TSTP Solution File: SWC214-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC214-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 22:02:32 EDT 2022
% Result : Unsatisfiable 9.14s 9.33s
% Output : Refutation 9.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 29
% Syntax : Number of clauses : 88 ( 36 unt; 6 nHn; 88 RR)
% Number of literals : 198 ( 0 equ; 123 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC214-1.p',unknown),
[] ).
cnf(2,axiom,
ssList(sk2),
file('SWC214-1.p',unknown),
[] ).
cnf(5,axiom,
equal(sk4,sk2),
file('SWC214-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC214-1.p',unknown),
[] ).
cnf(7,axiom,
neq(sk2,nil),
file('SWC214-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ ssList(u)
| ~ strictorderedP(u)
| ~ frontsegP(sk4,u)
| ~ segmentP(u,sk3)
| ~ neq(sk3,u) ),
file('SWC214-1.p',unknown),
[] ).
cnf(11,axiom,
~ neq(sk1,nil),
file('SWC214-1.p',unknown),
[] ).
cnf(24,axiom,
ssList(skaf82(u)),
file('SWC214-1.p',unknown),
[] ).
cnf(58,axiom,
ssItem(skaf44(u)),
file('SWC214-1.p',unknown),
[] ).
cnf(67,axiom,
( ~ ssList(u)
| segmentP(u,nil) ),
file('SWC214-1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC214-1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC214-1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC214-1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC214-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC214-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC214-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC214-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC214-1.p',unknown),
[] ).
cnf(96,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC214-1.p',unknown),
[] ).
cnf(97,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC214-1.p',unknown),
[] ).
cnf(110,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),u) ),
file('SWC214-1.p',unknown),
[] ).
cnf(113,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| equal(u,v)
| neq(u,v) ),
file('SWC214-1.p',unknown),
[] ).
cnf(120,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC214-1.p',unknown),
[] ).
cnf(127,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC214-1.p',unknown),
[] ).
cnf(128,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| ~ neq(u,v)
| ~ equal(u,v) ),
file('SWC214-1.p',unknown),
[] ).
cnf(131,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| equal(app(cons(v,nil),u),cons(v,u)) ),
file('SWC214-1.p',unknown),
[] ).
cnf(155,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(v,w),u)
| frontsegP(u,v) ),
file('SWC214-1.p',unknown),
[] ).
cnf(168,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC214-1.p',unknown),
[] ).
cnf(190,axiom,
( ~ ssList(u)
| ~ duplicatefreeP(u)
| ~ ssItem(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssList(y)
| ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
file('SWC214-1.p',unknown),
[] ).
cnf(202,plain,
( ~ strictorderedP(u)
| ~ ssList(u)
| ~ segmentP(u,sk1)
| ~ neq(sk1,u)
| ~ frontsegP(sk2,u) ),
inference(rew,[status(thm),theory(equality)],[6,10,5]),
[iquote('0:Rew:6.0,10.4,6.0,10.3,5.0,10.2')] ).
cnf(266,plain,
( equal(nil,sk2)
| equal(cons(skaf83(sk2),skaf82(sk2)),sk2) ),
inference(res,[status(thm),theory(equality)],[2,120]),
[iquote('0:Res:2.0,120.0')] ).
cnf(345,plain,
( ~ ssItem(u)
| ssList(cons(u,sk2)) ),
inference(res,[status(thm),theory(equality)],[2,97]),
[iquote('0:Res:2.0,97.1')] ).
cnf(514,plain,
( ~ ssItem(u)
| ~ equal(cons(u,sk1),sk1) ),
inference(res,[status(thm),theory(equality)],[1,110]),
[iquote('0:Res:1.0,110.1')] ).
cnf(517,plain,
( ~ ssItem(u)
| ssList(cons(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,97]),
[iquote('0:Res:1.0,97.1')] ).
cnf(559,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[83]),
[iquote('1:Spt:83.1')] ).
cnf(562,plain,
ssList(cons(u,sk1)),
inference(mrr,[status(thm)],[517,559]),
[iquote('1:MRR:517.0,559.0')] ).
cnf(565,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[81,559]),
[iquote('1:MRR:81.0,559.0')] ).
cnf(566,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[80,559]),
[iquote('1:MRR:80.0,559.0')] ).
cnf(567,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[79,559]),
[iquote('1:MRR:79.0,559.0')] ).
cnf(568,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[78,559]),
[iquote('1:MRR:78.0,559.0')] ).
cnf(569,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[77,559]),
[iquote('1:MRR:77.0,559.0')] ).
cnf(570,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[76,559]),
[iquote('1:MRR:76.0,559.0')] ).
cnf(571,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[75,559]),
[iquote('1:MRR:75.0,559.0')] ).
cnf(573,plain,
~ equal(cons(u,sk1),sk1),
inference(mrr,[status(thm)],[514,559]),
[iquote('1:MRR:514.0,559.0')] ).
cnf(590,plain,
( equal(u,v)
| neq(u,v) ),
inference(mrr,[status(thm)],[113,559]),
[iquote('1:MRR:113.1,113.0,559.0')] ).
