TSTP Solution File: NUM513+3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM513+3 : 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 10:44:39 EDT 2023
% Result : Theorem 1.33s 1.68s
% Output : Proof 1.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM513+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 14:03:06 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.49 %----Proving TF0_NAR, FOF, or CNF
% 1.33/1.68 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.rcfb4ZgpLg/cvc5---1.0.5_1537.p...
% 1.33/1.68 ------- get file name : TPTP file name is NUM513+3
% 1.33/1.68 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1537.smt2...
% 1.33/1.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.33/1.68 % SZS status Theorem for NUM513+3
% 1.33/1.68 % SZS output start Proof for NUM513+3
% 1.33/1.68 (
% 1.33/1.68 (let ((_let_1 (tptp.sdtsldt0 tptp.xn tptp.xr))) (let ((_let_2 (tptp.sdtasdt0 _let_1 tptp.xm))) (let ((_let_3 (tptp.sdtsldt0 tptp.xk tptp.xr))) (let ((_let_4 (tptp.sdtasdt0 tptp.xp _let_3))) (let ((_let_5 (= tptp.xn (tptp.sdtasdt0 tptp.xr _let_1)))) (let ((_let_6 (tptp.aNaturalNumber0 _let_1))) (let ((_let_7 (and _let_6 _let_5))) (let ((_let_8 (not (=> (and (tptp.aNaturalNumber0 _let_3) (= tptp.xk (tptp.sdtasdt0 tptp.xr _let_3))) (=> _let_7 (= _let_4 _let_2)))))) (let ((_let_9 (tptp.sdtasdt0 tptp.xp tptp.xk))) (let ((_let_10 (tptp.sdtsldt0 _let_9 tptp.xr))) (let ((_let_11 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_12 (and (not (=> _let_7 (= _let_1 tptp.xn))) _let_6 _let_5 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtsldt0 tptp.xn tptp.xr) W0) tptp.xn))) (tptp.sdtlseqdt0 _let_1 tptp.xn)))) (let ((_let_13 (tptp.doDivides0 tptp.xr tptp.xn))) (let ((_let_14 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xr W0)))) _let_13))) (let ((_let_15 (tptp.doDivides0 tptp.xr tptp.xk))) (let ((_let_16 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_17 (and _let_16 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xk (tptp.sdtasdt0 tptp.xr W0)))) _let_15 (not (= tptp.xr tptp.sz00)) (not (= tptp.xr tptp.sz10)) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= tptp.xr (tptp.sdtasdt0 W0 W1)))) (tptp.doDivides0 W0 tptp.xr))) (or (= W0 tptp.sz10) (= W0 tptp.xr)))) (tptp.isPrime0 tptp.xr)))) (let ((_let_18 (= tptp.xk tptp.sz10))) (let ((_let_19 (= tptp.xk tptp.sz00))) (let ((_let_20 (= _let_11 _let_9))) (let ((_let_21 (tptp.aNaturalNumber0 tptp.xk))) (let ((_let_22 (and _let_21 _let_20 (= tptp.xk (tptp.sdtsldt0 _let_11 tptp.xp))))) (let ((_let_23 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_24 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_25 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_26 (and _let_25 _let_24 _let_23))) (let ((_let_27 (forall ((W0 $$unsorted) (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 ((_let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_29 (= _let_2 _let_4))) (let ((_let_30 (tptp.sdtasdt0 tptp.xm tptp.xn))) (let ((_let_31 (= _let_11 _let_30))) (let ((_let_32 (tptp.sdtasdt0 tptp.xm _let_1))) (let ((_let_33 (= _let_2 _let_32))) (let ((_let_34 (= _let_10 _let_4))) (let ((_let_35 (= _let_32 (tptp.sdtsldt0 _let_30 tptp.xr)))) (let ((_let_36 (1))) (let ((_let_37 (ASSUME :args (_let_22)))) (let ((_let_38 (not _let_24))) (let ((_let_39 (not _let_25))) (let ((_let_40 (or _let_39 _let_38 _let_31))) (let ((_let_41 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_41))) (let ((_let_44 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_45 (ASSUME :args (_let_26)))) (let ((_let_46 (AND_ELIM _let_45 :args _let_36))) (let ((_let_47 (0))) (let ((_let_48 (AND_ELIM _let_45 :args _let_47))) (let ((_let_49 (not _let_6))) (let ((_let_50 (or _let_49 _let_38 _let_33))) (let ((_let_51 (not _let_23))) (let ((_let_52 (not _let_15))) (let ((_let_53 (= tptp.sz00 tptp.xr))) (let ((_let_54 (not _let_21))) (let ((_let_55 (not _let_16))) (let ((_let_56 (or _let_55 _let_54 _let_53 _let_52 _let_51 _let_34))) (let ((_let_57 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1934 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1934)) (= (tptp.sdtasdt0 BOUND_VARIABLE_1934 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 BOUND_VARIABLE_1934 W1) W0)))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (_let_57))) (let ((_let_60 ((tptp.sdtasdt0 BOUND_VARIABLE_1934 (tptp.sdtsldt0 W1 W0))))) (let ((_let_61 (2))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (AND_ELIM _let_62 :args _let_47))) (let ((_let_64 (AND_ELIM _let_62 :args (3)))) (let ((_let_65 (not _let_13))) (let ((_let_66 (or _let_55 _let_39 _let_53 _let_65 _let_38 _let_35))) (let ((_let_67 (not _let_35))) (let ((_let_68 (not _let_34))) (let ((_let_69 (not _let_33))) (let ((_let_70 (not _let_31))) (let ((_let_71 (not _let_20))) (let ((_let_72 (_let_67))) (let ((_let_73 (not _let_29))) (let ((_let_74 (ASSUME :args (_let_35)))) (let ((_let_75 (ASSUME :args (_let_73)))) (let ((_let_76 (ASSUME :args (_let_34)))) (let ((_let_77 (ASSUME :args (_let_20)))) (let ((_let_78 (ASSUME :args (_let_31)))) (let ((_let_79 (ASSUME :args (_let_33)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_79 _let_75 _let_76 _let_77 _let_78) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_79) (TRANS (CONG (TRANS (SYMM _let_78) (SYMM (SYMM _let_77))) (REFL :args (tptp.xr)) :args (APPLY_UF tptp.sdtsldt0)) (SYMM (SYMM _let_76))) :args (=)) (FALSE_INTRO _let_75))) :args (_let_33 _let_73 _let_34 _let_20 _let_31))) _let_74) :args (_let_20 _let_73 _let_31 _let_33 _let_34 _let_35)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_72))) (TRUE_INTRO _let_74))) :args (_let_67 _let_35)) :args ((not (and _let_20 _let_73 _let_31 _let_33 _let_34 _let_35)) SB_LITERAL))) (CONG (REFL :args (_let_71)) (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_29))) (REFL :args (_let_70)) (REFL :args (_let_69)) (REFL :args (_let_68)) (REFL :args _let_72) :args (or))) :args ((or _let_29 _let_71 _let_70 _let_69 _let_68 _let_67))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_53 _let_39 _let_38 _let_55 _let_65 _let_35 (not _let_66)))) _let_64 _let_48 _let_46 _let_63 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) :args _let_36) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.xr tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING _let_60)) :args _let_59)) _let_58 :args (_let_66 false _let_57)) :args (_let_35 true _let_53 false _let_25 false _let_24 false _let_16 false _let_13 false _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_53 _let_51 _let_54 _let_55 _let_52 _let_34 (not _let_56)))) _let_64 (AND_ELIM _let_45 :args _let_61) (AND_ELIM _let_37 :args _let_47) _let_63 (AND_ELIM _let_62 :args _let_61) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.xr tptp.xk tptp.xp QUANTIFIERS_INST_E_MATCHING _let_60)) :args _let_59))) _let_58 :args (_let_56 false _let_57)) :args (_let_34 true _let_53 false _let_23 false _let_21 false _let_16 false _let_15 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_38 _let_49 _let_33 (not _let_50)))) _let_46 (AND_ELIM (NOT_IMPLIES_ELIM1 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) :args _let_47)) :args _let_47) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_1 tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_50 false _let_41)) :args (_let_33 false _let_24 false _let_6 false _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_38 _let_31 (not _let_40)))) _let_48 _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_40 false _let_41)) :args (_let_31 false _let_25 false _let_24 false _let_40)) (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (AND_ELIM _let_37 :args _let_36) :args (false false _let_35 false _let_34 false _let_33 false _let_31 true _let_29 false _let_20)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (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))))) _let_28 (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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) (forall ((W0 $$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))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))) (forall ((W0 $$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)))) _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)))))))) (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 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (or (and (not (= W2 tptp.sz00)) (not (= W2 tptp.sz10)) (forall ((W3 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W3) (exists ((W4 $$unsorted)) (and (tptp.aNaturalNumber0 W4) (= W2 (tptp.sdtasdt0 W3 W4)))) (tptp.doDivides0 W3 W2)) (or (= W3 tptp.sz10) (= W3 W2))))) (tptp.isPrime0 W2)) (or (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W2 W3)))) (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 (and (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W0 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W0)) (and (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W1 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W1))))))) (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= tptp.xp (tptp.sdtasdt0 W0 W1)))) (tptp.doDivides0 W0 tptp.xp))) (or (= W0 tptp.sz10) (= W0 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xp W0)))) (tptp.doDivides0 tptp.xp _let_11)) (not (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xp W0) tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn))) (not (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xp W0) tptp.xm))) (tptp.sdtlseqdt0 tptp.xp tptp.xm))) (and (not (= tptp.xn tptp.xp)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xn W0) tptp.xp))) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xm W0) tptp.xp))) (tptp.sdtlseqdt0 tptp.xm tptp.xp)) _let_22 (not (or _let_19 _let_18)) (and (not _let_19) (not _let_18)) _let_17 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xr W0) tptp.xk))) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xr W0)))) (tptp.doDivides0 tptp.xr _let_11)) (and (not (= tptp.xk tptp.xp)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xk W0) tptp.xp))) (tptp.sdtlseqdt0 tptp.xk tptp.xp)) (or (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xr W0)))) _let_13) (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xm (tptp.sdtasdt0 tptp.xr W0)))) (tptp.doDivides0 tptp.xr tptp.xm))) _let_14 _let_12 (and _let_6 _let_5 (= (tptp.sdtasdt0 _let_2 tptp.xr) _let_11) (tptp.aNaturalNumber0 _let_10) (= _let_9 (tptp.sdtasdt0 tptp.xr _let_10)) (= _let_11 (tptp.sdtasdt0 _let_10 tptp.xr))) _let_8 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.33/1.69 )
% 1.33/1.69 % SZS output end Proof for NUM513+3
% 1.33/1.69 % cvc5---1.0.5 exiting
% 1.33/1.69 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------