TSTP Solution File: SWC110+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC110+1 : TPTP v8.1.0. Released v2.4.0.
% 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 : Tue Jul 19 22:01:47 EDT 2022
% Result : Theorem 35.24s 35.46s
% Output : Refutation 35.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 26
% Syntax : Number of clauses : 68 ( 31 unt; 6 nHn; 68 RR)
% Number of literals : 146 ( 0 equ; 86 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(skc7),
file('SWC110+1.p',unknown),
[] ).
cnf(2,axiom,
ssList(skc6),
file('SWC110+1.p',unknown),
[] ).
cnf(3,axiom,
ssList(skc5),
file('SWC110+1.p',unknown),
[] ).
cnf(4,axiom,
equalelemsP(skc5),
file('SWC110+1.p',unknown),
[] ).
cnf(7,axiom,
ssList(nil),
file('SWC110+1.p',unknown),
[] ).
cnf(8,axiom,
cyclefreeP(nil),
file('SWC110+1.p',unknown),
[] ).
cnf(9,axiom,
totalorderP(nil),
file('SWC110+1.p',unknown),
[] ).
cnf(10,axiom,
strictorderP(nil),
file('SWC110+1.p',unknown),
[] ).
cnf(11,axiom,
totalorderedP(nil),
file('SWC110+1.p',unknown),
[] ).
cnf(12,axiom,
strictorderedP(nil),
file('SWC110+1.p',unknown),
[] ).
cnf(13,axiom,
duplicatefreeP(nil),
file('SWC110+1.p',unknown),
[] ).
cnf(14,axiom,
equalelemsP(nil),
file('SWC110+1.p',unknown),
[] ).
cnf(60,axiom,
equal(app(skc5,skc7),skc6),
file('SWC110+1.p',unknown),
[] ).
cnf(61,axiom,
( skP0(u,v)
| equal(nil,v) ),
file('SWC110+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ ssList(u)
| segmentP(u,u) ),
file('SWC110+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ ssList(u)
| segmentP(u,nil) ),
file('SWC110+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ equal(skc5,nil)
| equal(skc6,nil) ),
file('SWC110+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ skP0(skc5,skc6)
| neq(skc6,nil) ),
file('SWC110+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ equal(nil,u)
| skP0(u,v) ),
file('SWC110+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC110+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ skP0(skc5,skc6)
| ~ segmentP(skc6,skc5)
| ~ neq(skc5,nil) ),
file('SWC110+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ ssList(u)
| ~ ssList(v)
| neq(v,u)
| equal(v,u) ),
file('SWC110+1.p',unknown),
[] ).
cnf(131,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(v,u),nil)
| equal(nil,v) ),
file('SWC110+1.p',unknown),
[] ).
cnf(154,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ strictorderedP(cons(v,u))
| lt(v,hd(u))
| equal(nil,u) ),
file('SWC110+1.p',unknown),
[] ).
cnf(160,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(app(w,v),u),app(w,app(v,u))) ),
file('SWC110+1.p',unknown),
[] ).
cnf(181,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ segmentP(u,v)
| segmentP(app(app(w,u),x),v) ),
file('SWC110+1.p',unknown),
[] ).
cnf(201,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ segmentP(x,w)
| segmentP(app(v,app(x,u)),w) ),
inference(rew,[status(thm),theory(equality)],[160,181]),
[iquote('0:Rew:160.3,181.5')] ).
cnf(250,plain,
( ~ ssList(u)
| ~ equal(app(skc5,u),nil)
| equal(skc5,nil) ),
inference(res,[status(thm),theory(equality)],[3,131]),
[iquote('0:Res:3.0,131.0')] ).
cnf(255,plain,
( ~ ssList(u)
| neq(skc5,u)
| equal(skc5,u) ),
inference(res,[status(thm),theory(equality)],[3,109]),
[iquote('0:Res:3.0,109.0')] ).
cnf(286,plain,
segmentP(skc5,skc5),
inference(res,[status(thm),theory(equality)],[3,67]),
[iquote('0:Res:3.0,67.0')] ).
cnf(287,plain,
segmentP(skc5,nil),
inference(res,[status(thm),theory(equality)],[3,68]),
[iquote('0:Res:3.0,68.0')] ).
cnf(312,plain,
( ~ ssItem(u)
| ~ strictorderedP(cons(u,skc5))
| lt(u,hd(skc5))
| equal(skc5,nil) ),
inference(res,[status(thm),theory(equality)],[3,154]),
[iquote('0:Res:3.0,154.1')] ).
cnf(453,plain,
equal(app(nil,skc6),skc6),
inference(res,[status(thm),theory(equality)],[2,82]),
[iquote('0:Res:2.0,82.0')] ).
