%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET640+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n013.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 14:39:42 EDT 2023

% Result   : Theorem 62.64s 62.90s
% Output   : Proof 62.64s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET640+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n013.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat Aug 26 09:48:32 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 62.64/62.90  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.uUKQUHLGaZ/cvc5---1.0.5_20855.p...
% 62.64/62.90  ------- get file name : TPTP file name is SET640+3
% 62.64/62.90  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20855.smt2...
% 62.64/62.90  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 62.64/62.90  --- Run --no-e-matching --full-saturate-quant at 5...
% 62.64/62.90  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 62.64/62.90  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 62.64/62.90  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 62.64/62.90  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 62.64/62.90  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 62.64/62.90  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 62.64/62.90  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 62.64/62.90  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 62.64/62.90  --- Run --relevant-triggers --full-saturate-quant at 5...
% 62.64/62.90  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 62.64/62.90  % SZS status Theorem for SET640+3
% 62.64/62.90  % SZS output start Proof for SET640+3
% 62.64/62.90  (
% 62.64/62.90  (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 $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (forall ((E $$unsorted)) (=> (tptp.ilf_type E (tptp.relation_type C D)) (=> (tptp.subset B E) (tptp.subset B (tptp.cross_product 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 $$unsorted)) (=> (and (not (tptp.empty C)) (tptp.ilf_type C tptp.set_type)) (= (tptp.ilf_type B (tptp.member_type C)) (tptp.member B C)))))))) (let ((_let_4 (forall ((B $$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 $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.ilf_type C (tptp.subset_type B)) (tptp.ilf_type C (tptp.member_type (tptp.power_set B)))))))))) (let ((_let_7 (forall ((B $$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_8 (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_9 (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_10 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (=> (and (tptp.subset B C) (tptp.subset C D)) (tptp.subset B D)))))))))) (let ((_let_11 (io_tptp.ilf_type_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 i_tptp.set_type_2))) (let ((_let_12 (io_tptp.ilf_type_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 i_tptp.set_type_2))) (let ((_let_13 (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_14 (io_tptp.subset_type_4 _let_13))) (let ((_let_15 (io_tptp.ilf_type_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_14))) (let ((_let_16 (io_tptp.relation_type_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_17 (io_tptp.ilf_type_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_16))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_15))) (let ((_let_20 (and (or (not (io_tptp.ilf_type_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_14)) (io_tptp.ilf_type_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_16)) _let_19))) (let ((_let_21 (not _let_12))) (let ((_let_22 (not _let_11))) (let ((_let_23 (or _let_22 _let_21 _let_20))) (let ((_let_24 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_13))) (let ((_let_27 (io_tptp.ilf_type_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 i_tptp.set_type_2))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_22 _let_21 _let_26 _let_18 _let_25))) (let ((_let_30 (forall ((B $$unsorted) (BOUND_VARIABLE_1505 $$unsorted) (BOUND_VARIABLE_1503 $$unsorted) (BOUND_VARIABLE_1501 $$unsorted)) (or (not (io_tptp.ilf_type_3 B i_tptp.set_type_2)) (not (io_tptp.ilf_type_3 BOUND_VARIABLE_1501 i_tptp.set_type_2)) (not (io_tptp.ilf_type_3 BOUND_VARIABLE_1505 i_tptp.set_type_2)) (tptp.subset B (tptp.cross_product BOUND_VARIABLE_1501 BOUND_VARIABLE_1505)) (not (io_tptp.ilf_type_3 BOUND_VARIABLE_1503 (io_tptp.relation_type_5 BOUND_VARIABLE_1501 BOUND_VARIABLE_1505))) (not (tptp.subset B BOUND_VARIABLE_1503)))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (not _let_30))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((B $$unsorted) (BOUND_VARIABLE_1505 $$unsorted) (BOUND_VARIABLE_1503 $$unsorted) (BOUND_VARIABLE_1501 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1501 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1505 tptp.set_type)) (tptp.subset