TSTP Solution File: COM012+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COM012+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 : Fri Jul 15 01:44:16 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 20 unt; 5 nHn; 31 RR)
% Number of literals : 67 ( 0 equ; 37 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aElement0(xx),
file('COM012+1.p',unknown),
[] ).
cnf(2,axiom,
aRewritingSystem0(xR),
file('COM012+1.p',unknown),
[] ).
cnf(3,axiom,
aElement0(xy),
file('COM012+1.p',unknown),
[] ).
cnf(4,axiom,
aElement0(xz),
file('COM012+1.p',unknown),
[] ).
cnf(5,axiom,
sdtmndtasgtdt0(xx,xR,xy),
file('COM012+1.p',unknown),
[] ).
cnf(6,axiom,
sdtmndtasgtdt0(xy,xR,xz),
file('COM012+1.p',unknown),
[] ).
cnf(7,axiom,
~ sdtmndtasgtdt0(xx,xR,xz),
file('COM012+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ aElement0(w)
| ~ sdtmndtplgtdt0(w,v,u)
| sdtmndtasgtdt0(w,v,u) ),
file('COM012+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ aElement0(u)
| ~ aRewritingSystem0(v)
| ~ aElement0(w)
| ~ sdtmndtasgtdt0(w,v,u)
| equal(w,u)
| sdtmndtplgtdt0(w,v,u) ),
file('COM012+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aRewritingSystem0(w)
| ~ aElement0(x)
| ~ sdtmndtplgtdt0(x,w,v)
| ~ sdtmndtplgtdt0(v,w,u)
| sdtmndtplgtdt0(x,w,u) ),
file('COM012+1.p',unknown),
[] ).
cnf(20,plain,
( ~ aElement0(xy)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xz)
| equal(xz,xy)
| sdtmndtplgtdt0(xy,xR,xz) ),
inference(res,[status(thm),theory(equality)],[6,13]),
[iquote('0:Res:6.0,13.3')] ).
cnf(21,plain,
( ~ aElement0(xx)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xy)
| equal(xy,xx)
| sdtmndtplgtdt0(xx,xR,xy) ),
inference(res,[status(thm),theory(equality)],[5,13]),
[iquote('0:Res:5.0,13.3')] ).
cnf(22,plain,
( ~ aElement0(xx)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xz)
| ~ sdtmndtplgtdt0(xx,xR,xz) ),
inference(res,[status(thm),theory(equality)],[12,7]),
[iquote('0:Res:12.4,7.0')] ).
cnf(25,plain,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(mrr,[status(thm)],[22,1,2,4]),
[iquote('0:MRR:22.0,22.1,22.2,1.0,2.0,4.0')] ).
cnf(26,plain,
( equal(xz,xy)
| sdtmndtplgtdt0(xy,xR,xz) ),
inference(mrr,[status(thm)],[20,3,2,4]),
[iquote('0:MRR:20.0,20.1,20.2,3.0,2.0,4.0')] ).
cnf(27,plain,
( equal(xy,xx)
| sdtmndtplgtdt0(xx,xR,xy) ),
inference(mrr,[status(thm)],[21,1,2,3]),
[iquote('0:MRR:21.0,21.1,21.2,1.0,2.0,3.0')] ).
cnf(34,plain,
equal(xz,xy),
inference(spt,[spt(split,[position(s1)])],[26]),
[iquote('1:Spt:26.0')] ).
cnf(39,plain,
~ sdtmndtasgtdt0(xx,xR,xy),
inference(rew,[status(thm),theory(equality)],[34,7]),
[iquote('1:Rew:34.0,7.0')] ).
cnf(42,plain,
$false,
inference(mrr,[status(thm)],[39,5]),
[iquote('1:MRR:39.0,5.0')] ).
cnf(43,plain,
~ equal(xz,xy),
inference(spt,[spt(split,[position(sa)])],[42,34]),
[iquote('1:Spt:42.0,26.0,34.0')] ).
cnf(44,plain,
sdtmndtplgtdt0(xy,xR,xz),
inference(spt,[spt(split,[position(s2)])],[26]),
[iquote('1:Spt:42.0,26.1')] ).
cnf(45,plain,
equal(xy,xx),
inference(spt,[spt(split,[position(s2s1)])],[27]),
[iquote('2:Spt:27.0')] ).
cnf(49,plain,
sdtmndtasgtdt0(xx,xR,xz),
inference(rew,[status(thm),theory(equality)],[45,6]),
[iquote('2:Rew:45.0,6.0')] ).
cnf(52,plain,
$false,
inference(mrr,[status(thm)],[49,7]),
[iquote('2:MRR:49.0,7.0')] ).
cnf(53,plain,
~ equal(xy,xx),
inference(spt,[spt(split,[position(s2sa)])],[52,45]),
[iquote('2:Spt:52.0,27.0,45.0')] ).
cnf(54,plain,
sdtmndtplgtdt0(xx,xR,xy),
inference(spt,[spt(split,[position(s2s2)])],[27]),
[iquote('2:Spt:52.0,27.1')] ).
cnf(67,plain,
( ~ aElement0(u)
| ~ aElement0(xy)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xx)
| ~ sdtmndtplgtdt0(xy,xR,u)
| sdtmndtplgtdt0(xx,xR,u) ),
inference(res,[status(thm),theory(equality)],[54,16]),
[iquote('2:Res:54.0,16.4')] ).
cnf(72,plain,
( ~ aElement0(u)
| ~ sdtmndtplgtdt0(xy,xR,u)
| sdtmndtplgtdt0(xx,xR,u) ),
inference(ssi,[status(thm)],[67,1,2,3]),
[iquote('2:SSi:67.3,67.2,67.1,1.0,2.0,3.0')] ).
cnf(82,plain,
( ~ aElement0(xz)
| sdtmndtplgtdt0(xx,xR,xz) ),
inference(res,[status(thm),theory(equality)],[44,72]),
[iquote('2:Res:44.0,72.1')] ).
cnf(84,plain,
sdtmndtplgtdt0(xx,xR,xz),
inference(ssi,[status(thm)],[82,4]),
[iquote('2:SSi:82.0,4.0')] ).
cnf(85,plain,
$false,
inference(mrr,[status(thm)],[84,25]),
[iquote('2:MRR:84.0,25.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : COM012+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 19:43:49 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.46
% 0.20/0.46 SPASS V 3.9
% 0.20/0.46 SPASS beiseite: Proof found.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 SPASS derived 35 clauses, backtracked 15 clauses, performed 2 splits and kept 55 clauses.
% 0.20/0.46 SPASS allocated 103985 KBytes.
% 0.20/0.46 SPASS spent 0:00:00.10 on the problem.
% 0.20/0.46 0:00:00.04 for the input.
% 0.20/0.46 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.46 0:00:00.00 for inferences.
% 0.20/0.46 0:00:00.00 for the backtracking.
% 0.20/0.46 0:00:00.00 for the reduction.
% 0.20/0.46
% 0.20/0.46
% 0.20/0.46 Here is a proof with depth 4, length 31 :
% 0.20/0.46 % SZS output start Refutation
% See solution above
% 0.20/0.46 Formulae used in the proof : m__349 m__ mTCRDef mTCTrans
% 0.20/0.46
%------------------------------------------------------------------------------