TSTP Solution File: KLE010+3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : KLE010+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.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 05:26:49 EDT 2023
% Result : Theorem 2.45s 2.80s
% Output : Proof 2.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE010+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 12:48:20 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 2.45/2.80 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.a7U7onvpVr/cvc5---1.0.5_30786.p...
% 2.45/2.80 ------- get file name : TPTP file name is KLE010+3
% 2.45/2.80 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30786.smt2...
% 2.45/2.80 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.45/2.80 % SZS status Theorem for KLE010+3
% 2.45/2.80 % SZS output start Proof for KLE010+3
% 2.45/2.80 (
% 2.45/2.80 (let ((_let_1 (not (forall ((X0 $$unsorted) (X1 $$unsorted)) (let ((_let_1 (tptp.c X1))) (let ((_let_2 (tptp.c X0))) (=> (and (tptp.test X1) (tptp.test X0)) (= tptp.one (tptp.addition (tptp.addition (tptp.addition (tptp.addition (tptp.multiplication X1 X0) (tptp.multiplication _let_1 X0)) (tptp.multiplication X0 X1)) (tptp.multiplication _let_2 X1)) (tptp.multiplication _let_2 _let_1)))))))))) (let ((_let_2 (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (and (tptp.test X0) (tptp.test X1)) (= (tptp.c (tptp.addition X0 X1)) (tptp.multiplication (tptp.c X0) (tptp.c X1))))))) (let ((_let_3 (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (tptp.test X0) (= (= (tptp.c X0) X1) (tptp.complement X0 X1)))))) (let ((_let_4 (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (tptp.complement X1 X0) (and (= (tptp.multiplication X0 X1) tptp.zero) (= (tptp.multiplication X1 X0) tptp.zero) (= (tptp.addition X0 X1) tptp.one)))))) (let ((_let_5 (forall ((X0 $$unsorted)) (= (tptp.test X0) (exists ((X1 $$unsorted)) (tptp.complement X1 X0)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication (tptp.addition A B) C) (tptp.addition (tptp.multiplication A C) (tptp.multiplication B C)))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.addition B C)) (tptp.addition (tptp.multiplication A B) (tptp.multiplication A C)))))) (let ((_let_8 (forall ((A $$unsorted)) (= (tptp.multiplication tptp.one A) A)))) (let ((_let_9 (forall ((A $$unsorted)) (= (tptp.multiplication A tptp.one) A)))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.multiplication B C)) (tptp.multiplication (tptp.multiplication A B) C))))) (let ((_let_11 (forall ((A $$unsorted)) (= (tptp.addition A A) A)))) (let ((_let_12 (forall ((A $$unsorted)) (= (tptp.addition A tptp.zero) A)))) (let ((_let_13 (forall ((C $$unsorted) (B $$unsorted) (A $$unsorted)) (= (tptp.addition A (tptp.addition B C)) (tptp.addition (tptp.addition A B) C))))) (let ((_let_14 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.addition A B) (tptp.addition B A))))) (let ((_let_15 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_16 (tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_17 (tptp.multiplication _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_18 (tptp.addition _let_15 _let_17))) (let ((_let_19 (= _let_18 (tptp.addition _let_17 _let_15)))) (let ((_let_20 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_21 (tptp.addition _let_18 _let_20))) (let ((_let_22 (= _let_21 (tptp.addition _let_20 _let_18)))) (let ((_let_23 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16))) (let ((_let_24 (tptp.multiplication _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_25 (= _let_18 _let_24))) (let ((_let_26 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_27 (tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (= (tptp.addition _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_27)))) (let ((_let_29 (tptp.addition _let_17 _let_20))) (let ((_let_30 (= _let_29 (tptp.addition _let_20 _let_17)))) (let ((_let_31 (tptp.multiplication _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (= (tptp.multiplication _let_18 _let_20) (tptp.multiplication _let_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_33 (tptp.multiplication _let_27 _let_16))) (let ((_let_34 (tptp.multiplication _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_35 (tptp.addition _let_34 _let_33))) (let ((_let_36 (= _let_35 (tptp.multiplication _let_27 _let_23)))) (let ((_let_37 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_27))) (let ((_let_38 (tptp.addition _let_20 _let_34))) (let ((_let_39 (= _let_38 (tptp.multiplication _let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_40 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_41 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_42 (= tptp.one _let_41))) (let ((_let_43 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_44 (= tptp.one _let_43))) (let ((_let_45 (tptp.complement _let_35 _let_21))) (let ((_let_46 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_47 (tptp.multiplication _let_46 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_48 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_20))) (let ((_let_49 (= _let_48 _let_47))) (let ((_let_50 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_23))) (let ((_let_51 (tptp.multiplication _let_20 _let_23))) (let ((_let_52 (= _let_51 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_50)))) (let ((_let_53 (= (tptp.multiplication _let_23 _let_46) (tptp.multiplication _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_54 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_16))) (let ((_let_55 (tptp.addition _let_20 _let_54))) (let ((_let_56 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_23))) (let ((_let_57 (= _let_56 _let_55))) (let ((_let_58 (tptp.multiplication _let_20 _let_16))) (let ((_let_59 (tptp.multiplication _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_60 (tptp.addition _let_59 _let_58))) (let ((_let_61 (= _let_51 _let_60))) (let ((_let_62 (tptp.multiplication _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_63 (tptp.multiplication _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_64 (tptp.addition _let_63 _let_62))) (let ((_let_65 (= _let_31 _let_64))) (let ((_let_66 (= (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_20) (tptp.addition _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_67 (= _let_55 (tptp.addition _let_54 _let_20)))) (let ((_let_68 (= _let_64 (tptp.addition _let_62 _let_63)))) (let ((_let_69 (= _let_60 (tptp.addition _let_58 _let_59)))) (let ((_let_70 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_71 (= _let_27 (tptp.addition _let_27 _let_27)))) (let ((_let_72 (= (tptp.multiplication _let_48 _let_23) (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_51)))) (let ((_let_73 (= (tptp.multiplication _let_23 _let_20) (tptp.multiplication _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_74 (= (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_24) (tptp.multiplication _let_56 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_75 (= (tptp.multiplication _let_46 _let_50) (tptp.multiplication _let_47 _let_23)))) (let ((_let_76 (= (tptp.multiplication _let_23 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_37)) (tptp.multiplication _let_24 _let_37)))) (let ((_let_77 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.one)))) (let ((_let_78 (= _let_23 (tptp.multiplication _let_23 tptp.one)))) (let ((_let_79 (= _let_27 (tptp.multiplication _let_27 tptp.one)))) (let ((_let_80 (= _let_16 (tptp.multiplication _let_16 tptp.one)))) (let ((_let_81 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.multiplication tptp.one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_82 (tptp.multiplication _let_18 _let_27))) (let ((_let_83 (= (tptp.multiplication _let_18 _let_37) (tptp.addition _let_31 _let_82)))) (let ((_let_84 (= _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_85 (= _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_86 (tptp.addition _let_15 _let_18))) (let ((_let_87 (tptp.addition _let_18 _let_15))) (let ((_let_88 (= _let_87 _let_86))) (let ((_let_89 (tptp.addition _let_18 _let_18))) (let ((_let_90 (= _let_89 (tptp.addition _let_87 _let_17)))) (let ((_let_91 (tptp.addition _let_15 _let_15))) (let ((_let_92 (= _let_86 (tptp.addition _let_91 _let_17)))) (let ((_let_93 (= (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_29) (tptp.addition (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_17) _let_20)))) (let ((_let_94 (= _let_31 (tptp.addition _let_31 tptp.zero)))) (let ((_let_95 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_96 (= _let_18 _let_89))) (let ((_let_97 (= _let_15 _let_91))) (let ((_let_98 (= (tptp.multiplication _let_18 _let_24) (tptp.multiplication (tptp.multiplication _let_18 _let_23) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_99 (= (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_54) (tptp.multiplication _let_46 _let_16)))) (let ((_let_100 (= (tptp.multiplication _let_37 _let_24) (tptp.multiplication (tptp.multiplication _let_37 _let_23) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_101 (= (tptp.multiplication _let_16 _let_24) (tptp.multiplication (tptp.multiplication _let_16 _let_23) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_102 (= (tptp.multiplication _let_23 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_18)) (tptp.multiplication _let_24 _let_18)))) (let ((_let_103 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.one)))) (let ((_let_104 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.multiplication tptp.one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_105 (tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_106 (= (tptp.c (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.multiplication _let_16 _let_105)))) (let ((_let_107 (= (tptp.c (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.multiplication _let_105 _let_16)))) (let ((_let_108 (= (tptp.c (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.multiplication _let_105 _let_105)))) (let ((_let_109 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_105))) (let ((_let_110 (_let_14))) (let ((_let_111 (ASSUME :args _let_110))) (let ((_let_112 ((tptp.addition A B)))) (let ((_let_113 (_let_6))) (let ((_let_114 (ASSUME :args _let_113))) (let ((_let_115 ((tptp.addition (tptp.multiplication A C) (tptp.multiplication B C))))) (let ((_let_116 (forall ((X1 $$unsorted)) (not (tptp.complement X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_117 (not _let_116))) (let ((_let_118 (tptp.test SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_119 (= _let_118 _let_117))) (let ((_let_120 (forall ((X0 $$unsorted)) (= (tptp.test X0) (not (forall ((X1 $$unsorted)) (not (tptp.complement X1 X0)))))))) (let ((_let_121 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_122 (_let_120))) (let ((_let_123 ((tptp.test X0)))) (let ((_let_124 (tptp.addition (tptp.addition _let_21 _let_34) _let_33))) (let ((_let_125 (= tptp.one _let_124))) (let ((_let_126 (not _let_118))) (let ((_let_127 (tptp.test SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_128 (not _let_127))) (let ((_let_129 (or _let_128 _let_126 _let_125))) (let ((_let_130 (forall ((X0 $$unsorted) (X1 $$unsorted)) (let ((_let_1 (tptp.c X1))) (let ((_let_2 (tptp.c X0))) (or (not (tptp.test X1)) (not (tptp.test X0)) (= tptp.one (tptp.addition (tptp.addition (tptp.addition (tptp.addition (tptp.multiplication X1 X0) (tptp.multiplication _let_1 X0)) (tptp.multiplication X0 X1)) (tptp.multiplication _let_2 X1)) (tptp.multiplication _let_2 _let_1))))))))) (let ((_let_131 (not _let_129))) (let ((_let_132 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_133 (or))) (let ((_let_134 (not _let_130))) (let ((_let_135 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_132) :args (_let_134))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_134) _let_130))) (REFL :args (_let_131)) :args _let_133)) _let_132 :args (_let_131 true _let_130)))) (let ((_let_136 (REFL :args (_let_129)))) (let ((_let_137 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_129 1)) (CONG _let_136 (MACRO_SR_PRED_INTRO :args ((= (not _let_126) _let_118))) :args _let_133)) :args ((or _let_118 _let_129))) _let_135 :args (_let_118 true _let_129)))) (let ((_let_138 (_let_26))) (let ((_let_139 (not _let_26))) (let ((_let_140 (_let_117))) (let ((_let_141 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_140)) :args _let_140) (REWRITE :args ((=> _let_117 (not _let_139)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_117) _let_116))) (REFL :args _let_138) :args _let_133)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_119)) :args ((or _let_126 _let_117 (not _let_119)))) _let_137 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_123)) :args _let_122)) _let_121 :args (_let_119 false _let_120)) :args (_let_117 false _let_118 false _let_119)) :args (_let_26 true _let_116)))) (let ((_let_142 (_let_10))) (let ((_let_143 (ASSUME :args _let_142))) (let ((_let_144 ((tptp.multiplication A (tptp.multiplication B C))))) (let ((_let_145 (_let_7))) (let ((_let_146 (ASSUME :args _let_145))) (let ((_let_147 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_148 (and _let_40 _let_147 _let_42))) (let ((_let_149 (= _let_26 _let_148))) (let ((_let_150 (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (tptp.complement X1 X0) (and (= tptp.zero (tptp.multiplication X0 X1)) (= tptp.zero (tptp.multiplication X1 X0)) (= tptp.one (tptp.addition X0 X1))))))) (let ((_let_151 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_152 (_let_150))) (let ((_let_153 ((tptp.complement X1 X0)))) (let ((_let_154 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_149)) :args ((or _let_139 _let_148 (not _let_149)))) _let_141 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_151 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_153)) :args _let_152)) _let_151 :args (_let_149 false _let_150)) :args (_let_148 false _let_26 false _let_149)))) (let ((_let_155 (not _let_148))) (let ((_let_156 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_148 0)) :args ((or _let_40 _let_155))) _let_154 :args (_let_40 false _let_148)))) (let ((_let_157 