TSTP Solution File: SET696+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET696+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 14:39:57 EDT 2023
% Result : Theorem 0.20s 0.54s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET696+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n031.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 09:39:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.54 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.YtCsRBg8H7/cvc5---1.0.5_22820.p...
% 0.20/0.54 ------- get file name : TPTP file name is SET696+4
% 0.20/0.54 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_22820.smt2...
% 0.20/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.54 % SZS status Theorem for SET696+4
% 0.20/0.54 % SZS output start Proof for SET696+4
% 0.20/0.54 (
% 0.20/0.54 (let ((_let_1 (not (forall ((A $$unsorted) (E $$unsorted)) (=> (tptp.subset A E) (tptp.equal_set (tptp.intersection (tptp.difference E A) A) tptp.empty_set)))))) (let ((_let_2 (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))))) (let ((_let_3 (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))))) (let ((_let_4 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_7 (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_7))) (let ((_let_9 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (not _let_9))) (let ((_let_11 (and (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_10))) (let ((_let_12 (= _let_8 _let_11))) (let ((_let_13 (and _let_8 _let_9))) (let ((_let_14 (tptp.intersection _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_14))) (let ((_let_16 (= _let_15 _let_13))) (let ((_let_17 (_let_4))) (let ((_let_18 (ASSUME :args _let_17))) (let ((_let_19 (not _let_15))) (let ((_let_20 (or _let_19 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.empty_set)))) (let ((_let_21 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.intersection (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (tptp.member X tptp.empty_set))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (tptp.subset _let_14 tptp.empty_set))) (let ((_let_24 (= _let_23 _let_21))) (let ((_let_25 (not _let_21))) (let ((_let_26 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (_let_26))) (let ((_let_29 ((tptp.subset A B)))) (let ((_let_30 (tptp.subset tptp.empty_set _let_14))) (let ((_let_31 (and _let_23 _let_30))) (let ((_let_32 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.empty_set)) (tptp.member X (tptp.intersection (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (let ((_let_33 (= _let_30 _let_32))) (let ((_let_34 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.empty_set))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_14)))) (let ((_let_37 (_let_3))) (let ((_let_38 (ASSUME :args _let_37))) (let ((_let_39 (or))) (let ((_let_40 (not _let_32))) (let ((_let_41 (_let_40))) (let ((_let_42 (tptp.equal_set _let_14 tptp.empty_set))) (let ((_let_43 (= _let_42 _let_31))) (let ((_let_44 (not _let_31))) (let ((_let_45 (_let_5))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 (or (not (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_42))) (let ((_let_48 (forall ((A $$unsorted) (E $$unsorted)) (or (not (tptp.subset A E)) (tptp.equal_set (tptp.intersection (tptp.difference E A) A) tptp.empty_set))))) (let ((_let_49 (not _let_47))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (not _let_48))) (let ((_let_52 (_let_25))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_16)) :args ((or _let_19 _let_13 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 0)) (CONG (REFL :args (_let_20)) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_15))) :args _let_39)) :args ((or _let_15 _let_20))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_52)) :args _let_52)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_21))) (REFL :args (_let_22)) :args _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_24)) :args ((or _let_23 _let_25 (not _let_24)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_43)) :args ((or _let_42 _let_44 (not _let_43)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_47 1)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_50) :args (_let_51))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_48))) (REFL :args (_let_49)) :args _let_39)) _let_50 :args (_let_49 true _let_48)) :args ((not _let_42) true _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_14 tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_45)) _let_46 :args (_let_43 false _let_5)) :args (_let_44 true _let_42 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_33)) :args ((or _let_30 _let_40 (not _let_33)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_41)) :args _let_41)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_32))) (REFL :args ((not _let_36))) :args _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 0)) (CONG (REFL :args (_let_36)) (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_39)) :args ((or _let_34 _let_36))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X tptp.empty_set) false))))) :args _let_37)) _let_38 :args (_let_35 false _let_3)) :args (_let_36 true _let_34)) :args (_let_32 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.empty_set _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_33 false _let_26)) :args (_let_30 false _let_32 false _let_33)) :args ((not _let_23) true _let_31 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (_let_14 tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_24 false _let_26)) :args (_let_25 true _let_23 false _let_24)) :args (_let_22 true _let_21)) :args (_let_15 true _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((tptp.member X (tptp.intersection A B))))) :args _let_17)) _let_18 :args (_let_16 false _let_4)) :args (_let_13 false _let_15 false _let_16)))) (let ((_let_54 (not _let_13))) (let ((_let_55 (not _let_11))) (let ((_let_56 (_let_2))) (let ((_let_57 (ASSUME :args _let_56))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_12)) :args ((or (not _let_8) _let_11 (not _let_12)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.member B (tptp.difference E A))))) :args _let_56)) _let_57 :args (_let_12 false _let_2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_11 1)) :args ((or _let_10 _let_55))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_13 1)) :args ((or _let_9 _let_54))) _let_53 :args (_let_9 false _let_13)) :args (_let_55 false _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_13 0)) :args ((or _let_8 _let_54))) _let_53 :args (_let_8 false _let_13)) :args (false false _let_12 true _let_11 false _let_8)) :args (_let_6 _let_5 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) _let_4 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))) _let_3 _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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.54 )
% 0.20/0.54 % SZS output end Proof for SET696+4
% 0.20/0.54 % cvc5---1.0.5 exiting
% 0.20/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------