TSTP Solution File: SWC230-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC230-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 22:02:39 EDT 2022
% Result : Unsatisfiable 11.61s 11.80s
% Output : Refutation 11.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 29
% Syntax : Number of clauses : 65 ( 27 unt; 3 nHn; 65 RR)
% Number of literals : 149 ( 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 : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC230-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(nil,sk1),
file('SWC230-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(v,sk5(u,v,w)) ),
file('SWC230-1.p',unknown),
[] ).
cnf(14,axiom,
equalelemsP(nil),
file('SWC230-1.p',unknown),
[] ).
cnf(15,axiom,
duplicatefreeP(nil),
file('SWC230-1.p',unknown),
[] ).
cnf(16,axiom,
strictorderedP(nil),
file('SWC230-1.p',unknown),
[] ).
cnf(17,axiom,
totalorderedP(nil),
file('SWC230-1.p',unknown),
[] ).
cnf(18,axiom,
strictorderP(nil),
file('SWC230-1.p',unknown),
[] ).
cnf(19,axiom,
totalorderP(nil),
file('SWC230-1.p',unknown),
[] ).
cnf(20,axiom,
cyclefreeP(nil),
file('SWC230-1.p',unknown),
[] ).
cnf(21,axiom,
ssList(nil),
file('SWC230-1.p',unknown),
[] ).
cnf(26,axiom,
ssList(skaf82(u)),
file('SWC230-1.p',unknown),
[] ).
cnf(60,axiom,
ssItem(skaf44(u)),
file('SWC230-1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC230-1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC230-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC230-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC230-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC230-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC230-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC230-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC230-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC230-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC230-1.p',unknown),
[] ).
cnf(98,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC230-1.p',unknown),
[] ).
cnf(99,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC230-1.p',unknown),
[] ).
cnf(122,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC230-1.p',unknown),
[] ).
cnf(129,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC230-1.p',unknown),
[] ).
cnf(170,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC230-1.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('SWC230-1.p',unknown),
[] ).
cnf(447,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(531,plain,
( ~ ssItem(u)
| ssList(cons(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,99]),
[iquote('0:Res:1.0,99.1')] ).
cnf(578,plain,
equal(cons(skaf83(sk1),skaf82(sk1)),sk1),
inference(mrr,[status(thm)],[447,7]),
[iquote('0:MRR:447.1,7.0')] ).
cnf(590,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[85]),
[iquote('1:Spt:85.1')] ).
cnf(595,plain,
~ memberP(nil,u),
inference(mrr,[status(thm)],[84,590]),
[iquote('1:MRR:84.0,590.0')] ).
cnf(596,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[83,590]),
[iquote('1:MRR:83.0,590.0')] ).
cnf(597,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[82,590]),
[iquote('1:MRR:82.0,590.0')] ).
cnf(598,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[81,590]),
[iquote('1:MRR:81.0,590.0')] ).
cnf(599,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[80,590]),
[iquote('1:MRR:80.0,590.0')] ).
cnf(600,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[79,590]),
[iquote('1:MRR:79.0,590.0')] ).
cnf(601,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[78,590]),
[iquote('1:MRR:78.0,590.0')] ).
cnf(602,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[77,590]),
[iquote('1:MRR:77.0,590.0')] ).
cnf(713,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[99,590]),
[iquote('1:MRR:99.1,590.0')] ).
cnf(718,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[129,590]),
[iquote('1:MRR:129.1,590.0')] ).
cnf(801,plain,
( ~ ssList(u)
| ~ ssList(v)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
inference(mrr,[status(thm)],[170,590]),
[iquote('1:MRR:170.2,590.0')] ).
cnf(806,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(v,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[9,590]),
[iquote('1:MRR:9.2,590.0')] ).
cnf(1724,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[718]),
[iquote('1:EqR:718.1')] ).
cnf(1725,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[1724,713,14,15,16,17,18,19,20,21,602,601,600,599,598,597,596]),
[iquote('1:SSi:1724.0,713.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,602.0,601.0,600.0,599.0,598.0,597.0,596.1')] ).
cnf(4850,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)],[87,806]),
[iquote('1:SpL:87.1,806.2')] ).
cnf(4864,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)],[87,4850,801]),
[iquote('1:Rew:87.1,4850.3,801.2,4850.3')] ).
cnf(4865,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1)
| memberP(nil,sk5(u,nil,v)) ),
inference(ssi,[status(thm)],[4864,14,15,16,17,18,19,20,21,713,602,601,600,599,598,597,596,1725]),
[iquote('1:SSi:4864.2,4864.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,713.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.1,602.0,601.0,600.0,599.0,598.0,597.0,596.0,1725.0')] ).
cnf(4866,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1) ),
inference(mrr,[status(thm)],[4865,595]),
[iquote('1:MRR:4865.2,595.0')] ).
cnf(5232,plain,
( ~ ssList(skaf82(sk1))
| ~ equal(sk1,sk1) ),
inference(spl,[status(thm),theory(equality)],[578,4866]),
[iquote('1:SpL:578.0,4866.1')] ).
cnf(5566,plain,
~ ssList(skaf82(sk1)),
inference(obv,[status(thm),theory(equality)],[5232]),
[iquote('1:Obv:5232.1')] ).
cnf(5567,plain,
$false,
inference(ssi,[status(thm)],[5566,26,1]),
[iquote('1:SSi:5566.0,26.0,1.0')] ).
cnf(5611,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[85]),
[iquote('1:Spt:5567.0,85.0,85.2')] ).
cnf(5622,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)],[192,5611]),
[iquote('1:MRR:192.1,5611.1')] ).
cnf(20911,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(20961,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[20911]),
[iquote('0:Obv:20911.0')] ).
cnf(20962,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[20961,99]),
[iquote('0:SSi:20961.2,99.2')] ).
cnf(23657,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)],[5622]),
[iquote('1:EqR:5622.5')] ).
cnf(23696,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[23657,98,99]),
[iquote('1:SSi:23657.0,98.2,98.2,99.2,99.2')] ).
cnf(23698,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[20962,23696]),
[iquote('1:MRR:20962.3,23696.1')] ).
cnf(23707,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[23698]),
[iquote('1:Con:23698.2')] ).
cnf(23709,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[531,23707]),
[iquote('1:MRR:531.1,23707.0')] ).
cnf(23719,plain,
$false,
inference(unc,[status(thm)],[23709,60]),
[iquote('1:UnC:23709.0,60.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC230-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.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 09:47:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 11.61/11.80
% 11.61/11.80 SPASS V 3.9
% 11.61/11.80 SPASS beiseite: Proof found.
% 11.61/11.80 % SZS status Theorem
% 11.61/11.80 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.61/11.80 SPASS derived 15409 clauses, backtracked 4783 clauses, performed 83 splits and kept 10856 clauses.
% 11.61/11.80 SPASS allocated 93354 KBytes.
% 11.61/11.80 SPASS spent 0:00:09.10 on the problem.
% 11.61/11.80 0:00:00.04 for the input.
% 11.61/11.80 0:00:00.00 for the FLOTTER CNF translation.
% 11.61/11.80 0:00:00.15 for inferences.
% 11.61/11.80 0:00:00.25 for the backtracking.
% 11.61/11.80 0:00:08.39 for the reduction.
% 11.61/11.80
% 11.61/11.80
% 11.61/11.80 Here is a proof with depth 2, length 65 :
% 11.61/11.80 % SZS output start Refutation
% See solution above
% 11.61/11.80 Formulae used in the proof : co1_1 co1_7 co1_9 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
% 11.61/11.80
%------------------------------------------------------------------------------