src/HOL/SMT_Examples/Boogie_Dijkstra.certs

-9d6b81d96fb21c8c08e3f1fd649ce37bdafb5f92 3044 0
+9d6b81d96fb21c8c08e3f1fd649ce37bdafb5f92 3015 0
 unsat
 ((set-logic AUFLIA)
 (declare-fun ?v0!19 () B_Vertex$)
 (declare-fun ?v1!18 () B_Vertex$)
 (declare-fun ?v0!20 () B_Vertex$)

 (let (($x1888 (<= (+ b_Infinity$ (* (- 1) ?x1885)) 0)))
 (let (($x1883 (fun_app$ v_b_Visited_G_2$ ?v1!18)))
 (let (($x2791 (not $x1883)))
 (let (($x2806 (or $x2791 $x1888 $x1896)))
 (let (($x2811 (not $x2806)))
-(let (($x3729 (forall ((?v1 B_Vertex$) )(!(let ((?x1911 (v_b_SP_G_2$ ?v0!20)))
+(let (($x3729 (forall ((?v1 B_Vertex$) )(! (let ((?x1911 (v_b_SP_G_2$ ?v0!20)))
 (let ((?x1912 (* (- 1) ?x1911)))
 (let ((?x273 (v_b_SP_G_2$ ?v1)))
 (let (($x2242 (= (+ ?x273 ?x1912 (b_G$ (pair$ ?v1 ?v0!20))) 0)))
 (let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
 (let (($x300 (not $x291)))
-(or (>= (+ ?x273 ?x1912) 0) $x300 (not $x2242)))))))) :pattern ( (v_b_SP_G_2$ ?v1) ) :pattern ( (fun_app$ v_b_Visited_G_2$ ?v1) ) :pattern ( (pair$ ?v1 ?v0!20) )))
+(or (>= (+ ?x273 ?x1912) 0) $x300 (not $x2242)))))))) :pattern ( (v_b_SP_G_2$ ?v1) ) :pattern ( (fun_app$ v_b_Visited_G_2$ ?v1) ) :pattern ( (pair$ ?v1 ?v0!20) ) :qid k!42))
 ))
 (let (($x3734 (not $x3729)))
 (let (($x1914 (<= (+ b_Infinity$ (* (- 1) (v_b_SP_G_2$ ?v0!20))) 0)))
 (let (($x1909 (= ?v0!20 b_Source$)))
-(let (($x3720 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let ((?x303 (v_b_SP_G_2$ ?v0)))
-(let ((?x1263 (* (- 1) ?x303)))
-(let ((?x273 (v_b_SP_G_2$ ?v1)))
+(let (($x3720 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x273 (v_b_SP_G_2$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
-(let (($x1282 (>= (+ ?x155 ?x273 ?x1263) 0)))
+(let (($x1282 (>= (+ ?x155 ?x273 (* (- 1) (v_b_SP_G_2$ ?v0))) 0)))
 (let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
 (let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
 (let (($x300 (not $x291)))
-(or $x300 $x922 $x1282))))))))) :pattern ( (pair$ ?v1 ?v0) )))
+(or $x300 $x922 $x1282))))))) :pattern ( (pair$ ?v1 ?v0) ) :qid k!42))
 ))
 (let (($x3725 (not $x3720)))
 (let (($x3737 (or $x3725 $x1909 $x1914 $x3734)))
 (let ((?x4393 (fun_app$c v_b_SP_G_1$ ?v0!20)))
 (let ((?x4418 (* (- 1) ?x4393)))

 (let ((?x3104 (v_b_SP_G_2$ v_b_v_G_1$)))
 (let ((?x3105 (* (- 1) ?x3104)))
 (let ((?x4546 (+ ?x1911 ?x3105 ?x4436)))
 (let (($x4569 (<= ?x4546 0)))
 (let (($x3740 (not $x3737)))
-(let ((@x8092 (hypothesis $x3740)))
+(let ((@x4391 (hypothesis $x3740)))
 (let ((@x3222 (def-axiom (or $x3737 $x3720))))
 (let (($x4161 (>= ?x3104 0)))
-(let (($x3703 (forall ((?v0 B_Vertex$) )(!(let ((?x273 (v_b_SP_G_2$ ?v0)))
-(>= ?x273 0)) :pattern ( (v_b_SP_G_2$ ?v0) )))
+(let (($x3703 (forall ((?v0 B_Vertex$) )(! (let ((?x273 (v_b_SP_G_2$ ?v0)))
+(>= ?x273 0)) :pattern ( (v_b_SP_G_2$ ?v0) ) :qid k!42))
 ))
 (let (($x3743 (or $x2811 $x3740)))
 (let (($x3746 (not $x3743)))
-(let (($x3712 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let (($x1262 (>= (+ (v_b_SP_G_2$ ?v1) (* (- 1) (v_b_SP_G_2$ ?v0))) 0)))
-(let (($x301 (fun_app$ v_b_Visited_G_2$ ?v0)))
-(let (($x2768 (not $x301)))
+(let (($x3712 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let (($x1262 (>= (+ (v_b_SP_G_2$ ?v1) (* (- 1) (v_b_SP_G_2$ ?v0))) 0)))
+(let (($x2768 (not (fun_app$ v_b_Visited_G_2$ ?v0))))
 (let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(or $x291 $x2768 $x1262))))) :pattern ( (v_b_SP_G_2$ ?v1) (v_b_SP_G_2$ ?v0) )))
+(or $x291 $x2768 $x1262)))) :pattern ( (v_b_SP_G_2$ ?v1) (v_b_SP_G_2$ ?v0) ) :qid k!42))
 ))
 (let (($x3717 (not $x3712)))
 (let (($x3749 (or $x3717 $x3746)))
 (let (($x3752 (not $x3749)))
 (let (($x1869 (>= (+ (v_b_SP_G_2$ ?v1!16) (* (- 1) (v_b_SP_G_2$ ?v0!17))) 0)))

 (let (($x3764 (not $x3761)))
 (let ((?x1846 (v_b_SP_G_2$ ?v0!15)))
 (let (($x1847 (>= ?x1846 0)))
 (let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
 (let (($x3904 (>= ?x257 0)))
-(let (($x3556 (forall ((?v0 B_Vertex$) )(!(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
-(>= ?x174 0)) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
+(let (($x3556 (forall ((?v0 B_Vertex$) )(! (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(>= ?x174 0)) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :qid k!42))
 ))
 (let (($x1848 (not $x1847)))
 (let (($x3767 (or $x1848 $x3764)))
 (let (($x3770 (not $x3767)))
 (let ((?x296 (v_b_SP_G_2$ b_Source$)))

 (let (($x773 (not $x297)))
 (let (($x3773 (or $x773 $x3770)))
 (let (($x3776 (not $x3773)))
 (let (($x3779 (or $x773 $x3776)))
 (let (($x3782 (not $x3779)))
-(let (($x3695 (forall ((?v0 B_Vertex$) )(!(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let (($x3695 (forall ((?v0 B_Vertex$) )(! (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let ((?x273 (v_b_SP_G_2$ ?v0)))
 (let (($x278 (= ?x273 ?x174)))
 (let (($x291 (fun_app$ v_b_Visited_G_2$ ?v0)))
 (let (($x300 (not $x291)))
-(or $x300 $x278)))))) :pattern ( (fun_app$ v_b_Visited_G_2$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
+(or $x300 $x278)))))) :pattern ( (fun_app$ v_b_Visited_G_2$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :qid k!42))
 ))
 (let (($x3700 (not $x3695)))
 (let (($x3785 (or $x3700 $x3782)))
 (let (($x3788 (not $x3785)))
 (let ((?x1827 (fun_app$c v_b_SP_G_1$ ?v0!14)))

 (let (($x1828 (= ?x1826 ?x1827)))
 (let (($x1829 (or (not (fun_app$ v_b_Visited_G_2$ ?v0!14)) $x1828)))
 (let (($x1830 (not $x1829)))
 (let (($x3791 (or $x1830 $x3788)))
 (let (($x3794 (not $x3791)))
-(let (($x3686 (forall ((?v0 B_Vertex$) )(!(>= (+ (fun_app$c v_b_SP_G_1$ ?v0) (* (- 1) (v_b_SP_G_2$ ?v0))) 0) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) )))
+(let (($x3686 (forall ((?v0 B_Vertex$) )(! (>= (+ (fun_app$c v_b_SP_G_1$ ?v0) (* (- 1) (v_b_SP_G_2$ ?v0))) 0) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) ) :qid k!42))
 ))
 (let (($x3691 (not $x3686)))
 (let (($x3797 (or $x3691 $x3794)))
 (let (($x3800 (not $x3797)))
 (let ((?x1809 (v_b_SP_G_2$ ?v0!13)))

 (let ((?x1811 (+ ?x1808 ?x1810)))
 (let (($x1812 (>= ?x1811 0)))
 (let (($x1813 (not $x1812)))
 (let (($x3803 (or $x1813 $x3800)))
 (let (($x3806 (not $x3803)))
-(let (($x3678 (forall ((?v0 B_Vertex$) )(!(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let (($x3678 (forall ((?v0 B_Vertex$) )(! (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let ((?x273 (v_b_SP_G_2$ ?v0)))
 (let (($x278 (= ?x273 ?x174)))
 (let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
 (let ((?x1173 (* (- 1) ?x257)))
 (let (($x1175 (<= (+ ?x174 ?x1173 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
 (let (($x1169 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
 (let (($x2717 (or $x1169 $x1175)))
 (let (($x2718 (not $x2717)))
-(or $x2718 $x278)))))))))) :pattern ( (pair$ v_b_v_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) )))
+(or $x2718 $x278)))))))))) :pattern ( (pair$ v_b_v_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) ) :qid k!42))
 ))
 (let (($x3683 (not $x3678)))
-(let (($x3670 (forall ((?v0 B_Vertex$) )(!(let ((?x273 (v_b_SP_G_2$ ?v0)))
+(let (($x3670 (forall ((?v0 B_Vertex$) )(! (let ((?x273 (v_b_SP_G_2$ ?v0)))
 (let ((?x1186 (* (- 1) ?x273)))
 (let ((?x268 (b_G$ (pair$ v_b_v_G_1$ ?v0))))
 (let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
 (let (($x1185 (= (+ ?x257 ?x268 ?x1186) 0)))
 (let (($x1175 (<= (+ (fun_app$c v_b_SP_G_1$ ?v0) (* (- 1) ?x257) (* (- 1) ?x268)) 0)))
 (let (($x1169 (<= (+ b_Infinity$ (* (- 1) ?x268)) 0)))
-(or $x1169 $x1175 $x1185)))))))) :pattern ( (pair$ v_b_v_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) )))
+(or $x1169 $x1175 $x1185)))))))) :pattern ( (pair$ v_b_v_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :pattern ( (v_b_SP_G_2$ ?v0) ) :qid k!42))
 ))
 (let (($x3675 (not $x3670)))
 (let ((?x263 (fun_upd$ v_b_Visited_G_1$)))
 (let ((?x264 (fun_app$b ?x263 v_b_v_G_1$)))
 (let ((?x265 (fun_app$a ?x264 true)))
 (let (($x266 (= v_b_Visited_G_2$ ?x265)))
 (let (($x2935 (not $x266)))
-(let (($x3660 (forall ((?v0 B_Vertex$) )(!(let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
+(let (($x3660 (forall ((?v0 B_Vertex$) )(! (let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
 (let ((?x1173 (* (- 1) ?x257)))
 (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v0)))
-(or $x178 (>= (+ ?x174 ?x1173) 0)))))) :pattern ( (fun_app$ v_b_Visited_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
+(or $x178 (>= (+ ?x174 ?x1173) 0)))))) :pattern ( (fun_app$ v_b_Visited_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :qid k!42))
 ))
 (let (($x3665 (not $x3660)))
 (let ((?x1173 (* (- 1) ?x257)))
 (let ((?x1212 (+ b_Infinity$ ?x1173)))
 (let (($x1213 (<= ?x1212 0)))

 (let (($x1773 (fun_app$ v_b_Visited_G_1$ ?v0!12)))
 (let (($x3809 (or $x1773 $x1778 $x255 $x1213 $x3665 $x2935 $x3675 $x3683 $x3806)))
 (let (($x3812 (not $x3809)))
 (let ((?x245 (fun_app$c v_b_SP_G_3$ b_Source$)))
 (let (($x246 (= ?x245 0)))
-(let (($x3622 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
+(let (($x3622 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
 (let (($x1140 (>= (+ ?x155 ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0))) 0)))
 (let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
 (let (($x1099 (<= (+ b_Infinity$ (* (- 1) ?x230)) 0)))
-(or $x1099 $x922 $x1140)))))) :pattern ( (pair$ ?v1 ?v0) )))
+(or $x1099 $x922 $x1140)))))) :pattern ( (pair$ ?v1 ?v0) ) :qid k!42))
 ))
 (let (($x3627 (not $x3622)))
 (let (($x3630 (or $x3627 $x246)))
 (let (($x3633 (not $x3630)))
 (let ((?x1734 (fun_app$c v_b_SP_G_3$ ?v0!11)))

 (let (($x1724 (<= (+ b_Infinity$ (* (- 1) ?x1721)) 0)))
 (let (($x2645 (or $x1724 $x1730 $x2209)))
 (let (($x2650 (not $x2645)))
 (let (($x3636 (or $x2650 $x3633)))
 (let (($x3639 (not $x3636)))
-(let (($x3614 (forall ((?v0 B_Vertex$) )(!(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v0)))
+(let (($x3614 (forall ((?v0 B_Vertex$) )(! (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v0)))
 (let ((?x2191 (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!9 ?v0) ?v0))))))
 (let (($x2192 (= ?x2191 0)))
 (let (($x2176 (<= (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0)))) 0)))
 (let (($x2617 (not (or $x2176 (not $x2192)))))
 (let (($x1099 (<= (+ b_Infinity$ (* (- 1) ?x230)) 0)))
 (let (($x127 (= ?v0 b_Source$)))
-(or $x127 $x1099 $x2617)))))))) :pattern ( (fun_app$c v_b_SP_G_3$ ?v0) )))
+(or $x127 $x1099 $x2617)))))))) :pattern ( (fun_app$c v_b_SP_G_3$ ?v0) ) :qid k!42))
 ))
 (let (($x3619 (not $x3614)))
 (let (($x3642 (or $x3619 $x3639)))
 (let (($x3645 (not $x3642)))
-(let (($x3600 (forall ((?v1 B_Vertex$) )(!(let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
+(let (($x3600 (forall ((?v1 B_Vertex$) )(! (let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
 (let ((?x1662 (* (- 1) ?x1661)))
 (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
 (let (($x2148 (= (+ ?x230 ?x1662 (b_G$ (pair$ ?v1 ?v0!8))) 0)))
-(or (>= (+ ?x230 ?x1662) 0) (not $x2148)))))) :pattern ( (fun_app$c v_b_SP_G_3$ ?v1) ) :pattern ( (pair$ ?v1 ?v0!8) )))
+(or (>= (+ ?x230 ?x1662) 0) (not $x2148)))))) :pattern ( (fun_app$c v_b_SP_G_3$ ?v1) ) :pattern ( (pair$ ?v1 ?v0!8) ) :qid k!42))
 ))
 (let (($x3605 (not $x3600)))
 (let (($x1664 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0!8))) 0)))
 (let (($x1659 (= ?v0!8 b_Source$)))
 (let (($x3608 (or $x1659 $x1664 $x3605)))

 (let (($x2708 (not $x217)))
 (let (($x215 (= v_b_v_G_2$ v_b_v_G_0$)))
 (let (($x2707 (not $x215)))
 (let (($x212 (= v_b_Visited_G_3$ v_b_Visited_G_1$)))
 (let (($x2706 (not $x212)))
-(let (($x3590 (forall ((?v0 B_Vertex$) )(!(let (($x1002 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
+(let (($x3590 (forall ((?v0 B_Vertex$) )(! (let (($x1002 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v0)))
-(or $x178 $x1002))) :pattern ( (fun_app$ v_b_Visited_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
+(or $x178 $x1002))) :pattern ( (fun_app$ v_b_Visited_G_1$ ?v0) ) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :qid k!42))
 ))
 (let (($x3595 (not $x3590)))
 (let (($x3654 (or $x3595 $x2706 $x2707 $x2708 $x2709 $x3651)))
 (let (($x3657 (not $x3654)))
 (let (($x3815 (or $x3657 $x3812)))
 (let (($x3818 (not $x3815)))
-(let (($x3581 (forall ((?v0 B_Vertex$) )(!(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let (($x3581 (forall ((?v0 B_Vertex$) )(! (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let ((?x2128 (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!7 ?v0) ?v0))))))
 (let (($x2129 (= ?x2128 0)))
 (let (($x2113 (<= (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0)))) 0)))
 (let (($x2551 (not (or $x2113 (not (fun_app$ v_b_Visited_G_1$ (?v1!7 ?v0))) (not $x2129)))))
 (let (($x1002 (<= (+ b_Infinity$ (* (- 1) ?x174)) 0)))
 (let (($x127 (= ?v0 b_Source$)))
-(or $x127 $x1002 $x2551)))))))) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) )))
+(or $x127 $x1002 $x2551)))))))) :pattern ( (fun_app$c v_b_SP_G_1$ ?v0) ) :qid k!42))
 ))
 (let (($x3586 (not $x3581)))
-(let (($x3573 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
+(let (($x3573 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x182 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let ((?x991 (* (- 1) ?x182)))
+(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
-(let (($x990 (>= (+ ?x155 ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
+(let (($x990 (>= (+ ?x155 ?x174 ?x991) 0)))
 (let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
 (let (($x179 (not $x178)))
-(or $x179 $x922 $x990))))))) :pattern ( (pair$ ?v1 ?v0) )))
+(or $x179 $x922 $x990))))))))) :pattern ( (pair$ ?v1 ?v0) ) :qid k!42))
 ))
 (let (($x3578 (not $x3573)))
-(let (($x3565 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
-(let (($x1015 (>= (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
+(let (($x3565 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x182 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let ((?x991 (* (- 1) ?x182)))
+(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
+(let (($x1015 (>= (+ ?x174 ?x991) 0)))
+(let (($x180 (fun_app$ v_b_Visited_G_1$ ?v0)))
+(let (($x2492 (not $x180)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
-(or $x178 (not (fun_app$ v_b_Visited_G_1$ ?v0)) $x1015)))) :pattern ( (fun_app$ v_b_Visited_G_1$ ?v1) (fun_app$ v_b_Visited_G_1$ ?v0) )))
+(or $x178 $x2492 $x1015)))))))) :pattern ( (fun_app$ v_b_Visited_G_1$ ?v1) (fun_app$ v_b_Visited_G_1$ ?v0) ) :qid k!42))
 ))
 (let (($x3570 (not $x3565)))
 (let (($x3561 (not $x3556)))
 (let ((?x172 (fun_app$c v_b_SP_G_1$ b_Source$)))
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+))
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 ))
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 ))
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-(let ((?x273 (v_b_SP_G_2$ ?v1)))
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+))
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+(let (($x617 (forall ((?v0 B_Vertex$) )(! (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let ((?x273 (v_b_SP_G_2$ ?v0)))
 (let (($x278 (= ?x273 ?x174)))
 (let ((?x268 (b_G$ (pair$ v_b_v_G_1$ ?v0))))
 (let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
 (let ((?x270 (+ ?x257 ?x268)))
 (let (($x272 (and (< ?x268 b_Infinity$) (< ?x270 ?x174))))
-(or $x272 $x278)))))))))
-))
-(let (($x611 (forall ((?v0 B_Vertex$) )(let ((?x268 (b_G$ (pair$ v_b_v_G_1$ ?v0))))
+(or $x272 $x278)))))))) :qid k!42))
+))
+(let (($x611 (forall ((?v0 B_Vertex$) )(! (let ((?x268 (b_G$ (pair$ v_b_v_G_1$ ?v0))))
 (let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
 (let ((?x270 (+ ?x257 ?x268)))
 (let ((?x273 (v_b_SP_G_2$ ?v0)))
 (let (($x274 (= ?x273 ?x270)))
 (let (($x272 (and (< ?x268 b_Infinity$) (< ?x270 (fun_app$c v_b_SP_G_1$ ?v0)))))
 (let (($x277 (not $x272)))
-(or $x277 $x274)))))))))
+(or $x277 $x274)))))))) :qid k!42))
 ))
 (let (($x620 (and $x611 $x617)))
 (let (($x623 (and $x266 $x620)))
-(let (($x605 (forall ((?v0 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let (($x605 (forall ((?v0 B_Vertex$) )(! (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
 (let (($x259 (<= ?x257 ?x174)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v0)))
-(or $x178 $x259))))))
+(or $x178 $x259))))) :qid k!42))
 ))
 (let (($x626 (and $x605 $x623)))
 (let (($x629 (and $x258 $x626)))
 (let (($x632 (and $x256 $x629)))
 (let (($x635 (and $x209 $x632)))
 (let (($x810 (or (not $x635) $x803)))
-(let (($x557 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
+(let (($x557 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
 (let ((?x521 (+ ?x155 ?x230)))
 (let ((?x233 (fun_app$c v_b_SP_G_3$ ?v0)))
 (let (($x545 (<= ?x233 ?x521)))
-(or (not (and (< ?x230 b_Infinity$) (< ?x155 b_Infinity$))) $x545)))))))
+(or (not (and (< ?x230 b_Infinity$) (< ?x155 b_Infinity$))) $x545)))))) :qid k!42))
 ))
 (let (($x573 (or (not $x557) $x246)))
 (let (($x578 (and $x557 $x573)))
-(let (($x542 (forall ((?v0 B_Vertex$) )(let (($x530 (exists ((?v1 B_Vertex$) )(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
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 (let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
 (let ((?x521 (+ ?x155 ?x230)))
 (let ((?x233 (fun_app$c v_b_SP_G_3$ ?v0)))
 (let (($x524 (= ?x233 ?x521)))
 (let (($x234 (< ?x230 ?x233)))
-(and $x234 $x524))))))))
+(and $x234 $x524))))))) :qid k!42))
 ))
 (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v0)))
 (let (($x231 (< ?x230 b_Infinity$)))
 (let (($x127 (= ?v0 b_Source$)))
 (let (($x132 (not $x127)))
 (let (($x232 (and $x132 $x231)))
-(or (not $x232) $x530))))))))
+(or (not $x232) $x530))))))) :qid k!42))
 ))
 (let (($x585 (or (not $x542) $x578)))
 (let (($x590 (and $x542 $x585)))
 (let (($x597 (or (not (and $x210 (and $x212 (and $x215 (and $x217 $x220))))) $x590)))
 (let (($x815 (and $x597 $x810)))
-(let (($x449 (forall ((?v0 B_Vertex$) )(let (($x437 (exists ((?v1 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
+(let (($x449 (forall ((?v0 B_Vertex$) )(! (let (($x437 (exists ((?v1 B_Vertex$) )(! (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
 (let ((?x410 (+ ?x155 ?x174)))
 (let ((?x182 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let (($x428 (= ?x182 ?x410)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
 (let (($x431 (and $x178 $x428)))
 (let (($x193 (< ?x174 ?x182)))
-(and $x193 $x431))))))))))
+(and $x193 $x431))))))))) :qid k!42))
 ))
 (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let (($x191 (< ?x174 b_Infinity$)))
 (let (($x127 (= ?v0 b_Source$)))
 (let (($x132 (not $x127)))
 (let (($x192 (and $x132 $x191)))
-(or (not $x192) $x437))))))))
-))
-(let (($x425 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
+(or (not $x192) $x437))))))) :qid k!42))
+))
+(let (($x425 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
 (let ((?x410 (+ ?x155 ?x174)))
 (let ((?x182 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let (($x413 (<= ?x182 ?x410)))
-(or (not (and (fun_app$ v_b_Visited_G_1$ ?v1) (< ?x155 b_Infinity$))) $x413)))))))
+(or (not (and (fun_app$ v_b_Visited_G_1$ ?v1) (< ?x155 b_Infinity$))) $x413)))))) :qid k!42))
 ))
 (let (($x459 (and $x425 $x449)))
-(let (($x407 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
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 (let ((?x182 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let (($x183 (<= ?x182 ?x174)))
 (let (($x180 (fun_app$ v_b_Visited_G_1$ ?v0)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
 (let (($x179 (not $x178)))
 (let (($x181 (and $x179 $x180)))
 (let (($x403 (not $x181)))
-(or $x403 $x183))))))))))
+(or $x403 $x183))))))))) :qid k!42))
 ))
 (let (($x462 (and $x407 $x459)))
 (let (($x465 (and $x176 $x462)))
 (let (($x468 (and $x173 $x465)))
-(let (($x400 (forall ((?v0 B_Vertex$) )(let (($x168 (exists ((?v1 B_Vertex$) )(let (($x136 (v_b_Visited_G_0$ ?v1)))
+(let (($x400 (forall ((?v0 B_Vertex$) )(! (let (($x168 (exists ((?v1 B_Vertex$) )(! (let (($x136 (v_b_Visited_G_0$ ?v1)))
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-(and (< (v_b_SP_G_0$ ?v1) (v_b_SP_G_0$ ?v0)) $x166))))
+(and (< (v_b_SP_G_0$ ?v1) (v_b_SP_G_0$ ?v0)) $x166))) :qid k!42))
 ))
 (let (($x127 (= ?v0 b_Source$)))
 (let (($x132 (not $x127)))
 (let (($x163 (and $x132 (< (v_b_SP_G_0$ ?v0) b_Infinity$))))
-(or (not $x163) $x168))))))
+(or (not $x163) $x168))))) :qid k!42))
 ))
 (let (($x482 (and $x400 $x468)))
 (let (($x822 (or (not $x482) $x815)))
 (let (($x827 (and $x400 $x822)))
-(let (($x393 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x150 (v_b_SP_G_0$ ?v0)))
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 (let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
 (let (($x156 (< ?x155 b_Infinity$)))
 (let (($x136 (v_b_Visited_G_0$ ?v1)))
 (let (($x157 (and $x136 $x156)))
-(or (not $x157) $x159))))))))
+(or (not $x157) $x159))))))) :qid k!42))
 ))
 (let (($x834 (or (not $x393) $x827)))
 (let (($x839 (and $x393 $x834)))
-(let (($x386 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x128 (v_b_SP_G_0$ ?v1)))
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 (let ((?x150 (v_b_SP_G_0$ ?v0)))
 (let (($x151 (<= ?x150 ?x128)))
 (let (($x148 (v_b_Visited_G_0$ ?v0)))
 (let (($x136 (v_b_Visited_G_0$ ?v1)))
 (let (($x137 (not $x136)))
 (let (($x149 (and $x137 $x148)))
 (let (($x382 (not $x149)))
-(or $x382 $x151))))))))))
+(or $x382 $x151))))))))) :qid k!42))
 ))
 (let (($x846 (or (not $x386) $x839)))
 (let (($x851 (and $x386 $x846)))
 (let (($x858 (or (not $x147) $x851)))
 (let (($x863 (and $x147 $x858)))
 (let (($x870 (or $x869 $x863)))
 (let (($x875 (and $x145 $x870)))
 (let (($x882 (or (not (and $x354 (and $x360 $x138))) $x875)))
-(let (($x1323 (exists ((?v1 B_Vertex$) )(let ((?x303 (v_b_SP_G_2$ ?0)))
-(let ((?x1263 (* (- 1) ?x303)))
-(let ((?x273 (v_b_SP_G_2$ ?v1)))
+(let (($x1323 (exists ((?v1 B_Vertex$) )(! (let ((?x273 (v_b_SP_G_2$ ?v1)))
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-(let (($x1306 (= (+ ?x155 ?x273 ?x1263) 0)))
+(let (($x1306 (= (+ ?x155 ?x273 (* (- 1) (v_b_SP_G_2$ ?0))) 0)))
 (let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(let (($x1262 (>= (+ ?x273 ?x1263) 0)))
+(let (($x1262 (>= (+ ?x273 (* (- 1) (v_b_SP_G_2$ ?0))) 0)))
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-(and $x1309 $x291 $x1306))))))))))
+(and $x1309 $x291 $x1306))))))) :qid k!42))
 ))
 (let (($x132 (not $x127)))
 (let (($x1300 (and $x132 (not (<= (+ b_Infinity$ (* (- 1) (v_b_SP_G_2$ ?0))) 0)))))
-(let (($x698 (exists ((?v1 B_Vertex$) )(let ((?x273 (v_b_SP_G_2$ ?v1)))
+(let (($x698 (exists ((?v1 B_Vertex$) )(! (let ((?x273 (v_b_SP_G_2$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?0))))
 (let ((?x671 (+ ?x155 ?x273)))
 (let ((?x303 (v_b_SP_G_2$ ?0)))
 (let (($x689 (= ?x303 ?x671)))
 (let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
 (let (($x692 (and $x291 $x689)))
 (let (($x314 (< ?x273 ?x303)))
-(and $x314 $x692))))))))))
+(and $x314 $x692))))))))) :qid k!42))
 ))
 (let (($x705 (or (not (and $x132 (< (v_b_SP_G_2$ ?0) b_Infinity$))) $x698)))
-(let ((?x303 (v_b_SP_G_2$ ?1)))
-(let ((?x1263 (* (- 1) ?x303)))
 (let ((?x273 (v_b_SP_G_2$ ?0)))
 (let ((?x155 (b_G$ (pair$ ?0 ?1))))
-(let (($x1306 (= (+ ?x155 ?x273 ?x1263) 0)))
+(let (($x1306 (= (+ ?x155 ?x273 (* (- 1) (v_b_SP_G_2$ ?1))) 0)))
 (let (($x291 (fun_app$ v_b_Visited_G_2$ ?0)))
-(let (($x1262 (>= (+ ?x273 ?x1263) 0)))
+(let (($x1262 (>= (+ ?x273 (* (- 1) (v_b_SP_G_2$ ?1))) 0)))
 (let (($x1309 (not $x1262)))
 (let (($x1318 (and $x1309 $x291 $x1306)))
 (let ((?x671 (+ ?x155 ?x273)))
+(let ((?x303 (v_b_SP_G_2$ ?1)))
 (let (($x689 (= ?x303 ?x671)))
 (let (($x692 (and $x291 $x689)))
 (let (($x314 (< ?x273 ?x303)))
 (let (($x695 (and $x314 $x692)))
 (let ((@x1317 (monotonicity (rewrite (= $x314 $x1309)) (monotonicity (rewrite (= $x689 $x1306)) (= $x692 (and $x291 $x1306))) (= $x695 (and $x1309 (and $x291 $x1306))))))
 (let ((@x1322 (trans @x1317 (rewrite (= (and $x1309 (and $x291 $x1306)) $x1318)) (= $x695 $x1318))))
 (let (($x1298 (= (< ?x273 b_Infinity$) (not (<= (+ b_Infinity$ (* (- 1) ?x273)) 0)))))
 (let ((@x1302 (monotonicity (rewrite $x1298) (= (and $x132 (< ?x273 b_Infinity$)) $x1300))))
 (let ((@x1305 (monotonicity @x1302 (= (not (and $x132 (< ?x273 b_Infinity$))) (not $x1300)))))
 (let ((@x1328 (monotonicity @x1305 (quant-intro @x1322 (= $x698 $x1323)) (= $x705 (or (not $x1300) $x1323)))))
-(let (($x1282 (>= (+ ?x155 ?x273 ?x1263) 0)))
+(let (($x1282 (>= (+ ?x155 ?x273 (* (- 1) ?x303)) 0)))
 (let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
 (let (($x923 (not $x922)))
 (let (($x1276 (and $x291 $x923)))
 (let (($x1279 (not $x1276)))
 (let (($x1286 (or $x1279 $x1282)))