B (tptp.cross_product BOUND_VARIABLE_1501 BOUND_VARIABLE_1505)) (not (tptp.ilf_type BOUND_VARIABLE_1503 (tptp.relation_type BOUND_VARIABLE_1501 BOUND_VARIABLE_1505))) (not (tptp.subset B BOUND_VARIABLE_1503))))) _let_32))))))) (let ((_let_34 (or))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_33) :args (_let_32))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_30))) (REFL :args (_let_31)) :args _let_34)) _let_33 :args (_let_31 true _let_30)))) (let ((_let_36 (REFL :args (_let_29)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_11))) :args _let_34)) :args ((or _let_11 _let_29))) _let_35 :args (_let_11 true _let_29)))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 2)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_12))) :args _let_34)) :args ((or _let_12 _let_29))) _let_35 :args (_let_12 true _let_29)))) (let ((_let_39 (forall ((B $$unsorted) (BOUND_VARIABLE_1129 $$unsorted) (BOUND_VARIABLE_1127 $$unsorted) (BOUND_VARIABLE_1125 $$unsorted)) (let ((_let_1 (io_tptp.subset_type_4 (tptp.cross_product B BOUND_VARIABLE_1125)))) (let ((_let_2 (io_tptp.relation_type_5 B BOUND_VARIABLE_1125))) (or (not (io_tptp.ilf_type_3 B i_tptp.set_type_2)) (not (io_tptp.ilf_type_3 BOUND_VARIABLE_1125 i_tptp.set_type_2)) (and (or (not (io_tptp.ilf_type_3 BOUND_VARIABLE_1129 _let_1)) (io_tptp.ilf_type_3 BOUND_VARIABLE_1129 _let_2)) (or (not (io_tptp.ilf_type_3 BOUND_VARIABLE_1127 _let_2)) (io_tptp.ilf_type_3 BOUND_VARIABLE_1127 _let_1))))))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((B $$unsorted) (BOUND_VARIABLE_1129 $$unsorted) (BOUND_VARIABLE_1127 $$unsorted) (BOUND_VARIABLE_1125 $$unsorted)) (let ((_let_1 (tptp.subset_type (tptp.cross_product B BOUND_VARIABLE_1125)))) (let ((_let_2 (tptp.relation_type B BOUND_VARIABLE_1125))) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1125 tptp.set_type)) (and (or (not (tptp.ilf_type BOUND_VARIABLE_1129 _let_1)) (tptp.ilf_type BOUND_VARIABLE_1129 _let_2)) (or (not (tptp.ilf_type BOUND_VARIABLE_1127 _let_2)) (tptp.ilf_type BOUND_VARIABLE_1127 _let_1))))))) _let_39))))))) (let ((_let_41 (not _let_20))) (let ((_let_42 (not _let_19))) (let ((_let_43 (tptp.power_set _let_13))) (let ((_let_44 (io_tptp.ilf_type_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 (io_tptp.member_type_6 _let_43)))) (let ((_let_45 (= _let_15 _let_44))) (let ((_let_46 (not _let_15))) (let ((_let_47 (io_tptp.ilf_type_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 i_tptp.set_type_2))) (let ((_let_48 (not _let_47))) (let ((_let_49 (io_tptp.ilf_type_3 _let_13 i_tptp.set_type_2))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_48 _let_45))) (let ((_let_52 (forall ((B $$unsorted) (BOUND_VARIABLE_1242 $$unsorted)) (or (not (io_tptp.ilf_type_3 B i_tptp.set_type_2)) (not (io_tptp.ilf_type_3 BOUND_VARIABLE_1242 i_tptp.set_type_2)) (= (io_tptp.ilf_type_3 BOUND_VARIABLE_1242 (io_tptp.subset_type_4 B)) (io_tptp.ilf_type_3 BOUND_VARIABLE_1242 (io_tptp.member_type_6 (tptp.power_set B)))))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_6)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((B $$unsorted) (BOUND_VARIABLE_1242 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1242 tptp.set_type)) (= (tptp.ilf_type BOUND_VARIABLE_1242 (tptp.subset_type B)) (tptp.ilf_type BOUND_VARIABLE_1242 (tptp.member_type (tptp.power_set B)))))) _let_52))))))) (let ((_let_54 (or _let_22 _let_21 _let_49))) (let ((_let_55 (forall ((B $$unsorted) (BOUND_VARIABLE_1079 $$unsorted)) (or (not (io_tptp.ilf_type_3 B i_tptp.set_type_2)) (not (io_tptp.ilf_type_3 BOUND_VARIABLE_1079 i_tptp.set_type_2)) (io_tptp.ilf_type_3 (tptp.cross_product B BOUND_VARIABLE_1079) i_tptp.set_type_2))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_9)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((B $$unsorted) (BOUND_VARIABLE_1079 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1079 tptp.set_type)) (tptp.ilf_type (tptp.cross_product B BOUND_VARIABLE_1079) tptp.set_type))) _let_55))))))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_22 _let_21 _let_49 (not _let_54)))) _let_37 _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cross_product B BOUND_VARIABLE_1079)))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_49 false _let_11 false _let_12 false _let_54)))) (let ((_let_58 (forall ((B $$unsorted)) (io_tptp.ilf_type_3 B i_tptp.set_type_2)))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 _let_58)))))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_58))) _let_59 :args (_let_47 false _let_58)))) (let ((_let_61 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_43))) (let ((_let_62 (= _let_61 _let_44))) (let ((_let_63 (not _let_44))) (let ((_let_64 (io_tptp.ilf_type_3 _let_43 i_tptp.set_type_2))) (let ((_let_65 (not _let_64))) (let ((_let_66 (tptp.empty _let_43))) (let ((_let_67 (or _let_48 _let_66 _let_65 _let_62))) (let ((_let_68 (forall ((B $$unsorted) (BOUND_VARIABLE_1316 $$unsorted)) (or (not (io_tptp.ilf_type_3 B i_tptp.set_type_2)) (tptp.empty BOUND_VARIABLE_1316) (not (io_tptp.ilf_type_3 BOUND_VARIABLE_1316 i_tptp.set_type_2)) (= (tptp.member B BOUND_VARIABLE_1316) (io_tptp.ilf_type_3 B (io_tptp.member_type_6 BOUND_VARIABLE_1316))))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((B $$unsorted) (BOUND_VARIABLE_1316 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (tptp.empty BOUND_VARIABLE_1316) (not (tptp.ilf_type BOUND_VARIABLE_1316 tptp.set_type)) (= (tptp.ilf_type B (tptp.member_type BOUND_VARIABLE_1316)) (tptp.member B BOUND_VARIABLE_1316)))) _let_68))))))) (let ((_let_70 (not _let_66))) (let ((_let_71 (and _let_70 _let_64))) (let ((_let_72 (or _let_50 _let_71))) (let ((_let_73 (forall ((B $$unsorted)) (let ((_let_1 (tptp.power_set B))) (or (not (io_tptp.ilf_type_3 B i_tptp.set_type_2)) (and (not (tptp.empty _let_1)) (io_tptp.ilf_type_3 _let_1 i_tptp.set_type_2))))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((B $$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_73))))))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_50 _let_71 (not _let_72)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (_let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.power_set B)))) :args (_let_73))) _let_74 :args (_let_72 false _let_73)) :args (_let_71 false _let_49 false _let_72)))) (let ((_let_76 (not _let_71))) (let ((_let_77 (forall ((D $$unsorted)) (or (not (io_tptp.ilf_type_3 D i_tptp.set_type_2)) (not (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) (tptp.member D (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))))) (let ((_let_78 (= _let_61 _let_77))) (let ((_let_79 (not _let_61))) (let ((_let_80 (or _let_48 _let_50 _let_78))) (let ((_let_81 (forall ((B $$unsorted) (BOUND_VARIABLE_1285 $$unsorted)) (or (not (io_tptp.ilf_type_3 B i_tptp.set_type_2)) (not (io_tptp.ilf_type_3 BOUND_VARIABLE_1285 i_tptp.set_type_2)) (= (tptp.member B (tptp.power_set BOUND_VARIABLE_1285)) (forall ((D $$unsorted)) (or (not (io_tptp.ilf_type_3 D i_tptp.set_type_2)) (not (tptp.member D B)) (tptp.member D BOUND_VARIABLE_1285)))))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((B $$unsorted) (BOUND_VARIABLE_1285 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1285 tptp.set_type)) (= (tptp.member B (tptp.power_set BOUND_VARIABLE_1285)) (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D B)) (tptp.member D BOUND_VARIABLE_1285)))))) _let_81))))))) (let ((_let_83 (forall ((D $$unsorted)) (or (not (io_tptp.ilf_type_3 D i_tptp.set_type_2)) (not (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) (tptp.member D (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))))) (let ((_let_84 (not _let_77))) (let ((_let_85 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_13))) (let ((_let_86 (= _let_85 _let_83))) (let ((_let_87 (not _let_83))) (let ((_let_88 (or _let_48 _let_50 _let_86))) (let ((_let_89 (forall ((B $$unsorted) (BOUND_VARIABLE_1197 $$unsorted)) (or (not (io_tptp.ilf_type_3 B i_tptp.set_type_2)) (not (io_tptp.ilf_type_3 BOUND_VARIABLE_1197 i_tptp.set_type_2)) (= (tptp.subset B BOUND_VARIABLE_1197) (forall ((D $$unsorted)) (or (not (io_tptp.ilf_type_3 D i_tptp.set_type_2)) (not (tptp.member D B)) (tptp.member D BOUND_VARIABLE_1197)))))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_7)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((B $$unsorted) (BOUND_VARIABLE_1197 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1197 tptp.set_type)) (= (tptp.subset B BOUND_VARIABLE_1197) (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D B)) (tptp.member D BOUND_VARIABLE_1197)))))) _let_89))))))) (let ((_let_91 (not _let_85))) (let ((_let_92 (or _let_28 _let_48 _let_25 _let_50 _let_91 _let_26))) (let ((_let_93 (forall ((B $$unsorted) (BOUND_VARIABLE_951 $$unsorted) (BOUND_VARIABLE_949 $$unsorted)) (or (not (io_tptp.ilf_type_3 B i_tptp.set_type_2)) (not (io_tptp.ilf_type_3 BOUND_VARIABLE_949 i_tptp.set_type_2)) (not (tptp.subset B BOUND_VARIABLE_949)) (not (io_tptp.ilf_type_3 BOUND_VARIABLE_951 i_tptp.set_type_2)) (not (tptp.subset BOUND_VARIABLE_949 BOUND_VARIABLE_951)) (tptp.subset B BOUND_VARIABLE_951))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_10)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((B $$unsorted) (BOUND_VARIABLE_951 $$unsorted) (BOUND_VARIABLE_949 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_949 tptp.set_type)) (not (tptp.subset B BOUND_VARIABLE_949)) (not (tptp.ilf_type BOUND_VARIABLE_951 tptp.set_type)) (not (tptp.subset BOUND_VARIABLE_949 BOUND_VARIABLE_951)) (tptp.subset B BOUND_VARIABLE_951))) _let_93))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_21 _let_20 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_20 