%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET765+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n027.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 14:40:15 EDT 2023

% Result   : Theorem 0.20s 0.56s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET765+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.17/0.35  % Computer : n027.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit   : 300
% 0.17/0.35  % WCLimit    : 300
% 0.17/0.35  % DateTime   : Sat Aug 26 15:04:50 EDT 2023
% 0.17/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.56  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.rHYHbjczkr/cvc5---1.0.5_29987.p...
% 0.20/0.56  ------- get file name : TPTP file name is SET765+4
% 0.20/0.56  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_29987.smt2...
% 0.20/0.56  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.56  % SZS status Theorem for SET765+4
% 0.20/0.56  % SZS output start Proof for SET765+4
% 0.20/0.56  (
% 0.20/0.56  (let ((_let_1 (not (forall ((E $$unsorted) (R $$unsorted) (X $$unsorted)) (=> (and (tptp.equivalence R E) (tptp.subset X E)) (tptp.equivalence R X)))))) (let ((_let_2 (forall ((A $$unsorted) (R $$unsorted)) (= (tptp.equivalence R A) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A)) (=> (tptp.apply R X Y) (tptp.apply R Y X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A) (tptp.member Z A)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y Z)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Z))))) (let ((_let_5 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_6 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_13 _let_11 _let_9 _let_7 _let_5))) (let ((_let_17 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y X))))) (let ((_let_18 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X X))))) (let ((_let_19 (and _let_18 _let_17 _let_4))) (let ((_let_20 (tptp.equivalence SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_21 (= _let_20 _let_19))) (let ((_let_22 (forall ((A $$unsorted) (R $$unsorted)) (= (tptp.equivalence R A) (and (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y A)) (not (tptp.apply R X Y)) (tptp.apply R Y X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y A)) (not (tptp.member Z A)) (not (tptp.apply R X Y)) (not (tptp.apply R Y Z)) (tptp.apply R X Z)))))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (_let_22))) (let ((_let_25 ((tptp.equivalence R A)))) (let ((_let_26 (tptp.equivalence SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_27 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (not _let_27))) (let ((_let_29 (not _let_20))) (let ((_let_30 (or _let_29 _let_28 _let_26))) (let ((_let_31 (forall ((E $$unsorted) (R $$unsorted) (X $$unsorted)) (or (not (tptp.equivalence R E)) (not (tptp.subset X E)) (tptp.equivalence R X))))) (let ((_let_32 (not _let_30))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (or))) (let ((_let_35 (not _let_31))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_33) :args (_let_35))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_31))) (REFL :args (_let_32)) :args _let_34)) _let_33 :args (_let_32 true _let_31)))) (let ((_let_37 (REFL :args (_let_30)))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_21)) :args ((or _let_29 _let_19 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_20))) :args _let_34)) :args ((or _let_20 _let_30))) _let_36 :args (_let_20 true _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24)) _let_23 :args (_let_21 false _let_22)) :args (_let_19 false _let_20 false _let_21)))) (let ((_let_39 (not _let_19))) (let ((_let_40 (not _let_16))) (let ((_let_41 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_13 _let_15 _let_42 _let_8))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_19 1)) :args ((or _let_17 _let_39))) _let_38 :args (_let_17 false _let_19)))) (let ((_let_45 (_let_17))) (let ((_let_46 ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y) false))))) (let ((_let_47 (ASSUME :args _let_45))) (let ((_let_48 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_14))) (let ((_let_51 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_52 (= _let_27 _let_51))) (let ((_let_53 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_52)) :args ((or _let_28 _let_51 (not _let_52)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 1)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_34)) :args ((or _let_27 _let_30))) _let_36 :args (_let_27 true _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args (_let_53))) _let_54 :args (_let_52 false _let_53)) :args (_let_51 false _let_27 false _let_52)))) (let ((_let_56 (_let_51))) (let ((_let_57 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false))))) (let ((_let_58 (ASSUME :args _let_56))) (let ((_let_59 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_60 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_61 (not _let_60))) (let ((_let_62 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_63 (not _let_62))) (let ((_let_64 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 _let_63 _let_49 _let_61 _let_42 _let_59))) (let ((_let_67 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y Z)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Z))))) (let ((_let_68 (not _let_66))) (let ((_let_69 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y X))))) (let ((_let_70 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X X))))) (let ((_let_71 (and _let_70 _let_69 _let_67))) (let ((_let_72 (not _let_67))) (let ((_let_73 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_74 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_75 (not _let_74))) (let ((_let_76 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_77 (not _let_76))) (let ((_let_78 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_79 (not _let_78))) (let ((_let_80 (or _let_79 _let_77 _let_75 _let_73))) (let ((_let_81 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_82 (or _let_79 _let_81))) (let ((_let_83 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_84 (or _let_77 _let_83))) (let ((_let_85 (not _let_83))) (let ((_let_86 (not _let_81))) (let ((_let_87 (or _let_86 _let_85 _let_75 _let_73))) (let ((_let_88 (REFL :args (_let_80)))) (let ((_let_89 (not _let_69))) (let ((_let_90 (_let_89))) (let ((_let_91 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_92 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_93 (not _let_92))) (let ((_let_94 (or _let_93 _let_91))) (let ((_let_95 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_96 (or _let_93 _let_95))) (let ((_let_97 (not _let_95))) (let ((_let_98 (or _let_97 _let_91))) (let ((_let_99 (_let_18))) (let ((_let_100 (not _let_70))) (let ((_let_101 (_let_100))) (let ((_let_102 (= _let_26 _let_71))) (let ((_let_103 (not _let_71))) (let ((_let_104 (_let_72))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_104)) :args _let_104)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_67))) (REFL :args (_let_68)) :args _let_34)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_102)) :args ((or _let_26 _let_103 (not _let_102)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_30 2)) _let_36 :args ((not _let_26) true _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24)) _let_23 :args (_let_102 false _let_22)) :args (_let_103 true _let_26 false _let_102)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_101)) :args _let_101)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_70))) (REFL :args ((not _let_94))) :args _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_91 _let_97 (not _let_98)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_99) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X X) true))))) :args _let_99)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_19 0)) :args ((or _let_18 _let_39))) _let_38 :args (_let_18 false _let_19)) :args (_let_98 false _let_18)) (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_93 _let_95 (not _let_96)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_57)) :args _let_56)) _let_55 :args (_let_96 false _let_51)) (CNF_OR_NEG :args (_let_94 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_94 0)) (CONG (REFL :args (_let_94)) (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_92))) :args _let_34)) :args ((or _let_92 _let_94))) :args (_let_94 false _let_98 false _let_95 false _let_96 true _let_91 false _let_92)) :args (_let_70 false _let_94)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_90)) :args _let_90)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_89) _let_69))) (REFL :args ((not _let_80))) :args _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_75 _let_73 _let_86 _let_85 (not _let_87)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_45)) _let_44 :args (_let_87 false _let_17)) (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_77 _let_83 (not _let_84)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_57)) :args _let_56)) _let_55 :args (_let_84 false _let_51)) (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_79 _let_81 (not _let_82)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_57)) :args _let_56)) _let_55 :args (_let_82 false _let_51)) (CNF_OR_NEG :args (_let_80 3)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_80 2)) (CONG _let_88 (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_74))) :args _let_34)) :args ((or _let_74 _let_80))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_80 1)) (CONG _let_88 (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_76))) :args _let_34)) :args ((or _let_76 _let_80))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_80 0)) (CONG _let_88 (MACRO_SR_PRED_INTRO :args ((= (not _let_79) _let_78))) :args _let_34)) :args ((or _let_78 _let_80))) :args (_let_80 false _let_87 false _let_83 false _let_84 false _let_81 