TSTP Solution File: NUM524+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM524+1 : 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 10:44:43 EDT 2023
% Result : Theorem 11.09s 11.34s
% Output : Proof 11.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM524+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n031.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Aug 25 08:14:37 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.51 %----Proving TF0_NAR, FOF, or CNF
% 11.09/11.34 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.uo3it40Ixy/cvc5---1.0.5_7883.p...
% 11.09/11.34 ------- get file name : TPTP file name is NUM524+1
% 11.09/11.34 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7883.smt2...
% 11.09/11.34 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 11.09/11.34 --- Run --no-e-matching --full-saturate-quant at 5...
% 11.09/11.34 % SZS status Theorem for NUM524+1
% 11.09/11.34 % SZS output start Proof for NUM524+1
% 11.09/11.34 (
% 11.09/11.34 (let ((_let_1 (tptp.sdtasdt0 tptp.xm tptp.xm))) (let ((_let_2 (not (= _let_1 (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xq tptp.xq)))))) (let ((_let_3 (tptp.sdtsldt0 tptp.xn tptp.xp))) (let ((_let_4 (= tptp.xq _let_3))) (let ((_let_5 (tptp.doDivides0 tptp.xp tptp.xn))) (let ((_let_6 (tptp.sdtasdt0 tptp.xn tptp.xn))) (let ((_let_7 (tptp.doDivides0 tptp.xp _let_6))) (let ((_let_8 (and _let_7 _let_5))) (let ((_let_9 (tptp.sdtasdt0 tptp.xp _let_1))) (let ((_let_10 (= _let_9 _let_6))) (let ((_let_11 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_12 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_13 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_14 (and _let_13 _let_12 _let_11 (not (= tptp.xn tptp.sz00)) (not (= tptp.xm tptp.sz00)) (not (= tptp.xp tptp.sz00))))) (let ((_let_15 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))))) (let ((_let_16 (forall ((W0 $$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_17 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))) (let ((_let_18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_19 (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 _let_3 _let_3)))) (let ((_let_20 (= _let_1 _let_19))) (let ((_let_21 (= (tptp.sdtasdt0 tptp.xn _let_3) (tptp.sdtsldt0 _let_6 tptp.xp)))) (let ((_let_22 (= _let_1 (tptp.sdtsldt0 _let_9 tptp.xp)))) (let ((_let_23 (tptp.sdtasdt0 tptp.xp _let_3))) (let ((_let_24 (= tptp.xn _let_23))) (let ((_let_25 (= _let_19 (tptp.sdtasdt0 _let_23 _let_3)))) (let ((_let_26 (ASSUME :args (_let_10)))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO (ASSUME :args (_let_4)) :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (not _let_13))) (let ((_let_29 (not _let_5))) (let ((_let_30 (= tptp.sz00 tptp.xp))) (let ((_let_31 (not _let_11))) (let ((_let_32 (or _let_31 _let_28 _let_30 _let_29 _let_28 _let_21))) (let ((_let_33 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1714 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1714)) (= (tptp.sdtasdt0 BOUND_VARIABLE_1714 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 BOUND_VARIABLE_1714 W1) W0)))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (1))) (let ((_let_36 (ASSUME :args (_let_8)))) (let ((_let_37 (AND_ELIM _let_36 :args _let_35))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (AND_ELIM _let_38 :args (2)))) (let ((_let_40 (0))) (let ((_let_41 (AND_ELIM _let_38 :args _let_40))) (let ((_let_42 (AND_ELIM _let_38 :args (5)))) (let ((_let_43 (tptp.aNaturalNumber0 _let_1))) (let ((_let_44 (= _let_43 _let_22))) (let ((_let_45 (tptp.doDivides0 tptp.xp _let_9))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.aNaturalNumber0 _let_9))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_31 _let_48 _let_30 _let_46 _let_44))) (let ((_let_50 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1622 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1622) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1622))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1622)))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (_let_50))) (let ((_let_53 (and _let_10 _let_7))) (let ((_let_54 (ASSUME :args (_let_7)))) (let ((_let_55 (SYMM _let_26))) (let ((_let_56 (REFL :args (tptp.xp)))) (let ((_let_57 (not _let_43))) (let ((_let_58 (or _let_31 _let_57 _let_47))) (let ((_let_59 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (_let_59))) (let ((_let_62 (not _let_12))) (let ((_let_63 (or _let_62 _let_62 _let_43))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_63))) :args ((or _let_62 _let_43 (not _let_63)))) (AND_ELIM _let_38 :args _let_35) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.xm tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_61)) _let_60 :args (_let_63 false _let_59)) :args (_let_43 false _let_12 false _let_63)))) (let ((_let_65 (tptp.aNaturalNumber0 _let_3))) (let ((_let_66 (and _let_65 _let_24))) (let ((_let_67 (or _let_31 _let_28 _let_30 _let_29 _let_66))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_30 _let_28 _let_31 _let_29 _let_66 (not _let_67)))) _let_42 _let_41 _let_39 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.xp tptp.xn _let_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_52))) _let_51 :args (_let_67 false _let_50)) :args (_let_66 