0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : do_CVC4 %s
0.03/0.23	% Computer   : n127.star.cs.uiowa.edu
0.03/0.23	% Model      : x86_64 x86_64
0.03/0.23	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.23	% Memory     : 32218.625MB
0.03/0.23	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.23	% CPULimit   : 300
0.03/0.23	% DateTime   : Sat Jul 14 05:07:54 CDT 2018
0.03/0.23	% CPUTime    : 
0.07/0.28	%----Proving with arithmetic mode
0.07/0.28	------- cvc4-tfa casc j9 : /export/starexec/sandbox2/benchmark/theBenchmark.p at ...
0.07/0.28	--- Run --cbqi-all --purify-triggers --full-saturate-quant at 15...
15.12/15.34	--- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 15...
30.20/30.51	--- Run --finite-model-find --decision=internal at 15...
30.21/30.60	% SZS status Theorem for theBenchmark
30.21/30.60	% SZS output start Proof for theBenchmark
30.21/30.60	(skolem (let ((_let_0 (t2tb Current))) (let ((_let_1 (is_empty vertex _let_0))) (let ((_let_2 (tb2t (remove vertex (t2tb1 BOUND_VARIABLE_1789) _let_0)))) (let ((_let_3 (= true1 BOUND_VARIABLE_1823))) (forall ((S vertex1) (T vertex1) (D Int) (Next set_vertex) (Current set_vertex) (Visited set_vertex) (BOUND_VARIABLE_1789 vertex1) (BOUND_VARIABLE_1790 set_vertex) (BOUND_VARIABLE_1791 set_vertex) (BOUND_VARIABLE_1792 vertex1) (BOUND_VARIABLE_1823 bool1)) (or (not (inv1 S T Visited Current Next D)) (not (forall ((X vertex1)) (closure1 Visited Current Next X) )) (not (>= D 0)) _let_1 (not (mem vertex (t2tb1 BOUND_VARIABLE_1789) _let_0)) (= T BOUND_VARIABLE_1789) (not (inv1 S T Visited _let_2 Next D)) (not (shortest_path1 S BOUND_VARIABLE_1789 D)) (not (forall ((X vertex1)) (or (= X BOUND_VARIABLE_1789) (closure1 Visited _let_2 Next X)) )) (not (is_empty vertex (t2tb _let_2))) (not (forall ((X vertex1)) (closure1 BOUND_VARIABLE_1791 _let_2 BOUND_VARIABLE_1790 X) )) (not (subset vertex (t2tb (succ1 BOUND_VARIABLE_1789)) (t2tb BOUND_VARIABLE_1791))) (not (inv1 S T BOUND_VARIABLE_1791 _let_2 BOUND_VARIABLE_1790 D)) (closure1 BOUND_VARIABLE_1791 BOUND_VARIABLE_1790 (tb2t (empty vertex)) BOUND_VARIABLE_1792) (= (not _let_1) _let_3) _let_3) )))))
30.21/31.08	  ( skv_1 skv_2 skv_3 skv_4 skv_5 skv_6 skv_7 skv_8 skv_9 skv_10 skv_11 )
30.21/31.08	)
30.21/31.08	(skolem (forall ((X uni)) (or (not (sort1 vertex X)) (not (mem vertex X (t2tb (succ1 skv_7))))) )
30.21/31.08	  ( skv_83 )
30.21/31.08	)
30.21/31.08	(skolem (forall ((V2 vertex1)) (or (not (path1 skv_1 V2 0)) (not (mem vertex (t2tb1 skv_1) (t2tb (succ1 V2))))) )
30.21/31.08	  ( skv_84 )
30.21/31.08	)
30.21/31.08	(skolem (forall ((X vertex1) (M Int)) (or (not (path1 skv_1 X M)) (>= M 1) (mem vertex (t2tb1 X) (t2tb skv_5))) )
30.21/31.08	  ( skv_85 skv_86 )
30.21/31.08	)
30.21/31.08	(skolem (forall ((X vertex1)) (or (not (mem vertex (t2tb1 X) (t2tb skv_5))) (not (forall ((M Int)) (or (>= M 2) (not (path1 skv_1 X M))) ))) )
30.21/31.08	  ( skv_87 )
30.21/31.08	)
30.21/31.08	(skolem (forall ((X vertex1)) (or (not (mem vertex (t2tb1 X) (t2tb skv_5))) (shortest_path1 skv_1 X 1)) )
30.21/31.08	  ( skv_88 )
30.21/31.08	)
30.21/31.08	(skolem (let ((_let_0 (t2tb1 Y))) (forall ((Y vertex1)) (or (not (mem vertex _let_0 (t2tb (succ1 skv_1)))) (mem vertex _let_0 (t2tb skv_5))) ))
30.21/31.08	  ( skv_89 )
30.21/31.08	)
30.21/31.08	(skolem (forall ((M Int)) (or (>= M 0) (not (path1 skv_1 skv_1 M))) )
30.21/31.08	  ( skv_90 )
30.21/31.08	)
30.21/31.08	(skolem (forall ((X vertex1)) (or (not (mem vertex (t2tb1 X) (t2tb skv_5))) (shortest_path1 skv_1 X 0)) )
30.21/31.08	  ( skv_91 )
30.21/31.08	)
30.21/31.08	(skolem (let ((_let_0 (t2tb1 Y))) (forall ((Y vertex1)) (or (not (mem vertex _let_0 (t2tb (succ1 skv_10)))) (mem vertex _let_0 (t2tb skv_9))) ))
30.21/31.08	  ( skv_92 )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty)) (is_empty A (empty A)) )
