TSTP Solution File: SWC092+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC092+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 22:01:39 EDT 2022
% Result : Theorem 77.36s 77.55s
% Output : Refutation 77.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 33
% Syntax : Number of clauses : 73 ( 40 unt; 6 nHn; 73 RR)
% Number of literals : 159 ( 0 equ; 95 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(skc7),
file('SWC092+1.p',unknown),
[] ).
cnf(2,axiom,
ssList(skc6),
file('SWC092+1.p',unknown),
[] ).
cnf(3,axiom,
ssList(skc5),
file('SWC092+1.p',unknown),
[] ).
cnf(4,axiom,
strictorderedP(skc5),
file('SWC092+1.p',unknown),
[] ).
cnf(7,axiom,
ssList(nil),
file('SWC092+1.p',unknown),
[] ).
cnf(8,axiom,
cyclefreeP(nil),
file('SWC092+1.p',unknown),
[] ).
cnf(9,axiom,
totalorderP(nil),
file('SWC092+1.p',unknown),
[] ).
cnf(10,axiom,
strictorderP(nil),
file('SWC092+1.p',unknown),
[] ).
cnf(11,axiom,
totalorderedP(nil),
file('SWC092+1.p',unknown),
[] ).
cnf(12,axiom,
strictorderedP(nil),
file('SWC092+1.p',unknown),
[] ).
cnf(13,axiom,
duplicatefreeP(nil),
file('SWC092+1.p',unknown),
[] ).
cnf(14,axiom,
equalelemsP(nil),
file('SWC092+1.p',unknown),
[] ).
cnf(15,axiom,
neq(skc6,nil),
file('SWC092+1.p',unknown),
[] ).
cnf(32,axiom,
ssList(skf69(u)),
file('SWC092+1.p',unknown),
[] ).
cnf(33,axiom,
ssList(skf68(u)),
file('SWC092+1.p',unknown),
[] ).
cnf(34,axiom,
ssList(skf67(u)),
file('SWC092+1.p',unknown),
[] ).
cnf(35,axiom,
ssItem(skf66(u)),
file('SWC092+1.p',unknown),
[] ).
cnf(36,axiom,
ssItem(skf65(u)),
file('SWC092+1.p',unknown),
[] ).
cnf(61,axiom,
equal(app(skc5,skc7),skc6),
file('SWC092+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ ssList(u)
| segmentP(u,u) ),
file('SWC092+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ ssList(u)
| segmentP(u,nil) ),
file('SWC092+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ equal(skc5,nil)
| equal(skc6,nil) ),
file('SWC092+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC092+1.p',unknown),
[] ).
cnf(90,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(v,u)) ),
file('SWC092+1.p',unknown),
[] ).
cnf(101,axiom,
( ~ ssList(u)
| ~ leq(skf65(u),skf66(u))
| totalorderedP(u) ),
file('SWC092+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ ssList(u)
| ~ ssList(v)
| neq(v,u)
| equal(v,u) ),
file('SWC092+1.p',unknown),
[] ).
cnf(117,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| ~ lt(v,u)
| leq(v,u) ),
file('SWC092+1.p',unknown),
[] ).
cnf(126,axiom,
( ~ ssList(u)
| ~ neq(u,nil)
| ~ segmentP(skc5,u)
| ~ segmentP(skc6,u) ),
file('SWC092+1.p',unknown),
[] ).
cnf(152,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ strictorderedP(cons(v,u))
| lt(v,hd(u))
| equal(nil,u) ),
file('SWC092+1.p',unknown),
[] ).
cnf(158,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(app(w,v),u),app(w,app(v,u))) ),
file('SWC092+1.p',unknown),
[] ).
cnf(173,axiom,
( ~ ssList(u)
| totalorderedP(u)
| equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u) ),
file('SWC092+1.p',unknown),
[] ).
cnf(184,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ equal(app(app(u,x),v),w)
| segmentP(w,x) ),
file('SWC092+1.p',unknown),
[] ).
cnf(190,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssItem(y)
| ~ ssItem(z)
| ~ strictorderedP(u)
| ~ equal(app(app(x,cons(z,w)),cons(y,v)),u)
| lt(z,y) ),
file('SWC092+1.p',unknown),
[] ).
cnf(200,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)],[158,184]),
[iquote('0:Rew:158.3,184.4')] ).
cnf(222,plain,
( totalorderedP(skc5)
| equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5) ),
inference(res,[status(thm),theory(equality)],[3,173]),
[iquote('0:Res:3.0,173.0')] ).
cnf(247,plain,
( ~ neq(skc5,nil)
| ~ segmentP(skc6,skc5)
| ~ segmentP(skc5,skc5) ),
inference(res,[status(thm),theory(equality)],[3,126]),
[iquote('0:Res:3.0,126.0')] ).
cnf(255,plain,
( ~ ssList(u)
| neq(skc5,u)
| equal(skc5,u) ),
inference(res,[status(thm),theory(equality)],[3,106]),
[iquote('0:Res:3.0,106.0')] ).
cnf(264,plain,
( ~ leq(skf65(skc5),skf66(skc5))
| totalorderedP(skc5) ),
inference(res,[status(thm),theory(equality)],[3,101]),
[iquote('0:Res:3.0,101.0')] ).
