%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM577+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n025.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 10:45:15 EDT 2023

% Result   : Theorem 29.45s 29.80s
% Output   : Proof 29.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : NUM577+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command    : do_cvc5 %s %d
% 0.11/0.32  % Computer : n025.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri Aug 25 15:54:07 EDT 2023
% 0.11/0.32  % CPUTime    : 
% 0.17/0.45  %----Proving TF0_NAR, FOF, or CNF
% 29.45/29.80  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.r35EssRkiU/cvc5---1.0.5_8994.p...
% 29.45/29.80  ------- get file name : TPTP file name is NUM577+1
% 29.45/29.80  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_8994.smt2...
% 29.45/29.80  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 29.45/29.80  --- Run --no-e-matching --full-saturate-quant at 5...
% 29.45/29.80  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 29.45/29.80  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 29.45/29.80  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 29.45/29.80  % SZS status Theorem for NUM577+1
% 29.45/29.80  % SZS output start Proof for NUM577+1
% 29.45/29.80  (
% 29.45/29.80  (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.sdtmndt0 _let_1 _let_2))) (let ((_let_6 (tptp.aSubsetOf0 _let_3 _let_5))) (let ((_let_7 (tptp.szszuzczcdt0 tptp.xn))) (let ((_let_8 (tptp.sdtlseqdt0 _let_7 tptp.xm))) (let ((_let_9 (not (=> _let_8 (and _let_6 (not (= _let_4 _let_2))))))) (let ((_let_10 (and (tptp.aElementOf0 tptp.xn tptp.szNzAzT0) (tptp.aElementOf0 tptp.xm 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) (tptp.aSubsetOf0 (tptp.sdtlpdtrp0 tptp.xN W0) (tptp.sdtlpdtrp0 tptp.xN W1))))))) (let ((_let_12 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aSubsetOf0 _let_1 tptp.szNzAzT0) (tptp.isCountable0 _let_1))))))) (let ((_let_13 (tptp.sdtlpdtrp0 tptp.xN tptp.sz00))) (let ((_let_14 (tptp.szDzozmdt0 tptp.xN))) (let ((_let_15 (tptp.aFunction0 tptp.xN))) (let ((_let_16 (and _let_15 (= _let_14 tptp.szNzAzT0) (= _let_13 tptp.xS) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (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_17 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK)))) (let ((_let_18 (not (= tptp.xK tptp.sz00)))) (let ((_let_19 (tptp.szDzozmdt0 tptp.xc))) (let ((_let_20 (tptp.slbdtrb0 tptp.sz00))) (let ((_let_21 (= _let_20 tptp.slcrc0))) (let ((_let_22 (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 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W1 W2)))))))))) (let ((_let_23 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (= (tptp.sbrdtbr0 W0) tptp.sz00) (= W0 tptp.slcrc0)))))) (let ((_let_24 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (tptp.aElementOf0 (tptp.sbrdtbr0 W0) tptp.szNzAzT0) (tptp.isFinite0 W0)))))) (let ((_let_25 (forall ((W0 $$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_26 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0))) (let ((_let_27 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0)))) (let ((_let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 W0) (not (= W3 W1)))))))))))) (let ((_let_29 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1) (tptp.aSet0 W2)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W2)) (tptp.aSubsetOf0 W0 W2)))))) (let ((_let_30 (forall ((W0 $$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_31 (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (= W0 tptp.slcrc0)))))) (let ((_let_32 (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (tptp.isFinite0 W0)))))) (let ((_let_33 (forall ((W0 $$unsorted)) (= (= W0 tptp.slcrc0) (and (tptp.aSet0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))))) (let ((_let_34 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_35 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN tptp.xm))) (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xn))))))) (let ((_let_36 (tptp.sdtlpdtrp0 tptp.xN _let_7))) (let ((_let_37 (tptp.aElementOf0 _let_2 _let_36))) (let ((_let_38 (tptp.aElementOf0 _let_2 _let_3))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37))) (let ((_let_41 (tptp.aSet0 _let_3))) (let ((_let_42 (and _let_41 _let_35))) (let ((_let_43 (tptp.aSubsetOf0 _let_3 _let_36))) (let ((_let_44 (= _let_43 _let_42))) (let ((_let_45 (tptp.aSet0 _let_36))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_44))) (let ((_let_48 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1792 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.aSubsetOf0 BOUND_VARIABLE_1792 W0) (and (tptp.aSet0 BOUND_VARIABLE_1792) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 BOUND_VARIABLE_1792)) (tptp.aElementOf0 W2 W0))))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (_let_48))) (let ((_let_51 ((tptp.aSubsetOf0 BOUND_VARIABLE_1792 W0)))) (let ((_let_52 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (or (not (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xn)))) (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))))) (let ((_let_53 (and _let_45 _let_52))) (let ((_let_54 (tptp.aSubsetOf0 _let_36 _let_5))) (let ((_let_55 (= _let_54 _let_53))) (let ((_let_56 (tptp.aSet0 _let_5))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_55))) (let ((_let_59 (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W3 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 _let_1) (not (= W3 _let_2))))))))) (let ((_let_60 (and _let_56 _let_59))) (let ((_let_61 (tptp.aElement0 _let_2))) (let ((_let_62 (not _let_61))) (let ((_let_63 (tptp.aSet0 _let_1))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_64 _let_62 _let_60))) (let ((_let_66 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1910 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElement0 W1)) (= (= (tptp.sdtmndt0 W0 W1) BOUND_VARIABLE_1910) (and (tptp.aSet0 BOUND_VARIABLE_1910) (forall ((W3 $$unsorted)) (= (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 W0) (not (= W1 W3))) (tptp.aElementOf0 W3 BOUND_VARIABLE_1910))))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (tptp.aElementOf0 _let_2 _let_1))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_64 _let_69 _let_61))) (let ((_let_71 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1727 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1727 W0)) (tptp.aElement0 BOUND_VARIABLE_1727))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (_let_1 _let_2 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_74 (and _let_68 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (or (not (tptp.aElementOf0 W2 _let_1)) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2))))))) (let ((_let_75 (= _let_20 _let_1))) (let ((_let_76 (tptp.aSubsetOf0 _let_1 _let_14))) (let ((_let_77 (not _let_76))) (let ((_let_78 (or _let_77 _let_75 _let_74))) (let ((_let_79 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2320 $$unsorted)) (or (not (tptp.aSubsetOf0 W0 (tptp.szDzozmdt0 tptp.xN))) (= W0 (tptp.slbdtrb0 tptp.sz00)) (= (and (tptp.aElementOf0 BOUND_VARIABLE_2320 W0) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_2320 W2)))) (= (tptp.szmzizndt0 W0) BOUND_VARIABLE_2320)))))) (let ((_let_80 (1))) (let ((_let_81 (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_82 (ASSUME :args (_let_16)))) (let ((_let_83 (EQ_RESOLVE _let_82 _let_81))) (let ((_let_84 (AND_INTRO (AND_ELIM _let_83 :args (2)) (AND_ELIM _let_83 :args _let_80) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) :args _let_80) (SYMM (ASSUME :args (_let_21)))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_22)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_84 :args ((forall ((W0 $$unsorted) (BOUND_VARIABLE_2320 $$unsorted)) (or (not (tptp.aSubsetOf0 W0 tptp.szNzAzT0)) (= tptp.slcrc0 W0) (= (and (tptp.aElementOf0 BOUND_VARIABLE_2320 W0) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_2320 W2)))) (= (tptp.szmzizndt0 W0) BOUND_VARIABLE_2320)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_86 (_let_79))) (let ((_let_87 (tptp.isCountable0 _let_20))) (let ((_let_88 (tptp.isCountable0 _let_1))) (let ((_let_89 (not _let_75))) (let ((_let_90 (tptp.aSet0 _let_20))) (let ((_let_91 (not _let_87))) (let ((_let_92 (and _let_90 (forall ((W1 $$unsorted)) (not (tptp.aElementOf0 W1 (tptp.slbdtrb0 tptp.sz00))))))) (let ((_let_93 (forall ((W0 $$unsorted)) (= (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (not (tptp.aElementOf0 W1 W0)))) (= W0 (tptp.slbdtrb0 tptp.sz00)))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_33)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_84 :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_95 (and _let_76 _let_88))) (let ((_let_96 (tptp.aElementOf0 tptp.xn _let_14))) (let ((_let_97 (not _let_96))) (let ((_let_98 (or _let_97 _let_95))) (let ((_let_99 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szDzozmdt0 tptp.xN))) (or (not (tptp.aElementOf0 W0 _let_2)) (and (tptp.aSubsetOf0 _let_1 _let_2) (tptp.isCountable0 _let_1)))))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_12)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_84 :args ((forall ((W0 $$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_101 (_let_99))) (let ((_let_102 ((not (= (tptp.aElementOf0 W0 _let_14) false))))) (let ((_let_103 (0))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO _let_84 :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (AND_ELIM _let_104 :args _let_103))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_97 _let_95 (not _let_98)))) _let_105 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_102)) :args _let_101)) _let_100 :args (_let_98 false _let_99)) :args (_let_95 false _let_96 false _let_98)))) (let ((_let_107 (not _let_95))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_95 1)) :args ((or _let_88 _let_107))) _let_106 :args (_let_88 false _let_95)))) (let ((_let_109 (or))) (let ((_let_110 (not _let_88))) (let ((_let_111 (ASSUME :args (_let_91)))) (let ((_let_112 (ASSUME :args (_let_75)))) (let ((_let_113 (ASSUME :args (_let_88)))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_95 0)) :args ((or _let_76 _let_107))) _let_106 :args (_let_76 false _let_95)))) (let ((_let_115 (and _let_63 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN tptp.xn))) (tptp.aElementOf0 W2 (tptp.szDzozmdt0 tptp.xN))))))) (let ((_let_116 (= _let_76 _let_115))) (let ((_let_117 (tptp.aSet0 _let_14))) (let ((_let_118 (not _let_117))) (let ((_let_119 (or _let_118 _let_116))) (let ((_let_120 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO _let_84 :args (_let_27 SB_DEFAULT SBA_FIXPOINT))) :args _let_103))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_115 0)) :args ((or _let_63 (not _let_115)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_116)) :args ((or _let_77 _let_115 (not _let_116)))) _let_114 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_118 _let_116 (not _let_119)))) _let_120 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_14 _let_1 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_50)) _let_49 :args (_let_119 false _let_48)) :args (_let_116 false _let_117 false _let_119)) :args (_let_115 false _let_76 false _let_116)) :args (_let_63 false _let_115)))) (let ((_let_122 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_64 _let_62 _let_60 (not _let_65)))) _let_121 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_64 _let_69 _let_61 (not _let_70)))) _let_121 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_74 0)) :args ((or _let_68 (not _let_74)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_77 _let_75 _let_74 (not _let_78)))) _let_114 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_111 _let_112 _let_113) :args (_let_91 _let_88 _let_75)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_113)) (CONG (SYMM _let_112) :args (APPLY_UF tptp.isCountable0)) (FALSE_INTRO _let_111))) :args (_let_91 _let_75 _let_88)) :args ((not (and _let_91 _let_88 _let_75)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_87))) (REFL :args (_let_110)) (REFL :args (_let_89)) :args _let_109)) _let_108 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_31)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_84 :args ((or (not (tptp.aSet0 tptp.slcrc0)) (not (tptp.isCountable0 tptp.slcrc0))) SB_DEFAULT SBA_FIXPOINT)))) :args ((or _let_91 (not _let_90)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_92 0)) :args ((or _let_90 (not _let_92)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_94 :args (_let_20 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_93)))) _let_94 :args (_let_92 false _let_93)) :args (_let_90 false _let_92)) :args (_let_91 false _let_90)) :args (_let_89 false _let_88 true _let_87)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_85 :args _let_73) :args _let_86))) _let_85 :args (_let_78 false _let_79)) :args (_let_74 false _let_76 true _let_75 false _let_78)) :args (_let_68 false _let_74)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args _let_73) :args (_let_71))) _let_72 :args (_let_70 false _let_71)) :args (_let_61 false _let_63 false _let_68 false _let_70)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_67 :args (_let_1 _let_2 _let_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_66)))) _let_67 :args (_let_65 false _let_66)) :args (_let_60 false _let_63 false _let_61 false _let_65)))) (let ((_let_123 (not _let_60))) (let ((_let_124 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_60 0)) :args ((or _let_56 _let_123))) _let_122 :args (_let_56 false _let_60)))) (let ((_let_125 (and _let_54 (tptp.isCountable0 _let_36)))) (let ((_let_126 (or _let_97 _let_77 _let_110 _let_125))) (let ((_let_127 (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.szDzozmdt0 tptp.xN))) (or (not (tptp.aElementOf0 W0 _let_3)) (not (tptp.aSubsetOf0 _let_2 _let_3)) (not (tptp.isCountable0 _let_2)) (and (tptp.aSubsetOf0 _let_1 (tptp.sdtmndt0 _let_2 (tptp.szmzizndt0 _let_2))) (tptp.isCountable0 _let_1))))))))) (let ((_let_128 (_let_127))) (let ((_let_129 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_125 0)) :args ((or _let_54 (not _let_125)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_126)) :args ((or _let_97 _let_110 _let_77 _let_125 (not _let_126)))) _let_105 _let_108 _let_114 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_128) :args (tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 _let_14) false))))) :args _let_128)) (AND_ELIM (EQ_RESOLVE _let_82 (TRANS _let_81 (MACRO_SR_EQ_INTRO _let_84 :args ((and _let_15 (= tptp.szNzAzT0 _let_14) (= tptp.xS _let_13) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aSubsetOf0 _let_2 tptp.szNzAzT0)) (not (tptp.isCountable0 _let_2)) (and (tptp.aSubsetOf0 _let_1 (tptp.sdtmndt0 _let_2 (tptp.szmzizndt0 _let_2))) (tptp.isCountable0 _let_1))))))) SB_DEFAULT SBA_FIXPOINT)))) :args _let_80) :args (_let_126 false _let_127)) :args (_let_125 false _let_96 false _let_88 false _let_76 false _let_126)) :args (_let_54 false _let_125)))) (let ((_let_130 (not _let_54))) (let ((_let_131 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_55)) :args ((or _let_130 _let_53 (not _let_55)))) _let_129 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_57 _let_55 (not _let_58)))) _let_124 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_5 _let_36 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_51)) :args _let_50)) _let_49 :args (_let_58 false _let_48)) :args (_let_55 false _let_56 false _let_58)) :args (_let_53 false _let_54 false _let_55)))) (let ((_let_132 (not _let_53))) (let ((_let_133 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_53 0)) :args ((or _let_45 _let_132))) _let_131 :args (_let_45 false _let_53)))) (let ((_let_134 (not _let_8))) (let ((_let_135 (tptp.aElementOf0 _let_7 _let_14))) (let ((_let_136 (not _let_135))) (let ((_let_137 (tptp.aElementOf0 tptp.xm _let_14))) (let ((_let_138 (not _let_137))) (let ((_let_139 (or _let_138 _let_136 _let_134 _let_43))) (let ((_let_140 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 tptp.xN))) (or (not (tptp.aElementOf0 W0 _let_1)) (not (tptp.aElementOf0 W1 _let_1)) (not (tptp.sdtlseqdt0 W1 W0)) (tptp.aSubsetOf0 (tptp.sdtlpdtrp0 tptp.xN W0) (tptp.sdtlpdtrp0 tptp.xN W1))))))) (let ((_let_141 (EQ_RESOLVE (ASSUME :args (_let_11)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_84 :args ((forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (tptp.sdtlseqdt0 W1 W0)) (tptp.aSubsetOf0 (tptp.sdtlpdtrp0 tptp.xN W0) (tptp.sdtlpdtrp0 tptp.xN W1)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_142 (and _let_135 (not (= tptp.sz00 _let_7))))) (let ((_let_143 (or _let_97 _let_142))) (let ((_let_144 (forall ((W0 $$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_145 (EQ_RESOLVE (ASSUME :args (_let_25)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_84 :args ((forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= tptp.sz00 _let_1)))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_146 (AND_ELIM _let_104 :args _let_80))) (let ((_let_147 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_148 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_139)) :args ((or _let_134 _let_138 _let_136 _let_43 (not _let_139)))) (NOT_IMPLIES_ELIM1 _let_147) _let_146 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_142 0)) :args ((or _let_135 (not _let_142)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_143)) :args ((or _let_97 _let_142 (not _let_143)))) _let_105 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_145 :args (tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.szszuzczcdt0 W0)))) :args (_let_144))) _let_145 :args (_let_143 false _let_144)) :args (_let_142 false _let_96 false _let_143)) :args (_let_135 false _let_142)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_141 :args (tptp.xm _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.sdtlseqdt0 W1 W0) false))))) :args (_let_140))) _let_141 :args (_let_139 false _let_140)) :args (_let_43 false _let_8 false _let_137 false _let_135 false _let_139)))) (let ((_let_149 (not _let_43))) (let ((_let_150 (not _let_40))) (let ((_let_151 (tptp.aElementOf0 _let_2 _let_5))) (let ((_let_152 (not _let_37))) (let ((_let_153 (or _let_152 _let_151))) (let ((_let_154 (_let_52))) (let ((_let_155 (_let_2 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_156 (_let_59))) (let ((_let_157 (tptp.aElementOf0 _let_4 _let_3))) (let ((_let_158 (= _let_2 _let_4))) (let ((_let_159 (and _let_157 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xm))) (or (not (tptp.aElementOf0 W2 _let_1)) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2))))))) (let ((_let_160 (= _let_20 _let_3))) (let ((_let_161 (tptp.aSubsetOf0 _let_3 _let_14))) (let ((_let_162 (not _let_161))) (let ((_let_163 (or _let_162 _let_160 _let_159))) (let ((_let_164 (tptp.sbrdtbr0 _let_3))) (let ((_let_165 (= tptp.sz00 _let_164))) (let ((_let_166 (= _let_165 _let_160))) (let ((_let_167 (not _let_160))) (let ((_let_168 (not _let_41))) (let ((_let_169 (or _let_168 _let_166))) (let ((_let_170 (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (= tptp.sz00 (tptp.sbrdtbr0 W0)) (= W0 (tptp.slbdtrb0 tptp.sz00))))))) (let ((_let_171 (EQ_RESOLVE (ASSUME :args (_let_23)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_84 :args ((forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (= tptp.sz00 (tptp.sbrdtbr0 W0)) (= tptp.slcrc0 W0)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_172 (and _let_41 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN tptp.xm))) (tptp.aElementOf0 W2 (tptp.szDzozmdt0 tptp.xN))))))) (let ((_let_173 (= _let_161 _let_172))) (let ((_let_174 (or _let_118 _let_173))) (let ((_let_175 (tptp.isCountable0 _let_3))) (let ((_let_176 (and _let_161 _let_175))) (let ((_let_177 (or _let_138 _let_176))) (let ((_let_178 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_177)) :args ((or _let_138 _let_176 (not _let_177)))) _let_146 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_102)) :args _let_101)) _let_100 :args (_let_177 false _let_99)) :args (_let_176 false _let_137 false _let_177)))) (let ((_let_179 (not _let_176))) (let ((_let_180 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_176 0)) :args ((or _let_161 _let_179))) _let_178 :args (_let_161 false _let_176)))) (let ((_let_181 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_172 0)) :args ((or _let_41 (not _let_172)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_173)) :args ((or _let_162 _let_172 (not _let_173)))) _let_180 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_174)) :args ((or _let_118 _let_173 (not _let_174)))) _let_120 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_14 _let_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_50)) _let_49 :args (_let_174 false _let_48)) :args (_let_173 false _let_117 false _let_174)) :args (_let_172 false _let_161 false _let_173)) :args (_let_41 false _let_172)))) (let ((_let_182 (tptp.aElementOf0 tptp.sz00 _let_14))) (let ((_let_183 (tptp.aElementOf0 _let_164 _let_14))) (let ((_let_184 (not _let_165))) (let ((_let_185 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO _let_84 :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_186 (tptp.isFinite0 _let_3))) (let ((_let_187 (= _let_186 _let_183))) (let ((_let_188 (not _let_183))) (let ((_let_189 (or _let_168 _let_187))) (let ((_let_190 (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.isFinite0 W0) (tptp.aElementOf0 (tptp.sbrdtbr0 W0) (tptp.szDzozmdt0 tptp.xN))))))) (let ((_let_191 (EQ_RESOLVE (ASSUME :args (_let_24)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_84 :args ((forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.aElementOf0 (tptp.sbrdtbr0 W0) tptp.szNzAzT0) (tptp.isFinite0 W0)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_192 (not _let_186))) (let ((_let_193 (not _let_175))) (let ((_let_194 (or _let_168 _let_193 _let_192))) (let ((_let_195 (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.isCountable0 W0)) (not (tptp.isFinite0 W0)))))) (let ((_let_196 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_197 (not _let_182))) (let ((_let_198 (APPLY_UF tptp.aElementOf0))) (let ((_let_199 (or _let_168 _let_46 _let_57 _let_149 _let_130 _let_6))) (let ((_let_200 (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_201 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_202 (not _let_6))) (let ((_let_203 (and _let_158 _let_157))) (let ((_let_204 (ASSUME :args (_let_157)))) (let ((_let_205 (ASSUME :args (_let_158)))) (let ((_let_206 (_let_35))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_206) :args _let_155) :args _let_206)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_37 _let_150))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_203)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_204 _let_205) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_205)) (REFL :args (_let_3)) :args _let_198) (TRUE_INTRO _let_204))) :args (_let_157 _let_158))) :args (_let_158 _let_157))) :args (true _let_203)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (NOT_IMPLIES_ELIM2 _let_147)) (CONG (REFL :args (_let_202)) (MACRO_SR_PRED_INTRO :args ((= (not (not _let_158)) _let_158))) :args _let_109)) :args ((or _let_158 _let_202))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_199)) :args ((or _let_6 _let_57 _let_168 _let_130 _let_149 _let_46 (not _let_199)))) _let_124 _let_181 _let_129 _let_148 _let_133 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_201 :args (_let_3 _let_36 _let_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_200))) _let_201 :args (_let_199 false _let_200)) :args (_let_6 false _let_56 false _let_41 false _let_54 false _let_43 false _let_45 false _let_199)) :args (_let_158 false _let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_159 0)) :args ((or _let_157 (not _let_159)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_163)) :args ((or _let_162 _let_160 _let_159 (not _let_163)))) _let_180 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_166)) :args ((or _let_165 _let_167 (not _let_166)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_188)))) (CONG (SYMM (ASSUME :args (_let_165))) (REFL :args (_let_14)) :args _let_198) (TRUE_INTRO _let_185))) :args (_let_182 _let_165 _let_188))) (CONG (REFL :args (_let_197)) (REFL :args (_let_184)) (MACRO_SR_PRED_INTRO :args ((= (not _let_188) _let_183))) :args _let_109)) :args ((or _let_197 _let_183 _let_184))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_187)) :args ((or _let_186 _let_188 (not _let_187)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_194)) :args ((or _let_193 _let_168 _let_192 (not _let_194)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_176 1)) :args ((or _let_175 _let_179))) _let_178 :args (_let_175 false _let_176)) _let_181 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_196 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aSet0 W0) false))))) :args (_let_195))) _let_196 :args (_let_194 false _let_195)) :args (_let_192 false _let_175 false _let_41 false _let_194)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_189)) :args ((or _let_168 _let_187 (not _let_189)))) _let_181 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_191 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aSet0 W0) false))))) :args (_let_190))) _let_191 :args (_let_189 false _let_190)) :args (_let_187 false _let_41 false _let_189)) :args (_let_188 true _let_186 false _let_187)) _let_185 :args (_let_184 true _let_183 false _let_182)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_169)) :args ((or _let_168 _let_166 (not _let_169)))) _let_181 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_171 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aSet0 W0) false))))) :args (_let_170)))) _let_171 :args (_let_169 false _let_170)) :args (_let_166 false _let_41 false _let_169)) :args (_let_167 true _let_165 false _let_166)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_85 :args (_let_3 _let_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_86))) _let_85 :args (_let_163 false _let_79)) :args (_let_159 false _let_161 true _let_160 false _let_163)) :args (_let_157 false _let_159)) :args (_let_38 false _let_158 false _let_157)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_153)) :args ((or _let_151 _let_152 (not _let_153)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_156) :args (_let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElement0 W3)))) :args _let_156))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_60 1)) :args ((or _let_59 _let_123))) _let_122 :args (_let_59 false _let_60)) :args ((not _let_151) false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_154) :args _let_155) :args _let_154)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_53 1)) :args ((or _let_52 _let_132))) _let_131 :args (_let_52 false _let_53)) :args (_let_153 false _let_52)) :args (_let_152 true _let_151 false _let_153)) :args (_let_150 false _let_38 true _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_42 1)) :args ((or _let_35 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_44)) :args ((or _let_149 _let_42 (not _let_44)))) _let_148 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_44 (not _let_47)))) _let_133 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_36 _let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_51)) :args _let_50)) _let_49 :args (_let_47 false _let_48)) :args (_let_44 false _let_45 false _let_47)) :args (_let_42 false _let_43 false _let_44)) :args (_let_35 false _let_42)) :args (false true _let_40 false _let_35)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) _let_34 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) _let_33 (tptp.isFinite0 tptp.slcrc0) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isCountable0 W0) true))) _let_32 _let_31 _let_30 (forall ((W0 $$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_29 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtpldt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElement0 W3) (or (tptp.aElementOf0 W3 W0) (= W3 W1)))))))))) _let_28 (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_27 _let_26 _let_25 (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)))) _let_24 _let_23 (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 $$unsorted)) (and (tptp.aSubsetOf0 W2 W0) (= (tptp.sbrdtbr0 W2) W1)))))) _let_22 (forall ((W0 $$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_21 (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_19 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xc _let_19) 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_18 _let_18 _let_17 _let_16 _let_12 _let_11 (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_10 _let_9 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 29.45/29.81  )
% 29.45/29.81  % SZS output end Proof for NUM577+1
% 29.45/29.81  % cvc5---1.0.5 exiting
% 29.45/29.81  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------