TSTP Solution File: NUM440+6 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM440+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 10:43:57 EDT 2023
% Result : Theorem 0.20s 0.69s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM440+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 13:55:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.69 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.St3RoVHOnr/cvc5---1.0.5_16568.p...
% 0.20/0.69 ------- get file name : TPTP file name is NUM440+6
% 0.20/0.69 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16568.smt2...
% 0.20/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.69 % SZS status Theorem for NUM440+6
% 0.20/0.69 % SZS output start Proof for NUM440+6
% 0.20/0.69 (
% 0.20/0.69 (let ((_let_1 (tptp.stldt0 tptp.xB))) (let ((_let_2 (tptp.stldt0 tptp.xA))) (let ((_let_3 (tptp.sdtbsmnsldt0 tptp.xA tptp.xB))) (let ((_let_4 (tptp.stldt0 _let_3))) (let ((_let_5 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sdtbsmnsldt0 tptp.xA tptp.xB))) (and (tptp.aInteger0 W0) (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xA)) (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xB))))))) (let ((_let_6 (or _let_5 (= _let_4 (tptp.sdtslmnbsdt0 _let_2 _let_1))))) (let ((_let_7 (=> (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xB)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 tptp.xB))))) _let_6))) (let ((_let_8 (=> (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xA)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 tptp.xA))))) _let_7))) (let ((_let_9 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtbsmnsldt0 tptp.xA tptp.xB))) (= (tptp.aElementOf0 W0 (tptp.stldt0 _let_1)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 _let_1)))))))) (let ((_let_10 (and (tptp.aSet0 _let_4) _let_9))) (let ((_let_11 (=> _let_10 _let_8))) (let ((_let_12 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtbsmnsldt0 tptp.xA tptp.xB)) (and (tptp.aInteger0 W0) (or (tptp.aElementOf0 W0 tptp.xA) (tptp.aElementOf0 W0 tptp.xB))))))) (let ((_let_13 (and (tptp.aSet0 _let_3) _let_12))) (let ((_let_14 (=> _let_13 _let_11))) (let ((_let_15 (tptp.aSubsetOf0 _let_1 tptp.cS1395))) (let ((_let_16 (tptp.aSet0 tptp.cS1395))) (let ((_let_17 (and _let_16 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.cS1395) (tptp.aInteger0 W0)))))) (let ((_let_18 (tptp.aSet0 _let_1))) (let ((_let_19 (and _let_18 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xB)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 tptp.xB)))))))) (let ((_let_20 (tptp.aSubsetOf0 _let_2 tptp.cS1395))) (let ((_let_21 (and _let_16 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.cS1395) (tptp.aInteger0 W0)))))) (let ((_let_22 (tptp.aSet0 _let_2))) (let ((_let_23 (and _let_22 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xA)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 tptp.xA)))))))) (let ((_let_24 (not (and (=> _let_23 (=> _let_21 (or (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xA)) (tptp.aElementOf0 W0 tptp.cS1395))) _let_20))) (=> _let_19 (=> _let_17 (or (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xB)) (tptp.aElementOf0 W0 tptp.cS1395))) _let_15))) _let_14)))) (let ((_let_25 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xB)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 tptp.xB))))))) (let ((_let_26 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xA)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 tptp.xA))))))) (let ((_let_27 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.cS1395) (tptp.aInteger0 W0))))) (let ((_let_28 (and _let_16 _let_27 (tptp.aSet0 tptp.xA) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xA) (tptp.aElementOf0 W0 tptp.cS1395))) (tptp.aSubsetOf0 tptp.xA tptp.cS1395) _let_16 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.cS1395) (tptp.aInteger0 W0))) (tptp.aSet0 tptp.xB) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xB) (tptp.aElementOf0 W0 tptp.cS1395))) (tptp.aSubsetOf0 tptp.xB tptp.cS1395) _let_22 _let_26 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xA)) (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 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1)) (tptp.aElementOf0 W2 (tptp.stldt0 tptp.xA)))) (tptp.aSubsetOf0 _let_1 (tptp.stldt0 tptp.xA))))))) (tptp.isOpen0 _let_2) (tptp.isClosed0 tptp.xA) _let_18 _let_25 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xB)) (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 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1)) (tptp.aElementOf0 W2 (tptp.stldt0 tptp.xB)))) (tptp.aSubsetOf0 _let_1 (tptp.stldt0 tptp.xB))))))) (tptp.isOpen0 _let_1) (tptp.isClosed0 tptp.xB)))) (let ((_let_29 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xB))) (let ((_let_30 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xA))) (let ((_let_31 (or _let_30 _let_29))) (let ((_let_32 (tptp.aInteger0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_33 (and _let_32 _let_31))) (let ((_let_34 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_3))) (let ((_let_35 (= _let_34 _let_33))) (let ((_let_36 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xB))) (tptp.aElementOf0 W0 tptp.cS1395))))) (let ((_let_37 (or _let_36 _let_15))) (let ((_let_38 (=> _let_17 _let_37))) (let ((_let_39 (=> _let_19 _let_38))) (let ((_let_40 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xA))) (tptp.aElementOf0 W0 tptp.cS1395))))) (let ((_let_41 (or _let_40 _let_20))) (let ((_let_42 (=> _let_21 _let_41))) (let ((_let_43 (=> _let_23 _let_42))) (let ((_let_44 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.cS1395))) (let ((_let_45 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_1))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_44))) (let ((_let_48 (tptp.aInteger0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_49 (and _let_48 (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xB))))) (let ((_let_50 (= _let_45 _let_49))) (let ((_let_51 (= _let_44 _let_48))) (let ((_let_52 (or))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (AND_ELIM _let_53 :args (16)))) (let ((_let_55 (_let_25))) (let ((_let_56 ((tptp.aElementOf0 W0 _let_1)))) (let ((_let_57 (ASSUME :args _let_55))) (let ((_let_58 (AND_ELIM _let_53 :args (1)))) (let ((_let_59 (_let_27))) (let ((_let_60 ((tptp.aElementOf0 W0 tptp.cS1395)))) (let ((_let_61 (ASSUME :args _let_59))) (let ((_let_62 (not _let_36))) (let ((_let_63 (_let_62))) (let ((_let_64 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.cS1395))) (let ((_let_65 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_2))) (let ((_let_66 (not _let_65))) (let ((_let_67 (or _let_66 _let_64))) (let ((_let_68 (tptp.aInteger0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_69 (and _let_68 (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xA))))) (let ((_let_70 (= _let_65 _let_69))) (let ((_let_71 (= _let_64 _let_68))) (let ((_let_72 (AND_ELIM _let_53 :args (11)))) (let ((_let_73 (_let_26))) (let ((_let_74 ((tptp.aElementOf0 W0 _let_2)))) (let ((_let_75 (ASSUME :args _let_73))) (let ((_let_76 (not _let_40))) (let ((_let_77 (_let_76))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT)))) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args (_let_43)) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args (_let_42)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_41 0)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_77)) :args _let_77)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_40))) (REFL :args ((not _let_67))) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_69 0)) :args ((or _let_68 (not _let_69)))) (REORDERING (CNF_EQUIV_POS2 :args (_let_71)) :args ((or _let_64 (not _let_68) (not _let_71)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_60)) :args _let_59)) _let_58 :args (_let_71 false _let_27)) (REORDERING (CNF_EQUIV_POS1 :args (_let_70)) :args ((or _let_66 _let_69 (not _let_70)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_74)) :args _let_73)) _let_72 :args (_let_70 false _let_26)) (CNF_OR_NEG :args (_let_67 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_67 0)) (CONG (REFL :args (_let_67)) (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_65))) :args _let_52)) :args ((or _let_65 _let_67))) :args (_let_67 true _let_68 false _let_71 false _let_69 false _let_70 true _let_64 false _let_65)) :args (_let_40 false _let_67)) :args (_let_41 false _let_40)) :args (_let_42 false _let_41)) :args (_let_43 false _let_42)) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args (_let_39)) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args (_let_38)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_37 0)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_63)) :args _let_63)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_36))) (REFL :args ((not _let_47))) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 0)) :args ((or _let_48 (not _let_49)))) (REORDERING (CNF_EQUIV_POS2 :args (_let_51)) :args ((or _let_44 (not _let_48) (not _let_51)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_60)) :args _let_59)) _let_58 :args (_let_51 false _let_27)) (REORDERING (CNF_EQUIV_POS1 :args (_let_50)) :args ((or _let_46 _let_49 (not _let_50)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_50 false _let_25)) (CNF_OR_NEG :args (_let_47 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 0)) (CONG (REFL :args (_let_47)) (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_52)) :args ((or _let_45 _let_47))) :args (_let_47 true _let_48 false _let_51 false _let_49 false _let_50 true _let_44 false _let_45)) :args (_let_36 false _let_47)) :args (_let_37 false _let_36)) :args (_let_38 false _let_37)) :args (_let_39 false _let_38)) :args ((not _let_14) false _let_43 false _let_39)))) (let ((_let_79 (_let_14))) (let ((_let_80 (_let_12))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_80) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aInteger0 W0)))) :args _let_80)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_13 1)) :args ((or _let_12 (not _let_13)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_NEG1 :args _let_79) :args ((or _let_13 _let_14))) _let_78 :args (_let_13 true _let_14)) :args (_let_12 false _let_13)) :args (_let_35 false _let_12)))) (let ((_let_82 (not _let_34))) (let ((_let_83 (and _let_32 _let_82))) (let ((_let_84 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_4))) (let ((_let_85 (= _let_84 _let_83))) (let ((_let_86 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_1))) (let ((_let_87 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_2))) (let ((_let_88 (and _let_32 _let_87 _let_86))) (let ((_let_89 (= _let_84 _let_88))) (let ((_let_90 (not _let_30))) (let ((_let_91 (and _let_32 _let_90))) (let ((_let_92 (not _let_29))) (let ((_let_93 (and _let_32 _let_92))) (let ((_let_94 (= _let_87 _let_91))) (let ((_let_95 (= _let_86 _let_93))) (let ((_let_96 (not _let_83))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args _let_79) _let_78 :args ((not _let_11) true _let_14)))) (let ((_let_98 (_let_11))) (let ((_let_99 (_let_9))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_99) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W0 _let_4)))) :args _let_99)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_10 1)) :args ((or _let_9 (not _let_10)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_NEG1 :args _let_98) :args ((or _let_10 _let_11))) _let_97 :args (_let_10 true _let_11)) :args (_let_9 false _let_10)) :args (_let_85 false _let_9)))) (let ((_let_101 (not _let_85))) (let ((_let_102 (_let_85))) (let ((_let_103 (not _let_35))) (let ((_let_104 (not _let_33))) (let ((_let_105 (_let_35))) (let ((_let_106 (not _let_89))) (let ((_let_107 (not _let_5))) (let ((_let_108 (_let_107))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_108)) :args _let_108)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_107) _let_5))) (REFL :args (_let_106)) :args _let_52)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_6 0)) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args (_let_7)) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args (_let_8)) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args _let_98) _let_97 :args ((not _let_8) true _let_11)) :args ((not _let_7) true _let_8)) :args ((not _let_6) true _let_7)) :args (_let_107 true _let_6)) :args (_let_106 true _let_5)))) (let ((_let_110 (_let_89))) (let ((_let_111 (not _let_88))) (let ((_let_112 (REORDERING (CNF_EQUIV_NEG1 :args _let_110) :args ((or _let_84 _let_88 _let_89))))) (let ((_let_113 (not _let_84))) (let ((_let_114 (REORDERING (CNF_EQUIV_POS1 :args _let_102) :args ((or _let_113 _let_83 _let_101))))) (let ((_let_115 (MACRO_RESOLUTION_TRUST _let_114 _let_100 _let_112 _let_109 (REORDERING (CNF_AND_POS :args (_let_83 0)) :args ((or _let_32 _let_96))) (REORDERING (CNF_AND_POS :args (_let_88 0)) :args ((or _let_32 _let_111))) :args (_let_32 false _let_85 false _let_84 true _let_89 true _let_83 true _let_88)))) (let ((_let_116 (not _let_31))) (let ((_let_117 (not _let_32))) (let ((_let_118 (REFL :args (_let_117)))) (let ((_let_119 (_let_91))) (let ((_let_120 (_let_93))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_74)) :args _let_73)) _let_72 :args (_let_94 false _let_26)))) (let ((_let_122 (not _let_94))) (let ((_let_123 (not _let_91))) (let ((_let_124 (_let_94))) (let ((_let_125 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_95 false _let_25)))) (let ((_let_126 (not _let_95))) (let ((_let_127 (not _let_93))) (let ((_let_128 (_let_95))) (let ((_let_129 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_88)) _let_115 (REORDERING (CNF_EQUIV_POS2 :args _let_128) :args ((or _let_86 _let_127 _let_126))) _let_125 (REORDERING (CNF_EQUIV_POS2 :args _let_124) :args ((or _let_87 _let_123 _let_122))) _let_121 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_120) (CONG (REFL :args _let_120) _let_118 (MACRO_SR_PRED_INTRO :args ((= (not _let_92) _let_29))) :args _let_52)) :args ((or _let_117 _let_29 _let_93))) _let_115 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_119) (CONG (REFL :args _let_119) _let_118 (MACRO_SR_PRED_INTRO :args ((= (not _let_90) _let_30))) :args _let_52)) :args ((or _let_117 _let_30 _let_91))) _let_115 (CNF_OR_NEG :args (_let_31 1)) (CNF_OR_NEG :args (_let_31 0)) (REORDERING (CNF_AND_NEG :args (_let_33)) :args ((or _let_117 _let_33 _let_116))) _let_115 (CNF_EQUIV_NEG2 :args _let_110) _let_109 (REORDERING (CNF_EQUIV_POS2 :args _let_105) :args ((or _let_34 _let_104 _let_103))) _let_81 (REORDERING (CNF_EQUIV_POS2 :args _let_102) :args ((or _let_84 _let_96 _let_101))) _let_100 (REORDERING (CNF_AND_POS :args (_let_83 1)) :args ((or _let_82 _let_96))) :args (_let_96 false _let_32 false _let_86 false _let_95 false _let_87 false _let_94 false _let_93 false _let_32 false _let_91 false _let_32 true _let_29 true _let_30 true _let_31 false _let_32 true _let_88 true _let_89 true _let_33 false _let_35 false _let_84 false _let_85 true _let_34)))) (let ((_let_130 (_let_83))) (let ((_let_131 (MACRO_RESOLUTION_TRUST _let_112 (MACRO_RESOLUTION_TRUST _let_114 _let_129 _let_100 :args (_let_113 true _let_83 false _let_85)) _let_109 :args (_let_88 true _let_84 true _let_89)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_29 _let_116))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_93 1)) :args ((or _let_92 _let_127))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_128) :args ((or (not _let_86) _let_93 _let_126))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_88 2)) :args ((or _let_86 _let_111))) _let_131 :args (_let_86 false _let_88)) _let_125 :args (_let_93 false _let_86 false _let_95)) :args (_let_92 false _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_91 1)) :args ((or _let_90 _let_123))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_124) :args ((or (not _let_87) _let_91 _let_122))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_88 1)) :args ((or _let_87 _let_111))) _let_131 :args (_let_87 false _let_88)) _let_121 :args (_let_91 false _let_87 false _let_94)) :args (_let_90 false _let_91)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_33 1)) :args ((or _let_31 _let_104))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_105) :args ((or _let_33 _let_82 _let_103))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_130) (CONG (REFL :args _let_130) _let_118 (MACRO_SR_PRED_INTRO :args ((= (not _let_82) _let_34))) :args _let_52)) :args ((or _let_117 _let_34 _let_83))) _let_115 _let_129 :args (_let_34 false _let_32 true _let_83)) _let_81 :args (_let_33 false _let_34 false _let_35)) :args (_let_31 false _let_33)) :args (false true _let_29 true _let_30 false _let_31)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) true)) (tptp.aInteger0 tptp.sz00) (tptp.aInteger0 tptp.sz10) (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (tptp.aInteger0 (tptp.smndt0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (tptp.aInteger0 (tptp.sdtpldt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (tptp.aInteger0 (tptp.sdtasdt0 W0 W1)))) (forall ((W0 $$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)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))) (forall ((W0 $$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)))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2)) (= (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2)) (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W2))) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2)) (and (= (tptp.sdtasdt0 W0 (tptp.sdtpldt0 W1 W2)) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) _let_1)) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 _let_1 (tptp.sdtasdt0 W1 W2))))))) (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 tptp.sz10))) (let ((_let_2 (tptp.smndt0 W0))) (=> (tptp.aInteger0 W0) (and (= (tptp.sdtasdt0 _let_1 W0) _let_2) (= _let_2 (tptp.sdtasdt0 W0 _let_1))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))) (forall ((W0 $$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)))) _let_28 _let_24 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.70 )
% 0.20/0.70 % SZS output end Proof for NUM440+6
% 0.20/0.70 % cvc5---1.0.5 exiting
% 0.20/0.70 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------