TSTP Solution File: NUM501+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM501+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 10:44:30 EDT 2023
% Result : Theorem 28.72s 29.02s
% Output : Proof 28.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM501+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 18:13:22 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 28.72/29.02 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.xyvOE6iEYp/cvc5---1.0.5_5138.p...
% 28.72/29.02 ------- get file name : TPTP file name is NUM501+3
% 28.72/29.02 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_5138.smt2...
% 28.72/29.02 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 28.72/29.02 --- Run --no-e-matching --full-saturate-quant at 5...
% 28.72/29.02 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 28.72/29.02 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 28.72/29.02 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 28.72/29.02 % SZS status Theorem for NUM501+3
% 28.72/29.02 % SZS output start Proof for NUM501+3
% 28.72/29.02 (
% 28.72/29.02 (let ((_let_1 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_2 (not (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xr W0)))) (tptp.doDivides0 tptp.xr _let_1))))) (let ((_let_3 (tptp.isPrime0 tptp.xr))) (let ((_let_4 (tptp.doDivides0 tptp.xr tptp.xk))) (let ((_let_5 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_6 (and _let_5 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xk (tptp.sdtasdt0 tptp.xr W0)))) _let_4 (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)))) _let_3))) (let ((_let_7 (= tptp.xk tptp.sz10))) (let ((_let_8 (= tptp.xk tptp.sz00))) (let ((_let_9 (tptp.sdtsldt0 _let_1 tptp.xp))) (let ((_let_10 (and (tptp.aNaturalNumber0 tptp.xk) (= _let_1 (tptp.sdtasdt0 tptp.xp tptp.xk)) (= tptp.xk _let_9)))) (let ((_let_11 (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 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xp W0)))) (tptp.doDivides0 tptp.xp _let_1)))) (let ((_let_12 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_13 (and (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xm) _let_12))) (let ((_let_14 (forall ((W0 $$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))))))))) (let ((_let_15 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))) (let ((_let_16 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_17 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_18 (tptp.sdtasdt0 tptp.xp _let_9))) (let ((_let_19 (= _let_1 _let_18))) (let ((_let_20 (tptp.sdtasdt0 tptp.xr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_21 (= _let_9 _let_20))) (let ((_let_22 (= _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_23 (tptp.sdtasdt0 _let_9 tptp.xp))) (let ((_let_24 (= _let_18 _let_23))) (let ((_let_25 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.xp))) (let ((_let_26 (tptp.sdtasdt0 tptp.xr _let_25))) (let ((_let_27 (= (tptp.sdtasdt0 _let_20 tptp.xp) _let_26))) (let ((_let_28 (= _let_1 _let_26))) (let ((_let_29 (1))) (let ((_let_30 (2))) (let ((_let_31 (ASSUME :args (_let_10)))) (let ((_let_32 (AND_ELIM _let_31 :args _let_30))) (let ((_let_33 (EQ_RESOLVE _let_31 (MACRO_SR_EQ_INTRO _let_32 :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (AND_ELIM _let_33 :args _let_29))) (let ((_let_35 (not _let_21))) (let ((_let_36 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35))) (let ((_let_39 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtsldt0 (tptp.sdtasdt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtasdt0 tptp.xr W0))))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_6)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_32 :args ((and _let_5 (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xk (tptp.sdtasdt0 tptp.xr W0)))))) _let_4 (not (= tptp.sz00 tptp.xr)) (not (= tptp.sz10 tptp.xr)) (forall ((W0 $$unsorted) (BOUND_VARIABLE_2164 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_2164)) (not (= tptp.xr (tptp.sdtasdt0 W0 BOUND_VARIABLE_2164)))) (not (tptp.doDivides0 W0 tptp.xr))) (= tptp.sz10 W0) (= tptp.xr W0))) _let_3) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_42 (or))) (let ((_let_43 (not _let_39))) (let ((_let_44 (_let_43))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_44)) :args _let_44)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_39))) (REFL :args (_let_40)) :args _let_42)) (AND_ELIM _let_41 :args _let_29) :args (_let_40 true _let_39)))) (let ((_let_46 (REFL :args (_let_38)))) (let ((_let_47 (tptp.sdtasdt0 tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_48 (= _let_18 _let_47))) (let ((_let_49 (not _let_48))) (let ((_let_50 (and _let_49 (not (= _let_23 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xp)))))) (let ((_let_51 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_52 (not _let_51))) (let ((_let_53 (tptp.aNaturalNumber0 _let_9))) (let ((_let_54 (not _let_53))) (let ((_let_55 (= tptp.sz00 tptp.xp))) (let ((_let_56 (not _let_12))) (let ((_let_57 (or _let_56 _let_55 _let_54 _let_52 _let_50 _let_22))) (let ((_let_58 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1474 $$unsorted) (BOUND_VARIABLE_1472 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= tptp.sz00 W0) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1472)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1474)) (and (not (= (tptp.sdtasdt0 W0 BOUND_VARIABLE_1472) (tptp.sdtasdt0 W0 BOUND_VARIABLE_1474))) (not (= (tptp.sdtasdt0 BOUND_VARIABLE_1472 W0) (tptp.sdtasdt0 BOUND_VARIABLE_1474 W0)))) (= BOUND_VARIABLE_1472 BOUND_VARIABLE_1474))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (not _let_50))) (let ((_let_61 (= _let_1 _let_47))) (let ((_let_62 (not _let_61))) (let ((_let_63 (or _let_52 _let_62))) (let ((_let_64 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xp W0))))))) (let ((_let_65 (not _let_63))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (not _let_64))) (let ((_let_68 (_let_67))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_68)) :args _let_68)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_64))) (REFL :args (_let_65)) :args _let_42)) (AND_ELIM _let_66 :args (4)) :args (_let_65 true _let_64)))) (let ((_let_70 (REFL :args (_let_63)))) (let ((_let_71 (and _let_19 _let_61))) (let ((_let_72 (ASSUME :args (_let_61)))) (let ((_let_73 (ASSUME :args (_let_19)))) (let ((_let_74 (SYMM (SYMM _let_73)))) (let ((_let_75 (0))) (let ((_let_76 (AND_ELIM _let_33 :args _let_75))) (let ((_let_77 (AND_ELIM (ASSUME :args (_let_13)) :args _let_30))) (let ((_let_78 (or _let_56 _let_54 _let_24))) (let ((_let_79 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (not _let_5))) (let ((_let_82 (or _let_81 _let_37 _let_56 _let_27))) (let ((_let_83 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_42)) :args ((or _let_36 _let_38))) _let_45 :args (_let_36 true _let_38)))) (let ((_let_86 (not _let_28))) (let ((_let_87 (tptp.aNaturalNumber0 _let_25))) (let ((_let_88 (not _let_87))) (let ((_let_89 (or _let_88 _let_86))) (let ((_let_90 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xr W0))))))) (let ((_let_91 (_let_90))) (let ((_let_92 (or _let_37 _let_56 _let_87))) (let ((_let_93 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (ASSUME :args (_let_86)))) (let ((_let_96 (ASSUME :args (_let_27)))) (let ((_let_97 (APPLY_UF tptp.sdtasdt0))) (let ((_let_98 (REFL :args (tptp.xp)))) (let ((_let_99 (ASSUME :args (_let_21)))) (let ((_let_100 (ASSUME :args (_let_22)))) (let ((_let_101 (ASSUME :args (_let_24)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_96 _let_99 _let_100 _let_101 _let_73) (SCOPE (TRANS _let_74 (SYMM (SYMM _let_101)) (CONG _let_100 _let_98 :args _let_97) (CONG (TRANS (SYMM _let_100) (SYMM (SYMM _let_99))) _let_98 :args _let_97) (SYMM (SYMM _let_96))) :args (_let_27 _let_21 _let_22 _let_24 _let_19))) _let_95) :args (_let_19 _let_21 _let_22 _let_24 _let_27 _let_86)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (SYMM (SYMM (ASSUME :args (_let_28)))))) (FALSE_INTRO _let_95))) :args (_let_28 _let_86)) :args ((not (and _let_19 _let_21 _let_22 _let_24 _let_27 _let_86)) SB_LITERAL))) (CONG (REFL :args ((not _let_19))) (REFL :args (_let_35)) (REFL :args ((not _let_22))) (REFL :args ((not _let_24))) (REFL :args ((not _let_27))) (MACRO_SR_PRED_INTRO :args ((= (not _let_86) _let_28))) :args _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_88 _let_86 (not _let_89)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_56 _let_37 _let_87 (not _let_92)))) _let_77 _let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 W0 W1)))) :args (_let_93))) _let_94 :args (_let_92 false _let_93)) :args (_let_87 false _let_12 false _let_36 false _let_92)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_91) :args (_let_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 tptp.xr W0)))) :args _let_91)) (NOT_NOT_ELIM (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args _let_75)) :args (_let_89 false _let_90)) :args (_let_86 false _let_87 false _let_89)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_56 _let_81 _let_37 _let_27 (not _let_82)))) _let_77 (AND_ELIM _let_41 :args _let_75) _let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (tptp.xr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.xp QUANTIFIERS_INST_E_MATCHING ((tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2)))) :args (_let_83))) _let_84 :args (_let_82 false _let_83)) :args (_let_27 false _let_12 false _let_5 false _let_36 false _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_56 _let_54 _let_24 (not _let_78)))) _let_77 _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (tptp.xp _let_9 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_79))) _let_80 :args (_let_78 false _let_79)) :args (_let_24 false _let_12 false _let_53 false _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_55 _let_56 _let_54 _let_52 _let_50 _let_22 (not _let_57)))) (AND_ELIM _let_66 :args _let_75) _let_77 _let_76 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_63 0)) (CONG _let_70 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) :args _let_42)) :args ((or _let_51 _let_63))) _let_69 :args (_let_51 true _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_50 0)) :args ((or _let_49 _let_60))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_71)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_72 _let_73) (SCOPE (TRANS (SYMM _let_74) (SYMM (SYMM _let_72))) :args (_let_61 _let_19))) :args (_let_19 _let_61))) :args (true _let_71)) _let_34 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_63 1)) (CONG _let_70 (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_61))) :args _let_42)) :args ((or _let_61 _let_63))) _let_69 :args (_let_61 true _let_63)) :args (_let_48 false _let_19 false _let_61)) :args (_let_60 false _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_58))) _let_59 :args (_let_57 false _let_58)) :args (_let_22 true _let_55 false _let_12 false _let_53 false _let_51 true _let_50 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 1)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_21))) :args _let_42)) :args ((or _let_21 _let_38))) _let_45 :args (_let_21 true _let_38)) _let_34 :args (false true _let_28 false _let_27 false _let_24 false _let_22 false _let_21 false _let_19)) :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)))) _let_17 (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_16 _let_15 (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)))) _let_14 (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)))) (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 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_13 (forall ((W0 $$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 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W1 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W1))))))) _let_11 (not (or (exists ((W0 $$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_10 (not (or _let_8 _let_7)) (and (not _let_8) (not _let_7)) _let_6 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 28.72/29.03 )
% 28.72/29.03 % SZS output end Proof for NUM501+3
% 28.72/29.03 % cvc5---1.0.5 exiting
% 28.72/29.03 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------