TSTP Solution File: KLE027+3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : KLE027+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:26:57 EDT 2023
% Result : Theorem 5.97s 6.21s
% Output : Proof 6.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE027+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n024.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 11:20:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 5.97/6.21 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.NrdlyFczaE/cvc5---1.0.5_26572.p...
% 5.97/6.21 ------- get file name : TPTP file name is KLE027+3
% 5.97/6.21 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_26572.smt2...
% 5.97/6.21 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 5.97/6.21 % SZS status Theorem for KLE027+3
% 5.97/6.21 % SZS output start Proof for KLE027+3
% 5.97/6.21 (
% 5.97/6.21 (let ((_let_1 (not (forall ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted)) (let ((_let_1 (tptp.c X3))) (let ((_let_2 (tptp.multiplication _let_1 X2))) (let ((_let_3 (tptp.multiplication X3 X0))) (=> (and (tptp.test X3) (tptp.test X4)) (= (tptp.addition (tptp.multiplication X3 (tptp.addition _let_3 (tptp.multiplication _let_1 X1))) _let_2) (tptp.addition _let_3 _let_2)))))))))) (let ((_let_2 (forall ((X0 $$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)) (=> (not (tptp.test X0)) (= (tptp.c X0) tptp.zero))))) (let ((_let_4 (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (tptp.test X0) (= (= (tptp.c X0) X1) (tptp.complement X0 X1)))))) (let ((_let_5 (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_6 (forall ((X0 $$unsorted)) (= (tptp.test X0) (exists ((X1 $$unsorted)) (tptp.complement X1 X0)))))) (let ((_let_7 (forall ((A $$unsorted)) (= (tptp.multiplication tptp.zero A) tptp.zero)))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.addition B C)) (tptp.addition (tptp.multiplication A B) (tptp.multiplication A C)))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.multiplication B C)) (tptp.multiplication (tptp.multiplication A B) C))))) (let ((_let_10 (forall ((A $$unsorted)) (= (tptp.addition A A) A)))) (let ((_let_11 (forall ((A $$unsorted)) (= (tptp.addition A tptp.zero) A)))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.addition A B) (tptp.addition B A))))) (let ((_let_13 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_14 (forall ((X1 $$unsorted)) (not (tptp.complement X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))))) (let ((_let_15 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_16 (= tptp.one _let_15))) (let ((_let_17 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_18 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_19 (and _let_18 _let_17 _let_16))) (let ((_let_20 (= _let_13 _let_19))) (let ((_let_21 (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_22 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (_let_21))) (let ((_let_24 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_25 (= _let_24 _let_15))) (let ((_let_26 (= tptp.one _let_24))) (let ((_let_27 (_let_12))) (let ((_let_28 (ASSUME :args _let_27))) (let ((_let_29 ((tptp.addition A B)))) (let ((_let_30 (and _let_17 _let_18 _let_26))) (let ((_let_31 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (= _let_31 _let_30))) (let ((_let_33 (forall ((X1 $$unsorted)) (not (tptp.complement X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.test SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_36 (= _let_35 _let_34))) (let ((_let_37 (forall ((X0 $$unsorted)) (= (tptp.test X0) (not (forall ((X1 $$unsorted)) (not (tptp.complement X1 X0)))))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (_let_37))) (let ((_let_40 ((tptp.test X0)))) (let ((_let_41 (tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_42 (tptp.multiplication _let_41 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_43 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_44 (tptp.addition _let_43 _let_42))) (let ((_let_45 (tptp.multiplication _let_41 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_46 (tptp.addition _let_43 _let_45))) (let ((_let_47 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_46))) (let ((_let_48 (tptp.addition _let_47 _let_42))) (let ((_let_49 (= _let_48 _let_44))) (let ((_let_50 (not _let_35))) (let ((_let_51 (or _let_50 _let_49))) (let ((_let_52 (forall ((X3 $$unsorted) (X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (tptp.c X3))) (let ((_let_2 (tptp.multiplication _let_1 X2))) (let ((_let_3 (tptp.multiplication X3 X0))) (or (not (tptp.test X3)) (= (tptp.addition (tptp.multiplication X3 (tptp.addition _let_3 (tptp.multiplication _let_1 X1))) _let_2) (tptp.addition _let_3 _let_2))))))))) (let ((_let_53 (not _let_51))) (let ((_let_54 (or))) (let ((_let_55 (not _let_52))) (let ((_let_56 (_let_55))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_56)) :args _let_56)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_52))) (REFL :args (_let_53)) :args _let_54)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (0)) :args (_let_53 true _let_52)))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 0)) (CONG (REFL :args (_let_51)) (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_35))) :args _let_54)) :args ((or _let_35 _let_51))) _let_57 :args (_let_35 true _let_51)))) (let ((_let_59 (not _let_31))) (let ((_let_60 (_let_34))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_60)) :args _let_60) (REWRITE :args ((=> _let_34 (not _let_59)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) (REFL :args (_let_31)) :args _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_36)) :args ((or _let_50 _let_34 (not _let_36)))) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_40)) :args _let_39)) _let_38 :args (_let_36 false _let_37)) :args (_let_34 false _let_35 false _let_36)) :args (_let_31 true _let_33)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_32)) :args ((or _let_59 _let_30 (not _let_32)))) _let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complement X1 X0)))) :args _let_23)) _let_22 :args (_let_32 false _let_21)) :args (_let_30 false _let_31 false _let_32)))) (let ((_let_63 (not _let_30))) (let ((_let_64 (and _let_26 _let_25))) (let ((_let_65 (ASSUME :args (_let_25)))) (let ((_let_66 (ASSUME :args (_let_26)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_30 1)) :args ((or _let_18 _let_63))) _let_62 :args (_let_18 false _let_30)))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_30 0)) :args ((or _let_17 _let_63))) _let_62 :args (_let_17 false _let_30)))) (let ((_let_69 (not _let_18))) (let ((_let_70 (not _let_17))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_20)) :args ((or _let_13 (not _let_19) (not _let_20)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_19)) :args ((or _let_70 _let_69 _let_19 (not _let_16)))) _let_68 _let_67 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_64)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_65 _let_66) (SCOPE (TRANS (SYMM (SYMM _let_66)) (SYMM (SYMM _let_65))) :args (_let_25 _let_26))) :args (_let_26 _let_25))) :args (true _let_64)) :args ((or (not _let_26) _let_16 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_30 2)) :args ((or _let_26 _let_63))) _let_62 :args (_let_26 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_27)) _let_28 :args (_let_25 false _let_12)) :args (_let_16 false _let_26 false _let_25)) :args (_let_19 false _let_17 false _let_18 false _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.multiplication X0 X1)))) :args _let_23)) _let_22 :args (_let_20 false _let_21)) :args (_let_13 false _let_19 false _let_20)))) (let ((_let_72 (not _let_14))) (let ((_let_73 (tptp.test SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_74 (= _let_73 _let_72))) (let ((_let_75 (tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_76 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_75))) (let ((_let_77 (= _let_31 _let_76))) (let ((_let_78 (not _let_73))) (let ((_let_79 (or _let_78 _let_77))) (let ((_let_80 (forall ((X0 $$unsorted) (X1 $$unsorted)) (or (not (tptp.test X0)) (= (tptp.complement X0 X1) (= X1 (tptp.c X0))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_80))) (let ((_let_83 ((tptp.complement X0 X1)))) (let ((_let_84 (not _let_77))) (let ((_let_85 (= _let_44 (tptp.addition _let_42 _let_43)))) (let ((_let_86 (= _let_48 (tptp.addition _let_42 _let_47)))) (let ((_let_87 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_45))) (let ((_let_88 (= _let_87 (tptp.multiplication (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_41) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_89 (= (tptp.addition _let_87 _let_42) (tptp.addition _let_42 _let_87)))) (let ((_let_90 (= _let_41 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_91 (= _let_42 (tptp.addition _let_42 tptp.zero)))) (let ((_let_92 (= tptp.zero (tptp.multiplication tptp.zero _let_46)))) (let ((_let_93 (= tptp.zero (tptp.multiplication tptp.zero SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_94 (= tptp.zero (tptp.multiplication tptp.zero SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_95 (= tptp.zero _let_75))) (let ((_let_96 (or _let_73 _let_95))) (let ((_let_97 (= (tptp.c (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) (tptp.multiplication _let_75 _let_75)))) (let ((_let_98 (or _let_78 _let_78 _let_97))) (let ((_let_99 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_43))) (let ((_let_100 (= _let_47 (tptp.addition _let_99 _let_87)))) (let ((_let_101 (= _let_99 (tptp.multiplication (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_102 (= _let_41 (tptp.addition _let_41 _let_41)))) (let ((_let_103 (= _let_99 (tptp.addition _let_99 tptp.zero)))) (let ((_let_104 (not _let_76))) (let ((_let_105 (not _let_49))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_51 1)) _let_57 :args (_let_105 true _let_51)))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_43 _let_42 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_27)) _let_28 :args (_let_85 false _let_12)))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_47 _let_42 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_27)) _let_28 :args (_let_86 false _let_12)))) (let ((_let_109 (_let_9))) (let ((_let_110 (ASSUME :args _let_109))) (let ((_let_111 ((tptp.multiplication A (tptp.multiplication B C))))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_41 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_111)) :args _let_109)) _let_110 :args (_let_88 false _let_9)))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_87 _let_42 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_27)) _let_28 :args (_let_89 false _let_12)))) (let ((_let_114 (= _let_13 _let_90))) (let ((_let_115 (or _let_50 _let_114))) (let ((_let_116 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_114)) :args ((or (not _let_13) _let_90 (not _let_114)))) _let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_115)) :args ((or _let_50 _let_114 (not _let_115)))) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_81 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_83)) :args _let_82))) _let_81 :args (_let_115 false _let_80)) :args (_let_114 false _let_35 false _let_115)) :args (_let_90 false _let_13 false _let_114)))) (let ((_let_117 (forall ((A $$unsorted)) (= A (tptp.addition A tptp.zero))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 (_let_117))) (let ((_let_120 ((tptp.addition A tptp.zero)))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_118 :args (_let_42 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_120)) :args _let_119)) _let_118 :args (_let_91 false _let_117)))) (let ((_let_122 (forall ((A $$unsorted)) (= tptp.zero (tptp.multiplication tptp.zero A))))) (let ((_let_123 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_124 (_let_122))) (let ((_let_125 ((not (= (tptp.multiplication tptp.zero A) tptp.zero))))) (let ((_let_126 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_123 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_125)) :args _let_124)) _let_123 :args (_let_93 false _let_122)))) (let ((_let_127 (not _let_93))) (let ((_let_128 (not _let_91))) (let ((_let_129 (not _let_90))) (let ((_let_130 (not _let_89))) (let ((_let_131 (not _let_88))) (let ((_let_132 (not _let_86))) (let ((_let_133 (not _let_85))) (let ((_let_134 (= _let_42 _let_48))) (let ((_let_135 (= _let_42 _let_44))) (let ((_let_136 (ASSUME :args (_let_91)))) (let ((_let_137 (SYMM _let_136))) (let ((_let_138 (SYMM _let_137))) (let ((_let_139 (ASSUME :args (_let_105)))) (let ((_let_140 (ASSUME :args (_let_86)))) (let ((_let_141 (SYMM _let_140))) (let ((_let_142 (APPLY_UF tptp.addition))) (let ((_let_143 (APPLY_UF tptp.multiplication))) (let ((_let_144 (REFL :args (_let_46)))) (let ((_let_145 (ASSUME :args (_let_76)))) (let ((_let_146 (APPLY_UF tptp.c))) (let ((_let_147 (ASSUME :args (_let_90)))) (let ((_let_148 (SYMM _let_147))) (let ((_let_149 (SYMM _let_148))) (let ((_let_150 (CONG _let_149 :args _let_146))) (let ((_let_151 (TRANS _let_150 (SYMM _let_145)))) (let ((_let_152 (ASSUME :args (_let_95)))) (let ((_let_153 (ASSUME :args (_let_18)))) (let ((_let_154 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_155 (TRANS (CONG _let_149 _let_154 :args _let_143) (SYMM _let_153)))) (let ((_let_156 (TRANS _let_155 (TRANS (SYMM (SYMM _let_152)) (SYMM _let_150)) _let_151))) (let ((_let_157 (SYMM _let_155))) (let ((_let_158 (ASSUME :args (_let_92)))) (let ((_let_159 (REFL :args (_let_42)))) (let ((_let_160 (ASSUME :args (_let_85)))) (let ((_let_161 (SYMM _let_160))) (let ((_let_162 (ASSUME :args (_let_93)))) (let ((_let_163 (SYMM _let_162))) (let ((_let_164 (ASSUME :args (_let_17)))) (let ((_let_165 (CONG _let_154 _let_149 :args _let_143))) (let ((_let_166 (TRANS _let_165 (SYMM _let_164)))) (let ((_let_167 (CONG _let_166 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) :args _let_143))) (let ((_let_168 (ASSUME :args (_let_88)))) (let ((_let_169 (SYMM (SYMM _let_168)))) (let ((_let_170 (ASSUME :args (_let_89)))) (let 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(forall ((A $$unsorted)) (= (tptp.multiplication A tptp.zero) tptp.zero)) _let_7 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.leq A B) (= (tptp.addition A B) B))) _let_6 _let_5 _let_4 _let_3 _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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 6.08/6.25 )
% 6.08/6.25 % SZS output end Proof for KLE027+3
% 6.08/6.25 % cvc5---1.0.5 exiting
% 6.08/6.25 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------