TSTP Solution File: SEU328+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU328+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 16:30:57 EDT 2023
% Result : Theorem 0.22s 0.59s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU328+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 23 17:40:56 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.59 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.ZafDuyfyCh/cvc5---1.0.5_10245.p...
% 0.22/0.59 ------- get file name : TPTP file name is SEU328+1
% 0.22/0.59 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10245.smt2...
% 0.22/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.59 % SZS status Theorem for SEU328+1
% 0.22/0.59 % SZS output start Proof for SEU328+1
% 0.22/0.59 (
% 0.22/0.59 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.union_of_subsets A (tptp.complements_of_subsets A B)) (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.meet_of_subsets A B)))))))) (let ((_let_2 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.union_of_subsets A (tptp.complements_of_subsets A B)) (tptp.subset_complement A (tptp.meet_of_subsets A B))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_difference A B C) (tptp.set_difference B C))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B (tptp.powerset _let_1)) (tptp.element (tptp.meet_of_subsets A B) _let_1)))))) (let ((_let_5 (forall ((A $$unsorted)) (tptp.element (tptp.cast_to_subset A) (tptp.powerset A))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A B) (tptp.set_difference A B)))))) (let ((_let_7 (forall ((A $$unsorted)) (= (tptp.cast_to_subset A) A)))) (let ((_let_8 (tptp.meet_of_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_9 (tptp.subset_complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_8))) (let ((_let_10 (tptp.union_of_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.complements_of_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (tptp.cast_to_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_13 (tptp.subset_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12 _let_8))) (let ((_let_14 (= _let_10 _let_13))) (let ((_let_15 (= _let_9 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_8)))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12))) (let ((_let_17 (= _let_13 (tptp.set_difference _let_12 _let_8)))) (let ((_let_18 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_19 (tptp.powerset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_20 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.powerset _let_19)))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_18 _let_11))) (let ((_let_23 (not _let_11))) (let ((_let_24 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset (tptp.powerset A)))) (= tptp.empty_set B) (= (tptp.union_of_subsets A (tptp.complements_of_subsets A B)) (tptp.subset_complement A (tptp.meet_of_subsets A B))))))) (let ((_let_25 (not _let_22))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (or))) (let ((_let_28 (not _let_24))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_26) :args (_let_28))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_24))) (REFL :args (_let_25)) :args _let_27)) _let_26 :args (_let_25 true _let_24)))) (let ((_let_30 (or _let_21 _let_18 _let_14))) (let ((_let_31 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset (tptp.powerset A)))) (= tptp.empty_set B) (= (tptp.union_of_subsets A (tptp.complements_of_subsets A B)) (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.meet_of_subsets A B))))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 0)) (CONG (REFL :args (_let_22)) (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_27)) :args ((or _let_20 _let_22))) _let_29 :args (_let_20 true _let_22)))) (let ((_let_34 (tptp.element _let_8 _let_19))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_15))) (let ((_let_37 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset A))) (= (tptp.subset_complement A B) (tptp.set_difference A B)))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (or _let_21 _let_34))) (let ((_let_40 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B (tptp.powerset _let_1))) (tptp.element (tptp.meet_of_subsets A B) _let_1)))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_21 _let_34 (not _let_39)))) _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B (tptp.powerset (tptp.powerset A))) false))))) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_34 false _let_20 false _let_39)))) (let ((_let_43 (forall ((A $$unsorted)) (= A (tptp.cast_to_subset A))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (tptp.element _let_12 _let_19))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_35 _let_17))) (let ((_let_48 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B _let_1)) (not (tptp.element C _let_1)) (= (tptp.subset_difference A B C) (tptp.set_difference B C))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (_let_5))) (let ((_let_51 (ASSUME :args _let_50))) (let ((_let_52 (and _let_23 _let_15 _let_14 _let_16))) (let ((_let_53 (ASSUME :args (_let_23)))) (let ((_let_54 (ASSUME :args (_let_15)))) (let ((_let_55 (ASSUME :args (_let_16)))) (let ((_let_56 (ASSUME :args (_let_14)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_52)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_53 _let_56 _let_54 _let_55) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_56) (TRANS (CONG (SYMM _let_55) (REFL :args (_let_8)) :args (APPLY_UF tptp.set_difference)) (SYMM _let_54)) :args (=)) (FALSE_INTRO _let_53))) :args (_let_23 _let_14 _let_15 _let_16))) :args (_let_23 _let_15 _let_14 _let_16))) :args (true _let_52)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_11))) (REFL :args ((not _let_15))) (REFL :args ((not _let_14))) (REFL :args ((not _let_16))) (REFL :args ((not _let_17))) :args _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_35 _let_46 _let_17 (not _let_47)))) _let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.powerset A)))) :args _let_50)) _let_51 :args (_let_45 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12 _let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset_difference A B C)))) :args (_let_48))) _let_49 :args (_let_47 false _let_48)) :args (_let_17 false _let_34 false _let_45 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cast_to_subset A)))) :args (_let_43))) _let_44 :args (_let_16 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_15 (not _let_36)))) _let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset_complement A B)))) :args (_let_37))) _let_38 :args (_let_36 false _let_37)) :args (_let_15 false _let_34 false _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_21 _let_18 _let_14 (not _let_30)))) _let_33 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 1)) _let_29 :args ((not _let_18) true _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B (tptp.powerset (tptp.powerset A))) false))))) :args (_let_31))) _let_32 :args (_let_30 false _let_31)) :args (_let_14 false _let_20 true _let_18 false _let_30)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 2)) _let_29 :args (_let_23 true _let_22)) :args (false false _let_17 false _let_16 false _let_15 false _let_14 true _let_11)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (tptp.v1_xcmplx_0 B))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.natural B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A)))) (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.v1_membered B))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (tptp.v4_membered A))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (tptp.v3_membered A))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (tptp.v2_membered A))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (tptp.v1_membered A))) _let_7 _let_6 true true true _let_5 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B _let_1) (tptp.element (tptp.subset_complement A B) _let_1)))) true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B (tptp.powerset _let_1)) (tptp.element (tptp.union_of_subsets A B) _let_1)))) _let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.subset_difference A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.powerset A)))) (=> (tptp.element B _let_1) (tptp.element (tptp.complements_of_subsets A B) _let_1)))) true (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_membered A) (tptp.v1_membered (tptp.set_difference A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.set_difference A B))) (=> (tptp.v2_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.set_difference A B))) (=> (tptp.v3_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.set_difference A B))) (=> (tptp.v4_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1) (tptp.v4_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.set_difference A B))) (=> (tptp.v5_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1) (tptp.v4_membered _let_1) (tptp.v5_membered _let_1))))) (and (tptp.empty tptp.empty_set) (tptp.v1_membered tptp.empty_set) (tptp.v2_membered tptp.empty_set) (tptp.v3_membered tptp.empty_set) (tptp.v4_membered tptp.empty_set) (tptp.v5_membered tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A (tptp.subset_complement A B)) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.complements_of_subsets A (tptp.complements_of_subsets A B)) B))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.union_of_subsets A B) (tptp.union B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.meet_of_subsets A B) (tptp.set_meet B)))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) _let_1 (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.59 )
% 0.22/0.59 % SZS output end Proof for SEU328+1
% 0.22/0.59 % cvc5---1.0.5 exiting
% 0.22/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------