 (let (($x681 (or (not (and $x291 (< ?x155 b_Infinity$))) $x674)))
 (let ((@x925 (rewrite (= (< ?x155 b_Infinity$) $x923))))
 (let ((@x1281 (monotonicity (monotonicity @x925 (= (and $x291 (< ?x155 b_Infinity$)) $x1276)) (= (not (and $x291 (< ?x155 b_Infinity$))) $x1279))))
 (let ((@x1291 (quant-intro (monotonicity @x1281 (rewrite (= $x674 $x1282)) (= $x681 $x1286)) (= $x686 $x1289))))
 (let ((@x1334 (monotonicity (monotonicity @x1291 (= (not $x686) $x1292)) (quant-intro @x1328 (= $x710 $x1329)) (= $x738 $x1332))))
-(let (($x301 (fun_app$ v_b_Visited_G_2$ ?1)))
 (let (($x300 (not $x291)))
-(let (($x302 (and $x300 $x301)))
+(let (($x302 (and $x300 (fun_app$ v_b_Visited_G_2$ ?1))))
 (let (($x664 (not $x302)))
 (let (($x1267 (or $x664 $x1262)))
 (let (($x304 (<= ?x303 ?x273)))
 (let (($x665 (or $x664 $x304)))
 (let ((@x1272 (quant-intro (monotonicity (rewrite (= $x304 $x1262)) (= $x665 $x1267)) (= $x668 $x1270))))

 (let (($x552 (or (not (and (< ?x230 b_Infinity$) (< ?x155 b_Infinity$))) $x545)))
 (let ((@x1136 (monotonicity (rewrite (= (< ?x230 b_Infinity$) $x1100)) @x925 (= (and (< ?x230 b_Infinity$) (< ?x155 b_Infinity$)) $x1134))))
 (let ((@x1139 (monotonicity @x1136 (= (not (and (< ?x230 b_Infinity$) (< ?x155 b_Infinity$))) $x1137))))
 (let ((@x1148 (quant-intro (monotonicity @x1139 (rewrite (= $x545 $x1140)) (= $x552 $x1143)) (= $x557 $x1146))))
 (let ((@x1154 (monotonicity (monotonicity @x1148 (= (not $x557) $x1149)) (= $x573 $x1152))))
-(let (($x1122 (exists ((?v1 B_Vertex$) )(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
+(let (($x1122 (exists ((?v1 B_Vertex$) )(! (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?0))))
-(and (not (>= (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ ?0))) 0)) (= (+ ?x155 ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ ?0))) 0)))))
+(and (not (>= (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ ?0))) 0)) (= (+ ?x155 ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ ?0))) 0)))) :qid k!42))
 ))
 (let (($x1103 (and $x132 $x1100)))
 (let (($x1106 (not $x1103)))
 (let (($x1125 (or $x1106 $x1122)))
-(let (($x530 (exists ((?v1 B_Vertex$) )(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
+(let (($x530 (exists ((?v1 B_Vertex$) )(! (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?0))))
 (let ((?x521 (+ ?x155 ?x230)))
 (let ((?x233 (fun_app$c v_b_SP_G_3$ ?0)))
 (let (($x524 (= ?x233 ?x521)))
 (let (($x234 (< ?x230 ?x233)))
-(and $x234 $x524))))))))
+(and $x234 $x524))))))) :qid k!42))
 ))
 (let (($x537 (or (not (and $x132 (< ?x230 b_Infinity$))) $x530)))
 (let (($x1119 (and (not (>= (+ ?x230 (* (- 1) ?x233)) 0)) (= (+ ?x155 ?x230 (* (- 1) ?x233)) 0))))
 (let (($x524 (= ?x233 ?x521)))
 (let (($x234 (< ?x230 ?x233)))

 (let ((@x1088 (monotonicity (monotonicity (quant-intro @x1079 (= $x209 $x1080)) (= $x210 $x1083)) (= $x507 (and $x1083 $x493)))))
 (let ((@x1096 (monotonicity (trans @x1088 @x1091 (= $x507 $x1089)) (= (not $x507) $x1094))))
 (let ((@x1166 (monotonicity @x1096 (monotonicity (quant-intro @x1127 (= $x542 $x1128)) @x1160 (= $x590 $x1161)) (= $x597 $x1164))))
 (let (($x1070 (= (and $x980 (and $x173 (and $x1051 (and $x1045 (and $x997 $x1037))))) $x1069)))
 (let (($x1067 (= $x482 (and $x980 (and $x173 (and $x1051 (and $x1045 (and $x997 $x1037))))))))
-(let (($x1031 (exists ((?v1 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
+(let (($x1031 (exists ((?v1 B_Vertex$) )(! (let ((?x182 (fun_app$c v_b_SP_G_1$ ?0)))
+(let ((?x991 (* (- 1) ?x182)))
+(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?0))))
-(let (($x1012 (= (+ ?x155 ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?0))) 0)))
+(let (($x1012 (= (+ ?x155 ?x174 ?x991) 0)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
-(let (($x1015 (>= (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?0))) 0)))
+(let (($x1015 (>= (+ ?x174 ?x991) 0)))
 (let (($x1017 (not $x1015)))
-(and $x1017 $x178 $x1012))))))))
+(and $x1017 $x178 $x1012))))))))) :qid k!42))
 ))
 (let (($x1006 (and $x132 $x1003)))
 (let (($x1009 (not $x1006)))
 (let (($x1034 (or $x1009 $x1031)))
-(let (($x437 (exists ((?v1 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
+(let (($x437 (exists ((?v1 B_Vertex$) )(! (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?0))))
 (let ((?x410 (+ ?x155 ?x174)))
 (let ((?x182 (fun_app$c v_b_SP_G_1$ ?0)))
 (let (($x428 (= ?x182 ?x410)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
 (let (($x431 (and $x178 $x428)))
 (let (($x193 (< ?x174 ?x182)))
-(and $x193 $x431))))))))))
+(and $x193 $x431))))))))) :qid k!42))
 ))
 (let (($x444 (or (not (and $x132 (< ?x174 b_Infinity$))) $x437)))
 (let (($x1012 (= (+ ?x155 ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?1))) 0)))
 (let (($x1015 (>= (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?1))) 0)))
 (let (($x1017 (not $x1015)))

 (let (($x404 (or $x403 $x183)))
 (let ((@x1047 (quant-intro (monotonicity (rewrite (= $x183 $x1015)) (= $x404 $x1042)) (= $x407 $x1045))))
 (let ((@x1053 (quant-intro (rewrite (= (<= 0 ?x174) (>= ?x174 0))) (= $x176 $x1051))))
 (let ((@x1062 (monotonicity @x1053 (monotonicity @x1047 @x1056 (= $x462 (and $x1045 (and $x997 $x1037)))) (= $x465 (and $x1051 (and $x1045 (and $x997 $x1037)))))))
 (let ((@x1065 (monotonicity @x1062 (= $x468 (and $x173 (and $x1051 (and $x1045 (and $x997 $x1037))))))))
-(let (($x974 (exists ((?v1 B_Vertex$) )(let ((?x155 (b_G$ (pair$ ?v1 ?0))))
+(let (($x974 (exists ((?v1 B_Vertex$) )(! (let ((?x155 (b_G$ (pair$ ?v1 ?0))))
 (let ((?x128 (v_b_SP_G_0$ ?v1)))
 (let (($x957 (= (+ ?x128 (* (- 1) (v_b_SP_G_0$ ?0)) ?x155) 0)))
 (let (($x136 (v_b_Visited_G_0$ ?v1)))
 (let (($x907 (>= (+ ?x128 (* (- 1) (v_b_SP_G_0$ ?0))) 0)))
 (let (($x960 (not $x907)))
-(and $x960 $x136 $x957))))))))
+(and $x960 $x136 $x957))))))) :qid k!42))
 ))
 (let (($x951 (and $x132 (not (<= (+ b_Infinity$ (* (- 1) (v_b_SP_G_0$ ?0))) 0)))))
 (let (($x954 (not $x951)))
 (let (($x977 (or $x954 $x974)))
-(let (($x168 (exists ((?v1 B_Vertex$) )(let (($x136 (v_b_Visited_G_0$ ?v1)))
+(let (($x168 (exists ((?v1 B_Vertex$) )(! (let (($x136 (v_b_Visited_G_0$ ?v1)))
 (let (($x166 (and $x136 (= (v_b_SP_G_0$ ?0) (+ (v_b_SP_G_0$ ?v1) (b_G$ (pair$ ?v1 ?0)))))))
-(and (< (v_b_SP_G_0$ ?v1) (v_b_SP_G_0$ ?0)) $x166))))
+(and (< (v_b_SP_G_0$ ?v1) (v_b_SP_G_0$ ?0)) $x166))) :qid k!42))
 ))
 (let (($x397 (or (not (and $x132 (< (v_b_SP_G_0$ ?0) b_Infinity$))) $x168)))
 (let (($x957 (= (+ (v_b_SP_G_0$ ?0) (* (- 1) (v_b_SP_G_0$ ?1)) ?x155) 0)))
 (let (($x136 (v_b_Visited_G_0$ ?0)))
 (let (($x907 (>= (+ (v_b_SP_G_0$ ?0) (* (- 1) (v_b_SP_G_0$ ?1))) 0)))

 (let ((@x901 (quant-intro (rewrite (= (<= 0 ?x128) (>= ?x128 0))) (= $x147 $x899))))
 (let ((@x1394 (monotonicity (monotonicity @x901 (= (not $x147) $x902)) (monotonicity @x916 @x1388 (= $x851 $x1389)) (= $x858 $x1392))))
 (let ((@x1400 (monotonicity (monotonicity @x901 @x1394 (= $x863 $x1395)) (= $x870 $x1398))))
 (let ((@x895 (monotonicity (rewrite (= (and $x354 (and $x360 $x138)) $x890)) (= (not (and $x354 (and $x360 $x138))) (not $x890)))))
 (let ((@x1406 (monotonicity @x895 (monotonicity @x1400 (= $x875 $x1401)) (= $x882 (or (not $x890) $x1401)))))
-(let (($x318 (exists ((?v1 B_Vertex$) )(let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
+(let (($x318 (exists ((?v1 B_Vertex$) )(! (let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
 (let (($x316 (and $x291 (= (v_b_SP_G_2$ ?0) (+ (v_b_SP_G_2$ ?v1) (b_G$ (pair$ ?v1 ?0)))))))
 (let ((?x303 (v_b_SP_G_2$ ?0)))
 (let ((?x273 (v_b_SP_G_2$ ?v1)))
 (let (($x314 (< ?x273 ?x303)))
-(and $x314 $x316)))))))
+(and $x314 $x316)))))) :qid k!42))
 ))
 (let (($x313 (and $x132 (< ?x273 b_Infinity$))))
 (let (($x319 (=> $x313 $x318)))
 (let ((@x691 (monotonicity (rewrite (= (+ ?x273 ?x155) ?x671)) (= (= ?x303 (+ ?x273 ?x155)) $x689))))
 (let ((@x697 (monotonicity (monotonicity @x691 (= (and $x291 (= ?x303 (+ ?x273 ?x155))) $x692)) (= (and $x314 (and $x291 (= ?x303 (+ ?x273 ?x155)))) $x695))))

 (let (($x243 (=> $x241 (<= ?x233 (+ ?x230 ?x155)))))
 (let ((@x547 (monotonicity (rewrite (= (+ ?x230 ?x155) ?x521)) (= (<= ?x233 (+ ?x230 ?x155)) $x545))))
 (let ((@x556 (trans (monotonicity @x547 (= $x243 (=> $x241 $x545))) (rewrite (= (=> $x241 $x545) $x552)) (= $x243 $x552))))
 (let ((@x571 (monotonicity (quant-intro @x556 (= $x244 $x557)) (trans @x564 (rewrite (= (and $x246 true) $x246)) (= $x248 $x246)) (= $x249 (=> $x557 $x246)))))
 (let ((@x580 (monotonicity (quant-intro @x556 (= $x244 $x557)) (trans @x571 (rewrite (= (=> $x557 $x246) $x573)) (= $x249 $x573)) (= (and $x244 $x249) $x578))))
-(let (($x238 (exists ((?v1 B_Vertex$) )(let ((?x155 (b_G$ (pair$ ?v1 ?0))))
+(let (($x238 (exists ((?v1 B_Vertex$) )(! (let ((?x155 (b_G$ (pair$ ?v1 ?0))))
 (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
 (let ((?x235 (+ ?x230 ?x155)))
 (let ((?x233 (fun_app$c v_b_SP_G_3$ ?0)))
 (let (($x234 (< ?x230 ?x233)))
-(and $x234 (= ?x233 ?x235))))))))
+(and $x234 (= ?x233 ?x235))))))) :qid k!42))
 ))
 (let (($x232 (and $x132 $x231)))
 (let (($x239 (=> $x232 $x238)))
 (let ((@x526 (monotonicity (rewrite (= (+ ?x230 ?x155) ?x521)) (= (= ?x233 (+ ?x230 ?x155)) $x524))))
 (let ((@x532 (quant-intro (monotonicity @x526 (= (and $x234 (= ?x233 (+ ?x230 ?x155))) $x527)) (= $x238 $x530))))

 (let ((@x506 (trans (monotonicity @x502 (= $x226 (and true $x493))) (rewrite (= (and true $x493) $x493)) (= $x226 $x493))))
 (let ((@x512 (monotonicity (monotonicity @x506 (= (and $x210 $x226) $x507)) (= $x228 (and true $x507)))))
 (let ((@x518 (monotonicity (trans @x512 (rewrite (= (and true $x507) $x507)) (= $x228 $x507)) (= $x229 (and true $x507)))))
 (let ((@x595 (monotonicity (trans @x518 (rewrite (= (and true $x507) $x507)) (= $x229 $x507)) @x592 (= $x253 (=> $x507 $x590)))))
 (let ((@x817 (monotonicity (trans @x595 (rewrite (= (=> $x507 $x590) $x597)) (= $x253 $x597)) (trans @x808 (rewrite (= (=> $x635 $x803) $x810)) (= $x336 $x810)) (= (and $x253 $x336) $x815))))
-(let (($x197 (exists ((?v1 B_Vertex$) )(let ((?x155 (b_G$ (pair$ ?v1 ?0))))
+(let (($x197 (exists ((?v1 B_Vertex$) )(! (let ((?x155 (b_G$ (pair$ ?v1 ?0))))
 (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
 (let ((?x187 (+ ?x174 ?x155)))
 (let ((?x182 (fun_app$c v_b_SP_G_1$ ?0)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
 (let (($x193 (< ?x174 ?x182)))
-(and $x193 (and $x178 (= ?x182 ?x187))))))))))
+(and $x193 (and $x178 (= ?x182 ?x187))))))))) :qid k!42))
 ))
 (let (($x191 (< ?x174 b_Infinity$)))
 (let (($x192 (and $x132 $x191)))
 (let (($x198 (=> $x192 $x197)))
 (let ((@x430 (monotonicity (rewrite (= (+ ?x174 ?x155) ?x410)) (= (= ?x182 (+ ?x174 ?x155)) $x428))))

 (let ((@x5777 (unit-resolution (hypothesis $x6457) (mp (unit-resolution @x5602 @x3498 (hypothesis $x1539) $x5616) @x5778 $x5625) false)))
 (let ((@x5735 (unit-resolution (lemma @x5777 (or $x5625 $x1538)) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x6457 $x1543)) @x6514 $x6457) @x6246 false)))
 (let (($x3544 (not $x3541)))
 (let (($x3827 (or $x3544 $x3824)))
 (let (($x3830 (not $x3827)))
-(let (($x3524 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
+(let (($x3524 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
 (let ((?x128 (v_b_SP_G_0$ ?v1)))
 (let (($x933 (>= (+ ?x128 (* (- 1) (v_b_SP_G_0$ ?v0)) ?x155) 0)))
 (let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
 (let (($x136 (v_b_Visited_G_0$ ?v1)))
 (let (($x137 (not $x136)))
-(or $x137 $x922 $x933))))))) :pattern ( (pair$ ?v1 ?v0) )))
+(or $x137 $x922 $x933))))))) :pattern ( (pair$ ?v1 ?v0) ) :qid k!42))
 ))
 (let (($x3529 (not $x3524)))
 (let (($x3833 (or $x3529 $x3830)))
 (let (($x3836 (not $x3833)))
 (let ((?x1522 (v_b_SP_G_0$ ?v0!4)))

