%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET669+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n009.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 14:39:50 EDT 2023

% Result   : Theorem 27.85s 28.05s
% Output   : Proof 27.85s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem    : SET669+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n009.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 12:06:05 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.52  %----Proving TF0_NAR, FOF, or CNF
% 27.85/28.05  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.dHI7kQyGUr/cvc5---1.0.5_4968.p...
% 27.85/28.05  ------- get file name : TPTP file name is SET669+3
% 27.85/28.05  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_4968.smt2...
% 27.85/28.05  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 27.85/28.05  --- Run --no-e-matching --full-saturate-quant at 5...
% 27.85/28.05  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 27.85/28.05  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 27.85/28.05  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.85/28.05  % SZS status Theorem for SET669+3
% 27.85/28.05  % SZS output start Proof for SET669+3
% 27.85/28.05  (
% 27.85/28.05  (let ((_let_1 (not (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.relation_type B C)) (=> (tptp.subset (tptp.identity_relation_of C) D) (and (tptp.subset C (tptp.domain B C D)) (= C (tptp.range B C D))))))))))))) (let ((_let_2 (forall ((B $$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 $$unsorted)) (=> (tptp.ilf_type D (tptp.relation_type B C)) (tptp.ilf_type (tptp.range B C D) (tptp.subset_type C)))))))))) (let ((_let_4 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (and (not (tptp.empty C)) (tptp.ilf_type C tptp.set_type)) (= (tptp.ilf_type B (tptp.member_type C)) (tptp.member B C)))))))) (let ((_let_5 (forall ((B $$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_6 (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 $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (=> (tptp.member D B) (tptp.member D C))))))))))) (let ((_let_7 (forall ((B $$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 $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.subset B C) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (=> (tptp.member D B) (tptp.member D 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 $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (forall ((E $$unsorted)) (=> (tptp.ilf_type E (tptp.relation_type B C)) (=> (tptp.subset (tptp.identity_relation_of D) E) (and (tptp.subset D (tptp.domain B C E)) (tptp.subset D (tptp.range B C E)))))))))))))) (let ((_let_10 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (=> (and (tptp.subset B C) (tptp.subset C B)) (= B C)))))))) (let ((_let_11 (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D (tptp.range SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_12 (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (tptp.range SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_14 (tptp.member _let_13 _let_12))) (let ((_let_15 (= _let_14 _let_11))) (let ((_let_16 (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D (tptp.range SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_17 (tptp.subset _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (= _let_17 _let_16))) (let ((_let_19 (not _let_16))) (let ((_let_20 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.set_type))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.ilf_type _let_13 tptp.set_type))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_18))) (let ((_let_25 (forall ((B $$unsorted) (BOUND_VARIABLE_1366 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1366 tptp.set_type)) (= (tptp.subset B BOUND_VARIABLE_1366) (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D B)) (tptp.member D BOUND_VARIABLE_1366)))))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (_let_2))) (let ((_let_28 (ASSUME :args _let_27))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_27)) _let_28 :args (_let_22 false _let_2)))) (let ((_let_30 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_13))) (let ((_let_31 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.domain SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_32 (and _let_31 _let_30))) (let ((_let_33 (tptp.subset (tptp.identity_relation_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.set_type))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_21 _let_36 _let_34 _let_32))) (let ((_let_40 (forall ((B $$unsorted) (BOUND_VARIABLE_1943 $$unsorted) (BOUND_VARIABLE_1941 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1941 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1943 (tptp.relation_type B BOUND_VARIABLE_1941))) (not (tptp.subset (tptp.identity_relation_of BOUND_VARIABLE_1941) BOUND_VARIABLE_1943)) (and (tptp.subset BOUND_VARIABLE_1941 (tptp.domain B BOUND_VARIABLE_1941 BOUND_VARIABLE_1943)) (= BOUND_VARIABLE_1941 (tptp.range B BOUND_VARIABLE_1941 BOUND_VARIABLE_1943))))))) (let ((_let_41 (not _let_39))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (or))) (let ((_let_44 (not _let_40))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_42) :args (_let_44))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_40))) (REFL :args (_let_41)) :args _let_43)) _let_42 :args (_let_41 true _let_40)))) (let ((_let_46 (REFL :args (_let_39)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 1)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_43)) :args ((or _let_20 _let_39))) _let_45 :args (_let_20 true _let_39)))) (let ((_let_48 (not _let_17))) (let ((_let_49 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_13))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_21 _let_23 _let_50 _let_48 _let_30))) (let ((_let_52 (forall ((B $$unsorted) (BOUND_VARIABLE_1105 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1105 tptp.set_type)) (not (tptp.subset B BOUND_VARIABLE_1105)) (not (tptp.subset BOUND_VARIABLE_1105 B)) (= B BOUND_VARIABLE_1105))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (and _let_31 _let_49))) (let ((_let_55 (or _let_38 _let_21 _let_21 _let_36 _let_34 _let_54))) (let ((_let_56 (forall ((B $$unsorted) (BOUND_VARIABLE_1184 $$unsorted) (BOUND_VARIABLE_1182 $$unsorted) (BOUND_VARIABLE_1180 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1180 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1184 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1182 (tptp.relation_type B BOUND_VARIABLE_1180))) (not (tptp.subset (tptp.identity_relation_of BOUND_VARIABLE_1184) BOUND_VARIABLE_1182)) (and (tptp.subset BOUND_VARIABLE_1184 (tptp.domain B BOUND_VARIABLE_1180 BOUND_VARIABLE_1182)) (tptp.subset BOUND_VARIABLE_1184 (tptp.range B BOUND_VARIABLE_1180 BOUND_VARIABLE_1182))))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 2)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_43)) :args ((or _let_35 _let_39))) _let_45 :args (_let_35 true _let_39)))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 0)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_43)) :args ((or _let_37 _let_39))) _let_45 :args (_let_37 true _let_39)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_55))) :args ((or _let_38 _let_21 _let_36 _let_34 _let_54 (not _let_55)))) _let_59 _let_47 _let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 3)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_43)) :args ((or _let_33 _let_39))) _let_45 :args (_let_33 true _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_56))) _let_57 :args (_let_55 false _let_56)) :args (_let_54 false _let_37 false _let_20 false _let_35 false _let_33 false _let_55)))) (let ((_let_61 (not _let_54))) (let ((_let_62 (or _let_23 _let_21 _let_15))) (let ((_let_63 (forall ((B $$unsorted) (BOUND_VARIABLE_1570 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1570 tptp.set_type)) (= (tptp.member B (tptp.power_set BOUND_VARIABLE_1570)) (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D B)) (tptp.member D BOUND_VARIABLE_1570)))))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (tptp.ilf_type _let_13 (tptp.member_type _let_12)))) (let ((_let_66 (= _let_65 _let_14))) (let ((_let_67 (tptp.ilf_type _let_12 tptp.set_type))) (let ((_let_68 (not _let_67))) (let ((_let_69 (tptp.empty _let_12))) (let ((_let_70 (or _let_23 _let_69 _let_68 _let_66))) (let ((_let_71 (forall ((B $$unsorted) (BOUND_VARIABLE_1601 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (tptp.empty BOUND_VARIABLE_1601) (not (tptp.ilf_type BOUND_VARIABLE_1601 tptp.set_type)) (= (tptp.ilf_type B (tptp.member_type BOUND_VARIABLE_1601)) (tptp.member B BOUND_VARIABLE_1601)))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (not _let_69))) (let ((_let_74 (and _let_73 _let_67))) (let ((_let_75 (or _let_21 _let_74))) (let ((_let_76 (forall ((B $$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_77 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_21 _let_74 (not _let_75)))) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.power_set B)))) :args (_let_76))) _let_77 :args (_let_75 false _let_76)) :args (_let_74 false _let_20 false _let_75)))) (let ((_let_79 (not _let_74))) (let ((_let_80 (tptp.ilf_type _let_13 (tptp.subset_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_81 (= _let_80 _let_65))) (let ((_let_82 (or _let_21 _let_23 _let_81))) (let ((_let_83 (forall ((B $$unsorted) (BOUND_VARIABLE_1523 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1523 tptp.set_type)) (= (tptp.ilf_type BOUND_VARIABLE_1523 (tptp.subset_type B)) (tptp.ilf_type BOUND_VARIABLE_1523 (tptp.member_type (tptp.power_set B)))))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (or _let_38 _let_21 _let_36 _let_80))) (let ((_let_86 (forall ((B $$unsorted) (BOUND_VARIABLE_1892 $$unsorted) (BOUND_VARIABLE_1890 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1890 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1892 (tptp.relation_type B BOUND_VARIABLE_1890))) (tptp.ilf_type (tptp.range B BOUND_VARIABLE_1890 BOUND_VARIABLE_1892) (tptp.subset_type BOUND_VARIABLE_1890)))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_15)) :args ((or _let_11 (not _let_14) (not _let_15)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_66)) :args ((or (not _let_65) _let_14 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_81)) :args ((or (not _let_80) _let_65 (not _let_81)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_38 _let_21 _let_36 _let_80 (not _let_85)))) _let_59 _let_47 _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.ilf_type BOUND_VARIABLE_1892 (tptp.relation_type B BOUND_VARIABLE_1890)) false))))) :args (_let_86))) _let_87 :args (_let_85 false _let_86)) :args (_let_80 false _let_37 false _let_20 false _let_35 false _let_85)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_21 _let_23 _let_81 (not _let_82)))) _let_47 _let_29 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_13 QUANTIFIERS_INST_E_MATCHING ((tptp.ilf_type BOUND_VARIABLE_1523 (tptp.subset_type B))))) :args (_let_83))) _let_84 :args (_let_82 false _let_83)) :args (_let_81 false _let_20 false _let_22 false _let_82)) :args (_let_65 false _let_80 false _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_23 _let_69 _let_68 _let_66 (not _let_70)))) _let_29 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_74 0)) :args ((or _let_73 _let_79))) _let_78 :args (_let_73 false _let_74)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_74 1)) :args ((or _let_67 _let_79))) _let_78 :args (_let_67 false _let_74)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (_let_13 _let_12 QUANTIFIERS_INST_E_MATCHING ((tptp.ilf_type B (tptp.member_type BOUND_VARIABLE_1601))))) :args (_let_71))) _let_72 :args (_let_70 false _let_71)) :args (_let_66 false _let_22 true _let_69 false _let_67 false _let_70)) :args (_let_14 false _let_65 false _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_21 _let_23 _let_15 (not _let_62)))) _let_47 _let_29 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.ilf_type B tptp.set_type) false)) (not (= (tptp.ilf_type BOUND_VARIABLE_1570 tptp.set_type) false))))) :args (_let_63))) _let_64 :args (_let_62 false _let_63)) :args (_let_15 false _let_20 false _let_22 false _let_62)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_16 (= D D)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_18)) :args ((or _let_17 _let_19 (not _let_18)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_21 _let_30 _let_50 _let_23 _let_48 (not _let_51)))) _let_47 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_32)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 4)) _let_45 :args ((not _let_32) true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_54 0)) :args ((or _let_31 _let_61))) _let_60 :args (_let_31 false _let_54)) :args ((not _let_30) true _let_32 false _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_54 1)) :args ((or _let_49 _let_61))) _let_60 :args (_let_49 false _let_54)) _let_29 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset B BOUND_VARIABLE_1105) false))))) :args (_let_52))) _let_53 :args (_let_51 false _let_52)) :args (_let_48 false _let_20 true _let_30 false _let_49 false _let_22 false _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_21 _let_23 _let_18 (not _let_24)))) _let_47 _let_29 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (_let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset B BOUND_VARIABLE_1366)))) :args (_let_25))) _let_26 :args (_let_24 false _let_25)) :args (_let_18 false _let_20 false _let_22 false _let_24)) :args (_let_19 true _let_17 false _let_18)) :args ((not _let_11) true _let_16)) :args (false false _let_14 false _let_15 true _let_11)) :args (_let_10 _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))))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.ilf_type (tptp.identity_relation_of B) tptp.binary_relation_type))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (and (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.subset_type (tptp.cross_product B C))) (tptp.ilf_type D (tptp.relation_type B C)))) (forall ((E $$unsorted)) (=> (tptp.ilf_type E (tptp.relation_type B C)) (tptp.ilf_type E (tptp.subset_type (tptp.cross_product B C)))))))))) (forall ((B $$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_8 (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)))))))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (= B C) (and (tptp.subset B C) (tptp.subset 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) (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.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))))) (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))) _let_6 _let_5 _let_4 (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))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.relation_type B C)) (= (tptp.domain B C D) (tptp.domain_of D)))))))) (forall ((B $$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)))))))) _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.85/28.06  )
% 27.85/28.06  % SZS output end Proof for SET669+3
% 27.85/28.06  % cvc5---1.0.5 exiting
% 27.85/28.07  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------