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(421,plain,
( ~ neq(skc6,nil)
| ~ segmentP(skc6,skc6)
| ~ segmentP(skc5,skc6) ),
inference(res,[status(thm),theory(equality)],[2,126]),
[iquote('0:Res:2.0,126.0')] ).
cnf(454,plain,
equal(app(nil,skc6),skc6),
inference(res,[status(thm),theory(equality)],[2,80]),
[iquote('0:Res:2.0,80.0')] ).
cnf(460,plain,
segmentP(skc6,skc6),
inference(res,[status(thm),theory(equality)],[2,67]),
[iquote('0:Res:2.0,67.0')] ).
cnf(486,plain,
( ~ ssItem(u)
| ~ strictorderedP(cons(u,skc6))
| lt(u,hd(skc6))
| equal(skc6,nil) ),
inference(res,[status(thm),theory(equality)],[2,152]),
[iquote('0:Res:2.0,152.1')] ).
cnf(552,plain,
( ~ segmentP(skc6,skc5)
| ~ neq(skc5,nil) ),
inference(mrr,[status(thm)],[247,286]),
[iquote('0:MRR:247.2,286.0')] ).
cnf(553,plain,
~ segmentP(skc5,skc6),
inference(mrr,[status(thm)],[421,15,460]),
[iquote('0:MRR:421.0,421.1,15.0,460.0')] ).
cnf(564,plain,
equal(skc6,nil),
inference(spt,[spt(split,[position(s1)])],[486]),
[iquote('1:Spt:486.3')] ).
cnf(677,plain,
~ segmentP(skc5,nil),
inference(rew,[status(thm),theory(equality)],[564,553]),
[iquote('1:Rew:564.0,553.0')] ).
cnf(722,plain,
$false,
inference(mrr,[status(thm)],[677,287]),
[iquote('1:MRR:677.0,287.0')] ).
cnf(841,plain,
~ equal(skc6,nil),
inference(spt,[spt(split,[position(sa)])],[722,564]),
[iquote('1:Spt:722.0,486.3,564.0')] ).
cnf(842,plain,
( ~ ssItem(u)
| ~ strictorderedP(cons(u,skc6))
| lt(u,hd(skc6)) ),
inference(spt,[spt(split,[position(s2)])],[486]),
[iquote('1:Spt:722.0,486.0,486.1,486.2')] ).
cnf(848,plain,
~ equal(skc5,nil),
inference(mrr,[status(thm)],[70,841]),
[iquote('1:MRR:70.1,841.0')] ).
cnf(870,plain,
totalorderedP(skc5),
inference(spt,[spt(split,[position(s2s1)])],[222]),
[iquote('2:Spt:222.0')] ).
cnf(39236,plain,
( ~ ssList(skc5)
| ~ ssList(u)
| ~ ssList(skc7)
| ~ ssList(v)
| ~ equal(app(v,skc6),u)
| segmentP(u,skc5) ),
inference(spl,[status(thm),theory(equality)],[61,200]),
[iquote('0:SpL:61.0,200.4')] ).
cnf(45398,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(v,skc6),u)
| segmentP(u,skc5) ),
inference(ssi,[status(thm)],[39236,1,870,4,3]),
[iquote('2:SSi:39236.2,39236.0,1.0,870.0,4.0,3.0')] ).
cnf(51619,plain,
( ~ ssList(app(u,skc6))
| ~ ssList(u)
| segmentP(app(u,skc6),skc5) ),
inference(eqr,[status(thm),theory(equality)],[45398]),
[iquote('2:EqR:45398.2')] ).
cnf(62488,plain,
( ~ ssList(u)
| segmentP(app(u,skc6),skc5) ),
inference(ssi,[status(thm)],[51619,90,2]),
[iquote('2:SSi:51619.0,90.0,2.2')] ).
cnf(64559,plain,
( ~ ssList(nil)
| segmentP(skc6,skc5) ),
inference(spr,[status(thm),theory(equality)],[454,62488]),
[iquote('2:SpR:454.0,62488.1')] ).
cnf(64565,plain,
segmentP(skc6,skc5),
inference(ssi,[status(thm)],[64559,14,13,10,9,8,12,11,7]),
[iquote('2:SSi:64559.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0')] ).
