TSTP Solution File: SWC243-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC243-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 22:02:45 EDT 2022
% Result : Unsatisfiable 11.04s 11.27s
% Output : Refutation 11.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 31
% Syntax : Number of clauses : 68 ( 30 unt; 3 nHn; 68 RR)
% Number of literals : 152 ( 0 equ; 94 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; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC243-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC243-1.p',unknown),
[] ).
cnf(7,axiom,
totalorderedP(sk3),
file('SWC243-1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(nil,sk1),
file('SWC243-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(v,sk5(u,v,w)) ),
file('SWC243-1.p',unknown),
[] ).
cnf(14,axiom,
equalelemsP(nil),
file('SWC243-1.p',unknown),
[] ).
cnf(15,axiom,
duplicatefreeP(nil),
file('SWC243-1.p',unknown),
[] ).
cnf(16,axiom,
strictorderedP(nil),
file('SWC243-1.p',unknown),
[] ).
cnf(17,axiom,
totalorderedP(nil),
file('SWC243-1.p',unknown),
[] ).
cnf(18,axiom,
strictorderP(nil),
file('SWC243-1.p',unknown),
[] ).
cnf(19,axiom,
totalorderP(nil),
file('SWC243-1.p',unknown),
[] ).
cnf(20,axiom,
cyclefreeP(nil),
file('SWC243-1.p',unknown),
[] ).
cnf(21,axiom,
ssList(nil),
file('SWC243-1.p',unknown),
[] ).
cnf(26,axiom,
ssList(skaf82(u)),
file('SWC243-1.p',unknown),
[] ).
cnf(60,axiom,
ssItem(skaf44(u)),
file('SWC243-1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC243-1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC243-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC243-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC243-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC243-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC243-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC243-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC243-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC243-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC243-1.p',unknown),
[] ).
cnf(98,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC243-1.p',unknown),
[] ).
cnf(99,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC243-1.p',unknown),
[] ).
cnf(122,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC243-1.p',unknown),
[] ).
cnf(129,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC243-1.p',unknown),
[] ).
cnf(170,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC243-1.p',unknown),
[] ).
cnf(192,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('SWC243-1.p',unknown),
[] ).
cnf(199,plain,
totalorderedP(sk1),
inference(rew,[status(thm),theory(equality)],[6,7]),
[iquote('0:Rew:6.0,7.0')] ).
cnf(445,plain,
( equal(cons(skaf83(sk1),skaf82(sk1)),sk1)
| equal(nil,sk1) ),
inference(res,[status(thm),theory(equality)],[1,122]),
[iquote('0:Res:1.0,122.0')] ).
cnf(529,plain,
( ~ ssItem(u)
| ssList(cons(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,99]),
[iquote('0:Res:1.0,99.1')] ).
cnf(574,plain,
equal(cons(skaf83(sk1),skaf82(sk1)),sk1),
inference(mrr,[status(thm)],[445,8]),
[iquote('0:MRR:445.1,8.0')] ).
cnf(588,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[85]),
[iquote('1:Spt:85.1')] ).
cnf(593,plain,
~ memberP(nil,u),
inference(mrr,[status(thm)],[84,588]),
[iquote('1:MRR:84.0,588.0')] ).
cnf(594,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[83,588]),
[iquote('1:MRR:83.0,588.0')] ).
cnf(595,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[82,588]),
[iquote('1:MRR:82.0,588.0')] ).
cnf(596,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[81,588]),
[iquote('1:MRR:81.0,588.0')] ).
cnf(597,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[80,588]),
[iquote('1:MRR:80.0,588.0')] ).
cnf(598,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[79,588]),
[iquote('1:MRR:79.0,588.0')] ).
cnf(599,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[78,588]),
[iquote('1:MRR:78.0,588.0')] ).
cnf(600,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[77,588]),
[iquote('1:MRR:77.0,588.0')] ).
cnf(709,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[99,588]),
[iquote('1:MRR:99.1,588.0')] ).
cnf(714,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[129,588]),
[iquote('1:MRR:129.1,588.0')] ).
cnf(793,plain,
( ~ ssList(u)
| ~ ssList(v)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
inference(mrr,[status(thm)],[170,588]),
[iquote('1:MRR:170.2,588.0')] ).
cnf(798,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(v,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[10,588]),
[iquote('1:MRR:10.2,588.0')] ).
cnf(1771,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[714]),
[iquote('1:EqR:714.1')] ).
