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