%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET664+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n016.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 21.49s 21.70s
% Output   : Proof 21.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET664+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n016.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sat Aug 26 12:30:12 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 21.49/21.70  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.n0ebqOZQwD/cvc5---1.0.5_13621.p...
% 21.49/21.70  ------- get file name : TPTP file name is SET664+3
% 21.49/21.70  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_13621.smt2...
% 21.49/21.70  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 21.49/21.70  --- Run --no-e-matching --full-saturate-quant at 5...
% 21.49/21.70  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 21.49/21.70  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 21.49/21.70  % SZS status Theorem for SET664+3
% 21.49/21.70  % SZS output start Proof for SET664+3
% 21.49/21.70  (
% 21.49/21.70  (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 $$unsorted)) (=> (tptp.ilf_type D (tptp.relation_type C B)) (=> (tptp.ilf_type D (tptp.relation_type C tptp.empty_set)) (= D tptp.empty_set))))))))))) (let ((_let_2 (forall ((B $$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 $$unsorted)) (=> (tptp.ilf_type D (tptp.subset_type (tptp.cross_product B C))) (tptp.relation_like D))))))))) (let ((_let_4 (forall ((B $$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 $$unsorted)) (=> (tptp.ilf_type B tptp.binary_relation_type) (tptp.ilf_type (tptp.range_of B) tptp.set_type))))) (let ((_let_6 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (and (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.subset_type (tptp.cross_product B C))) (tptp.ilf_type D (tptp.relation_type B C)))) (forall ((E $$unsorted)) (=> (tptp.ilf_type E (tptp.relation_type B C)) (tptp.ilf_type E (tptp.subset_type (tptp.cross_product B C)))))))))))) (let ((_let_7 (forall ((B $$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.relation_type B C)) (and (tptp.subset (tptp.domain_of D) B) (tptp.subset (tptp.range_of D) C)))))))))) (let ((_let_8 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.binary_relation_type) (=> (or (= (tptp.domain_of B) tptp.empty_set) (= (tptp.range_of B) tptp.empty_set)) (= B tptp.empty_set)))))) (let ((_let_9 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (=> (tptp.subset B tptp.empty_set) (= B tptp.empty_set)))))) (let ((_let_10 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.set_type))) (let ((_let_11 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.empty_set)))) (let ((_let_12 (tptp.ilf_type tptp.empty_set tptp.set_type))) (let ((_let_13 (tptp.range_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_14 (tptp.subset _let_13 tptp.empty_set))) (let ((_let_15 (tptp.domain_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_16 (and (tptp.subset _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) _let_14))) (let ((_let_17 (not _let_11))) (let ((_let_18 (not _let_12))) (let ((_let_19 (not _let_10))) (let ((_let_20 (or _let_19 _let_18 _let_17 _let_16))) (let ((_let_21 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_22 (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_23 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_22))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.set_type))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_19 _let_24 _let_17 _let_21))) (let ((_let_28 (forall ((B $$unsorted) (BOUND_VARIABLE_1810 $$unsorted) (BOUND_VARIABLE_1808 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1808 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1810 (tptp.relation_type BOUND_VARIABLE_1808 B))) (not (tptp.ilf_type BOUND_VARIABLE_1810 (tptp.relation_type BOUND_VARIABLE_1808 tptp.empty_set))) (= tptp.empty_set BOUND_VARIABLE_1810))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (or))) (let ((_let_32 (not _let_28))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_30) :args (_let_32))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_28))) (REFL :args (_let_29)) :args _let_31)) _let_30 :args (_let_29 true _let_28)))) (let ((_let_34 (REFL :args (_let_27)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 1)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_10))) :args _let_31)) :args ((or _let_10 _let_27))) _let_33 :args (_let_10 true _let_27)))) (let ((_let_36 (_let_2))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 (not _let_16))) (let ((_let_39 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.binary_relation_type))) (let ((_let_40 (not _let_14))) (let ((_let_41 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.set_type))) (let ((_let_42 (tptp.relation_like SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_43 (and _let_42 _let_41))) (let ((_let_44 (= _let_39 _let_43))) (let ((_let_45 (not _let_41))) (let ((_let_46 (or _let_45 _let_44))) (let ((_let_47 (forall ((B $$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_48 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args _let_49) :args _let_36)) _let_37 :args (_let_41 false _let_2)))) (let ((_let_51 (tptp.subset_type (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_52 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_51))) (let ((_let_53 (not _let_52))) (let ((_let_54 (or _let_19 _let_26 _let_53 _let_42))) (let ((_let_55 (forall ((B $$unsorted) (BOUND_VARIABLE_1583 $$unsorted) (BOUND_VARIABLE_1581 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1581 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1583 (tptp.subset_type (tptp.cross_product B BOUND_VARIABLE_1581)))) (tptp.relation_like BOUND_VARIABLE_1583))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (or _let_24 _let_52))) (let ((_let_58 (and (or (not (tptp.ilf_type tptp.set_type _let_51)) (tptp.ilf_type tptp.set_type _let_22)) _let_57))) (let ((_let_59 (or _let_19 _let_26 _let_58))) (let ((_let_60 (forall ((B $$unsorted) (BOUND_VARIABLE_1180 $$unsorted) (BOUND_VARIABLE_1178 $$unsorted) (BOUND_VARIABLE_1176 $$unsorted)) (let ((_let_1 (tptp.subset_type (tptp.cross_product B BOUND_VARIABLE_1176)))) (let ((_let_2 (tptp.relation_type B BOUND_VARIABLE_1176))) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1176 tptp.set_type)) (and (or (not (tptp.ilf_type BOUND_VARIABLE_1180 _let_1)) (tptp.ilf_type BOUND_VARIABLE_1180 _let_2)) (or (not (tptp.ilf_type BOUND_VARIABLE_1178 _let_2)) (tptp.ilf_type BOUND_VARIABLE_1178 _let_1))))))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_31)) :args ((or _let_25 _let_27))) _let_33 :args (_let_25 true _let_27)))) (let ((_let_63 (= tptp.empty_set _let_13))) (let ((_let_64 (not _let_63))) (let ((_let_65 (and (not (= tptp.empty_set _let_15)) _let_64))) (let ((_let_66 (not _let_39))) (let ((_let_67 (or _let_66 _let_65 _let_21))) (let ((_let_68 (tptp.ilf_type _let_13 tptp.set_type))) (let ((_let_69 (or _let_66 _let_68))) (let ((_let_70 (not _let_68))) (let ((_let_71 (or _let_70 _let_40 _let_63))) (let ((_let_72 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.binary_relation_type)) (and (not (= tptp.empty_set (tptp.domain_of B))) (not (= tptp.empty_set (tptp.range_of B)))) (= tptp.empty_set B))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_FMF_FMC_EXH))) (let ((_let_75 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.binary_relation_type)) (tptp.ilf_type (tptp.range_of B) tptp.set_type))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.subset B tptp.empty_set)) (= tptp.empty_set B))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (forall ((B $$unsorted) (BOUND_VARIABLE_1120 $$unsorted) (BOUND_VARIABLE_1118 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1118 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1120 (tptp.relation_type B BOUND_VARIABLE_1118))) (and (tptp.subset (tptp.domain_of BOUND_VARIABLE_1120) B) (tptp.subset (tptp.range_of BOUND_VARIABLE_1120) BOUND_VARIABLE_1118)))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_17 _let_18 _let_16 (not _let_20)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.empty_set QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_79))) _let_80 :args (_let_20 false _let_79)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_16 1)) :args ((or _let_14 _let_38))) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_63 _let_70 _let_40 (not _let_71)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (_let_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_77))) _let_78 :args (_let_71 false _let_77)) (REORDERING (CNF_AND_POS :args (_let_65 1)) :args ((or _let_64 (not _let_65)))) (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_66 _let_68 (not _let_69)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args _let_74) :args (_let_75))) _let_76 :args (_let_69 false _let_75)) (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_21 _let_66 _let_65 (not _let_67)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args _let_74) :args (_let_72))) _let_73 :args (_let_67 false _let_72)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_27 4)) _let_33 :args ((not _let_21) true _let_27)) :args ((or _let_66 _let_40) false _let_71 true _let_63 false _let_68 false _let_69 false _let_65 false _let_67 true _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_44)) :args ((or _let_39 (not _let_43) (not _let_44)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_43)) :args ((or _let_45 (not _let_42) _let_43))) _let_50 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_26 _let_19 _let_42 _let_53 (not _let_54)))) _let_62 _let_35 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_24 _let_52 (not _let_57)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 2)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_31)) :args ((or _let_23 _let_27))) _let_33 :args (_let_23 true _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 1)) :args ((or _let_57 (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_26 _let_19 _let_58 (not _let_59)))) _let_62 _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.set_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_60))) _let_61 :args (_let_59 false _let_60)) :args (_let_58 false _let_25 false _let_10 false _let_59)) :args (_let_57 false _let_58)) :args (_let_52 false _let_23 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_42 false _let_25 false _let_10 false _let_52 false _let_54)) :args (_let_43 false _let_41 false _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_44 (not _let_46)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args _let_49) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_44 false _let_41 false _let_46)) :args (_let_39 false _let_43 false _let_44)) :args (_let_40 false _let_39)) :args (_let_38 true _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.empty_set QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_36)) _let_37 :args (_let_12 false _let_2)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 3)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_11))) :args _let_31)) :args ((or _let_11 _let_27))) _let_33 :args (_let_11 true _let_27)) _let_35 :args (false false _let_20 true _let_16 false _let_12 false _let_11 false _let_10)) :args (_let_9 _let_8 _let_7 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (not (tptp.member B tptp.empty_set)))) (tptp.empty tptp.empty_set) (tptp.type tptp.empty_set tptp.set_type) _let_6 (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.binary_relation_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.binary_relation_type) (= (= B C) (forall ((D $$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.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))))) _let_5 (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 $$unsorted)) (tptp.ilf_type B tptp.binary_relation_type)) (forall ((B $$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.binary_relation_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.binary_relation_type) (=> (= B C) (= C B)))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.binary_relation_type) (= B B))) (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) (tptp.subset B 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 $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$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 $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (= (tptp.relation_like B) (forall ((C $$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 $$unsorted)) (=> (and (tptp.empty B) (tptp.ilf_type B tptp.set_type)) (tptp.relation_like B))) _let_3 (forall ((B $$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)))))))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 21.49/21.71  )
% 21.49/21.71  % SZS output end Proof for SET664+3
% 21.49/21.71  % cvc5---1.0.5 exiting
% 21.49/21.71  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------