TSTP Solution File: SET902+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET902+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 14:40:55 EDT 2023
% Result : Theorem 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET902+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 10:19:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.0W3gOszSge/cvc5---1.0.5_23009.p...
% 0.20/0.53 ------- get file name : TPTP file name is SET902+1
% 0.20/0.53 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_23009.smt2...
% 0.20/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.53 % SZS status Theorem for SET902+1
% 0.20/0.53 % SZS output start Proof for SET902+1
% 0.20/0.53 (
% 0.20/0.53 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A (tptp.set_union2 A B))))) (let ((_let_2 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.singleton A))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= C _let_1))) (not (and (= _let_1 (tptp.set_union2 B C)) (not (and _let_2 _let_3)) (not (and (= B tptp.empty_set) _let_3)) (not (and _let_2 (= C tptp.empty_set)))))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _let_1))))))) (let ((_let_4 (forall ((A $$unsorted)) (not (= (tptp.singleton A) tptp.empty_set))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))))) (let ((_let_7 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_7))) (let ((_let_9 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_10 (or _let_9 _let_8))) (let ((_let_11 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_7))) (let ((_let_12 (= _let_11 _let_10))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= tptp.empty_set A) (= A _let_1))))))) (let ((_let_14 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_15 (_let_13))) (let ((_let_16 ((tptp.subset A (tptp.singleton B))))) (let ((_let_17 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_17))) (let ((_let_19 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_20 (= _let_19 _let_17))) (let ((_let_21 (= _let_7 _let_19))) (let ((_let_22 (_let_1))) (let ((_let_23 (ASSUME :args _let_22))) (let ((_let_24 ((tptp.set_union2 A B)))) (let ((_let_25 (_let_6))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_union2 A B)))) :args _let_25)) _let_26 :args (_let_20 false _let_6)))) (let ((_let_28 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_7))) (let ((_let_29 (and _let_28 _let_9))) (let ((_let_30 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_31 (and _let_30 _let_8))) (let ((_let_32 (and _let_28 _let_8))) (let ((_let_33 (not _let_21))) (let ((_let_34 (or _let_33 _let_32 _let_31 _let_29))) (let ((_let_35 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.singleton A))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= C _let_1))) (or (not (= _let_1 (tptp.set_union2 B C))) (and _let_2 _let_3) (and (= tptp.empty_set B) _let_3) (and _let_2 (= tptp.empty_set C))))))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (or))) (let ((_let_39 (not _let_35))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_37) :args (_let_39))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_35))) (REFL :args (_let_36)) :args _let_38)) _let_37 :args (_let_36 true _let_35)))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG (REFL :args (_let_34)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_21))) :args _let_38)) :args ((or _let_21 _let_34))) _let_40 :args (_let_21 true _let_34)))) (let ((_let_42 (and _let_21 _let_20 _let_18))) (let ((_let_43 (ASSUME :args (_let_18)))) (let ((_let_44 (APPLY_UF tptp.subset))) (let ((_let_45 (ASSUME :args (_let_20)))) (let ((_let_46 (SYMM _let_45))) (let ((_let_47 (ASSUME :args (_let_21)))) (let ((_let_48 (SYMM _let_47))) (let ((_let_49 (SYMM _let_48))) (let ((_let_50 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_12)) :args ((or _let_10 (not _let_11) (not _let_12)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_42)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_43 _let_45 _let_47) (SCOPE (TRUE_ELIM (TRANS (CONG _let_50 (TRANS _let_49 (SYMM _let_46)) :args _let_44) (TRUE_INTRO _let_43))) :args (_let_18 _let_20 _let_21))) :args (_let_21 _let_20 _let_18))) :args (true _let_42)) _let_41 _let_27 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_24)) :args _let_22)) _let_23 :args (_let_18 false _let_1)) :args (_let_11 false _let_21 false _let_20 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_14 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_16)) :args _let_15)) _let_14 :args (_let_12 false _let_13)) :args (_let_10 false _let_11 false _let_12)))) (let ((_let_52 (not _let_8))) (let ((_let_53 (or _let_30 _let_28))) (let ((_let_54 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_7))) (let ((_let_55 (= _let_54 _let_53))) (let ((_let_56 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_19))) (let ((_let_57 (and _let_21 _let_56))) (let ((_let_58 (ASSUME :args (_let_56)))) (let ((_let_59 (= tptp.empty_set _let_7))) (let ((_let_60 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_61 (not _let_30))) (let ((_let_62 (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_8 _let_9 (not _let_10)))))) (let ((_let_63 (forall ((A $$unsorted)) (not (= tptp.empty_set (tptp.singleton A)))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (forall ((A $$unsorted)) (= A (tptp.set_union2 A A))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (not _let_9))) (let ((_let_68 (and _let_21 _let_30 _let_9 _let_20 _let_60))) (let ((_let_69 (ASSUME :args (_let_30)))) (let ((_let_70 (ASSUME :args (_let_9)))) (let ((_let_71 (ASSUME :args (_let_60)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_28 _let_30 (not _let_53)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_68)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_47 _let_45 _let_69 _let_70 _let_71) (SCOPE (TRANS _let_70 (SYMM (SYMM _let_71)) (CONG _let_50 (TRANS (SYMM _let_70) (SYMM (SYMM _let_69))) :args (APPLY_UF tptp.set_union2)) _let_46 _let_48) :args (_let_21 _let_20 _let_30 _let_9 _let_60))) :args (_let_21 _let_30 _let_9 _let_20 _let_60))) :args (true _let_68)) :args ((or _let_33 _let_61 _let_67 _let_59 (not _let_20) (not _let_60)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_union2 A A)))) :args (_let_65))) _let_66 :args (_let_60 false _let_65)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.singleton A)))) :args (_let_63))) _let_64 :args ((not _let_59) false _let_63)) _let_27 _let_41 _let_62 _let_51 (REORDERING (CNF_AND_NEG :args (_let_31)) :args ((or _let_31 _let_52 _let_61))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 2)) _let_40 :args ((not _let_31) true _let_34)) :args (_let_61 false _let_60 true _let_59 false _let_20 false _let_21 false _let_9 false _let_10 true _let_8 true _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_55)) :args ((or _let_53 (not _let_54) (not _let_55)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_57)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_58 _let_47) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_49 :args _let_44) (TRUE_INTRO _let_58))) :args (_let_56 _let_21))) :args (_let_21 _let_56))) :args (true _let_57)) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_24)) :args _let_22)) _let_23 :args (_let_56 false _let_1)) :args (_let_54 false _let_21 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_14 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_16)) :args _let_15)) _let_14 :args (_let_55 false _let_13)) :args (_let_53 false _let_54 false _let_55)) :args (_let_28 true _let_30 false _let_53)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST _let_62 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_29)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 3)) _let_40 :args ((not _let_29) true _let_34)) _let_72 :args (_let_67 true _let_29 false _let_28)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_32)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 1)) _let_40 :args ((not _let_32) true _let_34)) _let_72 :args (_let_52 true _let_32 false _let_28)) _let_51 :args (false true _let_9 true _let_8 false _let_10)) :args (_let_6 (tptp.empty tptp.empty_set) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) _let_5 _let_4 _let_3 (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.53 )
% 0.20/0.53 % SZS output end Proof for SET902+1
% 0.20/0.53 % cvc5---1.0.5 exiting
% 0.20/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------