TSTP Solution File: NUM475+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM475+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 14:26:34 EDT 2022

% Result   : Theorem 0.92s 1.12s
% Output   : Refutation 0.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   19
% Syntax   : Number of clauses     :   45 (  17 unt;   8 nHn;  45 RR)
%            Number of literals    :  125 (   0 equ;  74 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    aNaturalNumber0(xl),
    file('NUM475+1.p',unknown),
    [] ).

cnf(4,axiom,
    aNaturalNumber0(xm),
    file('NUM475+1.p',unknown),
    [] ).

cnf(5,axiom,
    aNaturalNumber0(xn),
    file('NUM475+1.p',unknown),
    [] ).

cnf(6,axiom,
    doDivides0(xl,xm),
    file('NUM475+1.p',unknown),
    [] ).

cnf(7,axiom,
    sdtlseqdt0(xp,xq),
    file('NUM475+1.p',unknown),
    [] ).

cnf(11,axiom,
    ~ equal(xl,sz00),
    file('NUM475+1.p',unknown),
    [] ).

cnf(12,axiom,
    doDivides0(xl,sdtpldt0(xm,xn)),
    file('NUM475+1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(sdtsldt0(xm,xl),xp),
    file('NUM475+1.p',unknown),
    [] ).

cnf(14,axiom,
    equal(sdtmndt0(xq,xp),xr),
    file('NUM475+1.p',unknown),
    [] ).

cnf(15,axiom,
    ~ equal(sdtasdt0(xl,xr),xn),
    file('NUM475+1.p',unknown),
    [] ).

cnf(17,axiom,
    equal(sdtsldt0(sdtpldt0(xm,xn),xl),xq),
    file('NUM475+1.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | aNaturalNumber0(sdtpldt0(v,u)) ),
    file('NUM475+1.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | aNaturalNumber0(sdtasdt0(v,u)) ),
    file('NUM475+1.p',unknown),
    [] ).

cnf(32,axiom,
    equal(sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)),sdtpldt0(sdtasdt0(xl,xp),xn)),
    file('NUM475+1.p',unknown),
    [] ).

cnf(41,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ equal(sdtpldt0(v,w),u)
    | sdtlseqdt0(v,u) ),
    file('NUM475+1.p',unknown),
    [] ).

cnf(42,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ sdtlseqdt0(v,u)
    | ~ equal(w,sdtmndt0(u,v))
    | aNaturalNumber0(w) ),
    file('NUM475+1.p',unknown),
    [] ).

cnf(50,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ doDivides0(v,u)
    | ~ equal(w,sdtsldt0(u,v))
    | aNaturalNumber0(w)
    | equal(v,sz00) ),
    file('NUM475+1.p',unknown),
    [] ).

cnf(59,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ doDivides0(v,u)
    | ~ equal(w,sdtsldt0(u,v))
    | equal(v,sz00)
    | equal(u,sdtasdt0(v,w)) ),
    file('NUM475+1.p',unknown),
    [] ).

cnf(62,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ sdtlseqdt0(v,w)
    | ~ equal(sdtpldt0(v,u),w)
    | equal(u,sdtmndt0(w,v)) ),
    file('NUM475+1.p',unknown),
    [] ).

cnf(68,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ equal(sdtpldt0(v,w),u)
    | equal(w,sdtmndt0(u,v)) ),
    inference(mrr,[status(thm)],[62,41]),
    [iquote('0:MRR:62.3,41.4')] ).

cnf(479,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ sdtlseqdt0(v,u)
    | aNaturalNumber0(sdtmndt0(u,v)) ),
    inference(eqr,[status(thm),theory(equality)],[42]),
    [iquote('0:EqR:42.3')] ).

cnf(652,plain,
    ( ~ aNaturalNumber0(xq)
    | ~ aNaturalNumber0(xp)
    | ~ sdtlseqdt0(xp,xq)
    | aNaturalNumber0(xr) ),
    inference(spr,[status(thm),theory(equality)],[14,479]),
    [iquote('0:SpR:14.0,479.3')] ).

