TSTP Solution File: NUM505+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM505+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 14:26:54 EDT 2022

% Result   : Theorem 0.45s 0.64s
% Output   : Refutation 0.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   18
% Syntax   : Number of clauses     :   43 (  18 unt;   4 nHn;  43 RR)
%            Number of literals    :  118 (   0 equ;  81 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    aNaturalNumber0(xn),
    file('NUM505+1.p',unknown),
    [] ).

cnf(4,axiom,
    aNaturalNumber0(xm),
    file('NUM505+1.p',unknown),
    [] ).

cnf(5,axiom,
    aNaturalNumber0(xp),
    file('NUM505+1.p',unknown),
    [] ).

cnf(6,axiom,
    isPrime0(xp),
    file('NUM505+1.p',unknown),
    [] ).

cnf(15,axiom,
    ~ sdtlseqdt0(xp,xk),
    file('NUM505+1.p',unknown),
    [] ).

cnf(17,axiom,
    aNaturalNumber0(skf4(u,v)),
    file('NUM505+1.p',unknown),
    [] ).

cnf(27,axiom,
    doDivides0(xp,sdtasdt0(xn,xm)),
    file('NUM505+1.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ aNaturalNumber0(u)
    | sdtlseqdt0(u,u) ),
    file('NUM505+1.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ sdtlseqdt0(xk,xp)
    | equal(xk,xp) ),
    file('NUM505+1.p',unknown),
    [] ).

cnf(31,axiom,
    equal(sdtsldt0(sdtasdt0(xn,xm),xp),xk),
    file('NUM505+1.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | aNaturalNumber0(sdtpldt0(v,u)) ),
    file('NUM505+1.p',unknown),
    [] ).

cnf(39,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | aNaturalNumber0(sdtasdt0(v,u)) ),
    file('NUM505+1.p',unknown),
    [] ).

cnf(40,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ isPrime0(u)
    | ~ equal(u,sz00) ),
    file('NUM505+1.p',unknown),
    [] ).

cnf(42,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | sdtlseqdt0(v,u)
    | sdtlseqdt0(u,v) ),
    file('NUM505+1.p',unknown),
    [] ).

cnf(62,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ equal(sdtpldt0(v,w),u)
    | sdtlseqdt0(v,u) ),
    file('NUM505+1.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ sdtlseqdt0(v,u)
    | ~ equal(w,sdtmndt0(u,v))
    | aNaturalNumber0(w) ),
    file('NUM505+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ doDivides0(v,u)
    | ~ equal(w,sdtsldt0(u,v))
    | aNaturalNumber0(w)
    | equal(v,sz00) ),
    file('NUM505+1.p',unknown),
    [] ).

cnf(85,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ sdtlseqdt0(v,w)
    | ~ equal(sdtpldt0(v,u),w)
    | equal(u,sdtmndt0(w,v)) ),
    file('NUM505+1.p',unknown),
    [] ).

cnf(93,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ equal(sdtpldt0(v,w),u)
    | equal(w,sdtmndt0(u,v)) ),
    inference(mrr,[status(thm)],[85,62]),
    [iquote('0:MRR:85.3,62.4')] ).

cnf(96,plain,
    ( ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(xp)
    | sdtlseqdt0(xk,xp) ),
    inference(res,[status(thm),theory(equality)],[42,15]),
    [iquote('0:Res:42.2,15.0')] ).

cnf(102,plain,
    ( ~ aNaturalNumber0(xk)
    | sdtlseqdt0(xk,xp) ),
    inference(mrr,[status(thm)],[96,5]),
    [iquote('0:MRR:96.1,5.0')] ).

cnf(107,plain,
    equal(xk,xp),
    inference(spt,[spt(split,[position(s1)])],[30]),
    [iquote('1:Spt:30.1')] ).

cnf(114,plain,
    ~ sdtlseqdt0(xp,xp),
    inference(rew,[status(thm),theory(equality)],[107,15]),
    [iquote('1:Rew:107.0,15.0')] ).

cnf(122,plain,
    ~ aNaturalNumber0(xp),
    inference(res,[status(thm),theory(equality)],[29,114]),
    [iquote('1:Res:29.1,114.0')] ).

cnf(123,plain,
    $false,
    inference(ssi,[status(thm)],[122,6,5]),
    [iquote('1:SSi:122.0,6.0,5.0')] ).

cnf(124,plain,
    ~ equal(xk,xp),
    inference(spt,[spt(split,[position(sa)])],[123,107]),
    [iquote('1:Spt:123.0,30.1,107.0')] ).

cnf(125,plain,
    ~ sdtlseqdt0(xk,xp),
    inference(spt,[spt(split,[position(s2)])],[30]),
    [iquote('1:Spt:123.0,30.0')] ).

cnf(126,plain,
    ~ aNaturalNumber0(xk),
    inference(mrr,[status(thm)],[102,125]),
    [iquote('1:MRR:102.1,125.0')] ).

cnf(141,plain,
    ~ equal(xp,sz00),
    inference(ems,[status(thm)],[40,5,6]),
    [iquote('0:EmS:40.0,40.1,5.0,6.0')] ).

