TSTP Solution File: SWC068+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC068+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 22:01:30 EDT 2022
% Result : Theorem 25.54s 25.73s
% Output : Refutation 25.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of clauses : 57 ( 29 unt; 7 nHn; 57 RR)
% Number of literals : 135 ( 0 equ; 80 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(skc5),
file('SWC068+1.p',unknown),
[] ).
cnf(2,axiom,
ssList(skc4),
file('SWC068+1.p',unknown),
[] ).
cnf(5,axiom,
ssList(nil),
file('SWC068+1.p',unknown),
[] ).
cnf(6,axiom,
cyclefreeP(nil),
file('SWC068+1.p',unknown),
[] ).
cnf(7,axiom,
totalorderP(nil),
file('SWC068+1.p',unknown),
[] ).
cnf(8,axiom,
strictorderP(nil),
file('SWC068+1.p',unknown),
[] ).
cnf(9,axiom,
totalorderedP(nil),
file('SWC068+1.p',unknown),
[] ).
cnf(10,axiom,
strictorderedP(nil),
file('SWC068+1.p',unknown),
[] ).
cnf(11,axiom,
duplicatefreeP(nil),
file('SWC068+1.p',unknown),
[] ).
cnf(12,axiom,
equalelemsP(nil),
file('SWC068+1.p',unknown),
[] ).
cnf(58,axiom,
equal(app(skc5,skc5),skc4),
file('SWC068+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ ssList(u)
| segmentP(u,u) ),
file('SWC068+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ equal(skc4,nil)
| ~ equal(skc5,nil) ),
file('SWC068+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC068+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssList(u)
| equal(app(u,nil),u) ),
file('SWC068+1.p',unknown),
[] ).
cnf(103,axiom,
( ~ ssList(u)
| ~ ssList(v)
| neq(v,u)
| equal(v,u) ),
file('SWC068+1.p',unknown),
[] ).
cnf(123,axiom,
( ~ ssList(u)
| ~ neq(u,nil)
| ~ segmentP(skc4,u)
| ~ segmentP(skc5,u) ),
file('SWC068+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(v,u),nil)
| equal(nil,u) ),
file('SWC068+1.p',unknown),
[] ).
cnf(155,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(app(w,v),u),app(w,app(v,u))) ),
file('SWC068+1.p',unknown),
[] ).
cnf(176,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ segmentP(u,v)
| segmentP(app(app(w,u),x),v) ),
file('SWC068+1.p',unknown),
[] ).
cnf(183,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('SWC068+1.p',unknown),
[] ).
cnf(195,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)],[155,176]),
[iquote('0:Rew:155.3,176.5')] ).
cnf(273,plain,
equal(app(nil,skc4),skc4),
inference(res,[status(thm),theory(equality)],[2,77]),
[iquote('0:Res:2.0,77.0')] ).
cnf(281,plain,
( ~ ssList(u)
| ~ equal(tl(skc4),tl(u))
| ~ equal(hd(skc4),hd(u))
| equal(nil,u)
| equal(skc4,u)
| equal(skc4,nil) ),
inference(res,[status(thm),theory(equality)],[2,183]),
[iquote('0:Res:2.0,183.1')] ).
cnf(420,plain,
( ~ ssList(u)
| neq(skc5,u)
| equal(skc5,u) ),
inference(res,[status(thm),theory(equality)],[1,103]),
[iquote('0:Res:1.0,103.0')] ).
cnf(446,plain,
equal(app(skc5,nil),skc5),
inference(res,[status(thm),theory(equality)],[1,78]),
[iquote('0:Res:1.0,78.0')] ).
cnf(451,plain,
segmentP(skc5,skc5),
inference(res,[status(thm),theory(equality)],[1,64]),
[iquote('0:Res:1.0,64.0')] ).
cnf(453,plain,
( ~ ssList(u)
| ~ equal(tl(skc5),tl(u))
| ~ equal(hd(skc5),hd(u))
| equal(nil,u)
| equal(skc5,u)
| equal(skc5,nil) ),
inference(res,[status(thm),theory(equality)],[1,183]),
[iquote('0:Res:1.0,183.1')] ).
cnf(486,plain,
( ~ ssList(u)
| ~ equal(app(u,skc5),nil)
| equal(skc5,nil) ),
inference(res,[status(thm),theory(equality)],[1,125]),
[iquote('0:Res:1.0,125.1')] ).
cnf(551,plain,
equal(skc4,nil),
inference(spt,[spt(split,[position(s1)])],[281]),
[iquote('1:Spt:281.5')] ).
cnf(558,plain,
( ~ equal(nil,nil)
| ~ equal(skc5,nil) ),
inference(rew,[status(thm),theory(equality)],[551,76]),
[iquote('1:Rew:551.0,76.0')] ).
cnf(665,plain,
equal(app(skc5,skc5),nil),
inference(rew,[status(thm),theory(equality)],[551,58]),
[iquote('1:Rew:551.0,58.0')] ).
cnf(717,plain,
~ equal(skc5,nil),
inference(obv,[status(thm),theory(equality)],[558]),
[iquote('1:Obv:558.0')] ).
cnf(725,plain,
( ~ ssList(u)
| ~ equal(app(u,skc5),nil) ),
inference(mrr,[status(thm)],[486,717]),
[iquote('1:MRR:486.2,717.0')] ).
cnf(938,plain,
( ~ ssList(skc5)
| ~ equal(nil,nil) ),
inference(spl,[status(thm),theory(equality)],[665,725]),
[iquote('1:SpL:665.0,725.1')] ).
cnf(1009,plain,
~ ssList(skc5),
inference(obv,[status(thm),theory(equality)],[938]),
[iquote('1:Obv:938.1')] ).
