TSTP Solution File: NUM620+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM620+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 34.86s 35.07s
% Output : Proof 34.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM620+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n018.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
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Aug 25 13:28:28 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.21/0.51 %----Proving TF0_NAR, FOF, or CNF
% 34.86/35.07 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.J99aix1Bzw/cvc5---1.0.5_18949.p...
% 34.86/35.07 ------- get file name : TPTP file name is NUM620+1
% 34.86/35.07 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_18949.smt2...
% 34.86/35.07 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 34.86/35.07 --- Run --no-e-matching --full-saturate-quant at 5...
% 34.86/35.07 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 34.86/35.07 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 34.86/35.07 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 34.86/35.07 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 34.86/35.07 % SZS status Theorem for NUM620+1
% 34.86/35.07 % SZS output start Proof for NUM620+1
% 34.86/35.07 (
% 34.86/35.07 (let ((_let_1 (tptp.szszuzczcdt0 tptp.xn))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN _let_1))) (let ((_let_3 (tptp.sdtlpdtrp0 tptp.xN tptp.xm))) (let ((_let_4 (tptp.aSubsetOf0 _let_3 _let_2))) (let ((_let_5 (not (=> _let_4 (tptp.aElementOf0 tptp.xx _let_2))))) (let ((_let_6 (tptp.szmzizndt0 _let_3))) (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.szDzizrdt0 tptp.xd))) (let ((_let_11 (tptp.sdtlpdtrp0 tptp.xe tptp.xn))) (let ((_let_12 (tptp.aElementOf0 tptp.xn tptp.szNzAzT0))) (let ((_let_13 (tptp.sdtlbdtrb0 tptp.xd _let_10))) (let ((_let_14 (tptp.aElementOf0 tptp.xn _let_13))) (let ((_let_15 (and _let_14 _let_12 (= _let_11 tptp.xp)))) (let ((_let_16 (tptp.sbrdtbr0 tptp.xP))) (let ((_let_17 (= _let_16 tptp.xk))) (let ((_let_18 (tptp.szmzizndt0 tptp.xQ))) (let ((_let_19 (and (tptp.aSet0 tptp.xP) (= tptp.xP (tptp.sdtmndt0 tptp.xQ _let_18))))) (let ((_let_20 (= tptp.xp _let_18))) (let ((_let_21 (tptp.szDzozmdt0 tptp.xc))) (let ((_let_22 (tptp.aSet0 tptp.xO))) (let ((_let_23 (and _let_22 (= tptp.xO (tptp.sdtlcdtrc0 tptp.xe _let_13))))) (let ((_let_24 (tptp.szDzozmdt0 tptp.xd))) (let ((_let_25 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aSubsetOf0 _let_1 tptp.szNzAzT0) (tptp.isCountable0 _let_1))))))) (let ((_let_26 (tptp.szDzozmdt0 tptp.xN))) (let ((_let_27 (and (tptp.aFunction0 tptp.xN) (= _let_26 tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xN tptp.sz00) tptp.xS) (forall ((W0 $$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_28 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK)))) (let ((_let_29 (not (= tptp.xK tptp.sz00)))) (let ((_let_30 (tptp.slbdtrb0 tptp.sz00))) (let ((_let_31 (= _let_30 tptp.slcrc0))) (let ((_let_32 (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 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W1 W2)))))))))) (let ((_let_33 (forall ((W0 $$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_34 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0)))) (let ((_let_35 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))))) (let ((_let_36 (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (= W0 tptp.slcrc0)))))) (let ((_let_37 (forall ((W0 $$unsorted)) (= (= W0 tptp.slcrc0) (and (tptp.aSet0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))))) (let ((_let_38 (tptp.aSubsetOf0 _let_3 _let_26))) (let ((_let_39 (= _let_30 _let_3))) (let ((_let_40 (tptp.aElementOf0 _let_8 _let_3))) (let ((_let_41 (and _let_40 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN tptp.xm))) (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xe tptp.xm) W2)))))) (let ((_let_42 (= _let_8 _let_6))) (let ((_let_43 (= _let_42 _let_41))) (let ((_let_44 (not _let_38))) (let ((_let_45 (or _let_44 _let_39 _let_43))) (let ((_let_46 (tptp.isCountable0 _let_3))) (let ((_let_47 (and _let_38 _let_46))) (let ((_let_48 (tptp.aElementOf0 tptp.xm _let_26))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_47))) (let ((_let_51 (forall ((W0 $$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_52 (SYMM (ASSUME :args (_let_31))))) (let ((_let_53 (1))) (let ((_let_54 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))) :args _let_53))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (AND_ELIM _let_55 :args _let_53))) (let ((_let_57 (AND_ELIM _let_55 :args (2)))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_25)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_57 _let_56 _let_54 _let_52) :args ((forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aSubsetOf0 _let_1 tptp.szNzAzT0) (tptp.isCountable0 _let_1))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_59 (_let_51))) (let ((_let_60 (AND_ELIM (ASSUME :args (_let_23)) :args _let_53))) (let ((_let_61 (ASSUME :args (_let_20)))) (let ((_let_62 (AND_ELIM (ASSUME :args (_let_19)) :args _let_53))) (let ((_let_63 (ASSUME :args (_let_9)))) (let ((_let_64 (AND_INTRO (AND_ELIM _let_63 :args _let_53) (EQ_RESOLVE (SYMM (ASSUME :args (_let_17))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_62 _let_61 _let_60 _let_57 _let_56 _let_54 _let_52) :args ((= tptp.xk _let_16) SB_DEFAULT SBA_FIXPOINT))) _let_62 _let_61 _let_60 _let_57 _let_56 _let_54 _let_52))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_49 _let_47 (not _let_50)))) (EQ_RESOLVE _let_63 (MACRO_SR_EQ_INTRO _let_64 :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 _let_26) false))))) :args _let_59)) _let_58 :args (_let_50 false _let_51)) :args (_let_47 false _let_48 false _let_50)))) (let ((_let_66 (not _let_47))) (let ((_let_67 (tptp.isCountable0 _let_30))) (let ((_let_68 (not _let_39))) (let ((_let_69 (tptp.aSet0 _let_30))) (let ((_let_70 (not _let_67))) (let ((_let_71 (and _let_69 (forall ((W1 $$unsorted)) (not (tptp.aElementOf0 W1 (tptp.slbdtrb0 tptp.sz00))))))) (let ((_let_72 (forall ((W0 $$unsorted)) (= (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (not (tptp.aElementOf0 W1 W0)))) (= W0 (tptp.slbdtrb0 tptp.sz00)))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_37)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_64 :args ((forall ((W0 $$unsorted)) (= (= tptp.slcrc0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (not (tptp.aElementOf0 W1 W0)))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_74 (not _let_46))) (let ((_let_75 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2558 $$unsorted)) (or (not (tptp.aSubsetOf0 W0 (tptp.szDzozmdt0 tptp.xN))) (= W0 (tptp.slbdtrb0 tptp.sz00)) (= (and (tptp.aElementOf0 BOUND_VARIABLE_2558 W0) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_2558 W2)))) (= (tptp.szmzizndt0 W0) BOUND_VARIABLE_2558)))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_32)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_64 :args ((forall ((W0 $$unsorted) (BOUND_VARIABLE_2558 $$unsorted)) (or (not (tptp.aSubsetOf0 W0 tptp.szNzAzT0)) (= tptp.slcrc0 W0) (= (and (tptp.aElementOf0 BOUND_VARIABLE_2558 W0) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_2558 W2)))) (= (tptp.szmzizndt0 W0) BOUND_VARIABLE_2558)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_77 (not _let_43))) (let ((_let_78 (not _let_41))) (let ((_let_79 (tptp.aElementOf0 _let_8 _let_2))) (let ((_let_80 (not _let_40))) (let ((_let_81 (or _let_80 _let_79))) (let ((_let_82 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN tptp.xm))) (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xn))))))) (let ((_let_83 (and (tptp.aSet0 _let_3) _let_82))) (let ((_let_84 (= _let_4 _let_83))) (let ((_let_85 (tptp.aSet0 _let_2))) (let ((_let_86 (not _let_85))) (let ((_let_87 (or _let_86 _let_84))) (let ((_let_88 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2030 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.aSubsetOf0 BOUND_VARIABLE_2030 W0) (and (tptp.aSet0 BOUND_VARIABLE_2030) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 BOUND_VARIABLE_2030)) (tptp.aElementOf0 W2 W0))))))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (_let_88))) (let ((_let_91 (and _let_85 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xn)))) (tptp.aElementOf0 W2 (tptp.szDzozmdt0 tptp.xN))))))) (let ((_let_92 (tptp.aSubsetOf0 _let_2 _let_26))) (let ((_let_93 (= _let_92 _let_91))) (let ((_let_94 (tptp.aSet0 _let_26))) (let ((_let_95 (not _let_94))) (let ((_let_96 (or _let_95 _let_93))) (let ((_let_97 (and _let_92 (tptp.isCountable0 _let_2)))) (let ((_let_98 (tptp.aElementOf0 _let_1 _let_26))) (let ((_let_99 (not _let_98))) (let ((_let_100 (or _let_99 _let_97))) (let ((_let_101 (and _let_98 (not (= tptp.sz00 _let_1))))) (let ((_let_102 (tptp.aElementOf0 tptp.xn _let_26))) (let ((_let_103 (not _let_102))) (let ((_let_104 (or _let_103 _let_101))) (let ((_let_105 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (let ((_let_2 (tptp.szDzozmdt0 tptp.xN))) (or (not (tptp.aElementOf0 W0 _let_2)) (and (tptp.aElementOf0 _let_1 _let_2) (not (= tptp.sz00 _let_1))))))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_33)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_64 :args ((forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= tptp.sz00 _let_1)))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO _let_64 :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (_let_82))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_44 _let_39 _let_43 (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_43)) :args ((or (not _let_42) _let_41 _let_77))) (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO _let_64 :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_41 0)) :args ((or _let_40 _let_78))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_79 _let_80 (not _let_81)))) (NOT_IMPLIES_ELIM2 _let_107) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_108) :args (_let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W2 _let_2) true))))) :args _let_108)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_83 1)) :args ((or _let_82 (not _let_83)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_84)) :args ((or (not _let_4) _let_83 (not _let_84)))) (NOT_IMPLIES_ELIM1 _let_107) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_86 _let_84 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_91 0)) :args ((or _let_85 (not _let_91)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_93)) :args ((or (not _let_92) _let_91 (not _let_93)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_97 0)) :args ((or _let_92 (not _let_97)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_99 _let_97 (not _let_100)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_101 0)) :args ((or _let_98 (not _let_101)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_103 _let_101 (not _let_104)))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_15)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_64 :args ((and _let_14 _let_12 (= tptp.xp _let_11)) SB_DEFAULT SBA_FIXPOINT)))) :args _let_53) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.szszuzczcdt0 W0)))) :args (_let_105))) _let_106 :args (_let_104 false _let_105)) :args (_let_101 false _let_102 false _let_104)) :args (_let_98 false _let_101)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (_let_1 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_59)) _let_58 :args (_let_100 false _let_51)) :args (_let_97 false _let_98 false _let_100)) :args (_let_92 false _let_97)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_95 _let_93 (not _let_96)))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO _let_64 :args (_let_34 SB_DEFAULT SBA_FIXPOINT))) :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (_let_26 _let_2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_90)) _let_89 :args (_let_96 false _let_88)) :args (_let_93 false _let_94 false _let_96)) :args (_let_91 false _let_92 false _let_93)) :args (_let_85 false _let_91)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (_let_2 _let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aSubsetOf0 BOUND_VARIABLE_2030 W0)))) :args _let_90)) _let_89 :args (_let_87 false _let_88)) :args (_let_84 false _let_85 false _let_87)) :args (_let_83 false _let_4 false _let_84)) :args (_let_82 false _let_83)) :args (_let_81 false _let_82)) :args (_let_80 true _let_79 false _let_81)) :args (_let_78 true _let_40)) :args (_let_77 false _let_42 true _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_76 :args (_let_3 _let_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_75)))) _let_76 :args (_let_45 false _let_75)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (ASSUME :args (_let_46)))) (CONG (SYMM (ASSUME :args (_let_39))) :args (APPLY_UF tptp.isCountable0)) (FALSE_INTRO (ASSUME :args (_let_70))))) :args (_let_70 _let_39 _let_46))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_67))) (REFL :args (_let_68)) (REFL :args (_let_74)) :args (or))) :args ((or _let_67 _let_74 _let_68))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_47 1)) :args ((or _let_46 _let_66))) _let_65 :args (_let_46 false _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_36)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_64 :args ((or (not (tptp.aSet0 tptp.slcrc0)) (not (tptp.isCountable0 tptp.slcrc0))) SB_DEFAULT SBA_FIXPOINT)))) :args ((or _let_70 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_71 0)) :args ((or _let_69 (not _let_71)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_73 :args (_let_30 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_72)))) _let_73 :args (_let_71 false _let_72)) :args (_let_69 false _let_71)) :args (_let_70 false _let_69)) :args (_let_68 false _let_46 true _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_47 0)) :args ((or _let_38 _let_66))) _let_65 :args (_let_38 false _let_47)) :args (false true _let_43 false _let_45 true _let_39 false _let_38)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) _let_37 (tptp.isFinite0 tptp.slcrc0) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isCountable0 W0) true))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (tptp.isFinite0 W0)))) _let_36 _let_35 (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (tptp.isFinite0 W1))))) (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)))))))))) (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)))))))))) (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_34 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0) _let_33 (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 $$unsorted)) (and (tptp.aSubsetOf0 W2 W0) (= (tptp.sbrdtbr0 W2) W1)))))) _let_32 (forall ((W0 $$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_31 (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_21 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xc _let_21) 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_29 _let_29 _let_28 _let_27 _let_25 (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 $$unsorted)) (=> (and (tptp.aSet0 W2) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)) tptp.xk))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W2) W1))))))) (and (tptp.aFunction0 tptp.xe) (= (tptp.szDzozmdt0 tptp.xe) tptp.szNzAzT0) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xe W0) (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)))))) (and (tptp.aFunction0 tptp.xd) (= _let_24 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_24) tptp.xT) (and (tptp.aElementOf0 _let_10 tptp.xT) (tptp.isCountable0 _let_13)) _let_23 (and _let_22 (tptp.isCountable0 tptp.xO)) (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_21) _let_20 _let_19 (tptp.aElementOf0 tptp.xp tptp.xQ) (tptp.aElementOf0 tptp.xp tptp.xO) (tptp.aSubsetOf0 tptp.xP tptp.xQ) (tptp.aSubsetOf0 tptp.xP tptp.xO) _let_17 (tptp.aElementOf0 tptp.xP (tptp.slbdtsldtrb0 tptp.xO tptp.xk)) _let_15 (= (tptp.sdtlpdtrp0 tptp.xd tptp.xn) _let_10) (tptp.aElementOf0 tptp.xx tptp.xP) (and (tptp.aElementOf0 tptp.xx tptp.szNzAzT0) (tptp.aElementOf0 tptp.xx tptp.xO)) _let_9 _let_7 _let_5 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 34.86/35.08 )
% 34.86/35.08 % SZS output end Proof for NUM620+1
% 34.86/35.08 % cvc5---1.0.5 exiting
% 34.86/35.08 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------