cnf(653,plain,
    ( ~ aNaturalNumber0(xq)
    | ~ aNaturalNumber0(xp)
    | aNaturalNumber0(xr) ),
    inference(mrr,[status(thm)],[652,7]),
    [iquote('0:MRR:652.2,7.0')] ).

cnf(656,plain,
    ( ~ aNaturalNumber0(sdtpldt0(u,v))
    | ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
    inference(eqr,[status(thm),theory(equality)],[68]),
    [iquote('0:EqR:68.3')] ).

cnf(664,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
    inference(ssi,[status(thm)],[656,24]),
    [iquote('0:SSi:656.0,24.2')] ).

cnf(1047,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl)
    | ~ doDivides0(xl,xm)
    | ~ equal(u,xp)
    | aNaturalNumber0(u)
    | equal(xl,sz00) ),
    inference(spl,[status(thm),theory(equality)],[13,50]),
    [iquote('0:SpL:13.0,50.3')] ).

cnf(1048,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl)
    | ~ doDivides0(xl,sdtpldt0(xm,xn))
    | ~ equal(u,xq)
    | aNaturalNumber0(u)
    | equal(xl,sz00) ),
    inference(spl,[status(thm),theory(equality)],[17,50]),
    [iquote('0:SpL:17.0,50.3')] ).

cnf(1049,plain,
    ( ~ doDivides0(xl,xm)
    | ~ equal(u,xp)
    | aNaturalNumber0(u)
    | equal(xl,sz00) ),
    inference(ssi,[status(thm)],[1047,3,4]),
    [iquote('0:SSi:1047.1,1047.0,3.0,4.0')] ).

cnf(1050,plain,
    ( ~ equal(u,xp)
    | aNaturalNumber0(u) ),
    inference(mrr,[status(thm)],[1049,6,11]),
    [iquote('0:MRR:1049.0,1049.3,6.0,11.0')] ).

cnf(1051,plain,
    ( ~ doDivides0(xl,sdtpldt0(xm,xn))
    | ~ equal(u,xq)
    | aNaturalNumber0(u)
    | equal(xl,sz00) ),
    inference(ssi,[status(thm)],[1048,3,24,4,5]),
    [iquote('0:SSi:1048.1,1048.0,3.0,24.0,4.2,5.0')] ).

cnf(1052,plain,
    ( ~ equal(u,xq)
    | aNaturalNumber0(u) ),
    inference(mrr,[status(thm)],[1051,12,11]),
    [iquote('0:MRR:1051.0,1051.3,12.0,11.0')] ).

cnf(1074,plain,
    ( ~ aNaturalNumber0(xq)
    | ~ equal(xp,xp)
    | aNaturalNumber0(xr) ),
    inference(sor,[status(thm)],[653,1050]),
    [iquote('0:SoR:653.1,1050.1')] ).

cnf(1083,plain,
    ( ~ aNaturalNumber0(xq)
    | aNaturalNumber0(xr) ),
    inference(obv,[status(thm),theory(equality)],[1074]),
    [iquote('0:Obv:1074.1')] ).

cnf(1160,plain,
    ( ~ equal(xq,xq)
    | aNaturalNumber0(xr) ),
    inference(sor,[status(thm)],[1083,1052]),
    [iquote('0:SoR:1083.0,1052.1')] ).

cnf(1161,plain,
    aNaturalNumber0(xr),
    inference(obv,[status(thm),theory(equality)],[1160]),
    [iquote('0:Obv:1160.0')] ).

cnf(2154,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl)
    | ~ doDivides0(xl,xm)
    | ~ equal(u,xp)
    | equal(xl,sz00)
    | equal(sdtasdt0(xl,u),xm) ),
    inference(spl,[status(thm),theory(equality)],[13,59]),
    [iquote('0:SpL:13.0,59.3')] ).