cnf(1010,plain,
$false,
inference(ssi,[status(thm)],[1009,1]),
[iquote('1:SSi:1009.0,1.0')] ).
cnf(1018,plain,
~ equal(skc4,nil),
inference(spt,[spt(split,[position(sa)])],[1010,551]),
[iquote('1:Spt:1010.0,281.5,551.0')] ).
cnf(1019,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)])],[281]),
[iquote('1:Spt:1010.0,281.0,281.1,281.2,281.3,281.4')] ).
cnf(1039,plain,
equal(skc5,nil),
inference(spt,[spt(split,[position(s2s1)])],[453]),
[iquote('2:Spt:453.5')] ).
cnf(1049,plain,
equal(app(nil,nil),nil),
inference(rew,[status(thm),theory(equality)],[1039,446]),
[iquote('2:Rew:1039.0,446.0')] ).
cnf(1188,plain,
equal(app(nil,nil),skc4),
inference(rew,[status(thm),theory(equality)],[1039,58]),
[iquote('2:Rew:1039.0,58.0')] ).
cnf(1195,plain,
equal(skc4,nil),
inference(rew,[status(thm),theory(equality)],[1049,1188]),
[iquote('2:Rew:1049.0,1188.0')] ).
cnf(1196,plain,
$false,
inference(mrr,[status(thm)],[1195,1018]),
[iquote('2:MRR:1195.0,1018.0')] ).
cnf(1298,plain,
~ equal(skc5,nil),
inference(spt,[spt(split,[position(s2sa)])],[1196,1039]),
[iquote('2:Spt:1196.0,453.5,1039.0')] ).
cnf(1299,plain,
( ~ ssList(u)
| ~ equal(tl(skc5),tl(u))
| ~ equal(hd(skc5),hd(u))
| equal(nil,u)
| equal(skc5,u) ),
inference(spt,[spt(split,[position(s2s2)])],[453]),
[iquote('2:Spt:1196.0,453.0,453.1,453.2,453.3,453.4')] ).
cnf(5803,plain,
( ~ ssList(skc5)
| ~ ssList(u)
| ~ ssList(v)
| ~ ssList(skc5)
| ~ segmentP(skc5,v)
| segmentP(app(u,skc4),v) ),
inference(spr,[status(thm),theory(equality)],[58,195]),
[iquote('0:SpR:58.0,195.5')] ).
cnf(5835,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(skc5)
| ~ segmentP(skc5,v)
| segmentP(app(u,skc4),v) ),
inference(obv,[status(thm),theory(equality)],[5803]),
[iquote('0:Obv:5803.0')] ).
cnf(25276,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ segmentP(skc5,v)
| segmentP(app(u,skc4),v) ),
inference(ssi,[status(thm)],[5835,1]),
[iquote('0:SSi:5835.2,1.0')] ).
cnf(26798,plain,
( ~ ssList(nil)
| ~ ssList(u)
| ~ segmentP(skc5,u)
| segmentP(skc4,u) ),
inference(spr,[status(thm),theory(equality)],[273,25276]),
[iquote('0:SpR:273.0,25276.3')] ).
cnf(26815,plain,
( ~ ssList(u)
| ~ segmentP(skc5,u)
| segmentP(skc4,u) ),
inference(ssi,[status(thm)],[26798,12,11,8,7,6,10,9,5]),
[iquote('0:SSi:26798.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0')] ).
cnf(26816,plain,
( ~ ssList(u)
| ~ neq(u,nil)
| ~ segmentP(skc5,u) ),
inference(mrr,[status(thm)],[123,26815]),
[iquote('0:MRR:123.2,26815.2')] ).
cnf(26850,plain,
( ~ ssList(skc5)
| ~ neq(skc5,nil) ),
inference(res,[status(thm),theory(equality)],[451,26816]),
[iquote('0:Res:451.0,26816.2')] ).
cnf(27590,plain,
~ neq(skc5,nil),
inference(ssi,[status(thm)],[26850,1]),
[iquote('0:SSi:26850.0,1.0')] ).
cnf(27824,plain,
( ~ ssList(nil)
| equal(skc5,nil) ),
inference(res,[status(thm),theory(equality)],[420,27590]),
[iquote('0:Res:420.1,27590.0')] ).
cnf(27827,plain,
equal(skc5,nil),
inference(ssi,[status(thm)],[27824,12,11,8,7,6,10,9,5]),
[iquote('0:SSi:27824.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0')] ).
cnf(27828,plain,
$false,
inference(mrr,[status(thm)],[27827,1298]),
[iquote('2:MRR:27827.0,1298.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWC068+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 12 12:51:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 25.54/25.73
% 25.54/25.73 SPASS V 3.9
% 25.54/25.73 SPASS beiseite: Proof found.
% 25.54/25.73 % SZS status Theorem
% 25.54/25.73 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.54/25.73 SPASS derived 16001 clauses, backtracked 7537 clauses, performed 102 splits and kept 10467 clauses.
% 25.54/25.73 SPASS allocated 120016 KBytes.
% 25.54/25.73 SPASS spent 0:0:22.77 on the problem.
% 25.54/25.73 0:00:00.04 for the input.
% 25.54/25.73 0:00:00.08 for the FLOTTER CNF translation.
% 25.54/25.73 0:00:00.30 for inferences.
% 25.54/25.73 0:00:00.61 for the backtracking.
% 25.54/25.73 0:0:21.42 for the reduction.
% 25.54/25.73
% 25.54/25.73
% 25.54/25.73 Here is a proof with depth 3, length 57 :
% 25.54/25.73 % SZS output start Refutation
% See solution above
% 25.54/25.73 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax55 ax28 ax84 ax15 ax83 ax82 ax56 ax77
% 25.54/25.73
%------------------------------------------------------------------------------