bbf19253181a221ae876ff5207c4e19acd49bcc5 5 0
unsat
((set-logic AUFLIA)
(proof
(mp (asserted (not true)) (rewrite (= (not true) false)) false)))
7da7317115e337fb9b3e7260dcd426df65d770ca 5 0
unsat
((set-logic AUFLIA)
(proof
(|unit-resolution| (|not-or-elim| (asserted (not (or |p$| (not |p$|)))) (not |p$|)) (|not-or-elim| (asserted (not (or |p$| (not |p$|)))) |p$|) false)))
491ce0f180688f8b3ad41fb77c37c188bb719912 9 0
unsat
((set-logic AUFLIA)
(proof
(let ((@x14 (monotonicity (rewrite (= (and |p$| true) |p$|)) (= (= (and |p$| true) |p$|) (= |p$| |p$|)))))
(let ((@x18 (trans @x14 (rewrite (= (= |p$| |p$|) true)) (= (= (and |p$| true) |p$|) true))))
(let ((@x21 (monotonicity @x18 (= (not (= (and |p$| true) |p$|)) (not true)))))
(let ((@x25 (trans @x21 (rewrite (= (not true) false)) (= (not (= (and |p$| true) |p$|)) false))))
(mp (asserted (not (= (and |p$| true) |p$|))) @x25 false)))))))
bcdca2390eec1cc7907ebb4fd43ef90102359e67 13 0
unsat
((set-logic AUFLIA)
(proof
(let (($x11 (not (=> (and (or |p$| |q$|) (not |p$|)) |q$|))))
(let (($x15 (= (=> (and (or |p$| |q$|) (not |p$|)) |q$|) (or (not (and (or |p$| |q$|) (not |p$|))) |q$|))))
(let ((@x19 (monotonicity (rewrite $x15) (= $x11 (not (or (not (and (or |p$| |q$|) (not |p$|))) |q$|))))))
(let ((@x20 (mp (asserted $x11) @x19 (not (or (not (and (or |p$| |q$|) (not |p$|))) |q$|)))))
(let ((@x23 (|and-elim| (|not-or-elim| @x20 (and (or |p$| |q$|) (not |p$|))) (not |p$|))))
(let ((@x32 (monotonicity (|iff-false| @x23 (= |p$| false)) (|iff-false| (|not-or-elim| @x20 (not |q$|)) (= |q$| false)) (= (or |p$| |q$|) (or false false)))))
(let ((@x36 (trans @x32 (rewrite (= (or false false) false)) (= (or |p$| |q$|) false))))
(let (($x7 (or |p$| |q$|)))
(mp (|and-elim| (|not-or-elim| @x20 (and $x7 (not |p$|))) $x7) @x36 false)))))))))))
33609f14221bd6366d7f13b136eb93ccf9841b7e 13 0
unsat
((set-logic AUFLIA)
(proof
(let (($x10 (and |c$| |d$|)))
(let (($x7 (and |a$| |b$|)))
(let (($x13 (not (=> (or $x7 $x10) (or $x7 $x10)))))
(let (($x17 (= (=> (or $x7 $x10) (or $x7 $x10)) (or (not (or $x7 $x10)) $x7 $x10))))
(let ((@x21 (monotonicity (rewrite $x17) (= $x13 (not (or (not (or $x7 $x10)) $x7 $x10))))))
(let ((@x22 (mp (asserted $x13) @x21 (not (or (not (or $x7 $x10)) $x7 $x10)))))
(let ((@x34 (monotonicity (|iff-false| (|not-or-elim| @x22 (not $x7)) (= $x7 false)) (|iff-false| (|not-or-elim| @x22 (not $x10)) (= $x10 false)) (= (or $x7 $x10) (or false false)))))
(let ((@x38 (trans @x34 (rewrite (= (or false false) false)) (= (or $x7 $x10) false))))
(mp (|not-or-elim| @x22 (or $x7 $x10)) @x38 false)))))))))))
41601ebe27811aa51768455eec7d63637aa09b37 15 0
unsat
((set-logic AUFLIA)
(proof
(let (($x14 (or (=> |p1$| (or (and |p3$| |p2$|) (and |p1$| |p3$|))) |p1$|)))
(let (($x15 (=> (or (and |p1$| |p2$|) |p3$|) $x14)))
(let (($x16 (not $x15)))
(let (($x25 (= (or (or (not |p1$|) (and |p3$| |p2$|) (and |p1$| |p3$|)) |p1$|) true)))
(let (($x23 (= $x14 (or (or (not |p1$|) (and |p3$| |p2$|) (and |p1$| |p3$|)) |p1$|))))
(let (($x20 (= (=> |p1$| (or (and |p3$| |p2$|) (and |p1$| |p3$|))) (or (not |p1$|) (and |p3$| |p2$|) (and |p1$| |p3$|)))))
(let ((@x28 (trans (monotonicity (rewrite $x20) $x23) (rewrite $x25) (= $x14 true))))
(let ((@x31 (monotonicity @x28 (= $x15 (=> (or (and |p1$| |p2$|) |p3$|) true)))))
(let ((@x35 (trans @x31 (rewrite (= (=> (or (and |p1$| |p2$|) |p3$|) true) true)) (= $x15 true))))
(let ((@x42 (trans (monotonicity @x35 (= $x16 (not true))) (rewrite (= (not true) false)) (= $x16 false))))
(mp (asserted $x16) @x42 false)))))))))))))
7f485e6a920dd309143a3ab1b4de9c4e47827bd1 24 0
unsat
((set-logic AUFLIA)
(proof
(let (($x6 (= |p$| |p$|)))
(let (($x7 (= $x6 |p$|)))
(let (($x8 (= $x7 |p$|)))
(let (($x9 (= $x8 |p$|)))
(let (($x10 (= $x9 |p$|)))
(let (($x11 (= $x10 |p$|)))
(let (($x12 (= $x11 |p$|)))
(let (($x13 (= $x12 |p$|)))
(let (($x14 (= $x13 |p$|)))
(let (($x15 (not $x14)))
(let ((@x18 (rewrite (= $x6 true))))
(let ((@x23 (rewrite (= (= true |p$|) |p$|))))
(let ((@x25 (trans (monotonicity @x18 (= $x7 (= true |p$|))) @x23 (= $x7 |p$|))))
(let ((@x31 (monotonicity (trans (monotonicity @x25 (= $x8 $x6)) @x18 (= $x8 true)) (= $x9 (= true |p$|)))))
(let ((@x37 (trans (monotonicity (trans @x31 @x23 (= $x9 |p$|)) (= $x10 $x6)) @x18 (= $x10 true))))
(let ((@x41 (trans (monotonicity @x37 (= $x11 (= true |p$|))) @x23 (= $x11 |p$|))))
(let ((@x47 (monotonicity (trans (monotonicity @x41 (= $x12 $x6)) @x18 (= $x12 true)) (= $x13 (= true |p$|)))))
(let ((@x53 (trans (monotonicity (trans @x47 @x23 (= $x13 |p$|)) (= $x14 $x6)) @x18 (= $x14 true))))
(let ((@x60 (trans (monotonicity @x53 (= $x15 (not true))) (rewrite (= (not true) false)) (= $x15 false))))
(mp (asserted $x15) @x60 false))))))))))))))))))))))
47fc1bdb5c81d2c954d3c9c4f6781abf20cd2ad5 33 0
unsat
((set-logic AUFLIA)
(proof
(let (($x101 (not |d$|)))
(let (($x39 (not (or |c$| (and (not |p$|) (or |p$| (and |q$| (not |q$|))))))))
(let ((@x109 (|iff-false| (|not-or-elim| (asserted $x39) (not |c$|)) (= |c$| false))))
(let ((@x116 (trans (monotonicity @x109 (= (or $x101 |c$|) (or $x101 false))) (rewrite (= (or $x101 false) $x101)) (= (or $x101 |c$|) $x101))))
(let (($x104 (or $x101 |c$|)))
(let ((@x103 (monotonicity (rewrite (= (or |d$| false) |d$|)) (= (not (or |d$| false)) $x101))))
(let ((@x107 (mp (asserted (or (not (or |d$| false)) |c$|)) (monotonicity @x103 (= (or (not (or |d$| false)) |c$|) $x104)) $x104)))
(let (($x92 (not |b$|)))
(let ((@x127 (trans (monotonicity @x109 (= (or $x92 |c$|) (or $x92 false))) (rewrite (= (or $x92 false) $x92)) (= (or $x92 |c$|) $x92))))
(let (($x95 (or $x92 |c$|)))
(let ((@x87 (monotonicity (rewrite (= (or |x$| (not |x$|)) true)) (= (and |b$| (or |x$| (not |x$|))) (and |b$| true)))))
(let ((@x91 (trans @x87 (rewrite (= (and |b$| true) |b$|)) (= (and |b$| (or |x$| (not |x$|))) |b$|))))
(let ((@x97 (monotonicity (monotonicity @x91 (= (not (and |b$| (or |x$| (not |x$|)))) $x92)) (= (or (not (and |b$| (or |x$| (not |x$|)))) |c$|) $x95))))
(let ((@x98 (mp (asserted (or (not (and |b$| (or |x$| (not |x$|)))) |c$|)) @x97 $x95)))
(let (($x76 (not |a$|)))
(let ((@x128 (monotonicity (|iff-false| (mp @x98 @x127 $x92) (= |b$| false)) (= (or $x76 |b$|) (or $x76 false)))))
(let ((@x133 (trans @x128 (rewrite (= (or $x76 false) $x76)) (= (or $x76 |b$|) $x76))))
(let (($x79 (or $x76 |b$|)))
(let ((@x71 (monotonicity (rewrite (= (and |c$| (not |c$|)) false)) (= (or |a$| (and |c$| (not |c$|))) (or |a$| false)))))
(let ((@x75 (trans @x71 (rewrite (= (or |a$| false) |a$|)) (= (or |a$| (and |c$| (not |c$|))) |a$|))))
(let ((@x81 (monotonicity (monotonicity @x75 (= (not (or |a$| (and |c$| (not |c$|)))) $x76)) (= (or (not (or |a$| (and |c$| (not |c$|)))) |b$|) $x79))))
(let ((@x82 (mp (asserted (or (not (or |a$| (and |c$| (not |c$|)))) |b$|)) @x81 $x79)))
(let ((@x155 (monotonicity (|iff-false| (mp @x82 @x133 $x76) (= |a$| false)) (|iff-false| (mp @x98 @x127 $x92) (= |b$| false)) @x109 (|iff-false| (mp @x107 @x116 $x101) (= |d$| false)) (= (or |a$| |b$| |c$| |d$|) (or false false false false)))))
(let ((@x159 (trans @x155 (rewrite (= (or false false false false) false)) (= (or |a$| |b$| |c$| |d$|) false))))
(let (($x57 (or |a$| |b$| |c$| |d$|)))
(let (($x11 (or |a$| (or |b$| (or |c$| |d$|)))))
(let ((@x56 (monotonicity (rewrite (= (or |b$| (or |c$| |d$|)) (or |b$| |c$| |d$|))) (= $x11 (or |a$| (or |b$| |c$| |d$|))))))
(let ((@x61 (trans @x56 (rewrite (= (or |a$| (or |b$| |c$| |d$|)) $x57)) (= $x11 $x57))))
(mp (mp (asserted $x11) @x61 $x57) @x159 false)))))))))))))))))))))))))))))))
8c24f75a894825932206d94b2ce1c08f0d064ba2 16 0
unsat
((set-logic AUFLIA)
(proof
(let (($x16 (= (|symm_f$| |a$| |b$|) (|symm_f$| |b$| |a$|))))
(let (($x30 (not $x16)))
(let ((@x25 (monotonicity (rewrite (= (= |a$| |a$|) true)) (= (and (= |a$| |a$|) $x16) (and true $x16)))))
(let ((@x29 (trans @x25 (rewrite (= (and true $x16) $x16)) (= (and (= |a$| |a$|) $x16) $x16))))
(let ((@x33 (mp (asserted (not (and (= |a$| |a$|) $x16))) (monotonicity @x29 (= (not (and (= |a$| |a$|) $x16)) $x30)) $x30)))
(let (($x483 (forall ((?v0 |A$|) (?v1 |A$|) )(!(= (|symm_f$| ?v0 ?v1) (|symm_f$| ?v1 ?v0)) :pattern ( (|symm_f$| ?v0 ?v1) ) :pattern ( (|symm_f$| ?v1 ?v0) )))
))
(let (($x10 (forall ((?v0 |A$|) (?v1 |A$|) )(= (|symm_f$| ?v0 ?v1) (|symm_f$| ?v1 ?v0)))
))
(let (($x9 (= (|symm_f$| ?1 ?0) (|symm_f$| ?0 ?1))))
(let ((@x63 (|mp~| (mp (asserted $x10) (|rewrite*| (= $x10 $x10)) $x10) (|nnf-pos| (refl (|~| $x9 $x9)) (|~| $x10 $x10)) $x10)))
(|unit-resolution| ((_ |quant-inst| |a$| |b$|) (or (not $x483) $x16)) (mp @x63 (|quant-intro| (refl (= $x9 $x9)) (= $x10 $x483)) $x483) (mp @x33 (|rewrite*| (= $x30 $x30)) $x30) false))))))))))))
b7bd810dad2f1e427087fcd2f0121b91d06c649f 37 0
unsat
((set-logic AUFLIA)
(declare-fun ?v0!0 () Int)
(declare-fun ?v1!1 () Int)
(proof
(let (($x49 (|p$| ?v0!0)))
(let (($x50 (not $x49)))
(let (($x63 (not (or $x49 (|p$| ?v1!1)))))
(let ((@x79 (monotonicity (rewrite (= (not $x50) $x49)) (= (and (not $x50) $x63) (and $x49 $x63)))))
(let (($x57 (not $x50)))
(let (($x67 (and $x57 $x63)))
(let (($x19 (forall ((?v0 Int) )(let (($x10 (forall ((?v1 Int) )(let (($x6 (|p$| ?v1)))
(or (|p$| ?v0) $x6)))
))
(or (not (|p$| ?v0)) $x10)))
))
(let (($x22 (not $x19)))
(let (($x52 (forall ((?v1 Int) )(let (($x6 (|p$| ?v1)))
(let (($x49 (|p$| ?v0!0)))
(or $x49 $x6))))
))
(let ((@x69 (|nnf-neg| (refl (|~| $x57 $x57)) (sk (|~| (not $x52) $x63)) (|~| (not (or $x50 $x52)) $x67))))
(let (($x12 (forall ((?v0 Int) )(let (($x10 (forall ((?v1 Int) )(let (($x6 (|p$| ?v1)))
(or (|p$| ?v0) $x6)))
))
(let (($x6 (|p$| ?v0)))
(=> $x6 $x10))))
))
(let (($x13 (not $x12)))
(let (($x10 (forall ((?v1 Int) )(let (($x6 (|p$| ?v1)))
(or (|p$| ?0) $x6)))
))
(let ((@x21 (|quant-intro| (rewrite (= (=> (|p$| ?0) $x10) (or (not (|p$| ?0)) $x10))) (= $x12 $x19))))
(let ((@x28 (mp (mp (asserted $x13) (monotonicity @x21 (= $x13 $x22)) $x22) (|rewrite*| (= $x22 $x22)) $x22)))
(let ((@x72 (|mp~| @x28 (trans (sk (|~| $x22 (not (or $x50 $x52)))) @x69 (|~| $x22 $x67)) $x67)))
(|unit-resolution| (|and-elim| (mp @x72 @x79 (and $x49 $x63)) $x49) (|not-or-elim| (|and-elim| (mp @x72 @x79 (and $x49 $x63)) $x63) $x50) false)))))))))))))))))))
6cf824ace40aded20fac37a6bbde5bb680ac2a1c 22 0
unsat
((set-logic AUFLIA)
(proof
(let (($x6 (|p$| |x$|)))
(let ((@x26 (monotonicity (rewrite (= (=> $x6 (|p$| |y$|)) (or (not $x6) (|p$| |y$|)))) (= (not (=> $x6 (|p$| |y$|))) (not (or (not $x6) (|p$| |y$|)))))))
(let ((@x27 (mp (asserted (not (=> $x6 (|p$| |y$|)))) @x26 (not (or (not $x6) (|p$| |y$|))))))
(let (($x492 (forall ((?v0 |A$|) )(!(let (($x8 (|p$| ?v0)))
(not $x8)) :pattern ( (|p$| ?v0) )))
))
(let (($x12 (forall ((?v0 |A$|) )(let (($x8 (|p$| ?v0)))
(not $x8)))
))
(let ((@x496 (|quant-intro| (refl (= (not (|p$| ?0)) (not (|p$| ?0)))) (= $x12 $x492))))
(let (($x9 (exists ((?v0 |A$|) )(|p$| ?v0))
))
(let (($x10 (not $x9)))
(let ((@x35 (monotonicity (|iff-true| (|not-or-elim| @x27 $x6) (= $x6 true)) (= (ite $x6 $x10 $x12) (ite true $x10 $x12)))))
(let ((@x39 (trans @x35 (rewrite (= (ite true $x10 $x12) $x10)) (= (ite $x6 $x10 $x12) $x10))))
(let ((@x43 (mp (mp (asserted (ite $x6 $x10 $x12)) @x39 $x10) (|rewrite*| (= $x10 $x10)) $x10)))
(let ((@x70 (|mp~| @x43 (|nnf-neg| (refl (|~| (not (|p$| ?0)) (not (|p$| ?0)))) (|~| $x10 $x12)) $x12)))
(|unit-resolution| ((_ |quant-inst| |x$|) (or (not $x492) (not $x6))) (mp @x70 @x496 $x492) (mp (|not-or-elim| @x27 $x6) (|rewrite*| (= $x6 $x6)) $x6) false)))))))))))))))
a89c726795a8d0e170934e5d099744330d95400b 7 0
unsat
((set-logic AUFLIA)
(proof
(let ((@x14 (monotonicity (rewrite (= (= 3 3) true)) (= (not (= 3 3)) (not true)))))
(let ((@x18 (trans @x14 (rewrite (= (not true) false)) (= (not (= 3 3)) false))))
(mp (asserted (not (= 3 3))) @x18 false)))))
f7b25fbc92a3db52d764adfa193cc9c7d084b0d6 7 0
unsat
((set-logic AUFLIRA)
(proof
(let ((@x14 (monotonicity (rewrite (= (= 3.0 3.0) true)) (= (not (= 3.0 3.0)) (not true)))))
(let ((@x18 (trans @x14 (rewrite (= (not true) false)) (= (not (= 3.0 3.0)) false))))
(mp (asserted (not (= 3.0 3.0))) @x18 false)))))
54ea7c923e2f51278ebed4a257f587326e98cb4d 9 0
unsat
((set-logic AUFLIA)
(proof
(let ((@x15 (monotonicity (rewrite (= (+ 3 1) 4)) (= (= (+ 3 1) 4) (= 4 4)))))
(let ((@x20 (trans @x15 (rewrite (= (= 4 4) true)) (= (= (+ 3 1) 4) true))))
(let ((@x23 (monotonicity @x20 (= (not (= (+ 3 1) 4)) (not true)))))
(let ((@x27 (trans @x23 (rewrite (= (not true) false)) (= (not (= (+ 3 1) 4)) false))))
(mp (asserted (not (= (+ 3 1) 4))) @x27 false)))))))
552d7f5bd067421657495756c4f47648a5eef581 10 0
unsat
((set-logic AUFLIA)
(proof
(let (($x12 (= (+ |x$| (+ |y$| |z$|)) (+ |y$| (+ |z$| |x$|)))))
(let (($x13 (not $x12)))
(let ((@x23 (monotonicity (rewrite (= (+ |x$| (+ |y$| |z$|)) (+ |x$| |y$| |z$|))) (rewrite (= (+ |y$| (+ |z$| |x$|)) (+ |y$| |z$| |x$|))) (= $x12 (= (+ |x$| |y$| |z$|) (+ |y$| |z$| |x$|))))))
(let ((@x28 (trans @x23 (rewrite (= (= (+ |x$| |y$| |z$|) (+ |y$| |z$| |x$|)) true)) (= $x12 true))))
(let ((@x35 (trans (monotonicity @x28 (= $x13 (not true))) (rewrite (= (not true) false)) (= $x13 false))))
(mp (asserted $x13) @x35 false))))))))
36faa6237c000d60624d7bc78360f9dad21b1321 15 0
unsat
((set-logic AUFLIA)
(proof
(let ((@x36 (monotonicity (rewrite (= (<= 8 5) false)) (= (not (<= 8 5)) (not false)))))
(let ((@x40 (trans @x36 (rewrite (= (not false) true)) (= (not (<= 8 5)) true))))
(let (($x27 (not (<= 8 5))))
(let ((?x9 (ite (<= 3 8) 8 3)))
(let (($x10 (< 5 ?x9)))
(let ((@x18 (monotonicity (rewrite (= (<= 3 8) true)) (= ?x9 (ite true 8 3)))))
(let ((@x22 (trans @x18 (rewrite (= (ite true 8 3) 8)) (= ?x9 8))))
(let ((@x31 (trans (monotonicity @x22 (= $x10 (< 5 8))) (rewrite (= (< 5 8) $x27)) (= $x10 $x27))))
(let ((@x45 (monotonicity (trans @x31 @x40 (= $x10 true)) (= (not $x10) (not true)))))
(let ((@x49 (trans @x45 (rewrite (= (not true) false)) (= (not $x10) false))))
(mp (asserted (not $x10)) @x49 false)))))))))))))
e8e28789ea05d7727096ba10500963856291639a 85 0
unsat
((set-logic AUFLIRA)
(proof
(let (($x194 (<= (+ |x$| (* (~ 1.0) (ite (>= |x$| 0.0) |x$| (* (~ 1.0) |x$|)))) 0.0)))
(let ((?x35 (* (~ 1.0) |x$|)))
(let (($x140 (>= |x$| 0.0)))
(let ((?x143 (ite $x140 |x$| ?x35)))
(let (($x176 (= |x$| ?x143)))
(let ((?x36 (* (~ 1.0) |y$|)))
(let ((?x37 (+ ?x35 ?x36)))
(let ((?x7 (+ |x$| |y$|)))
(let (($x134 (>= ?x7 0.0)))
(let ((?x137 (ite $x134 ?x7 ?x37)))
(let (($x226 (>= (+ ?x37 (* (~ 1.0) ?x137)) 0.0)))
(let (($x172 (= ?x37 ?x137)))
(let (($x133 (not $x134)))
(let (($x146 (>= |y$| 0.0)))
(let (($x185 (not $x146)))
(let (($x199 (>= (+ ?x7 (* (~ 1.0) ?x137)) 0.0)))
(let (($x171 (= ?x7 ?x137)))
(let (($x235 (not $x226)))
(let ((@x206 (hypothesis $x146)))
(let (($x161 (<= (+ ?x137 (* (~ 1.0) ?x143) (* (~ 1.0) (ite $x146 |y$| ?x36))) 0.0)))
(let (($x69 (<= 0.0 |y$|)))
(let ((?x83 (ite $x69 |y$| ?x36)))
(let (($x50 (<= 0.0 |x$|)))
(let ((?x64 (ite $x50 |x$| ?x35)))
(let ((?x88 (+ ?x64 ?x83)))
(let (($x22 (<= 0.0 ?x7)))
(let ((?x45 (ite $x22 ?x7 ?x37)))
(let (($x91 (<= ?x45 ?x88)))
(let (($x94 (not $x91)))
(let ((@x154 (monotonicity (monotonicity (rewrite (= $x50 $x140)) (= ?x64 ?x143)) (monotonicity (rewrite (= $x69 $x146)) (= ?x83 (ite $x146 |y$| ?x36))) (= ?x88 (+ ?x143 (ite $x146 |y$| ?x36))))))
(let ((@x157 (monotonicity (monotonicity (rewrite (= $x22 $x134)) (= ?x45 ?x137)) @x154 (= $x91 (<= ?x137 (+ ?x143 (ite $x146 |y$| ?x36)))))))
(let ((@x165 (trans @x157 (rewrite (= (<= ?x137 (+ ?x143 (ite $x146 |y$| ?x36))) $x161)) (= $x91 $x161))))
(let ((@x108 (monotonicity (monotonicity (rewrite (= $x50 $x50)) (= ?x64 ?x64)) (monotonicity (rewrite (= $x69 $x69)) (= ?x83 ?x83)) (= ?x88 ?x88))))
(let ((@x110 (monotonicity (monotonicity (rewrite (= $x22 $x22)) (= ?x45 ?x45)) @x108 (= $x91 $x91))))
(let ((?x17 (ite (< |y$| 0.0) (- |y$|) |y$|)))
(let ((?x14 (ite (< |x$| 0.0) (- |x$|) |x$|)))
(let ((?x10 (- ?x7)))
(let ((?x11 (ite (< ?x7 0.0) ?x10 ?x7)))
(let (($x20 (not (<= ?x11 (+ ?x14 ?x17)))))
(let ((@x77 (trans (rewrite (= (< |y$| 0.0) (not $x69))) (monotonicity (rewrite (= $x69 $x69)) (= (not $x69) (not $x69))) (= (< |y$| 0.0) (not $x69)))))
(let ((@x82 (monotonicity @x77 (rewrite (= (- |y$|) ?x36)) (= ?x17 (ite (not $x69) ?x36 |y$|)))))
(let ((@x87 (trans @x82 (rewrite (= (ite (not $x69) ?x36 |y$|) ?x83)) (= ?x17 ?x83))))
(let ((@x58 (trans (rewrite (= (< |x$| 0.0) (not $x50))) (monotonicity (rewrite (= $x50 $x50)) (= (not $x50) (not $x50))) (= (< |x$| 0.0) (not $x50)))))
(let ((@x63 (monotonicity @x58 (rewrite (= (- |x$|) ?x35)) (= ?x14 (ite (not $x50) ?x35 |x$|)))))
(let ((@x68 (trans @x63 (rewrite (= (ite (not $x50) ?x35 |x$|) ?x64)) (= ?x14 ?x64))))
(let ((@x41 (trans (rewrite (= ?x10 (* (~ 1.0) ?x7))) (rewrite (= (* (~ 1.0) ?x7) ?x37)) (= ?x10 ?x37))))
(let ((@x30 (trans (rewrite (= (< ?x7 0.0) (not $x22))) (monotonicity (rewrite (= $x22 $x22)) (= (not $x22) (not $x22))) (= (< ?x7 0.0) (not $x22)))))
(let ((@x49 (trans (monotonicity @x30 @x41 (= ?x11 (ite (not $x22) ?x37 ?x7))) (rewrite (= (ite (not $x22) ?x37 ?x7) ?x45)) (= ?x11 ?x45))))
(let ((@x93 (monotonicity @x49 (monotonicity @x68 @x87 (= (+ ?x14 ?x17) ?x88)) (= (<= ?x11 (+ ?x14 ?x17)) $x91))))
(let ((@x100 (mp (mp (asserted $x20) (monotonicity @x93 (= $x20 $x94)) $x94) (|rewrite*| (= $x94 $x94)) $x94)))
(let ((@x113 (mp (mp @x100 (monotonicity @x110 (= $x94 $x94)) $x94) (monotonicity @x110 (= $x94 $x94)) $x94)))
(let ((@x169 (mp @x113 (monotonicity @x165 (= $x94 (not $x161))) (not $x161))))
(let ((?x149 (ite $x146 |y$| ?x36)))
(let (($x183 (= |y$| ?x149)))
(let ((@x219 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x183) (<= (+ |y$| (* (~ 1.0) ?x149)) 0.0))) (|unit-resolution| (|def-axiom| (or $x185 $x183)) @x206 $x183) (<= (+ |y$| (* (~ 1.0) ?x149)) 0.0))))
(let (($x198 (<= (+ ?x35 (* (~ 1.0) ?x143)) 0.0)))
(let (($x177 (= ?x35 ?x143)))
(let (($x178 (not $x140)))
(let ((@x204 ((_ |th-lemma| arith triangle-eq) (or (not $x176) $x194))))
(let ((@x205 (|unit-resolution| @x204 (|unit-resolution| (|def-axiom| (or $x178 $x176)) (hypothesis $x140) $x176) $x194)))
(let ((@x209 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -1) (or $x134 $x178 $x185)) (hypothesis $x140) @x206 $x134)))
(let ((@x173 (|def-axiom| (or $x133 $x171))))
(let ((@x213 ((_ |th-lemma| arith triangle-eq) (or (not $x171) $x199))))
(let ((@x220 ((_ |th-lemma| arith farkas 1 -1 -1 1) @x219 (|unit-resolution| @x213 (|unit-resolution| @x173 @x209 $x171) $x199) @x169 @x205 false)))
(let ((@x229 (|unit-resolution| (|def-axiom| (or $x140 $x177)) (|unit-resolution| (lemma @x220 (or $x178 $x185)) @x206 $x178) $x177)))
(let ((@x234 ((_ |th-lemma| arith farkas 2 -1 -1 1 1) @x206 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x177) $x198)) @x229 $x198) @x219 @x169 (hypothesis $x226) false)))
(let ((@x243 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x172) $x226)) (hypothesis $x172) (hypothesis $x235) false)))
(let ((@x246 (|unit-resolution| (lemma @x243 (or (not $x172) $x226)) (|unit-resolution| (lemma @x234 (or $x235 $x185)) @x206 $x235) (not $x172))))
(let ((@x248 (|unit-resolution| @x173 (|unit-resolution| (|def-axiom| (or $x134 $x172)) @x246 $x134) $x171)))
(let ((@x250 ((_ |th-lemma| arith farkas 2 1 1 1 1) (|unit-resolution| (lemma @x220 (or $x178 $x185)) @x206 $x178) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x177) $x198)) @x229 $x198) @x219 @x169 (|unit-resolution| @x213 @x248 $x199) false)))
(let ((@x251 (lemma @x250 $x185)))
(let ((@x257 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1) (or $x140 $x146 $x133)) (hypothesis $x134) @x251 $x140)))
(let ((@x180 (|def-axiom| (or $x178 $x176))))
(let ((@x261 (|unit-resolution| @x213 (|unit-resolution| @x173 (hypothesis $x134) $x171) $x199)))
(let (($x184 (= ?x36 ?x149)))
(let ((@x266 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x184) (<= (+ ?x36 (* (~ 1.0) ?x149)) 0.0))) (|unit-resolution| (|def-axiom| (or $x146 $x184)) @x251 $x184) (<= (+ ?x36 (* (~ 1.0) ?x149)) 0.0))))
(let ((@x267 ((_ |th-lemma| arith farkas 2 1 1 1 1) @x251 @x266 @x169 @x261 (|unit-resolution| @x204 (|unit-resolution| @x180 @x257 $x176) $x194) false)))
(let ((@x271 (|unit-resolution| (lemma @x243 (or (not $x172) $x226)) (|unit-resolution| (|def-axiom| (or $x134 $x172)) (lemma @x267 $x133) $x172) $x226)))
(let ((@x276 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x177) $x198)) (hypothesis $x177) (lemma ((_ |th-lemma| arith farkas 1 -1 -1 1) @x266 @x169 @x271 (hypothesis $x198) false) (not $x198)) false)))
(let ((@x278 (|unit-resolution| (|def-axiom| (or $x140 $x177)) (lemma @x276 (not $x177)) $x140)))
((_ |th-lemma| arith farkas -2 1 -1 -1 1) @x278 @x266 @x169 @x271 (|unit-resolution| @x204 (|unit-resolution| @x180 @x278 $x176) $x194) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
d11fcb5f4744241869bf523344d4028dde874c74 15 0
unsat
((set-logic AUFLIA)
(proof
(let ((?x10 (|p$| true)))
(let (($x11 (= (|p$| (ite (< 2 3) true false)) ?x10)))
(let (($x12 (not $x11)))
(let ((@x23 (monotonicity (rewrite (= (<= 3 2) false)) (= (not (<= 3 2)) (not false)))))
(let ((@x27 (trans @x23 (rewrite (= (not false) true)) (= (not (<= 3 2)) true))))
(let ((@x29 (trans (rewrite (= (< 2 3) (not (<= 3 2)))) @x27 (= (< 2 3) true))))
(let ((@x32 (monotonicity @x29 (= (ite (< 2 3) true false) (ite true true false)))))
(let ((@x36 (trans @x32 (rewrite (= (ite true true false) true)) (= (ite (< 2 3) true false) true))))
(let ((@x44 (trans (monotonicity (monotonicity @x36 $x11) (= $x11 (= ?x10 ?x10))) (rewrite (= (= ?x10 ?x10) true)) (= $x11 true))))
(let ((@x51 (trans (monotonicity @x44 (= $x12 (not true))) (rewrite (= (not true) false)) (= $x12 false))))
(mp (asserted $x12) @x51 false)))))))))))))
118bd48c31dce91a7e08520c2c1fe2c904fc8d4f 16 0
unsat
((set-logic AUFLIA)
(proof
(let (($x25 (<= 1 |x$|)))
(let ((@x40 (trans (rewrite (= (< |x$| 1) (not $x25))) (monotonicity (rewrite (= $x25 $x25)) (= (not $x25) (not $x25))) (= (< |x$| 1) (not $x25)))))
(let ((@x47 (trans (monotonicity @x40 (= (not (< |x$| 1)) (not (not $x25)))) (rewrite (= (not (not $x25)) $x25)) (= (not (< |x$| 1)) $x25))))
(let (($x11 (< |x$| 1)))
(let (($x17 (not $x11)))
(let ((@x18 (|not-or-elim| (asserted (not (or (<= 4 (+ |x$| 3)) $x11))) $x17)))
(let (($x30 (not $x25)))
(let ((@x24 (monotonicity (rewrite (= (+ |x$| 3) (+ 3 |x$|))) (= (<= 4 (+ |x$| 3)) (<= 4 (+ 3 |x$|))))))
(let ((@x29 (trans @x24 (rewrite (= (<= 4 (+ 3 |x$|)) $x25)) (= (<= 4 (+ |x$| 3)) $x25))))
(let ((@x16 (|not-or-elim| (asserted (not (or (<= 4 (+ |x$| 3)) $x11))) (not (<= 4 (+ |x$| 3))))))
(let ((@x33 (mp @x16 (monotonicity @x29 (= (not (<= 4 (+ |x$| 3))) $x30)) $x30)))
(|unit-resolution| @x33 (mp @x18 @x47 $x25) false))))))))))))))
10f47384b1edbbe0088cb4f6641650cff9776ff0 23 0
unsat
((set-logic AUFLIA)
(proof
(let ((@x93 (rewrite (= (= |y$| (+ 4 |x$|)) (= (+ |x$| (* (~ 1) |y$|)) (~ 4))))))
(let (($x25 (= |y$| (+ 4 |x$|))))
(let ((@x29 (rewrite (= $x25 $x25))))
(let ((@x27 (monotonicity (rewrite (= (+ |x$| 4) (+ 4 |x$|))) (= (= |y$| (+ |x$| 4)) $x25))))
(let ((@x31 (mp (asserted (= |y$| (+ |x$| 4))) (trans @x27 @x29 (= (= |y$| (+ |x$| 4)) $x25)) $x25)))
(let ((@x64 (mp (mp (mp @x31 (|rewrite*| (= $x25 $x25)) $x25) @x29 $x25) @x29 $x25)))
(let ((@x110 (monotonicity (mp @x64 @x93 (= (+ |x$| (* (~ 1) |y$|)) (~ 4))) (= (>= (+ |x$| (* (~ 1) |y$|)) 0) (>= (~ 4) 0)))))
(let ((@x112 (trans @x110 (rewrite (= (>= (~ 4) 0) false)) (= (>= (+ |x$| (* (~ 1) |y$|)) 0) false))))
(let (($x100 (>= (+ |x$| (* (~ 1) |y$|)) 0)))
(let ((?x34 (+ |y$| (* (~ 1) |x$|))))
(let (($x40 (<= ?x34 0)))
(let ((@x99 (monotonicity (rewrite (= ?x34 (+ (* (~ 1) |x$|) |y$|))) (= $x40 (<= (+ (* (~ 1) |x$|) |y$|) 0)))))
(let ((@x104 (trans @x99 (rewrite (= (<= (+ (* (~ 1) |x$|) |y$|) 0) $x100)) (= $x40 $x100))))
(let ((@x39 (monotonicity (rewrite (= (- |y$| |x$|) ?x34)) (= (< 0 (- |y$| |x$|)) (< 0 ?x34)))))
(let ((@x45 (trans @x39 (rewrite (= (< 0 ?x34) (not $x40))) (= (< 0 (- |y$| |x$|)) (not $x40)))))
(let ((@x48 (monotonicity @x45 (= (not (< 0 (- |y$| |x$|))) (not (not $x40))))))
(let ((@x52 (trans @x48 (rewrite (= (not (not $x40)) $x40)) (= (not (< 0 (- |y$| |x$|))) $x40))))
(let ((@x60 (mp (mp (asserted (not (< 0 (- |y$| |x$|)))) @x52 $x40) (|rewrite*| (= $x40 $x40)) $x40)))
(mp (mp @x60 @x104 $x100) @x112 false)))))))))))))))))))))
aa7e091783f91e1fa3f52d47f54666f367d1bb36 11 0
unsat
((set-logic AUFLIA)
(proof
(let ((@x17 (monotonicity (rewrite (= (+ 2 2) 4)) (= (= (+ 2 2) 5) (= 4 5)))))
(let ((@x23 (trans @x17 (rewrite (= (= 4 5) false)) (= (= (+ 2 2) 5) false))))
(let ((@x26 (monotonicity @x23 (= (not (= (+ 2 2) 5)) (not false)))))
(let ((@x30 (trans @x26 (rewrite (= (not false) true)) (= (not (= (+ 2 2) 5)) true))))
(let ((@x33 (monotonicity @x30 (= (not (not (= (+ 2 2) 5))) (not true)))))
(let ((@x37 (trans @x33 (rewrite (= (not true) false)) (= (not (not (= (+ 2 2) 5))) false))))
(mp (asserted (not (not (= (+ 2 2) 5)))) @x37 false)))))))))
8f1ec6af8997aeb8e9888ff48bba8de209292f6d 22 0
unsat
((set-logic AUFLIRA)
(proof
(let ((?x11 (+ (* 3.0 |x$|) (* 7.0 |a$|))))
(let (($x23 (<= 4.0 ?x11)))
(let (($x24 (not $x23)))
(let ((@x100 (monotonicity (rewrite (= $x23 (>= ?x11 4.0))) (= $x24 (not (>= ?x11 4.0))))))
(let ((@x30 (monotonicity (rewrite (= $x23 $x23)) (= $x24 $x24))))
(let ((@x31 (trans (rewrite (= (< ?x11 4.0) $x24)) @x30 (= (< ?x11 4.0) $x24))))
(let ((@x65 (mp (mp (asserted (< ?x11 4.0)) @x31 $x24) (|rewrite*| (= $x24 $x24)) $x24)))
(let (($x47 (<= 0.0 |a$|)))
(let ((@x52 (rewrite (= $x47 $x47))))
(let ((@x55 (trans (rewrite (= (< |a$| 0.0) (not $x47))) (monotonicity @x52 (= (not $x47) (not $x47))) (= (< |a$| 0.0) (not $x47)))))
(let ((@x62 (trans (monotonicity @x55 (= (not (< |a$| 0.0)) (not (not $x47)))) (rewrite (= (not (not $x47)) $x47)) (= (not (< |a$| 0.0)) $x47))))
(let ((@x70 (mp (mp (asserted (not (< |a$| 0.0))) @x62 $x47) (|rewrite*| (= $x47 $x47)) $x47)))
(let ((@x105 (mp (mp (mp @x70 @x52 $x47) @x52 $x47) (rewrite (= $x47 (>= |a$| 0.0))) (>= |a$| 0.0))))
(let (($x41 (not (<= |x$| (/ 3.0 2.0)))))
(let ((@x43 (monotonicity (rewrite (= (<= (* 2.0 |x$|) 3.0) (<= |x$| (/ 3.0 2.0)))) (= (not (<= (* 2.0 |x$|) 3.0)) $x41))))
(let ((@x36 (rewrite (= (< 3.0 (* 2.0 |x$|)) (not (<= (* 2.0 |x$|) 3.0))))))
(let ((@x46 (mp (asserted (< 3.0 (* 2.0 |x$|))) (trans @x36 @x43 (= (< 3.0 (* 2.0 |x$|)) $x41)) $x41)))
((_ |th-lemma| arith farkas 3 7 1) (mp @x46 (|rewrite*| (= $x41 $x41)) $x41) @x105 (mp (mp (mp @x65 @x30 $x24) @x30 $x24) @x100 (not (>= ?x11 4.0))) false))))))))))))))))))))
123ff9b46d34a4f3a7f6c3b75522584cd621fb1d 22 0
unsat
((set-logic AUFLIA)
(proof
(let (($x13 (<= 0 |x$|)))
(let (($x14 (not $x13)))
(let (($x15 (or $x14 $x13)))
(let (($x16 (or (<= 0 (+ |y$| (* (- 1) |x$|))) $x15)))
(let (($x18 (= $x16 (not false))))
(let (($x19 (not $x18)))
(let ((@x49 (rewrite (= (or (<= 0 (+ |y$| (* (~ 1) |x$|))) true) true))))
(let ((@x41 (monotonicity (monotonicity (rewrite (= $x13 $x13)) (= $x14 $x14)) (rewrite (= $x13 $x13)) (= $x15 $x15))))
(let (($x30 (<= 0 (+ |y$| (* (~ 1) |x$|)))))
(let ((@x26 (monotonicity (rewrite (= (- 1) (~ 1))) (= (* (- 1) |x$|) (* (~ 1) |x$|)))))
(let ((@x29 (monotonicity @x26 (= (+ |y$| (* (- 1) |x$|)) (+ |y$| (* (~ 1) |x$|))))))
(let ((@x32 (monotonicity @x29 (= (<= 0 (+ |y$| (* (- 1) |x$|))) $x30))))
(let ((@x35 (trans @x32 (rewrite (= $x30 $x30)) (= (<= 0 (+ |y$| (* (- 1) |x$|))) $x30))))
(let ((@x47 (monotonicity @x35 (trans @x41 (rewrite (= $x15 true)) (= $x15 true)) (= $x16 (or $x30 true)))))
(let ((@x56 (monotonicity (trans @x47 @x49 (= $x16 true)) (rewrite (= (not false) true)) (= $x18 (= true true)))))
(let ((@x60 (trans @x56 (rewrite (= (= true true) true)) (= $x18 true))))
(let ((@x67 (trans (monotonicity @x60 (= $x19 (not true))) (rewrite (= (not true) false)) (= $x19 false))))
(mp (asserted $x19) @x67 false))))))))))))))))))))
3162fe55c0ec329908fcb4e022c32656696c4c11 223 0
unsat
((set-logic AUFLIA)
(proof
(let (($x22 (= |m$| |n$|)))
(let ((@x700 (symm (commutativity (= $x22 (= |n$| |m$|))) (= (= |n$| |m$|) $x22))))
(let (($x18 (= |n$| |m$|)))
(let (($x312 (>= (+ |n$| (* (~ 1) |m$|)) 0)))
(let (($x348 (<= (+ |m$| (* (~ 1) |n$a|)) 0)))
(let (($x342 (>= (+ |n$| (* (~ 1) |n$a|)) 0)))
(let (($x459 (or $x342 $x348)))
(let ((@x471 (monotonicity (rewrite (= (and (not $x342) (not $x348)) (not $x459))) (= (not (and (not $x342) (not $x348))) (not (not $x459))))))
(let ((@x491 (trans @x471 (rewrite (= (not (not $x459)) $x459)) (= (not (and (not $x342) (not $x348))) $x459))))
(let (($x351 (not $x348)))
(let (($x345 (not $x342)))
(let (($x354 (and $x345 $x351)))
(let (($x357 (not $x354)))
(let ((@x353 (monotonicity (rewrite (= (<= |m$| |n$a|) $x348)) (= (not (<= |m$| |n$a|)) $x351))))
(let ((@x347 (monotonicity (rewrite (= (<= |n$a| |n$|) $x342)) (= (not (<= |n$a| |n$|)) $x345))))
(let ((@x356 (monotonicity @x347 @x353 (= (and (not (<= |n$a| |n$|)) (not (<= |m$| |n$a|))) $x354))))
(let ((@x359 (monotonicity @x356 (= (not (and (not (<= |n$a| |n$|)) (not (<= |m$| |n$a|)))) $x357))))
(let (($x140 (not (<= |m$| |n$a|))))
(let (($x136 (not (<= |n$a| |n$|))))
(let (($x143 (and $x136 $x140)))
(let (($x146 (not $x143)))
(let ((@x142 (rewrite (= (< |n$a| |m$|) $x140))))
(let ((@x145 (monotonicity (rewrite (= (< |n$| |n$a|) $x136)) @x142 (= (and (< |n$| |n$a|) (< |n$a| |m$|)) $x143))))
(let ((@x148 (monotonicity @x145 (= (not (and (< |n$| |n$a|) (< |n$a| |m$|))) $x146))))
(let (($x37 (or (and $x22 (< |n$| |n$a|)) (or (and (= |m$| |n$a|) (< |n$a| |n$|)) (and (= |n$a| |m$|) $x22)))))
(let (($x24 (< |n$a| |n$|)))
(let (($x9 (< |m$| |n$a|)))
(let (($x32 (and $x9 $x24)))
(let (($x26 (= |n$a| |n$|)))
(let (($x20 (< |m$| |n$|)))
(let (($x31 (and $x20 $x26)))
(let (($x13 (< |n$| |n$a|)))
(let (($x30 (and $x20 $x13)))
(let (($x42 (or (and $x26 (< |n$| |m$|)) (or (and (= |n$a| |m$|) $x20) (or $x30 (or $x31 (or $x32 $x37)))))))
(let (($x7 (< |n$| |m$|)))
(let (($x25 (and $x24 $x7)))
(let (($x14 (< |n$a| |m$|)))
(let (($x23 (and $x14 $x22)))
(let (($x21 (and $x14 $x20)))
(let (($x19 (and $x18 $x9)))
(let (($x16 (= |n$| |n$a|)))
(let (($x17 (and $x16 $x14)))
(let (($x15 (and $x13 $x14)))
(let (($x59 (not (or $x15 (or $x17 (or $x19 (or $x21 (or $x23 (or $x25 $x42)))))))))
(let (($x11 (= |m$| |n$a|)))
(let (($x12 (and $x7 $x11)))
(let (($x49 (or $x12 (or $x15 (or $x17 (or $x19 (or $x21 (or $x23 (or $x25 $x42)))))))))
(let ((@x60 (|not-or-elim| (|not-or-elim| (asserted (not (or (and $x7 $x9) $x49))) (not $x49)) $x59)))
(let ((@x250 (mp (mp (|not-or-elim| @x60 (not $x15)) @x148 $x146) (|rewrite*| (= $x146 $x146)) $x146)))
(let ((@x674 (|unit-resolution| (mp (mp @x250 @x359 $x357) @x491 $x459) (hypothesis $x351) $x342)))
(let (($x493 (not $x16)))
(let (($x494 (or $x493 $x348)))
(let ((@x500 (monotonicity (rewrite (= (and $x16 $x351) (not $x494))) (= (not (and $x16 $x351)) (not (not $x494))))))
(let ((@x504 (trans @x500 (rewrite (= (not (not $x494)) $x494)) (= (not (and $x16 $x351)) $x494))))
(let (($x361 (and $x16 $x351)))
(let (($x364 (not $x361)))
(let ((@x366 (monotonicity (monotonicity @x353 (= (and $x16 $x140) $x361)) (= (not (and $x16 $x140)) $x364))))
(let (($x150 (and $x16 $x140)))
(let (($x153 (not $x150)))
(let ((@x155 (monotonicity (monotonicity @x142 (= $x17 $x150)) (= (not $x17) $x153))))
(let ((@x64 (|not-or-elim| @x60 (not (or $x17 (or $x19 (or $x21 (or $x23 (or $x25 $x42)))))))))
(let ((@x253 (mp (mp (|not-or-elim| @x64 (not $x17)) @x155 $x153) (|rewrite*| (= $x153 $x153)) $x153)))
(let ((@x675 (|unit-resolution| (mp (mp @x253 @x366 $x364) @x504 $x494) (hypothesis $x351) $x493)))
(let (($x395 (<= (+ |n$| (* (~ 1) |n$a|)) 0)))
(let (($x506 (not $x18)))
(let (($x531 (not $x22)))
(let (($x319 (>= (+ |m$| (* (~ 1) |n$a|)) 0)))
(let (($x398 (not $x395)))
(let ((@x654 (hypothesis $x398)))
(let (($x606 (or $x319 $x395)))
(let ((@x612 (monotonicity (rewrite (= (and (not $x319) $x398) (not $x606))) (= (not (and (not $x319) $x398)) (not (not $x606))))))
(let ((@x616 (trans @x612 (rewrite (= (not (not $x606)) $x606)) (= (not (and (not $x319) $x398)) $x606))))
(let (($x324 (not $x319)))
(let (($x436 (and $x324 $x398)))
(let (($x439 (not $x436)))
(let ((@x400 (monotonicity (rewrite (= (<= |n$| |n$a|) $x395)) (= (not (<= |n$| |n$a|)) $x398))))
(let ((@x326 (monotonicity (rewrite (= (<= |n$a| |m$|) $x319)) (= (not (<= |n$a| |m$|)) $x324))))
(let ((@x438 (monotonicity @x326 @x400 (= (and (not (<= |n$a| |m$|)) (not (<= |n$| |n$a|))) $x436))))
(let ((@x441 (monotonicity @x438 (= (not (and (not (<= |n$a| |m$|)) (not (<= |n$| |n$a|)))) $x439))))
(let (($x183 (not (<= |n$| |n$a|))))
(let (($x118 (not (<= |n$a| |m$|))))
(let (($x221 (and $x118 $x183)))
(let (($x224 (not $x221)))
(let ((@x185 (rewrite (= $x24 $x183))))
(let ((@x120 (rewrite (= $x9 $x118))))
(let ((@x226 (monotonicity (monotonicity @x120 @x185 (= $x32 $x221)) (= (not $x32) $x224))))
(let (($x87 (not (or (and (= |n$a| |m$|) $x20) (or $x30 (or $x31 (or $x32 $x37)))))))
(let ((@x68 (|not-or-elim| @x64 (not (or $x19 (or $x21 (or $x23 (or $x25 $x42))))))))
(let ((@x76 (|not-or-elim| (|not-or-elim| @x68 (not (or $x21 (or $x23 (or $x25 $x42))))) (not (or $x23 (or $x25 $x42))))))
(let ((@x88 (|not-or-elim| (|not-or-elim| (|not-or-elim| @x76 (not (or $x25 $x42))) (not $x42)) $x87)))
(let ((@x96 (|not-or-elim| (|not-or-elim| @x88 (not (or $x30 (or $x31 (or $x32 $x37))))) (not (or $x31 (or $x32 $x37))))))
(let ((@x227 (mp (|not-or-elim| (|not-or-elim| @x96 (not (or $x32 $x37))) (not $x32)) @x226 $x224)))
(let ((@x617 (mp (mp (mp @x227 (|rewrite*| (= $x224 $x224)) $x224) @x441 $x439) @x616 $x606)))
(let (($x466 (not $x11)))
(let (($x630 (or $x466 $x395)))
(let ((@x636 (monotonicity (rewrite (= (and $x11 $x398) (not $x630))) (= (not (and $x11 $x398)) (not (not $x630))))))
(let ((@x640 (trans @x636 (rewrite (= (not (not $x630)) $x630)) (= (not (and $x11 $x398)) $x630))))
(let (($x450 (and $x11 $x398)))
(let (($x453 (not $x450)))
(let ((@x455 (monotonicity (monotonicity @x400 (= (and $x11 $x183) $x450)) (= (not (and $x11 $x183)) $x453))))
(let (($x235 (and $x11 $x183)))
(let (($x238 (not $x235)))
(let ((@x240 (monotonicity (monotonicity @x185 (= (and $x11 $x24) $x235)) (= (not (and $x11 $x24)) $x238))))
(let ((@x108 (|not-or-elim| (|not-or-elim| (|not-or-elim| @x96 (not (or $x32 $x37))) (not $x37)) (not (or (and $x11 $x24) (and (= |n$a| |m$|) $x22))))))
(let ((@x286 (mp (mp (|not-or-elim| @x108 (not (and $x11 $x24))) @x240 $x238) (|rewrite*| (= $x238 $x238)) $x238)))
(let ((@x659 ((_ |th-lemma| arith triangle-eq) (or $x11 $x351 $x324))))
(let ((@x660 (|unit-resolution| @x659 (|unit-resolution| (mp (mp @x286 @x455 $x453) @x640 $x630) @x654 $x466) (|unit-resolution| @x617 @x654 $x319) $x351)))
(let (($x532 (or $x348 $x531)))
(let ((@x538 (monotonicity (rewrite (= (and $x351 $x22) (not $x532))) (= (not (and $x351 $x22)) (not (not $x532))))))
(let ((@x542 (trans @x538 (rewrite (= (not (not $x532)) $x532)) (= (not (and $x351 $x22)) $x532))))
(let (($x388 (and $x351 $x22)))
(let (($x391 (not $x388)))
(let ((@x393 (monotonicity (monotonicity @x353 (= (and $x140 $x22) $x388)) (= (not (and $x140 $x22)) $x391))))
(let (($x175 (and $x140 $x22)))
(let (($x178 (not $x175)))
(let ((@x180 (monotonicity (monotonicity @x142 (= $x23 $x175)) (= (not $x23) $x178))))
(let ((@x262 (mp (mp (|not-or-elim| @x76 (not $x23)) @x180 $x178) (|rewrite*| (= $x178 $x178)) $x178)))
(let ((@x670 (mp (|unit-resolution| (mp (mp @x262 @x393 $x391) @x542 $x532) @x660 $x531) (monotonicity (commutativity (= $x22 $x18)) (= $x531 $x506)) $x506)))
(let (($x544 (or $x395 $x312)))
(let ((@x550 (monotonicity (rewrite (= (and $x398 (not $x312)) (not $x544))) (= (not (and $x398 (not $x312))) (not (not $x544))))))
(let ((@x554 (trans @x550 (rewrite (= (not (not $x544)) $x544)) (= (not (and $x398 (not $x312))) $x544))))
(let (($x316 (not $x312)))
(let (($x401 (and $x398 $x316)))
(let (($x404 (not $x401)))
(let ((@x318 (monotonicity (rewrite (= (<= |m$| |n$|) $x312)) (= (not (<= |m$| |n$|)) $x316))))
(let ((@x406 (monotonicity (monotonicity @x400 @x318 (= (and $x183 (not (<= |m$| |n$|))) $x401)) (= (not (and $x183 (not (<= |m$| |n$|)))) $x404))))
(let (($x114 (not (<= |m$| |n$|))))
(let (($x186 (and $x183 $x114)))
(let (($x189 (not $x186)))
(let ((@x191 (monotonicity (monotonicity @x185 (rewrite (= $x7 $x114)) (= $x25 $x186)) (= (not $x25) $x189))))
(let ((@x192 (mp (|not-or-elim| (|not-or-elim| @x76 (not (or $x25 $x42))) (not $x25)) @x191 $x189)))
(let ((@x555 (mp (mp (mp @x192 (|rewrite*| (= $x189 $x189)) $x189) @x406 $x404) @x554 $x544)))
(let (($x375 (<= (+ |n$| (* (~ 1) |m$|)) 0)))
(let (($x519 (or $x348 $x375)))
(let ((@x525 (monotonicity (rewrite (= (and $x351 (not $x375)) (not $x519))) (= (not (and $x351 (not $x375))) (not (not $x519))))))
(let ((@x529 (trans @x525 (rewrite (= (not (not $x519)) $x519)) (= (not (and $x351 (not $x375))) $x519))))
(let (($x378 (not $x375)))
(let (($x381 (and $x351 $x378)))
(let (($x384 (not $x381)))
(let ((@x380 (monotonicity (rewrite (= (<= |n$| |m$|) $x375)) (= (not (<= |n$| |m$|)) $x378))))
(let ((@x386 (monotonicity (monotonicity @x353 @x380 (= (and $x140 (not (<= |n$| |m$|))) $x381)) (= (not (and $x140 (not (<= |n$| |m$|)))) $x384))))
(let (($x165 (not (<= |n$| |m$|))))
(let (($x168 (and $x140 $x165)))
(let (($x171 (not $x168)))
(let ((@x173 (monotonicity (monotonicity @x142 (rewrite (= $x20 $x165)) (= $x21 $x168)) (= (not $x21) $x171))))
(let ((@x74 (|not-or-elim| (|not-or-elim| @x68 (not (or $x21 (or $x23 (or $x25 $x42))))) (not $x21))))
(let ((@x387 (mp (mp (mp @x74 @x173 $x171) (|rewrite*| (= $x171 $x171)) $x171) @x386 $x384)))
(let ((@x664 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x18 $x378 $x316)) (|unit-resolution| (mp @x387 @x529 $x519) @x660 $x375) (|unit-resolution| @x555 @x654 $x312) $x18)))
(let ((@x679 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x16 $x398 $x345)) (lemma (|unit-resolution| @x664 @x670 false) $x395) (or $x16 $x345))))
(let (($x474 (or $x312 $x319)))
(let ((@x482 (monotonicity (rewrite (= (and $x316 $x324) (not $x474))) (= (not (and $x316 $x324)) (not (not $x474))))))
(let ((@x476 (trans @x482 (rewrite (= (not (not $x474)) $x474)) (= (not (and $x316 $x324)) $x474))))
(let (($x327 (and $x316 $x324)))
(let (($x330 (not $x327)))
(let ((@x332 (monotonicity (monotonicity @x318 @x326 (= (and $x114 $x118) $x327)) (= (not (and $x114 $x118)) $x330))))