cnf(599,plain,
( ~ neq(u,v)
| ~ equal(u,v) ),
inference(mrr,[status(thm)],[128,559]),
[iquote('1:MRR:128.1,128.0,559.0')] ).
cnf(687,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[127,559]),
[iquote('1:MRR:127.1,559.0')] ).
cnf(688,plain,
( ~ ssList(u)
| equal(app(cons(v,nil),u),cons(v,u)) ),
inference(mrr,[status(thm)],[131,559]),
[iquote('1:MRR:131.1,559.0')] ).
cnf(1981,plain,
equal(nil,sk1),
inference(res,[status(thm),theory(equality)],[590,11]),
[iquote('1:Res:590.1,11.0')] ).
cnf(1999,plain,
neq(sk2,sk1),
inference(rew,[status(thm),theory(equality)],[1981,7]),
[iquote('1:Rew:1981.0,7.0')] ).
cnf(2002,plain,
cyclefreeP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1981,565]),
[iquote('1:Rew:1981.0,565.0')] ).
cnf(2003,plain,
totalorderP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1981,566]),
[iquote('1:Rew:1981.0,566.0')] ).
cnf(2004,plain,
strictorderP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1981,567]),
[iquote('1:Rew:1981.0,567.0')] ).
cnf(2005,plain,
totalorderedP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1981,568]),
[iquote('1:Rew:1981.0,568.0')] ).
cnf(2006,plain,
strictorderedP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1981,569]),
[iquote('1:Rew:1981.0,569.0')] ).
cnf(2007,plain,
duplicatefreeP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1981,570]),
[iquote('1:Rew:1981.0,570.0')] ).
cnf(2008,plain,
equalelemsP(cons(u,sk1)),
inference(rew,[status(thm),theory(equality)],[1981,571]),
[iquote('1:Rew:1981.0,571.0')] ).
cnf(2019,plain,
( ~ ssList(u)
| segmentP(u,sk1) ),
inference(rew,[status(thm),theory(equality)],[1981,67]),
[iquote('1:Rew:1981.0,67.1')] ).
cnf(2051,plain,
( ~ ssList(u)
| ~ equal(cons(v,sk1),u)
| singletonP(u) ),
inference(rew,[status(thm),theory(equality)],[1981,687]),
[iquote('1:Rew:1981.0,687.1')] ).
cnf(2052,plain,
( ~ ssList(u)
| equal(app(cons(v,sk1),u),cons(v,u)) ),
inference(rew,[status(thm),theory(equality)],[1981,688]),
[iquote('1:Rew:1981.0,688.1')] ).
cnf(2074,plain,
( ~ strictorderedP(u)
| ~ ssList(u)
| ~ neq(sk1,u)
| ~ frontsegP(sk2,u) ),
inference(mrr,[status(thm)],[202,2019]),
[iquote('1:MRR:202.2,2019.1')] ).
cnf(2113,plain,
( equal(sk2,sk1)
| equal(cons(skaf83(sk2),skaf82(sk2)),sk2) ),
inference(rew,[status(thm),theory(equality)],[1981,266]),
[iquote('1:Rew:1981.0,266.0')] ).
cnf(2645,plain,
~ equal(sk2,sk1),
inference(res,[status(thm),theory(equality)],[1999,599]),
[iquote('1:Res:1999.0,599.0')] ).
cnf(2802,plain,
( ~ ssList(cons(u,sk1))
| singletonP(cons(u,sk1)) ),
inference(eqr,[status(thm),theory(equality)],[2051]),
[iquote('1:EqR:2051.1')] ).
cnf(2803,plain,
singletonP(cons(u,sk1)),
inference(ssi,[status(thm)],[2802,562,2002,2003,2004,2005,2006,2007,2008]),
[iquote('1:SSi:2802.0,562.0,2002.0,2003.0,2004.0,2005.0,2006.0,2007.0,2008.0')] ).
cnf(4680,plain,
( ~ ssList(app(u,v))
| ~ ssList(u)
| ~ ssList(v)
| frontsegP(app(u,v),u) ),
inference(eqr,[status(thm),theory(equality)],[155]),
[iquote('0:EqR:155.3')] ).
cnf(4695,plain,
( ~ ssList(u)
| ~ ssList(v)
| frontsegP(app(u,v),u) ),
inference(ssi,[status(thm)],[4680,96]),
[iquote('0:SSi:4680.0,96.2')] ).
cnf(4834,plain,
( ~ ssList(u)
| ~ ssList(cons(v,sk1))
| ~ ssList(u)
| frontsegP(cons(v,u),cons(v,sk1)) ),
inference(spr,[status(thm),theory(equality)],[2052,4695]),
[iquote('1:SpR:2052.1,4695.2')] ).
cnf(4852,plain,
( ~ ssList(cons(u,sk1))
| ~ ssList(v)
| frontsegP(cons(u,v),cons(u,sk1)) ),
inference(obv,[status(thm),theory(equality)],[4834]),
[iquote('1:Obv:4834.0')] ).
