TSTP Solution File: NUM503+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM503+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n026.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 10:44:31 EDT 2023
% Result : Theorem 15.28s 15.46s
% Output : Proof 15.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM503+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 10:41:32 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 15.28/15.46 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.pFP2p9rXps/cvc5---1.0.5_12605.p...
% 15.28/15.46 ------- get file name : TPTP file name is NUM503+3
% 15.28/15.46 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12605.smt2...
% 15.28/15.46 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 15.28/15.46 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.28/15.46 % SZS status Theorem for NUM503+3
% 15.28/15.46 % SZS output start Proof for NUM503+3
% 15.28/15.46 (
% 15.28/15.46 (let ((_let_1 (tptp.sdtasdt0 tptp.xp tptp.xk))) (let ((_let_2 (tptp.sdtasdt0 tptp.xp tptp.xm))) (let ((_let_3 (tptp.sdtlseqdt0 _let_2 _let_1))) (let ((_let_4 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_5 (tptp.sdtlseqdt0 _let_4 _let_2))) (let ((_let_6 (= _let_4 _let_2))) (let ((_let_7 (not _let_6))) (let ((_let_8 (not (and _let_7 (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xn tptp.xm) W0) (tptp.sdtasdt0 tptp.xp tptp.xm)))) _let_5) (not (= _let_2 _let_1)) (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xp tptp.xm) W0) (tptp.sdtasdt0 tptp.xp tptp.xk)))) _let_3))))) (let ((_let_9 (tptp.sdtlseqdt0 tptp.xp tptp.xk))) (let ((_let_10 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xp W0) tptp.xk))) _let_9))) (let ((_let_11 (= tptp.xk tptp.sz10))) (let ((_let_12 (= tptp.xk tptp.sz00))) (let ((_let_13 (not (or _let_12 _let_11)))) (let ((_let_14 (tptp.sdtsldt0 _let_4 tptp.xp))) (let ((_let_15 (and (tptp.aNaturalNumber0 tptp.xk) (= _let_4 _let_1) (= tptp.xk _let_14)))) (let ((_let_16 (tptp.sdtlseqdt0 tptp.xm tptp.xp))) (let ((_let_17 (tptp.sdtlseqdt0 tptp.xn tptp.xp))) (let ((_let_18 (= tptp.xn tptp.xp))) (let ((_let_19 (and (not _let_18) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xn W0) tptp.xp))) _let_17 (not (= tptp.xm tptp.xp)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xm W0) tptp.xp))) _let_16))) (let ((_let_20 (not (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xp W0) tptp.xm))) (tptp.sdtlseqdt0 tptp.xp tptp.xm))))) (let ((_let_21 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= tptp.xp (tptp.sdtasdt0 W0 W1)))) (tptp.doDivides0 W0 tptp.xp))) (or (= W0 tptp.sz10) (= W0 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xp W0)))) (tptp.doDivides0 tptp.xp _let_4)))) (let ((_let_22 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_23 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_24 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_25 (and _let_24 _let_23 _let_22))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W2 W0))) (let ((_let_2 (tptp.sdtasdt0 W1 W0))) (let ((_let_3 (tptp.sdtasdt0 W0 W2))) (let ((_let_4 (tptp.sdtasdt0 W0 W1))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 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 ((_let_27 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))))) (let ((_let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))))) (let ((_let_29 (forall ((W0 $$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_30 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_31 (= tptp.sz00 tptp.xp))) (let ((_let_32 (tptp.aNaturalNumber0 _let_14))) (let ((_let_33 (= tptp.xm _let_14))) (let ((_let_34 (tptp.sdtlseqdt0 tptp.xm _let_14))) (let ((_let_35 (tptp.sdtasdt0 _let_14 tptp.xp))) (let ((_let_36 (tptp.sdtasdt0 tptp.xm tptp.xp))) (let ((_let_37 (not (= _let_36 _let_35)))) (let ((_let_38 (tptp.sdtasdt0 tptp.xp _let_14))) (let ((_let_39 (tptp.sdtlseqdt0 _let_2 _let_38))) (let ((_let_40 (= _let_2 _let_38))) (let ((_let_41 (not _let_40))) (let ((_let_42 (and _let_41 _let_39 _let_37 (tptp.sdtlseqdt0 _let_36 _let_35)))) (let ((_let_43 (not _let_34))) (let ((_let_44 (not _let_32))) (let ((_let_45 (not _let_23))) (let ((_let_46 (not _let_22))) (let ((_let_47 (or _let_46 _let_45 _let_44 _let_31 _let_33 _let_43 _let_42))) (let ((_let_48 (1))) (let ((_let_49 (ASSUME :args (_let_25)))) (let ((_let_50 (AND_ELIM _let_49 :args _let_48))) (let ((_let_51 (2))) (let ((_let_52 (AND_ELIM _let_49 :args _let_51))) (let ((_let_53 (0))) (let ((_let_54 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))) :args _let_53))) (let ((_let_55 (ASSUME :args (_let_15)))) (let ((_let_56 (AND_ELIM _let_55 :args _let_51))) (let ((_let_57 (EQ_RESOLVE _let_55 (MACRO_SR_EQ_INTRO _let_56 :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (AND_ELIM _let_57 :args _let_53))) (let ((_let_59 (tptp.sdtpldt0 tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_60 (= tptp.xm _let_59))) (let ((_let_61 (= _let_14 _let_59))) (let ((_let_62 (not _let_33))) (let ((_let_63 (not _let_60))) (let ((_let_64 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 _let_63))) (let ((_let_67 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xm (tptp.sdtpldt0 tptp.xp W0))))))) (let ((_let_68 (_let_67))) (let ((_let_69 (not _let_61))) (let ((_let_70 (or _let_65 _let_69))) (let ((_let_71 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtsldt0 (tptp.sdtasdt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 tptp.xp W0))))))) (let ((_let_72 (not _let_70))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_10)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_56 :args ((and (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xk (tptp.sdtpldt0 tptp.xp W0)))))) _let_9) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_74 (or))) (let ((_let_75 (not _let_71))) (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_71))) (REFL :args (_let_72)) :args _let_74)) (AND_ELIM _let_73 :args _let_53) :args (_let_72 true _let_71)))) (let ((_let_78 (REFL :args (_let_70)))) (let ((_let_79 (and _let_61 _let_63))) (let ((_let_80 (ASSUME :args (_let_63)))) (let ((_let_81 (=))) (let ((_let_82 (ASSUME :args (_let_61)))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_79)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_80 _let_82) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.xm)) (SYMM (SYMM _let_82)) :args _let_81) (FALSE_INTRO _let_80))) :args (_let_63 _let_61))) :args (_let_61 _let_63))) :args (true _let_79)) (CONG (REFL :args (_let_69)) (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_60))) (REFL :args (_let_62)) :args _let_74)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_70 1)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_61))) :args _let_74)) :args ((or _let_61 _let_70))) _let_77 :args (_let_61 true _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_65 _let_63 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_70 0)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_64))) :args _let_74)) :args ((or _let_64 _let_70))) _let_77 :args (_let_64 true _let_70)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_68) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_CBQI_PROP)) :args _let_68)) (NOT_NOT_ELIM (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))) :args _let_53)) :args (_let_66 false _let_67)) :args (_let_63 false _let_64 false _let_66)) :args (_let_62 false _let_61 true _let_60)))) (let ((_let_84 (tptp.sdtlseqdt0 tptp.xp _let_14))) (let ((_let_85 (not _let_84))) (let ((_let_86 (not _let_16))) (let ((_let_87 (or _let_45 _let_46 _let_44 _let_86 _let_85 _let_34))) (let ((_let_88 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (not _let_42))) (let ((_let_92 (or (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xp tptp.xm) W0) (tptp.sdtasdt0 tptp.xp (tptp.sdtsldt0 (tptp.sdtasdt0 tptp.xn tptp.xm) tptp.xp))))))) _let_39))) (let ((_let_93 (or (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 tptp.xp tptp.xm) (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xn tptp.xm) W0)))))) _let_5))) (let ((_let_94 (not _let_92))) (let ((_let_95 (tptp.sdtasdt0 tptp.xm tptp.xn))) (let ((_let_96 (and (not (= _let_95 _let_36)) (tptp.sdtlseqdt0 _let_95 _let_36) _let_7 _let_5))) (let ((_let_97 (not _let_17))) (let ((_let_98 (= tptp.sz00 tptp.xm))) (let ((_let_99 (not _let_24))) (let ((_let_100 (or _let_45 _let_99 _let_46 _let_98 _let_18 _let_97 _let_96))) (let ((_let_101 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W2 W0))) (let ((_let_2 (tptp.sdtasdt0 W1 W0))) (let ((_let_3 (tptp.sdtasdt0 W0 W2))) (let ((_let_4 (tptp.sdtasdt0 W0 W1))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (= tptp.sz00 W0) (= W1 W2) (not (tptp.sdtlseqdt0 W1 W2)) (and (not (= _let_3 _let_4)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_1 _let_2)) (tptp.sdtlseqdt0 _let_2 _let_1)))))))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (_let_101))) (let ((_let_104 (= tptp.sz00 _let_4))) (let ((_let_105 (= tptp.sz00 (tptp.sdtasdt0 tptp.xn tptp.sz00)))) (let ((_let_106 (not _let_98))) (let ((_let_107 (= tptp.sz00 _let_38))) (let ((_let_108 (= _let_4 _let_38))) (let ((_let_109 (not _let_104))) (let ((_let_110 (= tptp.sz00 _let_14))) (let ((_let_111 (not _let_107))) (let ((_let_112 (or _let_46 _let_44 _let_111 _let_31 _let_110))) (let ((_let_113 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (= tptp.sz00 (tptp.sdtasdt0 W0 W1))) (= tptp.sz00 W0) (= tptp.sz00 W1))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (AND_ELIM _let_57 :args _let_48))) (let ((_let_116 (not _let_108))) (let ((_let_117 (REFL :args (_let_116)))) (let ((_let_118 (and _let_108 _let_111))) (let ((_let_119 (ASSUME :args (_let_111)))) (let ((_let_120 (ASSUME :args (_let_108)))) (let ((_let_121 (SYMM (SYMM _let_120)))) (let ((_let_122 (and _let_105 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xn))))) (let ((_let_123 (or _let_99 _let_122))) (let ((_let_124 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= tptp.sz00 (tptp.sdtasdt0 W0 tptp.sz00)) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_125 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_126 (AND_ELIM _let_49 :args _let_53))) (let ((_let_127 (and _let_98 _let_105))) (let ((_let_128 (_let_98 _let_105))) (let ((_let_129 (ASSUME :args (_let_98)))) (let ((_let_130 (ASSUME :args (_let_105)))) (let ((_let_131 (and _let_41 _let_37))) (let ((_let_132 (or _let_46 _let_31 _let_45 _let_44 _let_131 _let_33))) (let ((_let_133 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1514 $$unsorted) (BOUND_VARIABLE_1512 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= tptp.sz00 W0) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1512)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1514)) (and (not (= (tptp.sdtasdt0 W0 BOUND_VARIABLE_1512) (tptp.sdtasdt0 W0 BOUND_VARIABLE_1514))) (not (= (tptp.sdtasdt0 BOUND_VARIABLE_1512 W0) (tptp.sdtasdt0 BOUND_VARIABLE_1514 W0)))) (= BOUND_VARIABLE_1512 BOUND_VARIABLE_1514))))) (let ((_let_134 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_135 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_131 0)) :args ((or _let_41 (not _let_131)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_132)) :args ((or _let_31 _let_45 _let_46 _let_44 _let_131 _let_33 (not _let_132)))) _let_54 _let_50 _let_52 _let_58 _let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_134 :args (tptp.xp _let_14 tptp.xm QUANTIFIERS_INST_CBQI_PROP)) :args (_let_133))) _let_134 :args (_let_132 false _let_133)) :args (_let_131 true _let_31 false _let_23 false _let_22 false _let_32 true _let_33 false _let_132)) :args (_let_41 false _let_131)))) (let ((_let_136 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))))) (let ((_let_137 (ASSUME :args (_let_6)))) (let ((_let_138 (ASSUME :args (_let_41)))) (let ((_let_139 (not _let_93))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_31 _let_45 _let_46 _let_44 _let_33 _let_43 _let_42 (not _let_47)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_102 :args (tptp.xp tptp.xm _let_14 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_103))) _let_102 :args (_let_47 false _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_42 1)) :args ((or _let_39 _let_91))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_92 1)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_56 :args ((not (and _let_7 _let_93 (not (= _let_1 _let_2)) (or (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 tptp.xp tptp.xk) (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xp tptp.xm) W0)))))) _let_3))) SB_DEFAULT SBA_FIXPOINT))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) (REFL :args (_let_139)) _let_136 (REFL :args (_let_94)) :args _let_74)) :args ((or _let_6 _let_40 _let_139 _let_94))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_120 _let_138 _let_137) :args (_let_6 _let_108 _let_41)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_138)) (TRUE_INTRO (TRANS (SYMM _let_137) _let_121)))) :args (_let_108 _let_41 _let_6)) :args ((not (and _let_6 _let_108 _let_41)) SB_LITERAL))) (CONG (REFL :args (_let_7)) _let_117 _let_136 :args _let_74)) :args ((or _let_7 _let_40 _let_116))) _let_135 _let_115 :args (_let_7 true _let_40 false _let_108)) _let_135 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_93 1)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_96 3)) :args ((or _let_5 (not _let_96)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_18 _let_99 _let_45 _let_46 _let_97 _let_98 _let_96 (not _let_100)))) (AND_ELIM _let_90 :args _let_53) _let_126 _let_50 _let_52 (AND_ELIM _let_90 :args _let_51) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_127)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_129 _let_130) (SCOPE (TRANS (SYMM (SYMM _let_130)) (CONG (REFL :args (tptp.xn)) (SYMM (SYMM _let_129)) :args (APPLY_UF tptp.sdtasdt0))) :args _let_128)) :args _let_128)) :args (true _let_127)) :args ((or _let_104 _let_106 (not _let_105)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_122 0)) :args ((or _let_105 (not _let_122)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_123)) :args ((or _let_99 _let_122 (not _let_123)))) _let_126 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_125 :args (tptp.xn QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_124))) _let_125 :args (_let_123 false _let_124)) :args (_let_122 false _let_24 false _let_123)) :args (_let_105 false _let_122)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_118)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_119 _let_120) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.sz00)) _let_121 :args _let_81) (FALSE_INTRO _let_119))) :args (_let_111 _let_108))) :args (_let_108 _let_111))) :args (true _let_118)) (CONG _let_117 (MACRO_SR_PRED_INTRO :args ((= (not _let_111) _let_107))) (REFL :args (_let_109)) :args _let_74)) :args ((or _let_116 _let_109 _let_107))) _let_115 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_112)) :args ((or _let_31 _let_110 _let_46 _let_44 _let_111 (not _let_112)))) _let_54 (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_13)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_56 :args ((not (or (= tptp.sz00 tptp.xk) (= tptp.sz10 tptp.xk))) SB_DEFAULT SBA_FIXPOINT)))) :args _let_53) _let_52 _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (tptp.xp _let_14 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_113))) _let_114 :args (_let_112 false _let_113)) :args (_let_111 true _let_31 true _let_110 false _let_22 false _let_32 false _let_112)) :args (_let_109 false _let_108 true _let_107)) :args (_let_106 false _let_105 true _let_104)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_102 :args (tptp.xm tptp.xn tptp.xp QUANTIFIERS_INST_CBQI_PROP)) :args _let_103))) _let_102 :args (_let_100 false _let_101)) :args (_let_96 true _let_18 false _let_24 false _let_23 false _let_22 false _let_17 true _let_98 false _let_100)) :args (_let_5 false _let_96)) :args (_let_93 false _let_5)) :args (_let_94 true _let_6 true _let_40 false _let_93)) :args ((not _let_39) true _let_92)) :args (_let_91 true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_45 _let_46 _let_86 _let_44 _let_85 _let_34 (not _let_87)))) _let_50 _let_52 (AND_ELIM _let_90 :args (5)) _let_58 (AND_ELIM _let_73 :args _let_48) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (tptp.xm tptp.xp _let_14 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_88))) _let_89 :args (_let_87 false _let_88)) :args (_let_34 false _let_23 false _let_22 false _let_16 false _let_32 false _let_84 false _let_87)) _let_83 _let_58 _let_54 _let_52 _let_50 :args (false false _let_47 true _let_42 false _let_34 true _let_33 false _let_32 true _let_31 false _let_22 false _let_23)) :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)))) (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)))) (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))))) (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))))) _let_30 (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)))) _let_29 (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))))) _let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))) (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) _let_27 (forall ((W0 $$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_26 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (not (= W0 tptp.sz00)) (tptp.sdtlseqdt0 W1 (tptp.sdtasdt0 W1 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W1 W2)) (tptp.doDivides0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 W2)) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))) (tptp.doDivides0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.doDivides0 W0 W1) (not (= W1 tptp.sz00))) (tptp.sdtlseqdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.isPrime0 W0) (and (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10)) (forall ((W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0)) (or (= W1 tptp.sz10) (= W1 W0)))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_25 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (or (and (not (= W2 tptp.sz00)) (not (= W2 tptp.sz10)) (forall ((W3 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W3) (exists ((W4 $$unsorted)) (and (tptp.aNaturalNumber0 W4) (= W2 (tptp.sdtasdt0 W3 W4)))) (tptp.doDivides0 W3 W2)) (or (= W3 tptp.sz10) (= W3 W2))))) (tptp.isPrime0 W2)) (or (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1)))) (=> (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (and (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W0 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W0)) (and (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W1 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W1))))))) _let_21 (not (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xp W0) tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn))) _let_20 _let_19 _let_15 _let_13 (and (not _let_12) (not _let_11)) (and (tptp.aNaturalNumber0 tptp.xr) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xk (tptp.sdtasdt0 tptp.xr W0)))) (tptp.doDivides0 tptp.xr tptp.xk) (not (= tptp.xr tptp.sz00)) (not (= tptp.xr tptp.sz10)) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= tptp.xr (tptp.sdtasdt0 W0 W1)))) (tptp.doDivides0 W0 tptp.xr))) (or (= W0 tptp.sz10) (= W0 tptp.xr)))) (tptp.isPrime0 tptp.xr)) (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xr W0) tptp.xk))) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xr W0)))) (tptp.doDivides0 tptp.xr _let_4)) _let_10 _let_8 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 15.28/15.47 )
% 15.28/15.47 % SZS output end Proof for NUM503+3
% 15.28/15.47 % cvc5---1.0.5 exiting
% 15.28/15.47 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------