(let (($x121 (and $x114 $x118)))
(let (($x124 (not $x121)))
(let ((@x116 (rewrite (= $x7 $x114))))
(let ((@x126 (monotonicity (monotonicity @x116 @x120 (= (and $x7 $x9) $x121)) (= (not (and $x7 $x9)) $x124))))
(let ((@x54 (|not-or-elim| (asserted (not (or (and $x7 $x9) $x49))) (not (and $x7 $x9)))))
(let ((@x333 (mp (mp (mp @x54 @x126 $x124) (|rewrite*| (= $x124 $x124)) $x124) @x332 $x330)))
(let (($x467 (or $x312 $x466)))
(let ((@x479 (monotonicity (rewrite (= (and $x316 $x11) (not $x467))) (= (not (and $x316 $x11)) (not (not $x467))))))
(let ((@x465 (trans @x479 (rewrite (= (not (not $x467)) $x467)) (= (not (and $x316 $x11)) $x467))))
(let (($x334 (and $x316 $x11)))
(let (($x337 (not $x334)))
(let ((@x339 (monotonicity (monotonicity @x318 (= (and $x114 $x11) $x334)) (= (not (and $x114 $x11)) $x337))))
(let (($x128 (and $x114 $x11)))
(let (($x131 (not $x128)))
(let ((@x133 (monotonicity (monotonicity @x116 (= $x12 $x128)) (= (not $x12) $x131))))
(let ((@x58 (|not-or-elim| (|not-or-elim| (asserted (not (or (and $x7 $x9) $x49))) (not $x49)) (not $x12))))
(let ((@x340 (mp (mp (mp @x58 @x133 $x131) (|rewrite*| (= $x131 $x131)) $x131) @x339 $x337)))
(let ((@x685 (|unit-resolution| @x659 (|unit-resolution| (mp @x340 @x465 $x467) (hypothesis $x316) $x466) (|unit-resolution| (mp @x333 @x476 $x474) (hypothesis $x316) $x319) (lemma (|unit-resolution| @x679 @x675 @x674 false) $x348) false)))
(let (($x556 (not $x26)))
(let (($x594 (or $x375 $x556)))
(let ((@x600 (monotonicity (rewrite (= (and $x378 $x26) (not $x594))) (= (not (and $x378 $x26)) (not (not $x594))))))
(let ((@x604 (trans @x600 (rewrite (= (not (not $x594)) $x594)) (= (not (and $x378 $x26)) $x594))))
(let (($x429 (and $x378 $x26)))
(let (($x432 (not $x429)))
(let ((@x434 (monotonicity (monotonicity @x380 (= (and $x165 $x26) $x429)) (= (not (and $x165 $x26)) $x432))))
(let (($x214 (and $x165 $x26)))
(let (($x217 (not $x214)))
(let ((@x219 (monotonicity (monotonicity (rewrite (= $x20 $x165)) (= $x31 $x214)) (= (not $x31) $x217))))
(let ((@x277 (mp (mp (|not-or-elim| @x96 (not $x31)) @x219 $x217) (|rewrite*| (= $x217 $x217)) $x217)))
(let ((@x690 (|unit-resolution| (mp (mp @x277 @x434 $x432) @x604 $x594) (hypothesis $x378) $x556)))
(let ((@x695 (mp @x690 (monotonicity (commutativity (= $x26 $x16)) (= $x556 $x493)) $x493)))
(let (($x582 (or $x375 $x342)))
(let ((@x588 (monotonicity (rewrite (= (and $x378 $x345) (not $x582))) (= (not (and $x378 $x345)) (not (not $x582))))))
(let ((@x592 (trans @x588 (rewrite (= (not (not $x582)) $x582)) (= (not (and $x378 $x345)) $x582))))
(let (($x422 (and $x378 $x345)))
(let (($x425 (not $x422)))
(let ((@x427 (monotonicity (monotonicity @x380 @x347 (= (and $x165 $x136) $x422)) (= (not (and $x165 $x136)) $x425))))
(let (($x207 (and $x165 $x136)))
(let (($x210 (not $x207)))
(let ((@x167 (rewrite (= $x20 $x165))))
(let ((@x212 (monotonicity (monotonicity @x167 (rewrite (= $x13 $x136)) (= $x30 $x207)) (= (not $x30) $x210))))
(let ((@x94 (|not-or-elim| (|not-or-elim| @x88 (not (or $x30 (or $x31 (or $x32 $x37))))) (not $x30))))
(let ((@x428 (mp (mp (mp @x94 @x212 $x210) (|rewrite*| (= $x210 $x210)) $x210) @x427 $x425)))
(let ((@x689 (|unit-resolution| @x679 (|unit-resolution| (mp @x428 @x592 $x582) (hypothesis $x378) $x342) $x16)))
(let ((@x698 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x18 $x378 $x316)) (lemma (|unit-resolution| @x689 @x695 false) $x375) (lemma @x685 $x312) $x18)))
(let (($x28 (= |n$a| |m$|)))
(let (($x507 (or $x506 $x319)))
(let ((@x513 (monotonicity (rewrite (= (and $x18 $x324) (not $x507))) (= (not (and $x18 $x324)) (not (not $x507))))))
(let ((@x517 (trans @x513 (rewrite (= (not (not $x507)) $x507)) (= (not (and $x18 $x324)) $x507))))
(let (($x368 (and $x18 $x324)))
(let (($x371 (not $x368)))
(let ((@x373 (monotonicity (monotonicity @x326 (= (and $x18 $x118) $x368)) (= (not (and $x18 $x118)) $x371))))
(let (($x157 (and $x18 $x118)))
(let (($x160 (not $x157)))
(let ((@x162 (monotonicity (monotonicity @x120 (= $x19 $x157)) (= (not $x19) $x160))))
(let ((@x256 (mp (mp (|not-or-elim| @x68 (not $x19)) @x162 $x160) (|rewrite*| (= $x160 $x160)) $x160)))
(let ((@x703 (|unit-resolution| @x659 (|unit-resolution| (mp (mp @x256 @x373 $x371) @x517 $x507) @x698 $x319) (lemma (|unit-resolution| @x679 @x675 @x674 false) $x348) $x11)))
(let (($x642 (or (not $x28) $x531)))
(let ((@x648 (monotonicity (rewrite (= (and $x28 $x22) (not $x642))) (= (not (and $x28 $x22)) (not (not $x642))))))
(let ((@x652 (trans @x648 (rewrite (= (not (not $x642)) $x642)) (= (not (and $x28 $x22)) $x642))))
(let (($x35 (and $x28 $x22)))
(let (($x111 (not $x35)))
(let ((@x653 (mp (mp (|not-or-elim| @x108 $x111) (|rewrite*| (= $x111 $x111)) $x111) @x652 $x642)))
(|unit-resolution| @x653 (mp @x703 (symm (commutativity (= $x28 $x11)) (= $x11 $x28)) $x28) (mp @x698 @x700 $x22) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
4464df6a987862165c07a2bd783815dc9c588fb6 888 0
unsat
((set-logic AUFLIA)
(proof
(let (($x917 (>= (+ |x7$| (* (~ 1) (ite (>= |x7$| 0) |x7$| (* (~ 1) |x7$|)))) 0)))
(let (($x954 (not $x917)))
(let (($x904 (<= (+ |x2$| (* (~ 1) |x11$|)) 0)))
(let (($x1013 (not $x904)))
(let (($x71 (= |x2$| |x11$|)))
(let (($x808 (not $x71)))
(let (($x70 (= |x1$| |x10$|)))
(let (($x900 (<= (+ |x1$| (* (~ 1) |x10$|)) 0)))
(let (($x925 (<= (+ |x4$| (* (~ 1) (ite (>= |x4$| 0) |x4$| (* (~ 1) |x4$|)))) 0)))
(let (($x1023 (>= (+ |x5$| (* (~ 1) (ite (>= |x5$| 0) |x5$| (* (~ 1) |x5$|)))) 0)))
(let ((?x180 (* (~ 1) |x5$|)))
(let (($x642 (>= |x5$| 0)))
(let ((?x645 (ite $x642 |x5$| ?x180)))
(let (($x845 (= |x5$| ?x645)))
(let (($x1628 (<= (+ |x10$| (* (~ 1) (ite (>= |x10$| 0) |x10$| (* (~ 1) |x10$|)))) 0)))
(let ((?x335 (* (~ 1) |x10$|)))
(let (($x782 (>= |x10$| 0)))
(let ((?x785 (ite $x782 |x10$| ?x335)))
(let (($x890 (= |x10$| ?x785)))
(let (($x891 (= ?x335 ?x785)))
(let (($x1368 (not $x891)))
(let (($x1496 (<= (+ ?x335 (* (~ 1) ?x785)) 0)))
(let (($x1508 (not $x1496)))
(let ((?x304 (* (~ 1) |x9$|)))
(let (($x754 (>= |x9$| 0)))
(let ((?x757 (ite $x754 |x9$| ?x304)))
(let ((?x766 (* (~ 1) ?x757)))
(let (($x1616 (>= (+ ?x304 ?x766) 0)))
(let (($x882 (= ?x304 ?x757)))
(let (($x883 (not $x754)))
(let (($x847 (not $x642)))
(let ((@x1091 (hypothesis $x847)))
(let (($x670 (>= |x6$| 0)))
(let ((?x149 (* (~ 1) |x4$|)))
(let (($x614 (>= |x4$| 0)))
(let ((?x617 (ite $x614 |x4$| ?x149)))
(let (($x836 (= |x4$| ?x617)))
(let ((@x1325 (hypothesis $x754)))
(let (($x914 (>= (+ |x8$| (* (~ 1) (ite (>= |x8$| 0) |x8$| (* (~ 1) |x8$|)))) 0)))
(let (($x1107 (not $x914)))
(let (($x838 (not $x614)))
(let ((@x1010 (hypothesis $x838)))
(let ((?x654 (* (~ 1) ?x645)))
(let ((?x655 (+ |x4$| |x6$| ?x654)))
(let (($x853 (>= ?x655 0)))
(let (($x656 (= ?x655 0)))
(let (($x171 (<= 0 |x5$|)))
(let ((?x186 (ite $x171 |x5$| ?x180)))
(let ((?x636 (+ ?x149 ?x186)))
(let (($x639 (= |x6$| ?x636)))
(let ((@x650 (monotonicity (monotonicity (rewrite (= $x171 $x642)) (= ?x186 ?x645)) (= ?x636 (+ ?x149 ?x645)))))
(let ((@x660 (trans (monotonicity @x650 (= $x639 (= |x6$| (+ ?x149 ?x645)))) (rewrite (= (= |x6$| (+ ?x149 ?x645)) $x656)) (= $x639 $x656))))
(let ((@x641 (monotonicity (rewrite (= (+ ?x186 ?x149) ?x636)) (= (= |x6$| (+ ?x186 ?x149)) $x639))))
(let ((?x194 (+ ?x186 ?x149)))
(let (($x199 (= |x6$| ?x194)))
(let ((@x492 (monotonicity (monotonicity (rewrite (= $x171 $x171)) (= ?x186 ?x186)) (= ?x194 ?x194))))
(let (($x326 (<= 0 |x10$|)))
(let ((?x341 (ite $x326 |x10$| ?x335)))
(let ((?x349 (+ ?x341 ?x304)))
(let (($x354 (= |x11$| ?x349)))
(let ((?x273 (* (~ 1) |x8$|)))
(let (($x295 (<= 0 |x9$|)))
(let ((?x310 (ite $x295 |x9$| ?x304)))
(let ((?x318 (+ ?x310 ?x273)))
(let (($x323 (= |x10$| ?x318)))
(let ((?x242 (* (~ 1) |x7$|)))
(let (($x264 (<= 0 |x8$|)))
(let ((?x279 (ite $x264 |x8$| ?x273)))
(let ((?x287 (+ ?x279 ?x242)))
(let (($x292 (= |x9$| ?x287)))
(let ((?x211 (* (~ 1) |x6$|)))
(let (($x233 (<= 0 |x7$|)))
(let ((?x248 (ite $x233 |x7$| ?x242)))
(let ((?x256 (+ ?x248 ?x211)))
(let (($x261 (= |x8$| ?x256)))
(let (($x202 (<= 0 |x6$|)))
(let ((?x217 (ite $x202 |x6$| ?x211)))
(let ((?x225 (+ ?x217 ?x180)))
(let (($x230 (= |x7$| ?x225)))
(let ((?x118 (* (~ 1) |x3$|)))
(let (($x140 (<= 0 |x4$|)))
(let ((?x155 (ite $x140 |x4$| ?x149)))
(let ((?x163 (+ ?x155 ?x118)))
(let (($x168 (= |x5$| ?x163)))
(let ((?x86 (* (~ 1) |x2$|)))
(let (($x109 (<= 0 |x3$|)))
(let ((?x124 (ite $x109 |x3$| ?x118)))
(let ((?x132 (+ ?x124 ?x86)))
(let (($x137 (= |x4$| ?x132)))
(let ((?x100 (* (~ 1) |x1$|)))
(let (($x76 (<= 0 |x2$|)))
(let ((?x92 (ite $x76 |x2$| ?x86)))
(let ((?x101 (+ ?x92 ?x100)))
(let (($x106 (= |x3$| ?x101)))
(let (($x411 (and $x106 $x137 $x168 $x199 $x230 $x261 $x292 $x323 $x354)))
(let (($x72 (and $x70 $x71)))
(let (($x62 (and (= |x10$| (- (ite (< |x9$| 0) (- |x9$|) |x9$|) |x8$|)) (= |x11$| (- (ite (< |x10$| 0) (- |x10$|) |x10$|) |x9$|)))))
(let (($x63 (and (= |x9$| (- (ite (< |x8$| 0) (- |x8$|) |x8$|) |x7$|)) $x62)))
(let (($x64 (and (= |x8$| (- (ite (< |x7$| 0) (- |x7$|) |x7$|) |x6$|)) $x63)))
(let (($x65 (and (= |x7$| (- (ite (< |x6$| 0) (- |x6$|) |x6$|) |x5$|)) $x64)))
(let (($x66 (and (= |x6$| (- (ite (< |x5$| 0) (- |x5$|) |x5$|) |x4$|)) $x65)))
(let (($x67 (and (= |x5$| (- (ite (< |x4$| 0) (- |x4$|) |x4$|) |x3$|)) $x66)))
(let (($x68 (and (= |x4$| (- (ite (< |x3$| 0) (- |x3$|) |x3$|) |x2$|)) $x67)))
(let (($x69 (and (= |x3$| (- (ite (< |x2$| 0) (- |x2$|) |x2$|) |x1$|)) $x68)))
(let (($x73 (=> $x69 $x72)))
(let (($x74 (not $x73)))
(let ((@x413 (rewrite (= (and $x106 (and $x137 $x168 $x199 $x230 $x261 $x292 $x323 $x354)) $x411))))
(let (($x403 (and $x137 $x168 $x199 $x230 $x261 $x292 $x323 $x354)))
(let ((@x405 (rewrite (= (and $x137 (and $x168 $x199 $x230 $x261 $x292 $x323 $x354)) $x403))))
(let (($x395 (and $x168 $x199 $x230 $x261 $x292 $x323 $x354)))
(let (($x387 (and $x199 $x230 $x261 $x292 $x323 $x354)))
(let (($x379 (and $x230 $x261 $x292 $x323 $x354)))
(let ((@x373 (rewrite (= (and $x261 (and $x292 $x323 $x354)) (and $x261 $x292 $x323 $x354)))))
(let (($x355 (= (= |x11$| (- (ite (< |x10$| 0) (- |x10$|) |x10$|) |x9$|)) $x354)))
(let ((?x59 (ite (< |x10$| 0) (- |x10$|) |x10$|)))
(let ((?x60 (- ?x59 |x9$|)))
(let ((@x334 (trans (rewrite (= (< |x10$| 0) (not $x326))) (monotonicity (rewrite (= $x326 $x326)) (= (not $x326) (not $x326))) (= (< |x10$| 0) (not $x326)))))
(let ((@x340 (monotonicity @x334 (rewrite (= (- |x10$|) ?x335)) (= ?x59 (ite (not $x326) ?x335 |x10$|)))))
(let ((@x345 (trans @x340 (rewrite (= (ite (not $x326) ?x335 |x10$|) ?x341)) (= ?x59 ?x341))))
(let ((@x353 (trans (monotonicity @x345 (= ?x60 (- ?x341 |x9$|))) (rewrite (= (- ?x341 |x9$|) ?x349)) (= ?x60 ?x349))))
(let (($x324 (= (= |x10$| (- (ite (< |x9$| 0) (- |x9$|) |x9$|) |x8$|)) $x323)))
(let ((@x303 (trans (rewrite (= (< |x9$| 0) (not $x295))) (monotonicity (rewrite (= $x295 $x295)) (= (not $x295) (not $x295))) (= (< |x9$| 0) (not $x295)))))
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(let ((@x314 (trans @x309 (rewrite (= (ite (not $x295) ?x304 |x9$|) ?x310)) (= (ite (< |x9$| 0) (- |x9$|) |x9$|) ?x310))))
(let ((@x317 (monotonicity @x314 (= (- (ite (< |x9$| 0) (- |x9$|) |x9$|) |x8$|) (- ?x310 |x8$|)))))
(let ((@x322 (trans @x317 (rewrite (= (- ?x310 |x8$|) ?x318)) (= (- (ite (< |x9$| 0) (- |x9$|) |x9$|) |x8$|) ?x318))))
(let ((@x359 (monotonicity (monotonicity @x322 $x324) (monotonicity @x353 $x355) (= $x62 (and $x323 $x354)))))
(let ((@x272 (trans (rewrite (= (< |x8$| 0) (not $x264))) (monotonicity (rewrite (= $x264 $x264)) (= (not $x264) (not $x264))) (= (< |x8$| 0) (not $x264)))))
(let ((@x278 (monotonicity @x272 (rewrite (= (- |x8$|) ?x273)) (= (ite (< |x8$| 0) (- |x8$|) |x8$|) (ite (not $x264) ?x273 |x8$|)))))
(let ((@x283 (trans @x278 (rewrite (= (ite (not $x264) ?x273 |x8$|) ?x279)) (= (ite (< |x8$| 0) (- |x8$|) |x8$|) ?x279))))
(let ((@x286 (monotonicity @x283 (= (- (ite (< |x8$| 0) (- |x8$|) |x8$|) |x7$|) (- ?x279 |x7$|)))))
(let ((@x291 (trans @x286 (rewrite (= (- ?x279 |x7$|) ?x287)) (= (- (ite (< |x8$| 0) (- |x8$|) |x8$|) |x7$|) ?x287))))
(let ((@x294 (monotonicity @x291 (= (= |x9$| (- (ite (< |x8$| 0) (- |x8$|) |x8$|) |x7$|)) $x292))))
(let ((@x367 (trans (monotonicity @x294 @x359 (= $x63 (and $x292 (and $x323 $x354)))) (rewrite (= (and $x292 (and $x323 $x354)) (and $x292 $x323 $x354))) (= $x63 (and $x292 $x323 $x354)))))
(let ((@x241 (trans (rewrite (= (< |x7$| 0) (not $x233))) (monotonicity (rewrite (= $x233 $x233)) (= (not $x233) (not $x233))) (= (< |x7$| 0) (not $x233)))))
(let ((@x247 (monotonicity @x241 (rewrite (= (- |x7$|) ?x242)) (= (ite (< |x7$| 0) (- |x7$|) |x7$|) (ite (not $x233) ?x242 |x7$|)))))
(let ((@x252 (trans @x247 (rewrite (= (ite (not $x233) ?x242 |x7$|) ?x248)) (= (ite (< |x7$| 0) (- |x7$|) |x7$|) ?x248))))
(let ((@x255 (monotonicity @x252 (= (- (ite (< |x7$| 0) (- |x7$|) |x7$|) |x6$|) (- ?x248 |x6$|)))))
(let ((@x260 (trans @x255 (rewrite (= (- ?x248 |x6$|) ?x256)) (= (- (ite (< |x7$| 0) (- |x7$|) |x7$|) |x6$|) ?x256))))
(let ((@x263 (monotonicity @x260 (= (= |x8$| (- (ite (< |x7$| 0) (- |x7$|) |x7$|) |x6$|)) $x261))))
(let ((@x375 (trans (monotonicity @x263 @x367 (= $x64 (and $x261 (and $x292 $x323 $x354)))) @x373 (= $x64 (and $x261 $x292 $x323 $x354)))))
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(let ((@x221 (trans @x216 (rewrite (= (ite (not $x202) ?x211 |x6$|) ?x217)) (= (ite (< |x6$| 0) (- |x6$|) |x6$|) ?x217))))
(let ((@x224 (monotonicity @x221 (= (- (ite (< |x6$| 0) (- |x6$|) |x6$|) |x5$|) (- ?x217 |x5$|)))))
(let ((@x229 (trans @x224 (rewrite (= (- ?x217 |x5$|) ?x225)) (= (- (ite (< |x6$| 0) (- |x6$|) |x6$|) |x5$|) ?x225))))
(let ((@x232 (monotonicity @x229 (= (= |x7$| (- (ite (< |x6$| 0) (- |x6$|) |x6$|) |x5$|)) $x230))))
(let ((@x378 (monotonicity @x232 @x375 (= $x65 (and $x230 (and $x261 $x292 $x323 $x354))))))
(let ((@x383 (trans @x378 (rewrite (= (and $x230 (and $x261 $x292 $x323 $x354)) $x379)) (= $x65 $x379))))
(let ((@x179 (trans (rewrite (= (< |x5$| 0) (not $x171))) (monotonicity (rewrite (= $x171 $x171)) (= (not $x171) (not $x171))) (= (< |x5$| 0) (not $x171)))))
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(let ((@x190 (trans @x185 (rewrite (= (ite (not $x171) ?x180 |x5$|) ?x186)) (= (ite (< |x5$| 0) (- |x5$|) |x5$|) ?x186))))
(let ((@x193 (monotonicity @x190 (= (- (ite (< |x5$| 0) (- |x5$|) |x5$|) |x4$|) (- ?x186 |x4$|)))))
(let ((@x198 (trans @x193 (rewrite (= (- ?x186 |x4$|) ?x194)) (= (- (ite (< |x5$| 0) (- |x5$|) |x5$|) |x4$|) ?x194))))
(let ((@x201 (monotonicity @x198 (= (= |x6$| (- (ite (< |x5$| 0) (- |x5$|) |x5$|) |x4$|)) $x199))))
(let ((@x391 (trans (monotonicity @x201 @x383 (= $x66 (and $x199 $x379))) (rewrite (= (and $x199 $x379) $x387)) (= $x66 $x387))))
(let ((@x148 (trans (rewrite (= (< |x4$| 0) (not $x140))) (monotonicity (rewrite (= $x140 $x140)) (= (not $x140) (not $x140))) (= (< |x4$| 0) (not $x140)))))
(let ((@x154 (monotonicity @x148 (rewrite (= (- |x4$|) ?x149)) (= (ite (< |x4$| 0) (- |x4$|) |x4$|) (ite (not $x140) ?x149 |x4$|)))))
(let ((@x159 (trans @x154 (rewrite (= (ite (not $x140) ?x149 |x4$|) ?x155)) (= (ite (< |x4$| 0) (- |x4$|) |x4$|) ?x155))))
(let ((@x162 (monotonicity @x159 (= (- (ite (< |x4$| 0) (- |x4$|) |x4$|) |x3$|) (- ?x155 |x3$|)))))
(let ((@x167 (trans @x162 (rewrite (= (- ?x155 |x3$|) ?x163)) (= (- (ite (< |x4$| 0) (- |x4$|) |x4$|) |x3$|) ?x163))))
(let ((@x170 (monotonicity @x167 (= (= |x5$| (- (ite (< |x4$| 0) (- |x4$|) |x4$|) |x3$|)) $x168))))
(let ((@x399 (trans (monotonicity @x170 @x391 (= $x67 (and $x168 $x387))) (rewrite (= (and $x168 $x387) $x395)) (= $x67 $x395))))
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(let ((@x128 (trans @x123 (rewrite (= (ite (not $x109) ?x118 |x3$|) ?x124)) (= (ite (< |x3$| 0) (- |x3$|) |x3$|) ?x124))))
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(let ((@x136 (trans @x131 (rewrite (= (- ?x124 |x2$|) ?x132)) (= (- (ite (< |x3$| 0) (- |x3$|) |x3$|) |x2$|) ?x132))))
(let ((@x139 (monotonicity @x136 (= (= |x4$| (- (ite (< |x3$| 0) (- |x3$|) |x3$|) |x2$|)) $x137))))
(let ((@x407 (trans (monotonicity @x139 @x399 (= $x68 (and $x137 $x395))) @x405 (= $x68 $x403))))
(let ((@x84 (trans (rewrite (= (< |x2$| 0) (not $x76))) (monotonicity (rewrite (= $x76 $x76)) (= (not $x76) (not $x76))) (= (< |x2$| 0) (not $x76)))))
(let ((@x91 (monotonicity @x84 (rewrite (= (- |x2$|) ?x86)) (= (ite (< |x2$| 0) (- |x2$|) |x2$|) (ite (not $x76) ?x86 |x2$|)))))
(let ((@x96 (trans @x91 (rewrite (= (ite (not $x76) ?x86 |x2$|) ?x92)) (= (ite (< |x2$| 0) (- |x2$|) |x2$|) ?x92))))
(let ((@x99 (monotonicity @x96 (= (- (ite (< |x2$| 0) (- |x2$|) |x2$|) |x1$|) (- ?x92 |x1$|)))))
(let ((@x105 (trans @x99 (rewrite (= (- ?x92 |x1$|) ?x101)) (= (- (ite (< |x2$| 0) (- |x2$|) |x2$|) |x1$|) ?x101))))
(let ((@x108 (monotonicity @x105 (= (= |x3$| (- (ite (< |x2$| 0) (- |x2$|) |x2$|) |x1$|)) $x106))))
(let ((@x415 (trans (monotonicity @x108 @x407 (= $x69 (and $x106 $x403))) @x413 (= $x69 $x411))))
(let ((@x424 (trans (monotonicity @x415 (= $x73 (=> $x411 $x72))) (rewrite (= (=> $x411 $x72) (or (not $x411) $x72))) (= $x73 (or (not $x411) $x72)))))
(let ((@x428 (mp (asserted $x74) (monotonicity @x424 (= $x74 (not (or (not $x411) $x72)))) (not (or (not $x411) $x72)))))
(let ((@x429 (|not-or-elim| @x428 $x411)))
(let ((@x494 (mp (mp (|and-elim| @x429 $x199) (|rewrite*| (= $x199 $x199)) $x199) (monotonicity @x492 (= $x199 $x199)) $x199)))
(let ((@x663 (mp (mp @x494 (monotonicity @x492 (= $x199 $x199)) $x199) (trans @x641 @x660 (= $x199 $x656)) $x656)))
(let ((@x1046 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x656) $x853)) @x663 $x853)))
(let (($x1180 (<= (+ ?x180 ?x654) 0)))
(let (($x846 (= ?x180 ?x645)))
(let ((@x1247 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x846) $x1180)) (|unit-resolution| (|def-axiom| (or $x642 $x846)) @x1091 $x846) $x1180)))
(let (($x726 (>= |x8$| 0)))
(let ((?x729 (ite $x726 |x8$| ?x273)))
(let ((?x738 (* (~ 1) ?x729)))
(let ((?x739 (+ |x7$| |x9$| ?x738)))
(let (($x879 (<= ?x739 0)))
(let (($x740 (= ?x739 0)))
(let ((@x734 (monotonicity (monotonicity (rewrite (= $x264 $x726)) (= ?x279 ?x729)) (= (+ ?x242 ?x279) (+ ?x242 ?x729)))))
(let ((@x737 (monotonicity @x734 (= (= |x9$| (+ ?x242 ?x279)) (= |x9$| (+ ?x242 ?x729))))))
(let ((@x744 (trans @x737 (rewrite (= (= |x9$| (+ ?x242 ?x729)) $x740)) (= (= |x9$| (+ ?x242 ?x279)) $x740))))
(let ((@x725 (monotonicity (rewrite (= ?x287 (+ ?x242 ?x279))) (= $x292 (= |x9$| (+ ?x242 ?x279))))))
(let ((@x510 (monotonicity (monotonicity (rewrite (= $x264 $x264)) (= ?x279 ?x279)) (= ?x287 ?x287))))
(let ((@x512 (mp (mp (|and-elim| @x429 $x292) (|rewrite*| (= $x292 $x292)) $x292) (monotonicity @x510 (= $x292 $x292)) $x292)))
(let ((@x747 (mp (mp @x512 (monotonicity @x510 (= $x292 $x292)) $x292) (trans @x725 @x744 (= $x292 $x740)) $x740)))
(let ((@x1104 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x740) $x879)) @x747 $x879)))
(let (($x698 (>= |x7$| 0)))
(let ((?x701 (ite $x698 |x7$| ?x242)))
(let (($x863 (= |x7$| ?x701)))
(let (($x1027 (<= (+ ?x211 (* (~ 1) (ite $x670 |x6$| ?x211))) 0)))
(let ((?x673 (ite $x670 |x6$| ?x211)))
(let (($x855 (= ?x211 ?x673)))
(let (($x856 (not $x670)))
(let (($x865 (not $x698)))
(let ((@x1274 (hypothesis $x865)))
(let ((@x1273 (hypothesis $x670)))
(let ((?x682 (* (~ 1) ?x673)))
(let ((?x683 (+ |x5$| |x7$| ?x682)))
(let (($x862 (>= ?x683 0)))
(let (($x684 (= ?x683 0)))
(let ((@x678 (monotonicity (monotonicity (rewrite (= $x202 $x670)) (= ?x217 ?x673)) (= (+ ?x180 ?x217) (+ ?x180 ?x673)))))
(let ((@x681 (monotonicity @x678 (= (= |x7$| (+ ?x180 ?x217)) (= |x7$| (+ ?x180 ?x673))))))
(let ((@x688 (trans @x681 (rewrite (= (= |x7$| (+ ?x180 ?x673)) $x684)) (= (= |x7$| (+ ?x180 ?x217)) $x684))))
(let ((@x669 (monotonicity (rewrite (= ?x225 (+ ?x180 ?x217))) (= $x230 (= |x7$| (+ ?x180 ?x217))))))
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(let ((@x500 (mp (mp (|and-elim| @x429 $x230) (|rewrite*| (= $x230 $x230)) $x230) (monotonicity @x498 (= $x230 $x230)) $x230)))
(let ((@x691 (mp (mp @x500 (monotonicity @x498 (= $x230 $x230)) $x230) (trans @x669 @x688 (= $x230 $x684)) $x684)))
(let ((@x1100 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x684) $x862)) @x691 $x862)))
(let (($x1183 (<= (+ |x6$| ?x682) 0)))
(let (($x854 (= |x6$| ?x673)))
(let ((@x858 (|def-axiom| (or $x856 $x854))))
(let ((@x1197 ((_ |th-lemma| arith triangle-eq) (or (not $x854) $x1183))))
(let ((@x1276 (|unit-resolution| @x1197 (|unit-resolution| @x858 @x1273 $x854) $x1183)))
(let ((@x1279 (lemma ((_ |th-lemma| arith farkas 1 1 1 1 1) @x1276 @x1100 @x1274 @x1091 @x1273 false) (or $x698 $x642 $x856))))
(let ((@x860 (|def-axiom| (or $x670 $x855))))
(let ((@x1310 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x855) $x1027)) (|unit-resolution| @x860 (|unit-resolution| @x1279 @x1274 @x1091 $x856) $x855) $x1027)))
(let ((@x1311 ((_ |th-lemma| arith farkas 1 1 1 1 1) (|unit-resolution| @x1279 @x1274 @x1091 $x856) @x1274 @x1100 @x1091 @x1310 false)))
(let ((@x867 (|def-axiom| (or $x865 $x863))))
(let ((@x1334 (|unit-resolution| @x867 (|unit-resolution| (lemma @x1311 (or $x698 $x642)) @x1091 $x698) $x863)))
(let ((@x1173 ((_ |th-lemma| arith triangle-eq) (or (not $x863) $x917))))
(let ((@x1335 (|unit-resolution| @x1173 @x1334 $x917)))
(let ((?x710 (* (~ 1) ?x701)))
(let ((?x711 (+ |x6$| |x8$| ?x710)))
(let (($x870 (<= ?x711 0)))
(let (($x712 (= ?x711 0)))
(let ((@x706 (monotonicity (monotonicity (rewrite (= $x233 $x698)) (= ?x248 ?x701)) (= (+ ?x211 ?x248) (+ ?x211 ?x701)))))
(let ((@x709 (monotonicity @x706 (= (= |x8$| (+ ?x211 ?x248)) (= |x8$| (+ ?x211 ?x701))))))
(let ((@x716 (trans @x709 (rewrite (= (= |x8$| (+ ?x211 ?x701)) $x712)) (= (= |x8$| (+ ?x211 ?x248)) $x712))))
(let ((@x697 (monotonicity (rewrite (= ?x256 (+ ?x211 ?x248))) (= $x261 (= |x8$| (+ ?x211 ?x248))))))
(let ((@x504 (monotonicity (monotonicity (rewrite (= $x233 $x233)) (= ?x248 ?x248)) (= ?x256 ?x256))))
(let ((@x506 (mp (mp (|and-elim| @x429 $x261) (|rewrite*| (= $x261 $x261)) $x261) (monotonicity @x504 (= $x261 $x261)) $x261)))
(let ((@x719 (mp (mp @x506 (monotonicity @x504 (= $x261 $x261)) $x261) (trans @x697 @x716 (= $x261 $x712)) $x712)))
(let ((@x950 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x712) $x870)) @x719 $x870)))
(let ((@x1105 (hypothesis $x914)))
(let ((@x1351 (lemma ((_ |th-lemma| arith farkas 1 1 1 1 1 1 1 1 1) @x1105 @x950 @x1335 @x1104 @x1010 @x1247 @x1091 @x1046 @x1325 false) (or $x614 $x1107 $x642 $x883))))
(let (($x872 (= |x8$| ?x729)))
(let (($x1087 (<= (+ |x7$| ?x710) 0)))
(let ((@x1112 ((_ |th-lemma| arith triangle-eq) (or (not $x863) $x1087))))
(let ((@x1336 (|unit-resolution| @x1112 @x1334 $x1087)))
(let (($x871 (>= ?x711 0)))
(let ((@x1082 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x712) $x871)) @x719 $x871)))
(let ((@x1488 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1) (or $x614 (not $x1180) $x642 (not $x853) $x670)) @x1010 @x1046 @x1247 @x1091 $x670)))
(let ((@x1341 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1) (or $x726 (not $x871) (not $x1087) (not $x1183) (not $x862) $x642))))
(let ((@x1491 (|unit-resolution| @x1341 (|unit-resolution| @x1197 (|unit-resolution| @x858 @x1488 $x854) $x1183) @x1082 @x1091 @x1336 @x1100 $x726)))
(let ((@x876 (|def-axiom| (or (not $x726) $x872))))
(let ((@x1364 ((_ |th-lemma| arith triangle-eq) (or (not $x872) $x914))))
(let ((@x1493 (|unit-resolution| @x1364 (|unit-resolution| @x876 @x1491 $x872) (|unit-resolution| @x1351 @x1010 @x1091 @x1325 $x1107) false)))
(let ((@x840 (|def-axiom| (or $x838 $x836))))
(let ((@x1574 (|unit-resolution| @x840 (|unit-resolution| (lemma @x1493 (or $x614 $x642 $x883)) @x1091 @x1325 $x614) $x836)))
(let ((@x940 ((_ |th-lemma| arith triangle-eq) (or (not $x836) $x925))))
(let (($x908 (>= (+ |x9$| ?x766) 0)))
(let (($x881 (= |x9$| ?x757)))
(let ((@x885 (|def-axiom| (or $x883 $x881))))
(let ((@x1393 ((_ |th-lemma| arith triangle-eq) (or (not $x881) $x908))))
(let ((@x1394 (|unit-resolution| @x1393 (|unit-resolution| @x885 @x1325 $x881) $x908)))
(let (($x907 (<= (+ |x9$| ?x766) 0)))
(let ((@x1398 ((_ |th-lemma| arith triangle-eq) (or (not $x881) $x907))))
(let ((@x1399 (|unit-resolution| @x1398 (|unit-resolution| @x885 @x1325 $x881) $x907)))
(let (($x905 (>= (+ |x2$| (* (~ 1) |x11$|)) 0)))
(let (($x920 (>= (+ |x6$| ?x682) 0)))
(let (($x953 (not $x920)))
(let (($x910 (<= (+ |x8$| ?x738) 0)))
(let ((?x767 (+ |x8$| |x10$| ?x766)))
(let (($x889 (>= ?x767 0)))
(let (($x768 (= ?x767 0)))
(let ((@x762 (monotonicity (monotonicity (rewrite (= $x295 $x754)) (= ?x310 ?x757)) (= (+ ?x273 ?x310) (+ ?x273 ?x757)))))
(let ((@x765 (monotonicity @x762 (= (= |x10$| (+ ?x273 ?x310)) (= |x10$| (+ ?x273 ?x757))))))
(let ((@x772 (trans @x765 (rewrite (= (= |x10$| (+ ?x273 ?x757)) $x768)) (= (= |x10$| (+ ?x273 ?x310)) $x768))))
(let ((@x753 (monotonicity (rewrite (= ?x318 (+ ?x273 ?x310))) (= $x323 (= |x10$| (+ ?x273 ?x310))))))
(let ((@x516 (monotonicity (monotonicity (rewrite (= $x295 $x295)) (= ?x310 ?x310)) (= ?x318 ?x318))))
(let ((@x518 (mp (mp (|and-elim| @x429 $x323) (|rewrite*| (= $x323 $x323)) $x323) (monotonicity @x516 (= $x323 $x323)) $x323)))
(let ((@x775 (mp (mp @x518 (monotonicity @x516 (= $x323 $x323)) $x323) (trans @x753 @x772 (= $x323 $x768)) $x768)))
(let ((@x1385 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x768) $x889)) @x775 $x889)))
(let (($x892 (not $x782)))
(let (($x1411 (not $x890)))
(let (($x911 (>= (+ |x10$| (* (~ 1) ?x785)) 0)))
(let (($x981 (not $x911)))
(let (($x957 (not $x905)))
(let ((@x958 (hypothesis $x957)))
(let (($x586 (>= |x3$| 0)))
(let ((@x978 (hypothesis $x908)))
(let ((@x963 (hypothesis $x911)))
(let (($x864 (= ?x242 ?x701)))
(let (($x1070 (not $x864)))
(let (($x1026 (<= (+ ?x242 ?x710) 0)))
(let (($x1149 (not $x1026)))
(let (($x916 (>= (+ |x4$| (* (~ 1) ?x617)) 0)))
(let (($x829 (not $x586)))
(let ((@x935 (hypothesis $x829)))
(let (($x1094 (not $x855)))
(let (($x1086 (>= (+ ?x211 ?x682) 0)))
(let (($x1119 (not $x1086)))
(let (($x928 (<= (+ |x3$| (* (~ 1) (ite $x586 |x3$| ?x118))) 0)))
(let (($x926 (<= (+ ?x118 (* (~ 1) (ite $x586 |x3$| ?x118))) 0)))
(let ((?x589 (ite $x586 |x3$| ?x118)))
(let (($x828 (= ?x118 ?x589)))
(let ((@x1005 (|unit-resolution| (|def-axiom| (or $x586 $x828)) @x935 $x828)))
(let ((@x1009 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x828) $x926)) @x1005 $x926)))
(let (($x922 (<= (+ ?x149 (* (~ 1) ?x617)) 0)))
(let (($x837 (= ?x149 ?x617)))
(let ((@x1188 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x837) $x922)) (|unit-resolution| (|def-axiom| (or $x614 $x837)) @x1010 $x837) $x922)))
(let ((@x1191 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 1) (or $x925 $x614 (not $x922))) @x1188 @x1010 $x925)))
(let ((@x1116 (hypothesis $x928)))
(let ((@x1115 (hypothesis $x925)))
(let ((@x1114 (hypothesis $x1086)))
(let ((@x1113 (|unit-resolution| @x1112 (|unit-resolution| @x867 (hypothesis $x698) $x863) $x1087)))
(let ((@x1088 (hypothesis $x698)))
(let (($x861 (<= ?x683 0)))
(let ((@x945 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x684) $x861)) @x691 $x861)))
(let ((?x626 (* (~ 1) ?x617)))
(let ((?x627 (+ |x3$| |x5$| ?x626)))
(let (($x844 (>= ?x627 0)))
(let (($x628 (= ?x627 0)))
(let ((@x622 (monotonicity (monotonicity (rewrite (= $x140 $x614)) (= ?x155 ?x617)) (= (+ ?x118 ?x155) (+ ?x118 ?x617)))))
(let ((@x625 (monotonicity @x622 (= (= |x5$| (+ ?x118 ?x155)) (= |x5$| (+ ?x118 ?x617))))))
(let ((@x632 (trans @x625 (rewrite (= (= |x5$| (+ ?x118 ?x617)) $x628)) (= (= |x5$| (+ ?x118 ?x155)) $x628))))
(let ((@x613 (monotonicity (rewrite (= ?x163 (+ ?x118 ?x155))) (= $x168 (= |x5$| (+ ?x118 ?x155))))))
(let ((@x486 (monotonicity (monotonicity (rewrite (= $x140 $x140)) (= ?x155 ?x155)) (= ?x163 ?x163))))
(let ((@x488 (mp (mp (|and-elim| @x429 $x168) (|rewrite*| (= $x168 $x168)) $x168) (monotonicity @x486 (= $x168 $x168)) $x168)))
(let ((@x635 (mp (mp @x488 (monotonicity @x486 (= $x168 $x168)) $x168) (trans @x613 @x632 (= $x168 $x628)) $x628)))
(let ((@x934 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x628) $x844)) @x635 $x844)))
(let ((?x794 (* (~ 1) ?x785)))
(let ((?x795 (+ |x9$| |x11$| ?x794)))
(let (($x897 (<= ?x795 0)))
(let (($x796 (= ?x795 0)))
(let ((@x790 (monotonicity (monotonicity (rewrite (= $x326 $x782)) (= ?x341 ?x785)) (= (+ ?x304 ?x341) (+ ?x304 ?x785)))))
(let ((@x793 (monotonicity @x790 (= (= |x11$| (+ ?x304 ?x341)) (= |x11$| (+ ?x304 ?x785))))))
(let ((@x800 (trans @x793 (rewrite (= (= |x11$| (+ ?x304 ?x785)) $x796)) (= (= |x11$| (+ ?x304 ?x341)) $x796))))
(let ((@x781 (monotonicity (rewrite (= ?x349 (+ ?x304 ?x341))) (= $x354 (= |x11$| (+ ?x304 ?x341))))))
(let ((@x522 (monotonicity (monotonicity (rewrite (= $x326 $x326)) (= ?x341 ?x341)) (= ?x349 ?x349))))
(let ((@x524 (mp (mp (|and-elim| @x429 $x354) (|rewrite*| (= $x354 $x354)) $x354) (monotonicity @x522 (= $x354 $x354)) $x354)))
(let ((@x803 (mp (mp @x524 (monotonicity @x522 (= $x354 $x354)) $x354) (trans @x781 @x800 (= $x354 $x796)) $x796)))
(let ((@x962 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x796) $x897)) @x803 $x897)))
(let ((?x598 (* (~ 1) ?x589)))
(let ((?x599 (+ |x2$| |x4$| ?x598)))
(let (($x835 (>= ?x599 0)))
(let (($x600 (= ?x599 0)))
(let ((@x594 (monotonicity (monotonicity (rewrite (= $x109 $x586)) (= ?x124 ?x589)) (= (+ ?x86 ?x124) (+ ?x86 ?x589)))))
(let ((@x597 (monotonicity @x594 (= (= |x4$| (+ ?x86 ?x124)) (= |x4$| (+ ?x86 ?x589))))))
(let ((@x604 (trans @x597 (rewrite (= (= |x4$| (+ ?x86 ?x589)) $x600)) (= (= |x4$| (+ ?x86 ?x124)) $x600))))
(let ((@x585 (monotonicity (rewrite (= ?x132 (+ ?x86 ?x124))) (= $x137 (= |x4$| (+ ?x86 ?x124))))))
(let ((@x480 (monotonicity (monotonicity (rewrite (= $x109 $x109)) (= ?x124 ?x124)) (= ?x132 ?x132))))
(let ((@x482 (mp (mp (|and-elim| @x429 $x137) (|rewrite*| (= $x137 $x137)) $x137) (monotonicity @x480 (= $x137 $x137)) $x137)))
(let ((@x607 (mp (mp @x482 (monotonicity @x480 (= $x137 $x137)) $x137) (trans @x585 @x604 (= $x137 $x600)) $x600)))
(let ((@x967 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x600) $x835)) @x607 $x835)))
(let (($x888 (<= ?x767 0)))
(let ((@x977 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x768) $x888)) @x775 $x888)))
(let ((@x1117 ((_ |th-lemma| arith farkas -1 1 -1 1 -1 -1 1 1 -1 1 1 -1 -2 1) @x1082 @x1116 @x978 @x977 @x967 @x963 @x962 @x958 @x934 @x1115 @x945 @x1114 @x1088 @x1113 false)))
(let ((@x1121 (lemma @x1117 (or $x865 (not $x928) (not $x908) $x981 $x905 (not $x925) $x1119))))
(let ((@x869 (|def-axiom| (or $x698 $x864))))
(let ((@x1127 (|unit-resolution| @x869 (|unit-resolution| @x1121 @x1114 @x978 @x963 @x958 @x1115 @x1116 $x865) $x864)))
(let ((@x1129 ((_ |th-lemma| arith farkas -1 1 -1 1 -1 -1 1 1 -1 1 1 -1 1) @x1082 @x1116 @x978 @x977 @x967 @x963 @x962 @x958 @x934 @x1115 @x945 @x1114 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1070 $x1026)) @x1127 $x1026) false)))
(let ((@x1131 (lemma @x1129 (or $x1119 (not $x928) (not $x908) $x981 $x905 (not $x925)))))
(let ((@x1192 (|unit-resolution| @x1131 @x1191 @x978 @x963 @x958 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2) (or $x928 (not $x926) $x586)) @x1009 @x935 $x928) $x1119)))
(let ((@x1139 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1094 $x1086)) (hypothesis $x855) (hypothesis $x1119) false)))
(let ((@x1140 (lemma @x1139 (or $x1094 $x1086))))
(let ((@x1195 (|unit-resolution| @x858 (|unit-resolution| @x860 (|unit-resolution| @x1140 @x1192 $x1094) $x670) $x854)))
(let (($x1022 (<= (+ |x5$| ?x654) 0)))
(let ((@x1201 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1) (or $x642 (not $x922) (not $x844) $x586 $x614)) @x1010 @x934 @x935 @x1188 $x642)))
(let ((@x849 (|def-axiom| (or $x847 $x845))))
(let ((@x1041 ((_ |th-lemma| arith triangle-eq) (or (not $x845) $x1022))))
(let ((@x1207 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1) (or $x698 (not $x1183) (not $x862) $x614 (not $x1022) (not $x853)))))
(let ((@x1208 (|unit-resolution| @x1207 @x1010 @x1100 @x1046 (|unit-resolution| @x1041 (|unit-resolution| @x849 @x1201 $x845) $x1022) (|unit-resolution| @x1197 @x1195 $x1183) $x698)))
(let (($x843 (<= ?x627 0)))
(let ((@x1079 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x628) $x843)) @x635 $x843)))
(let (($x1179 (>= (+ ?x149 ?x626) 0)))
(let ((@x1213 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x837) $x1179)) (|unit-resolution| (|def-axiom| (or $x614 $x837)) @x1010 $x837) $x1179)))
(let ((@x1214 ((_ |th-lemma| arith farkas -1 -1 1 1 -1 -1 1 1 1 -1 -1 1 1) @x1082 @x978 @x977 @x1009 @x967 @x963 @x962 @x958 (|unit-resolution| @x1197 @x1195 $x1183) @x1100 @x1213 @x1079 (|unit-resolution| @x1112 (|unit-resolution| @x867 @x1208 $x863) $x1087) false)))
(let ((@x1221 (|unit-resolution| (lemma @x1214 (or $x614 (not $x908) $x981 $x905 $x586)) @x935 @x963 @x958 @x978 $x614)))
(let ((@x1075 ((_ |th-lemma| arith triangle-eq) (or (not $x836) $x916))))
(let ((@x1225 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1) (or $x642 (not $x844) $x586 $x838 (not $x925))) (|unit-resolution| @x940 (|unit-resolution| @x840 @x1221 $x836) $x925) @x934 @x935 @x1221 $x642)))
(let ((@x1038 ((_ |th-lemma| arith triangle-eq) (or (not $x845) $x1023))))
(let ((@x1228 (|unit-resolution| @x1131 (|unit-resolution| @x940 (|unit-resolution| @x840 @x1221 $x836) $x925) @x978 @x963 @x958 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2) (or $x928 (not $x926) $x586)) @x1009 @x935 $x928) $x1119)))
(let ((@x1231 (|unit-resolution| @x858 (|unit-resolution| @x860 (|unit-resolution| @x1140 @x1228 $x1094) $x670) $x854)))
(let ((@x1055 ((_ |th-lemma| arith triangle-eq) (or (not $x854) $x920))))
(let (($x1150 (not $x916)))
(let (($x1064 (not $x1023)))
(let (($x1060 (not $x926)))
(let (($x980 (not $x908)))
(let ((@x1147 (hypothesis $x916)))
(let (($x852 (<= ?x655 0)))
(let ((@x1059 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x656) $x852)) @x663 $x852)))
(let ((@x946 (hypothesis $x920)))
(let ((@x1181 (hypothesis $x926)))
(let ((@x1182 ((_ |th-lemma| arith farkas -1 -1 1 1 -1 -1 1 1 -1 1 -2 2 -1 1 1) @x1082 @x978 @x977 @x1181 @x967 @x963 @x962 @x958 @x946 @x945 (hypothesis $x1023) @x1059 @x1147 @x1079 (hypothesis $x1026) false)))
(let ((@x1233 (|unit-resolution| (lemma @x1182 (or $x1149 $x980 $x1060 $x981 $x905 $x953 $x1064 $x1150)) @x1009 @x978 @x963 @x958 (|unit-resolution| @x1055 @x1231 $x920) (|unit-resolution| @x1038 (|unit-resolution| @x849 @x1225 $x845) $x1023) (|unit-resolution| @x1075 (|unit-resolution| @x840 @x1221 $x836) $x916) $x1149)))
(let ((@x1153 (hypothesis $x1149)))
(let ((@x1155 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1070 $x1026)) (hypothesis $x864) @x1153 false)))
(let ((@x1156 (lemma @x1155 (or $x1070 $x1026))))
(let ((@x1236 (|unit-resolution| @x867 (|unit-resolution| @x869 (|unit-resolution| @x1156 @x1233 $x1070) $x698) $x863)))
(let ((@x1238 ((_ |th-lemma| arith farkas -1 -1 1 1 -1 -1 1 1 -1 1 -2 2 -2 -1 1 1) @x1082 @x978 @x977 @x1009 @x967 @x963 @x962 @x958 (|unit-resolution| @x1055 @x1231 $x920) @x945 (|unit-resolution| @x1038 (|unit-resolution| @x849 @x1225 $x845) $x1023) @x1059 (|unit-resolution| @x869 (|unit-resolution| @x1156 @x1233 $x1070) $x698) (|unit-resolution| @x1075 (|unit-resolution| @x840 @x1221 $x836) $x916) @x1079 (|unit-resolution| @x1112 @x1236 $x1087) false)))
(let ((@x1219 (|unit-resolution| (lemma @x1238 (or $x586 $x980 $x981 $x905)) @x963 @x978 @x958 $x586)))
(let (($x827 (= |x3$| ?x589)))
(let ((@x831 (|def-axiom| (or $x829 $x827))))
(let ((@x972 ((_ |th-lemma| arith triangle-eq) (or (not $x827) $x928))))
(let ((@x1241 (|unit-resolution| @x972 (|unit-resolution| @x831 @x1219 $x827) $x928)))
(let ((@x1258 (|unit-resolution| @x1140 (|unit-resolution| @x1131 @x1191 @x978 @x963 @x958 @x1241 $x1119) $x1094)))
(let ((@x1261 (|unit-resolution| @x1197 (|unit-resolution| @x858 (|unit-resolution| @x860 @x1258 $x670) $x854) $x1183)))
(let ((@x1248 (hypothesis $x1183)))
(let ((@x1251 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 2) (or $x698 (not $x1183) (not $x862) $x614 (not $x853) (not $x1180) $x642))))
(let ((@x1253 (|unit-resolution| @x867 (|unit-resolution| @x1251 @x1091 @x1046 @x1100 @x1010 @x1248 @x1247 $x698) $x863)))
(let ((@x1011 (hypothesis $x904)))
(let ((@x1255 ((_ |th-lemma| arith farkas 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1) @x1082 @x1248 @x1100 @x1091 @x978 @x977 @x967 @x963 @x962 @x1011 @x934 @x1188 @x1116 @x1010 (|unit-resolution| @x1112 @x1253 $x1087) false)))
(let ((@x1262 (|unit-resolution| (lemma @x1255 (or $x642 (not $x1183) $x980 $x981 $x1013 (not $x928) $x614)) @x1261 @x978 @x963 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x905 $x904)) @x958 $x904) @x1241 @x1010 $x642)))
(let ((@x1265 (|unit-resolution| @x1207 (|unit-resolution| @x1041 (|unit-resolution| @x849 @x1262 $x845) $x1022) @x1100 @x1010 @x1261 @x1046 $x698)))
(let ((@x1268 ((_ |th-lemma| arith farkas -1/2 1/2 -1/2 1/2 -1/2 1/2 1/2 -1/2 1/2 1/2 -1/2 -1/2 -1/2 1) @x1079 @x1213 (|unit-resolution| @x1112 (|unit-resolution| @x867 @x1265 $x863) $x1087) @x1082 @x1261 @x1100 @x978 @x977 @x967 @x963 @x962 @x958 @x1241 @x1219 false)))
(let ((@x1272 (|unit-resolution| (lemma @x1268 (or $x614 $x980 $x981 $x905)) @x963 @x978 @x958 $x614)))
(let ((@x1282 (|unit-resolution| @x1131 (|unit-resolution| @x940 (|unit-resolution| @x840 @x1272 $x836) $x925) @x978 @x963 @x958 @x1241 $x1119)))
(let ((@x1284 (|unit-resolution| @x860 (|unit-resolution| @x1140 @x1282 $x1094) $x670)))
(let (($x1271 (>= (+ ?x180 ?x654) 0)))
(let ((@x1287 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x846) $x1271)) (|unit-resolution| (|def-axiom| (or $x642 $x846)) @x1091 $x846) $x1271)))
(let ((@x1290 (|unit-resolution| @x1112 (|unit-resolution| @x867 (|unit-resolution| @x1279 @x1091 @x1284 $x698) $x863) $x1087)))
(let ((@x1293 ((_ |th-lemma| arith farkas -1 1 -1 1 1 -1 1 1 -1 -1 -1 1 -1 1 1) (|unit-resolution| @x1197 (|unit-resolution| @x858 @x1284 $x854) $x1183) @x1100 @x1290 @x1082 @x978 @x977 @x967 @x963 @x962 @x958 @x1241 @x1287 @x1059 @x1219 @x1284 false)))
(let ((@x1298 (|unit-resolution| (lemma @x1293 (or $x642 $x980 $x981 $x905)) @x963 @x978 @x958 $x642)))
(let ((@x1144 (|unit-resolution| @x972 (|unit-resolution| @x831 (hypothesis $x586) $x827) $x928)))