 (let (($x2048 (>= ?x2045 0)))
 (let (($x1517 (<= (+ b_Infinity$ (* (- 1) ?x1514)) 0)))
 (let (($x1512 (v_b_Visited_G_0$ ?v1!3)))
 (let (($x2394 (not $x1512)))
 (let (($x2409 (or $x2394 $x1517 $x2048)))
-(let (($x3500 (forall ((?v0 B_Vertex$) )(!(let (($x136 (v_b_Visited_G_0$ ?v0)))
-(not $x136)) :pattern ( (v_b_Visited_G_0$ ?v0) )))
+(let (($x3500 (forall ((?v0 B_Vertex$) )(! (let (($x136 (v_b_Visited_G_0$ ?v0)))
+(not $x136)) :pattern ( (v_b_Visited_G_0$ ?v0) ) :qid k!42))
 ))
 (let ((@x1468 (mp~ (and-elim @x1413 $x138) (nnf-pos (refl (~ $x137 $x137)) (~ $x138 $x138)) $x138)))
 (let ((@x3505 (mp @x1468 (quant-intro (refl (= $x137 $x137)) (= $x138 $x3500)) $x3500)))
 (let ((@x3073 (unit-resolution ((_ quant-inst ?v1!3) (or (not $x3500) $x2394)) @x3505 (hypothesis $x1512) false)))
 (let (($x2414 (not $x2409)))
 (let (($x3839 (or $x2414 $x3836)))
 (let (($x3842 (not $x3839)))
-(let (($x3515 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let (($x907 (>= (+ (v_b_SP_G_0$ ?v1) (* (- 1) (v_b_SP_G_0$ ?v0))) 0)))
+(let (($x3515 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let (($x907 (>= (+ (v_b_SP_G_0$ ?v1) (* (- 1) (v_b_SP_G_0$ ?v0))) 0)))
 (let (($x136 (v_b_Visited_G_0$ ?v1)))
-(or $x136 (not (v_b_Visited_G_0$ ?v0)) $x907))) :pattern ( (v_b_Visited_G_0$ ?v1) (v_b_Visited_G_0$ ?v0) )))
+(or $x136 (not (v_b_Visited_G_0$ ?v0)) $x907))) :pattern ( (v_b_Visited_G_0$ ?v1) (v_b_Visited_G_0$ ?v0) ) :qid k!42))
 ))
 (let (($x3520 (not $x3515)))
 (let (($x3845 (or $x3520 $x3842)))
 (let (($x3848 (not $x3845)))
 (let (($x1498 (>= (+ (v_b_SP_G_0$ ?v1!1) (* (- 1) (v_b_SP_G_0$ ?v0!2))) 0)))

 (let (($x1489 (v_b_Visited_G_0$ ?v1!1)))
 (let (($x2363 (or $x1489 $x2348 $x1498)))
 (let (($x2368 (not $x2363)))
 (let (($x3851 (or $x2368 $x3848)))
 (let (($x3854 (not $x3851)))
-(let (($x3506 (forall ((?v0 B_Vertex$) )(!(let ((?x128 (v_b_SP_G_0$ ?v0)))
-(>= ?x128 0)) :pattern ( (v_b_SP_G_0$ ?v0) )))
+(let (($x3506 (forall ((?v0 B_Vertex$) )(! (let ((?x128 (v_b_SP_G_0$ ?v0)))
+(>= ?x128 0)) :pattern ( (v_b_SP_G_0$ ?v0) ) :qid k!42))
 ))
 (let (($x3511 (not $x3506)))
 (let (($x3857 (or $x3511 $x3854)))
 (let (($x3860 (not $x3857)))
 (let ((?x1475 (v_b_SP_G_0$ ?v0!0)))

 (let ((@x4994 (symm (commutativity (= $x5734 (= ?x1475 b_Infinity$))) (= (= ?x1475 b_Infinity$) $x5734))))
 (let (($x5461 (= ?x1475 b_Infinity$)))
 (let (($x5589 (= ?v0!0 b_Source$)))
 (let (($x4695 (not $x5589)))
 (let ((@x5096 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1475 0)) $x1476)) @x5848 (not (= ?x1475 0)))))
-(let (($x3487 (forall ((?v0 B_Vertex$) )(!(let (($x127 (= ?v0 b_Source$)))
+(let (($x3487 (forall ((?v0 B_Vertex$) )(! (let (($x127 (= ?v0 b_Source$)))
 (let (($x132 (not $x127)))
-(or $x132 (= (v_b_SP_G_0$ ?v0) 0)))) :pattern ( (v_b_SP_G_0$ ?v0) )))
+(or $x132 (= (v_b_SP_G_0$ ?v0) 0)))) :pattern ( (v_b_SP_G_0$ ?v0) ) :qid k!42))
 ))
 (let ((@x3491 (quant-intro (refl (= (or $x132 (= ?x128 0)) (or $x132 (= ?x128 0)))) (= $x354 $x3487))))
 (let ((@x1457 (nnf-pos (refl (~ (or $x132 (= ?x128 0)) (or $x132 (= ?x128 0)))) (~ $x354 $x354))))
 (let ((@x3492 (mp (mp~ (and-elim @x1413 $x354) @x1457 $x354) @x3491 $x3487)))
 (let (($x5571 (= (or (not $x3487) (or $x4695 (= ?x1475 0))) (or (not $x3487) $x4695 (= ?x1475 0)))))

 (let ((@x5707 (trans @x5657 (rewrite (= (or false $x145) $x145)) (= (or (not (= b_Source$ b_Source$)) $x145) $x145))))
 (let ((@x5373 (monotonicity @x5707 (= (or $x5983 (or (not (= b_Source$ b_Source$)) $x145)) $x3194))))
 (let ((@x5431 (trans @x5373 (rewrite (= $x3194 $x3194)) (= (or $x5983 (or (not (= b_Source$ b_Source$)) $x145)) $x3194))))
 (let ((@x5763 (mp ((_ quant-inst b_Source$) (or $x5983 (or (not (= b_Source$ b_Source$)) $x145))) @x5431 $x3194)))
 (let (($x3875 (or $x869 $x3872)))
-(let (($x2848 (forall ((?v1 B_Vertex$) )(let ((?x1911 (v_b_SP_G_2$ ?v0!20)))
+(let (($x2848 (forall ((?v1 B_Vertex$) )(! (let ((?x1911 (v_b_SP_G_2$ ?v0!20)))
 (let ((?x1912 (* (- 1) ?x1911)))
 (let ((?x273 (v_b_SP_G_2$ ?v1)))
 (let (($x2242 (= (+ ?x273 ?x1912 (b_G$ (pair$ ?v1 ?v0!20))) 0)))
 (let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
 (let (($x300 (not $x291)))
-(or (>= (+ ?x273 ?x1912) 0) $x300 (not $x2242)))))))))
-))
-(let (($x2833 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x303 (v_b_SP_G_2$ ?v0)))
-(let ((?x1263 (* (- 1) ?x303)))
-(let ((?x273 (v_b_SP_G_2$ ?v1)))
+(or (>= (+ ?x273 ?x1912) 0) $x300 (not $x2242)))))))) :qid k!42))
+))
+(let (($x2833 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x273 (v_b_SP_G_2$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
-(let (($x1282 (>= (+ ?x155 ?x273 ?x1263) 0)))
+(let (($x1282 (>= (+ ?x155 ?x273 (* (- 1) (v_b_SP_G_2$ ?v0))) 0)))
 (let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
 (let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
 (let (($x300 (not $x291)))
-(or $x300 $x922 $x1282))))))))))
+(or $x300 $x922 $x1282))))))) :qid k!42))
 ))
 (let (($x2857 (not (or (not $x2833) $x1909 $x1914 (not $x2848)))))
 (let (($x2862 (or $x2811 $x2857)))
-(let (($x2788 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let (($x1262 (>= (+ (v_b_SP_G_2$ ?v1) (* (- 1) (v_b_SP_G_2$ ?v0))) 0)))
-(let (($x301 (fun_app$ v_b_Visited_G_2$ ?v0)))
-(let (($x2768 (not $x301)))
+(let (($x2788 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let (($x1262 (>= (+ (v_b_SP_G_2$ ?v1) (* (- 1) (v_b_SP_G_2$ ?v0))) 0)))
+(let (($x2768 (not (fun_app$ v_b_Visited_G_2$ ?v0))))
 (let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(or $x291 $x2768 $x1262))))))
+(or $x291 $x2768 $x1262)))) :qid k!42))
 ))
 (let (($x2871 (not (or (not $x2788) (not $x2862)))))
 (let (($x2876 (or $x2765 $x2871)))
 (let (($x2884 (not (or $x1259 (not $x2876)))))
 (let (($x2889 (or $x1848 $x2884)))

 (let (($x2902 (or $x773 $x2897)))
 (let (($x2910 (not (or $x785 (not $x2902)))))
 (let (($x2915 (or $x1830 $x2910)))
 (let (($x2923 (not (or $x1250 (not $x2915)))))
 (let (($x2928 (or $x1813 $x2923)))
-(let (($x2742 (forall ((?v0 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let (($x2742 (forall ((?v0 B_Vertex$) )(! (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let ((?x273 (v_b_SP_G_2$ ?v0)))
 (let (($x278 (= ?x273 ?x174)))
 (let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
 (let ((?x1173 (* (- 1) ?x257)))
 (let (($x1175 (<= (+ ?x174 ?x1173 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
 (let (($x1169 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
 (let (($x2717 (or $x1169 $x1175)))
 (let (($x2718 (not $x2717)))
-(or $x2718 $x278)))))))))))
-))
-(let (($x2736 (forall ((?v0 B_Vertex$) )(let ((?x273 (v_b_SP_G_2$ ?v0)))
+(or $x2718 $x278)))))))))) :qid k!42))
+))
+(let (($x2736 (forall ((?v0 B_Vertex$) )(! (let ((?x273 (v_b_SP_G_2$ ?v0)))
 (let ((?x1186 (* (- 1) ?x273)))
 (let ((?x268 (b_G$ (pair$ v_b_v_G_1$ ?v0))))
 (let ((?x257 (fun_app$c v_b_SP_G_1$ v_b_v_G_1$)))
 (let (($x1185 (= (+ ?x257 ?x268 ?x1186) 0)))
 (let (($x1175 (<= (+ (fun_app$c v_b_SP_G_1$ ?v0) (* (- 1) ?x257) (* (- 1) ?x268)) 0)))
 (let (($x1169 (<= (+ b_Infinity$ (* (- 1) ?x268)) 0)))
-(or $x1169 $x1175 $x1185)))))))))
+(or $x1169 $x1175 $x1185)))))))) :qid k!42))
 ))
 (let (($x2939 (or $x1773 $x1778 $x255 $x1213 (not $x1209) $x2935 (not $x2736) (not $x2742) (not $x2928))))
 (let (($x2940 (not $x2939)))
-(let (($x2672 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
+(let (($x2672 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
 (let (($x1140 (>= (+ ?x155 ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ ?v0))) 0)))
 (let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
 (let (($x1099 (<= (+ b_Infinity$ (* (- 1) ?x230)) 0)))
-(or $x1099 $x922 $x1140)))))))
+(or $x1099 $x922 $x1140)))))) :qid k!42))
 ))
 (let (($x2680 (not (or (not $x2672) $x246))))
 (let (($x2685 (or $x2650 $x2680)))
-(let (($x2628 (forall ((?v0 B_Vertex$) )(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v0)))
+(let (($x2628 (forall ((?v0 B_Vertex$) )(! (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v0)))
 (let ((?x2191 (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!9 ?v0) ?v0))))))
 (let (($x2192 (= ?x2191 0)))
 (let (($x2176 (<= (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0)))) 0)))
 (let (($x2617 (not (or $x2176 (not $x2192)))))
 (let (($x1099 (<= (+ b_Infinity$ (* (- 1) ?x230)) 0)))
 (let (($x127 (= ?v0 b_Source$)))
-(or $x127 $x1099 $x2617)))))))))
+(or $x127 $x1099 $x2617)))))))) :qid k!42))
 ))
 (let (($x2694 (not (or (not $x2628) (not $x2685)))))
-(let (($x2591 (forall ((?v1 B_Vertex$) )(let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
+(let (($x2591 (forall ((?v1 B_Vertex$) )(! (let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
 (let ((?x1662 (* (- 1) ?x1661)))
 (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
 (let (($x2148 (= (+ ?x230 ?x1662 (b_G$ (pair$ ?v1 ?v0!8))) 0)))
-(or (>= (+ ?x230 ?x1662) 0) (not $x2148)))))))
+(or (>= (+ ?x230 ?x1662) 0) (not $x2148)))))) :qid k!42))
 ))
 (let (($x2599 (not (or $x1659 $x1664 (not $x2591)))))
 (let (($x2699 (or $x2599 $x2694)))
-(let (($x2576 (forall ((?v0 B_Vertex$) )(let (($x1002 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
+(let (($x2576 (forall ((?v0 B_Vertex$) )(! (let (($x1002 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v0)))
-(or $x178 $x1002))))
+(or $x178 $x1002))) :qid k!42))
 ))
 (let (($x2712 (not (or (not $x2576) $x2706 $x2707 $x2708 $x2709 (not $x2699)))))
 (let (($x2945 (or $x2712 $x2940)))
-(let (($x2562 (forall ((?v0 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let (($x2562 (forall ((?v0 B_Vertex$) )(! (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let ((?x2128 (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!7 ?v0) ?v0))))))
 (let (($x2129 (= ?x2128 0)))
 (let (($x2113 (<= (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0)))) 0)))
 (let (($x2551 (not (or $x2113 (not (fun_app$ v_b_Visited_G_1$ (?v1!7 ?v0))) (not $x2129)))))
 (let (($x1002 (<= (+ b_Infinity$ (* (- 1) ?x174)) 0)))
 (let (($x127 (= ?v0 b_Source$)))
-(or $x127 $x1002 $x2551)))))))))
-))
-(let (($x2534 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
+(or $x127 $x1002 $x2551)))))))) :qid k!42))
+))
+(let (($x2534 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x182 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let ((?x991 (* (- 1) ?x182)))
+(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
 (let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
-(let (($x990 (>= (+ ?x155 ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
+(let (($x990 (>= (+ ?x155 ?x174 ?x991) 0)))
 (let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
 (let (($x179 (not $x178)))
-(or $x179 $x922 $x990))))))))
-))
-(let (($x2512 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
-(let (($x1015 (>= (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
+(or $x179 $x922 $x990))))))))) :qid k!42))
+))
+(let (($x2512 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x182 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let ((?x991 (* (- 1) ?x182)))
+(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v1)))
+(let (($x1015 (>= (+ ?x174 ?x991) 0)))
+(let (($x180 (fun_app$ v_b_Visited_G_1$ ?v0)))
+(let (($x2492 (not $x180)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v1)))
-(or $x178 (not (fun_app$ v_b_Visited_G_1$ ?v0)) $x1015)))))
-))
-(let (($x2489 (forall ((?v0 B_Vertex$) )(let ((?x128 (v_b_SP_G_0$ ?v0)))
+(or $x178 $x2492 $x1015)))))))) :qid k!42))
+))
+(let (($x2489 (forall ((?v0 B_Vertex$) )(! (let ((?x128 (v_b_SP_G_0$ ?v0)))
 (let ((?x2090 (+ ?x128 (* (- 1) (v_b_SP_G_0$ (?v1!6 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!6 ?v0) ?v0))))))
 (let (($x2091 (= ?x2090 0)))
 (let (($x2075 (<= (+ ?x128 (* (- 1) (v_b_SP_G_0$ (?v1!6 ?v0)))) 0)))
 (let (($x2478 (not (or $x2075 (not (v_b_Visited_G_0$ (?v1!6 ?v0))) (not $x2091)))))
 (let (($x947 (<= (+ b_Infinity$ (* (- 1) ?x128)) 0)))
 (let (($x127 (= ?v0 b_Source$)))
-(or $x127 $x947 $x2478)))))))))
+(or $x127 $x947 $x2478)))))))) :qid k!42))
 ))
 (let (($x2958 (or (not $x2489) $x2952 (not $x1051) (not $x2512) (not $x2534) (not $x2562) (not $x2945))))
 (let (($x2959 (not $x2958)))
-(let (($x2451 (forall ((?v1 B_Vertex$) )(let ((?x1540 (v_b_SP_G_0$ ?v0!5)))
+(let (($x2451 (forall ((?v1 B_Vertex$) )(! (let ((?x1540 (v_b_SP_G_0$ ?v0!5)))
 (let ((?x1541 (* (- 1) ?x1540)))
 (let ((?x128 (v_b_SP_G_0$ ?v1)))
 (let (($x136 (v_b_Visited_G_0$ ?v1)))
 (let (($x137 (not $x136)))
-(or (>= (+ ?x128 ?x1541) 0) $x137 (not (= (+ ?x128 ?x1541 (b_G$ (pair$ ?v1 ?v0!5))) 0)))))))))
+(or (>= (+ ?x128 ?x1541) 0) $x137 (not (= (+ ?x128 ?x1541 (b_G$ (pair$ ?v1 ?v0!5))) 0)))))))) :qid k!42))
 ))
 (let (($x2459 (not (or $x1538 $x1543 (not $x2451)))))
 (let (($x2964 (or $x2459 $x2959)))
-(let (($x2436 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
+(let (($x2436 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x155 (b_G$ (pair$ ?v1 ?v0))))
 (let ((?x128 (v_b_SP_G_0$ ?v1)))
 (let (($x933 (>= (+ ?x128 (* (- 1) (v_b_SP_G_0$ ?v0)) ?x155) 0)))
 (let (($x922 (<= (+ b_Infinity$ (* (- 1) ?x155)) 0)))
 (let (($x136 (v_b_Visited_G_0$ ?v1)))
 (let (($x137 (not $x136)))
-(or $x137 $x922 $x933))))))))
+(or $x137 $x922 $x933))))))) :qid k!42))
 ))
 (let (($x2973 (not (or (not $x2436) (not $x2964)))))
 (let (($x2978 (or $x2414 $x2973)))
-(let (($x2391 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let (($x907 (>= (+ (v_b_SP_G_0$ ?v1) (* (- 1) (v_b_SP_G_0$ ?v0))) 0)))
+(let (($x2391 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let (($x907 (>= (+ (v_b_SP_G_0$ ?v1) (* (- 1) (v_b_SP_G_0$ ?v0))) 0)))
 (let (($x136 (v_b_Visited_G_0$ ?v1)))
-(or $x136 (not (v_b_Visited_G_0$ ?v0)) $x907))))
+(or $x136 (not (v_b_Visited_G_0$ ?v0)) $x907))) :qid k!42))
 ))
 (let (($x2987 (not (or (not $x2391) (not $x2978)))))
 (let (($x2992 (or $x2368 $x2987)))
 (let (($x3000 (not (or $x902 (not $x2992)))))
 (let (($x3005 (or $x1477 $x3000)))

 (let (($x2837 (or (>= (+ ?x273 (* (- 1) ?x1911)) 0) $x300 (not (= (+ ?x273 (* (- 1) ?x1911) (b_G$ (pair$ ?0 ?v0!20))) 0)))))
 (let ((@x3736 (monotonicity (quant-intro (refl (= $x2837 $x2837)) (= $x2848 $x3729)) (= (not $x2848) $x3734))))
 (let ((@x3724 (quant-intro (refl (= (or $x300 $x922 $x1282) (or $x300 $x922 $x1282))) (= $x2833 $x3720))))
 (let ((@x3739 (monotonicity (monotonicity @x3724 (= (not $x2833) $x3725)) @x3736 (= (or (not $x2833) $x1909 $x1914 (not $x2848)) $x3737))))
 (let ((@x3748 (monotonicity (monotonicity (monotonicity @x3739 (= $x2857 $x3740)) (= $x2862 $x3743)) (= (not $x2862) $x3746))))
-(let ((@x3716 (quant-intro (refl (= (or $x291 (not $x301) $x1262) (or $x291 (not $x301) $x1262))) (= $x2788 $x3712))))
-(let ((@x3751 (monotonicity (monotonicity @x3716 (= (not $x2788) $x3717)) @x3748 (= (or (not $x2788) (not $x2862)) $x3749))))
-(let ((@x3760 (monotonicity (monotonicity (monotonicity @x3751 (= $x2871 $x3752)) (= $x2876 $x3755)) (= (not $x2876) $x3758))))
+(let (($x2768 (not (fun_app$ v_b_Visited_G_2$ ?1))))
+(let (($x2783 (or $x291 $x2768 $x1262)))
+(let ((@x3719 (monotonicity (quant-intro (refl (= $x2783 $x2783)) (= $x2788 $x3712)) (= (not $x2788) $x3717))))
+(let ((@x3754 (monotonicity (monotonicity @x3719 @x3748 (= (or (not $x2788) (not $x2862)) $x3749)) (= $x2871 $x3752))))
+(let ((@x3760 (monotonicity (monotonicity @x3754 (= $x2876 $x3755)) (= (not $x2876) $x3758))))
 (let ((@x3707 (quant-intro (refl (= (>= ?x273 0) (>= ?x273 0))) (= $x1256 $x3703))))
 (let ((@x3763 (monotonicity (monotonicity @x3707 (= $x1259 $x3708)) @x3760 (= (or $x1259 (not $x2876)) $x3761))))
 (let ((@x3772 (monotonicity (monotonicity (monotonicity @x3763 (= $x2884 $x3764)) (= $x2889 $x3767)) (= (not $x2889) $x3770))))
 (let ((@x3778 (monotonicity (monotonicity @x3772 (= (or $x773 (not $x2889)) $x3773)) (= $x2897 $x3776))))
 (let ((@x3784 (monotonicity (monotonicity @x3778 (= $x2902 $x3779)) (= (not $x2902) $x3782))))

 (let ((@x3856 (monotonicity (monotonicity (monotonicity @x3847 (= $x2987 $x3848)) (= $x2992 $x3851)) (= (not $x2992) $x3854))))
 (let ((@x3510 (quant-intro (refl (= (>= ?x128 0) (>= ?x128 0))) (= $x899 $x3506))))
 (let ((@x3859 (monotonicity (monotonicity @x3510 (= $x902 $x3511)) @x3856 (= (or $x902 (not $x2992)) $x3857))))
 (let ((@x3868 (monotonicity (monotonicity (monotonicity @x3859 (= $x3000 $x3860)) (= $x3005 $x3863)) (= (not $x3005) $x3866))))
 (let ((@x3874 (monotonicity (monotonicity @x3868 (= (or $x869 (not $x3005)) $x3869)) (= $x3013 $x3872))))
-(let (($x2251 (forall ((?v1 B_Vertex$) )(let ((?x1911 (v_b_SP_G_2$ ?v0!20)))
+(let (($x2251 (forall ((?v1 B_Vertex$) )(! (let ((?x1911 (v_b_SP_G_2$ ?v0!20)))
 (let ((?x1912 (* (- 1) ?x1911)))
 (let ((?x273 (v_b_SP_G_2$ ?v1)))
 (let (($x2242 (= (+ ?x273 ?x1912 (b_G$ (pair$ ?v1 ?v0!20))) 0)))
 (let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
 (let (($x2245 (and (not (>= (+ ?x273 ?x1912) 0)) $x291 $x2242)))
-(not $x2245))))))))
+(not $x2245))))))) :qid k!42))
 ))
 (let (($x1915 (not $x1914)))
 (let (($x1910 (not $x1909)))
 (let (($x2260 (and $x1289 $x1910 $x1915 $x2251)))
 (let (($x1891 (not (and $x1883 (not $x1888)))))

 (let (($x1752 (and $x1146 $x1749)))
 (let (($x1733 (not (and (not $x1724) (not $x1730)))))
 (let (($x2212 (or $x1733 $x2209)))
 (let (($x2215 (not $x2212)))
 (let (($x2218 (or $x2215 $x1752)))
-(let (($x2203 (forall ((?v0 B_Vertex$) )(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v0)))
+(let (($x2203 (forall ((?v0 B_Vertex$) )(! (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v0)))
 (let ((?x2191 (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!9 ?v0) ?v0))))))
 (let (($x2192 (= ?x2191 0)))
 (let (($x2176 (<= (+ ?x230 (* (- 1) (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0)))) 0)))
 (let (($x2197 (and (not $x2176) $x2192)))
 (let (($x1099 (<= (+ b_Infinity$ (* (- 1) ?x230)) 0)))
 (let (($x1100 (not $x1099)))
 (let (($x127 (= ?v0 b_Source$)))
 (let (($x132 (not $x127)))
 (let (($x1103 (and $x132 $x1100)))
 (let (($x1106 (not $x1103)))
-(or $x1106 $x2197)))))))))))))
+(or $x1106 $x2197)))))))))))) :qid k!42))
 ))
 (let (($x2221 (and $x2203 $x2218)))
-(let (($x2157 (forall ((?v1 B_Vertex$) )(let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
+(let (($x2157 (forall ((?v1 B_Vertex$) )(! (let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
 (let ((?x1662 (* (- 1) ?x1661)))
 (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
 (let (($x2148 (= (+ ?x230 ?x1662 (b_G$ (pair$ ?v1 ?v0!8))) 0)))
 (let (($x2151 (and (not (>= (+ ?x230 ?x1662) 0)) $x2148)))
-(not $x2151)))))))
+(not $x2151)))))) :qid k!42))
 ))
 (let (($x1665 (not $x1664)))
 (let (($x1660 (not $x1659)))
 (let (($x2163 (and $x1660 $x1665 $x2157)))
 (let (($x2224 (or $x2163 $x2221)))
-(let (($x1641 (forall ((?v0 B_Vertex$) )(let (($x1002 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
+(let (($x1641 (forall ((?v0 B_Vertex$) )(! (let (($x1002 (<= (+ b_Infinity$ (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0))) 0)))
 (let (($x1003 (not $x1002)))
 (let (($x178 (fun_app$ v_b_Visited_G_1$ ?v0)))
 (let (($x179 (not $x178)))
 (let (($x1077 (and $x179 $x1003)))
-(not $x1077)))))))
+(not $x1077)))))) :qid k!42))
 ))
 (let (($x2230 (and $x1641 $x212 $x215 $x217 $x220 $x2224)))
 (let (($x2306 (or $x2230 $x2301)))
-(let (($x2140 (forall ((?v0 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let (($x2140 (forall ((?v0 B_Vertex$) )(! (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let ((?x2128 (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ (?v1!7 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!7 ?v0) ?v0))))))
 (let (($x2129 (= ?x2128 0)))
 (let ((?x1613 (?v1!7 ?v0)))
 (let (($x1618 (fun_app$ v_b_Visited_G_1$ ?x1613)))
 (let (($x2134 (and (not (<= (+ ?x174 (* (- 1) (fun_app$c v_b_SP_G_1$ ?x1613))) 0)) $x1618 $x2129)))

