TSTP Solution File: NUM621+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM621+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 10:45:41 EDT 2023
% Result : Theorem 153.09s 153.29s
% Output : Proof 153.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM621+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n024.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 : Fri Aug 25 14:11:54 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 153.09/153.29 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.1MV0IeMztH/cvc5---1.0.5_15264.p...
% 153.09/153.29 ------- get file name : TPTP file name is NUM621+1
% 153.09/153.29 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15264.smt2...
% 153.09/153.29 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 153.09/153.29 --- Run --no-e-matching --full-saturate-quant at 5...
% 153.09/153.29 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 153.09/153.29 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 153.09/153.29 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 153.09/153.29 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 153.09/153.29 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 153.09/153.29 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 153.09/153.29 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 153.09/153.29 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 153.09/153.29 --- Run --relevant-triggers --full-saturate-quant at 5...
% 153.09/153.29 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 153.09/153.29 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 153.09/153.29 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 153.09/153.29 --- Run --no-cbqi --full-saturate-quant at 10...
% 153.09/153.29 --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 153.09/153.29 % SZS status Theorem for NUM621+1
% 153.09/153.29 % SZS output start Proof for NUM621+1
% 153.09/153.29 (
% 153.09/153.29 (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xn)))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN tptp.xm))) (let ((_let_3 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (let ((_let_4 (tptp.aSubsetOf0 _let_3 _let_2))) (let ((_let_5 (not (=> _let_4 (tptp.aElementOf0 tptp.xx _let_1))))) (let ((_let_6 (tptp.szmzizndt0 _let_2))) (let ((_let_7 (= tptp.xx _let_6))) (let ((_let_8 (tptp.sdtlpdtrp0 tptp.xe tptp.xm))) (let ((_let_9 (and (tptp.aElementOf0 tptp.xm tptp.szNzAzT0) (= tptp.xx _let_8)))) (let ((_let_10 (tptp.aElementOf0 tptp.xx tptp.xP))) (let ((_let_11 (tptp.szDzizrdt0 tptp.xd))) (let ((_let_12 (tptp.sdtlpdtrp0 tptp.xe tptp.xn))) (let ((_let_13 (tptp.aElementOf0 tptp.xn tptp.szNzAzT0))) (let ((_let_14 (tptp.sdtlbdtrb0 tptp.xd _let_11))) (let ((_let_15 (tptp.aElementOf0 tptp.xn _let_14))) (let ((_let_16 (and _let_15 _let_13 (= _let_12 tptp.xp)))) (let ((_let_17 (tptp.sbrdtbr0 tptp.xP))) (let ((_let_18 (= _let_17 tptp.xk))) (let ((_let_19 (tptp.aElementOf0 tptp.xp tptp.xO))) (let ((_let_20 (tptp.szmzizndt0 tptp.xQ))) (let ((_let_21 (tptp.sdtmndt0 tptp.xQ _let_20))) (let ((_let_22 (and (tptp.aSet0 tptp.xP) (= tptp.xP _let_21)))) (let ((_let_23 (= tptp.xp _let_20))) (let ((_let_24 (tptp.szDzozmdt0 tptp.xc))) (let ((_let_25 (tptp.aSubsetOf0 tptp.xQ tptp.szNzAzT0))) (let ((_let_26 (tptp.aSubsetOf0 tptp.xQ tptp.xO))) (let ((_let_27 (and _let_26 (not (= tptp.xQ tptp.slcrc0))))) (let ((_let_28 (tptp.aSet0 tptp.xO))) (let ((_let_29 (and _let_28 (tptp.isCountable0 tptp.xO)))) (let ((_let_30 (tptp.sdtlcdtrc0 tptp.xe _let_14))) (let ((_let_31 (and _let_28 (= tptp.xO _let_30)))) (let ((_let_32 (tptp.szDzozmdt0 tptp.xd))) (let ((_let_33 (tptp.szDzozmdt0 tptp.xe))) (let ((_let_34 (tptp.aFunction0 tptp.xe))) (let ((_let_35 (and _let_34 (= _let_33 tptp.szNzAzT0) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xe W0) (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)))))))) (let ((_let_36 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aSubsetOf0 _let_1 tptp.szNzAzT0) (tptp.isCountable0 _let_1))))))) (let ((_let_37 (tptp.szDzozmdt0 tptp.xN))) (let ((_let_38 (and (tptp.aFunction0 tptp.xN) (= _let_37 tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xN tptp.sz00) tptp.xS) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (=> (and (tptp.aSubsetOf0 _let_2 tptp.szNzAzT0) (tptp.isCountable0 _let_2)) (and (tptp.aSubsetOf0 _let_1 (tptp.sdtmndt0 _let_2 (tptp.szmzizndt0 _let_2))) (tptp.isCountable0 _let_1)))))))))) (let ((_let_39 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK)))) (let ((_let_40 (not (= tptp.xK tptp.sz00)))) (let ((_let_41 (tptp.slbdtrb0 tptp.sz00))) (let ((_let_42 (= _let_41 tptp.slcrc0))) (let ((_let_43 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szmzizndt0 W1))) (let ((_let_2 (tptp.szmzizndt0 W0))) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.aSubsetOf0 W1 tptp.szNzAzT0) (not (= W0 tptp.slcrc0)) (not (= W1 tptp.slcrc0))) (=> (and (tptp.aElementOf0 _let_2 W1) (tptp.aElementOf0 _let_1 W0)) (= _let_2 _let_1)))))))) (let ((_let_44 (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (not (= W0 tptp.slcrc0))) (forall ((W1 $$unsorted)) (= (= W1 (tptp.szmzizndt0 W0)) (and (tptp.aElementOf0 W1 W0) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W1 W2)))))))))) (let ((_let_45 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0)))) (let ((_let_46 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 W0) (not (= W3 W1)))))))))))) (let ((_let_47 (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (tptp.isFinite0 W1))))))) (let ((_let_48 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))))) (let ((_let_49 (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (= W0 tptp.slcrc0)))))) (let ((_let_50 (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (tptp.isFinite0 W0)))))) (let ((_let_51 (tptp.isFinite0 tptp.slcrc0))) (let ((_let_52 (forall ((W0 $$unsorted)) (= (= W0 tptp.slcrc0) (and (tptp.aSet0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))))) (let ((_let_53 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_54 (= _let_41 tptp.xQ))) (let ((_let_55 (tptp.aSubsetOf0 tptp.xQ _let_37))) (let ((_let_56 (tptp.aSubsetOf0 _let_2 _let_37))) (let ((_let_57 (= _let_41 _let_2))) (let ((_let_58 (tptp.aElementOf0 _let_6 tptp.xQ))) (let ((_let_59 (= _let_20 _let_6))) (let ((_let_60 (tptp.aElementOf0 _let_20 _let_2))) (let ((_let_61 (not _let_60))) (let ((_let_62 (not _let_58))) (let ((_let_63 (not _let_55))) (let ((_let_64 (not _let_56))) (let ((_let_65 (or _let_64 _let_63 _let_57 _let_54 _let_62 _let_61 _let_59))) (let ((_let_66 (1))) (let ((_let_67 (SYMM (ASSUME :args (_let_42))))) (let ((_let_68 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))) :args _let_66))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (AND_ELIM _let_69 :args _let_66))) (let ((_let_71 (2))) (let ((_let_72 (AND_ELIM _let_69 :args _let_71))) (let ((_let_73 (AND_ELIM (ASSUME :args (_let_31)) :args _let_66))) (let ((_let_74 (ASSUME :args (_let_23)))) (let ((_let_75 (AND_ELIM (ASSUME :args (_let_22)) :args _let_66))) (let ((_let_76 (AND_INTRO _let_75 _let_74 _let_73 _let_72 _let_70 _let_68 _let_67))) (let ((_let_77 (ASSUME :args (_let_9)))) (let ((_let_78 (AND_INTRO (AND_ELIM _let_77 :args _let_66) (EQ_RESOLVE (SYMM (ASSUME :args (_let_18))) (MACRO_SR_EQ_INTRO _let_76 :args ((= tptp.xk _let_17) SB_DEFAULT SBA_FIXPOINT))) _let_75 _let_74 _let_73 _let_72 _let_70 _let_68 _let_67))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_73 _let_72 _let_70 _let_68 _let_67) :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (and _let_56 (tptp.isCountable0 _let_2)))) (let ((_let_81 (tptp.aElementOf0 tptp.xm _let_37))) (let ((_let_82 (not _let_81))) (let ((_let_83 (or _let_82 _let_80))) (let ((_let_84 