(let ((@x1148 ((_ |th-lemma| arith farkas -1/2 1/2 1 -1 -1/2 1/2 -1/2 1/2 -1/2 1/2 1/2 -1/2 -1/2 -1/2 1/2 1) @x1079 @x1147 (hypothesis $x1023) @x1059 (hypothesis $x1026) @x1082 @x1144 @x978 @x977 @x967 @x963 @x962 @x958 @x945 @x946 (hypothesis $x586) false)))
(let ((@x1301 (|unit-resolution| (lemma @x1148 (or $x1149 $x1150 $x1064 $x980 $x981 $x905 $x953 $x829)) (|unit-resolution| @x1038 (|unit-resolution| @x849 @x1298 $x845) $x1023) @x1219 @x978 @x963 @x958 (|unit-resolution| @x1075 (|unit-resolution| @x840 @x1272 $x836) $x916) (|unit-resolution| @x1055 (|unit-resolution| @x858 @x1284 $x854) $x920) $x1149)))
(let ((@x1304 (|unit-resolution| @x867 (|unit-resolution| @x869 (|unit-resolution| @x1156 @x1301 $x1070) $x698) $x863)))
(let ((@x1306 ((_ |th-lemma| arith farkas 1 -1 1/2 -1/2 1 1/2 -1/2 -1/2 1/2 1/2 -1/2 1/2 1/2 -1/2 -1/2 -1/2 1) (|unit-resolution| @x1038 (|unit-resolution| @x849 @x1298 $x845) $x1023) @x1059 (|unit-resolution| @x1075 (|unit-resolution| @x840 @x1272 $x836) $x916) @x1079 (|unit-resolution| @x869 (|unit-resolution| @x1156 @x1301 $x1070) $x698) (|unit-resolution| @x1055 (|unit-resolution| @x858 @x1284 $x854) $x920) @x945 (|unit-resolution| @x1112 @x1304 $x1087) @x1082 @x978 @x977 @x967 @x963 @x962 @x958 @x1241 @x1219 false)))
(let ((@x1414 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1411 $x911)) (hypothesis $x890) (hypothesis $x981) false)))
(let ((@x1415 (lemma @x1414 (or $x1411 $x911))))
(let ((@x1417 (|unit-resolution| @x1415 (|unit-resolution| (lemma @x1306 (or $x981 $x980 $x905)) @x958 @x1394 $x981) $x1411)))
(let ((@x894 (|def-axiom| (or $x892 $x890))))
(let ((@x1418 (|unit-resolution| @x894 @x1417 $x892)))
(let ((@x1440 ((_ |th-lemma| arith assign-bounds 1 1 1 1) (or $x726 $x782 (not $x907) (not $x889) $x883))))
(let ((@x1465 (|unit-resolution| @x876 (|unit-resolution| @x1440 @x1418 @x1385 @x1325 @x1399 $x726) $x872)))
(let ((@x1376 ((_ |th-lemma| arith triangle-eq) (or (not $x872) $x910))))
(let ((@x1466 (|unit-resolution| @x1376 @x1465 $x910)))
(let (($x1031 (not $x925)))
(let (($x992 (not $x922)))
(let ((@x1092 (hypothesis $x856)))
(let ((@x1050 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1) (or $x670 (not $x1022) (not $x844) $x586 $x1031 (not $x853)))))
(let ((@x1317 (|unit-resolution| @x1050 @x1092 @x1046 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2) (or $x1022 (not $x1180) $x642)) @x1247 @x1091 $x1022) @x935 @x934 $x1031)))
(let ((@x1320 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1) (or $x614 (not $x1180) $x642 (not $x853) $x670)) @x1092 @x1046 @x1091 @x1247 $x614)))
(let ((@x1324 (lemma (|unit-resolution| @x940 (|unit-resolution| @x840 @x1320 $x836) @x1317 false) (or $x670 $x586 $x642))))
(let ((@x1330 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 1 -1 1 -1) (or $x992 (not $x844) $x586 (not $x1271) (not $x852) $x856)) (|unit-resolution| @x1324 @x935 @x1091 $x670) @x1059 @x934 @x935 @x1287 $x992)))
(let ((@x1332 (|unit-resolution| @x1055 (|unit-resolution| @x858 (|unit-resolution| @x1324 @x935 @x1091 $x670) $x854) $x920)))
(let ((@x1337 (|unit-resolution| @x1197 (|unit-resolution| @x858 (|unit-resolution| @x1324 @x935 @x1091 $x670) $x854) $x1183)))
(let ((@x930 (hypothesis $x917)))
(let ((@x941 (|unit-resolution| @x940 (|unit-resolution| @x840 (hypothesis $x614) $x836) $x925)))
(let ((@x952 ((_ |th-lemma| arith farkas 1 -1 1 -1 1 -1 -1 1 1) (hypothesis $x726) @x950 @x946 @x945 (hypothesis $x614) @x941 @x935 @x934 @x930 false)))
(let ((@x1343 (|unit-resolution| (lemma @x952 (or $x586 (not $x726) $x953 $x838 $x954)) (|unit-resolution| @x1341 @x1337 @x1082 @x1091 @x1100 @x1336 $x726) @x1335 @x935 @x1332 $x838)))
(let ((@x1345 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x837) $x922)) (|unit-resolution| (|def-axiom| (or $x614 $x837)) @x1343 $x837) @x1330 false)))
(let ((@x1379 (|unit-resolution| @x831 (|unit-resolution| (lemma @x1345 (or $x586 $x642)) @x1091 $x586) $x827)))
(let ((@x1380 (|unit-resolution| @x972 @x1379 $x928)))
(let (($x1352 (>= (+ ?x335 ?x794) 0)))
(let ((@x1407 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1368 $x1352)) (hypothesis $x891) (hypothesis (not $x1352)) false)))
(let ((@x1408 (lemma @x1407 (or $x1368 $x1352))))
(let ((@x1420 (|unit-resolution| @x1408 (|unit-resolution| (|def-axiom| (or $x782 $x891)) @x1418 $x891) $x1352)))
(let ((@x1097 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1094 $x1027)) (|unit-resolution| @x860 @x1092 $x855) $x1027)))
(let ((@x1359 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x1183 $x920)) (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2) (or $x953 (not $x1027) $x670)) @x1097 @x1092 $x953) $x1183)))
(let ((@x1361 (|unit-resolution| @x876 (|unit-resolution| @x1341 @x1359 @x1082 @x1100 @x1091 @x1336 $x726) $x872)))
(let ((@x1106 ((_ |th-lemma| arith farkas 1 1 1 1 1 1 1 1 1) @x1105 @x1104 @x1100 @x1092 @x978 @x977 @x1097 @x1091 (hypothesis $x782) false)))
(let ((@x1366 (|unit-resolution| (lemma @x1106 (or $x642 $x1107 $x670 $x980 $x892)) (|unit-resolution| @x1364 @x1361 $x914) @x1091 @x978 @x1092 $x892)))
(let ((@x896 (|def-axiom| (or $x782 $x891))))
(let ((@x1371 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1368 $x1352)) (|unit-resolution| @x896 @x1366 $x891) $x1352)))
(let (($x880 (>= ?x739 0)))
(let ((@x1374 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x740) $x880)) @x747 $x880)))
(let ((@x1382 (|unit-resolution| @x1140 (|unit-resolution| @x860 @x1092 $x855) $x1086)))
(let ((@x1386 (hypothesis $x907)))
(let ((@x1387 ((_ |th-lemma| arith farkas 1 -1 1 -1 -1 1 -1 -1 1 -1 1 -1 -2 2 1) @x1082 @x1386 @x1385 @x1336 @x945 @x1382 @x962 @x958 @x967 (|unit-resolution| @x940 (|unit-resolution| @x840 @x1320 $x836) $x925) @x934 @x1380 (|unit-resolution| @x1376 @x1361 $x910) @x1374 @x1371 false)))
(let ((@x1421 (|unit-resolution| (lemma @x1387 (or $x670 (not $x907) $x905 $x642 $x980)) @x1091 @x958 @x1399 @x1394 $x670)))
(let ((@x1401 ((_ |th-lemma| arith farkas -1/2 1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 -1/2 1/2 -1/2 1/2 -1/2 1) @x950 @x930 @x946 @x945 (hypothesis $x1352) @x1399 @x1385 @x962 @x958 @x967 @x1115 @x934 @x1116 @x1325 false)))
(let ((@x1424 (|unit-resolution| (lemma @x1401 (or (not $x1352) $x954 $x953 $x905 $x1031 (not $x928) $x883)) (|unit-resolution| @x1055 (|unit-resolution| @x858 @x1421 $x854) $x920) @x1420 @x958 @x1380 @x1335 @x1325 $x1031)))
(let ((@x1426 (|unit-resolution| @x1341 @x1336 @x1082 @x1091 (|unit-resolution| @x1197 (|unit-resolution| @x858 @x1421 $x854) $x1183) @x1100 $x726)))
(let ((@x1429 (|unit-resolution| @x1351 (|unit-resolution| @x1364 (|unit-resolution| @x876 @x1426 $x872) $x914) @x1091 @x1325 $x614)))
(let ((@x1433 (lemma (|unit-resolution| @x940 (|unit-resolution| @x840 @x1429 $x836) @x1424 false) (or $x642 $x883 $x905))))
(let ((@x1469 (|unit-resolution| @x1038 (|unit-resolution| @x849 (|unit-resolution| @x1433 @x958 @x1325 $x642) $x845) $x1023)))
(let ((@x1436 (|unit-resolution| @x1041 (|unit-resolution| @x849 (hypothesis $x642) $x845) $x1022)))
(let ((@x1442 (|unit-resolution| @x876 (|unit-resolution| @x1440 (hypothesis $x892) @x1385 @x1325 @x1399 $x726) $x872)))
(let ((@x1448 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1) (or $x698 $x782 (not $x910) (not $x880) (not $x907) (not $x889)))))
(let ((@x1449 (|unit-resolution| @x1448 (|unit-resolution| @x1376 @x1442 $x910) @x1385 (hypothesis $x892) @x1399 @x1374 $x698)))
(let ((@x1434 (hypothesis $x642)))
(let ((@x1452 ((_ |th-lemma| arith farkas -1 1 -1 -1 -1 1 1 -1 1) @x1434 @x950 (|unit-resolution| @x1173 (|unit-resolution| @x867 @x1449 $x863) $x917) @x1325 (|unit-resolution| @x1364 @x1442 $x914) @x1104 @x1010 @x1046 @x1436 false)))
(let ((@x1470 (|unit-resolution| (lemma @x1452 (or $x614 $x847 $x883 $x782)) (|unit-resolution| @x1433 @x958 @x1325 $x642) @x1325 @x1418 $x614)))
(let (($x1065 (not $x852)))
(let (($x1446 (not $x880)))
(let (($x1445 (not $x910)))
(let (($x1438 (not $x889)))
(let (($x1388 (not $x907)))
(let (($x990 (not $x861)))
(let ((@x1473 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -1 -1 1 1 -1 1 1 -1) (or $x953 $x990 $x782 $x1388 $x1438 $x1064 $x1445 $x1446 $x838 $x1065)) @x1418 @x945 @x1374 @x1385 @x1059 @x1399 @x1470 @x1469 @x1466 $x953)))
(let ((@x1474 (|unit-resolution| @x1041 (|unit-resolution| @x849 (|unit-resolution| @x1433 @x958 @x1325 $x642) $x845) $x1022)))
(let ((@x1478 (|unit-resolution| @x867 (|unit-resolution| @x1448 @x1466 @x1385 @x1418 @x1399 @x1374 $x698) $x863)))
(let ((@x1455 (hypothesis $x1087)))
(let ((@x1458 (|unit-resolution| @x831 (|unit-resolution| @x1050 @x1092 @x1046 (hypothesis $x1022) @x1115 @x934 $x586) $x827)))
(let ((@x1460 (hypothesis $x910)))
(let ((@x1461 ((_ |th-lemma| arith farkas -1 -2 2 -1 1 1 -1 -1 1 -1 1 -1 -1 1 1) @x945 @x1460 @x1374 @x1386 @x1385 (hypothesis $x1352) @x962 @x958 @x967 (|unit-resolution| @x972 @x1458 $x928) @x1082 @x1455 @x1115 @x934 @x1382 false)))
(let ((@x1463 (lemma @x1461 (or $x670 $x1445 $x1388 (not $x1352) $x905 (not $x1087) $x1031 (not $x1022)))))
(let ((@x1480 (|unit-resolution| @x1463 @x1466 @x1399 @x1420 @x958 (|unit-resolution| @x1112 @x1478 $x1087) (|unit-resolution| @x940 (|unit-resolution| @x840 @x1470 $x836) $x925) @x1474 $x670)))
(let ((@x1484 (lemma (|unit-resolution| @x1055 (|unit-resolution| @x858 @x1480 $x854) @x1473 false) (or $x905 $x883))))
(let (($x820 (not $x70)))
(let ((@x1514 (|unit-resolution| @x876 (|unit-resolution| @x1341 @x1359 @x1082 @x1091 @x1336 @x1100 $x726) $x872)))
(let (($x919 (>= (+ |x3$| ?x598) 0)))
(let ((@x1517 ((_ |th-lemma| arith triangle-eq) (or (not $x827) $x919))))
(let ((@x1518 (|unit-resolution| @x1517 @x1379 $x919)))
(let ((@x1519 (|unit-resolution| (lemma @x1106 (or $x642 $x1107 $x670 $x980 $x892)) (|unit-resolution| @x1364 @x1514 $x914) @x1091 @x978 @x1092 $x892)))
(let ((@x1523 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1368 $x1496)) (|unit-resolution| @x896 @x1519 $x891) $x1496)))
(let ((@x1497 (hypothesis $x1027)))
(let ((@x1498 (hypothesis $x919)))
(let (($x834 (<= ?x599 0)))
(let ((@x1501 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x600) $x834)) @x607 $x834)))
(let ((@x1502 (hypothesis $x1013)))
(let (($x898 (>= ?x795 0)))
(let ((@x1505 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x796) $x898)) @x803 $x898)))
(let ((@x1507 ((_ |th-lemma| arith farkas 1/2 -1 -1/2 -1/2 1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 1) @x930 @x1104 @x950 (hypothesis $x1496) @x1505 @x1502 @x1501 @x1498 @x1079 @x978 @x977 @x1147 @x1497 @x1100 @x1105 false)))
(let ((@x1511 (lemma @x1507 (or $x904 $x954 $x1508 (not $x919) $x980 $x1150 (not $x1027) $x1107))))
(let ((@x1524 (|unit-resolution| @x1511 @x1523 @x1335 @x1518 @x978 @x1147 @x1097 (|unit-resolution| @x1364 @x1514 $x914) $x904)))
(let ((@x1526 ((_ |th-lemma| arith triangle-eq) (or $x71 $x1013 $x957))))
(let (($x809 (or $x820 $x808)))
(let ((@x816 (monotonicity (rewrite (= $x72 (not $x809))) (= (not $x72) (not (not $x809))))))
(let ((@x806 (trans @x816 (rewrite (= (not (not $x809)) $x809)) (= (not $x72) $x809))))
(let (($x439 (not $x72)))
(let ((@x807 (mp (mp (|not-or-elim| @x428 $x439) (|rewrite*| (= $x439 $x439)) $x439) @x806 $x809)))
(let ((@x1528 (|unit-resolution| @x807 (|unit-resolution| @x1526 @x1524 (hypothesis $x905) $x71) $x820)))
(let (($x901 (>= (+ |x1$| ?x335) 0)))
(let (($x558 (>= |x2$| 0)))
(let ((?x561 (ite $x558 |x2$| ?x86)))
(let ((?x570 (* (~ 1) ?x561)))
(let ((?x571 (+ |x3$| |x1$| ?x570)))
(let (($x826 (>= ?x571 0)))
(let (($x572 (= ?x571 0)))
(let ((@x566 (monotonicity (monotonicity (rewrite (= $x76 $x558)) (= ?x92 ?x561)) (= (+ ?x100 ?x92) (+ ?x100 ?x561)))))
(let ((@x569 (monotonicity @x566 (= (= |x3$| (+ ?x100 ?x92)) (= |x3$| (+ ?x100 ?x561))))))
(let ((@x576 (trans @x569 (rewrite (= (= |x3$| (+ ?x100 ?x561)) $x572)) (= (= |x3$| (+ ?x100 ?x92)) $x572))))
(let ((@x557 (monotonicity (rewrite (= ?x101 (+ ?x100 ?x92))) (= $x106 (= |x3$| (+ ?x100 ?x92))))))
(let ((@x474 (monotonicity (monotonicity (rewrite (= $x76 $x76)) (= ?x92 ?x92)) (= ?x101 ?x101))))
(let ((@x476 (mp (mp (|and-elim| @x429 $x106) (|rewrite*| (= $x106 $x106)) $x106) (monotonicity @x474 (= $x106 $x106)) $x106)))
(let ((@x579 (mp (mp @x476 (monotonicity @x474 (= $x106 $x106)) $x106) (trans @x557 @x576 (= $x106 $x572)) $x572)))
(let ((@x1533 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x572) $x826)) @x579 $x826)))
(let (($x1485 (<= (+ |x2$| ?x570) 0)))
(let (($x822 (= |x2$| ?x561)))
(let ((@x1535 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1) (or $x558 (not $x835) $x642 $x1031 (not $x844) (not $x928)))))
(let ((@x812 (|def-axiom| (or (not $x558) $x822))))
(let ((@x1537 (|unit-resolution| @x812 (|unit-resolution| @x1535 @x1115 @x934 @x1091 @x1380 @x967 $x558) $x822)))
(let ((@x1540 ((_ |th-lemma| arith triangle-eq) (or (not $x822) $x1485))))
(let ((@x1542 ((_ |th-lemma| arith assign-bounds 1 -3/2 3/2 -1 1/2 -1/2 1/2 -1/2 -1 1 1/2 -1/2 -1/2 1/2 1/2 -1/2 1/2) (|unit-resolution| @x1540 @x1537 $x1485) @x967 @x1380 @x1533 @x1336 @x978 @x977 @x1082 @x1287 @x1059 @x1097 @x1100 (|unit-resolution| @x1408 (|unit-resolution| @x896 @x1519 $x891) $x1352) @x962 @x1524 @x934 @x1115 $x901)))
(let (($x825 (<= ?x571 0)))
(let ((@x1545 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x572) $x825)) @x579 $x825)))
(let (($x1486 (>= (+ |x2$| ?x570) 0)))
(let ((@x1547 ((_ |th-lemma| arith triangle-eq) (or (not $x822) $x1486))))
(let ((@x1549 ((_ |th-lemma| arith assign-bounds 1 -3/2 3/2 -1 1/2 -1/2 1/2 -1/2 -1 1 1/2 -1/2 -1/2 1/2 1/2 -1/2 1/2) (|unit-resolution| @x1547 @x1537 $x1486) @x1501 @x1518 @x1545 @x1335 @x1386 @x1385 @x950 @x1247 @x1046 @x1382 @x945 @x1523 @x1505 (hypothesis $x905) @x1079 @x1147 $x900)))
(let ((@x1553 ((_ |th-lemma| arith triangle-eq) (or $x70 (not $x900) (not $x901)))))
(let ((@x1556 (lemma (|unit-resolution| @x1553 @x1549 @x1542 @x1528 false) (or $x670 $x1388 $x957 $x1150 $x980 $x1031 $x642))))
(let ((@x1578 (|unit-resolution| @x1556 (|unit-resolution| @x1075 @x1574 $x916) (|unit-resolution| @x1484 @x1325 $x905) @x1399 @x1394 (|unit-resolution| @x940 @x1574 $x925) @x1091 $x670)))
(let (($x1551 (not $x901)))
(let ((@x1580 (|unit-resolution| @x1197 (|unit-resolution| @x858 @x1578 $x854) $x1183)))
(let ((@x1585 (|unit-resolution| @x876 (|unit-resolution| @x1341 @x1580 @x1082 @x1091 @x1336 @x1100 $x726) $x872)))
(let ((@x1586 (|unit-resolution| @x1364 @x1585 $x914)))
(let ((@x1562 (|unit-resolution| @x876 (|unit-resolution| @x1341 @x1276 @x1082 @x1091 @x1336 @x1100 $x726) $x872)))
(let ((@x1564 ((_ |th-lemma| arith farkas -1 -1 -1 1 -1 1 -1 1 1) @x1273 (hypothesis $x782) @x978 @x977 @x1100 @x1091 (|unit-resolution| @x1364 @x1562 $x914) @x1104 @x1276 false)))
(let ((@x1587 (|unit-resolution| (lemma @x1564 (or $x892 $x856 $x980 $x642)) @x1578 @x1394 @x1091 $x892)))
(let ((@x1558 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1368 $x1496)) (hypothesis $x891) (hypothesis $x1508) false)))
(let ((@x1559 (lemma @x1558 (or $x1368 $x1496))))
(let ((@x1590 (|unit-resolution| @x1511 (|unit-resolution| @x1559 (|unit-resolution| @x896 @x1587 $x891) $x1496) @x1586 @x1518 @x1394 (|unit-resolution| @x1075 @x1574 $x916) (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -1) (or $x1027 $x856 (not $x1183))) @x1580 @x1578 $x1027) @x1335 $x904)))
(let ((@x1592 (|unit-resolution| @x807 (|unit-resolution| @x1526 @x1590 (|unit-resolution| @x1484 @x1325 $x905) $x71) $x820)))
(let ((@x1593 (|unit-resolution| @x1535 (|unit-resolution| @x940 @x1574 $x925) @x934 @x1091 @x1380 @x967 $x558)))
(let ((@x1567 (hypothesis (not $x900))))
(let ((@x1569 ((_ |th-lemma| arith farkas 1 -1 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 1) @x930 @x950 @x1105 @x1104 @x946 @x1399 @x1385 @x945 (hypothesis $x1486) @x1501 @x1498 @x1545 @x1567 (hypothesis $x1180) @x1046 @x1325 false)))
(let ((@x1572 (lemma @x1569 (or $x900 $x954 $x1107 $x953 (not $x1486) (not $x919) (not $x1180) $x883))))
(let ((@x1597 (|unit-resolution| @x1572 @x1335 @x1586 (|unit-resolution| @x1055 (|unit-resolution| @x858 @x1578 $x854) $x920) (|unit-resolution| @x1547 (|unit-resolution| @x812 @x1593 $x822) $x1486) @x1518 @x1247 @x1325 $x900)))
(let ((@x1600 ((_ |th-lemma| arith farkas -1/2 1/2 -1/2 1/2 1/2 -1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1) @x1580 @x1394 @x977 @x1100 @x1586 @x1104 (|unit-resolution| @x1540 (|unit-resolution| @x812 @x1593 $x822) $x1485) @x967 @x1380 @x1533 (|unit-resolution| @x1553 @x1597 @x1592 $x1551) @x1287 @x1059 @x1578 false)))
(let ((@x887 (|def-axiom| (or $x754 $x882))))
(let ((@x1646 (|unit-resolution| @x887 (|unit-resolution| (lemma @x1600 (or $x642 $x883)) @x1091 $x883) $x882)))
(let ((@x1652 ((_ |th-lemma| arith triangle-eq) (or (not $x882) $x1616))))
(let ((@x1653 (|unit-resolution| @x1652 @x1646 $x1616)))
(let ((@x1617 (hypothesis $x883)))
(let ((@x1620 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1 1) (or $x1445 (not $x1087) $x1446 $x754 (not $x871) $x670)) @x1092 @x1374 @x1617 @x1113 @x1082 $x1445)))
(let ((@x1623 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1) (or $x726 $x865 (not $x1087) (not $x871) $x670)) @x1092 @x1082 @x1088 @x1113 $x726)))
(let ((@x1627 (lemma (|unit-resolution| @x1376 (|unit-resolution| @x876 @x1623 $x872) @x1620 false) (or $x670 $x865 $x754))))
(let ((@x1637 (|unit-resolution| @x1627 (|unit-resolution| (lemma @x1311 (or $x698 $x642)) @x1091 $x698) (|unit-resolution| (lemma @x1600 (or $x642 $x883)) @x1091 $x883) $x670)))
(let ((@x1639 (|unit-resolution| @x1197 (|unit-resolution| @x858 @x1637 $x854) $x1183)))
(let ((@x1642 (|unit-resolution| (|unit-resolution| @x1341 @x1082 @x1100 (or $x726 (not $x1087) (not $x1183) $x642)) @x1639 @x1091 @x1336 $x726)))
(let ((@x1644 (|unit-resolution| @x1364 (|unit-resolution| @x876 @x1642 $x872) $x914)))
(let ((@x1645 (|unit-resolution| @x1055 (|unit-resolution| @x858 @x1637 $x854) $x920)))
(let (($x1607 (<= (+ ?x304 ?x766) 0)))
(let ((@x1649 ((_ |th-lemma| arith triangle-eq) (or (not $x882) $x1607))))
(let ((@x1650 (|unit-resolution| @x1649 @x1646 $x1607)))
(let ((@x1654 (|unit-resolution| @x1376 (|unit-resolution| @x876 @x1642 $x872) $x910)))
(let ((@x1658 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 2) (or $x558 (not $x835) $x642 (not $x844) $x992 (not $x928) $x614)) @x934 @x967 (or $x558 $x642 $x992 (not $x928) $x614))))
(let ((@x1660 (|unit-resolution| @x812 (|unit-resolution| @x1658 @x1188 @x1380 @x1091 @x1010 $x558) $x822)))
(let (($x1205 (not $x862)))
(let (($x1204 (not $x1183)))
(let (($x1338 (not $x871)))
(let (($x1339 (not $x1087)))
(let (($x1061 (not $x888)))
(let (($x1633 (not $x1616)))
(let (($x1327 (not $x1271)))
(let (($x1118 (not $x928)))
(let (($x1663 (not $x826)))
(let (($x1062 (not $x835)))
(let (($x1662 (not $x1485)))
(let (($x1664 (or $x901 $x1662 $x1062 $x1663 $x1118 $x1327 $x1065 $x1633 $x1061 $x1339 $x1338 $x1204 $x1205 $x1445 $x1446)))
(let ((@x1666 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 -1 1 -1 1 2 -2 1 -1 1 -1) $x1664) (|unit-resolution| @x1540 @x1660 $x1485) @x1059 @x1100 @x1082 @x1374 @x977 @x1533 @x1380 @x1639 @x1336 @x1287 @x1654 @x1653 @x967 $x901)))
(let (($x1671 (not $x879)))
(let (($x989 (not $x870)))
(let (($x1670 (not $x1607)))
(let (($x1048 (not $x853)))
(let (($x1249 (not $x1180)))
(let (($x1509 (not $x919)))
(let (($x1669 (not $x825)))
(let (($x1668 (not $x834)))
(let (($x1570 (not $x1486)))
(let (($x1672 (or $x900 $x1570 $x1668 $x1669 $x1509 $x1249 $x1048 $x1670 $x1438 $x954 $x989 $x953 $x990 $x1107 $x1671)))
(let ((@x1673 ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 -1 1 -1 1 2 -2 1 -1 1 -1) $x1672)))
(let ((@x1674 (|unit-resolution| @x1673 (|unit-resolution| @x1547 @x1660 $x1486) @x1046 @x945 @x950 @x1104 @x1385 @x1545 @x1645 @x1335 @x1644 @x1518 @x1247 @x1501 @x1650 $x900)))
(let ((@x1678 ((_ |th-lemma| arith assign-bounds 1 1 2 2 1 1 1 1 1 1 1) (or $x782 $x1670 $x1438 $x954 $x989 $x953 $x990 $x1249 $x1048 $x614 $x1107 $x1671))))
(let ((@x1679 (|unit-resolution| @x1678 @x1010 @x945 @x950 @x1104 @x1385 @x1046 @x1645 @x1335 @x1644 @x1247 @x1650 $x782)))
(let ((@x1629 (hypothesis $x922)))
(let ((@x1632 ((_ |th-lemma| arith farkas -1 1 1 -1 1 -1 -2 2 -1 1 3 -3 1 -1 2 -2 1) @x963 @x962 @x958 @x967 @x1116 @x934 (hypothesis $x1271) @x1059 (hypothesis $x1616) @x977 @x1455 @x1082 @x1248 @x1100 @x1460 @x1374 @x1629 false)))
(let ((@x1682 (|unit-resolution| (lemma @x1632 (or $x905 $x981 $x1118 $x1327 $x1633 $x1339 $x1204 $x1445 $x992)) (|unit-resolution| @x1415 (|unit-resolution| @x894 @x1679 $x890) $x911) @x1380 @x1287 @x1653 @x1336 @x1639 @x1654 @x1188 $x905)))
(let ((@x1683 (|unit-resolution| @x1526 @x1682 (|unit-resolution| @x807 (|unit-resolution| @x1553 @x1674 @x1666 $x70) $x808) $x1013)))
(let ((@x1685 ((_ |th-lemma| arith triangle-eq) (or $x1411 $x1628))))
(let ((@x1687 ((_ |th-lemma| arith farkas -1 1 1 -1 1 -1 -2 2 -1 1 3 -3 1 -1 2 -2 1) (|unit-resolution| @x1685 (|unit-resolution| @x894 @x1679 $x890) $x1628) @x1505 @x1683 @x1501 @x1518 @x1079 @x1247 @x1046 @x1650 @x1385 @x1335 @x950 @x1645 @x945 @x1644 @x1104 @x1213 false)))
(let ((@x1700 (|unit-resolution| @x840 (|unit-resolution| (lemma @x1687 (or $x614 $x642)) @x1091 $x614) $x836)))
(let ((@x1702 (|unit-resolution| @x940 @x1700 $x925)))
(let ((@x1705 (|unit-resolution| (|unit-resolution| @x1535 @x934 @x967 (or $x558 $x642 $x1031 $x1118)) @x1702 @x1091 @x1380 $x558)))
(let ((@x1708 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 -1 1 -1 1 2 -2 1 -1 1 -1) $x1664) (|unit-resolution| @x1540 (|unit-resolution| @x812 @x1705 $x822) $x1485) @x1059 @x1100 @x1082 @x1374 @x977 @x967 @x1380 @x1639 @x1336 @x1287 @x1654 @x1653 @x1533 $x901)))
(let ((@x1710 (|unit-resolution| @x1673 (|unit-resolution| @x1547 (|unit-resolution| @x812 @x1705 $x822) $x1486) @x1046 @x945 @x950 @x1104 @x1385 @x1501 @x1645 @x1335 @x1644 @x1518 @x1247 @x1545 @x1650 $x900)))
(let ((@x1715 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -1) (or $x922 $x838 $x1031)) @x1702 (|unit-resolution| (lemma @x1687 (or $x614 $x642)) @x1091 $x614) $x922)))
(let ((@x1690 (|unit-resolution| (lemma @x1632 (or $x905 $x981 $x1118 $x1327 $x1633 $x1339 $x1204 $x1445 $x992)) @x958 @x1116 (hypothesis $x1271) (hypothesis $x1616) @x1455 @x1248 @x1460 @x1629 $x981)))
(let ((@x1693 (|unit-resolution| @x896 (|unit-resolution| @x894 (|unit-resolution| @x1415 @x1690 $x1411) $x892) $x891)))
(let ((@x1696 ((_ |th-lemma| arith farkas -1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 1) @x962 @x958 @x1115 @x934 @x967 @x1116 @x930 @x950 (hypothesis $x1607) @x1385 @x946 @x945 (|unit-resolution| @x1408 @x1693 $x1352) false)))
(let ((@x1698 (lemma @x1696 (or $x905 $x1031 $x1118 $x954 $x1670 $x953 $x1327 $x1633 $x1339 $x1204 $x1445 $x992))))
(let ((@x1716 (|unit-resolution| @x1698 @x1702 @x1380 @x1335 @x1650 @x1645 @x1287 @x1653 @x1336 @x1639 @x1654 @x1715 $x905)))
(let ((@x1717 (|unit-resolution| @x1526 @x1716 (|unit-resolution| @x807 (|unit-resolution| @x1553 @x1710 @x1708 $x70) $x808) $x1013)))
(let (($x1719 (not $x843)))
(let (($x1718 (not $x898)))
(let (($x1720 (or $x1508 $x1718 $x904 $x1150 $x1719 $x1668 $x1509 $x1339 $x1338 $x1633 $x1061 $x1204 $x1205)))
(let ((@x1722 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -1 -1 1 1 -1 1 -1 -1 1 1 -1) $x1720) @x1717 @x1100 @x1082 @x977 @x1505 @x1079 (|unit-resolution| @x1075 @x1700 $x916) @x1518 @x1639 @x1336 @x1501 @x1653 $x1508)))
(let ((@x1725 (|unit-resolution| @x894 (|unit-resolution| @x896 (|unit-resolution| @x1559 @x1722 $x1368) $x782) $x890)))
(let ((@x1727 ((_ |th-lemma| arith farkas -1 -1 -2 -1 1 1 -1 1 -1 -1 1 1 -1 1) @x1505 @x1717 (|unit-resolution| @x896 (|unit-resolution| @x1559 @x1722 $x1368) $x782) (|unit-resolution| @x1075 @x1700 $x916) @x1079 @x1501 @x1518 @x1336 @x1082 @x1653 @x977 @x1639 @x1100 (|unit-resolution| @x1685 @x1725 $x1628) false)))
(let ((@x1728 (lemma @x1727 $x642)))
(let ((@x1785 (|unit-resolution| @x1038 (|unit-resolution| @x849 @x1728 $x845) $x1023)))
(let (($x1946 (>= (+ ?x273 ?x738) 0)))
(let (($x873 (= ?x273 ?x729)))
(let (($x874 (not $x726)))
(let ((@x1948 (hypothesis $x874)))
(let ((@x878 (|def-axiom| (or $x726 $x873))))
(let ((@x1959 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x873) $x1946)) (|unit-resolution| @x878 @x1948 $x873) $x1946)))
(let (($x1122 (<= (+ ?x273 ?x738) 0)))
(let ((@x1882 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x873) $x1122)) (hypothesis $x873) (hypothesis (not $x1122)) false)))
(let ((@x1883 (lemma @x1882 (or (not $x873) $x1122))))
(let ((@x1950 (|unit-resolution| @x1883 (|unit-resolution| @x878 @x1948 $x873) $x1122)))
(let (($x1879 (not $x873)))
(let (($x1876 (not $x1122)))
(let ((@x1764 (|unit-resolution| @x1041 (|unit-resolution| @x849 @x1728 $x845) $x1022)))
(let ((@x1606 (lemma ((_ |th-lemma| arith farkas 1 1 1 1 1) @x1434 @x1046 @x1010 @x1092 @x1436 false) (or $x614 $x847 $x670))))
(let ((@x1767 (|unit-resolution| @x940 (|unit-resolution| @x840 (|unit-resolution| @x1606 @x1092 @x1728 $x614) $x836) $x925)))
(let ((@x1770 (|unit-resolution| (|unit-resolution| @x1050 @x1046 @x934 (or $x670 (not $x1022) $x586 $x1031)) @x1767 @x1764 @x1092 $x586)))
(let ((@x1772 (|unit-resolution| @x1517 (|unit-resolution| @x831 @x1770 $x827) $x919)))
(let ((@x1773 (|unit-resolution| @x1075 (|unit-resolution| @x840 (|unit-resolution| @x1606 @x1092 @x1728 $x614) $x836) $x916)))
(let ((@x1612 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -1) (or $x1026 $x865 $x1339)) (|unit-resolution| @x869 (|unit-resolution| @x1156 @x1153 $x1070) $x698) @x1153 $x1339)))
(let ((@x1613 (|unit-resolution| @x867 (|unit-resolution| @x869 (|unit-resolution| @x1156 @x1153 $x1070) $x698) $x863)))
(let ((@x1733 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 1 -1 1 -1) (or $x1149 $x1338 $x726 $x1119 $x990 $x847)) @x1082 (lemma (|unit-resolution| @x1112 @x1613 @x1612 false) $x1026) @x945 (or $x726 $x1119 $x847))))
(let ((@x1736 (|unit-resolution| @x1376 (|unit-resolution| @x876 (|unit-resolution| @x1733 @x1382 @x1728 $x726) $x872) $x910)))
(let ((@x1738 ((_ |th-lemma| arith assign-bounds 1 2 2 2 2 2) (or $x1119 $x1204 $x1445 $x1339 $x1446 $x754 $x1338))))
(let ((@x1742 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x1087 $x917)) (|unit-resolution| @x1738 @x1617 @x1374 @x1082 @x1382 @x1359 @x1736 $x1339) $x917)))
(let ((@x1746 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 1) (or $x954 $x698 $x1149)) (lemma (|unit-resolution| @x1112 @x1613 @x1612 false) $x1026) (or $x954 $x698))))
(let ((@x1747 (|unit-resolution| @x1746 @x1742 (|unit-resolution| @x1627 @x1617 @x1092 $x865) false)))
(let ((@x1756 (|unit-resolution| @x885 (|unit-resolution| (lemma @x1747 (or $x754 $x670)) @x1092 $x754) $x881)))
(let ((@x1757 (|unit-resolution| @x1398 @x1756 $x907)))
(let ((@x1755 (|unit-resolution| @x1484 (|unit-resolution| (lemma @x1747 (or $x754 $x670)) @x1092 $x754) $x905)))
(let (($x823 (= ?x86 ?x561)))
(let (($x1793 (not $x823)))
(let (($x1753 (>= (+ ?x86 ?x570) 0)))
(let (($x1805 (not $x1753)))
(let ((@x1819 (|unit-resolution| @x1376 (|unit-resolution| @x876 (|unit-resolution| @x1733 @x1114 @x1728 $x726) $x872) $x910)))
(let (($x1047 (not $x1022)))
(let (($x991 (not $x844)))
(let (($x1806 (or $x900 $x1805 $x1031 $x991 $x1062 $x1118 $x1669 $x1047 $x1048 $x1388 $x1438 $x990 $x1445 $x1446 $x1119)))
(let ((@x1820 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -2 2 1 -1 -1 -1 1 -1 1 -1 -1 1 1) $x1806) @x1567 @x934 @x1046 @x945 @x1374 @x1385 @x967 @x1386 @x1115 @x1764 @x1116 @x1114 @x1819 @x1545 $x1805)))
(let ((@x1815 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1793 $x1753)) (hypothesis $x823) (hypothesis $x1805) false)))
(let ((@x824 (|def-axiom| (or $x558 $x823))))
(let ((@x1822 (|unit-resolution| @x824 (|unit-resolution| (lemma @x1815 (or $x1793 $x1753)) @x1820 $x1793) $x558)))
(let ((@x1825 ((_ |th-lemma| arith farkas -1/2 1/2 -1/2 1/2 -1/2 1/2 1/2 -1/2 1/2 -1/2 1/2 -1/2 1/2 1) @x945 @x1114 @x1386 @x1385 @x1819 @x1374 (|unit-resolution| @x1547 (|unit-resolution| @x812 @x1822 $x822) $x1486) @x1545 @x1567 @x1764 @x1046 @x1501 @x1498 @x1728 false)))
(let ((@x1840 (|unit-resolution| (lemma @x1825 (or $x900 $x1119 $x1388 $x1509 $x1031 $x1118)) @x1382 @x1757 @x1772 @x1767 (|unit-resolution| @x972 (|unit-resolution| @x831 @x1770 $x827) $x928) $x900)))
(let ((@x1784 (|unit-resolution| @x1364 (|unit-resolution| @x876 (|unit-resolution| @x1733 @x1382 @x1728 $x726) $x872) $x914)))
(let ((@x1786 (|unit-resolution| @x1393 @x1756 $x908)))
(let (($x1752 (<= (+ ?x86 ?x570) 0)))
(let (($x1797 (not $x1752)))
(let (($x1353 (not $x1027)))
(let (($x1798 (or $x901 $x1797 $x1150 $x1719 $x1668 $x1509 $x1663 $x1064 $x1065 $x980 $x1061 $x1205 $x1107 $x1671 $x1353)))
(let ((@x1832 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -2 2 1 -1 -1 -1 1 -1 1 -1 -1 1 1) $x1798) (hypothesis $x1551) @x1079 @x1059 @x1100 @x1104 @x977 @x1501 @x978 @x1785 @x1105 @x1497 @x1147 @x1498 @x1533 $x1797)))
(let ((@x1829 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1793 $x1752)) (hypothesis $x823) (hypothesis $x1797) false)))
(let ((@x1834 (|unit-resolution| @x824 (|unit-resolution| (lemma @x1829 (or $x1793 $x1752)) @x1832 $x1793) $x558)))
(let ((@x1837 ((_ |th-lemma| arith farkas 1/2 -1/2 1 -1 -1/2 1/2 1/2 -1/2 1/2 -1/2 -1/2 1/2 -1/2 1/2 -1/2 1) @x1100 @x1497 @x1147 @x1079 @x1501 @x1498 @x978 @x977 @x1105 @x1104 (|unit-resolution| @x1540 (|unit-resolution| @x812 @x1834 $x822) $x1485) @x1533 (hypothesis $x1551) @x1785 @x1059 @x1834 false)))
(let ((@x1841 (|unit-resolution| (lemma @x1837 (or $x901 $x1353 $x1150 $x1509 $x980 $x1107)) @x1097 @x1773 @x1772 @x1786 @x1784 $x901)))
(let ((@x1844 (|unit-resolution| @x1526 (|unit-resolution| @x807 (|unit-resolution| @x1553 @x1841 @x1840 $x70) $x808) @x1755 $x1013)))
(let ((@x1760 (|unit-resolution| (|unit-resolution| @x1448 @x1385 @x1374 (or $x698 $x782 $x1445 $x1388)) @x1274 @x1736 @x1757 $x782)))
(let (($x1750 (>= (+ ?x242 ?x710) 0)))
(let ((@x1777 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1070 $x1750)) (|unit-resolution| @x869 @x1274 $x864) $x1750)))
(let (($x1779 (not $x1628)))
(let (($x1778 (not $x1750)))
(let (($x1780 (or $x904 $x1778 $x1779 $x1718 $x989 $x1150 $x1719 $x1668 $x1509 $x1388 $x1438 $x1205 $x1353)))
(let ((@x1781 ((_ |th-lemma| arith assign-bounds 1 -1 1 -1 1 -1 -1 1 -1 1 1 -1) $x1780)))
(let ((@x1782 (|unit-resolution| @x1781 @x1777 @x1100 @x950 @x1385 @x1505 @x1501 @x1757 @x1097 @x1773 @x1772 @x1079 (|unit-resolution| @x1685 (|unit-resolution| @x894 @x1760 $x890) $x1628) $x904)))
(let (($x810 (not $x558)))
(let ((@x1790 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 1 1 1) (or $x810 $x1509 $x1668 $x1719 $x1150 $x698 $x1205 $x670 $x1353)) @x1079 @x1100 @x1501 (or $x810 $x1509 $x1150 $x698 $x670 $x1353))))
(let ((@x1792 (|unit-resolution| @x824 (|unit-resolution| @x1790 @x1274 @x1092 @x1097 @x1773 @x1772 $x810) $x823)))
(let ((@x1800 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -2 2 1 -1 -1 -1 1 -1 1 -1 -1 1 1) $x1798) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1793 $x1752)) @x1792 $x1752) @x1079 @x1059 @x1100 @x1104 @x977 @x1533 @x1786 @x1785 @x1784 @x1097 @x1773 @x1772 @x1501 $x901)))
(let ((@x1808 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -2 2 1 -1 -1 -1 1 -1 1 -1 -1 1 1) $x1806) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1793 $x1753)) @x1792 $x1753) @x934 @x1046 @x945 @x1374 @x1385 @x1545 @x1757 @x1767 @x1764 (|unit-resolution| @x972 (|unit-resolution| @x831 @x1770 $x827) $x928) @x1382 @x1736 @x967 $x900)))
(let ((@x1810 (|unit-resolution| @x807 (|unit-resolution| @x1553 @x1808 @x1800 $x70) (|unit-resolution| @x1526 @x1782 @x1755 $x71) false)))
(let ((@x1846 (|unit-resolution| @x867 (|unit-resolution| (lemma @x1810 (or $x698 $x670)) @x1092 $x698) $x863)))
(let ((@x1848 (|unit-resolution| @x1511 @x1844 @x1784 @x1772 @x1786 @x1773 @x1097 (|unit-resolution| @x1173 @x1846 $x917) $x1508)))
(let ((@x1851 (|unit-resolution| @x894 (|unit-resolution| @x896 (|unit-resolution| @x1559 @x1848 $x1368) $x782) $x890)))
(let ((@x1855 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -2 2 -2 2 -1 -2) (or $x1750 $x980 $x1061 $x1107 $x1671 $x954 $x892)) (|unit-resolution| @x896 (|unit-resolution| @x1559 @x1848 $x1368) $x782) @x977 @x1786 (|unit-resolution| @x1173 @x1846 $x917) @x1784 @x1104 $x1750)))
(let ((@x1856 (|unit-resolution| @x1781 @x1855 (|unit-resolution| @x1685 @x1851 $x1628) @x1100 @x950 @x1385 @x1505 @x1844 @x1757 @x1097 @x1773 @x1772 @x1079 @x1501 false)))
(let ((@x1857 (lemma @x1856 $x670)))
(let ((@x1884 ((_ |th-lemma| arith assign-bounds -1 -1 1 1 -1) (or $x1876 $x1446 $x1778 $x989 $x754 $x856))))
(let ((@x1886 (|unit-resolution| @x1883 (|unit-resolution| @x1884 @x1777 @x1374 @x1617 @x1857 @x950 $x1876) $x1879)))
(let ((@x1889 (|unit-resolution| @x1376 (|unit-resolution| @x876 (|unit-resolution| @x878 @x1886 $x726) $x872) $x910)))
(let ((@x1890 ((_ |th-lemma| arith farkas 1 1 1 1 1) @x1617 @x1889 @x1374 @x1274 (|unit-resolution| @x878 @x1886 $x726) false)))
(let ((@x1135 (|unit-resolution| @x867 (|unit-resolution| (lemma @x1890 (or $x698 $x754)) @x1617 $x698) $x863)))
(let ((@x1895 (|unit-resolution| @x1484 @x958 $x883)))
(let ((@x1897 (|unit-resolution| @x867 (|unit-resolution| (lemma @x1890 (or $x698 $x754)) @x1895 $x698) $x863)))
(let ((@x1919 (|unit-resolution| @x1197 (|unit-resolution| @x858 @x1857 $x854) $x1183)))
(let ((@x1894 (hypothesis $x1122)))
(let ((@x1864 (|unit-resolution| @x1055 (|unit-resolution| @x858 @x1857 $x854) $x920)))
(let ((@x1898 (|unit-resolution| @x1173 @x1897 $x917)))
(let ((@x1903 ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 1 1 1) (or $x782 $x1438 $x1670 $x754 $x954 $x953 $x847 $x990 $x989))))
(let ((@x1904 (|unit-resolution| @x1903 @x1895 @x950 @x945 @x1385 @x1728 @x1864 @x1898 (|unit-resolution| @x1649 (|unit-resolution| @x887 @x1895 $x882) $x1607) $x782)))
(let ((@x1907 ((_ |th-lemma| arith assign-bounds -1 1 1 -1 -1 1 -1 -1 -3 3 1 1 2 -2 -2 2) (|unit-resolution| @x1415 (|unit-resolution| @x894 @x1904 $x890) $x911) @x962 @x958 @x934 @x967 @x977 (|unit-resolution| @x1652 (|unit-resolution| @x887 @x1895 $x882) $x1616) @x1898 @x1864 @x945 @x950 @x1629 @x1894 @x1374 @x1785 @x1059 $x1118)))
(let ((@x1909 ((_ |th-lemma| arith assign-bounds 1 1 1 2 2 1 1 1 1 1 1) (or $x586 $x991 $x992 $x954 $x953 $x990 $x989 $x1876 $x1446 $x754 $x1064 $x1065))))
(let ((@x1910 (|unit-resolution| @x1909 @x1894 @x1059 @x945 @x950 @x1374 @x1895 @x1864 @x1898 @x1629 @x1785 @x934 $x586)))
(let ((@x1914 (lemma (|unit-resolution| @x972 (|unit-resolution| @x831 @x1910 $x827) @x1907 false) (or $x1876 $x905 $x992))))
(let ((@x1916 (|unit-resolution| @x878 (|unit-resolution| @x1883 (|unit-resolution| @x1914 @x1188 @x958 $x1876) $x1879) $x726)))
(let ((@x1922 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 1 1 1) (or $x586 $x954 $x874 $x989 $x953 $x990 $x991 $x992 $x614)) @x934 @x945 @x950 (or $x586 $x954 $x874 $x953 $x992 $x614))))
(let ((@x1924 (|unit-resolution| @x831 (|unit-resolution| @x1922 @x1916 @x1898 @x1188 @x1864 @x1010 $x586) $x827)))
(let ((@x1928 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -2 -2 -2 2 2) (or $x1271 $x1064 $x874 $x954 $x953 $x990 $x989)) @x1916 @x950 @x1864 @x1898 @x1785 @x945 $x1271)))
(let ((@x1929 (|unit-resolution| @x1698 @x1928 (|unit-resolution| @x972 @x1924 $x928) @x958 (|unit-resolution| @x1649 (|unit-resolution| @x887 @x1895 $x882) $x1607) @x1898 @x1864 @x1188 (|unit-resolution| @x1652 (|unit-resolution| @x887 @x1895 $x882) $x1616) (|unit-resolution| @x1112 @x1897 $x1087) @x1919 (|unit-resolution| @x1376 (|unit-resolution| @x876 @x1916 $x872) $x910) @x1191 false)))
(let ((@x1935 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -2 2 -2 -2 2) (or $x1750 $x954 $x953 $x990 $x838 $x1064 $x1065)) @x1898 @x945 @x1864 @x1059 @x1785 (|unit-resolution| (lemma @x1929 (or $x614 $x905)) @x958 $x614) $x1750)))
(let ((@x1937 (|unit-resolution| @x1883 (|unit-resolution| @x1884 @x1935 @x1374 @x1895 @x1857 @x950 $x1876) $x1879)))
(let ((@x1940 (|unit-resolution| @x1376 (|unit-resolution| @x876 (|unit-resolution| @x878 @x1937 $x726) $x872) $x910)))
(let ((@x1943 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -3 -2 -2 2 2 -2 -2 2) (or $x1086 $x953 $x874 $x954 $x989 $x990 $x838 $x1064 $x1065)) (|unit-resolution| @x878 @x1937 $x726) @x945 @x950 @x1059 @x1864 @x1898 @x1785 (|unit-resolution| (lemma @x1929 (or $x614 $x905)) @x958 $x614) $x1086)))
(let ((@x1944 (|unit-resolution| @x1738 @x1943 @x1940 @x1374 @x1082 @x1895 @x1919 (|unit-resolution| @x1112 @x1897 $x1087) false)))
(let ((@x1945 (lemma @x1944 $x905)))
(let ((@x1859 (|unit-resolution| @x1649 (|unit-resolution| @x887 @x1617 $x882) $x1607)))
(let ((@x1988 (|unit-resolution| (|unit-resolution| @x1207 @x1100 @x1046 (or $x698 $x1204 $x614 $x1047)) @x1010 @x1919 @x1764 $x698)))
(let ((@x1990 (|unit-resolution| @x1173 (|unit-resolution| @x867 @x1988 $x863) $x917)))
(let ((@x1947 (hypothesis $x1179)))
(let ((@x1951 (|unit-resolution| @x1909 @x1950 @x1059 @x945 @x950 @x1374 @x1617 @x1864 @x930 @x1629 @x1785 @x934 $x586)))
(let ((@x1955 (|unit-resolution| @x894 (|unit-resolution| @x1903 @x1859 @x950 @x945 @x1385 @x1728 @x1864 @x930 @x1617 $x782) $x890)))
(let ((@x1956 (|unit-resolution| @x1685 @x1955 $x1628)))
(let ((@x1960 ((_ |th-lemma| arith assign-bounds 1 -1 -3/2 3/2 -1 1 -1/2 1/2 -1/2 -1/2 1/2 1/2 -1/2 -1/2 1/2 1/2) @x1959 @x1104 @x1919 @x1100 @x1764 @x1046 @x1956 @x1505 @x1079 @x1501 (|unit-resolution| @x1517 (|unit-resolution| @x831 @x1951 $x827) $x919) @x1385 @x1859 @x1455 @x1082 @x1947 $x904)))
(let ((@x1965 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 1 1 1 1 1 1) (or $x558 $x754 $x1779 $x1718 $x957 $x1438 $x1670 $x726)) @x1948 @x1617 @x1385 @x1505 @x1945 @x1859 @x1956 $x558)))
(let (($x1970 (not $x1179)))
(let (($x1971 (or $x901 $x1662 $x1663 $x1779 $x1718 $x957 $x1719 $x1970 $x1339 $x1204 $x1205 $x1338 $x1062 $x1118 $x1061 $x1633)))
(let ((@x1973 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 1/2 -1/2 -1/2 1/2 -1/2 1/2 1/2 -1/2 -1/2 -1/2 1/2 1/2 -1/2) $x1971) (|unit-resolution| @x972 (|unit-resolution| @x831 @x1951 $x827) $x928) @x1079 @x1100 @x1082 @x977 @x1505 @x1533 @x1945 @x967 @x1919 @x1947 @x1455 (|unit-resolution| @x1652 (|unit-resolution| @x887 @x1617 $x882) $x1616) (|unit-resolution| @x1540 (|unit-resolution| @x812 @x1965 $x822) $x1485) @x1956 $x901)))
