%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET816+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n018.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 14:40:26 EDT 2023

% Result   : Theorem 135.16s 135.37s
% Output   : Proof 135.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET816+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n018.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 16:43:15 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 135.16/135.37  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.YM3NcF4LUk/cvc5---1.0.5_23711.p...
% 135.16/135.37  ------- get file name : TPTP file name is SET816+4
% 135.16/135.37  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_23711.smt2...
% 135.16/135.37  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 135.16/135.37  --- Run --no-e-matching --full-saturate-quant at 5...
% 135.16/135.37  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 135.16/135.37  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 135.16/135.37  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 135.16/135.37  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 135.16/135.37  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 135.16/135.37  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 135.16/135.37  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 135.16/135.37  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 135.16/135.37  --- Run --relevant-triggers --full-saturate-quant at 5...
% 135.16/135.37  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 135.16/135.37  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 135.16/135.37  --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 135.16/135.37  --- Run --no-cbqi --full-saturate-quant at 10...
% 135.16/135.37  --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 135.16/135.37  % SZS status Theorem for SET816+4
% 135.16/135.37  % SZS output start Proof for SET816+4
% 135.16/135.37  (
% 135.16/135.37  (let ((_let_1 (not (forall ((A $$unsorted)) (=> (tptp.subset A tptp.on) (tptp.subset (tptp.sum A) tptp.on)))))) (let ((_let_2 (forall ((X $$unsorted)) (=> (tptp.set X) (forall ((Y $$unsorted)) (=> (tptp.member Y X) (tptp.set Y))))))) (let ((_let_3 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_order R E) (and (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E)) (not (and (tptp.apply R X Y) (tptp.apply R Y X))))) (forall ((X $$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 ((_let_4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.apply tptp.member_predicate X Y) (tptp.member X Y))))) (let ((_let_5 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.least M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (tptp.member X E) (or (= M X) (tptp.apply R M X))))))))) (let ((_let_6 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_well_order R E) (and (tptp.strict_order R E) (forall ((A $$unsorted)) (=> (and (tptp.subset A E) (exists ((X $$unsorted)) (tptp.member X A))) (exists ((Y $$unsorted)) (tptp.least Y R A))))))))) (let ((_let_7 (forall ((A $$unsorted)) (= (tptp.member A tptp.on) (and (tptp.set A) (tptp.strict_well_order tptp.member_predicate A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.subset X A)))))))) (let ((_let_8 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_11 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.apply tptp.member_predicate X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply tptp.member_predicate Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply tptp.member_predicate Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply tptp.member_predicate X Y)) (not (tptp.apply tptp.member_predicate Y Z)) (tptp.apply tptp.member_predicate X Z))))) (let ((_let_12 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_111 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_113))) (let ((_let_13 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_112 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_113))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_111 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_112))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_113 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_112 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_111 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_20 _let_18 _let_16 _let_14 _let_12))) (let ((_let_24 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.apply tptp.member_predicate X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply tptp.member_predicate Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply tptp.member_predicate X Y)) (not (tptp.apply tptp.member_predicate Y X)))))) (let ((_let_25 (forall ((A $$unsorted) (BOUND_VARIABLE_902 $$unsorted)) (or (not (forall ((X $$unsorted)) (or (not (tptp.apply tptp.member_predicate X A)) (tptp.apply tptp.member_predicate X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (not (tptp.apply tptp.member_predicate BOUND_VARIABLE_902 A)) (not (forall ((Y $$unsorted)) (or (not (tptp.apply tptp.member_predicate Y A)) (not (forall ((X $$unsorted)) (or (not (tptp.apply tptp.member_predicate X A)) (= Y X) (tptp.apply tptp.member_predicate Y X))))))))))) (let ((_let_26 (forall ((X $$unsorted) (BOUND_VARIABLE_1616 $$unsorted)) (or (not (tptp.apply tptp.member_predicate X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply tptp.member_predicate BOUND_VARIABLE_1616 X)) (tptp.apply tptp.member_predicate BOUND_VARIABLE_1616 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (let ((_let_27 (tptp.set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_28 (and _let_27 _let_26 _let_25 _let_24 _let_11))) (let ((_let_29 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.on))) (let ((_let_30 (= _let_29 _let_28))) (let ((_let_31 (forall ((A $$unsorted)) (= (and (tptp.set A) (forall ((X $$unsorted) (BOUND_VARIABLE_1616 $$unsorted)) (or (not (tptp.apply tptp.member_predicate X A)) (not (tptp.apply tptp.member_predicate BOUND_VARIABLE_1616 X)) (tptp.apply tptp.member_predicate BOUND_VARIABLE_1616 A))) (forall ((A $$unsorted) (BOUND_VARIABLE_902 $$unsorted)) (or (not (forall ((X $$unsorted)) (or (not (tptp.apply tptp.member_predicate X A)) (tptp.apply tptp.member_predicate X A)))) (not (tptp.apply tptp.member_predicate BOUND_VARIABLE_902 A)) (not (forall ((Y $$unsorted)) (or (not (tptp.apply tptp.member_predicate Y A)) (not (forall ((X $$unsorted)) (or (not (tptp.apply tptp.member_predicate X A)) (= Y X) (tptp.apply tptp.member_predicate Y X))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.apply tptp.member_predicate X A)) (not (tptp.apply tptp.member_predicate Y A)) (not (tptp.apply tptp.member_predicate X Y)) (not (tptp.apply tptp.member_predicate Y X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.apply tptp.member_predicate X A)) (not (tptp.apply tptp.member_predicate Y A)) (not (tptp.apply tptp.member_predicate Z A)) (not (tptp.apply tptp.member_predicate X Y)) (not (tptp.apply tptp.member_predicate Y Z)) (tptp.apply tptp.member_predicate X Z)))) (tptp.apply tptp.member_predicate A tptp.on))))) (let ((_let_32 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.subset (lambda ((BOUND_VARIABLE_976 $$unsorted) (BOUND_VARIABLE_977 $$unsorted)) (forall ((X $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_976)) (tptp.member X BOUND_VARIABLE_977))))))))) (let ((_let_33 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO _let_32 :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.equal_set (lambda ((BOUND_VARIABLE_1006 $$unsorted) (BOUND_VARIABLE_1007 $$unsorted)) (and (forall ((X $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1006)) (tptp.member X BOUND_VARIABLE_1007))) (forall ((X $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1007)) (tptp.member X BOUND_VARIABLE_1006)))))))))) (let ((_let_34 (TRUST_SUBS_EQ (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_33 _let_32) :args ((forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_well_order R E) (and (tptp.strict_order R E) (forall ((A $$unsorted) (BOUND_VARIABLE_902 $$unsorted)) (or (not (tptp.subset A E)) (not (tptp.member BOUND_VARIABLE_902 A)) (not (forall ((Y $$unsorted)) (not (tptp.least Y R A))))))))) SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.strict_well_order (lambda ((BOUND_VARIABLE_1080 $$unsorted) (BOUND_VARIABLE_1081 $$unsorted)) (and (tptp.strict_order BOUND_VARIABLE_1080 BOUND_VARIABLE_1081) (forall ((A $$unsorted) (BOUND_VARIABLE_902 $$unsorted)) (or (not (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X BOUND_VARIABLE_1081)))) (not (tptp.member BOUND_VARIABLE_902 A)) (not (forall ((Y $$unsorted)) (not (tptp.least Y BOUND_VARIABLE_1080 A))))))))))))) (let ((_let_35 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.least (lambda ((BOUND_VARIABLE_1099 $$unsorted) (BOUND_VARIABLE_1100 $$unsorted) (BOUND_VARIABLE_1101 $$unsorted)) (and (tptp.member BOUND_VARIABLE_1099 BOUND_VARIABLE_1101) (forall ((X $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1101)) (= BOUND_VARIABLE_1099 X) (tptp.apply BOUND_VARIABLE_1100 BOUND_VARIABLE_1099 X)))))))))) (let ((_let_36 (TRUST_SUBS_EQ (ASSUME :args (_let_4)) :args ((= tptp.member (lambda ((BOUND_VARIABLE_1121 $$unsorted) (BOUND_VARIABLE_1122 $$unsorted)) (tptp.apply tptp.member_predicate BOUND_VARIABLE_1121 BOUND_VARIABLE_1122))))))) (let ((_let_37 (AND_INTRO (TRUST_SUBS_EQ (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_36 _let_35 _let_34 _let_33 _let_32) :args ((forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_order R E) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X E)) (not (tptp.member Y E)) (not (tptp.apply R X Y)) (not (tptp.apply R Y X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X E)) (not (tptp.member Y E)) (not (tptp.member Z E)) (not (tptp.apply R X Y)) (not (tptp.apply R Y Z)) (tptp.apply R X Z)))))) SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.strict_order (lambda ((BOUND_VARIABLE_1165 $$unsorted) (BOUND_VARIABLE_1166 $$unsorted)) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.apply tptp.member_predicate X BOUND_VARIABLE_1166)) (not (tptp.apply tptp.member_predicate Y BOUND_VARIABLE_1166)) (not (tptp.apply BOUND_VARIABLE_1165 X Y)) (not (tptp.apply