%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n028.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 14:39:49 EDT 2023

% Result   : Theorem 46.79s 46.96s
% Output   : Proof 46.79s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.34  % Computer : n028.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sat Aug 26 13:27:37 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.48  %----Proving TF0_NAR, FOF, or CNF
% 46.79/46.96  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.XxbNt9RZ2n/cvc5---1.0.5_27205.p...
% 46.79/46.96  ------- get file name : TPTP file name is SET666+3
% 46.79/46.96  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27205.smt2...
% 46.79/46.96  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 46.79/46.96  --- Run --no-e-matching --full-saturate-quant at 5...
% 46.79/46.96  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 46.79/46.96  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 46.79/46.96  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 46.79/46.96  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 46.79/46.96  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 46.79/46.96  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 46.79/46.96  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 46.79/46.96  % SZS status Theorem for SET666+3
% 46.79/46.96  % SZS output start Proof for SET666+3
% 46.79/46.96  (
% 46.79/46.96  (let ((_let_1 (not (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.ilf_type (tptp.identity_relation_of B) (tptp.identity_relation_of_type B))))))) (let ((_let_2 (forall ((B $$unsorted)) (tptp.ilf_type B tptp.set_type)))) (let ((_let_3 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (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_4 (forall ((B $$unsorted)) (let ((_let_1 (tptp.power_set B))) (=> (tptp.ilf_type B tptp.set_type) (and (not (tptp.empty _let_1)) (tptp.ilf_type _let_1 tptp.set_type))))))) (let ((_let_5 (forall ((B $$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))))))))))) (let ((_let_6 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.subset B C) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (=> (tptp.member D B) (tptp.member D C))))))))))) (let ((_let_7 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.ilf_type C (tptp.subset_type B)) (tptp.ilf_type C (tptp.member_type (tptp.power_set B)))))))))) (let ((_let_8 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (tptp.ilf_type (tptp.cross_product B C) tptp.set_type))))))) (let ((_let_9 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.ilf_type C (tptp.identity_relation_of_type B)) (tptp.ilf_type C (tptp.relation_type B B))))))))) (let ((_let_10 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.subset (tptp.identity_relation_of B) (tptp.cross_product B B)))))) (let ((_let_11 (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_12 (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_13 (tptp.power_set _let_12))) (let ((_let_14 (tptp.identity_relation_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (tptp.member _let_14 _let_13))) (let ((_let_16 (tptp.ilf_type _let_14 (tptp.member_type _let_13)))) (let ((_let_17 (= _let_15 _let_16))) (let ((_let_18 (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D (tptp.identity_relation_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member D (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_19 (= _let_15 _let_18))) (let ((_let_20 (tptp.ilf_type _let_12 tptp.set_type))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19))) (let ((_let_23 (forall ((C $$unsorted)) (or (not (tptp.ilf_type C tptp.set_type)) (= (tptp.member (tptp.identity_relation_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.power_set C)) (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D (tptp.identity_relation_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member D C)))))))) (let ((_let_24 (tptp.ilf_type _let_14 tptp.set_type))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23))) (let ((_let_27 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (forall ((C $$unsorted)) (or (not (tptp.ilf_type C tptp.set_type)) (= (tptp.member B (tptp.power_set C)) (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D B)) (tptp.member D C)))))))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (_let_2))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_14 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_29)) _let_30 :args (_let_24 false _let_2)))) (let ((_let_32 (_let_23))) (let ((_let_33 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.set_type))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_20))) (let ((_let_36 (forall ((C $$unsorted)) (or (not (tptp.ilf_type C tptp.set_type)) (tptp.ilf_type (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 C) tptp.set_type))))) (let ((_let_37 (or _let_34 _let_36))) (let ((_let_38 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (forall ((C $$unsorted)) (or (not (tptp.ilf_type C tptp.set_type)) (tptp.ilf_type (tptp.cross_product B C) tptp.set_type))))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_CBQI_PROP))) (let ((_let_41 (tptp.identity_relation_of_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_42 (tptp.ilf_type _let_14 _let_41))) (let ((_let_43 (or _let_34 _let_42))) (let ((_let_44 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (tptp.ilf_type (tptp.identity_relation_of B) (tptp.identity_relation_of_type B)))))) (let ((_let_45 (not _let_43))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (or))) (let ((_let_48 (not _let_44))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_46) :args (_let_48))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_44))) (REFL :args (_let_45)) :args _let_47)) _let_46 :args (_let_45 true _let_44)))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 0)) (CONG (REFL :args (_let_43)) (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_47)) :args ((or _let_33 _let_43))) _let_49 :args (_let_33 true _let_43)))) (let ((_let_51 (_let_36))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_20 (not _let_35)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_51) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 C)))) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_34 _let_36 (not _let_37)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args _let_40) :args (_let_38))) _let_39 :args (_let_37 false _let_38)) :args (_let_36 false _let_33 false _let_37)) :args (_let_35 false _let_36)) :args (_let_20 false _let_33 false _let_35)))) (let ((_let_53 (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D (tptp.identity_relation_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member D (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_54 (tptp.subset _let_14 _let_12))) (let ((_let_55 (= _let_54 _let_53))) (let ((_let_56 (or _let_21 _let_55))) (let ((_let_57 (forall ((C $$unsorted)) (or (not (tptp.ilf_type C tptp.set_type)) (= (tptp.subset (tptp.identity_relation_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) C) (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D (tptp.identity_relation_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member D C)))))))) (let ((_let_58 (or _let_25 _let_57))) (let ((_let_59 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (forall ((C $$unsorted)) (or (not (tptp.ilf_type C tptp.set_type)) (= (tptp.subset B C) (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D B)) (tptp.member D C)))))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (_let_57))) (let ((_let_62 (or _let_34 _let_54))) (let ((_let_63 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (tptp.subset (tptp.identity_relation_of B) (tptp.cross_product B B)))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (tptp.ilf_type _let_14 (tptp.subset_type _let_12)))) (let ((_let_66 (= _let_65 _let_16))) (let ((_let_67 (not _let_16))) (let ((_let_68 (or _let_25 _let_66))) (let ((_let_69 (forall ((C $$unsorted)) (let ((_let_1 (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (or (not (tptp.ilf_type C tptp.set_type)) (= (tptp.ilf_type C (tptp.subset_type _let_1)) (tptp.ilf_type C (tptp.member_type (tptp.power_set _let_1))))))))) (let ((_let_70 (or _let_21 _let_69))) (let ((_let_71 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (forall ((C $$unsorted)) (or (not (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)))))))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (_let_69))) (let ((_let_74 (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_75 (tptp.ilf_type _let_14 _let_74))) (let ((_let_76 (not _let_65))) (let ((_let_77 (or _let_76 _let_75))) (let ((_let_78 (forall ((D $$unsorted)) (or (not (tptp.ilf_type D (tptp.subset_type (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (tptp.ilf_type D (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_79 (and _let_78 (forall ((E $$unsorted)) (or (not (tptp.ilf_type E (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.ilf_type E (tptp.subset_type (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))))) (let ((_let_80 (or _let_34 _let_79))) (let ((_let_81 (forall ((C $$unsorted)) (or (not (tptp.ilf_type C tptp.set_type)) (and (forall ((D $$unsorted)) (or (not (tptp.ilf_type D (tptp.subset_type (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 C)))) (tptp.ilf_type D (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 C)))) (forall ((E $$unsorted)) (or (not (tptp.ilf_type E (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 C))) (tptp.ilf_type E (tptp.subset_type (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 C)))))))))) (let ((_let_82 (or _let_34 _let_81))) (let ((_let_83 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (forall ((C $$unsorted)) (or (not (tptp.ilf_type C tptp.set_type)) (and (forall ((D $$unsorted)) (or (not (tptp.ilf_type D (tptp.subset_type (tptp.cross_product B C)))) (tptp.ilf_type D (tptp.relation_type B C)))) (forall ((E $$unsorted)) (or (not (tptp.ilf_type E (tptp.relation_type B C))) (tptp.ilf_type E (tptp.subset_type (tptp.cross_product B C)))))))))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (_let_81))) (let ((_let_86 (_let_78))) (let ((_let_87 (= _let_42 _let_75))) (let ((_let_88 (not _let_75))) (let ((_let_89 (or _let_25 _let_87))) (let ((_let_90 (forall ((C $$unsorted)) (or (not (tptp.ilf_type C tptp.set_type)) (= (tptp.ilf_type C (tptp.identity_relation_of_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.ilf_type C (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))))) (let ((_let_91 (or _let_34 _let_90))) (let ((_let_92 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (forall ((C $$unsorted)) (or (not (tptp.ilf_type C tptp.set_type)) (= (tptp.ilf_type C (tptp.identity_relation_of_type B)) (tptp.ilf_type C (tptp.relation_type B B))))))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (_let_90))) (let ((_let_95 (tptp.ilf_type _let_13 tptp.set_type))) (let ((_let_96 (not _let_95))) (let ((_let_97 (tptp.empty _let_13))) (let ((_let_98 (or _let_97 _let_96 _let_17))) (let ((_let_99 (forall ((C $$unsorted)) (let ((_let_1 (tptp.identity_relation_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (or (tptp.empty C) (not (tptp.ilf_type C tptp.set_type)) (= (tptp.ilf_type _let_1 (tptp.member_type C)) (tptp.member _let_1 C))))))) (let ((_let_100 (or _let_25 _let_99))) (let ((_let_101 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (forall ((C $$unsorted)) (or (tptp.empty C) (not (tptp.ilf_type C tptp.set_type)) (= (tptp.ilf_type B (tptp.member_type C)) (tptp.member B C)))))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (_let_99))) (let ((_let_104 (not _let_97))) (let ((_let_105 (and _let_104 _let_95))) (let ((_let_106 (or _let_21 _let_105))) (let ((_let_107 (forall ((B $$unsorted)) (let ((_let_1 (tptp.power_set B))) (or (not (tptp.ilf_type B tptp.set_type)) (and (not (tptp.empty _let_1)) (tptp.ilf_type _let_1 tptp.set_type))))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_21 _let_105 (not _let_106)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (_let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.power_set B)))) :args (_let_107))) _let_108 :args (_let_106 false _let_107)) :args (_let_105 false _let_20 false _let_106)))) (let ((_let_110 (not _let_105))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_17)) :args ((or (not _let_15) _let_16 (not _let_17)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_97 _let_96 _let_17 (not _let_98)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_105 0)) :args ((or _let_104 _let_110))) _let_109 :args (_let_104 false _let_105)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_105 1)) :args ((or _let_95 _let_110))) _let_109 :args (_let_95 false _let_105)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_103) :args (_let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.member _let_14 C)))) :args _let_103))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_25 _let_99 (not _let_100)))) _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type B tptp.set_type) false))))) :args (_let_101))) _let_102 :args (_let_100 false _let_101)) :args (_let_99 false _let_24 false _let_100)) :args (_let_98 false _let_99)) :args (_let_17 true _let_97 false _let_95 false _let_98)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_66)) :args ((or _let_65 _let_67 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_75 _let_76 (not _let_77)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_87)) :args ((or _let_42 _let_88 (not _let_87)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 1)) _let_49 :args ((not _let_42) true _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_25 _let_87 (not _let_89)))) _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_94) :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ilf_type C _let_41)))) :args _let_94)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_34 _let_90 (not _let_91)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args _let_40) :args (_let_92))) _let_93 :args (_let_91 false _let_92)) :args (_let_90 false _let_33 false _let_91)) :args (_let_89 false _let_90)) :args (_let_87 false _let_24 false _let_89)) :args (_let_88 true _let_42 false _let_87)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_86) :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type D _let_74) true))))) :args _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_79 0)) :args ((or _let_78 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_34 _let_79 (not _let_80)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_85) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type