TSTP Solution File: NUM516+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM516+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.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 10:44:41 EDT 2023
% Result : Theorem 1.52s 1.77s
% Output : Proof 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM516+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n023.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 09:45:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 1.52/1.77 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.xp8O0WUHXL/cvc5---1.0.5_20312.p...
% 1.52/1.77 ------- get file name : TPTP file name is NUM516+3
% 1.52/1.77 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_20312.smt2...
% 1.52/1.77 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.52/1.77 % SZS status Theorem for NUM516+3
% 1.52/1.77 % SZS output start Proof for NUM516+3
% 1.52/1.77 (
% 1.52/1.77 (let ((_let_1 (tptp.sdtpldt0 tptp.xn tptp.xm))) (let ((_let_2 (tptp.sdtpldt0 _let_1 tptp.xp))) (let ((_let_3 (tptp.sdtsldt0 tptp.xn tptp.xr))) (let ((_let_4 (tptp.sdtpldt0 _let_3 tptp.xm))) (let ((_let_5 (tptp.sdtpldt0 _let_4 tptp.xp))) (let ((_let_6 (tptp.sdtlseqdt0 _let_5 _let_2))) (let ((_let_7 (= tptp.xn (tptp.sdtasdt0 tptp.xr _let_3)))) (let ((_let_8 (tptp.aNaturalNumber0 _let_3))) (let ((_let_9 (and _let_8 _let_7))) (let ((_let_10 (not (and (not (and _let_8 _let_7 (= _let_5 _let_2))) (=> _let_9 (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtsldt0 tptp.xn tptp.xr) tptp.xm) tptp.xp) W0) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) _let_6)))))) (let ((_let_11 (tptp.sdtlseqdt0 _let_3 tptp.xn))) (let ((_let_12 (and (not (=> _let_9 (= _let_3 tptp.xn))) _let_8 _let_7 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtsldt0 tptp.xn tptp.xr) W0) tptp.xn))) _let_11))) (let ((_let_13 (tptp.doDivides0 tptp.xr tptp.xn))) (let ((_let_14 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_15 (= tptp.xk tptp.sz10))) (let ((_let_16 (= tptp.xk tptp.sz00))) (let ((_let_17 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_18 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_19 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_20 (and _let_19 _let_18 _let_17))) (let ((_let_21 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (let ((_let_2 (tptp.sdtpldt0 W0 W2))) (let ((_let_3 (tptp.sdtpldt0 W2 W1))) (let ((_let_4 (tptp.sdtpldt0 W2 W0))) (=> (tptp.aNaturalNumber0 W2) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))))))) (let ((_let_22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_23 (or (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtsldt0 tptp.xn tptp.xr) tptp.xm) tptp.xp) W0)))))) _let_6))) (let ((_let_24 (=> _let_9 _let_23))) (let ((_let_25 (= _let_2 _let_5))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.sdtpldt0 tptp.xp _let_1))) (let ((_let_28 (tptp.sdtpldt0 tptp.xp _let_4))) (let ((_let_29 (and (not (= _let_27 _let_28)) (tptp.sdtlseqdt0 _let_28 _let_27) _let_26 _let_6))) (let ((_let_30 (not _let_17))) (let ((_let_31 (tptp.sdtlseqdt0 _let_4 _let_1))) (let ((_let_32 (not _let_31))) (let ((_let_33 (= _let_1 _let_4))) (let ((_let_34 (tptp.aNaturalNumber0 _let_1))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.aNaturalNumber0 _let_4))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35 _let_33 _let_32 _let_30 _let_29))) (let ((_let_39 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1735 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1735))) (let ((_let_2 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1735))) (let ((_let_3 (tptp.sdtpldt0 BOUND_VARIABLE_1735 W1))) (let ((_let_4 (tptp.sdtpldt0 BOUND_VARIABLE_1735 W0))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1735)) (and (not (= _let_3 _let_4)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_1 _let_2)) (tptp.sdtlseqdt0 _let_2 _let_1)))))))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (_let_39))) (let ((_let_42 ((tptp.sdtlseqdt0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1735) (tptp.sdtpldt0 W1 BOUND_VARIABLE_1735))))) (let ((_let_43 (not _let_33))) (let ((_let_44 (tptp.sdtpldt0 tptp.xm tptp.xn))) (let ((_let_45 (tptp.sdtpldt0 tptp.xm _let_3))) (let ((_let_46 (and (not (= _let_44 _let_45)) (tptp.sdtlseqdt0 _let_45 _let_44) _let_43 _let_31))) (let ((_let_47 (not _let_18))) (let ((_let_48 (not _let_11))) (let ((_let_49 (= tptp.xn _let_3))) (let ((_let_50 (not _let_19))) (let ((_let_51 (not _let_8))) (let ((_let_52 (or _let_51 _let_50 _let_49 _let_48 _let_47 _let_46))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (0))) (let ((_let_55 (AND_ELIM _let_53 :args _let_54))) (let ((_let_56 (AND_ELIM (NOT_IMPLIES_ELIM1 _let_55) :args _let_54))) (let ((_let_57 (ASSUME :args (_let_20)))) (let ((_let_58 (AND_ELIM _let_57 :args (1)))) (let ((_let_59 (AND_ELIM _let_57 :args _let_54))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_49 _let_50 _let_47 _let_51 _let_48 _let_46 (not _let_52)))) (NOT_IMPLIES_ELIM2 _let_55) _let_59 _let_58 _let_56 (AND_ELIM _let_53 :args (4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_40 :args (_let_3 tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING _let_42)) :args _let_41))) _let_40 :args (_let_52 false _let_39)) :args (_let_46 true _let_49 false _let_19 false _let_18 false _let_8 false _let_11 false _let_52)))) (let ((_let_61 (not _let_46))) (let ((_let_62 (or _let_51 _let_47 _let_36))) (let ((_let_63 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (_let_63))) (let ((_let_66 ((tptp.sdtpldt0 W0 W1)))) (let ((_let_67 (or _let_50 _let_47 _let_34))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_30 _let_35 _let_37 _let_32 _let_29 _let_33 (not _let_38)))) (AND_ELIM _let_57 :args (2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_50 _let_47 _let_34 (not _let_67)))) _let_59 _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_66)) :args _let_65)) _let_64 :args (_let_67 false _let_63)) :args (_let_34 false _let_19 false _let_18 false _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_47 _let_51 _let_36 (not _let_62)))) _let_58 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_3 tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_66)) :args _let_65)) _let_64 :args (_let_62 false _let_63)) :args (_let_36 false _let_18 false _let_8 false _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_46 3)) :args ((or _let_31 _let_61))) _let_60 :args (_let_31 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_46 2)) :args ((or _let_43 _let_61))) _let_60 :args (_let_43 false _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_40 :args (_let_4 _let_1 tptp.xp QUANTIFIERS_INST_E_MATCHING _let_42)) :args _let_41))) _let_40 :args (_let_38 false _let_39)) :args (_let_29 false _let_17 false _let_34 false _let_36 false _let_31 true _let_33 false _let_38)))) (let ((_let_69 (not _let_29))) (let ((_let_70 (and _let_8 _let_7 _let_25))) (let ((_let_71 (not _let_24))) (let ((_let_72 (not _let_70))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args (_let_24)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_70))) (REFL :args (_let_71)) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_70 2)) :args ((or _let_25 _let_72))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 2)) :args ((or _let_26 _let_69))) _let_68 :args (_let_26 false _let_29)) :args (_let_72 true _let_25)) :args (_let_71 true _let_70)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 1)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 3)) :args ((or _let_6 _let_69))) _let_68 :args (_let_6 false _let_29)) :args (_let_23 false _let_6)) :args (false true _let_24 false _let_23)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))) _let_22 (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))))) _let_21 (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_20 (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 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xp W0)))) (tptp.doDivides0 tptp.xp _let_14)) (not (or (exists ((W0 $$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 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xm W0) tptp.xp))) (tptp.sdtlseqdt0 tptp.xm tptp.xp)) (and (tptp.aNaturalNumber0 tptp.xk) (= _let_14 (tptp.sdtasdt0 tptp.xp tptp.xk)) (= tptp.xk (tptp.sdtsldt0 _let_14 tptp.xp))) (not (or _let_16 _let_15)) (and (not _let_16) (not _let_15)) (and (tptp.aNaturalNumber0 tptp.xr) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xk (tptp.sdtasdt0 tptp.xr W0)))) (tptp.doDivides0 tptp.xr tptp.xk) (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)) (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_14)) (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 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xm (tptp.sdtasdt0 tptp.xr W0)))) (tptp.doDivides0 tptp.xr tptp.xm))) (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xr W0)))) _let_13) _let_12 (and _let_8 _let_7 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 (tptp.sdtsldt0 tptp.xn tptp.xr) tptp.xm) (tptp.sdtasdt0 tptp.xp W0)))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 _let_3 tptp.xm))) _let_10 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.59/1.78 )
% 1.59/1.78 % SZS output end Proof for NUM516+3
% 1.59/1.78 % cvc5---1.0.5 exiting
% 1.64/1.78 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------