0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : do_cvc5 %s %d 0.10/0.30 % Computer : n025.cluster.edu 0.10/0.30 % Model : x86_64 x86_64 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.30 % Memory : 8042.1875MB 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.30 % CPULimit : 960 0.10/0.30 % WCLimit : 120 0.10/0.30 % DateTime : Tue Aug 9 05:06:41 EDT 2022 0.10/0.30 % CPUTime : 0.15/0.41 %----Proving TF0_ARI 0.15/0.52 ------- cvc5-tfa casc j11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p... 0.15/0.52 --- Run --finite-model-find --decision=internal at 15... 0.15/0.52 % SZS status Theorem for theBenchmark 0.15/0.52 % SZS output start Proof for theBenchmark 0.15/0.52 (let ((_let_1 (forall ((Visited set_vertex) (Current set_vertex) (Next set_vertex) (X vertex1)) (let ((_let_1 (t2tb1 X))) (= (closure1 Visited Current Next X) (=> (mem vertex _let_1 (t2tb Visited)) (=> (not (mem vertex _let_1 (t2tb Current))) (=> (not (mem vertex _let_1 (t2tb Next))) (forall ((Y vertex1)) (let ((_let_1 (t2tb1 Y))) (=> (mem vertex _let_1 (t2tb (succ1 X))) (mem vertex _let_1 (t2tb Visited))))))))))))) (let ((_let_2 (not (forall ((S vertex1) (T vertex1) (D Int) (Next set_vertex) (Current set_vertex) (Visited set_vertex)) (=> (and (=> (is_empty vertex (t2tb Current)) (is_empty vertex (t2tb Next))) (forall ((X vertex1)) (closure1 Visited Current Next X)) (<= 0 D) (inv1 S T Visited Current Next D)) (forall ((O bool1)) (let ((_let_1 (is_empty vertex (t2tb Current)))) (let ((_let_2 (= O true1))) (=> (= _let_1 _let_2) (=> (not _let_2) (=> (not _let_1) (forall ((Current1 set_vertex) (V vertex1)) (let ((_let_1 (t2tb Current))) (let ((_let_2 (t2tb1 V))) (=> (and (mem vertex _let_2 _let_1) (= Current1 (tb2t (remove vertex _let_2 _let_1)))) (=> (not (= V T)) (=> (and (inv1 S T Visited Current1 Next D) (shortest_path1 S V D) (forall ((X vertex1)) (=> (not (= X V)) (closure1 Visited Current1 Next X)))) (forall ((Next1 set_vertex) (Visited1 set_vertex)) (=> (and (inv1 S T Visited1 Current1 Next1 D) (forall ((X vertex1)) (closure1 Visited1 Current1 Next1 X)) (subset vertex (t2tb (succ1 V)) (t2tb Visited1))) (forall ((Result bool1)) (let ((_let_1 (= Result true1))) (=> (= (is_empty vertex (t2tb Current1)) _let_1) (=> _let_1 (forall ((Current2 set_vertex)) (=> (= Current2 Next1) (forall ((Next2 set_vertex)) (=> (= Next2 (tb2t (empty vertex))) (forall ((D1 Int)) (=> (= D1 (+ D 1)) (forall ((X vertex1)) (closure1 Visited1 Current2 Next2 X))))))))))))))))))))))))))))))) (let ((_let_3 (forall ((A ty) (S uni)) (let ((_let_1 (is_empty A S))) (and (=> _let_1 (forall ((X uni)) (not (mem A X S)))) (=> (forall ((X uni)) (=> (sort1 A X) (not (mem A X S)))) _let_1)))))) (let ((_let_4 (forall ((BOUND_VARIABLE_1607 ty) (BOUND_VARIABLE_1609 uni) (BOUND_VARIABLE_1635 uni)) (or (not (is_empty BOUND_VARIABLE_1607 BOUND_VARIABLE_1609)) (not (mem BOUND_VARIABLE_1607 BOUND_VARIABLE_1635 BOUND_VARIABLE_1609)))))) (let ((_let_5 (t2tb skv_7))) (let ((_let_6 (t2tb1 skv_13))) (let ((_let_7 (tb2t (remove vertex _let_6 _let_5)))) (let ((_let_8 (t2tb _let_7))) (let ((_let_9 (t2tb1 