cnf(4853,plain,
( ~ ssList(u)
| frontsegP(cons(v,u),cons(v,sk1)) ),
inference(ssi,[status(thm)],[4852,562,2002,2003,2004,2005,2006,2007,2008,2803]),
[iquote('1:SSi:4852.0,562.0,2002.0,2003.0,2004.0,2005.0,2006.0,2007.0,2008.0,2803.0')] ).
cnf(5106,plain,
equal(cons(skaf83(sk2),skaf82(sk2)),sk2),
inference(mrr,[status(thm)],[2113,2645]),
[iquote('1:MRR:2113.0,2645.0')] ).
cnf(5406,plain,
( ~ ssList(skaf82(sk2))
| frontsegP(sk2,cons(skaf83(sk2),sk1)) ),
inference(spr,[status(thm),theory(equality)],[5106,4853]),
[iquote('1:SpR:5106.0,4853.1')] ).
cnf(6174,plain,
frontsegP(sk2,cons(skaf83(sk2),sk1)),
inference(ssi,[status(thm)],[5406,24,2]),
[iquote('1:SSi:5406.0,24.0,2.0')] ).
cnf(6451,plain,
( ~ strictorderedP(cons(skaf83(sk2),sk1))
| ~ ssList(cons(skaf83(sk2),sk1))
| ~ neq(sk1,cons(skaf83(sk2),sk1)) ),
inference(res,[status(thm),theory(equality)],[6174,2074]),
[iquote('1:Res:6174.0,2074.3')] ).
cnf(6452,plain,
~ neq(sk1,cons(skaf83(sk2),sk1)),
inference(ssi,[status(thm)],[6451,562,2002,2003,2004,2005,2006,2007,2008,2803]),
[iquote('1:SSi:6451.1,6451.0,562.0,2002.0,2003.0,2004.0,2005.0,2006.0,2007.0,2008.0,2803.0,562.0,2002.0,2003.0,2004.0,2005.0,2006.0,2007.0,2008.0,2803.0')] ).
cnf(6484,plain,
equal(cons(skaf83(sk2),sk1),sk1),
inference(res,[status(thm),theory(equality)],[590,6452]),
[iquote('1:Res:590.1,6452.0')] ).
cnf(6485,plain,
$false,
inference(mrr,[status(thm)],[6484,573]),
[iquote('1:MRR:6484.0,573.0')] ).
cnf(6486,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[83]),
[iquote('1:Spt:6485.0,83.0,83.2')] ).
cnf(6499,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssList(y)
| ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
inference(mrr,[status(thm)],[190,6486]),
[iquote('1:MRR:190.1,6486.1')] ).
cnf(18586,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ ssList(cons(w,v))
| ~ ssList(u)
| ssList(cons(w,app(v,u))) ),
inference(spr,[status(thm),theory(equality)],[168,96]),
[iquote('0:SpR:168.3,96.2')] ).
cnf(18631,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[18586]),
[iquote('0:Obv:18586.0')] ).
cnf(18632,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[18631,97]),
[iquote('0:SSi:18631.2,97.2')] ).
cnf(19795,plain,
( ~ ssList(app(app(u,cons(v,w)),cons(v,x)))
| ~ ssItem(v)
| ~ ssList(u)
| ~ ssList(w)
| ~ ssList(x) ),
inference(eqr,[status(thm),theory(equality)],[6499]),
[iquote('1:EqR:6499.5')] ).
cnf(19823,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[19795,96,97]),
[iquote('1:SSi:19795.0,96.2,96.2,97.2,97.2')] ).
cnf(19824,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[18632,19823]),
[iquote('1:MRR:18632.3,19823.1')] ).
cnf(19827,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[19824]),
[iquote('1:Con:19824.2')] ).
cnf(19829,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[345,19827]),
[iquote('1:MRR:345.1,19827.0')] ).
cnf(19831,plain,
$false,
inference(unc,[status(thm)],[19829,58]),
[iquote('1:UnC:19829.0,58.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWC214-1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 08:52:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 9.14/9.33
% 9.14/9.33 SPASS V 3.9
% 9.14/9.33 SPASS beiseite: Proof found.
% 9.14/9.33 % SZS status Theorem
% 9.14/9.33 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.14/9.33 SPASS derived 12908 clauses, backtracked 6934 clauses, performed 138 splits and kept 12093 clauses.
% 9.14/9.33 SPASS allocated 89999 KBytes.
% 9.14/9.33 SPASS spent 0:00:07.35 on the problem.
% 9.14/9.33 0:00:00.04 for the input.
% 9.14/9.33 0:00:00.00 for the FLOTTER CNF translation.
% 9.14/9.33 0:00:00.11 for inferences.
% 9.14/9.33 0:00:00.19 for the backtracking.
% 9.14/9.33 0:00:06.78 for the reduction.
% 9.14/9.33
% 9.14/9.33
% 9.14/9.33 Here is a proof with depth 5, length 88 :
% 9.14/9.33 % SZS output start Refutation
% See solution above
% 9.14/9.33 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_10 co1_11 clause13 clause47 clause56 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause85 clause86 clause99 clause102 clause109 clause116 clause117 clause120 clause144 clause157 clause179
% 9.14/9.33
%------------------------------------------------------------------------------