TSTP Solution File: SWC336+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC336+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 22:03:24 EDT 2022
% Result : Theorem 15.70s 15.87s
% Output : Refutation 15.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of clauses : 54 ( 28 unt; 15 nHn; 54 RR)
% Number of literals : 120 ( 0 equ; 55 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(skc5),
file('SWC336+1.p',unknown),
[] ).
cnf(2,axiom,
ssList(skc4),
file('SWC336+1.p',unknown),
[] ).
cnf(5,axiom,
ssList(nil),
file('SWC336+1.p',unknown),
[] ).
cnf(6,axiom,
cyclefreeP(nil),
file('SWC336+1.p',unknown),
[] ).
cnf(7,axiom,
totalorderP(nil),
file('SWC336+1.p',unknown),
[] ).
cnf(8,axiom,
strictorderP(nil),
file('SWC336+1.p',unknown),
[] ).
cnf(9,axiom,
totalorderedP(nil),
file('SWC336+1.p',unknown),
[] ).
cnf(10,axiom,
strictorderedP(nil),
file('SWC336+1.p',unknown),
[] ).
cnf(11,axiom,
duplicatefreeP(nil),
file('SWC336+1.p',unknown),
[] ).
cnf(12,axiom,
equalelemsP(nil),
file('SWC336+1.p',unknown),
[] ).
cnf(51,axiom,
ssList(skf48(u,v)),
file('SWC336+1.p',unknown),
[] ).
cnf(52,axiom,
ssList(skf47(u,v)),
file('SWC336+1.p',unknown),
[] ).
cnf(53,axiom,
ssItem(skf46(u,v)),
file('SWC336+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ ssList(u)
| segmentP(u,nil) ),
file('SWC336+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ skP0(skc5,skc4)
| equal(nil,skc4) ),
file('SWC336+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ totalorderedP(skc4)
| ~ segmentP(skc5,skc4) ),
file('SWC336+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC336+1.p',unknown),
[] ).
cnf(87,axiom,
( skP0(u,v)
| equal(cons(skf46(u,v),nil),v) ),
file('SWC336+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ssList(cons(u,v)) ),
file('SWC336+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(v,u)) ),
file('SWC336+1.p',unknown),
[] ).
cnf(120,axiom,
( skP0(u,v)
| equal(app(app(skf47(u,v),v),skf48(v,u)),u) ),
file('SWC336+1.p',unknown),
[] ).
cnf(162,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(app(w,v),u),app(w,app(v,u))) ),
file('SWC336+1.p',unknown),
[] ).
cnf(188,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ equal(app(app(u,x),v),w)
| segmentP(w,x) ),
file('SWC336+1.p',unknown),
[] ).
cnf(190,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(tl(u),tl(v))
| ~ equal(hd(u),hd(v))
| equal(u,v)
| equal(nil,v)
| equal(nil,u) ),
file('SWC336+1.p',unknown),
[] ).
cnf(204,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ equal(app(x,app(u,w)),v)
| segmentP(v,u) ),
inference(rew,[status(thm),theory(equality)],[162,188]),
[iquote('0:Rew:162.3,188.4')] ).
cnf(288,plain,
( ~ ssList(u)
| ~ equal(tl(skc4),tl(u))
| ~ equal(hd(skc4),hd(u))
| equal(nil,u)
| equal(skc4,u)
| equal(nil,skc4) ),
inference(res,[status(thm),theory(equality)],[2,190]),
[iquote('0:Res:2.0,190.1')] ).
cnf(458,plain,
segmentP(skc5,nil),
inference(res,[status(thm),theory(equality)],[1,67]),
[iquote('0:Res:1.0,67.0')] ).
cnf(1622,plain,
equal(nil,skc4),
inference(spt,[spt(split,[position(s1)])],[288]),
[iquote('1:Spt:288.5')] ).
cnf(1628,plain,
totalorderedP(skc4),
inference(rew,[status(thm),theory(equality)],[1622,9]),
[iquote('1:Rew:1622.0,9.0')] ).
cnf(1638,plain,
segmentP(skc5,skc4),
inference(rew,[status(thm),theory(equality)],[1622,458]),
[iquote('1:Rew:1622.0,458.0')] ).
cnf(1713,plain,
~ segmentP(skc5,skc4),
inference(mrr,[status(thm)],[71,1628]),
[iquote('1:MRR:71.0,1628.0')] ).
cnf(1721,plain,
$false,
inference(mrr,[status(thm)],[1713,1638]),
[iquote('1:MRR:1713.0,1638.0')] ).
cnf(1797,plain,
~ equal(nil,skc4),
inference(spt,[spt(split,[position(sa)])],[1721,1622]),
[iquote('1:Spt:1721.0,288.5,1622.0')] ).
cnf(1798,plain,
( ~ ssList(u)
| ~ equal(tl(skc4),tl(u))
| ~ equal(hd(skc4),hd(u))
| equal(nil,u)
| equal(skc4,u) ),
inference(spt,[spt(split,[position(s2)])],[288]),
[iquote('1:Spt:1721.0,288.0,288.1,288.2,288.3,288.4')] ).
cnf(1804,plain,
~ skP0(skc5,skc4),
inference(mrr,[status(thm)],[70,1797]),
[iquote('1:MRR:70.1,1797.0')] ).
cnf(1823,plain,
~ totalorderedP(skc4),
inference(spt,[spt(split,[position(s2s1)])],[71]),
[iquote('2:Spt:71.0')] ).
