TSTP Solution File: NUM495+3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM495+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 10:44:28 EDT 2023
% Result : Theorem 14.98s 15.18s
% Output : Proof 14.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM495+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n024.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 11:07:09 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 14.98/15.18 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.tipqxgOHl4/cvc5---1.0.5_10976.p...
% 14.98/15.18 ------- get file name : TPTP file name is NUM495+3
% 14.98/15.18 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10976.smt2...
% 14.98/15.18 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 14.98/15.18 --- Run --no-e-matching --full-saturate-quant at 5...
% 14.98/15.18 % SZS status Theorem for NUM495+3
% 14.98/15.18 % SZS output start Proof for NUM495+3
% 14.98/15.18 (
% 14.98/15.18 (let ((_let_1 (tptp.doDivides0 tptp.xp tptp.xm))) (let ((_let_2 (tptp.doDivides0 tptp.xp tptp.xr))) (let ((_let_3 (not (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xr (tptp.sdtasdt0 tptp.xp W0)))) _let_2 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xm (tptp.sdtasdt0 tptp.xp W0)))) _let_1)))) (let ((_let_4 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (let ((_let_5 (tptp.sdtpldt0 tptp.xr tptp.xm))) (let ((_let_6 (tptp.sdtpldt0 _let_5 tptp.xp))) (let ((_let_7 (tptp.sdtlseqdt0 _let_6 _let_4))) (let ((_let_8 (and (not (= _let_6 _let_4)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) W0) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) _let_7))) (let ((_let_9 (tptp.sdtasdt0 tptp.xr tptp.xm))) (let ((_let_10 (tptp.doDivides0 tptp.xp _let_9))) (let ((_let_11 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xr tptp.xm) (tptp.sdtasdt0 tptp.xp W0)))) _let_10))) (let ((_let_12 (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp)))) (let ((_let_13 (tptp.sdtpldt0 tptp.xp tptp.xr))) (let ((_let_14 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_15 (and _let_14 (= _let_13 tptp.xn) _let_12))) (let ((_let_16 (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xm)))) (let ((_let_17 (tptp.isPrime0 tptp.xp))) (let ((_let_18 (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)))) _let_17 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xp W0)))) _let_16))) (let ((_let_19 (forall ((W0 $$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 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W1 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W1))))))))) (let ((_let_20 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_21 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_22 (and (tptp.aNaturalNumber0 tptp.xn) _let_21 _let_20))) (let ((_let_23 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))))) (let ((_let_24 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_25 (tptp.aNaturalNumber0 tptp.sz10))) (let ((_let_26 (not _let_17))) (let ((_let_27 (= tptp.sz10 tptp.xp))) (let ((_let_28 (= tptp.sz00 tptp.xp))) (let ((_let_29 (and (or _let_28 _let_27 (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1906 $$unsorted)) (or (not (tptp.aNaturalNumber0 W3)) (not (tptp.doDivides0 W3 tptp.xp)) (= tptp.sz10 W3) (= tptp.xp W3) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1906)) (not (= tptp.xp (tptp.sdtasdt0 W3 BOUND_VARIABLE_1906))))))) _let_26))) (let ((_let_30 (tptp.sdtpldt0 (tptp.sdtpldt0 _let_13 tptp.xm) tptp.xp))) (let ((_let_31 (tptp.iLess0 _let_6 _let_30))) (let ((_let_32 (and (not (forall ((W3 $$unsorted)) (or (not (tptp.aNaturalNumber0 W3)) (not (= tptp.xm (tptp.sdtasdt0 tptp.xp W3)))))) _let_1))) (let ((_let_33 (and (not (forall ((W3 $$unsorted)) (or (not (tptp.aNaturalNumber0 W3)) (not (= tptp.xr (tptp.sdtasdt0 tptp.xp W3)))))) _let_2))) (let ((_let_34 (not _let_31))) (let ((_let_35 (not _let_10))) (let ((_let_36 (and (or (not _let_25) (not (= _let_9 (tptp.sdtasdt0 tptp.xp tptp.sz10)))) _let_35))) (let ((_let_37 (not _let_20))) (let ((_let_38 (not _let_21))) (let ((_let_39 (not _let_14))) (let ((_let_40 (or _let_39 _let_38 _let_37 _let_29 _let_36 _let_34 _let_33 _let_32))) (let ((_let_41 (1))) (let ((_let_42 (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_43 (ASSUME :args (_let_15)))) (let ((_let_44 (AND_ELIM (EQ_RESOLVE _let_43 _let_42) :args _let_41))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO _let_44 :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (AND_ELIM _let_45 :args _let_41))) (let ((_let_47 (2))) (let ((_let_48 (AND_ELIM _let_45 :args _let_47))) (let ((_let_49 (0))) (let ((_let_50 (AND_ELIM (EQ_RESOLVE _let_43 (TRANS _let_42 (MACRO_SR_EQ_INTRO _let_44 :args ((and _let_14 (= tptp.xn _let_13) _let_12) SB_DEFAULT SBA_FIXPOINT)))) :args _let_49))) (let ((_let_51 (not _let_29))) (let ((_let_52 (3))) (let ((_let_53 (tptp.sdtlseqdt0 _let_6 _let_30))) (let ((_let_54 (not _let_53))) (let ((_let_55 (= _let_6 _let_30))) (let ((_let_56 (tptp.aNaturalNumber0 _let_30))) (let ((_let_57 (not _let_56))) (let ((_let_58 (tptp.aNaturalNumber0 _let_6))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_59 _let_57 _let_55 _let_54 _let_31))) (let ((_let_61 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (tptp.sdtpldt0 _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_64 (tptp.aNaturalNumber0 _let_63))) (let ((_let_65 (= _let_30 _let_63))) (let ((_let_66 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_59 _let_67 _let_64))) (let ((_let_69 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (_let_69))) (let ((_let_72 (tptp.aNaturalNumber0 _let_5))) (let ((_let_73 (not _let_72))) (let ((_let_74 (or _let_73 _let_37 _let_58))) (let ((_let_75 (or _let_39 _let_38 _let_72))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_37 _let_73 _let_58 (not _let_74)))) _let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_38 _let_39 _let_72 (not _let_75)))) _let_46 _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (tptp.xr tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_71)) _let_70 :args (_let_75 false _let_69)) :args (_let_72 false _let_21 false _let_14 false _let_75)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (_let_5 tptp.xp QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_71)) _let_70 :args (_let_74 false _let_69)) :args (_let_58 false _let_20 false _let_72 false _let_74)))) (let ((_let_77 (not _let_65))) (let ((_let_78 (or _let_67 _let_77))) (let ((_let_79 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) W0) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xp tptp.xr) tptp.xm) tptp.xp))))))) (let ((_let_80 (not _let_78))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_44 :args ((and (not (= _let_4 _let_6)) (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) W0)))))) _let_7) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_82 (or))) (let ((_let_83 (not _let_79))) (let ((_let_84 (_let_83))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_84)) :args _let_84) (REWRITE :args ((=> _let_83 (not (or _let_67 (not (= _let_63 _let_30))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_79))) (REFL :args (_let_80)) :args _let_82)) (AND_ELIM _let_81 :args _let_41) :args (_let_80 true _let_79)))) (let ((_let_86 (REFL :args (_let_78)))) (let ((_let_87 (and _let_65 _let_64))) (let ((_let_88 (ASSUME :args (_let_64)))) (let ((_let_89 (ASSUME :args (_let_65)))) (let ((_let_90 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (BOUND_VARIABLE_1975 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W1))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (and (or (= tptp.sz00 W2) (= tptp.sz10 W2) (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1906 $$unsorted)) (or (not (tptp.aNaturalNumber0 W3)) (not (tptp.doDivides0 W3 W2)) (= tptp.sz10 W3) (= W2 W3) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1906)) (not (= W2 (tptp.sdtasdt0 W3 BOUND_VARIABLE_1906))))))) (not (tptp.isPrime0 W2))) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1975)) (not (= _let_1 (tptp.sdtasdt0 W2 BOUND_VARIABLE_1975)))) (not (tptp.doDivides0 W2 _let_1))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xp tptp.xr) tptp.xm) tptp.xp))) (and (not (forall ((W3 $$unsorted)) (or (not (tptp.aNaturalNumber0 W3)) (not (= W0 (tptp.sdtasdt0 W2 W3)))))) (tptp.doDivides0 W2 W0)) (and (not (forall ((W3 $$unsorted)) (or (not (tptp.aNaturalNumber0 W3)) (not (= W1 (tptp.sdtasdt0 W2 W3)))))) (tptp.doDivides0 W2 W1))))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_19)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_44 :args ((forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (BOUND_VARIABLE_1975 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W1))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (and (or (= tptp.sz00 W2) (= tptp.sz10 W2) (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1906 $$unsorted)) (or (not (tptp.aNaturalNumber0 W3)) (not (tptp.doDivides0 W3 W2)) (= tptp.sz10 W3) (= W2 W3) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1906)) (not (= W2 (tptp.sdtasdt0 W3 BOUND_VARIABLE_1906))))))) (not (tptp.isPrime0 W2))) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1975)) (not (= _let_1 (tptp.sdtasdt0 W2 BOUND_VARIABLE_1975)))) (not (tptp.doDivides0 W2 _let_1))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (and (not (forall ((W3 $$unsorted)) (or (not (tptp.aNaturalNumber0 W3)) (not (= W0 (tptp.sdtasdt0 W2 W3)))))) (tptp.doDivides0 W2 W0)) (and (not (forall ((W3 $$unsorted)) (or (not (tptp.aNaturalNumber0 W3)) (not (= W1 (tptp.sdtasdt0 W2 W3)))))) (tptp.doDivides0 W2 W1))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_92 (not _let_32))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (not _let_36))) (let ((_let_95 (not _let_33))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_38 _let_37 _let_39 _let_29 _let_34 _let_36 _let_33 _let_32 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_33 1)) :args ((or _let_2 _let_95))) (NOT_OR_ELIM _let_93 :args _let_41) :args (_let_95 true _let_2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_36 1)) :args ((or _let_35 _let_94))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) :args _let_41) :args (_let_94 false _let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_32 1)) :args ((or _let_1 _let_92))) (NOT_OR_ELIM _let_93 :args _let_52) :args (_let_92 true _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (tptp.xr tptp.xm tptp.xp tptp.sz10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_90))) _let_91 :args (_let_40 false _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_55 _let_54 _let_59 _let_57 _let_31 (not _let_60)))) (AND_ELIM _let_81 :args _let_49) (AND_ELIM _let_81 :args _let_47) _let_76 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_87)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_88 _let_89) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_89)) :args (APPLY_UF tptp.aNaturalNumber0)) (TRUE_INTRO _let_88))) :args (_let_64 _let_65))) :args (_let_65 _let_64))) :args (true _let_87)) :args ((or _let_77 _let_56 (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_78 1)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_65))) :args _let_82)) :args ((or _let_65 _let_78))) _let_85 :args (_let_65 true _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_67 _let_59 _let_64 (not _let_68)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_78 0)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) :args _let_82)) :args ((or _let_66 _let_78))) _let_85 :args (_let_66 true _let_78)) _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (_let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_71)) _let_70 :args (_let_68 false _let_69)) :args (_let_64 false _let_66 false _let_58 false _let_68)) :args (_let_56 false _let_65 false _let_64)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_6 _let_30 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_31 true _let_55 false _let_53 false _let_58 false _let_56 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 1)) :args ((or _let_26 _let_51))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_18)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_44 :args ((and (not _let_28) (not _let_27) (forall ((W0 $$unsorted) (BOUND_VARIABLE_2015 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_2015)) (not (= tptp.xp (tptp.sdtasdt0 W0 BOUND_VARIABLE_2015)))) (not (tptp.doDivides0 W0 tptp.xp))) (= tptp.sz10 W0) (= tptp.xp W0))) _let_17 (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xp W0)))))) _let_16) SB_DEFAULT SBA_FIXPOINT)))) :args _let_52) :args (_let_51 false _let_17)) _let_50 _let_48 _let_46 :args (false true _let_33 true _let_36 true _let_32 false _let_40 false _let_31 true _let_29 false _let_14 false _let_20 false _let_21)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) (and _let_25 (not (= tptp.sz10 tptp.sz00))) _let_24 (forall ((W0 $$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_23 (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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.doDivides0 W0 W1) (not (= W1 tptp.sz00))) (tptp.sdtlseqdt0 W0 W1)))) (forall ((W0 $$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))))))) (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_22 _let_19 _let_18 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xp W0) tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn)) _let_15 (and (not (= tptp.xr tptp.xn)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xr W0) tptp.xn))) (tptp.sdtlseqdt0 tptp.xr tptp.xn)) _let_11 _let_8 _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 14.98/15.19 )
% 14.98/15.19 % SZS output end Proof for NUM495+3
% 14.98/15.19 % cvc5---1.0.5 exiting
% 14.98/15.19 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------