%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM460+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n018.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 10:44:09 EDT 2023

% Result   : Theorem 3.11s 3.36s
% Output   : Proof 3.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : NUM460+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command    : do_cvc5 %s %d
% 0.14/0.32  % Computer : n018.cluster.edu
% 0.14/0.32  % Model    : x86_64 x86_64
% 0.14/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32  % Memory   : 8042.1875MB
% 0.14/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32  % CPULimit   : 300
% 0.14/0.32  % WCLimit    : 300
% 0.14/0.32  % DateTime   : Fri Aug 25 14:36:14 EDT 2023
% 0.14/0.33  % CPUTime    : 
% 0.18/0.44  %----Proving TF0_NAR, FOF, or CNF
% 3.11/3.36  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.pHOwGaXsT0/cvc5---1.0.5_31677.p...
% 3.11/3.36  ------- get file name : TPTP file name is NUM460+1
% 3.11/3.36  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31677.smt2...
% 3.11/3.36  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 3.11/3.36  % SZS status Theorem for NUM460+1
% 3.11/3.36  % SZS output start Proof for NUM460+1
% 3.11/3.36  (
% 3.11/3.36  (let ((_let_1 (tptp.sdtlseqdt0 tptp.xm tptp.xl))) (let ((_let_2 (tptp.sdtlseqdt0 tptp.xn tptp.xl))) (let ((_let_3 (tptp.sdtlseqdt0 tptp.xm tptp.xn))) (let ((_let_4 (not (=> (and _let_3 _let_2) _let_1)))) (let ((_let_5 (tptp.aNaturalNumber0 tptp.xl))) (let ((_let_6 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_7 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_8 (and _let_7 _let_6 _let_5))) (let ((_let_9 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))))) (let ((_let_10 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))))) (let ((_let_11 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_12 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_13 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_14 (tptp.aNaturalNumber0 _let_13))) (let ((_let_15 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_16 _let_14))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (not _let_19))) (let ((_let_22 (tptp.sdtpldt0 tptp.xm _let_13))) (let ((_let_23 (= tptp.xl _let_22))) (let ((_let_24 (not _let_23))) (let ((_let_25 (not _let_14))) (let ((_let_26 (or _let_25 _let_24))) (let ((_let_27 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= tptp.xl (tptp.sdtpldt0 tptp.xm W2))))))) (let ((_let_28 (not _let_27))) (let ((_let_29 (= _let_1 _let_28))) (let ((_let_30 (not _let_5))) (let ((_let_31 (not _let_7))) (let ((_let_32 (or _let_31 _let_30 _let_29))) (let ((_let_33 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtpldt0 W0 W2))))))))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (_let_33))) (let ((_let_36 ((tptp.sdtlseqdt0 W0 W1)))) (let ((_let_37 (ASSUME :args (_let_8)))) (let ((_let_38 (AND_ELIM _let_37 :args (2)))) (let ((_let_39 (0))) (let ((_let_40 (AND_ELIM _let_37 :args _let_39))) (let ((_let_41 (ASSUME :args (_let_4)))) (let ((_let_42 (not _let_29))) (let ((_let_43 (or))) (let ((_let_44 (_let_27))) (let ((_let_45 (tptp.sdtpldt0 tptp.xm SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_46 (= (tptp.sdtpldt0 _let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) _let_22))) (let ((_let_47 (= tptp.xl (tptp.sdtpldt0 tptp.xn SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_48 (= tptp.xn _let_45))) (let ((_let_49 (or _let_31 _let_18 _let_16 _let_46))) (let ((_let_50 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (not _let_47))) (let ((_let_53 (or _let_16 _let_52))) (let ((_let_54 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= tptp.xl (tptp.sdtpldt0 tptp.xn W2))))))) (let ((_let_55 (not _let_53))) (let ((_let_56 (not _let_54))) (let ((_let_57 (= _let_2 _let_56))) (let ((_let_58 (not _let_6))) (let ((_let_59 (or _let_58 _let_30 _let_57))) (let ((_let_60 (1))) (let ((_let_61 (AND_ELIM _let_37 :args _let_60))) (let ((_let_62 (NOT_IMPLIES_ELIM1 _let_41))) (let ((_let_63 (_let_56))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_63)) :args _let_63)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_54))) (REFL :args (_let_55)) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_57)) :args ((or (not _let_2) _let_56 (not _let_57)))) (AND_ELIM _let_62 :args _let_60) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_58 _let_30 _let_57 (not _let_59)))) _let_61 _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.xn tptp.xl QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_36)) :args _let_35)) _let_34 :args (_let_59 false _let_33)) :args (_let_57 false _let_6 false _let_5 false _let_59)) :args (_let_56 false _let_2 false _let_57)) :args (_let_55 true _let_54)))) (let ((_let_65 (REFL :args (_let_53)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 0)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_43)) :args ((or _let_15 _let_53))) _let_64 :args (_let_15 true _let_53)))) (let ((_let_67 (not _let_48))) (let ((_let_68 (or _let_18 _let_67))) (let ((_let_69 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= tptp.xn (tptp.sdtpldt0 tptp.xm W2))))))) (let ((_let_70 (not _let_68))) (let ((_let_71 (not _let_69))) (let ((_let_72 (= _let_3 _let_71))) (let ((_let_73 (or _let_31 _let_58 _let_72))) (let ((_let_74 (_let_71))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_74)) :args _let_74)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_69))) (REFL :args (_let_70)) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_72)) :args ((or (not _let_3) _let_71 (not _let_72)))) (AND_ELIM _let_62 :args _let_39) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_31 _let_58 _let_72 (not _let_73)))) _let_40 _let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.xm tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_36)) :args _let_35)) _let_34 :args (_let_73 false _let_33)) :args (_let_72 false _let_7 false _let_6 false _let_73)) :args (_let_71 false _let_3 false _let_72)) :args (_let_70 true _let_69)))) (let ((_let_76 (REFL :args (_let_68)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 0)) (CONG _let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_43)) :args ((or _let_17 _let_68))) _let_75 :args (_let_17 true _let_68)))) (let ((_let_78 (and _let_48 _let_47 _let_46))) (let ((_let_79 (ASSUME :args (_let_46)))) (let ((_let_80 (ASSUME :args (_let_48)))) (let ((_let_81 (ASSUME :args (_let_47)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtpldt0 W0 W1)))) :args (_let_12))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_18 _let_16 _let_14 _let_21))) _let_77 _let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_24 (not _let_26)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_78)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_79 _let_80 _let_81) (SCOPE (TRANS (SYMM (SYMM _let_81)) (CONG (SYMM (SYMM _let_80)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) :args (APPLY_UF tptp.sdtpldt0)) (SYMM (SYMM _let_79))) :args (_let_46 _let_48 _let_47))) :args (_let_48 _let_47 _let_46))) :args (true _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 1)) (CONG _let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_48))) :args _let_43)) :args ((or _let_48 _let_68))) _let_75 :args (_let_48 true _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 1)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_47))) :args _let_43)) :args ((or _let_47 _let_53))) _let_64 :args (_let_47 true _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_31 _let_18 _let_16 _let_46 (not _let_49)))) _let_40 _let_77 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.xm SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2)))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_46 false _let_7 false _let_17 false _let_15 false _let_49)) :args (_let_23 false _let_48 false _let_47 false _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_44) :args (_let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtpldt0 tptp.xm W2)))) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_29)) (CONG (REFL :args (_let_42)) (REFL :args (_let_1)) (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_43)) :args ((or _let_1 _let_27 _let_42))) (NOT_IMPLIES_ELIM2 _let_41) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_30 _let_29 (not _let_32)))) _let_40 _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.xm tptp.xl QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_36)) :args _let_35)) _let_34 :args (_let_32 false _let_33)) :args (_let_29 false _let_7 false _let_5 false _let_32)) :args (_let_27 true _let_1 false _let_29)) :args (_let_26 false _let_27)) :args (_let_25 false _let_23 false _let_26)) :args (_let_21 false _let_17 false _let_15 true _let_14)) _let_20 :args (false true _let_19 false _let_12)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))) _let_11 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))) _let_10 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (and (= (tptp.sdtasdt0 W0 _let_1) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 _let_1 W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtpldt0 W0 W1) tptp.sz00) (and (= W0 tptp.sz00) (= W1 tptp.sz00))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))) _let_9 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) _let_8 _let_4 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 3.20/3.38  )
% 3.20/3.38  % SZS output end Proof for NUM460+1
% 3.20/3.38  % cvc5---1.0.5 exiting
% 3.20/3.38  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------