cnf(1921,plain,
( ~ ssItem(skf46(u,v))
| ~ ssList(nil)
| skP0(u,v)
| ssList(v) ),
inference(spr,[status(thm),theory(equality)],[87,91]),
[iquote('0:SpR:87.1,91.2')] ).
cnf(1925,plain,
( ~ ssItem(skf46(u,v))
| skP0(u,v)
| totalorderedP(v) ),
inference(spr,[status(thm),theory(equality)],[87,76]),
[iquote('0:SpR:87.1,76.1')] ).
cnf(1933,plain,
( skP0(u,v)
| totalorderedP(v) ),
inference(ssi,[status(thm)],[1925,53]),
[iquote('0:SSi:1925.0,53.0')] ).
cnf(1937,plain,
( skP0(u,v)
| ssList(v) ),
inference(ssi,[status(thm)],[1921,12,11,10,9,8,7,6,5,53]),
[iquote('0:SSi:1921.1,1921.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0,5.0,53.0')] ).
cnf(1942,plain,
totalorderedP(skc4),
inference(res,[status(thm),theory(equality)],[1933,1804]),
[iquote('1:Res:1933.0,1804.0')] ).
cnf(1943,plain,
$false,
inference(mrr,[status(thm)],[1942,1823]),
[iquote('2:MRR:1942.0,1823.0')] ).
cnf(1944,plain,
totalorderedP(skc4),
inference(spt,[spt(split,[position(s2sa)])],[1943,1823]),
[iquote('2:Spt:1943.0,71.0,1823.0')] ).
cnf(1945,plain,
~ segmentP(skc5,skc4),
inference(spt,[spt(split,[position(s2s2)])],[71]),
[iquote('2:Spt:1943.0,71.1')] ).
cnf(4917,plain,
( ~ ssList(skf48(u,v))
| ~ ssList(u)
| ~ ssList(skf47(v,u))
| skP0(v,u)
| equal(app(skf47(v,u),app(u,skf48(u,v))),v) ),
inference(spr,[status(thm),theory(equality)],[162,120]),
[iquote('0:SpR:162.3,120.1')] ).
cnf(4978,plain,
( ~ ssList(u)
| skP0(v,u)
| equal(app(skf47(v,u),app(u,skf48(u,v))),v) ),
inference(ssi,[status(thm)],[4917,52,51]),
[iquote('0:SSi:4917.2,4917.0,52.0,51.0')] ).
cnf(4979,plain,
( skP0(u,v)
| equal(app(skf47(u,v),app(v,skf48(v,u))),u) ),
inference(mrr,[status(thm)],[4978,1937]),
[iquote('0:MRR:4978.0,1937.1')] ).
cnf(7068,plain,
( ~ ssList(u)
| ~ ssList(app(v,app(u,w)))
| ~ ssList(w)
| ~ ssList(v)
| segmentP(app(v,app(u,w)),u) ),
inference(eqr,[status(thm),theory(equality)],[204]),
[iquote('0:EqR:204.4')] ).
cnf(7105,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| segmentP(app(w,app(u,v)),u) ),
inference(ssi,[status(thm)],[7068,92]),
[iquote('0:SSi:7068.1,92.2,92.2')] ).
cnf(21086,plain,
( ~ ssList(u)
| ~ ssList(skf48(u,v))
| ~ ssList(skf47(v,u))
| skP0(v,u)
| segmentP(v,u) ),
inference(spr,[status(thm),theory(equality)],[4979,7105]),
[iquote('0:SpR:4979.1,7105.3')] ).
cnf(21117,plain,
( ~ ssList(u)
| skP0(v,u)
| segmentP(v,u) ),
inference(ssi,[status(thm)],[21086,52,51]),
[iquote('0:SSi:21086.2,21086.1,52.0,51.0')] ).
cnf(21118,plain,
( skP0(u,v)
| segmentP(u,v) ),
inference(mrr,[status(thm)],[21117,1937]),
[iquote('0:MRR:21117.0,1937.1')] ).
cnf(21192,plain,
segmentP(skc5,skc4),
inference(res,[status(thm),theory(equality)],[21118,1804]),
[iquote('1:Res:21118.0,1804.0')] ).
cnf(21193,plain,
$false,
inference(mrr,[status(thm)],[21192,1945]),
[iquote('2:MRR:21192.0,1945.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC336+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 12 07:59:08 EDT 2022
% 0.14/0.34 % CPUTime :
% 15.70/15.87
% 15.70/15.87 SPASS V 3.9
% 15.70/15.87 SPASS beiseite: Proof found.
% 15.70/15.87 % SZS status Theorem
% 15.70/15.87 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.70/15.87 SPASS derived 14173 clauses, backtracked 909 clauses, performed 51 splits and kept 6116 clauses.
% 15.70/15.87 SPASS allocated 118158 KBytes.
% 15.70/15.87 SPASS spent 0:0:14.04 on the problem.
% 15.70/15.87 0:00:00.04 for the input.
% 15.70/15.87 0:00:00.07 for the FLOTTER CNF translation.
% 15.70/15.87 0:00:00.26 for inferences.
% 15.70/15.87 0:00:00.57 for the backtracking.
% 15.70/15.87 0:0:12.80 for the reduction.
% 15.70/15.87
% 15.70/15.87
% 15.70/15.87 Here is a proof with depth 3, length 54 :
% 15.70/15.87 % SZS output start Refutation
% See solution above
% 15.70/15.87 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax57 ax65 ax16 ax26 ax82 ax7 ax77
% 15.70/15.87
%------------------------------------------------------------------------------