skv_12))) (let ((_let_10 (mem vertex _let_9 _let_8))) (let ((_let_11 (not _let_10))) (let ((_let_12 (is_empty vertex _let_8))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_11))) (let ((_let_15 (not _let_14))) (let ((_let_16 (forall ((Y vertex1)) (let ((_let_1 (t2tb1 Y))) (or (not (mem vertex _let_1 (t2tb (succ1 skv_12)))) (mem vertex _let_1 (t2tb skv_11))))))) (let ((_let_17 (mem vertex _let_9 (t2tb skv_10)))) (let ((_let_18 (t2tb skv_11))) (let ((_let_19 (mem vertex _let_9 _let_18))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_10 _let_17 _let_16))) (let ((_let_22 (closure1 skv_11 _let_7 skv_10 skv_12))) (let ((_let_23 (= _let_22 _let_21))) (let ((_let_24 (forall ((Visited set_vertex) (Current set_vertex) (Next set_vertex) (X vertex1)) (let ((_let_1 (t2tb1 X))) (= (closure1 Visited Current Next X) (or (not (mem vertex _let_1 (t2tb Visited))) (mem vertex _let_1 (t2tb Current)) (mem vertex _let_1 (t2tb Next)) (forall ((Y vertex1)) (let ((_let_1 (t2tb1 Y))) (or (not (mem vertex _let_1 (t2tb (succ1 X)))) (mem vertex _let_1 (t2tb Visited))))))))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (_let_24))) (let ((_let_27 (forall ((X vertex1)) (closure1 skv_11 (tb2t (remove vertex (t2tb1 skv_13) (t2tb skv_7))) skv_10 X)))) (let ((_let_28 (= true1 skv_9))) (let ((_let_29 (is_empty vertex _let_5))) (let ((_let_30 (tb2t (empty vertex)))) (let ((_let_31 (closure1 skv_11 skv_10 _let_30 skv_12))) (let ((_let_32 (not _let_27))) (let ((_let_33 (or (and _let_29 (not (is_empty vertex (t2tb skv_6)))) (not (forall ((X vertex1)) (closure1 skv_8 skv_7 skv_6 X))) (not (>= skv_5 0)) (not (inv1 skv_3 skv_4 skv_8 skv_7 skv_6 skv_5)) _let_29 (not (mem vertex _let_6 _let_5)) (= skv_4 skv_13) (not (inv1 skv_3 skv_4 skv_8 _let_7 skv_6 skv_5)) (not (shortest_path1 skv_3 skv_13 skv_5)) (not (forall ((X vertex1)) (or (= X skv_13) (closure1 skv_8 (tb2t (remove vertex (t2tb1 skv_13) (t2tb skv_7))) skv_6 X)))) _let_13 (not (inv1 skv_3 skv_4 skv_11 _let_7 skv_10 skv_5)) _let_32 (not (subset vertex (t2tb (succ1 skv_13)) _let_18)) _let_31 (= (not _let_29) _let_28) _let_28))) (let ((_let_34 (forall ((S vertex1) (T vertex1) (D Int) (Next set_vertex) (Current set_vertex) (Visited set_vertex) (BOUND_VARIABLE_1884 bool1) (BOUND_VARIABLE_1852 set_vertex) (BOUND_VARIABLE_1850 set_vertex) (BOUND_VARIABLE_1848 vertex1) (BOUND_VARIABLE_1846 vertex1)) (let ((_let_1 (= true1 BOUND_VARIABLE_1884))) (let ((_let_2 (t2tb Current))) (let ((_let_3 (is_empty vertex _let_2))) (let ((_let_4 (t2tb1 BOUND_VARIABLE_1846))) (let ((_let_5 (tb2t (remove vertex _let_4 _let_2)))) (or (and _let_3 (not (is_empty vertex (t2tb Next)))) (not (forall ((X vertex1)) (closure1 Visited Current Next X))) (not (>= D 0)) (not (inv1 S T Visited Current Next D)) _let_3 (not (mem vertex _let_4 _let_2)) (= T BOUND_VARIABLE_1846) (not (inv1 S T Visited _let_5 Next D)) (not (shortest_path1 S BOUND_VARIABLE_1846 D)) (not (forall ((X vertex1)) (or (= X BOUND_VARIABLE_1846) (closure1 Visited (tb2t (remove vertex (t2tb1 BOUND_VARIABLE_1846) (t2tb Current))) Next X)))) (not (is_empty vertex (t2tb _let_5))) (not (inv1 S T BOUND_VARIABLE_1850 _let_5 BOUND_VARIABLE_1852 D)) (not (forall ((X vertex1)) (closure1 BOUND_VARIABLE_1850 (tb2t (remove vertex (t2tb1 BOUND_VARIABLE_1846) (t2tb Current))) BOUND_VARIABLE_1852 X))) (not (subset vertex (t2tb (succ1 BOUND_VARIABLE_1846)) (t2tb BOUND_VARIABLE_1850))) (closure1 BOUND_VARIABLE_1850 BOUND_VARIABLE_1852 (tb2t (empty vertex)) BOUND_VARIABLE_1848) (= (not _let_3) _let_1) _let_1))))))))) (let ((_let_35 (not _let_33))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (OR))) (let ((_let_38 (not _let_34))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_36) :args (_let_38))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_34))) (REFL :args (_let_35)) :args _let_37)) _let_36 :args (_let_35 true _let_34)))) (let ((_let_40 (REFL :args (_let_33)))) (let ((_let_41 (_let_27))) (let ((_let_42 (or _let_20 _let_17 (mem vertex _let_9 (t2tb _let_30)) _let_16))) (let ((_let_43 (= _let_31 _let_42))) (let ((_let_44 (not _let_42))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_43)) :args ((or _let_31 _let_44 (not _let_43)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_33 14)) _let_39 :args ((not _let_31) true _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (skv_11 skv_10 _let_30 skv_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_26)) _let_25 :args (_let_43 false _let_24)) :args (_let_44 true _let_31 false _let_43)))) (let ((_let_46 (_let_4))) (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_46) :args (vertex _let_8 _let_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_13 _let_11 _let_15))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 10)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_37)) :args ((or _let_12 _let_33))) _let_39 :args (_let_12 true _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_20 _let_17 _let_16 _let_10 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG (REFL :args (_let_42)) (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_37)) :args ((or _let_19 _let_42))) _let_45 :args (_let_19 true _let_42)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_42 1)) _let_45 :args ((not _let_17) true _let_42)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_42 3)) _let_45 :args ((not _let_16) true _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_23)) :args ((or (not _let_22) _let_21 (not _let_23)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_41) :args (skv_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 12)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_27))) :args _let_37)) :args ((or _let_27 _let_33))) _let_39 :args (_let_27 true _let_33)) :args (_let_22 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (skv_11 _let_7 skv_10 skv_12 QUANTIFIERS_INST_CBQI_PROP)) :args _let_26)) _let_25 :args (_let_23 false _let_24)) :args (_let_21 false _let_22 false _let_23)) :args (_let_10 false _let_19 true _let_17 true _let_16 false _let_21)) :args (_let_15 false _let_12 false _let_10)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) :args (0)) :args (false true _let_14 false _let_4)) :args ((forall ((Z vertex1) (Z1 vertex1) (Z2 