false _let_82 true _let_73 false _let_74 false _let_76 false _let_78)) :args (_let_69 false _let_80)) :args (_let_72 true _let_71 false _let_70 false _let_69)) :args (_let_68 true _let_67)))) (let ((_let_106 (REFL :args (_let_66)))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_49 _let_14 (not _let_50)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 2)) (CONG _let_106 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_34)) :args ((or _let_48 _let_66))) _let_105 :args (_let_48 true _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_57)) :args _let_56)) _let_55 :args (_let_50 false _let_51)) :args (_let_14 false _let_48 false _let_50)))) (let ((_let_108 (or _let_63 _let_12))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_108)) :args ((or _let_63 _let_12 (not _let_108)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 1)) (CONG _let_106 (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_62))) :args _let_34)) :args ((or _let_62 _let_66))) _let_105 :args (_let_62 true _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_57)) :args _let_56)) _let_55 :args (_let_108 false _let_51)) :args (_let_12 false _let_62 false _let_108)))) (let ((_let_110 (or _let_11 _let_13 _let_61 _let_6))) (let ((_let_111 (or _let_65 _let_10))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_111)) :args ((or _let_65 _let_10 (not _let_111)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 0)) (CONG _let_106 (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_64))) :args _let_34)) :args ((or _let_64 _let_66))) _let_105 :args (_let_64 true _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_57)) :args _let_56)) _let_55 :args (_let_111 false _let_51)) :args (_let_10 false _let_64 false _let_111)))) (let ((_let_113 (not _let_5))) (let ((_let_114 (or _let_15 _let_11 _let_113 _let_59))) (let ((_let_115 (_let_4))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_115) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Z) true)) (not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y) false))))) :args _let_115)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_11 _let_13 _let_15 _let_5 _let_7 _let_9 _let_40))) _let_112 _let_109 _let_107 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_59 _let_11 _let_15 _let_113 (not _let_114)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_66 5)) _let_105 :args ((not _let_59) true _let_66)) _let_112 _let_107 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y X) true))))) :args _let_45)) _let_44 :args (_let_114 false _let_17)) :args (_let_113 true _let_59 false _let_10 false _let_14 false _let_114)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_110)) :args ((or _let_61 _let_11 _let_13 _let_6 (not _let_110)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 3)) (CONG _let_106 (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_60))) :args _let_34)) :args ((or _let_60 _let_66))) _let_105 :args (_let_60 true _let_66)) _let_112 _let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_45)) _let_44 :args (_let_110 false _let_17)) :args (_let_6 false _let_60 false _let_10 false _let_12 false _let_110)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_42 _let_13 _let_15 _let_8 (not _let_43)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 4)) (CONG _let_106 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_34)) :args ((or _let_41 _let_66))) _let_105 :args (_let_41 true _let_66)) _let_109 _let_107 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_45)) _let_44 :args (_let_43 false _let_17)) :args (_let_8 false _let_41 false _let_12 false _let_14 false _let_43)) :args (_let_40 false _let_10 false _let_12 false _let_14 true _let_5 false _let_6 false _let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_19 2)) :args ((or _let_4 _let_39))) _let_38 :args (_let_4 false _let_19)) :args (false true _let_16 false _let_4)) :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))) (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))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (not (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.member X B)))))) (forall ((A $$unsorted) (E $$unsorted)) (= (tptp.partition A E) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.subset X E))) (forall ((X $$unsorted)) (=> (tptp.member X E) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A)) (=> (exists ((Z $$unsorted)) (and (tptp.member Z X) (tptp.member Z Y))) (= X Y))))))) _let_2 (forall ((R $$unsorted) (E $$unsorted) (A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.equivalence_class A E R)) (and (tptp.member X E) (tptp.apply R A X)))) (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.pre_order R E) (and (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.56  )
% 0.20/0.56  % SZS output end Proof for SET765+4
% 0.20/0.56  % cvc5---1.0.5 exiting
% 0.20/0.57  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------