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szDzozmdt0 tptp.xN))) (or (not (tptp.aElementOf0 W0 _let_2)) (and (tptp.aSubsetOf0 _let_1 _let_2) (tptp.isCountable0 _let_1)))))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_36)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_72 _let_70 _let_68 _let_67) :args ((forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aSubsetOf0 _let_1 tptp.szNzAzT0) (tptp.isCountable0 _let_1))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_86 (_let_84))) (let ((_let_87 ((not (= (tptp.aElementOf0 W0 _let_37) false))))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_80 0)) :args ((or _let_56 (not _let_80)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_82 _let_80 (not _let_83)))) (EQ_RESOLVE _let_77 (MACRO_SR_EQ_INTRO _let_78 :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_87)) :args _let_86)) _let_85 :args (_let_83 false _let_84)) :args (_let_80 false _let_81 false _let_83)) :args (_let_56 false _let_80)))) (let ((_let_89 (tptp.isFinite0 _let_41))) (let ((_let_90 (tptp.isFinite0 _let_2))) (let ((_let_91 (not _let_57))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_51)) (MACRO_SR_EQ_INTRO _let_78 :args (_let_51 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (tptp.isFinite0 _let_3))) (let ((_let_94 (not _let_4))) (let ((_let_95 (not _let_90))) (let ((_let_96 (tptp.aSet0 _let_2))) (let ((_let_97 (not _let_96))) (let ((_let_98 (or _let_97 _let_95 _let_94 _let_93))) (let ((_let_99 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2058 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.isFinite0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_2058 W0)) (tptp.isFinite0 BOUND_VARIABLE_2058))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_47)) (MACRO_SR_EQ_INTRO :args (_let_47 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (not _let_93))) (let ((_let_102 (tptp.isCountable0 _let_3))) (let ((_let_103 (not _let_102))) (let ((_let_104 (tptp.aSet0 _let_3))) (let ((_let_105 (not _let_104))) (let ((_let_106 (or _let_105 _let_103 _let_101))) (let ((_let_107 (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.isCountable0 W0)) (not (tptp.isFinite0 W0)))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_50)) (MACRO_SR_EQ_INTRO :args (_let_50 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (tptp.aSubsetOf0 _let_3 _let_37))) (let ((_let_110 (and _let_109 _let_102))) (let ((_let_111 (tptp.aElementOf0 tptp.xn _let_37))) (let ((_let_112 (not _let_111))) (let ((_let_113 (or _let_112 _let_110))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_16)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_78 :args ((and _let_15 _let_13 (= tptp.xp _let_12)) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_115 (AND_ELIM _let_114 :args _let_66))) (let ((_let_116 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_112 _let_110 (not _let_113)))) _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_87)) :args _let_86)) _let_85 :args (_let_113 false _let_84)) :args (_let_110 false _let_111 false _let_113)))) (let ((_let_117 (not _let_110))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_110 1)) :args ((or _let_102 _let_117))) _let_116 :args (_let_102 false _let_110)))) (let ((_let_119 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN tptp.xm)))))) (let ((_let_120 (and _let_104 _let_119))) (let ((_let_121 (= _let_4 _let_120))) (let ((_let_122 (or _let_97 _let_121))) (let ((_let_123 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2033 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.aSubsetOf0 BOUND_VARIABLE_2033 W0) (and (tptp.aSet0 BOUND_VARIABLE_2033) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 BOUND_VARIABLE_2033)) (tptp.aElementOf0 W2 W0))))))))) (let ((_let_124 (EQ_RESOLVE (ASSUME :args (_let_48)) (MACRO_SR_EQ_INTRO :args (_let_48 