TSTP Solution File: NUM542+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM542+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:44:55 EDT 2023
% Result : Theorem 32.27s 32.53s
% Output : Proof 32.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM542+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.12 % Command : do_cvc5 %s %d
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Aug 25 17:45:39 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.17/0.45 %----Proving TF0_NAR, FOF, or CNF
% 32.27/32.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Zcmo1ySJkU/cvc5---1.0.5_19391.p...
% 32.27/32.53 ------- get file name : TPTP file name is NUM542+1
% 32.27/32.53 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19391.smt2...
% 32.27/32.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 32.27/32.53 --- Run --no-e-matching --full-saturate-quant at 5...
% 32.27/32.53 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 32.27/32.53 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 32.27/32.53 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 32.27/32.53 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 32.27/32.53 % SZS status Theorem for NUM542+1
% 32.27/32.53 % SZS output start Proof for NUM542+1
% 32.27/32.53 (
% 32.27/32.53 (let ((_let_1 (tptp.slbdtrb0 tptp.xn))) (let ((_let_2 (tptp.slbdtrb0 tptp.xm))) (let ((_let_3 (tptp.aSubsetOf0 _let_2 _let_1))) (let ((_let_4 (tptp.sdtlseqdt0 tptp.xm tptp.xn))) (let ((_let_5 (not (= _let_4 _let_3)))) (let ((_let_6 (tptp.aElementOf0 tptp.xn tptp.szNzAzT0))) (let ((_let_7 (tptp.aElementOf0 tptp.xm tptp.szNzAzT0))) (let ((_let_8 (and _let_7 _let_6))) (let ((_let_9 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (= (= W1 (tptp.slbdtrb0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) W0))))))))))) (let ((_let_10 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (or (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W1) W0)))))) (let ((_let_11 (forall ((W0 $$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)))))) (let ((_let_12 (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)))))) (let ((_let_13 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_14 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 (tptp.szszuzczcdt0 W0)))))) (let ((_let_15 (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))))))) (let ((_let_16 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) tptp.sz00)))))) (let ((_let_17 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 tptp.sz00 W0))))) (let ((_let_18 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (= W0 (tptp.szszuzczcdt0 W0))))))) (let ((_let_19 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (or (= W0 tptp.sz00) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (= W0 (tptp.szszuzczcdt0 W1))))))))) (let ((_let_20 (forall ((W0 $$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_21 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))))) (let ((_let_22 (tptp.sdtlseqdt0 tptp.sz00 tptp.xn))) (let ((_let_23 (= tptp.sz00 tptp.xm))) (let ((_let_24 (not _let_6))) (let ((_let_25 (or _let_24 _let_22))) (let ((_let_26 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (tptp.sdtlseqdt0 tptp.sz00 W0))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (ASSUME :args (_let_8)))) (let ((_let_29 (AND_ELIM _let_28 :args (1)))) (let ((_let_30 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.slbdtrb0 tptp.xm))) (tptp.aElementOf0 W2 (tptp.slbdtrb0 tptp.xn)))))) (let ((_let_31 (tptp.aSet0 _let_2))) (let ((_let_32 (and _let_31 _let_30))) (let ((_let_33 (= _let_3 _let_32))) (let ((_let_34 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_1))) (let ((_let_35 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_2))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_34))) (let ((_let_38 (tptp.szszuzczcdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_39 (tptp.sdtlseqdt0 _let_38 tptp.xm))) (let ((_let_40 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 tptp.szNzAzT0))) (let ((_let_41 (and _let_40 _let_39))) (let ((_let_42 (= _let_35 _let_41))) (let ((_let_43 (tptp.sdtlseqdt0 _let_38 tptp.sz00))) (let ((_let_44 (not _let_43))) (let ((_let_45 (not _let_40))) (let ((_let_46 (or _let_45 _let_44))) (let ((_let_47 (tptp.szszuzczcdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_48 (= tptp.xm _let_47))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.szNzAzT0))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49))) (let ((_let_53 (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (= (tptp.szszuzczcdt0 W1) tptp.xm)))))) (let ((_let_54 (not _let_53))) (let ((_let_55 (not _let_7))) (let ((_let_56 (or _let_55 _let_23 _let_54))) (let ((_let_57 (not _let_4))) (let ((_let_58 (ASSUME :args (_let_5)))) (let ((_let_59 (NOT_EQUIV_ELIM2 _let_58))) (let ((_let_60 (tptp.aSet0 _let_1))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_33))) (let ((_let_63 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1313 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.aSubsetOf0 BOUND_VARIABLE_1313 W0) (and (tptp.aSet0 BOUND_VARIABLE_1313) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 BOUND_VARIABLE_1313)) (tptp.aElementOf0 