TSTP Solution File: NUM527+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM527+3 : 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 10:44:47 EDT 2023
% Result : Theorem 28.44s 28.74s
% Output : Proof 28.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM527+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 09:01:00 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.47 %----Proving TF0_NAR, FOF, or CNF
% 28.44/28.74 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.I1dv8Jh6oY/cvc5---1.0.5_26536.p...
% 28.44/28.74 ------- get file name : TPTP file name is NUM527+3
% 28.44/28.74 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_26536.smt2...
% 28.44/28.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 28.44/28.74 --- Run --no-e-matching --full-saturate-quant at 5...
% 28.44/28.74 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 28.44/28.74 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 28.44/28.74 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 28.44/28.74 % SZS status Theorem for NUM527+3
% 28.44/28.74 % SZS output start Proof for NUM527+3
% 28.44/28.74 (
% 28.44/28.74 (let ((_let_1 (tptp.sdtasdt0 tptp.xm tptp.xm))) (let ((_let_2 (tptp.sdtasdt0 tptp.xn tptp.xn))) (let ((_let_3 (tptp.sdtlseqdt0 _let_2 _let_1))) (let ((_let_4 (tptp.sdtlseqdt0 tptp.xn tptp.xm))) (let ((_let_5 (not (=> (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xn W0) tptp.xm))) _let_4) (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xn tptp.xn) W0) (tptp.sdtasdt0 tptp.xm tptp.xm)))) _let_3))))) (let ((_let_6 (tptp.sdtasdt0 tptp.xq tptp.xq))) (let ((_let_7 (tptp.sdtasdt0 tptp.xp _let_6))) (let ((_let_8 (= _let_1 _let_7))) (let ((_let_9 (tptp.sdtasdt0 tptp.xp tptp.xq))) (let ((_let_10 (tptp.aNaturalNumber0 tptp.xq))) (let ((_let_11 (and _let_10 (= tptp.xn _let_9) (= tptp.xq (tptp.sdtsldt0 tptp.xn tptp.xp))))) (let ((_let_12 (tptp.doDivides0 tptp.xp tptp.xn))) (let ((_let_13 (tptp.doDivides0 tptp.xp _let_2))) (let ((_let_14 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W0)))) _let_13 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xp W0)))) _let_12))) (let ((_let_15 (and (not (= tptp.xp tptp.sz10)) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= tptp.xp (tptp.sdtasdt0 W0 W1)))) (tptp.doDivides0 W0 tptp.xp))) (or (= W0 tptp.sz10) (= W0 tptp.xp)))) (tptp.isPrime0 tptp.xp)))) (let ((_let_16 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_17 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_18 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_19 (and _let_18 _let_17 _let_16 (not (= tptp.xn tptp.sz00)) (not (= tptp.xm tptp.sz00)) (not (= tptp.xp tptp.sz00))))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (not (= W0 tptp.sz00)) (tptp.sdtlseqdt0 W1 (tptp.sdtasdt0 W1 W0))))))) (let ((_let_21 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W2 W0))) (let ((_let_2 (tptp.sdtasdt0 W1 W0))) (let ((_let_3 (tptp.sdtasdt0 W0 W2))) (let ((_let_4 (tptp.sdtasdt0 W0 W1))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 W2)) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))))) (let ((_let_22 (forall ((W0 $$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)))))) (let ((_let_23 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))))) (let ((_let_24 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))))) (let ((_let_25 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_26 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_27 (forall ((W0 $$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))))))) (let ((_let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_29 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_30 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_31 (tptp.aNaturalNumber0 tptp.sz10))) (let ((_let_32 (and _let_31 (not (= tptp.sz10 tptp.sz00))))) (let ((_let_33 (tptp.aNaturalNumber0 _let_1))) (let ((_let_34 (tptp.sdtasdt0 _let_9 tptp.xm))) (let ((_let_35 (tptp.sdtlseqdt0 _let_1 _let_34))) (let ((_let_36 (tptp.aNaturalNumber0 _let_34))) (let ((_let_37 (= _let_1 _let_34))) (let ((_let_38 (not _let_35))) (let ((_let_39 (tptp.sdtlseqdt0 _let_34 _let_1))) (let ((_let_40 (not _let_39))) (let ((_let_41 (not _let_33))) (let ((_let_42 (not _let_36))) (let ((_let_43 (or _let_42 _let_41 _let_40 _let_38 _let_37))) (let ((_let_44 (not _let_17))) (let ((_let_45 (or _let_44 _let_44 _let_33))) (let ((_let_46 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (_let_46))) (let ((_let_49 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_50 (1))) (let ((_let_51 (= tptp.sz00 tptp.xp))) (let ((_let_52 (= tptp.sz00 tptp.xm))) (let ((_let_53 (ASSUME :args (_let_11)))) (let ((_let_54 (AND_ELIM _let_53 :args _let_50))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_19)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_54 :args ((and _let_18 _let_17 _let_16 (not (= tptp.sz00 tptp.xn)) (not _let_52) (not _let_51)) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_56 (AND_ELIM _let_55 :args _let_50))) (let ((_let_57 (tptp.sdtasdt0 _let_9 tptp.xq))) (let ((_let_58 (tptp.sdtlseqdt0 _let_57 _let_34))) (let ((_let_59 (= _let_7 _let_57))) (let ((_let_60 (tptp.sdtasdt0 tptp.xm _let_9))) (let ((_let_61 (tptp.sdtasdt0 tptp.xq _let_9))) (let ((_let_62 (not (= _let_60 _let_61)))) (let ((_let_63 (= _let_34 _let_57))) (let ((_let_64 (not _let_63))) (let ((_let_65 (and _let_64 _let_58 _let_62 (tptp.sdtlseqdt0 _let_61 _let_60)))) (let ((_let_66 (tptp.sdtlseqdt0 tptp.xq tptp.xm))) (let ((_let_67 (not _let_66))) (let ((_let_68 (= tptp.xm tptp.xq))) (let ((_let_69 (= tptp.sz00 _let_9))) (let ((_let_70 (not _let_10))) (let ((_let_71 (tptp.aNaturalNumber0 _let_9))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_70 _let_44 _let_69 _let_68 _let_67 _let_65))) (let ((_let_74 (forall ((W0 $$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))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (= tptp.sz00 W0) (= W1 W2) (not (tptp.sdtlseqdt0 W1 W2)) (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_75 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (_let_74))) (let ((_let_77 (= (tptp.sdtasdt0 tptp.xq tptp.xm) (tptp.sdtasdt0 tptp.xm tptp.xq)))) (let ((_let_78 (= _let_61 _let_57))) (let ((_let_79 (= _let_6 _let_61))) (let ((_let_80 (= tptp.xq (tptp.sdtpldt0 tptp.sz00 tptp.xq)))) (let ((_let_81 (= tptp.xm (tptp.sdtpldt0 tptp.sz00 tptp.xm)))) (let ((_let_82 (not _let_68))) (let ((_let_83 (or _let_70 _let_44 _let_77))) (let ((_let_84 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (_let_84))) (let ((_let_87 (0))) (let ((_let_88 (EQ_RESOLVE _let_53 (MACRO_SR_EQ_INTRO _let_54 :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (AND_ELIM _let_88 :args _let_87))) (let ((_let_90 (or _let_70 _let_72 _let_78))) (let ((_let_91 (AND_ELIM _let_55 :args _let_87))) (let ((_let_92 (not _let_79))) (let ((_let_93 (and _let_92 (not (= _let_6 _let_57))))) (let ((_let_94 (= tptp.xq _let_9))) (let ((_let_95 (= tptp.sz00 tptp.xq))) (let ((_let_96 (or _let_70 _let_95 _let_70 _let_72 _let_93 _let_94))) (let ((_let_97 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1414 $$unsorted) (BOUND_VARIABLE_1412 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= tptp.sz00 W0) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1412)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1414)) (and (not (= (tptp.sdtasdt0 W0 BOUND_VARIABLE_1412) (tptp.sdtasdt0 W0 BOUND_VARIABLE_1414))) (not (= (tptp.sdtasdt0 BOUND_VARIABLE_1412 W0) (tptp.sdtasdt0 BOUND_VARIABLE_1414 W0)))) (= BOUND_VARIABLE_1412 BOUND_VARIABLE_1414))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (_let_97))) (let ((_let_100 (= tptp.xq (tptp.sdtsldt0 _let_9 tptp.xp)))) (let ((_let_101 (tptp.sdtasdt0 tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_102 (= _let_9 _let_101))) (let ((_let_103 (tptp.sdtasdt0 tptp.xq tptp.xp))) (let ((_let_104 (= _let_9 _let_103))) (let ((_let_105 (tptp.sdtasdt0 tptp.xq tptp.sz10))) (let ((_let_106 (= tptp.xq _let_105))) (let ((_let_107 (tptp.sdtasdt0 tptp.sz10 