TSTP Solution File: NUM443+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM443+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.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 4.13s 4.37s
% Output : Proof 4.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM443+4 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n002.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 18:19:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.49 %----Proving TF0_NAR, FOF, or CNF
% 4.13/4.37 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.ioOgoe1jU9/cvc5---1.0.5_10373.p...
% 4.13/4.37 ------- get file name : TPTP file name is NUM443+4
% 4.13/4.37 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10373.smt2...
% 4.13/4.37 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 4.13/4.37 % SZS status Theorem for NUM443+4
% 4.13/4.37 % SZS output start Proof for NUM443+4
% 4.13/4.37 (
% 4.13/4.37 (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.xa tptp.xq))) (let ((_let_2 (tptp.stldt0 _let_1))) (let ((_let_3 (tptp.aElementOf0 tptp.xc _let_1))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.aSet0 _let_1))) (let ((_let_6 (tptp.sdteqdtlpzmzozddtrp0 tptp.xc tptp.xb tptp.xq))) (let ((_let_7 (tptp.aElementOf0 tptp.xb _let_1))) (let ((_let_8 (not (=> (and _let_5 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.xa tptp.xq)))) (let ((_let_2 (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xa tptp.xq))) (let ((_let_3 (tptp.aDivisorOf0 tptp.xq (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xa))))) (let ((_let_4 (tptp.aInteger0 W0))) (and (=> _let_1 (and _let_4 (exists ((W1 $$unsorted)) (and (tptp.aInteger0 W1) (= (tptp.sdtasdt0 tptp.xq W1) (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xa))))) _let_3 _let_2)) (=> (and _let_4 (or (exists ((W1 $$unsorted)) (and (tptp.aInteger0 W1) (= (tptp.sdtasdt0 tptp.xq W1) (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xa))))) _let_3 _let_2)) _let_1))))))) (not _let_7) (tptp.aElementOf0 tptp.xb _let_2) (exists ((W0 $$unsorted)) (and (tptp.aInteger0 W0) (= (tptp.sdtasdt0 tptp.xq W0) (tptp.sdtpldt0 tptp.xc (tptp.smndt0 tptp.xb))))) (tptp.aDivisorOf0 tptp.xq (tptp.sdtpldt0 tptp.xc (tptp.smndt0 tptp.xb))) _let_6) (=> (and _let_5 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.xa tptp.xq)))) (let ((_let_2 (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xa tptp.xq))) (let ((_let_3 (tptp.aDivisorOf0 tptp.xq (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xa))))) (let ((_let_4 (tptp.aInteger0 W0))) (and (=> _let_1 (and _let_4 (exists ((W1 $$unsorted)) (and (tptp.aInteger0 W1) (= (tptp.sdtasdt0 tptp.xq W1) (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xa))))) _let_3 _let_2)) (=> (and _let_4 (or (exists ((W1 $$unsorted)) (and (tptp.aInteger0 W1) (= (tptp.sdtasdt0 tptp.xq W1) (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xa))))) _let_3 _let_2)) _let_1)))))))) (or _let_4 (tptp.aElementOf0 tptp.xc _let_2))))))) (let ((_let_9 (tptp.aInteger0 tptp.xc))) (let ((_let_10 (tptp.aInteger0 tptp.xb))) (let ((_let_11 (and _let_10 _let_9))) (let ((_let_12 (tptp.aInteger0 tptp.xq))) (let ((_let_13 (tptp.aInteger0 tptp.xa))) (let ((_let_14 (and _let_13 _let_12 (not (= tptp.xq tptp.sz00))))) (let ((_let_15 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2) (not (= W2 tptp.sz00)) (tptp.aInteger0 W3)) (=> (and (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.sdteqdtlpzmzozddtrp0 W1 W3 W2)) (tptp.sdteqdtlpzmzozddtrp0 W0 W3 W2)))))) (let ((_let_16 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2) (not (= W2 tptp.sz00))) (=> (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (let ((_let_17 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aInteger0 W0)) (not (tptp.aInteger0 W1)) (not (tptp.aInteger0 W2)) (= tptp.sz00 W2) (not (tptp.aInteger0 W3)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2)) (not (tptp.sdteqdtlpzmzozddtrp0 W1 W3 W2)) (tptp.sdteqdtlpzmzozddtrp0 W0 W3 W2))))) (let ((_let_18 (tptp.sdteqdtlpzmzozddtrp0 tptp.xa tptp.xb tptp.xq))) (let ((_let_19 (not _let_6))) (let ((_let_20 (tptp.sdteqdtlpzmzozddtrp0 tptp.xa tptp.xc tptp.xq))) (let ((_let_21 (not _let_20))) (let ((_let_22 (not _let_10))) (let ((_let_23 (= tptp.sz00 tptp.xq))) (let ((_let_24 (not _let_12))) (let ((_let_25 (not _let_9))) (let ((_let_26 (not _let_13))) (let ((_let_27 (or _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_19 _let_18))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (tptp.sdteqdtlpzmzozddtrp0 tptp.xc tptp.xa tptp.xq))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_25 _let_26 _let_24 _let_23 _let_31 _let_20))) (let ((_let_33 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aInteger0 W0)) (not (tptp.aInteger0 W1)) (not (tptp.aInteger0 W2)) (= tptp.sz00 W2) (not (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2)) (tptp.sdteqdtlpzmzozddtrp0 W1 W0 W2))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (_let_33))) (let ((_let_36 (tptp.smndt0 tptp.xa))) (let ((_let_37 (and _let_9 (not (forall ((W1 $$unsorted)) (or (not (tptp.aInteger0 W1)) (not (= (tptp.sdtasdt0 tptp.xq W1) (tptp.sdtpldt0 tptp.xc (tptp.smndt0 tptp.xa))))))) (tptp.aDivisorOf0 