W2 W0))))))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_1 _let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aSubsetOf0 BOUND_VARIABLE_1313 W0)))) :args (_let_63))))) (let ((_let_66 (forall ((W2 $$unsorted)) (= (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) tptp.xn)) (tptp.aElementOf0 W2 (tptp.slbdtrb0 tptp.xn)))))) (let ((_let_67 (and _let_60 _let_66))) (let ((_let_68 (or _let_24 _let_67))) (let ((_let_69 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1918 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (= (= (tptp.slbdtrb0 W0) BOUND_VARIABLE_1918) (and (tptp.aSet0 BOUND_VARIABLE_1918) (forall ((W2 $$unsorted)) (= (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) W0)) (tptp.aElementOf0 W2 BOUND_VARIABLE_1918))))))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (_let_69))) (let ((_let_72 (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_70 :args (tptp.xn _let_1 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_71))))) (let ((_let_73 (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_24 _let_67 (not _let_68)))))) (let ((_let_74 (MACRO_RESOLUTION_TRUST _let_73 _let_29 (MACRO_RESOLUTION_TRUST _let_72 _let_70 :args (_let_68 false _let_69)) :args (_let_67 false _let_6 false _let_68)))) (let ((_let_75 (not _let_67))) (let ((_let_76 (REORDERING (CNF_AND_POS :args (_let_67 0)) :args ((or _let_60 _let_75))))) (let ((_let_77 (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_61 _let_33 (not _let_62)))))) (let ((_let_78 (MACRO_RESOLUTION_TRUST _let_77 (MACRO_RESOLUTION_TRUST _let_76 _let_74 :args (_let_60 false _let_67)) (MACRO_RESOLUTION_TRUST _let_65 _let_64 :args (_let_62 false _let_63)) :args (_let_33 false _let_60 false _let_62)))) (let ((_let_79 (not _let_33))) (let ((_let_80 (not _let_32))) (let ((_let_81 (_let_33))) (let ((_let_82 (REORDERING (CNF_EQUIV_POS2 :args _let_81) :args ((or _let_3 _let_80 _let_79))))) (let ((_let_83 (forall ((W2 $$unsorted)) (= (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) tptp.xm)) (tptp.aElementOf0 W2 (tptp.slbdtrb0 tptp.xm)))))) (let ((_let_84 (and _let_31 _let_83))) (let ((_let_85 (or _let_55 _let_84))) (let ((_let_86 (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_70 :args (tptp.xm _let_2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_71))))) (let ((_let_87 (AND_ELIM _let_28 :args (0)))) (let ((_let_88 (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_55 _let_84 (not _let_85)))))) (let ((_let_89 (MACRO_RESOLUTION_TRUST _let_88 _let_87 (MACRO_RESOLUTION_TRUST _let_86 _let_70 :args (_let_85 false _let_69)) :args (_let_84 false _let_7 false _let_85)))) (let ((_let_90 (not _let_84))) (let ((_let_91 (REORDERING (CNF_AND_POS :args (_let_84 0)) :args ((or _let_31 _let_90))))) (let ((_let_92 (CNF_AND_NEG :args (_let_32)))) (let ((_let_93 (or))) (let ((_let_94 (not _let_30))) (let ((_let_95 (_let_94))) (let ((_let_96 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_95)) :args _let_95)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_94) _let_30))) (REFL :args ((not _let_37))) :args _let_93)))) (let ((_let_97 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 0)) (CONG (REFL :args (_let_37)) (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_93)) :args ((or _let_35 _let_37))))) (let ((_let_98 (REORDERING (CNF_AND_POS :args (_let_84 1)) :args ((or _let_83 _let_90))))) (let ((_let_99 (MACRO_RESOLUTION_TRUST _let_98 _let_89 :args (_let_83 false _let_84)))) (let ((_let_100 (_let_83))) (let ((_let_101 (ASSUME :args _let_100))) (let ((_let_102 (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_101 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W2 _let_2)))) :args _let_100))))) (let ((_let_103 (REORDERING (CNF_EQUIV_POS1 :args (_let_42)) :args ((or _let_36 _let_41 (not _let_42)))))) (let ((_let_104 (not _let_41))) (let ((_let_105 (REORDERING (CNF_AND_POS :args (_let_41 0)) :args ((or _let_40 _let_104))))) (let ((_let_106 (REORDERING (CNF_AND_POS :args (_let_41 1)) :args ((or _let_39 _let_104))))) (let ((_let_107 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) tptp.sz00)))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (tptp.sdtlseqdt0 _let_38 tptp.xn))) (let ((_let_110 (and _let_40 _let_109))) (let ((_let_111 (= _let_34 _let_110))) (let ((_let_112 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W1) W0))))) (let ((_let_113 (tptp.sdtlseqdt0 tptp.xn SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_114 (or _let_24 _let_45 _let_113 _let_109))) (let ((_let_115 (tptp.sdtlseqdt0 _let_38 _let_47))) (let ((_let_116 (tptp.sdtlseqdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_117 (= _let_116 _let_115))) (let ((_let_118 (or _let_45 _let_51 _let_117))) (let ((_let_119 (tptp.szszuzczcdt0 tptp.xn))) (let ((_let_120 (tptp.sdtlseqdt0 _let_119 _let_47))) (let ((_let_121 (tptp.sdtlseqdt0 tptp.xn SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_122 (= _let_121 _let_120))) (let ((_let_123 (or _let_24 _let_51 _let_122))) (let ((_let_124 (not _let_116))) (let ((_let_125 (not _let_113))) (let ((_let_126 (or _let_24 _let_45 _let_51 _let_125 _let_124 _let_121))) (let ((_let_127 (tptp.sdtlseqdt0 _let_119 tptp.xm))) (let ((_let_128 (tptp.sdtlseqdt0 tptp.xn _let_119))) (let ((_let_129 (tptp.aElementOf0 _let_119 tptp.szNzAzT0))) (let ((_let_130 (tptp.sdtlseqdt0 tptp.xn tptp.xm))) (let ((_let_131 (not _let_127))) (let ((_let_132 (not _let_128))) (let ((_let_133 (not _let_129))) (let ((_let_134 (or _let_24 _let_133 _let_55 _let_132 _let_131 _let_130))) (let ((_let_135 (= tptp.xm tptp.xn))) (let ((_let_136 (not _let_130))) (let ((_let_137 (or _let_55 _let_24 _let_57 _let_136 _let_135))) (let ((_let_138 (tptp.sdtlseqdt0 _let_119 tptp.xn))) (let ((_let_139 (REORDERING (CNF_AND_POS :args (_let_67 1)) :args ((or _let_66 _let_75))))) (let ((_let_140 (_let_66))) (let ((_let_141 (ASSUME :args _let_140))) (let ((_let_142 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_143 (REFL :args (_let_52)))) (let ((_let_144 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 0)) (CONG _let_143 (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_93)) :args ((or _let_50 _let_52))))) (let ((_let_145 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 1)) (CONG _let_143 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_93)) :args ((or _let_48 _let_52))))) (let ((_let_146 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1))))))) (let ((_let_147 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_148 (_let_146))) (let ((_let_149 ((tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1))))) (let ((_let_150 (and _let_48 _let_39))) (let ((_let_151 (ASSUME :args (_let_39)))) (let ((_let_152 (TRUE_INTRO _let_151))) (let ((_let_153 (APPLY_UF tptp.sdtlseqdt0))) (let ((_let_154 (ASSUME :args (_let_48)))) (let ((_let_155 (SYMM _let_154))) (let ((_let_156 (SYMM _let_155))) (let ((_let_157 (REFL :args (_let_38)))) (let ((_let_158 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (tptp.aElementOf0 W2 tptp.szNzAzT0)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2))))) (let ((_let_159 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_160 (_let_158))) (let ((_let_161 (not _let_120))) (let ((_let_162 (and _let_48 _let_120))) (let ((_let_163 (ASSUME :args (_let_120)))) (let ((_let_164 (TRUE_INTRO _let_163))) (let ((_let_165 (REFL :args (_let_119)))) (let ((_let_166 (CONG _let_165 _let_156 :args _let_153))) (let ((_let_167 (or _let_24 _let_128))) (let ((_let_168 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) 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QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_219)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_32 1)) :args ((or _let_30 _let_80))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_81) :args ((or (not _let_3) _let_32 _let_79))) (MACRO_RESOLUTION_TRUST (NOT_EQUIV_ELIM1 _let_58) _let_200 :args (_let_3 true _let_4)) _let_78 :args (_let_32 false _let_3 false _let_33)) :args (_let_30 false _let_32)) :args (_let_207 false _let_30)) (REORDERING (CNF_EQUIV_POS2 :args (_let_204)) :args ((or _let_202 (not _let_203) (not _let_204)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_141 :args _let_218) :args _let_140)) (MACRO_RESOLUTION_TRUST _let_139 _let_74 :args (_let_66 false _let_67)) :args (_let_204 false _let_66)) (REORDERING (CNF_AND_POS :args (_let_202 1)) :args ((or _let_201 (not _let_202)))) (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_213)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_215 _let_154) (SCOPE (FALSE_ELIM (TRANS (CONG _let_155 _let_217 :args _let_153) _let_216)) :args _let_214)) :args _let_214)) :args (true _let_213)) (CONG _let_212 _let_187 (REFL :args ((not _let_201))) :args _let_93)) _let_200 _let_145 _let_144 :args (_let_52 false _let_211 true _let_208 true _let_209 false _let_210 true _let_205 false _let_207 true _let_203 false _let_204 true _let_202 true _let_201 true _let_4 false _let_48 false _let_50)) :args (_let_53 false _let_52)) _let_194 :args (_let_23 false _let_7 false _let_53 false _let_56)) _let_200 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_22 (not _let_25)))) _let_29 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 tptp.szNzAzT0) false))))) :args (_let_26))) _let_27 :args (_let_25 false _let_26)) :args (_let_22 false _let_6 false _let_25)) :args (false false _let_23 true _let_4 false _let_22)) :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 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (= W0 tptp.slcrc0)))) _let_21 (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtmndt0 W1 W0)))))) (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0)) (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0) _let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (= (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1)) (= W0 W1)))) _let_19 _let_18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.sdtlseqdt0 W0 W1) true))) _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 (forall ((W0 $$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)))))) _let_9 (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))))) _let_8 _let_5 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 32.27/32.53 )
% 32.27/32.53 % SZS output end Proof for NUM542+1
% 32.27/32.53 % cvc5---1.0.5 exiting
% 32.27/32.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------