tptp.xq))) (let ((_let_108 (= tptp.xq _let_107))) (let ((_let_109 (= _let_103 _let_105))) (let ((_let_110 (not _let_94))) (let ((_let_111 (not _let_102))) (let ((_let_112 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_113 (not _let_112))) (let ((_let_114 (or _let_113 _let_111))) (let ((_let_115 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 tptp.xp W0) (tptp.sdtasdt0 tptp.xp tptp.xq))))))) (let ((_let_116 (not _let_114))) (let ((_let_117 (2))) (let ((_let_118 (or))) (let ((_let_119 (not _let_115))) (let ((_let_120 (_let_119))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_120)) :args _let_120) (REWRITE :args ((=> _let_119 (not (or _let_113 (not (= _let_101 _let_9))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_119) _let_115))) (REFL :args (_let_116)) :args _let_118)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_54 :args ((and (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W0)))))) _let_13 (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xn (tptp.sdtasdt0 tptp.xp W0)))))) _let_12) SB_DEFAULT SBA_FIXPOINT)))) :args _let_117) :args (_let_116 true _let_115)))) (let ((_let_122 (REFL :args (_let_114)))) (let ((_let_123 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_114 1)) (CONG _let_122 (MACRO_SR_PRED_INTRO :args ((= (not _let_111) _let_102))) :args _let_118)) :args ((or _let_102 _let_114))) _let_121 :args (_let_102 true _let_114)))) (let ((_let_124 (not _let_16))) (let ((_let_125 (or _let_124 _let_70 _let_104))) (let ((_let_126 (AND_ELIM _let_55 :args _let_117))) (let ((_let_127 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_125)) :args ((or _let_124 _let_70 _let_104 (not _let_125)))) _let_126 _let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (tptp.xp tptp.xq QUANTIFIERS_INST_CBQI_PROP)) :args _let_86)) _let_85 :args (_let_125 false _let_84)) :args (_let_104 false _let_16 false _let_10 false _let_125)))) (let ((_let_128 (and _let_106 _let_108))) (let ((_let_129 (or _let_70 _let_128))) (let ((_let_130 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= W0 (tptp.sdtasdt0 W0 tptp.sz10)) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_131 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_132 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_129)) :args ((or _let_70 _let_128 (not _let_129)))) _let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_131 :args (tptp.xq QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aNaturalNumber0 W0) false))))) :args (_let_130))) _let_131 :args (_let_129 false _let_130)) :args (_let_128 false _let_10 false _let_129)))) (let ((_let_133 (not _let_128))) (let ((_let_134 (not _let_109))) (let ((_let_135 (and _let_134 (not (= _let_9 _let_107))))) (let ((_let_136 (= tptp.sz10 tptp.xp))) (let ((_let_137 (not _let_31))) (let ((_let_138 (or _let_70 _let_95 _let_124 _let_137 _let_135 _let_136))) (let ((_let_139 (= tptp.sz00 (tptp.sdtasdt0 tptp.xp tptp.sz00)))) (let ((_let_140 (not _let_95))) (let ((_let_141 (AND_ELIM _let_55 :args (3)))) (let ((_let_142 (and _let_139 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xp))))) (let ((_let_143 (or _let_124 _let_142))) (let ((_let_144 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= tptp.sz00 (tptp.sdtasdt0 W0 tptp.sz00)) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_145 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_146 (and _let_95 _let_139))) (let ((_let_147 (_let_95 _let_139))) (let ((_let_148 (APPLY_UF tptp.sdtasdt0))) (let ((_let_149 (ASSUME :args (_let_95)))) (let ((_let_150 (REFL :args (tptp.xp)))) (let ((_let_151 (ASSUME :args (_let_139)))) (let ((_let_152 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_146)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_149 _let_151) (SCOPE (TRANS (SYMM (SYMM _let_151)) (CONG _let_150 (SYMM (SYMM _let_149)) :args _let_148)) :args _let_147)) :args _let_147)) :args (true _let_146)) :args ((or _let_69 _let_140 (not _let_139)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_142 