 (let (($x1003 (not $x1002)))
 (let (($x127 (= ?v0 b_Source$)))
 (let (($x132 (not $x127)))
 (let (($x1006 (and $x132 $x1003)))
 (let (($x1009 (not $x1006)))
-(or $x1009 $x2134))))))))))))))
-))
-(let (($x2102 (forall ((?v0 B_Vertex$) )(let ((?x128 (v_b_SP_G_0$ ?v0)))
+(or $x1009 $x2134))))))))))))) :qid k!42))
+))
+(let (($x2102 (forall ((?v0 B_Vertex$) )(! (let ((?x128 (v_b_SP_G_0$ ?v0)))
 (let ((?x2090 (+ ?x128 (* (- 1) (v_b_SP_G_0$ (?v1!6 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!6 ?v0) ?v0))))))
 (let (($x2091 (= ?x2090 0)))
 (let ((?x1578 (?v1!6 ?v0)))
 (let (($x1583 (v_b_Visited_G_0$ ?x1578)))
 (let (($x2096 (and (not (<= (+ ?x128 (* (- 1) (v_b_SP_G_0$ ?x1578))) 0)) $x1583 $x2091)))
 (let (($x127 (= ?v0 b_Source$)))
 (let (($x132 (not $x127)))
 (let (($x951 (and $x132 (not (<= (+ b_Infinity$ (* (- 1) ?x128)) 0)))))
 (let (($x954 (not $x951)))
-(or $x954 $x2096))))))))))))
+(or $x954 $x2096))))))))))) :qid k!42))
 ))
 (let (($x2315 (and $x2102 $x173 $x1051 $x1045 $x997 $x2140 $x2306)))
-(let (($x1567 (forall ((?v1 B_Vertex$) )(let ((?x1540 (v_b_SP_G_0$ ?v0!5)))
+(let (($x1567 (forall ((?v1 B_Vertex$) )(! (let ((?x1540 (v_b_SP_G_0$ ?v0!5)))
 (let ((?x1541 (* (- 1) ?x1540)))
 (let ((?x128 (v_b_SP_G_0$ ?v1)))
 (let (($x136 (v_b_Visited_G_0$ ?v1)))
 (let (($x1554 (and (not (>= (+ ?x128 ?x1541) 0)) $x136 (= (+ ?x128 ?x1541 (b_G$ (pair$ ?v1 ?v0!5))) 0))))
-(not $x1554)))))))
+(not $x1554)))))) :qid k!42))
 ))
 (let (($x2062 (and $x1539 $x1544 $x1567)))
 (let (($x2320 (or $x2062 $x2315)))
 (let (($x2323 (and $x939 $x2320)))
 (let (($x1520 (not (and $x1512 (not $x1517)))))

 (let ((@x2861 (trans @x2853 (rewrite (= (and $x2833 $x1910 $x1915 $x2848) $x2857)) (= $x2260 $x2857))))
 (let ((@x2798 (monotonicity (rewrite (= (and $x1883 (not $x1888)) (not (or $x2791 $x1888)))) (= $x1891 (not (not (or $x2791 $x1888)))))))
 (let ((@x2802 (trans @x2798 (rewrite (= (not (not (or $x2791 $x1888))) (or $x2791 $x1888))) (= $x1891 (or $x2791 $x1888)))))
 (let ((@x2810 (trans (monotonicity @x2802 (= $x1897 (or (or $x2791 $x1888) $x1896))) (rewrite (= (or (or $x2791 $x1888) $x1896) $x2806)) (= $x1897 $x2806))))
 (let ((@x2864 (monotonicity (monotonicity @x2810 (= $x1898 $x2811)) @x2861 (= $x2265 $x2862))))
-(let ((@x2785 (rewrite (= (or (or $x291 (not $x301)) $x1262) (or $x291 (not $x301) $x1262)))))
-(let ((@x2777 (rewrite (= (not (not (or $x291 (not $x301)))) (or $x291 (not $x301))))))
-(let ((@x2775 (monotonicity (rewrite (= $x302 (not (or $x291 (not $x301))))) (= $x664 (not (not (or $x291 (not $x301))))))))
-(let ((@x2782 (monotonicity (trans @x2775 @x2777 (= $x664 (or $x291 (not $x301)))) (= $x1267 (or (or $x291 (not $x301)) $x1262)))))
-(let ((@x2790 (quant-intro (trans @x2782 @x2785 (= $x1267 (or $x291 (not $x301) $x1262))) (= $x1270 $x2788))))
-(let ((@x2875 (trans (monotonicity @x2790 @x2864 (= $x2268 (and $x2788 $x2862))) (rewrite (= (and $x2788 $x2862) $x2871)) (= $x2268 $x2871))))
+(let ((@x2775 (monotonicity (rewrite (= $x302 (not (or $x291 $x2768)))) (= $x664 (not (not (or $x291 $x2768)))))))
+(let ((@x2779 (trans @x2775 (rewrite (= (not (not (or $x291 $x2768))) (or $x291 $x2768))) (= $x664 (or $x291 $x2768)))))
+(let ((@x2787 (trans (monotonicity @x2779 (= $x1267 (or (or $x291 $x2768) $x1262))) (rewrite (= (or (or $x291 $x2768) $x1262) $x2783)) (= $x1267 $x2783))))
+(let ((@x2867 (monotonicity (quant-intro @x2787 (= $x1270 $x2788)) @x2864 (= $x2268 (and $x2788 $x2862)))))
 (let ((@x2752 (monotonicity (rewrite (= (and (not $x1860) $x1862) (not (or $x1860 $x2745)))) (= $x1864 (not (not (or $x1860 $x2745)))))))
 (let ((@x2756 (trans @x2752 (rewrite (= (not (not (or $x1860 $x2745))) (or $x1860 $x2745))) (= $x1864 (or $x1860 $x2745)))))
 (let ((@x2764 (trans (monotonicity @x2756 (= $x1870 (or (or $x1860 $x2745) $x1869))) (rewrite (= (or (or $x1860 $x2745) $x1869) $x2760)) (= $x1870 $x2760))))
-(let ((@x2878 (monotonicity (monotonicity @x2764 (= $x1871 $x2765)) @x2875 (= $x2271 $x2876))))
+(let ((@x2878 (monotonicity (monotonicity @x2764 (= $x1871 $x2765)) (trans @x2867 (rewrite (= (and $x2788 $x2862) $x2871)) (= $x2268 $x2871)) (= $x2271 $x2876))))
 (let ((@x2888 (trans (monotonicity @x2878 (= $x2274 (and $x1256 $x2876))) (rewrite (= (and $x1256 $x2876) $x2884)) (= $x2274 $x2884))))
 (let ((@x2894 (monotonicity (monotonicity @x2888 (= $x2277 $x2889)) (= $x2280 (and $x297 $x2889)))))
 (let ((@x2904 (monotonicity (trans @x2894 (rewrite (= (and $x297 $x2889) $x2897)) (= $x2280 $x2897)) (= $x2283 $x2902))))
 (let ((@x2914 (trans (monotonicity @x2904 (= $x2286 (and $x652 $x2902))) (rewrite (= (and $x652 $x2902) $x2910)) (= $x2286 $x2910))))
 (let ((@x2920 (monotonicity (monotonicity @x2914 (= $x2289 $x2915)) (= $x2292 (and $x1247 $x2915)))))

 (let ((@x2367 (trans (monotonicity @x2359 (= $x1499 (or (or $x1489 $x2348) $x1498))) (rewrite (= (or (or $x1489 $x2348) $x1498) $x2363)) (= $x1499 $x2363))))
 (let ((@x2994 (monotonicity (monotonicity @x2367 (= $x1500 $x2368)) @x2991 (= $x2332 $x2992))))
 (let ((@x3004 (trans (monotonicity @x2994 (= $x2335 (and $x899 $x2992))) (rewrite (= (and $x899 $x2992) $x3000)) (= $x2335 $x3000))))
 (let ((@x3010 (monotonicity (monotonicity @x3004 (= $x2338 $x3005)) (= $x2341 (and $x145 $x3005)))))
 (let ((@x3020 (monotonicity (trans @x3010 (rewrite (= (and $x145 $x3005) $x3013)) (= $x2341 $x3013)) (= $x2344 $x3018))))
-(let (($x1938 (forall ((?v1 B_Vertex$) )(let ((?x1911 (v_b_SP_G_2$ ?v0!20)))
+(let (($x1938 (forall ((?v1 B_Vertex$) )(! (let ((?x1911 (v_b_SP_G_2$ ?v0!20)))
 (let ((?x1912 (* (- 1) ?x1911)))
 (let ((?x273 (v_b_SP_G_2$ ?v1)))
 (let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
 (let (($x1925 (and (not (>= (+ ?x273 ?x1912) 0)) $x291 (= (+ (b_G$ (pair$ ?v1 ?v0!20)) ?x273 ?x1912) 0))))
-(not $x1925)))))))
+(not $x1925)))))) :qid k!42))
 ))
 (let (($x1932 (not (not (and $x1910 $x1915)))))
 (let (($x1942 (and $x1932 $x1938)))
 (let (($x1947 (and $x1289 $x1942)))
 (let (($x1951 (or $x1898 $x1947)))

 (let (($x1991 (or $x1813 $x1987)))
 (let (($x1801 (and (and $x1774 $x1779) $x256 $x1214 $x1209 $x266 $x1193 $x1199)))
 (let (($x1995 (and $x1801 $x1991)))
 (let (($x1739 (not (or $x1733 (>= (+ ?x1727 ?x1721 ?x1735) 0)))))
 (let (($x1756 (or $x1739 $x1752)))
-(let (($x1713 (forall ((?v0 B_Vertex$) )(let ((?x230 (fun_app$c v_b_SP_G_3$ ?v0)))
+(let (($x1713 (forall ((?v0 B_Vertex$) )(! (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v0)))
 (let ((?x1097 (* (- 1) ?x230)))
 (let ((?x1699 (fun_app$c v_b_SP_G_3$ (?v1!9 ?v0))))
 (let ((?x1704 (b_G$ (pair$ (?v1!9 ?v0) ?v0))))
 (let (($x1706 (= (+ ?x1704 ?x1699 ?x1097) 0)))
 (let (($x1707 (and (not (>= (+ ?x1699 ?x1097) 0)) $x1706)))

 (let (($x1100 (not $x1099)))
 (let (($x127 (= ?v0 b_Source$)))
 (let (($x132 (not $x127)))
 (let (($x1103 (and $x132 $x1100)))
 (let (($x1106 (not $x1103)))
-(or $x1106 $x1707))))))))))))))
+(or $x1106 $x1707))))))))))))) :qid k!42))
 ))
 (let (($x1760 (and $x1713 $x1756)))
-(let (($x1687 (forall ((?v1 B_Vertex$) )(let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
+(let (($x1687 (forall ((?v1 B_Vertex$) )(! (let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
 (let ((?x1662 (* (- 1) ?x1661)))
 (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
 (let (($x1675 (and (not (>= (+ ?x230 ?x1662) 0)) (= (+ (b_G$ (pair$ ?v1 ?v0!8)) ?x230 ?x1662) 0))))
-(not $x1675))))))
+(not $x1675))))) :qid k!42))
 ))
 (let (($x1681 (not (not (and $x1660 $x1665)))))
 (let (($x1691 (and $x1681 $x1687)))
 (let (($x1764 (or $x1691 $x1760)))
 (let (($x1652 (and $x1641 $x212 $x215 $x217 $x220)))
 (let (($x1768 (and $x1652 $x1764)))
 (let (($x1999 (or $x1768 $x1995)))
-(let (($x1629 (forall ((?v0 B_Vertex$) )(let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
+(let (($x1629 (forall ((?v0 B_Vertex$) )(! (let ((?x174 (fun_app$c v_b_SP_G_1$ ?v0)))
 (let ((?x1000 (* (- 1) ?x174)))
 (let ((?x1613 (?v1!7 ?v0)))
 (let ((?x1614 (fun_app$c v_b_SP_G_1$ ?x1613)))
 (let ((?x1620 (b_G$ (pair$ ?x1613 ?v0))))
 (let (($x1622 (= (+ ?x1620 ?x1614 ?x1000) 0)))

 (let (($x1003 (not $x1002)))
 (let (($x127 (= ?v0 b_Source$)))
 (let (($x132 (not $x127)))
 (let (($x1006 (and $x132 $x1003)))
 (let (($x1009 (not $x1006)))
-(or $x1009 $x1623))))))))))))))))
-))
-(let (($x1594 (forall ((?v0 B_Vertex$) )(let ((?x1585 (b_G$ (pair$ (?v1!6 ?v0) ?v0))))
+(or $x1009 $x1623))))))))))))))) :qid k!42))
+))
+(let (($x1594 (forall ((?v0 B_Vertex$) )(! (let ((?x1585 (b_G$ (pair$ (?v1!6 ?v0) ?v0))))
 (let ((?x128 (v_b_SP_G_0$ ?v0)))
 (let ((?x945 (* (- 1) ?x128)))
 (let ((?x1578 (?v1!6 ?v0)))
 (let ((?x1579 (v_b_SP_G_0$ ?x1578)))
 (let (($x1587 (= (+ ?x1579 ?x945 ?x1585) 0)))

 (let (($x1588 (and (not (>= (+ ?x1579 ?x945) 0)) $x1583 $x1587)))
 (let (($x127 (= ?v0 b_Source$)))
 (let (($x132 (not $x127)))
 (let (($x951 (and $x132 (not (<= (+ b_Infinity$ ?x945) 0)))))
 (let (($x954 (not $x951)))
-(or $x954 $x1588))))))))))))))
+(or $x954 $x1588))))))))))))) :qid k!42))
 ))
 (let (($x1632 (and $x1594 $x173 $x1051 $x1045 $x997 $x1629)))
 (let (($x2003 (and $x1632 $x1999)))
 (let (($x1561 (not (not (and $x1539 $x1544)))))
 (let (($x1571 (and $x1561 $x1567)))

 (let ((@x2050 (monotonicity (rewrite (= (+ ?x1521 ?x1523 ?x1514) ?x2045)) (= (>= (+ ?x1521 ?x1523 ?x1514) 0) $x2048))))
 (let ((@x2053 (monotonicity @x2050 (= (or $x1520 (>= (+ ?x1521 ?x1523 ?x1514) 0)) $x2051))))
 (let ((@x2328 (monotonicity (monotonicity @x2053 (= $x1527 $x2054)) @x2325 (= $x2015 $x2326))))
 (let ((@x2337 (monotonicity (monotonicity (monotonicity @x2328 (= $x2019 $x2329)) (= $x2023 $x2332)) (= $x2027 $x2335))))
 (let ((@x2343 (monotonicity (rewrite (= $x1471 $x145)) (monotonicity @x2337 (= $x2031 $x2338)) (= $x2035 $x2341))))
-(let (($x1926 (exists ((?v1 B_Vertex$) )(let ((?x1911 (v_b_SP_G_2$ ?v0!20)))
+(let (($x1926 (exists ((?v1 B_Vertex$) )(! (let ((?x1911 (v_b_SP_G_2$ ?v0!20)))
 (let ((?x1912 (* (- 1) ?x1911)))
 (let ((?x273 (v_b_SP_G_2$ ?v1)))
 (let (($x291 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(and (not (>= (+ ?x273 ?x1912) 0)) $x291 (= (+ (b_G$ (pair$ ?v1 ?v0!20)) ?x273 ?x1912) 0)))))))
+(and (not (>= (+ ?x273 ?x1912) 0)) $x291 (= (+ (b_G$ (pair$ ?v1 ?v0!20)) ?x273 ?x1912) 0)))))) :qid k!42))
 ))
 (let ((@x1944 (nnf-neg (refl (~ $x1932 $x1932)) (nnf-neg (refl (~ $x1935 $x1935)) (~ (not $x1926) $x1938)) (~ (not (or (not (and $x1910 $x1915)) $x1926)) $x1942))))
 (let ((@x1946 (trans (sk (~ (not $x1329) (not (or (not (and $x1910 $x1915)) $x1926)))) @x1944 (~ (not $x1329) $x1942))))
 (let ((@x1907 (nnf-neg (nnf-pos (refl (~ $x1286 $x1286)) (~ $x1289 $x1289)) (~ (not $x1292) $x1289))))
 (let ((@x1954 (nnf-neg (sk (~ $x1292 $x1898)) (nnf-neg @x1907 @x1946 (~ (not $x1332) $x1947)) (~ (not $x1335) $x1951))))

 (let ((@x1998 (nnf-neg (nnf-neg @x1803 (~ (not $x1240) $x1801)) @x1994 (~ (not $x1368) $x1995))))
 (let ((@x1748 (nnf-neg (nnf-pos (refl (~ $x1143 $x1143)) (~ $x1146 $x1146)) (~ (not $x1149) $x1146))))
 (let ((@x1759 (nnf-neg (sk (~ $x1149 $x1739)) (nnf-neg @x1748 (refl (~ $x1749 $x1749)) (~ (not $x1152) $x1752)) (~ (not $x1155) $x1756))))
 (let ((@x1715 (nnf-pos (monotonicity (refl (~ $x1106 $x1106)) (sk (~ $x1122 $x1707)) (~ $x1125 $x1710)) (~ $x1128 $x1713))))
 (let ((@x1763 (nnf-neg (nnf-neg @x1715 (~ (not $x1131) $x1713)) @x1759 (~ (not $x1158) $x1760))))
-(let (($x1676 (exists ((?v1 B_Vertex$) )(let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
+(let (($x1676 (exists ((?v1 B_Vertex$) )(! (let ((?x1661 (fun_app$c v_b_SP_G_3$ ?v0!8)))
 (let ((?x1662 (* (- 1) ?x1661)))
 (let ((?x230 (fun_app$c v_b_SP_G_3$ ?v1)))
-(and (not (>= (+ ?x230 ?x1662) 0)) (= (+ (b_G$ (pair$ ?v1 ?v0!8)) ?x230 ?x1662) 0))))))
+(and (not (>= (+ ?x230 ?x1662) 0)) (= (+ (b_G$ (pair$ ?v1 ?v0!8)) ?x230 ?x1662) 0))))) :qid k!42))
 ))
 (let ((@x1693 (nnf-neg (refl (~ $x1681 $x1681)) (nnf-neg (refl (~ $x1684 $x1684)) (~ (not $x1676) $x1687)) (~ (not (or (not (and $x1660 $x1665)) $x1676)) $x1691))))
 (let ((@x1695 (trans (sk (~ $x1131 (not (or (not (and $x1660 $x1665)) $x1676)))) @x1693 (~ $x1131 $x1691))))
 (let ((@x1654 (monotonicity (nnf-neg (refl (~ (not $x1077) (not $x1077))) (~ $x1083 $x1641)) (refl (~ $x212 $x212)) (refl (~ $x215 $x215)) (refl (~ $x217 $x217)) (refl (~ $x220 $x220)) (~ $x1089 $x1652))))
 (let ((@x1771 (nnf-neg (nnf-neg @x1654 (~ (not $x1094) $x1652)) (nnf-neg @x1695 @x1763 (~ (not $x1161) $x1764)) (~ (not $x1164) $x1768))))
 (let ((@x1631 (nnf-pos (monotonicity (refl (~ $x1009 $x1009)) (sk (~ $x1031 $x1623)) (~ $x1034 $x1626)) (~ $x1037 $x1629))))
 (let ((@x1596 (nnf-pos (monotonicity (refl (~ $x954 $x954)) (sk (~ $x974 $x1588)) (~ $x977 $x1591)) (~ $x980 $x1594))))
 (let ((@x1634 (monotonicity @x1596 (refl (~ $x173 $x173)) (nnf-pos (refl (~ (>= ?x174 0) (>= ?x174 0))) (~ $x1051 $x1051)) (nnf-pos (refl (~ $x1042 $x1042)) (~ $x1045 $x1045)) (nnf-pos (refl (~ $x994 $x994)) (~ $x997 $x997)) @x1631 (~ $x1069 $x1632))))
 (let ((@x2006 (nnf-neg (nnf-neg @x1634 (~ (not $x1074) $x1632)) (nnf-neg @x1771 @x1998 (~ (not $x1371) $x1999)) (~ (not $x1374) $x2003))))
-(let (($x1555 (exists ((?v1 B_Vertex$) )(let ((?x1540 (v_b_SP_G_0$ ?v0!5)))
+(let (($x1555 (exists ((?v1 B_Vertex$) )(! (let ((?x1540 (v_b_SP_G_0$ ?v0!5)))
 (let ((?x1541 (* (- 1) ?x1540)))
 (let ((?x128 (v_b_SP_G_0$ ?v1)))
 (let (($x136 (v_b_Visited_G_0$ ?v1)))
-(and (not (>= (+ ?x128 ?x1541) 0)) $x136 (= (+ ?x128 ?x1541 (b_G$ (pair$ ?v1 ?v0!5))) 0)))))))
+(and (not (>= (+ ?x128 ?x1541) 0)) $x136 (= (+ ?x128 ?x1541 (b_G$ (pair$ ?v1 ?v0!5))) 0)))))) :qid k!42))
 ))
 (let ((@x1573 (nnf-neg (refl (~ $x1561 $x1561)) (nnf-neg (refl (~ $x1564 $x1564)) (~ (not $x1555) $x1567)) (~ (not (or (not (and $x1539 $x1544)) $x1555)) $x1571))))
 (let ((@x1575 (trans (sk (~ (not $x980) (not (or (not (and $x1539 $x1544)) $x1555)))) @x1573 (~ (not $x980) $x1571))))
 (let ((@x1536 (nnf-neg (nnf-pos (refl (~ $x936 $x936)) (~ $x939 $x939)) (~ (not $x942) $x939))))
 (let ((@x2014 (nnf-neg @x1536 (nnf-neg @x1575 @x2006 (~ (not $x1377) $x2007)) (~ (not $x1380) $x2011))))

