%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : KLE022+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n012.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 05:26:55 EDT 2023

% Result   : Theorem 0.70s 0.99s
% Output   : Proof 0.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : KLE022+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.34  % Computer : n012.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 29 11:11:09 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.47  %----Proving TF0_NAR, FOF, or CNF
% 0.70/0.99  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.hQ8wQXELxt/cvc5---1.0.5_21977.p...
% 0.70/0.99  ------- get file name : TPTP file name is KLE022+3
% 0.70/0.99  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21977.smt2...
% 0.70/0.99  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.70/0.99  % SZS status Theorem for KLE022+3
% 0.70/0.99  % SZS output start Proof for KLE022+3
% 0.70/0.99  (
% 0.70/0.99  (let ((_let_1 (not (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (tptp.test X1) (= X0 (tptp.addition (tptp.multiplication X0 X1) (tptp.multiplication X0 (tptp.c X1))))))))) (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 $$unsorted)) (= (tptp.multiplication A (tptp.addition B C)) (tptp.addition (tptp.multiplication A B) (tptp.multiplication A C)))))) (let ((_let_6 (forall ((A $$unsorted)) (= (tptp.multiplication A tptp.one) A)))) (let ((_let_7 (forall ((A $$unsorted)) (= (tptp.addition A A) A)))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.addition A B) (tptp.addition B A))))) (let ((_let_9 (tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (tptp.addition (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9)))) (let ((_let_11 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10))) (let ((_let_12 (= _let_10 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9))))) (let ((_let_13 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_14 (= tptp.one _let_13))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_16 (= _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.one)))) (let ((_let_18 (tptp.test SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 _let_11))) (let ((_let_21 (not _let_11))) (let ((_let_22 (forall ((X0 $$unsorted) (X1 $$unsorted)) (or (not (tptp.test X1)) (= X0 (tptp.addition (tptp.multiplication X0 X1) (tptp.multiplication X0 (tptp.c X1)))))))) (let ((_let_23 (not _let_20))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (or))) (let ((_let_26 (not _let_22))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_24) :args (_let_26))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_22))) (REFL :args (_let_23)) :args _let_25)) _let_24 :args (_let_23 true _let_22)))) (let ((_let_28 (_let_5))) (let ((_let_29 (ASSUME :args _let_28))) (let ((_let_30 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_31 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_32 (and _let_31 _let_30 _let_14))) (let ((_let_33 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_34 (= _let_33 _let_32))) (let ((_let_35 (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (tptp.complement X1 X0) (and (= tptp.zero (tptp.multiplication X0 X1)) (= tptp.zero (tptp.multiplication X1 X0)) (= tptp.one (tptp.addition X0 X1))))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (_let_35))) (let ((_let_38 (forall ((X1 $$unsorted)) (not (tptp.complement X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_39 (not _let_38))) (let ((_let_40 (= _let_18 _let_39))) (let ((_let_41 (forall ((X0 $$unsorted)) (= (tptp.test X0) (not (forall ((X1 $$unsorted)) (not (tptp.complement X1 X0)))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (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_25)) :args ((or _let_18 _let_20))) _let_27 :args (_let_18 true _let_20)))) (let ((_let_44 (not _let_33))) (let ((_let_45 (_let_39))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_34)) :args ((or _let_44 _let_32 (not _let_34)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_45)) :args _let_45) (REWRITE :args ((=> _let_39 (not _let_44)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) (REFL :args (_let_33)) :args _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_40)) :args ((or _let_19 _let_39 (not _let_40)))) _let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.test X0)))) :args (_let_41))) _let_42 :args (_let_40 false _let_41)) :args (_let_39 false _let_18 false _let_40)) :args (_let_33 true _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complement X1 X0)))) :args _let_37)) _let_36 :args (_let_34 false _let_35)) :args (_let_32 false _let_33 false _let_34)))) (let ((_let_47 (not _let_32))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_32 2)) :args ((or _let_14 _let_47))) _let_46 :args (_let_14 false _let_32)))) (let ((_let_49 (forall ((A $$unsorted)) (= A (tptp.addition A A))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_52 (= _let_51 _let_16))) (let ((_let_53 (or _let_19 _let_52))) (let ((_let_54 (forall ((X0 $$unsorted) (X1 $$unsorted)) (or (not (tptp.test X0)) (= (tptp.complement X0 X1) (= X1 (tptp.c X0))))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_57 (= tptp.one _let_56))) (let ((_let_58 (and _let_30 _let_31 _let_57))) (let ((_let_59 (= _let_51 _let_58))) (let ((_let_60 (= _let_13 _let_56))) (let ((_let_61 (_let_8))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 (not _let_14))) (let ((_let_64 (and _let_14 _let_60))) (let ((_let_65 (ASSUME :args (_let_60)))) (let ((_let_66 (ASSUME :args (_let_14)))) (let ((_let_67 (SYMM (SYMM _let_66)))) (let ((_let_68 (forall ((A $$unsorted)) (= A (tptp.multiplication A tptp.one))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (not _let_17))) (let ((_let_71 (_let_70))) (let ((_let_72 (ASSUME :args (_let_17)))) (let ((_let_73 (ASSUME :args (_let_21)))) (let ((_let_74 (ASSUME :args (_let_12)))) (let ((_let_75 (APPLY_UF tptp.addition))) (let ((_let_76 (ASSUME :args (_let_16)))) (let ((_let_77 (ASSUME :args (_let_15)))) (let ((_let_78 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_73 _let_74 _let_77 _let_76 _let_66) (SCOPE (FALSE_ELIM (TRANS (CONG _let_78 (TRANS (CONG _let_78 (TRANS _let_67 (CONG _let_77 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) :args _let_75) (CONG (SYMM _let_77) (SYMM _let_76) :args _let_75)) :args (APPLY_UF tptp.multiplication)) (SYMM _let_74)) :args (=)) (FALSE_INTRO _let_73))) :args (_let_21 _let_12 _let_15 _let_16 _let_14))) _let_72) :args (_let_21 _let_12 _let_14 _let_15 _let_16 _let_17)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_71))) (TRUE_INTRO _let_72))) :args (_let_70 _let_17)) :args ((not (and _let_21 _let_12 _let_14 _let_15 _let_16 _let_17)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_11))) (REFL :args ((not _let_12))) (REFL :args (_let_63)) (REFL :args ((not _let_15))) (REFL :args ((not _let_16))) (REFL :args _let_71) :args _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.multiplication A tptp.one)))) :args (_let_68))) _let_69 :args (_let_17 false _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_52)) :args ((or (not _let_51) _let_16 (not _let_52)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_59)) :args ((or _let_51 (not _let_58) (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_58)) :args ((or (not _let_31) (not _let_30) _let_58 (not _let_57)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_32 0)) :args ((or _let_31 _let_47))) _let_46 :args (_let_31 false _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_32 1)) :args ((or _let_30 _let_47))) _let_46 :args (_let_30 false _let_32)) (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_60 _let_14))) :args (_let_14 _let_60))) :args (true _let_64)) :args ((or _let_63 _let_57 (not _let_60)))) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.addition A B)))) :args _let_61)) _let_62 :args (_let_60 false _let_8)) :args (_let_57 false _let_14 false _let_60)) :args (_let_58 false _let_31 false _let_30 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.multiplication X0 X1)))) :args _let_37)) _let_36 :args (_let_59 false _let_35)) :args (_let_51 false _let_58 false _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_19 _let_52 (not _let_53)))) _let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complement X0 X1)))) :args (_let_54)))) _let_55 :args (_let_53 false _let_54)) :args (_let_52 false _let_18 false _let_53)) :args (_let_16 false _let_51 false _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.addition A A)))) :args (_let_49))) _let_50 :args (_let_15 false _let_49)) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9 QUANTIFIERS_INST_E_MATCHING ((tptp.addition (tptp.multiplication A B) (tptp.multiplication A C))))) :args _let_28))) _let_29 :args (_let_12 false _let_5)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_20 1)) _let_27 :args (_let_21 true _let_20)) :args (false false _let_17 false _let_16 false _let_15 false _let_14 false _let_12 true _let_11)) :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 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.multiplication B C)) (tptp.multiplication (tptp.multiplication A B) C))) _let_6 (forall ((A $$unsorted)) (= (tptp.multiplication tptp.one A) A)) _let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication (tptp.addition A B) C) (tptp.addition (tptp.multiplication A C) (tptp.multiplication B C)))) (forall ((A $$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))) (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (and (tptp.test X0) (tptp.test X1)) (= (tptp.c (tptp.addition X0 X1)) (tptp.multiplication (tptp.c X0) (tptp.c X1))))) (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (and (tptp.test X0) (tptp.test X1)) (= (tptp.c (tptp.multiplication X0 X1)) (tptp.addition (tptp.c X0) (tptp.c X1))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.70/1.00  )
% 0.70/1.00  % SZS output end Proof for KLE022+3
% 0.70/1.00  % cvc5---1.0.5 exiting
% 0.70/1.00  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------