TSTP Solution File: NUM452+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM452+1 : 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 10:44:02 EDT 2023
% Result : Theorem 40.45s 40.80s
% Output : Proof 40.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM452+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 13:51:25 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 40.45/40.80 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.jJwImpmifg/cvc5---1.0.5_23126.p...
% 40.45/40.80 ------- get file name : TPTP file name is NUM452+1
% 40.45/40.80 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_23126.smt2...
% 40.45/40.80 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 40.45/40.80 --- Run --no-e-matching --full-saturate-quant at 5...
% 40.45/40.80 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 40.45/40.80 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 40.45/40.80 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 40.45/40.80 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 40.45/40.80 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 40.45/40.80 % SZS status Theorem for NUM452+1
% 40.45/40.80 % SZS output start Proof for NUM452+1
% 40.45/40.80 (
% 40.45/40.80 (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp))) (let ((_let_2 (tptp.smndt0 tptp.xp))) (let ((_let_3 (tptp.sdtpldt0 tptp.sz10 _let_2))) (let ((_let_4 (tptp.aElementOf0 _let_3 _let_1))) (let ((_let_5 (tptp.sdtpldt0 tptp.sz10 tptp.xp))) (let ((_let_6 (tptp.aElementOf0 _let_5 _let_1))) (let ((_let_7 (not (and _let_6 _let_4)))) (let ((_let_8 (tptp.sbsmnsldt0 tptp.xS))) (let ((_let_9 (tptp.stldt0 _let_8))) (let ((_let_10 (tptp.aInteger0 tptp.xp))) (let ((_let_11 (and _let_10 (not (= tptp.xp tptp.sz00)) (tptp.aSubsetOf0 _let_1 _let_9)))) (let ((_let_12 (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))))))))))) (let ((_let_13 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2) (not (= W2 tptp.sz00))) (=> (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (let ((_let_14 (forall ((W0 $$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)))))))) (let ((_let_15 (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (forall ((W1 $$unsorted)) (= (tptp.aDivisorOf0 W1 W0) (and (tptp.aInteger0 W1) (not (= W1 tptp.sz00)) (exists ((W2 $$unsorted)) (and (tptp.aInteger0 W2) (= (tptp.sdtasdt0 W1 W2) W0)))))))))) (let ((_let_16 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))))) (let ((_let_17 (forall ((W0 $$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_18 (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_19 (forall ((W0 $$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_20 (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_21 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_22 (forall ((W0 $$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_23 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (=> (tptp.aInteger0 W0) (and (= (tptp.sdtpldt0 W0 _let_1) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 _let_1 W0)))))))) (let ((_let_24 (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_25 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2)) (= (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2)) (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2)))))) (let ((_let_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (tptp.aInteger0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (tptp.aInteger0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_29 (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (tptp.aInteger0 (tptp.smndt0 W0)))))) (let ((_let_30 (tptp.aInteger0 tptp.sz10))) (let ((_let_31 (tptp.aInteger0 tptp.sz00))) (let ((_let_32 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aInteger0 W0)) (not (tptp.aInteger0 W1)) (not (tptp.aInteger0 W2)) (= tptp.sz00 W2) (not (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2)) (tptp.sdteqdtlpzmzozddtrp0 W1 W0 W2))))) (let ((_let_33 (tptp.sdteqdtlpzmzozddtrp0 _let_3 tptp.sz10 tptp.xp))) (let ((_let_34 (tptp.sdteqdtlpzmzozddtrp0 tptp.sz10 _let_3 tptp.xp))) (let ((_let_35 (not _let_34))) (let ((_let_36 (= tptp.sz00 tptp.xp))) (let ((_let_37 (not _let_10))) (let ((_let_38 (tptp.aInteger0 _let_3))) (let ((_let_39 (not _let_38))) (let ((_let_40 (not _let_30))) (let ((_let_41 (or _let_40 _let_39 _let_37 _let_36 _let_35 _let_33))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (not _let_41))) (let ((_let_44 (and _let_38 _let_33))) (let ((_let_45 (not _let_33))) (let ((_let_46 (= _let_4 _let_44))) (let ((_let_47 (not _let_44))) (let ((_let_48 (forall ((W3 $$unsorted)) (= (and (tptp.aInteger0 W3) (tptp.sdteqdtlpzmzozddtrp0 W3 tptp.sz10 tptp.xp)) (tptp.aElementOf0 W3 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp)))))) (let ((_let_49 (and (tptp.aSet0 _let_1) _let_48))) (let ((_let_50 (or _let_40 _let_37 _let_36 _let_49))) (let ((_let_51 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1626 $$unsorted)) (or (not (tptp.aInteger0 W0)) (not (tptp.aInteger0 W1)) (= tptp.sz00 W1) (= (= (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1) BOUND_VARIABLE_1626) (and (tptp.aSet0 BOUND_VARIABLE_1626) (forall ((W3 $$unsorted)) (= (and (tptp.aInteger0 W3) (tptp.sdteqdtlpzmzozddtrp0 W3 W0 W1)) (tptp.aElementOf0 W3 BOUND_VARIABLE_1626))))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (AND_ELIM _let_53 :args (0)))) (let ((_let_55 (ASSUME :args (_let_30)))) (let ((_let_56 (AND_ELIM _let_53 :args (1)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 1)) :args ((or _let_48 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_36 _let_40 _let_37 _let_49 (not _let_50)))) _let_56 _let_55 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.sz10 tptp.xp _let_1 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.aInteger0 W0) false)) (not (= (tptp.aInteger0 W1) false)) (tptp.aSet0 BOUND_VARIABLE_1626)))) :args (_let_51)))) _let_52 :args (_let_50 false _let_51)) :args (_let_49 true _let_36 false _let_30 false _let_10 false _let_50)) :args (_let_48 false _let_49)))) (let ((_let_58 (_let_48))) (let ((_let_59 ((tptp.aInteger0 W3)))) (let ((_let_60 (ASSUME :args _let_58))) (let ((_let_61 (tptp.sdteqdtlpzmzozddtrp0 _let_5 tptp.sz10 tptp.xp))) (let ((_let_62 (tptp.aInteger0 _let_5))) (let ((_let_63 (and _let_62 _let_61))) (let ((_let_64 (= _let_6 _let_63))) (let ((_let_65 (tptp.sdtpldt0 tptp.xp tptp.sz10))) (let ((_let_66 (tptp.sdteqdtlpzmzozddtrp0 _let_65 tptp.sz10 tptp.xp))) (let ((_let_67 (= _let_5 _let_65))) (let ((_let_68 (tptp.smndt0 tptp.sz10))) (let ((_let_69 (tptp.aDivisorOf0 tptp.xp (tptp.sdtpldt0 _let_65 _let_68)))) (let ((_let_70 (= _let_66 _let_69))) (let ((_let_71 (tptp.aInteger0 _let_65))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_40 _let_37 _let_36 _let_70))) (let ((_let_74 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aInteger0 W0)) (not (tptp.aInteger0 W1)) (not (tptp.aInteger0 W2)) (= tptp.sz00 W2) (= (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.aDivisorOf0 W2 (tptp.sdtpldt0 W0 (tptp.smndt0 W1)))))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (_let_74))) (let ((_let_77 (or _let_40 _let_37 _let_67))) (let ((_let_78 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aInteger0 W0)) (not (tptp.aInteger0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (_let_78))) (let ((_let_81 ((tptp.sdtpldt0 W0 W1)))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_40 _let_37 _let_67 (not _let_77)))) _let_55 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (tptp.sz10 tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_81)) :args _let_80)) _let_79 :args (_let_77 false _let_78)) :args (_let_67 false _let_30 false _let_10 false _let_77)))) (let ((_let_83 (or _let_40 _let_37 _let_62))) (let ((_let_84 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aInteger0 W0)) (not (tptp.aInteger0 W1)) (tptp.aInteger0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (_let_84))) (let ((_let_87 ((tptp.sdtpldt0 W0 W1)))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_40 _let_37 _let_62 (not _let_83)))) _let_55 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (tptp.sz10 tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_87)) :args _let_86)) _let_85 :args (_let_83 false _let_84)) :args (_let_62 false _let_30 false _let_10 false _let_83)))) (let ((_let_89 (and _let_62 _let_67))) (let ((_let_90 (_let_62 _let_67))) (let ((_let_91 (ASSUME :args (_let_62)))) (let ((_let_92 (APPLY_UF tptp.aInteger0))) (let ((_let_93 (ASSUME :args (_let_67)))) (let ((_let_94 (SYMM _let_93))) (let ((_let_95 (SYMM _let_94))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_89)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_91 _let_93) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_95) :args _let_92) (TRUE_INTRO _let_91))) :args _let_90)) :args _let_90)) :args (true _let_89)) _let_88 _let_82 :args (_let_71 false _let_62 false _let_67)))) (let ((_let_97 (tptp.sdtasdt0 tptp.sz10 _let_68))) (let ((_let_98 (tptp.sdtpldt0 _let_65 _let_97))) (let ((_let_99 (tptp.sdtpldt0 tptp.sz10 _let_97))) (let ((_let_100 (= (tptp.sdtpldt0 tptp.xp _let_99) _let_98))) (let ((_let_101 (tptp.aDivisorOf0 tptp.xp tptp.xp))) (let ((_let_102 (= _let_68 _let_97))) (let ((_let_103 (= tptp.sz00 (tptp.sdtpldt0 tptp.sz10 _let_68)))) (let ((_let_104 (tptp.sdtpldt0 tptp.xp tptp.sz00))) (let ((_let_105 (= tptp.xp _let_104))) (let ((_let_106 (tptp.aInteger0 _let_97))) (let ((_let_107 (not _let_106))) (let ((_let_108 (or _let_37 _let_40 _let_107 _let_100))) (let ((_let_109 (forall ((W0 $$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_110 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (_let_109))) (let ((_let_112 (tptp.aInteger0 _let_68))) (let ((_let_113 (not _let_112))) (let ((_let_114 (or _let_40 _let_113 _let_106))) (let ((_let_115 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aInteger0 W0)) (not (tptp.aInteger0 W1)) (tptp.aInteger0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (_let_115))) (let ((_let_118 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_119 (or _let_40 _let_112))) (let ((_let_120 (forall ((W0 $$unsorted)) (or (not (tptp.aInteger0 W0)) (tptp.aInteger0 (tptp.smndt0 W0)))))) (let ((_let_121 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_122 (_let_120))) (let ((_let_123 ((tptp.smndt0 W0)))) (let ((_let_124 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_40 _let_112 (not _let_119)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (tptp.sz10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_123)) :args _let_122)) _let_121 :args (_let_119 false _let_120)) :args (_let_112 false _let_30 false _let_119)))) (let ((_let_125 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_40 _let_113 _let_106 (not _let_114)))) _let_55 _let_124 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_116 :args (tptp.sz10 _let_68 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_118)) :args _let_117)) _let_116 :args (_let_114 false _let_115)) :args (_let_106 false _let_30 false _let_112 false _let_114)))) (let ((_let_126 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_108)) :args ((or _let_40 _let_37 _let_107 _let_100 (not _let_108)))) _let_55 _let_54 _let_125 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (tptp.xp tptp.sz10 _let_97 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_111)) _let_110 :args (_let_108 false _let_109)) :args (_let_100 false _let_30 false _let_10 false _let_106 false _let_108)))) (let ((_let_127 (forall ((W2 $$unsorted)) (or (not (tptp.aInteger0 W2)) (not (= tptp.xp (tptp.sdtasdt0 tptp.xp W2))))))) (let ((_let_128 (not _let_127))) (let ((_let_129 (not _let_36))) (let ((_let_130 (and _let_10 _let_129 _let_128))) (let ((_let_131 (= _let_101 _let_130))) (let ((_let_132 (or _let_37 _let_131))) (let ((_let_133 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1339 $$unsorted)) (or (not (tptp.aInteger0 W0)) (= (tptp.aDivisorOf0 BOUND_VARIABLE_1339 W0) (and 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_let_36 _let_40 _let_37 _let_39 _let_206 (not _let_207)))) _let_56 _let_55 _let_54 _let_203 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args _let_208) :args _let_76)) _let_75 :args (_let_207 false _let_74)) :args (_let_206 true _let_36 false _let_30 false _let_10 false _let_38 false _let_207)) :args (_let_34 false _let_205 false _let_206)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_44)) :args ((or _let_39 _let_44 _let_45))) _let_203 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_46)) :args ((or _let_4 _let_47 (not _let_46)))) (MACRO_RESOLUTION_TRUST (NOT_AND (ASSUME :args (_let_7))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_64)) :args ((or _let_6 (not _let_63) (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_63)) :args ((or (not _let_62) _let_63 (not _let_61)))) _let_88 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_196)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_197 _let_93) (SCOPE (TRUE_ELIM (TRANS (CONG _let_95 _let_190 _let_192 :args (APPLY_UF tptp.sdteqdtlpzmzozddtrp0)) (TRUE_INTRO _let_197))) :args (_let_66 _let_67))) :args (_let_67 _let_66))) :args (true _let_196)) :args ((or (not _let_67) _let_61 (not _let_66)))) _let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_70)) :args ((or _let_66 (not _let_69) (not _let_70)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_180)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_181 _let_194 _let_187 _let_188 _let_184) (SCOPE (TRUE_ELIM (TRANS (CONG _let_192 (TRANS (CONG (REFL :args (_let_65)) _let_188 :args _let_186) _let_195 _let_193 _let_185) :args _let_183) _let_182)) :args (_let_101 _let_100 _let_103 _let_102 _let_105))) :args (_let_105 _let_103 _let_102 _let_101 _let_100))) :args (true _let_180)) _let_179 _let_172 _let_162 _let_151 _let_126 :args (_let_69 false _let_105 false _let_103 false _let_102 false _let_101 false _let_100)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_36 _let_40 _let_37 _let_72 _let_70 (not _let_73)))) _let_56 _let_55 _let_54 _let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (_let_65 tptp.sz10 tptp.xp QUANTIFIERS_INST_E_MATCHING ((tptp.aDivisorOf0 W2 (tptp.sdtpldt0 W0 (tptp.smndt0 W1)))))) :args _let_76)) _let_75 :args (_let_73 false _let_74)) :args (_let_70 true _let_36 false _let_30 false _let_10 false _let_71 false _let_73)) :args (_let_66 false _let_69 false _let_70)) :args (_let_61 false _let_67 false _let_66)) :args (_let_63 false _let_62 false _let_61)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_59)) :args _let_58))) _let_57 :args (_let_64 false _let_48)) :args (_let_6 false _let_63 false _let_64)) :args ((not _let_4) false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_59)) :args _let_58))) _let_57 :args (_let_46 false _let_48)) :args (_let_47 true _let_4 false _let_46)) :args (_let_45 false _let_38 true _let_44)) :args (_let_43 true _let_36 false _let_30 false _let_10 false _let_38 false _let_34 true _let_33)) _let_42 :args (false true _let_41 false _let_32)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) true)) _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (not (= W1 tptp.sz00))) (tptp.sdteqdtlpzmzozddtrp0 W0 W0 W1))) _let_13 (forall ((W0 $$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 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (and (tptp.aInteger0 W2) (not (tptp.aElementOf0 W2 W0)))))))))) _let_12 (forall ((W0 $$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))))) (= tptp.xS tptp.cS2043) (= _let_9 tptp.cS2076) (tptp.isFinite0 tptp.xS) (and (tptp.isClosed0 _let_8) (tptp.isOpen0 _let_9)) _let_11 _let_7 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 40.45/40.81 )
% 40.45/40.81 % SZS output end Proof for NUM452+1
% 40.45/40.81 % cvc5---1.0.5 exiting
% 40.45/40.81 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------