%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : KLE026+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n028.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 05:26:56 EDT 2023

% Result   : Theorem 13.11s 13.36s
% Output   : Proof 13.11s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : KLE026+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n028.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 12:35:41 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 13.11/13.36  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.ViFOkR2SJi/cvc5---1.0.5_26545.p...
% 13.11/13.36  ------- get file name : TPTP file name is KLE026+1
% 13.11/13.36  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_26545.smt2...
% 13.11/13.36  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 13.11/13.36  --- Run --no-e-matching --full-saturate-quant at 5...
% 13.11/13.36  % SZS status Theorem for KLE026+1
% 13.11/13.36  % SZS output start Proof for KLE026+1
% 13.11/13.36  (
% 13.11/13.36  (let ((_let_1 (not (forall ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (tptp.multiplication X1 X0))) (=> (and (tptp.test X1) (tptp.test X2)) (=> (= _let_1 (tptp.multiplication _let_1 X2)) (tptp.leq _let_1 (tptp.multiplication X0 X2))))))))) (let ((_let_2 (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (tptp.complement X1 X0) (and (= (tptp.multiplication X0 X1) tptp.zero) (= (tptp.multiplication X1 X0) tptp.zero) (= (tptp.addition X0 X1) tptp.one)))))) (let ((_let_3 (forall ((X0 $$unsorted)) (= (tptp.test X0) (exists ((X1 $$unsorted)) (tptp.complement X1 X0)))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.leq A B) (= (tptp.addition A B) B))))) (let ((_let_5 (forall ((A $$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 $$unsorted)) (= (tptp.multiplication tptp.one A) A)))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.multiplication B C)) (tptp.multiplication (tptp.multiplication A B) C))))) (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.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (tptp.multiplication _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_13 (= _let_11 _let_12))) (let ((_let_14 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_14))) (let ((_let_16 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (tptp.multiplication tptp.one _let_16))) (let ((_let_18 (= _let_16 _let_17))) (let ((_let_19 (= _let_16 (tptp.addition _let_11 _let_16)))) (let ((_let_20 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.one))) (let ((_let_21 (= _let_20 (tptp.addition tptp.one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_22 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16))) (let ((_let_23 (= (tptp.multiplication _let_20 _let_16) (tptp.addition _let_22 _let_17)))) (let ((_let_24 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_25 (= (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 _let_14) (tptp.addition _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_26 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26))) (let ((_let_27 (= _let_26 _let_24))) (let ((_let_28 (= tptp.one _let_26))) (let ((_let_29 (= _let_12 _let_22))) (let ((_let_30 (tptp.leq _let_11 _let_16))) (let ((_let_31 (not _let_13))) (let ((_let_32 (tptp.test SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 (not (tptp.test SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_31 _let_30))) (let ((_let_35 (forall ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (tptp.multiplication X1 X0))) (or (not (tptp.test X1)) (not (tptp.test X2)) (not (= _let_1 (tptp.multiplication _let_1 X2))) (tptp.leq _let_1 (tptp.multiplication X0 X2))))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (or))) (let ((_let_39 (not _let_35))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_37) :args (_let_39))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_35))) (REFL :args (_let_36)) :args _let_38)) _let_37 :args (_let_36 true _let_35)))) (let ((_let_41 (REFL :args (_let_34)))) (let ((_let_42 (forall ((A $$unsorted)) (= A (tptp.addition A A))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_ENUM))) (let ((_let_45 (forall ((A $$unsorted)) (= A (tptp.multiplication tptp.one A))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (= _let_30 _let_19))) (let ((_let_48 (not _let_19))) (let ((_let_49 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.leq A B) (= B (tptp.addition A B)))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (_let_10))) (let ((_let_52 (ASSUME :args _let_51))) (let ((_let_53 (_let_5))) (let ((_let_54 (ASSUME :args _let_53))) (let ((_let_55 (_let_9))) (let ((_let_56 (ASSUME :args _let_55))) (let ((_let_57 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 QUANTIFIERS_INST_ENUM))) (let ((_let_58 (and (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26)) (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_28))) (let ((_let_59 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_60 (= _let_59 _let_58))) (let ((_let_61 (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (tptp.complement X1 X0) (and (= tptp.zero (tptp.multiplication X0 X1)) (= tptp.zero (tptp.multiplication X1 X0)) (= tptp.one (tptp.addition X0 X1))))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (forall ((X1 $$unsorted)) (not (tptp.complement