TSTP Solution File: NUM629+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM629+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 10:45:49 EDT 2023
% Result : Theorem 55.97s 56.19s
% Output : Proof 55.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM629+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n024.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 14:05:24 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.51 %----Proving TF0_NAR, FOF, or CNF
% 55.97/56.19 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.nsUCvv7wpe/cvc5---1.0.5_11701.p...
% 55.97/56.19 ------- get file name : TPTP file name is NUM629+1
% 55.97/56.19 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11701.smt2...
% 55.97/56.19 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 55.97/56.19 --- Run --no-e-matching --full-saturate-quant at 5...
% 55.97/56.19 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 55.97/56.19 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 55.97/56.19 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 55.97/56.19 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 55.97/56.19 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 55.97/56.19 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 55.97/56.19 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 55.97/56.19 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 55.97/56.19 % SZS status Theorem for NUM629+1
% 55.97/56.19 % SZS output start Proof for NUM629+1
% 55.97/56.19 (
% 55.97/56.19 (let ((_let_1 (not (tptp.aElementOf0 tptp.xP (tptp.slbdtsldtrb0 tptp.xD tptp.xk))))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (let ((_let_3 (tptp.szmzizndt0 _let_2))) (let ((_let_4 (tptp.sdtmndt0 _let_2 _let_3))) (let ((_let_5 (= tptp.xD _let_4))) (let ((_let_6 (tptp.szszuzczcdt0 tptp.xn))) (let ((_let_7 (tptp.sdtlpdtrp0 tptp.xN _let_6))) (let ((_let_8 (tptp.aSubsetOf0 tptp.xP _let_7))) (let ((_let_9 (tptp.szDzizrdt0 tptp.xd))) (let ((_let_10 (tptp.sdtlpdtrp0 tptp.xe tptp.xn))) (let ((_let_11 (tptp.aElementOf0 tptp.xn tptp.szNzAzT0))) (let ((_let_12 (tptp.sdtlbdtrb0 tptp.xd _let_9))) (let ((_let_13 (tptp.aElementOf0 tptp.xn _let_12))) (let ((_let_14 (and _let_13 _let_11 (= _let_10 tptp.xp)))) (let ((_let_15 (tptp.sbrdtbr0 tptp.xP))) (let ((_let_16 (= _let_15 tptp.xk))) (let ((_let_17 (tptp.aElementOf0 tptp.xp tptp.xO))) (let ((_let_18 (tptp.szmzizndt0 tptp.xQ))) (let ((_let_19 (tptp.sdtmndt0 tptp.xQ _let_18))) (let ((_let_20 (and (tptp.aSet0 tptp.xP) (= tptp.xP _let_19)))) (let ((_let_21 (= tptp.xp _let_18))) (let ((_let_22 (tptp.szDzozmdt0 tptp.xc))) (let ((_let_23 (tptp.aSet0 tptp.xO))) (let ((_let_24 (and _let_23 (tptp.isCountable0 tptp.xO)))) (let ((_let_25 (tptp.sdtlcdtrc0 tptp.xe _let_12))) (let ((_let_26 (and _let_23 (= tptp.xO _let_25)))) (let ((_let_27 (tptp.szDzozmdt0 tptp.xd))) (let ((_let_28 (tptp.szDzozmdt0 tptp.xe))) (let ((_let_29 (tptp.aFunction0 tptp.xe))) (let ((_let_30 (and _let_29 (= _let_28 tptp.szNzAzT0) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xe W0) (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)))))))) (let ((_let_31 (forall ((W0 $$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_32 (tptp.sdtlpdtrp0 tptp.xN tptp.sz00))) (let ((_let_33 (tptp.szDzozmdt0 tptp.xN))) (let ((_let_34 (tptp.aFunction0 tptp.xN))) (let ((_let_35 (and _let_34 (= _let_33 tptp.szNzAzT0) (= _let_32 tptp.xS) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (=> (and (tptp.aSubsetOf0 _let_2 tptp.szNzAzT0) (tptp.isCountable0 _let_2)) (and (tptp.aSubsetOf0 _let_1 (tptp.sdtmndt0 _let_2 (tptp.szmzizndt0 _let_2))) (tptp.isCountable0 _let_1)))))))))) (let ((_let_36 (tptp.szszuzczcdt0 tptp.xk))) (let ((_let_37 (tptp.aElementOf0 tptp.xk tptp.szNzAzT0))) (let ((_let_38 (and _let_37 (= _let_36 tptp.xK)))) (let ((_let_39 (not (= tptp.xK tptp.sz00)))) (let ((_let_40 (forall ((W0 $$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 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aSubsetOf0 W3 W0) (= (tptp.sbrdtbr0 