BOUND_VARIABLE_1165 Y X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.apply tptp.member_predicate X BOUND_VARIABLE_1166)) (not (tptp.apply tptp.member_predicate Y BOUND_VARIABLE_1166)) (not (tptp.apply tptp.member_predicate Z BOUND_VARIABLE_1166)) (not (tptp.apply BOUND_VARIABLE_1165 X Y)) (not (tptp.apply BOUND_VARIABLE_1165 Y Z)) (tptp.apply BOUND_VARIABLE_1165 X Z)))))))) _let_36 _let_35 _let_34 _let_33 _let_32))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_7)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_37 :args ((forall ((A $$unsorted)) (= (tptp.member A tptp.on) (and (tptp.set A) (tptp.strict_well_order tptp.member_predicate A) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.subset X A)))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_39 (_let_31))) (let ((_let_40 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_29))) (let ((_let_43 (forall ((X $$unsorted)) (or (not (tptp.apply tptp.member_predicate X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.apply tptp.member_predicate X tptp.on))))) (let ((_let_44 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.on))) (let ((_let_45 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_46 (not _let_45))) (let ((_let_47 (not _let_43))) (let ((_let_48 (or _let_47 _let_46 _let_44))) (let ((_let_49 (forall ((A $$unsorted) (BOUND_VARIABLE_1306 $$unsorted)) (or (not (forall ((X $$unsorted)) (or (not (tptp.apply tptp.member_predicate X A)) (tptp.apply tptp.member_predicate X tptp.on)))) (not (tptp.apply tptp.member_predicate BOUND_VARIABLE_1306 (tptp.sum A))) (tptp.apply tptp.member_predicate BOUND_VARIABLE_1306 tptp.on))))) (let ((_let_50 (not _let_48))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_37 :args ((not (forall ((A $$unsorted)) (or (not (tptp.subset A tptp.on)) (tptp.subset (tptp.sum A) tptp.on)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_52 (or))) (let ((_let_53 (not _let_49))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_51) :args (_let_53))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_49))) (REFL :args (_let_50)) :args _let_52)) _let_51 :args (_let_50 true _let_49)))) (let ((_let_55 (REFL :args (_let_48)))) (let ((_let_56 (_let_43))) (let ((_let_57 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_41 _let_58))) (let ((_let_60 (forall ((Y $$unsorted)) (or (not (tptp.apply tptp.member_predicate Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y)))))) (let ((_let_61 (not _let_59))) (let ((_let_62 (not _let_60))) (let ((_let_63 (= _let_45 _let_62))) (let ((_let_64 (forall ((X $$unsorted) (A $$unsorted)) (= (not (forall ((Y $$unsorted)) (or (not (tptp.apply tptp.member_predicate Y A)) (not (tptp.apply tptp.member_predicate X Y))))) (tptp.apply tptp.member_predicate X (tptp.sum A)))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_37 :args ((forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y A)) (not (tptp.member X Y))))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_66 (_let_62))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_66)) :args _let_66)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_60))) (REFL :args (_let_61)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_63)) :args ((or _let_46 _let_62 (not _let_63)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 1)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_52)) :args ((or _let_45 _let_48))) _let_54 :args (_let_45 true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_65 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((tptp.apply tptp.member_predicate X (tptp.sum A))))) :args (_let_64)))) _let_65 :args (_let_63 false _let_64)) :args (_let_62 false _let_45 false _let_63)) :args (_let_61 true _let_60)))) (let ((_let_68 (REFL :args (_let_59)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_30)) :args ((or (not _let_29) _let_28 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_29 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 0)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_52)) :args ((or _let_40 _let_59))) _let_67 :args (_let_40 true _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_56) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.apply tptp.member_predicate X 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(MACRO_SR_PRED_INTRO :args ((= (not _let_128) _let_127))) :args _let_52)) :args ((or _let_127 _let_131))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_131 0)) (CONG _let_143 (MACRO_SR_PRED_INTRO :args ((= (not _let_130) _let_129))) :args _let_52)) :args ((or _let_129 _let_131))) :args (_let_131 false _let_142 false _let_132 true _let_139 false _let_133 true _let_140 true _let_136 false _let_138 false _let_135 false _let_125 false _let_127 false _let_129)) :args (_let_100 false _let_131)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_124)) :args _let_124)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_123) _let_99))) (REFL :args ((not _let_113))) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_108 _let_106 _let_118 _let_119 (not _let_120)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_122) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.apply