C tptp.set_type) false))))) :args _let_85)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_34 _let_81 (not _let_82)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type B tptp.set_type) false))))) :args (_let_83))) _let_84 :args (_let_82 false _let_83)) :args (_let_81 false _let_33 false _let_82)) :args (_let_80 false _let_81)) :args (_let_79 false _let_33 false _let_80)) :args (_let_78 false _let_79)) :args (_let_77 false _let_78)) :args (_let_76 true _let_75 false _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_25 _let_66 (not _let_68)))) _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_73) :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type C tptp.set_type) false))))) :args _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_21 _let_69 (not _let_70)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (_let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type B tptp.set_type) false))))) :args (_let_71))) _let_72 :args (_let_70 false _let_71)) :args (_let_69 false _let_20 false _let_70)) :args (_let_68 false _let_69)) :args (_let_66 false _let_24 false _let_68)) :args (_let_67 true _let_65 false _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_19)) :args ((or _let_15 (not _let_18) (not _let_19)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_53 (= D D)))) :args ((or _let_18 (not _let_53)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_55)) :args ((or (not _let_54) _let_53 (not _let_55)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_34 _let_54 (not _let_62)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type B tptp.set_type) false))))) :args (_let_63))) _let_64 :args (_let_62 false _let_63)) :args (_let_54 false _let_33 false _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_21 _let_55 (not _let_56)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_61) :args (_let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type C tptp.set_type) false))))) :args _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_25 _let_57 (not _let_58)))) _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type B tptp.set_type) false))))) :args (_let_59))) _let_60 :args (_let_58 false _let_59)) :args (_let_57 false _let_24 false _let_58)) :args (_let_56 false _let_57)) :args (_let_55 false _let_20 false _let_56)) :args (_let_53 false _let_54 false _let_55)) :args (_let_18 false _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_21 _let_19 (not _let_22)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_32) :args (_let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type C tptp.set_type) false))))) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_23 (not _let_26)))) _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type B tptp.set_type) false))))) :args (_let_27))) _let_28 :args (_let_26 false _let_27)) :args (_let_23 false _let_24 false _let_26)) :args (_let_22 false _let_23)) :args (_let_19 false _let_20 false _let_22)) :args (_let_15 false _let_18 false _let_19)) :args (false false _let_17 true _let_16 false _let_15)) :args (_let_11 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (exists ((D $$unsorted)) (tptp.ilf_type D (tptp.relation_type C B))))))) _let_10 (forall ((B $$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) (= (tptp.member (tptp.ordered_pair C D) (tptp.identity_relation_of B)) (and (tptp.member C B) (= C D))))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.ilf_type (tptp.identity_relation_of B) tptp.binary_relation_type))) _let_9 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (exists ((C $$unsorted)) (tptp.ilf_type C (tptp.identity_relation_of_type B))))) _let_8 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (tptp.ilf_type (tptp.ordered_pair B C) tptp.set_type))))) (forall ((B $$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))))) (exists ((B $$unsorted)) (tptp.ilf_type B tptp.binary_relation_type)) _let_7 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (exists ((C $$unsorted)) (tptp.ilf_type C (tptp.subset_type B))))) _let_6 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.subset B B))) _let_5 _let_4 _let_3 (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 $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (= (tptp.relation_like B) (forall ((C $$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 $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.subset_type (tptp.cross_product B C))) (tptp.relation_like D))))))) (forall ((B $$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)) (=> (and (tptp.empty B) (tptp.ilf_type B tptp.set_type)) (tptp.relation_like B))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 46.79/46.97  )
% 46.79/46.97  % SZS output end Proof for SET666+3
% 46.79/46.97  % cvc5---1.0.5 exiting
% 46.79/46.98  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------