(let (($x1063 (not $x897)))
(let (($x1976 (or $x900 $x1570 $x1669 $x981 $x1063 $x1013 $x991 $x992 $x954 $x953 $x990 $x989 $x1668 $x1509 $x1438 $x1670)))
(let ((@x1978 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 1/2 -1/2 -1/2 1/2 -1/2 1/2 1/2 -1/2 -1/2 -1/2 1/2 1/2 -1/2) $x1976) @x1960 @x934 @x945 @x950 @x1385 @x962 @x1545 @x1501 (|unit-resolution| @x1415 @x1955 $x911) @x1864 @x930 @x1629 (|unit-resolution| @x1517 (|unit-resolution| @x831 @x1951 $x827) $x919) (|unit-resolution| @x1547 (|unit-resolution| @x812 @x1965 $x822) $x1486) @x1859 $x900)))
(let ((@x1979 (|unit-resolution| @x1553 @x1978 @x1973 (|unit-resolution| @x807 (|unit-resolution| @x1526 @x1960 @x1945 $x71) $x820) false)))
(let ((@x1992 (|unit-resolution| (lemma @x1979 (or $x726 $x954 $x992 $x1970 $x1339 $x754)) @x1617 @x1188 @x1213 (|unit-resolution| @x1112 (|unit-resolution| @x867 @x1988 $x863) $x1087) @x1990 $x726)))
(let ((@x1994 (|unit-resolution| @x831 (|unit-resolution| @x1922 @x1992 @x1010 @x1188 @x1864 @x1990 $x586) $x827)))
(let ((@x1997 (|unit-resolution| @x894 (|unit-resolution| @x1903 @x1859 @x950 @x945 @x1385 @x1728 @x1864 @x1990 @x1617 $x782) $x890)))
(let ((@x1998 (|unit-resolution| @x1685 @x1997 $x1628)))
(let ((@x1982 (hypothesis $x1628)))
(let ((@x1983 ((_ |th-lemma| arith farkas 3/4 1/4 -1/4 -3/4 1/2 -1/2 -1/2 1/2 -1/4 1/4 1/4 -1/4 -1/4 1/4 1/4 -1/4 1/4 1) @x930 @x1864 @x945 @x950 @x1105 @x1104 @x1764 @x1046 @x1982 @x1505 @x1502 @x1079 @x1501 @x1498 @x1385 (hypothesis $x1607) @x1947 @x1728 false)))
(let ((@x2001 (|unit-resolution| (lemma @x1983 (or $x904 $x954 $x1107 $x1779 $x1509 $x1670 $x1970)) (|unit-resolution| @x1364 (|unit-resolution| @x876 @x1992 $x872) $x914) @x1990 @x1998 (|unit-resolution| @x1517 @x1994 $x919) @x1859 @x1213 $x904)))
(let ((@x2006 ((_ |th-lemma| arith assign-bounds 2 3/4 3/4 3/4 3/4 3/4 1/2 1/2 3/4 3/4 1/2 1/2 1/4 1/4 1/4 1/4 1/4 1/4) @x1617 @x1998 @x1505 @x1945 @x1385 @x1859 (|unit-resolution| @x1376 (|unit-resolution| @x876 @x1992 $x872) $x910) @x1374 @x1864 @x945 @x1785 @x1059 @x934 @x967 (|unit-resolution| @x972 @x1994 $x928) @x1990 @x950 @x1188 $x558)))
(let ((@x2009 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 1/2 -1/2 -1/2 1/2 -1/2 1/2 1/2 -1/2 -1/2 -1/2 1/2 1/2 -1/2) $x1971) (|unit-resolution| @x1540 (|unit-resolution| @x812 @x2006 $x822) $x1485) @x1079 @x1100 @x1082 @x977 @x1505 @x1533 @x1945 @x967 @x1919 @x1213 (|unit-resolution| @x1112 (|unit-resolution| @x867 @x1988 $x863) $x1087) (|unit-resolution| @x1652 (|unit-resolution| @x887 @x1617 $x882) $x1616) (|unit-resolution| @x972 @x1994 $x928) @x1998 $x901)))
(let ((@x2014 (|unit-resolution| @x1673 (|unit-resolution| @x1547 (|unit-resolution| @x812 @x2006 $x822) $x1486) @x1046 @x945 @x950 @x1104 @x1385 @x1864 @x1859 @x1990 (|unit-resolution| @x1364 (|unit-resolution| @x876 @x1992 $x872) $x914) (|unit-resolution| @x1517 @x1994 $x919) (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -1) (or $x1180 $x847 $x1047)) @x1764 @x1728 $x1180) @x1501 @x1545 $x900)))
(let ((@x2015 (|unit-resolution| @x1553 @x2014 @x2009 (|unit-resolution| @x807 (|unit-resolution| @x1526 @x2001 @x1945 $x71) $x820) false)))
(let ((@x1138 (|unit-resolution| (lemma @x2015 (or $x754 $x614)) @x1617 $x614)))
(let ((@x1030 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -2 2 -2 -2 2 -1) (or $x1179 $x1064 $x1065 $x953 $x865 $x990 $x1150)) @x945 @x1059 (or $x1179 $x1064 $x953 $x865 $x1150))))
(let ((@x1042 (|unit-resolution| (|unit-resolution| @x1030 @x1785 @x1864 (or $x1179 $x865 $x1150)) (|unit-resolution| @x1075 (|unit-resolution| @x840 @x1138 $x836) $x916) (|unit-resolution| (lemma @x1890 (or $x698 $x754)) @x1617 $x698) $x1179)))
(let ((@x1052 (|unit-resolution| (lemma @x952 (or $x586 $x874 $x953 $x838 $x954)) @x1864 (or $x586 $x874 $x838 $x954))))
(let ((@x1068 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -1) (or $x922 $x838 $x1031)) (|unit-resolution| @x940 (|unit-resolution| @x840 @x1138 $x836) $x925) @x1138 $x922)))
(let ((@x1069 (|unit-resolution| (lemma @x1979 (or $x726 $x954 $x992 $x1970 $x1339 $x754)) @x1068 (|unit-resolution| @x1052 (|unit-resolution| @x1173 @x1135 $x917) @x935 @x1138 $x874) @x1617 @x1042 (|unit-resolution| @x1112 @x1135 $x1087) (|unit-resolution| @x1173 @x1135 $x917) false)))
(let ((@x1165 (|unit-resolution| (lemma @x1069 (or $x754 $x586)) @x935 $x754)))
(let ((@x969 (|unit-resolution| @x1398 (|unit-resolution| @x885 @x1165 $x881) $x907)))
(let ((@x2054 (|unit-resolution| (|unit-resolution| @x1440 @x1385 (or $x726 $x782 $x1388 $x883)) @x1948 @x1165 @x969 $x782)))
(let ((@x1085 (|unit-resolution| (|unit-resolution| @x1207 @x1100 @x1046 (or $x698 $x1204 $x614 $x1047)) @x1919 @x1764 (or $x698 $x614))))
(let ((@x1157 (|unit-resolution| @x867 (|unit-resolution| @x1085 @x1010 $x698) $x863)))
(let ((@x1167 (|unit-resolution| @x1393 (|unit-resolution| @x885 @x1165 $x881) $x908)))
(let ((@x1163 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1) (or $x558 $x586 $x1060 $x1062 $x614)) @x967 (or $x558 $x586 $x1060 $x614))))
(let ((@x1170 (|unit-resolution| @x1540 (|unit-resolution| @x812 (|unit-resolution| @x1163 @x1010 @x935 @x1009 $x558) $x822) $x1485)))
(let ((@x1171 ((_ |th-lemma| arith assign-bounds 1 -1 1 -1 1 -1 1 3 -3 1 -1 -1 2 -2 2 -2) @x1170 @x1533 @x1009 @x967 @x977 (hypothesis $x1946) @x1104 @x1919 @x1100 @x1764 @x1046 @x1167 @x1079 @x1213 (|unit-resolution| @x1112 @x1157 $x1087) @x1082 $x901)))
(let (($x1133 (>= (+ ?x118 ?x598) 0)))
(let ((@x982 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x828) $x1133)) @x1005 $x1133)))
(let ((@x983 (|unit-resolution| @x1547 (|unit-resolution| @x812 (|unit-resolution| @x1163 @x1010 @x935 @x1009 $x558) $x822) $x1486)))
(let ((@x929 ((_ |th-lemma| arith assign-bounds 1 -1 1 -1 1 -1 1 3 -3 1 -1 -1 2 -2 2 -2) @x983 @x1545 @x982 @x1501 @x1385 @x1894 @x1374 @x1864 @x945 @x1785 @x1059 @x969 @x934 @x1188 (|unit-resolution| @x1173 @x1157 $x917) @x950 $x900)))
(let (($x988 (not $x1133)))
(let (($x995 (or $x904 $x988 $x1779 $x1718 $x1668 $x1438 $x953 $x990 $x991 $x992 $x954 $x989 $x1388)))
(let ((@x997 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 1 -1 1 1 -1 1 -1 1 -1 -1) $x995) (|unit-resolution| @x1173 @x1157 $x917) @x945 @x950 @x1385 @x1505 @x1501 @x969 @x1864 @x934 @x1188 @x1982 @x982 $x904)))
(let ((@x1002 (|unit-resolution| @x1526 @x1945 (or $x71 $x1013))))
(let ((@x1164 (|unit-resolution| @x807 (|unit-resolution| @x1002 @x997 $x71) (|unit-resolution| @x1553 @x929 @x1171 $x70) false)))
(let ((@x2057 (|unit-resolution| (lemma @x1164 (or $x614 $x1779 $x1876 (not $x1946) $x586)) (|unit-resolution| @x1685 (|unit-resolution| @x894 @x2054 $x890) $x1628) @x1950 @x1959 @x935 $x614)))
(let ((@x2027 (hypothesis $x1133)))
(let (($x2029 (or $x904 $x1778 $x988 $x1779 $x1718 $x1668 $x1438 $x1204 $x1205 $x991 $x989 $x1388 $x1031 $x1047 $x1048)))
(let ((@x2031 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 -1 1 -1 1 -1 1 1 -1 -1 -1 -2 2) $x2029) (hypothesis $x1750) @x1046 @x1100 @x950 @x1385 @x1505 @x1501 @x1386 @x1115 @x1764 @x1919 @x934 @x1982 @x2027 $x904)))
(let ((@x2036 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 1) (or $x558 $x726 $x1779 $x1718 $x957 $x1438 $x1388)) @x1948 @x1385 @x1505 @x1945 @x1386 @x1982 $x558)))
(let (($x1174 (not $x1946)))
(let (($x2039 (or $x901 $x1662 $x1663 $x988 $x1668 $x1438 $x1174 $x1671 $x1204 $x1205 $x1047 $x1048 $x1388 $x1779 $x1718 $x957)))
(let ((@x2041 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 -1 -1 1 1 -1 1 -1 1 2 -2 -2) $x2039) (|unit-resolution| @x1540 (|unit-resolution| @x812 @x2036 $x822) $x1485) @x1046 @x1100 @x1104 @x1385 @x1505 @x1533 @x1945 @x1386 @x1764 @x1919 @x1501 @x1982 @x2027 @x1959 $x901)))
(let (($x2043 (or $x900 $x1570 $x1669 $x1060 $x1062 $x1061 $x1876 $x1446 $x953 $x990 $x1064 $x1065 $x980 $x981 $x1063 $x1013)))
(let ((@x2045 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 -1 -1 1 1 -1 1 -1 1 2 -2 -2) $x2043) @x2031 @x1059 @x945 @x1374 @x977 @x962 @x1545 @x967 @x978 @x963 @x1864 @x1181 @x1785 @x1950 (|unit-resolution| @x1547 (|unit-resolution| @x812 @x2036 $x822) $x1486) $x900)))
(let ((@x2046 (|unit-resolution| @x1553 @x2045 @x2041 (|unit-resolution| @x807 (|unit-resolution| @x1002 @x2031 $x71) $x820) false)))
(let ((@x2061 (|unit-resolution| (lemma @x2046 (or $x1778 $x980 $x981 $x1060 $x1388 $x1779 $x988 $x1031 $x726)) (|unit-resolution| @x1415 (|unit-resolution| @x894 @x2054 $x890) $x911) @x1167 @x1009 @x969 (|unit-resolution| @x1685 (|unit-resolution| @x894 @x2054 $x890) $x1628) @x982 (|unit-resolution| @x940 (|unit-resolution| @x840 @x2057 $x836) $x925) @x1948 $x1778)))
(let ((@x2063 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -2 2 -2 -2 2) (or $x1750 $x954 $x953 $x990 $x838 $x1064 $x1065)) @x945 @x1864 @x1059 @x1785 (or $x1750 $x954 $x838))))
(let ((@x2050 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x1070 $x1750)) (hypothesis $x864) (hypothesis $x1778) false)))
(let ((@x2051 (lemma @x2050 (or $x1070 $x1750))))
(let ((@x2067 (|unit-resolution| @x867 (|unit-resolution| @x869 (|unit-resolution| @x2051 @x2061 $x1070) $x698) $x863)))
(let ((@x2068 (|unit-resolution| @x1173 @x2067 (|unit-resolution| @x2063 @x2061 @x2057 $x954) false)))
(let ((@x2108 (|unit-resolution| (lemma @x2068 (or $x726 $x586)) @x935 $x726)))
(let ((@x2074 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 -1 -1 -1 1 1 -1) (or $x1107 $x954 $x847 $x989 $x1671 $x1047 $x1048 $x883 $x614)) @x1046 @x950 @x1104 @x1728 @x1764 (or $x1107 $x954 $x883 $x614))))
(let ((@x2076 (|unit-resolution| @x1173 @x1157 (|unit-resolution| @x2074 @x1010 @x1325 @x1105 $x954) false)))
(let ((@x2111 (|unit-resolution| (lemma @x2076 (or $x614 $x883 $x1107)) @x1165 (|unit-resolution| @x1364 (|unit-resolution| @x876 @x2108 $x872) $x914) $x614)))
(let ((@x2115 (|unit-resolution| @x1376 (|unit-resolution| @x876 @x2108 $x872) $x910)))
(let ((@x1866 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -1 -1 1 1 -1 1 1 -1) (or $x953 $x990 $x782 $x1388 $x1438 $x1064 $x1445 $x1446 $x838 $x1065)) @x945 @x1374 @x1385 @x1059 (or $x953 $x782 $x1388 $x1064 $x1445 $x838))))
(let ((@x2118 (|unit-resolution| (|unit-resolution| @x1866 @x1785 @x1864 (or $x782 $x1388 $x1445 $x838)) @x2111 @x969 @x2115 $x782)))
(let ((@x2083 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 -1 -1 1 1 -1 1 -1 1 2 -2 -2) $x2043) @x1567 @x1059 @x945 @x1374 @x977 @x962 @x1545 @x967 @x978 @x963 @x1864 @x1181 @x1785 @x1894 @x1011 $x1570)))
(let ((@x2080 ((_ |th-lemma| arith farkas 1 -1 -1 1 -1 1 1 1 -1 1 -1 -1 1) @x1385 @x1386 @x1545 @x1567 @x1181 @x967 @x1374 @x1864 @x945 @x1785 @x1059 @x1460 (hypothesis $x1753) false)))
(let ((@x2084 (|unit-resolution| (lemma @x2080 (or $x1805 $x1388 $x900 $x1060 $x1445)) @x1567 @x1386 @x1181 @x1460 $x1805)))
(let ((@x2086 (|unit-resolution| @x824 (|unit-resolution| (lemma @x1815 (or $x1793 $x1753)) @x2084 $x1793) $x558)))
(let ((@x2090 (lemma (|unit-resolution| @x1547 (|unit-resolution| @x812 @x2086 $x822) @x2083 false) (or $x900 $x1388 $x1060 $x1445 $x980 $x981 $x1876 $x1013))))
(let ((@x2094 (|unit-resolution| @x1553 (|unit-resolution| @x2090 @x1011 @x1181 @x1460 @x978 @x963 @x1894 @x1386 $x900) (|unit-resolution| @x807 (|unit-resolution| @x1002 @x1011 $x71) $x820) $x1551)))
(let (($x2095 (or $x1797 $x1061 $x980 $x1663 $x901 $x988 $x1668 $x1671 $x1204 $x1205 $x1047 $x1048 $x1107)))
(let ((@x2097 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 -1 1 1 1 -1 1 -1 -1) $x2095) @x2094 @x1046 @x1100 @x1104 @x977 @x1501 @x978 @x1764 @x1105 @x1919 @x1533 @x2027 $x1797)))
(let ((@x2099 (|unit-resolution| @x824 (|unit-resolution| (lemma @x1829 (or $x1793 $x1752)) @x2097 $x1793) $x558)))
(let ((@x2104 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -2 -2 2 2 2 -2) (or $x1946 $x1107 $x810 $x981 $x1063 $x1013 $x1061 $x980)) @x1011 @x962 @x977 @x978 @x963 @x1105 @x2099 $x1946)))
(let ((@x2105 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 -1 1 -1 -1 1 1 -1 1 -1 1 2 -2 -2) $x2039) @x2104 (|unit-resolution| @x1540 (|unit-resolution| @x812 @x2099 $x822) $x1485) @x1046 @x1100 @x1104 @x1385 @x1505 @x1982 @x1945 @x1386 @x1764 @x1919 @x2094 @x1501 @x2027 @x1533 false)))
(let ((@x2125 (|unit-resolution| (lemma @x2105 (or $x1013 $x1779 $x1388 $x988 $x980 $x981 $x1107 $x1060 $x1445 $x1876)) (|unit-resolution| @x1685 (|unit-resolution| @x894 @x2118 $x890) $x1628) @x969 @x982 @x1167 (|unit-resolution| @x1415 (|unit-resolution| @x894 @x2118 $x890) $x911) (|unit-resolution| @x1364 (|unit-resolution| @x876 @x2108 $x872) $x914) @x1009 @x2115 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -2) (or $x1122 $x1445 $x874)) @x2108 @x2115 $x1122) $x1013)))
(let ((@x2126 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 -1 1 -1 1 -1 1 1 -1 -1 -1 -2 2) $x2029) @x2125 @x1046 @x1100 @x950 @x1385 @x1505 (|unit-resolution| @x1685 (|unit-resolution| @x894 @x2118 $x890) $x1628) @x969 (|unit-resolution| @x940 (|unit-resolution| @x840 @x2111 $x836) $x925) @x1764 @x1919 @x934 @x1501 @x982 $x1778)))
(let ((@x2129 (|unit-resolution| @x867 (|unit-resolution| @x869 (|unit-resolution| @x2051 @x2126 $x1070) $x698) $x863)))
(let ((@x2130 (|unit-resolution| @x1173 @x2129 (|unit-resolution| @x1052 @x2111 @x935 @x2108 $x954) false)))
(let ((@x2131 (lemma @x2130 $x586)))
(let ((@x2190 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -1 1 -1 1) (or $x925 $x856 $x1719 $x1064 $x1065 $x829)) @x1079 @x1059 @x1857 @x2131 @x1785 $x925)))
(let ((@x2153 (|unit-resolution| (lemma @x2015 (or $x754 $x614)) @x1010 $x754)))
(let ((@x2156 (|unit-resolution| (lemma @x1452 (or $x614 $x847 $x883 $x782)) @x1728 (or $x614 $x883 $x782))))
(let ((@x2159 (|unit-resolution| @x1415 (|unit-resolution| @x894 (|unit-resolution| @x2156 @x1010 @x2153 $x782) $x890) $x911)))
(let ((@x2162 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x910 $x914)) (|unit-resolution| (lemma @x2076 (or $x614 $x883 $x1107)) @x2153 @x1010 $x1107) $x910)))
(let ((@x2163 (|unit-resolution| @x1685 (|unit-resolution| @x894 (|unit-resolution| @x2156 @x1010 @x2153 $x782) $x890) $x1628)))
(let ((@x2133 (|unit-resolution| @x1517 (|unit-resolution| @x831 @x2131 $x827) $x919)))
(let ((@x2134 ((_ |th-lemma| arith farkas -1 1 -1 1 -3/2 3/2 -1/2 1/2 1/2 -1/2 1/2 -1/2 1/2 1/2 -1/2 -1/2 1/2 1) @x1104 @x1325 @x1764 @x1046 @x1919 @x1100 @x1982 @x1505 @x1502 @x1501 @x1947 @x1079 @x2133 @x1385 @x1399 @x1455 @x1082 (hypothesis $x1946) false)))
(let ((@x2137 (|unit-resolution| (lemma @x2134 (or $x904 $x883 $x1779 $x1970 $x1339 $x1174)) @x1959 @x1982 @x1947 @x1455 @x1325 $x904)))
(let ((@x2019 (hypothesis $x1118)))
(let ((@x2021 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x828) $x926)) @x1005 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 2) (or $x928 $x1060 $x586)) @x935 @x2019 $x1060) false)))
(let ((@x2024 (|unit-resolution| @x831 (|unit-resolution| (lemma @x2021 (or $x586 $x928)) @x2019 $x586) $x827)))
(let ((@x2143 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -1) (or $x926 $x829 $x1118)) (lemma (|unit-resolution| @x972 @x2024 @x2019 false) $x928) (or $x926 $x829))))
(let ((@x2145 (|unit-resolution| @x2090 @x2137 (|unit-resolution| @x2143 @x2131 $x926) @x1460 @x1394 @x963 @x1950 @x1399 $x900)))
(let ((@x2146 (|unit-resolution| @x1553 @x2145 (|unit-resolution| @x807 (|unit-resolution| @x1002 @x2137 $x71) $x820) $x1551)))
(let ((@x2147 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1 1 1 1 1) (or $x558 $x726 $x1779 $x1718 $x957 $x1438 $x1388)) @x1948 @x1385 @x1505 @x1945 @x1399 @x1982 $x558)))
(let ((@x2150 ((_ |th-lemma| arith farkas -1 -1 1 -2 2 -1 1 1 1 -1 -1 1 -1 1 -1 1) @x1104 @x1764 @x1046 @x1919 @x1100 @x1982 @x1505 @x1945 @x1947 @x1079 @x1455 @x1082 (|unit-resolution| @x1540 (|unit-resolution| @x812 @x2147 $x822) $x1485) @x1533 @x2146 @x1959 false)))
(let ((@x2164 (|unit-resolution| (lemma @x2150 (or $x726 $x1779 $x1970 $x1339 $x1445 $x981 $x883)) @x2163 @x1213 (|unit-resolution| @x1112 @x1157 $x1087) @x2162 @x2159 @x2153 $x726)))
(let ((@x2166 (|unit-resolution| @x1364 (|unit-resolution| @x876 @x2164 $x872) (|unit-resolution| (lemma @x2076 (or $x614 $x883 $x1107)) @x2153 @x1010 $x1107) false)))
(let ((@x2167 (lemma @x2166 $x614)))
(let ((@x2169 (|unit-resolution| @x1075 (|unit-resolution| @x840 @x2167 $x836) $x916)))
(let ((@x2172 (|unit-resolution| ((_ |th-lemma| arith assign-bounds -1 -2 2 -2 -2 2) (or $x1086 $x953 $x1064 $x1065 $x829 $x1150 $x1719)) @x1079 @x1059 @x1864 @x1785 @x2131 @x2169 $x1086)))
(let ((@x2176 (|unit-resolution| @x876 (|unit-resolution| (|unit-resolution| @x1733 @x1728 (or $x726 $x1119)) @x2172 $x726) $x872)))
(let ((@x2177 (|unit-resolution| @x1376 @x2176 $x910)))
(let ((@x2180 (|unit-resolution| (|unit-resolution| @x1738 @x1374 @x1082 @x1919 (or $x1119 $x1445 $x1339 $x754)) @x1617 @x2172 @x2177 $x1339)))
(let ((@x2181 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 -2) (or $x1122 $x1445 $x874)) @x2177 (|unit-resolution| (|unit-resolution| @x1733 @x1728 (or $x726 $x1119)) @x2172 $x726) $x1122)))
(let ((@x2184 (|unit-resolution| (|unit-resolution| @x1884 @x1374 @x1857 @x950 (or $x1876 $x1778 $x754)) @x1617 @x2181 $x1778)))
(let ((@x2186 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x1087 $x917)) (|unit-resolution| @x2063 @x2184 @x2167 $x954) @x2180 false)))
(let ((@x2192 (|unit-resolution| @x1398 (|unit-resolution| @x885 (lemma @x2186 $x754) $x881) $x907)))
(let ((@x2194 (|unit-resolution| (lemma @x1825 (or $x900 $x1119 $x1388 $x1509 $x1031 $x1118)) (lemma (|unit-resolution| @x972 @x2024 @x2019 false) $x928) (or $x900 $x1119 $x1388 $x1509 $x1031))))
(let ((@x2197 (|unit-resolution| @x1393 (|unit-resolution| @x885 (lemma @x2186 $x754) $x881) $x908)))
(let ((@x2198 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -1) (or $x1027 $x856 $x1204)) @x1919 @x1857 $x1027)))
(let ((@x2200 (|unit-resolution| (lemma @x1837 (or $x901 $x1353 $x1150 $x1509 $x980 $x1107)) @x2198 (or $x901 $x1150 $x1509 $x980 $x1107))))
(let ((@x2201 (|unit-resolution| @x2200 @x2197 @x2133 @x2169 (|unit-resolution| @x1364 @x2176 $x914) $x901)))
(let ((@x2202 (|unit-resolution| @x1553 @x2201 (|unit-resolution| @x2194 @x2192 @x2133 @x2172 @x2190 $x900) $x70)))
(let ((@x2205 (|unit-resolution| (|unit-resolution| @x1866 @x1785 @x1864 (or $x782 $x1388 $x1445 $x838)) @x2192 @x2167 @x2177 $x782)))
(let ((@x2210 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 2 -1) (or $x1496 $x892 $x1779)) (|unit-resolution| @x1685 (|unit-resolution| @x894 @x2205 $x890) $x1628) @x2205 $x1496)))
(let ((@x2213 (|unit-resolution| (|unit-resolution| @x1511 @x2198 (or $x904 $x954 $x1508 $x1509 $x980 $x1150 $x1107)) @x2210 @x2133 (|unit-resolution| @x1364 @x2176 $x914) @x2197 @x2169 (|unit-resolution| @x1002 (|unit-resolution| @x807 @x2202 $x808) $x1013) $x954)))
(let ((@x2215 (|unit-resolution| @x1781 @x1100 @x950 @x1385 @x1505 @x2198 @x1079 @x1501 (or $x904 $x1778 $x1779 $x1150 $x1509 $x1388))))
(let ((@x2216 (|unit-resolution| @x2215 (|unit-resolution| @x1685 (|unit-resolution| @x894 @x2205 $x890) $x1628) @x2133 @x2169 @x2192 (|unit-resolution| @x1002 (|unit-resolution| @x807 @x2202 $x808) $x1013) $x1778)))
(let ((@x2219 (|unit-resolution| @x867 (|unit-resolution| @x869 (|unit-resolution| @x2051 @x2216 $x1070) $x698) $x863)))
(|unit-resolution| @x1173 @x2219 @x2213 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
6a3a89e24d8df556f7ea5217b40c76ff1c882fab 13 0
unsat
((set-logic AUFLIRA)
(proof
(let (($x11 (< (+ |x$| |x$|) (+ (* 2.0 |x$|) 1.0))))
(let (($x16 (not $x11)))
(let (($x32 (not (<= (+ 1.0 (* 2.0 |x$|)) (* 2.0 |x$|)))))
(let ((@x39 (rewrite (= (<= (+ 1.0 (* 2.0 |x$|)) (* 2.0 |x$|)) false))))
(let ((@x45 (trans (monotonicity @x39 (= $x32 (not false))) (rewrite (= (not false) true)) (= $x32 true))))
(let ((@x30 (monotonicity (rewrite (= (+ |x$| |x$|) (* 2.0 |x$|))) (rewrite (= (+ (* 2.0 |x$|) 1.0) (+ 1.0 (* 2.0 |x$|)))) (= $x11 (< (* 2.0 |x$|) (+ 1.0 (* 2.0 |x$|)))))))
(let ((@x36 (trans @x30 (rewrite (= (< (* 2.0 |x$|) (+ 1.0 (* 2.0 |x$|))) $x32)) (= $x11 $x32))))
(let ((@x50 (monotonicity (trans @x36 @x45 (= $x11 true)) (= $x16 (not true)))))
(mp (|not-or-elim| (asserted (not (or $x11 (or false $x11)))) $x16) (trans @x50 (rewrite (= (not true) false)) (= $x16 false)) false)))))))))))
b3a64ab4fe7d5720729351a375772727b97cece2 81 0
unsat
((set-logic <null>)
(proof
(let (($x591 (= (+ (|mod$| |x$| 2) (* (~ 1) (mod |x$| 2))) 0)))
(let (($x607 (forall ((?v0 Int) (?v1 Int) )(!(let (($x68 (<= ?v1 0)))
(let (($x178 (ite $x68 (= (+ (|mod$| ?v0 ?v1) (mod (* (~ 1) ?v0) (* (~ 1) ?v1))) 0) (= (+ (|mod$| ?v0 ?v1) (* (~ 1) (mod ?v0 ?v1))) 0))))
(let (($x19 (= ?v1 0)))
(ite $x19 (= (|mod$| ?v0 ?v1) ?v0) $x178)))) :pattern ( (|mod$| ?v0 ?v1) )))
))
(let (($x182 (forall ((?v0 Int) (?v1 Int) )(let (($x68 (<= ?v1 0)))
(let (($x178 (ite $x68 (= (+ (|mod$| ?v0 ?v1) (mod (* (~ 1) ?v0) (* (~ 1) ?v1))) 0) (= (+ (|mod$| ?v0 ?v1) (* (~ 1) (mod ?v0 ?v1))) 0))))
(let (($x19 (= ?v1 0)))
(ite $x19 (= (|mod$| ?v0 ?v1) ?v0) $x178)))))
))
(let (($x68 (<= ?0 0)))
(let (($x178 (ite $x68 (= (+ (|mod$| ?1 ?0) (mod (* (~ 1) ?1) (* (~ 1) ?0))) 0) (= (+ (|mod$| ?1 ?0) (* (~ 1) (mod ?1 ?0))) 0))))
(let (($x19 (= ?0 0)))
(let (($x179 (ite $x19 (= (|mod$| ?1 ?0) ?1) $x178)))
(let (($x125 (forall ((?v0 Int) (?v1 Int) )(let ((?x30 (mod ?v0 ?v1)))
(let ((?x100 (mod (* (~ 1) ?v0) (* (~ 1) ?v1))))
(let ((?x106 (* (~ 1) ?x100)))
(let (($x68 (<= ?v1 0)))
(let ((?x114 (ite $x68 ?x106 ?x30)))
(let (($x19 (= ?v1 0)))
(let ((?x29 (|mod$| ?v0 ?v1)))
(= ?x29 (ite $x19 ?v0 ?x114))))))))))
))
(let ((?x30 (mod ?1 ?0)))
(let ((?x100 (mod (* (~ 1) ?1) (* (~ 1) ?0))))
(let ((?x106 (* (~ 1) ?x100)))
(let ((?x114 (ite $x68 ?x106 ?x30)))
(let ((?x29 (|mod$| ?1 ?0)))
(let (($x122 (= ?x29 (ite $x19 ?1 ?x114))))
(let (($x36 (forall ((?v0 Int) (?v1 Int) )(let ((?x32 (- (mod (- ?v0) (- ?v1)))))
(let ((?x30 (mod ?v0 ?v1)))
(let (($x20 (< 0 ?v1)))
(let ((?x33 (ite $x20 ?x30 ?x32)))
(let (($x19 (= ?v1 0)))
(let ((?x29 (|mod$| ?v0 ?v1)))
(= ?x29 (ite $x19 ?v0 ?x33)))))))))
))
(let ((?x32 (- (mod (- ?1) (- ?0)))))
(let (($x20 (< 0 ?0)))
(let ((?x33 (ite $x20 ?x30 ?x32)))
(let ((@x102 (monotonicity (rewrite (= (- ?1) (* (~ 1) ?1))) (rewrite (= (- ?0) (* (~ 1) ?0))) (= (mod (- ?1) (- ?0)) ?x100))))
(let ((@x110 (trans (monotonicity @x102 (= ?x32 (- ?x100))) (rewrite (= (- ?x100) ?x106)) (= ?x32 ?x106))))
(let ((@x113 (monotonicity (rewrite (= $x20 (not $x68))) @x110 (= ?x33 (ite (not $x68) ?x30 ?x106)))))
(let ((@x118 (trans @x113 (rewrite (= (ite (not $x68) ?x30 ?x106) ?x114)) (= ?x33 ?x114))))
(let ((@x124 (monotonicity (monotonicity @x118 (= (ite $x19 ?1 ?x33) (ite $x19 ?1 ?x114))) (= (= ?x29 (ite $x19 ?1 ?x33)) $x122))))
(let ((@x156 (|mp~| (mp (asserted $x36) (|quant-intro| @x124 (= $x36 $x125)) $x125) (|nnf-pos| (refl (|~| $x122 $x122)) (|~| $x125 $x125)) $x125)))
(let ((@x185 (mp @x156 (|quant-intro| (rewrite (= $x122 $x179)) (= $x125 $x182)) $x182)))
(let (($x583 (or (not $x607) $x591)))
(let (($x275 (= (+ (|mod$| |x$| 2) (mod (* (~ 1) |x$|) (* (~ 1) 2))) 0)))
(let (($x592 (ite (<= 2 0) $x275 $x591)))
(let (($x248 (ite (= 2 0) (= (|mod$| |x$| 2) |x$|) $x592)))
(let (($x233 (ite false (= (+ (|mod$| |x$| 2) (mod (* (~ 1) |x$|) (~ 2))) 0) $x591)))
(let (($x254 (= $x275 (= (+ (|mod$| |x$| 2) (mod (* (~ 1) |x$|) (~ 2))) 0))))
(let (($x251 (= (+ (|mod$| |x$| 2) (mod (* (~ 1) |x$|) (* (~ 1) 2))) (+ (|mod$| |x$| 2) (mod (* (~ 1) |x$|) (~ 2))))))
(let ((@x598 (monotonicity (rewrite (= (* (~ 1) 2) (~ 2))) (= (mod (* (~ 1) |x$|) (* (~ 1) 2)) (mod (* (~ 1) |x$|) (~ 2))))))
(let ((@x236 (monotonicity (rewrite (= (<= 2 0) false)) (monotonicity (monotonicity @x598 $x251) $x254) (= $x592 $x233))))
(let ((@x578 (monotonicity (rewrite (= (= 2 0) false)) (trans @x236 (rewrite (= $x233 $x591)) (= $x592 $x591)) (= $x248 (ite false (= (|mod$| |x$| 2) |x$|) $x591)))))
(let ((@x219 (trans @x578 (rewrite (= (ite false (= (|mod$| |x$| 2) |x$|) $x591) $x591)) (= $x248 $x591))))
(let ((@x573 (trans (monotonicity @x219 (= (or (not $x607) $x248) $x583)) (rewrite (= $x583 $x583)) (= (or (not $x607) $x248) $x583))))
(let ((@x416 (|unit-resolution| (mp ((_ |quant-inst| |x$| 2) (or (not $x607) $x248)) @x573 $x583) (mp @x185 (|quant-intro| (refl (= $x179 $x179)) (= $x182 $x607)) $x607) $x591)))
(let (($x418 (or (not $x591) (>= (+ (|mod$| |x$| 2) (* (~ 1) (mod |x$| 2))) 0))))
(let ((@x528 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) $x418) @x416 (>= (+ (|mod$| |x$| 2) (* (~ 1) (mod |x$| 2))) 0))))
(let ((@x530 (|unit-resolution| ((_ |th-lemma| arith) (or false (>= (mod |x$| 2) 0))) (|true-axiom| true) (>= (mod |x$| 2) 0))))
(let ((?x12 (+ |x$| (+ (* 2 (|mod$| |x$| 2)) 1))))
(let (($x13 (<= (+ |x$| 1) ?x12)))
(let (($x14 (not $x13)))
(let ((?x9 (|mod$| |x$| 2)))
(let (($x59 (>= ?x9 0)))
(let ((@x61 (rewrite (= (<= (+ 1 |x$|) (+ 1 |x$| (* 2 ?x9))) $x59))))
(let ((?x10 (* 2 ?x9)))
(let ((?x51 (+ 1 |x$| ?x10)))
(let ((@x50 (monotonicity (rewrite (= (+ ?x10 1) (+ 1 ?x10))) (= ?x12 (+ |x$| (+ 1 ?x10))))))
(let ((@x55 (trans @x50 (rewrite (= (+ |x$| (+ 1 ?x10)) ?x51)) (= ?x12 ?x51))))
(let ((@x58 (monotonicity (rewrite (= (+ |x$| 1) (+ 1 |x$|))) @x55 (= $x13 (<= (+ 1 |x$|) ?x51)))))
(let ((@x66 (monotonicity (trans @x58 @x61 (= $x13 $x59)) (= $x14 (not $x59)))))
((_ |th-lemma| arith farkas -1 1 1) (mp (asserted $x14) @x66 (not $x59)) @x530 @x528 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))
f204450f48b701dc1991b41c92d8f0455c6a933e 80 0
unsat
((set-logic <null>)
(proof
(let ((@x426 (|unit-resolution| ((_ |th-lemma| arith) (or false (not (>= (mod |x$| 2) 2)))) (|true-axiom| true) (not (>= (mod |x$| 2) 2)))))
(let (($x599 (= (+ (|mod$| |x$| 2) (* (~ 1) (mod |x$| 2))) 0)))
(let (($x615 (forall ((?v0 Int) (?v1 Int) )(!(let (($x75 (<= ?v1 0)))
(let (($x185 (ite $x75 (= (+ (|mod$| ?v0 ?v1) (mod (* (~ 1) ?v0) (* (~ 1) ?v1))) 0) (= (+ (|mod$| ?v0 ?v1) (* (~ 1) (mod ?v0 ?v1))) 0))))
(let (($x18 (= ?v1 0)))
(ite $x18 (= (|mod$| ?v0 ?v1) ?v0) $x185)))) :pattern ( (|mod$| ?v0 ?v1) )))
))
(let (($x189 (forall ((?v0 Int) (?v1 Int) )(let (($x75 (<= ?v1 0)))
(let (($x185 (ite $x75 (= (+ (|mod$| ?v0 ?v1) (mod (* (~ 1) ?v0) (* (~ 1) ?v1))) 0) (= (+ (|mod$| ?v0 ?v1) (* (~ 1) (mod ?v0 ?v1))) 0))))
(let (($x18 (= ?v1 0)))
(ite $x18 (= (|mod$| ?v0 ?v1) ?v0) $x185)))))
))
(let (($x75 (<= ?0 0)))
(let (($x185 (ite $x75 (= (+ (|mod$| ?1 ?0) (mod (* (~ 1) ?1) (* (~ 1) ?0))) 0) (= (+ (|mod$| ?1 ?0) (* (~ 1) (mod ?1 ?0))) 0))))
(let (($x18 (= ?0 0)))
(let (($x186 (ite $x18 (= (|mod$| ?1 ?0) ?1) $x185)))
(let (($x132 (forall ((?v0 Int) (?v1 Int) )(let ((?x29 (mod ?v0 ?v1)))
(let ((?x107 (mod (* (~ 1) ?v0) (* (~ 1) ?v1))))
(let ((?x113 (* (~ 1) ?x107)))
(let (($x75 (<= ?v1 0)))
(let ((?x121 (ite $x75 ?x113 ?x29)))
(let (($x18 (= ?v1 0)))
(let ((?x28 (|mod$| ?v0 ?v1)))
(= ?x28 (ite $x18 ?v0 ?x121))))))))))
))
(let ((?x29 (mod ?1 ?0)))
(let ((?x107 (mod (* (~ 1) ?1) (* (~ 1) ?0))))
(let ((?x113 (* (~ 1) ?x107)))
(let ((?x121 (ite $x75 ?x113 ?x29)))
(let ((?x28 (|mod$| ?1 ?0)))
(let (($x129 (= ?x28 (ite $x18 ?1 ?x121))))
(let (($x35 (forall ((?v0 Int) (?v1 Int) )(let ((?x31 (- (mod (- ?v0) (- ?v1)))))
(let ((?x29 (mod ?v0 ?v1)))
(let (($x19 (< 0 ?v1)))
(let ((?x32 (ite $x19 ?x29 ?x31)))
(let (($x18 (= ?v1 0)))
(let ((?x28 (|mod$| ?v0 ?v1)))
(= ?x28 (ite $x18 ?v0 ?x32)))))))))
))
(let ((?x31 (- (mod (- ?1) (- ?0)))))
(let (($x19 (< 0 ?0)))
(let ((?x32 (ite $x19 ?x29 ?x31)))
(let ((@x109 (monotonicity (rewrite (= (- ?1) (* (~ 1) ?1))) (rewrite (= (- ?0) (* (~ 1) ?0))) (= (mod (- ?1) (- ?0)) ?x107))))
(let ((@x117 (trans (monotonicity @x109 (= ?x31 (- ?x107))) (rewrite (= (- ?x107) ?x113)) (= ?x31 ?x113))))
(let ((@x120 (monotonicity (rewrite (= $x19 (not $x75))) @x117 (= ?x32 (ite (not $x75) ?x29 ?x113)))))
(let ((@x125 (trans @x120 (rewrite (= (ite (not $x75) ?x29 ?x113) ?x121)) (= ?x32 ?x121))))
(let ((@x131 (monotonicity (monotonicity @x125 (= (ite $x18 ?1 ?x32) (ite $x18 ?1 ?x121))) (= (= ?x28 (ite $x18 ?1 ?x32)) $x129))))
(let ((@x163 (|mp~| (mp (asserted $x35) (|quant-intro| @x131 (= $x35 $x132)) $x132) (|nnf-pos| (refl (|~| $x129 $x129)) (|~| $x132 $x132)) $x132)))
(let ((@x192 (mp @x163 (|quant-intro| (rewrite (= $x129 $x186)) (= $x132 $x189)) $x189)))
(let (($x591 (or (not $x615) $x599)))
(let (($x283 (= (+ (|mod$| |x$| 2) (mod (* (~ 1) |x$|) (* (~ 1) 2))) 0)))
(let (($x600 (ite (<= 2 0) $x283 $x599)))
(let (($x256 (ite (= 2 0) (= (|mod$| |x$| 2) |x$|) $x600)))
(let (($x241 (ite false (= (+ (|mod$| |x$| 2) (mod (* (~ 1) |x$|) (~ 2))) 0) $x599)))
(let (($x262 (= $x283 (= (+ (|mod$| |x$| 2) (mod (* (~ 1) |x$|) (~ 2))) 0))))
(let (($x259 (= (+ (|mod$| |x$| 2) (mod (* (~ 1) |x$|) (* (~ 1) 2))) (+ (|mod$| |x$| 2) (mod (* (~ 1) |x$|) (~ 2))))))
(let ((@x606 (monotonicity (rewrite (= (* (~ 1) 2) (~ 2))) (= (mod (* (~ 1) |x$|) (* (~ 1) 2)) (mod (* (~ 1) |x$|) (~ 2))))))
(let ((@x244 (monotonicity (rewrite (= (<= 2 0) false)) (monotonicity (monotonicity @x606 $x259) $x262) (= $x600 $x241))))
(let ((@x586 (monotonicity (rewrite (= (= 2 0) false)) (trans @x244 (rewrite (= $x241 $x599)) (= $x600 $x599)) (= $x256 (ite false (= (|mod$| |x$| 2) |x$|) $x599)))))
(let ((@x227 (trans @x586 (rewrite (= (ite false (= (|mod$| |x$| 2) |x$|) $x599) $x599)) (= $x256 $x599))))
(let ((@x581 (trans (monotonicity @x227 (= (or (not $x615) $x256) $x591)) (rewrite (= $x591 $x591)) (= (or (not $x615) $x256) $x591))))
(let ((@x390 (|unit-resolution| (mp ((_ |quant-inst| |x$| 2) (or (not $x615) $x256)) @x581 $x591) (mp @x192 (|quant-intro| (refl (= $x186 $x186)) (= $x189 $x615)) $x615) $x599)))
(let (($x440 (or (not $x599) (<= (+ (|mod$| |x$| 2) (* (~ 1) (mod |x$| 2))) 0))))
(let ((@x538 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) $x440) @x390 (<= (+ (|mod$| |x$| 2) (* (~ 1) (mod |x$| 2))) 0))))
(let ((?x7 (|mod$| |x$| 2)))
(let (($x59 (>= ?x7 2)))
(let (($x12 (< (+ |x$| (+ ?x7 ?x7)) (+ |x$| 3))))
(let (($x13 (not $x12)))
(let ((@x64 (monotonicity (rewrite (= (<= (+ 3 |x$|) (+ |x$| (* 2 ?x7))) $x59)) (= (not (<= (+ 3 |x$|) (+ |x$| (* 2 ?x7)))) (not $x59)))))
(let (($x54 (not (<= (+ 3 |x$|) (+ |x$| (* 2 ?x7))))))
(let ((@x46 (monotonicity (rewrite (= (+ ?x7 ?x7) (* 2 ?x7))) (= (+ |x$| (+ ?x7 ?x7)) (+ |x$| (* 2 ?x7))))))
(let ((@x52 (monotonicity @x46 (rewrite (= (+ |x$| 3) (+ 3 |x$|))) (= $x12 (< (+ |x$| (* 2 ?x7)) (+ 3 |x$|))))))
(let ((@x58 (trans @x52 (rewrite (= (< (+ |x$| (* 2 ?x7)) (+ 3 |x$|)) $x54)) (= $x12 $x54))))
(let ((@x69 (monotonicity (trans @x58 @x64 (= $x12 (not $x59))) (= $x13 (not (not $x59))))))
(let ((@x74 (mp (asserted $x13) (trans @x69 (rewrite (= (not (not $x59)) $x59)) (= $x13 $x59)) $x59)))
((_ |th-lemma| arith farkas -1 1 1) @x74 @x538 @x426 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))
31f44b6ec36399ae0bf7b30f056d07862ad51205 29 0
unsat
((set-logic <null>)
(proof
(let (($x7 (= |x$| 0.0)))
(let ((?x13 (ite (< |x$| 0.0) (- |x$|) |x$|)))
(let (($x14 (< 1.0 ?x13)))
(let (($x15 (not $x14)))
(let (($x16 (or $x14 $x15)))
(let ((?x19 (ite $x16 4.0 2.0)))
(let (($x21 (= (+ |x$| |x$|) (* ?x19 |x$|))))
(let (($x23 (not (not $x21))))
(let ((?x41 (* (~ 1.0) |x$|)))
(let (($x31 (<= 0.0 |x$|)))
(let ((?x47 (ite $x31 |x$| ?x41)))
(let (($x55 (<= ?x47 1.0)))
(let (($x56 (not $x55)))
(let ((@x39 (trans (rewrite (= (< |x$| 0.0) (not $x31))) (monotonicity (rewrite (= $x31 $x31)) (= (not $x31) (not $x31))) (= (< |x$| 0.0) (not $x31)))))
(let ((@x46 (monotonicity @x39 (rewrite (= (- |x$|) ?x41)) (= ?x13 (ite (not $x31) ?x41 |x$|)))))
(let ((@x51 (trans @x46 (rewrite (= (ite (not $x31) ?x41 |x$|) ?x47)) (= ?x13 ?x47))))
(let ((@x60 (trans (monotonicity @x51 (= $x14 (< 1.0 ?x47))) (rewrite (= (< 1.0 ?x47) $x56)) (= $x14 $x56))))
(let ((@x67 (trans (monotonicity @x60 (= $x15 (not $x56))) (rewrite (= (not $x56) $x55)) (= $x15 $x55))))
(let ((@x74 (trans (monotonicity @x60 @x67 (= $x16 (or $x56 $x55))) (rewrite (= (or $x56 $x55) true)) (= $x16 true))))
(let ((@x81 (trans (monotonicity @x74 (= ?x19 (ite true 4.0 2.0))) (rewrite (= (ite true 4.0 2.0) 4.0)) (= ?x19 4.0))))
(let ((@x87 (monotonicity (rewrite (= (+ |x$| |x$|) (* 2.0 |x$|))) (monotonicity @x81 (= (* ?x19 |x$|) (* 4.0 |x$|))) (= $x21 (= (* 2.0 |x$|) (* 4.0 |x$|))))))
(let ((@x91 (trans @x87 (rewrite (= (= (* 2.0 |x$|) (* 4.0 |x$|)) $x7)) (= $x21 $x7))))
(let ((@x96 (monotonicity (monotonicity @x91 (= (not $x21) (not $x7))) (= $x23 (not (not $x7))))))
(let ((@x101 (mp (asserted $x23) (trans @x96 (rewrite (= (not (not $x7)) $x7)) (= $x23 $x7)) $x7)))
(|unit-resolution| (asserted (not $x7)) @x101 false)))))))))))))))))))))))))))
0af106a1a4c411ecd84e866591819b17883ffc09 178 0
unsat
((set-logic <null>)
(proof
(let ((?x436 (* (~ 1) (mod |n$| 4))))
(let ((?x336 (mod |n$| 2)))
(let ((?x339 (* (~ 1) ?x336)))
(let ((?x13 (|mod$| |n$| 4)))
(let ((?x193 (+ |n$| ?x13 ?x339 ?x436 (* (~ 2) (div |n$| 4)) (* (~ 1) (div |n$| 2)))))
(let ((@x129 (|true-axiom| true)))
(let ((@x662 (|unit-resolution| ((_ |th-lemma| arith) (or false (>= ?x336 0))) @x129 (>= ?x336 0))))
(let ((?x203 (+ |n$| ?x339 (* (~ 2) (div |n$| 2)))))
(let (($x201 (= ?x203 0)))
(let ((@x525 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x201) (<= ?x203 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x201)) @x129 $x201) (<= ?x203 0))))
(let ((?x529 (+ ?x13 ?x436)))
(let (($x530 (= ?x529 0)))
(let (($x604 (forall ((?v0 Int) (?v1 Int) )(!(let (($x51 (<= ?v1 0)))
(let (($x175 (ite $x51 (= (+ (|mod$| ?v0 ?v1) (mod (* (~ 1) ?v0) (* (~ 1) ?v1))) 0) (= (+ (|mod$| ?v0 ?v1) (* (~ 1) (mod ?v0 ?v1))) 0))))
(let (($x26 (= ?v1 0)))
(ite $x26 (= (|mod$| ?v0 ?v1) ?v0) $x175)))) :pattern ( (|mod$| ?v0 ?v1) )))
))
(let (($x179 (forall ((?v0 Int) (?v1 Int) )(let (($x51 (<= ?v1 0)))
(let (($x175 (ite $x51 (= (+ (|mod$| ?v0 ?v1) (mod (* (~ 1) ?v0) (* (~ 1) ?v1))) 0) (= (+ (|mod$| ?v0 ?v1) (* (~ 1) (mod ?v0 ?v1))) 0))))
(let (($x26 (= ?v1 0)))
(ite $x26 (= (|mod$| ?v0 ?v1) ?v0) $x175)))))
))
(let (($x51 (<= ?0 0)))
(let (($x175 (ite $x51 (= (+ (|mod$| ?1 ?0) (mod (* (~ 1) ?1) (* (~ 1) ?0))) 0) (= (+ (|mod$| ?1 ?0) (* (~ 1) (mod ?1 ?0))) 0))))
(let (($x26 (= ?0 0)))
(let (($x176 (ite $x26 (= (|mod$| ?1 ?0) ?1) $x175)))
(let (($x108 (forall ((?v0 Int) (?v1 Int) )(let ((?x37 (mod ?v0 ?v1)))
(let ((?x83 (mod (* (~ 1) ?v0) (* (~ 1) ?v1))))
(let ((?x89 (* (~ 1) ?x83)))
(let (($x51 (<= ?v1 0)))
(let ((?x97 (ite $x51 ?x89 ?x37)))
(let (($x26 (= ?v1 0)))
(let ((?x36 (|mod$| ?v0 ?v1)))
(= ?x36 (ite $x26 ?v0 ?x97))))))))))
))
(let ((?x37 (mod ?1 ?0)))
(let ((?x83 (mod (* (~ 1) ?1) (* (~ 1) ?0))))
(let ((?x89 (* (~ 1) ?x83)))
(let ((?x97 (ite $x51 ?x89 ?x37)))
(let ((?x36 (|mod$| ?1 ?0)))
(let (($x105 (= ?x36 (ite $x26 ?1 ?x97))))
(let (($x43 (forall ((?v0 Int) (?v1 Int) )(let ((?x39 (- (mod (- ?v0) (- ?v1)))))
(let ((?x37 (mod ?v0 ?v1)))
(let (($x27 (< 0 ?v1)))
(let ((?x40 (ite $x27 ?x37 ?x39)))
(let (($x26 (= ?v1 0)))
(let ((?x36 (|mod$| ?v0 ?v1)))
(= ?x36 (ite $x26 ?v0 ?x40)))))))))
))
(let ((?x39 (- (mod (- ?1) (- ?0)))))
(let (($x27 (< 0 ?0)))
(let ((?x40 (ite $x27 ?x37 ?x39)))
(let ((@x85 (monotonicity (rewrite (= (- ?1) (* (~ 1) ?1))) (rewrite (= (- ?0) (* (~ 1) ?0))) (= (mod (- ?1) (- ?0)) ?x83))))
(let ((@x93 (trans (monotonicity @x85 (= ?x39 (- ?x83))) (rewrite (= (- ?x83) ?x89)) (= ?x39 ?x89))))
(let ((@x96 (monotonicity (rewrite (= $x27 (not $x51))) @x93 (= ?x40 (ite (not $x51) ?x37 ?x89)))))
(let ((@x101 (trans @x96 (rewrite (= (ite (not $x51) ?x37 ?x89) ?x97)) (= ?x40 ?x97))))
(let ((@x107 (monotonicity (monotonicity @x101 (= (ite $x26 ?1 ?x40) (ite $x26 ?1 ?x97))) (= (= ?x36 (ite $x26 ?1 ?x40)) $x105))))
(let ((@x135 (|mp~| (mp (asserted $x43) (|quant-intro| @x107 (= $x43 $x108)) $x108) (|nnf-pos| (refl (|~| $x105 $x105)) (|~| $x108 $x108)) $x108)))
(let ((@x182 (mp @x135 (|quant-intro| (rewrite (= $x105 $x176)) (= $x108 $x179)) $x179)))
(let ((@x609 (mp @x182 (|quant-intro| (refl (= $x176 $x176)) (= $x179 $x604)) $x604)))
(let (($x289 (not $x604)))
(let (($x480 (or $x289 $x530)))
(let (($x531 (ite (<= 4 0) (= (+ ?x13 (mod (* (~ 1) |n$|) (* (~ 1) 4))) 0) $x530)))
(let (($x518 (ite (= 4 0) (= ?x13 |n$|) $x531)))
(let (($x505 (= (ite false (= (+ ?x13 (mod (* (~ 1) |n$|) (~ 4))) 0) $x530) $x530)))
(let (($x503 (= $x531 (ite false (= (+ ?x13 (mod (* (~ 1) |n$|) (~ 4))) 0) $x530))))
(let (($x517 (= (= (+ ?x13 (mod (* (~ 1) |n$|) (* (~ 1) 4))) 0) (= (+ ?x13 (mod (* (~ 1) |n$|) (~ 4))) 0))))
(let (($x514 (= (+ ?x13 (mod (* (~ 1) |n$|) (* (~ 1) 4))) (+ ?x13 (mod (* (~ 1) |n$|) (~ 4))))))
(let ((@x512 (monotonicity (rewrite (= (* (~ 1) 4) (~ 4))) (= (mod (* (~ 1) |n$|) (* (~ 1) 4)) (mod (* (~ 1) |n$|) (~ 4))))))
(let ((@x504 (monotonicity (rewrite (= (<= 4 0) false)) (monotonicity (monotonicity @x512 $x514) $x517) $x503)))
(let ((@x496 (monotonicity (rewrite (= (= 4 0) false)) (trans @x504 (rewrite $x505) (= $x531 $x530)) (= $x518 (ite false (= ?x13 |n$|) $x530)))))
(let ((@x500 (trans @x496 (rewrite (= (ite false (= ?x13 |n$|) $x530) $x530)) (= $x518 $x530))))
(let ((@x487 (trans (monotonicity @x500 (= (or $x289 $x518) $x480)) (rewrite (= $x480 $x480)) (= (or $x289 $x518) $x480))))
(let ((@x232 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x530) (<= ?x529 0))) (|unit-resolution| (mp ((_ |quant-inst| |n$| 4) (or $x289 $x518)) @x487 $x480) @x609 $x530) (<= ?x529 0))))
(let ((?x466 (+ |n$| ?x436 (* (~ 4) (div |n$| 4)))))
(let (($x464 (= ?x466 0)))
(let ((@x243 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x464) (<= ?x466 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x464)) @x129 $x464) (<= ?x466 0))))
(let ((@x227 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x13 3)) (<= ?x13 3))) (asserted (= ?x13 3)) (<= ?x13 3))))
(let ((@x626 ((_ |th-lemma| arith farkas 2 -1 -1 -1 -1 1) (hypothesis (>= ?x193 2)) @x227 @x243 @x232 @x525 @x662 false)))
(let ((@x621 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x201) (>= ?x203 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x201)) @x129 $x201) (>= ?x203 0))))
(let ((@x353 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x530) (>= ?x529 0))) (|unit-resolution| (mp ((_ |quant-inst| |n$| 4) (or $x289 $x518)) @x487 $x480) @x609 $x530) (>= ?x529 0))))
(let ((@x560 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x464) (>= ?x466 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x464)) @x129 $x464) (>= ?x466 0))))
