%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET656+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 14:39:47 EDT 2023

% Result   : Theorem 81.26s 77.32s
% Output   : Proof 81.26s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET656+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.16/0.35  % Computer : n016.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit   : 300
% 0.16/0.35  % WCLimit    : 300
% 0.16/0.35  % DateTime   : Sat Aug 26 14:19:42 EDT 2023
% 0.16/0.36  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 81.26/77.32  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.cvnIXda7q1/cvc5---1.0.5_29488.p...
% 81.26/77.32  ------- get file name : TPTP file name is SET656+3
% 81.26/77.32  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_29488.smt2...
% 81.26/77.32  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 81.26/77.32  --- Run --no-e-matching --full-saturate-quant at 5...
% 81.26/77.32  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 81.26/77.32  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 81.26/77.32  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 81.26/77.32  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 81.26/77.32  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 81.26/77.32  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 81.26/77.32  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 81.26/77.32  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 81.26/77.32  --- Run --relevant-triggers --full-saturate-quant at 5...
% 81.26/77.32  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 81.26/77.32  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 81.26/77.32  --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 81.26/77.32  % SZS status Theorem for SET656+3
% 81.26/77.32  % SZS output start Proof for SET656+3
% 81.26/77.32  (
% 81.26/77.32  (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 $$unsorted)) (=> (tptp.ilf_type D (tptp.relation_type B C)) (= (tptp.intersection D (tptp.cross_product B C)) D)))))))))) (let ((_let_2 (forall ((B $$unsorted)) (tptp.ilf_type B tptp.set_type)))) (let ((_let_3 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (and (not (tptp.empty C)) (tptp.ilf_type C tptp.set_type)) (= (tptp.ilf_type B (tptp.member_type C)) (tptp.member B C)))))))) (let ((_let_4 (forall ((B $$unsorted)) (let ((_let_1 (tptp.power_set B))) (=> (tptp.ilf_type B tptp.set_type) (and (not (tptp.empty _let_1)) (tptp.ilf_type _let_1 tptp.set_type))))))) (let ((_let_5 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.member B (tptp.power_set C)) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (=> (tptp.member D B) (tptp.member D C))))))))))) (let ((_let_6 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.subset B C) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (=> (tptp.member D B) (tptp.member D C))))))))))) (let ((_let_7 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.ilf_type C (tptp.subset_type B)) (tptp.ilf_type C (tptp.member_type (tptp.power_set B)))))))))) (let ((_let_8 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (and (forall ((D $$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 $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (=> (tptp.subset B C) (= (tptp.intersection B C) B)))))))) (let ((_let_11 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.set_type))) (let ((_let_12 (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (tptp.power_set _let_12))) (let ((_let_14 (tptp.empty _let_13))) (let ((_let_15 (tptp.ilf_type _let_13 tptp.set_type))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_13))) (let ((_let_17 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.member_type _let_13)))) (let ((_let_18 (= _let_17 _let_16))) (let ((_let_19 (not _let_15))) (let ((_let_20 (not _let_11))) (let ((_let_21 (or _let_20 _let_14 _let_19 _let_18))) (let ((_let_22 (_let_2))) (let ((_let_23 (ASSUME :args _let_22))) (let ((_let_24 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_22)) _let_23 :args (_let_11 false _let_2)))) (let ((_let_25 (not _let_14))) (let ((_let_26 (and _let_25 _let_15))) (let ((_let_27 (tptp.ilf_type _let_12 tptp.set_type))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26))) (let ((_let_30 (forall ((B $$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_31 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.set_type))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.set_type))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33 _let_27))) (let ((_let_37 (forall ((B $$unsorted) (BOUND_VARIABLE_1217 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1217 tptp.set_type)) (tptp.ilf_type (tptp.cross_product B BOUND_VARIABLE_1217) tptp.set_type))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12)))) (let ((_let_40 (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_41 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_40))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_35 _let_33 _let_42 _let_39))) (let ((_let_44 (forall ((B $$unsorted) (BOUND_VARIABLE_1949 $$unsorted) (BOUND_VARIABLE_1947 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1947 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1949 (tptp.relation_type B BOUND_VARIABLE_1947))) (= BOUND_VARIABLE_1949 (tptp.intersection BOUND_VARIABLE_1949 (tptp.cross_product B BOUND_VARIABLE_1947))))))) (let ((_let_45 (not _let_43))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (or))) (let ((_let_48 (not _let_44))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_46) :args (_let_48))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_44))) (REFL :args (_let_45)) :args _let_47)) _let_46 :args (_let_45 true _let_44)))) (let ((_let_50 (REFL :args (_let_43)))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 1)) (CONG _let_50 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_47)) :args ((or _let_32 _let_43))) _let_49 :args (_let_32 true _let_43)))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 0)) (CONG _let_50 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_47)) :args ((or _let_34 _let_43))) _let_49 :args (_let_34 true _let_43)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_33 _let_27 (not _let_36)))) _let_52 _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cross_product B BOUND_VARIABLE_1217)))) :args (_let_37))) _let_38 :args (_let_36 false _let_37)) :args (_let_27 false _let_34 false _let_32 false _let_36)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_28 _let_26 (not _let_29)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (_let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.power_set B)))) :args (_let_30))) _let_31 :args (_let_29 false _let_30)) :args (_let_26 false _let_27 false _let_29)))) (let ((_let_55 (not _let_26))) (let ((_let_56 (not _let_18))) (let ((_let_57 (tptp.subset_type _let_12))) (let ((_let_58 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_57))) (let ((_let_59 (= _let_58 _let_17))) (let ((_let_60 (or _let_28 _let_20 _let_59))) (let ((_let_61 (forall ((B $$unsorted) (BOUND_VARIABLE_1498 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1498 tptp.set_type)) (= (tptp.ilf_type BOUND_VARIABLE_1498 (tptp.subset_type B)) (tptp.ilf_type BOUND_VARIABLE_1498 (tptp.member_type (tptp.power_set B)))))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (or _let_42 _let_58))) (let ((_let_64 (and (or (not (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_57)) (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_40)) _let_63))) (let ((_let_65 (or _let_35 _let_33 _let_64))) (let ((_let_66 (forall ((B $$unsorted) (BOUND_VARIABLE_1337 $$unsorted) (BOUND_VARIABLE_1335 $$unsorted) (BOUND_VARIABLE_1333 $$unsorted)) (let ((_let_1 (tptp.subset_type (tptp.cross_product B BOUND_VARIABLE_1333)))) (let ((_let_2 (tptp.relation_type B BOUND_VARIABLE_1333))) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1333 tptp.set_type)) (and (or (not (tptp.ilf_type BOUND_VARIABLE_1337 _let_1)) (tptp.ilf_type BOUND_VARIABLE_1337 _let_2)) (or (not (tptp.ilf_type BOUND_VARIABLE_1335 _let_2)) (tptp.ilf_type BOUND_VARIABLE_1335 _let_1))))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.member D (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_69 (= _let_16 _let_68))) (let ((_let_70 (not _let_16))) (let ((_let_71 (or _let_20 _let_28 _let_69))) (let ((_let_72 (forall ((B $$unsorted) (BOUND_VARIABLE_1587 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1587 tptp.set_type)) (= (tptp.member B (tptp.power_set BOUND_VARIABLE_1587)) (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D B)) (tptp.member D BOUND_VARIABLE_1587)))))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.member D (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_75 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12))) (let ((_let_76 (= _let_75 _let_74))) (let ((_let_77 (not _let_74))) (let ((_let_78 (or _let_20 _let_28 _let_76))) (let ((_let_79 (forall ((B $$unsorted) (BOUND_VARIABLE_1551 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1551 tptp.set_type)) (= (tptp.subset B BOUND_VARIABLE_1551) (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D B)) (tptp.member D BOUND_VARIABLE_1551)))))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (not _let_75))) (let ((_let_82 (or _let_20 _let_28 _let_81 _let_39))) (let ((_let_83 (forall ((B $$unsorted) (BOUND_VARIABLE_1092 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1092 tptp.set_type)) (not (tptp.subset B BOUND_VARIABLE_1092)) (= B (tptp.intersection B BOUND_VARIABLE_1092)))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (forall ((B $$unsorted) (BOUND_VARIABLE_1618 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (tptp.empty BOUND_VARIABLE_1618) (not (tptp.ilf_type BOUND_VARIABLE_1618 tptp.set_type)) (= (tptp.ilf_type B (tptp.member_type BOUND_VARIABLE_1618)) (tptp.member B BOUND_VARIABLE_1618)))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_20 _let_14 _let_19 _let_18 (not _let_21)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_85))) _let_86 :args (_let_21 false _let_85)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_18)) :args ((or _let_16 (not _let_17) _let_56))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_69)) :args ((or _let_68 _let_70 (not _let_69)))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_74 (= D D)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_76)) :args ((or _let_75 _let_77 (not _let_76)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_39 _let_20 _let_28 _let_81 (not _let_82)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 3)) _let_49 :args ((not _let_39) true _let_43)) _let_24 _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.intersection B BOUND_VARIABLE_1092)))) :args (_let_83))) _let_84 :args (_let_82 false _let_83)) :args (_let_81 true _let_39 false _let_11 false _let_27 false _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_20 _let_28 _let_76 (not _let_78)))) _let_24 _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset B BOUND_VARIABLE_1551)))) :args (_let_79))) _let_80 :args (_let_78 false _let_79)) :args (_let_76 false _let_11 false _let_27 false _let_78)) :args (_let_77 true _let_75 false _let_76)) :args ((not _let_68) true _let_74)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_20 _let_28 _let_69 (not _let_71)))) _let_24 _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12 QUANTIFIERS_INST_E_MATCHING ((tptp.power_set BOUND_VARIABLE_1587) (not (= (tptp.ilf_type B tptp.set_type) false))))) :args (_let_72))) _let_73 :args (_let_71 false _let_72)) :args (_let_69 false _let_11 false _let_27 false _let_71)) :args (_let_70 true _let_68 false _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_59)) :args ((or (not _let_58) _let_17 (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_42 _let_58 (not _let_63)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 2)) (CONG _let_50 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_47)) :args ((or _let_41 _let_43))) _let_49 :args (_let_41 true _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_64 1)) :args ((or _let_63 (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_35 _let_33 _let_64 (not _let_65)))) _let_52 _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((tptp.ilf_type BOUND_VARIABLE_1337 (tptp.subset_type (tptp.cross_product B BOUND_VARIABLE_1333))) (tptp.ilf_type BOUND_VARIABLE_1335 (tptp.relation_type B BOUND_VARIABLE_1333))))) :args (_let_66))) _let_67 :args (_let_65 false _let_66)) :args (_let_64 false _let_34 false _let_32 false _let_65)) :args (_let_63 false _let_64)) :args (_let_58 false _let_41 false _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_20 _let_28 _let_59 (not _let_60)))) _let_24 _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.ilf_type BOUND_VARIABLE_1498 (tptp.subset_type B))))) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_59 false _let_11 false _let_27 false _let_60)) :args (_let_17 false _let_58 false _let_59)) :args (_let_56 true _let_16 false _let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_26 1)) :args ((or _let_15 _let_55))) _let_54 :args (_let_15 false _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_26 0)) :args ((or _let_25 _let_55))) _let_54 :args (_let_25 false _let_26)) _let_24 :args (false false _let_21 true _let_18 false _let_15 true _let_14 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 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (= (tptp.member D (tptp.intersection B C)) (and (tptp.member D B) (tptp.member D C))))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (tptp.ilf_type (tptp.intersection B C) tptp.set_type))))) _let_8 (forall ((B $$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))))))) (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 $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.intersection B C) (tptp.intersection C B)))))) (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 $$unsorted)) (=> (tptp.ilf_type B tptp.binary_relation_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.binary_relation_type) (=> (= B C) (= C B)))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.binary_relation_type) (= B B))) _let_6 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.subset B B))) _let_5 _let_4 _let_3 (forall ((B $$unsorted)) (=> (and (not (tptp.empty B)) (tptp.ilf_type B tptp.set_type)) (exists ((C $$unsorted)) (tptp.ilf_type C (tptp.member_type B))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (= 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.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)) (forall ((E $$unsorted)) (=> (tptp.ilf_type E (tptp.relation_type B C)) (= (tptp.intersection4 B C D E) (tptp.intersection D E)))))))))) (forall ((B $$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.relation_type B C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.relation_type B C))) (=> (tptp.ilf_type E _let_1) (tptp.ilf_type (tptp.intersection4 B C D E) _let_1)))))))))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 81.26/77.32  )
% 81.26/77.32  % SZS output end Proof for SET656+3
% 81.26/77.32  % cvc5---1.0.5 exiting
% 81.26/77.32  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------