30.21/31.08	  ( vertex )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((X set_vertex)) (sort1 (set vertex) (t2tb X)) )
30.21/31.08	  ( skv_5 )
30.21/31.08	  ( (tb2t (remove vertex (t2tb1 skv_7) (t2tb skv_5))) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((V vertex1)) (path1 V V 0) )
30.21/31.08	  ( skv_1 )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (S1 uni) (S2 uni) (X uni)) (= (and (mem A X S1) (not (mem A X S2))) (mem A X (diff A S1 S2))) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)), (t2tb (succ1 skv_7)), (t2tb (succ1 skv_7)) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)), (t2tb (succ1 skv_7)), skv_83 )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)), (t2tb skv_9), (t2tb1 skv_10) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (S1 uni) (S2 uni) (BOUND_VARIABLE_1176 uni)) (or (not (subset A S1 S2)) (not (mem A BOUND_VARIABLE_1176 S1)) (mem A BOUND_VARIABLE_1176 S2)) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)), (t2tb skv_9), (t2tb1 skv_92) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (U uni)) (or (not (sort1 A U)) (= U (contents A (mk_ref A U)))) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((I vertex1)) (= I (tb2t1 (t2tb1 I))) )
30.21/31.08	  ( skv_1 )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((V1 vertex1) (V2 vertex1) (N Int)) (= (and (forall ((M Int)) (or (not (>= (+ N (* (- 1) M)) 1)) (not (path1 V1 V2 M))) ) (path1 V1 V2 N)) (shortest_path1 V1 V2 N)) )
30.21/31.08	  ( skv_1, skv_1, 0 )
30.21/31.08	)
30.21/31.08	(instantiation (let ((_let_0 (t2tb1 X))) (let ((_let_1 (t2tb Visited))) (let ((_let_2 (t2tb1 Y))) (forall ((Visited set_vertex) (Current set_vertex) (Next set_vertex) (X vertex1)) (= (or (not (mem vertex _let_0 _let_1)) (mem vertex _let_0 (t2tb Current)) (mem vertex _let_0 (t2tb Next)) (forall ((Y vertex1)) (or (not (mem vertex _let_2 (t2tb (succ1 X)))) (mem vertex _let_2 _let_1)) )) (closure1 Visited Current Next X)) ))))
30.21/31.08	  ( skv_5, skv_5, (tb2t (empty vertex)), skv_1 )
30.21/31.08	  ( skv_9, skv_8, (tb2t (empty vertex)), skv_10 )
30.21/31.08	  ( skv_9, (tb2t (remove vertex (t2tb1 skv_7) (t2tb skv_5))), skv_8, skv_10 )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (S uni)) (= (= (cardinal1 A S) 0) (is_empty A S)) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)) )
30.21/31.08	  ( vertex, (let ((_let_0 (t2tb (succ1 skv_7)))) (remove vertex _let_0 _let_0)) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (Z uni) (Z1 uni)) (or (not (sort1 A Z1)) (= Z1 (match_bool1 A false1 Z Z1))) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)), (t2tb (succ1 skv_7)) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (X uni)) (not (mem A X (empty A))) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)) )
30.21/31.08	  ( vertex, (t2tb1 skv_92) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (X uni) (Y uni) (BOUND_VARIABLE_1388 uni)) (or (not (sort1 A X)) (not (sort1 A Y)) (= (mem A X (add A Y BOUND_VARIABLE_1388)) (or (= X Y) (mem A X BOUND_VARIABLE_1388)))) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)), (t2tb (succ1 skv_7)), (let ((_let_0 (t2tb (succ1 skv_7)))) (remove vertex _let_0 _let_0)) )
30.21/31.08	)
30.21/31.08	(instantiation (let ((_let_0 (t2tb Current))) (let ((_let_1 (t2tb Visited))) (let ((_let_2 (t2tb Next))) (let ((_let_3 (t2tb1 T))) (let ((_let_4 (t2tb1 X))) (let ((_let_5 (+ 1 D))) (forall ((S vertex1) (T vertex1) (Visited set_vertex) (Current set_vertex) (Next set_vertex) (D Int)) (= (and (subset vertex _let_0 _let_1) (forall ((X vertex1)) (or (not (mem vertex (t2tb1 X) _let_0)) (shortest_path1 S X D)) ) (subset vertex _let_2 _let_1) (forall ((X vertex1)) (or (not (mem vertex (t2tb1 X) _let_2)) (shortest_path1 S X _let_5)) ) (forall ((X vertex1)) (or (not (mem vertex (t2tb1 X) _let_1)) (not (forall ((M Int)) (or (not (>= (+ D (* (- 1) M)) (- 1))) (not (path1 S X M))) ))) ) (or (not (mem vertex _let_3 _let_1)) (mem vertex _let_3 _let_2) (mem vertex _let_3 _let_0)) (forall ((X vertex1)) (or (not (shortest_path1 S X _let_5)) (mem vertex _let_4 _let_2) (not (mem vertex _let_4 _let_1))) ) (forall ((X vertex1) (M Int)) (or (not (path1 S X M)) (not (>= (+ D (* (- 1) M)) 0)) (mem vertex (t2tb1 X) _let_1)) )) (inv1 S T Visited Current Next D)) )))))))