tptp.xq (tptp.sdtpldt0 tptp.xc _let_36)) _let_30))) (let ((_let_38 (or _let_4 _let_37))) (let ((_let_39 (forall ((BOUND_VARIABLE_1820 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1820 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.xa tptp.xq))) (and (tptp.aInteger0 BOUND_VARIABLE_1820) (not (forall ((W1 $$unsorted)) (or (not (tptp.aInteger0 W1)) (not (= (tptp.sdtasdt0 tptp.xq W1) (tptp.sdtpldt0 BOUND_VARIABLE_1820 (tptp.smndt0 tptp.xa))))))) (tptp.aDivisorOf0 tptp.xq (tptp.sdtpldt0 BOUND_VARIABLE_1820 (tptp.smndt0 tptp.xa))) (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_1820 tptp.xa tptp.xq)))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (NOT_IMPLIES_ELIM1 _let_40))) (let ((_let_42 (_let_39))) (let ((_let_43 (0))) (let ((_let_44 (1))) (let ((_let_45 (ASSUME :args (_let_11)))) (let ((_let_46 (AND_ELIM _let_45 :args _let_44))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (AND_ELIM _let_47 :args _let_44))) (let ((_let_49 (AND_ELIM _let_47 :args _let_43))) (let ((_let_50 (AND_ELIM _let_47 :args (2)))) (let ((_let_51 (tptp.sdteqdtlpzmzozddtrp0 tptp.xb tptp.xa tptp.xq))) (let ((_let_52 (not _let_18))) (let ((_let_53 (or _let_26 _let_22 _let_24 _let_23 _let_52 _let_51))) (let ((_let_54 (not _let_51))) (let ((_let_55 (tptp.sdtpldt0 tptp.xb _let_36))) (let ((_let_56 (and (or _let_22 (not (= _let_55 (tptp.sdtasdt0 tptp.xq tptp.xb)))) (not (tptp.aDivisorOf0 tptp.xq _let_55)) _let_54))) (let ((_let_57 (or _let_22 _let_56 _let_7))) (let ((_let_58 (forall ((BOUND_VARIABLE_1837 $$unsorted) (BOUND_VARIABLE_1871 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 BOUND_VARIABLE_1837 (tptp.smndt0 tptp.xa)))) (or (not (tptp.aInteger0 BOUND_VARIABLE_1837)) (and (or (not (tptp.aInteger0 BOUND_VARIABLE_1871)) (not (= _let_1 (tptp.sdtasdt0 tptp.xq BOUND_VARIABLE_1871)))) (not (tptp.aDivisorOf0 tptp.xq _let_1)) (not (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_1837 tptp.xa tptp.xq))) (tptp.aElementOf0 BOUND_VARIABLE_1837 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.xa tptp.xq))))))) (let ((_let_59 (_let_58))) (let ((_let_60 (AND_ELIM _let_45 :args _let_43))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (tptp.xa tptp.xc tptp.xq tptp.xb QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.sdteqdtlpzmzozddtrp0 W0 W3 W2) true)) (not (= (tptp.sdteqdtlpzmzozddtrp0 W1 W3 W2) false))))) :args (_let_17))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_23 _let_26 _let_24 _let_22 _let_25 _let_19 _let_18 _let_21 _let_29))) _let_50 _let_49 _let_48 _let_60 _let_46 (AND_ELIM _let_41 :args (5)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_23 _let_26 _let_24 _let_22 _let_51 _let_52 (not _let_53)))) _let_50 _let_49 _let_48 _let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_56 2)) :args ((or _let_54 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_7 _let_22 _let_56 (not _let_57)))) (AND_ELIM _let_41 :args _let_44) _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_59) :args (tptp.xb tptp.xb QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.aInteger0 BOUND_VARIABLE_1837) false)) (tptp.aInteger0 BOUND_VARIABLE_1871)))) :args _let_59)) (AND_ELIM _let_41 :args (7)) :args (_let_57 false _let_58)) :args (_let_56 true _let_7 false _let_10 false _let_57)) :args (_let_54 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.xa tptp.xb tptp.xq QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.sdteqdtlpzmzozddtrp0 W1 W0 W2) true))))) :args _let_35)) _let_34 :args (_let_53 false _let_33)) :args (_let_52 true _let_23 false _let_13 false _let_12 false _let_10 true _let_51 false _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_23 _let_26 _let_24 _let_25 _let_31 _let_20 (not _let_32)))) _let_50 _let_49 _let_48 _let_46 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_37 3)) :args ((or _let_30 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_4 _let_37 (not _let_38)))) (NOT_NOT_ELIM (NOT_OR_ELIM (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 _let_40)) :args _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_42) :args (tptp.xc QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 BOUND_VARIABLE_1820 _let_1) false))))) :args _let_42)) (AND_ELIM _let_41 :args (6)) :args (_let_38 false _let_39)) :args (_let_37 false _let_3 false _let_38)) :args (_let_30 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.xc tptp.xa tptp.xq QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) false))))) :args _let_35)) _let_34 :args (_let_32 false _let_33)) :args (_let_20 true _let_23 false _let_13 false _let_12 false _let_9 false _let_30 false _let_32)) :args (_let_29 true _let_23 false _let_13 false _let_12 false _let_10 false _let_9 false _let_6 true _let_18 false _let_20)) _let_28 :args (false true _let_27 false _let_17)) :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))) _let_16 _let_15 (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)))) _let_14 _let_11 _let_8 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 4.23/4.40 )
% 4.23/4.40 % SZS output end Proof for NUM443+4
% 4.23/4.40 % cvc5---1.0.5 exiting
% 4.23/4.40 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------