cnf(1772,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[1771,709,14,15,16,17,18,19,20,21,600,599,598,597,596,595,594]),
[iquote('1:SSi:1771.0,709.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,600.0,599.0,598.0,597.0,596.0,595.0,594.1')] ).
cnf(4967,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ equal(app(cons(u,nil),v),sk1)
| memberP(nil,sk5(v,nil,u)) ),
inference(spl,[status(thm),theory(equality)],[87,798]),
[iquote('1:SpL:87.1,798.2')] ).
cnf(4981,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ equal(cons(u,v),sk1)
| memberP(nil,sk5(v,nil,u)) ),
inference(rew,[status(thm),theory(equality)],[87,4967,793]),
[iquote('1:Rew:87.1,4967.3,793.2,4967.3')] ).
cnf(4982,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1)
| memberP(nil,sk5(u,nil,v)) ),
inference(ssi,[status(thm)],[4981,14,15,16,17,18,19,20,21,709,600,599,598,597,596,595,594,1772]),
[iquote('1:SSi:4981.2,4981.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,709.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.1,600.0,599.0,598.0,597.0,596.0,595.0,594.0,1772.0')] ).
cnf(4983,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1) ),
inference(mrr,[status(thm)],[4982,593]),
[iquote('1:MRR:4982.2,593.0')] ).
cnf(5396,plain,
( ~ ssList(skaf82(sk1))
| ~ equal(sk1,sk1) ),
inference(spl,[status(thm),theory(equality)],[574,4983]),
[iquote('1:SpL:574.0,4983.1')] ).
cnf(5590,plain,
~ ssList(skaf82(sk1)),
inference(obv,[status(thm),theory(equality)],[5396]),
[iquote('1:Obv:5396.1')] ).
cnf(5591,plain,
$false,
inference(ssi,[status(thm)],[5590,26,199,1]),
[iquote('1:SSi:5590.0,26.0,199.0,1.0')] ).
cnf(5667,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[85]),
[iquote('1:Spt:5591.0,85.0,85.2')] ).
cnf(5678,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)],[192,5667]),
[iquote('1:MRR:192.1,5667.1')] ).
cnf(21080,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)],[170,98]),
[iquote('0:SpR:170.3,98.2')] ).
cnf(21137,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[21080]),
[iquote('0:Obv:21080.0')] ).
cnf(21138,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[21137,99]),
[iquote('0:SSi:21137.2,99.2')] ).
cnf(23274,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)],[5678]),
[iquote('1:EqR:5678.5')] ).
cnf(23312,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[23274,98,99]),
[iquote('1:SSi:23274.0,98.2,98.2,99.2,99.2')] ).
cnf(23314,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[21138,23312]),
[iquote('1:MRR:21138.3,23312.1')] ).
cnf(23323,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[23314]),
[iquote('1:Con:23314.2')] ).
cnf(23325,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[529,23323]),
[iquote('1:MRR:529.1,23323.0')] ).
cnf(23335,plain,
$false,
inference(unc,[status(thm)],[23325,60]),
[iquote('1:UnC:23325.0,60.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC243-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 12 18:36:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 11.04/11.27
% 11.04/11.27 SPASS V 3.9
% 11.04/11.27 SPASS beiseite: Proof found.
% 11.04/11.27 % SZS status Theorem
% 11.04/11.27 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.04/11.27 SPASS derived 15360 clauses, backtracked 4269 clauses, performed 67 splits and kept 10492 clauses.
% 11.04/11.27 SPASS allocated 93141 KBytes.
% 11.04/11.27 SPASS spent 0:00:08.68 on the problem.
% 11.04/11.27 0:00:00.04 for the input.
% 11.04/11.27 0:00:00.00 for the FLOTTER CNF translation.
% 11.04/11.27 0:00:00.15 for inferences.
% 11.04/11.27 0:00:00.21 for the backtracking.
% 11.04/11.27 0:00:08.02 for the reduction.
% 11.04/11.27
% 11.04/11.27
% 11.04/11.27 Here is a proof with depth 2, length 68 :
% 11.04/11.27 % SZS output start Refutation
% See solution above
% 11.04/11.27 Formulae used in the proof : co1_1 co1_6 co1_7 co1_8 co1_10 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause13 clause47 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause74 clause85 clause86 clause109 clause116 clause157 clause179
% 11.04/11.28
%------------------------------------------------------------------------------