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_148 2)) :args ((or _let_42 _let_155))) _let_154 :args (_let_42 false _let_148)))) (let ((_let_158 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_159 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_160 (and _let_159 _let_158 _let_44))) (let ((_let_161 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_162 (= _let_161 _let_160))) (let ((_let_163 (forall ((X1 $$unsorted)) (not (tptp.complement X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_164 (not _let_163))) (let ((_let_165 (= _let_127 _let_164))) (let ((_let_166 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_129 0)) (CONG _let_136 (MACRO_SR_PRED_INTRO :args ((= (not _let_128) _let_127))) :args _let_133)) :args ((or _let_127 _let_129))) _let_135 :args (_let_127 true _let_129)))) (let ((_let_167 (not _let_161))) (let ((_let_168 (_let_164))) (let ((_let_169 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_162)) :args ((or 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(MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_146 :args (_let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_27 QUANTIFIERS_INST_E_MATCHING _let_188)) :args _let_145)) _let_146 :args (_let_83 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_198 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_200)) :args _let_199)) _let_198 :args (_let_81 false _let_197)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_194 :args (_let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_196)) :args _let_195)) _let_194 :args (_let_80 false _let_193)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_194 :args (_let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_196)) :args _let_195)) _let_194 :args (_let_79 false _let_193)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_194 :args (_let_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_196)) :args _let_195)) _let_194 :args (_let_78 false _let_193)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_194 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_196)) :args _let_195)) _let_194 :args (_let_77 false _let_193)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_143 :args (_let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_37 QUANTIFIERS_INST_E_MATCHING _let_187)) :args _let_142)) _let_143 :args (_let_76 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_143 :args (_let_46 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_23 QUANTIFIERS_INST_E_MATCHING _let_187)) :args _let_142)) _let_143 :args (_let_75 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_143 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_144)) :args _let_142)) _let_143 :args (_let_74 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_143 :args (_let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_144)) :args _let_142)) _let_143 :args (_let_73 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_143 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_20 _let_23 QUANTIFIERS_INST_E_MATCHING _let_144)) :args _let_142))) _let_143 :args (_let_72 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_190 :args (_let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_192)) :args _let_191)) _let_190 :args (_let_71 false _let_189)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_190 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_192)) :args _let_191)) _let_190 :args (_let_70 false _let_189)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (_let_59 _let_58 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_110)) _let_111 :args (_let_69 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (_let_63 _let_62 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_110)) _let_111 :args (_let_68 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (_let_20 _let_54 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_110)) _let_111 :args (_let_67 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_110)) _let_111 :args (_let_66 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (_let_15 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((tptp.multiplication (tptp.addition A B) C)))) :args _let_113)) _let_114 :args (_let_65 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_146 :args (_let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16 QUANTIFIERS_INST_E_MATCHING _let_188)) :args _let_145)) _let_146 :args (_let_61 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_146 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16 QUANTIFIERS_INST_E_MATCHING _let_188)) :args _let_145)) _let_146 :args (_let_57 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_143 :args (_let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_187)) :args _let_142)) _let_143 :args (_let_53 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_143 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_23 QUANTIFIERS_INST_E_MATCHING _let_187)) :args _let_142))) _let_143 :args (_let_52 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_143 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_144)) :args _let_142)) _let_143 :args (_let_49 false _let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_175)) :args ((or _let_174 _let_176 (not _let_175)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_174 2)) :args ((or _let_173 _let_177))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_183)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_185 _let_186) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.one)) (SYMM _let_186) :args (=)) (FALSE_INTRO _let_185))) :args _let_184)) :args _let_184)) :args (true _let_183)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_182) _let_125))) (REFL :args ((not _let_178))) (REFL :args (_let_179)) :args _let_133)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_129 2)) _let_135 :args (_let_182 true _let_129)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_181 :args (_let_33 _let_34 _let_21 QUANTIFIERS_INST_E_MATCHING ((tptp.addition (tptp.addition A B) C)))) :args _let_180))) _let_181 :args (_let_178 false _let_13)) :args (_let_179 true _let_125 false _let_178)) :args (_let_177 true _let_173)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_151 :args (_let_21 _let_35 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.addition X0 X1)))) :args _let_152)) _let_151 :args (_let_175 false _let_150)) :args (_let_176 true _let_174 false _let_175)) _let_171 _let_157 _let_156 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_114 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_115)) :args _let_113))) _let_114 :args (_let_39 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_146 :args (_let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16 QUANTIFIERS_INST_E_MATCHING ((tptp.addition (tptp.multiplication A B) (tptp.multiplication A C))))) :args _let_145))) _let_146 :args (_let_36 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_143 :args (_let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_144)) :args _let_142)) _let_143 :args (_let_32 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (_let_17 _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_110)) _let_111 :args (_let_30 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_111 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_110))) _let_111 :args (_let_28 false _let_14)) _let_141 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_114 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_115)) :args _let_113))) _let_114 :args (_let_25 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (_let_18 _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_110)) _let_111 :args (_let_22 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (_let_15 _let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_110)) _let_111 :args (_let_19 false _let_14)) :args (false false _let_109 false _let_108 false _let_107 false _let_106 false _let_104 false _let_103 false _let_102 false _let_101 false _let_100 false _let_99 false _let_98 false _let_97 false _let_96 false _let_95 false _let_94 false _let_93 false _let_92 false _let_90 false _let_88 false _let_85 false _let_84 false _let_83 false _let_81 false _let_80 false _let_79 false _let_78 false _let_77 false _let_76 false _let_75 false _let_74 false _let_73 false _let_72 false _let_71 false _let_70 false _let_69 false _let_68 false _let_67 false _let_66 false _let_65 false _let_61 false _let_57 false _let_53 false _let_52 false _let_49 true _let_45 false _let_44 false _let_42 false _let_40 false _let_39 false _let_36 false _let_32 false _let_30 false _let_28 false _let_26 false _let_25 false _let_22 false _let_19)) :args (_let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 (forall ((A $$unsorted)) (= (tptp.multiplication A tptp.zero) tptp.zero)) (forall ((A $$unsorted)) (= (tptp.multiplication tptp.zero A) tptp.zero)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.leq A B) (= (tptp.addition A B) B))) _let_5 _let_4 _let_3 (forall ((X0 $$unsorted)) (=> (not (tptp.test X0)) (= (tptp.c X0) tptp.zero))) _let_2 (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (and (tptp.test X0) (tptp.test X1)) (= (tptp.c (tptp.multiplication X0 X1)) (tptp.addition (tptp.c X0) (tptp.c X1))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 2.45/2.82 )
% 2.45/2.82 % SZS output end Proof for KLE010+3
% 2.45/2.82 % cvc5---1.0.5 exiting
% 2.45/2.82 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------