 (let (($x6583 (not $x6582)))
 (let (($x6156 (= v_b_v_G_1$ ?v0!15)))
 (let (($x5538 (not $x6156)))
 (let ((@x7337 (symm (commutativity (= $x6156 (= ?v0!15 v_b_v_G_1$))) (= (= ?v0!15 v_b_v_G_1$) $x6156))))
 (let (($x6631 (= ?v0!15 v_b_v_G_1$)))
-(let (($x7483 (not $x6631)))
+(let (($x7452 (not $x6631)))
 (let (($x6269 (fun_app$ v_b_Visited_G_1$ ?v0!15)))
 (let (($x7698 (or $x6631 $x6269)))
 (let (($x6630 (fun_app$ ?x265 ?v0!15)))
 (let (($x7702 (= $x6630 $x7698)))
-(let (($x3468 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(!(let (($x67 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
-(= $x67 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))) :pattern ( (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3) )))
-))
-(let (($x77 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(let (($x67 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
-(= $x67 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))))
+(let (($x3468 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(! (let (($x67 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
+(= $x67 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))) :pattern ( (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3) ) :qid k!38))
+))
+(let (($x77 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(! (let (($x67 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
+(= $x67 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))) :qid k!38))
 ))
 (let (($x67 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?3) ?2) ?1) ?0)))
 (let (($x74 (= $x67 (ite (= ?0 ?2) ?1 (fun_app$ ?3 ?0)))))
-(let (($x72 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(let (($x67 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
-(= $x67 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))))
+(let (($x72 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(! (let (($x67 (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v3)))
+(= $x67 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))) :qid k!38))
 ))
 (let ((@x76 (rewrite (= (= $x67 (ite (= ?0 ?2) ?1 (fun_app$ ?3 ?0))) $x74))))
 (let ((@x1443 (mp~ (mp (asserted $x72) (quant-intro @x76 (= $x72 $x77)) $x77) (nnf-pos (refl (~ $x74 $x74)) (~ $x77 $x77)) $x77)))
 (let ((@x3473 (mp @x1443 (quant-intro (refl (= $x74 $x74)) (= $x77 $x3468)) $x3468)))
 (let (($x4114 (not $x3468)))
 (let (($x6435 (or $x4114 $x7702)))
 (let ((@x5925 (monotonicity (rewrite (= (ite $x6631 true $x6269) $x7698)) (= (= $x6630 (ite $x6631 true $x6269)) $x7702))))
 (let ((@x6213 (monotonicity @x5925 (= (or $x4114 (= $x6630 (ite $x6631 true $x6269))) $x6435))))
-(let ((@x7487 (trans @x6213 (rewrite (= $x6435 $x6435)) (= (or $x4114 (= $x6630 (ite $x6631 true $x6269))) $x6435))))
-(let ((@x7488 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!15) (or $x4114 (= $x6630 (ite $x6631 true $x6269)))) @x7487 $x6435)))
+(let ((@x7485 (trans @x6213 (rewrite (= $x6435 $x6435)) (= (or $x4114 (= $x6630 (ite $x6631 true $x6269))) $x6435))))
+(let ((@x7486 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!15) (or $x4114 (= $x6630 (ite $x6631 true $x6269)))) @x7485 $x6435)))
 (let ((@x5875 (symm (unit-resolution (def-axiom (or $x3809 $x266)) @x6181 $x266) (= ?x265 v_b_Visited_G_2$))))
 (let ((@x7321 (symm (monotonicity @x5875 (= $x6630 (fun_app$ v_b_Visited_G_2$ ?v0!15))) (= (fun_app$ v_b_Visited_G_2$ ?v0!15) $x6630))))
 (let ((@x7322 (monotonicity @x7321 (= (not (fun_app$ v_b_Visited_G_2$ ?v0!15)) (not $x6630)))))
 (let (($x4415 (fun_app$ v_b_Visited_G_2$ ?v0!15)))
 (let (($x4479 (not $x4415)))

 (let ((@x6283 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x6491 0)) $x5826)) (hypothesis (not $x5826)) (not (= ?x6491 0)))))
 (let (($x5742 (= v_b_v_G_1$ ?v0!14)))
 (let (($x5751 (<= ?x6491 0)))
 (let ((@x6302 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x5826 $x5751)) (hypothesis (not $x5826)) $x5751)))
 (let (($x5738 (or $x5742 (not $x5751))))
-(let (($x3480 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(let (($x84 (= ?v0 ?v1)))
-(or $x84 (not (<= (b_G$ (pair$ ?v0 ?v1)) 0)))) :pattern ( (pair$ ?v0 ?v1) )))
-))
-(let (($x120 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let (($x84 (= ?v0 ?v1)))
-(or $x84 (not (<= (b_G$ (pair$ ?v0 ?v1)) 0)))))
+(let (($x3480 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let (($x84 (= ?v0 ?v1)))
+(or $x84 (not (<= (b_G$ (pair$ ?v0 ?v1)) 0)))) :pattern ( (pair$ ?v0 ?v1) ) :qid k!41))
+))
+(let (($x120 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let (($x84 (= ?v0 ?v1)))
+(or $x84 (not (<= (b_G$ (pair$ ?v0 ?v1)) 0)))) :qid k!41))
 ))
 (let (($x84 (= ?1 ?0)))
 (let (($x117 (or $x84 (not (<= (b_G$ (pair$ ?1 ?0)) 0)))))
-(let (($x105 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x29 (pair$ ?v0 ?v1)))
+(let (($x105 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x29 (pair$ ?v0 ?v1)))
 (let ((?x85 (b_G$ ?x29)))
 (let (($x102 (< 0 ?x85)))
-(=> (not (= ?v0 ?v1)) $x102)))))
-))
-(let (($x110 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let ((?x29 (pair$ ?v0 ?v1)))
+(=> (not (= ?v0 ?v1)) $x102)))) :qid k!41))
+))
+(let (($x110 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x29 (pair$ ?v0 ?v1)))
 (let ((?x85 (b_G$ ?x29)))
 (let (($x102 (< 0 ?x85)))
 (let (($x84 (= ?v0 ?v1)))
-(or $x84 $x102))))))
+(or $x84 $x102))))) :qid k!41))
 ))
 (let ((?x29 (pair$ ?1 ?0)))
 (let ((?x85 (b_G$ ?x29)))
 (let (($x102 (< 0 ?x85)))
 (let ((@x119 (monotonicity (rewrite (= $x102 (not (<= ?x85 0)))) (= (or $x84 $x102) $x117))))

 (let ((@x125 (mp (asserted $x105) (trans @x112 (quant-intro @x119 (= $x110 $x120)) (= $x105 $x120)) $x120)))
 (let ((@x3485 (mp (mp~ @x125 (nnf-pos (refl (~ $x117 $x117)) (~ $x120 $x120)) $x120) (quant-intro (refl (= $x117 $x117)) (= $x120 $x3480)) $x3480)))
 (let ((@x5780 (mp ((_ quant-inst v_b_v_G_1$ ?v0!14) (or (not $x3480) $x5738)) (rewrite (= (or (not $x3480) $x5738) (or (not $x3480) $x5742 (not $x5751)))) (or (not $x3480) $x5742 (not $x5751)))))
 (let (($x5739 (= ?x6491 0)))
 (let (($x5781 (or (not $x5742) $x5739)))
-(let (($x3474 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(!(or (not (= ?v0 ?v1)) (= (b_G$ (pair$ ?v0 ?v1)) 0)) :pattern ( (pair$ ?v0 ?v1) )))
-))
-(let (($x99 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(or (not (= ?v0 ?v1)) (= (b_G$ (pair$ ?v0 ?v1)) 0)))
+(let (($x3474 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (or (not (= ?v0 ?v1)) (= (b_G$ (pair$ ?v0 ?v1)) 0)) :pattern ( (pair$ ?v0 ?v1) ) :qid k!40))
+))
+(let (($x99 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (or (not (= ?v0 ?v1)) (= (b_G$ (pair$ ?v0 ?v1)) 0)) :qid k!40))
 ))
 (let ((@x3476 (refl (= (or (not $x84) (= ?x85 0)) (or (not $x84) (= ?x85 0))))))
 (let ((@x1447 (refl (~ (or (not $x84) (= ?x85 0)) (or (not $x84) (= ?x85 0))))))
-(let (($x93 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(let (($x84 (= ?v0 ?v1)))
-(=> $x84 (= (b_G$ (pair$ ?v0 ?v1)) 0))))
+(let (($x93 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let (($x84 (= ?v0 ?v1)))
+(=> $x84 (= (b_G$ (pair$ ?v0 ?v1)) 0))) :qid k!40))
 ))
 (let ((@x98 (rewrite (= (=> $x84 (= ?x85 0)) (or (not $x84) (= ?x85 0))))))
 (let ((@x1448 (mp~ (mp (asserted $x93) (quant-intro @x98 (= $x93 $x99)) $x99) (nnf-pos @x1447 (~ $x99 $x99)) $x99)))
 (let ((@x3479 (mp @x1448 (quant-intro @x3476 (= $x99 $x3474)) $x3474)))
 (let ((@x5817 (mp ((_ quant-inst v_b_v_G_1$ ?v0!14) (or (not $x3474) $x5781)) (rewrite (= (or (not $x3474) $x5781) (or (not $x3474) (not $x5742) $x5739))) (or (not $x3474) (not $x5742) $x5739))))

 (let ((@x4258 (trans @x4254 (rewrite (= (or $x3683 (or $x4245 $x3052)) $x3975)) (= $x3958 $x3975))))
 (let ((@x4259 (mp ((_ quant-inst v_b_v_G_1$) $x3958) @x4258 $x3975)))
 (let ((@x6268 (monotonicity (unit-resolution (def-axiom (or (not $x4963) $x6050 $x5678)) @x5057 @x5037 $x6050) (= ?x1826 ?x3104))))
 (let ((@x6107 (trans @x6268 (unit-resolution @x4259 @x5944 (unit-resolution @x4316 @x6019 $x4242) $x3052) (= ?x1826 ?x257))))
 (let ((@x6162 (unit-resolution @x5065 (trans @x6107 (symm @x6293 (= ?x257 ?x1827)) $x1828) false)))
-(let ((@x7615 (unit-resolution (def-axiom (or $x3794 $x1830 $x3788)) (lemma @x6162 $x1829) (unit-resolution (def-axiom (or $x3797 $x3791)) @x6891 $x3791) $x3788)))
-(let ((@x7616 (unit-resolution (def-axiom (or $x3785 $x3695)) @x7615 $x3695)))
-(let ((@x7443 (mp ((_ quant-inst ?v0!15) (or $x3700 (or $x4479 $x4481))) (rewrite (= (or $x3700 (or $x4479 $x4481)) (or $x3700 $x4479 $x4481))) (or $x3700 $x4479 $x4481))))
-(let ((@x7323 (mp (unit-resolution @x7443 @x7616 (unit-resolution @x6242 @x6183 (not $x4481)) $x4479) @x7322 (not $x6630))))
-(let ((@x7334 (unit-resolution (def-axiom (or (not $x7702) $x6630 (not $x7698))) @x7323 (unit-resolution @x7488 @x3473 $x7702) (not $x7698))))
-(let ((@x7344 (mp (unit-resolution (def-axiom (or $x7698 $x7483)) @x7334 $x7483) (monotonicity @x7337 (= $x7483 $x5538)) $x5538)))
+(let ((@x7617 (unit-resolution (def-axiom (or $x3794 $x1830 $x3788)) (lemma @x6162 $x1829) (unit-resolution (def-axiom (or $x3797 $x3791)) @x6891 $x3791) $x3788)))
+(let ((@x7618 (unit-resolution (def-axiom (or $x3785 $x3695)) @x7617 $x3695)))
+(let ((@x7447 (mp ((_ quant-inst ?v0!15) (or $x3700 (or $x4479 $x4481))) (rewrite (= (or $x3700 (or $x4479 $x4481)) (or $x3700 $x4479 $x4481))) (or $x3700 $x4479 $x4481))))
+(let ((@x7323 (mp (unit-resolution @x7447 @x7618 (unit-resolution @x6242 @x6183 (not $x4481)) $x4479) @x7322 (not $x6630))))
+(let ((@x7334 (unit-resolution (def-axiom (or (not $x7702) $x6630 (not $x7698))) @x7323 (unit-resolution @x7486 @x3473 $x7702) (not $x7698))))
+(let ((@x7344 (mp (unit-resolution (def-axiom (or $x7698 $x7452)) @x7334 $x7452) (monotonicity @x7337 (= $x7452 $x5538)) $x5538)))
 (let (($x5470 (or $x6156 $x6583)))
 (let ((@x6577 (mp ((_ quant-inst v_b_v_G_1$ ?v0!15) (or (not $x3480) $x5470)) (rewrite (= (or (not $x3480) $x5470) (or (not $x3480) $x6156 $x6583))) (or (not $x3480) $x6156 $x6583))))
 (let ((@x7345 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x6603 $x6582)) (unit-resolution (unit-resolution @x6577 @x3485 $x5470) @x7344 $x6583) $x6603)))
 (let (($x4153 (<= ?x296 0)))
 (let ((?x4058 (* (- 1) ?x296)))

 (let ((@x5596 (unit-resolution @x5938 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4079) $x4096)) @x5623 $x4096) (hypothesis $x4153) @x5049 $x5310)))
 (let (($x5886 (= (or (not $x3480) (or $x3887 (not $x5310))) (or (not $x3480) $x3887 (not $x5310)))))
 (let ((@x5952 (mp ((_ quant-inst v_b_v_G_1$ b_Source$) (or (not $x3480) (or $x3887 (not $x5310)))) (rewrite $x5886) (or (not $x3480) $x3887 (not $x5310)))))
 (let ((@x5597 (unit-resolution @x5952 @x3485 @x5596 (unit-resolution (lemma @x5283 (or $x5313 $x3683 $x297)) @x5202 @x4739 $x5313) false)))
 (let ((@x6788 (unit-resolution (lemma @x5597 (or $x297 (not $x4153) $x3675 $x3683)) @x6900 @x6588 @x5944 $x297)))
-(let ((@x7810 (unit-resolution (def-axiom (or $x3782 $x773 $x3776)) (unit-resolution (def-axiom (or $x3785 $x3779)) @x7615 $x3779) @x6788 $x3776)))
+(let ((@x7810 (unit-resolution (def-axiom (or $x3782 $x773 $x3776)) (unit-resolution (def-axiom (or $x3785 $x3779)) @x7617 $x3779) @x6788 $x3776)))
 (let ((@x3347 (def-axiom (or $x3770 $x1848 $x3764))))
-(let ((@x9293 (unit-resolution @x3347 (unit-resolution (def-axiom (or $x3773 $x3767)) @x7810 $x3767) $x3767)))
-(let ((@x9294 (unit-resolution @x9293 (lemma ((_ th-lemma arith farkas 1 1 -1 1) @x5703 @x7345 @x6959 @x5049 false) $x1847) $x3764)))
+(let ((@x9303 (unit-resolution @x3347 (unit-resolution (def-axiom (or $x3773 $x3767)) @x7810 $x3767) $x3767)))
+(let ((@x9304 (unit-resolution @x9303 (lemma ((_ th-lemma arith farkas 1 1 -1 1) @x5703 @x7345 @x6959 @x5049 false) $x1847) $x3764)))
 (let ((@x3367 (def-axiom (or $x3761 $x3703))))
 (let (($x4335 (or $x3708 $x4161)))
 (let ((@x4337 ((_ quant-inst v_b_v_G_1$) $x4335)))
 (let (($x4126 (fun_app$ v_b_Visited_G_2$ v_b_v_G_1$)))
 (let (($x3136 (fun_app$ ?x265 v_b_v_G_1$)))
-(let (($x3461 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(!(= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v1) ?v2) :pattern ( (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) )))
-))
-(let (($x57 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v1) ?v2))
+(let (($x3461 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(! (= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v1) ?v2) :pattern ( (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ) :qid k!37))
+))
+(let (($x57 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(! (= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v1) ?v2) :qid k!37))
 ))
 (let (($x54 (= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?2) ?1) ?0) ?1) ?0)))
-(let (($x52 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v1) ?v2))
+(let (($x52 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(! (= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?v0) ?v1) ?v2) ?v1) ?v2) :qid k!37))
 ))
 (let (($x51 (= (fun_app$ (fun_app$a (fun_app$b (fun_upd$ ?2) ?1) ?0) ?1) ?0)))
 (let ((@x62 (mp (asserted $x52) (quant-intro (rewrite (= $x51 $x54)) (= $x52 $x57)) $x57)))
 (let ((@x3466 (mp (mp~ @x62 (nnf-pos (refl (~ $x54 $x54)) (~ $x57 $x57)) $x57) (quant-intro (refl (= $x54 $x54)) (= $x57 $x3461)) $x3461)))
 (let (($x6140 (or (not $x3461) $x3136)))
 (let ((@x6106 (monotonicity (rewrite (= (= $x3136 true) $x3136)) (= (or (not $x3461) (= $x3136 true)) $x6140))))
 (let ((@x5837 (trans @x6106 (rewrite (= $x6140 $x6140)) (= (or (not $x3461) (= $x3136 true)) $x6140))))
 (let ((@x5928 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true) (or (not $x3461) (= $x3136 true))) @x5837 $x6140)))
-(let ((@x7482 (mp (unit-resolution @x5928 @x3466 $x3136) (monotonicity @x5875 (= $x3136 $x4126)) $x4126)))
+(let ((@x7413 (mp (unit-resolution @x5928 @x3466 $x3136) (monotonicity @x5875 (= $x3136 $x4126)) $x4126)))
 (let (($x4570 (>= ?x4546 0)))
 (let ((@x5420 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x4570 $x4569)) (hypothesis (not $x4569)) $x4570)))
 (let (($x4438 (<= (+ b_Infinity$ ?x4436) 0)))
 (let (($x4127 (not $x4126)))
 (let (($x5352 (or $x3725 $x4127 $x4438 $x4569)))

 (let ((@x5348 (trans @x5344 (rewrite (= (>= (+ (* (- 1) ?x1911) ?x3104 ?x4435) 0) $x4569)) (= $x5336 $x4569))))
 (let ((@x5357 (monotonicity (monotonicity @x5348 (= $x5339 (or $x4127 $x4438 $x4569))) (= $x5353 (or $x3725 (or $x4127 $x4438 $x4569))))))
 (let ((@x5361 (trans @x5357 (rewrite (= (or $x3725 (or $x4127 $x4438 $x4569)) $x5352)) (= $x5353 $x5352))))
 (let ((@x5424 (unit-resolution (mp ((_ quant-inst ?v0!20 v_b_v_G_1$) $x5353) @x5361 $x5352) (hypothesis $x3720) (hypothesis $x4126) (hypothesis (not $x4569)) $x4438)))
 (let ((@x5428 (lemma ((_ th-lemma arith farkas 1 1 1 1) @x5424 (hypothesis $x4161) @x5420 (hypothesis $x1915) false) (or $x4569 (not $x4161) $x1914 $x3725 $x4127))))
-(let ((@x7692 (unit-resolution (unit-resolution @x5428 @x7482 (or $x4569 (not $x4161) $x1914 $x3725)) (unit-resolution @x4337 (unit-resolution @x3367 @x9294 $x3703) $x4161) (or $x4569 $x1914 $x3725))))
-(let ((@x7751 (unit-resolution @x7692 (unit-resolution (def-axiom (or $x3737 $x1915)) @x8092 $x1915) (unit-resolution @x3222 @x8092 $x3720) $x4569)))
+(let ((@x7705 (unit-resolution (unit-resolution @x5428 @x7413 (or $x4569 (not $x4161) $x1914 $x3725)) (unit-resolution @x4337 (unit-resolution @x3367 @x9304 $x3703) $x4161) (or $x4569 $x1914 $x3725))))
+(let ((@x4467 (unit-resolution @x7705 (unit-resolution (def-axiom (or $x3737 $x1915)) @x4391 $x1915) (unit-resolution @x3222 @x4391 $x3720) $x4569)))
 (let (($x5386 (= v_b_v_G_1$ ?v0!20)))
 (let (($x5390 (not $x5386)))
-(let ((@x9325 (symm (commutativity (= $x5386 (= ?v0!20 v_b_v_G_1$))) (= (= ?v0!20 v_b_v_G_1$) $x5386))))
+(let ((@x9335 (symm (commutativity (= $x5386 (= ?v0!20 v_b_v_G_1$))) (= (= ?v0!20 v_b_v_G_1$) $x5386))))
 (let (($x5240 (= ?v0!20 v_b_v_G_1$)))
-(let (($x9145 (not $x5240)))
+(let (($x9098 (not $x5240)))
 (let (($x4609 (fun_app$ v_b_Visited_G_1$ ?v0!20)))
-(let (($x9130 (or $x5240 $x4609)))
+(let (($x9110 (or $x5240 $x4609)))
 (let (($x5237 (fun_app$ ?x265 ?v0!20)))
-(let (($x9133 (= $x5237 $x9130)))
-(let (($x9136 (or $x4114 $x9133)))
-(let ((@x9135 (monotonicity (rewrite (= (ite $x5240 true $x4609) $x9130)) (= (= $x5237 (ite $x5240 true $x4609)) $x9133))))
-(let ((@x9140 (monotonicity @x9135 (= (or $x4114 (= $x5237 (ite $x5240 true $x4609))) $x9136))))
-(let ((@x9143 (trans @x9140 (rewrite (= $x9136 $x9136)) (= (or $x4114 (= $x5237 (ite $x5240 true $x4609))) $x9136))))
-(let ((@x9144 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!20) (or $x4114 (= $x5237 (ite $x5240 true $x4609)))) @x9143 $x9136)))
-(let ((@x9316 (symm (monotonicity @x5875 (= $x5237 (fun_app$ v_b_Visited_G_2$ ?v0!20))) (= (fun_app$ v_b_Visited_G_2$ ?v0!20) $x5237))))
-(let ((@x9318 (monotonicity @x9316 (= (not (fun_app$ v_b_Visited_G_2$ ?v0!20)) (not $x5237)))))
+(let (($x9115 (= $x5237 $x9110)))
+(let (($x9118 (or $x4114 $x9115)))
+(let ((@x9117 (monotonicity (rewrite (= (ite $x5240 true $x4609) $x9110)) (= (= $x5237 (ite $x5240 true $x4609)) $x9115))))
+(let ((@x9122 (monotonicity @x9117 (= (or $x4114 (= $x5237 (ite $x5240 true $x4609))) $x9118))))
+(let ((@x9099 (trans @x9122 (rewrite (= $x9118 $x9118)) (= (or $x4114 (= $x5237 (ite $x5240 true $x4609))) $x9118))))
+(let ((@x9100 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!20) (or $x4114 (= $x5237 (ite $x5240 true $x4609)))) @x9099 $x9118)))
+(let ((@x9326 (symm (monotonicity @x5875 (= $x5237 (fun_app$ v_b_Visited_G_2$ ?v0!20))) (= (fun_app$ v_b_Visited_G_2$ ?v0!20) $x5237))))
+(let ((@x9328 (monotonicity @x9326 (= (not (fun_app$ v_b_Visited_G_2$ ?v0!20)) (not $x5237)))))
 (let (($x4278 (fun_app$ v_b_Visited_G_2$ ?v0!20)))
 (let (($x4279 (not $x4278)))
 (let (($x4403 (or $x4279 $x4400)))
-(let ((@x8012 (mp ((_ quant-inst ?v0!20) (or $x3700 $x4403)) (rewrite (= (or $x3700 $x4403) (or $x3700 $x4279 $x4400))) (or $x3700 $x4279 $x4400))))
-(let ((@x9292 (unit-resolution (unit-resolution @x8012 @x7616 $x4403) (hypothesis (not $x4400)) $x4279)))
-(let ((@x9320 (unit-resolution (def-axiom (or (not $x9133) $x5237 (not $x9130))) (mp @x9292 @x9318 (not $x5237)) (unit-resolution @x9144 @x3473 $x9133) (not $x9130))))
-(let ((@x9328 (mp (unit-resolution (def-axiom (or $x9130 $x9145)) @x9320 $x9145) (monotonicity @x9325 (= $x9145 $x5390)) $x5390)))
+(let ((@x7926 (mp ((_ quant-inst ?v0!20) (or $x3700 $x4403)) (rewrite (= (or $x3700 $x4403) (or $x3700 $x4279 $x4400))) (or $x3700 $x4279 $x4400))))
+(let ((@x9302 (unit-resolution (unit-resolution @x7926 @x7618 $x4403) (hypothesis (not $x4400)) $x4279)))
+(let ((@x9330 (unit-resolution (def-axiom (or (not $x9115) $x5237 (not $x9110))) (mp @x9302 @x9328 (not $x5237)) (unit-resolution @x9100 @x3473 $x9115) (not $x9110))))
+(let ((@x9338 (mp (unit-resolution (def-axiom (or $x9110 $x9098)) @x9330 $x9098) (monotonicity @x9335 (= $x9098 $x5390)) $x5390)))
 (let (($x5387 (<= ?x4435 0)))
 (let (($x5391 (= ?x4435 0)))
 (let ((?x3106 (+ ?x257 ?x3096 ?x3105)))
 (let (($x4239 (<= ?x3106 0)))
 (let ((?x3884 (+ ?x257 ?x3105)))

