%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET016+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n021.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 14:36:47 EDT 2023

% Result   : Theorem 63.02s 63.28s
% Output   : Proof 63.02s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SET016+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.15/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.37  % Computer : n021.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Sat Aug 26 10:28:11 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.23/0.51  %----Proving TF0_NAR, FOF, or CNF
% 63.02/63.28  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.FKOij2urVX/cvc5---1.0.5_22251.p...
% 63.02/63.28  ------- get file name : TPTP file name is SET016+1
% 63.02/63.28  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22251.smt2...
% 63.02/63.28  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 63.02/63.28  --- Run --no-e-matching --full-saturate-quant at 5...
% 63.02/63.28  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 63.02/63.28  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 63.02/63.28  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 63.02/63.28  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 63.02/63.28  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 63.02/63.28  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 63.02/63.28  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 63.02/63.28  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 63.02/63.28  --- Run --relevant-triggers --full-saturate-quant at 5...
% 63.02/63.28  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 63.02/63.28  % SZS status Theorem for SET016+1
% 63.02/63.28  % SZS output start Proof for SET016+1
% 63.02/63.28  (
% 63.02/63.28  (let ((_let_1 (not (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (= (tptp.ordered_pair W X) (tptp.ordered_pair Y Z)) (tptp.member W tptp.universal_class)) (= W Y)))))) (let ((_let_2 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))))))) (let ((_let_4 (forall ((X $$unsorted)) (= (tptp.singleton X) (tptp.unordered_pair X X))))) (let ((_let_5 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))) (let ((_let_6 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.member U (tptp.unordered_pair X Y)) (and (tptp.member U tptp.universal_class) (or (= U X) (= U Y))))))) (let ((_let_7 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_7))) (let ((_let_9 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_10 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_9))) (let ((_let_11 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_10))) (let ((_let_12 (= _let_10 _let_7))) (let ((_let_13 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_14 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.universal_class))) (let ((_let_15 (and _let_14 _let_13))) (let ((_let_16 (= _let_8 _let_15))) (let ((_let_17 (not _let_8))) (let ((_let_18 (_let_6))) (let ((_let_19 (ASSUME :args _let_18))) (let ((_let_20 (not _let_15))) (let ((_let_21 (not _let_14))) (let ((_let_22 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_23 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_24 (= _let_23 _let_22))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_21 _let_13))) (let ((_let_27 (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (= (tptp.ordered_pair W X) (tptp.ordered_pair Y Z))) (not (tptp.member W tptp.universal_class)) (= W Y))))) (let ((_let_28 (not _let_26))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (or))) (let ((_let_31 (not _let_27))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_29) :args (_let_31))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_27))) (REFL :args (_let_28)) :args _let_30)) _let_29 :args (_let_28 true _let_27)))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_16)) :args ((or _let_15 _let_17 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_15 1)) :args ((or _let_13 _let_20))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 2)) _let_32 :args ((not _let_13) true _let_26)) :args (_let_20 true _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_18))) _let_19 :args (_let_16 false _let_6)) :args (_let_17 true _let_15 false _let_16)))) (let ((_let_34 (= _let_14 _let_11))) (let ((_let_35 (REFL :args (_let_26)))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 1)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_14))) :args _let_30)) :args ((or _let_14 _let_26))) _let_32 :args (_let_14 true _let_26)))) (let ((_let_37 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_38 (= _let_37 _let_7))) (let ((_let_39 (or _let_38 _let_12))) (let ((_let_40 (tptp.member _let_7 tptp.universal_class))) (let ((_let_41 (and _let_40 _let_39))) (let ((_let_42 (tptp.unordered_pair _let_37 _let_10))) (let ((_let_43 (tptp.member _let_7 _let_42))) (let ((_let_44 (= _let_43 _let_41))) (let ((_let_45 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_46 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_47 (tptp.unordered_pair _let_46 _let_45))) (let ((_let_48 (tptp.member _let_7 _let_47))) (let ((_let_49 (= _let_23 _let_42))) (let ((_let_50 (= _let_22 _let_47))) (let ((_let_51 (= _let_46 _let_7))) (let ((_let_52 (or _let_51 (= _let_45 _let_7)))) (let ((_let_53 (and _let_40 _let_52))) (let ((_let_54 (= _let_48 _let_53))) (let ((_let_55 (_let_4))) (let ((_let_56 (ASSUME :args _let_55))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_PROP)) :args _let_55)) _let_56 :args (_let_51 false _let_4)))) (let ((_let_58 (not _let_51))) (let ((_let_59 (_let_5))) (let ((_let_60 (ASSUME :args _let_59))) (let ((_let_61 (_let_3))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 ((tptp.ordered_pair X Y)))) (let ((_let_64 (and _let_24 _let_50 _let_49 _let_48))) (let ((_let_65 (ASSUME :args (_let_48)))) (let ((_let_66 (APPLY_UF tptp.member))) (let ((_let_67 (ASSUME :args (_let_50)))) (let ((_let_68 (ASSUME :args (_let_24)))) (let ((_let_69 (ASSUME :args (_let_49)))) (let ((_let_70 (= _let_46 _let_37))) (let ((_let_71 (not _let_38))) (let ((_let_72 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_73 (= _let_37 _let_72))) (let ((_let_74 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_72))) (let ((_let_75 (not _let_70))) (let ((_let_76 (= _let_14 _let_74))) (let ((_let_77 (not _let_74))) (let ((_let_78 (not _let_73))) (let ((_let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_8))))) (let ((_let_80 (REFL :args (_let_58)))) (let ((_let_81 (_let_75))) (let ((_let_82 (ASSUME :args (_let_74)))) (let ((_let_83 (ASSUME :args (_let_73)))) (let ((_let_84 (ASSUME :args (_let_70)))) (let ((_let_85 (ASSUME :args (_let_51)))) (let ((_let_86 (SYMM _let_85))) (let ((_let_87 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_88 (ASSUME :args (_let_17)))) (let ((_let_89 (FALSE_INTRO _let_88))) (let ((_let_90 (and _let_51 _let_75))) (let ((_let_91 (_let_51 _let_75))) (let ((_let_92 (ASSUME :args _let_81))) (let ((_let_93 (not _let_12))) (let ((_let_94 (not _let_11))) (let ((_let_95 (ASSUME :args (_let_12)))) (let ((_let_96 (ASSUME :args (_let_11)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_88 _let_95 _let_96) :args (_let_12 _let_17 _let_11)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_96)) (CONG _let_87 (SYMM (SYMM _let_95)) :args _let_66) _let_89)) :args (_let_17 _let_12 _let_11)) :args ((not (and _let_12 _let_17 _let_11)) SB_LITERAL))) (CONG (REFL :args (_let_93)) _let_79 (REFL :args (_let_94)) :args _let_30)) :args ((or _let_8 _let_94 _let_93))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_12 _let_38 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_90)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_85 _let_92) (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG _let_86 (REFL :args (_let_37)) :args (=)) (FALSE_INTRO _let_92)) :args ((= _let_38 false)))) :args _let_91)) :args _let_91)) :args (true _let_90)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_70))) (REFL :args (_let_71)) :args _let_30)) :args ((or _let_70 _let_58 _let_71))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_82 _let_83 _let_84 _let_85 _let_88) :args (_let_70 _let_73 _let_74 _let_51 _let_17)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM _let_89) (CONG _let_87 (TRANS _let_86 (SYMM (SYMM _let_84)) (SYMM (SYMM _let_83))) :args _let_66) (TRUE_INTRO _let_82))) :args (_let_74 _let_73 _let_70 _let_51 _let_17)) :args ((not (and _let_70 _let_73 _let_74 _let_51 _let_17)) SB_LITERAL))) (CONG (REFL :args _let_81) (REFL :args (_let_78)) (REFL :args (_let_77)) _let_80 _let_79 :args _let_30)) :args ((or _let_78 _let_77 _let_58 _let_75 _let_8))) _let_33 _let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_76)) :args ((or _let_21 _let_74 (not _let_76)))) _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_18))) _let_19 :args (_let_76 false _let_6)) :args (_let_74 false _let_14 false _let_76)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_55)) _let_56 :args (_let_73 false _let_4)) :args (_let_75 true _let_8 false _let_51 false _let_74 false _let_73)) _let_57 :args (_let_71 true _let_70 false _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_41 1)) :args ((or _let_39 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_44)) :args ((or _let_41 (not _let_43) (not _let_44)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_64)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_65 _let_67 _let_68 _let_69) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_7)) (TRANS (SYMM _let_69) (SYMM (SYMM _let_68)) (SYMM (SYMM _let_67))) :args _let_66) (TRUE_INTRO _let_65))) :args (_let_48 _let_50 _let_24 _let_49))) :args (_let_24 _let_50 _let_49 _let_48))) :args (true _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_30)) :args ((or _let_24 _let_26))) _let_32 :args (_let_24 true _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_63)) :args _let_61)) _let_62 :args (_let_50 false _let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_63)) :args _let_61)) _let_62 :args (_let_49 false _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_54)) :args ((or _let_48 (not _let_53) (not _let_54)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_53)) :args ((or (not _let_40) _let_53 (not _let_52)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_59)) _let_60 :args (_let_40 false _let_5)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_52 0)) :args ((or _let_58 _let_52))) _let_57 :args (_let_52 false _let_51)) :args (_let_53 false _let_40 false _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_19 :args (_let_7 _let_46 _let_45 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_18))) _let_19 :args (_let_54 false _let_6)) :args (_let_48 false _let_53 false _let_54)) :args (_let_43 false _let_24 false _let_50 false _let_49 false _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_19 :args (_let_7 _let_37 _let_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_18))) _let_19 :args (_let_44 false _let_6)) :args (_let_41 false _let_43 false _let_44)) :args (_let_39 false _let_41)) :args (_let_12 true _let_38 false _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_34)) :args ((or _let_21 _let_11 (not _let_34)))) _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_18))) _let_19 :args (_let_34 false _let_6)) :args (_let_11 false _let_14 false _let_34)) _let_33 :args (false false _let_12 false _let_11 true _let_8)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.subclass X Y) (forall ((U $$unsorted)) (=> (tptp.member U X) (tptp.member U Y))))) (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)) (forall ((X $$unsorted) (Y $$unsorted)) (= (= X Y) (and (tptp.subclass X Y) (tptp.subclass Y X)))) _let_6 _let_5 _let_4 _let_3 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)) (and (tptp.member U X) (tptp.member V Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (=> (and (tptp.member X tptp.universal_class) (tptp.member Y tptp.universal_class)) (and (= (tptp.first _let_1) X) (= (tptp.second _let_1) Y))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.member Z (tptp.cross_product X Y)) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.member (tptp.ordered_pair X Y) tptp.element_relation) (and (tptp.member Y tptp.universal_class) (tptp.member X Y)))) (tptp.subclass tptp.element_relation _let_2) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.member Z (tptp.intersection X Y)) (and (tptp.member Z X) (tptp.member Z Y)))) (forall ((X $$unsorted) (Z $$unsorted)) (= (tptp.member Z (tptp.complement X)) (and (tptp.member Z tptp.universal_class) (not (tptp.member Z X))))) (forall ((X $$unsorted) (XR $$unsorted) (Y $$unsorted)) (= (tptp.restrict XR X Y) (tptp.intersection XR (tptp.cross_product X Y)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.null_class))) (forall ((X $$unsorted) (Z $$unsorted)) (= (tptp.member Z (tptp.domain_of X)) (and (tptp.member Z tptp.universal_class) (not (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class))))) (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (= (tptp.member _let_1 (tptp.rotate X)) (and (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X))))) (forall ((X $$unsorted)) (tptp.subclass (tptp.rotate X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (= (tptp.member _let_1 (tptp.flip X)) (and (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X))))) (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.member Z (tptp.union X Y)) (or (tptp.member Z X) (tptp.member Z Y)))) (forall ((X $$unsorted)) (= (tptp.successor X) (tptp.union X (tptp.singleton X)))) (tptp.subclass tptp.successor_relation _let_2) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation) (and (tptp.member X tptp.universal_class) (tptp.member Y tptp.universal_class) (= (tptp.successor X) Y)))) (forall ((Y $$unsorted)) (= (tptp.inverse Y) (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))))) (forall ((Z $$unsorted)) (= (tptp.range_of Z) (tptp.domain_of (tptp.inverse Z)))) (forall ((X $$unsorted) (XR $$unsorted)) (= (tptp.image XR X) (tptp.range_of (tptp.restrict XR X tptp.universal_class)))) (forall ((X $$unsorted)) (= (tptp.inductive X) (and (tptp.member tptp.null_class X) (tptp.subclass (tptp.image tptp.successor_relation X) X)))) (exists ((X $$unsorted)) (and (tptp.member X tptp.universal_class) (tptp.inductive X) (forall ((Y $$unsorted)) (=> (tptp.inductive Y) (tptp.subclass X Y))))) (forall ((U $$unsorted) (X $$unsorted)) (= (tptp.member U (tptp.sum_class X)) (exists ((Y $$unsorted)) (and (tptp.member U Y) (tptp.member Y X))))) (forall ((X $$unsorted)) (=> (tptp.member X tptp.universal_class) (tptp.member (tptp.sum_class X) tptp.universal_class))) (forall ((U $$unsorted) (X $$unsorted)) (= (tptp.member U (tptp.power_class X)) (and (tptp.member U tptp.universal_class) (tptp.subclass U X)))) (forall ((U $$unsorted)) (=> (tptp.member U tptp.universal_class) (tptp.member (tptp.power_class U) tptp.universal_class))) (forall ((XR $$unsorted) (YR $$unsorted)) (tptp.subclass (tptp.compose YR XR) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((XR $$unsorted) (YR $$unsorted) (U $$unsorted) (V $$unsorted)) (= (tptp.member (tptp.ordered_pair U V) (tptp.compose YR XR)) (and (tptp.member U tptp.universal_class) (tptp.member V (tptp.image YR (tptp.image XR (tptp.singleton U))))))) (forall ((Z $$unsorted)) (= (tptp.member Z tptp.identity_relation) (exists ((X $$unsorted)) (and (tptp.member X tptp.universal_class) (= Z (tptp.ordered_pair X X)))))) (forall ((XF $$unsorted)) (= (tptp.function XF) (and (tptp.subclass XF (tptp.cross_product tptp.universal_class tptp.universal_class)) (tptp.subclass (tptp.compose XF (tptp.inverse XF)) tptp.identity_relation)))) (forall ((X $$unsorted) (XF $$unsorted)) (=> (and (tptp.member X tptp.universal_class) (tptp.function XF)) (tptp.member (tptp.image XF X) tptp.universal_class))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.disjoint X Y) (forall ((U $$unsorted)) (not (and (tptp.member U X) (tptp.member U Y)))))) (forall ((X $$unsorted)) (=> (not (= X tptp.null_class)) (exists ((U $$unsorted)) (and (tptp.member U tptp.universal_class) (tptp.member U X) (tptp.disjoint U X))))) (forall ((XF $$unsorted) (Y $$unsorted)) (= (tptp.apply XF Y) (tptp.sum_class (tptp.image XF (tptp.singleton Y))))) (exists ((XF $$unsorted)) (and (tptp.function XF) (forall ((Y $$unsorted)) (=> (tptp.member Y tptp.universal_class) (or (= Y tptp.null_class) (tptp.member (tptp.apply XF Y) Y)))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 63.02/63.29  )
% 63.02/63.29  % SZS output end Proof for SET016+1
% 63.02/63.29  % cvc5---1.0.5 exiting
% 63.02/63.29  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------