TSTP Solution File: COM012+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COM012+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 01:44:17 EDT 2022
% Result : Theorem 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of clauses : 36 ( 21 unt; 8 nHn; 36 RR)
% Number of literals : 66 ( 0 equ; 30 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aElement0(skc2),
file('COM012+3.p',unknown),
[] ).
cnf(4,axiom,
aRewritingSystem0(xR),
file('COM012+3.p',unknown),
[] ).
cnf(5,axiom,
aElement0(xy),
file('COM012+3.p',unknown),
[] ).
cnf(6,axiom,
aElement0(xz),
file('COM012+3.p',unknown),
[] ).
cnf(8,axiom,
sdtmndtasgtdt0(xy,xR,xz),
file('COM012+3.p',unknown),
[] ).
cnf(9,axiom,
~ equal(xz,xx),
file('COM012+3.p',unknown),
[] ).
cnf(11,axiom,
~ sdtmndtplgtdt0(xx,xR,xz),
file('COM012+3.p',unknown),
[] ).
cnf(12,axiom,
~ sdtmndtasgtdt0(xx,xR,xz),
file('COM012+3.p',unknown),
[] ).
cnf(14,axiom,
( equal(xy,xx)
| sdtmndtplgtdt0(xx,xR,xy) ),
file('COM012+3.p',unknown),
[] ).
cnf(15,axiom,
( equal(xy,xz)
| sdtmndtplgtdt0(xy,xR,xz) ),
file('COM012+3.p',unknown),
[] ).
cnf(16,axiom,
( equal(xy,xx)
| aReductOfIn0(xy,xx,xR)
| aReductOfIn0(skc2,xx,xR) ),
file('COM012+3.p',unknown),
[] ).
cnf(17,axiom,
( equal(xy,xx)
| aReductOfIn0(xy,xx,xR)
| sdtmndtplgtdt0(skc2,xR,xy) ),
file('COM012+3.p',unknown),
[] ).
cnf(20,axiom,
( ~ aElement0(u)
| ~ sdtmndtplgtdt0(u,xR,xz)
| ~ aReductOfIn0(u,xx,xR) ),
file('COM012+3.p',unknown),
[] ).
cnf(28,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aRewritingSystem0(w)
| ~ aElement0(x)
| ~ sdtmndtplgtdt0(x,w,v)
| ~ sdtmndtplgtdt0(v,w,u)
| sdtmndtplgtdt0(x,w,u) ),
file('COM012+3.p',unknown),
[] ).
cnf(40,plain,
equal(xy,xz),
inference(spt,[spt(split,[position(s1)])],[15]),
[iquote('1:Spt:15.0')] ).
cnf(43,plain,
( equal(xz,xx)
| sdtmndtplgtdt0(xx,xR,xy) ),
inference(rew,[status(thm),theory(equality)],[40,14]),
[iquote('1:Rew:40.0,14.0')] ).
cnf(48,plain,
( equal(xz,xx)
| sdtmndtplgtdt0(xx,xR,xz) ),
inference(rew,[status(thm),theory(equality)],[40,43]),
[iquote('1:Rew:40.0,43.1')] ).
cnf(49,plain,
$false,
inference(mrr,[status(thm)],[48,9,11]),
[iquote('1:MRR:48.0,48.1,9.0,11.0')] ).
cnf(54,plain,
~ equal(xy,xz),
inference(spt,[spt(split,[position(sa)])],[49,40]),
[iquote('1:Spt:49.0,15.0,40.0')] ).
cnf(55,plain,
sdtmndtplgtdt0(xy,xR,xz),
inference(spt,[spt(split,[position(s2)])],[15]),
[iquote('1:Spt:49.0,15.1')] ).
cnf(58,plain,
equal(xy,xx),
inference(spt,[spt(split,[position(s2s1)])],[14]),
[iquote('2:Spt:14.0')] ).
cnf(62,plain,
sdtmndtasgtdt0(xx,xR,xz),
inference(rew,[status(thm),theory(equality)],[58,8]),
[iquote('2:Rew:58.0,8.0')] ).
cnf(67,plain,
$false,
inference(mrr,[status(thm)],[62,12]),
[iquote('2:MRR:62.0,12.0')] ).