 (let ((@x6725 (trans @x6945 (rewrite (= (<= (+ ?x1173 ?x4393 ?x4436) 0) $x6827)) (= (<= (+ ?x4393 ?x1173 ?x4436) 0) $x6827))))
 (let ((@x6730 (monotonicity @x6725 (= (or $x4438 (<= (+ ?x4393 ?x1173 ?x4436) 0)) $x6723))))
 (let ((@x6830 (monotonicity @x6730 (= (not (or $x4438 (<= (+ ?x4393 ?x1173 ?x4436) 0))) $x6684))))
 (let ((@x6829 (monotonicity (monotonicity @x6830 (= $x4443 $x6831)) (= $x6790 (or $x3683 $x6831)))))
 (let ((@x6824 (mp ((_ quant-inst ?v0!20) $x6790) (trans @x6829 (rewrite (= (or $x3683 $x6831) $x6789)) (= $x6790 $x6789)) $x6789)))
-(let ((@x9281 (unit-resolution (unit-resolution @x6824 @x5944 $x6831) (hypothesis (not $x4400)) $x6684)))
-(let ((@x7436 (unit-resolution (def-axiom (or $x6723 (not $x4438))) (hypothesis $x6684) (not $x4438))))
-(let ((@x7494 (unit-resolution (def-axiom (or $x6723 (not $x6827))) (hypothesis $x6684) (not $x6827))))
+(let ((@x9291 (unit-resolution (unit-resolution @x6824 @x5944 $x6831) (hypothesis (not $x4400)) $x6684)))
+(let ((@x7434 (unit-resolution (def-axiom (or $x6723 (not $x4438))) (hypothesis $x6684) (not $x4438))))
+(let ((@x7480 (unit-resolution (def-axiom (or $x6723 (not $x6827))) (hypothesis $x6684) (not $x6827))))
 (let (($x6621 (or $x4438 $x6827 $x5673)))
 (let (($x6987 (or $x3675 $x4438 $x6827 $x5673)))
 (let (($x4440 (<= (+ ?x4393 ?x1173 ?x4436) 0)))
 (let (($x4486 (or $x4438 $x4440 (= (+ ?x257 ?x4435 ?x1912) 0))))
 (let (($x6624 (or $x3675 $x4486)))
 (let ((@x5324 (monotonicity (rewrite (= (+ ?x257 ?x4435 ?x1912) ?x4487)) (= (= (+ ?x257 ?x4435 ?x1912) 0) $x5673))))
 (let ((@x6996 (monotonicity (monotonicity @x6725 @x5324 (= $x4486 $x6621)) (= $x6624 (or $x3675 $x6621)))))
 (let ((@x7057 (mp ((_ quant-inst ?v0!20) $x6624) (trans @x6996 (rewrite (= (or $x3675 $x6621) $x6987)) (= $x6624 $x6987)) $x6987)))
-(let ((@x7649 (unit-resolution (unit-resolution @x7057 @x6588 $x6621) @x7494 @x7436 (hypothesis (not $x5673)) false)))
+(let ((@x7649 (unit-resolution (unit-resolution @x7057 @x6588 $x6621) @x7480 @x7434 (hypothesis (not $x5673)) false)))
 (let ((@x7699 (lemma @x7649 (or $x6723 $x5673))))
-(let ((@x9285 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x5673) $x4507)) (unit-resolution @x7699 @x9281 $x5673) $x4507)))
-(let ((@x9287 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1) (or (not $x4507) $x4570 (not $x3886))) @x6925 (or (not $x4507) $x4570))))
-(let ((@x7251 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x7135 (not $x4569) (not $x4570))) (hypothesis $x4569) (or $x7135 (not $x4570)))))
+(let ((@x9295 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x5673) $x4507)) (unit-resolution @x7699 @x9291 $x5673) $x4507)))
+(let ((@x9297 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1) (or (not $x4507) $x4570 (not $x3886))) @x6925 (or (not $x4507) $x4570))))
+(let ((@x7017 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x7135 (not $x4569) (not $x4570))) (hypothesis $x4569) (or $x7135 (not $x4570)))))
 (let (($x7151 (not $x7135)))
 (let (($x7157 (or $x3734 $x7049 $x4127 $x7151)))
 (let (($x4516 (>= (+ ?x3104 ?x1912) 0)))
 (let (($x4528 (or $x4516 $x4127 (not (= (+ ?x3104 ?x1912 ?x4435) 0)))))
 (let (($x7317 (or $x3734 $x4528)))

 (let ((@x7149 (trans @x7137 (rewrite (= (= (+ ?x1912 ?x3104 ?x4435) 0) $x7135)) (= (= (+ ?x3104 ?x1912 ?x4435) 0) $x7135))))
 (let ((@x7063 (monotonicity (rewrite (= (+ ?x3104 ?x1912) (+ ?x1912 ?x3104))) (= $x4516 (>= (+ ?x1912 ?x3104) 0)))))
 (let ((@x7144 (trans @x7063 (rewrite (= (>= (+ ?x1912 ?x3104) 0) $x7049)) (= $x4516 $x7049))))
 (let ((@x7156 (monotonicity @x7144 (monotonicity @x7149 (= (not (= (+ ?x3104 ?x1912 ?x4435) 0)) $x7151)) (= $x4528 (or $x7049 $x4127 $x7151)))))
 (let ((@x7313 (trans (monotonicity @x7156 (= $x7317 (or $x3734 (or $x7049 $x4127 $x7151)))) (rewrite (= (or $x3734 (or $x7049 $x4127 $x7151)) $x7157)) (= $x7317 $x7157))))
-(let ((@x7502 (unit-resolution (mp ((_ quant-inst v_b_v_G_1$) $x7317) @x7313 $x7157) (hypothesis $x3729) @x7482 (or $x7049 $x7151))))
-(let ((@x9290 (unit-resolution @x7502 (unit-resolution @x7251 (unit-resolution @x9287 @x9285 $x4570) $x7135) $x7049)))
+(let ((@x7506 (unit-resolution (mp ((_ quant-inst v_b_v_G_1$) $x7317) @x7313 $x7157) (hypothesis $x3729) @x7413 (or $x7049 $x7151))))
+(let ((@x9300 (unit-resolution @x7506 (unit-resolution @x7017 (unit-resolution @x9297 @x9295 $x4570) $x7135) $x7049)))
 (let (($x4382 (>= ?x4381 0)))
-(let (($x6813 (= ?v1!16 v_b_v_G_1$)))
-(let (($x7202 (= v_b_v_G_1$ ?v1!16)))
 (let ((?x6481 (pair$ v_b_v_G_1$ ?v1!16)))
 (let ((?x6374 (b_G$ ?x6481)))
 (let (($x7203 (<= ?x6374 0)))
+(let (($x7206 (not $x7203)))
+(let (($x7202 (= v_b_v_G_1$ ?v1!16)))
+(let (($x7265 (not $x7202)))
+(let (($x6813 (= ?v1!16 v_b_v_G_1$)))
+(let (($x6712 (not $x6813)))
+(let (($x6814 (fun_app$ v_b_Visited_G_1$ ?v1!16)))
+(let (($x8313 (or $x6813 $x6814)))
+(let (($x6812 (fun_app$ ?x265 ?v1!16)))
+(let (($x4356 (= $x6812 $x8313)))
+(let (($x6492 (or $x4114 $x4356)))
+(let ((@x6175 (monotonicity (rewrite (= (ite $x6813 true $x6814) $x8313)) (= (= $x6812 (ite $x6813 true $x6814)) $x4356))))
+(let ((@x7654 (monotonicity @x6175 (= (or $x4114 (= $x6812 (ite $x6813 true $x6814))) $x6492))))
+(let ((@x7598 (trans @x7654 (rewrite (= $x6492 $x6492)) (= (or $x4114 (= $x6812 (ite $x6813 true $x6814))) $x6492))))
+(let ((@x7600 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v1!16) (or $x4114 (= $x6812 (ite $x6813 true $x6814)))) @x7598 $x6492)))
+(let ((@x8661 (monotonicity (symm (monotonicity @x5875 (= $x6812 $x1860)) (= $x1860 $x6812)) (= (not $x1860) (not $x6812)))))
+(let (($x1861 (not $x1860)))
+(let ((@x8145 (hypothesis $x2765)))
+(let ((@x8181 (mp (unit-resolution (def-axiom (or $x2760 $x1861)) @x8145 $x1861) @x8661 (not $x6812))))
+(let ((@x8616 (unit-resolution (def-axiom (or (not $x4356) $x6812 (not $x8313))) @x8181 (unit-resolution @x7600 @x3473 $x4356) (not $x8313))))
+(let ((@x8179 (unit-resolution (hypothesis $x6712) (symm (hypothesis $x7202) $x6813) false)))
+(let ((@x8586 (unit-resolution (lemma @x8179 (or $x7265 $x6813)) (unit-resolution (def-axiom (or $x8313 $x6712)) @x8616 $x6712) $x7265)))
+(let ((@x7214 (rewrite (= (or (not $x3480) (or $x7202 $x7206)) (or (not $x3480) $x7202 $x7206)))))
+(let ((@x7215 (mp ((_ quant-inst v_b_v_G_1$ ?v1!16) (or (not $x3480) (or $x7202 $x7206))) @x7214 (or (not $x3480) $x7202 $x7206))))
+(let ((@x8872 (lemma (unit-resolution @x7215 @x3485 (hypothesis $x7203) (hypothesis $x7265) false) (or $x7206 $x7202))))
+(let ((?x1865 (v_b_SP_G_2$ ?v1!16)))
+(let ((?x6126 (* (- 1) ?x1865)))
+(let ((?x6400 (+ ?x257 ?x6126 ?x6374)))
+(let (($x6319 (<= ?x6400 0)))
+(let (($x7408 (= ?x6400 0)))
+(let (($x6238 (<= (+ b_Infinity$ (* (- 1) ?x6374)) 0)))
+(let (($x7360 (not $x6238)))
+(let (($x7540 (>= (+ ?x257 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v1!16)) ?x6374) 0)))
+(let (($x4492 (or $x6238 $x7540)))
+(let (($x4445 (not $x4492)))
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+(let (($x6378 (= ?x1865 ?x6234)))
+(let (($x8060 (not $x6378)))
+(let (($x7372 (>= (+ ?x1865 (* (- 1) ?x6234)) 0)))
+(let (($x8588 (not $x7372)))
+(let (($x8639 (<= (+ ?x257 (* (- 1) ?x6234)) 0)))
+(let (($x7946 (or $x6814 $x8639)))
+(let (($x8076 (or $x3665 $x6814 $x8639)))
+(let ((@x8377 (monotonicity (rewrite (= (+ ?x6234 ?x1173) (+ ?x1173 ?x6234))) (= (>= (+ ?x6234 ?x1173) 0) (>= (+ ?x1173 ?x6234) 0)))))
+(let ((@x8401 (trans @x8377 (rewrite (= (>= (+ ?x1173 ?x6234) 0) $x8639)) (= (>= (+ ?x6234 ?x1173) 0) $x8639))))
+(let ((@x8438 (monotonicity (monotonicity @x8401 (= (or $x6814 (>= (+ ?x6234 ?x1173) 0)) $x7946)) (= (or $x3665 (or $x6814 (>= (+ ?x6234 ?x1173) 0))) (or $x3665 $x7946)))))
+(let ((@x8439 (trans @x8438 (rewrite (= (or $x3665 $x7946) $x8076)) (= (or $x3665 (or $x6814 (>= (+ ?x6234 ?x1173) 0))) $x8076))))
+(let ((@x8127 (mp ((_ quant-inst ?v1!16) (or $x3665 (or $x6814 (>= (+ ?x6234 ?x1173) 0)))) @x8439 $x8076)))
+(let ((@x8777 (unit-resolution @x8127 (unit-resolution (def-axiom (or $x3809 $x3660)) @x6181 $x3660) $x7946)))
+(let ((@x8778 (unit-resolution @x8777 (unit-resolution (def-axiom (or $x8313 (not $x6814))) @x8616 (not $x6814)) $x8639)))
 (let ((?x1866 (v_b_SP_G_2$ ?v0!17)))
 (let ((?x6890 (+ ?x1866 ?x3105)))
 (let (($x6886 (<= ?x6890 0)))
-(let ((?x4496 (fun_app$c v_b_SP_G_1$ ?v0!17)))
-(let ((?x6307 (* (- 1) ?x4496)))
-(let ((?x5972 (+ ?x257 ?x6307)))
-(let (($x7220 (>= ?x5972 0)))
 (let (($x3187 (fun_app$ v_b_Visited_G_1$ ?v0!17)))
 (let (($x4478 (= ?v0!17 v_b_v_G_1$)))
 (let (($x4499 (or $x4478 $x3187)))
 (let (($x4471 (fun_app$ ?x265 ?v0!17)))
 (let (($x4593 (= $x4471 $x4499)))
 (let (($x4712 (or $x4114 $x4593)))
 (let ((@x4495 (monotonicity (rewrite (= (ite $x4478 true $x3187) $x4499)) (= (= $x4471 (ite $x4478 true $x3187)) $x4593))))
 (let ((@x5371 (monotonicity @x4495 (= (or $x4114 (= $x4471 (ite $x4478 true $x3187))) $x4712))))
 (let ((@x5958 (trans @x5371 (rewrite (= $x4712 $x4712)) (= (or $x4114 (= $x4471 (ite $x4478 true $x3187))) $x4712))))
 (let ((@x6125 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!17) (or $x4114 (= $x4471 (ite $x4478 true $x3187)))) @x5958 $x4712)))
-(let ((@x8166 (mp (unit-resolution (def-axiom (or $x2760 $x1862)) (hypothesis $x2765) $x1862) (symm (monotonicity @x5875 (= $x4471 $x1862)) (= $x1862 $x4471)) $x4471)))
-(let ((@x8237 (unit-resolution (def-axiom (or (not $x4593) (not $x4471) $x4499)) @x8166 (unit-resolution @x6125 @x3473 $x4593) $x4499)))
+(let ((@x8749 (mp (unit-resolution (def-axiom (or $x2760 $x1862)) @x8145 $x1862) (symm (monotonicity @x5875 (= $x4471 $x1862)) (= $x1862 $x4471)) $x4471)))
+(let ((@x8750 (unit-resolution (def-axiom (or (not $x4593) (not $x4471) $x4499)) @x8749 (unit-resolution @x6125 @x3473 $x4593) $x4499)))
+(let ((?x4496 (fun_app$c v_b_SP_G_1$ ?v0!17)))
+(let ((?x6307 (* (- 1) ?x4496)))
+(let ((?x5972 (+ ?x257 ?x6307)))
+(let (($x7220 (>= ?x5972 0)))
+(let (($x7299 (not $x7220)))
+(let ((?x5902 (+ ?x1866 ?x6307)))
+(let (($x6327 (<= ?x5902 0)))
+(let (($x6088 (or $x3691 $x6327)))
+(let (($x6436 (>= (+ ?x4496 (* (- 1) ?x1866)) 0)))
+(let ((@x6464 (monotonicity (rewrite (= (+ ?x4496 (* (- 1) ?x1866)) (+ (* (- 1) ?x1866) ?x4496))) (= $x6436 (>= (+ (* (- 1) ?x1866) ?x4496) 0)))))
+(let ((@x5905 (trans @x6464 (rewrite (= (>= (+ (* (- 1) ?x1866) ?x4496) 0) $x6327)) (= $x6436 $x6327))))
+(let ((@x5843 (trans (monotonicity @x5905 (= (or $x3691 $x6436) $x6088)) (rewrite (= $x6088 $x6088)) (= (or $x3691 $x6436) $x6088))))
+(let ((@x7292 (unit-resolution (mp ((_ quant-inst ?v0!17) (or $x3691 $x6436)) @x5843 $x6088) @x6892 $x6327)))
+(let (($x6936 (not $x6886)))
+(let ((@x6513 (hypothesis $x6936)))
+(let ((@x8452 (unit-resolution ((_ th-lemma arith assign-bounds -1 1 1 -1) (or $x7299 (not $x6327) $x6886 $x4315 (not $x4239))) @x6513 @x7292 @x6019 @x7839 $x7299)))
 (let (($x6485 (not $x4478)))
-(let (($x8046 (<= (+ ?x257 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v1!16))) 0)))
-(let (($x6814 (fun_app$ v_b_Visited_G_1$ ?v1!16)))
-(let (($x8334 (or $x6813 $x6814)))
-(let (($x6812 (fun_app$ ?x265 ?v1!16)))
-(let (($x7683 (= $x6812 $x8334)))
-(let (($x6622 (or $x4114 $x7683)))
-(let ((@x6719 (monotonicity (rewrite (= (ite $x6813 true $x6814) $x8334)) (= (= $x6812 (ite $x6813 true $x6814)) $x7683))))
-(let ((@x8777 (monotonicity @x6719 (= (or $x4114 (= $x6812 (ite $x6813 true $x6814))) $x6622))))
-(let ((@x8650 (trans @x8777 (rewrite (= $x6622 $x6622)) (= (or $x4114 (= $x6812 (ite $x6813 true $x6814))) $x6622))))
-(let ((@x8651 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v1!16) (or $x4114 (= $x6812 (ite $x6813 true $x6814)))) @x8650 $x6622)))
-(let ((@x8121 (monotonicity (symm (monotonicity @x5875 (= $x6812 $x1860)) (= $x1860 $x6812)) (= (not $x1860) (not $x6812)))))
-(let (($x1861 (not $x1860)))
-(let ((@x7803 (hypothesis $x2765)))
-(let ((@x8141 (mp (unit-resolution (def-axiom (or $x2760 $x1861)) @x7803 $x1861) @x8121 (not $x6812))))
-(let ((@x8147 (unit-resolution (def-axiom (or (not $x7683) $x6812 (not $x8334))) @x8141 (unit-resolution @x8651 @x3473 $x7683) (not $x8334))))
-(let (($x8156 (or $x6814 $x8046)))
-(let (($x8160 (or $x3665 $x6814 $x8046)))
-(let (($x6666 (>= (+ (fun_app$c v_b_SP_G_1$ ?v1!16) ?x1173) 0)))
-(let (($x6673 (or $x6814 $x6666)))
-(let (($x8163 (or $x3665 $x6673)))
-(let ((@x7990 (rewrite (= (>= (+ ?x1173 (fun_app$c v_b_SP_G_1$ ?v1!16)) 0) $x8046))))
-(let (($x8213 (= (+ (fun_app$c v_b_SP_G_1$ ?v1!16) ?x1173) (+ ?x1173 (fun_app$c v_b_SP_G_1$ ?v1!16)))))
-(let ((@x8047 (monotonicity (rewrite $x8213) (= $x6666 (>= (+ ?x1173 (fun_app$c v_b_SP_G_1$ ?v1!16)) 0)))))
-(let ((@x8089 (monotonicity (monotonicity (trans @x8047 @x7990 (= $x6666 $x8046)) (= $x6673 $x8156)) (= $x8163 (or $x3665 $x8156)))))
-(let ((@x8093 (mp ((_ quant-inst ?v1!16) $x8163) (trans @x8089 (rewrite (= (or $x3665 $x8156) $x8160)) (= $x8163 $x8160)) $x8160)))
-(let ((@x8217 (unit-resolution @x8093 (unit-resolution (def-axiom (or $x3809 $x3660)) @x6181 $x3660) $x8156)))
-(let ((@x8239 (unit-resolution @x8217 (unit-resolution (def-axiom (or $x8334 (not $x6814))) @x8147 (not $x6814)) $x8046)))
-(let (($x3386 (not $x1869)))
-(let ((@x3390 (def-axiom (or $x2760 $x3386))))
-(let ((@x8240 (unit-resolution @x3390 @x7803 $x3386)))
-(let ((?x6009 (pair$ v_b_v_G_1$ ?v0!17)))
-(let ((?x6010 (b_G$ ?x6009)))
-(let ((?x1867 (* (- 1) ?x1866)))
-(let ((?x6187 (+ ?x257 ?x1867 ?x6010)))
-(let ((@x8743 (monotonicity (monotonicity (hypothesis $x4478) (= ?x6009 ?x3130)) (= ?x6010 ?x3096))))
 (let (($x6889 (= ?x1866 ?x3104)))
-(let ((@x6922 (hypothesis $x4478)))
-(let ((@x6921 (unit-resolution (hypothesis (not $x6889)) (monotonicity @x6922 $x6889) false)))
+(let (($x6250 (not $x6889)))
+(let ((@x6214 ((_ th-lemma arith triangle-eq) (or $x6250 $x6886))))
+(let ((@x6921 (unit-resolution (hypothesis $x6250) (monotonicity (hypothesis $x4478) $x6889) false)))
 (let ((@x6939 (lemma @x6921 (or $x6485 $x6889))))
-(let ((@x6214 ((_ th-lemma arith triangle-eq) (or (not $x6889) $x6886))))
-(let (($x7675 (>= ?x6890 0)))
-(let ((@x8362 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x6889) $x7675)) (unit-resolution @x6939 @x6922 $x6889) $x7675)))
-(let ((@x7970 ((_ th-lemma arith eq-propagate 1 1 1 1 -1 -1) @x8362 (unit-resolution @x6214 (unit-resolution @x6939 @x6922 $x6889) $x6886) @x6019 @x6933 @x6930 @x7839 (= ?x6010 ?x6187))))
-(let ((@x8765 (trans (trans (symm @x7970 (= ?x6187 ?x6010)) @x8743 (= ?x6187 ?x3096)) @x4849 (= ?x6187 0))))
-(let (($x6564 (>= ?x6187 0)))
-(let (($x7274 (not $x6564)))
-(let ((@x7271 (hypothesis $x3386)))
-(let ((?x1865 (v_b_SP_G_2$ ?v1!16)))
-(let ((?x6126 (* (- 1) ?x1865)))
-(let ((?x6400 (+ ?x257 ?x6126 ?x6374)))
-(let (($x6319 (<= ?x6400 0)))
-(let (($x8008 (= ?x6400 0)))
-(let (($x6238 (<= (+ b_Infinity$ (* (- 1) ?x6374)) 0)))
-(let (($x8646 (not $x6238)))
-(let (($x7241 (>= (+ ?x257 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v1!16)) ?x6374) 0)))
-(let (($x7239 (or $x6238 $x7241)))
-(let (($x4416 (not $x7239)))
-(let ((?x6234 (fun_app$c v_b_SP_G_1$ ?v1!16)))
-(let (($x6378 (= ?x1865 ?x6234)))
-(let (($x8565 (not $x6378)))
-(let (($x8664 (>= (+ ?x1865 (* (- 1) ?x6234)) 0)))
-(let (($x8549 (not $x8664)))
-(let ((@x8517 ((_ th-lemma arith assign-bounds -1 -1 -1 -1 1) (or $x8549 (not $x8046) $x1869 (not $x6886) (not $x4177) (not $x3044)))))
-(let ((@x8321 (unit-resolution @x8517 (unit-resolution @x6214 (unit-resolution @x6939 @x6922 $x6889) $x6886) @x6933 @x6930 @x7271 (hypothesis $x8046) $x8549)))
-(let (($x8358 (or $x4416 $x6378)))
-(let (($x8640 (or $x3683 $x4416 $x6378)))
-(let (($x6219 (or (not (or $x6238 (<= (+ ?x6234 ?x1173 (* (- 1) ?x6374)) 0))) $x6378)))
-(let (($x8252 (or $x3683 $x6219)))
-(let (($x6539 (<= (+ ?x6234 ?x1173 (* (- 1) ?x6374)) 0)))
-(let ((@x7664 (rewrite (= (+ ?x6234 ?x1173 (* (- 1) ?x6374)) (+ ?x1173 ?x6234 (* (- 1) ?x6374))))))
-(let ((@x7697 (monotonicity @x7664 (= $x6539 (<= (+ ?x1173 ?x6234 (* (- 1) ?x6374)) 0)))))
-(let ((@x4371 (trans @x7697 (rewrite (= (<= (+ ?x1173 ?x6234 (* (- 1) ?x6374)) 0) $x7241)) (= $x6539 $x7241))))
-(let ((@x8352 (monotonicity (monotonicity @x4371 (= (or $x6238 $x6539) $x7239)) (= (not (or $x6238 $x6539)) $x4416))))
-(let ((@x8173 (monotonicity (monotonicity @x8352 (= $x6219 $x8358)) (= $x8252 (or $x3683 $x8358)))))
-(let ((@x8649 (mp ((_ quant-inst ?v1!16) $x8252) (trans @x8173 (rewrite (= (or $x3683 $x8358) $x8640)) (= $x8252 $x8640)) $x8640)))
-(let ((@x8632 (unit-resolution (unit-resolution @x8649 @x5944 $x8358) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x8565 $x8664)) @x8321 $x8565) $x4416)))
-(let (($x8029 (or $x6238 $x7241 $x8008)))
-(let (($x8118 (or $x3675 $x6238 $x7241 $x8008)))
-(let (($x6399 (or $x6238 $x6539 (= (+ ?x257 ?x6374 ?x6126) 0))))
-(let (($x8113 (or $x3675 $x6399)))
-(let ((@x8010 (monotonicity (rewrite (= (+ ?x257 ?x6374 ?x6126) ?x6400)) (= (= (+ ?x257 ?x6374 ?x6126) 0) $x8008))))
-(let ((@x5909 (monotonicity (monotonicity @x4371 @x8010 (= $x6399 $x8029)) (= $x8113 (or $x3675 $x8029)))))
-(let ((@x7712 (mp ((_ quant-inst ?v1!16) $x8113) (trans @x5909 (rewrite (= (or $x3675 $x8029) $x8118)) (= $x8113 $x8118)) $x8118)))
-(let ((@x8635 (unit-resolution (unit-resolution @x7712 @x6588 $x8029) (unit-resolution (def-axiom (or $x7239 (not $x7241))) @x8632 (not $x7241)) (unit-resolution (def-axiom (or $x7239 $x8646)) @x8632 $x8646) $x8008)))
-(let ((@x7288 (monotonicity (commutativity (= (= v_b_v_G_1$ ?v0!17) $x4478)) (= (not (= v_b_v_G_1$ ?v0!17)) $x6485))))
-(let (($x7176 (= v_b_v_G_1$ ?v0!17)))
-(let (($x7180 (not $x7176)))
-(let (($x7177 (<= ?x6010 0)))
-(let (($x7178 (not $x7177)))
-(let (($x7206 (not $x7203)))
-(let ((@x7267 (monotonicity (symm (commutativity (= $x7202 $x6813)) (= $x6813 $x7202)) (= (not $x6813) (not $x7202)))))
-(let (($x7207 (or $x7202 $x7206)))
-(let ((@x7215 (mp ((_ quant-inst v_b_v_G_1$ ?v1!16) (or (not $x3480) $x7207)) (rewrite (= (or (not $x3480) $x7207) (or (not $x3480) $x7202 $x7206))) (or (not $x3480) $x7202 $x7206))))
-(let ((@x7270 (unit-resolution (unit-resolution @x7215 @x3485 $x7207) (mp (hypothesis (not $x6813)) @x7267 (not $x7202)) $x7206)))
-(let ((@x7278 (unit-resolution ((_ th-lemma arith assign-bounds 1 1 1 1) (or $x7178 $x7274 $x1869 $x7203 (not $x6319))) (hypothesis $x6319) (hypothesis $x6564) @x7271 @x7270 $x7178)))
-(let ((@x7282 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x6010 0)) $x7177)) @x7278 (not (= ?x6010 0)))))
-(let (($x7181 (= ?x6010 0)))
-(let (($x7188 (or $x7180 $x7181)))
-(let ((@x7196 (mp ((_ quant-inst v_b_v_G_1$ ?v0!17) (or $x3151 $x7188)) (rewrite (= (or $x3151 $x7188) (or $x3151 $x7180 $x7181))) (or $x3151 $x7180 $x7181))))
-(let ((@x7289 (mp (unit-resolution (unit-resolution @x7196 @x3479 $x7188) @x7282 $x7180) @x7288 $x6485)))
 (let ((@x5812 (def-axiom (or (not $x4499) $x4478 $x3187))))
+(let ((@x8341 (unit-resolution @x5812 (unit-resolution @x6939 (unit-resolution @x6214 @x6513 $x6250) $x6485) (hypothesis $x4499) $x3187)))
 (let (($x7229 (= (or $x3570 (or $x255 (not $x3187) $x7220)) (or $x3570 $x255 (not $x3187) $x7220))))
 (let ((@x7231 (mp ((_ quant-inst ?v0!17 v_b_v_G_1$) (or $x3570 (or $x255 (not $x3187) $x7220))) (rewrite $x7229) (or $x3570 $x255 (not $x3187) $x7220))))
-(let ((@x7291 (unit-resolution @x7231 @x5748 @x6225 (unit-resolution @x5812 @x7289 (hypothesis $x4499) $x3187) $x7220)))
-(let (($x6327 (<= (+ ?x1866 ?x6307) 0)))
-(let (($x6088 (or $x3691 $x6327)))
-(let ((@x6464 (monotonicity (rewrite (= (+ ?x4496 ?x1867) (+ ?x1867 ?x4496))) (= (>= (+ ?x4496 ?x1867) 0) (>= (+ ?x1867 ?x4496) 0)))))
-(let ((@x5905 (trans @x6464 (rewrite (= (>= (+ ?x1867 ?x4496) 0) $x6327)) (= (>= (+ ?x4496 ?x1867) 0) $x6327))))
-(let ((@x5843 (trans (monotonicity @x5905 (= (or $x3691 (>= (+ ?x4496 ?x1867) 0)) $x6088)) (rewrite (= $x6088 $x6088)) (= (or $x3691 (>= (+ ?x4496 ?x1867) 0)) $x6088))))
-(let ((@x7292 (unit-resolution (mp ((_ quant-inst ?v0!17) (or $x3691 (>= (+ ?x4496 ?x1867) 0))) @x5843 $x6088) @x6892 $x6327)))
-(let ((@x7295 (lemma ((_ th-lemma arith farkas 1 1 1 1 1) @x7292 @x7271 @x7270 (hypothesis $x6319) @x7291 false) (or (not $x6319) $x1869 (not $x4499) $x7274 $x6813))))
-(let ((@x8734 (unit-resolution @x7295 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x8008) $x6319)) @x8635 $x6319) (hypothesis $x4499) (hypothesis (not $x6813)) @x7271 $x7274)))
-(let ((@x8324 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x6187 0)) $x6564)) @x8734 (not (= ?x6187 0)))))
-(let ((@x8494 (lemma (unit-resolution @x8324 @x8765 false) (or $x6485 (not $x4499) $x6813 $x1869 (not $x8046)))))
-(let ((@x8211 (unit-resolution @x8494 @x8237 (unit-resolution (def-axiom (or $x8334 (not $x6813))) @x8147 (not $x6813)) @x8240 @x8239 $x6485)))
-(let ((@x8909 (unit-resolution @x7231 @x5748 @x6225 (hypothesis $x3187) (hypothesis (not $x7220)) false)))
-(let ((@x8256 (unit-resolution (lemma @x8909 (or (not $x3187) $x7220)) (unit-resolution @x5812 @x8211 @x8237 $x3187) $x7220)))
-(let ((@x8314 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1 1 -1) (or $x6886 (not $x7220) (not $x6327) $x4315 (not $x4239))) @x7292 @x7839 @x8256 @x6019 $x6886)))
-(let ((@x8385 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x8565 $x8664)) (unit-resolution @x8517 @x8314 @x6933 @x6930 @x8240 @x8239 $x8549) $x8565)))
-(let ((@x8386 (unit-resolution (def-axiom (or $x7239 $x8646)) (unit-resolution (unit-resolution @x8649 @x5944 $x8358) @x8385 $x4416) $x8646)))
-(let (($x8654 (not $x7241)))
-(let ((@x8390 (unit-resolution (def-axiom (or $x7239 $x8654)) (unit-resolution (unit-resolution @x8649 @x5944 $x8358) @x8385 $x4416) $x8654)))
-(let ((@x8410 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x8008) $x6319)) (unit-resolution (unit-resolution @x7712 @x6588 $x8029) @x8390 @x8386 $x8008) $x6319)))
-(let ((@x8411 ((_ th-lemma arith assign-bounds 1 1 1 1 1) (or $x7203 (not $x6319) $x1869 (not $x6886) (not $x4177) (not $x3044)))))
-(let ((@x8413 (unit-resolution @x7215 @x3485 (unit-resolution @x8411 @x8410 @x6933 @x6930 @x8240 @x8314 $x7203) $x7202)))
-(let ((@x8417 (unit-resolution (unit-resolution (def-axiom (or $x8334 (not $x6813))) @x8147 (not $x6813)) (symm @x8413 $x6813) false)))
+(let ((@x8111 (lemma (unit-resolution @x7231 @x5748 @x6225 @x8341 @x8452 false) (or $x6886 (not $x4499)))))
+(let ((@x8747 (unit-resolution ((_ th-lemma arith assign-bounds 1 1 1 -1 1) (or $x8588 (not $x8639) $x1869 $x6936 (not $x4177) (not $x3044))) (unit-resolution @x8111 @x8750 $x6886) @x6933 @x6930 (unit-resolution (def-axiom (or $x2760 (not $x1869))) @x8145 (not $x1869)) @x8778 $x8588)))
+(let (($x6079 (or $x4445 $x6378)))
+(let (($x6188 (or $x3683 $x4445 $x6378)))
+(let (($x6219 (or (not (or $x6238 (<= (+ ?x6234 ?x1173 (* (- 1) ?x6374)) 0))) $x6378)))
+(let (($x6365 (or $x3683 $x6219)))
+(let (($x6539 (<= (+ ?x6234 ?x1173 (* (- 1) ?x6374)) 0)))
+(let ((@x6817 (rewrite (= (+ ?x6234 ?x1173 (* (- 1) ?x6374)) (+ ?x1173 ?x6234 (* (- 1) ?x6374))))))
+(let ((@x7239 (monotonicity @x6817 (= $x6539 (<= (+ ?x1173 ?x6234 (* (- 1) ?x6374)) 0)))))
+(let ((@x4408 (trans @x7239 (rewrite (= (<= (+ ?x1173 ?x6234 (* (- 1) ?x6374)) 0) $x7540)) (= $x6539 $x7540))))
+(let ((@x6718 (monotonicity (monotonicity @x4408 (= (or $x6238 $x6539) $x4492)) (= (not (or $x6238 $x6539)) $x4445))))
+(let ((@x7376 (monotonicity (monotonicity @x6718 (= $x6219 $x6079)) (= $x6365 (or $x3683 $x6079)))))
+(let ((@x7375 (mp ((_ quant-inst ?v1!16) $x6365) (trans @x7376 (rewrite (= (or $x3683 $x6079) $x6188)) (= $x6365 $x6188)) $x6188)))
+(let ((@x8141 (unit-resolution (unit-resolution @x7375 @x5944 $x6079) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x8060 $x7372)) @x8747 $x8060) $x4445)))
+(let (($x7378 (or $x6238 $x7540 $x7408)))
+(let (($x7022 (or $x3675 $x6238 $x7540 $x7408)))
+(let (($x6399 (or $x6238 $x6539 (= (+ ?x257 ?x6374 ?x6126) 0))))
+(let (($x6139 (or $x3675 $x6399)))
+(let ((@x7409 (monotonicity (rewrite (= (+ ?x257 ?x6374 ?x6126) ?x6400)) (= (= (+ ?x257 ?x6374 ?x6126) 0) $x7408))))
+(let ((@x6535 (monotonicity (monotonicity @x4408 @x7409 (= $x6399 $x7378)) (= $x6139 (or $x3675 $x7378)))))
+(let ((@x7425 (mp ((_ quant-inst ?v1!16) $x6139) (trans @x6535 (rewrite (= (or $x3675 $x7378) $x7022)) (= $x6139 $x7022)) $x7022)))
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+(let ((@x8386 ((_ th-lemma arith farkas 1 1 1 1 1 1) (unit-resolution (def-axiom (or $x2760 (not $x1869))) @x8145 (not $x1869)) (unit-resolution @x8111 @x8750 $x6886) @x6933 @x6930 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x7408) $x6319)) @x8177 $x6319) (unit-resolution @x8872 @x8586 $x7206) false)))
 (let ((@x3365 (def-axiom (or $x3758 $x2765 $x3752))))
-(let ((@x9296 (unit-resolution @x3365 (lemma @x8417 $x2760) (unit-resolution (def-axiom (or $x3761 $x3755)) @x9294 $x3755) $x3752)))
-(let ((@x8225 (rewrite (= (or $x3717 (or $x4278 $x4127 $x4382)) (or $x3717 $x4278 $x4127 $x4382)))))
-(let ((@x8229 (mp ((_ quant-inst v_b_v_G_1$ ?v0!20) (or $x3717 (or $x4278 $x4127 $x4382))) @x8225 (or $x3717 $x4278 $x4127 $x4382))))
-(let ((@x9299 (unit-resolution @x8229 (unit-resolution (def-axiom (or $x3749 $x3712)) @x9296 $x3712) @x7482 (or $x4278 $x4382))))
+(let ((@x9306 (unit-resolution @x3365 (lemma @x8386 $x2760) (unit-resolution (def-axiom (or $x3761 $x3755)) @x9304 $x3755) $x3752)))
+(let ((@x8028 (rewrite (= (or $x3717 (or $x4278 $x4127 $x4382)) (or $x3717 $x4278 $x4127 $x4382)))))
+(let ((@x7980 (mp ((_ quant-inst v_b_v_G_1$ ?v0!20) (or $x3717 (or $x4278 $x4127 $x4382))) @x8028 (or $x3717 $x4278 $x4127 $x4382))))
+(let ((@x9309 (unit-resolution @x7980 (unit-resolution (def-axiom (or $x3749 $x3712)) @x9306 $x3712) @x7413 (or $x4278 $x4382))))
 (let (($x4508 (>= ?x4487 0)))
-(let ((@x9304 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1) (or $x4508 (not $x4569) (not $x3886))) @x6925 (or $x4508 (not $x4569)))))
-(let ((@x9306 ((_ th-lemma arith eq-propagate -1 -1 -1 -1 -1 -1 1 1) (unit-resolution @x9304 (hypothesis $x4569) $x4508) @x9285 (unit-resolution @x9299 @x9292 $x4382) @x9290 @x6019 @x6933 @x6930 @x7839 $x5391)))
+(let ((@x9314 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1) (or $x4508 (not $x4569) (not $x3886))) @x6925 (or $x4508 (not $x4569)))))
+(let ((@x9316 ((_ th-lemma arith eq-propagate -1 -1 -1 -1 -1 -1 1 1) (unit-resolution @x9314 (hypothesis $x4569) $x4508) @x9295 (unit-resolution @x9309 @x9302 $x4382) @x9300 @x6019 @x6933 @x6930 @x7839 $x5391)))
 (let (($x5388 (not $x5387)))
 (let (($x5389 (or $x5386 $x5388)))
-(let ((@x7598 (mp ((_ quant-inst v_b_v_G_1$ ?v0!20) (or (not $x3480) $x5389)) (rewrite (= (or (not $x3480) $x5389) (or (not $x3480) $x5386 $x5388))) (or (not $x3480) $x5386 $x5388))))
-(let ((@x9311 (unit-resolution (unit-resolution @x7598 @x3485 $x5389) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x5391) $x5387)) @x9306 $x5387) $x5386)))
-(let ((@x8045 (unit-resolution (lemma (unit-resolution @x9311 @x9328 false) (or $x4400 $x3734 (not $x4569))) (unit-resolution (def-axiom (or $x3737 $x3729)) @x8092 $x3729) @x7751 $x4400)))
-(let ((@x8812 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4400) $x5977)) @x8045 $x5977)))
+(let ((@x7596 (mp ((_ quant-inst v_b_v_G_1$ ?v0!20) (or (not $x3480) $x5389)) (rewrite (= (or (not $x3480) $x5389) (or (not $x3480) $x5386 $x5388))) (or (not $x3480) $x5386 $x5388))))
+(let ((@x9321 (unit-resolution (unit-resolution @x7596 @x3485 $x5389) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x5391) $x5387)) @x9316 $x5387) $x5386)))
+(let ((@x8870 (unit-resolution (lemma (unit-resolution @x9321 @x9338 false) (or $x4400 $x3734 (not $x4569))) (unit-resolution (def-axiom (or $x3737 $x3729)) @x4391 $x3729) @x4467 $x4400)))
+(let ((@x8892 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4400) $x5977)) @x8870 $x5977)))
 (let ((?x4641 (?v1!7 ?v0!20)))
 (let ((?x4648 (pair$ ?x4641 ?v0!20)))
 (let ((?x4649 (b_G$ ?x4648)))
 (let ((?x4650 (* (- 1) ?x4649)))
 (let ((?x4642 (fun_app$c v_b_SP_G_1$ ?x4641)))
 (let ((?x4643 (* (- 1) ?x4642)))
 (let ((?x4651 (+ ?x4393 ?x4643 ?x4650)))
-(let (($x4391 (>= ?x4651 0)))
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 (let (($x4652 (= ?x4651 0)))
 (let (($x4653 (not $x4652)))
 (let (($x4646 (fun_app$ v_b_Visited_G_1$ ?x4641)))
 (let (($x4647 (not $x4646)))
 (let ((?x4644 (+ ?x4393 ?x4643)))
 (let (($x4645 (<= ?x4644 0)))
 (let (($x4654 (or $x4645 $x4647 $x4653)))
 (let (($x4655 (not $x4654)))
 (let (($x4640 (<= (+ b_Infinity$ ?x4418) 0)))
 (let (($x7886 (not $x4640)))
-(let ((@x8816 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1) (or (not $x5977) $x1914 $x7886)) @x8812 (unit-resolution (def-axiom (or $x3737 $x1915)) @x8092 $x1915) $x7886)))
+(let ((@x8893 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1) (or (not $x5977) $x1914 $x7886)) @x8892 (unit-resolution (def-axiom (or $x3737 $x1915)) @x4391 $x1915) $x7886)))
 (let ((@x7414 (rewrite (= (or $x3586 (or $x1909 $x4640 $x4655)) (or $x3586 $x1909 $x4640 $x4655)))))
 (let ((@x7415 (mp ((_ quant-inst ?v0!20) (or $x3586 (or $x1909 $x4640 $x4655))) @x7414 (or $x3586 $x1909 $x4640 $x4655))))
-(let ((@x8817 (unit-resolution @x7415 @x4545 (unit-resolution (def-axiom (or $x3737 $x1910)) @x8092 $x1910) (or $x4640 $x4655))))
-(let ((@x8826 (unit-resolution @x8817 @x8816 $x4655)))
-(let ((@x6085 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x4653 $x4391)) (unit-resolution (def-axiom (or $x4654 $x4652)) @x8826 $x4652) $x4391)))
-(let (($x7707 (<= ?x4651 0)))
-(let ((@x8177 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x4653 $x7707)) (unit-resolution (def-axiom (or $x4654 $x4652)) @x8826 $x4652) $x7707)))
+(let ((@x8894 (unit-resolution @x7415 @x4545 (unit-resolution (def-axiom (or $x3737 $x1910)) @x4391 $x1910) (or $x4640 $x4655))))
+(let ((@x8897 (unit-resolution @x8894 @x8893 $x4655)))
+(let ((@x8280 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x4653 $x8653)) (unit-resolution (def-axiom (or $x4654 $x4652)) @x8897 $x4652) $x8653)))
+(let (($x8584 (<= ?x4651 0)))
+(let ((@x7677 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x4653 $x8584)) (unit-resolution (def-axiom (or $x4654 $x4652)) @x8897 $x4652) $x8584)))
 (let (($x4689 (fun_app$ v_b_Visited_G_2$ ?x4641)))
 (let ((@x6032 (monotonicity (symm (hypothesis $x266) (= ?x265 v_b_Visited_G_2$)) (= (fun_app$ ?x265 ?x4641) $x4689))))
 (let ((@x6036 (monotonicity (symm @x6032 (= $x4689 (fun_app$ ?x265 ?x4641))) (= (not $x4689) (not (fun_app$ ?x265 ?x4641))))))
 (let (($x5978 (fun_app$ ?x265 ?x4641)))
 (let (($x5985 (= ?x4641 v_b_v_G_1$)))

