TSTP Solution File: COM022+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : COM022+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 : Fri Jul 15 01:44:22 EDT 2022

% Result   : Theorem 0.40s 0.59s
% Output   : Refutation 0.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   54 (  24 unt;   5 nHn;  54 RR)
%            Number of literals    :  131 (   0 equ;  89 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;  10 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    aElement0(skc6),
    file('COM022+1.p',unknown),
    [] ).

cnf(4,axiom,
    aRewritingSystem0(xR),
    file('COM022+1.p',unknown),
    [] ).

cnf(5,axiom,
    isLocallyConfluent0(xR),
    file('COM022+1.p',unknown),
    [] ).

cnf(6,axiom,
    isTerminating0(xR),
    file('COM022+1.p',unknown),
    [] ).

cnf(7,axiom,
    aElement0(xa),
    file('COM022+1.p',unknown),
    [] ).

cnf(8,axiom,
    aElement0(xb),
    file('COM022+1.p',unknown),
    [] ).

cnf(9,axiom,
    aElement0(xc),
    file('COM022+1.p',unknown),
    [] ).

cnf(18,axiom,
    sdtmndtasgtdt0(xb,xR,skc7),
    file('COM022+1.p',unknown),
    [] ).

cnf(19,axiom,
    sdtmndtasgtdt0(xa,xR,xb),
    file('COM022+1.p',unknown),
    [] ).

cnf(20,axiom,
    sdtmndtasgtdt0(xa,xR,xc),
    file('COM022+1.p',unknown),
    [] ).

cnf(31,axiom,
    ( ~ aElement0(u)
    | ~ sdtmndtasgtdt0(xc,xR,u)
    | ~ sdtmndtasgtdt0(xb,xR,u) ),
    file('COM022+1.p',unknown),
    [] ).

cnf(33,axiom,
    ( ~ aRewritingSystem0(u)
    | ~ aElement0(v)
    | ~ aNormalFormOfIn0(w,v,u)
    | aElement0(w) ),
    file('COM022+1.p',unknown),
    [] ).

cnf(40,axiom,
    ( ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | aNormalFormOfIn0(skc7,skc6,xR) ),
    file('COM022+1.p',unknown),
    [] ).

cnf(41,axiom,
    ( ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | sdtmndtasgtdt0(xc,xR,skc7) ),
    file('COM022+1.p',unknown),
    [] ).

cnf(45,axiom,
    ( ~ aElement0(u)
    | ~ aRewritingSystem0(v)
    | ~ aElement0(w)
    | ~ equal(w,u)
    | sdtmndtasgtdt0(w,v,u) ),
    file('COM022+1.p',unknown),
    [] ).

cnf(51,axiom,
    ( ~ aElement0(u)
    | ~ aRewritingSystem0(v)
    | ~ aElement0(w)
    | ~ sdtmndtasgtdt0(w,v,u)
    | equal(w,u)
    | sdtmndtplgtdt0(w,v,u) ),
    file('COM022+1.p',unknown),
    [] ).

cnf(55,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aRewritingSystem0(w)
    | ~ aElement0(x)
    | ~ sdtmndtasgtdt0(x,w,v)
    | ~ sdtmndtasgtdt0(v,w,u)
    | sdtmndtasgtdt0(x,w,u) ),
    file('COM022+1.p',unknown),
    [] ).

cnf(197,plain,
    ~ sdtmndtplgtdt0(xa,xR,xc),
    inference(spt,[spt(split,[position(s1)])],[40]),
    [iquote('1:Spt:40.0')] ).

cnf(370,plain,
    ( ~ aElement0(xc)
    | ~ aRewritingSystem0(xR)
    | ~ aElement0(xa)
    | equal(xc,xa)
    | sdtmndtplgtdt0(xa,xR,xc) ),
    inference(res,[status(thm),theory(equality)],[20,51]),
    [iquote('0:Res:20.0,51.3')] ).

cnf(371,plain,
    ( ~ aElement0(xb)
    | ~ aRewritingSystem0(xR)
    | ~ aElement0(xa)
    | equal(xb,xa)
    | sdtmndtplgtdt0(xa,xR,xb) ),
    inference(res,[status(thm),theory(equality)],[19,51]),
    [iquote('0:Res:19.0,51.3')] ).

cnf(383,plain,
    ( equal(xc,xa)
    | sdtmndtplgtdt0(xa,xR,xc) ),
    inference(ssi,[status(thm)],[370,7,6,5,4,9]),
    [iquote('0:SSi:370.2,370.1,370.0,7.0,6.0,5.0,4.0,9.0')] ).

cnf(384,plain,
    equal(xc,xa),
    inference(mrr,[status(thm)],[383,197]),
    [iquote('1:MRR:383.1,197.0')] ).

