TSTP Solution File: NUM493+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM493+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.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 10:44:27 EDT 2023
% Result : Theorem 34.76s 35.15s
% Output : Proof 34.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM493+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.19/0.35 % Computer : n020.cluster.edu
% 0.19/0.35 % Model : x86_64 x86_64
% 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35 % Memory : 8042.1875MB
% 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Fri Aug 25 17:49:15 EDT 2023
% 0.19/0.35 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 34.76/35.15 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.X1cwljuxPi/cvc5---1.0.5_32066.p...
% 34.76/35.15 ------- get file name : TPTP file name is NUM493+1
% 34.76/35.15 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_32066.smt2...
% 34.76/35.15 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 34.76/35.15 --- Run --no-e-matching --full-saturate-quant at 5...
% 34.76/35.15 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 34.76/35.15 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 34.76/35.15 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 34.76/35.15 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 34.76/35.15 % SZS status Theorem for NUM493+1
% 34.76/35.15 % SZS output start Proof for NUM493+1
% 34.76/35.15 (
% 34.76/35.15 (let ((_let_1 (tptp.doDivides0 tptp.xp tptp.xm))) (let ((_let_2 (not (or (tptp.doDivides0 tptp.xp tptp.xr) _let_1)))) (let ((_let_3 (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xr tptp.xm)))) (let ((_let_4 (tptp.sdtlseqdt0 tptp.xr tptp.xn))) (let ((_let_5 (and (not (= tptp.xr tptp.xn)) _let_4))) (let ((_let_6 (tptp.sdtmndt0 tptp.xn tptp.xp))) (let ((_let_7 (= tptp.xr _let_6))) (let ((_let_8 (tptp.sdtlseqdt0 tptp.xp tptp.xn))) (let ((_let_9 (tptp.isPrime0 tptp.xp))) (let ((_let_10 (and _let_9 (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xm))))) (let ((_let_11 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.isPrime0 W2) (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (=> (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))))))) (let ((_let_12 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_13 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_14 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_15 (and _let_14 _let_13 _let_12))) (let ((_let_16 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.isPrime0 W0) (and (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10)) (forall ((W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0)) (or (= W1 tptp.sz10) (= W1 W0)))))))))) (let ((_let_17 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))))) (let ((_let_18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (let ((_let_2 (tptp.sdtpldt0 W0 W2))) (let ((_let_3 (tptp.sdtpldt0 W2 W1))) (let ((_let_4 (tptp.sdtpldt0 W2 W0))) (=> (tptp.aNaturalNumber0 W2) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))))))) (let ((_let_19 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))))) (let ((_let_21 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))))) (let ((_let_22 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_23 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))))) (let ((_let_24 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_25 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_26 (tptp.aNaturalNumber0 tptp.sz00))) (let ((_let_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_28 (tptp.sdtpldt0 tptp.xm tptp.xp))) (let ((_let_29 (tptp.aNaturalNumber0 _let_28))) (let ((_let_30 (not _let_12))) (let ((_let_31 (not _let_13))) (let ((_let_32 (or _let_31 _let_30 _let_29))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (not _let_32))) (let ((_let_35 (tptp.sdtpldt0 tptp.xn _let_28))) (let ((_let_36 (tptp.sdtpldt0 _let_6 _let_28))) (let ((_let_37 (tptp.sdtlseqdt0 _let_36 _let_35))) (let ((_let_38 (tptp.sdtpldt0 _let_28 tptp.xn))) (let ((_let_39 (tptp.sdtpldt0 _let_28 _let_6))) (let ((_let_40 (and (not (= _let_38 _let_39)) (tptp.sdtlseqdt0 _let_39 _let_38) (not (= _let_35 _let_36)) _let_37))) (let ((_let_41 (not _let_29))) (let ((_let_42 (tptp.sdtlseqdt0 _let_6 tptp.xn))) (let ((_let_43 (not _let_42))) (let ((_let_44 (= tptp.xn _let_6))) (let ((_let_45 (not _let_14))) (let ((_let_46 (tptp.aNaturalNumber0 _let_6))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_47 _let_45 _let_44 _let_43 _let_41 _let_40))) (let ((_let_49 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1486 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1486))) (let ((_let_2 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1486))) (let ((_let_3 (tptp.sdtpldt0 BOUND_VARIABLE_1486 W1))) (let ((_let_4 (tptp.sdtpldt0 BOUND_VARIABLE_1486 W0))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1486)) (and (not (= _let_3 _let_4)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_1 _let_2)) (tptp.sdtlseqdt0 _let_2 _let_1)))))))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (not _let_40))) (let ((_let_52 (tptp.sdtpldt0 _let_6 tptp.xm))) (let ((_let_53 (tptp.sdtpldt0 _let_52 tptp.xp))) (let ((_let_54 (= _let_53 _let_36))) (let ((_let_55 (tptp.sdtpldt0 tptp.xn tptp.xm))) (let ((_let_56 (tptp.sdtpldt0 _let_55 tptp.xp))) (let ((_let_57 (= _let_56 _let_35))) (let ((_let_58 (tptp.sdtlseqdt0 _let_53 _let_56))) (let ((_let_59 (not _let_37))) (let ((_let_60 (or _let_47 _let_31 _let_30 _let_54))) (let ((_let_61 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (_let_61))) (let ((_let_64 ((tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2)))) (let ((_let_65 (tptp.sdtpldt0 tptp.xp _let_6))) (let ((_let_66 (= tptp.xn _let_65))) (let ((_let_67 (and _let_46 _let_66))) (let ((_let_68 (not _let_8))) (let ((_let_69 (or _let_30 _let_45 _let_68 _let_67))) (let ((_let_70 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1404 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1404) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1404))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1404)))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (ASSUME :args (_let_15)))) (let ((_let_73 (AND_ELIM _let_72 :args (2)))) (let ((_let_74 (0))) (let ((_let_75 (AND_ELIM _let_72 :args _let_74))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_45 _let_30 _let_68 _let_67 (not _let_69)))) _let_75 _let_73 (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_71 :args (tptp.xp tptp.xn _let_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_70)))) _let_71 :args (_let_69 false _let_70)) :args (_let_67 false _let_14 false _let_12 false _let_8 false _let_69)))) (let ((_let_77 (not _let_67))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 0)) :args ((or _let_46 _let_77))) _let_76 :args (_let_46 false _let_67)))) (let ((_let_79 (1))) (let ((_let_80 (AND_ELIM _let_72 :args _let_79))) (let ((_let_81 (or _let_45 _let_31 _let_30 _let_57))) (let ((_let_82 (tptp.iLess0 _let_53 _let_56))) (let ((_let_83 (not _let_58))) (let ((_let_84 (= _let_56 _let_53))) (let ((_let_85 (tptp.aNaturalNumber0 _let_56))) (let ((_let_86 (not _let_85))) (let ((_let_87 (tptp.aNaturalNumber0 _let_53))) (let ((_let_88 (not _let_87))) (let ((_let_89 (or _let_88 _let_86 _let_84 _let_83 _let_82))) (let ((_let_90 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (tptp.sdtpldt0 tptp.sz00 tptp.xm))) (let ((_let_93 (= tptp.xm _let_92))) (let ((_let_94 (= tptp.xp (tptp.sdtpldt0 tptp.sz00 tptp.xp)))) (let ((_let_95 (tptp.sdtpldt0 _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_96 (= tptp.xn _let_95))) (let ((_let_97 (tptp.sdtpldt0 tptp.xm tptp.xn))) (let ((_let_98 (= _let_55 _let_97))) (let ((_let_99 (= tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_100 (tptp.sdtpldt0 tptp.xm _let_6))) (let ((_let_101 (= _let_52 _let_100))) (let ((_let_102 (= (tptp.sdtpldt0 _let_92 tptp.xn) (tptp.sdtpldt0 tptp.sz00 _let_97)))) (let ((_let_103 (= (tptp.sdtpldt0 _let_100 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) (tptp.sdtpldt0 tptp.xm _let_95)))) (let ((_let_104 (= _let_56 (tptp.sdtpldt0 tptp.xp _let_55)))) (let ((_let_105 (= (tptp.sdtpldt0 tptp.sz00 _let_56) (tptp.sdtpldt0 tptp.xp _let_56)))) (let ((_let_106 (and (= tptp.xm (tptp.sdtpldt0 tptp.xm tptp.sz00)) _let_93))) (let ((_let_107 (or _let_31 _let_106))) (let ((_let_108 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= W0 (tptp.sdtpldt0 W0 tptp.sz00)) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_109 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (_let_108))) (let ((_let_111 ((not (= (tptp.aNaturalNumber0 W0) false))))) (let ((_let_112 (and (= tptp.xp (tptp.sdtpldt0 tptp.xp tptp.sz00)) _let_94))) (let ((_let_113 (or _let_30 _let_112))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_112 1)) :args ((or _let_94 (not _let_112)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_30 _let_112 (not _let_113)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_109 :args (tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_111)) :args _let_110)) _let_109 :args (_let_113 false _let_108)) :args (_let_112 false _let_12 false _let_113)) :args (_let_94 false _let_112)))) (let ((_let_115 (not _let_96))) (let ((_let_116 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_117 (not _let_116))) (let ((_let_118 (or _let_117 _let_115))) (let ((_let_119 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= tptp.xn (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) W2))))))) (let ((_let_120 (not _let_118))) (let ((_let_121 (not _let_119))) (let ((_let_122 (= _let_42 _let_121))) (let ((_let_123 (or _let_47 _let_45 _let_122))) (let ((_let_124 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtpldt0 W0 W2))))))))))) (let ((_let_125 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_126 (ASSUME :args (_let_7)))) (let ((_let_127 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_126 :args ((and (not (= tptp.xn tptp.xr)) _let_4) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_128 (AND_ELIM _let_127 :args _let_79))) (let ((_let_129 (or))) (let ((_let_130 (_let_121))) (let ((_let_131 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_130)) :args _let_130)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_121) _let_119))) (REFL :args (_let_120)) :args _let_129)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_122)) :args ((or _let_43 _let_121 (not _let_122)))) _let_128 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_123)) :args ((or _let_45 _let_47 _let_122 (not _let_123)))) _let_75 _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_125 :args (_let_6 tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtlseqdt0 W0 W1)))) :args (_let_124))) _let_125 :args (_let_123 false _let_124)) :args (_let_122 false _let_14 false _let_46 false _let_123)) :args (_let_121 false _let_42 false _let_122)) :args (_let_120 true _let_119)))) (let ((_let_132 (REFL :args (_let_118)))) (let ((_let_133 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_118 1)) (CONG _let_132 (MACRO_SR_PRED_INTRO :args ((= (not _let_115) _let_96))) :args _let_129)) :args ((or _let_96 _let_118))) _let_131 :args (_let_96 true _let_118)))) (let ((_let_134 (or _let_45 _let_31 _let_98))) (let ((_let_135 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_136 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_137 (_let_135))) (let ((_let_138 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_134)) :args ((or _let_45 _let_31 _let_98 (not _let_134)))) _let_75 _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_136 :args (tptp.xn tptp.xm QUANTIFIERS_INST_CBQI_PROP)) :args _let_137)) _let_136 :args (_let_134 false _let_135)) :args (_let_98 false _let_14 false _let_13 false _let_134)))) (let ((_let_139 (tptp.sdtpldt0 _let_6 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_let_208 (not _let_209)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_210)) :args ((or _let_215 _let_209 (not _let_210)))) _let_214 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_211)) :args ((or _let_30 _let_210 (not _let_211)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_213 :args (tptp.xp QUANTIFIERS_INST_CBQI_PROP)) :args (_let_212)))) _let_213 :args (_let_211 false _let_212)) :args (_let_210 false _let_12 false _let_211)) :args (_let_209 false _let_9 false _let_210)) :args (_let_208 false _let_209)) _let_207 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_145 :args (_let_56 tptp.sz00 tptp.xp QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_146)) _let_145 :args (_let_174 false _let_144)) :args (_let_172 false _let_26 false _let_12 true _let_173 false _let_85 false _let_174)) :args (_let_171 false _let_172)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_167)) :args ((or _let_30 _let_166 _let_104 (not _let_167)))) _let_73 _let_170 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_136 :args (_let_55 tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_158)) :args _let_137)) _let_136 :args (_let_167 false _let_135)) :args (_let_104 false _let_12 false _let_165 false _let_167)) _let_164 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_161)) :args ((or _let_160 _let_45 _let_31 _let_102 (not _let_161)))) _let_162 _let_75 _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.sz00 tptp.xm tptp.xn QUANTIFIERS_INST_E_MATCHING _let_64)) :args _let_63)) _let_62 :args (_let_161 false _let_61)) :args (_let_102 false _let_26 false _let_14 false _let_13 false _let_161)) _let_159 _let_156 _let_138 _let_133 _let_114 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_106 1)) :args ((or _let_93 (not _let_106)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_107)) :args ((or _let_31 _let_106 (not _let_107)))) _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_109 :args (tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_111)) :args _let_110)) _let_109 :args (_let_107 false _let_108)) :args (_let_106 false _let_13 false _let_107)) :args (_let_93 false _let_106)) :args ((not _let_84) true _let_105 false _let_104 false _let_103 false _let_102 false _let_101 false _let_99 false _let_98 false _let_96 false _let_94 false _let_93)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_91 :args (_let_53 _let_56 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.iLess0 W0 W1) true))))) :args (_let_90)))) _let_91 :args (_let_89 false _let_90)) :args (_let_83 true _let_82 false _let_87 false _let_85 true _let_84 false _let_89)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_45 _let_31 _let_30 _let_57 (not _let_81)))) _let_75 _let_80 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.xn tptp.xm tptp.xp QUANTIFIERS_INST_E_MATCHING _let_64)) :args _let_63)) _let_62 :args (_let_81 false _let_61)) :args (_let_57 false _let_14 false _let_13 false _let_12 false _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_31 _let_30 _let_47 _let_54 (not _let_60)))) _let_80 _let_73 _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_6 tptp.xm tptp.xp QUANTIFIERS_INST_E_MATCHING _let_64)) :args _let_63)) _let_62 :args (_let_60 false _let_61)) :args (_let_54 false _let_13 false _let_12 false _let_46 false _let_60)) :args (_let_59 true _let_58 false _let_57 false _let_54)) :args (_let_51 true _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_6 tptp.xn _let_28 QUANTIFIERS_INST_E_MATCHING ((tptp.sdtlseqdt0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1486) (tptp.sdtpldt0 W1 BOUND_VARIABLE_1486))))) :args (_let_49)))) _let_50 :args (_let_48 false _let_49)) :args (_let_41 true _let_44 false _let_14 false _let_42 false _let_46 true _let_40 false _let_48)) :args (_let_34 false _let_13 false _let_12 true _let_29)) _let_33 :args (false true _let_32 false _let_27)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) _let_26 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))) _let_25 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) _let_24 _let_23 _let_22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (and (= (tptp.sdtasdt0 W0 _let_1) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 _let_1 W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))))))) _let_21 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtpldt0 W0 W1) tptp.sz00) (and (= W0 tptp.sz00) (= W1 tptp.sz00))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))) _let_20 _let_19 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))) _let_18 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W2 W0))) (let ((_let_2 (tptp.sdtasdt0 W1 W0))) (let ((_let_3 (tptp.sdtasdt0 W0 W2))) (let ((_let_4 (tptp.sdtasdt0 W0 W1))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 W2)) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (not (= W0 tptp.sz00)) (tptp.sdtlseqdt0 W1 (tptp.sdtasdt0 W1 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) _let_17 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W1 W2)) (tptp.doDivides0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 W2)) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))) (tptp.doDivides0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.doDivides0 W0 W1) (not (= W1 tptp.sz00))) (tptp.sdtlseqdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) _let_16 (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_15 _let_11 _let_10 _let_8 _let_7 _let_5 _let_3 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 34.76/35.16 )
% 34.76/35.16 % SZS output end Proof for NUM493+1
% 34.76/35.16 % cvc5---1.0.5 exiting
% 34.76/35.16 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------