TSTP Solution File: KLE027+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : KLE027+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 1.65s 1.86s
% Output : Proof 1.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : KLE027+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n021.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 11:20:29 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.49 %----Proving TF0_NAR, FOF, or CNF
% 1.65/1.86 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.h5hGez5fR2/cvc5---1.0.5_3165.p...
% 1.65/1.86 ------- get file name : TPTP file name is KLE027+2
% 1.65/1.86 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_3165.smt2...
% 1.65/1.86 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.65/1.86 % SZS status Theorem for KLE027+2
% 1.65/1.86 % SZS output start Proof for KLE027+2
% 1.65/1.86 (
% 1.65/1.86 (let ((_let_1 (not (forall ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted) (X4 $$unsorted)) (let ((_let_1 (tptp.c X3))) (let ((_let_2 (tptp.multiplication _let_1 X2))) (let ((_let_3 (tptp.multiplication X3 X0))) (let ((_let_4 (tptp.addition (tptp.multiplication X3 (tptp.addition _let_3 (tptp.multiplication _let_1 X1))) _let_2))) (let ((_let_5 (tptp.addition _let_3 _let_2))) (=> (and (tptp.test X3) (tptp.test X4)) (and (tptp.leq _let_4 _let_5) (tptp.leq _let_5 _let_4)))))))))))) (let ((_let_2 (forall ((X0 $$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 $$unsorted)) (= (tptp.leq A B) (= (tptp.addition A B) B))))) (let ((_let_6 (forall ((A $$unsorted)) (= (tptp.multiplication tptp.zero A) tptp.zero)))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication (tptp.addition A B) C) (tptp.addition (tptp.multiplication A C) (tptp.multiplication B C)))))) (let ((_let_8 (forall ((A $$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 $$unsorted)) (= (tptp.multiplication tptp.one A) A)))) (let ((_let_10 (forall ((A $$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 $$unsorted)) (= (tptp.addition A B) (tptp.addition B A))))) (let ((_let_15 (tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_16 (tptp.multiplication _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_17 (tptp.multiplication _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_18 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_19 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.addition _let_18 _let_17)))) (let ((_let_20 (tptp.addition _let_19 _let_16))) (let ((_let_21 (tptp.addition _let_18 _let_16))) (let ((_let_22 (tptp.leq _let_21 _let_20))) (let ((_let_23 (tptp.leq _let_20 _let_21))) (let ((_let_24 (and _let_23 _let_22))) (let ((_let_25 (tptp.test SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_24))) (let ((_let_28 (forall ((X3 $$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))) (let ((_let_4 (tptp.addition (tptp.multiplication X3 (tptp.addition _let_3 (tptp.multiplication _let_1 X1))) _let_2))) (let ((_let_5 (tptp.addition _let_3 _let_2))) (or (not (tptp.test X3)) (and (tptp.leq _let_4 _let_5) (tptp.leq _let_5 _let_4))))))))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (or))) (let ((_let_31 (not _let_28))) (let ((_let_32 (_let_31))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_32)) :args _let_32)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_28))) (REFL :args (_let_29)) :args _let_30)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (0)) :args (_let_29 true _let_28)))) (let ((_let_34 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_35 (= _let_34 (tptp.addition _let_34 tptp.zero)))) (let ((_let_36 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_37 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_38 (= (tptp.multiplication _let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.addition _let_34 _let_36)))) (let ((_let_39 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_40 (= (tptp.addition _let_34 _let_34) (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_39)))) (let ((_let_41 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.multiplication tptp.one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_42 (= _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_43 (tptp.leq _let_20 _let_20))) (let ((_let_44 (= tptp.zero (tptp.multiplication tptp.zero SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_45 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.multiplication tptp.one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_46 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_39))) (let ((_let_47 (= _let_16 (tptp.addition _let_16 tptp.zero)))) (let ((_let_48 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_17))) (let ((_let_49 (tptp.addition _let_48 _let_16))) (let ((_let_50 (= _let_49 (tptp.addition _let_16 _let_48)))) (let ((_let_51 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_18))) (let ((_let_52 (tptp.addition _let_51 _let_49))) (let ((_let_53 (= _let_52 (tptp.addition _let_49 _let_51)))) (let ((_let_54 (= tptp.one _let_37))) (let ((_let_55 (= tptp.zero _let_36))) (let ((_let_56 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_57 (= _let_51 (tptp.multiplication _let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_58 (= _let_48 (tptp.multiplication (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_15) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_59 (tptp.addition _let_51 _let_48))) (let ((_let_60 (= _let_52 (tptp.addition _let_59 _let_16)))) (let ((_let_61 (= _let_19 _let_59))) (let ((_let_62 (= _let_21 (tptp.addition _let_16 _let_18)))) (let ((_let_63 (forall ((A $$unsorted)) (= A (tptp.addition A tptp.zero))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (_let_63))) (let ((_let_66 ((tptp.addition A tptp.zero)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_34 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_66)) :args _let_65)) _let_64 :args (_let_35 false _let_63)))) (let ((_let_68 (_let_7))) (let ((_let_69 (ASSUME :args _let_68))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((tptp.addition (tptp.multiplication A C) (tptp.multiplication B C))))) :args _let_68)) _let_69 :args (_let_38 false _let_7)))) (let ((_let_71 (_let_8))) (let ((_let_72 (ASSUME :args _let_71))) (let ((_let_73 ((tptp.multiplication A (tptp.addition B C))))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_73)) :args _let_71))) _let_72 :args (_let_40 false _let_8)))) (let ((_let_75 (forall ((A $$unsorted)) (= A (tptp.multiplication tptp.one A))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (_let_75))) (let ((_let_78 ((tptp.multiplication tptp.one A)))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_78)) :args _let_77)) _let_76 :args (_let_41 false _let_75)))) (let ((_let_80 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_81 (= _let_80 _let_42))) (let ((_let_82 (or _let_26 _let_81))) (let ((_let_83 (forall ((X0 $$unsorted) (X1 $$unsorted)) (or (not (tptp.test X0)) (= (tptp.complement X0 X1) (= X1 (tptp.c X0))))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG (REFL :args (_let_27)) (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_30)) :args ((or _let_25 _let_27))) _let_33 :args (_let_25 true _let_27)))) (let ((_let_86 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_87 (= tptp.one _let_86))) (let ((_let_88 (and _let_55 _let_56 _let_87))) (let ((_let_89 (= _let_80 _let_88))) (let ((_let_90 (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (tptp.complement X1 X0) (and (= tptp.zero (tptp.multiplication X0 X1)) (= tptp.zero (tptp.multiplication X1 X0)) (= tptp.one (tptp.addition X0 X1))))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (_let_90))) (let ((_let_93 (= _let_37 _let_86))) (let ((_let_94 (_let_14))) (let ((_let_95 (ASSUME :args _let_94))) (let ((_let_96 ((tptp.addition A B)))) (let ((_let_97 (and _let_56 _let_55 _let_54))) (let ((_let_98 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_99 (= _let_98 _let_97))) (let ((_let_100 (forall ((X1 $$unsorted)) (not (tptp.complement X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_101 (not _let_100))) (let ((_let_102 (= _let_25 _let_101))) (let ((_let_103 (forall ((X0 $$unsorted)) (= (tptp.test X0) (not (forall ((X1 $$unsorted)) (not (tptp.complement X1 X0)))))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (not _let_98))) (let ((_let_106 (_let_101))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_99)) :args ((or _let_105 _let_97 (not _let_99)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_106)) :args _let_106) (REWRITE :args ((=> _let_101 (not _let_105)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_101) _let_100))) (REFL :args (_let_98)) :args _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_102)) :args ((or _let_26 _let_101 (not _let_102)))) _let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.test X0)))) :args (_let_103))) _let_104 :args (_let_102 false _let_103)) :args (_let_101 false _let_25 false _let_102)) :args (_let_98 true _let_100)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complement X1 X0)))) :args _let_92)) _let_91 :args (_let_99 false _let_90)) :args (_let_97 false _let_98 false _let_99)))) (let ((_let_108 (not _let_97))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_97 2)) :args ((or _let_54 _let_108))) _let_107 :args (_let_54 false _let_97)))) (let ((_let_110 (not _let_54))) (let ((_let_111 (and _let_54 _let_93))) (let ((_let_112 (ASSUME :args (_let_93)))) (let ((_let_113 (ASSUME :args (_let_54)))) (let ((_let_114 (SYMM (SYMM _let_113)))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_97 1)) :args ((or _let_55 _let_108))) _let_107 :args (_let_55 false _let_97)))) (let ((_let_116 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_97 0)) :args ((or _let_56 _let_108))) _let_107 :args (_let_56 false _let_97)))) (let ((_let_117 (not _let_55))) (let ((_let_118 (not _let_56))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_81)) :args ((or (not _let_80) _let_42 (not _let_81)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_89)) :args ((or _let_80 (not _let_88) (not _let_89)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_88)) :args ((or _let_118 _let_117 _let_88 (not _let_87)))) _let_116 _let_115 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_111)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_112 _let_113) (SCOPE (TRANS _let_114 (SYMM (SYMM _let_112))) :args (_let_93 _let_54))) :args (_let_54 _let_93))) :args (true _let_111)) :args ((or _let_110 _let_87 (not _let_93)))) _let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_96)) :args _let_94)) _let_95 :args (_let_93 false _let_14)) :args (_let_87 false _let_54 false _let_93)) :args (_let_88 false _let_56 false _let_55 false _let_87)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.multiplication X0 X1)))) :args _let_92)) _let_91 :args (_let_89 false _let_90)) :args (_let_80 false _let_88 false _let_89)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_26 _let_81 (not _let_82)))) _let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complement X0 X1)))) :args (_let_83)))) _let_84 :args (_let_82 false _let_83)) :args (_let_81 false _let_25 false _let_82)) :args (_let_42 false _let_80 false _let_81)))) (let ((_let_120 (= _let_20 (tptp.addition _let_20 _let_20)))) (let ((_let_121 (= _let_120 _let_43))) (let ((_let_122 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.leq A B) (= B (tptp.addition A B)))))) (let ((_let_123 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_124 (forall ((A $$unsorted)) (= A (tptp.addition A A))))) (let ((_let_125 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_126 (_let_124))) (let ((_let_127 ((tptp.addition A A)))) (let ((_let_128 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_121)) :args ((or (not _let_120) _let_43 (not _let_121)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_125 :args (_let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_127)) :args _let_126)) _let_125 :args (_let_120 false _let_124)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_123 :args (_let_20 _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.addition A B)))) :args (_let_122)))) _let_123 :args (_let_121 false _let_122)) :args (_let_43 false _let_120 false _let_121)))) (let ((_let_129 (forall ((A $$unsorted)) (= tptp.zero (tptp.multiplication tptp.zero A))))) (let ((_let_130 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_131 