cnf(485,plain,
( ~ ssItem(u)
| ~ strictorderedP(cons(u,skc6))
| lt(u,hd(skc6))
| equal(skc6,nil) ),
inference(res,[status(thm),theory(equality)],[2,154]),
[iquote('0:Res:2.0,154.1')] ).
cnf(560,plain,
equal(skc5,nil),
inference(spt,[spt(split,[position(s1)])],[312]),
[iquote('1:Spt:312.3')] ).
cnf(563,plain,
( ~ skP0(nil,skc6)
| ~ segmentP(skc6,skc5)
| ~ neq(skc5,nil) ),
inference(rew,[status(thm),theory(equality)],[560,106]),
[iquote('1:Rew:560.0,106.0')] ).
cnf(564,plain,
( ~ skP0(nil,skc6)
| neq(skc6,nil) ),
inference(rew,[status(thm),theory(equality)],[560,71]),
[iquote('1:Rew:560.0,71.0')] ).
cnf(569,plain,
( ~ equal(nil,nil)
| equal(skc6,nil) ),
inference(rew,[status(thm),theory(equality)],[560,70]),
[iquote('1:Rew:560.0,70.0')] ).
cnf(667,plain,
segmentP(nil,nil),
inference(rew,[status(thm),theory(equality)],[560,287]),
[iquote('1:Rew:560.0,287.0')] ).
cnf(719,plain,
equal(skc6,nil),
inference(obv,[status(thm),theory(equality)],[569]),
[iquote('1:Obv:569.0')] ).
cnf(871,plain,
( ~ skP0(nil,nil)
| neq(skc6,nil) ),
inference(rew,[status(thm),theory(equality)],[719,564]),
[iquote('1:Rew:719.0,564.0')] ).
cnf(892,plain,
( ~ skP0(nil,nil)
| neq(nil,nil) ),
inference(rew,[status(thm),theory(equality)],[719,871]),
[iquote('1:Rew:719.0,871.1')] ).
cnf(927,plain,
( ~ skP0(nil,nil)
| ~ segmentP(nil,nil)
| ~ neq(nil,nil) ),
inference(rew,[status(thm),theory(equality)],[560,563,719]),
[iquote('1:Rew:560.0,563.2,719.0,563.1,560.0,563.1,719.0,563.0')] ).
cnf(928,plain,
~ skP0(nil,nil),
inference(mrr,[status(thm)],[927,667,892]),
[iquote('1:MRR:927.1,927.2,667.0,892.1')] ).
cnf(1076,plain,
~ equal(nil,nil),
inference(res,[status(thm),theory(equality)],[72,928]),
[iquote('1:Res:72.1,928.0')] ).
cnf(1077,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1076]),
[iquote('1:Obv:1076.0')] ).
cnf(1078,plain,
~ equal(skc5,nil),
inference(spt,[spt(split,[position(sa)])],[1077,560]),
[iquote('1:Spt:1077.0,312.3,560.0')] ).
cnf(1079,plain,
( ~ ssItem(u)
| ~ strictorderedP(cons(u,skc5))
| lt(u,hd(skc5)) ),
inference(spt,[spt(split,[position(s2)])],[312]),
[iquote('1:Spt:1077.0,312.0,312.1,312.2')] ).
cnf(1088,plain,
( ~ ssList(u)
| ~ equal(app(skc5,u),nil) ),
inference(mrr,[status(thm)],[250,1078]),
[iquote('1:MRR:250.2,1078.0')] ).
cnf(1093,plain,
equal(skc6,nil),
inference(spt,[spt(split,[position(s2s1)])],[485]),
[iquote('2:Spt:485.3')] ).
cnf(1101,plain,
equal(app(skc5,skc7),nil),
inference(rew,[status(thm),theory(equality)],[1093,60]),
[iquote('2:Rew:1093.0,60.0')] ).
cnf(1408,plain,
( ~ ssList(skc7)
| ~ equal(nil,nil) ),
inference(spl,[status(thm),theory(equality)],[1101,1088]),
[iquote('2:SpL:1101.0,1088.1')] ).
cnf(1411,plain,
~ ssList(skc7),
inference(obv,[status(thm),theory(equality)],[1408]),
[iquote('2:Obv:1408.1')] ).
cnf(1412,plain,
$false,
inference(ssi,[status(thm)],[1411,1]),
[iquote('2:SSi:1411.0,1.0')] ).
cnf(1413,plain,
~ equal(skc6,nil),
inference(spt,[spt(split,[position(s2sa)])],[1412,1093]),
[iquote('2:Spt:1412.0,485.3,1093.0')] ).