true _let_30 false _let_13 false _let_11 false _let_5 false _let_67)))) (let ((_let_69 (not _let_66))) (let ((_let_70 (not _let_65))) (let ((_let_71 (or _let_31 _let_70 _let_70 _let_25))) (let ((_let_72 (forall ((W0 $$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_73 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (not _let_25))) (let ((_let_75 (not _let_24))) (let ((_let_76 (not _let_22))) (let ((_let_77 (not _let_21))) (let ((_let_78 (not _let_10))) (let ((_let_79 (_let_74))) (let ((_let_80 (not _let_20))) (let ((_let_81 (ASSUME :args (_let_25)))) (let ((_let_82 (ASSUME :args (_let_22)))) (let ((_let_83 (ASSUME :args (_let_21)))) (let ((_let_84 (ASSUME :args (_let_24)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_81 (MODUS_PONENS (AND_INTRO _let_82 _let_26 _let_83 _let_84 _let_27) (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG (TRANS (CONG (SYMM _let_84) (REFL :args (_let_3)) :args (APPLY_UF tptp.sdtasdt0)) (SYMM (SYMM _let_83)) (CONG _let_55 _let_56 :args (APPLY_UF tptp.sdtsldt0)) (SYMM _let_82)) (REFL :args (_let_19)) :args (=)) (FALSE_INTRO _let_27)) :args ((= _let_25 false)))) :args (_let_22 _let_10 _let_21 _let_24 _let_80)))) :args (_let_10 _let_80 _let_21 _let_22 _let_24 _let_25)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_79))) (TRUE_INTRO (SYMM (SYMM _let_81))))) :args (_let_25 _let_74)) :args ((not (and _let_10 _let_80 _let_21 _let_22 _let_24 _let_25)) SB_LITERAL))) (CONG (REFL :args (_let_78)) (MACRO_SR_PRED_INTRO :args ((= (not _let_80) _let_20))) (REFL :args (_let_77)) (REFL :args (_let_76)) (REFL :args (_let_75)) (REFL :args _let_79) :args (or))) :args ((or _let_20 _let_78 _let_77 _let_76 _let_75 _let_74))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_71))) :args ((or _let_31 _let_70 _let_25 (not _let_71)))) _let_39 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_66 0)) :args ((or _let_65 _let_69))) _let_68 :args (_let_65 false _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_73 :args (tptp.xp _let_3 _let_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_72)))) _let_73 :args (_let_71 false _let_72)) :args (_let_25 false _let_11 false _let_65 false _let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_66 1)) :args ((or _let_24 _let_69))) _let_68 :args (_let_24 false _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_44)) :args ((or _let_57 _let_22 (not _let_44)))) _let_64 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_30 _let_31 _let_48 _let_46 _let_44 (not _let_49)))) _let_42 _let_39 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_31 _let_57 _let_47 (not _let_58)))) _let_39 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.xp _let_1 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_61)) _let_60 :args (_let_58 false _let_59)) :args (_let_47 false _let_11 false _let_43 false _let_58)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_53)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_54 _let_26) (SCOPE (TRUE_ELIM (TRANS (CONG _let_56 (SYMM _let_55) :args (APPLY_UF tptp.doDivides0)) (TRUE_INTRO _let_54))) :args (_let_7 _let_10))) :args (_let_10 _let_7))) :args (true _let_53)) _let_26 (AND_ELIM _let_36 :args _let_40) :args (_let_45 false _let_10 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.xp _let_9 _let_1 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_52))) _let_51 :args (_let_49 false _let_50)) :args (_let_44 true _let_30 false _let_11 false _let_47 false _let_45 false _let_49)) :args (_let_22 false _let_43 false _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_32))) :args ((or _let_30 _let_28 _let_31 _let_29 _let_21 (not _let_32)))) _let_42 _let_41 _let_39 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.xp tptp.xn tptp.xn QUANTIFIERS_INST_CBQI_PROP)) :args (_let_33))) _let_34 :args (_let_32 false _let_33)) :args (_let_21 true _let_30 false _let_13 false _let_11 false _let_5 false _let_32)) _let_27 _let_26 :args (false false _let_25 false _let_24 false _let_22 false _let_21 true _let_20 false _let_10)) :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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) _let_18 (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))) _let_17 (forall ((W0 $$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))))))) _let_16 (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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.doDivides0 W0 W1) (not (= W1 tptp.sz00))) (tptp.sdtlseqdt0 W0 W1)))) _let_15 (forall ((W0 $$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 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) (forall ((W0 $$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))) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))) _let_14 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2) (not (= W0 tptp.sz00)) (not (= W1 tptp.sz00)) (not (= W2 tptp.sz00))) (=> (= (tptp.sdtasdt0 W2 (tptp.sdtasdt0 W1 W1)) (tptp.sdtasdt0 W0 W0)) (=> (tptp.iLess0 W0 tptp.xn) (not (tptp.isPrime0 W2)))))) _let_10 (tptp.isPrime0 tptp.xp) _let_8 _let_4 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.09/11.34 )
% 11.09/11.34 % SZS output end Proof for NUM524+1
% 11.09/11.34 % cvc5---1.0.5 exiting
% 11.09/11.34 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------