%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : KLE021+3 : 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 05:26:54 EDT 2023

% Result   : Theorem 0.68s 0.91s
% Output   : Proof 0.68s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : KLE021+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n009.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 11:26:05 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.68/0.91  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.c0741ihO3B/cvc5---1.0.5_10824.p...
% 0.68/0.91  ------- get file name : TPTP file name is KLE021+3
% 0.68/0.91  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10824.smt2...
% 0.68/0.91  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.68/0.91  % SZS status Theorem for KLE021+3
% 0.68/0.91  % SZS output start Proof for KLE021+3
% 0.68/0.91  (
% 0.68/0.91  (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 $$unsorted)) (= (tptp.addition A A) A)))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.addition A B) (tptp.addition B A))))) (let ((_let_9 (tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (tptp.addition (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.multiplication _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_11 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10))) (let ((_let_12 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9))) (let ((_let_13 (= _let_10 (tptp.multiplication _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_14 (= _let_12 (tptp.addition _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_15 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_16 (= tptp.one _let_15))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_18 (= _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_19 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.multiplication tptp.one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_20 (tptp.test SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_11))) (let ((_let_23 (not _let_11))) (let ((_let_24 (forall ((X0 $$unsorted) (X1 $$unsorted)) (or (not (tptp.test X1)) (= X0 (tptp.addition (tptp.multiplication X1 X0) (tptp.multiplication (tptp.c X1) X0))))))) (let ((_let_25 (not _let_22))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (or))) (let ((_let_28 (not _let_24))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_26) :args (_let_28))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_24))) (REFL :args (_let_25)) :args _let_27)) _let_26 :args (_let_25 true _let_24)))) (let ((_let_30 (_let_5))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (_let_8))) (let ((_let_33 (ASSUME :args _let_32))) (let ((_let_34 ((tptp.addition A B)))) (let ((_let_35 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_36 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_37 (and _let_36 _let_35 _let_16))) (let ((_let_38 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_39 (= _let_38 _let_37))) (let ((_let_40 (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (tptp.complement X1 X0) (and (= tptp.zero (tptp.multiplication X0 X1)) (= tptp.zero (tptp.multiplication X1 X0)) (= tptp.one (tptp.addition X0 X1))))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (_let_40))) (let ((_let_43 (forall ((X1 $$unsorted)) (not (tptp.complement X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_44 (not _let_43))) (let ((_let_45 (= _let_20 _let_44))) (let ((_let_46 (forall ((X0 $$unsorted)) (= (tptp.test X0) (not (forall ((X1 $$unsorted)) (not (tptp.complement X1 X0)))))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 0)) (CONG (REFL :args (_let_22)) (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_27)) :args ((or _let_20 _let_22))) _let_29 :args (_let_20 true _let_22)))) (let ((_let_49 (not _let_38))) (let ((_let_50 (_let_44))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_39)) :args ((or _let_49 _let_37 (not _let_39)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_50)) :args _let_50) (REWRITE :args ((=> _let_44 (not _let_49)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) (REFL :args (_let_38)) :args _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_45)) :args ((or _let_21 _let_44 (not _let_45)))) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.test X0)))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_44 false _let_20 false _let_45)) :args (_let_38 true _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complement X1 X0)))) :args _let_42)) _let_41 :args (_let_39 false _let_40)) :args (_let_37 false _let_38 false _let_39)))) (let ((_let_52 (not _let_37))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_37 2)) :args ((or _let_16 _let_52))) _let_51 :args (_let_16 false _let_37)))) (let ((_let_54 (forall ((A $$unsorted)) (= A (tptp.addition A A))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_57 (= _let_56 _let_18))) (let ((_let_58 (or _let_21 _let_57))) (let ((_let_59 (forall ((X0 $$unsorted) (X1 $$unsorted)) (or (not (tptp.test X0)) (= (tptp.complement X0 X1) (= X1 (tptp.c X0))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_62 (= tptp.one _let_61))) (let ((_let_63 (and _let_35 _let_36 _let_62))) (let ((_let_64 (= _let_56 _let_63))) (let ((_let_65 (= _let_15 _let_61))) (let ((_let_66 (not _let_16))) (let ((_let_67 (and _let_16 _let_65))) (let ((_let_68 (ASSUME :args (_let_65)))) (let ((_let_69 (ASSUME :args (_let_16)))) (let ((_let_70 (SYMM (SYMM _let_69)))) (let ((_let_71 (forall ((A $$unsorted)) (= A (tptp.multiplication tptp.one A))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (not _let_19))) (let ((_let_74 (_let_73))) (let ((_let_75 (ASSUME :args (_let_19)))) (let ((_let_76 (ASSUME :args (_let_23)))) (let ((_let_77 (ASSUME :args (_let_13)))) (let ((_let_78 (APPLY_UF tptp.multiplication))) (let ((_let_79 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_80 (ASSUME :args (_let_14)))) (let ((_let_81 (APPLY_UF tptp.addition))) (let ((_let_82 (ASSUME :args (_let_18)))) (let ((_let_83 (ASSUME :args (_let_17)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_76 _let_77 _let_80 _let_83 _let_82 _let_69) (SCOPE (FALSE_ELIM (TRANS (CONG _let_79 (TRANS (CONG (TRANS (TRANS _let_70 (CONG _let_83 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) :args _let_81) (CONG (SYMM _let_83) (SYMM _let_82) :args _let_81)) _let_80) _let_79 :args _let_78) (CONG (SYMM _let_80) _let_79 :args _let_78) (SYMM _let_77)) :args (=)) (FALSE_INTRO _let_76))) :args (_let_23 _let_13 _let_14 _let_17 _let_18 _let_16))) _let_75) :args (_let_23 _let_13 _let_14 _let_16 _let_17 _let_18 _let_19)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_74))) (TRUE_INTRO _let_75))) :args (_let_73 _let_19)) :args ((not (and _let_23 _let_13 _let_14 _let_16 _let_17 _let_18 _let_19)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_11))) (REFL :args ((not _let_13))) (REFL :args ((not _let_14))) (REFL :args (_let_66)) (REFL :args ((not _let_17))) (REFL :args ((not _let_18))) (REFL :args _let_74) :args _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.multiplication tptp.one A)))) :args (_let_71))) _let_72 :args (_let_19 false _let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_57)) :args ((or (not _let_56) _let_18 (not _let_57)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_64)) :args ((or _let_56 (not _let_63) (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_63)) :args ((or (not _let_36) (not _let_35) _let_63 (not _let_62)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_37 0)) :args ((or _let_36 _let_52))) _let_51 :args (_let_36 false _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_37 1)) :args ((or _let_35 _let_52))) _let_51 :args (_let_35 false _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_67)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_68 _let_69) (SCOPE (TRANS _let_70 (SYMM (SYMM _let_68))) :args (_let_65 _let_16))) :args (_let_16 _let_65))) :args (true _let_67)) :args ((or _let_66 _let_62 (not _let_65)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_34)) :args _let_32)) _let_33 :args (_let_65 false _let_8)) :args (_let_62 false _let_16 false _let_65)) :args (_let_63 false _let_36 false _let_35 false _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.multiplication X0 X1)))) :args _let_42)) _let_41 :args (_let_64 false _let_40)) :args (_let_56 false _let_63 false _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_21 _let_57 (not _let_58)))) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complement X0 X1)))) :args (_let_59)))) _let_60 :args (_let_58 false _let_59)) :args (_let_57 false _let_20 false _let_58)) :args (_let_18 false _let_56 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.addition A A)))) :args (_let_54))) _let_55 :args (_let_17 false _let_54)) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_34)) :args _let_32)) _let_33 :args (_let_14 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((tptp.addition (tptp.multiplication A C) (tptp.multiplication B C))))) :args _let_30))) _let_31 :args (_let_13 false _let_5)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 1)) _let_29 :args (_let_23 true _let_22)) :args (false false _let_19 false _let_18 false _let_17 false _let_16 false _let_14 false _let_13 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 $$unsorted)) (= (tptp.multiplication A (tptp.multiplication B C)) (tptp.multiplication (tptp.multiplication A B) C))) (forall ((A $$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))) (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.68/0.92  )
% 0.68/0.92  % SZS output end Proof for KLE021+3
% 0.68/0.92  % cvc5---1.0.5 exiting
% 0.68/0.92  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------