0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.11 % Command : do_CVC4 %s %d 0.10/0.31 % Computer : n018.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 960 0.10/0.31 % WCLimit : 120 0.10/0.31 % DateTime : Thu Jul 2 08:07:22 EDT 2020 0.10/0.31 % CPUTime : 0.15/0.43 %----Proving TF0_ARI 0.15/0.44 ------- cvc4-tfa casc j10 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 960... 0.15/0.44 --- Run --finite-model-find --decision=internal at 15... 0.43/0.71 % SZS status Theorem for theBenchmark 0.43/0.71 % SZS output start Proof for theBenchmark 0.43/0.71 (skolem (forall ((S vertex1) (T vertex1) (D Int) (Next set_vertex) (Current set_vertex) (Visited set_vertex) (BOUND_VARIABLE_1678 vertex1) (BOUND_VARIABLE_1679 set_vertex) (BOUND_VARIABLE_1680 set_vertex) (BOUND_VARIABLE_1681 vertex1) (BOUND_VARIABLE_1712 bool1)) (let ((_let_0 (t2tb Current))) (let ((_let_1 (is_empty vertex _let_0))) (let ((_let_2 (t2tb1 BOUND_VARIABLE_1678))) (let ((_let_3 (tb2t (remove vertex _let_2 _let_0)))) (let ((_let_4 (= true1 BOUND_VARIABLE_1712))) (or (not (inv1 S T Visited Current Next D)) (and _let_1 (not (is_empty vertex (t2tb Next)))) (not (>= D 0)) (not (forall ((X vertex1)) (closure1 Visited Current Next X) )) _let_1 (not (mem vertex _let_2 _let_0)) (= T BOUND_VARIABLE_1678) (not (forall ((X vertex1)) (or (= X BOUND_VARIABLE_1678) (closure1 Visited _let_3 Next X)) )) (not (shortest_path1 S BOUND_VARIABLE_1678 D)) (not (inv1 S T Visited _let_3 Next D)) (not (is_empty vertex (t2tb _let_3))) (not (inv1 S T BOUND_VARIABLE_1680 _let_3 BOUND_VARIABLE_1679 D)) (not (forall ((X vertex1)) (closure1 BOUND_VARIABLE_1680 _let_3 BOUND_VARIABLE_1679 X) )) (not (subset vertex (t2tb (succ1 BOUND_VARIABLE_1678)) (t2tb BOUND_VARIABLE_1680))) (closure1 BOUND_VARIABLE_1680 BOUND_VARIABLE_1679 (tb2t (empty vertex)) BOUND_VARIABLE_1681) (= (not _let_1) _let_4) _let_4)))))) ) 0.43/0.71 ( skv_2 skv_3 skv_4 skv_5 skv_6 skv_7 skv_8 skv_9 skv_10 skv_11 skv_12 ) 0.43/0.71 ) 0.43/0.71 (skolem (forall ((X vertex1)) (or (not (mem vertex (t2tb1 X) (t2tb skv_5))) (shortest_path1 skv_2 X 0)) ) 0.43/0.71 ( skv_84 ) 0.43/0.71 ) 0.43/0.71 (skolem (forall ((X vertex1)) (or (not (mem vertex (t2tb1 X) (t2tb skv_5))) (shortest_path1 skv_2 X 1)) ) 0.43/0.71 ( skv_85 ) 0.43/0.71 ) 0.43/0.71 (skolem (forall ((X vertex1)) (or (not (mem vertex (t2tb1 X) (t2tb skv_5))) (not (forall ((M Int)) (or (not (path1 skv_2 X M)) (>= M 2)) ))) ) 0.43/0.71 ( skv_86 ) 0.43/0.71 ) 0.43/0.71 (skolem (forall ((X vertex1) (M Int)) (or (not (path1 skv_2 X M)) (>= M 1) (mem vertex (t2tb1 X) (t2tb skv_5))) ) 0.43/0.71 ( skv_87 skv_88 ) 0.43/0.71 ) 0.43/0.71 (skolem (forall ((Y vertex1)) (let ((_let_0 (t2tb1 Y))) (or (not (mem vertex _let_0 (t2tb (succ1 skv_2)))) (mem vertex _let_0 (t2tb skv_10)))) ) 0.43/0.71 ( skv_89 ) 0.43/0.71 ) 0.43/0.71 (skolem (forall ((V2 vertex1)) (or (not (path1 skv_2 V2 0)) (not (mem vertex (t2tb1 skv_2) (t2tb (succ1 V2))))) ) 0.43/0.71 ( skv_90 ) 0.43/0.71 ) 0.43/0.71 (skolem (forall ((X uni)) (or (not (sort1 vertex X)) (not (mem vertex X e_uni_13))) ) 0.43/0.71 ( skv_91 ) 0.43/0.71 ) 0.43/0.71 (skolem (forall ((M Int)) (or (>= M 0) (not (path1 skv_2 skv_2 M))) ) 0.43/0.71 ( skv_92 ) 0.43/0.71 ) 0.43/0.71 (skolem (forall ((Y vertex1)) (let ((_let_0 (t2tb1 Y))) (or (not (mem vertex _let_0 (t2tb (succ1 skv_11)))) (mem vertex _let_0 (t2tb skv_10)))) ) 0.43/0.71 ( skv_93 ) 0.43/0.71 ) 0.43/0.71 (skolem (forall ((M Int)) (or (not (path1 skv_2 skv_86 M)) (>= M 2)) ) 0.43/0.71 ( skv_94 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((I set_vertex)) (= I (tb2t (t2tb I))) ) 0.43/0.71 ( skv_6 ) 0.43/0.71 ( skv_10 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((A ty) (S1 uni) (S2 uni) (X uni)) (= (mem A X (diff A S1 S2)) (and (mem A X S1) (not (mem A X S2)))) ) 0.43/0.71 ( vertex, e_uni_13, e_uni_13, e_uni_13 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((A ty)) (is_empty A (empty A)) ) 0.43/0.71 ( vertex ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((A ty) (S uni)) (= (is_empty A S) (= (cardinal1 A S) 0)) ) 0.43/0.71 ( vertex, (t2tb skv_5) ) 0.43/0.71 ( vertex, e_uni_13 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((V vertex1)) (path1 V V 0) ) 0.43/0.71 ( skv_2 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((A ty)) (sort1 (set A) (empty A)) ) 0.43/0.71 ( vertex ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((X set_vertex)) (sort1 (set vertex) (t2tb X)) ) 0.43/0.71 ( skv_6 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((I vertex1)) (= I (tb2t1 (t2tb1 I))) ) 0.43/0.71 ( skv_2 ) 0.43/0.71 ( skv_8 ) 0.43/0.71 ( skv_11 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((U bool1)) (or (= true1 U) (= false1 U)) ) 0.43/0.71 ( skv_12 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((X Int) (Y Int) (Z Int)) (or (>= (+ X (* (- 1) Y)) 1) (not (>= Z 0)) (not (>= (+ (* X Z) (* (- 1) (* Y Z))) 1))) ) 0.43/0.71 ( 0, 0, 0 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((BOUND_VARIABLE_1193 ty) (BOUND_VARIABLE_1194 uni)) (or (not (forall ((X uni)) (or (not (sort1 BOUND_VARIABLE_1193 X)) (not (mem BOUND_VARIABLE_1193 X BOUND_VARIABLE_1194))) )) (is_empty BOUND_VARIABLE_1193 BOUND_VARIABLE_1194)) ) 0.43/0.71 ( vertex, e_uni_13 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((BOUND_VARIABLE_1206 ty) (BOUND_VARIABLE_1207 uni) (BOUND_VARIABLE_1217 uni)) (or (not (is_empty BOUND_VARIABLE_1206 BOUND_VARIABLE_1207)) (not (mem BOUND_VARIABLE_1206 BOUND_VARIABLE_1217 BOUND_VARIABLE_1207))) ) 0.43/0.71 ( vertex, (t2tb skv_5), (t2tb1 skv_8) ) 0.43/0.71 ( vertex, (t2tb skv_5), (t2tb1 skv_2) ) 0.43/0.71 ( vertex, (t2tb skv_5), (t2tb1 skv_84) ) 0.43/0.71 ( vertex, (t2tb skv_5), (t2tb1 skv_85) ) 0.43/0.71 ( vertex, (t2tb skv_5), (t2tb1 skv_86) ) 0.43/0.71 ( vertex, (t2tb skv_5), (t2tb1 skv_11) ) 0.43/0.71 ( vertex, (remove vertex (t2tb1 skv_8) (t2tb skv_6)), e_uni_13 ) 0.43/0.71 ( vertex, (t2tb (tb2t (remove vertex (t2tb1 skv_8) (t2tb skv_6)))), (t2tb1 skv_11) ) 0.43/0.71 ( vertex, (t2tb (tb2t (remove vertex (t2tb1 skv_8) (t2tb skv_6)))), (t2tb1 skv_93) ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((V1 vertex1) (V2 vertex1) (N Int)) (or (not (path1 V1 V2 N)) (>= N 0)) ) 0.43/0.71 ( skv_2, skv_2, 0 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((V1 vertex1) (V2 vertex1) (N Int)) (= (and (path1 V1 V2 N) (forall ((M Int)) (or (not (>= (+ N (* (- 1) M)) 1)) (not (path1 V1 V2 M))) )) (shortest_path1 V1 V2 N)) ) 0.43/0.71 ( skv_2, skv_2, 0 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((A ty) (X uni)) (not (mem A X (empty A))) ) 0.43/0.71 ( vertex, e_uni_13 ) 0.43/0.71 ) 0.43/0.71 (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))))) ))) ) 0.43/0.71 ( skv_2, skv_2, 0 ) 0.43/0.71 ) 0.43/0.71 (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)))) ) 0.43/0.71 ( vertex, e_uni_13, e_uni_13 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((A ty) (X uni) (S uni)) (or (not (mem A X S)) (= (cardinal1 A (remove A X S)) (+ (- 1) (cardinal1 A S)))) ) 0.43/0.71 ( vertex, e_uni_13, e_uni_13 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((BOUND_VARIABLE_1420 ty) (BOUND_VARIABLE_1421 uni) (BOUND_VARIABLE_1422 uni) (BOUND_VARIABLE_1449 uni)) (or (not (subset BOUND_VARIABLE_1420 BOUND_VARIABLE_1421 BOUND_VARIABLE_1422)) (not (mem BOUND_VARIABLE_1420 BOUND_VARIABLE_1449 BOUND_VARIABLE_1421)) (mem BOUND_VARIABLE_1420 BOUND_VARIABLE_1449 BOUND_VARIABLE_1422)) ) 0.43/0.71 ( vertex, (t2tb (succ1 skv_8)), (t2tb skv_10), (t2tb1 skv_8) ) 0.43/0.71 ( vertex, (t2tb (succ1 skv_8)), (t2tb skv_10), e_uni_13 ) 0.43/0.71 ( vertex, (t2tb (succ1 skv_8)), (t2tb skv_10), (t2tb1 skv_93) ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((A ty) (U uni)) (or (not (sort1 (ref A) U)) (= U (mk_ref A (contents A U)))) ) 0.43/0.71 ( vertex, e_uni_13 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((A ty) (X uni) (Y uni) (S uni)) (or (not (sort1 A X)) (not (sort1 A Y)) (= (mem A X (remove A Y S)) (and (not (= X Y)) (mem A X S)))) ) 0.43/0.71 ( vertex, (t2tb skv_6), (t2tb skv_6), e_uni_13 ) 0.43/0.71 ( vertex, (t2tb skv_6), e_uni_13, (t2tb skv_10) ) 0.43/0.71 ( vertex, (remove vertex (t2tb1 skv_8) (t2tb skv_6)), (remove vertex (t2tb1 skv_8) (t2tb skv_6)), e_uni_13 ) 0.43/0.71 ( vertex, (remove vertex (t2tb1 skv_8) (t2tb skv_6)), e_uni_13, (t2tb skv_10) ) 0.43/0.71 ( (set vertex), e_uni_13, (t2tb skv_6), (t2tb skv_5) ) 0.43/0.71 ( (set vertex), e_uni_13, (t2tb skv_6), (t2tb (succ1 skv_8)) ) 0.43/0.71 ( (set vertex), e_uni_13, (t2tb skv_6), (t2tb skv_10) ) 0.43/0.71 ( (set vertex), e_uni_13, (remove vertex (t2tb1 skv_8) (t2tb skv_6)), e_uni_13 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((Visited set_vertex) (Current set_vertex) (Next set_vertex) (X vertex1)) (let ((_let_0 (t2tb1 X))) (= (closure1 Visited Current Next X) (or (not (mem vertex _let_0 (t2tb Visited))) (mem vertex _let_0 (t2tb Current)) (mem vertex _let_0 (t2tb Next)) (forall ((Y vertex1)) (let ((_let_0 (t2tb1 Y))) (or (not (mem vertex _let_0 (t2tb (succ1 X)))) (mem vertex _let_0 (t2tb Visited)))) )))) ) 0.43/0.71 ( skv_10, skv_9, (tb2t (empty vertex)), skv_11 ) 0.43/0.71 ( skv_10, skv_10, skv_5, skv_2 ) 0.43/0.71 ( skv_10, (tb2t (remove vertex (t2tb1 skv_8) (t2tb skv_6))), skv_9, skv_11 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((S vertex1) (T vertex1) (Visited set_vertex) (Current set_vertex) (Next set_vertex) (D Int)) (let ((_let_0 (t2tb Next))) (let ((_let_1 (t2tb Visited))) (let ((_let_2 (t2tb1 T))) (let ((_let_3 (t2tb Current))) (= (and (subset vertex _let_0 _let_1) (forall ((X vertex1) (M Int)) (or (not (path1 S X M)) (not (>= (+ D (* (- 1) M)) 0)) (mem vertex (t2tb1 X) _let_1)) ) (or (not (mem vertex _let_2 _let_1)) (mem vertex _let_2 _let_0) (mem vertex _let_2 _let_3)) (forall ((X vertex1)) (let ((_let_2 (t2tb1 X))) (or (not (shortest_path1 S X (+ 1 D))) (not (mem vertex _let_2 _let_1)) (mem vertex _let_2 _let_0))) ) (forall ((X vertex1)) (or (not (mem vertex (t2tb1 X) _let_1)) (not (forall ((M Int)) (or (not (path1 S X M)) (not (>= (+ D (* (- 1) M)) (- 1)))) ))) ) (forall ((X vertex1)) (or (not (mem vertex (t2tb1 X) _let_0)) (shortest_path1 S X (+ 1 D))) ) (forall ((X vertex1)) (or (not (mem vertex (t2tb1 X) _let_3)) (shortest_path1 S X D)) ) (subset vertex _let_3 _let_1)) (inv1 S T Visited Current Next D)))))) ) 0.43/0.71 ( skv_2, skv_2, skv_5, skv_5, skv_5, 0 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((A ty) (Z uni) (Z1 uni)) (or (not (sort1 A Z1)) (= Z1 (match_bool1 A false1 Z Z1))) ) 0.43/0.71 ( vertex, e_uni_13, e_uni_13 ) 0.43/0.71 ) 0.43/0.71 (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))) ) 0.43/0.71 ( skv_2, skv_2, skv_2, 0 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((A ty) (S1 uni) (S2 uni)) (let ((_let_0 (set A))) (or (not (sort1 _let_0 S1)) (not (sort1 _let_0 S2)) (not (infix_eqeq A S1 S2)) (= S1 S2))) ) 0.43/0.71 ( vertex, e_uni_13, e_uni_13 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((A ty) (X uni) (S uni)) (= (remove A X (add A X S)) (remove A X S)) ) 0.43/0.71 ( vertex, (t2tb1 skv_8), (remove vertex e_uni_13 e_uni_13) ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((J uni)) (or (not (sort1 vertex J)) (= J (t2tb1 (tb2t1 J)))) ) 0.43/0.71 ( e_uni_13 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((A ty) (U uni)) (or (not (sort1 A U)) (= U (contents A (mk_ref A U)))) ) 0.43/0.71 ( vertex, e_uni_13 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((A ty) (Z uni) (Z1 uni)) (or (not (sort1 A Z)) (= Z (match_bool1 A true1 Z Z1))) ) 0.43/0.71 ( vertex, e_uni_13, e_uni_13 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((X vertex1)) (closure1 skv_10 (tb2t (remove vertex (t2tb1 skv_8) (t2tb skv_6))) skv_9 X) ) 0.43/0.71 ( skv_11 ) 0.43/0.71 ) 0.43/0.71 (instantiation (forall ((Y vertex1)) (let ((_let_0 (t2tb1 Y))) (or (not (mem vertex _let_0 (t2tb (succ1 skv_2)))) (mem vertex _let_0 (t2tb skv_10)))) ) 0.43/0.71 ( skv_93 ) 0.43/0.71 ) 0.43/0.71 % SZS output end Proof for theBenchmark 0.43/0.72 EOF