30.21/31.08	  ( skv_1, skv_1, skv_5, skv_5, skv_5, 0 )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (X uni) (Y uni) (S uni)) (or (not (sort1 A X)) (not (sort1 A Y)) (= (and (mem A X S) (not (= X Y))) (mem A X (remove A Y S)))) )
30.21/31.08	  ( vertex, (remove vertex (t2tb1 skv_7) (t2tb skv_5)), (remove vertex (t2tb1 skv_7) (t2tb skv_5)), (t2tb (succ1 skv_7)) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)), (t2tb (succ1 skv_7)), (t2tb (succ1 skv_7)) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((U bool1)) (or (= true1 U) (= false1 U)) )
30.21/31.08	  ( skv_11 )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (U uni)) (or (not (sort1 (ref A) U)) (= U (mk_ref A (contents A U)))) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((V1 vertex1) (V3 vertex1) (N Int)) (or (not (>= N 0)) (not (path1 V1 V3 (+ 1 N))) (not (forall ((V2 vertex1)) (or (not (path1 V1 V2 N)) (not (mem vertex (t2tb1 V3) (t2tb (succ1 V2))))) ))) )
30.21/31.08	  ( skv_1, skv_1, 0 )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (X uni) (S uni)) (or (not (mem A X S)) (= (cardinal1 A (remove A X S)) (+ (- 1) (cardinal1 A S)))) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)), (t2tb (succ1 skv_7)) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((V1 vertex1) (V2 vertex1) (V3 vertex1) (N Int)) (or (not (path1 V1 V2 N)) (not (mem vertex (t2tb1 V3) (t2tb (succ1 V2)))) (path1 V1 V3 (+ 1 N))) )
30.21/31.08	  ( skv_1, skv_1, skv_1, 0 )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((J uni)) (or (not (sort1 vertex J)) (= J (t2tb1 (tb2t1 J)))) )
30.21/31.08	  ( (t2tb (succ1 skv_7)) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((V1 vertex1) (V2 vertex1) (N Int)) (or (not (path1 V1 V2 N)) (>= N 0)) )
30.21/31.08	  ( skv_1, skv_1, 0 )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((I set_vertex)) (= I (tb2t (t2tb I))) )
30.21/31.08	  ( skv_5 )
30.21/31.08	  ( (succ1 skv_7) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (Z uni) (Z1 uni)) (or (not (sort1 A Z)) (= Z (match_bool1 A true1 Z Z1))) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)), (t2tb (succ1 skv_7)) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (X uni) (S uni)) (or (not (sort1 (set A) S)) (not (mem A X S)) (= S (add A X (remove A X S)))) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)), (t2tb (succ1 skv_7)) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (S uni)) (or (not (forall ((X uni)) (or (not (sort1 A X)) (not (mem A X S))) )) (is_empty A S)) )
30.21/31.08	  ( vertex, (t2tb (succ1 skv_7)) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((A ty) (S uni) (BOUND_VARIABLE_1867 uni)) (or (not (is_empty A S)) (not (mem A BOUND_VARIABLE_1867 S))) )
30.21/31.08	  ( vertex, (remove vertex (t2tb1 skv_7) (t2tb skv_5)), (t2tb (succ1 skv_7)) )
30.21/31.08	  ( vertex, (t2tb (tb2t (remove vertex (t2tb1 skv_7) (t2tb skv_5)))), (t2tb1 skv_10) )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((X Int) (Y Int) (Z Int)) (or (>= (+ X (* (- 1) Y)) 1) (not (>= Z 0)) (not (>= (+ (* X Z) (* (- 1) (* Y Z))) 1))) )
30.21/31.08	  ( 0, 0, 0 )
30.21/31.08	)
30.21/31.08	(instantiation (forall ((X vertex1)) (closure1 skv_9 (tb2t (remove vertex (t2tb1 skv_7) (t2tb skv_5))) skv_8 X) )
30.21/31.08	  ( skv_10 )
30.21/31.08	)
30.21/31.08	% SZS output end Proof for theBenchmark
30.21/31.08	EOF