TSTP Solution File: NUM469+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM469+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 14:26:31 EDT 2022

% Result   : Theorem 5.44s 5.67s
% Output   : Refutation 5.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   47 (  24 unt;   3 nHn;  47 RR)
%            Number of literals    :   98 (   0 equ;  58 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    aNaturalNumber0(sz00),
    file('NUM469+1.p',unknown),
    [] ).

cnf(3,axiom,
    aNaturalNumber0(xl),
    file('NUM469+1.p',unknown),
    [] ).

cnf(4,axiom,
    aNaturalNumber0(xm),
    file('NUM469+1.p',unknown),
    [] ).

cnf(5,axiom,
    aNaturalNumber0(xn),
    file('NUM469+1.p',unknown),
    [] ).

cnf(6,axiom,
    doDivides0(xl,xm),
    file('NUM469+1.p',unknown),
    [] ).

cnf(7,axiom,
    doDivides0(xl,xn),
    file('NUM469+1.p',unknown),
    [] ).

cnf(10,axiom,
    aNaturalNumber0(skf3(u,v)),
    file('NUM469+1.p',unknown),
    [] ).

cnf(11,axiom,
    ~ doDivides0(xl,sdtpldt0(xm,xn)),
    file('NUM469+1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ aNaturalNumber0(u)
    | equal(sdtpldt0(u,sz00),u) ),
    file('NUM469+1.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ aNaturalNumber0(u)
    | equal(sdtasdt0(sz00,u),sz00) ),
    file('NUM469+1.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | aNaturalNumber0(sdtpldt0(v,u)) ),
    file('NUM469+1.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | aNaturalNumber0(sdtasdt0(v,u)) ),
    file('NUM469+1.p',unknown),
    [] ).

cnf(31,axiom,
    ( equal(xl,sz00)
    | equal(sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),sdtpldt0(xm,xn)) ),
    file('NUM469+1.p',unknown),
    [] ).

cnf(34,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ doDivides0(v,u)
    | equal(sdtasdt0(v,skf3(v,u)),u) ),
    file('NUM469+1.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ equal(u,sdtasdt0(v,w))
    | doDivides0(v,u) ),
    file('NUM469+1.p',unknown),
    [] ).

cnf(45,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ doDivides0(v,u)
    | ~ equal(w,sdtsldt0(u,v))
    | aNaturalNumber0(w)
    | equal(v,sz00) ),
    file('NUM469+1.p',unknown),
    [] ).

cnf(68,plain,
    equal(xl,sz00),
    inference(spt,[spt(split,[position(s1)])],[31]),
    [iquote('1:Spt:31.0')] ).

cnf(70,plain,
    doDivides0(sz00,xn),
    inference(rew,[status(thm),theory(equality)],[68,7]),
    [iquote('1:Rew:68.0,7.0')] ).

cnf(71,plain,
    doDivides0(sz00,xm),
    inference(rew,[status(thm),theory(equality)],[68,6]),
    [iquote('1:Rew:68.0,6.0')] ).

cnf(72,plain,
    ~ doDivides0(sz00,sdtpldt0(xm,xn)),
    inference(rew,[status(thm),theory(equality)],[68,11]),
    [iquote('1:Rew:68.0,11.0')] ).

cnf(182,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(skf3(sz00,u))
    | ~ doDivides0(sz00,u)
    | equal(u,sz00) ),
    inference(spr,[status(thm),theory(equality)],[34,18]),
    [iquote('0:SpR:34.3,18.1')] ).

cnf(188,plain,
    ( ~ aNaturalNumber0(u)
    | ~ doDivides0(sz00,u)
    | equal(u,sz00) ),
    inference(ssi,[status(thm)],[182,10,1]),
    [iquote('0:SSi:182.2,182.1,10.0,1.0,1.0')] ).

cnf(204,plain,
    ( ~ aNaturalNumber0(xn)
    | equal(xn,sz00) ),
    inference(res,[status(thm),theory(equality)],[70,188]),
    [iquote('1:Res:70.0,188.1')] ).

cnf(205,plain,
    ( ~ aNaturalNumber0(xm)
    | equal(xm,sz00) ),
    inference(res,[status(thm),theory(equality)],[71,188]),
    [iquote('1:Res:71.0,188.1')] ).

cnf(206,plain,
    equal(xn,sz00),
    inference(ssi,[status(thm)],[204,5]),
    [iquote('1:SSi:204.0,5.0')] ).

cnf(208,plain,
    doDivides0(sz00,sz00),
    inference(rew,[status(thm),theory(equality)],[206,70]),
    [iquote('1:Rew:206.0,70.0')] ).

cnf(209,plain,
    ~ doDivides0(sz00,sdtpldt0(xm,sz00)),
    inference(rew,[status(thm),theory(equality)],[206,72]),
    [iquote('1:Rew:206.0,72.0')] ).

cnf(212,plain,
    equal(xm,sz00),
    inference(ssi,[status(thm)],[205,4]),
    [iquote('1:SSi:205.0,4.0')] ).

cnf(215,plain,
    ~ doDivides0(sz00,sdtpldt0(sz00,sz00)),
    inference(rew,[status(thm),theory(equality)],[212,209]),
    [iquote('1:Rew:212.0,209.0')] ).

