%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM462+2 : 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 10:44:10 EDT 2023

% Result   : Theorem 1.41s 1.66s
% Output   : Proof 1.48s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : NUM462+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.37  % Computer : n018.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Fri Aug 25 16:57:44 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 1.41/1.66  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.S4HikECDfj/cvc5---1.0.5_21958.p...
% 1.41/1.66  ------- get file name : TPTP file name is NUM462+2
% 1.41/1.66  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_21958.smt2...
% 1.41/1.66  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.41/1.66  % SZS status Theorem for NUM462+2
% 1.41/1.66  % SZS output start Proof for NUM462+2
% 1.41/1.66  (
% 1.41/1.66  (let ((_let_1 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_2 (tptp.sdtasdt0 tptp.xl tptp.xm))) (let ((_let_3 (tptp.sdtlseqdt0 _let_2 _let_1))) (let ((_let_4 (tptp.sdtasdt0 tptp.xm tptp.xn))) (let ((_let_5 (tptp.sdtasdt0 tptp.xm tptp.xl))) (let ((_let_6 (tptp.sdtlseqdt0 _let_5 _let_4))) (let ((_let_7 (not (and (not (= _let_5 _let_4)) (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xm tptp.xl) W0) (tptp.sdtasdt0 tptp.xm tptp.xn)))) _let_6) (not (= _let_2 _let_1)) (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xl tptp.xm) W0) (tptp.sdtasdt0 tptp.xn tptp.xm)))) _let_3))))) (let ((_let_8 (= tptp.xl tptp.xn))) (let ((_let_9 (and (not (= tptp.xm tptp.sz00)) (not _let_8) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xl W0) tptp.xn))) (tptp.sdtlseqdt0 tptp.xl tptp.xn)))) (let ((_let_10 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_11 (tptp.aNaturalNumber0 tptp.xl))) (let ((_let_12 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_13 (and _let_12 _let_11 _let_10))) (let ((_let_14 (forall ((W0 $$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_15 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))))) (let ((_let_16 (forall ((W0 $$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))))))))) (let ((_let_17 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_19 (= tptp.sz00 tptp.xm))) (let ((_let_20 (= _let_1 _let_2))) (let ((_let_21 (not _let_20))) (let ((_let_22 (= _let_4 _let_5))) (let ((_let_23 (not _let_22))) (let ((_let_24 (and _let_23 _let_21))) (let ((_let_25 (not _let_10))) (let ((_let_26 (not _let_11))) (let ((_let_27 (not _let_12))) (let ((_let_28 (or _let_27 _let_19 _let_26 _let_25 _let_24 _let_8))) (let ((_let_29 (0))) (let ((_let_30 (ASSUME :args (_let_13)))) (let ((_let_31 (AND_ELIM _let_30 :args _let_29))) (let ((_let_32 (1))) (let ((_let_33 (AND_ELIM _let_30 :args _let_32))) (let ((_let_34 (2))) (let ((_let_35 (AND_ELIM _let_30 :args _let_34))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (not _let_24))) (let ((_let_38 (= _let_2 _let_5))) (let ((_let_39 (= _let_1 _let_4))) (let ((_let_40 (or _let_27 _let_26 _let_38))) (let ((_let_41 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_41))) (let ((_let_44 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_45 (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_42 :args (tptp.xm tptp.xl QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43))))) (let ((_let_46 (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_27 _let_26 _let_38 (not _let_40)))))) (let ((_let_47 (MACRO_RESOLUTION_TRUST _let_46 _let_31 _let_33 (MACRO_RESOLUTION_TRUST _let_45 _let_42 :args (_let_40 false _let_41)) :args (_let_38 false _let_12 false _let_11 false _let_40)))) (let ((_let_48 (or _let_27 _let_25 _let_39))) (let ((_let_49 (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_42 :args (tptp.xm tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43))))) (let ((_let_50 (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_27 _let_25 _let_39 (not _let_48)))))) (let ((_let_51 (MACRO_RESOLUTION_TRUST _let_50 _let_31 _let_35 (MACRO_RESOLUTION_TRUST _let_49 _let_42 :args (_let_48 false _let_41)) :args (_let_39 false _let_12 false _let_10 false _let_48)))) (let ((_let_52 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 tptp.xm tptp.xn) (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xm tptp.xl) W0))))))) (let ((_let_53 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xm))) (let ((_let_54 (= _let_4 (tptp.sdtpldt0 _let_5 _let_53)))) (let ((_let_55 (not _let_54))) (let ((_let_56 (tptp.aNaturalNumber0 _let_53))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_55))) (let ((_let_59 (not _let_52))) (let ((_let_60 (not _let_58))) (let ((_let_61 (tptp.sdtpldt0 tptp.xl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_62 (= (tptp.sdtasdt0 _let_61 tptp.xm) (tptp.sdtpldt0 _let_2 _let_53)))) (let ((_let_63 (= tptp.xn _let_61))) (let ((_let_64 (and (= (tptp.sdtasdt0 tptp.xm _let_61) (tptp.sdtpldt0 _let_5 (tptp.sdtasdt0 tptp.xm SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) _let_62))) (let ((_let_65 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_66 (not _let_65))) (let ((_let_67 (or _let_27 _let_26 _let_66 _let_64))) (let ((_let_68 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (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))))))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (not _let_63))) (let ((_let_71 (or _let_66 _let_70))) (let ((_let_72 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xn (tptp.sdtpldt0 tptp.xl W0))))))) (let ((_let_73 (not _let_71))) (let ((_let_74 (or))) (let ((_let_75 (not _let_72))) (let ((_let_76 (_let_75))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_76)) :args _let_76)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_72))) (REFL :args (_let_73)) :args _let_74)) (AND_ELIM _let_36 :args _let_34) :args (_let_73 true _let_72)))) (let ((_let_78 (REFL :args (_let_71)))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_71 0)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_65))) :args _let_74)) :args ((or _let_65 _let_71))) _let_77 :args (_let_65 true _let_71)))) (let ((_let_80 (and _let_63 _let_38 _let_39 _let_62))) (let ((_let_81 (ASSUME :args (_let_38)))) (let ((_let_82 (SYMM _let_81))) (let ((_let_83 (SYMM _let_82))) (let ((_let_84 (ASSUME :args (_let_62)))) (let ((_let_85 (ASSUME :args (_let_63)))) (let ((_let_86 (ASSUME :args (_let_39)))) (let ((_let_87 (SYMM _let_86))) (let ((_let_88 (or _let_66 _let_27 _let_56))) (let ((_let_89 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (_let_89))) (let ((_let_92 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_93 (_let_52))) (let ((_let_94 (or _let_59 _let_6))) (let ((_let_95 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xm tptp.xn) (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xm tptp.xl) W2))))))) (let ((_let_96 (or (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xl tptp.xm) W0)))))) _let_3))) (let ((_let_97 (not _let_95))) (let ((_let_98 (= _let_6 _let_97))) (let ((_let_99 (not _let_39))) (let ((_let_100 (not _let_38))) (let ((_let_101 (_let_23))) (let ((_let_102 (REFL :args (_let_99)))) (let ((_let_103 (REFL :args (_let_100)))) (let ((_let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))))) (let ((_let_105 (and _let_21 _let_38 _let_39))) (let ((_let_106 (_let_21))) (let ((_let_107 (ASSUME :args _let_106))) (let ((_let_108 (=))) (let ((_let_109 (not _let_96))) (let ((_let_110 (not _let_94))) (let ((_let_111 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))))) (let ((_let_112 (tptp.aNaturalNumber0 _let_4))) (let ((_let_113 (not _let_112))) (let ((_let_114 (tptp.aNaturalNumber0 _let_5))) (let ((_let_115 (not _let_114))) (let ((_let_116 (or _let_115 _let_113 _let_98))) (let ((_let_117 (forall ((W0 $$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_118 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 (or _let_27 _let_25 _let_112))) (let ((_let_120 (or _let_27 _let_26 _let_114))) (let ((_let_121 (not _let_98))) (let ((_let_122 (_let_6))) (let ((_let_123 (and _let_6 _let_38 _let_39))) (let ((_let_124 (_let_6 _let_38 _let_39))) (let ((_let_125 (ASSUME :args _let_122))) (let ((_let_126 (SYMM _let_87))) (let ((_let_127 (and _let_23 _let_38 _let_39))) (let ((_let_128 (ASSUME :args _let_101))) (let ((_let_129 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1068 $$unsorted) (BOUND_VARIABLE_1066 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= tptp.sz00 W0) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1066)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1068)) (and (not (= (tptp.sdtasdt0 W0 BOUND_VARIABLE_1066) (tptp.sdtasdt0 W0 BOUND_VARIABLE_1068))) (not (= (tptp.sdtasdt0 BOUND_VARIABLE_1066 W0) (tptp.sdtasdt0 BOUND_VARIABLE_1068 W0)))) (= BOUND_VARIABLE_1066 BOUND_VARIABLE_1068))))) (let ((_let_130 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_8 _let_19 _let_27 _let_26 _let_25 _let_24 (not _let_28)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_130 :args (tptp.xm tptp.xn tptp.xl QUANTIFIERS_INST_E_MATCHING ((tptp.sdtasdt0 W0 BOUND_VARIABLE_1068) (not (= (tptp.aNaturalNumber0 BOUND_VARIABLE_1066) false))))) :args (_let_129)))) _let_130 :args (_let_28 false _let_129)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_24 0)) :args ((or _let_23 _let_37))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_127)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_128 _let_86 _let_81) (SCOPE (FALSE_ELIM (TRANS (CONG _let_126 _let_83 :args _let_108) (FALSE_INTRO _let_128))) :args (_let_23 _let_39 _let_38))) :args (_let_23 _let_38 _let_39))) :args (true _let_127)) (CONG _let_111 _let_103 _let_102 (REFL :args _let_106) :args _let_74)) :args ((or _let_22 _let_21 _let_100 _let_99))) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_123)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_125 _let_81 _let_86) (SCOPE (TRUE_ELIM (TRANS (CONG _let_83 _let_126 :args (APPLY_UF tptp.sdtlseqdt0)) (TRUE_INTRO _let_125))) :args _let_124)) :args _let_124)) :args (true _let_123)) :args ((or _let_3 (not _let_6) _let_100 _let_99))) _let_51 _let_47 (CNF_OR_NEG :args (_let_96 1)) (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_98)) (CONG (REFL :args (_let_121)) (REFL :args _let_122) (MACRO_SR_PRED_INTRO :args ((= (not _let_97) _let_95))) :args _let_74)) :args ((or _let_6 _let_95 _let_121))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_116)) :args ((or _let_115 _let_113 _let_98 (not _let_116)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_27 _let_26 _let_114 (not _let_120)))) _let_31 _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (tptp.xm tptp.xl QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_92)) :args _let_91)) _let_90 :args (_let_120 false _let_89)) :args (_let_114 false _let_12 false _let_11 false _let_120)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_27 _let_25 _let_112 (not _let_119)))) _let_31 _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (tptp.xm tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_92)) :args _let_91)) _let_90 :args (_let_119 false _let_89)) :args (_let_112 false _let_12 false _let_10 false _let_119)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_118 :args (_let_5 _let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtlseqdt0 W0 W1)))) :args (_let_117))) _let_118 :args (_let_116 false _let_117)) :args (_let_98 false _let_114 false _let_112 false _let_116)) (REORDERING (EQ_RESOLVE (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT)))) (CONG _let_111 (REFL :args (_let_110)) _let_104 (REFL :args (_let_109)) :args _let_74)) :args ((or _let_22 _let_20 _let_110 _let_109))) (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_52 (= W0 W2)))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_94 0)) (CONG (REFL :args (_let_94)) (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_52))) :args _let_74)) :args ((or _let_52 _let_94))) (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_105)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_107 _let_86 _let_81) (SCOPE (FALSE_ELIM (TRANS (CONG _let_87 _let_82 :args _let_108) (FALSE_INTRO _let_107))) :args (_let_21 _let_39 _let_38))) :args (_let_21 _let_38 _let_39))) :args (true _let_105)) (CONG _let_104 _let_103 _let_102 (REFL :args _let_101) :args _let_74)) :args ((or _let_23 _let_20 _let_100 _let_99))) _let_46 _let_33 _let_45 _let_50 _let_31 _let_35 _let_49 _let_42 :args ((or _let_52 _let_20) false _let_39 false _let_38 true _let_3 false _let_6 false _let_98 true _let_96 true _let_95 false _let_94 true _let_22 false _let_38 false _let_11 false _let_40 false _let_39 false _let_12 false _let_10 false _let_48 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_93) :args (_let_53 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtpldt0 _let_5 W0)))) :args _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_57 _let_55 _let_60))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_27 _let_66 _let_56 (not _let_88)))) _let_31 _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_92)) :args _let_91)) _let_90 :args (_let_88 false _let_89)) :args (_let_56 false _let_12 false _let_65 false _let_88)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_80)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_81 _let_84 _let_85 _let_86) (SCOPE (TRANS _let_87 (CONG (SYMM (SYMM _let_85)) (REFL :args (tptp.xm)) :args (APPLY_UF tptp.sdtasdt0)) (SYMM (SYMM _let_84)) (CONG _let_83 (REFL :args (_let_53)) :args (APPLY_UF tptp.sdtpldt0))) :args (_let_38 _let_62 _let_63 _let_39))) :args (_let_63 _let_38 _let_39 _let_62))) :args (true _let_80)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_71 1)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_63))) :args _let_74)) :args ((or _let_63 _let_71))) _let_77 :args (_let_63 true _let_71)) _let_47 _let_51 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_64 1)) :args ((or _let_62 (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_27 _let_26 _let_66 _let_64 (not _let_67)))) _let_31 _let_33 _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (tptp.xm tptp.xl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((tptp.sdtasdt0 W0 (tptp.sdtpldt0 W1 W2))))) :args (_let_68))) _let_69 :args (_let_67 false _let_68)) :args (_let_64 false _let_12 false _let_11 false _let_65 false _let_67)) :args (_let_62 false _let_64)) :args (_let_54 false _let_63 false _let_38 false _let_39 false _let_62)) :args (_let_60 false _let_56 false _let_54)) :args (_let_59 true _let_58)) :args (_let_20 true _let_52)) _let_51 _let_47 :args (_let_22 false _let_20 false _let_39 false _let_38)) :args (_let_37 false _let_22)) (AND_ELIM _let_36 :args _let_32) (AND_ELIM _let_36 :args _let_29) _let_35 _let_33 _let_31 :args (false false _let_28 true _let_24 true _let_8 true _let_19 false _let_10 false _let_11 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))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) _let_18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))) _let_17 (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 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))) _let_16 (forall ((W0 $$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)))) _let_15 (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_14 (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)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (let ((_let_2 (tptp.sdtpldt0 W0 W2))) (let ((_let_3 (tptp.sdtpldt0 W2 W1))) (let ((_let_4 (tptp.sdtpldt0 W2 W0))) (=> (tptp.aNaturalNumber0 W2) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))))) _let_13 _let_9 _let_7 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.48/1.67  )
% 1.48/1.67  % SZS output end Proof for NUM462+2
% 1.48/1.67  % cvc5---1.0.5 exiting
% 1.48/1.68  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------