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_125 (_let_123))) (let ((_let_126 ((tptp.aSubsetOf0 BOUND_VARIABLE_2033 W0)))) (let ((_let_127 (and _let_96 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN tptp.xm))) (tptp.aElementOf0 W2 (tptp.szDzozmdt0 tptp.xN))))))) (let ((_let_128 (= _let_56 _let_127))) (let ((_let_129 (tptp.aSet0 _let_37))) (let ((_let_130 (not _let_129))) (let ((_let_131 (or _let_130 _let_128))) (let ((_let_132 (0))) (let ((_let_133 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_45)) (MACRO_SR_EQ_INTRO _let_78 :args (_let_45 SB_DEFAULT SBA_FIXPOINT))) :args _let_132))) (let ((_let_134 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_127 0)) :args ((or _let_96 (not _let_127)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_128)) :args ((or _let_64 _let_127 (not _let_128)))) 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_let_124 :args (_let_122 false _let_123)) :args (_let_121 false _let_96 false _let_122)) :args (_let_120 false _let_4 false _let_121)))) (let ((_let_137 (not _let_120))) (let ((_let_138 (or))) (let ((_let_139 (ASSUME :args (_let_57)))) (let ((_let_140 (ASSUME :args (_let_95)))) (let ((_let_141 (tptp.aElementOf0 _let_8 tptp.xQ))) (let ((_let_142 (= _let_8 _let_6))) (let ((_let_143 (= _let_12 _let_8))) (let ((_let_144 (not _let_143))) (let ((_let_145 (and (tptp.aElement0 _let_8) _let_141 _let_144))) (let ((_let_146 (tptp.aElementOf0 _let_8 _let_21))) (let ((_let_147 (= _let_146 _let_145))) (let ((_let_148 (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 (tptp.sdtmndt0 tptp.xQ (tptp.szmzizndt0 tptp.xQ))) (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 tptp.xQ) (not (= W3 (tptp.sdtlpdtrp0 tptp.xe tptp.xn)))))))) (let ((_let_149 (and (tptp.aSet0 _let_21) _let_148))) (let ((_let_150 (= _let_21 (tptp.sdtmndt0 tptp.xQ _let_12)))) (let ((_let_151 (= _let_150 _let_149))) (let ((_let_152 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(NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_92 _let_139 _let_140) :args (_let_89 _let_95 _let_57)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_140)) (CONG (SYMM _let_139) :args (APPLY_UF tptp.isFinite0)) (TRUE_INTRO _let_92))) :args (_let_89 _let_57 _let_95)) :args ((not (and _let_89 _let_95 _let_57)) SB_LITERAL))) (CONG (REFL :args ((not _let_89))) (MACRO_SR_PRED_INTRO :args ((= (not _let_95) _let_90))) (REFL :args (_let_91)) :args _let_138)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_94 _let_97 _let_95 _let_93 (not _let_98)))) _let_135 _let_134 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_105 _let_103 _let_101 (not _let_106)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_120 0)) :args ((or _let_104 _let_137))) _let_136 :args (_let_104 false _let_120)) _let_118 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (_let_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_107))) _let_108 :args (_let_106 false _let_107)) :args (_let_101 false _let_104 false _let_102 false _let_106)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (_let_2 _let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aSubsetOf0 BOUND_VARIABLE_2058 W0) false))))) :args (_let_99))) _let_100 :args (_let_98 false _let_99)) :args (_let_95 false _let_4 false _let_96 true _let_93 false _let_98)) _let_92 :args (_let_91 true _let_90 false _let_89)) _let_88 _let_79 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_27)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_78 :args ((and _let_26 (not (= tptp.slcrc0 tptp.xQ))) SB_DEFAULT SBA_FIXPOINT)))) :args _let_66) :args (false false _let_60 true _let_59 false _let_65 false _let_58 true _let_57 false _let_56 false _let_55 true _let_54)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) _let_53 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) _let_52 _let_51 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isCountable0 