cnf(64566,plain,
~ neq(skc5,nil),
inference(mrr,[status(thm)],[552,64565]),
[iquote('2:MRR:552.0,64565.0')] ).
cnf(64581,plain,
( ~ ssList(nil)
| equal(skc5,nil) ),
inference(res,[status(thm),theory(equality)],[255,64566]),
[iquote('2:Res:255.1,64566.0')] ).
cnf(64584,plain,
equal(skc5,nil),
inference(ssi,[status(thm)],[64581,14,13,10,9,8,12,11,7]),
[iquote('2:SSi:64581.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0')] ).
cnf(64585,plain,
$false,
inference(mrr,[status(thm)],[64584,848]),
[iquote('2:MRR:64584.0,848.0')] ).
cnf(64589,plain,
~ totalorderedP(skc5),
inference(spt,[spt(split,[position(s2sa)])],[64585,870]),
[iquote('2:Spt:64585.0,222.0,870.0')] ).
cnf(64590,plain,
equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5),
inference(spt,[spt(split,[position(s2s2)])],[222]),
[iquote('2:Spt:64585.0,222.1')] ).
cnf(64591,plain,
~ leq(skf65(skc5),skf66(skc5)),
inference(mrr,[status(thm)],[264,64589]),
[iquote('2:MRR:264.1,64589.0')] ).
cnf(64790,plain,
( ~ ssList(u)
| ~ ssList(skf69(skc5))
| ~ ssList(skf68(skc5))
| ~ ssList(skf67(skc5))
| ~ ssItem(skf66(skc5))
| ~ ssItem(skf65(skc5))
| ~ strictorderedP(u)
| ~ equal(skc5,u)
| lt(skf65(skc5),skf66(skc5)) ),
inference(spl,[status(thm),theory(equality)],[64590,190]),
[iquote('2:SpL:64590.0,190.7')] ).
cnf(64813,plain,
( ~ ssList(u)
| ~ strictorderedP(u)
| ~ equal(skc5,u)
| lt(skf65(skc5),skf66(skc5)) ),
inference(ssi,[status(thm)],[64790,36,4,3,35,34,33,32]),
[iquote('2:SSi:64790.5,64790.4,64790.3,64790.2,64790.1,36.0,4.0,3.0,35.0,4.0,3.0,34.0,4.0,3.0,33.0,4.0,3.0,32.0,4.0,3.0')] ).
cnf(64880,plain,
( ~ ssItem(skf66(skc5))
| ~ ssItem(skf65(skc5))
| ~ lt(skf65(skc5),skf66(skc5)) ),
inference(res,[status(thm),theory(equality)],[117,64591]),
[iquote('2:Res:117.3,64591.0')] ).
cnf(67622,plain,
~ lt(skf65(skc5),skf66(skc5)),
inference(ssi,[status(thm)],[64880,36,4,3,35]),
[iquote('2:SSi:64880.1,64880.0,36.0,4.0,3.0,35.0,4.0,3.0')] ).
cnf(67623,plain,
( ~ ssList(u)
| ~ strictorderedP(u)
| ~ equal(skc5,u) ),
inference(mrr,[status(thm)],[64813,67622]),
[iquote('2:MRR:64813.3,67622.0')] ).
cnf(67941,plain,
~ equal(skc5,skc5),
inference(ems,[status(thm)],[67623,3,4]),
[iquote('2:EmS:67623.0,67623.1,3.0,4.0')] ).
cnf(67943,plain,
$false,
inference(obv,[status(thm),theory(equality)],[67941]),
[iquote('2:Obv:67941.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC092+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n010.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 21:15:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 77.36/77.55
% 77.36/77.55 SPASS V 3.9
% 77.36/77.55 SPASS beiseite: Proof found.
% 77.36/77.55 % SZS status Theorem
% 77.36/77.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 77.36/77.55 SPASS derived 46441 clauses, backtracked 24317 clauses, performed 154 splits and kept 26512 clauses.
% 77.36/77.55 SPASS allocated 147053 KBytes.
% 77.36/77.55 SPASS spent 0:0:57.40 on the problem.
% 77.36/77.55 0:00:00.04 for the input.
% 77.36/77.55 0:00:00.07 for the FLOTTER CNF translation.
% 77.36/77.55 0:00:00.67 for inferences.
% 77.36/77.55 0:00:01.08 for the backtracking.
% 77.36/77.55 0:0:54.95 for the reduction.
% 77.36/77.55
% 77.36/77.55
% 77.36/77.55 Here is a proof with depth 4, length 73 :
% 77.36/77.55 % SZS output start Refutation
% See solution above
% 77.36/77.55 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax11 ax2 ax55 ax57 ax28 ax26 ax15 ax93 ax70 ax82 ax7 ax12
% 77.36/77.55
%------------------------------------------------------------------------------