TSTP Solution File: NUM441+6 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM441+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 10:43:58 EDT 2023
% Result : Theorem 0.22s 0.61s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM441+6 : TPTP v8.1.2. Released v4.0.0.
% 0.15/0.14 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 15:49:40 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.61 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.NTgUio5Jfo/cvc5---1.0.5_16236.p...
% 0.22/0.61 ------- get file name : TPTP file name is NUM441+6
% 0.22/0.61 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16236.smt2...
% 0.22/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.61 % SZS status Theorem for NUM441+6
% 0.22/0.61 % SZS output start Proof for NUM441+6
% 0.22/0.61 (
% 0.22/0.61 (let ((_let_1 (tptp.sdtbsmnsldt0 tptp.xA tptp.xB))) (let ((_let_2 (tptp.stldt0 _let_1))) (let ((_let_3 (tptp.isOpen0 _let_2))) (let ((_let_4 (tptp.aSet0 _let_2))) (let ((_let_5 (tptp.aSet0 _let_1))) (let ((_let_6 (not (=> (and _let_5 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtbsmnsldt0 tptp.xA tptp.xB)) (and (tptp.aInteger0 W0) (or (tptp.aElementOf0 W0 tptp.xA) (tptp.aElementOf0 W0 tptp.xB)))))) (or (=> (and _let_4 (forall ((W0 $$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))))))) (or (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sdtbsmnsldt0 tptp.xA tptp.xB))) (exists ((W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1))) (and (tptp.aInteger0 W1) (not (= W1 tptp.sz00)) (=> (and (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 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 W0))))) _let_3 _let_2)) _let_1)))))))) (or (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1)) (tptp.aElementOf0 W2 (tptp.stldt0 (tptp.sdtbsmnsldt0 tptp.xA tptp.xB))))) (tptp.aSubsetOf0 _let_1 (tptp.stldt0 (tptp.sdtbsmnsldt0 tptp.xA tptp.xB)))))))))) _let_3)) (tptp.isClosed0 _let_1)))))) (let ((_let_7 (tptp.stldt0 tptp.xB))) (let ((_let_8 (tptp.stldt0 tptp.xA))) (let ((_let_9 (tptp.sdtslmnbsdt0 _let_8 _let_7))) (let ((_let_10 (= _let_2 _let_9))) (let ((_let_11 (tptp.aSubsetOf0 _let_7 tptp.cS1395))) (let ((_let_12 (tptp.aSet0 tptp.cS1395))) (let ((_let_13 (tptp.aSet0 _let_7))) (let ((_let_14 (tptp.aSubsetOf0 _let_8 tptp.cS1395))) (let ((_let_15 (tptp.aSet0 _let_8))) (let ((_let_16 (and _let_15 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xA)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 tptp.xA))))) _let_12 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.cS1395) (tptp.aInteger0 W0))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xA)) (tptp.aElementOf0 W0 tptp.cS1395))) _let_14 _let_13 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xB)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 tptp.xB))))) _let_12 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.cS1395) (tptp.aInteger0 W0))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xB)) (tptp.aElementOf0 W0 tptp.cS1395))) _let_11 _let_5 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtbsmnsldt0 tptp.xA tptp.xB)) (and (tptp.aInteger0 W0) (or (tptp.aElementOf0 W0 tptp.xA) (tptp.aElementOf0 W0 tptp.xB))))) _let_4 (forall ((W0 $$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)))))) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xA)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 tptp.xA))))) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xB)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 tptp.xB))))) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sdtbsmnsldt0 tptp.xA tptp.xB))) (and (tptp.aInteger0 W0) (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xA)) (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xB))))) _let_10))) (let ((_let_17 (tptp.isOpen0 _let_7))) (let ((_let_18 (tptp.isOpen0 _let_8))) (let ((_let_19 (and _let_12 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.cS1395) (tptp.aInteger0 W0))) (tptp.aSet0 tptp.xA) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xA) (tptp.aElementOf0 W0 tptp.cS1395))) (tptp.aSubsetOf0 tptp.xA tptp.cS1395) _let_12 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.cS1395) (tptp.aInteger0 W0))) (tptp.aSet0 tptp.xB) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xB) (tptp.aElementOf0 W0 tptp.cS1395))) (tptp.aSubsetOf0 tptp.xB tptp.cS1395) _let_15 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xA)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 tptp.xA))))) (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))))))) _let_18 (tptp.isClosed0 tptp.xA) _let_13 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 tptp.xB)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 tptp.xB))))) (forall ((W0 $$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 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1)) (tptp.aElementOf0 W2 (tptp.stldt0 tptp.xB)))) (tptp.aSubsetOf0 _let_1 (tptp.stldt0 tptp.xB))))))) _let_17 (tptp.isClosed0 tptp.xB)))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.cS1395) (tptp.aSubsetOf0 W1 tptp.cS1395) (tptp.isOpen0 W0) (tptp.isOpen0 W1)) (tptp.isOpen0 (tptp.sdtslmnbsdt0 W0 W1)))))) (let ((_let_21 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aSubsetOf0 W0 tptp.cS1395)) (not (tptp.aSubsetOf0 W1 tptp.cS1395)) (not (tptp.isOpen0 W0)) (not (tptp.isOpen0 W1)) (tptp.isOpen0 (tptp.sdtslmnbsdt0 W0 W1)))))) (let ((_let_22 (tptp.isOpen0 _let_9))) (let ((_let_23 (not _let_17))) (let ((_let_24 (not _let_18))) (let ((_let_25 (not _let_11))) (let ((_let_26 (not _let_14))) (let ((_let_27 (or _let_26 _let_25 _let_24 _let_23 _let_22))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (not _let_22))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (not _let_10))) (let ((_let_33 (not _let_3))) (let ((_let_34 (and _let_10 _let_33))) (let ((_let_35 (ASSUME :args (_let_33)))) (let ((_let_36 (ASSUME :args (_let_10)))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_8 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtslmnbsdt0 W0 W1)))) :args (_let_21))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_24 _let_23 _let_26 _let_25 _let_22 _let_29))) (AND_ELIM _let_37 :args (13)) (AND_ELIM _let_37 :args (18)) (AND_ELIM _let_31 :args (5)) (AND_ELIM _let_31 :args (11)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_34)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_35 _let_36) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_36) :args (APPLY_UF tptp.isOpen0)) (FALSE_INTRO _let_35))) :args (_let_33 _let_10))) :args (_let_10 _let_33))) :args (true _let_34)) (CONG (REFL :args (_let_32)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_3))) (REFL :args (_let_30)) :args (or))) :args ((or _let_3 _let_32 _let_30))) (NOT_OR_ELIM (NOT_IMPLIES_ELIM2 (NOT_OR_ELIM (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)))) :args (0))) :args (1)) (AND_ELIM _let_31 :args (19)) :args (_let_30 true _let_3 false _let_10)) :args (_let_29 false _let_18 false _let_17 false _let_14 false _let_11 true _let_22)) _let_28 :args (false true _let_27 false _let_21)) :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)))) _let_20 _let_19 _let_16 _let_6 true))))))))))))))))))))))))))))))))))))))))
% 0.22/0.62 )
% 0.22/0.62 % SZS output end Proof for NUM441+6
% 0.22/0.62 % cvc5---1.0.5 exiting
% 0.22/0.62 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------