%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET665+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 14:39:48 EDT 2023

% Result   : Theorem 3.32s 3.51s
% Output   : Proof 3.32s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET665+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n005.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 10:12:53 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.48  %----Proving TF0_NAR, FOF, or CNF
% 3.32/3.51  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.jRVIeSdyQT/cvc5---1.0.5_25022.p...
% 3.32/3.51  ------- get file name : TPTP file name is SET665+3
% 3.32/3.51  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_25022.smt2...
% 3.32/3.51  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 3.32/3.51  % SZS status Theorem for SET665+3
% 3.32/3.51  % SZS output start Proof for SET665+3
% 3.32/3.51  (
% 3.32/3.51  (let ((_let_1 (not (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.subset (tptp.identity_relation_of B) (tptp.cross_product B B))))))) (let ((_let_2 (forall ((B $$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_3 (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_4 (forall ((B $$unsorted)) (let ((_let_1 (tptp.ilf_type B tptp.set_type))) (=> _let_1 (= (tptp.ilf_type B tptp.binary_relation_type) (and (tptp.relation_like B) _let_1))))))) (let ((_let_5 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.ilf_type (tptp.identity_relation_of B) tptp.binary_relation_type))))) (let ((_let_6 (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_7 (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.relation_type 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) (= (tptp.member (tptp.ordered_pair B C) (tptp.cross_product D E)) (and (tptp.member B D) (tptp.member C E))))))))))))) (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 $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (= (tptp.member (tptp.ordered_pair C D) (tptp.identity_relation_of B)) (and (tptp.member C B) (= C D))))))))))) (let ((_let_10 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.binary_relation_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.binary_relation_type) (= (tptp.subset B C) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (forall ((E $$unsorted)) (let ((_let_1 (tptp.ordered_pair D E))) (=> (tptp.ilf_type E tptp.set_type) (=> (tptp.member _let_1 B) (tptp.member _let_1 C)))))))))))))) (let ((_let_11 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_12 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95))) (let ((_let_13 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_14 (and _let_11 _let_12))) (let ((_let_15 (tptp.identity_relation_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95))) (let ((_let_17 (tptp.member _let_16 _let_15))) (let ((_let_18 (= _let_17 _let_14))) (let ((_let_19 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95 tptp.set_type))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 tptp.set_type))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.set_type))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22 _let_20 _let_18))) (let ((_let_26 (forall ((B $$unsorted) (BOUND_VARIABLE_1097 $$unsorted) (BOUND_VARIABLE_1095 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1095 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1097 tptp.set_type)) (= (tptp.member (tptp.ordered_pair BOUND_VARIABLE_1095 BOUND_VARIABLE_1097) (tptp.identity_relation_of B)) (and (tptp.member BOUND_VARIABLE_1095 B) (= BOUND_VARIABLE_1095 BOUND_VARIABLE_1097))))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_29 (tptp.member _let_16 _let_28))) (let ((_let_30 (not _let_17))) (let ((_let_31 (or _let_22 _let_20 _let_30 _let_29))) (let ((_let_32 (forall ((D $$unsorted) (BOUND_VARIABLE_1026 $$unsorted)) (let ((_let_1 (tptp.ordered_pair D BOUND_VARIABLE_1026))) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1026 tptp.set_type)) (not (tptp.member _let_1 (tptp.identity_relation_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member _let_1 (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))))) (let ((_let_33 (not _let_31))) (let ((_let_34 (tptp.subset _let_15 _let_28))) (let ((_let_35 (= _let_34 _let_32))) (let ((_let_36 (not _let_32))) (let ((_let_37 (tptp.ilf_type _let_28 tptp.binary_relation_type))) (let ((_let_38 (not _let_37))) (let ((_let_39 (tptp.ilf_type _let_15 tptp.binary_relation_type))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38 _let_35))) (let ((_let_42 (forall ((B $$unsorted) (BOUND_VARIABLE_1051 $$unsorted)) (or (not (tptp.ilf_type B tptp.binary_relation_type)) (not (tptp.ilf_type BOUND_VARIABLE_1051 tptp.binary_relation_type)) (= (tptp.subset B BOUND_VARIABLE_1051) (forall ((D $$unsorted) (BOUND_VARIABLE_1026 $$unsorted)) (let ((_let_1 (tptp.ordered_pair D BOUND_VARIABLE_1026))) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1026 tptp.set_type)) (not (tptp.member _let_1 B)) (tptp.member _let_1 BOUND_VARIABLE_1051))))))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (tptp.ilf_type _let_28 tptp.set_type))) (let ((_let_45 (tptp.relation_like _let_28))) (let ((_let_46 (and _let_45 _let_44))) (let ((_let_47 (= _let_37 _let_46))) (let ((_let_48 (not _let_44))) (let ((_let_49 (or _let_48 _let_47))) (let ((_let_50 (forall ((B $$unsorted)) (let ((_let_1 (tptp.ilf_type B tptp.set_type))) (or (not _let_1) (= (tptp.ilf_type B tptp.binary_relation_type) (and (tptp.relation_like B) _let_1))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (or _let_24 _let_24 _let_44))) (let ((_let_53 (forall ((B $$unsorted) (BOUND_VARIABLE_1327 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1327 tptp.set_type)) (tptp.ilf_type (tptp.cross_product B BOUND_VARIABLE_1327) tptp.set_type))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (or _let_24 _let_34))) (let ((_let_56 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (tptp.subset (tptp.identity_relation_of B) (tptp.cross_product B B)))))) (let ((_let_57 (not _let_55))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (or))) (let ((_let_60 (not _let_56))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_58) :args (_let_60))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_56))) (REFL :args (_let_57)) :args _let_59)) _let_58 :args (_let_57 true _let_56)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_55 0)) (CONG (REFL :args (_let_55)) (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_59)) :args ((or _let_23 _let_55))) _let_61 :args (_let_23 true _let_55)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_52))) :args ((or _let_24 _let_44 (not _let_52)))) _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cross_product B BOUND_VARIABLE_1327)))) :args (_let_53))) _let_54 :args (_let_52 false _let_53)) :args (_let_44 false _let_23 false _let_52)))) (let ((_let_64 (tptp.subset_type _let_28))) (let ((_let_65 (tptp.ilf_type _let_28 _let_64))) (let ((_let_66 (not _let_65))) (let ((_let_67 (or _let_24 _let_24 _let_66 _let_45))) (let ((_let_68 (forall ((B $$unsorted) (BOUND_VARIABLE_1653 $$unsorted) (BOUND_VARIABLE_1651 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1651 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1653 (tptp.subset_type (tptp.cross_product B BOUND_VARIABLE_1651)))) (tptp.relation_like BOUND_VARIABLE_1653))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_71 (tptp.ilf_type _let_28 _let_70))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_65))) (let ((_let_74 (and (or (not (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_64)) (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_70)) _let_73))) (let ((_let_75 (or _let_24 _let_24 _let_74))) (let ((_let_76 (forall ((B $$unsorted) (BOUND_VARIABLE_1491 $$unsorted) (BOUND_VARIABLE_1489 $$unsorted) (BOUND_VARIABLE_1487 $$unsorted)) (let ((_let_1 (tptp.subset_type (tptp.cross_product B BOUND_VARIABLE_1487)))) (let ((_let_2 (tptp.relation_type B BOUND_VARIABLE_1487))) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1487 tptp.set_type)) (and (or (not (tptp.ilf_type BOUND_VARIABLE_1491 _let_1)) (tptp.ilf_type BOUND_VARIABLE_1491 _let_2)) (or (not (tptp.ilf_type BOUND_VARIABLE_1489 _let_2)) (tptp.ilf_type BOUND_VARIABLE_1489 _let_1))))))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (or _let_24 _let_24 _let_71))) (let ((_let_79 (forall ((B $$unsorted) (BOUND_VARIABLE_1203 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1203 tptp.set_type)) (tptp.ilf_type (tptp.cross_product B BOUND_VARIABLE_1203) (tptp.relation_type B BOUND_VARIABLE_1203)))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (or _let_24 _let_39))) (let ((_let_82 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (tptp.ilf_type (tptp.identity_relation_of B) tptp.binary_relation_type))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (_let_36))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_84)) :args _let_84)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_32))) (REFL :args (_let_33)) :args _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_35)) :args ((or _let_34 _let_36 (not _let_35)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_55 1)) _let_61 :args ((not _let_34) true _let_55)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_38 _let_35 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_24 _let_39 (not _let_81)))) _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type B tptp.set_type) false))))) :args (_let_82))) _let_83 :args (_let_81 false _let_82)) :args (_let_39 false _let_23 false _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_47)) :args ((or _let_37 (not _let_46) (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_46)) :args ((or _let_48 _let_46 (not _let_45)))) _let_63 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_67))) :args ((or _let_24 _let_45 _let_66 (not _let_67)))) _let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_72 _let_65 (not _let_73)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_78))) :args ((or _let_24 _let_71 (not _let_78)))) _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cross_product B BOUND_VARIABLE_1203)))) :args (_let_79))) _let_80 :args (_let_78 false _let_79)) :args (_let_71 false _let_23 false _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_74 1)) :args ((or _let_73 (not _let_74)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_75))) :args ((or _let_24 _let_74 (not _let_75)))) _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.ilf_type BOUND_VARIABLE_1491 (tptp.subset_type (tptp.cross_product B BOUND_VARIABLE_1487))) (tptp.ilf_type BOUND_VARIABLE_1489 (tptp.relation_type B BOUND_VARIABLE_1487))))) :args (_let_76))) _let_77 :args (_let_75 false _let_76)) :args (_let_74 false _let_23 false _let_75)) :args (_let_73 false _let_74)) :args (_let_65 false _let_71 false _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.ilf_type BOUND_VARIABLE_1653 (tptp.subset_type (tptp.cross_product B BOUND_VARIABLE_1651))) false))))) :args (_let_68))) _let_69 :args (_let_67 false _let_68)) :args (_let_45 false _let_23 false _let_65 false _let_67)) :args (_let_46 false _let_44 false _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_47 (not _let_49)))) _let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (_let_28 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type B tptp.set_type) false))))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_47 false _let_44 false _let_49)) :args (_let_37 false _let_46 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (_let_15 _let_28 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset B BOUND_VARIABLE_1051)))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_35 false _let_39 false _let_37 false _let_41)) :args (_let_36 true _let_34 false _let_35)) :args (_let_33 true _let_32)))) (let ((_let_86 (REFL :args (_let_31)))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 1)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_59)) :args ((or _let_19 _let_31))) _let_85 :args (_let_19 true _let_31)))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 0)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_59)) :args ((or _let_21 _let_31))) _let_85 :args (_let_21 true _let_31)))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_18)) :args ((or _let_30 _let_14 (not _let_18)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 2)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_17))) :args _let_59)) :args ((or _let_17 _let_31))) _let_85 :args (_let_17 true _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_22 _let_20 _let_18 (not _let_25)))) _let_62 _let_88 _let_87 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 QUANTIFIERS_INST_E_MATCHING ((tptp.member (tptp.ordered_pair BOUND_VARIABLE_1095 BOUND_VARIABLE_1097) (tptp.identity_relation_of B))))) :args (_let_26))) _let_27 :args (_let_25 false _let_26)) :args (_let_18 false _let_23 false _let_21 false _let_19 false _let_25)) :args (_let_14 false _let_17 false _let_18)))) (let ((_let_90 (not _let_14))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_14 0)) :args ((or _let_11 _let_90))) _let_89 :args (_let_11 false _let_14)))) (let ((_let_92 (and _let_11 _let_13))) (let ((_let_93 (= _let_29 _let_92))) (let ((_let_94 (not _let_92))) (let ((_let_95 (or _let_22 _let_20 _let_24 _let_24 _let_93))) (let ((_let_96 (forall ((B $$unsorted) (BOUND_VARIABLE_1173 $$unsorted) (BOUND_VARIABLE_1171 $$unsorted) (BOUND_VARIABLE_1169 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1169 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1173 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1171 tptp.set_type)) (= (tptp.member (tptp.ordered_pair B BOUND_VARIABLE_1169) (tptp.cross_product BOUND_VARIABLE_1173 BOUND_VARIABLE_1171)) (and (tptp.member B BOUND_VARIABLE_1173) (tptp.member BOUND_VARIABLE_1169 BOUND_VARIABLE_1171))))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (_let_11 _let_12))) (let ((_let_99 (ASSUME :args (_let_11)))) (let ((_let_100 (ASSUME :args (_let_12)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_14)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_99 _let_100) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_100) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) :args (APPLY_UF tptp.member)) (TRUE_INTRO _let_99))) :args _let_98)) :args _let_98)) :args (true _let_14)) :args ((or _let_13 (not _let_11) (not _let_12)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_92)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_93)) :args ((or _let_29 _let_94 (not _let_93)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_31 3)) _let_85 :args ((not _let_29) true _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_95))) :args ((or _let_24 _let_22 _let_20 _let_93 (not _let_95)))) _let_62 _let_88 _let_87 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95 QUANTIFIERS_INST_E_MATCHING ((tptp.member (tptp.ordered_pair B BOUND_VARIABLE_1169) (tptp.cross_product BOUND_VARIABLE_1173 BOUND_VARIABLE_1171))))) :args (_let_96))) _let_97 :args (_let_95 false _let_96)) :args (_let_93 false _let_23 false _let_21 false _let_19 false _let_95)) :args (_let_94 true _let_29 false _let_93)) _let_91 :args ((not _let_13) true _let_92 false _let_11)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_14 1)) :args ((or _let_12 _let_90))) _let_89 :args (_let_12 false _let_14)) _let_91 :args (false true _let_13 false _let_12 false _let_11)) :args (_let_10 _let_9 _let_8 _let_7 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (= (tptp.member D (tptp.cross_product B C)) (exists ((E $$unsorted)) (and (tptp.ilf_type E tptp.set_type) (exists ((F $$unsorted)) (and (tptp.ilf_type F tptp.set_type) (tptp.member E B) (tptp.member F C) (= D (tptp.ordered_pair E F))))))))))))) _let_6 (forall ((B $$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))))))))) _let_5 (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 $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (=> (tptp.member D B) (tptp.member D C))))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (tptp.ilf_type (tptp.ordered_pair B C) tptp.set_type))))) _let_4 (exists ((B $$unsorted)) (tptp.ilf_type B tptp.binary_relation_type)) _let_3 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (exists ((D $$unsorted)) (tptp.ilf_type D (tptp.relation_type C B))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.subset B B))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.binary_relation_type) (tptp.subset B B))) (forall ((B $$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) (= (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 $$unsorted)) (and (tptp.ilf_type E tptp.set_type) (= C (tptp.ordered_pair D E)))))))))))) _let_2 (forall ((B $$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) (forall ((C $$unsorted)) (=> (and (not (tptp.empty C)) (tptp.ilf_type C tptp.set_type)) (= (tptp.ilf_type B (tptp.member_type C)) (tptp.member B C)))))) (forall ((B $$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)) (=> (and (tptp.empty B) (tptp.ilf_type B tptp.set_type)) (tptp.relation_like B))) (forall ((B $$unsorted)) (tptp.ilf_type B tptp.set_type)) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 3.32/3.53  )
% 3.32/3.53  % SZS output end Proof for SET665+3
% 3.32/3.53  % cvc5---1.0.5 exiting
% 3.32/3.53  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------