%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : KLE022+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n001.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 0.21s 0.61s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : KLE022+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n001.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 13:08:52 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.61  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.PKifP2oU54/cvc5---1.0.5_5293.p...
% 0.21/0.61  ------- get file name : TPTP file name is KLE022+1
% 0.21/0.61  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_5293.smt2...
% 0.21/0.61  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.61  % SZS status Theorem for KLE022+1
% 0.21/0.61  % SZS output start Proof for KLE022+1
% 0.21/0.61  (
% 0.21/0.61  (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 $$unsorted) (B $$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_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8)))) (let ((_let_10 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_11 (= _let_9 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_8))))) (let ((_let_12 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_13 (= tptp.one _let_12))) (let ((_let_14 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.one)))) (let ((_let_15 (= _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_16 (tptp.test SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_10))) (let ((_let_19 (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_20 (not _let_18))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (or))) (let ((_let_23 (not _let_19))) (let ((_let_24 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_21) :args (_let_23))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_19))) (REFL :args (_let_20)) :args _let_22)) _let_21 :args (_let_20 true _let_19)))) (let ((_let_25 (_let_5))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_28 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_29 (and _let_28 _let_27 _let_13))) (let ((_let_30 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_31 (= _let_30 _let_29))) (let ((_let_32 (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_33 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (_let_32))) (let ((_let_35 (forall ((X1 $$unsorted)) (not (tptp.complement X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_36 (not _let_35))) (let ((_let_37 (= _let_16 _let_36))) (let ((_let_38 (forall ((X0 $$unsorted)) (= (tptp.test X0) (not (forall ((X1 $$unsorted)) (not (tptp.complement X1 X0)))))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 0)) (CONG (REFL :args (_let_18)) (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_22)) :args ((or _let_16 _let_18))) _let_24 :args (_let_16 true _let_18)))) (let ((_let_41 (not _let_30))) (let ((_let_42 (_let_36))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_31)) :args ((or _let_41 _let_29 (not _let_31)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_42)) :args _let_42) (REWRITE :args ((=> _let_36 (not _let_41)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) (REFL :args (_let_30)) :args _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_37)) :args ((or _let_17 _let_36 (not _let_37)))) _let_40 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.test X0)))) :args (_let_38))) _let_39 :args (_let_37 false _let_38)) :args (_let_36 false _let_16 false _let_37)) :args (_let_30 true _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complement X1 X0)))) :args _let_34)) _let_33 :args (_let_31 false _let_32)) :args (_let_29 false _let_30 false _let_31)))) (let ((_let_44 (not _let_29))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 2)) :args ((or _let_13 _let_44))) _let_43 :args (_let_13 false _let_29)))) (let ((_let_46 (forall ((A $$unsorted)) (= A (tptp.multiplication A tptp.one))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (tptp.complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_49 (= _let_48 _let_15))) (let ((_let_50 (or _let_17 _let_49))) (let ((_let_51 (forall ((X0 $$unsorted) (X1 $$unsorted)) (or (not (tptp.test X0)) (= (tptp.complement X0 X1) (= X1 (tptp.c X0))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (tptp.addition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_54 (= tptp.one _let_53))) (let ((_let_55 (and _let_27 _let_28 _let_54))) (let ((_let_56 (= _let_48 _let_55))) (let ((_let_57 (= _let_12 _let_53))) (let ((_let_58 (_let_7))) (let ((_let_59 (ASSUME :args _let_58))) (let ((_let_60 (not _let_13))) (let ((_let_61 (and _let_13 _let_57))) (let ((_let_62 (ASSUME :args (_let_57)))) (let ((_let_63 (ASSUME :args (_let_13)))) (let ((_let_64 (SYMM (SYMM _let_63)))) (let ((_let_65 (and _let_11 _let_13 _let_14 _let_15))) (let ((_let_66 (ASSUME :args (_let_11)))) (let ((_let_67 (ASSUME :args (_let_15)))) (let ((_let_68 (ASSUME :args (_let_14)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_65)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_66 _let_67 _let_63 _let_68) (SCOPE (TRANS (SYMM (SYMM _let_68)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (TRANS _let_64 (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (SYMM _let_67) :args (APPLY_UF tptp.addition))) :args (APPLY_UF tptp.multiplication)) (SYMM _let_66)) :args (_let_11 _let_15 _let_13 _let_14))) :args (_let_11 _let_13 _let_14 _let_15))) :args (true _let_65)) :args ((or _let_10 (not _let_11) _let_60 (not _let_14) (not _let_15)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_49)) :args ((or (not _let_48) _let_15 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_56)) :args ((or _let_48 (not _let_55) (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_55)) :args ((or (not _let_28) (not _let_27) _let_55 (not _let_54)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 0)) :args ((or _let_28 _let_44))) _let_43 :args (_let_28 false _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 1)) :args ((or _let_27 _let_44))) _let_43 :args (_let_27 false _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_61)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_62 _let_63) (SCOPE (TRANS _let_64 (SYMM (SYMM _let_62))) :args (_let_57 _let_13))) :args (_let_13 _let_57))) :args (true _let_61)) :args ((or _let_60 _let_54 (not _let_57)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.addition A B)))) :args _let_58)) _let_59 :args (_let_57 false _let_7)) :args (_let_54 false _let_13 false _let_57)) :args (_let_55 false _let_28 false _let_27 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.multiplication X0 X1)))) :args _let_34)) _let_33 :args (_let_56 false _let_32)) :args (_let_48 false _let_55 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_17 _let_49 (not _let_50)))) _let_40 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complement X0 X1)))) :args (_let_51)))) _let_52 :args (_let_50 false _let_51)) :args (_let_49 false _let_16 false _let_50)) :args (_let_15 false _let_48 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.multiplication A tptp.one)))) :args (_let_46))) _let_47 :args (_let_14 false _let_46)) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_8 QUANTIFIERS_INST_E_MATCHING ((tptp.addition (tptp.multiplication A B) (tptp.multiplication A C))))) :args _let_25))) _let_26 :args (_let_11 false _let_5)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_18 1)) _let_24 :args ((not _let_10) true _let_18)) :args (false false _let_15 false _let_14 false _let_13 false _let_11 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))) _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))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.62  )
% 0.21/0.62  % SZS output end Proof for KLE022+1
% 0.21/0.62  % cvc5---1.0.5 exiting
% 0.21/0.62  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------