cnf(2156,plain,
    ( ~ doDivides0(xl,xm)
    | ~ equal(u,xp)
    | equal(xl,sz00)
    | equal(sdtasdt0(xl,u),xm) ),
    inference(ssi,[status(thm)],[2154,3,4]),
    [iquote('0:SSi:2154.1,2154.0,3.0,4.0')] ).

cnf(2157,plain,
    ( ~ equal(u,xp)
    | equal(sdtasdt0(xl,u),xm) ),
    inference(mrr,[status(thm)],[2156,6,11]),
    [iquote('0:MRR:2156.0,2156.2,6.0,11.0')] ).

cnf(2520,plain,
    ( ~ equal(xp,xp)
    | equal(sdtpldt0(xm,sdtasdt0(xl,xr)),sdtpldt0(xm,xn)) ),
    inference(spr,[status(thm),theory(equality)],[2157,32]),
    [iquote('0:SpR:2157.1,32.0')] ).

cnf(2535,plain,
    equal(sdtpldt0(xm,sdtasdt0(xl,xr)),sdtpldt0(xm,xn)),
    inference(obv,[status(thm),theory(equality)],[2520]),
    [iquote('0:Obv:2520.0')] ).

cnf(2651,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sdtasdt0(xl,xr))
    | equal(sdtmndt0(sdtpldt0(xm,xn),xm),sdtasdt0(xl,xr)) ),
    inference(spr,[status(thm),theory(equality)],[2535,664]),
    [iquote('0:SpR:2535.0,664.2')] ).

cnf(2669,plain,
    equal(sdtmndt0(sdtpldt0(xm,xn),xm),sdtasdt0(xl,xr)),
    inference(ssi,[status(thm)],[2651,25,3,1161,4]),
    [iquote('0:SSi:2651.1,2651.0,25.0,3.0,1161.0,4.2')] ).

cnf(2752,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | equal(sdtasdt0(xl,xr),xn) ),
    inference(spr,[status(thm),theory(equality)],[2669,664]),
    [iquote('0:SpR:2669.0,664.2')] ).

cnf(2757,plain,
    equal(sdtasdt0(xl,xr),xn),
    inference(ssi,[status(thm)],[2752,5,4]),
    [iquote('0:SSi:2752.1,2752.0,5.0,4.0')] ).

cnf(2758,plain,
    $false,
    inference(mrr,[status(thm)],[2757,15]),
    [iquote('0:MRR:2757.0,15.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : NUM475+1 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.09  % Command  : run_spass %d %s
% 0.09/0.29  % Computer : n020.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 600
% 0.09/0.29  % DateTime : Tue Jul  5 15:31:44 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 0.92/1.12  
% 0.92/1.12  SPASS V 3.9 
% 0.92/1.12  SPASS beiseite: Proof found.
% 0.92/1.12  % SZS status Theorem
% 0.92/1.12  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.92/1.12  SPASS derived 1640 clauses, backtracked 79 clauses, performed 1 splits and kept 805 clauses.
% 0.92/1.12  SPASS allocated 100240 KBytes.
% 0.92/1.12  SPASS spent	0:00:00.77 on the problem.
% 0.92/1.12  		0:00:00.03 for the input.
% 0.92/1.12  		0:00:00.03 for the FLOTTER CNF translation.
% 0.92/1.12  		0:00:00.03 for inferences.
% 0.92/1.12  		0:00:00.00 for the backtracking.
% 0.92/1.12  		0:00:00.65 for the reduction.
% 0.92/1.12  
% 0.92/1.12  
% 0.92/1.12  Here is a proof with depth 4, length 45 :
% 0.92/1.12  % SZS output start Refutation
% See solution above
% 0.92/1.12  Formulae used in the proof : m__1324 m__1324_04 m__1395 m__1347 m__1360 m__1422 m__ m__1379 mSortsB mSortsB_02 m__1459 mDefLE mDefDiff mDefQuot
% 0.92/1.12  
%------------------------------------------------------------------------------