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_130 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.multiplication tptp.zero A) tptp.zero))))) :args (_let_129))) _let_130 :args (_let_44 false _let_129)))) (let ((_let_132 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_78)) :args _let_77)) _let_76 :args (_let_45 false _let_75)))) (let ((_let_133 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_125 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_127)) :args _let_126)) _let_125 :args (_let_46 false _let_124)))) (let ((_let_134 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_66)) :args _let_65)) _let_64 :args (_let_47 false _let_63)))) (let ((_let_135 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (_let_48 _let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_96)) :args _let_94)) _let_95 :args (_let_50 false _let_14)))) (let ((_let_136 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (_let_51 _let_49 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_96)) :args _let_94)) _let_95 :args (_let_53 false _let_14)))) (let ((_let_137 (_let_10))) (let ((_let_138 (ASSUME :args _let_137))) (let ((_let_139 ((tptp.multiplication A (tptp.multiplication B C))))) (let ((_let_140 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_138 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_139)) :args _let_137)) _let_138 :args (_let_57 false _let_10)))) (let ((_let_141 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_138 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_139)) :args _let_137)) _let_138 :args (_let_58 false _let_10)))) (let ((_let_142 (_let_13))) (let ((_let_143 (ASSUME :args _let_142))) (let ((_let_144 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_143 :args (_let_16 _let_48 _let_51 QUANTIFIERS_INST_E_MATCHING ((tptp.addition (tptp.addition A B) C)))) :args _let_142)) _let_143 :args (_let_60 false _let_13)))) (let ((_let_145 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_18 _let_17 QUANTIFIERS_INST_E_MATCHING _let_73)) :args _let_71)) _let_72 :args (_let_61 false _let_8)))) (let ((_let_146 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (_let_18 _let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_96)) :args _let_94)) _let_95 :args (_let_62 false _let_14)))) (let ((_let_147 (not _let_35))) (let ((_let_148 (not _let_38))) (let ((_let_149 (not _let_40))) (let ((_let_150 (not _let_41))) (let ((_let_151 (not _let_42))) (let ((_let_152 (not _let_43))) (let ((_let_153 (not _let_44))) (let ((_let_154 (not _let_45))) (let ((_let_155 (not _let_46))) (let ((_let_156 (not _let_47))) (let ((_let_157 (not _let_50))) (let ((_let_158 (not _let_53))) (let ((_let_159 (not _let_57))) (let ((_let_160 (not _let_58))) (let ((_let_161 (not _let_60))) (let ((_let_162 (not _let_61))) (let ((_let_163 (not _let_62))) (let ((_let_164 (and _let_62 _let_61 _let_60 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_50 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_38 _let_35))) (let ((_let_165 (true _let_164))) (let ((_let_166 (_let_62 _let_61 _let_60 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_50 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_38 _let_35))) (let ((_let_167 (_let_43 _let_61 _let_60 _let_53 _let_50 _let_58 _let_42 _let_56 _let_44 _let_47 _let_57 _let_41 _let_46 _let_40 _let_35 _let_55 _let_38 _let_54 _let_45 _let_62))) (let ((_let_168 (ASSUME :args (_let_43)))) (let ((_let_169 (TRUE_INTRO _let_168))) (let ((_let_170 (APPLY_UF tptp.leq))) (let ((_let_171 (APPLY_UF tptp.addition))) (let ((_let_172 (REFL :args (_let_16)))) (let ((_let_173 (ASSUME :args (_let_61)))) (let ((_let_174 (CONG (SYMM _let_173) _let_172 :args _let_171))) (let ((_let_175 (ASSUME :args (_let_60)))) (let ((_let_176 (SYMM (SYMM _let_175)))) (let ((_let_177 (ASSUME :args (_let_53)))) (let ((_let_178 (SYMM _let_177))) (let ((_let_179 (ASSUME :args (_let_57)))) (let ((_let_180 (APPLY_UF tptp.multiplication))) (let ((_let_181 (ASSUME :args (_let_41)))) (let ((_let_182 (REFL :args (_let_34)))) (let ((_let_183 (ASSUME :args (_let_46)))) (let ((_let_184 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_185 (CONG _let_184 (SYMM _let_183) :args _let_180))) (let ((_let_186 (ASSUME :args (_let_40)))) (let ((_let_187 (SYMM _let_186))) (let ((_let_188 (ASSUME :args (_let_35)))) (let ((_let_189 (ASSUME :args (_let_55)))) (let ((_let_190 (ASSUME :args (_let_38)))) (let ((_let_191 (ASSUME :args (_let_45)))) (let ((_let_192 (ASSUME :args (_let_50)))) (let ((_let_193 (ASSUME :args (_let_58)))) (let ((_let_194 (ASSUME :args (_let_42)))) (let ((_let_195 (ASSUME :args (_let_56)))) (let ((_let_196 (ASSUME :args (_let_44)))) (let ((_let_197 (ASSUME :args (_let_47)))) (let ((_let_198 (CONG (TRANS (SYMM (SYMM _let_197)) (CONG _let_172 (TRANS (SYMM (SYMM _let_196)) (CONG (TRANS (SYMM (SYMM _let_195)) (CONG _let_184 (SYMM _let_194) :args _let_180)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) :args _let_180) (SYMM _let_193)) :args _let_171) (SYMM _let_192)) (TRANS (CONG (TRANS (TRANS (SYMM (SYMM _let_191)) (CONG _let_114 _let_184 :args _let_180) (SYMM (SYMM _let_190)) (CONG _let_182 (SYMM _let_189) :args _let_171) (SYMM _let_188) (SYMM _let_185) _let_187) (TRANS (SYMM _let_187) _let_185)) _let_181 :args _let_180) (CONG _let_182 (SYMM _let_181) :args _let_180) (SYMM _let_179)) :args _let_171))) (let ((_let_199 (ASSUME :args (_let_62)))) (let ((_let_200 (SYMM (SYMM _let_199)))) (let ((_let_201 (REFL :args (_let_20)))) (let ((_let_202 (AND_INTRO _let_168 _let_173 _let_175 _let_177 _let_192 _let_193 _let_194 _let_195 _let_196 _let_197 _let_179 _let_181 _let_183 _let_186 _let_188 _let_189 _let_190 _let_113 _let_191 _let_199))) (let ((_let_203 (CNF_AND_NEG :args (_let_164)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION _let_203 (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_202 (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS _let_200 (TRANS _let_198 _let_178 _let_176 _let_174)) _let_201 :args _let_170) _let_169)) :args _let_167)) :args _let_166)) :args _let_165) :args ((or _let_22 _let_163 _let_162 _let_161 _let_160 _let_159 _let_118 _let_117 _let_110 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147))) _let_146 _let_145 _let_144 _let_141 _let_140 _let_116 _let_115 _let_109 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_128 _let_119 _let_79 _let_74 _let_70 _let_67 :args (_let_22 false _let_62 false _let_61 false _let_60 false _let_58 false _let_57 false _let_56 false _let_55 false _let_54 false _let_53 false _let_50 false _let_47 false _let_46 false _let_45 false _let_44 false _let_43 false _let_42 false _let_41 false _let_40 false _let_38 false _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION _let_203 (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_202 (SCOPE (TRUE_ELIM (TRANS (CONG _let_201 (TRANS _let_200 _let_198 _let_178 _let_176 _let_174) :args _let_170) _let_169)) :args _let_167)) :args _let_166)) :args _let_165) :args ((or _let_23 _let_163 _let_162 _let_161 _let_160 _let_159 _let_118 _let_117 _let_110 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147))) _let_146 _let_145 _let_144 _let_141 _let_140 _let_116 _let_115 _let_109 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_128 _let_119 _let_79 _let_74 _let_70 _let_67 :args (_let_23 false _let_62 false _let_61 false _let_60 false _let_58 false _let_57 false _let_56 false _let_55 false _let_54 false _let_53 false _let_50 false _let_47 false _let_46 false _let_45 false _let_44 false _let_43 false _let_42 false _let_41 false _let_40 false _let_38 false _let_35)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_27 1)) _let_33 :args ((not _let_24) true _let_27)) :args (false false _let_22 false _let_23 true _let_24)) :args (_let_14 _let_13 _let_12 _let_11 _let_10 (forall ((A $$unsorted)) (= (tptp.multiplication A tptp.one) A)) _let_9 _let_8 _let_7 (forall ((A $$unsorted)) (= (tptp.multiplication A tptp.zero) tptp.zero)) _let_6 _let_5 _let_4 _let_3 _let_2 (forall ((X0 $$unsorted)) (=> (not (tptp.test X0)) (= (tptp.c X0) tptp.zero))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.65/1.88 )
% 1.65/1.88 % SZS output end Proof for KLE027+2
% 1.65/1.88 % cvc5---1.0.5 exiting
% 1.65/1.88 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------