W3) W1))))))))))) (let ((_let_41 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0))) (let ((_let_42 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= _let_1 tptp.sz00)))))))) (let ((_let_43 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0)))) (let ((_let_44 (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_45 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1) (tptp.aSet0 W2)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W2)) (tptp.aSubsetOf0 W0 W2)))))) (let ((_let_46 (forall ((W0 $$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_47 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_48 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSet0 W1)) (not (tptp.aSet0 W2)) (not (tptp.aSubsetOf0 W0 W1)) (not (tptp.aSubsetOf0 W1 W2)) (tptp.aSubsetOf0 W0 W2))))) (let ((_let_49 (tptp.aSubsetOf0 _let_19 _let_4))) (let ((_let_50 (tptp.aSubsetOf0 _let_7 _let_4))) (let ((_let_51 (not _let_50))) (let ((_let_52 (tptp.aSubsetOf0 _let_19 _let_7))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.aSet0 _let_4))) (let ((_let_55 (not _let_54))) (let ((_let_56 (tptp.aSet0 _let_7))) (let ((_let_57 (not _let_56))) (let ((_let_58 (tptp.aSet0 _let_19))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_59 _let_57 _let_55 _let_53 _let_51 _let_49))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_45)) (MACRO_SR_EQ_INTRO :args (_let_45 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (not _let_60))) (let ((_let_63 (tptp.sbrdtbr0 _let_19))) (let ((_let_64 (tptp.slbdtsldtrb0 _let_4 _let_63))) (let ((_let_65 (tptp.aElementOf0 _let_19 _let_64))) (let ((_let_66 (= _let_65 _let_49))) (let ((_let_67 (not _let_49))) (let ((_let_68 (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sbrdtbr0 (tptp.sdtmndt0 tptp.xQ (tptp.szmzizndt0 tptp.xQ))))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (let ((_let_3 (tptp.sdtmndt0 _let_2 (tptp.szmzizndt0 _let_2)))) (= (tptp.aElementOf0 W3 (tptp.slbdtsldtrb0 _let_3 _let_1)) (and (tptp.aSubsetOf0 W3 _let_3) (= (tptp.sbrdtbr0 W3) _let_1))))))))) (let ((_let_69 (and (tptp.aSet0 _let_64) _let_68))) (let ((_let_70 (tptp.aElementOf0 _let_63 _let_33))) (let ((_let_71 (not _let_70))) (let ((_let_72 (or _let_55 _let_71 _let_69))) (let ((_let_73 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_2706 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 W1 (tptp.szDzozmdt0 tptp.xN))) (= (= (tptp.slbdtsldtrb0 W0 W1) BOUND_VARIABLE_2706) (and (tptp.aSet0 BOUND_VARIABLE_2706) (forall ((W3 $$unsorted)) (= (and (tptp.aSubsetOf0 W3 W0) (= W1 (tptp.sbrdtbr0 W3))) (tptp.aElementOf0 W3 BOUND_VARIABLE_2706))))))))) (let ((_let_74 (SYMM (ASSUME :args (_let_41))))) (let ((_let_75 (1))) (let ((_let_76 (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_77 (ASSUME :args (_let_38)))) (let ((_let_78 (AND_ELIM (EQ_RESOLVE _let_77 _let_76) :args _let_75))) (let ((_let_79 (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_80 (ASSUME :args (_let_35)))) (let ((_let_81 (EQ_RESOLVE _let_80 _let_79))) (let ((_let_82 (AND_ELIM _let_81 :args _let_75))) (let ((_let_83 (2))) (let ((_let_84 (AND_ELIM _let_81 :args _let_83))) (let ((_let_85 (AND_ELIM (ASSUME :args (_let_26)) :args _let_75))) (let ((_let_86 (ASSUME :args (_let_21)))) (let ((_let_87 (ASSUME :args (_let_20)))) (let ((_let_88 (AND_ELIM _let_87 :args _let_75))) (let ((_let_89 (AND_INTRO _let_88 _let_86 _let_85 _let_84 _let_82 _let_78 _let_74))) (let ((_let_90 (EQ_RESOLVE (SYMM (ASSUME :args (_let_16))) (MACRO_SR_EQ_INTRO _let_89 :args ((= tptp.xk _let_15) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (AND_INTRO (ASSUME :args (_let_5)) _let_90 _let_88 _let_86 _let_85 _let_84 _let_82 _let_78 _let_74))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_40)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_40 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_91 :args ((forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_2706 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (= (tptp.slbdtsldtrb0 W0 W1) BOUND_VARIABLE_2706) (and (tptp.aSet0 