(let ((@x360 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x13 3)) (>= ?x13 3))) (asserted (= ?x13 3)) (>= ?x13 3))))
(let ((?x16 (|mod$| |n$| 2)))
(let ((?x344 (+ ?x16 ?x339)))
(let (($x346 (= ?x344 0)))
(let (($x467 (or $x289 $x346)))
(let (($x268 (<= 2 0)))
(let (($x354 (ite $x268 (= (+ ?x16 (mod (* (~ 1) |n$|) (* (~ 1) 2))) 0) $x346)))
(let (($x183 (= 2 0)))
(let (($x355 (ite $x183 (= ?x16 |n$|) $x354)))
(let (($x315 (= (ite false (= (+ ?x16 (mod (* (~ 1) |n$|) (~ 2))) 0) $x346) $x346)))
(let (($x558 (= $x354 (ite false (= (+ ?x16 (mod (* (~ 1) |n$|) (~ 2))) 0) $x346))))
(let (($x311 (= (= (+ ?x16 (mod (* (~ 1) |n$|) (* (~ 1) 2))) 0) (= (+ ?x16 (mod (* (~ 1) |n$|) (~ 2))) 0))))
(let (($x330 (= (+ ?x16 (mod (* (~ 1) |n$|) (* (~ 1) 2))) (+ ?x16 (mod (* (~ 1) |n$|) (~ 2))))))
(let ((@x230 (rewrite (= (* (~ 1) 2) (~ 2)))))
(let ((@x328 (monotonicity @x230 (= (mod (* (~ 1) |n$|) (* (~ 1) 2)) (mod (* (~ 1) |n$|) (~ 2))))))
(let ((@x594 (rewrite (= $x268 false))))
(let ((@x305 (trans (monotonicity @x594 (monotonicity (monotonicity @x328 $x330) $x311) $x558) (rewrite $x315) (= $x354 $x346))))
(let ((@x584 (rewrite (= $x183 false))))
(let ((@x463 (trans (monotonicity @x584 @x305 (= $x355 (ite false (= ?x16 |n$|) $x346))) (rewrite (= (ite false (= ?x16 |n$|) $x346) $x346)) (= $x355 $x346))))
(let ((@x555 (trans (monotonicity @x463 (= (or $x289 $x355) $x467)) (rewrite (= $x467 $x467)) (= (or $x289 $x355) $x467))))
(let ((@x647 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x346) (>= ?x344 0))) (|unit-resolution| (mp ((_ |quant-inst| |n$| 2) (or $x289 $x355)) @x555 $x467) @x609 $x346) (>= ?x344 0))))
(let (($x629 (not (>= ?x16 1))))
(let (($x617 (<= ?x16 1)))
(let (($x394 (<= ?x344 0)))
(let ((@x651 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x346) $x394)) (|unit-resolution| (mp ((_ |quant-inst| |n$| 2) (or $x289 $x355)) @x555 $x467) @x609 $x346) $x394)))
(let ((@x184 (|unit-resolution| ((_ |th-lemma| arith) (or false (not (>= ?x336 2)))) @x129 (not (>= ?x336 2)))))
(let ((@x611 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1) (or $x617 (>= ?x336 2) (not $x394))) @x184 @x651 $x617)))
(let ((?x19 (|mod$| |m$| 2)))
(let (($x20 (= ?x19 1)))
(let ((?x274 (* (~ 1) (mod (+ |n$| |m$|) 2))))
(let ((?x7 (+ |n$| |m$|)))
(let ((?x9 (|mod$| ?x7 2)))
(let ((?x316 (+ |n$| |m$| ?x9 ?x13 ?x274 (* (~ 1) (div ?x7 2)) (* (~ 1) (div |m$| 2)) ?x436 (* (~ 2) (div |n$| 4)))))
(let (($x307 (not (>= ?x19 1))))
(let (($x318 (<= ?x19 1)))
(let ((?x400 (+ ?x19 (* (~ 1) (mod |m$| 2)))))
(let (($x371 (<= ?x400 0)))
(let (($x401 (= ?x400 0)))
(let (($x363 (or $x289 $x401)))
(let (($x402 (ite $x268 (= (+ ?x19 (mod (* (~ 1) |m$|) (* (~ 1) 2))) 0) $x401)))
(let (($x403 (ite $x183 (= ?x19 |m$|) $x402)))
(let (($x382 (= (ite false (= (+ ?x19 (mod (* (~ 1) |m$|) (~ 2))) 0) $x401) $x401)))
(let (($x378 (= $x402 (ite false (= (+ ?x19 (mod (* (~ 1) |m$|) (~ 2))) 0) $x401))))
(let (($x411 (= (= (+ ?x19 (mod (* (~ 1) |m$|) (* (~ 1) 2))) 0) (= (+ ?x19 (mod (* (~ 1) |m$|) (~ 2))) 0))))
(let (($x408 (= (+ ?x19 (mod (* (~ 1) |m$|) (* (~ 1) 2))) (+ ?x19 (mod (* (~ 1) |m$|) (~ 2))))))
(let ((@x406 (monotonicity @x230 (= (mod (* (~ 1) |m$|) (* (~ 1) 2)) (mod (* (~ 1) |m$|) (~ 2))))))
(let ((@x386 (trans (monotonicity @x594 (monotonicity (monotonicity @x406 $x408) $x411) $x378) (rewrite $x382) (= $x402 $x401))))
(let ((@x393 (trans (monotonicity @x584 @x386 (= $x403 (ite false (= ?x19 |m$|) $x401))) (rewrite (= (ite false (= ?x19 |m$|) $x401) $x401)) (= $x403 $x401))))
(let ((@x212 (trans (monotonicity @x393 (= (or $x289 $x403) $x363)) (rewrite (= $x363 $x363)) (= (or $x289 $x403) $x363))))
(let ((@x557 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x401) $x371)) (|unit-resolution| (mp ((_ |quant-inst| |m$| 2) (or $x289 $x403)) @x212 $x363) @x609 $x401) $x371)))
(let ((@x385 (|unit-resolution| ((_ |th-lemma| arith) (or false (not (>= (mod |m$| 2) 2)))) @x129 (not (>= (mod |m$| 2) 2)))))
(let ((@x448 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1) (or $x318 (>= (mod |m$| 2) 2) (not $x371))) @x385 @x557 $x318)))
(let ((@x546 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x20 (not $x318) $x307)) (hypothesis (not $x20)) (or (not $x318) $x307))))
(let ((?x351 (+ |m$| (* (~ 2) (div |m$| 2)) (* (~ 1) (mod |m$| 2)))))
(let (($x362 (= ?x351 0)))
(let ((@x449 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x362) (<= ?x351 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x362)) @x129 $x362) (<= ?x351 0))))
(let ((?x554 (+ |n$| |m$| ?x274 (* (~ 2) (div ?x7 2)))))
(let (($x552 (= ?x554 0)))
(let ((@x261 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x552) (<= ?x554 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x552)) @x129 $x552) (<= ?x554 0))))
(let ((?x253 (+ ?x9 ?x274)))
(let (($x588 (= ?x253 0)))
(let (($x290 (or $x289 $x588)))
(let (($x589 (ite $x268 (= (+ ?x9 (mod (* (~ 1) ?x7) (* (~ 1) 2))) 0) $x588)))
(let (($x245 (ite $x183 (= ?x9 ?x7) $x589)))
(let ((@x569 (rewrite (= (ite false (= (+ |n$| |m$| (* (~ 1) ?x9)) 0) $x588) $x588))))
(let (($x576 (ite false (= (+ ?x9 (mod (+ (* (~ 1) |n$|) (* (~ 1) |m$|)) (~ 2))) 0) $x588)))
(let (($x574 (= (= (+ ?x9 (mod (* (~ 1) ?x7) (* (~ 1) 2))) 0) (= (+ ?x9 (mod (+ (* (~ 1) |n$|) (* (~ 1) |m$|)) (~ 2))) 0))))
(let (($x236 (= (+ ?x9 (mod (* (~ 1) ?x7) (* (~ 1) 2))) (+ ?x9 (mod (+ (* (~ 1) |n$|) (* (~ 1) |m$|)) (~ 2))))))
(let (($x233 (= (mod (* (~ 1) ?x7) (* (~ 1) 2)) (mod (+ (* (~ 1) |n$|) (* (~ 1) |m$|)) (~ 2)))))
(let ((@x234 (monotonicity (rewrite (= (* (~ 1) ?x7) (+ (* (~ 1) |n$|) (* (~ 1) |m$|)))) @x230 $x233)))
(let ((@x578 (monotonicity @x594 (monotonicity (monotonicity @x234 $x236) $x574) (= $x589 $x576))))
(let ((@x257 (rewrite (= (= ?x9 ?x7) (= (+ |n$| |m$| (* (~ 1) ?x9)) 0)))))
(let ((@x582 (monotonicity @x584 @x257 (trans @x578 (rewrite (= $x576 $x588)) (= $x589 $x588)) (= $x245 (ite false (= (+ |n$| |m$| (* (~ 1) ?x9)) 0) $x588)))))
(let ((@x564 (monotonicity (trans @x582 @x569 (= $x245 $x588)) (= (or $x289 $x245) $x290))))
(let ((@x566 (mp ((_ |quant-inst| (+ |n$| |m$|) 2) (or $x289 $x245)) (trans @x564 (rewrite (= $x290 $x290)) (= (or $x289 $x245) $x290)) $x290)))
(let ((@x266 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x588) (<= ?x253 0))) (|unit-resolution| @x566 @x609 $x588) (<= ?x253 0))))
(let ((@x286 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x9 0)) (<= ?x9 0))) (asserted (= ?x9 0)) (<= ?x9 0))))
(let ((@x455 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x401) (>= ?x400 0))) (|unit-resolution| (mp ((_ |quant-inst| |m$| 2) (or $x289 $x403)) @x212 $x363) @x609 $x401) (>= ?x400 0))))
(let ((@x456 ((_ |th-lemma| arith farkas -1 1 1 -2 1 1 1 1 1 1) @x455 @x286 @x227 (hypothesis (>= ?x316 2)) @x243 @x266 @x261 @x449 @x232 (hypothesis $x307) false)))
(let ((@x373 (|unit-resolution| (lemma @x456 (or (not (>= ?x316 2)) (>= ?x19 1))) (|unit-resolution| @x546 @x448 $x307) (not (>= ?x316 2)))))
(let ((@x471 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x9 0)) (>= ?x9 0))) (asserted (= ?x9 0)) (>= ?x9 0))))
(let ((@x276 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x552) (>= ?x554 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x552)) @x129 $x552) (>= ?x554 0))))
(let ((@x475 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x588) (>= ?x253 0))) (|unit-resolution| @x566 @x609 $x588) (>= ?x253 0))))
(let ((@x532 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x362) (>= ?x351 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x362)) @x129 $x362) (>= ?x351 0))))
(let ((@x342 (|unit-resolution| ((_ |th-lemma| arith) (or false (>= (mod |m$| 2) 0))) @x129 (>= (mod |m$| 2) 0))))
(let ((@x349 (lemma ((_ |th-lemma| arith farkas -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 1) @x360 @x560 @x353 @x342 @x532 @x475 @x276 @x471 @x373 false) $x20)))
(let (($x142 (or (not (= ?x16 1)) (not $x20))))
(let ((@x148 (monotonicity (rewrite (= (and (= ?x16 1) $x20) (not $x142))) (= (not (and (= ?x16 1) $x20)) (not (not $x142))))))
(let ((@x152 (trans @x148 (rewrite (= (not (not $x142)) $x142)) (= (not (and (= ?x16 1) $x20)) $x142))))
(let ((@x627 (|unit-resolution| (mp (asserted (not (and (= ?x16 1) $x20))) @x152 $x142) @x349 (not (= ?x16 1)))))
(let ((@x636 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (= ?x16 1) (not $x617) $x629)) @x627 (or (not $x617) $x629))))
((_ |th-lemma| arith farkas 1/2 -1/2 -1/2 -1/2 -1/2 -1/2 1) (|unit-resolution| @x636 @x611 $x629) @x647 @x360 @x560 @x353 @x621 (lemma @x626 (not (>= ?x193 2))) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
6b708fee38e9bf7615ccc8723328495d7f62521e 11 0
unsat
((set-logic AUFLIA)
(proof
(let (($x6 (exists ((?v0 Int) )false)
))
(let (($x5 (not $x6)))
(let (($x7 (not $x5)))
(let ((@x13 (monotonicity (|elim-unused| (= $x6 false)) (= $x5 (not false)))))
(let ((@x20 (monotonicity (trans @x13 (rewrite (= (not false) true)) (= $x5 true)) (= $x7 (not true)))))
(mp (asserted $x7) (trans @x20 (rewrite (= (not true) false)) (= $x7 false)) false))))))))
531451869d81515a9a811b564209ab76519736be 11 0
unsat
((set-logic AUFLIRA)
(proof
(let (($x6 (exists ((?v0 Real) )false)
))
(let (($x5 (not $x6)))
(let (($x7 (not $x5)))
(let ((@x13 (monotonicity (|elim-unused| (= $x6 false)) (= $x5 (not false)))))
(let ((@x20 (monotonicity (trans @x13 (rewrite (= (not false) true)) (= $x5 true)) (= $x7 (not true)))))
(mp (asserted $x7) (trans @x20 (rewrite (= (not true) false)) (= $x7 false)) false))))))))
365761b65f00d147ff0728b709645c1e95a5cb22 22 0
unsat
((set-logic AUFLIA)
(proof
(let (($x54 (forall ((?v0 Int) )(<= ?v0 0))
))
(let (($x46 (forall ((?v0 Int) )(let (($x11 (<= ?v0 0)))
(let (($x12 (not $x11)))
(not $x12))))
))
(let ((@x56 (|quant-intro| (rewrite (= (not (not (<= ?0 0))) (<= ?0 0))) (= $x46 $x54))))
(let (($x15 (exists ((?v0 Int) )(let (($x11 (<= ?v0 0)))
(not $x11)))
))
(let (($x18 (not $x15)))
(let ((@x48 (|nnf-neg| (refl (|~| (not (not (<= ?0 0))) (not (not (<= ?0 0))))) (|~| $x18 $x46))))
(let (($x8 (exists ((?v0 Int) )(< 0 ?v0))
))
(let (($x9 (not $x8)))
(let ((@x17 (|quant-intro| (rewrite (= (< 0 ?0) (not (<= ?0 0)))) (= $x8 $x15))))
(let ((@x24 (mp (mp (asserted $x9) (monotonicity @x17 (= $x9 $x18)) $x18) (|rewrite*| (= $x18 $x18)) $x18)))
(mp (mp (|mp~| @x24 @x48 $x46) @x56 $x54) (rewrite (= $x54 false)) false)))))))))))))
a524cbe0a36c63dd22a617bca8ac628c3c4e0003 22 0
unsat
((set-logic AUFLIRA)
(proof
(let (($x54 (forall ((?v0 Real) )(<= ?v0 0.0))
))
(let (($x46 (forall ((?v0 Real) )(let (($x11 (<= ?v0 0.0)))
(let (($x12 (not $x11)))
(not $x12))))
))
(let ((@x56 (|quant-intro| (rewrite (= (not (not (<= ?0 0.0))) (<= ?0 0.0))) (= $x46 $x54))))
(let (($x15 (exists ((?v0 Real) )(let (($x11 (<= ?v0 0.0)))
(not $x11)))
))
(let (($x18 (not $x15)))
(let ((@x48 (|nnf-neg| (refl (|~| (not (not (<= ?0 0.0))) (not (not (<= ?0 0.0))))) (|~| $x18 $x46))))
(let (($x8 (exists ((?v0 Real) )(< 0.0 ?v0))
))
(let (($x9 (not $x8)))
(let ((@x17 (|quant-intro| (rewrite (= (< 0.0 ?0) (not (<= ?0 0.0)))) (= $x8 $x15))))
(let ((@x24 (mp (mp (asserted $x9) (monotonicity @x17 (= $x9 $x18)) $x18) (|rewrite*| (= $x18 $x18)) $x18)))
(mp (mp (|mp~| @x24 @x48 $x46) @x56 $x54) (rewrite (= $x54 false)) false)))))))))))))
52fc23e5db1b35bf2465aff4abeba68b99d17123 40 0
unsat
((set-logic AUFLIA)
(declare-fun ?v0!0 () Int)
(proof
(let (($x89 (forall ((?v1 Int) )(<= (+ ?v1 (* (~ 1) ?v0!0)) 0))
))
(let (($x79 (forall ((?v1 Int) )(not (not (<= (+ ?v1 (* (~ 1) ?v0!0)) 0))))
))
(let (($x70 (<= (+ ?0 (* (~ 1) ?v0!0)) 0)))
(let (($x76 (not (not $x70))))
(let (($x61 (forall ((?v0 Int) )(exists ((?v1 Int) )(not (<= (+ ?v1 (* (~ 1) ?v0)) 0)))
)
))
(let (($x64 (not $x61)))
(let (($x72 (exists ((?v1 Int) )(let (($x70 (<= (+ ?v1 (* (~ 1) ?v0!0)) 0)))
(not $x70)))
))
(let ((@x83 (trans (sk (|~| $x64 (not $x72))) (|nnf-neg| (refl (|~| $x76 $x76)) (|~| (not $x72) $x79)) (|~| $x64 $x79))))
(let (($x19 (forall ((?v0 Int) )(exists ((?v1 Int) )(not (<= ?v1 ?v0)))
)
))
(let (($x22 (not $x19)))
(let (($x58 (exists ((?v1 Int) )(not (<= (+ ?v1 (* (~ 1) ?0)) 0)))
))
(let (($x16 (exists ((?v1 Int) )(not (<= ?v1 ?0)))
))
(let ((@x57 (monotonicity (rewrite (= (<= ?0 ?1) (<= (+ ?0 (* (~ 1) ?1)) 0))) (= (not (<= ?0 ?1)) (not (<= (+ ?0 (* (~ 1) ?1)) 0))))))
(let ((@x66 (monotonicity (|quant-intro| (|quant-intro| @x57 (= $x16 $x58)) (= $x19 $x61)) (= $x22 $x64))))
(let (($x9 (forall ((?v0 Int) )(exists ((?v1 Int) )(< ?v0 ?v1))
)
))
(let (($x10 (not $x9)))
(let (($x8 (exists ((?v1 Int) )(< ?0 ?v1))
))
(let ((@x18 (|quant-intro| (rewrite (= (< ?1 ?0) (not (<= ?0 ?1)))) (= $x8 $x16))))
(let ((@x25 (mp (asserted $x10) (monotonicity (|quant-intro| @x18 (= $x9 $x19)) (= $x10 $x22)) $x22)))
(let ((@x84 (|mp~| (mp (mp @x25 (|rewrite*| (= $x22 $x22)) $x22) @x66 $x64) @x83 $x79)))
(let ((@x85 (mp @x84 (|quant-intro| (rewrite (= $x76 $x70)) (= $x79 $x89)) $x89)))
(mp @x85 (rewrite (= $x89 false)) false))))))))))))))))))))))))
750c85c0e2958b1508ba7c582f2bdbbb46fc0552 20 0
unsat
((set-logic AUFLIA)
(declare-fun ?v1!0 () Int)
(declare-fun ?v0!1 () Int)
(proof
(let (($x58 (or (not (and (= ?v0!1 0) (= ?v1!0 1))) (not (= ?v0!1 ?v1!0)))))
(let (($x22 (forall ((?v0 Int) (?v1 Int) )(or (not (and (= ?v0 0) (= ?v1 1))) (not (= ?v0 ?v1))))
))
(let (($x25 (not $x22)))
(let (($x15 (forall ((?v0 Int) (?v1 Int) )(=> (and (= ?v0 0) (= ?v1 1)) (not (= ?v0 ?v1))))
))
(let (($x16 (not $x15)))
(let (($x20 (= (=> (and (= ?1 0) (= ?0 1)) (not (= ?1 ?0))) (or (not (and (= ?1 0) (= ?0 1))) (not (= ?1 ?0))))))
(let ((@x27 (monotonicity (|quant-intro| (rewrite $x20) (= $x15 $x22)) (= $x16 $x25))))
(let ((@x62 (|mp~| (mp (mp (asserted $x16) @x27 $x25) (|rewrite*| (= $x25 $x25)) $x25) (sk (|~| $x25 (not $x58))) (not $x58))))
(let ((@x67 (|and-elim| (|not-or-elim| @x62 (and (= ?v0!1 0) (= ?v1!0 1))) (= ?v1!0 1))))
(let ((@x66 (|and-elim| (|not-or-elim| @x62 (and (= ?v0!1 0) (= ?v1!0 1))) (= ?v0!1 0))))
(let ((@x70 (trans (symm @x66 (= 0 ?v0!1)) (|not-or-elim| @x62 (= ?v0!1 ?v1!0)) (= 0 ?v1!0))))
(mp (trans @x70 @x67 (= 0 1)) (rewrite (= (= 0 1) false)) false))))))))))))))
76c68fc9857d9b1bea2540fac5de5d93a85faffa 30 0
unsat
((set-logic AUFLIA)
(proof
(let (($x14 (exists ((?v0 Int) )(forall ((?v1 Int) )(let (($x10 (<= 0 ?v1)))
(let (($x11 (or (< ?v1 0) $x10)))
(=> (< ?v0 ?v1) $x11))))
)
))
(let (($x15 (not $x14)))
(let (($x50 (exists ((?v0 Int) )true)
))
(let (($x13 (forall ((?v1 Int) )(let (($x10 (<= 0 ?v1)))
(let (($x11 (or (< ?v1 0) $x10)))
(=> (< ?0 ?v1) $x11))))
))
(let (($x43 (forall ((?v1 Int) )true)
))
(let (($x10 (<= 0 ?0)))
(let (($x11 (or (< ?0 0) $x10)))
(let (($x12 (=> (< ?1 ?0) $x11)))
(let ((@x28 (trans (rewrite (= (< ?0 0) (not $x10))) (monotonicity (rewrite (= $x10 $x10)) (= (not $x10) (not $x10))) (= (< ?0 0) (not $x10)))))
(let ((@x31 (monotonicity @x28 (rewrite (= $x10 $x10)) (= $x11 (or (not $x10) $x10)))))
(let ((@x35 (trans @x31 (rewrite (= (or (not $x10) $x10) true)) (= $x11 true))))
(let ((@x38 (monotonicity (rewrite (= (< ?1 ?0) (not (<= ?0 ?1)))) @x35 (= $x12 (=> (not (<= ?0 ?1)) true)))))
(let ((@x42 (trans @x38 (rewrite (= (=> (not (<= ?0 ?1)) true) true)) (= $x12 true))))
(let ((@x49 (trans (|quant-intro| @x42 (= $x13 $x43)) (|elim-unused| (= $x43 true)) (= $x13 true))))
(let ((@x56 (trans (|quant-intro| @x49 (= $x14 $x50)) (|elim-unused| (= $x50 true)) (= $x14 true))))
(let ((@x63 (trans (monotonicity @x56 (= $x15 (not true))) (rewrite (= (not true) false)) (= $x15 false))))
(mp (asserted $x15) @x63 false)))))))))))))))))))
a26ec0d452d6ecde84fa66db969e7d6c80150605 38 0
unsat
((set-logic AUFLIA)
(proof
(let (($x47 (forall ((?v0 Int) (?v1 Int) )(let ((?x22 (+ 1 (* 2 ?v0))))
(let ((?x12 (* 2 ?v1)))
(let (($x28 (<= ?x12 ?x22)))
(let (($x29 (not $x28)))
(let (($x18 (<= ?v1 ?v0)))
(or $x18 $x29)))))))
))
(let (($x50 (not $x47)))
(let (($x95 (forall ((?v0 Int) (?v1 Int) )true)
))
(let ((?x22 (+ 1 (* 2 ?1))))
(let ((?x12 (* 2 ?0)))
(let (($x28 (<= ?x12 ?x22)))
(let (($x29 (not $x28)))
(let (($x18 (<= ?0 ?1)))
(let (($x42 (or $x18 $x29)))
(let (($x79 (>= (+ ?1 (* (~ 1) ?0)) 0)))
(let ((@x90 (monotonicity (rewrite (= $x18 $x79)) (monotonicity (rewrite (= $x28 $x79)) (= $x29 (not $x79))) (= $x42 (or $x79 (not $x79))))))
(let ((@x94 (trans @x90 (rewrite (= (or $x79 (not $x79)) true)) (= $x42 true))))
(let ((@x101 (trans (|quant-intro| @x94 (= $x47 $x95)) (|elim-unused| (= $x95 true)) (= $x47 true))))
(let ((@x108 (trans (monotonicity @x101 (= $x50 (not true))) (rewrite (= (not true) false)) (= $x50 false))))
(let (($x15 (forall ((?v0 Int) (?v1 Int) )(let ((?x12 (* 2 ?v1)))
(let (($x13 (< (+ (* 2 ?v0) 1) ?x12)))
(=> (< ?v0 ?v1) $x13))))
))
(let (($x16 (not $x15)))
(let (($x13 (< (+ (* 2 ?1) 1) ?x12)))
(let (($x14 (=> (< ?1 ?0) $x13)))
(let ((@x27 (monotonicity (rewrite (= (+ (* 2 ?1) 1) ?x22)) (= $x13 (< ?x22 ?x12)))))
(let ((@x38 (trans (trans @x27 (rewrite (= (< ?x22 ?x12) $x29)) (= $x13 $x29)) (monotonicity (rewrite (= $x28 $x28)) (= $x29 $x29)) (= $x13 $x29))))
(let ((@x41 (monotonicity (rewrite (= (< ?1 ?0) (not $x18))) @x38 (= $x14 (=> (not $x18) $x29)))))
(let ((@x46 (trans @x41 (rewrite (= (=> (not $x18) $x29) $x42)) (= $x14 $x42))))
(let ((@x53 (mp (asserted $x16) (monotonicity (|quant-intro| @x46 (= $x15 $x47)) (= $x16 $x50)) $x50)))
(mp (mp @x53 (|rewrite*| (= $x50 $x50)) $x50) @x108 false))))))))))))))))))))))))))
bd9c4497c082a3945939358cc22879f4906afd6a 29 0
unsat
((set-logic AUFLIA)
(proof
(let (($x33 (forall ((?v0 Int) (?v1 Int) )(let ((?x8 (* 2 ?v0)))
(let (($x25 (= ?x8 (+ (~ 1) (* 2 ?v1)))))
(not $x25))))
))
(let (($x36 (not $x33)))
(let (($x72 (forall ((?v0 Int) (?v1 Int) )true)
))
(let ((?x8 (* 2 ?1)))
(let (($x25 (= ?x8 (+ (~ 1) (* 2 ?0)))))
(let (($x30 (not $x25)))
(let ((@x71 (trans (monotonicity (rewrite (= $x25 false)) (= $x30 (not false))) (rewrite (= (not false) true)) (= $x30 true))))
(let ((@x78 (trans (|quant-intro| @x71 (= $x33 $x72)) (|elim-unused| (= $x72 true)) (= $x33 true))))
(let ((@x85 (trans (monotonicity @x78 (= $x36 (not true))) (rewrite (= (not true) false)) (= $x36 false))))
(let (($x14 (forall ((?v0 Int) (?v1 Int) )(let ((?x11 (* 2 ?v1)))
(let (($x12 (= (+ (* 2 ?v0) 1) ?x11)))
(not $x12))))
))
(let (($x15 (not $x14)))
(let ((?x11 (* 2 ?0)))
(let (($x12 (= (+ ?x8 1) ?x11)))
(let ((@x22 (monotonicity (rewrite (= (+ ?x8 1) (+ 1 ?x8))) (= $x12 (= (+ 1 ?x8) ?x11)))))
(let ((@x29 (trans @x22 (rewrite (= (= (+ 1 ?x8) ?x11) $x25)) (= $x12 $x25))))
(let ((@x35 (|quant-intro| (monotonicity @x29 (= (not $x12) $x30)) (= $x14 $x33))))
(let ((@x42 (mp (mp (asserted $x15) (monotonicity @x35 (= $x15 $x36)) $x36) (|rewrite*| (= $x36 $x36)) $x36)))
(mp @x42 @x85 false))))))))))))))))))))
4561e7f574918fb0fcb2d1c3600b5565bf981ede 52 0
unsat
((set-logic AUFLIA)
(declare-fun ?v0!1 () Int)
(declare-fun ?v1!0 () Int)
(proof
(let ((?x101 (+ ?v1!0 ?v0!1)))
(let (($x113 (>= ?x101 2)))
(let (($x116 (not $x113)))
(let (($x110 (= ?x101 2)))
(let (($x104 (<= ?x101 2)))
(let (($x107 (not $x104)))
(let (($x94 (or (not (<= (+ ?v0!1 ?v1!0) 2)) (= (+ ?v0!1 ?v1!0) 2) (not (>= (+ ?v0!1 ?v1!0) 2)))))
(let (($x95 (not $x94)))
(let ((@x103 (rewrite (= (+ ?v0!1 ?v1!0) ?x101))))
(let ((@x118 (monotonicity (monotonicity @x103 (= (>= (+ ?v0!1 ?v1!0) 2) $x113)) (= (not (>= (+ ?v0!1 ?v1!0) 2)) $x116))))
(let ((@x109 (monotonicity (monotonicity @x103 (= (<= (+ ?v0!1 ?v1!0) 2) $x104)) (= (not (<= (+ ?v0!1 ?v1!0) 2)) $x107))))
(let ((@x121 (monotonicity @x109 (monotonicity @x103 (= (= (+ ?v0!1 ?v1!0) 2) $x110)) @x118 (= $x94 (or $x107 $x110 $x116)))))
(let (($x80 (forall ((?v0 Int) (?v1 Int) )(let ((?x8 (+ ?v0 ?v1)))
(let (($x10 (= ?x8 2)))
(let (($x18 (not (<= ?x8 2))))
(or $x18 $x10 (not (>= ?x8 2)))))))
))
(let (($x83 (not $x80)))
(let (($x41 (forall ((?v0 Int) (?v1 Int) )(let ((?x8 (+ ?v0 ?v1)))
(let (($x21 (<= 2 ?x8)))
(let (($x22 (not $x21)))
(let (($x10 (= ?x8 2)))
(let (($x18 (not (<= ?x8 2))))
(or $x18 $x10 $x22)))))))
))
(let (($x44 (not $x41)))
(let ((?x8 (+ ?1 ?0)))
(let (($x10 (= ?x8 2)))
(let (($x18 (not (<= ?x8 2))))
(let (($x21 (<= 2 ?x8)))
(let (($x22 (not $x21)))
(let (($x36 (or $x18 $x10 $x22)))
(let ((@x76 (monotonicity (rewrite (= $x21 (>= ?x8 2))) (= $x22 (not (>= ?x8 2))))))
(let ((@x82 (|quant-intro| (monotonicity @x76 (= $x36 (or $x18 $x10 (not (>= ?x8 2))))) (= $x41 $x80))))
(let (($x14 (forall ((?v0 Int) (?v1 Int) )(or (< 2 (+ ?v0 ?v1)) (or (= (+ ?v0 ?v1) 2) (< (+ ?v0 ?v1) 2))))
))
(let (($x15 (not $x14)))
(let (($x13 (or (< 2 ?x8) (or $x10 (< ?x8 2)))))
(let ((@x29 (trans (rewrite (= (< ?x8 2) $x22)) (monotonicity (rewrite (= $x21 $x21)) (= $x22 $x22)) (= (< ?x8 2) $x22))))
(let ((@x35 (monotonicity (rewrite (= (< 2 ?x8) $x18)) (monotonicity @x29 (= (or $x10 (< ?x8 2)) (or $x10 $x22))) (= $x13 (or $x18 (or $x10 $x22))))))
(let ((@x40 (trans @x35 (rewrite (= (or $x18 (or $x10 $x22)) $x36)) (= $x13 $x36))))
(let ((@x47 (mp (asserted $x15) (monotonicity (|quant-intro| @x40 (= $x14 $x41)) (= $x15 $x44)) $x44)))
(let ((@x86 (mp (mp @x47 (|rewrite*| (= $x44 $x44)) $x44) (monotonicity @x82 (= $x44 $x83)) $x83)))
(let ((@x99 (mp (|mp~| @x86 (sk (|~| $x83 $x95)) $x95) (monotonicity @x121 (= $x95 (not (or $x107 $x110 $x116)))) (not (or $x107 $x110 $x116)))))
(let ((@x131 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x110 $x107 $x116)) (|not-or-elim| @x99 $x104) (or $x110 $x116))))
(|unit-resolution| @x131 (|not-or-elim| @x99 $x113) (|not-or-elim| @x99 (not $x110)) false)))))))))))))))))))))))))))))))))))))
230760924531c91da933509839308feff344fdd2 50 0
unsat
((set-logic AUFLIA)
(declare-fun ?v0!0 () Int)
(proof
(let (($x103 (<= ?v0!0 0)))
(let (($x106 (<= ?v0!0 (~ 1))))
(let (($x107 (not $x106)))
(let ((@x125 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x107 $x103)) (hypothesis (not $x103)) $x107)))
(let (($x96 (forall ((?v0 Int) )(let (($x36 (not (<= ?v0 (~ 1)))))
(let (($x16 (<= ?v0 0)))
(ite $x16 (not (>= ?v0 1)) $x36))))
))
(let (($x99 (not $x96)))
(let (($x58 (forall ((?v0 Int) )(let (($x36 (not (<= ?v0 (~ 1)))))
(let (($x41 (<= 1 ?v0)))
(let (($x42 (not $x41)))
(let (($x16 (<= ?v0 0)))
(ite $x16 $x42 $x36))))))
))
(let (($x61 (not $x58)))
(let (($x36 (not (<= ?0 (~ 1)))))
(let (($x41 (<= 1 ?0)))
(let (($x42 (not $x41)))
(let (($x16 (<= ?0 0)))
(let (($x53 (ite $x16 $x42 $x36)))
(let ((@x92 (monotonicity (rewrite (= $x41 (>= ?0 1))) (= $x42 (not (>= ?0 1))))))
(let ((@x98 (|quant-intro| (monotonicity @x92 (= $x53 (ite $x16 (not (>= ?0 1)) $x36))) (= $x58 $x96))))
(let (($x13 (forall ((?v0 Int) )(let (($x10 (< 0 (+ ?v0 1))))
(ite (< 0 ?v0) $x10 (< ?v0 1))))
))
(let (($x14 (not $x13)))
(let (($x10 (< 0 (+ ?0 1))))
(let (($x12 (ite (< 0 ?0) $x10 (< ?0 1))))
(let ((@x49 (trans (rewrite (= (< ?0 1) $x42)) (monotonicity (rewrite (= $x41 $x41)) (= $x42 $x42)) (= (< ?0 1) $x42))))
(let ((@x38 (monotonicity (rewrite (= (<= (+ 1 ?0) 0) (<= ?0 (~ 1)))) (= (not (<= (+ 1 ?0) 0)) $x36))))
(let ((@x29 (rewrite (= (< 0 (+ 1 ?0)) (not (<= (+ 1 ?0) 0))))))
(let ((@x25 (monotonicity (rewrite (= (+ ?0 1) (+ 1 ?0))) (= $x10 (< 0 (+ 1 ?0))))))
(let ((@x40 (trans (trans @x25 @x29 (= $x10 (not (<= (+ 1 ?0) 0)))) @x38 (= $x10 $x36))))
(let ((@x52 (monotonicity (rewrite (= (< 0 ?0) (not $x16))) @x40 @x49 (= $x12 (ite (not $x16) $x36 $x42)))))
(let ((@x57 (trans @x52 (rewrite (= (ite (not $x16) $x36 $x42) $x53)) (= $x12 $x53))))
(let ((@x64 (mp (asserted $x14) (monotonicity (|quant-intro| @x57 (= $x13 $x58)) (= $x14 $x61)) $x61)))
(let ((@x102 (mp (mp @x64 (|rewrite*| (= $x61 $x61)) $x61) (monotonicity @x98 (= $x61 $x99)) $x99)))
(let ((@x112 (|mp~| @x102 (sk (|~| $x99 (not (ite $x103 (not (>= ?v0!0 1)) $x107)))) (not (ite $x103 (not (>= ?v0!0 1)) $x107)))))
(let ((@x127 (|unit-resolution| (|def-axiom| (or (ite $x103 (not (>= ?v0!0 1)) $x107) $x103 $x106)) @x112 (or $x103 $x106))))
(let ((@x129 (lemma (|unit-resolution| @x127 @x125 (hypothesis (not $x103)) false) $x103)))
(let (($x104 (>= ?v0!0 1)))
(let (($x105 (not $x104)))
(let ((@x134 (|unit-resolution| (|def-axiom| (or (ite $x103 $x105 $x107) (not $x103) $x104)) @x112 (or (not $x103) $x104))))
(|unit-resolution| @x134 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x105 (not $x103))) @x129 $x105) @x129 false)))))))))))))))))))))))))))))))))))))
1e9c0d6f38cf8e68fc9ae85612e77618e349b0b4 40 0
unsat
((set-logic AUFLIA)
(proof
(let (($x80 (forall ((?v0 Int) )(let (($x24 (not (<= ?v0 0))))
(or (not (>= ?v0 0)) $x24)))
))
(let (($x479 (not $x80)))
(let (($x89 (not (<= 0 0))))
(let (($x164 (not (>= 0 0))))
(let (($x175 (or $x164 $x89)))
(let (($x140 (or $x479 $x175)))
(let ((@x501 (monotonicity (rewrite (= (<= 0 0) true)) (= $x89 (not true)))))
(let ((@x160 (monotonicity (rewrite (= (>= 0 0) true)) (= $x164 (not true)))))
(let ((@x156 (monotonicity (trans @x160 (rewrite (= (not true) false)) (= $x164 false)) (trans @x501 (rewrite (= (not true) false)) (= $x89 false)) (= $x175 (or false false)))))
(let ((@x137 (trans @x156 (rewrite (= (or false false) false)) (= $x175 false))))
(let ((@x484 (trans (monotonicity @x137 (= $x140 (or $x479 false))) (rewrite (= (or $x479 false) $x479)) (= $x140 $x479))))
(let (($x24 (not (<= ?0 0))))
(let (($x77 (or (not (>= ?0 0)) $x24)))
(let (($x30 (forall ((?v0 Int) )(let (($x24 (not (<= ?v0 0))))
(let (($x14 (<= 0 ?v0)))
(let (($x15 (not $x14)))
(or $x15 $x24)))))
))
(let ((@x76 (monotonicity (rewrite (= (<= 0 ?0) (>= ?0 0))) (= (not (<= 0 ?0)) (not (>= ?0 0))))))
(let ((@x82 (|quant-intro| (monotonicity @x76 (= (or (not (<= 0 ?0)) $x24) $x77)) (= $x30 $x80))))
(let (($x10 (forall ((?v0 Int) )(or (< ?v0 0) (< 0 ?v0)))
))
(let (($x11 (ite $x10 false true)))
(let (($x12 (not $x11)))
(let (($x14 (<= 0 ?0)))
(let (($x15 (not $x14)))
(let (($x27 (or $x15 $x24)))
(let ((@x22 (trans (rewrite (= (< ?0 0) $x15)) (monotonicity (rewrite (= $x14 $x14)) (= $x15 $x15)) (= (< ?0 0) $x15))))
(let ((@x29 (monotonicity @x22 (rewrite (= (< 0 ?0) $x24)) (= (or (< ?0 0) (< 0 ?0)) $x27))))
(let ((@x35 (monotonicity (|quant-intro| @x29 (= $x10 $x30)) (= $x11 (ite $x30 false true)))))
(let ((@x40 (trans @x35 (rewrite (= (ite $x30 false true) (not $x30))) (= $x11 (not $x30)))))
(let ((@x47 (trans (monotonicity @x40 (= $x12 (not (not $x30)))) (rewrite (= (not (not $x30)) $x30)) (= $x12 $x30))))
(let ((@x83 (mp (mp (mp (asserted $x12) @x47 $x30) (|rewrite*| (= $x30 $x30)) $x30) @x82 $x80)))
(|unit-resolution| (|mp~| @x83 (|nnf-pos| (refl (|~| $x77 $x77)) (|~| $x80 $x80)) $x80) (mp ((_ |quant-inst| 0) $x140) @x484 $x479) false)))))))))))))))))))))))))))))))
ce79a1fda8f32a486e67471071f239d5db3b39f0 47 0
unsat
((set-logic AUFLIA)
(proof
(let (($x111 (forall ((?v0 Int) )(let (($x28 (not (<= ?v0 0))))
(or (not (>= ?v0 0)) $x28)))
))
(let (($x507 (not $x111)))
(let (($x119 (not (<= 0 0))))
(let (($x193 (not (>= 0 0))))
(let (($x204 (or $x193 $x119)))
(let (($x169 (or $x507 $x204)))
(let ((@x529 (monotonicity (rewrite (= (<= 0 0) true)) (= $x119 (not true)))))
(let ((@x189 (monotonicity (rewrite (= (>= 0 0) true)) (= $x193 (not true)))))
(let ((@x185 (monotonicity (trans @x189 (rewrite (= (not true) false)) (= $x193 false)) (trans @x529 (rewrite (= (not true) false)) (= $x119 false)) (= $x204 (or false false)))))
(let ((@x166 (trans @x185 (rewrite (= (or false false) false)) (= $x204 false))))
(let ((@x512 (trans (monotonicity @x166 (= $x169 (or $x507 false))) (rewrite (= (or $x507 false) $x507)) (= $x169 $x507))))
(let (($x28 (not (<= ?0 0))))
(let (($x108 (or (not (>= ?0 0)) $x28)))
(let (($x34 (forall ((?v0 Int) )(let (($x28 (not (<= ?v0 0))))
(let (($x18 (<= 0 ?v0)))
(let (($x19 (not $x18)))
(or $x19 $x28)))))
))
(let ((@x107 (monotonicity (rewrite (= (<= 0 ?0) (>= ?0 0))) (= (not (<= 0 ?0)) (not (>= ?0 0))))))
(let ((@x113 (|quant-intro| (monotonicity @x107 (= (or (not (<= 0 ?0)) $x28) $x108)) (= $x34 $x111))))
(let (($x67 (ite $x34 (<= (~ 1) 0) (<= 3 0))))
(let ((@x76 (monotonicity (rewrite (= (<= (~ 1) 0) true)) (rewrite (= (<= 3 0) false)) (= $x67 (ite $x34 true false)))))
(let ((@x80 (trans @x76 (rewrite (= (ite $x34 true false) $x34)) (= $x67 $x34))))
(let ((@x82 (trans (rewrite (= (<= (ite $x34 (~ 1) 3) 0) $x67)) @x80 (= (<= (ite $x34 (~ 1) 3) 0) $x34))))
(let ((?x40 (ite $x34 (~ 1) 3)))
(let (($x46 (<= ?x40 0)))
(let (($x10 (forall ((?v0 Int) )(or (< ?v0 0) (< 0 ?v0)))
))
(let (($x15 (< 0 (ite $x10 (- 1) 3))))
(let (($x16 (not $x15)))
(let (($x18 (<= 0 ?0)))
(let (($x19 (not $x18)))
(let (($x31 (or $x19 $x28)))
(let ((@x26 (trans (rewrite (= (< ?0 0) $x19)) (monotonicity (rewrite (= $x18 $x18)) (= $x19 $x19)) (= (< ?0 0) $x19))))
(let ((@x33 (monotonicity @x26 (rewrite (= (< 0 ?0) $x28)) (= (or (< ?0 0) (< 0 ?0)) $x31))))
(let ((@x42 (monotonicity (|quant-intro| @x33 (= $x10 $x34)) (rewrite (= (- 1) (~ 1))) (= (ite $x10 (- 1) 3) ?x40))))
(let ((@x51 (trans (monotonicity @x42 (= $x15 (< 0 ?x40))) (rewrite (= (< 0 ?x40) (not $x46))) (= $x15 (not $x46)))))
(let ((@x58 (trans (monotonicity @x51 (= $x16 (not (not $x46)))) (rewrite (= (not (not $x46)) $x46)) (= $x16 $x46))))
(let ((@x83 (mp (mp (mp (asserted $x16) @x58 $x46) (|rewrite*| (= $x46 $x46)) $x46) @x82 $x34)))
(let ((@x117 (|mp~| (mp @x83 @x113 $x111) (|nnf-pos| (refl (|~| $x108 $x108)) (|~| $x111 $x111)) $x111)))
(|unit-resolution| @x117 (mp ((_ |quant-inst| 0) $x169) @x512 $x507) false))))))))))))))))))))))))))))))))))))))
a8c954d45da95df62d2ec9e6e7c43aa1fee0cd56 21 0
unsat
((set-logic AUFLIA)
(proof
(let (($x39 (exists ((?v0 Int) (?v1 Int) )(= (+ (* 4 ?v0) (* (~ 6) ?v1)) 1))
))
(let (($x79 (exists ((?v0 Int) (?v1 Int) )false)
))
(let ((@x83 (|quant-intro| (rewrite (= (= (+ (* 4 ?1) (* (~ 6) ?0)) 1) false)) (= $x39 $x79))))
(let (($x16 (exists ((?v0 Int) (?v1 Int) (?v2 Int) )(= (+ (* 4 ?v0) (* (- 6) ?v1)) 1))
))
(let (($x17 (not (not $x16))))
(let (($x31 (exists ((?v0 Int) (?v1 Int) (?v2 Int) )(= (+ (* 4 ?v0) (* (~ 6) ?v1)) 1))
))
(let (($x29 (= (= (+ (* 4 ?2) (* (- 6) ?1)) 1) (= (+ (* 4 ?2) (* (~ 6) ?1)) 1))))
(let (($x26 (= (+ (* 4 ?2) (* (- 6) ?1)) (+ (* 4 ?2) (* (~ 6) ?1)))))
(let ((@x24 (monotonicity (rewrite (= (- 6) (~ 6))) (= (* (- 6) ?1) (* (~ 6) ?1)))))
(let ((@x33 (|quant-intro| (monotonicity (monotonicity @x24 $x26) $x29) (= $x16 $x31))))
(let ((@x46 (monotonicity (trans @x33 (|elim-unused| (= $x31 $x39)) (= $x16 $x39)) (= (not $x16) (not $x39)))))
(let ((@x53 (trans (monotonicity @x46 (= $x17 (not (not $x39)))) (rewrite (= (not (not $x39)) $x39)) (= $x17 $x39))))
(mp (mp (mp (asserted $x17) @x53 $x39) (|rewrite*| (= $x39 $x39)) $x39) (trans @x83 (|elim-unused| (= $x79 false)) (= $x39 false)) false)))))))))))))))
a029fa4a7b0e95c1814546efbbdea2800c05d654 41 0
unsat
((set-logic AUFLIA)
(declare-fun ?v1!1 () Int)
(declare-fun ?v2!0 () Int)
(proof
(let (($x107 (or (not (and (not (<= ?v1!1 0)) (not (<= ?v2!0 0)))) (not (<= (+ ?v2!0 ?v1!1) 0)))))
(let (($x89 (forall ((?v1 Int) (?v2 Int) )(or (not (and (not (<= ?v1 0)) (not (<= ?v2 0)))) (not (<= (+ ?v2 ?v1) 0))))
))
(let (($x92 (not $x89)))
(let (($x42 (forall ((?v1 Int) (?v2 Int) )(let (($x30 (not (<= (+ ?v1 ?v2) 0))))
(or (not (and (not (<= ?v1 0)) (not (<= ?v2 0)))) $x30)))
))
(let (($x52 (not $x42)))
(let (($x86 (or (not (and (not (<= ?1 0)) (not (<= ?0 0)))) (not (<= (+ ?0 ?1) 0)))))
(let (($x30 (not (<= (+ ?1 ?0) 0))))
(let (($x37 (or (not (and (not (<= ?1 0)) (not (<= ?0 0)))) $x30)))
(let ((@x82 (monotonicity (rewrite (= (+ ?1 ?0) (+ ?0 ?1))) (= (<= (+ ?1 ?0) 0) (<= (+ ?0 ?1) 0)))))
(let ((@x88 (monotonicity (monotonicity @x82 (= $x30 (not (<= (+ ?0 ?1) 0)))) (= $x37 $x86))))
(let (($x15 (exists ((?v0 Int) )(forall ((?v1 Int) (?v2 Int) )(=> (and (< 0 ?v1) (< 0 ?v2)) (< 0 (+ ?v1 ?v2))))
)
))
(let (($x16 (not $x15)))
(let (($x45 (exists ((?v0 Int) )(forall ((?v1 Int) (?v2 Int) )(let (($x30 (not (<= (+ ?v1 ?v2) 0))))
(or (not (and (not (<= ?v1 0)) (not (<= ?v2 0)))) $x30)))
)
))
(let (($x14 (forall ((?v1 Int) (?v2 Int) )(=> (and (< 0 ?v1) (< 0 ?v2)) (< 0 (+ ?v1 ?v2))))
))
(let (($x13 (=> (and (< 0 ?1) (< 0 ?0)) (< 0 (+ ?1 ?0)))))
(let (($x38 (= (=> (and (not (<= ?1 0)) (not (<= ?0 0))) $x30) $x37)))
(let (($x34 (= $x13 (=> (and (not (<= ?1 0)) (not (<= ?0 0))) $x30))))
(let (($x26 (and (not (<= ?1 0)) (not (<= ?0 0)))))
(let ((@x28 (monotonicity (rewrite (= (< 0 ?1) (not (<= ?1 0)))) (rewrite (= (< 0 ?0) (not (<= ?0 0)))) (= (and (< 0 ?1) (< 0 ?0)) $x26))))
(let ((@x41 (trans (monotonicity @x28 (rewrite (= (< 0 (+ ?1 ?0)) $x30)) $x34) (rewrite $x38) (= $x13 $x37))))
(let ((@x51 (trans (|quant-intro| (|quant-intro| @x41 (= $x14 $x42)) (= $x15 $x45)) (|elim-unused| (= $x45 $x42)) (= $x15 $x42))))
(let ((@x58 (mp (mp (asserted $x16) (monotonicity @x51 (= $x16 $x52)) $x52) (|rewrite*| (= $x52 $x52)) $x52)))
(let ((@x97 (mp @x58 (monotonicity (|quant-intro| @x88 (= $x42 $x89)) (= $x52 $x92)) $x92)))
(let ((@x117 (|not-or-elim| (|mp~| @x97 (sk (|~| $x92 (not $x107))) (not $x107)) (<= (+ ?v2!0 ?v1!1) 0))))
(let ((@x114 (|not-or-elim| (|mp~| @x97 (sk (|~| $x92 (not $x107))) (not $x107)) (and (not (<= ?v1!1 0)) (not (<= ?v2!0 0))))))
((_ |th-lemma| arith farkas 1 1 1) (|and-elim| @x114 (not (<= ?v2!0 0))) (|and-elim| @x114 (not (<= ?v1!1 0))) @x117 false))))))))))))))))))))))))))))
d41dfe74c924188d8570a9d71b541c5781066b63 41 0
unsat
((set-logic AUFLIRA)
(declare-fun ?v1!1 () Int)
(declare-fun ?v2!0 () Real)
(proof
(let (($x95 (not (<= ?v1!1 (~ 1)))))
(let (($x96 (or (not (and (not (<= ?v1!1 0)) (not (<= ?v2!0 0.0)))) $x95)))
(let (($x52 (forall ((?v1 Int) (?v2 Real) )(let (($x38 (not (<= ?v1 (~ 1)))))
(or (not (and (not (<= ?v1 0)) (not (<= ?v2 0.0)))) $x38)))
))
(let (($x62 (not $x52)))
(let (($x18 (exists ((?v0 Int) )(forall ((?v1 Int) (?v2 Real) )(let (($x15 (< (- 1) ?v1)))
(=> (and (< 0 ?v1) (< 0.0 ?v2)) $x15)))
)
))
(let (($x5 (not $x18)))
(let (($x55 (exists ((?v0 Int) )(forall ((?v1 Int) (?v2 Real) )(let (($x38 (not (<= ?v1 (~ 1)))))
(or (not (and (not (<= ?v1 0)) (not (<= ?v2 0.0)))) $x38)))
)
))
(let (($x17 (forall ((?v1 Int) (?v2 Real) )(let (($x15 (< (- 1) ?v1)))
(=> (and (< 0 ?v1) (< 0.0 ?v2)) $x15)))
))
(let (($x38 (not (<= ?1 (~ 1)))))
(let (($x47 (or (not (and (not (<= ?1 0)) (not (<= ?0 0.0)))) $x38)))
(let (($x15 (< (- 1) ?1)))
(let (($x16 (=> (and (< 0 ?1) (< 0.0 ?0)) $x15)))
(let (($x48 (= (=> (and (not (<= ?1 0)) (not (<= ?0 0.0))) $x38) $x47)))
(let (($x44 (= $x16 (=> (and (not (<= ?1 0)) (not (<= ?0 0.0))) $x38))))
(let ((@x36 (monotonicity (rewrite (= (- 1) (~ 1))) (= $x15 (< (~ 1) ?1)))))
(let (($x28 (and (not (<= ?1 0)) (not (<= ?0 0.0)))))
(let ((@x30 (monotonicity (rewrite (= (< 0 ?1) (not (<= ?1 0)))) (rewrite (= (< 0.0 ?0) (not (<= ?0 0.0)))) (= (and (< 0 ?1) (< 0.0 ?0)) $x28))))
(let ((@x45 (monotonicity @x30 (trans @x36 (rewrite (= (< (~ 1) ?1) $x38)) (= $x15 $x38)) $x44)))
(let ((@x54 (|quant-intro| (trans @x45 (rewrite $x48) (= $x16 $x47)) (= $x17 $x52))))
(let ((@x61 (trans (|quant-intro| @x54 (= $x18 $x55)) (|elim-unused| (= $x55 $x52)) (= $x18 $x52))))
(let ((@x68 (mp (mp (asserted $x5) (monotonicity @x61 (= $x5 $x62)) $x62) (|rewrite*| (= $x62 $x62)) $x62)))
(let ((@x106 (|not-or-elim| (|mp~| @x68 (sk (|~| $x62 (not $x96))) (not $x96)) (<= ?v1!1 (~ 1)))))
(let ((@x103 (|not-or-elim| (|mp~| @x68 (sk (|~| $x62 (not $x96))) (not $x96)) (and (not (<= ?v1!1 0)) (not (<= ?v2!0 0.0))))))
(let ((@x107 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x95 (<= ?v1!1 0))) (|and-elim| @x103 (not (<= ?v1!1 0))) $x95)))
(|unit-resolution| @x107 @x106 false)))))))))))))))))))))))))))
9c97136863512513fe9fd8b8cb83fdb885e5f3a5 115 0
unsat
((set-logic AUFLIA)
(proof
(let (($x156 (forall ((?v0 Int) )(let (($x16 (<= ?v0 0)))
(let (($x17 (not $x16)))
(let (($x150 (or (not false) $x17)))
(not $x150)))))
))
(let (($x178 (forall ((?v0 Int) )false)
))
(let (($x16 (<= ?0 0)))
(let (($x17 (not $x16)))
(let (($x150 (or (not false) $x17)))
(let ((@x166 (monotonicity (rewrite (= (not false) true)) (= $x150 (or true $x17)))))
(let ((@x170 (trans @x166 (rewrite (= (or true $x17) true)) (= $x150 true))))
(let ((@x177 (trans (monotonicity @x170 (= (not $x150) (not true))) (rewrite (= (not true) false)) (= (not $x150) false))))
(let ((@x184 (trans (|quant-intro| @x177 (= $x156 $x178)) (|elim-unused| (= $x178 false)) (= $x156 false))))
(let (($x126 (forall ((?v0 Int) )(let (($x16 (<= ?v0 0)))
(let (($x17 (not $x16)))
(let (($x82 (forall ((?v1 Int) )(let (($x16 (<= ?v1 0)))
(let (($x17 (not $x16)))
(or (not (>= (+ ?v1 (* (~ 1) ?v0)) 0)) $x17))))
))
(let (($x85 (not $x82)))
(let (($x88 (or $x85 $x17)))
(not $x88)))))))
))
(let (($x142 (forall ((?v0 Int) )(let (($x16 (<= ?v0 0)))
(let (($x17 (not $x16)))
(let (($x130 (forall ((?v1 Int) )(let (($x16 (<= ?v1 0)))
(not $x16)))
))
(not (or (not $x130) $x17))))))
))
(let ((@x160 (trans (rewrite (= $x126 $x142)) (rewrite (= $x142 $x156)) (= $x126 $x156))))
(let (($x122 (forall ((?v0 Int) )(let (($x16 (<= ?v0 0)))
(let (($x82 (forall ((?v1 Int) )(let (($x16 (<= ?v1 0)))
(let (($x17 (not $x16)))
(or (not (>= (+ ?v1 (* (~ 1) ?v0)) 0)) $x17))))
))
(and $x82 $x16))))
))
(let (($x82 (forall ((?v1 Int) )(let (($x16 (<= ?v1 0)))
(let (($x17 (not $x16)))
(or (not (>= (+ ?v1 (* (~ 1) ?0)) 0)) $x17))))
))
(let (($x85 (not $x82)))
(let (($x88 (or $x85 $x17)))
(let (($x108 (not $x88)))
(let (($x119 (and $x82 $x16)))
(let (($x111 (forall ((?v0 Int) )(let (($x16 (<= ?v0 0)))
(let (($x17 (not $x16)))
(let (($x104 (not $x17)))
(let (($x82 (forall ((?v1 Int) )(let (($x16 (<= ?v1 0)))
(let (($x17 (not $x16)))
(or (not (>= (+ ?v1 (* (~ 1) ?v0)) 0)) $x17))))
))
(and $x82 $x104))))))
))
(let ((@x121 (monotonicity (rewrite (= (not $x17) $x16)) (= (and $x82 (not $x17)) $x119))))
(let (($x91 (exists ((?v0 Int) )(let (($x16 (<= ?v0 0)))
(let (($x17 (not $x16)))
(let (($x82 (forall ((?v1 Int) )(let (($x16 (<= ?v1 0)))
(let (($x17 (not $x16)))
(or (not (>= (+ ?v1 (* (~ 1) ?v0)) 0)) $x17))))
))
(let (($x85 (not $x82)))
(or $x85 $x17))))))
))
(let (($x94 (not $x91)))
(let (($x79 (or (not (>= (+ ?0 (* (~ 1) ?1)) 0)) $x17)))
(let ((@x103 (|nnf-neg| (|nnf-pos| (refl (|~| $x79 $x79)) (|~| $x82 $x82)) (|~| (not $x85) $x82))))
(let ((@x110 (|nnf-neg| @x103 (refl (|~| (not $x17) (not $x17))) (|~| $x108 (and $x82 (not $x17))))))
(let (($x41 (exists ((?v0 Int) )(let (($x16 (<= ?v0 0)))
(let (($x17 (not $x16)))
(let (($x29 (forall ((?v1 Int) )(let (($x16 (<= ?v1 0)))
(let (($x17 (not $x16)))
(or (not (<= ?v0 ?v1)) $x17))))
))
(or (not $x29) $x17)))))
))
(let (($x44 (not $x41)))
(let (($x29 (forall ((?v1 Int) )(let (($x16 (<= ?v1 0)))
