TSTP Solution File: NUM508+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM508+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 14:26:56 EDT 2022

% Result   : Theorem 0.19s 0.53s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   29 (  15 unt;   3 nHn;  29 RR)
%            Number of literals    :   78 (   0 equ;  54 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    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    aNaturalNumber0(xn),
    file('NUM508+1.p',unknown),
    [] ).

cnf(4,axiom,
    aNaturalNumber0(xm),
    file('NUM508+1.p',unknown),
    [] ).

cnf(5,axiom,
    aNaturalNumber0(xp),
    file('NUM508+1.p',unknown),
    [] ).

cnf(6,axiom,
    isPrime0(xp),
    file('NUM508+1.p',unknown),
    [] ).

cnf(7,axiom,
    aNaturalNumber0(xr),
    file('NUM508+1.p',unknown),
    [] ).

cnf(8,axiom,
    isPrime0(xr),
    file('NUM508+1.p',unknown),
    [] ).

cnf(16,axiom,
    ~ doDivides0(xr,xn),
    file('NUM508+1.p',unknown),
    [] ).

cnf(17,axiom,
    ~ doDivides0(xr,xm),
    file('NUM508+1.p',unknown),
    [] ).

cnf(31,axiom,
    doDivides0(xr,sdtasdt0(xn,xm)),
    file('NUM508+1.p',unknown),
    [] ).

cnf(40,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | aNaturalNumber0(sdtpldt0(v,u)) ),
    file('NUM508+1.p',unknown),
    [] ).

cnf(44,axiom,
    sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
    file('NUM508+1.p',unknown),
    [] ).

cnf(48,axiom,
    ~ equal(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
    file('NUM508+1.p',unknown),
    [] ).

cnf(58,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ sdtlseqdt0(v,u)
    | iLess0(v,u)
    | equal(v,u) ),
    file('NUM508+1.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
    file('NUM508+1.p',unknown),
    [] ).

cnf(96,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('NUM508+1.p',unknown),
    [] ).

cnf(99,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)],[75,96]),
    [iquote('0:Rew:75.3,96.4')] ).

cnf(105,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xr)
    | ~ isPrime0(xr)
    | ~ iLess0(sdtpldt0(xn,sdtpldt0(u,xr)),sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ doDivides0(xr,sdtasdt0(xn,u))
    | doDivides0(xr,u) ),
    inference(res,[status(thm),theory(equality)],[99,16]),
    [iquote('0:Res:99.6,16.0')] ).

cnf(117,plain,
    ( ~ aNaturalNumber0(u)
    | ~ doDivides0(xr,sdtasdt0(xn,u))
    | ~ iLess0(sdtpldt0(xn,sdtpldt0(u,xr)),sdtpldt0(sdtpldt0(xn,xm),xp))
    | doDivides0(xr,u) ),
    inference(mrr,[status(thm)],[105,3,7,8]),
    [iquote('0:MRR:105.0,105.2,105.3,3.0,7.0,8.0')] ).

cnf(126,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ iLess0(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ doDivides0(xr,sdtasdt0(xn,xm)) ),
    inference(res,[status(thm),theory(equality)],[117,17]),
    [iquote('0:Res:117.3,17.0')] ).

cnf(129,plain,
    ~ iLess0(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(sdtpldt0(xn,xm),xp)),
    inference(mrr,[status(thm)],[126,4,31]),
    [iquote('0:MRR:126.0,126.2,4.0,31.0')] ).

cnf(543,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xr)))
    | ~ sdtlseqdt0(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(sdtpldt0(xn,xm),xp))
    | equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xr))) ),
    inference(res,[status(thm),theory(equality)],[58,129]),
    [iquote('0:Res:58.3,129.0')] ).

cnf(546,plain,
    ( ~ sdtlseqdt0(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(sdtpldt0(xn,xm),xp))
    | equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xr))) ),
    inference(ssi,[status(thm)],[543,40,3,4,8,7,6,5]),
    [iquote('0:SSi:543.1,543.0,40.0,3.0,40.0,4.0,8.2,7.2,40.0,40.0,3.0,4.2,6.0,5.2')] ).

cnf(880,plain,
    ( ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | sdtlseqdt0(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(spr,[status(thm),theory(equality)],[75,44]),
    [iquote('0:SpR:75.3,44.0')] ).

cnf(895,plain,
    ( ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | ~ equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xr))) ),
    inference(spl,[status(thm),theory(equality)],[75,48]),
    [iquote('0:SpL:75.3,48.0')] ).

cnf(908,plain,
    sdtlseqdt0(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(sdtpldt0(xn,xm),xp)),
    inference(ssi,[status(thm)],[880,3,4,8,7]),
    [iquote('0:SSi:880.2,880.1,880.0,3.0,4.0,8.0,7.0')] ).

cnf(909,plain,
    equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xr))),
    inference(mrr,[status(thm)],[546,908]),
    [iquote('0:MRR:546.0,908.0')] ).

cnf(930,plain,
    ( ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | ~ equal(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(xn,sdtpldt0(xm,xr))) ),
    inference(rew,[status(thm),theory(equality)],[909,895]),
    [iquote('0:Rew:909.0,895.3')] ).

cnf(931,plain,
    ( ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(obv,[status(thm),theory(equality)],[930]),
    [iquote('0:Obv:930.3')] ).

cnf(932,plain,
    $false,
    inference(ssi,[status(thm)],[931,3,4,8,7]),
    [iquote('0:SSi:931.2,931.1,931.0,3.0,4.0,8.0,7.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : NUM508+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n028.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 11:24:06 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.53  
% 0.19/0.53  SPASS V 3.9 
% 0.19/0.53  SPASS beiseite: Proof found.
% 0.19/0.53  % SZS status Theorem
% 0.19/0.53  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.53  SPASS derived 542 clauses, backtracked 76 clauses, performed 3 splits and kept 395 clauses.
% 0.19/0.53  SPASS allocated 98431 KBytes.
% 0.19/0.53  SPASS spent	0:00:00.19 on the problem.
% 0.19/0.53  		0:00:00.04 for the input.
% 0.19/0.53  		0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.53  		0:00:00.01 for inferences.
% 0.19/0.53  		0:00:00.00 for the backtracking.
% 0.19/0.53  		0:00:00.07 for the reduction.
% 0.19/0.53  
% 0.19/0.53  
% 0.19/0.53  Here is a proof with depth 3, length 29 :
% 0.19/0.53  % SZS output start Refutation
% See solution above
% 0.19/0.53  Formulae used in the proof : m__1837 m__1860 m__2342 m__ m__2362 mSortsB m__2478 mIH_03 mAddAsso m__1799
% 0.19/0.53  
%------------------------------------------------------------------------------