TSTP Solution File: NUM514+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM514+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.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 10:44:40 EDT 2023
% Result : Theorem 26.00s 26.23s
% Output : Proof 26.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM514+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n013.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 13:21:17 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.48 %----Proving TF0_NAR, FOF, or CNF
% 26.00/26.23 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.evAfUYi3tK/cvc5---1.0.5_21415.p...
% 26.00/26.23 ------- get file name : TPTP file name is NUM514+1
% 26.00/26.23 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21415.smt2...
% 26.00/26.23 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.00/26.23 --- Run --no-e-matching --full-saturate-quant at 5...
% 26.00/26.23 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.00/26.23 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.00/26.23 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.00/26.23 % SZS status Theorem for NUM514+1
% 26.00/26.23 % SZS output start Proof for NUM514+1
% 26.00/26.23 (
% 26.00/26.23 (let ((_let_1 (tptp.sdtsldt0 tptp.xn tptp.xr))) (let ((_let_2 (tptp.sdtasdt0 _let_1 tptp.xm))) (let ((_let_3 (tptp.doDivides0 tptp.xp _let_2))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.sdtasdt0 tptp.xp (tptp.sdtsldt0 tptp.xk tptp.xr)))) (let ((_let_6 (= _let_5 _let_2))) (let ((_let_7 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_8 (= _let_7 (tptp.sdtasdt0 (tptp.sdtsldt0 (tptp.sdtasdt0 tptp.xp tptp.xk) tptp.xr) tptp.xr)))) (let ((_let_9 (tptp.sdtasdt0 _let_2 tptp.xr))) (let ((_let_10 (and (= _let_9 _let_7) _let_8))) (let ((_let_11 (tptp.doDivides0 tptp.xr tptp.xn))) (let ((_let_12 (tptp.isPrime0 tptp.xr))) (let ((_let_13 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_14 (and _let_13 (tptp.doDivides0 tptp.xr tptp.xk) _let_12))) (let ((_let_15 (= tptp.xk tptp.sz10))) (let ((_let_16 (= tptp.xk tptp.sz00))) (let ((_let_17 (tptp.sdtsldt0 _let_7 tptp.xp))) (let ((_let_18 (= tptp.xk _let_17))) (let ((_let_19 (tptp.doDivides0 tptp.xp _let_7))) (let ((_let_20 (tptp.isPrime0 tptp.xp))) (let ((_let_21 (and _let_20 _let_19))) (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 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.isPrime0 W0) (and (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10)) (forall ((W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0)) (or (= W1 tptp.sz10) (= W1 W0)))))))))) (let ((_let_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (let ((_let_28 (forall ((W0 $$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 ((_let_29 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_30 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 (tptp.sdtsldt0 tptp.xn tptp.xr) tptp.xm) (tptp.sdtasdt0 tptp.xp W2))))))) (let ((_let_31 (tptp.sdtsldt0 _let_17 tptp.xr))) (let ((_let_32 (= _let_2 (tptp.sdtasdt0 tptp.xp _let_31)))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.aNaturalNumber0 _let_31))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33))) (let ((_let_37 (not _let_30))) (let ((_let_38 (= _let_3 _let_37))) (let ((_let_39 (tptp.aNaturalNumber0 _let_2))) (let ((_let_40 (not _let_39))) (let ((_let_41 (not _let_22))) (let ((_let_42 (or _let_41 _let_40 _let_38))) (let ((_let_43 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (not _let_23))) (let ((_let_46 (tptp.aNaturalNumber0 _let_1))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_47 _let_45 _let_39))) (let ((_let_49 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (_let_49))) (let ((_let_52 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_53 (and _let_46 (= tptp.xn (tptp.sdtasdt0 tptp.xr _let_1))))) (let ((_let_54 (not _let_11))) (let ((_let_55 (= tptp.sz00 tptp.xr))) (let ((_let_56 (not _let_24))) (let ((_let_57 (not _let_13))) (let ((_let_58 (or _let_57 _let_56 _let_55 _let_54 _let_53))) (let ((_let_59 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1640 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1640) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1640))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1640)))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (_let_59))) (let ((_let_62 (not _let_55))) (let ((_let_63 (and _let_62 (not (= tptp.sz10 tptp.xr)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xr)) (= tptp.sz10 W1) (= W1 tptp.xr)))))) (let ((_let_64 (= _let_12 _let_63))) (let ((_let_65 (or _let_57 _let_64))) (let ((_let_66 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= (tptp.isPrime0 W0) (and (not (= tptp.sz00 W0)) (not (= tptp.sz10 W0)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 W0)) (= tptp.sz10 