(let (($x17 (not $x16)))
(or (not (<= ?0 ?v1)) $x17))))
))
(let (($x36 (or (not $x29) $x17)))
(let ((@x78 (monotonicity (rewrite (= (<= ?1 ?0) (>= (+ ?0 (* (~ 1) ?1)) 0))) (= (not (<= ?1 ?0)) (not (>= (+ ?0 (* (~ 1) ?1)) 0))))))
(let ((@x84 (|quant-intro| (monotonicity @x78 (= (or (not (<= ?1 ?0)) $x17) $x79)) (= $x29 $x82))))
(let ((@x90 (monotonicity (monotonicity @x84 (= (not $x29) $x85)) (= $x36 $x88))))
(let (($x13 (exists ((?v0 Int) )(let (($x9 (< 0 ?v0)))
(let (($x11 (forall ((?v1 Int) )(let (($x9 (< 0 ?v1)))
(let (($x7 (<= ?v0 ?v1)))
(=> $x7 $x9))))
))
(=> $x11 $x9))))
))
(let (($x14 (not $x13)))
(let (($x9 (< 0 ?0)))
(let (($x11 (forall ((?v1 Int) )(let (($x9 (< 0 ?v1)))
(let (($x7 (<= ?0 ?v1)))
(=> $x7 $x9))))
))
(let (($x12 (=> $x11 $x9)))
(let ((@x26 (rewrite (= (=> (<= ?1 ?0) $x17) (or (not (<= ?1 ?0)) $x17)))))
(let ((@x22 (monotonicity (rewrite (= $x9 $x17)) (= (=> (<= ?1 ?0) $x9) (=> (<= ?1 ?0) $x17)))))
(let ((@x28 (trans @x22 @x26 (= (=> (<= ?1 ?0) $x9) (or (not (<= ?1 ?0)) $x17)))))
(let ((@x34 (monotonicity (|quant-intro| @x28 (= $x11 $x29)) (rewrite (= $x9 $x17)) (= $x12 (=> $x29 $x17)))))
(let ((@x43 (|quant-intro| (trans @x34 (rewrite (= (=> $x29 $x17) $x36)) (= $x12 $x36)) (= $x13 $x41))))
(let ((@x50 (mp (mp (asserted $x14) (monotonicity @x43 (= $x14 $x44)) $x44) (|rewrite*| (= $x44 $x44)) $x44)))
(let ((@x97 (mp @x50 (monotonicity (|quant-intro| @x90 (= $x41 $x91)) (= $x44 $x94)) $x94)))
(let ((@x115 (mp (|mp~| @x97 (|nnf-neg| @x110 (|~| $x94 $x111)) $x111) (|quant-intro| @x121 (= $x111 $x122)) $x122)))
(let ((@x129 (mp @x115 (|quant-intro| (rewrite (= $x119 $x108)) (= $x122 $x126)) $x126)))
(mp (mp @x129 @x160 $x156) @x184 false)))))))))))))))))))))))))))))))))))))))))))))))))
cf41882047cdb0b0d0cbb2e29bd4abf71d67b407 28 0
unsat
((set-logic AUFLIA)
(proof
(let (($x32 (forall ((?v0 Int) )(let (($x21 (not (<= (* 2 |a$|) (* 2 ?v0)))))
(let (($x16 (<= |a$| ?v0)))
(or $x16 $x21))))
))
(let (($x35 (not $x32)))
(let (($x80 (forall ((?v0 Int) )true)
))
(let (($x21 (not (<= (* 2 |a$|) (* 2 ?0)))))
(let (($x16 (<= |a$| ?0)))
(let (($x27 (or $x16 $x21)))
(let (($x64 (>= (+ ?0 (* (~ 1) |a$|)) 0)))
(let ((@x72 (monotonicity (rewrite (= (<= (* 2 |a$|) (* 2 ?0)) $x64)) (= $x21 (not $x64)))))
(let ((@x75 (monotonicity (rewrite (= $x16 $x64)) @x72 (= $x27 (or $x64 (not $x64))))))
(let ((@x79 (trans @x75 (rewrite (= (or $x64 (not $x64)) true)) (= $x27 true))))
(let ((@x86 (trans (|quant-intro| @x79 (= $x32 $x80)) (|elim-unused| (= $x80 true)) (= $x32 true))))
(let ((@x93 (trans (monotonicity @x86 (= $x35 (not true))) (rewrite (= (not true) false)) (= $x35 false))))
(let (($x13 (forall ((?v0 Int) )(=> (< ?v0 |a$|) (< (* 2 ?v0) (* 2 |a$|))))
))
(let (($x14 (not $x13)))
(let (($x12 (=> (< ?0 |a$|) (< (* 2 ?0) (* 2 |a$|)))))
(let ((@x26 (monotonicity (rewrite (= (< ?0 |a$|) (not $x16))) (rewrite (= (< (* 2 ?0) (* 2 |a$|)) $x21)) (= $x12 (=> (not $x16) $x21)))))
(let ((@x31 (trans @x26 (rewrite (= (=> (not $x16) $x21) $x27)) (= $x12 $x27))))
(let ((@x38 (mp (asserted $x14) (monotonicity (|quant-intro| @x31 (= $x13 $x32)) (= $x14 $x35)) $x35)))
(mp (mp @x38 (|rewrite*| (= $x35 $x35)) $x35) @x93 false)))))))))))))))))))))
2cfb4d9213b7aff75941c49db378297fcba62a29 38 0
unsat
((set-logic AUFLIA)
(declare-fun ?v1!0 () Int)
(proof
(let (($x73 (forall ((?v1 Int) )(let (($x15 (not (<= ?v1 0))))
(or $x15 (not (>= ?v1 1)))))
))
(let (($x76 (not $x73)))
(let (($x86 (|~| $x76 (not (or (not (<= ?v1!0 0)) (not (>= ?v1!0 1)))))))
(let (($x33 (forall ((?v1 Int) )(let (($x18 (<= 1 ?v1)))
(let (($x19 (not $x18)))
(let (($x15 (not (<= ?v1 0))))
(or $x15 $x19)))))
))
(let (($x38 (not $x33)))
(let (($x18 (<= 1 ?0)))
(let (($x19 (not $x18)))
(let (($x15 (not (<= ?0 0))))
(let (($x27 (or $x15 $x19)))
(let ((@x69 (monotonicity (rewrite (= $x18 (>= ?0 1))) (= $x19 (not (>= ?0 1))))))
(let ((@x75 (|quant-intro| (monotonicity @x69 (= $x27 (or $x15 (not (>= ?0 1))))) (= $x33 $x73))))
(let (($x12 (forall ((?v0 Int) (?v1 Int) )(or (< 0 ?v1) (< ?v1 1)))
))
(let (($x5 (not $x12)))
(let (($x30 (forall ((?v0 Int) (?v1 Int) )(let (($x18 (<= 1 ?v1)))
(let (($x19 (not $x18)))
(let (($x15 (not (<= ?v1 0))))
(or $x15 $x19)))))
))
(let ((@x26 (trans (rewrite (= (< ?0 1) $x19)) (monotonicity (rewrite (= $x18 $x18)) (= $x19 $x19)) (= (< ?0 1) $x19))))
(let ((@x29 (monotonicity (rewrite (= (< 0 ?0) $x15)) @x26 (= (or (< 0 ?0) (< ?0 1)) $x27))))
(let ((@x37 (trans (|quant-intro| @x29 (= $x12 $x30)) (|elim-unused| (= $x30 $x33)) (= $x12 $x33))))
(let ((@x44 (mp (mp (asserted $x5) (monotonicity @x37 (= $x5 $x38)) $x38) (|rewrite*| (= $x38 $x38)) $x38)))
(let ((@x88 (|mp~| (mp @x44 (monotonicity @x75 (= $x38 $x76)) $x76) (sk $x86) (not (or (not (<= ?v1!0 0)) (not (>= ?v1!0 1)))))))
(let (($x83 (not (>= ?v1!0 1))))
(let ((@x93 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x83 (not (<= ?v1!0 0)))) (|not-or-elim| @x88 (<= ?v1!0 0)) $x83)))
(|unit-resolution| @x93 (|not-or-elim| @x88 (>= ?v1!0 1)) false))))))))))))))))))))))))
abbcc5cc077b58e7142b658090ed462f7a37de5b 19 0
unsat
((set-logic <null>)
(proof
(let (($x29 (<= |b$| 0)))
(let (($x30 (not $x29)))
(let (($x37 (or (not (and (not (<= |a$| 0)) (not (<= (* |a$| |b$|) 0)))) $x30)))
(let (($x13 (=> (and (< 0 |a$|) (< 0 (* |a$| |b$|))) (< 0 |b$|))))
(let (($x14 (not $x13)))
(let (($x23 (not (<= (* |a$| |b$|) 0))))
(let (($x19 (not (<= |a$| 0))))
(let (($x26 (and $x19 $x23)))
(let ((@x28 (monotonicity (rewrite (= (< 0 |a$|) $x19)) (rewrite (= (< 0 (* |a$| |b$|)) $x23)) (= (and (< 0 |a$|) (< 0 (* |a$| |b$|))) $x26))))
(let ((@x35 (monotonicity @x28 (rewrite (= (< 0 |b$|) $x30)) (= $x13 (=> $x26 $x30)))))
(let ((@x44 (monotonicity (trans @x35 (rewrite (= (=> $x26 $x30) $x37)) (= $x13 $x37)) (= $x14 (not $x37)))))
(let ((@x58 (mp (|not-or-elim| (mp (asserted $x14) @x44 (not $x37)) $x29) (|rewrite*| (= $x29 $x29)) $x29)))
(let ((@x47 (|and-elim| (|not-or-elim| (mp (asserted $x14) @x44 (not $x37)) $x26) $x19)))
(let ((@x48 (|and-elim| (|not-or-elim| (mp (asserted $x14) @x44 (not $x37)) $x26) $x23)))
((_ |th-lemma| arith farkas 1 1 1) (mp @x48 (|rewrite*| (= $x23 $x23)) $x23) (mp @x47 (|rewrite*| (= $x19 $x19)) $x19) @x58 false)))))))))))))))))
4ef1d4e9c1eb07f7b6dde03db0c786dd6cdb3835 28 0
unsat
((set-logic <null>)
(proof
(let ((?x35 (+ 1 |y$|)))
(let ((?x38 (* |a$| ?x35)))
(let ((?x41 (+ (* |a$| |x$|) ?x38)))
(let ((?x27 (+ 1 |x$| |y$|)))
(let ((?x32 (* |a$| ?x27)))
(let (($x44 (= ?x32 ?x41)))
(let (($x47 (not $x44)))
(let ((@x72 (monotonicity (rewrite (= ?x35 ?x35)) (= (+ |x$| ?x35) (+ |x$| ?x35)))))
(let ((@x75 (trans @x72 (rewrite (= (+ |x$| ?x35) ?x27)) (= (+ |x$| ?x35) ?x27))))
(let ((@x80 (monotonicity (monotonicity @x75 (= (* |a$| (+ |x$| ?x35)) ?x32)) (= (+ (* |a$| (+ |x$| ?x35)) 0) (+ ?x32 0)))))
(let ((@x84 (trans @x80 (rewrite (= (+ ?x32 0) ?x32)) (= (+ (* |a$| (+ |x$| ?x35)) 0) ?x32))))
(let ((@x63 (monotonicity (monotonicity (rewrite (= ?x35 ?x35)) (= ?x38 ?x38)) (= ?x41 ?x41))))
(let ((@x70 (trans @x63 (rewrite (= ?x41 (+ (* |a$| (+ |x$| ?x35)) 0))) (= ?x41 (+ (* |a$| (+ |x$| ?x35)) 0)))))
(let ((@x88 (monotonicity (monotonicity (rewrite (= ?x27 ?x27)) (= ?x32 ?x32)) (trans @x70 @x84 (= ?x41 ?x32)) (= $x44 (= ?x32 ?x32)))))
(let ((@x95 (monotonicity (trans @x88 (rewrite (= (= ?x32 ?x32) true)) (= $x44 true)) (= $x47 (not true)))))
(let (($x16 (= (* |a$| (+ (+ |x$| 1) |y$|)) (+ (* |a$| |x$|) (* |a$| (+ |y$| 1))))))
(let (($x17 (not $x16)))
(let ((@x40 (monotonicity (rewrite (= (+ |y$| 1) ?x35)) (= (* |a$| (+ |y$| 1)) ?x38))))
(let ((@x43 (monotonicity @x40 (= (+ (* |a$| |x$|) (* |a$| (+ |y$| 1))) ?x41))))
(let ((@x26 (monotonicity (rewrite (= (+ |x$| 1) (+ 1 |x$|))) (= (+ (+ |x$| 1) |y$|) (+ (+ 1 |x$|) |y$|)))))
(let ((@x31 (trans @x26 (rewrite (= (+ (+ 1 |x$|) |y$|) ?x27)) (= (+ (+ |x$| 1) |y$|) ?x27))))
(let ((@x46 (monotonicity (monotonicity @x31 (= (* |a$| (+ (+ |x$| 1) |y$|)) ?x32)) @x43 (= $x16 $x44))))
(let ((@x53 (mp (mp (asserted $x17) (monotonicity @x46 (= $x17 $x47)) $x47) (|rewrite*| (= $x47 $x47)) $x47)))
(mp @x53 (trans @x95 (rewrite (= (not true) false)) (= $x47 false)) false))))))))))))))))))))))))))
d53ca0a1797e1fff3e579ce36e7f8e25e5b2afcb 25 0
unsat
((set-logic <null>)
(proof
(let ((?x38 (* |x$| |y$|)))
(let ((?x39 (* 2.0 ?x38)))
(let ((?x26 (* |x$| (+ 1.0 (* (~ 1.0) |y$|)))))
(let ((?x32 (* (~ 1.0) ?x26)))
(let ((?x9 (* |x$| (+ 1.0 |y$|))))
(let ((?x33 (+ ?x9 ?x32)))
(let (($x42 (= ?x33 ?x39)))
(let (($x45 (not $x42)))
(let ((@x81 (rewrite (= (* (~ 1.0) (+ |x$| (* (~ 1.0) ?x38))) (+ (* (~ 1.0) |x$|) ?x38)))))
(let ((@x77 (monotonicity (rewrite (= ?x26 (+ |x$| (* (~ 1.0) ?x38)))) (= ?x32 (* (~ 1.0) (+ |x$| (* (~ 1.0) ?x38)))))))
(let ((@x86 (monotonicity (rewrite (= ?x9 (+ |x$| ?x38))) (trans @x77 @x81 (= ?x32 (+ (* (~ 1.0) |x$|) ?x38))) (= ?x33 (+ (+ |x$| ?x38) (+ (* (~ 1.0) |x$|) ?x38))))))
(let ((@x89 (trans @x86 (rewrite (= (+ (+ |x$| ?x38) (+ (* (~ 1.0) |x$|) ?x38)) ?x39)) $x42)))
(let ((@x96 (trans (monotonicity @x89 (= $x42 (= ?x39 ?x39))) (rewrite (= (= ?x39 ?x39) true)) (= $x42 true))))
(let ((@x103 (trans (monotonicity @x96 (= $x45 (not true))) (rewrite (= (not true) false)) (= $x45 false))))
(let (($x17 (not (= (- ?x9 (* |x$| (- 1.0 |y$|))) (* (* 2.0 |x$|) |y$|)))))
(let (($x43 (= (= (- ?x9 (* |x$| (- 1.0 |y$|))) (* (* 2.0 |x$|) |y$|)) $x42)))
(let ((@x28 (monotonicity (rewrite (= (- 1.0 |y$|) (+ 1.0 (* (~ 1.0) |y$|)))) (= (* |x$| (- 1.0 |y$|)) ?x26))))
(let ((@x31 (monotonicity @x28 (= (- ?x9 (* |x$| (- 1.0 |y$|))) (- ?x9 ?x26)))))
(let ((@x37 (trans @x31 (rewrite (= (- ?x9 ?x26) ?x33)) (= (- ?x9 (* |x$| (- 1.0 |y$|))) ?x33))))
(let ((@x47 (monotonicity (monotonicity @x37 (rewrite (= (* (* 2.0 |x$|) |y$|) ?x39)) $x43) (= $x17 $x45))))
(mp (mp (asserted $x17) @x47 $x45) @x103 false)))))))))))))))))))))))
3d315c543a59bb7c2ba5e19237e3c8b29ad17b62 74 0
unsat
((set-logic <null>)
(proof
(let ((?x165 (* (~ 1) |e$|)))
(let ((?x163 (* (~ 1) |b$|)))
(let ((?x176 (+ ?x163 ?x165)))
(let ((?x8 (+ 1 |p$|)))
(let ((?x181 (* ?x8 ?x176)))
(let ((?x51 (+ 2 (* 2 |p$|))))
(let ((?x11 (+ |b$| |e$|)))
(let ((?x59 (* ?x11 ?x51)))
(let ((?x187 (+ ?x59 ?x181)))
(let ((?x12 (* ?x8 ?x11)))
(let (($x194 (= ?x12 ?x187)))
(let (($x197 (not $x194)))
(let ((?x220 (* |p$| |e$|)))
(let ((?x219 (* |p$| |b$|)))
(let ((?x221 (+ |b$| |e$| ?x219 ?x220)))
(let ((?x236 (+ (+ (* 2 |b$|) (* 2 |e$|) (* 2 ?x219) (* 2 ?x220)) (+ ?x163 ?x165 (* (~ 1) ?x219) (* (~ 1) ?x220)))))
(let (($x229 (= ?x59 (+ (* 2 |b$|) (* 2 |e$|) (* 2 ?x219) (* 2 ?x220)))))
(let ((@x238 (monotonicity (rewrite $x229) (rewrite (= ?x181 (+ ?x163 ?x165 (* (~ 1) ?x219) (* (~ 1) ?x220)))) (= ?x187 ?x236))))
(let ((@x245 (monotonicity (rewrite (= ?x12 ?x221)) (trans @x238 (rewrite (= ?x236 ?x221)) (= ?x187 ?x221)) (= $x194 (= ?x221 ?x221)))))
(let ((@x252 (monotonicity (trans @x245 (rewrite (= (= ?x221 ?x221) true)) (= $x194 true)) (= $x197 (not true)))))
(let ((?x86 (+ |b$| |d$| |e$|)))
(let ((?x89 (* ?x8 ?x86)))
(let ((?x96 (* (~ 1) ?x89)))
(let ((?x64 (* |d$| ?x8)))
(let ((?x121 (+ ?x59 ?x64 ?x96)))
(let (($x124 (= ?x12 ?x121)))
(let (($x127 (not $x124)))
(let ((?x157 (+ ?x59 (* ?x8 (+ |d$| (* (~ 1) ?x86))) 0)))
(let ((?x166 (+ ?x163 (* (~ 1) |d$|) ?x165)))
(let ((?x154 (* (~ 1) ?x86)))
(let (($x167 (= ?x154 ?x166)))
(let ((@x169 (trans (monotonicity (rewrite (= ?x86 ?x86)) (= ?x154 ?x154)) (rewrite $x167) $x167)))
(let ((@x175 (monotonicity (trans @x169 (rewrite (= ?x166 ?x166)) $x167) (= (+ |d$| ?x154) (+ |d$| ?x166)))))
(let ((@x180 (trans @x175 (rewrite (= (+ |d$| ?x166) ?x176)) (= (+ |d$| ?x154) ?x176))))
(let ((@x135 (rewrite (= ?x8 ?x8))))
(let ((@x143 (monotonicity (rewrite (= ?x11 ?x11)) (rewrite (= ?x51 ?x51)) (= ?x59 ?x59))))
(let ((@x186 (monotonicity @x143 (monotonicity @x135 @x180 (= (* ?x8 (+ |d$| ?x154)) ?x181)) (= ?x157 (+ ?x59 ?x181 0)))))
(let ((@x151 (monotonicity (monotonicity @x135 (rewrite (= ?x86 ?x86)) (= ?x89 ?x89)) (= ?x96 ?x96))))
(let ((@x153 (monotonicity @x143 (monotonicity @x135 (= ?x64 ?x64)) @x151 (= ?x121 ?x121))))
(let ((@x193 (trans (trans @x153 (rewrite (= ?x121 ?x157)) (= ?x121 ?x157)) (trans @x186 (rewrite (= (+ ?x59 ?x181 0) ?x187)) (= ?x157 ?x187)) (= ?x121 ?x187))))
(let ((@x196 (monotonicity (monotonicity @x135 (rewrite (= ?x11 ?x11)) (= ?x12 ?x12)) @x193 (= $x124 $x194))))
(let ((@x126 (monotonicity (rewrite (= (+ 0 ?x59 ?x64 ?x96) ?x121)) (= (= ?x12 (+ 0 ?x59 ?x64 ?x96)) $x124))))
(let ((@x129 (monotonicity @x126 (= (not (= ?x12 (+ 0 ?x59 ?x64 ?x96))) $x127))))
(let (($x112 (= ?x12 (+ 0 ?x59 ?x64 ?x96))))
(let (($x117 (not $x112)))
(let ((?x22 (* |d$| |p$|)))
(let ((?x23 (+ (+ (* (* 2 ?x8) ?x11) (* ?x8 |d$|)) ?x22)))
(let ((?x24 (+ |u$| ?x23)))
(let ((?x28 (- ?x24 (* ?x8 (+ (+ |b$| |d$|) |e$|)))))
(let ((?x16 (+ (+ |u$| ?x12) (* |p$| |d$|))))
(let (($x29 (= ?x16 ?x28)))
(let (($x30 (not $x29)))
(let ((@x114 (rewrite (= (= (+ |u$| ?x12 ?x22) (+ |u$| ?x59 ?x64 ?x22 ?x96)) $x112))))
(let ((@x104 (rewrite (= (+ (+ |u$| ?x59 ?x64 ?x22) ?x96) (+ |u$| ?x59 ?x64 ?x22 ?x96)))))
(let ((?x81 (+ |u$| ?x59 ?x64 ?x22)))
(let ((?x97 (+ ?x81 ?x96)))
(let ((@x91 (monotonicity (rewrite (= (+ (+ |b$| |d$|) |e$|) ?x86)) (= (* ?x8 (+ (+ |b$| |d$|) |e$|)) ?x89))))
(let ((@x53 (monotonicity (rewrite (= (* 2 1) 2)) (= (+ (* 2 1) (* 2 |p$|)) ?x51))))
(let ((@x55 (trans (rewrite (= (* 2 ?x8) (+ (* 2 1) (* 2 |p$|)))) @x53 (= (* 2 ?x8) ?x51))))
(let ((@x63 (trans (monotonicity @x55 (= (* (* 2 ?x8) ?x11) (* ?x51 ?x11))) (rewrite (= (* ?x51 ?x11) ?x59)) (= (* (* 2 ?x8) ?x11) ?x59))))
(let ((@x69 (monotonicity @x63 (rewrite (= (* ?x8 |d$|) ?x64)) (= (+ (* (* 2 ?x8) ?x11) (* ?x8 |d$|)) (+ ?x59 ?x64)))))
(let ((@x77 (trans (monotonicity @x69 (= ?x23 (+ (+ ?x59 ?x64) ?x22))) (rewrite (= (+ (+ ?x59 ?x64) ?x22) (+ ?x59 ?x64 ?x22))) (= ?x23 (+ ?x59 ?x64 ?x22)))))
(let ((@x85 (trans (monotonicity @x77 (= ?x24 (+ |u$| (+ ?x59 ?x64 ?x22)))) (rewrite (= (+ |u$| (+ ?x59 ?x64 ?x22)) ?x81)) (= ?x24 ?x81))))
(let ((@x101 (trans (monotonicity @x85 @x91 (= ?x28 (- ?x81 ?x89))) (rewrite (= (- ?x81 ?x89) ?x97)) (= ?x28 ?x97))))
(let ((@x38 (monotonicity (rewrite (= (* |p$| |d$|) ?x22)) (= ?x16 (+ (+ |u$| ?x12) ?x22)))))
(let ((@x43 (trans @x38 (rewrite (= (+ (+ |u$| ?x12) ?x22) (+ |u$| ?x12 ?x22))) (= ?x16 (+ |u$| ?x12 ?x22)))))
(let ((@x109 (monotonicity @x43 (trans @x101 @x104 (= ?x28 (+ |u$| ?x59 ?x64 ?x22 ?x96))) (= $x29 (= (+ |u$| ?x12 ?x22) (+ |u$| ?x59 ?x64 ?x22 ?x96))))))
(let ((@x120 (mp (asserted $x30) (monotonicity (trans @x109 @x114 (= $x29 $x112)) (= $x30 $x117)) $x117)))
(let ((@x200 (mp (mp (mp @x120 @x129 $x127) (|rewrite*| (= $x127 $x127)) $x127) (monotonicity @x196 (= $x127 $x197)) $x197)))
(mp @x200 (trans @x252 (rewrite (= (not true) false)) (= $x197 false)) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
895910b3e061efd8f207e0c25a2edc00b81271b2 97 0
unsat
((set-logic AUFLIA)
(proof
(let ((?x8 (* 2 (|of_nat$| |x$|))))
(let ((?x545 (+ ?x8 (* (~ 1) (|of_nat$| (|nat$| ?x8))))))
(let (($x543 (= ?x545 0)))
(let (($x205 (>= (|of_nat$| |x$|) 0)))
(let ((?x224 (|of_nat$| (|nat$| ?x8))))
(let (($x499 (>= ?x224 1)))
(let (($x517 (= (|of_nat$| (|nat$| 1)) 1)))
(let (($x558 (forall ((?v0 Int) )(!(let (($x25 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x25)) :pattern ( (|nat$| ?v0) )))
))
(let (($x109 (forall ((?v0 Int) )(let (($x25 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x25)))
))
(let (($x25 (= (|of_nat$| (|nat$| ?0)) ?0)))
(let (($x106 (or (not (>= ?0 0)) $x25)))
(let (($x48 (forall ((?v0 Int) )(let (($x25 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(let (($x22 (<= 0 ?v0)))
(let (($x43 (not $x22)))
(or $x43 $x25)))))
))
(let ((@x105 (monotonicity (rewrite (= (<= 0 ?0) (>= ?0 0))) (= (not (<= 0 ?0)) (not (>= ?0 0))))))
(let ((@x111 (|quant-intro| (monotonicity @x105 (= (or (not (<= 0 ?0)) $x25) $x106)) (= $x48 $x109))))
(let (($x27 (forall ((?v0 Int) )(let (($x25 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(let (($x22 (<= 0 ?v0)))
(=> $x22 $x25))))
))
(let ((@x46 (rewrite (= (=> (<= 0 ?0) $x25) (or (not (<= 0 ?0)) $x25)))))
(let ((@x42 (monotonicity (rewrite (= (<= 0 ?0) (<= 0 ?0))) (= (=> (<= 0 ?0) $x25) (=> (<= 0 ?0) $x25)))))
(let ((@x47 (trans @x42 @x46 (= (=> (<= 0 ?0) $x25) (or (not (<= 0 ?0)) $x25)))))
(let ((@x77 (mp (mp (asserted $x27) (|quant-intro| @x47 (= $x27 $x48)) $x48) (|rewrite*| (= $x48 $x48)) $x48)))
(let ((@x128 (|mp~| (mp @x77 @x111 $x109) (|nnf-pos| (refl (|~| $x106 $x106)) (|~| $x109 $x109)) $x109)))
(let (($x538 (not $x558)))
(let (($x501 (or $x538 $x517)))
(let ((@x521 (monotonicity (rewrite (= (>= 1 0) true)) (= (not (>= 1 0)) (not true)))))
(let ((@x231 (trans @x521 (rewrite (= (not true) false)) (= (not (>= 1 0)) false))))
(let ((@x235 (monotonicity @x231 (= (or (not (>= 1 0)) $x517) (or false $x517)))))
(let ((@x515 (trans @x235 (rewrite (= (or false $x517) $x517)) (= (or (not (>= 1 0)) $x517) $x517))))
(let ((@x505 (monotonicity @x515 (= (or $x538 (or (not (>= 1 0)) $x517)) $x501))))
(let ((@x508 (trans @x505 (rewrite (= $x501 $x501)) (= (or $x538 (or (not (>= 1 0)) $x517)) $x501))))
(let ((@x509 (mp ((_ |quant-inst| 1) (or $x538 (or (not (>= 1 0)) $x517))) @x508 $x501)))
(let ((@x329 (|unit-resolution| @x509 (mp @x128 (|quant-intro| (refl (= $x106 $x106)) (= $x109 $x558)) $x558) $x517)))
(let (($x12 (= (|nat$| ?x8) (|nat$| 1))))
(let ((@x38 (mp (asserted (not (not $x12))) (rewrite (= (not (not $x12)) $x12)) $x12)))
(let ((@x367 (monotonicity (mp @x38 (|rewrite*| (= $x12 $x12)) $x12) (= ?x224 (|of_nat$| (|nat$| 1))))))
(let ((@x479 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x224 1)) $x499)) (trans @x367 @x329 (= ?x224 1)) $x499)))
(let ((@x383 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x499) (not (<= ?x224 0)))) @x479 (not (<= ?x224 0)))))
(let ((@x386 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x224 0)) (<= ?x224 0))) @x383 (not (= ?x224 0)))))
(let (($x527 (= ?x224 0)))
(let (($x529 (or $x205 $x527)))
(let (($x564 (forall ((?v0 Int) )(!(let (($x29 (= (|of_nat$| (|nat$| ?v0)) 0)))
(let (($x102 (>= ?v0 0)))
(or $x102 $x29))) :pattern ( (|nat$| ?v0) )))
))
(let (($x116 (forall ((?v0 Int) )(let (($x29 (= (|of_nat$| (|nat$| ?v0)) 0)))
(let (($x102 (>= ?v0 0)))
(or $x102 $x29))))
))
(let (($x29 (= (|of_nat$| (|nat$| ?0)) 0)))
(let (($x102 (>= ?0 0)))
(let (($x113 (or $x102 $x29)))
(let (($x65 (forall ((?v0 Int) )(let (($x29 (= (|of_nat$| (|nat$| ?v0)) 0)))
(let (($x22 (<= 0 ?v0)))
(or $x22 $x29))))
))
(let ((@x115 (monotonicity (rewrite (= (<= 0 ?0) $x102)) (= (or (<= 0 ?0) $x29) $x113))))
(let (($x31 (forall ((?v0 Int) )(let (($x29 (= (|of_nat$| (|nat$| ?v0)) 0)))
(=> (< ?v0 0) $x29)))
))
(let ((@x62 (rewrite (= (=> (not (<= 0 ?0)) $x29) (or (<= 0 ?0) $x29)))))
(let ((@x55 (monotonicity (rewrite (= (<= 0 ?0) (<= 0 ?0))) (= (not (<= 0 ?0)) (not (<= 0 ?0))))))
(let ((@x56 (trans (rewrite (= (< ?0 0) (not (<= 0 ?0)))) @x55 (= (< ?0 0) (not (<= 0 ?0))))))
(let ((@x59 (monotonicity @x56 (= (=> (< ?0 0) $x29) (=> (not (<= 0 ?0)) $x29)))))
(let ((@x64 (trans @x59 @x62 (= (=> (< ?0 0) $x29) (or (<= 0 ?0) $x29)))))
(let ((@x80 (mp (mp (asserted $x31) (|quant-intro| @x64 (= $x31 $x65)) $x65) (|rewrite*| (= $x65 $x65)) $x65)))
(let ((@x133 (|mp~| (mp @x80 (|quant-intro| @x115 (= $x65 $x116)) $x116) (|nnf-pos| (refl (|~| $x113 $x113)) (|~| $x116 $x116)) $x116)))
(let (($x168 (not $x564)))
(let (($x532 (or $x168 $x205 $x527)))
(let ((@x531 (monotonicity (rewrite (= (>= ?x8 0) $x205)) (= (or (>= ?x8 0) $x527) $x529))))
(let ((@x535 (monotonicity @x531 (= (or $x168 (or (>= ?x8 0) $x527)) (or $x168 $x529)))))
(let ((@x227 (trans @x535 (rewrite (= (or $x168 $x529) $x532)) (= (or $x168 (or (>= ?x8 0) $x527)) $x532))))
(let ((@x387 (|unit-resolution| (mp ((_ |quant-inst| (* 2 (|of_nat$| |x$|))) (or $x168 (or (>= ?x8 0) $x527))) @x227 $x532) (mp @x133 (|quant-intro| (refl (= $x113 $x113)) (= $x116 $x564)) $x564) $x529)))
(let (($x197 (not $x205)))
(let (($x546 (or $x197 $x543)))
(let (($x200 (or $x538 $x197 $x543)))
(let (($x201 (or $x538 (or (not (>= ?x8 0)) (= ?x224 ?x8)))))
(let ((@x537 (monotonicity (rewrite (= (>= ?x8 0) $x205)) (= (not (>= ?x8 0)) $x197))))
(let ((@x548 (monotonicity @x537 (rewrite (= (= ?x224 ?x8) $x543)) (= (or (not (>= ?x8 0)) (= ?x224 ?x8)) $x546))))
(let ((@x187 (trans (monotonicity @x548 (= $x201 (or $x538 $x546))) (rewrite (= (or $x538 $x546) $x200)) (= $x201 $x200))))
(let ((@x389 (|unit-resolution| (mp ((_ |quant-inst| (* 2 (|of_nat$| |x$|))) $x201) @x187 $x200) (mp @x128 (|quant-intro| (refl (= $x106 $x106)) (= $x109 $x558)) $x558) $x546)))
(let ((@x472 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x543) (<= ?x545 0))) (|unit-resolution| @x389 (|unit-resolution| @x387 @x386 $x205) $x543) (<= ?x545 0))))
(let ((@x463 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x543) (>= ?x545 0))) (|unit-resolution| @x389 (|unit-resolution| @x387 @x386 $x205) $x543) (>= ?x545 0))))
(let ((@x475 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x224 1)) (<= ?x224 1))) (trans @x367 @x329 (= ?x224 1)) (<= ?x224 1))))
((_ |th-lemma| arith gcd-test -1/2 -1/2 -1/2 -1/2) @x479 @x475 @x463 @x472 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
348e0e0e2aff481fb0a9d832ecbb8299820ba5ad 23 0
unsat
((set-logic AUFLIA)
(proof
(let ((?x6 (|of_nat$| |a$|)))
(let (($x50 (>= ?x6 4)))
(let (($x12 (< (* 2 ?x6) 7)))
(let (($x13 (=> (< ?x6 3) $x12)))
(let (($x14 (not $x13)))
(let (($x53 (not $x50)))
(let (($x36 (<= 3 ?x6)))
(let (($x61 (or $x36 $x53)))
(let ((@x55 (monotonicity (rewrite (= (<= 7 (* 2 ?x6)) $x50)) (= (not (<= 7 (* 2 ?x6))) $x53))))
(let ((@x57 (trans (rewrite (= $x12 (not (<= 7 (* 2 ?x6))))) @x55 (= $x12 $x53))))
(let ((@x43 (monotonicity (rewrite (= $x36 $x36)) (= (not $x36) (not $x36)))))
(let ((@x44 (trans (rewrite (= (< ?x6 3) (not $x36))) @x43 (= (< ?x6 3) (not $x36)))))
(let ((@x65 (trans (monotonicity @x44 @x57 (= $x13 (=> (not $x36) $x53))) (rewrite (= (=> (not $x36) $x53) $x61)) (= $x13 $x61))))
(let ((@x69 (mp (asserted $x14) (monotonicity @x65 (= $x14 (not $x61))) (not $x61))))
(let ((@x142 (monotonicity (rewrite (= $x36 (>= ?x6 3))) (= (not $x36) (not (>= ?x6 3))))))
(let (($x37 (not $x36)))
(let ((@x116 (mp (mp (|not-or-elim| @x69 $x37) (|rewrite*| (= $x37 $x37)) $x37) @x43 $x37)))
(let ((@x265 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or $x53 (>= ?x6 3))) (mp (mp @x116 @x43 $x37) @x142 (not (>= ?x6 3))) $x53)))
(|unit-resolution| @x265 (mp (|not-or-elim| @x69 $x50) (|rewrite*| (= $x50 $x50)) $x50) false)))))))))))))))))))))
754dd3a2aa33c6ad39bf93726c67d09ed642aeda 115 0
unsat
((set-logic AUFLIA)
(proof
(let ((?x11 (|of_nat$| (|nat$| (+ 1 (|of_nat$| |y$|))))))
(let ((?x128 (+ (* (~ 1) (|of_nat$| |y$|)) ?x11)))
(let ((?x134 (|of_nat$| (|nat$| ?x128))))
(let ((?x8 (|of_nat$| |y$|)))
(let (($x554 (= (+ ?x8 (* (~ 1) ?x11) ?x134) 0)))
(let ((?x589 (+ ?x8 (* (~ 1) ?x11))))
(let (($x270 (<= ?x589 0)))
(let (($x572 (<= ?x589 (~ 1))))
(let (($x579 (= ?x589 (~ 1))))
(let (($x251 (>= ?x8 (~ 1))))
(let (($x409 (>= ?x8 0)))
(let (($x519 (= (|of_nat$| (|nat$| ?x8)) 0)))
(let (($x605 (forall ((?v0 Int) )(!(let (($x31 (= (|of_nat$| (|nat$| ?v0)) 0)))
(let (($x143 (>= ?v0 0)))
(or $x143 $x31))) :pattern ( (|nat$| ?v0) )))
))
(let (($x158 (forall ((?v0 Int) )(let (($x31 (= (|of_nat$| (|nat$| ?v0)) 0)))
(let (($x143 (>= ?v0 0)))
(or $x143 $x31))))
))
(let (($x31 (= (|of_nat$| (|nat$| ?0)) 0)))
(let (($x143 (>= ?0 0)))
(let (($x155 (or $x143 $x31)))
(let (($x94 (forall ((?v0 Int) )(let (($x31 (= (|of_nat$| (|nat$| ?v0)) 0)))
(let (($x24 (<= 0 ?v0)))
(or $x24 $x31))))
))
(let ((@x157 (monotonicity (rewrite (= (<= 0 ?0) $x143)) (= (or (<= 0 ?0) $x31) $x155))))
(let (($x33 (forall ((?v0 Int) )(let (($x31 (= (|of_nat$| (|nat$| ?v0)) 0)))
(=> (< ?v0 0) $x31)))
))
(let ((@x91 (rewrite (= (=> (not (<= 0 ?0)) $x31) (or (<= 0 ?0) $x31)))))
(let ((@x84 (monotonicity (rewrite (= (<= 0 ?0) (<= 0 ?0))) (= (not (<= 0 ?0)) (not (<= 0 ?0))))))
(let ((@x85 (trans (rewrite (= (< ?0 0) (not (<= 0 ?0)))) @x84 (= (< ?0 0) (not (<= 0 ?0))))))
(let ((@x88 (monotonicity @x85 (= (=> (< ?0 0) $x31) (=> (not (<= 0 ?0)) $x31)))))
(let ((@x93 (trans @x88 @x91 (= (=> (< ?0 0) $x31) (or (<= 0 ?0) $x31)))))
(let ((@x109 (mp (mp (asserted $x33) (|quant-intro| @x93 (= $x33 $x94)) $x94) (|rewrite*| (= $x94 $x94)) $x94)))
(let ((@x175 (|mp~| (mp @x109 (|quant-intro| @x157 (= $x94 $x158)) $x158) (|nnf-pos| (refl (|~| $x155 $x155)) (|~| $x158 $x158)) $x158)))
(let ((@x425 (rewrite (= (or (not $x605) (or $x409 $x519)) (or (not $x605) $x409 $x519)))))
(let ((@x418 (mp ((_ |quant-inst| (|of_nat$| |y$|)) (or (not $x605) (or $x409 $x519))) @x425 (or (not $x605) $x409 $x519))))
(let ((@x508 (|unit-resolution| @x418 (mp @x175 (|quant-intro| (refl (= $x155 $x155)) (= $x158 $x605)) $x605) (or $x409 $x519))))
(let (($x591 (forall ((?v0 |Nat$|) )(!(= (|nat$| (|of_nat$| ?v0)) ?v0) :pattern ( (|of_nat$| ?v0) )))
))
(let (($x22 (forall ((?v0 |Nat$|) )(= (|nat$| (|of_nat$| ?v0)) ?v0))
))
(let ((@x596 (trans (rewrite (= $x22 $x591)) (rewrite (= $x591 $x591)) (= $x22 $x591))))
(let ((@x166 (refl (|~| (= (|nat$| (|of_nat$| ?0)) ?0) (= (|nat$| (|of_nat$| ?0)) ?0)))))
(let ((@x163 (|mp~| (mp (asserted $x22) (|rewrite*| (= $x22 $x22)) $x22) (|nnf-pos| @x166 (|~| $x22 $x22)) $x22)))
(let ((@x510 (|unit-resolution| ((_ |quant-inst| |y$|) (or (not $x591) (= (|nat$| ?x8) |y$|))) (mp @x163 @x596 $x591) (= (|nat$| ?x8) |y$|))))
(let ((@x497 (monotonicity (symm @x510 (= |y$| (|nat$| ?x8))) (= ?x8 (|of_nat$| (|nat$| ?x8))))))
(let ((@x498 (trans @x497 (|unit-resolution| @x508 (hypothesis (not $x409)) $x519) (= ?x8 0))))
(let ((@x502 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x8 0)) $x409)) (hypothesis (not $x409)) @x498 false)))
(let ((@x490 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x409) $x251)) (lemma @x502 $x409) $x251)))
(let (($x585 (not $x251)))
(let (($x580 (or $x585 $x579)))
(let (($x599 (forall ((?v0 Int) )(!(let (($x27 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x27)) :pattern ( (|nat$| ?v0) )))
))
(let (($x151 (forall ((?v0 Int) )(let (($x27 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x27)))
))
(let (($x27 (= (|of_nat$| (|nat$| ?0)) ?0)))
(let (($x148 (or (not $x143) $x27)))
(let (($x77 (forall ((?v0 Int) )(let (($x27 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(let (($x24 (<= 0 ?v0)))
(let (($x72 (not $x24)))
(or $x72 $x27)))))
))
(let ((@x147 (monotonicity (rewrite (= (<= 0 ?0) $x143)) (= (not (<= 0 ?0)) (not $x143)))))
(let ((@x153 (|quant-intro| (monotonicity @x147 (= (or (not (<= 0 ?0)) $x27) $x148)) (= $x77 $x151))))
(let (($x29 (forall ((?v0 Int) )(let (($x27 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(let (($x24 (<= 0 ?v0)))
(=> $x24 $x27))))
))
(let ((@x75 (rewrite (= (=> (<= 0 ?0) $x27) (or (not (<= 0 ?0)) $x27)))))
(let ((@x71 (monotonicity (rewrite (= (<= 0 ?0) (<= 0 ?0))) (= (=> (<= 0 ?0) $x27) (=> (<= 0 ?0) $x27)))))
(let ((@x76 (trans @x71 @x75 (= (=> (<= 0 ?0) $x27) (or (not (<= 0 ?0)) $x27)))))
(let ((@x106 (mp (mp (asserted $x29) (|quant-intro| @x76 (= $x29 $x77)) $x77) (|rewrite*| (= $x77 $x77)) $x77)))
(let ((@x170 (|mp~| (mp @x106 @x153 $x151) (|nnf-pos| (refl (|~| $x148 $x148)) (|~| $x151 $x151)) $x151)))
(let (($x224 (not $x599)))
(let (($x565 (or $x224 $x585 $x579)))
(let (($x227 (or $x224 (or (not (>= (+ 1 ?x8) 0)) (= ?x11 (+ 1 ?x8))))))
(let (($x245 (= (or (not (>= (+ 1 ?x8) 0)) (= ?x11 (+ 1 ?x8))) $x580)))
(let ((@x587 (monotonicity (rewrite (= (>= (+ 1 ?x8) 0) $x251)) (= (not (>= (+ 1 ?x8) 0)) $x585))))
(let ((@x566 (monotonicity (monotonicity @x587 (rewrite (= (= ?x11 (+ 1 ?x8)) $x579)) $x245) (= $x227 (or $x224 $x580)))))
(let ((@x571 (mp ((_ |quant-inst| (+ 1 ?x8)) $x227) (trans @x566 (rewrite (= (or $x224 $x580) $x565)) (= $x227 $x565)) $x565)))
(let ((@x491 (|unit-resolution| @x571 (mp @x170 (|quant-intro| (refl (= $x148 $x148)) (= $x151 $x599)) $x599) $x580)))
(let ((@x475 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x579) $x572)) (|unit-resolution| @x491 @x490 $x579) $x572)))
(let (($x551 (not $x270)))
(let (($x542 (or $x551 $x554)))
(let (($x545 (or $x224 $x551 $x554)))
(let (($x546 (or $x224 (or (not (>= ?x128 0)) (= ?x134 ?x128)))))
(let ((@x276 (monotonicity (rewrite (= (>= ?x128 0) $x270)) (= (not (>= ?x128 0)) $x551))))
(let ((@x544 (monotonicity @x276 (rewrite (= (= ?x134 ?x128) $x554)) (= (or (not (>= ?x128 0)) (= ?x134 ?x128)) $x542))))
(let ((@x532 (trans (monotonicity @x544 (= $x546 (or $x224 $x542))) (rewrite (= (or $x224 $x542) $x545)) (= $x546 $x545))))
(let ((@x480 (|unit-resolution| (mp ((_ |quant-inst| (+ (* (~ 1) ?x8) ?x11)) $x546) @x532 $x545) (mp @x170 (|quant-intro| (refl (= $x148 $x148)) (= $x151 $x599)) $x599) $x542)))
(let ((@x481 (|unit-resolution| @x480 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x572) $x270)) @x475 $x270) $x554)))
(let ((@x485 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x554) (>= (+ ?x8 (* (~ 1) ?x11) ?x134) 0))) @x481 (>= (+ ?x8 (* (~ 1) ?x11) ?x134) 0))))
(let ((?x42 (+ ?x11 (* (~ 1) ?x8))))
(let ((?x45 (|nat$| ?x42)))
(let ((?x48 (|of_nat$| ?x45)))
(let (($x54 (<= ?x48 0)))
(let ((@x136 (monotonicity (monotonicity (rewrite (= ?x42 ?x128)) (= ?x45 (|nat$| ?x128))) (= ?x48 ?x134))))
(let (($x16 (< (* 0 ?x11) (|of_nat$| (|nat$| (- ?x11 ?x8))))))
(let (($x17 (not $x16)))
(let ((@x47 (monotonicity (rewrite (= (- ?x11 ?x8) ?x42)) (= (|nat$| (- ?x11 ?x8)) ?x45))))
(let ((@x53 (monotonicity (rewrite (= (* 0 ?x11) 0)) (monotonicity @x47 (= (|of_nat$| (|nat$| (- ?x11 ?x8))) ?x48)) (= $x16 (< 0 ?x48)))))
(let ((@x59 (trans @x53 (rewrite (= (< 0 ?x48) (not $x54))) (= $x16 (not $x54)))))
(let ((@x66 (trans (monotonicity @x59 (= $x17 (not (not $x54)))) (rewrite (= (not (not $x54)) $x54)) (= $x17 $x54))))
(let ((@x142 (mp (mp (mp (asserted $x17) @x66 $x54) (|rewrite*| (= $x54 $x54)) $x54) (monotonicity @x136 (= $x54 (<= ?x134 0))) (<= ?x134 0))))
((_ |th-lemma| arith farkas -1 -1 1) @x142 @x475 @x485 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
0f5c33836eb7c04b103caf9bdb4756aba933ece2 112 0
unsat
((set-logic AUFLIA)
(proof
(let ((?x11 (|of_nat$| (|nat$| (+ 1 (|of_nat$| |y$|))))))
(let ((?x75 (+ (~ 1) ?x11)))
(let ((?x82 (|nat$| ?x75)))
(let ((?x335 (|of_nat$| ?x82)))
(let ((?x8 (|of_nat$| |y$|)))
(let (($x419 (>= (+ ?x8 (* (~ 1) ?x335)) 0)))
(let (($x85 (= ?x82 |y$|)))
(let (($x54 (<= ?x11 0)))
(let (($x13 (ite (< 0 ?x11) true false)))
(let (($x18 (not $x13)))
(let (($x19 (=> $x18 false)))
(let (($x46 (not $x19)))
(let ((@x60 (monotonicity (rewrite (= (< 0 ?x11) (not $x54))) (= $x13 (ite (not $x54) true false)))))
(let ((@x64 (trans @x60 (rewrite (= (ite (not $x54) true false) (not $x54))) (= $x13 (not $x54)))))
(let ((@x106 (trans (monotonicity @x64 (= $x18 (not (not $x54)))) (rewrite (= (not (not $x54)) $x54)) (= $x18 $x54))))
(let ((@x113 (trans (monotonicity @x106 (= $x19 (=> $x54 false))) (rewrite (= (=> $x54 false) (not $x54))) (= $x19 (not $x54)))))
(let ((@x117 (trans (monotonicity @x113 (= $x46 (not (not $x54)))) (rewrite (= (not (not $x54)) $x54)) (= $x46 $x54))))
(let (($x22 (not (or false (or (= $x13 (= (|nat$| (- ?x11 1)) |y$|)) $x19)))))
(let ((@x43 (|not-or-elim| (asserted $x22) (not (or (= $x13 (= (|nat$| (- ?x11 1)) |y$|)) $x19)))))
(let ((@x51 (monotonicity (|iff-true| (mp (|not-or-elim| @x43 $x46) @x117 $x54) (= $x54 true)) (= (= $x54 $x85) (= true $x85)))))
(let ((@x152 (trans @x51 (rewrite (= (= true $x85) $x85)) (= (= $x54 $x85) $x85))))
(let (($x94 (= $x54 $x85)))
(let (($x17 (= $x13 (= (|nat$| (- ?x11 1)) |y$|))))
(let (($x44 (not $x17)))
(let ((@x74 (monotonicity (rewrite (= (* (~ 1) 1) (~ 1))) (= (+ ?x11 (* (~ 1) 1)) (+ ?x11 (~ 1))))))
(let ((@x79 (trans @x74 (rewrite (= (+ ?x11 (~ 1)) ?x75)) (= (+ ?x11 (* (~ 1) 1)) ?x75))))
(let ((@x81 (trans (rewrite (= (- ?x11 1) (+ ?x11 (* (~ 1) 1)))) @x79 (= (- ?x11 1) ?x75))))
(let ((@x87 (monotonicity (monotonicity @x81 (= (|nat$| (- ?x11 1)) ?x82)) (= (= (|nat$| (- ?x11 1)) |y$|) $x85))))
(let ((@x93 (monotonicity (monotonicity @x64 @x87 (= $x17 (= (not $x54) $x85))) (= $x44 (not (= (not $x54) $x85))))))
(let ((@x98 (trans @x93 (rewrite (= (not (= (not $x54) $x85)) $x94)) (= $x44 $x94))))
(let ((@x156 (mp (mp (mp (|not-or-elim| @x43 $x44) @x98 $x94) @x152 $x85) (|rewrite*| (= $x85 $x85)) $x85)))
(let ((@x569 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x8 ?x335)) $x419)) (monotonicity (symm @x156 (= |y$| ?x82)) (= ?x8 ?x335)) $x419)))
(let (($x631 (= (+ ?x8 (* (~ 1) ?x11)) (~ 1))))
(let (($x629 (>= ?x8 (~ 1))))
(let (($x577 (>= ?x335 0)))
(let (($x579 (= ?x335 0)))
(let ((@x159 (mp (mp (|not-or-elim| @x43 $x46) @x117 $x54) (|rewrite*| (= $x54 $x54)) $x54)))
(let ((@x558 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not (>= ?x11 1)) (not $x54))) @x159 (not (>= ?x11 1)))))
(let (($x651 (forall ((?v0 Int) )(!(let (($x36 (= (|of_nat$| (|nat$| ?v0)) 0)))
(let (($x189 (>= ?v0 0)))
(or $x189 $x36))) :pattern ( (|nat$| ?v0) )))
))
(let (($x204 (forall ((?v0 Int) )(let (($x36 (= (|of_nat$| (|nat$| ?v0)) 0)))
(let (($x189 (>= ?v0 0)))
(or $x189 $x36))))
))
(let (($x36 (= (|of_nat$| (|nat$| ?0)) 0)))
(let (($x189 (>= ?0 0)))
(let (($x201 (or $x189 $x36)))
(let (($x145 (forall ((?v0 Int) )(let (($x36 (= (|of_nat$| (|nat$| ?v0)) 0)))
(let (($x29 (<= 0 ?v0)))
(or $x29 $x36))))
))
(let ((@x203 (monotonicity (rewrite (= (<= 0 ?0) $x189)) (= (or (<= 0 ?0) $x36) $x201))))
(let (($x38 (forall ((?v0 Int) )(let (($x36 (= (|of_nat$| (|nat$| ?v0)) 0)))
(=> (< ?v0 0) $x36)))
))
(let ((@x142 (rewrite (= (=> (not (<= 0 ?0)) $x36) (or (<= 0 ?0) $x36)))))
(let ((@x135 (monotonicity (rewrite (= (<= 0 ?0) (<= 0 ?0))) (= (not (<= 0 ?0)) (not (<= 0 ?0))))))
(let ((@x136 (trans (rewrite (= (< ?0 0) (not (<= 0 ?0)))) @x135 (= (< ?0 0) (not (<= 0 ?0))))))
(let ((@x139 (monotonicity @x136 (= (=> (< ?0 0) $x36) (=> (not (<= 0 ?0)) $x36)))))
(let ((@x144 (trans @x139 @x142 (= (=> (< ?0 0) $x36) (or (<= 0 ?0) $x36)))))
(let ((@x168 (mp (mp (asserted $x38) (|quant-intro| @x144 (= $x38 $x145)) $x145) (|rewrite*| (= $x145 $x145)) $x145)))
(let ((@x221 (|mp~| (mp @x168 (|quant-intro| @x203 (= $x145 $x204)) $x204) (|nnf-pos| (refl (|~| $x201 $x201)) (|~| $x204 $x204)) $x204)))
(let (($x606 (>= ?x11 1)))
(let (($x620 (not $x651)))
(let (($x584 (or $x620 $x606 $x579)))
(let ((@x583 (monotonicity (rewrite (= (>= ?x75 0) $x606)) (= (or (>= ?x75 0) $x579) (or $x606 $x579)))))
(let ((@x415 (monotonicity @x583 (= (or $x620 (or (>= ?x75 0) $x579)) (or $x620 (or $x606 $x579))))))
(let ((@x574 (trans @x415 (rewrite (= (or $x620 (or $x606 $x579)) $x584)) (= (or $x620 (or (>= ?x75 0) $x579)) $x584))))
(let ((@x559 (|unit-resolution| (mp ((_ |quant-inst| (+ (~ 1) ?x11)) (or $x620 (or (>= ?x75 0) $x579))) @x574 $x584) (mp @x221 (|quant-intro| (refl (= $x201 $x201)) (= $x204 $x651)) $x651) @x558 $x579)))
(let ((@x552 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1) (or $x629 (not $x577) (not $x419))) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x579) $x577)) @x559 $x577) @x569 $x629)))
(let (($x624 (not $x629)))
(let (($x635 (or $x624 $x631)))
(let (($x645 (forall ((?v0 Int) )(!(let (($x32 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x32)) :pattern ( (|nat$| ?v0) )))
))
(let (($x197 (forall ((?v0 Int) )(let (($x32 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x32)))
))
(let (($x32 (= (|of_nat$| (|nat$| ?0)) ?0)))
(let (($x194 (or (not $x189) $x32)))
(let (($x128 (forall ((?v0 Int) )(let (($x32 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(let (($x29 (<= 0 ?v0)))
(let (($x123 (not $x29)))
(or $x123 $x32)))))
))
(let ((@x193 (monotonicity (rewrite (= (<= 0 ?0) $x189)) (= (not (<= 0 ?0)) (not $x189)))))
(let ((@x199 (|quant-intro| (monotonicity @x193 (= (or (not (<= 0 ?0)) $x32) $x194)) (= $x128 $x197))))
(let (($x34 (forall ((?v0 Int) )(let (($x32 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(let (($x29 (<= 0 ?v0)))
(=> $x29 $x32))))
))
(let ((@x126 (rewrite (= (=> (<= 0 ?0) $x32) (or (not (<= 0 ?0)) $x32)))))
(let ((@x122 (monotonicity (rewrite (= (<= 0 ?0) (<= 0 ?0))) (= (=> (<= 0 ?0) $x32) (=> (<= 0 ?0) $x32)))))
(let ((@x127 (trans @x122 @x126 (= (=> (<= 0 ?0) $x32) (or (not (<= 0 ?0)) $x32)))))
(let ((@x165 (mp (mp (asserted $x34) (|quant-intro| @x127 (= $x34 $x128)) $x128) (|rewrite*| (= $x128 $x128)) $x128)))
(let ((@x216 (|mp~| (mp @x165 @x199 $x197) (|nnf-pos| (refl (|~| $x194 $x194)) (|~| $x197 $x197)) $x197)))
(let (($x289 (not $x645)))
(let (($x626 (or $x289 $x624 $x631)))
(let (($x291 (or $x289 (or (not (>= (+ 1 ?x8) 0)) (= ?x11 (+ 1 ?x8))))))
(let (($x625 (= (or (not (>= (+ 1 ?x8) 0)) (= ?x11 (+ 1 ?x8))) $x635)))
(let ((@x298 (monotonicity (rewrite (= (>= (+ 1 ?x8) 0) $x629)) (= (not (>= (+ 1 ?x8) 0)) $x624))))
(let ((@x273 (monotonicity (monotonicity @x298 (rewrite (= (= ?x11 (+ 1 ?x8)) $x631)) $x625) (= $x291 (or $x289 $x635)))))
(let ((@x613 (mp ((_ |quant-inst| (+ 1 ?x8)) $x291) (trans @x273 (rewrite (= (or $x289 $x635) $x626)) (= $x291 $x626)) $x626)))
(let ((@x553 (|unit-resolution| @x613 (mp @x216 (|quant-intro| (refl (= $x194 $x194)) (= $x197 $x645)) $x645) $x635)))
(let ((@x541 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x631) (<= (+ ?x8 (* (~ 1) ?x11)) (~ 1)))) (|unit-resolution| @x553 @x552 $x631) (<= (+ ?x8 (* (~ 1) ?x11)) (~ 1)))))
((_ |th-lemma| arith farkas 1 -1 -1 1) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x579) $x577)) @x559 $x577) @x159 @x541 @x569 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
0c9ea539f37d7b052d3668e6cc284a6b6fb59ca4 60 0
unsat
((set-logic AUFLIA)
(proof
(let ((?x44 (* (~ 1) |x$|)))
(let (($x140 (>= |x$| 0)))
(let ((?x143 (ite $x140 |x$| ?x44)))
(let (($x279 (= ?x44 ?x143)))
(let (($x193 (= |x$| ?x143)))
(let ((@x585 (|unit-resolution| (|def-axiom| (or (not $x140) $x193)) (hypothesis $x140) $x193)))
(let ((@x589 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x193) (<= (+ |x$| (* (~ 1) ?x143)) 0))) @x585 (<= (+ |x$| (* (~ 1) ?x143)) 0))))
(let (($x286 (not (>= ?x143 0))))
(let (($x617 (forall ((?v0 Int) )(!(let (($x23 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x23)) :pattern ( (|nat$| ?v0) )))
))
(let (($x168 (forall ((?v0 Int) )(let (($x23 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x23)))
))
(let (($x23 (= (|of_nat$| (|nat$| ?0)) ?0)))
