TSTP Solution File: NUM449+6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM449+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.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 10:44:01 EDT 2023
% Result : Theorem 0.68s 0.90s
% Output : Proof 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM449+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 18:09:51 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.68/0.90 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.72JN0Mn9zX/cvc5---1.0.5_27982.p...
% 0.68/0.90 ------- get file name : TPTP file name is NUM449+6
% 0.68/0.90 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_27982.smt2...
% 0.68/0.90 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.68/0.90 % SZS status Theorem for NUM449+6
% 0.68/0.90 % SZS output start Proof for NUM449+6
% 0.68/0.90 (
% 0.68/0.90 (let ((_let_1 (tptp.sbsmnsldt0 tptp.xS))) (let ((_let_2 (tptp.isClosed0 _let_1))) (let ((_let_3 (tptp.stldt0 _let_1))) (let ((_let_4 (tptp.aSet0 _let_1))) (let ((_let_5 (not (=> (and _let_4 (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))))))) (or (=> (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sbsmnsldt0 tptp.xS))) (= (tptp.aElementOf0 W0 (tptp.stldt0 _let_1)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 _let_1)))))) (or (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))) (exists ((W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1))) (and (tptp.aInteger0 W1) (not (= W1 tptp.sz00)) (=> (and (tptp.aSet0 _let_1) (forall ((W2 $$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 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1)) (tptp.aElementOf0 W2 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))))) (tptp.aSubsetOf0 _let_1 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS)))))))))) (tptp.isOpen0 _let_3))) _let_2))))) (let ((_let_6 (tptp.isFinite0 tptp.xS))) (let ((_let_7 (tptp.aSet0 tptp.xS))) (let ((_let_8 (and _let_7 (forall ((W0 $$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 ((_let_9 (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))))))) (let ((_let_10 (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)))))) (let ((_let_11 (tptp.aInteger0 tptp.sz00))) (let ((_let_12 (tptp.isClosed0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_13 (tptp.aSubsetOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.cS1395))) (let ((_let_14 (and _let_13 _let_12))) (let ((_let_15 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.xS))) (let ((_let_16 (not _let_15))) (let ((_let_17 (or _let_16 _let_14))) (let ((_let_18 (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xS)) (and (tptp.aSubsetOf0 W1 tptp.cS1395) (tptp.isClosed0 W1)))))) (let ((_let_19 (not _let_17))) (let ((_let_20 (not _let_18))) (let ((_let_21 (not _let_6))) (let ((_let_22 (not _let_7))) (let ((_let_23 (or _let_22 _let_21 _let_20 _let_2))) (let ((_let_24 (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.isFinite0 W0)) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (and (tptp.aSubsetOf0 W1 tptp.cS1395) (tptp.isClosed0 W1))))) (tptp.isClosed0 (tptp.sbsmnsldt0 W0)))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (or))) (let ((_let_28 (_let_20))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_28)) :args _let_28)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_18))) (REFL :args (_let_19)) :args _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_2 _let_22 _let_21 _let_20 (not _let_23)))) (NOT_OR_ELIM (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)))) :args (1)) (AND_ELIM _let_26 :args (0)) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (tptp.xS QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aSet0 W0) false))))) :args (_let_24))) _let_25 :args (_let_23 false _let_24)) :args (_let_20 true _let_2 false _let_7 false _let_6 false _let_23)) :args (_let_19 true _let_18)))) (let ((_let_30 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_31 (tptp.aSubsetOf0 _let_30 tptp.cS1395))) (let ((_let_32 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_30))) (let ((_let_33 (tptp.isClosed0 _let_30))) (let ((_let_34 (and _let_31 _let_33))) (let ((_let_35 (= tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_36 (tptp.aInteger0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_37 (not _let_36))) (let ((_let_38 (not _let_11))) (let ((_let_39 (or _let_38 _let_37 _let_35 _let_34))) (let ((_let_40 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1))) (or (not (tptp.aInteger0 W0)) (not (tptp.aInteger0 W1)) (= tptp.sz00 W1) (and (tptp.aSubsetOf0 _let_1 tptp.cS1395) (tptp.isClosed0 _let_1))))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (not (forall ((BOUND_VARIABLE_1980 $$unsorted) (BOUND_VARIABLE_2014 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 BOUND_VARIABLE_1980 (tptp.smndt0 tptp.sz00)))) (or (not (tptp.aInteger0 BOUND_VARIABLE_1980)) (and (or (not (tptp.aInteger0 BOUND_VARIABLE_2014)) (not (= _let_1 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 BOUND_VARIABLE_2014)))) (not (tptp.aDivisorOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_1)) (not (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_1980 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (tptp.aElementOf0 BOUND_VARIABLE_1980 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))))))) (let ((_let_43 (not _let_32))) (let ((_let_44 (not (tptp.aSet0 _let_30)))) (let ((_let_45 (not (tptp.isPrime0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))) (let ((_let_46 (or _let_37 _let_35 _let_45 _let_44 _let_43 (not (forall ((BOUND_VARIABLE_1963 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1963 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (and (tptp.aInteger0 BOUND_VARIABLE_1963) (not (forall ((W3 $$unsorted)) (or (not (tptp.aInteger0 W3)) (not (= (tptp.sdtpldt0 BOUND_VARIABLE_1963 (tptp.smndt0 tptp.sz00)) (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 W3)))))) (tptp.aDivisorOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 (tptp.sdtpldt0 BOUND_VARIABLE_1963 (tptp.smndt0 tptp.sz00))) (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_1963 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))))) _let_42))) (let ((_let_47 (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1))) (or (not (tptp.aInteger0 W1)) (= tptp.sz00 W1) (not (tptp.isPrime0 W1)) (not (tptp.aSet0 _let_1)) (not (= _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((BOUND_VARIABLE_1963 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1963 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1))) (and (tptp.aInteger0 BOUND_VARIABLE_1963) (not (forall ((W3 $$unsorted)) (or (not (tptp.aInteger0 W3)) (not (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 BOUND_VARIABLE_1963 (tptp.smndt0 tptp.sz00))))))) (tptp.aDivisorOf0 W1 (tptp.sdtpldt0 BOUND_VARIABLE_1963 (tptp.smndt0 tptp.sz00))) (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_1963 tptp.sz00 W1))))) (not (forall ((BOUND_VARIABLE_1980 $$unsorted) (BOUND_VARIABLE_2014 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 BOUND_VARIABLE_1980 (tptp.smndt0 tptp.sz00)))) (or (not (tptp.aInteger0 BOUND_VARIABLE_1980)) (and (or (not (tptp.aInteger0 BOUND_VARIABLE_2014)) (not (= _let_1 (tptp.sdtasdt0 W1 BOUND_VARIABLE_2014)))) (not (tptp.aDivisorOf0 W1 _let_1)) (not (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_1980 tptp.sz00 W1))) (tptp.aElementOf0 BOUND_VARIABLE_1980 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1))))))))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (not _let_47))) (let ((_let_50 (or _let_16 _let_49))) (let ((_let_51 (forall ((BOUND_VARIABLE_2227 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_2227 tptp.xS)) (not (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1))) (or (not (tptp.aInteger0 W1)) (= tptp.sz00 W1) (not (tptp.isPrime0 W1)) (not (tptp.aSet0 _let_1)) (not (= _let_1 BOUND_VARIABLE_2227)) (not (forall ((BOUND_VARIABLE_1963 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1963 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1))) (and (tptp.aInteger0 BOUND_VARIABLE_1963) (not (forall ((W3 $$unsorted)) (or (not (tptp.aInteger0 W3)) (not (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 BOUND_VARIABLE_1963 (tptp.smndt0 tptp.sz00))))))) (tptp.aDivisorOf0 W1 (tptp.sdtpldt0 BOUND_VARIABLE_1963 (tptp.smndt0 tptp.sz00))) (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_1963 tptp.sz00 W1))))) (not (forall ((BOUND_VARIABLE_1980 $$unsorted) (BOUND_VARIABLE_2014 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 BOUND_VARIABLE_1980 (tptp.smndt0 tptp.sz00)))) (or (not (tptp.aInteger0 BOUND_VARIABLE_1980)) (and (or (not (tptp.aInteger0 BOUND_VARIABLE_2014)) (not (= _let_1 (tptp.sdtasdt0 W1 BOUND_VARIABLE_2014)))) (not (tptp.aDivisorOf0 W1 _let_1)) (not (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_1980 tptp.sz00 W1))) (tptp.aElementOf0 BOUND_VARIABLE_1980 