TSTP Solution File: NUM524+3 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM524+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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  : 600s
% DateTime : Mon Jul 18 14:27:06 EDT 2022

% Result   : Theorem 9.07s 9.25s
% Output   : Refutation 9.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   18
% Syntax   : Number of clauses     :   42 (  19 unt;  10 nHn;  42 RR)
%            Number of literals    :  110 (   0 equ;  66 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    aNaturalNumber0(xn),
    file('NUM524+3.p',unknown),
    [] ).

cnf(4,axiom,
    aNaturalNumber0(xm),
    file('NUM524+3.p',unknown),
    [] ).

cnf(5,axiom,
    aNaturalNumber0(xp),
    file('NUM524+3.p',unknown),
    [] ).

cnf(6,axiom,
    isPrime0(xp),
    file('NUM524+3.p',unknown),
    [] ).

cnf(8,axiom,
    aNaturalNumber0(skc2),
    file('NUM524+3.p',unknown),
    [] ).

cnf(9,axiom,
    aNaturalNumber0(xq),
    file('NUM524+3.p',unknown),
    [] ).

cnf(14,axiom,
    doDivides0(xp,xn),
    file('NUM524+3.p',unknown),
    [] ).

cnf(20,axiom,
    ~ equal(xp,sz00),
    file('NUM524+3.p',unknown),
    [] ).

cnf(24,axiom,
    equal(sdtasdt0(xp,xq),xn),
    file('NUM524+3.p',unknown),
    [] ).

cnf(25,axiom,
    equal(sdtsldt0(xn,xp),xq),
    file('NUM524+3.p',unknown),
    [] ).

cnf(27,axiom,
    equal(sdtasdt0(xp,skc2),sdtasdt0(xn,xn)),
    file('NUM524+3.p',unknown),
    [] ).

cnf(34,axiom,
    equal(sdtasdt0(xp,sdtasdt0(xm,xm)),sdtasdt0(xn,xn)),
    file('NUM524+3.p',unknown),
    [] ).

cnf(35,axiom,
    ~ equal(sdtasdt0(xp,sdtasdt0(xq,xq)),sdtasdt0(xm,xm)),
    file('NUM524+3.p',unknown),
    [] ).

cnf(37,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | aNaturalNumber0(sdtasdt0(v,u)) ),
    file('NUM524+3.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ equal(u,sdtasdt0(v,w))
    | doDivides0(v,u) ),
    file('NUM524+3.p',unknown),
    [] ).

cnf(70,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
    file('NUM524+3.p',unknown),
    [] ).

cnf(89,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ doDivides0(w,u)
    | equal(w,sz00)
    | equal(sdtasdt0(v,sdtsldt0(u,w)),sdtsldt0(sdtasdt0(v,u),w)) ),
    file('NUM524+3.p',unknown),
    [] ).

cnf(90,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ doDivides0(v,w)
    | ~ equal(w,sdtasdt0(v,u))
    | equal(u,sdtsldt0(w,v))
    | equal(v,sz00) ),
    file('NUM524+3.p',unknown),
    [] ).

cnf(99,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ equal(u,sdtasdt0(v,w))
    | equal(v,sz00)
    | equal(w,sdtsldt0(u,v)) ),
    inference(mrr,[status(thm)],[90,63]),
    [iquote('0:MRR:90.3,63.4')] ).

cnf(1127,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xq)
    | ~ aNaturalNumber0(xp)
    | equal(sdtasdt0(xp,sdtasdt0(xq,u)),sdtasdt0(xn,u)) ),
    inference(spr,[status(thm),theory(equality)],[24,70]),
    [iquote('0:SpR:24.0,70.3')] ).

cnf(1141,plain,
    ( ~ aNaturalNumber0(u)
    | equal(sdtasdt0(xp,sdtasdt0(xq,u)),sdtasdt0(xn,u)) ),
    inference(ssi,[status(thm)],[1127,6,5,9]),
    [iquote('0:SSi:1127.2,1127.1,6.0,5.0,9.0')] ).

cnf(5132,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xp)
    | ~ doDivides0(xp,xn)
    | equal(xp,sz00)
    | equal(sdtasdt0(u,xq),sdtsldt0(sdtasdt0(u,xn),xp)) ),
    inference(spr,[status(thm),theory(equality)],[25,89]),
    [iquote('0:SpR:25.0,89.5')] ).

cnf(5138,plain,
    ( ~ aNaturalNumber0(u)
    | ~ doDivides0(xp,xn)
    | equal(xp,sz00)
    | equal(sdtasdt0(u,xq),sdtsldt0(sdtasdt0(u,xn),xp)) ),
    inference(ssi,[status(thm)],[5132,5,6,3]),
    [iquote('0:SSi:5132.2,5132.0,5.0,6.0,3.0')] ).

cnf(5139,plain,
    ( ~ aNaturalNumber0(u)
    | equal(sdtasdt0(u,xq),sdtsldt0(sdtasdt0(u,xn),xp)) ),
    inference(mrr,[status(thm)],[5138,14,20]),
    [iquote('0:MRR:5138.1,5138.2,14.0,20.0')] ).

cnf(5200,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(skc2)
    | ~ equal(u,sdtasdt0(xn,xn))
    | equal(xp,sz00)
    | equal(sdtsldt0(u,xp),skc2) ),
    inference(spl,[status(thm),theory(equality)],[27,99]),
    [iquote('0:SpL:27.0,99.3')] ).

