TSTP Solution File: NUM454+6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM454+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.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 10:44:03 EDT 2023
% Result : Theorem 2.16s 2.39s
% Output : Proof 2.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM454+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n017.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 08:13:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.20/0.50 %----Proving TF0_NAR, FOF, or CNF
% 2.16/2.39 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.u7z8CtZFFI/cvc5---1.0.5_14351.p...
% 2.16/2.39 ------- get file name : TPTP file name is NUM454+6
% 2.16/2.39 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_14351.smt2...
% 2.16/2.39 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.16/2.39 % SZS status Theorem for NUM454+6
% 2.16/2.39 % SZS output start Proof for NUM454+6
% 2.16/2.39 (
% 2.16/2.39 (let ((_let_1 (tptp.smndt0 tptp.sz10))) (let ((_let_2 (tptp.smndt0 tptp.xp))) (let ((_let_3 (tptp.sdtpldt0 tptp.sz10 _let_2))) (let ((_let_4 (tptp.sdtpldt0 tptp.sz10 tptp.xp))) (let ((_let_5 (not (or (not (= _let_4 _let_1)) (not (= _let_3 _let_1)))))) (let ((_let_6 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp))) (let ((_let_7 (tptp.sbsmnsldt0 tptp.xS))) (let ((_let_8 (tptp.stldt0 _let_7))) (let ((_let_9 (tptp.aSet0 _let_7))) (let ((_let_10 (tptp.aInteger0 tptp.xp))) (let ((_let_11 (and _let_10 (not (= tptp.xp tptp.sz00)) (tptp.aSet0 _let_6) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp)))) (let ((_let_2 (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.sz10 tptp.xp))) (let ((_let_3 (tptp.aDivisorOf0 tptp.xp (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.sz10))))) (let ((_let_4 (tptp.aInteger0 W0))) (and (=> _let_1 (and _let_4 (exists ((W1 $$unsorted)) (and (tptp.aInteger0 W1) (= (tptp.sdtasdt0 tptp.xp W1) (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.sz10))))) _let_3 _let_2)) (=> (and _let_4 (or (exists ((W1 $$unsorted)) (and (tptp.aInteger0 W1) (= (tptp.sdtasdt0 tptp.xp W1) (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.sz10))))) _let_3 _let_2)) _let_1))))))) _let_9 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sbsmnsldt0 tptp.xS)) (and (tptp.aInteger0 W0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xS) (tptp.aElementOf0 W0 W1)))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sbsmnsldt0 tptp.xS))) (= (tptp.aElementOf0 W0 (tptp.stldt0 _let_1)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 _let_1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp)) (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))))) (tptp.aSubsetOf0 _let_6 _let_8)))) (let ((_let_12 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))))) (let ((_let_13 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 tptp.sz10))) (let ((_let_2 (tptp.smndt0 W0))) (=> (tptp.aInteger0 W0) (and (= (tptp.sdtasdt0 _let_1 W0) _let_2) (= _let_2 (tptp.sdtasdt0 W0 _let_1))))))))) (let ((_let_14 (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_15 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W2))) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2)) (and (= (tptp.sdtasdt0 W0 (tptp.sdtpldt0 W1 W2)) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) _let_1)) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 _let_1 (tptp.sdtasdt0 W1 W2))))))))) (let ((_let_16 (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_17 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2)) (= (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2)) (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2)))))) (let ((_let_18 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (=> (tptp.aInteger0 W0) (and (= (tptp.sdtpldt0 W0 _let_1) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 _let_1 W0)))))))) (let ((_let_19 (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_21 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2)) (= (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2)) (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2)))))) (let ((_let_22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (tptp.aInteger0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_23 (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (tptp.aInteger0 (tptp.smndt0 W0)))))) (let ((_let_24 (tptp.aInteger0 tptp.sz10))) (let ((_let_25 (= _let_1 _let_4))) (let ((_let_26 (= _let_1 _let_3))) (let ((_let_27 (tptp.sdtpldt0 tptp.xp tptp.sz10))) (let ((_let_28 (= _let_4 _let_27))) (let ((_let_29 (tptp.sdtpldt0 _let_2 tptp.sz10))) (let ((_let_30 (= _let_3 _let_29))) (let ((_let_31 (= tptp.sz10 (tptp.sdtpldt0 tptp.sz00 tptp.sz10)))) (let ((_let_32 (= tptp.xp (tptp.sdtpldt0 tptp.xp tptp.sz00)))) (let ((_let_33 (tptp.sdtpldt0 tptp.sz10 _let_1))) (let ((_let_34 (= tptp.sz00 _let_33))) (let ((_let_35 (= tptp.sz00 (tptp.sdtpldt0 _let_1 tptp.sz10)))) (let ((_let_36 (tptp.sdtpldt0 tptp.xp _let_2))) (let ((_let_37 (= tptp.sz00 _let_36))) (let ((_let_38 (tptp.sdtasdt0 tptp.xp tptp.sz10))) (let ((_let_39 (= tptp.xp _let_38))) (let ((_let_40 (tptp.sdtasdt0 tptp.sz10 tptp.xp))) (let ((_let_41 (= tptp.xp _let_40))) (let ((_let_42 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xp)))) (let ((_let_43 (= _let_1 (tptp.sdtasdt0 tptp.sz10 _let_1)))) (let ((_let_44 (tptp.sdtasdt0 _let_1 tptp.xp))) (let ((_let_45 (= _let_2 _let_44))) (let ((_let_46 (tptp.sdtasdt0 tptp.xp _let_1))) (let ((_let_47 (= _let_2 _let_46))) (let ((_let_48 (= (tptp.sdtpldt0 tptp.xp _let_29) (tptp.sdtpldt0 _let_36 tptp.sz10)))) (let ((_let_49 (= (tptp.sdtpldt0 _let_2 _let_33) (tptp.sdtpldt0 _let_29 _let_1)))) (let ((_let_50 (tptp.sdtpldt0 tptp.sz10 tptp.sz10))) (let ((_let_51 (= (tptp.sdtpldt0 _let_2 _let_50) (tptp.sdtpldt0 _let_29 tptp.sz10)))) (let ((_let_52 (= (tptp.sdtpldt0 tptp.xp _let_1) (tptp.sdtpldt0 _let_1 tptp.xp)))) (let ((_let_53 (= (tptp.sdtasdt0 _let_1 _let_38) (tptp.sdtasdt0 _let_44 tptp.sz10)))) (let ((_let_54 (= tptp.sz00 (tptp.sdtasdt0 tptp.xp tptp.xp)))) (let ((_let_55 (= _let_2 (tptp.sdtpldt0 _let_2 tptp.sz00)))) (let ((_let_56 (= (tptp.sdtasdt0 _let_50 tptp.xp) (tptp.sdtpldt0 _let_40 _let_40)))) (let ((_let_57 (tptp.sdtasdt0 _let_2 tptp.sz10))) (let ((_let_58 (= (tptp.sdtasdt0 _let_2 _let_50) (tptp.sdtpldt0 _let_57 _let_57)))) (let ((_let_59 (= (tptp.sdtasdt0 tptp.xp _let_50) (tptp.sdtpldt0 _let_38 _let_38)))) (let ((_let_60 (= (tptp.sdtpldt0 _let_4 _let_27) (tptp.sdtpldt0 (tptp.sdtpldt0 _let_4 tptp.xp) tptp.sz10)))) (let ((_let_61 (= (tptp.sdtpldt0 tptp.xp _let_33) (tptp.sdtpldt0 _let_27 _let_1)))) (let ((_let_62 (0))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (1))) (let ((_let_65 (not _let_10))) (let ((_let_66 (not _let_24))) (let ((_let_67 (or _let_66 _let_65 _let_28))) (let ((_let_68 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aInteger0 W0)) (not (tptp.aInteger0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (_let_68))) (let ((_let_71 ((tptp.sdtpldt0 W0 W1)))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (AND_ELIM _let_72 :args _let_62))) (let ((_let_74 (ASSUME :args (_let_24)))) (let ((_let_75 (tptp.aInteger0 _let_2))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_66 _let_76 _let_30))) (let ((_let_78 (or _let_65 _let_75))) (let ((_let_79 (forall ((W0 $$unsorted)) (or (not (tptp.aInteger0 W0)) (tptp.aInteger0 (tptp.smndt0 W0)))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (_let_79))) (let ((_let_82 ((tptp.smndt0 W0)))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_65 _let_75 (not _let_78)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_82)) :args _let_81)) _let_80 :args (_let_78 false _let_79)) :args (_let_75 false _let_10 false _let_78)))) (let ((_let_84 (and (= tptp.sz10 (tptp.sdtpldt0 tptp.sz10 tptp.sz00)) _let_31))) (let ((_let_85 (or _let_66 _let_84))) (let ((_let_86 (forall ((W0 $$unsorted)) (or (not (tptp.aInteger0 W0)) (and (= W0 (tptp.sdtpldt0 W0 tptp.sz00)) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (_let_86))) (let ((_let_89 ((not (= (tptp.aInteger0 W0) false))))) (let ((_let_90 (and _let_32 (= tptp.xp (tptp.sdtpldt0 tptp.sz00 tptp.xp))))) (let ((_let_91 (or _let_65 _let_90))) (let ((_let_92 (and _let_34 _let_35))) (let ((_let_93 (or _let_66 _let_92))) (let ((_let_94 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (or (not (tptp.aInteger0 W0)) (and (= tptp.sz00 (tptp.sdtpldt0 W0 _let_1)) (= tptp.sz00 (tptp.sdtpldt0 _let_1 W0)))))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (_let_94))) (let ((_let_97 ((not (= (tptp.aInteger0 W0) false))))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_66 _let_92 (not _let_93)))) _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (tptp.sz10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_97)) :args _let_96)) _let_95 :args (_let_93 false _let_94)) :args (_let_92 false _let_24 false _let_93)))) (let ((_let_99 (not _let_92))) (let ((_let_100 (and _let_37 (= tptp.sz00 (tptp.sdtpldt0 _let_2 tptp.xp))))) (let ((_let_101 (or _let_65 _let_100))) (let ((_let_102 (and _let_39 _let_41))) (let ((_let_103 (or _let_65 _let_102))) (let ((_let_104 (forall ((W0 $$unsorted)) (or (not (tptp.aInteger0 W0)) (and (= W0 (tptp.sdtasdt0 W0 tptp.sz10)) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_105 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_65 _let_102 (not _let_103)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_105 :args (tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aInteger0 W0) false))))) :args (_let_104))) _let_105 :args (_let_103 false _let_104)) :args (_let_102 false _let_10 false _let_103)))) (let ((_let_107 (not _let_102))) (let ((_let_108 (and (= tptp.sz00 (tptp.sdtasdt0 tptp.xp tptp.sz00)) _let_42))) (let ((_let_109 (or _let_65 _let_108))) (let ((_let_110 (forall ((W0 $$unsorted)) (or (not (tptp.aInteger0 W0)) (and (= tptp.sz00 (tptp.sdtasdt0 W0 tptp.sz00)) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_111 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_112 (and (= _let_1 (tptp.sdtasdt0 _let_1 tptp.sz10)) _let_43))) (let ((_let_113 (or _let_66 _let_112))) (let ((_let_114 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 tptp.sz10))) (let ((_let_2 (tptp.smndt0 W0))) (or (not (tptp.aInteger0 W0)) (and (= _let_2 (tptp.sdtasdt0 _let_1 W0)) (= _let_2 (tptp.sdtasdt0 W0 _let_1))))))))) (let ((_let_115 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_116 (_let_114))) (let ((_let_117 ((not (= (tptp.aInteger0 W0) false))))) (let ((_let_118 (and _let_45 _let_47))) (let ((_let_119 (or _let_65 _let_118))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_65 _let_118 (not _let_119)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_115 :args (tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_117)) :args _let_116)) _let_115 :args (_let_119 false _let_114)) :args (_let_118 false _let_10 false _let_119)))) (let ((_let_121 (not _let_118))) (let ((_let_122 (or _let_65 _let_76 _let_66 _let_48))) (let ((_let_123 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aInteger0 W0)) (not (tptp.aInteger0 W1)) (not (tptp.aInteger0 W2)) (= (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2)) (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2)))))) (let ((_let_124 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_125 (_let_123))) (let ((_let_126 ((tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) (let ((_let_127 (tptp.aInteger0 _let_1))) (let ((_let_128 (not _let_127))) (let ((_let_129 (or _let_76 _let_66 _let_128 _let_49))) (let ((_let_130 ((tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2)))) (let ((_let_131 (or _let_66 _let_127))) (let ((_let_132 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_131)) :args ((or _let_66 _let_127 (not _let_131)))) _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (tptp.sz10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_82)) :args _let_81)) _let_80 :args (_let_131 false _let_79)) :args (_let_127 false _let_24 false _let_131)))) (let ((_let_133 (or _let_76 _let_66 _let_66 _let_51))) (let ((_let_134 (or _let_65 _let_128 _let_52))) (let ((_let_135 (or _let_128 _let_65 _let_66 _let_53))) (let ((_let_136 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aInteger0 W0)) (not (tptp.aInteger0 W1)) (not (tptp.aInteger0 W2)) (= (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2)) (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2)))))) (let ((_let_137 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_138 (= tptp.sz00 tptp.xp))) (let ((_let_139 (not _let_54))) (let ((_let_140 (or _let_65 _let_65 _let_139 _let_138 _let_138))) (let ((_let_141 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aInteger0 W0)) (not (tptp.aInteger0 W1)) (not (= tptp.sz00 (tptp.sdtasdt0 W0 W1))) (= tptp.sz00 W0) (= tptp.sz00 W1))))) (let ((_let_142 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_143 (and _let_55 (= _let_2 (tptp.sdtpldt0 tptp.sz00 _let_2))))) (let ((_let_144 (or _let_76 _let_143))) (let ((_let_145 (tptp.sdtasdt0 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false _let_85)) :args (_let_31 false _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_66 _let_76 _let_30 (not _let_77)))) _let_74 _let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (tptp.sz10 _let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) _let_69 :args (_let_77 false _let_68)) :args (_let_30 false _let_24 false _let_75 false _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_66 _let_65 _let_28 (not _let_67)))) _let_74 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (tptp.sz10 tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) _let_69 :args (_let_67 false _let_68)) :args (_let_28 false _let_24 false _let_10 false _let_67)) (NOT_NOT_ELIM (NOT_OR_ELIM _let_63 :args _let_64)) (NOT_NOT_ELIM (NOT_OR_ELIM _let_63 :args _let_62)) :args (false false _let_61 false _let_60 false _let_59 false _let_58 false _let_56 false _let_55 true _let_54 false _let_53 false _let_52 false _let_51 false _let_49 false _let_48 false _let_47 false _let_45 false _let_43 false _let_42 false _let_41 false _let_39 false _let_37 false _let_35 false _let_34 false _let_32 false _let_31 false _let_30 false _let_28 false _let_26 false _let_25)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) true)) (tptp.aInteger0 tptp.sz00) _let_24 _let_23 _let_22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (tptp.aInteger0 (tptp.sdtasdt0 W0 W1)))) _let_21 _let_20 _let_19 _let_18 _let_17 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))) _let_16 _let_15 _let_14 _let_13 _let_12 (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (forall ((W1 $$unsorted)) (= (tptp.aDivisorOf0 W1 W0) (and (tptp.aInteger0 W1) (not (= W1 tptp.sz00)) (exists ((W2 $$unsorted)) (and (tptp.aInteger0 W2) (= (tptp.sdtasdt0 W1 W2) W0)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2) (not (= W2 tptp.sz00))) (= (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.aDivisorOf0 W2 (tptp.sdtpldt0 W0 (tptp.smndt0 W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (not (= W1 tptp.sz00))) (tptp.sdteqdtlpzmzozddtrp0 W0 W0 W1))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2) (not (= W2 tptp.sz00))) (=> (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.sdteqdtlpzmzozddtrp0 W1 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2) (not (= W2 tptp.sz00)) (tptp.aInteger0 W3)) (=> (and (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.sdteqdtlpzmzozddtrp0 W1 W3 W2)) (tptp.sdteqdtlpzmzozddtrp0 W0 W3 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2) (not (= W2 tptp.sz00)) (tptp.aInteger0 W3) (not (= W3 tptp.sz00))) (=> (tptp.sdteqdtlpzmzozddtrp0 W0 W1 (tptp.sdtasdt0 W2 W3)) (and (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W3))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aInteger0 W0) (not (= W0 tptp.sz00))) (=> (tptp.isPrime0 W0) true))) (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (= (exists ((W1 $$unsorted)) (and (tptp.aDivisorOf0 W1 W0) (tptp.isPrime0 W1))) (and (not (= W0 tptp.sz10)) (not (= W0 (tptp.smndt0 tptp.sz10))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) true)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.cS1395) (tptp.aSubsetOf0 