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1)))))))))))))) (let ((_let_52 (_let_51))) (let ((_let_53 (_let_49))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_53)) :args _let_53) (REWRITE :args ((=> _let_49 (not (or _let_37 _let_35 _let_45 _let_44 (not (= _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((BOUND_VARIABLE_1963 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1963 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (and (tptp.aInteger0 BOUND_VARIABLE_1963) (not (forall ((W3 $$unsorted)) (or (not (tptp.aInteger0 W3)) (not (= (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 W3) (tptp.sdtpldt0 BOUND_VARIABLE_1963 (tptp.smndt0 tptp.sz00))))))) (tptp.aDivisorOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 (tptp.sdtpldt0 BOUND_VARIABLE_1963 (tptp.smndt0 tptp.sz00))) (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_1963 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))))) _let_42))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_47))) (REFL :args (_let_48)) :args _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_16 _let_49 (not _let_50)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_17 0)) (CONG (REFL :args (_let_17)) (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_27)) :args ((or _let_15 _let_17))) _let_29 :args (_let_15 true _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_52) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 BOUND_VARIABLE_2227 tptp.xS) false))))) :args _let_52)) (AND_ELIM _let_26 :args (2)) :args (_let_50 false _let_51)) :args (_let_49 false _let_15 false _let_50)) :args (_let_48 true _let_47)))) (let ((_let_55 (REFL :args (_let_46)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_38 _let_37 _let_35 _let_34 (not _let_39)))) (ASSUME :args (_let_11)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_27)) :args ((or _let_36 _let_46))) _let_54 :args (_let_36 true _let_46)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 1)) _let_54 :args ((not _let_35) true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1)))) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_34 false _let_11 false _let_36 true _let_35 false _let_39)))) (let ((_let_57 (not _let_34))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 4)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_32))) :args _let_27)) :args ((or _let_32 _let_46))) _let_54 :args (_let_32 true _let_46)))) (let ((_let_59 (and _let_32 _let_31))) (let ((_let_60 (ASSUME :args (_let_31)))) (let ((_let_61 (ASSUME :args (_let_32)))) (let ((_let_62 (SYMM (SYMM _let_61)))) (let ((_let_63 (and _let_32 _let_33))) (let ((_let_64 (ASSUME :args (_let_33)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_63)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_64 _let_61) (SCOPE (TRUE_ELIM (TRANS (CONG _let_62 :args (APPLY_UF tptp.isClosed0)) (TRUE_INTRO _let_64))) :args (_let_33 _let_32))) :args (_let_32 _let_33))) :args (true _let_63)) :args ((or _let_12 _let_43 (not _let_33)))) _let_58 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 1)) :args ((or _let_33 _let_57))) _let_56 :args (_let_33 false _let_34)) :args (_let_12 false _let_32 false _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_59)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_60 _let_61) (SCOPE (TRUE_ELIM (TRANS (CONG _let_62 (REFL :args (tptp.cS1395)) :args (APPLY_UF tptp.aSubsetOf0)) (TRUE_INTRO _let_60))) :args (_let_31 _let_32))) :args (_let_32 _let_31))) :args (true _let_59)) :args ((or _let_13 _let_43 (not _let_31)))) _let_58 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 0)) :args ((or _let_31 _let_57))) _let_56 :args (_let_31 false _let_34)) :args (_let_13 false _let_32 false _let_31)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_17 1)) _let_29 :args ((not _let_14) true _let_17)) :args (false false _let_12 false _let_13 true _let_14)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) true)) _let_11 (tptp.aInteger0 tptp.sz10) (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.cS1395) (tptp.aSubsetOf0 W1 tptp.cS1395) (tptp.isClosed0 W0) (tptp.isClosed0 W1)) (tptp.isClosed0 (tptp.sdtbsmnsldt0 W0 W1)))) _let_10 _let_9 _let_8 (and _let_4 (forall ((W0 $$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_6 _let_5 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.68/0.91 )
% 0.68/0.91 % SZS output end Proof for NUM449+6
% 0.68/0.91 % cvc5---1.0.5 exiting
% 0.68/0.91 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------