tptp.member_predicate X Y) false))))) :args _let_122)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_28 3)) :args ((or _let_24 _let_70))) _let_69 :args (_let_24 false _let_28)) :args (_let_120 false _let_24)) (REORDERING (CNF_OR_POS :args (_let_117)) :args ((or _let_110 _let_116 (not _let_117)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_90)) :args _let_89)) _let_88 :args (_let_117 false _let_76)) (REORDERING (CNF_OR_POS :args (_let_115)) :args ((or _let_112 _let_114 (not _let_115)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_90)) :args _let_89)) _let_88 :args (_let_115 false _let_76)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 3)) (CONG _let_121 (MACRO_SR_PRED_INTRO :args ((= (not _let_106) _let_105))) :args _let_52)) :args ((or _let_105 _let_113))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 2)) (CONG _let_121 (MACRO_SR_PRED_INTRO :args ((= (not _let_108) _let_107))) :args _let_52)) :args ((or _let_107 _let_113))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 1)) (CONG _let_121 (MACRO_SR_PRED_INTRO :args ((= (not _let_110) _let_109))) :args _let_52)) :args ((or _let_109 _let_113))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 0)) (CONG _let_121 (MACRO_SR_PRED_INTRO :args ((= (not _let_112) _let_111))) :args _let_52)) :args ((or _let_111 _let_113))) :args (_let_113 false _let_120 false _let_116 false _let_117 false _let_114 false _let_115 false _let_105 false _let_107 false _let_109 false _let_111)) :args (_let_99 false _let_113)) :args (_let_104 true _let_103 false _let_102 false _let_101 false _let_100 false _let_99)) :args (_let_98 true _let_97)))) (let ((_let_176 (REFL :args (_let_96)))) (let ((_let_177 (or _let_93 _let_17))) (let ((_let_178 (or _let_95 _let_19))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_165 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_111 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_112 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_113 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_164)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_16 _let_14 _let_12 _let_20 _let_18 _let_22 _let_72))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_96 3)) (CONG _let_176 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_52)) :args ((or _let_15 _let_96))) _let_175 :args (_let_15 true _let_96)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_96 4)) (CONG _let_176 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_52)) :args ((or _let_13 _let_96))) _let_175 :args (_let_13 true _let_96)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_96 5)) _let_175 :args ((not _let_12) true _let_96)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_178)) :args ((or _let_95 _let_19 (not _let_178)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_96 1)) (CONG _let_176 (MACRO_SR_PRED_INTRO :args ((= (not _let_95) _let_94))) :args _let_52)) :args ((or _let_94 _let_96))) _let_175 :args (_let_94 true _let_96)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_112 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_90)) :args _let_89)) _let_88 :args (_let_178 false _let_76)) :args (_let_19 false _let_94 false _let_178)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_177)) :args ((or _let_93 _let_17 (not _let_177)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_96 2)) (CONG _let_176 (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_92))) :args _let_52)) :args ((or _let_92 _let_96))) _let_175 :args (_let_92 true _let_96)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_113 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_90)) :args _let_89)) _let_88 :args (_let_177 false _let_76)) :args (_let_17 false _let_92 false _let_177)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_74 _let_21 (not _let_75)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_96 0)) (CONG _let_176 (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_73))) :args _let_52)) :args ((or _let_73 _let_96))) _let_175 :args (_let_73 true _let_96)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_111 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_90)) :args _let_89)) _let_88 :args (_let_75 false _let_76)) :args (_let_21 false _let_73 false _let_75)) :args (_let_72 false _let_15 false _let_13 true _let_12 false _let_19 false _let_17 false _let_21)) _let_71 :args (false true _let_23 false _let_11)) :args (_let_10 _let_9 (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 $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) _let_8 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 (forall ((X $$unsorted) (R $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.initial_segment X R A)) (and (tptp.member Y A) (tptp.apply R Y X)))) (forall ((A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.suc A)) (tptp.member X (tptp.union A (tptp.singleton A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 135.16/135.41  )
% 135.16/135.41  % SZS output end Proof for SET816+4
% 135.16/135.41  % cvc5---1.0.5 exiting
% 135.16/135.42  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------