X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_64 (not _let_63))) (let ((_let_65 (= _let_32 _let_64))) (let ((_let_66 (forall ((X0 $$unsorted)) (= (tptp.test X0) (not (forall ((X1 $$unsorted)) (not (tptp.complement X1 X0)))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (not _let_59))) (let ((_let_69 (_let_64))) (let ((_let_70 (_let_7))) (let ((_let_71 (ASSUME :args _let_70))) (let ((_let_72 (and _let_13 _let_15 _let_18 _let_21 _let_23 _let_28 _let_25 _let_27 _let_29))) (let ((_let_73 (APPLY_UF tptp.addition))) (let ((_let_74 (ASSUME :args (_let_18)))) (let ((_let_75 (ASSUME :args (_let_13)))) (let ((_let_76 (ASSUME :args (_let_29)))) (let ((_let_77 (ASSUME :args (_let_23)))) (let ((_let_78 (ASSUME :args (_let_21)))) (let ((_let_79 (ASSUME :args (_let_28)))) (let ((_let_80 (ASSUME :args (_let_27)))) (let ((_let_81 (ASSUME :args (_let_25)))) (let ((_let_82 (ASSUME :args (_let_15)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_72)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_75 _let_76 _let_74 _let_77 _let_78 _let_79 _let_80 _let_81 _let_82) (SCOPE (TRANS _let_74 (CONG (TRANS _let_79 _let_80 (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26)) (SYMM (SYMM _let_82)) :args _let_73) (SYMM (SYMM _let_81)) (CONG (TRANS (SYMM _let_80) (SYMM _let_79)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) :args _let_73) (SYMM _let_78)) (REFL :args (_let_16)) :args (APPLY_UF tptp.multiplication)) (SYMM (SYMM _let_77)) (CONG (TRANS (SYMM _let_76) (SYMM _let_75)) (SYMM _let_74) :args _let_73)) :args (_let_13 _let_29 _let_18 _let_23 _let_21 _let_28 _let_27 _let_25 _let_15))) :args (_let_13 _let_15 _let_18 _let_21 _let_23 _let_28 _let_25 _let_27 _let_29))) :args (true _let_72)) :args ((or _let_31 (not _let_15) (not _let_18) _let_19 (not _let_21) (not _let_23) (not _let_28) (not _let_25) (not _let_27) (not _let_29)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_PROP)) :args _let_70))) _let_71 :args (_let_29 false _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 2)) :args ((or _let_28 (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_60)) :args ((or _let_68 _let_58 (not _let_60)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_69)) :args _let_69) (REWRITE :args ((=> _let_64 (not _let_68)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) (REFL :args (_let_59)) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_65)) :args ((or _let_33 _let_64 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_38)) :args ((or _let_32 _let_34))) _let_40 :args (_let_32 true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args _let_44) :args (_let_66))) _let_67 :args (_let_65 false _let_66)) :args (_let_64 false _let_32 false _let_65)) :args (_let_59 true _let_63)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args _let_57) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_58 false _let_59 false _let_60)) :args (_let_28 false _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args _let_57) :args _let_51)) _let_52 :args (_let_27 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 QUANTIFIERS_INST_ENUM)) :args _let_55)) _let_56 :args (_let_25 false _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.one _let_16 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_53)) _let_54 :args (_let_23 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.one QUANTIFIERS_INST_ENUM)) :args _let_51)) _let_52 :args (_let_21 false _let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_47)) :args ((or _let_30 _let_48 (not _let_47)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 3)) _let_40 :args ((not _let_30) true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_11 _let_16 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_49))) _let_50 :args (_let_47 false _let_49)) :args (_let_48 true _let_30 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_16 QUANTIFIERS_INST_ENUM)) :args (_let_45))) _let_46 :args (_let_18 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args _let_44) :args (_let_42))) _let_43 :args (_let_15 false _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 2)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_13))) :args _let_38)) :args ((or _let_13 _let_34))) _let_40 :args (_let_13 true _let_34)) :args (false false _let_29 false _let_28 false _let_27 false _let_25 false _let_23 false _let_21 true _let_19 false _let_18 false _let_15 false _let_13)) :args (_let_10 _let_9 (forall ((A $$unsorted)) (= (tptp.addition A tptp.zero) A)) _let_8 _let_7 (forall ((A $$unsorted)) (= (tptp.multiplication A tptp.one) A)) _let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.addition B C)) (tptp.addition (tptp.multiplication A B) (tptp.multiplication A C)))) _let_5 (forall ((A $$unsorted)) (= (tptp.multiplication A tptp.zero) tptp.zero)) (forall ((A $$unsorted)) (= (tptp.multiplication tptp.zero A) tptp.zero)) _let_4 _let_3 _let_2 (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (tptp.test X0) (= (= (tptp.c X0) X1) (tptp.complement X0 X1)))) (forall ((X0 $$unsorted)) (=> (not (tptp.test X0)) (= (tptp.c X0) tptp.zero))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 13.11/13.37  )
% 13.11/13.37  % SZS output end Proof for KLE026+1
% 13.11/13.37  % cvc5---1.0.5 exiting
% 13.22/13.37  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------