TSTP Solution File: NUM581+3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM581+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 10:45:19 EDT 2023
% Result : Theorem 8.02s 8.27s
% Output : Proof 8.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM581+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n001.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 12:33:43 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 8.02/8.27 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.cSQz6FWkjk/cvc5---1.0.5_1479.p...
% 8.02/8.27 ------- get file name : TPTP file name is NUM581+3
% 8.02/8.27 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_1479.smt2...
% 8.02/8.27 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 8.02/8.27 % SZS status Theorem for NUM581+3
% 8.02/8.27 % SZS output start Proof for NUM581+3
% 8.02/8.27 (
% 8.02/8.27 (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xi))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtpldt0 tptp.xQ _let_2))) (let ((_let_4 (tptp.aSet0 _let_3))) (let ((_let_5 (tptp.aElementOf0 _let_2 _let_1))) (let ((_let_6 (not (=> (and _let_5 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xi))) (=> (tptp.aElementOf0 W0 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W0))))) (=> (and _let_4 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN tptp.xi)))) (= (tptp.aElementOf0 W0 (tptp.sdtpldt0 tptp.xQ _let_1)) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 W0 tptp.xQ) (= W0 _let_1))))))) (or (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.sdtpldt0 tptp.xQ (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN tptp.xi)))) (tptp.aElementOf0 W0 tptp.xS))) (tptp.aSubsetOf0 _let_3 tptp.xS))))))) (let ((_let_7 (and _let_5 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xi))) (=> (tptp.aElementOf0 W0 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W0)))) _let_4 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN tptp.xi)))) (= (tptp.aElementOf0 W0 (tptp.sdtpldt0 tptp.xQ _let_1)) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 W0 tptp.xQ) (= W0 _let_1)))))) (= (tptp.sbrdtbr0 _let_3) tptp.xK)))) (let ((_let_8 (tptp.sdtmndt0 _let_1 _let_2))) (let ((_let_9 (and _let_5 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xi))) (=> (tptp.aElementOf0 W0 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W0)))) (tptp.aSet0 _let_8) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xi))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W0 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W0) (tptp.aElementOf0 W0 _let_1) (not (= W0 _let_2))))))) (tptp.aSet0 tptp.xQ) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xi))) (=> (tptp.aElementOf0 W0 tptp.xQ) (tptp.aElementOf0 W0 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) (tptp.aSubsetOf0 tptp.xQ _let_8) (= (tptp.sbrdtbr0 tptp.xQ) tptp.xk) (tptp.aElementOf0 tptp.xQ (tptp.slbdtsldtrb0 _let_8 tptp.xk))))) (let ((_let_10 (tptp.aElementOf0 tptp.xi tptp.szNzAzT0))) (let ((_let_11 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.sdtlseqdt0 W1 W0) (and (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN W1)))) (tptp.aSubsetOf0 (tptp.sdtlpdtrp0 tptp.xN W0) (tptp.sdtlpdtrp0 tptp.xN W1)))))))) (let ((_let_12 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aSet0 _let_1) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.aElementOf0 W1 tptp.szNzAzT0))) (tptp.aSubsetOf0 _let_1 tptp.szNzAzT0) (tptp.isCountable0 _let_1))))))) (let ((_let_13 (tptp.sdtlpdtrp0 tptp.xN tptp.sz00))) (let ((_let_14 (and (tptp.aFunction0 tptp.xN) (= (tptp.szDzozmdt0 tptp.xN) tptp.szNzAzT0) (= _let_13 tptp.xS) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_3 (tptp.szmzizndt0 _let_2))) (let ((_let_4 (tptp.sdtmndt0 _let_2 _let_3))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (=> (and (or (and (tptp.aSet0 _let_2) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.aElementOf0 W1 tptp.szNzAzT0)))) (tptp.aSubsetOf0 _let_2 tptp.szNzAzT0)) (tptp.isCountable0 _let_2)) (and (tptp.aElementOf0 _let_3 _let_2) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W1 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W1)))) (tptp.aSet0 _let_4) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W1 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W1) (tptp.aElementOf0 W1 _let_1) (not (= W1 _let_2))))))) (tptp.aSet0 _let_1) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0))) (tptp.aElementOf0 W1 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) (tptp.aSubsetOf0 _let_1 _let_4) (tptp.isCountable0 _let_1)))))))))))) (let ((_let_15 (not (= tptp.xK tptp.sz00)))) (let ((_let_16 (tptp.szDzozmdt0 tptp.xc))) (let ((_let_17 (tptp.sdtlcdtrc0 tptp.xc _let_16))) (let ((_let_18 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 tptp.sz00 W0))))) (let ((_let_19 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0))) (let ((_let_20 (forall ((W0 $$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_21 (= tptp.xS _let_13))) (let ((_let_22 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xS))) (let ((_let_23 (tptp.aElementOf0 _let_2 _let_13))) (let ((_let_24 (= _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_25 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) :args (2)))) (let ((_let_26 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_3))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_22))) (let ((_let_29 (not _let_22))) (let ((_let_30 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.sdtpldt0 tptp.xQ (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN tptp.xi))))) (tptp.aElementOf0 W0 tptp.xS))))) (let ((_let_31 (not _let_28))) (let ((_let_32 (0))) (let ((_let_33 (or))) (let ((_let_34 (not _let_30))) (let ((_let_35 (_let_34))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_35)) :args _let_35)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_30))) (REFL :args (_let_31)) :args _let_33)) (NOT_OR_ELIM (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) :args _let_32) :args (_let_31 true _let_30)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_28 1)) _let_36 :args (_let_29 true _let_28)))) (let ((_let_38 (not _let_5))) (let ((_let_39 (or _let_38 _let_23))) (let ((_let_40 (tptp.aSubsetOf0 _let_1 _let_13))) (let ((_let_41 (and _let_39 _let_40))) (let ((_let_42 (tptp.sdtlseqdt0 tptp.sz00 tptp.xi))) (let ((_let_43 (not _let_42))) (let ((_let_44 (not _let_19))) (let ((_let_45 (not _let_10))) (let ((_let_46 (or _let_45 _let_44 _let_43 _let_41))) (let ((_let_47 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_3852 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W1))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (tptp.sdtlseqdt0 W1 W0)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_3852 _let_2)) (tptp.aElementOf0 BOUND_VARIABLE_3852 _let_1)) (tptp.aSubsetOf0 _let_2 _let_1)))))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (or _let_45 _let_42))) (let ((_let_50 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (tptp.sdtlseqdt0 tptp.sz00 W0))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (ASSUME :args (_let_10)))) (let ((_let_53 (ASSUME :args (_let_19)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_44 _let_45 _let_43 _let_41 (not _let_46)))) _let_53 _let_52 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_45 _let_42 (not _let_49)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.xi QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 tptp.szNzAzT0) false))))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_42 false _let_10 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (tptp.xi tptp.sz00 _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.aElementOf0 W1 tptp.szNzAzT0) false)) (tptp.aElementOf0 BOUND_VARIABLE_3852 (tptp.sdtlpdtrp0 tptp.xN W0))))) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_41 false _let_19 false _let_10 false _let_42 false _let_46)))) (let ((_let_55 (not _let_41))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xQ))) (let ((_let_58 (or _let_57 _let_24))) (let ((_let_59 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_60 (and _let_59 _let_58))) (let ((_let_61 (= _let_26 _let_60))) (let ((_let_62 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN tptp.xi)))) (= (tptp.aElementOf0 W0 (tptp.sdtpldt0 tptp.xQ _let_1)) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 W0 tptp.xQ) (= _let_1 W0)))))))) (let ((_let_63 (3))) (let ((_let_64 (_let_62))) (let ((_let_65 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8))) (let ((_let_66 (not _let_57))) (let ((_let_67 (or _let_66 _let_65))) (let ((_let_68 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xi))) (or (not (tptp.aElementOf0 W0 tptp.xQ)) (tptp.aElementOf0 W0 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))))) (let ((_let_69 (_let_68))) (let ((_let_70 (not _let_24))) (let ((_let_71 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_1))) (let ((_let_72 (and _let_59 _let_71 _let_70))) (let ((_let_73 (= _let_65 _let_72))) (let ((_let_74 (not _let_65))) (let ((_let_75 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xi))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W0 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W0) (tptp.aElementOf0 W0 _let_1) (not (= _let_2 W0))))))))) (let ((_let_76 (_let_75))) (let ((_let_77 (not _let_72))) (let ((_let_78 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_13))) (let ((_let_79 (not _let_71))) (let ((_let_80 (or _let_79 _let_78))) (let ((_let_81 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN tptp.xi))) (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN tptp.sz00)))))) (let ((_let_82 (and (tptp.aSet0 _let_1) _let_81))) (let ((_let_83 (= _let_40 _let_82))) (let ((_let_84 (tptp.aSet0 _let_13))) (let ((_let_85 (not _let_84))) (let ((_let_86 (or _let_85 _let_83))) (let ((_let_87 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2063 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.aSubsetOf0 BOUND_VARIABLE_2063 W0) (and (tptp.aSet0 BOUND_VARIABLE_2063) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 BOUND_VARIABLE_2063)) (tptp.aElementOf0 W2 W0))))))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (tptp.szmzizndt0 _let_13))) (let ((_let_90 (and _let_84 (or (not (tptp.aElementOf0 _let_89 _let_13)) (tptp.aElementOf0 _let_89 tptp.szNzAzT0)) (tptp.aSubsetOf0 _let_13 tptp.szNzAzT0) (tptp.isCountable0 _let_13)))) (let ((_let_91 (or _let_44 _let_90))) (let ((_let_92 (forall ((W0 $$unsorted) (BOUND_VARIABLE_3826 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aSet0 _let_1) (or (not (tptp.aElementOf0 BOUND_VARIABLE_3826 _let_1)) (tptp.aElementOf0 BOUND_VARIABLE_3826 tptp.szNzAzT0)) (tptp.aSubsetOf0 _let_1 tptp.szNzAzT0) (tptp.isCountable0 _let_1))))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (_let_81))) (let ((_let_95 (not _let_78))) (let ((_let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_22))))) (let ((_let_97 (REFL :args ((not _let_21))))) (let ((_let_98 (and _let_21 _let_29))) (let ((_let_99 (ASSUME :args (_let_29)))) (let ((_let_100 (FALSE_INTRO _let_99))) (let ((_let_101 (APPLY_UF tptp.aElementOf0))) (let ((_let_102 (ASSUME :args (_let_21)))) (let ((_let_103 (SYMM (SYMM _let_102)))) (let ((_let_104 (ASSUME :args (_let_23)))) (let ((_let_105 (ASSUME :args (_let_24)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_104 _let_105 _let_102 _let_99) :args (_let_21 _let_29 _let_23 _let_24)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM _let_100) (CONG (SYMM _let_105) _let_103 :args _let_101) (TRUE_INTRO _let_104))) :args (_let_23 _let_24 _let_21 _let_29)) :args ((not (and _let_21 _let_29 _let_23 _let_24)) SB_LITERAL))) (CONG _let_97 _let_96 (REFL :args ((not _let_23))) (REFL :args (_let_70)) :args _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_57 _let_24 (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_66 _let_65 (not _let_67)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_73)) :args ((or _let_72 _let_74 (not _let_73)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_72 1)) :args ((or _let_71 _let_77))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_78 _let_79 (not _let_80)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_98)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_99 _let_102) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (SYMM _let_103) :args _let_101) _let_100)) :args (_let_29 _let_21))) :args (_let_21 _let_29))) :args (true _let_98)) (CONG _let_97 _let_96 (REFL :args (_let_95)) :args _let_33)) _let_25 _let_37 :args (_let_95 false _let_21 true _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_94) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W2 _let_1) false))))) :args _let_94)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_82 1)) :args ((or _let_81 (not _let_82)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_83)) :args ((or (not _let_40) _let_82 (not _let_83)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_41 1)) :args ((or _let_40 _let_55))) _let_54 :args (_let_40 false _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_85 _let_83 (not _let_86)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_90 0)) :args ((or _let_84 (not _let_90)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_44 _let_90 (not _let_91)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args (tptp.sz00 _let_89 QUANTIFIERS_INST_E_MATCHING ((tptp.aElementOf0 BOUND_VARIABLE_3826 (tptp.sdtlpdtrp0 tptp.xN W0))))) :args (_let_92))) _let_93 :args (_let_91 false _let_92)) :args (_let_90 false _let_19 false _let_91)) :args (_let_84 false _let_90)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (_let_13 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aSubsetOf0 BOUND_VARIABLE_2063 W0)))) :args (_let_87))) _let_88 :args (_let_86 false _let_87)) :args (_let_83 false _let_84 false _let_86)) :args (_let_82 false _let_40 false _let_83)) :args (_let_81 false _let_82)) :args (_let_80 false _let_81)) :args (_let_79 true _let_78 false _let_80)) :args (_let_77 true _let_71)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_76) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElement0 W0)))) :args _let_76)) (AND_ELIM _let_56 :args _let_63) :args (_let_73 false _let_75)) :args (_let_74 true _let_72 false _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_69) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 tptp.xQ) false))))) :args _let_69)) (AND_ELIM _let_56 :args (5)) :args (_let_67 false _let_68)) :args (_let_66 true _let_65 false _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_60 1)) :args ((or _let_58 (not _let_60)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_61)) :args ((or _let_27 _let_60 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 0)) (CONG (REFL :args (_let_28)) (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_33)) :args ((or _let_26 _let_28))) _let_36 :args (_let_26 true _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_64) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W0 _let_3)))) :args _let_64)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) :args _let_63) :args (_let_61 false _let_62)) :args (_let_60 false _let_26 false _let_61)) :args (_let_58 false _let_60)) :args (_let_24 true _let_57 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_38 _let_23 (not _let_39)))) (AND_ELIM _let_56 :args _let_32) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_41 0)) :args ((or _let_39 _let_55))) _let_54 :args (_let_39 false _let_41)) :args (_let_23 false _let_5 false _let_39)) _let_37 _let_25 :args (false false _let_24 false _let_23 true _let_22 false _let_21)) :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 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) (forall ((W0 $$unsorted)) (= (= W0 tptp.slcrc0) (and (tptp.aSet0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))) (tptp.isFinite0 tptp.slcrc0) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isCountable0 W0) true))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (tptp.isFinite0 W0)))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (= W0 tptp.slcrc0)))) _let_20 (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)))))) (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0)) _let_19 (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))) _let_18 (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 $$unsorted)) (and (tptp.aSubsetOf0 W2 W0) (= (tptp.sbrdtbr0 W2) W1)))))) (forall ((W0 $$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 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 (tptp.slbdtrb0 