cnf(71,plain,
~ equal(xy,xx),
inference(spt,[spt(split,[position(s2sa)])],[67,58]),
[iquote('2:Spt:67.0,14.0,58.0')] ).
cnf(72,plain,
sdtmndtplgtdt0(xx,xR,xy),
inference(spt,[spt(split,[position(s2s2)])],[14]),
[iquote('2:Spt:67.0,14.1')] ).
cnf(73,plain,
( aReductOfIn0(xy,xx,xR)
| sdtmndtplgtdt0(skc2,xR,xy) ),
inference(mrr,[status(thm)],[17,71]),
[iquote('2:MRR:17.0,71.0')] ).
cnf(74,plain,
( aReductOfIn0(xy,xx,xR)
| aReductOfIn0(skc2,xx,xR) ),
inference(mrr,[status(thm)],[16,71]),
[iquote('2:MRR:16.0,71.0')] ).
cnf(75,plain,
( ~ aElement0(xy)
| ~ aReductOfIn0(xy,xx,xR) ),
inference(res,[status(thm),theory(equality)],[55,20]),
[iquote('1:Res:55.0,20.1')] ).
cnf(77,plain,
~ aReductOfIn0(xy,xx,xR),
inference(ssi,[status(thm)],[75,5]),
[iquote('1:SSi:75.0,5.0')] ).
cnf(78,plain,
sdtmndtplgtdt0(skc2,xR,xy),
inference(mrr,[status(thm)],[73,77]),
[iquote('2:MRR:73.0,77.0')] ).
cnf(79,plain,
aReductOfIn0(skc2,xx,xR),
inference(mrr,[status(thm)],[74,77]),
[iquote('2:MRR:74.0,77.0')] ).
cnf(115,plain,
( ~ aElement0(u)
| ~ aElement0(xy)
| ~ aRewritingSystem0(xR)
| ~ aElement0(skc2)
| ~ sdtmndtplgtdt0(xy,xR,u)
| sdtmndtplgtdt0(skc2,xR,u) ),
inference(res,[status(thm),theory(equality)],[78,28]),
[iquote('2:Res:78.0,28.4')] ).
cnf(123,plain,
( ~ aElement0(u)
| ~ sdtmndtplgtdt0(xy,xR,u)
| sdtmndtplgtdt0(skc2,xR,u) ),
inference(ssi,[status(thm)],[115,2,4,5]),
[iquote('2:SSi:115.3,115.2,115.1,2.0,4.0,5.0')] ).
cnf(137,plain,
( ~ aElement0(xz)
| ~ aElement0(skc2)
| ~ sdtmndtplgtdt0(xy,xR,xz)
| ~ aReductOfIn0(skc2,xx,xR) ),
inference(res,[status(thm),theory(equality)],[123,20]),
[iquote('2:Res:123.2,20.1')] ).
cnf(141,plain,
( ~ sdtmndtplgtdt0(xy,xR,xz)
| ~ aReductOfIn0(skc2,xx,xR) ),
inference(ssi,[status(thm)],[137,2,6]),
[iquote('2:SSi:137.1,137.0,2.0,6.0')] ).
cnf(142,plain,
$false,
inference(mrr,[status(thm)],[141,55,79]),
[iquote('2:MRR:141.0,141.1,55.0,79.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : COM012+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 19:52:51 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.48
% 0.21/0.48 SPASS V 3.9
% 0.21/0.48 SPASS beiseite: Proof found.
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48 SPASS derived 55 clauses, backtracked 21 clauses, performed 3 splits and kept 85 clauses.
% 0.21/0.48 SPASS allocated 104006 KBytes.
% 0.21/0.48 SPASS spent 0:00:00.11 on the problem.
% 0.21/0.48 0:00:00.03 for the input.
% 0.21/0.48 0:00:00.04 for the FLOTTER CNF translation.
% 0.21/0.48 0:00:00.00 for inferences.
% 0.21/0.48 0:00:00.00 for the backtracking.
% 0.21/0.48 0:00:00.01 for the reduction.
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 Here is a proof with depth 2, length 36 :
% 0.21/0.48 % SZS output start Refutation
% See solution above
% 0.21/0.48 Formulae used in the proof : m__ m__349 mTCTrans
% 0.21/0.48
%------------------------------------------------------------------------------