cnf(223,plain,
    ( ~ aNaturalNumber0(sz00)
    | ~ doDivides0(sz00,sz00) ),
    inference(spl,[status(thm),theory(equality)],[13,215]),
    [iquote('1:SpL:13.1,215.0')] ).

cnf(227,plain,
    ~ doDivides0(sz00,sz00),
    inference(ssi,[status(thm)],[223,1]),
    [iquote('1:SSi:223.0,1.0')] ).

cnf(228,plain,
    $false,
    inference(mrr,[status(thm)],[227,208]),
    [iquote('1:MRR:227.0,208.0')] ).

cnf(231,plain,
    ~ equal(xl,sz00),
    inference(spt,[spt(split,[position(sa)])],[228,68]),
    [iquote('1:Spt:228.0,31.0,68.0')] ).

cnf(232,plain,
    equal(sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),sdtpldt0(xm,xn)),
    inference(spt,[spt(split,[position(s2)])],[31]),
    [iquote('1:Spt:228.0,31.1')] ).

cnf(386,plain,
    ( ~ aNaturalNumber0(sdtasdt0(u,v))
    | ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | doDivides0(u,sdtasdt0(u,v)) ),
    inference(eqr,[status(thm),theory(equality)],[38]),
    [iquote('0:EqR:38.3')] ).

cnf(395,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | doDivides0(u,sdtasdt0(u,v)) ),
    inference(ssi,[status(thm)],[386,20]),
    [iquote('0:SSi:386.0,20.2')] ).

cnf(433,plain,
    ( ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
    | doDivides0(xl,sdtpldt0(xm,xn)) ),
    inference(spr,[status(thm),theory(equality)],[232,395]),
    [iquote('1:SpR:232.0,395.2')] ).

cnf(447,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
    | doDivides0(xl,sdtpldt0(xm,xn)) ),
    inference(ssi,[status(thm)],[433,3]),
    [iquote('1:SSi:433.0,3.0')] ).

cnf(448,plain,
    ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
    inference(mrr,[status(thm)],[447,11]),
    [iquote('1:MRR:447.1,11.0')] ).

cnf(511,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
    | ~ aNaturalNumber0(sdtsldt0(xn,xl)) ),
    inference(sor,[status(thm)],[448,19]),
    [iquote('1:SoR:448.0,19.2')] ).

cnf(939,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ doDivides0(v,u)
    | aNaturalNumber0(sdtsldt0(u,v))
    | equal(v,sz00) ),
    inference(eqr,[status(thm),theory(equality)],[45]),
    [iquote('0:EqR:45.3')] ).

cnf(18107,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xn,xl))
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm)
    | ~ doDivides0(xl,xm)
    | equal(xl,sz00) ),
    inference(sor,[status(thm)],[511,939]),
    [iquote('1:SoR:511.0,939.3')] ).

cnf(18125,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xn,xl))
    | ~ doDivides0(xl,xm)
    | equal(xl,sz00) ),
    inference(ssi,[status(thm)],[18107,4,3]),
    [iquote('1:SSi:18107.2,18107.1,4.0,3.0')] ).

cnf(18126,plain,
    ~ aNaturalNumber0(sdtsldt0(xn,xl)),
    inference(mrr,[status(thm)],[18125,6,231]),
    [iquote('1:MRR:18125.1,18125.2,6.0,231.0')] ).

cnf(18140,plain,
    ( ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xn)
    | ~ doDivides0(xl,xn)
    | equal(xl,sz00) ),
    inference(sor,[status(thm)],[18126,939]),
    [iquote('1:SoR:18126.0,939.3')] ).

cnf(18146,plain,
    ( ~ doDivides0(xl,xn)
    | equal(xl,sz00) ),
    inference(ssi,[status(thm)],[18140,5,3]),
    [iquote('1:SSi:18140.1,18140.0,5.0,3.0')] ).

cnf(18147,plain,
    $false,
    inference(mrr,[status(thm)],[18146,7,231]),
    [iquote('1:MRR:18146.0,18146.1,7.0,231.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM469+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jul  5 08:36:12 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 5.44/5.67  
% 5.44/5.67  SPASS V 3.9 
% 5.44/5.67  SPASS beiseite: Proof found.
% 5.44/5.67  % SZS status Theorem
% 5.44/5.67  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 5.44/5.67  SPASS derived 10676 clauses, backtracked 3027 clauses, performed 7 splits and kept 5051 clauses.
% 5.44/5.67  SPASS allocated 109709 KBytes.
% 5.44/5.67  SPASS spent	0:00:03.82 on the problem.
% 5.44/5.67  		0:00:00.04 for the input.
% 5.44/5.67  		0:00:00.04 for the FLOTTER CNF translation.
% 5.44/5.67  		0:00:00.10 for inferences.
% 5.44/5.67  		0:00:00.02 for the backtracking.
% 5.44/5.67  		0:00:03.58 for the reduction.
% 5.44/5.67  
% 5.44/5.67  
% 5.44/5.67  Here is a proof with depth 5, length 47 :
% 5.44/5.67  % SZS output start Refutation
% See solution above
% 5.44/5.67  Formulae used in the proof : mSortsC m__1240 m__1240_04 mDefDiv m__ m_AddZero m_MulZero mSortsB mSortsB_02 m__1298 mDefQuot
% 5.44/5.67  
%------------------------------------------------------------------------------