Int)) (=> (path1 Z Z1 Z2) (or (exists ((V vertex1)) (and (= Z V) (= Z1 V) (= Z2 0))) (exists ((V1 vertex1) (V2 vertex1) (V3 vertex1) (N Int)) (and (mem vertex (t2tb1 V3) (t2tb (succ1 V2))) (= Z2 (+ N 1)) (= Z1 V3) (= Z V1) (path1 V1 V2 N)))))) (forall ((A ty) (S1 uni) (S2 uni) (X uni)) (= (or (mem A X S2) (mem A X S1)) (mem A X (union A S1 S2)))) (forall ((A ty) (X uni) (X1 uni)) (sort1 (set A) (diff A X X1))) (forall ((S vertex1) (T vertex1) (Visited set_vertex) (Current set_vertex) (Next set_vertex) (D Int)) (let ((_let_1 (t2tb Visited))) (let ((_let_2 (t2tb Current))) (let ((_let_3 (t2tb1 T))) (let ((_let_4 (t2tb Next))) (= (inv1 S T Visited Current Next D) (and (subset vertex _let_4 _let_1) (forall ((X vertex1)) (=> (mem vertex (t2tb1 X) (t2tb Next)) (shortest_path1 S X (+ D 1)))) (forall ((X vertex1)) (=> (mem vertex (t2tb1 X) (t2tb Visited)) (exists ((M Int)) (and (<= M (+ D 1)) (path1 S X M))))) (=> (mem vertex _let_3 _let_1) (or (mem vertex _let_3 _let_4) (mem vertex _let_3 _let_2))) (forall ((X vertex1)) (let ((_let_1 (t2tb1 X))) (=> (shortest_path1 S X (+ D 1)) (or (mem vertex _let_1 (t2tb Next)) (not (mem vertex _let_1 (t2tb Visited))))))) (forall ((X vertex1) (M Int)) (=> (path1 S X M) (=> (<= M D) (mem vertex (t2tb1 X) (t2tb Visited))))) (forall ((X vertex1)) (=> (mem vertex (t2tb1 X) (t2tb Current)) (shortest_path1 S X D))) (subset vertex _let_2 _let_1)))))))) (forall ((A ty) (X uni) (X1 uni)) (sort1 (set A) (union A X X1))) (forall ((A ty) (Z uni) (Z1 uni)) (=> (sort1 A Z1) (= (match_bool1 A false1 Z Z1) Z1))) (forall ((A ty) (X uni) (Y uni) (S uni)) (=> (sort1 A X) (=> (sort1 A Y) (= (mem A X (remove A Y S)) (and (not (= X Y)) (mem A X S)))))) (forall ((A ty) (X uni) (Y uni)) (=> (sort1 A X) (=> (sort1 A Y) (forall ((S uni)) (= (or (mem A X S) (= X Y)) (mem A X (add A Y S))))))) (forall ((A ty) (X uni) (X1 uni)) (sort1 (set A) (remove A X X1))) (forall ((A ty) (S1 uni) (S2 uni)) (subset A (diff A S1 S2) S1)) (forall ((U bool1)) (or (= U false1) (= U true1))) (forall ((A ty) (X uni) (S uni)) (= (remove A X (add A X S)) (remove A X S))) (forall ((A ty) (X uni) (X1 uni)) (sort1 (set A) (add A X X1))) (forall ((V1 vertex1) (V2 vertex1) (N Int)) (= (and (forall ((M Int)) (=> (< M N) (not (path1 V1 V2 M)))) (path1 V1 V2 N)) (shortest_path1 V1 V2 N))) (forall ((A ty) (S uni)) (subset A S S)) (forall ((I vertex1)) (= (tb2t1 (t2tb1 I)) I)) (forall ((A ty)) (sort1 (set A) (empty A))) (forall ((A ty) (X uni) (S uni)) (=> (mem A X S) (= (cardinal1 A S) (+ 1 (cardinal1 A (remove A X S)))))) (forall ((S set_vertex)) (=> (forall ((X vertex1)) (=> (mem vertex (t2tb1 X) (t2tb S)) (forall ((Y vertex1)) (let ((_let_1 (t2tb1 Y))) (=> (mem vertex _let_1 (t2tb (succ1 X))) (mem vertex _let_1 (t2tb S))))))) (forall ((V1 vertex1) (V2 vertex1) (N Int)) (let ((_let_1 (t2tb S))) (=> (path1 V1 V2 N) (=> (mem vertex (t2tb1 V1) _let_1) (mem vertex (t2tb1 V2) _let_1))))))) (forall ((X Int) (Y Int) (Z Int)) (=> (<= X Y) (=> (<= 0 Z) (<= (* X Z) (* Y Z))))) (forall ((V1 vertex1) (V2 vertex1) (V3 vertex1) (N Int)) (=> (path1 V1 V2 N) (=> (mem vertex (t2tb1 V3) (t2tb (succ1 V2))) (path1 V1 V3 (+ N 1))))) (forall ((A ty) (X uni) (S uni)) (=> (sort1 (set A) S) (=> (mem A X S) (= (add A X (remove A X S)) S)))) (forall ((A ty) (U uni)) (=> (sort1 (ref A) U) (= U (mk_ref A (contents A U))))) (forall ((A ty) (X uni)) (sort1 (ref A) (mk_ref A X))) (forall ((A ty) (X uni) (S uni)) (=> (not (mem A X S)) (= (cardinal1 A (add A X S)) (+ 1 (cardinal1 A S))))) (forall ((A ty) (S1 uni) (S2 uni) (S3 uni)) (=> (subset A S1 S2) (=> (subset A S2 S3) (subset A S1 S3)))) (forall ((A ty)) (is_empty A (empty A))) (forall ((A ty) (S uni)) (=> (= (cardinal1 A S) 1) (forall ((X uni)) (=> (sort1 A X) (=> (mem A X S) (= X (choose A S))))))) (forall ((I set_vertex)) (= (tb2t (t2tb I)) I)) (forall ((A ty) (S1 uni) (S2 uni)) (let ((_let_1 (set A))) (=> (sort1 _let_1 S1) (=> (sort1 _let_1 S2) (=> (infix_eqeq A S1 S2) (= S1 S2)))))) (forall ((A ty) (X uni) (X1 uni)) (sort1 (set A) (inter A X X1))) (forall ((A ty) (S1 uni) (S2 uni) (X uni)) (= (mem A X (diff A S1 S2)) (and (not (mem A X S2)) (mem A X S1)))) (forall ((A ty) (Z uni) (Z1 uni)) (=> (sort1 A Z) (= (match_bool1 A true1 Z Z1) Z))) (forall ((A ty) (X uni)) (sort1 A (choose A X))) (forall ((V1 vertex1) (V3 vertex1) (N Int)) (=> (<= 0 N) (=> (path1 V1 V3 (+ N 1)) (exists ((V2 vertex1)) (and (path1 V1 V2 N) (mem vertex (t2tb1 V3) (t2tb (succ1 V2)))))))) (not (= true1 false1)) (forall ((A ty) (S1 uni) (S2 uni)) (let ((_let_1 (infix_eqeq A S1 S2))) (and (=> _let_1 (forall ((X uni)) (= (mem A X S2) (mem A X S1)))) (=> (forall ((X uni)) (=> (sort1 A X) (= (mem A X S2) (mem A X S1)))) _let_1)))) _let_3 _let_2 (forall ((A ty) (S1 uni) (S2 uni) (X uni)) (= (and (mem A X S1) (mem A X S2)) (mem A X (inter A S1 S2)))) (forall ((A ty)) (sort1 A (witness1 A))) (forall ((A ty) (X bool1) (X1 uni) (X2 uni)) (sort1 A (match_bool1 A X X1 X2))) (forall ((A ty) (X uni)) (= false (mem A X (empty A)))) (forall ((A ty) (S uni)) (<= 0 (cardinal1 A S))) (forall ((A ty) (X uni) (S uni)) (subset A (remove A X S) S)) (forall ((J uni)) (=> (sort1 (set vertex) J) (= (t2tb (tb2t J)) J))) _let_1 (forall ((A ty) (S1 uni) (S2 uni)) (let ((_let_1 (subset A S1 S2))) (and (=> (forall ((X uni)) (=> (sort1 A X) (=> (mem A X S1) (mem A X S2)))) _let_1) (=> _let_1 (forall ((X uni)) (=> (mem A X S1) (mem A X S2))))))) (forall ((U tuple02)) (= U tuple03)) (forall ((A ty) (S uni)) (=> (not (is_empty A S)) (mem A (choose A S) S))) (forall ((A ty) (X uni)) (sort1 A (contents A X))) (forall ((X set_vertex)) (sort1 (set vertex) (t2tb X))) (forall ((V1 vertex1) (V2 vertex1) (N Int)) (=> (path1 V1 V2 N) (<= 0 N))) (forall ((A ty) (U uni)) (=> (sort1 A U) (= (contents A (mk_ref A U)) U))) (forall ((V vertex1)) (path1 V V 0)) (forall ((J uni)) (=> (sort1 vertex J) (= (t2tb1 (tb2t1 J)) J))) (forall ((X vertex1)) (sort1 vertex (t2tb1 X))) (forall ((A ty) (S uni)) (= (is_empty A S) (= (cardinal1 A S) 0))) (forall ((A ty) (S1 uni) (S2 uni)) (=> (subset A S1 S2) (<= (cardinal1 A S1) (cardinal1 A S2)))) true)))))))))))))))))))))))))))))))))))))))))))))))) 0.15/0.52 % SZS output end Proof for theBenchmark 0.15/0.52 EOF