0)) :args ((or _let_139 (not _let_142)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_143)) :args ((or _let_124 _let_142 (not _let_143)))) _let_126 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_145 :args (tptp.xp QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_144))) _let_145 :args (_let_143 false _let_144)) :args (_let_142 false _let_16 false _let_143)) :args (_let_139 false _let_142)) _let_141 :args (_let_140 false _let_139 true _let_69)))) (let ((_let_153 (not _let_108))) (let ((_let_154 (not _let_106))) (let ((_let_155 (not _let_104))) (let ((_let_156 (not _let_100))) (let ((_let_157 (ASSUME :args (_let_100)))) (let ((_let_158 (ASSUME :args (_let_106)))) (let ((_let_159 (ASSUME :args (_let_108)))) (let ((_let_160 (ASSUME :args (_let_102)))) (let ((_let_161 (SYMM (SYMM _let_160)))) (let ((_let_162 (ASSUME :args (_let_94)))) (let ((_let_163 (ASSUME :args (_let_104)))) (let ((_let_164 (SYMM _let_163))) (let ((_let_165 (ASSUME 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_let_17 false _let_196 true _let_228 false _let_241)) :args (_let_39 false _let_240)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_227 1)) :args ((or _let_225 (not _let_227)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_229))) :args ((or _let_52 _let_72 _let_44 _let_227 _let_228 (not _let_229)))) _let_239 _let_91 _let_56 _let_238 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_98 :args (tptp.xm tptp.xm _let_9 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.aNaturalNumber0 W0) false)) (not (= (tptp.aNaturalNumber0 BOUND_VARIABLE_1412) false)) (not (= (tptp.aNaturalNumber0 BOUND_VARIABLE_1414) false))))) :args _let_99))) _let_98 :args (_let_229 false _let_97)) :args (_let_227 true _let_52 false _let_71 false _let_17 true _let_228 false _let_229)) :args (_let_225 false _let_227)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_224 :args (_let_34 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.sdtlseqdt0 W0 W1) false))))) :args (_let_223)))) _let_224 :args (_let_43 false _let_223)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_222)) :args ((or _let_72 _let_44 _let_36 (not _let_222)))) _let_91 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (_let_9 tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_49)) :args _let_48)) _let_47 :args (_let_222 false _let_46)) :args (_let_36 false _let_71 false _let_17 false _let_222)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_220)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_221 _let_185 _let_179) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS _let_187 _let_186) (REFL :args (_let_34)) :args _let_216) (TRUE_INTRO _let_221))) :args (_let_58 _let_59 _let_8))) :args (_let_8 _let_59 _let_58))) :args (true _let_220)) :args ((or _let_182 _let_180 _let_35 (not _let_58)))) _let_179 _let_169 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_65 1)) :args ((or _let_58 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_69 _let_72 _let_44 _let_70 _let_67 _let_68 _let_65 (not _let_73)))) _let_141 _let_91 _let_56 _let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_200)) :args ((or _let_72 _let_44 _let_70 _let_197 _let_66 _let_199 (not _let_200)))) _let_91 _let_56 _let_89 _let_219 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_214)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_215 _let_217 _let_163) (SCOPE (TRUE_ELIM (TRANS (CONG _let_218 (TRANS (SYMM _let_164) (CONG _let_218 _let_150 :args _let_148)) :args _let_216) (TRUE_INTRO _let_215))) :args (_let_204 _let_205 _let_104))) :args (_let_205 _let_104 _let_204))) :args (true _let_214)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_212)) :args ((or _let_51 _let_124 _let_70 _let_113 _let_211 _let_205 (not _let_212)))) _let_210 _let_126 _let_89 _let_209 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_211 0)) :args ((or _let_111 _let_213))) _let_123 :args (_let_213 false _let_102)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xq