TSTP Solution File: NUM505+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM505+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 10:44:32 EDT 2023
% Result : Theorem 11.66s 11.88s
% Output : Proof 11.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : NUM505+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n004.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 09:05:08 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_NAR, FOF, or CNF
% 11.66/11.88 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.dviBvjQlTn/cvc5---1.0.5_19913.p...
% 11.66/11.88 ------- get file name : TPTP file name is NUM505+1
% 11.66/11.88 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19913.smt2...
% 11.66/11.88 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 11.66/11.88 --- Run --no-e-matching --full-saturate-quant at 5...
% 11.66/11.88 % SZS status Theorem for NUM505+1
% 11.66/11.88 % SZS output start Proof for NUM505+1
% 11.66/11.88 (
% 11.66/11.88 (let ((_let_1 (tptp.sdtlseqdt0 tptp.xk tptp.xp))) (let ((_let_2 (not (tptp.sdtlseqdt0 tptp.xp tptp.xk)))) (let ((_let_3 (not (=> _let_2 (and (not (= tptp.xk tptp.xp)) _let_1))))) (let ((_let_4 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_5 (= tptp.xk tptp.sz10))) (let ((_let_6 (= tptp.xk tptp.sz00))) (let ((_let_7 (tptp.sdtsldt0 _let_4 tptp.xp))) (let ((_let_8 (= tptp.xk _let_7))) (let ((_let_9 (tptp.doDivides0 tptp.xp _let_4))) (let ((_let_10 (tptp.isPrime0 tptp.xp))) (let ((_let_11 (and _let_10 _let_9))) (let ((_let_12 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_13 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_14 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_15 (and _let_14 _let_13 _let_12))) (let ((_let_16 (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_17 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (let ((_let_18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))))) (let ((_let_19 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_21 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_22 (tptp.aNaturalNumber0 _let_4))) (let ((_let_23 (not _let_13))) (let ((_let_24 (not _let_14))) (let ((_let_25 (or _let_24 _let_23 _let_22))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (tptp.aNaturalNumber0 _let_7))) (let ((_let_29 (and _let_28 (= _let_4 (tptp.sdtasdt0 tptp.xp _let_7))))) (let ((_let_30 (not _let_9))) (let ((_let_31 (= tptp.sz00 tptp.xp))) (let ((_let_32 (not _let_22))) (let ((_let_33 (not _let_12))) (let ((_let_34 (or _let_33 _let_32 _let_31 _let_30 _let_29))) (let ((_let_35 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1623 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1623) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1623))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1623)))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (not _let_29))) (let ((_let_38 (tptp.sdtlseqdt0 tptp.xp _let_7))) (let ((_let_39 (= tptp.xp _let_7))) (let ((_let_40 (not _let_39))) (let ((_let_41 (and _let_40 _let_38))) (let ((_let_42 (tptp.sdtlseqdt0 _let_7 tptp.xp))) (let ((_let_43 (not _let_28))) (let ((_let_44 (or _let_43 _let_33 _let_42 _let_41))) (let ((_let_45 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.sdtlseqdt0 W0 W1) (and (not (= W0 W1)) (tptp.sdtlseqdt0 W1 W0)))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (not _let_41))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (ASSUME :args (_let_8)) :args ((not (=> _let_2 (and (not (= tptp.xp tptp.xk)) _let_1))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_49 (NOT_IMPLIES_ELIM1 _let_48))) (let ((_let_50 (ASSUME :args (_let_15)))) (let ((_let_51 (AND_ELIM _let_50 :args (2)))) (let ((_let_52 (not _let_42))) (let ((_let_53 (tptp.sdtlseqdt0 tptp.xp tptp.xp))) (let ((_let_54 (or _let_33 _let_53))) (let ((_let_55 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (or))) (let ((_let_58 (not _let_38))) (let ((_let_59 (ASSUME :args (_let_53)))) (let ((_let_60 (ASSUME :args (_let_39)))) (let ((_let_61 (ASSUME :args (_let_58)))) (let ((_let_62 (not _let_31))) (let ((_let_63 (and _let_62 (not (= tptp.sz10 tptp.xp)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xp)) (= tptp.sz10 W1) (= W1 tptp.xp)))))) (let ((_let_64 (= _let_10 _let_63))) (let ((_let_65 (or _let_33 _let_64))) (let ((_let_66 (forall ((W0 $$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_67 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (0))) (let ((_let_69 (ASSUME :args (_let_11)))) (let ((_let_70 (1))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (tptp.xn tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_21))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_23 _let_22 _let_27))) (AND_ELIM _let_50 :args _let_68) (AND_ELIM _let_50 :args _let_70) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_30 _let_31 _let_32 _let_29 (not _let_34)))) _let_51 (AND_ELIM _let_69 :args _let_70) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_63 0)) :args ((or _let_62 (not _let_63)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_64)) :args ((or (not _let_10) _let_63 (not _let_64)))) (AND_ELIM _let_69 :args _let_68) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_33 _let_64 (not _let_65)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_67 :args (tptp.xp QUANTIFIERS_INST_CBQI_PROP)) :args (_let_66)))) _let_67 :args (_let_65 false _let_66)) :args (_let_64 false _let_12 false _let_65)) :args (_let_63 false _let_10 false _let_64)) :args (_let_62 false _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 0)) :args ((or _let_28 _let_37))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_42 _let_33 _let_43 _let_41 (not _let_44)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (NOT_IMPLIES_ELIM2 _let_48)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) (REFL :args (_let_52)) :args _let_57)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_59 _let_60 _let_61) :args (_let_58 _let_39 _let_53)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_61)) (CONG (REFL :args (tptp.xp)) (SYMM _let_60) :args (APPLY_UF tptp.sdtlseqdt0)) (TRUE_INTRO _let_59))) :args (_let_53 _let_39 _let_58)) :args ((not (and _let_58 _let_39 _let_53)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_38))) (REFL :args (_let_40)) (REFL :args ((not _let_53))) :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_33 _let_53 (not _let_54)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.xp QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_53 false _let_12 false _let_54)) _let_49 :args (_let_40 false _let_53 true _let_38)) :args (_let_52 true _let_39)) _let_51 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_41 1)) :args ((or _let_38 _let_47))) _let_49 :args (_let_47 true _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_7 tptp.xp QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_45)))) _let_46 :args (_let_44 false _let_45)) :args (_let_43 true _let_42 false _let_12 true _let_41 false _let_44)) :args (_let_37 true _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.xp _let_4 _let_7 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_35)))) _let_36 :args (_let_34 false _let_35)) :args (_let_32 false _let_12 false _let_9 true _let_31 true _let_29 false _let_34)) :args (_let_27 false _let_14 false _let_13 true _let_22)) _let_26 :args (false true _let_25 false _let_21)) :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_20 (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))))))) _let_19 (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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) _let_18 (forall ((W0 $$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 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))) _let_17 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) _let_16 (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_15 (forall ((W0 $$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_11 (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_8 (not (or _let_6 _let_5)) (and (not _let_6) (not _let_5)) (and (tptp.aNaturalNumber0 tptp.xr) (tptp.doDivides0 tptp.xr tptp.xk) (tptp.isPrime0 tptp.xr)) (and (tptp.sdtlseqdt0 tptp.xr tptp.xk) (tptp.doDivides0 tptp.xr _let_4)) _let_3 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.66/11.89 )
% 11.66/11.89 % SZS output end Proof for NUM505+1
% 11.66/11.89 % cvc5---1.0.5 exiting
% 11.66/11.89 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------