cnf(390,plain,
    ( ~ aElement0(u)
    | ~ sdtmndtasgtdt0(xa,xR,u)
    | ~ sdtmndtasgtdt0(xb,xR,u) ),
    inference(rew,[status(thm),theory(equality)],[384,31]),
    [iquote('1:Rew:384.0,31.1')] ).

cnf(436,plain,
    ( equal(xb,xa)
    | sdtmndtplgtdt0(xa,xR,xb) ),
    inference(ssi,[status(thm)],[371,7,6,5,4,8]),
    [iquote('0:SSi:371.2,371.1,371.0,7.0,6.0,5.0,4.0,8.0')] ).

cnf(568,plain,
    ( ~ aElement0(u)
    | ~ aElement0(xb)
    | ~ aRewritingSystem0(xR)
    | ~ aElement0(xa)
    | ~ sdtmndtasgtdt0(xb,xR,u)
    | sdtmndtasgtdt0(xa,xR,u) ),
    inference(res,[status(thm),theory(equality)],[19,55]),
    [iquote('0:Res:19.0,55.4')] ).

cnf(582,plain,
    ( ~ aElement0(u)
    | ~ sdtmndtasgtdt0(xb,xR,u)
    | sdtmndtasgtdt0(xa,xR,u) ),
    inference(ssi,[status(thm)],[568,7,6,5,4,8]),
    [iquote('0:SSi:568.3,568.2,568.1,7.0,6.0,5.0,4.0,8.0')] ).

cnf(583,plain,
    ( ~ aElement0(u)
    | ~ sdtmndtasgtdt0(xb,xR,u) ),
    inference(mrr,[status(thm)],[582,390]),
    [iquote('1:MRR:582.2,390.1')] ).

cnf(607,plain,
    ( ~ aElement0(u)
    | ~ aRewritingSystem0(xR)
    | ~ aElement0(xb)
    | ~ aElement0(u)
    | ~ equal(xb,u) ),
    inference(res,[status(thm),theory(equality)],[45,583]),
    [iquote('1:Res:45.4,583.1')] ).

cnf(610,plain,
    ( ~ aRewritingSystem0(xR)
    | ~ aElement0(xb)
    | ~ aElement0(u)
    | ~ equal(xb,u) ),
    inference(obv,[status(thm),theory(equality)],[607]),
    [iquote('1:Obv:607.0')] ).

cnf(611,plain,
    ( ~ aElement0(u)
    | ~ equal(xb,u) ),
    inference(ssi,[status(thm)],[610,8,6,5,4]),
    [iquote('1:SSi:610.1,610.0,8.0,6.0,5.0,4.0')] ).

cnf(637,plain,
    ~ equal(xb,xb),
    inference(ems,[status(thm)],[611,8]),
    [iquote('1:EmS:611.0,8.0')] ).

cnf(638,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[637]),
    [iquote('1:Obv:637.0')] ).

cnf(639,plain,
    sdtmndtplgtdt0(xa,xR,xc),
    inference(spt,[spt(split,[position(sa)])],[638,197]),
    [iquote('1:Spt:638.0,40.0,197.0')] ).

cnf(640,plain,
    ( ~ sdtmndtplgtdt0(xa,xR,xb)
    | aNormalFormOfIn0(skc7,skc6,xR) ),
    inference(spt,[spt(split,[position(s2)])],[40]),
    [iquote('1:Spt:638.0,40.1,40.2')] ).

cnf(641,plain,
    ( ~ sdtmndtplgtdt0(xa,xR,xb)
    | sdtmndtasgtdt0(xc,xR,skc7) ),
    inference(mrr,[status(thm)],[41,639]),
    [iquote('1:MRR:41.0,639.0')] ).

cnf(650,plain,
    ( ~ aRewritingSystem0(xR)
    | ~ aElement0(skc6)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | aElement0(skc7) ),
    inference(res,[status(thm),theory(equality)],[640,33]),
    [iquote('1:Res:640.1,33.2')] ).

cnf(651,plain,
    ( ~ sdtmndtplgtdt0(xa,xR,xb)
    | aElement0(skc7) ),
    inference(ssi,[status(thm)],[650,1,6,5,4]),
    [iquote('1:SSi:650.1,650.0,1.0,6.0,5.0,4.0')] ).

cnf(656,plain,
    ( ~ aElement0(u)
    | ~ aElement0(xc)
    | ~ aRewritingSystem0(xR)
    | ~ aElement0(xa)
    | ~ sdtmndtasgtdt0(xc,xR,u)
    | sdtmndtasgtdt0(xa,xR,u) ),
    inference(res,[status(thm),theory(equality)],[20,55]),
    [iquote('0:Res:20.0,55.4')] ).

cnf(658,plain,
    ( ~ aElement0(u)
    | ~ sdtmndtasgtdt0(xc,xR,u)
    | sdtmndtasgtdt0(xa,xR,u) ),
    inference(ssi,[status(thm)],[656,7,6,5,4,9]),
    [iquote('0:SSi:656.3,656.2,656.1,7.0,6.0,5.0,4.0,9.0')] ).

