%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET695+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n014.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 0.21s 0.67s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET695+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n014.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 09:44:32 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.67  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ekHTYK0faH/cvc5---1.0.5_10510.p...
% 0.21/0.67  ------- get file name : TPTP file name is SET695+4
% 0.21/0.67  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10510.smt2...
% 0.21/0.67  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.67  % SZS status Theorem for SET695+4
% 0.21/0.67  % SZS output start Proof for SET695+4
% 0.21/0.67  (
% 0.21/0.67  (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted) (E $$unsorted)) (=> (and (tptp.subset A E) (tptp.subset B E)) (= (tptp.subset A B) (tptp.subset (tptp.difference E B) (tptp.difference E A)))))))) (let ((_let_2 (forall ((B $$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.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_4 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_5 (not _let_4))) (let ((_let_6 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_7 (and _let_6 _let_5))) (let ((_let_8 (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_9 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 _let_8))) (let ((_let_10 (= _let_9 _let_7))) (let ((_let_11 (not _let_7))) (let ((_let_12 (_let_2))) (let ((_let_13 (ASSUME :args _let_12))) (let ((_let_14 ((tptp.member B (tptp.difference E A))))) (let ((_let_15 (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 _let_15))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_9))) (let ((_let_19 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member X (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (let ((_let_20 (not _let_18))) (let ((_let_21 (tptp.subset _let_15 _let_8))) (let ((_let_22 (= _let_21 _let_19))) (let ((_let_23 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_8))) (let ((_let_24 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_15))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23))) (let ((_let_27 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_28 (= _let_27 _let_21))) (let ((_let_29 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_30 (= _let_27 _let_29))) (let ((_let_31 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_32 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31))) (let ((_let_35 (not _let_31))) (let ((_let_36 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_37 (and _let_36 _let_35))) (let ((_let_38 (and _let_36 _let_33))) (let ((_let_39 (= _let_24 _let_37))) (let ((_let_40 (= _let_23 _let_38))) (let ((_let_41 (not _let_19))) (let ((_let_42 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (_let_42))) (let ((_let_45 ((tptp.subset A B)))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (_let_15 _let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_45)) :args _let_44)) _let_43 :args (_let_22 false _let_42)))) (let ((_let_47 (not _let_22))) (let ((_let_48 (_let_22))) (let ((_let_49 (_let_19))) (let ((_let_50 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 (not (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_28))) (let ((_let_53 (forall ((A $$unsorted) (B $$unsorted) (E $$unsorted)) (or (not (tptp.subset A E)) (not (tptp.subset B E)) (= (tptp.subset A B) (tptp.subset (tptp.difference E B) (tptp.difference E A))))))) (let ((_let_54 (not _let_52))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (or))) (let ((_let_57 (not _let_53))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_55) :args (_let_57))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_53))) (REFL :args (_let_54)) :args _let_56)) _let_55 :args (_let_54 true _let_53)))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_52 2)) _let_58 :args ((not _let_28) true _let_52)))) (let ((_let_60 (_let_28))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_45)) :args _let_44)) _let_43 :args (_let_30 false _let_42)))) (let ((_let_62 (not _let_30))) (let ((_let_63 (not _let_29))) (let ((_let_64 (_let_30))) (let ((_let_65 (_let_63))) (let ((_let_66 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG (REFL :args (_let_34)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_56)) :args ((or _let_32 _let_34))))) (let ((_let_67 (or _let_33 _let_36))) (let ((_let_68 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_69 (= _let_50 _let_68))) (let ((_let_70 (_let_68))) (let ((_let_71 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) (let ((_let_72 (not _let_36))) (let ((_let_73 (_let_37))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_23 (not _let_26)))) (REORDERING (CNF_EQUIV_POS1 :args (_let_40)) :args ((or (not _let_23) _let_38 (not _let_40)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_40 false _let_2)) (REORDERING (CNF_EQUIV_POS2 :args (_let_39)) :args ((or _let_24 (not _let_37) (not _let_39)))) (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_39 false _let_2)) (REORDERING (CNF_AND_POS :args (_let_38 1)) :args ((or _let_33 (not _let_38)))) (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_35) _let_31))) :args _let_56)) :args ((or _let_31 _let_72 _let_37))) (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_33 _let_36 (not _let_67)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_70) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_69)) :args ((or _let_51 _let_68 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 0)) (CONG (REFL :args (_let_52)) (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_56)) :args ((or _let_50 _let_52))) _let_58 :args (_let_50 true _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_45)) :args _let_44)) _let_43 :args (_let_69 false _let_42)) :args (_let_68 false _let_50 false _let_69)) :args (_let_67 false _let_68)) (CNF_OR_NEG :args (_let_34 1)) _let_66 :args ((or _let_34 _let_37) false _let_36 false _let_67 true _let_31 false _let_32)) _let_66 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_65)) :args _let_65)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_29))) (REFL :args ((not _let_34))) :args _let_56)) (REORDERING (CNF_EQUIV_POS2 :args _let_64) :args ((or _let_27 _let_63 _let_62))) _let_61 (CNF_EQUIV_NEG2 :args _let_60) _let_59 (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_49) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X _let_15) false))))) :args _let_49)) (REORDERING (CNF_EQUIV_POS2 :args _let_48) :args ((or _let_21 _let_41 _let_47))) _let_46 :args (_let_41 true _let_23 false _let_40 false _let_24 false _let_39 true _let_38 false _let_37 false _let_32 true _let_34 true _let_29 false _let_30 true _let_27 true _let_28 false _let_26 false _let_21 false _let_22)))) (let ((_let_75 (_let_41))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_75)) :args _let_75)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_19))) (REFL :args (_let_20)) :args _let_56)) _let_74 :args (_let_20 true _let_19)))) (let ((_let_77 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_78 (not _let_77))) (let ((_let_79 (and _let_6 _let_78))) (let ((_let_80 (= _let_16 _let_79))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_80)) :args ((or _let_17 _let_79 (not _let_80)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 0)) (CONG (REFL :args (_let_18)) (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_56)) :args ((or _let_16 _let_18))) _let_76 :args (_let_16 true _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_80 false _let_2)) :args (_let_79 false _let_16 false _let_80)))) (let ((_let_82 (not _let_79))) (let ((_let_83 (or _let_5 _let_77))) (let ((_let_84 (not _let_21))) (let ((_let_85 (_let_29))) (let ((_let_86 (not _let_6))) (let ((_let_87 (_let_7))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_87) (CONG (REFL :args _let_87) (REFL :args (_let_86)) (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) :args _let_56)) :args ((or _let_4 _let_7 _let_86))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_77 _let_5 (not _let_83)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_79 1)) :args ((or _let_78 _let_82))) _let_81 :args (_let_78 false _let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_85) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_85)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_64) :args ((or (not _let_27) _let_29 _let_62))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_60) :args ((or _let_27 _let_21 _let_28))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_48) :args ((or _let_84 _let_19 _let_47))) _let_74 _let_46 :args (_let_84 true _let_19 false _let_22)) _let_59 :args (_let_27 true _let_21 true _let_28)) _let_61 :args (_let_29 false _let_27 false _let_30)) :args (_let_83 false _let_29)) :args (_let_5 true _let_77 false _let_83)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_79 0)) :args ((or _let_6 _let_82))) _let_81 :args (_let_6 false _let_79)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_10)) :args ((or _let_9 _let_11 (not _let_10)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_18 1)) _let_76 :args ((not _let_9) true _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_10 false _let_2)) :args (_let_11 true _let_9 false _let_10)) :args (false true _let_4 false _let_6 true _let_7)) :args (_let_3 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))) (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.68  )
% 0.21/0.68  % SZS output end Proof for SET695+4
% 0.21/0.68  % cvc5---1.0.5 exiting
% 0.21/0.68  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------