%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : KLE021+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n025.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 05:26:53 EDT 2023

% Result   : Theorem 0.22s 0.59s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : KLE021+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n025.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 12:36:10 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.22/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.59  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.mHX6EDRjvw/cvc5---1.0.5_12561.p...
% 0.22/0.59  ------- get file name : TPTP file name is KLE021+1
% 0.22/0.59  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_12561.smt2...
% 0.22/0.59  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.59  % SZS status Theorem for KLE021+1
% 0.22/0.59  % SZS output start Proof for KLE021+1
% 0.22/0.59  (
% 0.22/0.59  (let ((_let_1 (not (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (tptp.test X1) (= X0 (tptp.addition (tptp.multiplication X1 X0) (tptp.multiplication (tptp.c X1) X0)))))))) (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) (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)) (= (tptp.addition A B) (tptp.addition B A))))) (let ((_let_8 (tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_9 (tptp.addition (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.multiplication _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_10 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_11 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_8))) (let ((_let_12 (= _let_9 (tptp.multiplication _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_13 (= _let_11 (tptp.addition _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_14 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_15 (= tptp.one _let_14))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.multiplication tptp.one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_17 (= _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_18 (tptp.test SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 _let_10))) (let ((_let_21 (forall ((X0 $$unsorted) (X1 $$unsorted)) (or (not (tptp.test X1)) (= X0 (tptp.addition (tptp.multiplication X1 X0) (tptp.multiplication (tptp.c X1) X0))))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (or))) (let ((_let_25 (not _let_21))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_23) :args (_let_25))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_21))) (REFL :args (_let_22)) :args _let_24)) _let_23 :args (_let_22 true _let_21)))) (let ((_let_27 (_let_5))) (let ((_let_28 (ASSUME :args _let_27))) (let ((_let_29 (_let_7))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 ((tptp.addition A B)))) (let ((_let_32 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_33 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_34 (and _let_33 _let_32 _let_15))) (let ((_let_35 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_36 (= _let_35 _let_34))) (let ((_let_37 (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_38 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (_let_37))) (let ((_let_40 (forall ((X1 $$unsorted)) (not (tptp.complement X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_41 (not _let_40))) (let ((_let_42 (= _let_18 _let_41))) (let ((_let_43 (forall ((X0 $$unsorted)) (= (tptp.test X0) (not (forall ((X1 $$unsorted)) (not (tptp.complement X1 X0)))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 0)) (CONG (REFL :args (_let_20)) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_24)) :args ((or _let_18 _let_20))) _let_26 :args (_let_18 true _let_20)))) (let ((_let_46 (not _let_35))) (let ((_let_47 (_let_41))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_36)) :args ((or _let_46 _let_34 (not _let_36)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_47)) :args _let_47) (REWRITE :args ((=> _let_41 (not _let_46)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) (REFL :args (_let_35)) :args _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_42)) :args ((or _let_19 _let_41 (not _let_42)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.test X0)))) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_41 false _let_18 false _let_42)) :args (_let_35 true _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complement X1 X0)))) :args _let_39)) _let_38 :args (_let_36 false _let_37)) :args (_let_34 false _let_35 false _let_36)))) (let ((_let_49 (not _let_34))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 2)) :args ((or _let_15 _let_49))) _let_48 :args (_let_15 false _let_34)))) (let ((_let_51 (forall ((A $$unsorted)) (= A (tptp.multiplication tptp.one A))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_54 (= _let_53 _let_17))) (let ((_let_55 (or _let_19 _let_54))) (let ((_let_56 (forall ((X0 $$unsorted) (X1 $$unsorted)) (or (not (tptp.test X0)) (= (tptp.complement X0 X1) (= X1 (tptp.c X0))))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_59 (= tptp.one _let_58))) (let ((_let_60 (and _let_32 _let_33 _let_59))) (let ((_let_61 (= _let_53 _let_60))) (let ((_let_62 (= _let_14 _let_58))) (let ((_let_63 (not _let_15))) (let ((_let_64 (and _let_15 _let_62))) (let ((_let_65 (ASSUME :args (_let_62)))) (let ((_let_66 (ASSUME :args (_let_15)))) (let ((_let_67 (SYMM (SYMM _let_66)))) (let ((_let_68 (and _let_12 _let_13 _let_15 _let_16 _let_17))) (let ((_let_69 (ASSUME :args (_let_12)))) (let ((_let_70 (APPLY_UF tptp.multiplication))) (let ((_let_71 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_72 (ASSUME :args (_let_13)))) (let ((_let_73 (ASSUME :args (_let_17)))) (let ((_let_74 (ASSUME :args (_let_16)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_68)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_69 _let_72 _let_73 _let_66 _let_74) (SCOPE (TRANS (SYMM (SYMM _let_74)) (CONG (TRANS (TRANS _let_67 (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (SYMM _let_73) :args (APPLY_UF tptp.addition))) _let_72) _let_71 :args _let_70) (CONG (SYMM _let_72) _let_71 :args _let_70) (SYMM _let_69)) :args (_let_12 _let_13 _let_17 _let_15 _let_16))) :args (_let_12 _let_13 _let_15 _let_16 _let_17))) :args (true _let_68)) :args ((or _let_10 (not _let_12) (not _let_13) _let_63 (not _let_16) (not _let_17)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_54)) :args ((or (not _let_53) _let_17 (not _let_54)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_61)) :args ((or _let_53 (not _let_60) (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_60)) :args ((or (not _let_33) (not _let_32) _let_60 (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 0)) :args ((or _let_33 _let_49))) _let_48 :args (_let_33 false _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 1)) :args ((or _let_32 _let_49))) _let_48 :args (_let_32 false _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_64)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_65 _let_66) (SCOPE (TRANS _let_67 (SYMM (SYMM _let_65))) :args (_let_62 _let_15))) :args (_let_15 _let_62))) :args (true _let_64)) :args ((or _let_63 _let_59 (not _let_62)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_31)) :args _let_29)) _let_30 :args (_let_62 false _let_7)) :args (_let_59 false _let_15 false _let_62)) :args (_let_60 false _let_33 false _let_32 false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.multiplication X0 X1)))) :args _let_39)) _let_38 :args (_let_61 false _let_37)) :args (_let_53 false _let_60 false _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_19 _let_54 (not _let_55)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complement X0 X1)))) :args (_let_56)))) _let_57 :args (_let_55 false _let_56)) :args (_let_54 false _let_18 false _let_55)) :args (_let_17 false _let_53 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.multiplication tptp.one A)))) :args (_let_51))) _let_52 :args (_let_16 false _let_51)) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_31)) :args _let_29)) _let_30 :args (_let_13 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((tptp.addition (tptp.multiplication A C) (tptp.multiplication B C))))) :args _let_27))) _let_28 :args (_let_12 false _let_5)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_20 1)) _let_26 :args ((not _let_10) true _let_20)) :args (false false _let_17 false _let_16 false _let_15 false _let_13 false _let_12 true _let_10)) :args (_let_7 (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)) (forall ((A $$unsorted)) (= (tptp.addition A A) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.multiplication B C)) (tptp.multiplication (tptp.multiplication A B) C))) (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)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.leq A B) (= (tptp.addition A B) B))) _let_4 _let_3 _let_2 (forall ((X0 $$unsorted)) (=> (not (tptp.test X0)) (= (tptp.c X0) tptp.zero))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.60  )
% 0.22/0.60  % SZS output end Proof for KLE021+1
% 0.22/0.60  % cvc5---1.0.5 exiting
% 0.22/0.60  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------