W1 tptp.cS1395)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtbsmnsldt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aInteger0 W3) (or (tptp.aElementOf0 W3 W0) (tptp.aElementOf0 W3 W1)))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.cS1395) (tptp.aSubsetOf0 W1 tptp.cS1395)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtslmnbsdt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aInteger0 W3) (tptp.aElementOf0 W3 W0) (tptp.aElementOf0 W3 W1))))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aSubsetOf0 W1 tptp.cS1395)))) (forall ((W1 $$unsorted)) (= (= W1 (tptp.sbsmnsldt0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (and (tptp.aInteger0 W2) (exists ((W3 $$unsorted)) (and (tptp.aElementOf0 W3 W0) (tptp.aElementOf0 W2 W3))))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSubsetOf0 W0 tptp.cS1395) (forall ((W1 $$unsorted)) (= (= W1 (tptp.stldt0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (and (tptp.aInteger0 W2) (not (tptp.aElementOf0 W2 W0)))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (not (= W1 tptp.sz00))) (forall ((W2 $$unsorted)) (= (= W2 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aInteger0 W3) (tptp.sdteqdtlpzmzozddtrp0 W3 W0 W1))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSubsetOf0 W0 tptp.cS1395) (= (tptp.isOpen0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (exists ((W2 $$unsorted)) (and (tptp.aInteger0 W2) (not (= W2 tptp.sz00)) (tptp.aSubsetOf0 (tptp.szAzrzSzezqlpdtcmdtrp0 W1 W2) W0)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSubsetOf0 W0 tptp.cS1395) (= (tptp.isClosed0 W0) (tptp.isOpen0 (tptp.stldt0 W0))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (and (tptp.aSubsetOf0 W1 tptp.cS1395) (tptp.isOpen0 W1))))) (tptp.isOpen0 (tptp.sbsmnsldt0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.cS1395) (tptp.aSubsetOf0 W1 tptp.cS1395) (tptp.isOpen0 W0) (tptp.isOpen0 W1)) (tptp.isOpen0 (tptp.sdtslmnbsdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.cS1395) (tptp.aSubsetOf0 W1 tptp.cS1395) (tptp.isClosed0 W0) (tptp.isClosed0 W1)) (tptp.isClosed0 (tptp.sdtbsmnsldt0 W0 W1)))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (and (tptp.aSubsetOf0 W1 tptp.cS1395) (tptp.isClosed0 W1))))) (tptp.isClosed0 (tptp.sbsmnsldt0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1))) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (not (= W1 tptp.sz00))) (and (tptp.aSubsetOf0 _let_1 tptp.cS1395) (tptp.isClosed0 _let_1))))) (and (tptp.aSet0 tptp.xS) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 tptp.xS))) (and (=> _let_1 (exists ((W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1))) (and (tptp.aInteger0 W1) (not (= W1 tptp.sz00)) (tptp.isPrime0 W1) (tptp.aSet0 _let_1) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1)))) (let ((_let_2 (tptp.sdteqdtlpzmzozddtrp0 W2 tptp.sz00 W1))) (let ((_let_3 (tptp.aDivisorOf0 W1 (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) (let ((_let_4 (tptp.aInteger0 W2))) (and (=> _let_1 (and _let_4 (exists ((W3 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) _let_3 _let_2)) (=> (and _let_4 (or (exists ((W3 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) _let_3 _let_2)) _let_1))))))) (= _let_1 W0))))) (=> (exists ((W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1))) (and (tptp.aInteger0 W1) (not (= W1 tptp.sz00)) (tptp.isPrime0 W1) (=> (and (tptp.aSet0 _let_1) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1)))) (let ((_let_2 (tptp.sdteqdtlpzmzozddtrp0 W2 tptp.sz00 W1))) (let ((_let_3 (tptp.aDivisorOf0 W1 (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) (let ((_let_4 (tptp.aInteger0 W2))) (and (=> _let_1 (and _let_4 (exists ((W3 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) _let_3 _let_2)) (=> (and _let_4 (or (exists ((W3 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) _let_3 _let_2)) _let_1)))))))) (= _let_1 W0))))) _let_1)))) (= tptp.xS tptp.cS2043)) (and _let_9 