cnf(1414,plain,
( ~ ssItem(u)
| ~ strictorderedP(cons(u,skc6))
| lt(u,hd(skc6)) ),
inference(spt,[spt(split,[position(s2s2)])],[485]),
[iquote('2:Spt:1412.0,485.0,485.1,485.2')] ).
cnf(36845,plain,
( ~ ssList(skc7)
| ~ ssList(u)
| ~ ssList(v)
| ~ ssList(skc5)
| ~ segmentP(skc5,v)
| segmentP(app(u,skc6),v) ),
inference(spr,[status(thm),theory(equality)],[60,201]),
[iquote('0:SpR:60.0,201.5')] ).
cnf(37386,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ segmentP(skc5,v)
| segmentP(app(u,skc6),v) ),
inference(ssi,[status(thm)],[36845,3,4,1]),
[iquote('0:SSi:36845.3,36845.0,3.0,4.0,1.0')] ).
cnf(40222,plain,
( ~ ssList(nil)
| ~ ssList(u)
| ~ segmentP(skc5,u)
| segmentP(skc6,u) ),
inference(spr,[status(thm),theory(equality)],[453,37386]),
[iquote('0:SpR:453.0,37386.3')] ).
cnf(40238,plain,
( ~ ssList(u)
| ~ segmentP(skc5,u)
| segmentP(skc6,u) ),
inference(ssi,[status(thm)],[40222,14,13,10,9,8,12,11,7]),
[iquote('0:SSi:40222.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0')] ).
cnf(40256,plain,
( ~ ssList(skc5)
| ~ segmentP(skc5,skc5)
| ~ skP0(skc5,skc6)
| ~ neq(skc5,nil) ),
inference(res,[status(thm),theory(equality)],[40238,106]),
[iquote('0:Res:40238.2,106.1')] ).
cnf(40984,plain,
( ~ segmentP(skc5,skc5)
| ~ skP0(skc5,skc6)
| ~ neq(skc5,nil) ),
inference(ssi,[status(thm)],[40256,3,4]),
[iquote('0:SSi:40256.0,3.0,4.0')] ).
cnf(40985,plain,
( ~ skP0(skc5,skc6)
| ~ neq(skc5,nil) ),
inference(mrr,[status(thm)],[40984,286]),
[iquote('0:MRR:40984.0,286.0')] ).
cnf(41159,plain,
( ~ ssList(nil)
| ~ skP0(skc5,skc6)
| equal(skc5,nil) ),
inference(res,[status(thm),theory(equality)],[255,40985]),
[iquote('0:Res:255.1,40985.1')] ).
cnf(41162,plain,
( ~ skP0(skc5,skc6)
| equal(skc5,nil) ),
inference(ssi,[status(thm)],[41159,14,13,10,9,8,12,11,7]),
[iquote('0:SSi:41159.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0')] ).
cnf(41163,plain,
~ skP0(skc5,skc6),
inference(mrr,[status(thm)],[41162,1078]),
[iquote('1:MRR:41162.1,1078.0')] ).
cnf(41170,plain,
equal(skc6,nil),
inference(res,[status(thm),theory(equality)],[61,41163]),
[iquote('1:Res:61.0,41163.0')] ).
cnf(41171,plain,
$false,
inference(mrr,[status(thm)],[41170,1413]),
[iquote('2:MRR:41170.0,1413.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC110+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 12 21:58:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 35.24/35.46
% 35.24/35.46 SPASS V 3.9
% 35.24/35.46 SPASS beiseite: Proof found.
% 35.24/35.46 % SZS status Theorem
% 35.24/35.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.24/35.46 SPASS derived 27227 clauses, backtracked 9117 clauses, performed 111 splits and kept 13179 clauses.
% 35.24/35.46 SPASS allocated 129559 KBytes.
% 35.24/35.46 SPASS spent 0:0:28.86 on the problem.
% 35.24/35.46 0:00:00.04 for the input.
% 35.24/35.46 0:00:00.07 for the FLOTTER CNF translation.
% 35.24/35.46 0:00:00.43 for inferences.
% 35.24/35.46 0:00:00.69 for the backtracking.
% 35.24/35.46 0:0:27.18 for the reduction.
% 35.24/35.46
% 35.24/35.46
% 35.24/35.46 Here is a proof with depth 5, length 68 :
% 35.24/35.46 % SZS output start Refutation
% See solution above
% 35.24/35.46 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax55 ax57 ax28 ax15 ax83 ax70 ax82 ax56
% 35.24/35.46
%------------------------------------------------------------------------------