TSTP Solution File: KLE150+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : KLE150+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 05:27:27 EDT 2023
% Result : Theorem 0.70s 0.87s
% Output : Proof 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : KLE150+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n009.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 29 11:06:50 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.70/0.87 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.AnlZQ5SWLj/cvc5---1.0.5_21826.p...
% 0.70/0.87 ------- get file name : TPTP file name is KLE150+2
% 0.70/0.87 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_21826.smt2...
% 0.70/0.87 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.70/0.87 % SZS status Theorem for KLE150+2
% 0.70/0.87 % SZS output start Proof for KLE150+2
% 0.70/0.87 (
% 0.70/0.87 (let ((_let_1 (not (forall ((X0 $$unsorted)) (let ((_let_1 (tptp.multiplication X0 tptp.zero))) (let ((_let_2 (tptp.strong_iteration _let_1))) (let ((_let_3 (tptp.addition tptp.one _let_1))) (and (tptp.leq _let_2 _let_3) (tptp.leq _let_3 _let_2))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.leq A B) (= (tptp.addition A B) B))))) (let ((_let_3 (forall ((A $$unsorted)) (let ((_let_1 (tptp.strong_iteration A))) (= _let_1 (tptp.addition (tptp.star A) (tptp.multiplication _let_1 tptp.zero))))))) (let ((_let_4 (forall ((A $$unsorted)) (let ((_let_1 (tptp.strong_iteration A))) (= _let_1 (tptp.addition (tptp.multiplication A _let_1) tptp.one)))))) (let ((_let_5 (forall ((A $$unsorted)) (= (tptp.multiplication tptp.zero A) tptp.zero)))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.multiplication B C)) (tptp.multiplication (tptp.multiplication A B) C))))) (let ((_let_7 (forall ((A $$unsorted)) (= (tptp.addition A A) A)))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.addition A B) (tptp.addition B A))))) (let ((_let_9 (forall ((BOUND_VARIABLE_777 $$unsorted)) (let ((_let_1 (tptp.multiplication BOUND_VARIABLE_777 tptp.zero))) (tptp.leq (tptp.strong_iteration _let_1) (tptp.addition tptp.one _let_1)))))) (let ((_let_10 (forall ((BOUND_VARIABLE_785 $$unsorted)) (let ((_let_1 (tptp.multiplication BOUND_VARIABLE_785 tptp.zero))) (tptp.leq (tptp.addition tptp.one _let_1) (tptp.strong_iteration _let_1)))))) (let ((_let_11 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.zero))) (let ((_let_12 (tptp.addition tptp.one _let_11))) (let ((_let_13 (tptp.strong_iteration _let_11))) (let ((_let_14 (tptp.leq _let_13 _let_12))) (let ((_let_15 (= _let_12 (tptp.addition _let_13 _let_12)))) (let ((_let_16 (= _let_14 _let_15))) (let ((_let_17 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.leq A B) (= B (tptp.addition A B)))))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (_let_17))) (let ((_let_20 ((tptp.leq A B)))) (let ((_let_21 (= _let_12 (tptp.addition _let_12 _let_12)))) (let ((_let_22 (tptp.multiplication tptp.zero _let_13))) (let ((_let_23 (= tptp.zero _let_22))) (let ((_let_24 (tptp.multiplication _let_11 _let_13))) (let ((_let_25 (= _let_24 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_22)))) (let ((_let_26 (tptp.star _let_11))) (let ((_let_27 (tptp.multiplication _let_13 tptp.zero))) (let ((_let_28 (tptp.addition _let_26 _let_27))) (let ((_let_29 (= _let_28 (tptp.addition _let_27 _let_26)))) (let ((_let_30 (tptp.addition _let_24 tptp.one))) (let ((_let_31 (= _let_30 (tptp.addition tptp.one _let_24)))) (let ((_let_32 (= _let_13 _let_28))) (let ((_let_33 (= _let_13 _let_30))) (let ((_let_34 (forall ((A $$unsorted)) (= A (tptp.addition A A))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (_let_34))) (let ((_let_37 ((tptp.addition A A)))) (let ((_let_38 (forall ((A $$unsorted)) (= tptp.zero (tptp.multiplication tptp.zero A))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (_let_38))) (let ((_let_41 ((not (= (tptp.multiplication tptp.zero A) tptp.zero))))) (let ((_let_42 (_let_6))) (let ((_let_43 (ASSUME :args _let_42))) (let ((_let_44 ((tptp.multiplication (tptp.multiplication A B) C)))) (let ((_let_45 (_let_8))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 ((tptp.addition A B)))) (let ((_let_48 (_let_3))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 (_let_4))) (let ((_let_51 (ASSUME :args _let_50))) (let ((_let_52 ((tptp.strong_iteration A)))) (let ((_let_53 (and _let_33 _let_32 _let_31 _let_29 _let_25 _let_23 _let_21))) (let ((_let_54 (APPLY_UF tptp.addition))) (let ((_let_55 (REFL :args (_let_12)))) (let ((_let_56 (ASSUME :args (_let_32)))) (let ((_let_57 (SYMM _let_56))) (let ((_let_58 (ASSUME :args (_let_29)))) (let ((_let_59 (SYMM _let_58))) (let ((_let_60 (APPLY_UF tptp.multiplication))) (let ((_let_61 (ASSUME :args (_let_23)))) (let ((_let_62 (ASSUME :args (_let_25)))) (let ((_let_63 (REFL :args (tptp.one)))) (let ((_let_64 (CONG _let_63 (TRANS (SYMM (SYMM _let_62)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (SYMM _let_61) :args _let_60)) :args _let_54))) (let ((_let_65 (ASSUME :args (_let_31)))) (let ((_let_66 (SYMM _let_65))) (let ((_let_67 (TRANS (SYMM _let_66) _let_64))) (let ((_let_68 (ASSUME :args (_let_33)))) (let ((_let_69 (ASSUME :args (_let_21)))) (let ((_let_70 (or))) (let ((_let_71 (not _let_9))) (let ((_let_72 (_let_71))) (let ((_let_73 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.zero))) (let ((_let_74 (tptp.strong_iteration _let_73))) (let ((_let_75 (tptp.addition tptp.one _let_73))) (let ((_let_76 (tptp.leq _let_75 _let_74))) (let ((_let_77 (= _let_74 (tptp.addition _let_75 _let_74)))) (let ((_let_78 (= _let_76 _let_77))) (let ((_let_79 (= _let_74 (tptp.addition _let_74 _let_74)))) (let ((_let_80 (tptp.multiplication tptp.zero _let_74))) (let ((_let_81 (= tptp.zero _let_80))) (let ((_let_82 (tptp.multiplication _let_73 _let_74))) (let ((_let_83 (= _let_82 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_80)))) (let ((_let_84 (tptp.addition _let_82 tptp.one))) (let ((_let_85 (= _let_84 (tptp.addition tptp.one _let_82)))) (let ((_let_86 (= _let_74 _let_84))) (let ((_let_87 (and _let_86 _let_85 _let_83 _let_81 _let_79))) (let ((_let_88 (ASSUME :args (_let_81)))) (let ((_let_89 (ASSUME :args (_let_83)))) (let ((_let_90 (ASSUME :args (_let_85)))) (let ((_let_91 (ASSUME :args (_let_86)))) (let ((_let_92 (ASSUME :args (_let_79)))) (let ((_let_93 (not _let_10))) (let ((_let_94 (_let_93))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_94)) :args _let_94)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_10))) (REFL :args ((not _let_76))) :args _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_78)) :args ((or _let_76 (not _let_77) (not _let_78)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_87)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_88 _let_89 _let_90 _let_91 _let_92) (SCOPE (TRANS (SYMM (SYMM _let_92)) (CONG (TRANS (SYMM (SYMM _let_91)) (SYMM (SYMM _let_90)) (CONG _let_63 (TRANS (SYMM (SYMM _let_89)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (SYMM _let_88) :args _let_60)) :args _let_54)) (REFL :args (_let_74)) :args _let_54)) :args (_let_81 _let_83 _let_85 _let_86 _let_79))) :args (_let_86 _let_85 _let_83 _let_81 _let_79))) :args (true _let_87)) :args ((or _let_77 (not _let_86) (not _let_85) (not _let_83) (not _let_81) (not _let_79)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (_let_73 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_52)) :args _let_50)) _let_51 :args (_let_86 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_82 tptp.one QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_47)) :args _let_45)) _let_46 :args (_let_85 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.zero _let_74 QUANTIFIERS_INST_E_MATCHING _let_44)) :args _let_42))) _let_43 :args (_let_83 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_74 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_41)) :args _let_40)) _let_39 :args (_let_81 false _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (_let_74 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_35 :args (_let_79 false _let_34)) :args (_let_77 false _let_86 false _let_85 false _let_83 false _let_81 false _let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (_let_75 _let_74 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_20)) :args _let_19)) _let_18 :args (_let_78 false _let_17)) :args (_let_76 false _let_77 false _let_78)) :args (_let_10 false _let_76)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_72)) :args _let_72)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_9))) (REFL :args ((not _let_14))) :args _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_16)) :args ((or _let_14 (not _let_15) (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_53)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_56 _let_58 _let_61 _let_62 _let_65 _let_68 _let_69) (SCOPE (TRANS (SYMM (SYMM _let_69)) (CONG (TRANS (SYMM _let_64) _let_66 (SYMM _let_68)) (SYMM _let_67) :args _let_54) (CONG (SYMM (TRANS _let_59 _let_57)) _let_67 :args _let_54) (CONG _let_59 _let_55 :args _let_54) (CONG _let_57 _let_55 :args _let_54)) :args (_let_32 _let_29 _let_23 _let_25 _let_31 _let_33 _let_21))) :args (_let_33 _let_32 _let_31 _let_29 _let_25 _let_23 _let_21))) :args (true _let_53)) :args ((or _let_15 (not _let_33) (not _let_32) (not _let_31) (not _let_29) (not _let_25) (not _let_23) (not _let_21)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (_let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_52)) :args _let_50)) _let_51 :args (_let_33 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.strong_iteration A)))) :args _let_48)) _let_49 :args (_let_32 false _let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_24 tptp.one QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_47)) :args _let_45)) _let_46 :args (_let_31 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_26 _let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_47)) :args _let_45)) _let_46 :args (_let_29 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.zero _let_13 QUANTIFIERS_INST_E_MATCHING _let_44)) :args _let_42))) _let_43 :args (_let_25 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_41)) :args _let_40)) _let_39 :args (_let_23 false _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (_let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_35 :args (_let_21 false _let_34)) :args (_let_15 false _let_33 false _let_32 false _let_31 false _let_29 false _let_25 false _let_23 false _let_21)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (_let_13 _let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_20)) :args _let_19)) _let_18 :args (_let_16 false _let_17)) :args (_let_14 false _let_15 false _let_16)) :args (_let_9 false _let_14)) :args (false false _let_10 false _let_9)) :args (_let_8 (forall ((C $$unsorted) (B $$unsorted) (A $$unsorted)) (= (tptp.addition A (tptp.addition B C)) (tptp.addition (tptp.addition A B) C))) (forall ((A $$unsorted)) (= (tptp.addition A tptp.zero) A)) _let_7 _let_6 (forall ((A $$unsorted)) (= (tptp.multiplication A tptp.one) A)) (forall ((A $$unsorted)) (= (tptp.multiplication tptp.one A) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.addition B C)) (tptp.addition (tptp.multiplication A B) (tptp.multiplication A C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication (tptp.addition A B) C) (tptp.addition (tptp.multiplication A C) (tptp.multiplication B C)))) _let_5 (forall ((A $$unsorted)) (let ((_let_1 (tptp.star A))) (= (tptp.addition tptp.one (tptp.multiplication A _let_1)) _let_1))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.star A))) (= (tptp.addition tptp.one (tptp.multiplication _let_1 A)) _let_1))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.leq (tptp.addition (tptp.multiplication A C) B) C) (tptp.leq (tptp.multiplication (tptp.star A) B) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.leq (tptp.addition (tptp.multiplication C A) B) C) (tptp.leq (tptp.multiplication B (tptp.star A)) C))) _let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.leq C (tptp.addition (tptp.multiplication A C) B)) (tptp.leq C (tptp.multiplication (tptp.strong_iteration A) B)))) _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.70/0.87 )
% 0.70/0.87 % SZS output end Proof for KLE150+2
% 0.70/0.87 % cvc5---1.0.5 exiting
% 0.70/0.87 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------