cnf(5210,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,sdtasdt0(xn,xn))
    | equal(xp,sz00)
    | equal(sdtsldt0(u,xp),skc2) ),
    inference(ssi,[status(thm)],[5200,8,5,6]),
    [iquote('0:SSi:5200.2,5200.1,8.0,5.0,6.0')] ).

cnf(5211,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,sdtasdt0(xn,xn))
    | equal(sdtsldt0(u,xp),skc2) ),
    inference(mrr,[status(thm)],[5210,20]),
    [iquote('0:MRR:5210.2,20.0')] ).

cnf(5258,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(sdtasdt0(xm,xm))
    | ~ equal(u,sdtasdt0(xn,xn))
    | equal(xp,sz00)
    | equal(sdtasdt0(xm,xm),sdtsldt0(u,xp)) ),
    inference(spl,[status(thm),theory(equality)],[34,99]),
    [iquote('0:SpL:34.0,99.3')] ).

cnf(5269,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(sdtasdt0(xm,xm))
    | ~ equal(u,sdtasdt0(xn,xn))
    | equal(xp,sz00)
    | equal(sdtasdt0(xm,xm),skc2) ),
    inference(rew,[status(thm),theory(equality)],[5211,5258]),
    [iquote('0:Rew:5211.2,5258.5')] ).

cnf(5270,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,sdtasdt0(xn,xn))
    | equal(xp,sz00)
    | equal(sdtasdt0(xm,xm),skc2) ),
    inference(ssi,[status(thm)],[5269,37,4,5,6]),
    [iquote('0:SSi:5269.2,5269.1,37.0,4.0,4.0,5.0,6.2')] ).

cnf(5271,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,sdtasdt0(xn,xn))
    | equal(sdtasdt0(xm,xm),skc2) ),
    inference(mrr,[status(thm)],[5270,20]),
    [iquote('0:MRR:5270.2,20.0')] ).

cnf(12744,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xn,xn))
    | equal(sdtasdt0(xm,xm),skc2) ),
    inference(eqr,[status(thm),theory(equality)],[5271]),
    [iquote('0:EqR:5271.1')] ).

cnf(12747,plain,
    equal(sdtasdt0(xm,xm),skc2),
    inference(ssi,[status(thm)],[12744,37,3]),
    [iquote('0:SSi:12744.0,37.0,3.0,3.2')] ).

cnf(12754,plain,
    ~ equal(sdtasdt0(xp,sdtasdt0(xq,xq)),skc2),
    inference(rew,[status(thm),theory(equality)],[12747,35]),
    [iquote('0:Rew:12747.0,35.0')] ).

cnf(12917,plain,
    ( ~ aNaturalNumber0(xq)
    | ~ equal(sdtasdt0(xn,xq),skc2) ),
    inference(spl,[status(thm),theory(equality)],[1141,12754]),
    [iquote('0:SpL:1141.1,12754.0')] ).

cnf(17692,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xn,xn))
    | equal(sdtsldt0(sdtasdt0(xn,xn),xp),skc2) ),
    inference(eqr,[status(thm),theory(equality)],[5211]),
    [iquote('0:EqR:5211.1')] ).

cnf(17695,plain,
    equal(sdtsldt0(sdtasdt0(xn,xn),xp),skc2),
    inference(ssi,[status(thm)],[17692,37,3]),
    [iquote('0:SSi:17692.0,37.0,3.0,3.2')] ).

cnf(17713,plain,
    ~ equal(sdtasdt0(xn,xq),skc2),
    inference(ssi,[status(thm)],[12917,9]),
    [iquote('0:SSi:12917.0,9.0')] ).

cnf(18110,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ equal(sdtsldt0(sdtasdt0(xn,xn),xp),skc2) ),
    inference(spl,[status(thm),theory(equality)],[5139,17713]),
    [iquote('0:SpL:5139.1,17713.0')] ).

cnf(18111,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ equal(skc2,skc2) ),
    inference(rew,[status(thm),theory(equality)],[17695,18110]),
    [iquote('0:Rew:17695.0,18110.1')] ).

cnf(18112,plain,
    ~ aNaturalNumber0(xn),
    inference(obv,[status(thm),theory(equality)],[18111]),
    [iquote('0:Obv:18111.1')] ).

cnf(18113,plain,
    $false,
    inference(ssi,[status(thm)],[18112,3]),
    [iquote('0:SSi:18112.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : NUM524+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n007.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Tue Jul  5 21:21:43 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 9.07/9.25  
% 9.07/9.25  SPASS V 3.9 
% 9.07/9.25  SPASS beiseite: Proof found.
% 9.07/9.25  % SZS status Theorem
% 9.07/9.25  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 9.07/9.25  SPASS derived 11828 clauses, backtracked 2961 clauses, performed 25 splits and kept 5314 clauses.
% 9.07/9.25  SPASS allocated 111514 KBytes.
% 9.07/9.25  SPASS spent	0:00:07.24 on the problem.
% 9.07/9.25  		0:00:00.04 for the input.
% 9.07/9.25  		0:00:00.04 for the FLOTTER CNF translation.
% 9.07/9.25  		0:00:00.14 for inferences.
% 9.07/9.25  		0:00:00.08 for the backtracking.
% 9.07/9.25  		0:00:06.87 for the reduction.
% 9.07/9.25  
% 9.07/9.25  
% 9.07/9.25  Here is a proof with depth 3, length 42 :
% 9.07/9.25  % SZS output start Refutation
% See solution above
% 9.07/9.25  Formulae used in the proof : m__2987 m__3025 m__3046 m__3059 m__3014 m__ mSortsB_02 mDefDiv mMulAsso mDivAsso mDefQuot
% 9.07/9.25  
%------------------------------------------------------------------------------