QUANTIFIERS_INST_CBQI_PROP)) :args _let_99)) _let_98 :args (_let_212 false _let_97)) :args (_let_205 true _let_51 false _let_16 false _let_10 false _let_112 true _let_211 false _let_212)) _let_127 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_206)) :args ((or _let_51 _let_124 _let_113 _let_204 (not _let_206)))) _let_210 _let_126 _let_209 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_208 :args (tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 W1 W0)))) :args (_let_207))) _let_208 :args (_let_206 false _let_207)) :args (_let_204 true _let_51 false _let_16 false _let_112 false _let_206)) :args (_let_198 false _let_205 false _let_104 false _let_204)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_202 :args (tptp.xq _let_9 tptp.xm QUANTIFIERS_INST_CBQI_PROP)) :args (_let_201))) _let_202 :args (_let_200 false _let_201)) :args (_let_66 false _let_71 false _let_17 false _let_10 false _let_196 false _let_198 false _let_200)) _let_195 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_75 :args (_let_9 tptp.xq tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_76))) _let_75 :args (_let_73 false _let_74)) :args (_let_65 true _let_69 false _let_71 false _let_17 false _let_10 false _let_66 true _let_68 false _let_73)) :args (_let_58 false _let_65)) :args (_let_35 false _let_8 false _let_59 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_45))) :args ((or _let_44 _let_33 (not _let_45)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.xm tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_49)) :args _let_48)) _let_47 :args (_let_45 false _let_46)) :args (_let_33 false _let_17 false _let_45)) :args (false false _let_39 true _let_37 false _let_43 false _let_36 false _let_35 false _let_33)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) _let_32 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) _let_30 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))) (forall ((W0 $$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_29 _let_28 _let_27 _let_26 _let_25 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (and (= (tptp.sdtasdt0 W0 _let_1) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 _let_1 W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))))))) (forall ((W0 $$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_24 (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))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))) (forall ((W0 $$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))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))) _let_23 _let_22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))) (forall ((W0 $$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_21 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))) _let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.isPrime0 W0) (and (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10)) (forall ((W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0)) (or (= W1 tptp.sz10) (= W1 W0)))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) (forall ((W0 $$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))) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))) _let_19 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2) (not (= W0 tptp.sz00)) (not (= W1 tptp.sz00)) (not (= W2 tptp.sz00))) (=> (= (tptp.sdtasdt0 W2 (tptp.sdtasdt0 W1 W1)) (tptp.sdtasdt0 W0 W0)) (=> (tptp.iLess0 W0 tptp.xn) (not (or (and (not (= W2 tptp.sz10)) (forall ((W3 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W3) (exists ((W4 $$unsorted)) (and (tptp.aNaturalNumber0 W4) (= W2 (tptp.sdtasdt0 W3 W4)))) (tptp.doDivides0 W3 W2)) (or (= W3 tptp.sz10) (= W3 W2))))) (tptp.isPrime0 W2))))))) (= (tptp.sdtasdt0 tptp.xp _let_1) _let_2) _let_15 _let_14 _let_11 _let_8 _let_5 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 28.44/28.74 )
% 28.44/28.74 % SZS output end Proof for NUM527+3
% 28.44/28.74 % cvc5---1.0.5 exiting
% 28.44/28.75 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------