1)) :args ((or _let_19 _let_41))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_18 _let_15 _let_42))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 4)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_34)) :args ((or _let_17 _let_29))) _let_35 :args (_let_17 true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_45)) :args ((or _let_46 _let_44 (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_62)) :args ((or _let_61 _let_63 (not _let_62)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_78)) :args ((or _let_77 _let_79 (not _let_78)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_77 (= D D)))) :args ((or _let_83 _let_84))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_86)) :args ((or _let_85 _let_87 (not _let_86)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_28 _let_26 _let_25 _let_48 _let_50 _let_91 (not _let_92)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_34)) :args ((or _let_27 _let_29))) _let_35 :args (_let_27 true _let_29)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 3)) _let_35 :args ((not _let_26) true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 5)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_34)) :args ((or _let_24 _let_29))) _let_35 :args (_let_24 true _let_29)) _let_60 _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.subset B BOUND_VARIABLE_951) true)) (not (= (tptp.subset B BOUND_VARIABLE_949) false))))) :args (_let_93))) _let_94 :args (_let_92 false _let_93)) :args (_let_91 false _let_27 true _let_26 false _let_24 false _let_47 false _let_49 false _let_92)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_48 _let_50 _let_86 (not _let_88)))) _let_60 _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset B BOUND_VARIABLE_1197)))) :args (_let_89))) _let_90 :args (_let_88 false _let_89)) :args (_let_86 false _let_47 false _let_49 false _let_88)) :args (_let_87 true _let_85 false _let_86)) :args (_let_84 true _let_83)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_48 _let_50 _let_78 (not _let_80)))) _let_60 _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_13 QUANTIFIERS_INST_E_MATCHING ((not (= (io_tptp.ilf_type_3 B i_tptp.set_type_2) false)) (not (= (io_tptp.ilf_type_3 BOUND_VARIABLE_1285 i_tptp.set_type_2) false))))) :args (_let_81))) _let_82 :args (_let_80 false _let_81)) :args (_let_78 false _let_47 false _let_49 false _let_80)) :args (_let_79 true _let_77 false _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_48 _let_66 _let_65 _let_62 (not _let_67)))) _let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_71 0)) :args ((or _let_70 _let_76))) _let_75 :args (_let_70 false _let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_71 1)) :args ((or _let_64 _let_76))) _let_75 :args (_let_64 false _let_71)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_43 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_68))) _let_69 :args (_let_67 false _let_68)) :args (_let_62 false _let_47 true _let_66 false _let_64 false _let_67)) :args (_let_63 true _let_61 false _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_48 _let_50 _let_45 (not _let_51)))) _let_60 _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (_let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_52))) _let_53 :args (_let_51 false _let_52)) :args (_let_45 false _let_47 false _let_49 false _let_51)) :args (_let_46 true _let_44 false _let_45)) :args (_let_42 false _let_17 true _let_15)) :args (_let_41 true _let_19)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_39))) _let_40 :args (_let_23 false _let_39)) _let_38 _let_37 :args (false true _let_20 false _let_23 false _let_12 false _let_11)) :args (_let_10 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (= (tptp.member D (tptp.cross_product B C)) (exists ((E $$unsorted)) (and (tptp.ilf_type E tptp.set_type) (exists ((F $$unsorted)) (and (tptp.ilf_type F tptp.set_type) (tptp.member E B) (tptp.member F C) (= D (tptp.ordered_pair E F))))))))))))) _let_9 _let_8 (forall ((B $$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_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.ordered_pair B C) tptp.set_type))))) _let_6 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (exists ((C $$unsorted)) (tptp.ilf_type C (tptp.subset_type B))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.subset B B))) _let_5 _let_4 _let_3 (forall ((B $$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.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) (= (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))) (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_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 62.64/62.91  )
% 62.64/62.91  % SZS output end Proof for SET640+3
% 62.64/62.91  % cvc5---1.0.5 exiting
% 62.64/62.91  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------