TSTP Solution File: NUM452+6 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM452+6 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 14:26:20 EDT 2022

% Result   : Theorem 6.14s 6.34s
% Output   : Refutation 6.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   45 (  11 unt;   0 nHn;  45 RR)
%            Number of literals    :  112 (   0 equ;  82 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    5 (   4 usr;   2 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    aInteger0(sz10),
    file('NUM452+6.p',unknown),
    [] ).

cnf(5,axiom,
    aInteger0(xp),
    file('NUM452+6.p',unknown),
    [] ).

cnf(25,axiom,
    equal(stldt0(sbsmnsldt0(xS)),cS2076),
    file('NUM452+6.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ aInteger0(u)
    | aInteger0(smndt0(u)) ),
    file('NUM452+6.p',unknown),
    [] ).

cnf(37,axiom,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(sz00,u),u) ),
    file('NUM452+6.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(u,sz10),u) ),
    file('NUM452+6.p',unknown),
    [] ).

cnf(47,axiom,
    ( ~ aElementOf0(u,stldt0(sbsmnsldt0(xS)))
    | aInteger0(u) ),
    file('NUM452+6.p',unknown),
    [] ).

cnf(49,axiom,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(u,smndt0(u)),sz00) ),
    file('NUM452+6.p',unknown),
    [] ).

cnf(50,axiom,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(u),u),sz00) ),
    file('NUM452+6.p',unknown),
    [] ).

cnf(69,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | aInteger0(sdtpldt0(v,u)) ),
    file('NUM452+6.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(u,smndt0(sz10)),smndt0(u)) ),
    file('NUM452+6.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ equal(u,smndt0(sz10))
    | aElementOf0(u,stldt0(sbsmnsldt0(xS))) ),
    file('NUM452+6.p',unknown),
    [] ).

cnf(101,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
    file('NUM452+6.p',unknown),
    [] ).

cnf(119,axiom,
    ( ~ aInteger0(u)
    | ~ equal(sdtasdt0(xp,u),sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
    | skC0 ),
    file('NUM452+6.p',unknown),
    [] ).

cnf(138,axiom,
    ( ~ aInteger0(u)
    | ~ skC0
    | ~ equal(sdtasdt0(xp,u),sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))) ),
    file('NUM452+6.p',unknown),
    [] ).

cnf(163,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
    file('NUM452+6.p',unknown),
    [] ).

cnf(210,plain,
    ( ~ aElementOf0(u,cS2076)
    | aInteger0(u) ),
    inference(rew,[status(thm),theory(equality)],[25,47]),
    [iquote('0:Rew:25.0,47.0')] ).

cnf(214,plain,
    ( ~ equal(u,smndt0(sz10))
    | aElementOf0(u,cS2076) ),
    inference(rew,[status(thm),theory(equality)],[25,80]),
    [iquote('0:Rew:25.0,80.1')] ).

cnf(280,plain,
    ( ~ aInteger0(u)
    | ~ equal(sdtasdt0(xp,u),sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) ),
    inference(spt,[spt(split,[position(s1)])],[119]),
    [iquote('1:Spt:119.0,119.1')] ).

cnf(450,plain,
    aElementOf0(smndt0(sz10),cS2076),
    inference(eqr,[status(thm),theory(equality)],[214]),
    [iquote('0:EqR:214.0')] ).

cnf(456,plain,
    aInteger0(smndt0(sz10)),
    inference(res,[status(thm),theory(equality)],[450,210]),
    [iquote('0:Res:450.0,210.0')] ).

cnf(477,plain,
    ( ~ aInteger0(xp)
    | ~ aInteger0(sz10)
    | ~ equal(sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)),xp) ),
    inference(spl,[status(thm),theory(equality)],[38,280]),
    [iquote('1:SpL:38.1,280.1')] ).

cnf(480,plain,
    ~ equal(sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)),xp),
    inference(ssi,[status(thm)],[477,2,5]),
    [iquote('1:SSi:477.1,477.0,2.0,5.0')] ).

cnf(5923,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(sdtpldt0(sz10,xp))
    | ~ equal(sdtpldt0(smndt0(sz10),sdtpldt0(sz10,xp)),xp) ),
    inference(spl,[status(thm),theory(equality)],[101,480]),
    [iquote('1:SpL:101.2,480.0')] ).

cnf(5945,plain,
    ~ equal(sdtpldt0(smndt0(sz10),sdtpldt0(sz10,xp)),xp),
    inference(ssi,[status(thm)],[5923,69,2,5,456]),
    [iquote('1:SSi:5923.1,5923.0,69.0,2.0,5.0,456.2')] ).

cnf(7858,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(u)
    | ~ aInteger0(smndt0(u))
    | equal(sdtpldt0(smndt0(u),sdtpldt0(u,v)),sdtpldt0(sz00,v)) ),
    inference(spr,[status(thm),theory(equality)],[50,163]),
    [iquote('0:SpR:50.1,163.3')] ).

cnf(7862,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(smndt0(u))
    | ~ aInteger0(u)
    | equal(sdtpldt0(u,sdtpldt0(smndt0(u),v)),sdtpldt0(sz00,v)) ),
    inference(spr,[status(thm),theory(equality)],[49,163]),
    [iquote('0:SpR:49.1,163.3')] ).

cnf(7988,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(v))
    | ~ aInteger0(v)
    | equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(sz00,u)) ),
    inference(obv,[status(thm),theory(equality)],[7862]),
    [iquote('0:Obv:7862.0')] ).