(let (($x165 (or (not (>= ?0 0)) $x23)))
(let (($x77 (forall ((?v0 Int) )(let (($x23 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (<= 0 ?v0)) $x23)))
))
(let ((@x164 (monotonicity (rewrite (= (<= 0 ?0) (>= ?0 0))) (= (not (<= 0 ?0)) (not (>= ?0 0))))))
(let ((@x170 (|quant-intro| (monotonicity @x164 (= (or (not (<= 0 ?0)) $x23) $x165)) (= $x77 $x168))))
(let (($x25 (forall ((?v0 Int) )(let (($x23 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(let (($x20 (<= 0 ?v0)))
(=> $x20 $x23))))
))
(let ((@x75 (rewrite (= (=> (<= 0 ?0) $x23) (or (not (<= 0 ?0)) $x23)))))
(let ((@x71 (monotonicity (rewrite (= (<= 0 ?0) (<= 0 ?0))) (= (=> (<= 0 ?0) $x23) (=> (<= 0 ?0) $x23)))))
(let ((@x76 (trans @x71 @x75 (= (=> (<= 0 ?0) $x23) (or (not (<= 0 ?0)) $x23)))))
(let ((@x106 (mp (mp (asserted $x25) (|quant-intro| @x76 (= $x25 $x77)) $x77) (|rewrite*| (= $x77 $x77)) $x77)))
(let ((@x187 (|mp~| (mp @x106 @x170 $x168) (|nnf-pos| (refl (|~| $x165 $x165)) (|~| $x168 $x168)) $x168)))
(let (($x34 (<= 0 |x$|)))
(let ((?x50 (ite $x34 |x$| ?x44)))
(let ((?x55 (|nat$| ?x50)))
(let ((?x58 (|of_nat$| ?x55)))
(let (($x61 (= ?x58 ?x50)))
(let (($x64 (not $x61)))
(let ((@x148 (monotonicity (monotonicity (rewrite (= $x34 $x140)) (= ?x50 ?x143)) (= ?x55 (|nat$| ?x143)))))
(let ((@x154 (monotonicity (monotonicity @x148 (= ?x58 (|of_nat$| (|nat$| ?x143)))) (monotonicity (rewrite (= $x34 $x140)) (= ?x50 ?x143)) (= $x61 (= (|of_nat$| (|nat$| ?x143)) ?x143)))))
(let ((@x113 (monotonicity (monotonicity (rewrite (= $x34 $x34)) (= ?x50 ?x50)) (= ?x55 ?x55))))
(let ((@x117 (monotonicity (monotonicity @x113 (= ?x58 ?x58)) (monotonicity (rewrite (= $x34 $x34)) (= ?x50 ?x50)) (= $x61 $x61))))
(let ((?x9 (ite (< |x$| 0) (- |x$|) |x$|)))
(let (($x13 (not (= (|of_nat$| (|nat$| ?x9)) ?x9))))
(let ((@x42 (trans (rewrite (= (< |x$| 0) (not $x34))) (monotonicity (rewrite (= $x34 $x34)) (= (not $x34) (not $x34))) (= (< |x$| 0) (not $x34)))))
(let ((@x49 (monotonicity @x42 (rewrite (= (- |x$|) ?x44)) (= ?x9 (ite (not $x34) ?x44 |x$|)))))
(let ((@x54 (trans @x49 (rewrite (= (ite (not $x34) ?x44 |x$|) ?x50)) (= ?x9 ?x50))))
(let ((@x60 (monotonicity (monotonicity @x54 (= (|nat$| ?x9) ?x55)) (= (|of_nat$| (|nat$| ?x9)) ?x58))))
(let ((@x66 (monotonicity (monotonicity @x60 @x54 (= (= (|of_nat$| (|nat$| ?x9)) ?x9) $x61)) (= $x13 $x64))))
(let ((@x119 (mp (mp (mp (asserted $x13) @x66 $x64) (|rewrite*| (= $x64 $x64)) $x64) (monotonicity @x117 (= $x64 $x64)) $x64)))
(let ((@x158 (mp (mp @x119 (monotonicity @x117 (= $x64 $x64)) $x64) (monotonicity @x154 (= $x64 (not (= (|of_nat$| (|nat$| ?x143)) ?x143)))) (not (= (|of_nat$| (|nat$| ?x143)) ?x143)))))
(let (($x604 (= (or (not $x617) (or $x286 (= (|of_nat$| (|nat$| ?x143)) ?x143))) (or (not $x617) $x286 (= (|of_nat$| (|nat$| ?x143)) ?x143)))))
(let ((@x606 (mp ((_ |quant-inst| (ite $x140 |x$| ?x44)) (or (not $x617) (or $x286 (= (|of_nat$| (|nat$| ?x143)) ?x143)))) (rewrite $x604) (or (not $x617) $x286 (= (|of_nat$| (|nat$| ?x143)) ?x143)))))
(let ((@x590 (|unit-resolution| @x606 @x158 (mp @x187 (|quant-intro| (refl (= $x165 $x165)) (= $x168 $x617)) $x617) $x286)))
(let ((@x233 (|unit-resolution| (|def-axiom| (or $x140 $x279)) (lemma ((_ |th-lemma| arith farkas -1 1 1) (hypothesis $x140) @x590 @x589 false) (not $x140)) $x279)))
(let ((@x581 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x279) (<= (+ ?x44 (* (~ 1) ?x143)) 0))) @x233 (<= (+ ?x44 (* (~ 1) ?x143)) 0))))
(let ((@x301 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (<= ?x143 0) (>= ?x143 0))) @x590 (<= ?x143 0))))
((_ |th-lemma| arith farkas 1 1 1) @x301 (lemma ((_ |th-lemma| arith farkas -1 1 1) (hypothesis $x140) @x590 @x589 false) (not $x140)) @x581 false)))))))))))))))))))))))))))))))))))))))))))))))))
2f8af7e6fa968818bbe306cb947f5460272d1297 255 0
unsat
((set-logic AUFLIA)
(declare-fun ?v1!0 (|Nat$|) |Nat$|)
(proof
(let ((?x23 (|of_nat$| |m$|)))
(let ((?x24 (* 4 ?x23)))
(let (($x601 (= (+ ?x24 (* (~ 1) (|of_nat$| (|nat$| (+ 1 ?x24))))) (~ 1))))
(let (($x614 (>= ?x23 0)))
(let (($x705 (forall ((?v1 |Nat$|) )(!(let ((?x12 (|nat$| 1)))
(let (($x13 (= ?v1 ?x12)))
(or (not (|dvd$| ?v1 (|nat$| (+ 1 (* 4 (|of_nat$| |m$|)))))) $x13 (= ?v1 (|nat$| (+ 1 (* 4 (|of_nat$| |m$|)))))))) :pattern ( (|dvd$| ?v1 (|nat$| (+ 1 (* 4 (|of_nat$| |m$|))))) )))
))
(let ((?x72 (+ 1 ?x24)))
(let ((?x75 (|nat$| ?x72)))
(let ((?x299 (|of_nat$| ?x75)))
(let (($x384 (<= ?x299 1)))
(let (($x373 (not (or $x384 (not $x705)))))
(let (($x78 (|prime_nat$| ?x75)))
(let (($x86 (not $x78)))
(let (($x374 (or $x86 $x373)))
(let (($x703 (or (not (|dvd$| (?v1!0 ?x75) ?x75)) (= (?v1!0 ?x75) (|nat$| 1)) (= (?v1!0 ?x75) ?x75))))
(let (($x707 (not $x374)))
(let (($x742 (forall ((?v0 |Nat$|) )(!(let (($x223 (or (not (|dvd$| (?v1!0 ?v0) ?v0)) (= (?v1!0 ?v0) (|nat$| 1)) (= (?v1!0 ?v0) ?v0))))
(let (($x224 (not $x223)))
(let ((?x8 (|of_nat$| ?v0)))
(let (($x51 (<= ?x8 1)))
(let (($x6 (|prime_nat$| ?v0)))
(let (($x251 (or $x6 $x51 $x224)))
(let (($x714 (forall ((?v1 |Nat$|) )(!(let ((?x12 (|nat$| 1)))
(let (($x13 (= ?v1 ?x12)))
(or (not (|dvd$| ?v1 ?v0)) $x13 (= ?v1 ?v0)))) :pattern ( (|dvd$| ?v1 ?v0) )))
))
(let (($x204 (not $x6)))
(not (or (not (or $x204 (not (or $x51 (not $x714))))) (not $x251))))))))))) :pattern ( (|prime_nat$| ?v0) ) :pattern ( (|of_nat$| ?v0) )))
))
(let (($x294 (forall ((?v0 |Nat$|) )(let (($x223 (or (not (|dvd$| (?v1!0 ?v0) ?v0)) (= (?v1!0 ?v0) (|nat$| 1)) (= (?v1!0 ?v0) ?v0))))
(let (($x224 (not $x223)))
(let ((?x8 (|of_nat$| ?v0)))
(let (($x51 (<= ?x8 1)))
(let (($x6 (|prime_nat$| ?v0)))
(let (($x251 (or $x6 $x51 $x224)))
(let (($x59 (forall ((?v1 |Nat$|) )(let ((?x12 (|nat$| 1)))
(let (($x13 (= ?v1 ?x12)))
(or (not (|dvd$| ?v1 ?v0)) $x13 (= ?v1 ?v0)))))
))
(let (($x225 (not $x59)))
(let (($x279 (not (or $x51 $x225))))
(let (($x204 (not $x6)))
(let (($x280 (or $x204 $x279)))
(not (or (not $x280) (not $x251)))))))))))))))
))
(let (($x223 (or (not (|dvd$| (?v1!0 ?0) ?0)) (= (?v1!0 ?0) (|nat$| 1)) (= (?v1!0 ?0) ?0))))
(let (($x224 (not $x223)))
(let ((?x8 (|of_nat$| ?0)))
(let (($x51 (<= ?x8 1)))
(let (($x6 (|prime_nat$| ?0)))
(let (($x251 (or $x6 $x51 $x224)))
(let (($x714 (forall ((?v1 |Nat$|) )(!(let ((?x12 (|nat$| 1)))
(let (($x13 (= ?v1 ?x12)))
(or (not (|dvd$| ?v1 ?0)) $x13 (= ?v1 ?0)))) :pattern ( (|dvd$| ?v1 ?0) )))
))
(let (($x204 (not $x6)))
(let (($x59 (forall ((?v1 |Nat$|) )(let ((?x12 (|nat$| 1)))
(let (($x13 (= ?v1 ?x12)))
(or (not (|dvd$| ?v1 ?0)) $x13 (= ?v1 ?0)))))
))
(let (($x225 (not $x59)))
(let (($x279 (not (or $x51 $x225))))
(let (($x280 (or $x204 $x279)))
(let (($x289 (not (or (not $x280) (not $x251)))))
(let (($x738 (= $x289 (not (or (not (or $x204 (not (or $x51 (not $x714))))) (not $x251))))))
(let (($x735 (= (or (not $x280) (not $x251)) (or (not (or $x204 (not (or $x51 (not $x714))))) (not $x251)))))
(let ((?x12 (|nat$| 1)))
(let (($x13 (= ?0 ?x12)))
(let (($x56 (or (not (|dvd$| ?0 ?1)) $x13 (= ?0 ?1))))
(let ((@x721 (monotonicity (|quant-intro| (refl (= $x56 $x56)) (= $x59 $x714)) (= $x225 (not $x714)))))
(let ((@x727 (monotonicity (monotonicity @x721 (= (or $x51 $x225) (or $x51 (not $x714)))) (= $x279 (not (or $x51 (not $x714)))))))
(let ((@x733 (monotonicity (monotonicity @x727 (= $x280 (or $x204 (not (or $x51 (not $x714)))))) (= (not $x280) (not (or $x204 (not (or $x51 (not $x714)))))))))
(let ((@x744 (|quant-intro| (monotonicity (monotonicity @x733 $x735) $x738) (= $x294 $x742))))
(let (($x259 (forall ((?v0 |Nat$|) )(let (($x223 (or (not (|dvd$| (?v1!0 ?v0) ?v0)) (= (?v1!0 ?v0) (|nat$| 1)) (= (?v1!0 ?v0) ?v0))))
(let (($x224 (not $x223)))
(let ((?x8 (|of_nat$| ?v0)))
(let (($x51 (<= ?x8 1)))
(let (($x6 (|prime_nat$| ?v0)))
(let (($x251 (or $x6 $x51 $x224)))
(let (($x59 (forall ((?v1 |Nat$|) )(let ((?x12 (|nat$| 1)))
(let (($x13 (= ?v1 ?x12)))
(or (not (|dvd$| ?v1 ?v0)) $x13 (= ?v1 ?v0)))))
))
(let (($x52 (not $x51)))
(let (($x62 (and $x52 $x59)))
(let (($x204 (not $x6)))
(let (($x233 (or $x204 $x62)))
(and $x233 $x251)))))))))))))
))
(let ((@x282 (monotonicity (rewrite (= (and (not $x51) $x59) $x279)) (= (or $x204 (and (not $x51) $x59)) $x280))))
(let ((@x285 (monotonicity @x282 (= (and (or $x204 (and (not $x51) $x59)) $x251) (and $x280 $x251)))))
(let ((@x293 (trans @x285 (rewrite (= (and $x280 $x251) $x289)) (= (and (or $x204 (and (not $x51) $x59)) $x251) $x289))))
(let (($x237 (forall ((?v0 |Nat$|) )(let (($x223 (or (not (|dvd$| (?v1!0 ?v0) ?v0)) (= (?v1!0 ?v0) (|nat$| 1)) (= (?v1!0 ?v0) ?v0))))
(let (($x224 (not $x223)))
(let ((?x8 (|of_nat$| ?v0)))
(let (($x51 (<= ?x8 1)))
(let (($x52 (not $x51)))
(let (($x215 (not $x52)))
(let (($x228 (or $x215 $x224)))
(let (($x6 (|prime_nat$| ?v0)))
(let (($x232 (or $x6 $x228)))
(let (($x59 (forall ((?v1 |Nat$|) )(let ((?x12 (|nat$| 1)))
(let (($x13 (= ?v1 ?x12)))
(or (not (|dvd$| ?v1 ?v0)) $x13 (= ?v1 ?v0)))))
))
(let (($x62 (and $x52 $x59)))
(let (($x204 (not $x6)))
(let (($x233 (or $x204 $x62)))
(and $x233 $x232)))))))))))))))
))
(let (($x52 (not $x51)))
(let (($x62 (and $x52 $x59)))
(let (($x233 (or $x204 $x62)))
(let (($x256 (and $x233 $x251)))
(let (($x215 (not $x52)))
(let (($x228 (or $x215 $x224)))
(let (($x232 (or $x6 $x228)))
(let (($x234 (and $x233 $x232)))
(let ((@x250 (monotonicity (monotonicity (rewrite (= $x215 $x51)) (= $x228 (or $x51 $x224))) (= $x232 (or $x6 (or $x51 $x224))))))
(let ((@x255 (trans @x250 (rewrite (= (or $x6 (or $x51 $x224)) $x251)) (= $x232 $x251))))
(let (($x171 (forall ((?v0 |Nat$|) )(let (($x59 (forall ((?v1 |Nat$|) )(let ((?x12 (|nat$| 1)))
(let (($x13 (= ?v1 ?x12)))
(or (not (|dvd$| ?v1 ?v0)) $x13 (= ?v1 ?v0)))))
))
(let ((?x8 (|of_nat$| ?v0)))
(let (($x51 (<= ?x8 1)))
(let (($x52 (not $x51)))
(let (($x62 (and $x52 $x59)))
(let (($x6 (|prime_nat$| ?v0)))
(= $x6 $x62))))))))
))
(let ((@x231 (|nnf-neg| (refl (|~| $x215 $x215)) (sk (|~| $x225 $x224)) (|~| (not $x62) $x228))))
(let ((@x214 (monotonicity (refl (|~| $x52 $x52)) (|nnf-pos| (refl (|~| $x56 $x56)) (|~| $x59 $x59)) (|~| $x62 $x62))))
(let ((@x236 (|nnf-pos| (refl (|~| $x6 $x6)) (refl (|~| $x204 $x204)) @x214 @x231 (|~| (= $x6 $x62) $x234))))
(let (($x68 (forall ((?v0 |Nat$|) )(let (($x59 (forall ((?v1 |Nat$|) )(let ((?x12 (|nat$| 1)))
(let (($x13 (= ?v1 ?x12)))
(or (not (|dvd$| ?v1 ?v0)) $x13 (= ?v1 ?v0)))))
))
(let ((?x8 (|of_nat$| ?v0)))
(let (($x51 (<= ?x8 1)))
(let (($x52 (not $x51)))
(let (($x62 (and $x52 $x59)))
(let (($x6 (|prime_nat$| ?v0)))
(= $x6 $x62))))))))
))
(let ((@x173 (|quant-intro| (rewrite (= (= $x6 $x62) (= $x6 $x62))) (= $x68 $x171))))
(let (($x20 (forall ((?v0 |Nat$|) )(let (($x17 (forall ((?v1 |Nat$|) )(let (($x11 (|dvd$| ?v1 ?v0)))
(=> $x11 (or (= ?v1 (|nat$| 1)) (= ?v1 ?v0)))))
))
(let (($x6 (|prime_nat$| ?v0)))
(= $x6 (and (< 1 (|of_nat$| ?v0)) $x17)))))
))
(let (($x65 (= $x6 $x62)))
(let (($x17 (forall ((?v1 |Nat$|) )(let (($x11 (|dvd$| ?v1 ?0)))
(=> $x11 (or (= ?v1 (|nat$| 1)) (= ?v1 ?0)))))
))
(let ((@x61 (|quant-intro| (rewrite (= (=> (|dvd$| ?0 ?1) (or $x13 (= ?0 ?1))) $x56)) (= $x17 $x59))))
(let ((@x64 (monotonicity (rewrite (= (< 1 ?x8) $x52)) @x61 (= (and (< 1 ?x8) $x17) $x62))))
(let ((@x70 (|quant-intro| (monotonicity @x64 (= (= $x6 (and (< 1 ?x8) $x17)) $x65)) (= $x20 $x68))))
(let ((@x176 (mp (mp (mp (asserted $x20) @x70 $x68) (|rewrite*| (= $x68 $x68)) $x68) @x173 $x171)))
(let ((@x241 (mp (|mp~| @x176 (|nnf-pos| @x236 (|~| $x171 $x237)) $x237) (|quant-intro| (monotonicity @x255 (= $x234 $x256)) (= $x237 $x259)) $x259)))
(let ((@x691 ((_ |quant-inst| (|nat$| ?x72)) (or (not $x742) (not (or $x707 (not (or $x78 $x384 (not $x703)))))))))
(let ((@x572 (|unit-resolution| @x691 (mp (mp @x241 (|quant-intro| @x293 (= $x259 $x294)) $x294) @x744 $x742) (not (or $x707 (not (or $x78 $x384 (not $x703))))))))
(let ((@x573 (|unit-resolution| (|def-axiom| (or (or $x707 (not (or $x78 $x384 (not $x703)))) $x374)) @x572 $x374)))
(let (($x28 (<= 1 ?x23)))
(let (($x29 (=> (|prime_nat$| (|nat$| (+ ?x24 1))) $x28)))
(let (($x30 (not $x29)))
(let ((@x77 (monotonicity (rewrite (= (+ ?x24 1) ?x72)) (= (|nat$| (+ ?x24 1)) ?x75))))
(let ((@x85 (monotonicity (monotonicity @x77 (= (|prime_nat$| (|nat$| (+ ?x24 1))) $x78)) (rewrite (= $x28 $x28)) (= $x29 (=> $x78 $x28)))))
(let ((@x91 (trans @x85 (rewrite (= (=> $x78 $x28) (or $x86 $x28))) (= $x29 (or $x86 $x28)))))
(let ((@x95 (mp (asserted $x30) (monotonicity @x91 (= $x30 (not (or $x86 $x28)))) (not (or $x86 $x28)))))
(let ((@x575 (|unit-resolution| (|def-axiom| (or $x707 $x86 $x373)) (mp (|not-or-elim| @x95 $x78) (|rewrite*| (= $x78 $x78)) $x78) (or $x707 $x373))))
(let ((@x577 (|unit-resolution| (|def-axiom| (or (or $x384 (not $x705)) (not $x384))) (|unit-resolution| @x575 @x573 $x373) (not $x384))))
(let ((@x534 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not (<= ?x299 0)) $x384)) @x577 (not (<= ?x299 0)))))
(let ((@x565 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x299 0)) (<= ?x299 0))) @x534 (not (= ?x299 0)))))
(let (($x579 (= ?x299 0)))
(let (($x581 (or $x614 $x579)))
(let (($x760 (forall ((?v0 Int) )(!(let (($x43 (= (|of_nat$| (|nat$| ?v0)) 0)))
(let (($x178 (>= ?v0 0)))
(or $x178 $x43))) :pattern ( (|nat$| ?v0) )))
))
(let (($x192 (forall ((?v0 Int) )(let (($x43 (= (|of_nat$| (|nat$| ?v0)) 0)))
(let (($x178 (>= ?v0 0)))
(or $x178 $x43))))
))
(let (($x43 (= (|of_nat$| (|nat$| ?0)) 0)))
(let (($x178 (>= ?0 0)))
(let (($x189 (or $x178 $x43)))
(let (($x125 (forall ((?v0 Int) )(let (($x43 (= (|of_nat$| (|nat$| ?v0)) 0)))
(let (($x36 (<= 0 ?v0)))
(or $x36 $x43))))
))
(let ((@x191 (monotonicity (rewrite (= (<= 0 ?0) $x178)) (= (or (<= 0 ?0) $x43) $x189))))
(let (($x45 (forall ((?v0 Int) )(let (($x43 (= (|of_nat$| (|nat$| ?v0)) 0)))
(=> (< ?v0 0) $x43)))
))
(let ((@x122 (rewrite (= (=> (not (<= 0 ?0)) $x43) (or (<= 0 ?0) $x43)))))
(let ((@x115 (monotonicity (rewrite (= (<= 0 ?0) (<= 0 ?0))) (= (not (<= 0 ?0)) (not (<= 0 ?0))))))
(let ((@x116 (trans (rewrite (= (< ?0 0) (not (<= 0 ?0)))) @x115 (= (< ?0 0) (not (<= 0 ?0))))))
(let ((@x119 (monotonicity @x116 (= (=> (< ?0 0) $x43) (=> (not (<= 0 ?0)) $x43)))))
(let ((@x124 (trans @x119 @x122 (= (=> (< ?0 0) $x43) (or (<= 0 ?0) $x43)))))
(let ((@x143 (mp (mp (asserted $x45) (|quant-intro| @x124 (= $x45 $x125)) $x125) (|rewrite*| (= $x125 $x125)) $x125)))
(let ((@x275 (|mp~| (mp @x143 (|quant-intro| @x191 (= $x125 $x192)) $x192) (|nnf-pos| (refl (|~| $x189 $x189)) (|~| $x192 $x192)) $x192)))
(let (($x584 (not $x760)))
(let (($x585 (or $x584 $x614 $x579)))
(let ((@x583 (monotonicity (rewrite (= (>= ?x72 0) $x614)) (= (or (>= ?x72 0) $x579) $x581))))
(let ((@x559 (monotonicity @x583 (= (or $x584 (or (>= ?x72 0) $x579)) (or $x584 $x581)))))
(let ((@x568 (trans @x559 (rewrite (= (or $x584 $x581) $x585)) (= (or $x584 (or (>= ?x72 0) $x579)) $x585))))
(let ((@x533 (|unit-resolution| (mp ((_ |quant-inst| (+ 1 ?x24)) (or $x584 (or (>= ?x72 0) $x579))) @x568 $x585) (mp @x275 (|quant-intro| (refl (= $x189 $x189)) (= $x192 $x760)) $x760) $x581)))
(let (($x617 (not $x614)))
(let (($x604 (or $x617 $x601)))
(let (($x754 (forall ((?v0 Int) )(!(let (($x39 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x39)) :pattern ( (|nat$| ?v0) )))
))
(let (($x185 (forall ((?v0 Int) )(let (($x39 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x39)))
))
(let (($x39 (= (|of_nat$| (|nat$| ?0)) ?0)))
(let (($x182 (or (not $x178) $x39)))
(let (($x108 (forall ((?v0 Int) )(let (($x39 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(let (($x36 (<= 0 ?v0)))
(let (($x103 (not $x36)))
(or $x103 $x39)))))
))
(let ((@x181 (monotonicity (rewrite (= (<= 0 ?0) $x178)) (= (not (<= 0 ?0)) (not $x178)))))
(let ((@x187 (|quant-intro| (monotonicity @x181 (= (or (not (<= 0 ?0)) $x39) $x182)) (= $x108 $x185))))
(let (($x41 (forall ((?v0 Int) )(let (($x39 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(let (($x36 (<= 0 ?v0)))
(=> $x36 $x39))))
))
(let ((@x106 (rewrite (= (=> (<= 0 ?0) $x39) (or (not (<= 0 ?0)) $x39)))))
(let ((@x102 (monotonicity (rewrite (= (<= 0 ?0) (<= 0 ?0))) (= (=> (<= 0 ?0) $x39) (=> (<= 0 ?0) $x39)))))
(let ((@x107 (trans @x102 @x106 (= (=> (<= 0 ?0) $x39) (or (not (<= 0 ?0)) $x39)))))
(let ((@x140 (mp (mp (asserted $x41) (|quant-intro| @x107 (= $x41 $x108)) $x108) (|rewrite*| (= $x108 $x108)) $x108)))
(let ((@x270 (|mp~| (mp @x140 @x187 $x185) (|nnf-pos| (refl (|~| $x182 $x182)) (|~| $x185 $x185)) $x185)))
(let (($x607 (not $x754)))
(let (($x608 (or $x607 $x617 $x601)))
(let (($x609 (or $x607 (or (not (>= ?x72 0)) (= ?x299 ?x72)))))
(let ((@x598 (monotonicity (rewrite (= (>= ?x72 0) $x614)) (= (not (>= ?x72 0)) $x617))))
(let ((@x606 (monotonicity @x598 (rewrite (= (= ?x299 ?x72) $x601)) (= (or (not (>= ?x72 0)) (= ?x299 ?x72)) $x604))))
(let ((@x594 (trans (monotonicity @x606 (= $x609 (or $x607 $x604))) (rewrite (= (or $x607 $x604) $x608)) (= $x609 $x608))))
(let ((@x498 (|unit-resolution| (mp ((_ |quant-inst| (+ 1 ?x24)) $x609) @x594 $x608) (mp @x270 (|quant-intro| (refl (= $x182 $x182)) (= $x185 $x754)) $x754) $x604)))
(let ((@x542 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x601) (>= (+ ?x24 (* (~ 1) ?x299)) (~ 1)))) (|unit-resolution| @x498 (|unit-resolution| @x533 @x565 $x614) $x601) (>= (+ ?x24 (* (~ 1) ?x299)) (~ 1)))))
(let ((@x201 (monotonicity (rewrite (= $x28 (>= ?x23 1))) (= (not $x28) (not (>= ?x23 1))))))
(let (($x97 (not $x28)))
(let ((@x152 (mp (mp (|not-or-elim| @x95 $x97) (|rewrite*| (= $x97 $x97)) $x97) (monotonicity (rewrite (= $x28 $x28)) (= $x97 $x97)) $x97)))
(let ((@x153 (mp @x152 (monotonicity (rewrite (= $x28 $x28)) (= $x97 $x97)) $x97)))
((_ |th-lemma| arith farkas -4 1 1) (mp @x153 @x201 (not (>= ?x23 1))) @x577 @x542 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
382f4199d494d0df860c17de3f08dc5bef5af830 20 0
unsat
((set-logic AUFLIA)
(proof
(let (($x17 (= |x$| |a$|)))
(let ((?x14 (|fst$| (|pair$| |x$| |y$|))))
(let (($x16 (= ?x14 |a$|)))
(let ((@x28 (monotonicity (rewrite (= (=> $x16 $x17) (or (not $x16) $x17))) (= (not (=> $x16 $x17)) (not (or (not $x16) $x17))))))
(let ((@x30 (|not-or-elim| (mp (asserted (not (=> $x16 $x17))) @x28 (not (or (not $x16) $x17))) $x16)))
(let (($x484 (forall ((?v0 |A$|) (?v1 |B$|) )(!(= (|fst$| (|pair$| ?v0 ?v1)) ?v0) :pattern ( (|pair$| ?v0 ?v1) )))
))
(let (($x10 (forall ((?v0 |A$|) (?v1 |B$|) )(= (|fst$| (|pair$| ?v0 ?v1)) ?v0))
))
(let (($x9 (= (|fst$| (|pair$| ?1 ?0)) ?1)))
(let ((@x61 (|mp~| (mp (asserted $x10) (|rewrite*| (= $x10 $x10)) $x10) (|nnf-pos| (refl (|~| $x9 $x9)) (|~| $x10 $x10)) $x10)))
(let ((@x153 (|unit-resolution| ((_ |quant-inst| |x$| |y$|) (or (not $x484) (= ?x14 |x$|))) (mp @x61 (|quant-intro| (refl (= $x9 $x9)) (= $x10 $x484)) $x484) (= ?x14 |x$|))))
(let ((@x156 (trans (symm @x153 (= |x$| ?x14)) (mp @x30 (|rewrite*| (= $x16 $x16)) $x16) $x17)))
(let (($x31 (not $x17)))
(let ((@x32 (|not-or-elim| (mp (asserted (not (=> $x16 $x17))) @x28 (not (or (not $x16) $x17))) $x31)))
(|unit-resolution| (mp @x32 (|rewrite*| (= $x31 $x31)) $x31) @x156 false))))))))))))))))
2e6ad6073b328dff58f57dea99b605ad0bcd9bbc 32 0
unsat
((set-logic AUFLIA)
(proof
(let ((?x33 (|snd$a| |p2$|)))
(let ((?x32 (|fst$a| |p1$|)))
(let (($x34 (= ?x32 ?x33)))
(let (($x30 (= |p2$| (|pair$| |y$| |x$|))))
(let (($x27 (= |p1$| (|pair$a| |x$| |y$|))))
(let (($x31 (and $x27 $x30)))
(let ((@x48 (monotonicity (rewrite (= (=> $x31 $x34) (or (not $x31) $x34))) (= (not (=> $x31 $x34)) (not (or (not $x31) $x34))))))
(let ((@x50 (|not-or-elim| (mp (asserted (not (=> $x31 $x34))) @x48 (not (or (not $x31) $x34))) $x31)))
(let ((@x531 (monotonicity (mp (|and-elim| @x50 $x30) (|rewrite*| (= $x30 $x30)) $x30) (= ?x33 (|snd$a| (|pair$| |y$| |x$|))))))
(let (($x552 (forall ((?v0 |B$|) (?v1 |A$|) )(!(= (|snd$a| (|pair$| ?v0 ?v1)) ?v1) :pattern ( (|pair$| ?v0 ?v1) )))
))
(let (($x22 (forall ((?v0 |B$|) (?v1 |A$|) )(= (|snd$a| (|pair$| ?v0 ?v1)) ?v1))
))
(let (($x21 (= (|snd$a| (|pair$| ?1 ?0)) ?0)))
(let ((@x114 (|mp~| (mp (asserted $x22) (|rewrite*| (= $x22 $x22)) $x22) (|nnf-pos| (refl (|~| $x21 $x21)) (|~| $x22 $x22)) $x22)))
(let ((@x520 (|unit-resolution| ((_ |quant-inst| |y$| |x$|) (or (not $x552) (= (|snd$a| (|pair$| |y$| |x$|)) |x$|))) (mp @x114 (|quant-intro| (refl (= $x21 $x21)) (= $x22 $x552)) $x552) (= (|snd$a| (|pair$| |y$| |x$|)) |x$|))))
(let (($x540 (forall ((?v0 |A$|) (?v1 |B$|) )(!(= (|fst$a| (|pair$a| ?v0 ?v1)) ?v0) :pattern ( (|pair$a| ?v0 ?v1) )))
))
(let (($x16 (forall ((?v0 |A$|) (?v1 |B$|) )(= (|fst$a| (|pair$a| ?v0 ?v1)) ?v0))
))
(let (($x15 (= (|fst$a| (|pair$a| ?1 ?0)) ?1)))
(let ((@x108 (|mp~| (mp (asserted $x16) (|rewrite*| (= $x16 $x16)) $x16) (|nnf-pos| (refl (|~| $x15 $x15)) (|~| $x16 $x16)) $x16)))
(let ((@x192 (|unit-resolution| ((_ |quant-inst| |x$| |y$|) (or (not $x540) (= (|fst$a| (|pair$a| |x$| |y$|)) |x$|))) (mp @x108 (|quant-intro| (refl (= $x15 $x15)) (= $x16 $x540)) $x540) (= (|fst$a| (|pair$a| |x$| |y$|)) |x$|))))
(let ((@x529 (monotonicity (mp (|and-elim| @x50 $x27) (|rewrite*| (= $x27 $x27)) $x27) (= ?x32 (|fst$a| (|pair$a| |x$| |y$|))))))
(let ((@x507 (trans (trans @x529 @x192 (= ?x32 |x$|)) (symm @x520 (= |x$| (|snd$a| (|pair$| |y$| |x$|)))) (= ?x32 (|snd$a| (|pair$| |y$| |x$|))))))
(let (($x53 (not $x34)))
(let ((@x54 (|not-or-elim| (mp (asserted (not (=> $x31 $x34))) @x48 (not (or (not $x31) $x34))) $x53)))
(|unit-resolution| (mp @x54 (|rewrite*| (= $x53 $x53)) $x53) (trans @x507 (symm @x531 (= (|snd$a| (|pair$| |y$| |x$|)) ?x33)) $x34) false))))))))))))))))))))))))))
aeb8771903a6c70ea67dddc8b5f3cfb927335a01 42 0
unsat
((set-logic AUFLIA)
(proof
(let ((?x41 (|fun_app$b| (|fun_upd$| (|fun_app$a| (|fun_app$b| (|fun_upd$| |f$|) |i1$|) |v1$|)) |i2$|)))
(let ((?x44 (|fun_app$| (|fun_app$a| ?x41 |v2$|) |i$|)))
(let (($x46 (= ?x44 (|fun_app$| |f$| |i$|))))
(let ((?x39 (|fun_app$a| (|fun_app$b| (|fun_upd$| |f$|) |i1$|) |v1$|)))
(let ((?x209 (|fun_app$| ?x39 |i$|)))
(let (($x217 (= ?x209 (|fun_app$| |f$| |i$|))))
(let (($x29 (= |i$| |i1$|)))
(let (($x496 (ite $x29 (= ?x209 |v1$|) $x217)))
(let (($x543 (forall ((?v0 |A_b_fun$|) (?v1 |A$|) (?v2 |B$|) (?v3 |A$|) )(!(let ((?x21 (|fun_app$| (|fun_app$a| (|fun_app$b| (|fun_upd$| ?v0) ?v1) ?v2) ?v3)))
(ite (= ?v3 ?v1) (= ?x21 ?v2) (= ?x21 (|fun_app$| ?v0 ?v3)))) :pattern ( (|fun_app$| (|fun_app$a| (|fun_app$b| (|fun_upd$| ?v0) ?v1) ?v2) ?v3) )))
))
(let (($x114 (forall ((?v0 |A_b_fun$|) (?v1 |A$|) (?v2 |B$|) (?v3 |A$|) )(let ((?x21 (|fun_app$| (|fun_app$a| (|fun_app$b| (|fun_upd$| ?v0) ?v1) ?v2) ?v3)))
(ite (= ?v3 ?v1) (= ?x21 ?v2) (= ?x21 (|fun_app$| ?v0 ?v3)))))
))
(let ((?x21 (|fun_app$| (|fun_app$a| (|fun_app$b| (|fun_upd$| ?3) ?2) ?1) ?0)))
(let (($x111 (ite (= ?0 ?2) (= ?x21 ?1) (= ?x21 (|fun_app$| ?3 ?0)))))
(let (($x26 (forall ((?v0 |A_b_fun$|) (?v1 |A$|) (?v2 |B$|) (?v3 |A$|) )(let ((?x21 (|fun_app$| (|fun_app$a| (|fun_app$b| (|fun_upd$| ?v0) ?v1) ?v2) ?v3)))
(= ?x21 (ite (= ?v3 ?v1) ?v2 (|fun_app$| ?v0 ?v3)))))
))
(let ((@x113 (rewrite (= (= ?x21 (ite (= ?0 ?2) ?1 (|fun_app$| ?3 ?0))) $x111))))
(let (($x25 (= ?x21 (ite (= ?0 ?2) ?1 (|fun_app$| ?3 ?0)))))
(let ((@x108 (|mp~| (mp (asserted $x26) (|rewrite*| (= $x26 $x26)) $x26) (|nnf-pos| (refl (|~| $x25 $x25)) (|~| $x26 $x26)) $x26)))
(let ((@x548 (mp (mp @x108 (|quant-intro| @x113 (= $x26 $x114)) $x114) (|quant-intro| (refl (= $x111 $x111)) (= $x114 $x543)) $x543)))
(let (($x30 (not $x29)))
(let (($x32 (= |i$| |i2$|)))
(let (($x33 (not $x32)))
(let (($x34 (and $x30 $x33)))
(let ((@x58 (monotonicity (rewrite (= (=> $x34 $x46) (or (not $x34) $x46))) (= (not (=> $x34 $x46)) (not (or (not $x34) $x46))))))
(let ((@x60 (|not-or-elim| (mp (asserted (not (=> $x34 $x46))) @x58 (not (or (not $x34) $x46))) $x34)))
(let ((@x333 (|unit-resolution| (|def-axiom| (or (not $x496) $x29 $x217)) (mp (|and-elim| @x60 $x30) (|rewrite*| (= $x30 $x30)) $x30) (or (not $x496) $x217))))
(let ((@x334 (|unit-resolution| @x333 (|unit-resolution| ((_ |quant-inst| |f$| |i1$| |v1$| |i$|) (or (not $x543) $x496)) @x548 $x496) $x217)))
(let (($x212 (= ?x44 ?x209)))
(let (($x191 (ite $x32 (= ?x44 |v2$|) $x212)))
(let ((@x478 (|unit-resolution| (|def-axiom| (or (not $x191) $x32 $x212)) (mp (|and-elim| @x60 $x33) (|rewrite*| (= $x33 $x33)) $x33) (or (not $x191) $x212))))
(let ((@x479 (|unit-resolution| @x478 (|unit-resolution| ((_ |quant-inst| (|fun_app$a| (|fun_app$b| (|fun_upd$| |f$|) |i1$|) |v1$|) |i2$| |v2$| |i$|) (or (not $x543) $x191)) @x548 $x191) $x212)))
(let (($x63 (not $x46)))
(let ((@x64 (|not-or-elim| (mp (asserted (not (=> $x34 $x46))) @x58 (not (or (not $x34) $x46))) $x63)))
(|unit-resolution| (mp @x64 (|rewrite*| (= $x63 $x63)) $x63) (trans @x479 @x334 $x46) false))))))))))))))))))))))))))))))))))
c4b4af33aa30da357345c646af342edc4d415cfd 19 0
unsat
((set-logic AUFLIA)
(proof
(let (($x8 (|fun_app$| |g$| |x$|)))
(let (($x7 (|f$| |g$| |x$|)))
(let (($x33 (not $x7)))
(let (($x34 (= $x33 $x8)))
(let ((@x49 (monotonicity (rewrite (= (= $x8 true) $x8)) (= (not (= $x8 true)) (not $x8)))))
(let (($x10 (= $x7 (and $x8 true))))
(let (($x15 (not (or $x10 (or (= $x7 true) (= $x8 true))))))
(let ((@x20 (|not-or-elim| (asserted $x15) (not (or (= $x7 true) (= $x8 true))))))
(let ((@x56 (|iff-false| (mp (|not-or-elim| @x20 (not (= $x8 true))) @x49 (not $x8)) (= $x8 false))))
(let ((@x43 (monotonicity (rewrite (= (= $x7 true) $x7)) (= (not (= $x7 true)) $x33))))
(let ((@x52 (|iff-true| (mp (|not-or-elim| @x20 (not (= $x7 true))) @x43 $x33) (= $x33 true))))
(let ((@x61 (trans (monotonicity @x52 @x56 (= $x34 (= true false))) (rewrite (= (= true false) false)) (= $x34 false))))
(let ((@x29 (monotonicity (rewrite (= (and $x8 true) $x8)) (= $x10 (= $x7 $x8)))))
(let ((@x38 (trans (monotonicity @x29 (= (not $x10) (not (= $x7 $x8)))) (rewrite (= (not (= $x7 $x8)) $x34)) (= (not $x10) $x34))))
(mp (mp (|not-or-elim| (asserted $x15) (not $x10)) @x38 $x34) @x61 false)))))))))))))))))
fb8b7f74f922a8d00662632480052b1430519f93 12 0
unsat
((set-logic AUFLIA)
(proof
(let (($x7 (exists ((?v0 |A$|) )(|g$| ?v0))
))
(let (($x10 (=> (|f$| (ite $x7 true false)) true)))
(let (($x11 (not $x10)))
(let ((@x17 (monotonicity (rewrite (= (ite $x7 true false) $x7)) (= (|f$| (ite $x7 true false)) (|f$| $x7)))))
(let ((@x24 (trans (monotonicity @x17 (= $x10 (=> (|f$| $x7) true))) (rewrite (= (=> (|f$| $x7) true) true)) (= $x10 true))))
(let ((@x31 (trans (monotonicity @x24 (= $x11 (not true))) (rewrite (= (not true) false)) (= $x11 false))))
(mp (asserted $x11) @x31 false)))))))))
d62e2b1dea713f6de1a49810c6dcc90c07962d7b 12 0
unsat
((set-logic AUFLIA)
(proof
(let (($x7 (forall ((?v0 |A$|) )(|g$| ?v0))
))
(let (($x10 (=> (|f$| (ite $x7 true false)) true)))
(let (($x11 (not $x10)))
(let ((@x17 (monotonicity (rewrite (= (ite $x7 true false) $x7)) (= (|f$| (ite $x7 true false)) (|f$| $x7)))))
(let ((@x24 (trans (monotonicity @x17 (= $x10 (=> (|f$| $x7) true))) (rewrite (= (=> (|f$| $x7) true) true)) (= $x10 true))))
(let ((@x31 (trans (monotonicity @x24 (= $x11 (not true))) (rewrite (= (not true) false)) (= $x11 false))))
(mp (asserted $x11) @x31 false)))))))))
95d5c3c67c271c191a1aa0777fcf993d700adecd 43 0
unsat
((set-logic AUFLIA)
(proof
(let (($x19 (|fun_app$| (|fun_app$a| |le$| 3) 42)))
(let (($x33 (not $x19)))
(let (($x15 (= |le$| |uu$|)))
(let ((@x30 (monotonicity (rewrite (= (=> $x15 $x19) (or (not $x15) $x19))) (= (not (=> $x15 $x19)) (not (or (not $x15) $x19))))))
(let ((@x32 (|not-or-elim| (mp (asserted (not (=> $x15 $x19))) @x30 (not (or (not $x15) $x19))) $x15)))
(let ((@x487 (monotonicity (symm (mp @x32 (|rewrite*| (= $x15 $x15)) $x15) (= |uu$| |le$|)) (= (|fun_app$a| |uu$| 3) (|fun_app$a| |le$| 3)))))
(let ((@x489 (symm (monotonicity @x487 (= (|fun_app$| (|fun_app$a| |uu$| 3) 42) $x19)) (= $x19 (|fun_app$| (|fun_app$a| |uu$| 3) 42)))))
(let ((@x477 (monotonicity @x489 (= $x33 (not (|fun_app$| (|fun_app$a| |uu$| 3) 42))))))
(let ((@x34 (|not-or-elim| (mp (asserted (not (=> $x15 $x19))) @x30 (not (or (not $x15) $x19))) $x33)))
(let ((@x195 (mp (mp @x34 (|rewrite*| (= $x33 $x33)) $x33) @x477 (not (|fun_app$| (|fun_app$a| |uu$| 3) 42)))))
(let (($x174 (|fun_app$| (|fun_app$a| |uu$| 3) 42)))
(let (($x78 (forall ((?v0 Int) (?v1 Int) )(!(let (($x9 (|fun_app$| (|fun_app$a| |uu$| ?v0) ?v1)))
(= $x9 (<= (+ ?v0 (* (~ 1) ?v1)) 0))) :pattern ( (|fun_app$| (|fun_app$a| |uu$| ?v0) ?v1) )))
))
(let (($x9 (|fun_app$| (|fun_app$a| |uu$| ?1) ?0)))
(let (($x75 (= $x9 (<= (+ ?1 (* (~ 1) ?0)) 0))))
(let (($x13 (forall ((?v0 Int) (?v1 Int) )(!(let (($x10 (<= ?v0 ?v1)))
(let (($x9 (|fun_app$| (|fun_app$a| |uu$| ?v0) ?v1)))
(= $x9 $x10))) :pattern ( (|fun_app$| (|fun_app$a| |uu$| ?v0) ?v1) )))
))
(let (($x66 (forall ((?v0 Int) (?v1 Int) )(!(let (($x10 (<= ?v0 ?v1)))
(let (($x9 (|fun_app$| (|fun_app$a| |uu$| ?v0) ?v1)))
(= $x9 $x10))) :pattern ( (|fun_app$| (|fun_app$a| |uu$| ?v0) ?v1) )))
))
(let ((@x77 (monotonicity (rewrite (= (<= ?1 ?0) (<= (+ ?1 (* (~ 1) ?0)) 0))) (= (= $x9 (<= ?1 ?0)) $x75))))
(let ((@x68 (|quant-intro| (rewrite (= (= $x9 (<= ?1 ?0)) (= $x9 (<= ?1 ?0)))) (= $x13 $x66))))
(let ((@x83 (mp (mp (asserted $x13) (|rewrite*| (= $x13 $x13)) $x13) (trans @x68 (|quant-intro| @x77 (= $x66 $x78)) (= $x13 $x78)) $x78)))
(let (($x140 (or (not $x78) $x174)))
(let (($x143 (= (or (not $x78) (= $x174 (<= (+ 3 (* (~ 1) 42)) 0))) $x140)))
(let ((?x176 (+ 3 (* (~ 1) 42))))
(let (($x166 (<= ?x176 0)))
(let (($x177 (= $x174 $x166)))
(let ((@x495 (monotonicity (rewrite (= (* (~ 1) 42) (~ 42))) (= ?x176 (+ 3 (~ 42))))))
(let ((@x498 (monotonicity (trans @x495 (rewrite (= (+ 3 (~ 42)) (~ 39))) (= ?x176 (~ 39))) (= $x166 (<= (~ 39) 0)))))
(let ((@x502 (trans @x498 (rewrite (= (<= (~ 39) 0) true)) (= $x166 true))))
(let ((@x137 (trans (monotonicity @x502 (= $x177 (= $x174 true))) (rewrite (= (= $x174 true) $x174)) (= $x177 $x174))))
(let ((@x483 (mp ((_ |quant-inst| 3 42) (or (not $x78) $x177)) (trans (monotonicity @x137 $x143) (rewrite (= $x140 $x140)) $x143) $x140)))
(let ((@x484 (|unit-resolution| @x483 (|mp~| @x83 (|nnf-pos| (refl (|~| $x75 $x75)) (|~| $x78 $x78)) $x78) $x174)))
(|unit-resolution| @x484 @x195 false)))))))))))))))))))))))))))))))))
7fbbdb30adaccd1cbc0fc92d3a2f74bf98a088ab 143 0
unsat
((set-logic AUFLIA)
(proof
(let ((?x37 (|nat$| 2)))
(let ((?x38 (|cons$| ?x37 |nil$|)))
(let ((?x32 (|nat$| 1)))
(let ((?x39 (|cons$| ?x32 ?x38)))
(let ((?x33 (|cons$| ?x32 |nil$|)))
(let ((?x285 (|map$| |uu$| ?x33)))
(let ((?x31 (|nat$| 0)))
(let ((?x284 (|fun_app$| |uu$| ?x31)))
(let ((?x286 (|cons$| ?x284 ?x285)))
(let (($x619 (forall ((?v0 |Nat_nat_fun$|) (?v1 |Nat$|) (?v2 |Nat_list$|) )(!(= (|map$| ?v0 (|cons$| ?v1 ?v2)) (|cons$| (|fun_app$| ?v0 ?v1) (|map$| ?v0 ?v2))) :pattern ( (|map$| ?v0 (|cons$| ?v1 ?v2)) ) :pattern ( (|cons$| (|fun_app$| ?v0 ?v1) (|map$| ?v0 ?v2)) )))
))
(let (($x29 (forall ((?v0 |Nat_nat_fun$|) (?v1 |Nat$|) (?v2 |Nat_list$|) )(= (|map$| ?v0 (|cons$| ?v1 ?v2)) (|cons$| (|fun_app$| ?v0 ?v1) (|map$| ?v0 ?v2))))
))
(let (($x28 (= (|map$| ?2 (|cons$| ?1 ?0)) (|cons$| (|fun_app$| ?2 ?1) (|map$| ?2 ?0)))))
(let ((@x179 (|mp~| (mp (asserted $x29) (|rewrite*| (= $x29 $x29)) $x29) (|nnf-pos| (refl (|~| $x28 $x28)) (|~| $x29 $x29)) $x29)))
(let (($x545 (or (not $x619) (= ?x285 (|cons$| (|fun_app$| |uu$| ?x32) (|map$| |uu$| |nil$|))))))
(let ((@x378 (|unit-resolution| ((_ |quant-inst| |uu$| (|nat$| 1) |nil$|) $x545) (mp @x179 (|quant-intro| (refl (= $x28 $x28)) (= $x29 $x619)) $x619) (= ?x285 (|cons$| (|fun_app$| |uu$| ?x32) (|map$| |uu$| |nil$|))))))
(let ((@x335 (symm @x378 (= (|cons$| (|fun_app$| |uu$| ?x32) (|map$| |uu$| |nil$|)) ?x285))))
(let (($x611 (forall ((?v0 |Nat_nat_fun$|) )(!(= (|map$| ?v0 |nil$|) |nil$|) :pattern ( (|map$| ?v0 |nil$|) )))
))
(let (($x19 (forall ((?v0 |Nat_nat_fun$|) )(= (|map$| ?v0 |nil$|) |nil$|))
))
(let ((@x613 (refl (= (= (|map$| ?0 |nil$|) |nil$|) (= (|map$| ?0 |nil$|) |nil$|)))))
(let ((@x173 (refl (|~| (= (|map$| ?0 |nil$|) |nil$|) (= (|map$| ?0 |nil$|) |nil$|)))))
(let ((@x168 (|mp~| (mp (asserted $x19) (|rewrite*| (= $x19 $x19)) $x19) (|nnf-pos| @x173 (|~| $x19 $x19)) $x19)))
(let ((@x379 (|unit-resolution| ((_ |quant-inst| |uu$|) (or (not $x611) (= (|map$| |uu$| |nil$|) |nil$|))) (mp @x168 (|quant-intro| @x613 (= $x19 $x611)) $x611) (= (|map$| |uu$| |nil$|) |nil$|))))
(let (($x72 (forall ((?v0 |Nat$|) )(!(let ((?x7 (|fun_app$| |uu$| ?v0)))
(= ?x7 (|nat$| (+ 1 (|of_nat$| ?v0))))) :pattern ( (|fun_app$| |uu$| ?v0) )))
))
(let ((?x7 (|fun_app$| |uu$| ?0)))
(let (($x69 (= ?x7 (|nat$| (+ 1 (|of_nat$| ?0))))))
(let (($x14 (forall ((?v0 |Nat$|) )(!(let ((?x7 (|fun_app$| |uu$| ?v0)))
(= ?x7 (|nat$| (+ (|of_nat$| ?v0) 1)))) :pattern ( (|fun_app$| |uu$| ?v0) )))
))
(let ((@x68 (monotonicity (rewrite (= (+ (|of_nat$| ?0) 1) (+ 1 (|of_nat$| ?0)))) (= (|nat$| (+ (|of_nat$| ?0) 1)) (|nat$| (+ 1 (|of_nat$| ?0)))))))
(let ((@x71 (monotonicity @x68 (= (= ?x7 (|nat$| (+ (|of_nat$| ?0) 1))) $x69))))
(let ((@x108 (mp (mp (asserted $x14) (|quant-intro| @x71 (= $x14 $x72)) $x72) (|rewrite*| (= $x72 $x72)) $x72)))
(let (($x515 (or (not $x72) (= (|fun_app$| |uu$| ?x32) (|nat$| (+ 1 (|of_nat$| ?x32)))))))
(let ((@x225 (|unit-resolution| ((_ |quant-inst| (|nat$| 1)) $x515) (|mp~| @x108 (|nnf-pos| (refl (|~| $x69 $x69)) (|~| $x72 $x72)) $x72) (= (|fun_app$| |uu$| ?x32) (|nat$| (+ 1 (|of_nat$| ?x32)))))))
(let ((?x302 (|of_nat$| ?x32)))
(let ((?x537 (+ 1 ?x302)))
(let ((?x538 (|nat$| ?x537)))
(let (($x626 (forall ((?v0 |Nat$|) )(!(= (|nat$| (|of_nat$| ?v0)) ?v0) :pattern ( (|of_nat$| ?v0) )))
))
(let (($x44 (forall ((?v0 |Nat$|) )(= (|nat$| (|of_nat$| ?v0)) ?v0))
))
(let ((@x631 (trans (rewrite (= $x44 $x626)) (rewrite (= $x626 $x626)) (= $x44 $x626))))
(let ((@x180 (refl (|~| (= (|nat$| (|of_nat$| ?0)) ?0) (= (|nat$| (|of_nat$| ?0)) ?0)))))
(let ((@x184 (|mp~| (mp (asserted $x44) (|rewrite*| (= $x44 $x44)) $x44) (|nnf-pos| @x180 (|~| $x44 $x44)) $x44)))
(let ((@x384 (|unit-resolution| ((_ |quant-inst| (|nat$| ?x537)) (or (not $x626) (= (|nat$| (|of_nat$| ?x538)) ?x538))) (mp @x184 @x631 $x626) (= (|nat$| (|of_nat$| ?x538)) ?x538))))
(let ((?x431 (+ ?x302 (* (~ 1) (|of_nat$| ?x538)))))
(let (($x399 (= ?x431 (~ 1))))
(let (($x469 (>= ?x302 (~ 1))))
(let (($x463 (>= ?x302 1)))
(let (($x303 (= ?x302 1)))
(let (($x634 (forall ((?v0 Int) )(!(let (($x49 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x49)) :pattern ( (|nat$| ?v0) )))
))
(let (($x155 (forall ((?v0 Int) )(let (($x49 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x49)))
))
(let (($x49 (= (|of_nat$| (|nat$| ?0)) ?0)))
(let (($x152 (or (not (>= ?0 0)) $x49)))
(let (($x85 (forall ((?v0 Int) )(let (($x49 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (<= 0 ?v0)) $x49)))
))
(let ((@x151 (monotonicity (rewrite (= (<= 0 ?0) (>= ?0 0))) (= (not (<= 0 ?0)) (not (>= ?0 0))))))
(let ((@x157 (|quant-intro| (monotonicity @x151 (= (or (not (<= 0 ?0)) $x49) $x152)) (= $x85 $x155))))
(let (($x51 (forall ((?v0 Int) )(let (($x49 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(let (($x46 (<= 0 ?v0)))
(=> $x46 $x49))))
))
(let ((@x83 (rewrite (= (=> (<= 0 ?0) $x49) (or (not (<= 0 ?0)) $x49)))))
(let ((@x79 (monotonicity (rewrite (= (<= 0 ?0) (<= 0 ?0))) (= (=> (<= 0 ?0) $x49) (=> (<= 0 ?0) $x49)))))
(let ((@x84 (trans @x79 @x83 (= (=> (<= 0 ?0) $x49) (or (not (<= 0 ?0)) $x49)))))
(let ((@x123 (mp (mp (asserted $x51) (|quant-intro| @x84 (= $x51 $x85)) $x85) (|rewrite*| (= $x85 $x85)) $x85)))
(let ((@x189 (|mp~| (mp @x123 @x157 $x155) (|nnf-pos| (refl (|~| $x152 $x152)) (|~| $x155 $x155)) $x155)))
(let ((@x639 (mp @x189 (|quant-intro| (refl (= $x152 $x152)) (= $x155 $x634)) $x634)))
(let (($x248 (not $x634)))
(let (($x292 (or $x248 $x303)))
(let ((@x578 (monotonicity (rewrite (= (>= 1 0) true)) (= (not (>= 1 0)) (not true)))))
(let ((@x310 (trans @x578 (rewrite (= (not true) false)) (= (not (>= 1 0)) false))))
(let ((@x581 (monotonicity @x310 (= (or (not (>= 1 0)) $x303) (or false $x303)))))
(let ((@x291 (trans @x581 (rewrite (= (or false $x303) $x303)) (= (or (not (>= 1 0)) $x303) $x303))))
(let ((@x573 (monotonicity @x291 (= (or $x248 (or (not (>= 1 0)) $x303)) $x292))))
(let ((@x576 (trans @x573 (rewrite (= $x292 $x292)) (= (or $x248 (or (not (>= 1 0)) $x303)) $x292))))
(let ((@x562 (mp ((_ |quant-inst| 1) (or $x248 (or (not (>= 1 0)) $x303))) @x576 $x292)))
(let ((@x372 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x303) $x463)) (|unit-resolution| @x562 @x639 $x303) $x463)))
(let (($x472 (not $x469)))
(let (($x430 (or $x248 $x472 $x399)))
(let (($x432 (or $x248 (or (not (>= ?x537 0)) (= (|of_nat$| ?x538) ?x537)))))
(let (($x461 (= (or (not (>= ?x537 0)) (= (|of_nat$| ?x538) ?x537)) (or $x472 $x399))))
(let ((@x474 (monotonicity (rewrite (= (>= ?x537 0) $x469)) (= (not (>= ?x537 0)) $x472))))
(let ((@x436 (monotonicity (monotonicity @x474 (rewrite (= (= (|of_nat$| ?x538) ?x537) $x399)) $x461) (= $x432 (or $x248 (or $x472 $x399))))))
(let ((@x441 (trans @x436 (rewrite (= (or $x248 (or $x472 $x399)) $x430)) (= $x432 $x430))))
(let ((@x364 (|unit-resolution| (mp ((_ |quant-inst| (+ 1 ?x302)) $x432) @x441 $x430) @x639 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x463) $x469)) @x372 $x469) $x399)))
(let ((@x370 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x399) (<= ?x431 (~ 1)))) @x364 (<= ?x431 (~ 1)))))
(let ((@x351 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x399) (>= ?x431 (~ 1)))) @x364 (>= ?x431 (~ 1)))))
(let ((@x356 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x303) (<= ?x302 1))) (|unit-resolution| @x562 @x639 $x303) (<= ?x302 1))))
(let ((@x363 (symm ((_ |th-lemma| arith eq-propagate -1 -1 1 1) @x372 @x356 @x351 @x370 (= (|of_nat$| ?x538) 2)) (= 2 (|of_nat$| ?x538)))))
(let ((@x348 (trans (monotonicity @x363 (= ?x37 (|nat$| (|of_nat$| ?x538)))) @x384 (= ?x37 ?x538))))
(let ((@x350 (trans @x348 (symm @x225 (= ?x538 (|fun_app$| |uu$| ?x32))) (= ?x37 (|fun_app$| |uu$| ?x32)))))
(let ((@x333 (monotonicity @x350 (symm @x379 (= |nil$| (|map$| |uu$| |nil$|))) (= ?x38 (|cons$| (|fun_app$| |uu$| ?x32) (|map$| |uu$| |nil$|))))))
(let ((@x338 (|unit-resolution| ((_ |quant-inst| (|nat$| 0)) (or (not $x72) (= ?x284 (|nat$| (+ 1 (|of_nat$| ?x31)))))) (|mp~| @x108 (|nnf-pos| (refl (|~| $x69 $x69)) (|~| $x72 $x72)) $x72) (= ?x284 (|nat$| (+ 1 (|of_nat$| ?x31)))))))
(let ((?x598 (|of_nat$| ?x31)))
(let ((?x543 (+ 1 ?x598)))
(let ((?x544 (|nat$| ?x543)))
