TSTP Solution File: SET012+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET012+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 14:36:42 EDT 2023
% Result : Theorem 0.36s 0.55s
% Output : Proof 0.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET012+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 08:46:35 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.36/0.55 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.mt37wEWBU7/cvc5---1.0.5_16353.p...
% 0.36/0.55 ------- get file name : TPTP file name is SET012+4
% 0.36/0.55 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16353.smt2...
% 0.36/0.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.36/0.55 % SZS status Theorem for SET012+4
% 0.36/0.55 % SZS output start Proof for SET012+4
% 0.36/0.55 (
% 0.36/0.55 (let ((_let_1 (not (forall ((A $$unsorted) (E $$unsorted)) (=> (tptp.subset A E) (tptp.equal_set (tptp.difference E (tptp.difference E A)) A)))))) (let ((_let_2 (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_5 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_6 (not _let_5))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_8 (and _let_7 _let_6))) (let ((_let_9 (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_9))) (let ((_let_11 (= _let_10 _let_8))) (let ((_let_12 (_let_2))) (let ((_let_13 (ASSUME :args _let_12))) (let ((_let_14 ((tptp.member B (tptp.difference E A))))) (let ((_let_15 (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_15))) (let ((_let_17 (or _let_6 _let_16))) (let ((_let_18 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.member X (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))))) (let ((_let_19 (not _let_17))) (let ((_let_20 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_15))) (let ((_let_21 (= _let_20 _let_18))) (let ((_let_22 (not _let_18))) (let ((_let_23 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (_let_23))) (let ((_let_26 ((tptp.subset A B)))) (let ((_let_27 (tptp.subset _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (and _let_27 _let_20))) (let ((_let_29 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_30 (= _let_27 _let_29))) (let ((_let_31 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_15))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31))) (let ((_let_35 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_9))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_38 (and _let_37 _let_36))) (let ((_let_39 (= _let_32 _let_38))) (let ((_let_40 (not _let_31))) (let ((_let_41 (and _let_37 _let_40))) (let ((_let_42 (= _let_35 _let_41))) (let ((_let_43 (or))) (let ((_let_44 (not _let_38))) (let ((_let_45 (not _let_37))) (let ((_let_46 (_let_41))) (let ((_let_47 (not _let_29))) (let ((_let_48 (_let_47))) (let ((_let_49 (tptp.equal_set _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_50 (= _let_49 _let_28))) (let ((_let_51 (not _let_28))) (let ((_let_52 (_let_3))) (let ((_let_53 (ASSUME :args _let_52))) (let ((_let_54 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_49))) (let ((_let_57 (forall ((A $$unsorted) (E $$unsorted)) (or (not (tptp.subset A E)) (tptp.equal_set (tptp.difference E (tptp.difference E A)) A))))) (let ((_let_58 (not _let_56))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (not _let_57))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_59) :args (_let_60))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_57))) (REFL :args (_let_58)) :args _let_43)) _let_59 :args (_let_58 true _let_57)))) (let ((_let_62 (_let_22))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_62)) :args _let_62)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_18))) (REFL :args (_let_19)) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_21)) :args ((or _let_20 _let_22 (not _let_21)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_50)) :args ((or _let_49 _let_51 (not _let_50)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_56 1)) _let_61 :args ((not _let_49) true _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (_let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_52)) _let_53 :args (_let_50 false _let_3)) :args (_let_51 true _let_49 false _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_30)) :args ((or _let_27 _let_47 (not _let_30)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_48)) :args _let_48)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_29))) (REFL :args ((not _let_34))) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_42)) :args ((or _let_35 (not _let_41) (not _let_42)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_42 false _let_2)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_46) (CONG (REFL :args _let_46) (REFL :args (_let_45)) (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_31))) :args _let_43)) :args ((or _let_31 _let_45 _let_41))) (REORDERING (CNF_AND_POS :args (_let_38 1)) :args ((or _let_36 _let_44))) (REORDERING (CNF_AND_POS :args (_let_38 0)) :args ((or _let_37 _let_44))) (REORDERING (CNF_EQUIV_POS1 :args (_let_39)) :args ((or _let_33 _let_38 (not _let_39)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_39 false _let_2)) (CNF_OR_NEG :args (_let_34 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG (REFL :args (_let_34)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_43)) :args ((or _let_32 _let_34))) :args (_let_34 false _let_42 false _let_41 true _let_35 false _let_37 false _let_38 false _let_39 true _let_31 false _let_32)) :args (_let_29 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (_let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_25)) _let_24 :args (_let_30 false _let_23)) :args (_let_27 false _let_29 false _let_30)) :args ((not _let_20) true _let_28 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_25)) _let_24 :args (_let_21 false _let_23)) :args (_let_22 true _let_20 false _let_21)) :args (_let_19 true _let_18)))) (let ((_let_64 (or _let_6 _let_7))) (let ((_let_65 (not _let_10))) (let ((_let_66 (and _let_7 _let_65))) (let ((_let_67 (= _let_16 _let_66))) (let ((_let_68 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_17 0)) (CONG (REFL :args (_let_17)) (MACRO_SR_PRED_INTRO :args ((= (not _let_6) _let_5))) :args _let_43)) :args ((or _let_5 _let_17))))) (let ((_let_69 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_70 (= _let_54 _let_69))) (let ((_let_71 (_let_69))) (let ((_let_72 (not _let_7))) (let ((_let_73 (_let_66))) (let ((_let_74 (not _let_8))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_11)) :args ((or _let_65 _let_8 (not _let_11)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_8 1)) :args ((or _let_6 _let_74))) (MACRO_RESOLUTION_TRUST _let_68 _let_63 :args (_let_5 true _let_17)) :args (_let_74 false _let_5)) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_73) (CONG (REFL :args _let_73) (REFL :args (_let_72)) (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_10))) :args _let_43)) :args ((or _let_10 _let_66 _let_72))) (REORDERING (CNF_EQUIV_POS2 :args (_let_67)) :args ((or _let_16 (not _let_66) (not _let_67)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_67 false _let_2)) (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_6 _let_7 (not _let_64)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_71) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) :args _let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_70)) :args ((or _let_55 _let_69 (not _let_70)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 0)) (CONG (REFL :args (_let_56)) (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_43)) :args ((or _let_54 _let_56))) _let_61 :args (_let_54 true _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_25)) _let_24 :args (_let_70 false _let_23)) :args (_let_69 false _let_54 false _let_70)) :args (_let_64 false _let_69)) (CNF_OR_NEG :args (_let_17 1)) _let_68 :args ((or _let_17 _let_10) true _let_66 false _let_67 false _let_7 false _let_64 true _let_16 false _let_5)) _let_63 :args (_let_10 true _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_11 false _let_2)) :args (false true _let_8 false _let_10 false _let_11)) :args (_let_4 _let_3 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))) _let_2 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.36/0.56 )
% 0.36/0.56 % SZS output end Proof for SET012+4
% 0.36/0.56 % cvc5---1.0.5 exiting
% 0.36/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------