W0) true))) _let_50 _let_49 _let_48 _let_47 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aSubsetOf0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1) (tptp.aSet0 W2)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W2)) (tptp.aSubsetOf0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtpldt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElement0 W3) (or (tptp.aElementOf0 W3 W0) (= W3 W1)))))))))) _let_46 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (= (tptp.sdtpldt0 (tptp.sdtmndt0 W0 W1) W1) W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aSet0 W1)) (=> (not (tptp.aElementOf0 W0 W1)) (= (tptp.sdtmndt0 (tptp.sdtpldt0 W1 W0) W0) W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isCountable0 W1)) (tptp.isCountable0 (tptp.sdtpldt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isCountable0 W1)) (tptp.isCountable0 (tptp.sdtmndt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtpldt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtmndt0 W1 W0)))))) _let_45 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= _let_1 tptp.sz00)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (= (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1)) (= W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (or (= W0 tptp.sz00) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (= W0 (tptp.szszuzczcdt0 W1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (= W0 (tptp.szszuzczcdt0 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.sdtlseqdt0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 tptp.sz00 W0))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) tptp.sz00)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 (tptp.szszuzczcdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aElementOf0 W2 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (or (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W1) W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.iLess0 W0 (tptp.szszuzczcdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aElement0 (tptp.sbrdtbr0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (tptp.aElementOf0 (tptp.sbrdtbr0 W0) tptp.szNzAzT0) (tptp.isFinite0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (= (tptp.sbrdtbr0 W0) tptp.sz00) (= W0 tptp.slcrc0)))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (=> (not (tptp.aElementOf0 W1 W0)) (= (tptp.sbrdtbr0 (tptp.sdtpldt0 W0 W1)) (tptp.szszuzczcdt0 (tptp.sbrdtbr0 W0)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.isFinite0 W0) (tptp.aElementOf0 W1 W0)) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 (tptp.sdtmndt0 W0 W1))) (tptp.sbrdtbr0 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.isFinite0 W0) (tptp.aSubsetOf0 W1 W0)) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 W1) (tptp.sbrdtbr0 W0)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (and (tptp.isFinite0 W0) (tptp.sdtlseqdt0 W1 (tptp.sbrdtbr0 W0))) (exists ((W2 $$unsorted)) (and (tptp.aSubsetOf0 W2 W0) (= (tptp.sbrdtbr0 W2) W1)))))) _let_44 (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 W0) (not (= W0 tptp.slcrc0))) (forall ((W1 $$unsorted)) (= (= W1 (tptp.szmzazxdt0 W0)) (and (tptp.aElementOf0 W1 W0) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W2 W1)))))))) _let_43 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (= (= W1 (tptp.slbdtrb0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) W0))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 (tptp.slbdtrb0 W0)))) _let_42 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.aElementOf0 W0 (tptp.slbdtrb0 (tptp.szszuzczcdt0 W1))) (or (tptp.aElementOf0 W0 (tptp.slbdtrb0 W1)) (= W0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.sdtlseqdt0 W0 W1) (tptp.aSubsetOf0 (tptp.slbdtrb0 W0) (tptp.slbdtrb0 W1))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 