TSTP Solution File: KLE009+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : KLE009+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 05:26:48 EDT 2023
% Result : Theorem 1.00s 1.22s
% Output : Proof 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE009+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n010.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 : Tue Aug 29 12:15:33 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.48 %----Proving TF0_NAR, FOF, or CNF
% 1.00/1.22 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.K9bQnIhroI/cvc5---1.0.5_15888.p...
% 1.00/1.22 ------- get file name : TPTP file name is KLE009+2
% 1.00/1.22 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15888.smt2...
% 1.00/1.22 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.00/1.22 % SZS status Theorem for KLE009+2
% 1.00/1.22 % SZS output start Proof for KLE009+2
% 1.00/1.22 (
% 1.00/1.22 (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.multiplication X0 X1) (tptp.multiplication X0 _let_1)) (tptp.multiplication _let_2 X1)) (tptp.multiplication _let_2 _let_1)))))))))) (let ((_let_2 (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (tptp.test X0) (= (= (tptp.c X0) X1) (tptp.complement X0 X1)))))) (let ((_let_3 (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_4 (forall ((X0 $$unsorted)) (= (tptp.test X0) (exists ((X1 $$unsorted)) (tptp.complement X1 X0)))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication (tptp.addition A B) C) (tptp.addition (tptp.multiplication A C) (tptp.multiplication B C)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.addition B C)) (tptp.addition (tptp.multiplication A B) (tptp.multiplication A C)))))) (let ((_let_7 (forall ((A $$unsorted)) (= (tptp.multiplication A tptp.one) A)))) (let ((_let_8 (forall ((A $$unsorted)) (= (tptp.addition A A) A)))) (let ((_let_9 (forall ((C $$unsorted) (B $$unsorted) (A $$unsorted)) (= (tptp.addition A (tptp.addition B C)) (tptp.addition (tptp.addition A B) C))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.addition A B) (tptp.addition B A))))) (let ((_let_11 (tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_12 (tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_13 (tptp.multiplication _let_12 _let_11))) (let ((_let_14 (tptp.multiplication _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (tptp.addition (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_11)))) (let ((_let_16 (tptp.addition (tptp.addition _let_15 _let_14) _let_13))) (let ((_let_17 (= tptp.one _let_16))) (let ((_let_18 (tptp.addition _let_14 _let_13))) (let ((_let_19 (= _let_16 (tptp.addition _let_15 _let_18)))) (let ((_let_20 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_11))) (let ((_let_21 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_20))) (let ((_let_22 (= _let_15 _let_21))) (let ((_let_23 (tptp.multiplication _let_12 _let_20))) (let ((_let_24 (= _let_18 _let_23))) (let ((_let_25 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_26 (= tptp.one _let_25))) (let ((_let_27 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_28 (= tptp.one _let_27))) (let ((_let_29 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_30 (= _let_27 _let_29))) (let ((_let_31 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12))) (let ((_let_32 (= (tptp.multiplication _let_31 _let_20) (tptp.addition _let_21 _let_23)))) (let ((_let_33 (tptp.addition _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_34 (= _let_31 _let_33))) (let ((_let_35 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_36 (= _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_37 (= _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_38 (= _let_33 (tptp.multiplication _let_33 tptp.one)))) (let ((_let_39 (tptp.test SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_40 (not _let_39))) (let ((_let_41 (tptp.test SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_42 _let_40 _let_17))) (let ((_let_44 (not _let_17))) (let ((_let_45 (forall ((X0 $$unsorted) (X1 $$unsorted)) (let ((_let_1 (tptp.c X1))) (let ((_let_2 (tptp.c X0))) (or (not (tptp.test X1)) (not (tptp.test X0)) (= tptp.one (tptp.addition (tptp.addition (tptp.addition (tptp.multiplication X0 X1) (tptp.multiplication X0 _let_1)) (tptp.multiplication _let_2 X1)) (tptp.multiplication _let_2 _let_1))))))))) (let ((_let_46 (not _let_43))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (or))) (let ((_let_49 (not _let_45))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_47) :args (_let_49))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_45))) (REFL :args (_let_46)) :args _let_48)) _let_47 :args (_let_46 true _let_45)))) (let ((_let_51 (_let_9))) (let ((_let_52 (ASSUME :args _let_51))) (let ((_let_53 (_let_6))) (let ((_let_54 (ASSUME :args _let_53))) (let ((_let_55 ((tptp.addition (tptp.multiplication A B) (tptp.multiplication A C))))) (let ((_let_56 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_57 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_58 (and _let_57 _let_56 _let_26))) (let ((_let_59 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_60 (= _let_59 _let_58))) (let ((_let_61 (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (tptp.complement X1 X0) (and (= tptp.zero (tptp.multiplication X0 X1)) (= tptp.zero (tptp.multiplication X1 X0)) (= tptp.one (tptp.addition X0 X1))))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (_let_61))) (let ((_let_64 ((tptp.complement X1 X0)))) (let ((_let_65 (forall ((X1 $$unsorted)) (not (tptp.complement X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_66 (not _let_65))) (let ((_let_67 (= _let_39 _let_66))) (let ((_let_68 (forall ((X0 $$unsorted)) (= (tptp.test X0) (not (forall ((X1 $$unsorted)) (not (tptp.complement X1 X0)))))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (_let_68))) (let ((_let_71 ((tptp.test X0)))) (let ((_let_72 (REFL :args (_let_43)))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 1)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_48)) :args ((or _let_39 _let_43))) _let_50 :args (_let_39 true _let_43)))) (let ((_let_74 (not _let_59))) (let ((_let_75 (_let_66))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_60)) :args ((or _let_74 _let_58 (not _let_60)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_75)) :args _let_75) (REWRITE :args ((=> _let_66 (not _let_74)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_65))) (REFL :args (_let_59)) :args _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_67)) :args ((or _let_40 _let_66 (not _let_67)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) _let_69 :args (_let_67 false _let_68)) :args (_let_66 false _let_39 false _let_67)) :args (_let_59 true _let_65)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_64)) :args _let_63)) _let_62 :args (_let_60 false _let_61)) :args (_let_58 false _let_59 false _let_60)))) (let ((_let_77 (not _let_58))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 2)) :args ((or _let_26 _let_77))) _let_76 :args (_let_26 false _let_58)))) (let ((_let_79 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_80 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_81 (and _let_80 _let_79 _let_28))) (let ((_let_82 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_83 (= _let_82 _let_81))) (let ((_let_84 (forall ((X1 $$unsorted)) (not (tptp.complement X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_85 (not _let_84))) (let ((_let_86 (= _let_41 _let_85))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 0)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_48)) :args ((or _let_41 _let_43))) _let_50 :args (_let_41 true _let_43)))) (let ((_let_88 (not _let_82))) (let ((_let_89 (_let_85))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_83)) :args ((or _let_88 _let_81 (not _let_83)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_89)) :args _let_89) (REWRITE :args ((=> _let_85 (not _let_88)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_85) _let_84))) (REFL :args (_let_82)) :args _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_86)) :args ((or _let_42 _let_85 (not _let_86)))) _let_87 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) _let_69 :args (_let_86 false _let_68)) :args (_let_85 false _let_41 false _let_86)) :args (_let_82 true _let_84)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_64)) :args _let_63)) _let_62 :args (_let_83 false _let_61)) :args (_let_81 false _let_82 false _let_83)))) (let ((_let_91 (not _let_81))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_81 2)) :args ((or _let_28 _let_91))) _let_90 :args (_let_28 false _let_81)))) (let ((_let_93 (_let_10))) (let ((_let_94 (ASSUME :args _let_93))) (let ((_let_95 ((tptp.addition A B)))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_95)) :args _let_93)) _let_94 :args (_let_30 false _let_10)))) (let ((_let_97 (_let_5))) (let ((_let_98 (ASSUME :args _let_97))) (let ((_let_99 (forall ((A $$unsorted)) (= A (tptp.addition A A))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_102 (= _let_101 _let_36))) (let ((_let_103 (or _let_40 _let_102))) (let ((_let_104 (forall ((X0 $$unsorted) (X1 $$unsorted)) (or (not (tptp.test X0)) (= (tptp.complement X0 X1) (= X1 (tptp.c X0))))))) (let ((_let_105 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_106 (_let_104))) (let ((_let_107 ((tptp.complement X0 X1)))) (let ((_let_108 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_109 (= tptp.one _let_108))) (let ((_let_110 (and _let_56 _let_57 _let_109))) (let ((_let_111 (= _let_101 _let_110))) (let ((_let_112 ((tptp.multiplication X0 X1)))) (let ((_let_113 (= _let_25 _let_108))) (let ((_let_114 (not _let_26))) (let ((_let_115 (and _let_26 _let_113))) (let ((_let_116 (ASSUME :args (_let_113)))) (let ((_let_117 (ASSUME :args (_let_26)))) (let ((_let_118 (SYMM _let_117))) (let ((_let_119 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_120 (= _let_119 _let_37))) (let ((_let_121 (or _let_42 _let_120))) (let ((_let_122 (= tptp.one _let_29))) (let ((_let_123 (and _let_79 _let_80 _let_122))) (let ((_let_124 (= _let_119 _let_123))) (let ((_let_125 (not _let_30))) (let ((_let_126 (not _let_28))) (let ((_let_127 (and _let_28 _let_30))) (let ((_let_128 (ASSUME :args (_let_30)))) (let ((_let_129 (ASSUME :args (_let_28)))) (let ((_let_130 (SYMM (SYMM _let_129)))) (let ((_let_131 (forall ((A $$unsorted)) (= A (tptp.multiplication A tptp.one))))) (let ((_let_132 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_133 (not _let_38))) (let ((_let_134 (_let_133))) (let ((_let_135 (ASSUME :args (_let_38)))) (let ((_let_136 (ASSUME :args (_let_44)))) (let ((_let_137 (ASSUME :args (_let_19)))) (let ((_let_138 (APPLY_UF tptp.addition))) (let ((_let_139 (ASSUME :args (_let_24)))) (let ((_let_140 (ASSUME :args (_let_22)))) (let ((_let_141 (ASSUME :args (_let_32)))) (let ((_let_142 (APPLY_UF tptp.multiplication))) (let ((_let_143 (ASSUME :args (_let_37)))) (let ((_let_144 (ASSUME :args (_let_35)))) (let ((_let_145 (CONG (SYMM _let_144) (SYMM _let_143) :args _let_138))) (let ((_let_146 (CONG _let_144 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) :args _let_138))) (let ((_let_147 (ASSUME :args (_let_36)))) (let ((_let_148 (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (SYMM (SYMM _let_147)) :args _let_138))) (let ((_let_149 (TRANS _let_148 _let_118 _let_130 _let_146 _let_145))) (let ((_let_150 (ASSUME :args (_let_34)))) (let ((_let_151 (SYMM _let_150))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_117 _let_147 _let_150 _let_136 _let_137 _let_140 _let_139 _let_141 _let_129 _let_128 _let_144 _let_143) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS _let_151 _let_148 _let_118) (TRANS (CONG (TRANS (TRANS _let_151 _let_148 _let_118 _let_130 _let_128) (SYMM (TRANS (SYMM _let_145) (SYMM _let_146) _let_128))) (TRANS _let_117 (SYMM _let_148)) :args _let_142) (CONG (SYMM _let_149) _let_149 :args _let_142) (SYMM (SYMM _let_141)) (CONG (SYMM _let_140) (SYMM _let_139) :args _let_138) (SYMM _let_137)) :args (=)) (FALSE_INTRO _let_136))) :args (_let_26 _let_36 _let_34 _let_44 _let_19 _let_22 _let_24 _let_32 _let_28 _let_30 _let_35 _let_37))) _let_135) :args (_let_44 _let_19 _let_22 _let_24 _let_26 _let_28 _let_30 _let_32 _let_34 _let_35 _let_36 _let_37 _let_38)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_134))) (TRUE_INTRO _let_135))) :args (_let_133 _let_38)) :args ((not (and _let_44 _let_19 _let_22 _let_24 _let_26 _let_28 _let_30 _let_32 _let_34 _let_35 _let_36 _let_37 _let_38)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_17))) (REFL :args ((not _let_19))) (REFL :args ((not _let_22))) (REFL :args ((not _let_24))) (REFL :args (_let_114)) (REFL :args (_let_126)) (REFL :args (_let_125)) (REFL :args ((not _let_32))) (REFL :args ((not _let_34))) (REFL :args ((not _let_35))) (REFL :args ((not _let_36))) (REFL :args ((not _let_37))) (REFL :args _let_134) :args _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_132 :args (_let_33 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.multiplication A tptp.one)))) :args (_let_131))) _let_132 :args (_let_38 false _let_131)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_120)) :args ((or (not _let_119) _let_37 (not _let_120)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_124)) :args ((or _let_119 (not _let_123) (not _let_124)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_123)) :args ((or (not _let_80) (not _let_79) _let_123 (not _let_122)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_81 0)) :args ((or _let_80 _let_91))) _let_90 :args (_let_80 false _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_81 1)) :args ((or _let_79 _let_91))) _let_90 :args (_let_79 false _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_127)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_128 _let_129) (SCOPE (TRANS _let_130 (SYMM (SYMM _let_128))) :args (_let_30 _let_28))) :args (_let_28 _let_30))) :args (true _let_127)) :args ((or _let_126 _let_122 _let_125))) _let_92 _let_96 :args (_let_122 false _let_28 false _let_30)) :args (_let_123 false _let_80 false _let_79 false _let_122)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_63)) _let_62 :args (_let_124 false _let_61)) :args (_let_119 false _let_123 false _let_124)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_121)) :args ((or _let_42 _let_120 (not _let_121)))) _let_87 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_105 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_107)) :args _let_106))) _let_105 :args (_let_121 false _let_104)) :args (_let_120 false _let_41 false _let_121)) :args (_let_37 false _let_119 false _let_120)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_102)) :args ((or (not _let_101) _let_36 (not _let_102)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_111)) :args ((or _let_101 (not _let_110) (not _let_111)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_110)) :args ((or (not _let_57) (not _let_56) _let_110 (not _let_109)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 0)) :args ((or _let_57 _let_77))) _let_76 :args (_let_57 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 1)) :args ((or _let_56 _let_77))) _let_76 :args (_let_56 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_115)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_116 _let_117) (SCOPE (TRANS (SYMM _let_118) (SYMM (SYMM _let_116))) :args (_let_113 _let_26))) :args (_let_26 _let_113))) :args (true _let_115)) :args ((or _let_114 _let_109 (not _let_113)))) _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_95)) :args _let_93)) _let_94 :args (_let_113 false _let_10)) :args (_let_109 false _let_26 false _let_113)) :args (_let_110 false _let_57 false _let_56 false _let_109)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_63)) _let_62 :args (_let_111 false _let_61)) :args (_let_101 false _let_110 false _let_111)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_40 _let_102 (not _let_103)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_105 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_107)) :args _let_106))) _let_105 :args (_let_103 false _let_104)) :args (_let_102 false _let_39 false _let_103)) :args (_let_36 false _let_101 false _let_102)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.addition A A)))) :args (_let_99))) _let_100 :args (_let_35 false _let_99)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_95)) :args _let_93)) _let_94 :args (_let_34 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12 _let_20 QUANTIFIERS_INST_E_MATCHING ((tptp.addition (tptp.multiplication A C) (tptp.multiplication B C))))) :args _let_97)) _let_98 :args (_let_32 false _let_5)) _let_96 _let_92 _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_11 QUANTIFIERS_INST_E_MATCHING _let_55)) :args _let_53))) _let_54 :args (_let_24 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_11 QUANTIFIERS_INST_E_MATCHING _let_55)) :args _let_53))) _let_54 :args (_let_22 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (_let_13 _let_14 _let_15 QUANTIFIERS_INST_E_MATCHING ((tptp.addition (tptp.addition A B) C)))) :args _let_51))) _let_52 :args (_let_19 false _let_9)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 2)) _let_50 :args (_let_44 true _let_43)) :args (false false _let_38 false _let_37 false _let_36 false _let_35 false _let_34 false _let_32 false _let_30 false _let_28 false _let_26 false _let_24 false _let_22 false _let_19 true _let_17)) :args (_let_10 _let_9 (forall ((A $$unsorted)) (= (tptp.addition A tptp.zero) A)) _let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.multiplication B C)) (tptp.multiplication (tptp.multiplication A B) C))) _let_7 (forall ((A $$unsorted)) (= (tptp.multiplication tptp.one A) A)) _let_6 _let_5 (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_4 _let_3 _let_2 (forall ((X0 $$unsorted)) (=> (not (tptp.test X0)) (= (tptp.c X0) tptp.zero))) (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (and (tptp.test X0) (tptp.test X1)) (= (tptp.c (tptp.addition X0 X1)) (tptp.multiplication (tptp.c X0) (tptp.c X1))))) (forall ((X0 $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.00/1.23 )
% 1.00/1.23 % SZS output end Proof for KLE009+2
% 1.00/1.23 % cvc5---1.0.5 exiting
% 1.00/1.23 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------