BOUND_VARIABLE_2706) (forall ((W3 $$unsorted)) (= (and (tptp.aSubsetOf0 W3 W0) (= W1 (tptp.sbrdtbr0 W3))) (tptp.aElementOf0 W3 BOUND_VARIABLE_2706))))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_93 (and _let_54 (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (= (tptp.aElementOf0 W3 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1))) (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 _let_1) (not (= W3 (tptp.sdtlpdtrp0 tptp.xe tptp.xn)))))))))) (let ((_let_94 (= _let_4 (tptp.sdtmndt0 _let_2 _let_10)))) (let ((_let_95 (= _let_94 _let_93))) (let ((_let_96 (tptp.aElement0 _let_10))) (let ((_let_97 (not _let_96))) (let ((_let_98 (tptp.aSet0 _let_2))) (let ((_let_99 (not _let_98))) (let ((_let_100 (or _let_99 _let_97 _let_95))) (let ((_let_101 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_2140 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElement0 W1)) (= (= (tptp.sdtmndt0 W0 W1) BOUND_VARIABLE_2140) (and (tptp.aSet0 BOUND_VARIABLE_2140) (forall ((W3 $$unsorted)) (= (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 W0) (not (= W1 W3))) (tptp.aElementOf0 W3 BOUND_VARIABLE_2140))))))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_44)) (MACRO_SR_EQ_INTRO :args (_let_44 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (tptp.aElement0 _let_18))) (let ((_let_104 (= _let_18 _let_10))) (let ((_let_105 (tptp.aElementOf0 _let_18 _let_25))) (let ((_let_106 (not _let_105))) (let ((_let_107 (tptp.aSet0 _let_25))) (let ((_let_108 (not _let_107))) (let ((_let_109 (or _let_108 _let_106 _let_103))) (let ((_let_110 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1957 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1957 W0)) (tptp.aElement0 BOUND_VARIABLE_1957))))) (let ((_let_111 (EQ_RESOLVE (ASSUME :args (_let_47)) (MACRO_SR_EQ_INTRO :args (_let_47 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_112 (0))) (let ((_let_113 (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_91 :args ((and _let_13 _let_11 (= tptp.xp _let_10)) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_114 (and _let_104 _let_103))) (let ((_let_115 (ASSUME :args (_let_103)))) (let ((_let_116 (ASSUME :args (_let_104)))) (let ((_let_117 (and _let_98 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (tptp.aElementOf0 W2 (tptp.szDzozmdt0 tptp.xN))))))) (let ((_let_118 (tptp.aSubsetOf0 _let_2 _let_33))) (let ((_let_119 (= _let_118 _let_117))) (let ((_let_120 (tptp.aSet0 _let_33))) (let ((_let_121 (not _let_120))) (let ((_let_122 (or _let_121 _let_119))) (let ((_let_123 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2022 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.aSubsetOf0 BOUND_VARIABLE_2022 W0) (and (tptp.aSet0 BOUND_VARIABLE_2022) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 BOUND_VARIABLE_2022)) (tptp.aElementOf0 W2 W0))))))))) (let ((_let_124 (EQ_RESOLVE (ASSUME :args (_let_46)) (MACRO_SR_EQ_INTRO :args (_let_46 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_125 (_let_123))) (let ((_let_126 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO _let_91 :args (_let_43 SB_DEFAULT SBA_FIXPOINT))) :args _let_112))) (let ((_let_127 (tptp.isCountable0 _let_2))) (let ((_let_128 (and _let_118 _let_127))) (let ((_let_129 (tptp.aElementOf0 tptp.xn _let_33))) (let ((_let_130 (not _let_129))) (let ((_let_131 (or _let_130 _let_128))) (let ((_let_132 (forall ((W0 $$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_133 (EQ_RESOLVE (ASSUME :args (_let_31)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_84 _let_82 _let_78 _let_74) :args ((forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aSubsetOf0 _let_1 tptp.szNzAzT0) (tptp.isCountable0 _let_1))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_134 (_let_132))) (let ((_let_135 (AND_ELIM _let_113 :args _let_75))) (let ((_let_136 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_131)) :args ((or _let_130 _let_128 (not _let_131)))) _let_135 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_133 :args (tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 _let_33) false))))) :args _let_134)) _let_133 :args (_let_131 false _let_132)) :args (_let_128 false _let_129 false _let_131)))) (let ((_let_137 (not _let_128))) (let ((_let_138 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_128 0)) :args ((or _let_118 _let_137))) _let_136 :args (_let_118 false _let_128)))) (let ((_let_139 (not _let_118))) (let ((_let_140 (= _let_10 _let_3))) (let ((_let_141 (or _let_130 _let_140))) (let ((_let_142 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.szDzozmdt0 tptp.xN))) (= (tptp.sdtlpdtrp0 tptp.xe W0) (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0))))))) (let ((_let_143 (_let_142))) (let ((_let_144 (_let_140))) (let ((_let_145 (ASSUME :args _let_144))) (let ((_let_146 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_93 0)) :args ((or _let_54 (not _let_93)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_95)) :args ((or _let_93 (not _let_94) (not _let_95)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_145 (SCOPE (CONG (REFL :args (_let_2)) (SYMM _let_145) :args (APPLY_UF tptp.sdtmndt0)) :args _let_144)) :args _let_144)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_141)) :args ((or _let_130 _let_140 (not _let_141)))) _let_135 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_143) :args (tptp.xn QUANTIFIERS_INST_CBQI_PROP)) :args _let_143)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_30)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_91 :args ((and _let_29 (= tptp.szNzAzT0 _let_28) (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (= (tptp.sdtlpdtrp0 tptp.xe W0) (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)))))) SB_DEFAULT SBA_FIXPOINT)))) :args _let_83) :args (_let_141 false _let_142)) :args 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W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aElementOf0 W2 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$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)))))) (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 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W1 W2)))))))) (forall ((W0 $$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)))))))) (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)))))) (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_41 (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 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (= (tptp.sbrdtbr0 (tptp.slbdtrb0 W0)) W0))) _let_40 (forall ((W0 $$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_22 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xc _let_22) 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_39 _let_39 _let_38 _let_35 _let_31 (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 $$unsorted)) (=> (and (tptp.aSet0 W2) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)) tptp.xk))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W2) W1))))))) _let_30 (and (tptp.aFunction0 tptp.xd) (= _let_27 tptp.szNzAzT0) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)) tptp.xk))) (= (tptp.sdtlpdtrp0 tptp.xd W0) (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W1))))))) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xd _let_27) tptp.xT) (and (tptp.aElementOf0 _let_9 tptp.xT) (tptp.isCountable0 _let_12)) _let_26 _let_24 (forall ((W0 $$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)) (and (tptp.aSubsetOf0 tptp.xQ tptp.xO) (not (= tptp.xQ tptp.slcrc0))) (tptp.aSubsetOf0 tptp.xQ tptp.szNzAzT0) (tptp.aElementOf0 tptp.xQ _let_22) _let_21 _let_20 (tptp.aElementOf0 tptp.xp tptp.xQ) _let_17 (tptp.aSubsetOf0 tptp.xP tptp.xQ) (tptp.aSubsetOf0 tptp.xP tptp.xO) _let_16 (tptp.aElementOf0 tptp.xP (tptp.slbdtsldtrb0 tptp.xO tptp.xk)) _let_14 (= (tptp.sdtlpdtrp0 tptp.xd tptp.xn) _let_9) _let_8 _let_5 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 55.97/56.20 )
% 55.97/56.20 % SZS output end Proof for NUM629+1
% 55.97/56.20 % cvc5---1.0.5 exiting
% 55.97/56.20 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------