TSTP Solution File: SET680+3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET680+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 14:39:53 EDT 2023
% Result : Theorem 228.66s 228.89s
% Output : Proof 228.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET680+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n003.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 09:40:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 228.66/228.89 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.i9fhWtjGMk/cvc5---1.0.5_15489.p...
% 228.66/228.89 ------- get file name : TPTP file name is SET680+3
% 228.66/228.89 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15489.smt2...
% 228.66/228.89 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 228.66/228.89 --- Run --no-e-matching --full-saturate-quant at 5...
% 228.66/228.89 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 228.66/228.89 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 228.66/228.89 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 228.66/228.89 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 228.66/228.89 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 228.66/228.89 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 228.66/228.89 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 228.66/228.89 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 228.66/228.89 --- Run --relevant-triggers --full-saturate-quant at 5...
% 228.66/228.89 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 228.66/228.89 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 228.66/228.89 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 228.66/228.89 --- Run --no-cbqi --full-saturate-quant at 10...
% 228.66/228.89 --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 228.66/228.89 % SZS status Theorem for SET680+3
% 228.66/228.89 % SZS output start Proof for SET680+3
% 228.66/228.89 (
% 228.66/228.89 (let ((_let_1 (not (forall ((B $$unsorted)) (=> (and (not (tptp.empty B)) (tptp.ilf_type B tptp.set_type)) (forall ((C $$unsorted)) (=> (and (not (tptp.empty C)) (tptp.ilf_type C tptp.set_type)) (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.relation_type B C)) (forall ((E $$unsorted)) (=> (tptp.ilf_type E (tptp.member_type B)) (= (tptp.member E (tptp.domain B C D)) (exists ((F $$unsorted)) (and (tptp.ilf_type F (tptp.member_type C)) (tptp.member (tptp.ordered_pair E F) D))))))))))))))) (let ((_let_2 (forall ((B $$unsorted)) (tptp.ilf_type B tptp.set_type)))) (let ((_let_3 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.relation_type B C)) (= (tptp.domain B C D) (tptp.domain_of D)))))))))) (let ((_let_4 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.subset_type (tptp.cross_product B C))) (tptp.relation_like D))))))))) (let ((_let_5 (forall ((B $$unsorted)) (let ((_let_1 (tptp.ilf_type B tptp.set_type))) (=> _let_1 (= (tptp.ilf_type B tptp.binary_relation_type) (and (tptp.relation_like B) _let_1))))))) (let ((_let_6 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (and (not (tptp.empty C)) (tptp.ilf_type C tptp.set_type)) (= (tptp.ilf_type B (tptp.member_type C)) (tptp.member B C)))))))) (let ((_let_7 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (and (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.subset_type (tptp.cross_product B C))) (tptp.ilf_type D (tptp.relation_type B C)))) (forall ((E $$unsorted)) (=> (tptp.ilf_type E (tptp.relation_type B C)) (tptp.ilf_type E (tptp.subset_type (tptp.cross_product B C)))))))))))) (let ((_let_8 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (forall ((E $$unsorted)) (=> (tptp.ilf_type E tptp.set_type) (forall ((F $$unsorted)) (=> (tptp.ilf_type F (tptp.relation_type B C)) (=> (tptp.member (tptp.ordered_pair D E) F) (and (tptp.member D B) (tptp.member E C))))))))))))))) (let ((_let_9 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.binary_relation_type) (=> (tptp.member (tptp.ordered_pair B C) D) (and (tptp.member B (tptp.domain_of D)) (tptp.member C (tptp.range_of D)))))))))))) (let ((_let_10 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.binary_relation_type) (= (tptp.member B (tptp.domain_of C)) (exists ((D $$unsorted)) (and (tptp.ilf_type D tptp.set_type) (tptp.member (tptp.ordered_pair B D) C)))))))))) (let ((_let_11 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_252 tptp.set_type))) (let ((_let_12 (_let_2))) (let ((_let_13 (ASSUME :args _let_12))) (let ((_let_14 (tptp.domain_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_15 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_14))) (let ((_let_16 (and _let_15 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_252 (tptp.range_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_17 (tptp.member (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_252) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.binary_relation_type))) (let ((_let_20 (not _let_19))) (let ((_let_21 (not _let_11))) (let ((_let_22 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.set_type))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_20 _let_18 _let_16))) (let ((_let_25 (forall ((B $$unsorted) (BOUND_VARIABLE_1192 $$unsorted) (BOUND_VARIABLE_1190 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1190 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1192 tptp.binary_relation_type)) (not (tptp.member (tptp.ordered_pair B BOUND_VARIABLE_1190) BOUND_VARIABLE_1192)) (and (tptp.member B (tptp.domain_of BOUND_VARIABLE_1192)) (tptp.member BOUND_VARIABLE_1190 (tptp.range_of BOUND_VARIABLE_1192))))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (not _let_16))) (let ((_let_28 (tptp.domain SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_29 (= _let_28 _let_14))) (let ((_let_30 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_28))) (let ((_let_31 (not _let_15))) (let ((_let_32 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.set_type))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.set_type))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35 _let_33 _let_29))) (let ((_let_39 (forall ((B $$unsorted) (BOUND_VARIABLE_1857 $$unsorted) (BOUND_VARIABLE_1855 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1855 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1857 (tptp.relation_type B BOUND_VARIABLE_1855))) (= (tptp.domain B BOUND_VARIABLE_1855 BOUND_VARIABLE_1857) (tptp.domain_of BOUND_VARIABLE_1857)))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (forall ((F $$unsorted)) (or (not (tptp.ilf_type F (tptp.member_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (not (tptp.member (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 F) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_42 (not _let_41))) (let ((_let_43 (= _let_30 _let_42))) (let ((_let_44 (tptp.empty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_45 (or (tptp.empty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_37 _let_44 _let_35 _let_33 (not (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.member_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) _let_43))) (let ((_let_46 (forall ((B $$unsorted) (BOUND_VARIABLE_2084 $$unsorted) (BOUND_VARIABLE_2082 $$unsorted) (BOUND_VARIABLE_2080 $$unsorted)) (or (tptp.empty B) (not (tptp.ilf_type B tptp.set_type)) (tptp.empty BOUND_VARIABLE_2080) (not (tptp.ilf_type BOUND_VARIABLE_2080 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_2084 (tptp.relation_type B BOUND_VARIABLE_2080))) (not (tptp.ilf_type BOUND_VARIABLE_2082 (tptp.member_type B))) (= (tptp.member BOUND_VARIABLE_2082 (tptp.domain B BOUND_VARIABLE_2080 BOUND_VARIABLE_2084)) (not (forall ((F $$unsorted)) (or (not (tptp.ilf_type F (tptp.member_type BOUND_VARIABLE_2080))) (not (tptp.member (tptp.ordered_pair BOUND_VARIABLE_2082 F) BOUND_VARIABLE_2084)))))))))) (let ((_let_47 (not _let_45))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (or))) (let ((_let_50 (not _let_46))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_48) :args (_let_50))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_46))) (REFL :args (_let_47)) :args _let_49)) _let_48 :args (_let_47 true _let_46)))) (let ((_let_52 (REFL :args (_let_45)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 4)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_49)) :args ((or _let_32 _let_45))) _let_51 :args (_let_32 true _let_45)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 3)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_49)) :args ((or _let_34 _let_45))) _let_51 :args (_let_34 true _let_45)))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 1)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_49)) :args ((or _let_36 _let_45))) _let_51 :args (_let_36 true _let_45)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_35 _let_33 _let_29 (not _let_38)))) _let_55 _let_54 _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.ilf_type BOUND_VARIABLE_1857 (tptp.relation_type B BOUND_VARIABLE_1855)) false))))) :args (_let_39))) _let_40 :args (_let_38 false _let_39)) :args (_let_29 false _let_36 false _let_34 false _let_32 false _let_38)))) (let ((_let_57 (tptp.member (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_53) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_58 (not _let_57))) (let ((_let_59 (tptp.member_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_60 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_53 _let_59))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_58))) (let ((_let_63 (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_64 (not _let_63))) (let ((_let_65 (= _let_15 _let_64))) (let ((_let_66 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_53 tptp.set_type))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_67 _let_58))) (let ((_let_69 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_53 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_70 (= _let_60 _let_69))) (let ((_let_71 (or _let_67 _let_44 _let_35 _let_70))) (let ((_let_72 (and (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_69))) (let ((_let_73 (or _let_37 _let_35 _let_23 _let_67 _let_72 _let_33 _let_58))) (let ((_let_74 (not _let_30))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_45 6)) _let_51 :args ((not _let_43) true _let_45)))) (let ((_let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))))) (let ((_let_77 (_let_74))) (let ((_let_78 (_let_43))) (let ((_let_79 (and _let_30 _let_29))) (let ((_let_80 (_let_30 _let_29))) (let ((_let_81 (ASSUME :args (_let_30)))) (let ((_let_82 (ASSUME :args (_let_29)))) (let ((_let_83 (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (SYMM _let_82) :args (APPLY_UF tptp.member)))) (let ((_let_84 (_let_41))) (let ((_let_85 (or _let_23 _let_20 _let_65))) (let ((_let_86 (forall ((B $$unsorted) (BOUND_VARIABLE_1139 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1139 tptp.binary_relation_type)) (= (tptp.member B (tptp.domain_of BOUND_VARIABLE_1139)) (not (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member (tptp.ordered_pair B D) BOUND_VARIABLE_1139)))))))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.set_type))) (let ((_let_89 (tptp.relation_like SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_90 (and _let_89 _let_88))) (let ((_let_91 (= _let_19 _let_90))) (let ((_let_92 (not _let_88))) (let ((_let_93 (or _let_92 _let_91))) (let ((_let_94 (forall ((B $$unsorted)) (let ((_let_1 (tptp.ilf_type B tptp.set_type))) (or (not _let_1) (= (tptp.ilf_type B tptp.binary_relation_type) (and (tptp.relation_like B) _let_1))))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type B tptp.set_type) true))))) :args _let_12)) _let_13 :args (_let_88 false _let_2)))) (let ((_let_97 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.subset_type (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (let ((_let_98 (not _let_97))) (let ((_let_99 (or _let_37 _let_35 _let_98 _let_89))) (let ((_let_100 (forall ((B $$unsorted) (BOUND_VARIABLE_1813 $$unsorted) (BOUND_VARIABLE_1811 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1811 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1813 (tptp.subset_type (tptp.cross_product B BOUND_VARIABLE_1811)))) (tptp.relation_like BOUND_VARIABLE_1813))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (or _let_33 _let_97))) (let ((_let_103 (and (or _let_98 _let_32) _let_102))) (let ((_let_104 (or _let_37 _let_35 _let_103))) (let ((_let_105 (forall ((B $$unsorted) (BOUND_VARIABLE_1453 $$unsorted) (BOUND_VARIABLE_1451 $$unsorted) (BOUND_VARIABLE_1449 $$unsorted)) (let ((_let_1 (tptp.subset_type (tptp.cross_product B BOUND_VARIABLE_1449)))) (let ((_let_2 (tptp.relation_type B BOUND_VARIABLE_1449))) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1449 tptp.set_type)) (and (or (not (tptp.ilf_type BOUND_VARIABLE_1453 _let_1)) (tptp.ilf_type BOUND_VARIABLE_1453 _let_2)) (or (not (tptp.ilf_type BOUND_VARIABLE_1451 _let_2)) (tptp.ilf_type BOUND_VARIABLE_1451 _let_1))))))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (tptp.relation_type B BOUND_VARIABLE_1449))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_91)) :args ((or _let_19 (not _let_90) (not _let_91)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_90)) :args ((or _let_92 _let_90 (not _let_89)))) _let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_37 _let_35 _let_89 _let_98 (not _let_99)))) _let_55 _let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_33 _let_97 (not _let_102)))) _let_53 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_103 1)) :args ((or _let_102 (not _let_103)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_37 _let_35 _let_103 (not _let_104)))) _let_55 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((tptp.ilf_type BOUND_VARIABLE_1451 _let_107) (tptp.ilf_type BOUND_VARIABLE_1453 _let_107)))) :args (_let_105))) _let_106 :args (_let_104 false _let_105)) :args (_let_103 false _let_36 false _let_34 false _let_104)) :args (_let_102 false _let_103)) :args (_let_97 false _let_32 false _let_102)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_100))) _let_101 :args (_let_99 false _let_100)) :args (_let_89 false _let_36 false _let_34 false _let_97 false _let_99)) :args (_let_90 false _let_88 false _let_89)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_92 _let_91 (not _let_93)))) _let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type B tptp.set_type) false))))) :args (_let_94))) _let_95 :args (_let_93 false _let_94)) :args (_let_91 false _let_88 false _let_93)) :args (_let_19 false _let_90 false _let_91)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_12)) _let_13 :args (_let_22 false _let_2)))) (let ((_let_110 (_let_64))) (let ((_let_111 (REFL :args (_let_68)))) (let ((_let_112 (forall ((B $$unsorted) (BOUND_VARIABLE_1515 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (tptp.empty BOUND_VARIABLE_1515) (not (tptp.ilf_type BOUND_VARIABLE_1515 tptp.set_type)) (= (tptp.ilf_type B (tptp.member_type BOUND_VARIABLE_1515)) (tptp.member B BOUND_VARIABLE_1515)))))) (let ((_let_113 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_114 (forall ((B $$unsorted) (BOUND_VARIABLE_1302 $$unsorted) (BOUND_VARIABLE_1300 $$unsorted) (BOUND_VARIABLE_1298 $$unsorted) (BOUND_VARIABLE_1296 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1296 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1302 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1298 tptp.set_type)) (and (tptp.member BOUND_VARIABLE_1302 B) (tptp.member BOUND_VARIABLE_1298 BOUND_VARIABLE_1296)) (not (tptp.ilf_type BOUND_VARIABLE_1300 (tptp.relation_type B BOUND_VARIABLE_1296))) (not (tptp.member (tptp.ordered_pair BOUND_VARIABLE_1302 BOUND_VARIABLE_1298) BOUND_VARIABLE_1300)))))) (let ((_let_115 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_116 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_72 1)) :args ((or _let_69 (not _let_72)))) (REORDERING (CNF_EQUIV_POS2 :args (_let_70)) :args ((or _let_60 (not _let_69) (not _let_70)))) (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_37 _let_35 _let_33 _let_23 _let_67 _let_58 _let_72 (not _let_73)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_115 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_53 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_114))) _let_115 :args (_let_73 false _let_114)) _let_109 _let_53 _let_54 _let_55 (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_58 _let_61 (not _let_62)))) (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_44 _let_35 _let_67 _let_70 (not _let_71)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_53 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_112))) _let_113 :args (_let_71 false _let_112)) _let_54 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_45 2)) _let_51 :args ((not _let_44) true _let_45)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 1)) (CONG _let_111 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_49)) :args ((or _let_57 _let_68))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 0)) (CONG _let_111 (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) :args _let_49)) :args ((or _let_66 _let_68))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_110)) :args _let_110)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) (REFL :args ((not _let_68))) :args _let_49)) (REORDERING (CNF_EQUIV_POS1 :args (_let_65)) :args ((or _let_64 _let_31 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_23 _let_20 _let_65 (not _let_85)))) _let_109 _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.member B (tptp.domain_of BOUND_VARIABLE_1139))))) :args (_let_86))) _let_87 :args (_let_85 false _let_86)) :args (_let_65 false _let_22 false _let_19 false _let_85)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_84) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_53 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 F)))) :args _let_84)) (RESOLUTION (CNF_AND_NEG :args (_let_79)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_81 _let_82) (SCOPE (TRUE_ELIM (TRANS _let_83 (TRUE_INTRO _let_81))) :args _let_80)) :args _let_80)) :args (true _let_79)) _let_56 (REORDERING (EQ_RESOLVE (CNF_EQUIV_NEG2 :args _let_78) (CONG (REFL :args _let_78) (REFL :args _let_77) _let_76 :args _let_49)) :args ((or _let_41 _let_43 _let_74))) _let_75 :args (_let_74 true _let_69 false _let_72 false _let_73 false _let_22 false _let_32 false _let_34 false _let_36 true _let_60 false _let_70 false _let_71 false _let_34 true _let_44 false _let_57 false _let_66 true _let_68 true _let_63 false _let_65 false _let_62 false _let_15 false _let_29 false _let_41 true _let_43)))) (let ((_let_117 (and _let_74 _let_29))) (let ((_let_118 (_let_74 _let_29))) (let ((_let_119 (ASSUME :args _let_77))) (let ((_let_120 (or (not (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_252 _let_59)) _let_18))) (let ((_let_121 (not _let_120))) (let ((_let_122 (_let_42))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_252 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_12)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_20 _let_18 _let_21 _let_16 (not _let_24)))) _let_109 _let_108 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_120 1)) (CONG (REFL :args (_let_120)) (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_49)) :args ((or _let_17 _let_120))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_122)) :args _let_122)) (CONG _let_76 (REFL :args (_let_121)) :args _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_78) :args ((or _let_30 _let_42 _let_43))) _let_116 _let_75 :args (_let_42 true _let_30 true _let_43)) :args (_let_121 true _let_41)) :args (_let_17 true _let_120)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_16 0)) :args ((or _let_15 _let_27))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_117)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_119 _let_82) (SCOPE (FALSE_ELIM (TRANS _let_83 (FALSE_INTRO _let_119))) :args _let_118)) :args _let_118)) :args (true _let_117)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_30))) (REFL :args ((not _let_29))) (REFL :args (_let_31)) :args _let_49)) _let_116 _let_56 :args (_let_31 true _let_30 false _let_29)) :args (_let_27 true _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_252 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member (tptp.ordered_pair B BOUND_VARIABLE_1190) BOUND_VARIABLE_1192) false))))) :args (_let_25))) _let_26 :args (_let_24 false _let_25)) :args (_let_21 false _let_22 false _let_19 false _let_17 true _let_16 false _let_24)) _let_13 :args (false true _let_11 false _let_2)) :args (_let_10 _let_9 _let_8 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (forall ((E $$unsorted)) (=> (tptp.ilf_type E tptp.set_type) (forall ((F $$unsorted)) (=> (tptp.ilf_type F tptp.set_type) (= (= F (tptp.ordered_pair D E)) (= F (tptp.unordered_pair (tptp.unordered_pair D E) (tptp.singleton D)))))))))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (tptp.ilf_type (tptp.ordered_pair B C) tptp.set_type))))) _let_7 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (exists ((D $$unsorted)) (tptp.ilf_type D (tptp.relation_type C B))))))) _let_6 (forall ((B $$unsorted)) (=> (and (not (tptp.empty B)) (tptp.ilf_type B tptp.set_type)) (exists ((C $$unsorted)) (tptp.ilf_type C (tptp.member_type B))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (= (tptp.empty B) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (not (tptp.member C B))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.binary_relation_type) (tptp.ilf_type (tptp.domain_of B) tptp.set_type))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.ilf_type (tptp.singleton B) tptp.set_type))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (tptp.ilf_type (tptp.cross_product B C) tptp.set_type))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.binary_relation_type) (tptp.ilf_type (tptp.range_of B) tptp.set_type))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (tptp.ilf_type (tptp.unordered_pair B C) tptp.set_type))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.unordered_pair B C) (tptp.unordered_pair C B)))))) _let_5 (exists ((B $$unsorted)) (tptp.ilf_type B tptp.binary_relation_type)) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.ilf_type C (tptp.subset_type B)) (tptp.ilf_type C (tptp.member_type (tptp.power_set B)))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (exists ((C $$unsorted)) (tptp.ilf_type C (tptp.subset_type B))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (= B C) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (= (tptp.member D B) (tptp.member D C))))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.member B (tptp.power_set C)) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (=> (tptp.member D B) (tptp.member D C))))))))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.power_set B))) (=> (tptp.ilf_type B tptp.set_type) (and (not (tptp.empty _let_1)) (tptp.ilf_type _let_1 tptp.set_type))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (= (tptp.relation_like B) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (=> (tptp.member C B) (exists ((D $$unsorted)) (and (tptp.ilf_type D tptp.set_type) (exists ((E $$unsorted)) (and (tptp.ilf_type E tptp.set_type) (= C (tptp.ordered_pair D E)))))))))))) (forall ((B $$unsorted)) (=> (and (tptp.empty B) (tptp.ilf_type B tptp.set_type)) (tptp.relation_like B))) _let_4 _let_3 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.relation_type B C)) (tptp.ilf_type (tptp.domain B C D) (tptp.subset_type B)))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.relation_type B C)) (= (tptp.range B C D) (tptp.range_of D)))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.relation_type B C)) (tptp.ilf_type (tptp.range B C D) (tptp.subset_type C)))))))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 228.66/228.91 )
% 228.66/228.91 % SZS output end Proof for SET680+3
% 228.66/228.91 % cvc5---1.0.5 exiting
% 228.66/228.91 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------