W0)) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aSubsetOf0 W0 (tptp.slbdtrb0 W1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (= (tptp.sbrdtbr0 (tptp.slbdtrb0 W0)) W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.slbdtsldtrb0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aSubsetOf0 W3 W0) (= (tptp.sbrdtbr0 W3) W1))))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.isFinite0 (tptp.slbdtsldtrb0 W0 W1)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (not (tptp.isFinite0 W0))) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= (tptp.slbdtsldtrb0 W0 W1) tptp.slcrc0)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (forall ((W1 $$unsorted)) (=> (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= W1 tptp.sz00))) (tptp.isCountable0 (tptp.slbdtsldtrb0 W0 W1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.slbdtsldtrb0 W1 W0))) (=> (and (tptp.aSet0 W1) (tptp.aSet0 W2) (not (= W0 tptp.sz00))) (=> (and (tptp.aSubsetOf0 _let_1 (tptp.slbdtsldtrb0 W2 W0)) (not (= _let_1 tptp.slcrc0))) (tptp.aSubsetOf0 W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (forall ((W2 $$unsorted)) (=> (and (tptp.aSubsetOf0 W2 (tptp.slbdtsldtrb0 W0 W1)) (tptp.isFinite0 W2)) (exists ((W3 $$unsorted)) (and (tptp.aSubsetOf0 W3 W0) (tptp.isFinite0 W3) (tptp.aSubsetOf0 W2 (tptp.slbdtsldtrb0 W3 W1)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (tptp.aSet0 (tptp.szDzozmdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.szDzozmdt0 W0)) (tptp.aElement0 (tptp.sdtlpdtrp0 W0 W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aFunction0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtlbdtrb0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElementOf0 W3 (tptp.szDzozmdt0 W0)) (= (tptp.sdtlpdtrp0 W0 W3) W1))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aFunction0 W0) (tptp.aElement0 W1)) (tptp.aSubsetOf0 (tptp.sdtlbdtrb0 W0 W1) (tptp.szDzozmdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 (tptp.szDzozmdt0 W0)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtlcdtrc0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (exists ((W4 $$unsorted)) (and (tptp.aElementOf0 W4 W1) (= (tptp.sdtlpdtrp0 W0 W4) W3)))))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W0))) (=> (tptp.aElementOf0 W1 _let_1) (tptp.aElementOf0 (tptp.sdtlpdtrp0 W0 W1) (tptp.sdtlcdtrc0 W0 _let_1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 (tptp.szDzozmdt0 W0)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtexdt0 W0 W1)) (and (tptp.aFunction0 W2) (= (tptp.szDzozmdt0 W2) W1) (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W1) (= (tptp.sdtlpdtrp0 W2 W3) (tptp.sdtlpdtrp0 W0 W3))))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W1 (tptp.szDzozmdt0 W0)) (tptp.isCountable0 W1)) (=> (forall ((W2 $$unsorted) (W3 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W0))) (=> (and (tptp.aElementOf0 W2 _let_1) (tptp.aElementOf0 W3 _let_1) (not (= W2 W3))) (not (= (tptp.sdtlpdtrp0 W0 W2) (tptp.sdtlpdtrp0 W0 W3)))))) (tptp.isCountable0 (tptp.sdtlcdtrc0 W0 W1))))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szDzizrdt0 W0))) (let ((_let_2 (tptp.szDzozmdt0 W0))) (=> (tptp.aFunction0 W0) (=> (and (tptp.isCountable0 _let_2) (tptp.isFinite0 (tptp.sdtlcdtrc0 W0 _let_2))) (and (tptp.aElement0 _let_1) (tptp.isCountable0 (tptp.sdtlbdtrb0 W0 _let_1)))))))) (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT)) (tptp.aElementOf0 tptp.xK tptp.szNzAzT0) (and (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS)) (and (tptp.aFunction0 tptp.xc) (= _let_24 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xc _let_24) tptp.xT)) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W1 tptp.szNzAzT0) (tptp.isCountable0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W2))) (=> (and (tptp.aFunction0 W2) (= _let_1 (tptp.slbdtsldtrb0 W1 W0)) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 