 (let ((@x5998 (monotonicity @x5993 (= (or $x4114 (= $x5978 (ite $x5985 true $x4646))) $x5994))))
 (let ((@x6001 (trans @x5998 (rewrite (= $x5994 $x5994)) (= (or $x4114 (= $x5978 (ite $x5985 true $x4646))) $x5994))))
 (let ((@x6002 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true (?v1!7 ?v0!20)) (or $x4114 (= $x5978 (ite $x5985 true $x4646)))) @x6001 $x5994)))
 (let ((@x6025 (unit-resolution (def-axiom (or (not $x5991) $x5978 (not $x5988))) (unit-resolution (def-axiom (or $x5988 $x4647)) (hypothesis $x4646) $x5988) (or (not $x5991) $x5978))))
 (let ((@x6038 (unit-resolution (unit-resolution @x6025 (unit-resolution @x6002 @x3473 $x5991) $x5978) (mp (hypothesis (not $x4689)) @x6036 (not $x5978)) false)))
-(let ((@x8986 (unit-resolution (lemma @x6038 (or $x4689 $x2935 $x4647)) (unit-resolution (def-axiom (or $x3809 $x266)) @x6181 $x266) (or $x4689 $x4647))))
-(let ((@x8987 (unit-resolution @x8986 (unit-resolution (def-axiom (or $x4654 $x4646)) @x8826 $x4646) $x4689)))
+(let ((@x8188 (unit-resolution (lemma @x6038 (or $x4689 $x2935 $x4647)) (unit-resolution (def-axiom (or $x3809 $x266)) @x6181 $x266) (or $x4689 $x4647))))
+(let ((@x8763 (unit-resolution @x8188 (unit-resolution (def-axiom (or $x4654 $x4646)) @x8897 $x4646) $x4689)))
 (let ((?x4697 (v_b_SP_G_2$ ?x4641)))
 (let ((?x4700 (* (- 1) ?x4697)))
 (let ((?x4868 (+ ?x1911 ?x4700)))
-(let (($x9248 (<= ?x4868 0)))
-(let (($x8507 (not $x9248)))
+(let (($x7732 (<= ?x4868 0)))
+(let (($x9853 (not $x7732)))
 (let ((?x4701 (+ ?x4642 ?x4700)))
 (let (($x4708 (>= ?x4701 0)))
-(let ((@x8348 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 -1) (or $x8507 (not $x4708) $x4645 (not $x5977))) @x8812 (unit-resolution ((_ quant-inst (?v1!7 ?v0!20)) (or $x3691 $x4708)) @x6892 $x4708) (unit-resolution (def-axiom (or $x4654 (not $x4645))) @x8826 (not $x4645)) $x8507)))
-(let ((?x8311 (+ ?x1911 ?x4650 ?x4700)))
-(let (($x8266 (>= ?x8311 0)))
-(let ((@x10143 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 -1) (or $x8266 (not $x4391) (not $x4708) (not $x5977))) (unit-resolution ((_ quant-inst (?v1!7 ?v0!20)) (or $x3691 $x4708)) @x6892 $x4708) (hypothesis $x4391) (hypothesis $x5977) $x8266)))
-(let (($x8534 (<= ?x8311 0)))
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+(let ((?x7938 (+ ?x1911 ?x4650 ?x4700)))
+(let (($x8292 (<= ?x7938 0)))
 (let (($x5038 (<= ?x4701 0)))
-(let (($x5863 (= ?x4642 ?x4697)))
-(let ((@x10149 (symm (commutativity (= $x5863 (= ?x4697 ?x4642))) (= (= ?x4697 ?x4642) $x5863))))
+(let (($x8272 (= ?x4642 ?x4697)))
+(let ((@x9865 (symm (commutativity (= $x8272 (= ?x4697 ?x4642))) (= (= ?x4697 ?x4642) $x8272))))
 (let (($x4698 (= ?x4697 ?x4642)))
-(let ((@x7939 (rewrite (= (or $x3700 (or (not $x4689) $x4698)) (or $x3700 (not $x4689) $x4698)))))
-(let ((@x7943 (mp ((_ quant-inst (?v1!7 ?v0!20)) (or $x3700 (or (not $x4689) $x4698))) @x7939 (or $x3700 (not $x4689) $x4698))))
-(let ((@x7980 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x5863) $x5038)) (mp (unit-resolution @x7943 @x7616 (hypothesis $x4689) $x4698) @x10149 $x5863) $x5038)))
-(let (($x8014 (<= ?x4419 0)))
-(let (($x8221 (or $x3691 $x8014)))
-(let ((@x8001 (monotonicity (rewrite (= (+ ?x4393 ?x1912) (+ ?x1912 ?x4393))) (= (>= (+ ?x4393 ?x1912) 0) (>= (+ ?x1912 ?x4393) 0)))))
-(let ((@x8035 (trans @x8001 (rewrite (= (>= (+ ?x1912 ?x4393) 0) $x8014)) (= (>= (+ ?x4393 ?x1912) 0) $x8014))))
-(let ((@x8178 (trans (monotonicity @x8035 (= (or $x3691 (>= (+ ?x4393 ?x1912) 0)) $x8221)) (rewrite (= $x8221 $x8221)) (= (or $x3691 (>= (+ ?x4393 ?x1912) 0)) $x8221))))
-(let ((@x8659 (unit-resolution (mp ((_ quant-inst ?v0!20) (or $x3691 (>= (+ ?x4393 ?x1912) 0))) @x8178 $x8221) @x6892 $x8014)))
-(let ((@x8083 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 -1) (or $x8534 (not $x7707) (not $x5038) (not $x8014))) @x8659 (hypothesis $x7707) @x7980 $x8534)))
-(let (($x9251 (= ?x8311 0)))
-(let (($x8749 (not $x9251)))
+(let ((@x8267 (rewrite (= (or $x3700 (or (not $x4689) $x4698)) (or $x3700 (not $x4689) $x4698)))))
+(let ((@x8268 (mp ((_ quant-inst (?v1!7 ?v0!20)) (or $x3700 (or (not $x4689) $x4698))) @x8267 (or $x3700 (not $x4689) $x4698))))
+(let ((@x9794 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x8272) $x5038)) (mp (unit-resolution @x8268 @x7618 (hypothesis $x4689) $x4698) @x9865 $x8272) $x5038)))
+(let (($x7927 (<= ?x4419 0)))
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+(let ((@x8030 (monotonicity (rewrite (= (+ ?x4393 ?x1912) (+ ?x1912 ?x4393))) (= (>= (+ ?x4393 ?x1912) 0) (>= (+ ?x1912 ?x4393) 0)))))
+(let ((@x8091 (trans @x8030 (rewrite (= (>= (+ ?x1912 ?x4393) 0) $x7927)) (= (>= (+ ?x4393 ?x1912) 0) $x7927))))
+(let ((@x8854 (trans (monotonicity @x8091 (= (or $x3691 (>= (+ ?x4393 ?x1912) 0)) $x8009)) (rewrite (= $x8009 $x8009)) (= (or $x3691 (>= (+ ?x4393 ?x1912) 0)) $x8009))))
+(let ((@x9860 (unit-resolution (mp ((_ quant-inst ?v0!20) (or $x3691 (>= (+ ?x4393 ?x1912) 0))) @x8854 $x8009) @x6892 $x7927)))
+(let ((@x10107 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 -1) (or $x8292 (not $x8584) (not $x7927) (not $x5038))) @x9860 (hypothesis $x8584) @x9794 $x8292)))
+(let (($x8954 (>= ?x7938 0)))
+(let ((@x10056 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 -1) (or $x8954 (not $x8653) (not $x5977) (not $x4708))) (unit-resolution ((_ quant-inst (?v1!7 ?v0!20)) (or $x3691 $x4708)) @x6892 $x4708) (hypothesis $x8653) (hypothesis $x5977) $x8954)))
+(let (($x8665 (= ?x7938 0)))
+(let (($x9226 (not $x8665)))
 (let (($x4690 (not $x4689)))
-(let (($x8567 (or $x3734 $x9248 $x4690 $x8749)))
+(let (($x6495 (or $x3734 $x7732 $x4690 $x9226)))
 (let (($x4857 (>= (+ ?x4697 ?x1912) 0)))
 (let (($x4861 (or $x4857 $x4690 (not (= (+ ?x4697 ?x1912 ?x4649) 0)))))
-(let (($x8927 (or $x3734 $x4861)))
-(let ((@x8955 (monotonicity (rewrite (= (+ ?x4697 ?x1912 ?x4649) (+ ?x1912 ?x4649 ?x4697))) (= (= (+ ?x4697 ?x1912 ?x4649) 0) (= (+ ?x1912 ?x4649 ?x4697) 0)))))
-(let ((@x8627 (trans @x8955 (rewrite (= (= (+ ?x1912 ?x4649 ?x4697) 0) $x9251)) (= (= (+ ?x4697 ?x1912 ?x4649) 0) $x9251))))
-(let ((@x8965 (monotonicity (rewrite (= (+ ?x4697 ?x1912) (+ ?x1912 ?x4697))) (= $x4857 (>= (+ ?x1912 ?x4697) 0)))))
-(let ((@x8985 (trans @x8965 (rewrite (= (>= (+ ?x1912 ?x4697) 0) $x9248)) (= $x4857 $x9248))))
-(let ((@x9087 (monotonicity @x8985 (monotonicity @x8627 (= (not (= (+ ?x4697 ?x1912 ?x4649) 0)) $x8749)) (= $x4861 (or $x9248 $x4690 $x8749)))))
-(let ((@x8874 (trans (monotonicity @x9087 (= $x8927 (or $x3734 (or $x9248 $x4690 $x8749)))) (rewrite (= (or $x3734 (or $x9248 $x4690 $x8749)) $x8567)) (= $x8927 $x8567))))
-(let ((@x8397 (unit-resolution (mp ((_ quant-inst (?v1!7 ?v0!20)) $x8927) @x8874 $x8567) (hypothesis $x3729) (hypothesis $x4689) (or $x9248 $x8749))))
-(let ((@x5592 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x9251 (not $x8534) (not $x8266))) (unit-resolution @x8397 (hypothesis $x8507) $x8749) @x8083 @x10143 false)))
-(let ((@x8013 (unit-resolution (lemma @x5592 (or $x9248 $x3734 $x4690 (not $x7707) (not $x4391) (not $x5977))) @x8348 (unit-resolution (def-axiom (or $x3737 $x3729)) @x8092 $x3729) @x8987 @x8177 @x6085 @x8812 false)))
+(let (($x9201 (or $x3734 $x4861)))
+(let ((@x8630 (monotonicity (rewrite (= (+ ?x4697 ?x1912 ?x4649) (+ ?x1912 ?x4649 ?x4697))) (= (= (+ ?x4697 ?x1912 ?x4649) 0) (= (+ ?x1912 ?x4649 ?x4697) 0)))))
+(let ((@x8460 (trans @x8630 (rewrite (= (= (+ ?x1912 ?x4649 ?x4697) 0) $x8665)) (= (= (+ ?x4697 ?x1912 ?x4649) 0) $x8665))))
+(let ((@x7449 (monotonicity (rewrite (= (+ ?x4697 ?x1912) (+ ?x1912 ?x4697))) (= $x4857 (>= (+ ?x1912 ?x4697) 0)))))
+(let ((@x7972 (trans @x7449 (rewrite (= (>= (+ ?x1912 ?x4697) 0) $x7732)) (= $x4857 $x7732))))
+(let ((@x4476 (monotonicity @x7972 (monotonicity @x8460 (= (not (= (+ ?x4697 ?x1912 ?x4649) 0)) $x9226)) (= $x4861 (or $x7732 $x4690 $x9226)))))
+(let ((@x8430 (trans (monotonicity @x4476 (= $x9201 (or $x3734 (or $x7732 $x4690 $x9226)))) (rewrite (= (or $x3734 (or $x7732 $x4690 $x9226)) $x6495)) (= $x9201 $x6495))))
+(let ((@x10015 (unit-resolution (mp ((_ quant-inst (?v1!7 ?v0!20)) $x9201) @x8430 $x6495) (hypothesis $x3729) (hypothesis $x4689) (or $x7732 $x9226))))
+(let ((@x10016 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x8665 (not $x8292) (not $x8954))) (unit-resolution @x10015 (hypothesis $x9853) $x9226) @x10056 @x10107 false)))
+(let ((@x8164 (unit-resolution (lemma @x10016 (or $x7732 $x3734 $x4690 (not $x8584) (not $x8653) (not $x5977))) @x8509 (unit-resolution (def-axiom (or $x3737 $x3729)) @x4391 $x3729) @x8763 @x7677 @x8280 @x8892 false)))
 (let ((@x3278 (def-axiom (or $x3746 $x2811 $x3740))))
-(let ((@x8433 (unit-resolution @x3278 (unit-resolution (def-axiom (or $x3749 $x3743)) @x9296 $x3743) $x3743)))
+(let ((@x8072 (unit-resolution @x3278 (unit-resolution (def-axiom (or $x3749 $x3743)) @x9306 $x3743) $x3743)))
 (let (($x3378 (not $x1896)))
 (let ((@x3380 (def-axiom (or $x2806 $x3378))))
-(let ((@x8434 (unit-resolution @x3380 (unit-resolution @x8433 (lemma @x8013 $x3737) $x2811) $x3378)))
+(let ((@x8073 (unit-resolution @x3380 (unit-resolution @x8072 (lemma @x8164 $x3737) $x2811) $x3378)))
 (let ((?x6619 (fun_app$c v_b_SP_G_1$ ?v1!18)))
 (let (($x6615 (= ?x1892 ?x6619)))
-(let (($x7618 (not $x6615)))
-(let ((@x7591 (hypothesis $x2811)))
-(let ((@x7607 (unit-resolution (def-axiom (or $x2806 $x1883)) @x7591 $x1883)))
-(let ((@x7571 (hypothesis $x3378)))
+(let (($x7620 (not $x6615)))
+(let ((@x7607 (hypothesis $x2811)))
+(let ((@x7608 (unit-resolution (def-axiom (or $x2806 $x1883)) @x7607 $x1883)))
+(let ((@x7570 (hypothesis $x3378)))
 (let (($x1889 (not $x1888)))
-(let ((@x7592 (unit-resolution (def-axiom (or $x2806 $x1889)) @x7591 $x1889)))
+(let ((@x7615 (unit-resolution (def-axiom (or $x2806 $x1889)) @x7607 $x1889)))
+(let ((?x6721 (* (- 1) ?x6619)))
+(let ((?x5600 (+ ?x1892 ?x6721)))
+(let (($x7353 (>= ?x5600 0)))
+(let ((@x9059 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x7620 $x7353)) (hypothesis $x6615) $x7353)))
 (let ((?x7110 (pair$ v_b_v_G_1$ ?v0!19)))
 (let ((?x7111 (b_G$ ?x7110)))
 (let ((?x7100 (* (- 1) ?x7111)))
 (let ((?x7554 (+ ?x1885 ?x7100)))
 (let (($x7556 (>= ?x7554 0)))