cnf(7989,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(v))
    | ~ aInteger0(v)
    | equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
    inference(rew,[status(thm),theory(equality)],[37,7988]),
    [iquote('0:Rew:37.1,7988.3')] ).

cnf(7990,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
    inference(ssi,[status(thm)],[7989,26]),
    [iquote('0:SSi:7989.1,26.1')] ).

cnf(7991,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(smndt0(v))
    | equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),sdtpldt0(sz00,u)) ),
    inference(obv,[status(thm),theory(equality)],[7858]),
    [iquote('0:Obv:7858.0')] ).

cnf(7992,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(smndt0(v))
    | equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
    inference(rew,[status(thm),theory(equality)],[37,7991]),
    [iquote('0:Rew:37.1,7991.3')] ).

cnf(7993,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
    inference(ssi,[status(thm)],[7992,26]),
    [iquote('0:SSi:7992.2,26.1')] ).

cnf(16255,plain,
    ( ~ aInteger0(xp)
    | ~ aInteger0(sz10)
    | ~ equal(xp,xp) ),
    inference(spl,[status(thm),theory(equality)],[7993,5945]),
    [iquote('1:SpL:7993.2,5945.0')] ).

cnf(16261,plain,
    ( ~ aInteger0(xp)
    | ~ aInteger0(sz10) ),
    inference(obv,[status(thm),theory(equality)],[16255]),
    [iquote('1:Obv:16255.2')] ).

cnf(16262,plain,
    $false,
    inference(ssi,[status(thm)],[16261,2,5]),
    [iquote('1:SSi:16261.1,16261.0,2.0,5.0')] ).

cnf(16288,plain,
    skC0,
    inference(spt,[spt(split,[position(s2)])],[119]),
    [iquote('1:Spt:16262.0,119.2')] ).

cnf(16343,plain,
    ( ~ aInteger0(u)
    | ~ equal(sdtasdt0(xp,u),sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))) ),
    inference(mrr,[status(thm)],[138,16288]),
    [iquote('1:MRR:138.1,16288.0')] ).

cnf(17217,plain,
    ( ~ aInteger0(xp)
    | ~ aInteger0(smndt0(sz10))
    | ~ equal(sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)),smndt0(xp)) ),
    inference(spl,[status(thm),theory(equality)],[72,16343]),
    [iquote('1:SpL:72.1,16343.1')] ).

cnf(17223,plain,
    ~ equal(sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)),smndt0(xp)),
    inference(ssi,[status(thm)],[17217,456,5]),
    [iquote('1:SSi:17217.1,17217.0,456.0,5.0')] ).

cnf(22514,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(smndt0(xp))
    | ~ aInteger0(sz10)
    | ~ equal(sdtpldt0(sz10,sdtpldt0(smndt0(xp),smndt0(sz10))),smndt0(xp)) ),
    inference(spl,[status(thm),theory(equality)],[163,17223]),
    [iquote('1:SpL:163.3,17223.0')] ).

cnf(22608,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(smndt0(xp))
    | ~ aInteger0(sz10)
    | ~ equal(sdtpldt0(sz10,sdtpldt0(smndt0(sz10),smndt0(xp))),smndt0(xp)) ),
    inference(rew,[status(thm),theory(equality)],[101,22514]),
    [iquote('1:Rew:101.2,22514.3')] ).

cnf(22609,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(smndt0(xp))
    | ~ aInteger0(sz10)
    | ~ equal(smndt0(xp),smndt0(xp)) ),
    inference(rew,[status(thm),theory(equality)],[7990,22608]),
    [iquote('1:Rew:7990.2,22608.3')] ).

cnf(22610,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(smndt0(xp))
    | ~ aInteger0(sz10) ),
    inference(obv,[status(thm),theory(equality)],[22609]),
    [iquote('1:Obv:22609.3')] ).

cnf(22611,plain,
    $false,
    inference(ssi,[status(thm)],[22610,2,26,5,456]),
    [iquote('1:SSi:22610.2,22610.1,22610.0,2.0,26.0,5.1,456.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : NUM452+6 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n026.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 : Wed Jul  6 03:33:53 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 6.14/6.34  
% 6.14/6.34  SPASS V 3.9 
% 6.14/6.34  SPASS beiseite: Proof found.
% 6.14/6.34  % SZS status Theorem
% 6.14/6.34  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 6.14/6.34  SPASS derived 14130 clauses, backtracked 5242 clauses, performed 78 splits and kept 9452 clauses.
% 6.14/6.34  SPASS allocated 112655 KBytes.
% 6.14/6.34  SPASS spent	0:00:05.30 on the problem.
% 6.14/6.34  		0:00:00.04 for the input.
% 6.14/6.34  		0:00:00.24 for the FLOTTER CNF translation.
% 6.14/6.34  		0:00:00.17 for inferences.
% 6.14/6.34  		0:00:00.16 for the backtracking.
% 6.14/6.34  		0:00:04.58 for the reduction.
% 6.14/6.34  
% 6.14/6.34  
% 6.14/6.34  Here is a proof with depth 4, length 45 :
% 6.14/6.34  % SZS output start Refutation
% See solution above
% 6.14/6.34  Formulae used in the proof : mIntOne m__2171 m__2079 mIntNeg mAddZero mMulOne mAddNeg mIntPlus mMulMinOne mAddComm m__ mAddAsso
% 6.14/6.34  
%------------------------------------------------------------------------------