TSTP Solution File: NUM577+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM577+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 10:45:17 EDT 2023
% Result : Theorem 20.41s 20.96s
% Output : Proof 20.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM577+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : do_cvc5 %s %d
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Aug 25 16:48:28 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.15/0.40 %----Proving TF0_NAR, FOF, or CNF
% 20.41/20.96 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.vorDfWnJvV/cvc5---1.0.5_5885.p...
% 20.41/20.96 ------- get file name : TPTP file name is NUM577+3
% 20.41/20.96 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_5885.smt2...
% 20.41/20.96 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 20.41/20.96 --- Run --no-e-matching --full-saturate-quant at 5...
% 20.41/20.96 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.41/20.96 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 20.41/20.96 % SZS status Theorem for NUM577+3
% 20.41/20.96 % SZS output start Proof for NUM577+3
% 20.41/20.96 (
% 20.41/20.96 (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtlpdtrp0 tptp.xN tptp.xm))) (let ((_let_4 (tptp.szmzizndt0 _let_3))) (let ((_let_5 (tptp.aElementOf0 _let_4 _let_1))) (let ((_let_6 (tptp.aElementOf0 _let_4 _let_3))) (let ((_let_7 (tptp.sdtmndt0 _let_1 _let_2))) (let ((_let_8 (tptp.aSubsetOf0 _let_3 _let_7))) (let ((_let_9 (tptp.aSet0 _let_7))) (let ((_let_10 (tptp.aElementOf0 _let_2 _let_1))) (let ((_let_11 (tptp.szszuzczcdt0 tptp.xn))) (let ((_let_12 (tptp.sdtlseqdt0 _let_11 tptp.xm))) (let ((_let_13 (not (=> _let_12 (and (=> (and _let_10 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (=> (tptp.aElementOf0 W0 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W0))))) (=> (and _let_9 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (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)))))))) (or (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (=> (tptp.aElementOf0 W0 (tptp.sdtlpdtrp0 tptp.xN tptp.xm)) (tptp.aElementOf0 W0 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) _let_8))) (not (and _let_6 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xm))) (=> (tptp.aElementOf0 W0 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W0)))) _let_5 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.sdtlpdtrp0 tptp.xN tptp.xn)) (tptp.sdtlseqdt0 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN tptp.xm)) W0))) (= _let_4 _let_2)))))))) (let ((_let_14 (and (tptp.aElementOf0 tptp.xn tptp.szNzAzT0) (tptp.aElementOf0 tptp.xm tptp.szNzAzT0)))) (let ((_let_15 (forall ((W0 $$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_16 (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_17 (tptp.sdtlpdtrp0 tptp.xN tptp.sz00))) (let ((_let_18 (tptp.szDzozmdt0 tptp.xN))) (let ((_let_19 (tptp.aFunction0 tptp.xN))) (let ((_let_20 (and _let_19 (= _let_18 tptp.szNzAzT0) (= _let_17 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 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0))) (tptp.aElementOf0 W1 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) (tptp.aSubsetOf0 _let_1 _let_4) (tptp.isCountable0 _let_1)))))))))))) (let ((_let_21 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK)))) (let ((_let_22 (not (= tptp.xK tptp.sz00)))) (let ((_let_23 (tptp.szDzozmdt0 tptp.xc))) (let ((_let_24 (tptp.sdtlcdtrc0 tptp.xc _let_23))) (let ((_let_25 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0))) (let ((_let_26 (forall ((W0 $$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_27 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1) (tptp.aSet0 W2)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W2)) (tptp.aSubsetOf0 W0 W2)))))) (let ((_let_28 (= _let_2 _let_4))) (let ((_let_29 (tptp.aElementOf0 _let_2 _let_3))) (let ((_let_30 (and _let_6 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xm))) (or (not (tptp.aElementOf0 W0 _let_1)) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W0)))) _let_5 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (tptp.sdtlseqdt0 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN tptp.xm)) W0))) _let_28))) (let ((_let_31 (or (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (or (not (tptp.aElementOf0 W0 (tptp.sdtlpdtrp0 tptp.xN tptp.xm))) (tptp.aElementOf0 W0 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) _let_8))) (let ((_let_32 (=> (and _let_9 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W0 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W0) (tptp.aElementOf0 W0 _let_1) (not (= _let_2 W0)))))))) _let_31))) (let ((_let_33 (=> (and _let_10 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (or (not (tptp.aElementOf0 W0 _let_1)) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W0))))) _let_32))) (let ((_let_34 (tptp.sdtlpdtrp0 tptp.xN _let_11))) (let ((_let_35 (tptp.aSubsetOf0 _let_34 _let_7))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.aSubsetOf0 _let_3 _let_34))) (let ((_let_38 (not _let_37))) (let ((_let_39 (not _let_9))) (let ((_let_40 (tptp.aSet0 _let_34))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.aSet0 _let_3))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_41 _let_39 _let_38 _let_36 _let_8))) (let ((_let_45 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSet0 W1)) (not (tptp.aSet0 W2)) (not (tptp.aSubsetOf0 W0 W1)) (not (tptp.aSubsetOf0 W1 W2)) (tptp.aSubsetOf0 W0 W2))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (tptp.aElementOf0 tptp.sz00 _let_34))) (let ((_let_48 (not (tptp.aElementOf0 tptp.sz00 _let_3)))) (let ((_let_49 (and (or _let_48 _let_47) _let_37))) (let ((_let_50 (not _let_12))) (let ((_let_51 (tptp.aElementOf0 _let_11 _let_18))) (let ((_let_52 (not _let_51))) (let ((_let_53 (tptp.aElementOf0 tptp.xm _let_18))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_54 _let_52 _let_50 _let_49))) (let ((_let_56 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_3806 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W1))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_3 (tptp.szDzozmdt0 tptp.xN))) (or (not (tptp.aElementOf0 W0 _let_3)) (not (tptp.aElementOf0 W1 _let_3)) (not (tptp.sdtlseqdt0 W1 W0)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_3806 _let_2)) (tptp.aElementOf0 BOUND_VARIABLE_3806 _let_1)) (tptp.aSubsetOf0 _let_2 _let_1))))))))) (let ((_let_57 (1))) (let ((_let_58 (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_59 (ASSUME :args (_let_20)))) (let ((_let_60 (EQ_RESOLVE _let_59 _let_58))) (let ((_let_61 (AND_INTRO (AND_ELIM _let_60 :args (2)) (AND_ELIM _let_60 :args _let_57) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))) :args _let_57) (SYMM (ASSUME :args (_let_25)))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_15)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_61 :args ((forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_3806 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W1))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (tptp.sdtlseqdt0 W1 W0)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_3806 _let_2)) (tptp.aElementOf0 BOUND_VARIABLE_3806 _let_1)) (tptp.aSubsetOf0 _let_2 _let_1)))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_63 (_let_56))) (let ((_let_64 (and _let_51 (not (= tptp.sz00 _let_11))))) (let ((_let_65 (tptp.aElementOf0 tptp.xn _let_18))) (let ((_let_66 (not _let_65))) (let ((_let_67 (or _let_66 _let_64))) (let ((_let_68 (forall ((W0 $$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_69 (EQ_RESOLVE (ASSUME :args (_let_26)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_61 :args ((forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= tptp.sz00 _let_1)))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO _let_61 :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (AND_ELIM _let_70 :args (0)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_64 0)) :args ((or _let_51 (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_66 _let_64 (not _let_67)))) _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (tptp.xn QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_68))) _let_69 :args (_let_67 false _let_68)) :args (_let_64 false _let_65 false _let_67)) :args (_let_51 false _let_64)))) (let ((_let_73 (AND_ELIM _let_70 :args _let_57))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (NOT_IMPLIES_ELIM1 _let_74))) (let ((_let_76 (tptp.aElementOf0 tptp.sz00 _let_18))) (let ((_let_77 (and _let_42 (or _let_48 _let_76) (tptp.aSubsetOf0 _let_3 _let_18) (tptp.isCountable0 _let_3)))) (let ((_let_78 (or _let_54 _let_77))) (let ((_let_79 (forall ((W0 $$unsorted) (BOUND_VARIABLE_3780 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szDzozmdt0 tptp.xN))) (or (not (tptp.aElementOf0 W0 _let_2)) (and (tptp.aSet0 _let_1) (or (not (tptp.aElementOf0 BOUND_VARIABLE_3780 _let_1)) (tptp.aElementOf0 BOUND_VARIABLE_3780 _let_2)) (tptp.aSubsetOf0 _let_1 _let_2) (tptp.isCountable0 _let_1)))))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_16)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_61 :args ((forall ((W0 $$unsorted) (BOUND_VARIABLE_3780 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aSet0 _let_1) (or (not (tptp.aElementOf0 BOUND_VARIABLE_3780 _let_1)) (tptp.aElementOf0 BOUND_VARIABLE_3780 tptp.szNzAzT0)) (tptp.aSubsetOf0 _let_1 tptp.szNzAzT0) (tptp.isCountable0 _let_1))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_81 (_let_79))) (let ((_let_82 (tptp.isCountable0 _let_34))) (let ((_let_83 (tptp.aElementOf0 tptp.sz00 _let_7))) (let ((_let_84 (or (not _let_47) _let_83))) (let ((_let_85 (tptp.aElementOf0 tptp.sz00 _let_1))) (let ((_let_86 (= _let_83 (and (tptp.aElement0 tptp.sz00) _let_85 (not (= tptp.sz00 _let_2)))))) (let ((_let_87 (not _let_85))) (let ((_let_88 (or _let_87 (tptp.sdtlseqdt0 _let_2 tptp.sz00)))) (let ((_let_89 (and _let_10 _let_88 _let_9 _let_86 _let_40 _let_84 _let_35 _let_82))) (let ((_let_90 (tptp.isCountable0 _let_1))) (let ((_let_91 (not _let_90))) (let ((_let_92 (tptp.aSubsetOf0 _let_1 _let_18))) (let ((_let_93 (not _let_92))) (let ((_let_94 (tptp.aSet0 _let_1))) (let ((_let_95 (and (or (not _let_94) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (tptp.aElementOf0 W1 (tptp.szDzozmdt0 tptp.xN)))))) _let_93))) (let ((_let_96 (or _let_66 _let_95 _let_91 _let_89))) (let ((_let_97 (forall ((W0 $$unsorted) (BOUND_VARIABLE_3759 $$unsorted) (BOUND_VARIABLE_3750 $$unsorted) (BOUND_VARIABLE_3744 $$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))) (let ((_let_5 (tptp.szDzozmdt0 tptp.xN))) (or (not (tptp.aElementOf0 W0 _let_5)) (and (or (not (tptp.aSet0 _let_2)) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN W0))) (tptp.aElementOf0 W1 (tptp.szDzozmdt0 tptp.xN)))))) (not (tptp.aSubsetOf0 _let_2 _let_5))) (not (tptp.isCountable0 _let_2)) (and (tptp.aElementOf0 _let_3 _let_2) (or (not (tptp.aElementOf0 BOUND_VARIABLE_3744 _let_2)) (tptp.sdtlseqdt0 _let_3 BOUND_VARIABLE_3744)) (tptp.aSet0 _let_4) (= (tptp.aElementOf0 BOUND_VARIABLE_3750 _let_4) (and (tptp.aElement0 BOUND_VARIABLE_3750) (tptp.aElementOf0 BOUND_VARIABLE_3750 _let_2) (not (= _let_3 BOUND_VARIABLE_3750)))) (tptp.aSet0 _let_1) (or (not (tptp.aElementOf0 BOUND_VARIABLE_3759 _let_1)) (tptp.aElementOf0 BOUND_VARIABLE_3759 _let_4)) (tptp.aSubsetOf0 _let_1 _let_4) (tptp.isCountable0 _let_1))))))))))) (let ((_let_98 (AND_ELIM (EQ_RESOLVE _let_59 (TRANS _let_58 (MACRO_SR_EQ_INTRO _let_61 :args ((and _let_19 (= tptp.szNzAzT0 _let_18) (= tptp.xS _let_17) (forall ((W0 $$unsorted) (BOUND_VARIABLE_3759 $$unsorted) (BOUND_VARIABLE_3750 $$unsorted) (BOUND_VARIABLE_3744 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_3 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(let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_66 _let_91 _let_95 _let_89 (not _let_96)))) _let_71 _let_107 _let_106 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_100 :args (tptp.xn tptp.sz00 tptp.sz00 tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_99))) _let_98 :args (_let_96 false _let_97)) :args (_let_89 false _let_65 false _let_90 true _let_95 false _let_96)))) (let ((_let_109 (not _let_89))) (let ((_let_110 (not _let_33))) (let ((_let_111 (or))) (let ((_let_112 (not _let_30))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (NOT_IMPLIES_ELIM2 _let_74)) (CONG (REFL :args (_let_110)) (MACRO_SR_PRED_INTRO :args ((= (not _let_112) _let_30))) :args _let_111)) :args ((or _let_30 _let_110))) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args (_let_33)) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args (_let_32)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_31 1)) 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_let_99))) _let_98 :args (_let_126 false _let_97)) :args (_let_125 false _let_65 false _let_90 true _let_95 false _let_126)) :args (_let_124 false _let_125)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_122 5)) :args ((or _let_121 (not _let_122)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_123)) :args ((or _let_66 _let_91 _let_95 _let_122 (not _let_123)))) _let_71 _let_107 _let_106 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_100 :args (tptp.xn _let_2 tptp.sz00 tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_99))) _let_98 :args (_let_123 false _let_97)) :args (_let_122 false _let_65 false _let_90 true _let_95 false _let_123)) :args (_let_121 false _let_122)) :args (_let_120 true _let_119 false _let_121)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_117 0)) :args ((or _let_116 (not _let_117)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_50 _let_54 _let_52 _let_117 (not _let_118)))) _let_75 _let_73 _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.xm _let_11 _let_2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_63)) _let_62 :args (_let_118 false _let_56)) :args (_let_117 false _let_12 false _let_53 false _let_51 false _let_118)) :args (_let_116 false _let_117)) :args (_let_115 true _let_114 false _let_116)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_30 4)) :args ((or _let_28 _let_112))) _let_113 :args (_let_28 false _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_30 0)) :args ((or _let_6 _let_112))) _let_113 :args (_let_6 false _let_30)) :args (false true _let_29 false _let_28 false _let_6)) :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 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (= W0 tptp.slcrc0)))) (forall ((W0 $$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)))))))) (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 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W0)) (= W0 W1)))) _let_27 (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtmndt0 W1 W0)))))) (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0)) (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0) _let_26 (forall ((W0 $$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)))))) (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_25 (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_23 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSet0 _let_24) (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 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.sdtlcdtrc0 tptp.xc (tptp.szDzozmdt0 tptp.xc))) (tptp.aElementOf0 W0 tptp.xT))) (tptp.aSubsetOf0 _let_24 tptp.xT)) (forall ((W0 $$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_22 _let_22 _let_21 _let_20 _let_16 _let_15 (and (tptp.aElementOf0 tptp.xi tptp.szNzAzT0) (tptp.aElementOf0 tptp.xj tptp.szNzAzT0)) (=> (not (= tptp.xi tptp.xj)) (or (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 tptp.xj) tptp.xi) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 tptp.xi) tptp.xj))) _let_14 _let_13 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 20.41/20.97 )
% 20.41/20.97 % SZS output end Proof for NUM577+3
% 20.41/20.97 % cvc5---1.0.5 exiting
% 20.41/20.97 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------