cnf(663,plain,
    equal(xb,xa),
    inference(spt,[spt(split,[position(s2s1)])],[436]),
    [iquote('2:Spt:436.0')] ).

cnf(716,plain,
    ( ~ aElement0(u)
    | ~ sdtmndtasgtdt0(xc,xR,u)
    | ~ sdtmndtasgtdt0(xa,xR,u) ),
    inference(rew,[status(thm),theory(equality)],[663,31]),
    [iquote('2:Rew:663.0,31.2')] ).

cnf(732,plain,
    ( ~ aElement0(u)
    | ~ sdtmndtasgtdt0(xc,xR,u) ),
    inference(mrr,[status(thm)],[716,658]),
    [iquote('2:MRR:716.2,658.2')] ).

cnf(746,plain,
    ( ~ aElement0(u)
    | ~ aRewritingSystem0(xR)
    | ~ aElement0(xc)
    | ~ aElement0(u)
    | ~ equal(xc,u) ),
    inference(res,[status(thm),theory(equality)],[45,732]),
    [iquote('2:Res:45.4,732.1')] ).

cnf(749,plain,
    ( ~ aRewritingSystem0(xR)
    | ~ aElement0(xc)
    | ~ aElement0(u)
    | ~ equal(xc,u) ),
    inference(obv,[status(thm),theory(equality)],[746]),
    [iquote('2:Obv:746.0')] ).

cnf(750,plain,
    ( ~ aElement0(u)
    | ~ equal(xc,u) ),
    inference(ssi,[status(thm)],[749,9,6,5,4]),
    [iquote('2:SSi:749.1,749.0,9.0,6.0,5.0,4.0')] ).

cnf(753,plain,
    ~ equal(xc,xc),
    inference(ems,[status(thm)],[750,9]),
    [iquote('2:EmS:750.0,9.0')] ).

cnf(773,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[753]),
    [iquote('2:Obv:753.0')] ).

cnf(774,plain,
    ~ equal(xb,xa),
    inference(spt,[spt(split,[position(s2sa)])],[773,663]),
    [iquote('2:Spt:773.0,436.0,663.0')] ).

cnf(775,plain,
    sdtmndtplgtdt0(xa,xR,xb),
    inference(spt,[spt(split,[position(s2s2)])],[436]),
    [iquote('2:Spt:773.0,436.1')] ).

cnf(776,plain,
    aElement0(skc7),
    inference(mrr,[status(thm)],[651,775]),
    [iquote('2:MRR:651.0,775.0')] ).

cnf(779,plain,
    sdtmndtasgtdt0(xc,xR,skc7),
    inference(mrr,[status(thm)],[641,775]),
    [iquote('2:MRR:641.0,775.0')] ).

cnf(854,plain,
    ( ~ aElement0(skc7)
    | ~ sdtmndtasgtdt0(xb,xR,skc7) ),
    inference(res,[status(thm),theory(equality)],[779,31]),
    [iquote('2:Res:779.0,31.1')] ).

cnf(859,plain,
    ~ sdtmndtasgtdt0(xb,xR,skc7),
    inference(ssi,[status(thm)],[854,776]),
    [iquote('2:SSi:854.0,776.0')] ).

cnf(860,plain,
    $false,
    inference(mrr,[status(thm)],[859,18]),
    [iquote('2:MRR:859.0,18.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : COM022+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n029.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 : Thu Jun 16 20:06:42 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.40/0.59  
% 0.40/0.59  SPASS V 3.9 
% 0.40/0.59  SPASS beiseite: Proof found.
% 0.40/0.59  % SZS status Theorem
% 0.40/0.59  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.40/0.59  SPASS derived 499 clauses, backtracked 135 clauses, performed 2 splits and kept 585 clauses.
% 0.40/0.59  SPASS allocated 104659 KBytes.
% 0.40/0.59  SPASS spent	0:00:00.24 on the problem.
% 0.40/0.59  		0:00:00.04 for the input.
% 0.40/0.59  		0:00:00.08 for the FLOTTER CNF translation.
% 0.40/0.59  		0:00:00.01 for inferences.
% 0.40/0.59  		0:00:00.00 for the backtracking.
% 0.40/0.59  		0:00:00.07 for the reduction.
% 0.40/0.59  
% 0.40/0.59  
% 0.40/0.59  Here is a proof with depth 3, length 54 :
% 0.40/0.59  % SZS output start Refutation
% See solution above
% 0.40/0.60  Formulae used in the proof : m__ m__731 m__656 m__656_01 mTermNF mNFRDef mTCRDef mTCRTrans
% 0.40/0.60  
%------------------------------------------------------------------------------