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sbsmnsldt0 tptp.xS)) (and (tptp.aInteger0 W0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xS) (tptp.aElementOf0 W0 W1)))))) (tptp.aSet0 _let_8) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sbsmnsldt0 tptp.xS))) (= (tptp.aElementOf0 W0 (tptp.stldt0 _let_1)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 _let_1)))))) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))) (or (= W0 tptp.sz10) (= W0 (tptp.smndt0 tptp.sz10))))) (= _let_8 tptp.cS2076)) (tptp.isFinite0 tptp.xS) (and _let_9 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sbsmnsldt0 tptp.xS)) (and (tptp.aInteger0 W0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xS) (tptp.aElementOf0 W0 W1)))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sbsmnsldt0 tptp.xS))) (= (tptp.aElementOf0 W0 (tptp.stldt0 _let_1)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 _let_1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))) (exists ((W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1))) (and (tptp.aInteger0 W1) (not (= W1 tptp.sz00)) (tptp.aSet0 _let_1) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1)))) (let ((_let_2 (tptp.sdteqdtlpzmzozddtrp0 W2 W0 W1))) (let ((_let_3 (tptp.aDivisorOf0 W1 (tptp.sdtpldt0 W2 (tptp.smndt0 W0))))) (let ((_let_4 (tptp.aInteger0 W2))) (and (=> _let_1 (and _let_4 (exists ((W3 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 W0))))) _let_3 _let_2)) (=> (and _let_4 (or (exists ((W3 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 W0))))) _let_3 _let_2)) _let_1))))))) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1)) (tptp.aElementOf0 W2 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))))) (tptp.aSubsetOf0 _let_1 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS)))))))) (tptp.isOpen0 _let_8) (tptp.isClosed0 _let_7) _let_9 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sbsmnsldt0 tptp.xS)) (and (tptp.aInteger0 W0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xS) (tptp.aElementOf0 W0 W1)))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sbsmnsldt0 tptp.xS))) (= (tptp.aElementOf0 W0 (tptp.stldt0 _let_1)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 _let_1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))) (exists ((W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1))) (and (tptp.aInteger0 W1) (not (= W1 tptp.sz00)) (tptp.aSet0 _let_1) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1)))) (let ((_let_2 (tptp.sdteqdtlpzmzozddtrp0 W2 W0 W1))) (let ((_let_3 (tptp.aDivisorOf0 W1 (tptp.sdtpldt0 W2 (tptp.smndt0 W0))))) (let ((_let_4 (tptp.aInteger0 W2))) (and (=> _let_1 (and _let_4 (exists ((W3 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 W0))))) _let_3 _let_2)) (=> (and _let_4 (or (exists ((W3 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 W0))))) _let_3 _let_2)) _let_1))))))) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1)) (tptp.aElementOf0 W2 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))))) (tptp.aSubsetOf0 _let_1 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))))))))) _let_11 (and (exists ((W0 $$unsorted)) (and (tptp.aInteger0 W0) (= (tptp.sdtasdt0 tptp.xp W0) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.sz10 tptp.xp) (tptp.smndt0 tptp.sz10))))) (tptp.aDivisorOf0 tptp.xp (tptp.sdtpldt0 _let_4 _let_1)) (tptp.sdteqdtlpzmzozddtrp0 _let_4 tptp.sz10 tptp.xp) (tptp.aElementOf0 _let_4 _let_6) (exists ((W0 $$unsorted)) (and (tptp.aInteger0 W0) (= (tptp.sdtasdt0 tptp.xp W0) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.sz10 (tptp.smndt0 tptp.xp)) (tptp.smndt0 tptp.sz10))))) (tptp.aDivisorOf0 tptp.xp (tptp.sdtpldt0 _let_3 _let_1)) (tptp.sdteqdtlpzmzozddtrp0 _let_3 tptp.sz10 tptp.xp) (tptp.aElementOf0 _let_3 _let_6)) (and (not (= _let_4 tptp.sz10)) (not (= _let_3 tptp.sz10))) _let_5 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 2.21/2.41 )
% 2.21/2.41 % SZS output end Proof for NUM454+6
% 2.21/2.41 % cvc5---1.0.5 exiting
% 2.21/2.41 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------