TSTP Solution File: NUM456+6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM456+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 10:44:05 EDT 2023
% Result : Theorem 0.45s 0.73s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM456+6 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n024.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 16:17:39 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.45/0.73 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.aMsafyOotS/cvc5---1.0.5_19222.p...
% 0.45/0.73 ------- get file name : TPTP file name is NUM456+6
% 0.45/0.73 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_19222.smt2...
% 0.45/0.73 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.45/0.73 % SZS status Theorem for NUM456+6
% 0.45/0.73 % SZS output start Proof for NUM456+6
% 0.45/0.73 (
% 0.45/0.73 (let ((_let_1 (exists ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 tptp.sz10))) (and (tptp.aInteger0 W0) (exists ((W1 $$unsorted)) (and (tptp.aInteger0 W1) (= (tptp.sdtasdt0 tptp.xp W1) (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.sz10))))) (tptp.aDivisorOf0 tptp.xp (tptp.sdtpldt0 W0 _let_1)) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.sz10 tptp.xp) (tptp.aElementOf0 W0 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp)) (not (or (= W0 tptp.sz10) (= W0 _let_1) (tptp.aElementOf0 W0 tptp.cS2200)))))))) (let ((_let_2 (tptp.sbsmnsldt0 tptp.xS))) (let ((_let_3 (tptp.stldt0 _let_2))) (let ((_let_4 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp))) (let ((_let_5 (tptp.aSet0 _let_2))) (let ((_let_6 (and (tptp.aInteger0 tptp.xp) (not (= tptp.xp tptp.sz00)) (tptp.aSet0 _let_4) (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 $$unsorted)) (and (tptp.aInteger0 W1) (= (tptp.sdtasdt0 tptp.xp W1) (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.sz10))))) _let_3 _let_2)) _let_1))))))) _let_5 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp)) (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))))) (tptp.aSubsetOf0 _let_4 _let_3)))) (let ((_let_7 (and _let_5 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sbsmnsldt0 tptp.xS)) (and (tptp.aInteger0 W0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xS) (tptp.aElementOf0 W0 W1)))))) (tptp.aSet0 _let_3) (forall ((W0 $$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 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))) (or (= W0 tptp.sz10) (= W0 (tptp.smndt0 tptp.sz10))))) (= _let_3 tptp.cS2076)))) (let ((_let_8 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_3))) (let ((_let_9 (tptp.smndt0 tptp.sz10))) (let ((_let_10 (= _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (= tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (or _let_11 _let_10))) (let ((_let_13 (= _let_8 _let_12))) (let ((_let_14 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_4))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_8))) (let ((_let_17 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp))) (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))))))) (let ((_let_18 (_let_17))) (let ((_let_19 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_20 (or (not (tptp.aInteger0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.aDivisorOf0 tptp.xp _let_19)) (not (tptp.sdteqdtlpzmzozddtrp0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.sz10 tptp.xp)) _let_15 _let_11 _let_10 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.cS2200) (not (tptp.aInteger0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (= _let_19 (tptp.sdtasdt0 tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_21 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2945 $$unsorted)) (let ((_let_1 (tptp.smndt0 tptp.sz10))) (let ((_let_2 (tptp.sdtpldt0 W0 _let_1))) (or (not (tptp.aInteger0 W0)) (not (tptp.aDivisorOf0 tptp.xp _let_2)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.sz10 tptp.xp)) (not (tptp.aElementOf0 W0 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp))) (= tptp.sz10 W0) (= _let_1 W0) (tptp.aElementOf0 W0 tptp.cS2200) (not (tptp.aInteger0 BOUND_VARIABLE_2945)) (not (= _let_2 (tptp.sdtasdt0 tptp.xp BOUND_VARIABLE_2945))))))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (or))) (let ((_let_25 (not _let_21))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_23) :args (_let_25))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_21))) (REFL :args (_let_22)) :args _let_24)) _let_23 :args (_let_22 true _let_21)))) (let ((_let_27 (not _let_12))) (let ((_let_28 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))) (or (= tptp.sz10 W0) (= (tptp.smndt0 tptp.sz10) W0)))))) (let ((_let_29 (_let_28))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_13)) :args ((or (not _let_8) _let_12 (not _let_13)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_29) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W0 _let_3)))) :args _let_29)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) :args (4)) :args (_let_13 false _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_12)) :args ((or _let_11 _let_10 _let_27))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_20 4)) _let_26 :args ((not _let_11) true _let_20)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_20 5)) _let_26 :args ((not _let_10) true _let_20)) :args (_let_27 true _let_11 true _let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_15 _let_8 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 3)) (CONG (REFL :args (_let_20)) (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_24)) :args ((or _let_14 _let_20))) _let_26 :args (_let_14 true _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_18) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 _let_4) false))))) :args _let_18)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) :args (6)) :args (_let_16 false _let_17)) :args (_let_8 false _let_14 false _let_16)) :args (false false _let_13 true _let_12 false _let_8)) :args ((forall ((W0 $$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)))) (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 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) _let_3 _let_2)) _let_1)))))))) (= _let_1 W0))))) _let_1)))) (= tptp.xS tptp.cS2043)) _let_7 (tptp.isFinite0 tptp.xS) (and _let_5 (forall ((W0 $$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_3) (tptp.isClosed0 _let_2) _let_5 (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_6 _let_1 (not false) true))))))))))))))))))))))))))))))))
% 0.45/0.73 )
% 0.45/0.73 % SZS output end Proof for NUM456+6
% 0.45/0.73 % cvc5---1.0.5 exiting
% 0.45/0.74 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------