 (let (($x7243 (= ?v1!18 v_b_v_G_1$)))
 (let (($x7246 (fun_app$ v_b_Visited_G_1$ ?v1!18)))
 (let (($x6211 (not $x7246)))
 (let (($x7248 (>= (+ ?x1885 ?x6619 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!19))) 0)))
 (let (($x7499 (not $x7248)))
-(let ((?x6721 (* (- 1) ?x6619)))
-(let ((?x5600 (+ ?x1892 ?x6721)))
-(let (($x7353 (>= ?x5600 0)))
-(let ((@x8658 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x7618 $x7353)) (hypothesis $x6615) $x7353)))
-(let (($x7076 (<= (+ ?x1893 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!19))) 0)))
+(let ((@x7004 (hypothesis $x7353)))
+(let ((?x7053 (fun_app$c v_b_SP_G_1$ ?v0!19)))
+(let ((?x7074 (* (- 1) ?x7053)))
+(let ((?x7075 (+ ?x1893 ?x7074)))
+(let (($x7076 (<= ?x7075 0)))
 (let (($x7084 (or $x3691 $x7076)))
-(let (($x7081 (= (or $x3691 (>= (+ (fun_app$c v_b_SP_G_1$ ?v0!19) ?x1894) 0)) $x7084)))
-(let ((@x7078 (rewrite (= (>= (+ ?x1894 (fun_app$c v_b_SP_G_1$ ?v0!19)) 0) $x7076))))
-(let (($x7048 (>= (+ (fun_app$c v_b_SP_G_1$ ?v0!19) ?x1894) 0)))
-(let (($x7069 (= (+ (fun_app$c v_b_SP_G_1$ ?v0!19) ?x1894) (+ ?x1894 (fun_app$c v_b_SP_G_1$ ?v0!19)))))
-(let ((@x7073 (monotonicity (rewrite $x7069) (= $x7048 (>= (+ ?x1894 (fun_app$c v_b_SP_G_1$ ?v0!19)) 0)))))
-(let ((@x7090 (trans (monotonicity (trans @x7073 @x7078 (= $x7048 $x7076)) $x7081) (rewrite (= $x7084 $x7084)) $x7081)))
-(let ((@x7496 (unit-resolution (mp ((_ quant-inst ?v0!19) (or $x3691 $x7048)) @x7090 $x7084) @x6892 $x7076)))
-(let ((@x7501 (lemma ((_ th-lemma arith farkas 1 -1 -1 1) (hypothesis $x7248) @x7571 @x7496 (hypothesis $x7353) false) (or $x7499 $x1896 (not $x7353)))))
+(let ((@x7073 (monotonicity (rewrite (= (+ ?x7053 ?x1894) (+ ?x1894 ?x7053))) (= (>= (+ ?x7053 ?x1894) 0) (>= (+ ?x1894 ?x7053) 0)))))
+(let ((@x7080 (trans @x7073 (rewrite (= (>= (+ ?x1894 ?x7053) 0) $x7076)) (= (>= (+ ?x7053 ?x1894) 0) $x7076))))
+(let ((@x7090 (trans (monotonicity @x7080 (= (or $x3691 (>= (+ ?x7053 ?x1894) 0)) $x7084)) (rewrite (= $x7084 $x7084)) (= (or $x3691 (>= (+ ?x7053 ?x1894) 0)) $x7084))))
+(let ((@x7496 (unit-resolution (mp ((_ quant-inst ?v0!19) (or $x3691 (>= (+ ?x7053 ?x1894) 0))) @x7090 $x7084) @x6892 $x7076)))
+(let ((@x7501 (lemma ((_ th-lemma arith farkas 1 -1 -1 1) (hypothesis $x7248) @x7570 @x7496 @x7004 false) (or $x7499 $x1896 (not $x7353)))))
 (let ((@x6992 (rewrite (= (or $x3578 (or $x6211 $x1888 $x7248)) (or $x3578 $x6211 $x1888 $x7248)))))
 (let ((@x7051 (mp ((_ quant-inst ?v0!19 ?v1!18) (or $x3578 (or $x6211 $x1888 $x7248))) @x6992 (or $x3578 $x6211 $x1888 $x7248))))
-(let ((@x8673 (unit-resolution (unit-resolution @x7051 @x4223 (hypothesis $x1889) (or $x6211 $x7248)) (unit-resolution @x7501 @x8658 @x7571 $x7499) $x6211)))
+(let ((@x9076 (unit-resolution (unit-resolution @x7051 @x4223 (hypothesis $x1889) (or $x6211 $x7248)) (unit-resolution @x7501 @x9059 @x7570 $x7499) $x6211)))
 (let (($x7222 (or $x7243 $x7246)))
 (let (($x6667 (fun_app$ ?x265 ?v1!18)))
 (let (($x6740 (= $x6667 $x7222)))
 (let (($x6746 (or $x4114 $x6740)))
 (let ((@x6743 (monotonicity (rewrite (= (ite $x7243 true $x7246) $x7222)) (= (= $x6667 (ite $x7243 true $x7246)) $x6740))))
 (let ((@x6845 (monotonicity @x6743 (= (or $x4114 (= $x6667 (ite $x7243 true $x7246))) $x6746))))
 (let ((@x4954 (trans @x6845 (rewrite (= $x6746 $x6746)) (= (or $x4114 (= $x6667 (ite $x7243 true $x7246))) $x6746))))
 (let ((@x6537 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v1!18) (or $x4114 (= $x6667 (ite $x7243 true $x7246)))) @x4954 $x6746)))
-(let ((@x8675 (mp (hypothesis $x1883) (symm (monotonicity @x5875 (= $x6667 $x1883)) (= $x1883 $x6667)) $x6667)))
-(let ((@x8676 (unit-resolution (def-axiom (or (not $x6740) (not $x6667) $x7222)) @x8675 (unit-resolution @x6537 @x3473 $x6740) $x7222)))
+(let ((@x9160 (mp (hypothesis $x1883) (symm (monotonicity @x5875 (= $x6667 $x1883)) (= $x1883 $x6667)) $x6667)))
+(let ((@x9163 (unit-resolution (def-axiom (or (not $x6740) (not $x6667) $x7222)) @x9160 (unit-resolution @x6537 @x3473 $x6740) $x7222)))
 (let ((@x4955 (def-axiom (or (not $x7222) $x7243 $x7246))))
 (let ((@x7000 (unit-resolution (hypothesis (not $x7003)) (monotonicity (monotonicity (hypothesis $x7243) (= ?x1884 ?x7110)) $x7003) false)))
 (let ((@x7002 (lemma @x7000 (or (not $x7243) $x7003))))
 (let ((@x7011 ((_ th-lemma arith triangle-eq) (or (not $x7003) $x7556))))
-(let ((@x8679 (unit-resolution @x7011 (unit-resolution @x7002 (unit-resolution @x4955 @x8676 @x8673 $x7243) $x7003) $x7556)))
+(let ((@x9060 (unit-resolution @x7011 (unit-resolution @x7002 (unit-resolution @x4955 @x9163 @x9076 $x7243) $x7003) $x7556)))
+(let (($x7366 (<= (+ ?x257 ?x6721) 0)))
+(let (($x8813 (or $x3665 $x7246 $x7366)))
+(let (($x7357 (>= (+ ?x6619 ?x1173) 0)))
+(let (($x7358 (or $x7246 $x7357)))
+(let (($x8814 (or $x3665 $x7358)))
+(let ((@x8805 (monotonicity (rewrite (= (+ ?x6619 ?x1173) (+ ?x1173 ?x6619))) (= $x7357 (>= (+ ?x1173 ?x6619) 0)))))
+(let ((@x8809 (trans @x8805 (rewrite (= (>= (+ ?x1173 ?x6619) 0) $x7366)) (= $x7357 $x7366))))
+(let ((@x8818 (monotonicity (monotonicity @x8809 (= $x7358 (or $x7246 $x7366))) (= $x8814 (or $x3665 (or $x7246 $x7366))))))
+(let ((@x8822 (trans @x8818 (rewrite (= (or $x3665 (or $x7246 $x7366)) $x8813)) (= $x8814 $x8813))))
+(let ((@x8620 (unit-resolution (mp ((_ quant-inst ?v1!18) $x8814) @x8822 $x8813) (unit-resolution (def-axiom (or $x3809 $x3660)) @x6181 $x3660) @x9076 $x7366)))
 (let (($x7102 (<= (+ b_Infinity$ ?x7100) 0)))
+(let (($x7158 (not $x7102)))
+(let ((@x8621 (unit-resolution ((_ th-lemma arith assign-bounds 1 1) (or $x7158 $x1888 (not $x7556))) @x9060 (hypothesis $x1889) $x7158)))
 (let ((?x7171 (+ ?x257 ?x1894 ?x7111)))
 (let (($x7252 (>= ?x7171 0)))
-(let (($x7576 (not $x7252)))
-(let (($x7366 (<= (+ ?x257 ?x6721) 0)))
-(let (($x8449 (or $x3665 $x7246 $x7366)))
-(let (($x7357 (>= (+ ?x6619 ?x1173) 0)))
-(let (($x7358 (or $x7246 $x7357)))
-(let (($x8450 (or $x3665 $x7358)))
-(let ((@x8441 (monotonicity (rewrite (= (+ ?x6619 ?x1173) (+ ?x1173 ?x6619))) (= $x7357 (>= (+ ?x1173 ?x6619) 0)))))
-(let ((@x8445 (trans @x8441 (rewrite (= (>= (+ ?x1173 ?x6619) 0) $x7366)) (= $x7357 $x7366))))
-(let ((@x8454 (monotonicity (monotonicity @x8445 (= $x7358 (or $x7246 $x7366))) (= $x8450 (or $x3665 (or $x7246 $x7366))))))
-(let ((@x8458 (trans @x8454 (rewrite (= (or $x3665 (or $x7246 $x7366)) $x8449)) (= $x8450 $x8449))))
-(let ((@x8681 (unit-resolution (mp ((_ quant-inst ?v1!18) $x8450) @x8458 $x8449) (unit-resolution (def-axiom (or $x3809 $x3660)) @x6181 $x3660) @x8673 $x7366)))
-(let ((@x8685 (unit-resolution ((_ th-lemma arith assign-bounds -1 1 -1 1) (or $x7576 $x1896 (not $x7353) (not $x7366) (not $x7556))) @x8681 @x8679 @x7571 @x8658 $x7576)))
-(let ((@x8686 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x7171 0)) $x7252)) @x8685 (not (= ?x7171 0)))))
-(let (($x7117 (>= (+ ?x257 (* (- 1) (fun_app$c v_b_SP_G_1$ ?v0!19)) ?x7111) 0)))
+(let (($x7575 (not $x7252)))
+(let ((@x8781 (unit-resolution ((_ th-lemma arith assign-bounds -1 1 -1 1) (or $x7575 $x1896 (not $x7353) (not $x7366) (not $x7556))) @x8620 @x9060 @x7570 @x9059 $x7575)))
+(let (($x7117 (>= (+ ?x257 ?x7074 ?x7111) 0)))
 (let (($x7161 (not $x7117)))
-(let ((@x8688 ((_ th-lemma arith assign-bounds -1 -1 1 -1 1) (or $x7161 (not $x7076) $x1896 (not $x7353) (not $x7366) (not $x7556)))))
+(let ((@x9234 ((_ th-lemma arith assign-bounds -1 -1 1 -1 1) (or $x7161 (not $x7076) $x1896 (not $x7353) (not $x7366) (not $x7556)))))
+(let ((@x9235 (unit-resolution @x9234 (hypothesis $x7366) (hypothesis $x7556) @x7570 @x7004 @x7496 $x7161)))
+(let ((@x9237 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x7171 0)) $x7252)) (hypothesis $x7575) (not (= ?x7171 0)))))
 (let (($x7174 (= ?x7171 0)))
 (let (($x7184 (or $x7102 $x7117 $x7174)))
 (let (($x7186 (or $x3675 $x7102 $x7117 $x7174)))
-(let (($x7104 (<= (+ (fun_app$c v_b_SP_G_1$ ?v0!19) ?x1173 ?x7100) 0)))
+(let (($x7104 (<= (+ ?x7053 ?x1173 ?x7100) 0)))
 (let (($x7165 (or $x7102 $x7104 (= (+ ?x257 ?x7111 ?x1894) 0))))
 (let (($x7187 (or $x3675 $x7165)))
 (let ((@x7183 (monotonicity (rewrite (= (+ ?x257 ?x7111 ?x1894) ?x7171)) (= (= (+ ?x257 ?x7111 ?x1894) 0) $x7174))))
-(let ((@x7119 (rewrite (= (<= (+ ?x1173 (fun_app$c v_b_SP_G_1$ ?v0!19) ?x7100) 0) $x7117))))
-(let (($x7112 (= (+ (fun_app$c v_b_SP_G_1$ ?v0!19) ?x1173 ?x7100) (+ ?x1173 (fun_app$c v_b_SP_G_1$ ?v0!19) ?x7100))))
-(let ((@x7115 (monotonicity (rewrite $x7112) (= $x7104 (<= (+ ?x1173 (fun_app$c v_b_SP_G_1$ ?v0!19) ?x7100) 0)))))
-(let ((@x7205 (monotonicity (monotonicity (trans @x7115 @x7119 (= $x7104 $x7117)) @x7183 (= $x7165 $x7184)) (= $x7187 (or $x3675 $x7184)))))
+(let ((@x7115 (monotonicity (rewrite (= (+ ?x7053 ?x1173 ?x7100) (+ ?x1173 ?x7053 ?x7100))) (= $x7104 (<= (+ ?x1173 ?x7053 ?x7100) 0)))))
+(let ((@x7128 (trans @x7115 (rewrite (= (<= (+ ?x1173 ?x7053 ?x7100) 0) $x7117)) (= $x7104 $x7117))))
+(let ((@x7205 (monotonicity (monotonicity @x7128 @x7183 (= $x7165 $x7184)) (= $x7187 (or $x3675 $x7184)))))
 (let ((@x7250 (mp ((_ quant-inst ?v0!19) $x7187) (trans @x7205 (rewrite (= (or $x3675 $x7184) $x7186)) (= $x7187 $x7186)) $x7186)))
-(let ((@x8690 (unit-resolution (unit-resolution @x7250 @x6588 $x7184) (unit-resolution @x8688 @x8681 @x8679 @x7571 @x8658 @x7496 $x7161) @x8686 $x7102)))
-(let ((@x8693 (lemma ((_ th-lemma arith farkas -1 1 1) @x8690 @x8679 (hypothesis $x1889) false) (or $x7618 $x1888 $x1896 $x2791))))
+(let ((@x9238 (unit-resolution (unit-resolution @x7250 @x6588 $x7184) @x9237 @x9235 (hypothesis $x7158) false)))
+(let ((@x8782 (unit-resolution (lemma @x9238 (or $x7252 $x7102 (not $x7366) (not $x7556) $x1896 (not $x7353))) @x8781 @x8621 @x8620 @x9060 @x7570 @x9059 false)))
+(let ((@x8908 (unit-resolution (lemma @x8782 (or $x7620 $x1896 $x1888 $x2791)) @x7615 @x7570 @x7608 $x7620)))
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