W2 _let_1) tptp.xT)) (=> (tptp.iLess0 W0 tptp.xK) (exists ((W3 $$unsorted)) (and (tptp.aElementOf0 W3 tptp.xT) (exists ((W4 $$unsorted)) (and (tptp.aSubsetOf0 W4 W1) (tptp.isCountable0 W4) (forall ((W5 $$unsorted)) (=> (tptp.aElementOf0 W5 (tptp.slbdtsldtrb0 W4 W0)) (= (tptp.sdtlpdtrp0 W2 W5) W3))))))))))))))) _let_40 _let_40 _let_39 _let_38 _let_36 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.sdtlseqdt0 W1 W0) (tptp.aSubsetOf0 (tptp.sdtlpdtrp0 tptp.xN W0) (tptp.sdtlpdtrp0 tptp.xN W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= W0 W1))) (not (= (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (=> (and (tptp.aSet0 W1) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 _let_2) tptp.xk))) (tptp.aElementOf0 (tptp.sdtpldt0 W1 _let_2) (tptp.slbdtsldtrb0 tptp.xS tptp.xK)))))))) (and (tptp.aFunction0 tptp.xC) (= (tptp.szDzozmdt0 tptp.xC) tptp.szNzAzT0) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xC W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aFunction0 _let_2) (= (tptp.szDzozmdt0 _let_2) (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)) tptp.xk)) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (=> (and (tptp.aSet0 W1) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 _let_2) tptp.xk))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W1) (tptp.sdtlpdtrp0 tptp.xc (tptp.sdtpldt0 W1 _let_2))))))))))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 _let_1 (tptp.szDzozmdt0 _let_1)) tptp.xT)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (and (tptp.aSubsetOf0 W1 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1))) (tptp.isCountable0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (and (tptp.aSet0 W2) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 W1 tptp.xk))) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)) tptp.xk)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xT) (exists ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (and (tptp.aSubsetOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1))) (tptp.isCountable0 W2) (forall ((W3 $$unsorted)) (=> (and (tptp.aSet0 W3) (tptp.aElementOf0 W3 (tptp.slbdtsldtrb0 W2 tptp.xk))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W3) W1)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xT) (forall ((W2 $$unsorted)) (=> (and (tptp.aSet0 W2) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)) tptp.xk))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W2) W1))))))) _let_35 (and (tptp.aFunction0 tptp.xd) (= _let_32 tptp.szNzAzT0) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)) tptp.xk))) (= (tptp.sdtlpdtrp0 tptp.xd W0) (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W1))))))) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xd _let_32) tptp.xT) (and (tptp.aElementOf0 _let_11 tptp.xT) (tptp.isCountable0 _let_14)) _let_31 _let_29 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xO) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aElementOf0 W1 (tptp.sdtlbdtrb0 tptp.xd (tptp.szDzizrdt0 tptp.xd))) (= (tptp.sdtlpdtrp0 tptp.xe W1) W0))))) (tptp.aSubsetOf0 tptp.xO tptp.xS) (tptp.aElementOf0 tptp.xQ (tptp.slbdtsldtrb0 tptp.xO tptp.xK)) _let_27 _let_25 (tptp.aElementOf0 tptp.xQ _let_24) _let_23 _let_22 (tptp.aElementOf0 tptp.xp tptp.xQ) _let_19 (tptp.aSubsetOf0 tptp.xP tptp.xQ) (tptp.aSubsetOf0 tptp.xP tptp.xO) _let_18 (tptp.aElementOf0 tptp.xP (tptp.slbdtsldtrb0 tptp.xO tptp.xk)) _let_16 (= (tptp.sdtlpdtrp0 tptp.xd tptp.xn) _let_11) _let_10 (and (tptp.aElementOf0 tptp.xx tptp.szNzAzT0) (tptp.aElementOf0 tptp.xx tptp.xO)) _let_9 _let_7 (not (tptp.aSubsetOf0 _let_2 _let_1)) _let_5 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 153.09/153.33 )
% 153.09/153.33 % SZS output end Proof for NUM621+1
% 153.09/153.33 % cvc5---1.0.5 exiting
% 153.09/153.33 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------