W0)))) (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0) (forall ((W0 $$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 $$unsorted)) (let ((_let_1 (tptp.szDzizrdt0 W0))) (let ((_let_2 (tptp.szDzozmdt0 W0))) (=> (tptp.aFunction0 W0) (=> (and (tptp.isCountable0 _let_2) (tptp.isFinite0 (tptp.sdtlcdtrc0 W0 _let_2))) (and (tptp.aElement0 _let_1) (tptp.isCountable0 (tptp.sdtlbdtrb0 W0 _let_1)))))))) (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT)) (tptp.aElementOf0 tptp.xK tptp.szNzAzT0) (and (tptp.aSet0 tptp.xS) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xS) (tptp.aElementOf0 W0 tptp.szNzAzT0))) (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS)) (and (tptp.aFunction0 tptp.xc) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.szDzozmdt0 tptp.xc)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xK))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xS))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS)))) _let_3) _let_2) _let_1))))))) (= _let_16 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSet0 _let_17) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtlcdtrc0 tptp.xc (tptp.szDzozmdt0 tptp.xc))) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.szDzozmdt0 tptp.xc)) (= (tptp.sdtlpdtrp0 tptp.xc W1) W0))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.sdtlcdtrc0 tptp.xc (tptp.szDzozmdt0 tptp.xc))) (tptp.aElementOf0 W0 tptp.xT))) (tptp.aSubsetOf0 _let_17 tptp.xT)) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (=> (and (or (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 tptp.szNzAzT0)))) (tptp.aSubsetOf0 W1 tptp.szNzAzT0)) (tptp.isCountable0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W2))) (let ((_let_2 (tptp.sdtlcdtrc0 W2 _let_1))) (=> (and (tptp.aFunction0 W2) (or (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W3 (tptp.szDzozmdt0 W2)))) (let ((_let_2 (= (tptp.sbrdtbr0 W3) W0))) (let ((_let_3 (tptp.aSubsetOf0 W3 W1))) (let ((_let_4 (tptp.aSet0 W3))) (and (=> _let_1 (and (or (and _let_4 (forall ((W4 $$unsorted)) (=> (tptp.aElementOf0 W4 W3) (tptp.aElementOf0 W4 W1)))) _let_3) _let_2)) (=> (and _let_4 (forall ((W4 $$unsorted)) (=> (tptp.aElementOf0 W4 W3) (tptp.aElementOf0 W4 W1))) _let_3 _let_2) _let_1))))))) (= _let_1 (tptp.slbdtsldtrb0 W1 W0))) (=> (and (tptp.aSet0 _let_2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 (tptp.sdtlcdtrc0 W2 (tptp.szDzozmdt0 W2))) (exists ((W4 $$unsorted)) (and (tptp.aElementOf0 W4 (tptp.szDzozmdt0 W2)) (= (tptp.sdtlpdtrp0 W2 W4) W3)))))) (or (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 (tptp.sdtlcdtrc0 W2 (tptp.szDzozmdt0 W2))) (tptp.aElementOf0 W3 tptp.xT))) (tptp.aSubsetOf0 _let_2 tptp.xT)))) (=> (tptp.iLess0 W0 tptp.xK) (exists ((W3 $$unsorted)) (and (tptp.aElementOf0 W3 tptp.xT) (exists ((W4 $$unsorted)) (and (tptp.aSet0 W4) (forall ((W5 $$unsorted)) (=> (tptp.aElementOf0 W5 W4) (tptp.aElementOf0 W5 W1))) (tptp.aSubsetOf0 W4 W1) (tptp.isCountable0 W4) (forall ((W5 $$unsorted)) (=> (or (and (or (and (tptp.aSet0 W5) (forall ((W6 $$unsorted)) (=> (tptp.aElementOf0 W6 W5) (tptp.aElementOf0 W6 W4)))) (tptp.aSubsetOf0 W5 W4)) (= (tptp.sbrdtbr0 W5) W0)) (tptp.aElementOf0 W5 (tptp.slbdtsldtrb0 W4 W0))) (= (tptp.sdtlpdtrp0 W2 W5) W3)))))))))))))))) _let_15 _let_15 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK)) _let_14 _let_12 _let_11 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W1))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_3 (tptp.szmzizndt0 _let_2))) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= W0 W1))) (not (=> (and (tptp.aElementOf0 _let_3 _let_2) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2))))) (or (and (tptp.aElementOf0 _let_3 _let_1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN W1)) (tptp.sdtlseqdt0 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)) W2)))) (= _let_3 (tptp.szmzizndt0 _let_1)))))))))) _let_10 _let_9 _let_7 _let_6 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 8.12/8.29 )
% 8.12/8.29 % SZS output end Proof for NUM581+3
% 8.12/8.29 % cvc5---1.0.5 exiting
% 8.12/8.29 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------