TSTP Solution File: KLE151+1 by cvc5---1.0.5

View Problem - Process Solution 
%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : KLE151+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 05:27:28 EDT 2023

% Result   : Theorem 25.55s 25.92s
% Output   : Proof 25.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : KLE151+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12  % Command    : do_cvc5 %s %d
% 0.13/0.33  % Computer : n005.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 29 10:55:07 EDT 2023
% 0.13/0.33  % CPUTime    : 
% 0.19/0.46  %----Proving TF0_NAR, FOF, or CNF
% 25.55/25.92  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.U1BBZTxc6G/cvc5---1.0.5_10519.p...
% 25.55/25.92  ------- get file name : TPTP file name is KLE151+1
% 25.55/25.92  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10519.smt2...
% 25.55/25.92  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.55/25.92  --- Run --no-e-matching --full-saturate-quant at 5...
% 25.55/25.92  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.55/25.92  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.55/25.92  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.55/25.92  % SZS status Theorem for KLE151+1
% 25.55/25.92  % SZS output start Proof for KLE151+1
% 25.55/25.92  (
% 25.55/25.92  (let ((_let_1 (forall ((X0 $$unsorted) (X1 $$unsorted)) (tptp.leq (tptp.multiplication X0 (tptp.strong_iteration (tptp.multiplication X1 X0))) (tptp.multiplication (tptp.strong_iteration (tptp.multiplication X0 X1)) X0))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.leq A B) (= (tptp.addition A B) B))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.leq C (tptp.addition (tptp.multiplication A C) B)) (tptp.leq C (tptp.multiplication (tptp.strong_iteration A) B)))))) (let ((_let_5 (forall ((A $$unsorted)) (let ((_let_1 (tptp.strong_iteration A))) (= _let_1 (tptp.addition (tptp.multiplication A _let_1) tptp.one)))))) (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 $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.multiplication B C)) (tptp.multiplication (tptp.multiplication A B) C))))) (let ((_let_9 (forall ((A $$unsorted)) (= (tptp.addition A A) A)))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.addition A B) (tptp.addition B A))))) (let ((_let_11 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (tptp.strong_iteration _let_11))) (let ((_let_13 (tptp.multiplication _let_11 _let_12))) (let ((_let_14 (tptp.addition _let_13 tptp.one))) (let ((_let_15 (= _let_12 _let_14))) (let ((_let_16 (tptp.addition tptp.one _let_13))) (let ((_let_17 (= _let_14 _let_16))) (let ((_let_18 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12))) (let ((_let_19 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_20 (tptp.multiplication _let_19 _let_18))) (let ((_let_21 (tptp.addition _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_22 (= _let_21 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_20)))) (let ((_let_23 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_18))) (let ((_let_24 (= _let_13 _let_23))) (let ((_let_25 (= _let_20 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_23)))) (let ((_let_26 (= _let_21 (tptp.addition _let_18 _let_21)))) (let ((_let_27 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.one))) (let ((_let_28 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_27))) (let ((_let_29 (= _let_18 (tptp.addition _let_18 _let_18)))) (let ((_let_30 (= (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_16) (tptp.addition _let_27 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_13))))) (let ((_let_31 (_let_5))) (let ((_let_32 (ASSUME :args _let_31))) (let ((_let_33 (_let_10))) (let ((_let_34 (ASSUME :args _let_33))) (let ((_let_35 ((tptp.addition A B)))) (let ((_let_36 (_let_8))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 ((tptp.multiplication (tptp.multiplication A B) C)))) (let ((_let_39 (tptp.leq _let_18 _let_21))) (let ((_let_40 (= _let_39 _let_26))) (let ((_let_41 (not _let_26))) (let ((_let_42 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.leq A B) (= B (tptp.addition A B)))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (tptp.leq _let_18 (tptp.multiplication (tptp.strong_iteration _let_19) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_45 (not _let_39))) (let ((_let_46 (or _let_45 _let_44))) (let ((_let_47 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.leq C (tptp.addition (tptp.multiplication A C) B))) (tptp.leq C (tptp.multiplication (tptp.strong_iteration A) B)))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (not _let_44))) (let ((_let_50 (_let_2))) (let ((_let_51 (ASSUME :args _let_50))) (let ((_let_52 (forall ((A $$unsorted)) (= A (tptp.multiplication A tptp.one))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (forall ((A $$unsorted)) (= A (tptp.addition A A))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (_let_6))) (let ((_let_57 (ASSUME :args _let_56))) (let ((_let_58 (and _let_15 _let_17 _let_22 _let_24 _let_25 _let_28 _let_29 _let_30))) (let ((_let_59 (APPLY_UF tptp.addition))) (let ((_let_60 (ASSUME :args (_let_22)))) (let ((_let_61 (ASSUME :args (_let_25)))) (let ((_let_62 (APPLY_UF tptp.multiplication))) (let ((_let_63 (ASSUME :args (_let_24)))) (let ((_let_64 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_65 (ASSUME :args (_let_28)))) (let ((_let_66 (CONG (SYMM _let_65) (TRANS (CONG _let_64 (SYMM (SYMM _let_63)) :args _let_62) (SYMM _let_61)) :args _let_59))) (let ((_let_67 (ASSUME :args (_let_30)))) (let ((_let_68 (SYMM _let_67))) (let ((_let_69 (ASSUME :args (_let_17)))) (let ((_let_70 (ASSUME :args (_let_15)))) (let ((_let_71 (CONG _let_64 (TRANS (SYMM (SYMM _let_70)) (SYMM (SYMM _let_69))) :args _let_62))) (let ((_let_72 (ASSUME :args (_let_29)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_58)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_60 _let_65 _let_61 _let_63 _let_67 _let_69 _let_70 _let_72) (SCOPE (TRANS _let_60 (SYMM _let_66) _let_68 (SYMM _let_71) (SYMM (SYMM _let_72)) (CONG (REFL :args (_let_18)) (TRANS _let_71 (SYMM _let_68) _let_66 (SYMM _let_60)) :args _let_59)) :args (_let_22 _let_28 _let_25 _let_24 _let_30 _let_17 _let_15 _let_29))) :args (_let_15 _let_17 _let_22 _let_24 _let_25 _let_28 _let_29 _let_30))) :args (true _let_58)) :args ((or (not _let_15) _let_26 (not _let_17) (not _let_22) (not _let_24) (not _let_25) (not _let_28) (not _let_29) (not _let_30)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.one _let_13 QUANTIFIERS_INST_CBQI_PROP)) :args _let_56)) _let_57 :args (_let_30 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_18 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_54))) _let_55 :args (_let_29 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_52))) _let_53 :args (_let_28 false _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_40)) :args ((or _let_39 _let_41 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_44 _let_45 (not _let_46)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_51) :args _let_50)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_49)) :args (or))) _let_51 :args (_let_49 true _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (_let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_18 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.leq C (tptp.multiplication (tptp.strong_iteration A) B)) true))))) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_45 true _let_44 false _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (_let_18 _let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.leq A B)))) :args (_let_42))) _let_43 :args (_let_40 false _let_42)) :args (_let_41 true _let_39 false _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_18 QUANTIFIERS_INST_E_MATCHING _let_38)) :args _let_36))) _let_37 :args (_let_25 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12 QUANTIFIERS_INST_E_MATCHING _let_38)) :args _let_36))) _let_37 :args (_let_24 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_33)) _let_34 :args (_let_22 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_13 tptp.one QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_33)) _let_34 :args (_let_17 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.strong_iteration A)))) :args _let_31)) _let_32 :args (_let_15 false _let_5)) :args (false false _let_30 false _let_29 false _let_28 true _let_26 false _let_25 false _let_24 false _let_22 false _let_17 false _let_15)) :args (_let_10 (forall ((C $$unsorted) (B $$unsorted) (A $$unsorted)) (= (tptp.addition A (tptp.addition B C)) (tptp.addition (tptp.addition A B) C))) (forall ((A $$unsorted)) (= (tptp.addition A tptp.zero) A)) _let_9 _let_8 _let_7 (forall ((A $$unsorted)) (= (tptp.multiplication tptp.one A) A)) _let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication (tptp.addition A B) C) (tptp.addition (tptp.multiplication A C) (tptp.multiplication B C)))) (forall ((A $$unsorted)) (= (tptp.multiplication tptp.zero A) tptp.zero)) (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_5 _let_4 (forall ((A $$unsorted)) (let ((_let_1 (tptp.strong_iteration A))) (= _let_1 (tptp.addition (tptp.star A) (tptp.multiplication _let_1 tptp.zero))))) _let_3 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.55/25.93  )
% 25.55/25.93  % SZS output end Proof for KLE151+1
% 25.55/25.93  % cvc5---1.0.5 exiting
% 25.55/25.93  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------