TSTP Solution File: NUM517+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM517+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.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 10:44:41 EDT 2023
% Result : Theorem 25.74s 26.16s
% Output : Proof 25.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM517+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n025.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 17:22:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 25.74/26.16 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.hEBpeLupIs/cvc5---1.0.5_788.p...
% 25.74/26.16 ------- get file name : TPTP file name is NUM517+1
% 25.74/26.16 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_788.smt2...
% 25.74/26.16 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.74/26.16 --- Run --no-e-matching --full-saturate-quant at 5...
% 25.74/26.16 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.74/26.16 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.74/26.16 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.74/26.16 % SZS status Theorem for NUM517+1
% 25.74/26.16 % SZS output start Proof for NUM517+1
% 25.74/26.16 (
% 25.74/26.16 (let ((_let_1 (tptp.doDivides0 tptp.xp tptp.xm))) (let ((_let_2 (tptp.sdtsldt0 tptp.xn tptp.xr))) (let ((_let_3 (tptp.doDivides0 tptp.xp _let_2))) (let ((_let_4 (not (or _let_3 _let_1)))) (let ((_let_5 (tptp.sdtpldt0 tptp.xn tptp.xm))) (let ((_let_6 (tptp.sdtpldt0 _let_5 tptp.xp))) (let ((_let_7 (tptp.sdtpldt0 _let_2 tptp.xm))) (let ((_let_8 (tptp.sdtpldt0 _let_7 tptp.xp))) (let ((_let_9 (tptp.sdtlseqdt0 _let_8 _let_6))) (let ((_let_10 (and (not (= _let_8 _let_6)) _let_9))) (let ((_let_11 (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 _let_2 tptp.xm)))) (let ((_let_12 (tptp.doDivides0 tptp.xr tptp.xn))) (let ((_let_13 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_14 (tptp.isPrime0 tptp.xr))) (let ((_let_15 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_16 (and _let_15 (tptp.doDivides0 tptp.xr tptp.xk) _let_14))) (let ((_let_17 (= tptp.xk tptp.sz10))) (let ((_let_18 (= tptp.xk tptp.sz00))) (let ((_let_19 (= tptp.xk (tptp.sdtsldt0 _let_13 tptp.xp)))) (let ((_let_20 (tptp.isPrime0 tptp.xp))) (let ((_let_21 (and _let_20 (tptp.doDivides0 tptp.xp _let_13)))) (let ((_let_22 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.isPrime0 W2) (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (=> (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))))))) (let ((_let_23 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_24 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_25 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_26 (and _let_25 _let_24 _let_23))) (let ((_let_27 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.isPrime0 W0) (and (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10)) (forall ((W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0)) (or (= W1 tptp.sz10) (= W1 W0)))))))))) (let ((_let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (let ((_let_29 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))))) (let ((_let_30 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_31 (= _let_6 _let_8))) (let ((_let_32 (tptp.iLess0 _let_8 _let_6))) (let ((_let_33 (not _let_9))) (let ((_let_34 (tptp.aNaturalNumber0 _let_6))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.aNaturalNumber0 _let_8))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35 _let_31 _let_33 _let_32))) (let ((_let_39 (0))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (1))) (let ((_let_42 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (not _let_23))) (let ((_let_45 (tptp.aNaturalNumber0 _let_5))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_44 _let_34))) (let ((_let_48 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (_let_48))) (let ((_let_51 ((tptp.sdtpldt0 W0 W1)))) (let ((_let_52 (not _let_24))) (let ((_let_53 (not _let_25))) (let ((_let_54 (or _let_53 _let_52 _let_45))) (let ((_let_55 (ASSUME :args (_let_26)))) (let ((_let_56 (AND_ELIM _let_55 :args _let_41))) (let ((_let_57 (AND_ELIM _let_55 :args _let_39))) (let ((_let_58 (2))) (let ((_let_59 (AND_ELIM _let_55 :args _let_58))) (let ((_let_60 (not _let_32))) (let ((_let_61 (not _let_11))) (let ((_let_62 (not _let_20))) (let ((_let_63 (tptp.aNaturalNumber0 _let_2))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_64 _let_52 _let_44 _let_62 _let_61 _let_60 _let_3 _let_1))) (let ((_let_66 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (and _let_63 (= tptp.xn (tptp.sdtasdt0 tptp.xr _let_2))))) (let ((_let_69 (not _let_12))) (let ((_let_70 (= tptp.sz00 tptp.xr))) (let ((_let_71 (not _let_15))) (let ((_let_72 (or _let_71 _let_53 _let_70 _let_69 _let_68))) (let ((_let_73 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1639 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1639) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1639))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1639)))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (not _let_70))) (let ((_let_76 (and _let_75 (not (= tptp.sz10 tptp.xr)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xr)) (= tptp.sz10 W1) (= W1 tptp.xr)))))) (let ((_let_77 (= _let_14 _let_76))) (let ((_let_78 (or _let_71 _let_77))) (let ((_let_79 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= (tptp.isPrime0 W0) (and (not (= tptp.sz00 W0)) (not (= tptp.sz10 W0)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 W0)) (= tptp.sz10 W1) (= W0 W1))))))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO (ASSUME :args (_let_19)) :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (AND_ELIM _let_81 :args _let_39))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_68 0)) :args ((or _let_63 (not _let_68)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_69 _let_53 _let_71 _let_70 _let_68 (not _let_72)))) (ASSUME :args (_let_12)) _let_57 _let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_76 0)) :args ((or _let_75 (not _let_76)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_77)) :args ((or (not _let_14) _let_76 (not _let_77)))) (AND_ELIM _let_81 :args _let_58) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_71 _let_77 (not _let_78)))) _let_82 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_80 :args (tptp.xr QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.isPrime0 W0)))) :args (_let_79)))) _let_80 :args (_let_78 false _let_79)) :args (_let_77 false _let_15 false _let_78)) :args (_let_76 false _let_14 false _let_77)) :args (_let_75 false _let_76)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_74 :args (tptp.xr tptp.xn _let_2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_73)))) _let_74 :args (_let_72 false _let_73)) :args (_let_68 false _let_12 false _let_25 false _let_15 true _let_70 false _let_72)) :args (_let_63 false _let_68)))) (let ((_let_84 (ASSUME :args (_let_4)))) (let ((_let_85 (tptp.aNaturalNumber0 _let_7))) (let ((_let_86 (not _let_85))) (let ((_let_87 (or _let_86 _let_44 _let_36))) (let ((_let_88 (or _let_64 _let_52 _let_85))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_31 _let_33 _let_37 _let_35 _let_32 (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_44 _let_36 _let_86 (not _let_87)))) _let_59 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_52 _let_64 _let_85 (not _let_88)))) _let_56 _let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_2 tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_51)) :args _let_50)) _let_49 :args (_let_88 false _let_48)) :args (_let_85 false _let_24 false _let_63 false _let_88)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_7 tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_51)) :args _let_50)) _let_49 :args (_let_87 false _let_48)) :args (_let_36 false _let_23 false _let_85 false _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_3 _let_1 _let_52 _let_44 _let_62 _let_61 _let_64 _let_60 (not _let_65)))) (NOT_OR_ELIM _let_84 :args _let_39) (NOT_OR_ELIM _let_84 :args _let_41) _let_56 _let_59 (AND_ELIM (ASSUME :args (_let_21)) :args _let_39) (ASSUME :args (_let_11)) _let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (_let_2 tptp.xm tptp.xp QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1)) false))))) :args (_let_66))) _let_67 :args (_let_65 false _let_66)) :args (_let_60 true _let_3 true _let_1 false _let_24 false _let_23 false _let_20 false _let_11 false _let_63 false _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_44 _let_34 _let_46 (not _let_47)))) _let_59 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_52 _let_45 (not _let_54)))) _let_57 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_51)) :args _let_50)) _let_49 :args (_let_54 false _let_48)) :args (_let_45 false _let_25 false _let_24 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_5 tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_51)) :args _let_50)) _let_49 :args (_let_47 false _let_48)) :args (_let_34 false _let_23 false _let_45 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_43 :args (_let_8 _let_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.sdtlseqdt0 W0 W1) false))))) :args (_let_42)))) _let_43 :args (_let_38 false _let_42)) (AND_ELIM _let_40 :args _let_41) (AND_ELIM _let_40 :args _let_39) :args (false false _let_36 true _let_32 false _let_34 false _let_38 false _let_9 true _let_31)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))) _let_30 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (and (= (tptp.sdtasdt0 W0 _let_1) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 _let_1 W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtpldt0 W0 W1) tptp.sz00) (and (= W0 tptp.sz00) (= W1 tptp.sz00))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (let ((_let_2 (tptp.sdtpldt0 W0 W2))) (let ((_let_3 (tptp.sdtpldt0 W2 W1))) (let ((_let_4 (tptp.sdtpldt0 W2 W0))) (=> (tptp.aNaturalNumber0 W2) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W2 W0))) (let ((_let_2 (tptp.sdtasdt0 W1 W0))) (let ((_let_3 (tptp.sdtasdt0 W0 W2))) (let ((_let_4 (tptp.sdtasdt0 W0 W1))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 W2)) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (not (= W0 tptp.sz00)) (tptp.sdtlseqdt0 W1 (tptp.sdtasdt0 W1 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) _let_29 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))) _let_28 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W1 W2)) (tptp.doDivides0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 W2)) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))) (tptp.doDivides0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.doDivides0 W0 W1) (not (= W1 tptp.sz00))) (tptp.sdtlseqdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) _let_27 (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_26 _let_22 _let_21 (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xm)) (and (not (= tptp.xn tptp.xp)) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (tptp.sdtlseqdt0 tptp.xm tptp.xp)) _let_19 (not (or _let_18 _let_17)) (and (not _let_18) (not _let_17)) _let_16 (and (tptp.sdtlseqdt0 tptp.xr tptp.xk) (tptp.doDivides0 tptp.xr _let_13)) (and (not (= tptp.xk tptp.xp)) (tptp.sdtlseqdt0 tptp.xk tptp.xp)) (or _let_12 (tptp.doDivides0 tptp.xr tptp.xm)) _let_12 (and (not (= _let_2 tptp.xn)) (tptp.sdtlseqdt0 _let_2 tptp.xn)) _let_11 _let_10 _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.74/26.16 )
% 25.74/26.16 % SZS output end Proof for NUM517+1
% 25.74/26.16 % cvc5---1.0.5 exiting
% 25.74/26.16 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------