TSTP Solution File: NUM506+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM506+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 10:44:32 EDT 2023
% Result : Theorem 29.99s 30.32s
% Output : Proof 29.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM506+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.12 % Command : do_cvc5 %s %d
% 0.13/0.33 % Computer : n031.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 12:18:52 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.46 %----Proving TF0_NAR, FOF, or CNF
% 29.99/30.32 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Wq7euXx3us/cvc5---1.0.5_2800.p...
% 29.99/30.32 ------- get file name : TPTP file name is NUM506+1
% 29.99/30.32 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_2800.smt2...
% 29.99/30.32 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 29.99/30.32 --- Run --no-e-matching --full-saturate-quant at 5...
% 29.99/30.32 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 29.99/30.32 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 29.99/30.32 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 29.99/30.32 % SZS status Theorem for NUM506+1
% 29.99/30.32 % SZS output start Proof for NUM506+1
% 29.99/30.32 (
% 29.99/30.32 (let ((_let_1 (tptp.doDivides0 tptp.xr tptp.xm))) (let ((_let_2 (tptp.doDivides0 tptp.xr tptp.xn))) (let ((_let_3 (not (or _let_2 _let_1)))) (let ((_let_4 (tptp.sdtlseqdt0 tptp.xk tptp.xp))) (let ((_let_5 (and (not (= tptp.xk tptp.xp)) _let_4))) (let ((_let_6 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_7 (tptp.doDivides0 tptp.xr _let_6))) (let ((_let_8 (and (tptp.sdtlseqdt0 tptp.xr tptp.xk) _let_7))) (let ((_let_9 (tptp.isPrime0 tptp.xr))) (let ((_let_10 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_11 (and _let_10 (tptp.doDivides0 tptp.xr tptp.xk) _let_9))) (let ((_let_12 (= tptp.xk tptp.sz10))) (let ((_let_13 (= tptp.xk tptp.sz00))) (let ((_let_14 (tptp.sdtsldt0 _let_6 tptp.xp))) (let ((_let_15 (= tptp.xk _let_14))) (let ((_let_16 (tptp.doDivides0 tptp.xp _let_6))) (let ((_let_17 (tptp.isPrime0 tptp.xp))) (let ((_let_18 (and _let_17 _let_16))) (let ((_let_19 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.isPrime0 W2) (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (=> (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))))))) (let ((_let_20 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_21 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_22 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_23 (and _let_22 _let_21 _let_20))) (let ((_let_24 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.isPrime0 W0) (and (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10)) (forall ((W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0)) (or (= W1 tptp.sz10) (= W1 W0)))))))))) (let ((_let_25 (forall ((W0 $$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)))))))))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))))) (let ((_let_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (let ((_let_2 (tptp.sdtpldt0 W0 W2))) (let ((_let_3 (tptp.sdtpldt0 W2 W1))) (let ((_let_4 (tptp.sdtpldt0 W2 W0))) (=> (tptp.aNaturalNumber0 W2) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))))))) (let ((_let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))))) (let ((_let_29 (forall ((W0 $$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_30 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))))) (let ((_let_31 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_32 (forall ((W0 $$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 ((_let_33 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_34 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_35 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_36 (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_37 (tptp.sdtlseqdt0 tptp.xp _let_14))) (let ((_let_38 (tptp.sdtlseqdt0 tptp.xr _let_14))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.sdtlseqdt0 tptp.xp tptp.xr))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.aNaturalNumber0 _let_14))) (let ((_let_43 (not _let_42))) (let ((_let_44 (not _let_10))) (let ((_let_45 (not _let_20))) (let ((_let_46 (or _let_45 _let_44 _let_43 _let_41 _let_39 _let_37))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (tptp.sdtlseqdt0 tptp.xp tptp.xp))) (let ((_let_50 (= tptp.xp tptp.xr))) (let ((_let_51 (tptp.sdtlseqdt0 tptp.xr tptp.xp))) (let ((_let_52 (not _let_50))) (let ((_let_53 (and _let_52 _let_51))) (let ((_let_54 (or _let_45 _let_44 _let_40 _let_53))) (let ((_let_55 (tptp.sdtpldt0 tptp.xm tptp.xn))) (let ((_let_56 (tptp.aNaturalNumber0 _let_55))) (let ((_let_57 (tptp.sdtpldt0 tptp.xr _let_55))) (let ((_let_58 (tptp.sdtpldt0 tptp.xp _let_55))) (let ((_let_59 (not (= _let_58 _let_57)))) (let ((_let_60 (tptp.sdtpldt0 _let_55 tptp.xr))) (let ((_let_61 (tptp.sdtpldt0 _let_55 tptp.xp))) (let ((_let_62 (= _let_61 _let_60))) (let ((_let_63 (not _let_62))) (let ((_let_64 (and _let_63 _let_59))) (let ((_let_65 (not _let_56))) (let ((_let_66 (or _let_65 _let_45 _let_44 _let_64 _let_50))) (let ((_let_67 (tptp.sdtlseqdt0 _let_60 _let_61))) (let ((_let_68 (and _let_63 _let_67 _let_59 (tptp.sdtlseqdt0 _let_57 _let_58)))) (let ((_let_69 (not _let_51))) (let ((_let_70 (or _let_44 _let_45 _let_50 _let_69 _let_65 _let_68))) (let ((_let_71 (tptp.sdtpldt0 tptp.xn tptp.xm))) (let ((_let_72 (= _let_71 _let_55))) (let ((_let_73 (tptp.sdtpldt0 _let_71 tptp.xr))) (let ((_let_74 (tptp.sdtpldt0 _let_71 tptp.xp))) (let ((_let_75 (= _let_74 _let_73))) (let ((_let_76 (= _let_74 (tptp.sdtpldt0 tptp.xp _let_71)))) (let ((_let_77 (= _let_73 (tptp.sdtpldt0 tptp.xr _let_71)))) (let ((_let_78 (tptp.sdtlseqdt0 _let_73 _let_74))) (let ((_let_79 (tptp.iLess0 _let_73 _let_74))) (let ((_let_80 (not _let_78))) (let ((_let_81 (tptp.aNaturalNumber0 _let_74))) (let ((_let_82 (not _let_81))) (let ((_let_83 (tptp.aNaturalNumber0 _let_73))) (let ((_let_84 (not _let_83))) (let ((_let_85 (or _let_84 _let_82 _let_75 _let_80 _let_79))) (let ((_let_86 (or _let_45 _let_49))) (let ((_let_87 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (2))) (let ((_let_90 (ASSUME :args (_let_23)))) (let ((_let_91 (AND_ELIM _let_90 :args _let_89))) (let ((_let_92 (not _let_49))) (let ((_let_93 (or))) (let ((_let_94 (APPLY_UF tptp.sdtlseqdt0))) (let ((_let_95 (REFL :args (tptp.xp)))) (let ((_let_96 (0))) (let ((_let_97 (ASSUME :args (_let_15)))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO _let_97 :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (AND_ELIM _let_98 :args _let_96))) (let ((_let_100 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.sdtlseqdt0 W0 W1) (and (not (= W0 W1)) (tptp.sdtlseqdt0 W1 W0)))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (not _let_22))) (let ((_let_103 (not _let_21))) (let ((_let_104 (or _let_103 _let_102 _let_56))) (let ((_let_105 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (_let_105))) (let ((_let_108 ((tptp.sdtpldt0 W0 W1)))) (let ((_let_109 (1))) (let ((_let_110 (AND_ELIM _let_90 :args _let_109))) (let ((_let_111 (AND_ELIM _let_90 :args _let_96))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_102 _let_103 _let_56 (not _let_104)))) _let_111 _let_110 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (tptp.xm tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_108)) :args _let_107)) _let_106 :args (_let_104 false _let_105)) :args (_let_56 false _let_22 false _let_21 false _let_104)))) (let ((_let_113 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (and (not (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2))) (not (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0)))) (= W1 W2))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1509 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1509))) (let ((_let_2 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1509))) (let ((_let_3 (tptp.sdtpldt0 BOUND_VARIABLE_1509 W1))) (let ((_let_4 (tptp.sdtpldt0 BOUND_VARIABLE_1509 W0))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1509)) (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_116 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (or _let_102 _let_103 _let_72))) (let ((_let_118 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_119 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_120 (_let_118))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_117)) :args ((or _let_102 _let_103 _let_72 (not _let_117)))) _let_111 _let_110 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_119 :args (tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.aNaturalNumber0 W0) false)) (not (= (tptp.aNaturalNumber0 W1) false))))) :args _let_120)) _let_119 :args (_let_117 false _let_118)) :args (_let_72 false _let_22 false _let_21 false _let_117)))) (let ((_let_122 (not _let_75))) (let ((_let_123 (not _let_72))) (let ((_let_124 (and _let_72 _let_63))) (let ((_let_125 (ASSUME :args (_let_63)))) (let ((_let_126 (APPLY_UF tptp.sdtpldt0))) (let ((_let_127 (REFL :args (tptp.xr)))) (let ((_let_128 (ASSUME :args (_let_72)))) (let ((_let_129 (SYMM _let_128))) (let ((_let_130 (SYMM _let_129))) (let ((_let_131 (CONG _let_130 _let_127 :args _let_126))) (let ((_let_132 (CONG _let_130 _let_95 :args _let_126))) (let ((_let_133 (tptp.aNaturalNumber0 _let_71))) (let ((_let_134 (not _let_133))) (let ((_let_135 (or _let_134 _let_45 _let_76))) (let ((_let_136 ((tptp.sdtpldt0 W0 W1)))) (let ((_let_137 (or _let_102 _let_103 _let_133))) (let ((_let_138 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_137)) :args ((or _let_102 _let_103 _let_133 (not _let_137)))) _let_111 _let_110 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_108)) :args _let_107)) _let_106 :args (_let_137 false _let_105)) :args (_let_133 false _let_22 false _let_21 false _let_137)))) (let ((_let_139 (or _let_134 _let_44 _let_77))) (let ((_let_140 (and _let_72 _let_76 _let_77 _let_67))) (let ((_let_141 (ASSUME :args (_let_67)))) (let ((_let_142 (ASSUME :args (_let_76)))) (let ((_let_143 (CONG _let_95 _let_129 :args _let_126))) (let ((_let_144 (ASSUME :args (_let_77)))) (let ((_let_145 (TRANS (CONG _let_127 _let_129 :args _let_126) (SYMM _let_144)))) (let ((_let_146 (not _let_79))) (let ((_let_147 (not _let_7))) (let ((_let_148 (not _let_9))) (let ((_let_149 (or _let_102 _let_103 _let_44 _let_148 _let_147 _let_146 _let_2 _let_1))) (let ((_let_150 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))) (let ((_let_151 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_152 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO _let_97 :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_153 (ASSUME :args (_let_3)))) (let ((_let_154 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))))) (let ((_let_155 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_156 (or _let_134 _let_44 _let_83))) (let ((_let_157 (or _let_134 _let_45 _let_81))) (let ((_let_158 (= tptp.xp _let_14))) (let ((_let_159 (not _let_37))) (let ((_let_160 (tptp.sdtlseqdt0 _let_14 tptp.xp))) (let ((_let_161 (not _let_160))) (let ((_let_162 (or _let_43 _let_45 _let_161 _let_159 _let_158))) (let ((_let_163 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))))) (let ((_let_164 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_165 (and _let_42 (= _let_6 (tptp.sdtasdt0 tptp.xp _let_14))))) (let ((_let_166 (not _let_16))) (let ((_let_167 (= tptp.sz00 tptp.xp))) (let ((_let_168 (tptp.aNaturalNumber0 _let_6))) (let ((_let_169 (not _let_168))) (let ((_let_170 (or _let_45 _let_169 _let_167 _let_166 _let_165))) (let ((_let_171 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1623 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1623) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1623))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1623)))))) (let ((_let_172 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let 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(tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))) _let_31 _let_30 _let_29 _let_28 _let_27 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W2 W0))) (let ((_let_2 (tptp.sdtasdt0 W1 W0))) (let ((_let_3 (tptp.sdtasdt0 W0 W2))) (let ((_let_4 (tptp.sdtasdt0 W0 W1))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 W2)) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))) (forall ((W0 $$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))) _let_26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))) _let_25 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) _let_24 (forall ((W0 $$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_23 _let_19 _let_18 (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xm)) (and (not (= tptp.xn tptp.xp)) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (tptp.sdtlseqdt0 tptp.xm tptp.xp)) _let_15 (not (or _let_13 _let_12)) (and (not _let_13) (not _let_12)) _let_11 _let_8 _let_5 _let_3 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 29.99/30.32 )
% 29.99/30.32 % SZS output end Proof for NUM506+1
% 29.99/30.32 % cvc5---1.0.5 exiting
% 29.99/30.33 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------