cnf(429,plain,
    ( ~ aNaturalNumber0(sdtpldt0(u,v))
    | ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | sdtlseqdt0(u,sdtpldt0(u,v)) ),
    inference(eqr,[status(thm),theory(equality)],[62]),
    [iquote('0:EqR:62.3')] ).

cnf(435,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | sdtlseqdt0(u,sdtpldt0(u,v)) ),
    inference(ssi,[status(thm)],[429,38]),
    [iquote('0:SSi:429.0,38.2')] ).

cnf(819,plain,
    ( ~ aNaturalNumber0(sdtpldt0(u,v))
    | ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
    inference(eqr,[status(thm),theory(equality)],[93]),
    [iquote('0:EqR:93.3')] ).

cnf(826,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
    inference(ssi,[status(thm)],[819,38]),
    [iquote('0:SSi:819.0,38.2')] ).

cnf(845,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(sdtpldt0(u,v))
    | ~ aNaturalNumber0(u)
    | ~ sdtlseqdt0(u,sdtpldt0(u,v))
    | ~ equal(w,v)
    | aNaturalNumber0(w) ),
    inference(spl,[status(thm),theory(equality)],[826,63]),
    [iquote('0:SpL:826.2,63.3')] ).

cnf(860,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(sdtpldt0(v,u))
    | ~ aNaturalNumber0(v)
    | ~ sdtlseqdt0(v,sdtpldt0(v,u))
    | ~ equal(w,u)
    | aNaturalNumber0(w) ),
    inference(obv,[status(thm),theory(equality)],[845]),
    [iquote('0:Obv:845.0')] ).

cnf(861,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ sdtlseqdt0(v,sdtpldt0(v,u))
    | ~ equal(w,u)
    | aNaturalNumber0(w) ),
    inference(ssi,[status(thm)],[860,38]),
    [iquote('0:SSi:860.1,38.2')] ).

cnf(862,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ equal(w,u)
    | aNaturalNumber0(w) ),
    inference(mrr,[status(thm)],[861,435]),
    [iquote('0:MRR:861.2,435.2')] ).

cnf(957,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(v,u)
    | aNaturalNumber0(v) ),
    inference(ems,[status(thm)],[862,17]),
    [iquote('0:EmS:862.1,17.0')] ).

cnf(987,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(xk,u) ),
    inference(sor,[status(thm)],[126,957]),
    [iquote('1:SoR:126.0,957.2')] ).

cnf(1257,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
    | ~ aNaturalNumber0(xp)
    | ~ doDivides0(xp,sdtasdt0(xn,xm))
    | ~ equal(u,xk)
    | aNaturalNumber0(u)
    | equal(xp,sz00) ),
    inference(spl,[status(thm),theory(equality)],[31,72]),
    [iquote('0:SpL:31.0,72.3')] ).

cnf(1258,plain,
    ( ~ doDivides0(xp,sdtasdt0(xn,xm))
    | ~ equal(u,xk)
    | aNaturalNumber0(u)
    | equal(xp,sz00) ),
    inference(ssi,[status(thm)],[1257,6,5,39,3,4]),
    [iquote('0:SSi:1257.1,1257.0,6.0,5.0,39.2,3.0,4.0')] ).

cnf(1259,plain,
    ~ equal(u,xk),
    inference(mrr,[status(thm)],[1258,27,987,141]),
    [iquote('1:MRR:1258.0,1258.2,1258.3,27.0,987.0,141.0')] ).

cnf(1260,plain,
    $false,
    inference(unc,[status(thm)],[1259,31]),
    [iquote('1:UnC:1259.0,31.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : NUM505+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue Jul  5 11:49:43 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.45/0.64  
% 0.45/0.64  SPASS V 3.9 
% 0.45/0.64  SPASS beiseite: Proof found.
% 0.45/0.64  % SZS status Theorem
% 0.45/0.64  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.45/0.64  SPASS derived 748 clauses, backtracked 31 clauses, performed 4 splits and kept 370 clauses.
% 0.45/0.64  SPASS allocated 98725 KBytes.
% 0.45/0.64  SPASS spent	0:00:00.28 on the problem.
% 0.45/0.64  		0:00:00.04 for the input.
% 0.45/0.64  		0:00:00.04 for the FLOTTER CNF translation.
% 0.45/0.64  		0:00:00.01 for inferences.
% 0.45/0.64  		0:00:00.00 for the backtracking.
% 0.45/0.64  		0:00:00.16 for the reduction.
% 0.45/0.64  
% 0.45/0.64  
% 0.45/0.64  Here is a proof with depth 4, length 43 :
% 0.45/0.64  % SZS output start Refutation
% See solution above
% 0.45/0.64  Formulae used in the proof : m__1837 m__1860 m__ mDefLE m__2342 mLERefl m__2306 mSortsB mSortsB_02 mDefPrime mLETotal mDefDiff mDefQuot
% 0.45/0.64  
%------------------------------------------------------------------------------