W1) (= W0 W1))))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (_let_66))) (let ((_let_69 (0))) (let ((_let_70 (ASSUME :args (_let_18)))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO _let_70 :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (AND_ELIM _let_71 :args _let_69))) (let ((_let_73 (2))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_63 0)) :args ((or _let_62 (not _let_63)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_64)) :args ((or (not _let_12) _let_63 (not _let_64)))) (AND_ELIM _let_71 :args _let_73) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_57 _let_64 (not _let_65)))) _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_67 :args (tptp.xr QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.isPrime0 W0)))) :args _let_68))) _let_67 :args (_let_65 false _let_66)) :args (_let_64 false _let_13 false _let_65)) :args (_let_63 false _let_12 false _let_64)) :args (_let_62 false _let_63)))) (let ((_let_75 (ASSUME :args (_let_25)))) (let ((_let_76 (AND_ELIM _let_75 :args _let_69))) (let ((_let_77 (1))) (let ((_let_78 (AND_ELIM _let_75 :args _let_77))) (let ((_let_79 (AND_ELIM _let_75 :args _let_73))) (let ((_let_80 (not _let_38))) (let ((_let_81 (not _let_36))) (let ((_let_82 (and _let_34 (= _let_17 (tptp.sdtasdt0 tptp.xr _let_31))))) (let ((_let_83 (tptp.doDivides0 tptp.xr _let_17))) (let ((_let_84 (not _let_83))) (let ((_let_85 (tptp.aNaturalNumber0 _let_17))) (let ((_let_86 (not _let_85))) (let ((_let_87 (or _let_57 _let_86 _let_55 _let_84 _let_82))) (let ((_let_88 (tptp.sdtasdt0 tptp.xp _let_17))) (let ((_let_89 (tptp.sdtasdt0 (tptp.sdtsldt0 _let_88 tptp.xr) tptp.xr))) (let ((_let_90 (and _let_85 (= _let_88 _let_89)))) (let ((_let_91 (= _let_17 (tptp.sdtsldt0 _let_89 tptp.xp)))) (let ((_let_92 (= _let_90 _let_91))) (let ((_let_93 (tptp.doDivides0 tptp.xp _let_89))) (let ((_let_94 (not _let_93))) (let ((_let_95 (= tptp.sz00 tptp.xp))) (let ((_let_96 (tptp.aNaturalNumber0 _let_89))) (let ((_let_97 (not _let_96))) (let ((_let_98 (or _let_41 _let_97 _let_95 _let_94 _let_92))) (let ((_let_99 (= _let_7 _let_89))) (let ((_let_100 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_10)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_70 :args ((and (= _let_7 _let_9) _let_8) SB_DEFAULT SBA_FIXPOINT)))) :args _let_77))) (let ((_let_101 (ASSUME :args (_let_21)))) (let ((_let_102 (and _let_19 _let_99))) (let ((_let_103 (_let_19 _let_99))) (let ((_let_104 (ASSUME :args (_let_19)))) (let ((_let_105 (_let_99))) (let ((_let_106 (ASSUME :args _let_105))) (let ((_let_107 (SYMM (SYMM _let_106)))) (let ((_let_108 (SYMM _let_107))) (let ((_let_109 (REFL :args (tptp.xp)))) (let ((_let_110 (tptp.aNaturalNumber0 _let_7))) (let ((_let_111 (or _let_56 _let_45 _let_110))) (let ((_let_112 (and _let_99 _let_110))) (let ((_let_113 (ASSUME :args (_let_110)))) (let ((_let_114 (not _let_95))) (let ((_let_115 (and _let_114 (not (= tptp.sz10 tptp.xp)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xp)) (= tptp.sz10 W1) (= W1 tptp.xp)))))) (let ((_let_116 (= _let_20 _let_115))) (let ((_let_117 (or _let_41 _let_116))) (let ((_let_118 (_let_30))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_118) :args (_let_31 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_118)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_33 _let_35 _let_81))) (EQ_RESOLVE (ASSUME :args (_let_6)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_70 :args ((= _let_2 _let_5) SB_DEFAULT SBA_FIXPOINT)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_82 0)) :args ((or _let_34 (not _let_82)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_57 _let_84 _let_55 _let_86 _let_82 (not _let_87)))) _let_72 (AND_ELIM _let_71 :args _let_77) _let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_90 0)) :args ((or _let_85 (not _let_90)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_92)) :args ((or _let_90 (not _let_91) (not _let_92)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_106 (SCOPE (CONG _let_107 _let_109 :args (APPLY_UF tptp.sdtsldt0)) :args _let_105)) :args _let_105)) _let_100 :args (_let_91 false _let_99)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_41 _let_95 _let_97 _let_94 _let_92 (not _let_98)))) _let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_115 0)) :args ((or _let_114 (not _let_115)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_116)) :args ((or (not _let_20) _let_115 (not _let_116)))) (AND_ELIM _let_101 :args _let_69) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_117)) :args ((or _let_41 _let_116 (not _let_117)))) _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_67 :args (tptp.xp QUANTIFIERS_INST_CBQI_PROP)) :args _let_68))) _let_67 :args (_let_117 false _let_66)) :args (_let_116 false _let_22 false _let_117)) :args (_let_115 false _let_20 false _let_116)) :args (_let_114 false _let_115)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_112)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_113 _let_106) (SCOPE (TRUE_ELIM (TRANS (CONG _let_108 :args (APPLY_UF tptp.aNaturalNumber0)) (TRUE_INTRO _let_113))) :args (_let_110 _let_99))) :args (_let_99 _let_110))) :args (true _let_112)) :args ((or (not _let_99) _let_96 (not _let_110)))) _let_100 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_111)) :args ((or _let_56 _let_45 _let_110 (not _let_111)))) _let_76 _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_52)) :args _let_51)) _let_50 :args (_let_111 false _let_49)) :args (_let_110 false _let_24 false _let_23 false _let_111)) :args (_let_96 false _let_99 false _let_110)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_102)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_104 _let_106) (SCOPE (TRUE_ELIM (TRANS (CONG _let_109 _let_108 :args (APPLY_UF tptp.doDivides0)) (TRUE_INTRO _let_104))) :args _let_103)) :args _let_103)) :args (true _let_102)) (AND_ELIM _let_101 :args _let_77) _let_100 :args (_let_93 false _let_19 false _let_99)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.xp _let_89 _let_17 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_61))) _let_60 :args (_let_98 false _let_59)) :args (_let_92 false _let_22 true _let_95 false _let_96 false _let_93 false _let_98)) :args (_let_90 false _let_91 false _let_92)) :args (_let_85 false _let_90)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.xr _let_17 _let_31 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_61))) _let_60 :args (_let_87 false _let_59)) :args (_let_82 false _let_13 false _let_83 true _let_55 false _let_85 false _let_87)) :args (_let_34 false _let_82)) :args (_let_81 false _let_32 false _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_38)) (CONG (REFL :args (_let_80)) (REFL :args (_let_3)) (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_30))) :args (or))) :args ((or _let_3 _let_30 _let_80))) (ASSUME :args (_let_4)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_40 _let_38 (not _let_42)))) _let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_45 _let_47 _let_39 (not _let_48)))) _let_78 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_53 0)) :args ((or _let_46 (not _let_53)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_54 _let_56 _let_57 _let_55 _let_53 (not _let_58)))) (ASSUME :args (_let_11)) _let_76 _let_72 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.xr tptp.xn _let_1 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_61))) _let_60 :args (_let_58 false _let_59)) :args (_let_53 false _let_11 false _let_24 false _let_13 true _let_55 false _let_58)) :args (_let_46 false _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_1 tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_52)) :args _let_51)) _let_50 :args (_let_48 false _let_49)) :args (_let_39 false _let_23 false _let_46 false _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.xp _let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.doDivides0 W0 W1)))) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_38 false _let_22 false _let_39 false _let_42)) :args (_let_30 true _let_3 false _let_38)) :args (false true _let_36 false _let_30)) :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_29 (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))))) (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))))) (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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$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 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (let ((_let_2 (tptp.sdtpldt0 W0 W2))) (let ((_let_3 (tptp.sdtpldt0 W2 W1))) (let ((_let_4 (tptp.sdtpldt0 W2 W0))) (=> (tptp.aNaturalNumber0 W2) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))))) (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) _let_28 _let_27 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) _let_26 (forall ((W0 $$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 (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_21 (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_18 (not (or _let_16 _let_15)) (and (not _let_16) (not _let_15)) _let_14 (and (tptp.sdtlseqdt0 tptp.xr tptp.xk) (tptp.doDivides0 tptp.xr _let_7)) (and (not (= tptp.xk tptp.xp)) (tptp.sdtlseqdt0 tptp.xk tptp.xp)) (or _let_11 (tptp.doDivides0 tptp.xr tptp.xm)) _let_11 (and (not (= _let_1 tptp.xn)) (tptp.sdtlseqdt0 _let_1 tptp.xn)) _let_10 _let_6 _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.00/26.24 )
% 26.00/26.24 % SZS output end Proof for NUM514+1
% 26.00/26.24 % cvc5---1.0.5 exiting
% 26.00/26.24 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------