(let ((@x339 (|unit-resolution| ((_ |quant-inst| (|nat$| ?x543)) (or (not $x626) (= (|nat$| (|of_nat$| ?x544)) ?x544))) (mp @x184 @x631 $x626) (= (|nat$| (|of_nat$| ?x544)) ?x544))))
(let ((?x517 (|of_nat$| ?x544)))
(let ((?x512 (+ ?x517 (* (~ 1) ?x598))))
(let (($x513 (= ?x512 1)))
(let (($x520 (>= ?x598 (~ 1))))
(let (($x523 (>= ?x598 0)))
(let (($x270 (= ?x598 0)))
(let (($x249 (or $x248 $x270)))
(let ((@x608 (monotonicity (rewrite (= (>= 0 0) true)) (= (not (>= 0 0)) (not true)))))
(let ((@x262 (trans @x608 (rewrite (= (not true) false)) (= (not (>= 0 0)) false))))
(let ((@x601 (monotonicity @x262 (= (or (not (>= 0 0)) $x270) (or false $x270)))))
(let ((@x247 (trans @x601 (rewrite (= (or false $x270) $x270)) (= (or (not (>= 0 0)) $x270) $x270))))
(let ((@x589 (monotonicity @x247 (= (or $x248 (or (not (>= 0 0)) $x270)) $x249))))
(let ((@x592 (trans @x589 (rewrite (= $x249 $x249)) (= (or $x248 (or (not (>= 0 0)) $x270)) $x249))))
(let ((@x229 (mp ((_ |quant-inst| 0) (or $x248 (or (not (>= 0 0)) $x270))) @x592 $x249)))
(let ((@x344 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x270) $x523)) (|unit-resolution| @x229 @x639 $x270) $x523)))
(let (($x508 (not $x520)))
(let (($x498 (or $x248 $x508 $x513)))
(let (($x499 (or $x248 (or (not (>= ?x543 0)) (= ?x517 ?x543)))))
(let ((@x510 (monotonicity (rewrite (= (>= ?x543 0) $x520)) (= (not (>= ?x543 0)) $x508))))
(let ((@x497 (monotonicity @x510 (rewrite (= (= ?x517 ?x543) $x513)) (= (or (not (>= ?x543 0)) (= ?x517 ?x543)) (or $x508 $x513)))))
(let ((@x507 (trans (monotonicity @x497 (= $x499 (or $x248 (or $x508 $x513)))) (rewrite (= (or $x248 (or $x508 $x513)) $x498)) (= $x499 $x498))))
(let ((@x325 (|unit-resolution| (mp ((_ |quant-inst| (+ 1 ?x598)) $x499) @x507 $x498) @x639 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x523) $x520)) @x344 $x520) $x513)))
(let ((@x329 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x513) (<= ?x512 1))) @x325 (<= ?x512 1))))
(let ((@x316 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x513) (>= ?x512 1))) @x325 (>= ?x512 1))))
(let ((@x319 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x270) (<= ?x598 0))) (|unit-resolution| @x229 @x639 $x270) (<= ?x598 0))))
(let ((@x311 (monotonicity (symm ((_ |th-lemma| arith eq-propagate -1 -1 -1 -1) @x344 @x319 @x316 @x329 (= ?x517 1)) (= 1 ?x517)) (= ?x32 (|nat$| ?x517)))))
(let ((@x294 (trans (trans @x311 @x339 (= ?x32 ?x544)) (symm @x338 (= ?x544 ?x284)) (= ?x32 ?x284))))
(let ((@x300 (symm (monotonicity @x294 (trans @x333 @x335 (= ?x38 ?x285)) (= ?x39 ?x286)) (= ?x286 ?x39))))
(let ((@x295 (|unit-resolution| ((_ |quant-inst| |uu$| (|nat$| 0) (|cons$| ?x32 |nil$|)) (or (not $x619) (= (|map$| |uu$| (|cons$| ?x31 ?x33)) ?x286))) (mp @x179 (|quant-intro| (refl (= $x28 $x28)) (= $x29 $x619)) $x619) (= (|map$| |uu$| (|cons$| ?x31 ?x33)) ?x286))))
(let (($x41 (not (= (|map$| |uu$| (|cons$| ?x31 ?x33)) ?x39))))
(|unit-resolution| (mp (asserted $x41) (|rewrite*| (= $x41 $x41)) $x41) (trans @x295 @x300 (= (|map$| |uu$| (|cons$| ?x31 ?x33)) ?x39)) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
c2aa9b07a380b6b94c7b3a0cba48d13d4241c907 7 0
unsat
((set-logic AUFLIA)
(proof
(let (($x7 (forall ((?v0 |A$|) )(|p$| ?v0))
))
(|unit-resolution| (|not-or-elim| (asserted (not (or $x7 (not $x7)))) (not $x7)) (|not-or-elim| (asserted (not (or $x7 (not $x7)))) $x7) false))))
e807e5ca142c0da5a6842f0271c430bac373ca49 147 0
unsat
((set-logic AUFLIA)
(proof
(let ((?x24 (|nat$| 6)))
(let ((?x17 (|nat$| 4)))
(let ((?x18 (|dec_10$| ?x17)))
(let ((?x19 (|of_nat$| ?x18)))
(let ((?x20 (* 4 ?x19)))
(let ((?x21 (|nat$| ?x20)))
(let ((?x22 (|dec_10$| ?x21)))
(let ((?x496 (|dec_10$| ?x24)))
(let (($x456 (= ?x496 ?x24)))
(let ((?x522 (|of_nat$| ?x24)))
(let (($x495 (>= ?x522 10)))
(let (($x484 (ite $x495 (= ?x496 (|dec_10$| (|nat$| (+ (~ 10) ?x522)))) $x456)))
(let (($x637 (forall ((?v0 |Nat$|) )(!(let ((?x7 (|of_nat$| ?v0)))
(let (($x160 (>= ?x7 10)))
(ite $x160 (= (|dec_10$| ?v0) (|dec_10$| (|nat$| (+ (~ 10) ?x7)))) (= (|dec_10$| ?v0) ?v0)))) :pattern ( (|of_nat$| ?v0) ) :pattern ( (|dec_10$| ?v0) )))
))
(let (($x216 (forall ((?v0 |Nat$|) )(let ((?x7 (|of_nat$| ?v0)))
(let (($x160 (>= ?x7 10)))
(ite $x160 (= (|dec_10$| ?v0) (|dec_10$| (|nat$| (+ (~ 10) ?x7)))) (= (|dec_10$| ?v0) ?v0)))))
))
(let ((?x7 (|of_nat$| ?0)))
(let (($x160 (>= ?x7 10)))
(let (($x213 (ite $x160 (= (|dec_10$| ?0) (|dec_10$| (|nat$| (+ (~ 10) ?x7)))) (= (|dec_10$| ?0) ?0))))
(let (($x168 (forall ((?v0 |Nat$|) )(let ((?x77 (|dec_10$| (|nat$| (+ (~ 10) (|of_nat$| ?v0))))))
(let ((?x7 (|of_nat$| ?v0)))
(let (($x160 (>= ?x7 10)))
(let ((?x6 (|dec_10$| ?v0)))
(= ?x6 (ite $x160 ?x77 ?v0)))))))
))
(let ((?x6 (|dec_10$| ?0)))
(let (($x165 (= ?x6 (ite $x160 (|dec_10$| (|nat$| (+ (~ 10) ?x7))) ?0))))
(let (($x91 (forall ((?v0 |Nat$|) )(let ((?x77 (|dec_10$| (|nat$| (+ (~ 10) (|of_nat$| ?v0))))))
(let ((?x7 (|of_nat$| ?v0)))
(let (($x47 (<= 10 ?x7)))
(let ((?x83 (ite $x47 ?x77 ?v0)))
(let ((?x6 (|dec_10$| ?v0)))
(= ?x6 ?x83)))))))
))
(let ((?x77 (|dec_10$| (|nat$| (+ (~ 10) ?x7)))))
(let (($x47 (<= 10 ?x7)))
(let ((?x83 (ite $x47 ?x77 ?0)))
(let (($x88 (= ?x6 ?x83)))
(let ((@x167 (monotonicity (monotonicity (rewrite (= $x47 $x160)) (= ?x83 (ite $x160 ?x77 ?0))) (= $x88 $x165))))
(let (($x15 (forall ((?v0 |Nat$|) )(let ((?x13 (ite (< (|of_nat$| ?v0) 10) ?v0 (|dec_10$| (|nat$| (- (|of_nat$| ?v0) 10))))))
(let ((?x6 (|dec_10$| ?v0)))
(= ?x6 ?x13))))
))
(let (($x89 (= (= ?x6 (ite (< ?x7 10) ?0 (|dec_10$| (|nat$| (- ?x7 10))))) $x88)))
(let ((?x13 (ite (< ?x7 10) ?0 (|dec_10$| (|nat$| (- ?x7 10))))))
(let ((@x66 (monotonicity (rewrite (= (* (~ 1) 10) (~ 10))) (= (+ ?x7 (* (~ 1) 10)) (+ ?x7 (~ 10))))))
(let ((@x71 (trans @x66 (rewrite (= (+ ?x7 (~ 10)) (+ (~ 10) ?x7))) (= (+ ?x7 (* (~ 1) 10)) (+ (~ 10) ?x7)))))
(let ((@x73 (trans (rewrite (= (- ?x7 10) (+ ?x7 (* (~ 1) 10)))) @x71 (= (- ?x7 10) (+ (~ 10) ?x7)))))
(let ((@x79 (monotonicity (monotonicity @x73 (= (|nat$| (- ?x7 10)) (|nat$| (+ (~ 10) ?x7)))) (= (|dec_10$| (|nat$| (- ?x7 10))) ?x77))))
(let ((@x55 (trans (rewrite (= (< ?x7 10) (not $x47))) (monotonicity (rewrite (= $x47 $x47)) (= (not $x47) (not $x47))) (= (< ?x7 10) (not $x47)))))
(let ((@x87 (trans (monotonicity @x55 @x79 (= ?x13 (ite (not $x47) ?0 ?x77))) (rewrite (= (ite (not $x47) ?0 ?x77) ?x83)) (= ?x13 ?x83))))
(let ((@x94 (mp (asserted $x15) (|quant-intro| (monotonicity @x87 $x89) (= $x15 $x91)) $x91)))
(let ((@x171 (mp (mp @x94 (|rewrite*| (= $x91 $x91)) $x91) (|quant-intro| @x167 (= $x91 $x168)) $x168)))
(let ((@x219 (mp (|mp~| @x171 (|nnf-pos| (refl (|~| $x165 $x165)) (|~| $x168 $x168)) $x168) (|quant-intro| (rewrite (= $x165 $x213)) (= $x168 $x216)) $x216)))
(let ((@x642 (mp @x219 (|quant-intro| (refl (= $x213 $x213)) (= $x216 $x637)) $x637)))
(let (($x485 (<= ?x522 6)))
(let (($x523 (= ?x522 6)))
(let (($x651 (forall ((?v0 Int) )(!(let (($x35 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x35)) :pattern ( (|nat$| ?v0) )))
))
(let (($x181 (forall ((?v0 Int) )(let (($x35 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (>= ?v0 0)) $x35)))
))
(let (($x35 (= (|of_nat$| (|nat$| ?0)) ?0)))
(let (($x178 (or (not (>= ?0 0)) $x35)))
(let (($x104 (forall ((?v0 Int) )(let (($x35 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(or (not (<= 0 ?v0)) $x35)))
))
(let ((@x177 (monotonicity (rewrite (= (<= 0 ?0) (>= ?0 0))) (= (not (<= 0 ?0)) (not (>= ?0 0))))))
(let ((@x183 (|quant-intro| (monotonicity @x177 (= (or (not (<= 0 ?0)) $x35) $x178)) (= $x104 $x181))))
(let (($x37 (forall ((?v0 Int) )(let (($x35 (= (|of_nat$| (|nat$| ?v0)) ?v0)))
(let (($x32 (<= 0 ?v0)))
(=> $x32 $x35))))
))
(let ((@x102 (rewrite (= (=> (<= 0 ?0) $x35) (or (not (<= 0 ?0)) $x35)))))
(let ((@x98 (monotonicity (rewrite (= (<= 0 ?0) (<= 0 ?0))) (= (=> (<= 0 ?0) $x35) (=> (<= 0 ?0) $x35)))))
(let ((@x103 (trans @x98 @x102 (= (=> (<= 0 ?0) $x35) (or (not (<= 0 ?0)) $x35)))))
(let ((@x136 (mp (mp (asserted $x37) (|quant-intro| @x103 (= $x37 $x104)) $x104) (|rewrite*| (= $x104 $x104)) $x104)))
(let ((@x205 (|mp~| (mp @x136 @x183 $x181) (|nnf-pos| (refl (|~| $x178 $x178)) (|~| $x181 $x181)) $x181)))
(let ((@x656 (mp @x205 (|quant-intro| (refl (= $x178 $x178)) (= $x181 $x651)) $x651)))
(let (($x579 (not $x651)))
(let (($x515 (or $x579 $x523)))
(let ((@x528 (monotonicity (rewrite (= (>= 6 0) true)) (= (not (>= 6 0)) (not true)))))
(let ((@x530 (trans @x528 (rewrite (= (not true) false)) (= (not (>= 6 0)) false))))
(let ((@x510 (monotonicity @x530 (= (or (not (>= 6 0)) $x523) (or false $x523)))))
(let ((@x514 (trans @x510 (rewrite (= (or false $x523) $x523)) (= (or (not (>= 6 0)) $x523) $x523))))
(let ((@x500 (monotonicity @x514 (= (or $x579 (or (not (>= 6 0)) $x523)) $x515))))
(let ((@x503 (trans @x500 (rewrite (= $x515 $x515)) (= (or $x579 (or (not (>= 6 0)) $x523)) $x515))))
(let ((@x504 (mp ((_ |quant-inst| 6) (or $x579 (or (not (>= 6 0)) $x523))) @x503 $x515)))
(let ((@x450 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x523) $x485)) (|unit-resolution| @x504 @x656 $x523) $x485)))
(let ((@x419 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x485) (not $x495))) @x450 (not $x495))))
(let ((@x421 (|unit-resolution| (|def-axiom| (or (not $x484) $x495 $x456)) @x419 (|unit-resolution| ((_ |quant-inst| (|nat$| 6)) (or (not $x637) $x484)) @x642 $x484) $x456)))
(let (($x273 (= ?x18 ?x17)))
(let ((?x624 (|of_nat$| ?x17)))
(let (($x287 (>= ?x624 10)))
(let (($x274 (ite $x287 (= ?x18 (|dec_10$| (|nat$| (+ (~ 10) ?x624)))) $x273)))
(let (($x415 (<= ?x624 4)))
(let (($x598 (= ?x624 4)))
(let (($x580 (or $x579 $x598)))
(let ((@x589 (monotonicity (rewrite (= (>= 4 0) true)) (= (not (>= 4 0)) (not true)))))
(let ((@x593 (trans @x589 (rewrite (= (not true) false)) (= (not (>= 4 0)) false))))
(let ((@x433 (monotonicity @x593 (= (or (not (>= 4 0)) $x598) (or false $x598)))))
(let ((@x578 (trans @x433 (rewrite (= (or false $x598) $x598)) (= (or (not (>= 4 0)) $x598) $x598))))
(let ((@x584 (monotonicity @x578 (= (or $x579 (or (not (>= 4 0)) $x598)) $x580))))
(let ((@x412 (trans @x584 (rewrite (= $x580 $x580)) (= (or $x579 (or (not (>= 4 0)) $x598)) $x580))))
(let ((@x414 (mp ((_ |quant-inst| 4) (or $x579 (or (not (>= 4 0)) $x598))) @x412 $x580)))
(let ((@x428 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x598) $x415)) (|unit-resolution| @x414 @x656 $x598) $x415)))
(let ((@x432 (|unit-resolution| ((_ |th-lemma| arith farkas 1 1) (or (not $x415) (not $x287))) @x428 (not $x287))))
(let ((@x402 (|unit-resolution| (|def-axiom| (or (not $x274) $x287 $x273)) @x432 (|unit-resolution| ((_ |quant-inst| (|nat$| 4)) (or (not $x637) $x274)) @x642 $x274) $x273)))
(let ((@x408 ((_ |th-lemma| arith triangle-eq) (or (not (= ?x19 ?x624)) (<= (+ ?x19 (* (~ 1) ?x624)) 0)))))
(let ((@x251 (|unit-resolution| @x408 (monotonicity @x402 (= ?x19 ?x624)) (<= (+ ?x19 (* (~ 1) ?x624)) 0))))
(let (($x492 (>= (+ ?x19 (* (~ 1) ?x624)) 0)))
(let ((@x411 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x19 ?x624)) $x492)) (monotonicity @x402 (= ?x19 ?x624)) $x492)))
(let (($x571 (>= ?x624 4)))
(let ((@x397 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x598) $x571)) (|unit-resolution| @x414 @x656 $x598) $x571)))
(let ((?x475 (+ ?x20 (* (~ 1) (|of_nat$| ?x21)))))
(let (($x552 (<= ?x475 0)))
(let (($x473 (= ?x475 0)))
(let (($x567 (>= ?x19 0)))
(let ((@x389 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 1) (or $x567 (not $x571) (not $x492))) @x397 @x411 $x567)))
(let (($x469 (not $x567)))
(let (($x568 (or $x469 $x473)))
(let (($x557 (or $x579 $x469 $x473)))
(let (($x558 (or $x579 (or (not (>= ?x20 0)) (= (|of_nat$| ?x21) ?x20)))))
(let ((@x463 (monotonicity (rewrite (= (>= ?x20 0) $x567)) (= (not (>= ?x20 0)) $x469))))
(let ((@x570 (monotonicity @x463 (rewrite (= (= (|of_nat$| ?x21) ?x20) $x473)) (= (or (not (>= ?x20 0)) (= (|of_nat$| ?x21) ?x20)) $x568))))
(let ((@x563 (trans (monotonicity @x570 (= $x558 (or $x579 $x568))) (rewrite (= (or $x579 $x568) $x557)) (= $x558 $x557))))
(let ((@x393 (|unit-resolution| (|unit-resolution| (mp ((_ |quant-inst| (* 4 ?x19)) $x558) @x563 $x557) @x656 $x568) @x389 $x473)))
(let ((@x380 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x473) (>= ?x475 0))) @x393 (>= ?x475 0))))
(let ((@x382 ((_ |th-lemma| arith eq-propagate 1 1 -4 -4 -4 -4) @x380 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x473) $x552)) @x393 $x552) @x397 @x428 @x411 @x251 (= (+ (~ 10) (|of_nat$| ?x21)) 6))))
(let ((@x374 (monotonicity (monotonicity @x382 (= (|nat$| (+ (~ 10) (|of_nat$| ?x21))) ?x24)) (= (|dec_10$| (|nat$| (+ (~ 10) (|of_nat$| ?x21)))) ?x496))))
(let (($x328 (= ?x22 (|dec_10$| (|nat$| (+ (~ 10) (|of_nat$| ?x21)))))))
(let ((?x275 (|of_nat$| ?x21)))
(let (($x611 (>= ?x275 10)))
(let (($x330 (ite $x611 $x328 (= ?x22 ?x21))))
(let ((@x371 (|unit-resolution| ((_ |th-lemma| arith assign-bounds 1 4 4) (or $x611 (not $x552) (not $x571) (not $x492))) @x397 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x473) $x552)) @x393 $x552) @x411 $x611)))
(let ((@x372 (|unit-resolution| (|def-axiom| (or (not $x330) (not $x611) $x328)) @x371 (|unit-resolution| ((_ |quant-inst| (|nat$| ?x20)) (or (not $x637) $x330)) @x642 $x330) $x328)))
(let (($x26 (not (= ?x22 ?x24))))
(|unit-resolution| (mp (asserted $x26) (|rewrite*| (= $x26 $x26)) $x26) (trans (trans @x372 @x374 (= ?x22 ?x496)) @x421 (= ?x22 ?x24)) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
b6d06ee5e346cf098143de9de1b69fb576a485c2 289 0
unsat
((set-logic <null>)
(proof
(let ((?x45 (|mod$| |l$| 2)))
(let ((?x43 (|eval_dioph$| |ks$| (|map$| |uu$| |xs$|))))
(let ((?x44 (|mod$| ?x43 2)))
(let (($x46 (= ?x44 ?x45)))
(let ((?x39 (|eval_dioph$| |ks$| |xs$|)))
(let (($x41 (= ?x39 |l$|)))
(let ((?x116 (* (~ 1) ?x43)))
(let ((?x117 (+ |l$| ?x116)))
(let ((?x120 (|div$| ?x117 2)))
(let ((?x48 (|eval_dioph$| |ks$| (|map$| |uua$| |xs$|))))
(let (($x123 (= ?x48 ?x120)))
(let (($x338 (not $x123)))
(let (($x337 (not $x46)))
(let (($x339 (or $x337 $x338)))
(let ((?x686 (|mod$| ?x39 2)))
(let ((?x441 (* (~ 1) ?x686)))
(let ((?x678 (* (~ 1) (mod |l$| 2))))
(let ((?x946 (+ |l$| ?x45 (* (~ 1) (div ?x39 2)) (* (~ 1) (div |l$| 2)) ?x678 ?x441)))
(let (($x864 (<= (+ ?x45 ?x441) 0)))
(let (($x796 (forall ((?v0 |Int_list$|) (?v1 |Nat_list$|) )(!(= (|mod$| (|eval_dioph$| ?v0 ?v1) 2) (|mod$| (|eval_dioph$| ?v0 (|map$| |uu$| ?v1)) 2)) :pattern ( (|eval_dioph$| ?v0 (|map$| |uu$| ?v1)) )))
))
(let (($x30 (forall ((?v0 |Int_list$|) (?v1 |Nat_list$|) )(= (|mod$| (|eval_dioph$| ?v0 ?v1) 2) (|mod$| (|eval_dioph$| ?v0 (|map$| |uu$| ?v1)) 2)))
))
(let (($x29 (= (|mod$| (|eval_dioph$| ?1 ?0) 2) (|mod$| (|eval_dioph$| ?1 (|map$| |uu$| ?0)) 2))))
(let ((@x300 (|mp~| (asserted $x30) (|nnf-pos| (refl (|~| $x29 $x29)) (|~| $x30 $x30)) $x30)))
(let ((@x910 (|unit-resolution| ((_ |quant-inst| |ks$| |xs$|) (or (not $x796) (= ?x686 ?x44))) (mp @x300 (|quant-intro| (refl (= $x29 $x29)) (= $x30 $x796)) $x796) (= ?x686 ?x44))))
(let (($x340 (not $x339)))
(let ((@x605 (hypothesis $x340)))
(let ((@x896 (symm (|unit-resolution| (|def-axiom| (or $x339 $x46)) @x605 $x46) (= ?x45 ?x44))))
(let ((@x1028 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x45 ?x686)) $x864)) (trans @x896 (symm @x910 (= ?x44 ?x686)) (= ?x45 ?x686)) $x864)))
(let (($x505 (>= (+ ?x48 (* (~ 1) ?x120)) 0)))
(let ((@x1032 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x338 $x505)) (|unit-resolution| (|def-axiom| (or $x339 $x123)) @x605 $x123) $x505)))
(let ((@x249 (|true-axiom| true)))
(let ((@x998 (|unit-resolution| ((_ |th-lemma| arith) (or false (not (>= (mod (+ |l$| ?x43) 2) 2)))) @x249 (not (>= (mod (+ |l$| ?x43) 2) 2)))))
(let ((?x596 (+ |l$| (* (~ 2) (div |l$| 2)) ?x678)))
(let (($x637 (= ?x596 0)))
(let ((@x894 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x637) (<= ?x596 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x637)) @x249 $x637) (<= ?x596 0))))
(let ((?x660 (+ ?x45 ?x678)))
(let (($x661 (= ?x660 0)))
(let (($x838 (forall ((?v0 Int) (?v1 Int) )(!(let (($x172 (<= ?v1 0)))
(let (($x373 (ite $x172 (= (+ (|mod$| ?v0 ?v1) (mod (* (~ 1) ?v0) (* (~ 1) ?v1))) 0) (= (+ (|mod$| ?v0 ?v1) (* (~ 1) (mod ?v0 ?v1))) 0))))
(let (($x72 (= ?v1 0)))
(ite $x72 (= (|mod$| ?v0 ?v1) ?v0) $x373)))) :pattern ( (|mod$| ?v0 ?v1) )))
))
(let (($x377 (forall ((?v0 Int) (?v1 Int) )(let (($x172 (<= ?v1 0)))
(let (($x373 (ite $x172 (= (+ (|mod$| ?v0 ?v1) (mod (* (~ 1) ?v0) (* (~ 1) ?v1))) 0) (= (+ (|mod$| ?v0 ?v1) (* (~ 1) (mod ?v0 ?v1))) 0))))
(let (($x72 (= ?v1 0)))
(ite $x72 (= (|mod$| ?v0 ?v1) ?v0) $x373)))))
))
(let (($x172 (<= ?0 0)))
(let (($x373 (ite $x172 (= (+ (|mod$| ?1 ?0) (mod (* (~ 1) ?1) (* (~ 1) ?0))) 0) (= (+ (|mod$| ?1 ?0) (* (~ 1) (mod ?1 ?0))) 0))))
(let (($x72 (= ?0 0)))
(let (($x374 (ite $x72 (= (|mod$| ?1 ?0) ?1) $x373)))
(let (($x228 (forall ((?v0 Int) (?v1 Int) )(let ((?x83 (mod ?v0 ?v1)))
(let ((?x179 (* (~ 1) ?v1)))
(let ((?x176 (* (~ 1) ?v0)))
(let ((?x203 (mod ?x176 ?x179)))
(let ((?x209 (* (~ 1) ?x203)))
(let (($x172 (<= ?v1 0)))
(let ((?x217 (ite $x172 ?x209 ?x83)))
(let (($x72 (= ?v1 0)))
(let ((?x82 (|mod$| ?v0 ?v1)))
(= ?x82 (ite $x72 ?v0 ?x217))))))))))))
))
(let ((?x83 (mod ?1 ?0)))
(let ((?x179 (* (~ 1) ?0)))
(let ((?x176 (* (~ 1) ?1)))
(let ((?x203 (mod ?x176 ?x179)))
(let ((?x209 (* (~ 1) ?x203)))
(let ((?x217 (ite $x172 ?x209 ?x83)))
(let ((?x82 (|mod$| ?1 ?0)))
(let (($x225 (= ?x82 (ite $x72 ?1 ?x217))))
(let (($x89 (forall ((?v0 Int) (?v1 Int) )(let ((?x85 (- (mod (- ?v0) (- ?v1)))))
(let ((?x83 (mod ?v0 ?v1)))
(let (($x73 (< 0 ?v1)))
(let ((?x86 (ite $x73 ?x83 ?x85)))
(let (($x72 (= ?v1 0)))
(let ((?x82 (|mod$| ?v0 ?v1)))
(= ?x82 (ite $x72 ?v0 ?x86)))))))))
))
(let ((?x85 (- (mod (- ?1) (- ?0)))))
(let (($x73 (< 0 ?0)))
(let ((?x86 (ite $x73 ?x83 ?x85)))
(let ((@x205 (monotonicity (rewrite (= (- ?1) ?x176)) (rewrite (= (- ?0) ?x179)) (= (mod (- ?1) (- ?0)) ?x203))))
(let ((@x213 (trans (monotonicity @x205 (= ?x85 (- ?x203))) (rewrite (= (- ?x203) ?x209)) (= ?x85 ?x209))))
(let ((@x216 (monotonicity (rewrite (= $x73 (not $x172))) @x213 (= ?x86 (ite (not $x172) ?x83 ?x209)))))
(let ((@x221 (trans @x216 (rewrite (= (ite (not $x172) ?x83 ?x209) ?x217)) (= ?x86 ?x217))))
(let ((@x227 (monotonicity (monotonicity @x221 (= (ite $x72 ?1 ?x86) (ite $x72 ?1 ?x217))) (= (= ?x82 (ite $x72 ?1 ?x86)) $x225))))
(let ((@x336 (|mp~| (mp (asserted $x89) (|quant-intro| @x227 (= $x89 $x228)) $x228) (|nnf-pos| (refl (|~| $x225 $x225)) (|~| $x228 $x228)) $x228)))
(let ((@x380 (mp @x336 (|quant-intro| (rewrite (= $x225 $x374)) (= $x228 $x377)) $x377)))
(let (($x584 (not $x838)))
(let (($x643 (or $x584 $x661)))
(let (($x448 (<= 2 0)))
(let (($x662 (ite $x448 (= (+ ?x45 (mod (* (~ 1) |l$|) (* (~ 1) 2))) 0) $x661)))
(let (($x784 (= 2 0)))
(let (($x663 (ite $x784 (= ?x45 |l$|) $x662)))
(let (($x650 (= (ite false (= (+ ?x45 (mod (* (~ 1) |l$|) (~ 2))) 0) $x661) $x661)))
(let (($x648 (= $x662 (ite false (= (+ ?x45 (mod (* (~ 1) |l$|) (~ 2))) 0) $x661))))
(let (($x640 (= (= (+ ?x45 (mod (* (~ 1) |l$|) (* (~ 1) 2))) 0) (= (+ ?x45 (mod (* (~ 1) |l$|) (~ 2))) 0))))
(let (($x668 (= (+ ?x45 (mod (* (~ 1) |l$|) (* (~ 1) 2))) (+ ?x45 (mod (* (~ 1) |l$|) (~ 2))))))
(let ((@x780 (rewrite (= (* (~ 1) 2) (~ 2)))))
(let ((@x666 (monotonicity @x780 (= (mod (* (~ 1) |l$|) (* (~ 1) 2)) (mod (* (~ 1) |l$|) (~ 2))))))
(let ((@x777 (rewrite (= $x448 false))))
(let ((@x653 (trans (monotonicity @x777 (monotonicity (monotonicity @x666 $x668) $x640) $x648) (rewrite $x650) (= $x662 $x661))))
(let ((@x775 (rewrite (= $x784 false))))
(let ((@x642 (trans (monotonicity @x775 @x653 (= $x663 (ite false (= ?x45 |l$|) $x661))) (rewrite (= (ite false (= ?x45 |l$|) $x661) $x661)) (= $x663 $x661))))
(let ((@x617 (trans (monotonicity @x642 (= (or $x584 $x663) $x643)) (rewrite (= $x643 $x643)) (= (or $x584 $x663) $x643))))
(let ((@x968 (|unit-resolution| (mp ((_ |quant-inst| |l$| 2) (or $x584 $x663)) @x617 $x643) (mp @x380 (|quant-intro| (refl (= $x374 $x374)) (= $x377 $x838)) $x838) $x661)))
(let ((@x899 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x661) (<= ?x660 0))) @x968 (<= ?x660 0))))
(let ((?x442 (+ (mod ?x39 2) ?x441)))
(let (($x443 (= ?x442 0)))
(let (($x413 (or $x584 $x443)))
(let (($x485 (= (+ ?x686 (* (~ 1) (mod ?x39 2))) 0)))
(let (($x486 (ite $x448 (= (+ ?x686 (mod (* (~ 1) ?x39) (* (~ 1) 2))) 0) $x485)))
(let (($x453 (ite $x784 (= ?x686 ?x39) $x486)))
(let (($x418 (= (ite false (= (+ (mod (* (~ 1) ?x39) (~ 2)) ?x686) 0) $x443) $x443)))
(let (($x416 (= $x486 (ite false (= (+ (mod (* (~ 1) ?x39) (~ 2)) ?x686) 0) $x443))))
(let (($x436 (= (+ ?x686 (* (~ 1) (mod ?x39 2))) (+ (* (~ 1) (mod ?x39 2)) ?x686))))
(let ((@x440 (monotonicity (rewrite $x436) (= $x485 (= (+ (* (~ 1) (mod ?x39 2)) ?x686) 0)))))
(let ((@x427 (trans @x440 (rewrite (= (= (+ (* (~ 1) (mod ?x39 2)) ?x686) 0) $x443)) (= $x485 $x443))))
(let (($x451 (= (= (+ ?x686 (mod (* (~ 1) ?x39) (* (~ 1) 2))) 0) (= (+ (mod (* (~ 1) ?x39) (~ 2)) ?x686) 0))))
(let ((?x454 (mod (* (~ 1) ?x39) (~ 2))))
(let ((?x462 (+ ?x454 ?x686)))
(let ((?x479 (+ ?x686 (mod (* (~ 1) ?x39) (* (~ 1) 2)))))
(let ((@x461 (monotonicity (monotonicity @x780 (= (mod (* (~ 1) ?x39) (* (~ 1) 2)) ?x454)) (= ?x479 (+ ?x686 ?x454)))))
(let ((@x430 (monotonicity (trans @x461 (rewrite (= (+ ?x686 ?x454) ?x462)) (= ?x479 ?x462)) $x451)))
(let ((@x423 (trans (monotonicity @x777 @x430 @x427 $x416) (rewrite $x418) (= $x486 $x443))))
(let ((@x412 (trans (monotonicity @x775 @x423 (= $x453 (ite false (= ?x686 ?x39) $x443))) (rewrite (= (ite false (= ?x686 ?x39) $x443) $x443)) (= $x453 $x443))))
(let ((@x405 (trans (monotonicity @x412 (= (or $x584 $x453) $x413)) (rewrite (= $x413 $x413)) (= (or $x584 $x453) $x413))))
(let ((@x927 (|unit-resolution| (mp ((_ |quant-inst| (|eval_dioph$| |ks$| |xs$|) 2) (or $x584 $x453)) @x405 $x413) (mp @x380 (|quant-intro| (refl (= $x374 $x374)) (= $x377 $x838)) $x838) $x443)))
(let ((@x1008 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x443) (<= ?x442 0))) @x927 (<= ?x442 0))))
(let ((?x483 (* (~ 1) (mod ?x39 2))))
(let ((?x383 (+ ?x39 (* (~ 2) (div ?x39 2)) ?x483)))
(let (($x395 (= ?x383 0)))
(let ((@x1015 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x395) (<= ?x383 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x395)) @x249 $x395) (<= ?x383 0))))
(let ((?x684 (+ ?x39 ?x116 (* (~ 2) ?x48))))
(let (($x685 (= ?x684 0)))
(let (($x803 (forall ((?v0 |Int_list$|) (?v1 |Nat_list$|) )(!(let ((?x24 (|eval_dioph$| ?v0 ?v1)))
(let ((?x264 (+ ?x24 (* (~ 1) (|eval_dioph$| ?v0 (|map$| |uu$| ?v1))) (* (~ 2) (|eval_dioph$| ?v0 (|map$| |uua$| ?v1))))))
(= ?x264 0))) :pattern ( (|eval_dioph$| ?v0 (|map$| |uu$| ?v1)) ) :pattern ( (|eval_dioph$| ?v0 (|map$| |uua$| ?v1)) )))
))
(let (($x266 (forall ((?v0 |Int_list$|) (?v1 |Nat_list$|) )(let ((?x24 (|eval_dioph$| ?v0 ?v1)))
(let ((?x264 (+ ?x24 (* (~ 1) (|eval_dioph$| ?v0 (|map$| |uu$| ?v1))) (* (~ 2) (|eval_dioph$| ?v0 (|map$| |uua$| ?v1))))))
(= ?x264 0))))
))
(let ((?x24 (|eval_dioph$| ?1 ?0)))
(let ((?x264 (+ ?x24 (* (~ 1) (|eval_dioph$| ?1 (|map$| |uu$| ?0))) (* (~ 2) (|eval_dioph$| ?1 (|map$| |uua$| ?0))))))
(let (($x260 (= ?x264 0)))
(let (($x111 (forall ((?v0 |Int_list$|) (?v1 |Nat_list$|) )(let ((?x24 (|eval_dioph$| ?v0 ?v1)))
(let ((?x27 (|eval_dioph$| ?v0 (|map$| |uu$| ?v1))))
(let ((?x32 (|eval_dioph$| ?v0 (|map$| |uua$| ?v1))))
(let ((?x102 (* 2 ?x32)))
(let ((?x105 (+ ?x102 ?x27)))
(= ?x105 ?x24)))))))
))
(let (($x256 (forall ((?v0 |Int_list$|) (?v1 |Nat_list$|) )(let ((?x24 (|eval_dioph$| ?v0 ?v1)))
(let ((?x32 (|eval_dioph$| ?v0 (|map$| |uua$| ?v1))))
(let ((?x102 (* 2 ?x32)))
(let ((?x27 (|eval_dioph$| ?v0 (|map$| |uu$| ?v1))))
(= (+ ?x27 ?x102) ?x24))))))
))
(let ((?x32 (|eval_dioph$| ?1 (|map$| |uua$| ?0))))
(let ((?x102 (* 2 ?x32)))
(let ((?x27 (|eval_dioph$| ?1 (|map$| |uu$| ?0))))
(let (($x253 (= (+ ?x27 ?x102) ?x24)))
(let ((@x255 (monotonicity (rewrite (= (+ ?x102 ?x27) (+ ?x27 ?x102))) (= (= (+ ?x102 ?x27) ?x24) $x253))))
(let ((@x270 (trans (|quant-intro| @x255 (= $x111 $x256)) (|quant-intro| (rewrite (= $x253 $x260)) (= $x256 $x266)) (= $x111 $x266))))
(let (($x36 (forall ((?v0 |Int_list$|) (?v1 |Nat_list$|) )(let ((?x24 (|eval_dioph$| ?v0 ?v1)))
(let ((?x27 (|eval_dioph$| ?v0 (|map$| |uu$| ?v1))))
(= (+ (* (|eval_dioph$| ?v0 (|map$| |uua$| ?v1)) 2) ?x27) ?x24))))
))
(let ((@x107 (monotonicity (rewrite (= (* ?x32 2) ?x102)) (= (+ (* ?x32 2) ?x27) (+ ?x102 ?x27)))))
(let ((@x110 (monotonicity @x107 (= (= (+ (* ?x32 2) ?x27) ?x24) (= (+ ?x102 ?x27) ?x24)))))
(let ((@x271 (mp (mp (asserted $x36) (|quant-intro| @x110 (= $x36 $x111)) $x111) @x270 $x266)))
(let ((@x808 (mp (|mp~| @x271 (|nnf-pos| (refl (|~| $x260 $x260)) (|~| $x266 $x266)) $x266) (|quant-intro| (refl (= $x260 $x260)) (= $x266 $x803)) $x803)))
(let ((@x1019 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x685) (>= ?x684 0))) (|unit-resolution| ((_ |quant-inst| |ks$| |xs$|) (or (not $x803) $x685)) @x808 $x685) (>= ?x684 0))))
(let ((?x435 (+ ?x120 (* (~ 1) (div ?x117 2)))))
(let (($x771 (= ?x435 0)))
(let (($x831 (forall ((?v0 Int) (?v1 Int) )(!(let (($x355 (= (+ (|div$| ?v0 ?v1) (* (~ 1) (div (* (~ 1) ?v0) (* (~ 1) ?v1)))) 0)))
(let (($x172 (<= ?v1 0)))
(let (($x359 (ite $x172 $x355 (= (+ (|div$| ?v0 ?v1) (* (~ 1) (div ?v0 ?v1))) 0))))
(let (($x72 (= ?v1 0)))
(ite $x72 (= (|div$| ?v0 ?v1) 0) $x359))))) :pattern ( (|div$| ?v0 ?v1) )))
))
(let (($x363 (forall ((?v0 Int) (?v1 Int) )(let (($x355 (= (+ (|div$| ?v0 ?v1) (* (~ 1) (div (* (~ 1) ?v0) (* (~ 1) ?v1)))) 0)))
(let (($x172 (<= ?v1 0)))
(let (($x359 (ite $x172 $x355 (= (+ (|div$| ?v0 ?v1) (* (~ 1) (div ?v0 ?v1))) 0))))
(let (($x72 (= ?v1 0)))
(ite $x72 (= (|div$| ?v0 ?v1) 0) $x359))))))
))
(let (($x359 (ite $x172 (= (+ (|div$| ?1 ?0) (* (~ 1) (div ?x176 ?x179))) 0) (= (+ (|div$| ?1 ?0) (* (~ 1) (div ?1 ?0))) 0))))
(let (($x360 (ite $x72 (= (|div$| ?1 ?0) 0) $x359)))
(let (($x199 (forall ((?v0 Int) (?v1 Int) )(let ((?x74 (div ?v0 ?v1)))
(let ((?x179 (* (~ 1) ?v1)))
(let ((?x176 (* (~ 1) ?v0)))
(let ((?x182 (div ?x176 ?x179)))
(let (($x172 (<= ?v1 0)))
(let ((?x188 (ite $x172 ?x182 ?x74)))
(let (($x72 (= ?v1 0)))
(let ((?x71 (|div$| ?v0 ?v1)))
(= ?x71 (ite $x72 0 ?x188)))))))))))
))
(let ((?x71 (|div$| ?1 ?0)))
(let (($x196 (= ?x71 (ite $x72 0 (ite $x172 (div ?x176 ?x179) (div ?1 ?0))))))
(let (($x81 (forall ((?v0 Int) (?v1 Int) )(let ((?x74 (div ?v0 ?v1)))
(let (($x73 (< 0 ?v1)))
(let ((?x78 (ite $x73 ?x74 (div (- ?v0) (- ?v1)))))
(let (($x72 (= ?v1 0)))
(let ((?x71 (|div$| ?v0 ?v1)))
(= ?x71 (ite $x72 0 ?x78))))))))
))
(let (($x80 (= ?x71 (ite $x72 0 (ite $x73 (div ?1 ?0) (div (- ?1) (- ?0)))))))
(let (($x194 (= (ite $x72 0 (ite $x73 (div ?1 ?0) (div (- ?1) (- ?0)))) (ite $x72 0 (ite $x172 (div ?x176 ?x179) (div ?1 ?0))))))
(let ((?x74 (div ?1 ?0)))
(let ((?x182 (div ?x176 ?x179)))
(let ((?x188 (ite $x172 ?x182 ?x74)))
(let ((?x78 (ite $x73 ?x74 (div (- ?1) (- ?0)))))
(let ((@x184 (monotonicity (rewrite (= (- ?1) ?x176)) (rewrite (= (- ?0) ?x179)) (= (div (- ?1) (- ?0)) ?x182))))
(let ((@x187 (monotonicity (rewrite (= $x73 (not $x172))) @x184 (= ?x78 (ite (not $x172) ?x74 ?x182)))))
(let ((@x192 (trans @x187 (rewrite (= (ite (not $x172) ?x74 ?x182) ?x188)) (= ?x78 ?x188))))
(let ((@x201 (|quant-intro| (monotonicity (monotonicity @x192 $x194) (= $x80 $x196)) (= $x81 $x199))))
(let ((@x331 (|mp~| (mp (asserted $x81) @x201 $x199) (|nnf-pos| (refl (|~| $x196 $x196)) (|~| $x199 $x199)) $x199)))
(let ((@x366 (mp @x331 (|quant-intro| (rewrite (= $x196 $x360)) (= $x199 $x363)) $x363)))
(let (($x761 (or (not $x831) $x771)))
(let (($x772 (ite $x448 (= (+ ?x120 (* (~ 1) (div (* (~ 1) ?x117) (* (~ 1) 2)))) 0) $x771)))
(let (($x773 (ite $x784 (= ?x120 0) $x772)))
(let (($x495 (ite false (= (+ ?x120 (* (~ 1) (div (+ (* (~ 1) |l$|) ?x43) (~ 2)))) 0) $x771)))
(let (($x763 (= (= (+ ?x120 (* (~ 1) (div (* (~ 1) ?x117) (* (~ 1) 2)))) 0) (= (+ ?x120 (* (~ 1) (div (+ (* (~ 1) |l$|) ?x43) (~ 2)))) 0))))
(let (($x490 (= (+ ?x120 (* (~ 1) (div (* (~ 1) ?x117) (* (~ 1) 2)))) (+ ?x120 (* (~ 1) (div (+ (* (~ 1) |l$|) ?x43) (~ 2)))))))
(let (($x487 (= (* (~ 1) (div (* (~ 1) ?x117) (* (~ 1) 2))) (* (~ 1) (div (+ (* (~ 1) |l$|) ?x43) (~ 2))))))
(let (($x782 (= (div (* (~ 1) ?x117) (* (~ 1) 2)) (div (+ (* (~ 1) |l$|) ?x43) (~ 2)))))
(let ((@x768 (monotonicity (rewrite (= (* (~ 1) ?x117) (+ (* (~ 1) |l$|) ?x43))) @x780 $x782)))
(let ((@x765 (monotonicity @x777 (monotonicity (monotonicity (monotonicity @x768 $x487) $x490) $x763) (= $x772 $x495))))
(let ((@x756 (monotonicity @x775 (trans @x765 (rewrite (= $x495 $x771)) (= $x772 $x771)) (= $x773 (ite false (= ?x120 0) $x771)))))
(let ((@x759 (trans @x756 (rewrite (= (ite false (= ?x120 0) $x771) $x771)) (= $x773 $x771))))
(let ((@x753 (trans (monotonicity @x759 (= (or (not $x831) $x773) $x761)) (rewrite (= $x761 $x761)) (= (or (not $x831) $x773) $x761))))
(let ((@x881 (|unit-resolution| (mp ((_ |quant-inst| (+ |l$| ?x116) 2) (or (not $x831) $x773)) @x753 $x761) (mp @x366 (|quant-intro| (refl (= $x360 $x360)) (= $x363 $x831)) $x831) $x771)))
(let ((@x992 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x771) (>= ?x435 0))) @x881 (>= ?x435 0))))
(let ((?x613 (+ |l$| ?x116 (* (~ 2) (div ?x117 2)) (* (~ 1) (mod (+ |l$| ?x43) 2)))))
(let (($x735 (= ?x613 0)))
(let ((@x995 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x735) (<= ?x613 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x735)) @x249 $x735) (<= ?x613 0))))
(let ((@x1020 ((_ |th-lemma| arith farkas 1 -2 -2 -1 -2 1 1 1 1 1 1) @x995 @x992 (hypothesis $x505) @x1019 (hypothesis (>= ?x946 1)) @x1015 @x1008 (hypothesis $x864) @x899 @x894 @x998 false)))
(let ((@x1033 (|unit-resolution| (lemma @x1020 (or (not (>= ?x946 1)) (not $x505) (not $x864))) @x1032 @x1028 (not (>= ?x946 1)))))
(let ((@x972 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x661) (>= ?x660 0))) @x968 (>= ?x660 0))))
(let ((@x987 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x637) (>= ?x596 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x637)) @x249 $x637) (>= ?x596 0))))
(let ((@x1036 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not (= ?x45 ?x686)) (>= (+ ?x45 ?x441) 0))) (trans @x896 (symm @x910 (= ?x44 ?x686)) (= ?x45 ?x686)) (>= (+ ?x45 ?x441) 0))))
(let ((@x1039 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x443) (>= ?x442 0))) @x927 (>= ?x442 0))))
(let (($x498 (>= (+ ?x39 (* (~ 1) |l$|)) 0)))
(let (($x1045 (not $x498)))
(let (($x497 (<= (+ ?x39 (* (~ 1) |l$|)) 0)))
(let (($x504 (<= (+ ?x48 (* (~ 1) ?x120)) 0)))
(let ((@x1042 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x338 $x504)) (|unit-resolution| (|def-axiom| (or $x339 $x123)) @x605 $x123) $x504)))
(let (($x726 (>= ?x613 0)))
(let ((@x872 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x735) $x726)) (|unit-resolution| ((_ |th-lemma| arith) (or false $x735)) @x249 $x735) $x726)))
(let (($x691 (<= ?x684 0)))
(let ((@x879 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x685) $x691)) (|unit-resolution| ((_ |quant-inst| |ks$| |xs$|) (or (not $x803) $x685)) @x808 $x685) $x691)))
(let (($x593 (<= ?x435 0)))
(let ((?x745 (mod (+ |l$| ?x43) 2)))
(let (($x730 (>= ?x745 0)))
(let ((@x889 ((_ |th-lemma| arith farkas 1 -2 -2 -1 1 1) (|unit-resolution| ((_ |th-lemma| arith) (or false $x730)) @x249 $x730) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x771) $x593)) @x881 $x593) (hypothesis $x504) @x879 (hypothesis (not $x497)) @x872 false)))
(let (($x135 (not $x41)))
(let (($x346 (= $x41 $x339)))
(let ((@x345 (monotonicity (rewrite (= (and $x46 $x123) $x340)) (= (= $x135 (and $x46 $x123)) (= $x135 $x340)))))
(let ((@x350 (trans @x345 (rewrite (= (= $x135 $x340) $x346)) (= (= $x135 (and $x46 $x123)) $x346))))
(let (($x126 (and $x46 $x123)))
(let (($x136 (= $x135 $x126)))
(let (($x54 (not (= $x41 (and $x46 (= ?x48 (|div$| (- |l$| ?x43) 2)))))))
(let (($x130 (= (= $x41 (and $x46 (= ?x48 (|div$| (- |l$| ?x43) 2)))) (= $x41 $x126))))
(let ((@x122 (monotonicity (rewrite (= (- |l$| ?x43) ?x117)) (= (|div$| (- |l$| ?x43) 2) ?x120))))
(let ((@x128 (monotonicity (monotonicity @x122 (= (= ?x48 (|div$| (- |l$| ?x43) 2)) $x123)) (= (and $x46 (= ?x48 (|div$| (- |l$| ?x43) 2))) $x126))))
(let ((@x140 (trans (monotonicity (monotonicity @x128 $x130) (= $x54 (not (= $x41 $x126)))) (rewrite (= (not (= $x41 $x126)) $x136)) (= $x54 $x136))))
(let ((@x794 (|unit-resolution| (|def-axiom| (or $x135 $x339 (not $x346))) (mp (mp (asserted $x54) @x140 $x136) @x350 $x346) (or $x135 $x339))))
(let ((@x1049 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x41 (not $x497) $x1045)) (|unit-resolution| @x794 @x605 $x135) (or (not $x497) $x1045))))
(let ((@x1050 (|unit-resolution| @x1049 (|unit-resolution| (lemma @x889 (or $x497 (not $x504))) @x1042 $x497) $x1045)))
(let ((@x1053 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x395) (>= ?x383 0))) (|unit-resolution| ((_ |th-lemma| arith) (or false $x395)) @x249 $x395) (>= ?x383 0))))
(let ((@x790 (|unit-resolution| (|def-axiom| (or $x41 $x340 (not $x346))) (mp (mp (asserted $x54) @x140 $x136) @x350 $x346) (or $x41 $x340))))
(let ((@x1123 (|unit-resolution| @x790 (lemma ((_ |th-lemma| arith farkas -1/2 1/2 -1/2 -1/2 -1/2 -1/2 1) @x1053 @x1050 @x1039 @x1036 @x987 @x972 @x1033 false) $x339) $x41)))
(let ((@x932 (trans (symm @x910 (= ?x44 ?x686)) (monotonicity @x1123 (= ?x686 ?x45)) $x46)))
(let (($x890 (not $x504)))
(let ((@x1135 ((_ |th-lemma| arith assign-bounds 1 -1/2 -1/2 1/2 -1/2) (or $x505 (not $x593) (not $x730) (not $x726) (not $x691) $x1045))))
(let ((@x1136 (|unit-resolution| @x1135 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or (not $x771) $x593)) @x881 $x593) (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x135 $x498)) @x1123 $x498) @x872 (|unit-resolution| ((_ |th-lemma| arith) (or false $x730)) @x249 $x730) @x879 $x505)))
(let ((@x1141 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x123 $x890 (not $x505))) (hypothesis $x338) (or $x890 (not $x505)))))
(let ((@x1143 ((_ |th-lemma| arith farkas -2 -2 1 -1 1 1) (|unit-resolution| @x1141 @x1136 $x890) @x992 @x995 @x1019 (|unit-resolution| ((_ |th-lemma| arith triangle-eq) (or $x135 $x497)) @x1123 $x497) @x998 false)))
(let ((@x575 (|unit-resolution| (|def-axiom| (or $x340 $x337 $x338)) (lemma ((_ |th-lemma| arith farkas -1/2 1/2 -1/2 -1/2 -1/2 -1/2 1) @x1053 @x1050 @x1039 @x1036 @x987 @x972 @x1033 false) $x339) $x339)))
(|unit-resolution| (|unit-resolution| @x575 (lemma @x1143 $x123) $x337) @x932 false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
4e21a28a63259a50737712606d48d7d4a769c900 46 0
unsat
((set-logic AUFLIA)
(proof
(let ((?x33 (|sup$| (|collect$| |uu$|))))
(let (($x38 (|less_eq$| ?x33 ?x33)))
(let (($x39 (not $x38)))
(let ((?x35 (|sup$| (|collect$| |uua$|))))
(let (($x37 (|less_eq$| ?x35 ?x33)))
(let (($x36 (|less_eq$| ?x33 ?x35)))
(let (($x597 (forall ((?v0 |A$|) (?v1 |A$|) (?v2 |A$|) )(!(let (($x29 (|less_eq$| ?v0 ?v2)))
(or (not (|less_eq$| ?v0 ?v1)) (not (|less_eq$| ?v1 ?v2)) $x29)) :pattern ( (|less_eq$| ?v0 ?v1) (|less_eq$| ?v1 ?v2) )))
))
(let (($x175 (forall ((?v0 |A$|) (?v1 |A$|) (?v2 |A$|) )(let (($x29 (|less_eq$| ?v0 ?v2)))
(or (not (|less_eq$| ?v0 ?v1)) (not (|less_eq$| ?v1 ?v2)) $x29)))
))
(let ((@x602 (trans (rewrite (= $x175 $x597)) (rewrite (= $x597 $x597)) (= $x175 $x597))))
(let (($x84 (forall ((?v0 |A$|) (?v1 |A$|) (?v2 |A$|) )(let (($x29 (|less_eq$| ?v0 ?v2)))
(let (($x27 (|less_eq$| ?v1 ?v2)))
(let (($x26 (|less_eq$| ?v0 ?v1)))
(let (($x28 (and $x26 $x27)))
(let (($x80 (not $x28)))
(or $x80 $x29)))))))
))
(let (($x29 (|less_eq$| ?2 ?0)))
(let (($x170 (or (not (|less_eq$| ?2 ?1)) (not (|less_eq$| ?1 ?0)) $x29)))
(let (($x27 (|less_eq$| ?1 ?0)))
(let (($x26 (|less_eq$| ?2 ?1)))
(let (($x28 (and $x26 $x27)))
(let (($x80 (not $x28)))
(let (($x81 (or $x80 $x29)))
(let (($x156 (or (not $x26) (not $x27))))
(let ((@x162 (monotonicity (rewrite (= $x28 (not $x156))) (= $x80 (not (not $x156))))))
(let ((@x169 (monotonicity (trans @x162 (rewrite (= (not (not $x156)) $x156)) (= $x80 $x156)) (= $x81 (or $x156 $x29)))))
(let ((@x177 (|quant-intro| (trans @x169 (rewrite (= (or $x156 $x29) $x170)) (= $x81 $x170)) (= $x84 $x175))))
(let (($x31 (forall ((?v0 |A$|) (?v1 |A$|) (?v2 |A$|) )(let (($x29 (|less_eq$| ?v0 ?v2)))
(let (($x27 (|less_eq$| ?v1 ?v2)))
(let (($x26 (|less_eq$| ?v0 ?v1)))
(let (($x28 (and $x26 $x27)))
(=> $x28 $x29))))))
))
(let ((@x87 (mp (asserted $x31) (|quant-intro| (rewrite (= (=> $x28 $x29) $x81)) (= $x31 $x84)) $x84)))
(let ((@x153 (|mp~| (mp @x87 (|rewrite*| (= $x84 $x84)) $x84) (|nnf-pos| (refl (|~| $x81 $x81)) (|~| $x84 $x84)) $x84)))
(let (($x252 (= (or (not $x597) (or (not $x36) (not $x37) $x38)) (or (not $x597) (not $x36) (not $x37) $x38))))
(let ((@x589 (mp ((_ |quant-inst| (|sup$| (|collect$| |uu$|)) (|sup$| (|collect$| |uua$|)) (|sup$| (|collect$| |uu$|))) (or (not $x597) (or (not $x36) (not $x37) $x38))) (rewrite $x252) (or (not $x597) (not $x36) (not $x37) $x38))))
(|unit-resolution| @x589 (mp (mp @x153 @x177 $x175) @x602 $x597) (mp (asserted $x36) (|rewrite*| (= $x36 $x36)) $x36) (mp (asserted $x37) (|rewrite*| (= $x37 $x37)) $x37) (mp (asserted $x39) (|rewrite*| (= $x39 $x39)) $x39) false)))))))))))))))))))))))))))))
dbbd203b9296b09c05b52742aa274aa3af897311 20 0
unsat
((set-logic AUFLIA)
(proof
(let (($x52 (not (|pred$e| 1))))
(let (($x630 (forall ((?v0 Int) )(!(|pred$e| ?v0) :pattern ( (|pred$e| ?v0) )))
))
(let (($x120 (forall ((?v0 Int) )(|pred$e| ?v0))
))
(let (($x49 (forall ((?v0 Int) )(let (($x47 (or (|pred$d| (|cons$d| ?v0 |nil$d|)) (not (|pred$d| (|cons$d| ?v0 |nil$d|))))))
(let (($x42 (|pred$e| ?v0)))
(and $x42 $x47))))
))
(let (($x42 (|pred$e| ?0)))
(let (($x47 (or (|pred$d| (|cons$d| ?0 |nil$d|)) (not (|pred$d| (|cons$d| ?0 |nil$d|))))))
(let (($x48 (and $x42 $x47)))
(let ((@x115 (monotonicity (rewrite (= $x47 true)) (= $x48 (and $x42 true)))))
(let ((@x122 (|quant-intro| (trans @x115 (rewrite (= (and $x42 true) $x42)) (= $x48 $x42)) (= $x49 $x120))))
(let ((@x185 (|mp~| (mp (mp (asserted $x49) @x122 $x120) (|rewrite*| (= $x120 $x120)) $x120) (|nnf-pos| (refl (|~| $x42 $x42)) (|~| $x120 $x120)) $x120)))
(|unit-resolution| ((_ |quant-inst| 1) (or (not $x630) (|pred$e| 1))) (mp @x185 (|quant-intro| (refl (= $x42 $x42)) (= $x120 $x630)) $x630) (mp (asserted $x52) (|rewrite*| (= $x52 $x52)) $x52) false)))))))))))))