TSTP Solution File: NUM495+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM495+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 14:26:47 EDT 2022

% Result   : Theorem 1.20s 1.46s
% Output   : Refutation 1.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   39 (  16 unt;   3 nHn;  39 RR)
%            Number of literals    :  105 (   0 equ;  72 neg)
%            Maximal clause size   :    8 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    aNaturalNumber0(xn),
    file('NUM495+1.p',unknown),
    [] ).

cnf(4,axiom,
    aNaturalNumber0(xm),
    file('NUM495+1.p',unknown),
    [] ).

cnf(5,axiom,
    aNaturalNumber0(xp),
    file('NUM495+1.p',unknown),
    [] ).

cnf(6,axiom,
    isPrime0(xp),
    file('NUM495+1.p',unknown),
    [] ).

cnf(9,axiom,
    sdtlseqdt0(xp,xn),
    file('NUM495+1.p',unknown),
    [] ).

cnf(11,axiom,
    ~ doDivides0(xp,xr),
    file('NUM495+1.p',unknown),
    [] ).

cnf(12,axiom,
    ~ doDivides0(xp,xm),
    file('NUM495+1.p',unknown),
    [] ).

cnf(18,axiom,
    equal(sdtmndt0(xn,xp),xr),
    file('NUM495+1.p',unknown),
    [] ).

cnf(19,axiom,
    doDivides0(xp,sdtasdt0(xr,xm)),
    file('NUM495+1.p',unknown),
    [] ).

cnf(27,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | aNaturalNumber0(sdtpldt0(v,u)) ),
    file('NUM495+1.p',unknown),
    [] ).

cnf(31,axiom,
    sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
    file('NUM495+1.p',unknown),
    [] ).

cnf(35,axiom,
    ~ equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
    file('NUM495+1.p',unknown),
    [] ).

cnf(45,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ sdtlseqdt0(v,u)
    | iLess0(v,u)
    | equal(v,u) ),
    file('NUM495+1.p',unknown),
    [] ).

cnf(54,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ sdtlseqdt0(v,u)
    | ~ equal(w,sdtmndt0(u,v))
    | aNaturalNumber0(w) ),
    file('NUM495+1.p',unknown),
    [] ).

cnf(62,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
    file('NUM495+1.p',unknown),
    [] ).

cnf(83,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ isPrime0(w)
    | ~ iLess0(sdtpldt0(sdtpldt0(u,v),w),sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ doDivides0(w,sdtasdt0(u,v))
    | doDivides0(w,u)
    | doDivides0(w,v) ),
    file('NUM495+1.p',unknown),
    [] ).

cnf(86,plain,
    ( ~ isPrime0(u)
    | ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ doDivides0(u,sdtasdt0(w,v))
    | ~ iLess0(sdtpldt0(w,sdtpldt0(v,u)),sdtpldt0(sdtpldt0(xn,xm),xp))
    | doDivides0(u,v)
    | doDivides0(u,w) ),
    inference(rew,[status(thm),theory(equality)],[62,83]),
    [iquote('0:Rew:62.3,83.4')] ).

cnf(91,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xp)
    | ~ isPrime0(xp)
    | ~ iLess0(sdtpldt0(u,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ doDivides0(xp,sdtasdt0(u,xm))
    | doDivides0(xp,u) ),
    inference(res,[status(thm),theory(equality)],[86,12]),
    [iquote('0:Res:86.7,12.0')] ).

cnf(106,plain,
    ( ~ aNaturalNumber0(u)
    | ~ doDivides0(xp,sdtasdt0(u,xm))
    | ~ iLess0(sdtpldt0(u,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp))
    | doDivides0(xp,u) ),
    inference(mrr,[status(thm)],[91,4,5,6]),
    [iquote('0:MRR:91.1,91.2,91.3,4.0,5.0,6.0')] ).

cnf(109,plain,
    ( ~ aNaturalNumber0(xr)
    | ~ iLess0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ doDivides0(xp,sdtasdt0(xr,xm)) ),
    inference(res,[status(thm),theory(equality)],[106,11]),
    [iquote('0:Res:106.3,11.0')] ).

cnf(117,plain,
    ( ~ aNaturalNumber0(xr)
    | ~ iLess0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(mrr,[status(thm)],[109,19]),
    [iquote('0:MRR:109.2,19.0')] ).

cnf(713,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ sdtlseqdt0(v,u)
    | aNaturalNumber0(sdtmndt0(u,v)) ),
    inference(eqr,[status(thm),theory(equality)],[54]),
    [iquote('0:EqR:54.3')] ).

cnf(714,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp)
    | ~ sdtlseqdt0(xp,xn)
    | ~ equal(u,xr)
    | aNaturalNumber0(u) ),
    inference(spl,[status(thm),theory(equality)],[18,54]),
    [iquote('0:SpL:18.0,54.3')] ).

cnf(715,plain,
    ( ~ sdtlseqdt0(xp,xn)
    | ~ equal(u,xr)
    | aNaturalNumber0(u) ),
    inference(ssi,[status(thm)],[714,6,5,3]),
    [iquote('0:SSi:714.1,714.0,6.0,5.0,3.0')] ).

