TSTP Solution File: NUM450+6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM450+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 10.42s 10.77s
% Output : Proof 10.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM450+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n019.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 13:35:58 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 10.42/10.77 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.5LOnpHHaXr/cvc5---1.0.5_22217.p...
% 10.42/10.77 ------- get file name : TPTP file name is NUM450+6
% 10.42/10.77 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22217.smt2...
% 10.42/10.77 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.42/10.77 --- Run --no-e-matching --full-saturate-quant at 5...
% 10.42/10.77 % SZS status Theorem for NUM450+6
% 10.42/10.77 % SZS output start Proof for NUM450+6
% 10.42/10.77 (
% 10.42/10.77 (let ((_let_1 (not (exists ((W0 $$unsorted)) (let ((_let_1 (tptp.sbsmnsldt0 tptp.xS))) (let ((_let_2 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 W0))) (and (tptp.aInteger0 W0) (not (= W0 tptp.sz00)) (=> (and (tptp.aSet0 _let_2) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W1 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 W0)))) (let ((_let_2 (tptp.sdteqdtlpzmzozddtrp0 W1 tptp.sz10 W0))) (let ((_let_3 (tptp.aDivisorOf0 W0 (tptp.sdtpldt0 W1 (tptp.smndt0 tptp.sz10))))) (let ((_let_4 (tptp.aInteger0 W1))) (and (=> _let_1 (and _let_4 (exists ((W2 $$unsorted)) (and (tptp.aInteger0 W2) (= (tptp.sdtasdt0 W0 W2) (tptp.sdtpldt0 W1 (tptp.smndt0 tptp.sz10))))) _let_3 _let_2)) (=> (and _let_4 (or (exists ((W2 $$unsorted)) (and (tptp.aInteger0 W2) (= (tptp.sdtasdt0 W0 W2) (tptp.sdtpldt0 W1 (tptp.smndt0 tptp.sz10))))) _let_3 _let_2)) _let_1)))))))) (=> (and (tptp.aSet0 _let_1) (forall ((W1 $$unsorted)) (= (tptp.aElementOf0 W1 (tptp.sbsmnsldt0 tptp.xS)) (and (tptp.aInteger0 W1) (exists ((W2 $$unsorted)) (and (tptp.aElementOf0 W2 tptp.xS) (tptp.aElementOf0 W1 W2))))))) (=> (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sbsmnsldt0 tptp.xS))) (= (tptp.aElementOf0 W1 (tptp.stldt0 _let_1)) (and (tptp.aInteger0 W1) (not (tptp.aElementOf0 W1 _let_1)))))) (or (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 W0)) (tptp.aElementOf0 W1 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))))) (tptp.aSubsetOf0 _let_2 (tptp.stldt0 _let_1))))))))))))) (let ((_let_2 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sbsmnsldt0 tptp.xS))) (= (tptp.aElementOf0 W0 (tptp.stldt0 _let_1)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 _let_1)))))))) (let ((_let_3 (tptp.sbsmnsldt0 tptp.xS))) (let ((_let_4 (tptp.aSet0 _let_3))) (let ((_let_5 (tptp.isClosed0 _let_3))) (let ((_let_6 (tptp.stldt0 _let_3))) (let ((_let_7 (tptp.isOpen0 _let_6))) (let ((_let_8 (forall ((W0 $$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)))))))) (let ((_let_9 (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)))))) _let_8 (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_7 _let_5 _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)))))) _let_2 (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 ((_let_10 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sbsmnsldt0 tptp.xS))) (= (tptp.aElementOf0 W0 (tptp.stldt0 _let_1)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 _let_1)))))))) (let ((_let_11 (tptp.aSet0 _let_6))) (let ((_let_12 (and _let_4 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sbsmnsldt0 tptp.xS)) (and (tptp.aInteger0 W0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xS) (tptp.aElementOf0 W0 W1)))))) _let_11 _let_10 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))) (or (= W0 tptp.sz10) (= W0 (tptp.smndt0 tptp.sz10))))) (= _let_6 tptp.cS2076)))) (let ((_let_13 (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 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) _let_3 _let_2)) _let_1)))))))) (= _let_1 W0))))) _let_1)))) (= tptp.xS tptp.cS2043)))) (let ((_let_14 (tptp.aInteger0 tptp.sz10))) (let ((_let_15 (tptp.aInteger0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51))) (let ((_let_16 (= tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51))) (let ((_let_17 (tptp.sbsmnsldt0 tptp.cS2043))) (let ((_let_18 (tptp.stldt0 _let_17))) (let ((_let_19 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51))) (let ((_let_20 (tptp.aSubsetOf0 _let_19 _let_18))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.aElementOf0 tptp.sz10 _let_18))) (let ((_let_23 (tptp.aElementOf0 tptp.sz10 _let_17))) (let ((_let_24 (tptp.aElementOf0 tptp.sz10 _let_19))) (let ((_let_25 (tptp.sdteqdtlpzmzozddtrp0 tptp.sz10 tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51))) (let ((_let_26 (tptp.sdtpldt0 tptp.sz10 (tptp.smndt0 tptp.sz10)))) (let ((_let_27 (tptp.aDivisorOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51 _let_26))) (let ((_let_28 (not _let_14))) (let ((_let_29 (tptp.aSet0 _let_19))) (let ((_let_30 (and _let_29 (or (not _let_24) (and _let_14 (not (forall ((W2 $$unsorted)) (or (not (tptp.aInteger0 W2)) (not (= (tptp.sdtpldt0 tptp.sz10 (tptp.smndt0 tptp.sz10)) (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51 W2)))))) _let_27 _let_25)) (or _let_28 (and (or _let_28 (not (= _let_26 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51 tptp.sz10)))) (not _let_27) (not _let_25)) _let_24) (tptp.aSet0 _let_17) (= _let_23 (and _let_14 (not (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.cS2043)) (not (tptp.aElementOf0 tptp.sz10 W2))))))) (= (and _let_14 (not _let_23)) _let_22) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51))) (tptp.aElementOf0 W1 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.cS2043)))))) _let_21))) (let ((_let_31 (not _let_15))) (let ((_let_32 (or _let_31 _let_16 _let_30))) (let ((_let_33 (not (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51))) (tptp.aElementOf0 W2 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.cS2043)))))))) (let ((_let_34 (not _let_29))) (let ((_let_35 (or _let_31 _let_16 _let_34 _let_33 _let_21 (not (forall ((BOUND_VARIABLE_2537 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_2537 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51))) (and (tptp.aInteger0 BOUND_VARIABLE_2537) (not (forall ((W3 $$unsorted)) (or (not (tptp.aInteger0 W3)) (not (= (tptp.sdtpldt0 BOUND_VARIABLE_2537 (tptp.smndt0 tptp.sz10)) (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51 W3)))))) (tptp.aDivisorOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51 (tptp.sdtpldt0 BOUND_VARIABLE_2537 (tptp.smndt0 tptp.sz10))) (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_2537 tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51))))) (not (forall ((BOUND_VARIABLE_2554 $$unsorted) (BOUND_VARIABLE_2588 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 BOUND_VARIABLE_2554 (tptp.smndt0 tptp.sz10)))) (or (not (tptp.aInteger0 BOUND_VARIABLE_2554)) (and (or (not (tptp.aInteger0 BOUND_VARIABLE_2588)) (not (= _let_1 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51 BOUND_VARIABLE_2588)))) (not (tptp.aDivisorOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51 _let_1)) (not (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_2554 tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51))) (tptp.aElementOf0 BOUND_VARIABLE_2554 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51))))))))) (let ((_let_36 (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 W1))) (or (not (tptp.aInteger0 W1)) (= tptp.sz00 W1) (not (tptp.aSet0 _let_1)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 W1))) (tptp.aElementOf0 W2 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.cS2043)))))) (not (tptp.aSubsetOf0 _let_1 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.cS2043)))) (not (forall ((BOUND_VARIABLE_2537 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_2537 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 W1))) (and (tptp.aInteger0 BOUND_VARIABLE_2537) (not (forall ((W3 $$unsorted)) (or (not (tptp.aInteger0 W3)) (not (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 BOUND_VARIABLE_2537 (tptp.smndt0 tptp.sz10))))))) (tptp.aDivisorOf0 W1 (tptp.sdtpldt0 BOUND_VARIABLE_2537 (tptp.smndt0 tptp.sz10))) (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_2537 tptp.sz10 W1))))) (not (forall ((BOUND_VARIABLE_2554 $$unsorted) (BOUND_VARIABLE_2588 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 BOUND_VARIABLE_2554 (tptp.smndt0 tptp.sz10)))) (or (not (tptp.aInteger0 BOUND_VARIABLE_2554)) (and (or (not (tptp.aInteger0 BOUND_VARIABLE_2588)) (not (= (tptp.sdtasdt0 W1 BOUND_VARIABLE_2588) _let_1))) (not (tptp.aDivisorOf0 W1 _let_1)) (not (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_2554 tptp.sz10 W1))) (tptp.aElementOf0 BOUND_VARIABLE_2554 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 W1))))))))))) (let ((_let_37 (not _let_35))) (let ((_let_38 (not _let_36))) (let ((_let_39 (not _let_22))) (let ((_let_40 (or _let_39 _let_38))) (let ((_let_41 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.cS2043)))) (not (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1))) (or (not (tptp.aInteger0 W1)) (= tptp.sz00 W1) (not (tptp.aSet0 _let_1)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1))) (tptp.aElementOf0 W2 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.cS2043)))))) (not (tptp.aSubsetOf0 _let_1 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.cS2043)))) (not (forall ((BOUND_VARIABLE_2537 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_2537 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1))) (and (tptp.aInteger0 BOUND_VARIABLE_2537) (not (forall ((W3 $$unsorted)) (or (not (tptp.aInteger0 W3)) (not (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 BOUND_VARIABLE_2537 (tptp.smndt0 W0))))))) (tptp.aDivisorOf0 W1 (tptp.sdtpldt0 BOUND_VARIABLE_2537 (tptp.smndt0 W0))) (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_2537 W0 W1))))) (not (forall ((BOUND_VARIABLE_2554 $$unsorted) (BOUND_VARIABLE_2588 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 BOUND_VARIABLE_2554 (tptp.smndt0 W0)))) (or (not (tptp.aInteger0 BOUND_VARIABLE_2554)) (and (or (not (tptp.aInteger0 BOUND_VARIABLE_2588)) (not (= _let_1 (tptp.sdtasdt0 W1 BOUND_VARIABLE_2588)))) (not (tptp.aDivisorOf0 W1 _let_1)) (not (tptp.sdteqdtlpzmzozddtrp0 BOUND_VARIABLE_2554 W0 W1))) (tptp.aElementOf0 BOUND_VARIABLE_2554 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1)))))))))))))) (let ((_let_42 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) :args (1)))) (let ((_let_43 (= tptp.cS2076 _let_6))) (let ((_let_44 (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_45 (ASSUME :args (_let_12)))) (let ((_let_46 (AND_INTRO (EQ_RESOLVE (AND_ELIM (EQ_RESOLVE _let_45 _let_44) :args (5)) (MACRO_SR_EQ_INTRO _let_42 :args (_let_43 SB_DEFAULT SBA_FIXPOINT))) _let_42))) (let ((_let_47 (_let_41))) (let ((_let_48 (tptp.sz10 QUANTIFIERS_INST_ENUM))) (let ((_let_49 (forall ((W0 $$unsorted)) (= (or (= tptp.sz10 W0) (= (tptp.smndt0 tptp.sz10) W0)) (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.cS2043))))))) (let ((_let_50 (_let_49))) (let ((_let_51 (or))) (let ((_let_52 (_let_38))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_52)) :args _let_52) (REWRITE :args ((=> _let_38 (not (or _let_31 _let_16 _let_34 _let_33 _let_21 (not (forall ((BOUND_VARIABLE_2537 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_2537 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51))) (and (tptp.aInteger0 BOUND_VARIABLE_2537) (not (forall ((W3 $$unsorted)) (or (not (tptp.aInteger0 W3)) (not (= (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51 W3) (tptp.sdtpldt0 BOUND_VARIABLE_2537 (tptp.smndt0 tptp.sz10))))))) (tptp.aDivisorOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51 (tptp.sdtpldt0 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(not (tptp.aElementOf0 BOUND_VARIABLE_2977 _let_1))) (tptp.aElementOf0 BOUND_VARIABLE_2977 _let_2)) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 W0))) (tptp.aElementOf0 W1 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.cS2043)))))) (not (tptp.aSubsetOf0 _let_3 _let_2)))))))))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_46 :args ((forall ((W0 $$unsorted) (BOUND_VARIABLE_2977 $$unsorted) (BOUND_VARIABLE_2966 $$unsorted) (BOUND_VARIABLE_2948 $$unsorted) (BOUND_VARIABLE_2946 $$unsorted) (BOUND_VARIABLE_2931 $$unsorted)) (let ((_let_1 (tptp.sbsmnsldt0 tptp.xS))) (let ((_let_2 (tptp.stldt0 _let_1))) (let ((_let_3 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 W0))) (let ((_let_4 (tptp.smndt0 tptp.sz10))) (let ((_let_5 (tptp.sdtpldt0 BOUND_VARIABLE_2946 _let_4))) (or (not (tptp.aInteger0 W0)) (= tptp.sz00 W0) (and (tptp.aSet0 _let_3) (or (not (tptp.aElementOf0 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:args (_let_20 true _let_35)) :args (_let_55 false _let_20)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_35 1)) _let_53 :args ((not _let_16) true _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 0)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_15))) :args _let_51)) :args ((or _let_15 _let_35))) _let_53 :args (_let_15 true _let_35)) :args (false false _let_32 true _let_30 true _let_16 false _let_15)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) true)) (tptp.aInteger0 tptp.sz00) _let_14 (forall ((W0 $$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))))) _let_13 _let_12 (tptp.isFinite0 tptp.xS) _let_9 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 10.58/10.77 )
% 10.58/10.77 % SZS output end Proof for NUM450+6
% 10.58/10.77 % cvc5---1.0.5 exiting
% 10.58/10.78 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------