TSTP Solution File: SET143+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET143+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 14:37:54 EDT 2023
% Result : Theorem 0.21s 0.54s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET143+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n007.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 : Sat Aug 26 09:11:26 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.54 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.LYnhkW14ny/cvc5---1.0.5_19311.p...
% 0.21/0.54 ------- get file name : TPTP file name is SET143+4
% 0.21/0.54 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19311.smt2...
% 0.21/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.54 % SZS status Theorem for SET143+4
% 0.21/0.54 % SZS output start Proof for SET143+4
% 0.21/0.54 (
% 0.21/0.54 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.equal_set (tptp.intersection (tptp.intersection A B) C) (tptp.intersection A (tptp.intersection B C)))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_6 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_8 (and _let_7 _let_6))) (let ((_let_9 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_9))) (let ((_let_11 (= _let_10 _let_8))) (let ((_let_12 (_let_3))) (let ((_let_13 (ASSUME :args _let_12))) (let ((_let_14 ((tptp.member X (tptp.intersection A B))))) (let ((_let_15 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_16 (and _let_6 _let_15))) (let ((_let_17 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_18 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_17))) (let ((_let_19 (= _let_18 _let_16))) (let ((_let_20 (and _let_7 _let_18))) (let ((_let_21 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_17))) (let ((_let_22 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_21))) (let ((_let_23 (= _let_22 _let_20))) (let ((_let_24 (tptp.intersection _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_24))) (let ((_let_26 (not _let_22))) (let ((_let_27 (or _let_26 _let_25))) (let ((_let_28 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (tptp.member X (tptp.intersection (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (tptp.subset _let_21 _let_24))) (let ((_let_31 (= _let_30 _let_28))) (let ((_let_32 (not _let_28))) (let ((_let_33 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (_let_33))) (let ((_let_36 ((tptp.subset A B)))) (let ((_let_37 (tptp.subset _let_24 _let_21))) (let ((_let_38 (and _let_37 _let_30))) (let ((_let_39 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.intersection (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.member X (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_40 (= _let_37 _let_39))) (let ((_let_41 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_21))) (let ((_let_42 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_24))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_41))) (let ((_let_45 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_46 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_9))) (let ((_let_47 (and _let_46 _let_45))) (let ((_let_48 (= _let_42 _let_47))) (let ((_let_49 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_17))) (let ((_let_50 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_51 (and _let_50 _let_49))) (let ((_let_52 (= _let_41 _let_51))) (let ((_let_53 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_54 (and _let_50 _let_53))) (let ((_let_55 (= _let_46 _let_54))) (let ((_let_56 (and _let_53 _let_45))) (let ((_let_57 (= _let_49 _let_56))) (let ((_let_58 (or))) (let ((_let_59 (not _let_47))) (let ((_let_60 (not _let_54))) (let ((_let_61 (not _let_39))) (let ((_let_62 (_let_61))) (let ((_let_63 (tptp.equal_set _let_24 _let_21))) (let ((_let_64 (= _let_63 _let_38))) (let ((_let_65 (not _let_38))) (let ((_let_66 (_let_4))) (let ((_let_67 (ASSUME :args _let_66))) (let ((_let_68 (not _let_63))) (let ((_let_69 (_let_2))) (let ((_let_70 (ASSUME :args _let_69))) (let ((_let_71 (_let_32))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_71)) :args _let_71)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_28))) (REFL :args (_let_29)) :args _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_31)) :args ((or _let_30 _let_32 (not _let_31)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_64)) :args ((or _let_63 _let_65 (not _let_64)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_70) :args _let_69)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_68)) :args _let_58)) _let_70 :args (_let_68 true _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (_let_24 _let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_66)) _let_67 :args (_let_64 false _let_4)) :args (_let_65 true _let_63 false _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_40)) :args ((or _let_37 _let_61 (not _let_40)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_62)) :args _let_62)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_39))) (REFL :args ((not _let_44))) :args _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_57)) :args ((or _let_49 (not _let_56) (not _let_57)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_57 false _let_3)) (REORDERING (CNF_AND_NEG :args (_let_56)) :args ((or (not _let_45) _let_56 (not _let_53)))) (CNF_AND_NEG :args (_let_51)) (REORDERING (CNF_AND_POS :args (_let_54 1)) :args ((or _let_53 _let_60))) (REORDERING (CNF_AND_POS :args (_let_54 0)) :args ((or _let_50 _let_60))) (REORDERING (CNF_EQUIV_POS1 :args (_let_55)) :args ((or (not _let_46) _let_54 (not _let_55)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_55 false _let_3)) (REORDERING (CNF_AND_POS :args (_let_47 1)) :args ((or _let_45 _let_59))) (REORDERING (CNF_AND_POS :args (_let_47 0)) :args ((or _let_46 _let_59))) (REORDERING (CNF_EQUIV_POS2 :args (_let_52)) :args ((or _let_41 (not _let_51) (not _let_52)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_17 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_52 false _let_3)) (REORDERING (CNF_EQUIV_POS1 :args (_let_48)) :args ((or _let_43 _let_47 (not _let_48)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_48 false _let_3)) (CNF_OR_NEG :args (_let_44 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_44 0)) (CONG (REFL :args (_let_44)) (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_42))) :args _let_58)) :args ((or _let_42 _let_44))) :args (_let_44 false _let_57 false _let_56 true _let_49 false _let_53 false _let_50 false _let_54 false _let_55 false _let_45 false _let_46 true _let_51 false _let_52 false _let_47 false _let_48 true _let_41 false _let_42)) :args (_let_39 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_24 _let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_36)) :args _let_35)) _let_34 :args (_let_40 false _let_33)) :args (_let_37 false _let_39 false _let_40)) :args ((not _let_30) true _let_38 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_21 _let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_36)) :args _let_35)) _let_34 :args (_let_31 false _let_33)) :args (_let_32 true _let_30 false _let_31)) :args (_let_29 true _let_28)))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_23)) :args ((or _let_26 _let_20 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG (REFL :args (_let_27)) (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_22))) :args _let_58)) :args ((or _let_22 _let_27))) _let_72 :args (_let_22 true _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_17 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_23 false _let_3)) :args (_let_20 false _let_22 false _let_23)))) (let ((_let_74 (not _let_20))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_19)) :args ((or (not _let_18) _let_16 (not _let_19)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_20 1)) :args ((or _let_18 _let_74))) _let_73 :args (_let_18 false _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_19 false _let_3)) :args (_let_16 false _let_18 false _let_19)))) (let ((_let_76 (not _let_16))) (let ((_let_77 (and _let_10 _let_15))) (let ((_let_78 (= _let_25 _let_77))) (let ((_let_79 (not _let_77))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_11)) :args ((or _let_10 (not _let_8) (not _let_11)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_78)) :args ((or _let_25 _let_79 (not _let_78)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_27 1)) _let_72 :args ((not _let_25) true _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_78 false _let_3)) :args (_let_79 true _let_25 false _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_16 1)) :args ((or _let_15 _let_76))) _let_75 :args (_let_15 false _let_16)) :args ((not _let_10) true _let_77 false _let_15)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_8)) :args ((or (not _let_7) _let_8 (not _let_6)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_20 0)) :args ((or _let_7 _let_74))) _let_73 :args (_let_7 false _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_16 0)) :args ((or _let_6 _let_76))) _let_75 :args (_let_6 false _let_16)) :args (_let_8 false _let_7 false _let_6)) (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_3)) :args (false true _let_10 false _let_8 false _let_11)) :args (_let_5 _let_4 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) _let_3 (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))) (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$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_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.55 )
% 0.21/0.55 % SZS output end Proof for SET143+4
% 0.21/0.55 % cvc5---1.0.5 exiting
% 0.21/0.55 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------