cnf(716,plain,
    ( ~ equal(u,xr)
    | aNaturalNumber0(u) ),
    inference(mrr,[status(thm)],[715,9]),
    [iquote('0:MRR:715.0,9.0')] ).

cnf(851,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xr)
    | sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(spr,[status(thm),theory(equality)],[62,31]),
    [iquote('0:SpR:62.3,31.0')] ).

cnf(862,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xr)
    | ~ equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xr,sdtpldt0(xm,xp))) ),
    inference(spl,[status(thm),theory(equality)],[62,35]),
    [iquote('0:SpL:62.3,35.0')] ).

cnf(864,plain,
    ( ~ aNaturalNumber0(xr)
    | sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(ssi,[status(thm)],[851,4,6,5]),
    [iquote('0:SSi:851.1,851.0,4.0,6.0,5.0')] ).

cnf(866,plain,
    ( ~ aNaturalNumber0(xr)
    | ~ equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xr,sdtpldt0(xm,xp))) ),
    inference(ssi,[status(thm)],[862,4,6,5]),
    [iquote('0:SSi:862.1,862.0,4.0,6.0,5.0')] ).

cnf(3382,plain,
    ( ~ equal(xr,xr)
    | sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(sor,[status(thm)],[864,716]),
    [iquote('0:SoR:864.0,716.1')] ).

cnf(3384,plain,
    sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)),
    inference(obv,[status(thm),theory(equality)],[3382]),
    [iquote('0:Obv:3382.0')] ).

cnf(3797,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp)
    | ~ sdtlseqdt0(xp,xn)
    | aNaturalNumber0(xr) ),
    inference(spr,[status(thm),theory(equality)],[18,713]),
    [iquote('0:SpR:18.0,713.3')] ).

cnf(3800,plain,
    ( ~ sdtlseqdt0(xp,xn)
    | aNaturalNumber0(xr) ),
    inference(ssi,[status(thm)],[3797,6,5,3]),
    [iquote('0:SSi:3797.1,3797.0,6.0,5.0,3.0')] ).

cnf(3801,plain,
    aNaturalNumber0(xr),
    inference(mrr,[status(thm)],[3800,9]),
    [iquote('0:MRR:3800.0,9.0')] ).

cnf(3803,plain,
    ~ equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xr,sdtpldt0(xm,xp))),
    inference(mrr,[status(thm)],[866,3801]),
    [iquote('0:MRR:866.0,3801.0')] ).

cnf(3804,plain,
    ~ iLess0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)),
    inference(mrr,[status(thm)],[117,3801]),
    [iquote('0:MRR:117.0,3801.0')] ).

cnf(4295,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ aNaturalNumber0(sdtpldt0(xr,sdtpldt0(xm,xp)))
    | ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp))
    | equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xr,sdtpldt0(xm,xp))) ),
    inference(res,[status(thm),theory(equality)],[45,3804]),
    [iquote('0:Res:45.3,3804.0')] ).

cnf(4298,plain,
    ( ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp))
    | equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xr,sdtpldt0(xm,xp))) ),
    inference(ssi,[status(thm)],[4295,27,3801,4,6,5,3]),
    [iquote('0:SSi:4295.1,4295.0,27.0,3801.0,27.0,4.0,6.2,5.2,27.0,27.0,3.0,4.2,6.0,5.2')] ).

cnf(4299,plain,
    $false,
    inference(mrr,[status(thm)],[4298,3384,3803]),
    [iquote('0:MRR:4298.0,4298.1,3384.0,3803.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : NUM495+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12  % 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 06:38:58 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.20/1.46  
% 1.20/1.46  SPASS V 3.9 
% 1.20/1.46  SPASS beiseite: Proof found.
% 1.20/1.46  % SZS status Theorem
% 1.20/1.46  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.20/1.46  SPASS derived 2619 clauses, backtracked 252 clauses, performed 6 splits and kept 1342 clauses.
% 1.20/1.46  SPASS allocated 101513 KBytes.
% 1.20/1.46  SPASS spent	0:00:01.02 on the problem.
% 1.20/1.46  		0:00:00.04 for the input.
% 1.20/1.46  		0:00:00.04 for the FLOTTER CNF translation.
% 1.20/1.46  		0:00:00.05 for inferences.
% 1.20/1.46  		0:00:00.00 for the backtracking.
% 1.20/1.46  		0:00:00.86 for the reduction.
% 1.20/1.46  
% 1.20/1.46  
% 1.20/1.46  Here is a proof with depth 3, length 39 :
% 1.20/1.46  % SZS output start Refutation
% See solution above
% 1.20/1.46  Formulae used in the proof : m__1837 m__1860 m__1870 m__ m__1883 m__1913 mSortsB m__2062 mIH_03 mDefDiff mAddAsso m__1799
% 1.20/1.46  
%------------------------------------------------------------------------------