TSTP Solution File: SWC249-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC249-1 : 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 22:02:48 EDT 2022
% Result : Unsatisfiable 8.26s 8.42s
% Output : Refutation 8.26s
% 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 : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC249-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC249-1.p',unknown),
[] ).
cnf(8,axiom,
strictorderedP(sk3),
file('SWC249-1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(nil,sk1),
file('SWC249-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(v,sk5(u,v,w)) ),
file('SWC249-1.p',unknown),
[] ).
cnf(16,axiom,
equalelemsP(nil),
file('SWC249-1.p',unknown),
[] ).
cnf(17,axiom,
duplicatefreeP(nil),
file('SWC249-1.p',unknown),
[] ).
cnf(18,axiom,
strictorderedP(nil),
file('SWC249-1.p',unknown),
[] ).
cnf(19,axiom,
totalorderedP(nil),
file('SWC249-1.p',unknown),
[] ).
cnf(20,axiom,
strictorderP(nil),
file('SWC249-1.p',unknown),
[] ).
cnf(21,axiom,
totalorderP(nil),
file('SWC249-1.p',unknown),
[] ).
cnf(22,axiom,
cyclefreeP(nil),
file('SWC249-1.p',unknown),
[] ).
cnf(23,axiom,
ssList(nil),
file('SWC249-1.p',unknown),
[] ).
cnf(27,axiom,
ssItem(skaf83(u)),
file('SWC249-1.p',unknown),
[] ).
cnf(28,axiom,
ssList(skaf82(u)),
file('SWC249-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC249-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC249-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC249-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC249-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC249-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC249-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC249-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC249-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC249-1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC249-1.p',unknown),
[] ).
cnf(100,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC249-1.p',unknown),
[] ).
cnf(101,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC249-1.p',unknown),
[] ).
cnf(124,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC249-1.p',unknown),
[] ).
cnf(131,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC249-1.p',unknown),
[] ).
cnf(172,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC249-1.p',unknown),
[] ).
cnf(194,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('SWC249-1.p',unknown),
[] ).
cnf(201,plain,
strictorderedP(sk1),
inference(rew,[status(thm),theory(equality)],[6,8]),
[iquote('0:Rew:6.0,8.0')] ).
cnf(452,plain,
( equal(cons(skaf83(sk1),skaf82(sk1)),sk1)
| equal(nil,sk1) ),
inference(res,[status(thm),theory(equality)],[1,124]),
[iquote('0:Res:1.0,124.0')] ).
cnf(536,plain,
( ~ ssItem(u)
| ssList(cons(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,101]),
[iquote('0:Res:1.0,101.1')] ).
cnf(581,plain,
equal(cons(skaf83(sk1),skaf82(sk1)),sk1),
inference(mrr,[status(thm)],[452,9]),
[iquote('0:MRR:452.1,9.0')] ).
cnf(596,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[87]),
[iquote('1:Spt:87.1')] ).
cnf(601,plain,
~ memberP(nil,u),
inference(mrr,[status(thm)],[86,596]),
[iquote('1:MRR:86.0,596.0')] ).
cnf(602,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[85,596]),
[iquote('1:MRR:85.0,596.0')] ).
cnf(603,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[84,596]),
[iquote('1:MRR:84.0,596.0')] ).
cnf(604,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[83,596]),
[iquote('1:MRR:83.0,596.0')] ).
cnf(605,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[82,596]),
[iquote('1:MRR:82.0,596.0')] ).
cnf(606,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[81,596]),
[iquote('1:MRR:81.0,596.0')] ).
cnf(607,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[80,596]),
[iquote('1:MRR:80.0,596.0')] ).
cnf(608,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[79,596]),
[iquote('1:MRR:79.0,596.0')] ).
cnf(717,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[101,596]),
[iquote('1:MRR:101.1,596.0')] ).
cnf(722,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[131,596]),
[iquote('1:MRR:131.1,596.0')] ).
cnf(801,plain,
( ~ ssList(u)
| ~ ssList(v)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
inference(mrr,[status(thm)],[172,596]),
[iquote('1:MRR:172.2,596.0')] ).
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)],[12,596]),
[iquote('1:MRR:12.2,596.0')] ).
cnf(1238,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[722]),
[iquote('1:EqR:722.1')] ).
cnf(1239,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[1238,717,16,17,18,19,20,21,22,23,608,607,606,605,604,603,602]),
[iquote('1:SSi:1238.0,717.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,23.0,608.0,607.0,606.0,605.0,604.0,603.0,602.1')] ).
cnf(4460,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)],[89,806]),
[iquote('1:SpL:89.1,806.2')] ).
cnf(4474,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)],[89,4460,801]),
[iquote('1:Rew:89.1,4460.3,801.2,4460.3')] ).
cnf(4475,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1)
| memberP(nil,sk5(u,nil,v)) ),
inference(ssi,[status(thm)],[4474,16,17,18,19,20,21,22,23,717,608,607,606,605,604,603,602,1239]),
[iquote('1:SSi:4474.2,4474.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,23.0,717.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,23.1,608.0,607.0,606.0,605.0,604.0,603.0,602.0,1239.0')] ).
cnf(4476,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1) ),
inference(mrr,[status(thm)],[4475,601]),
[iquote('1:MRR:4475.2,601.0')] ).
cnf(5014,plain,
( ~ ssList(skaf82(sk1))
| ~ equal(sk1,sk1) ),
inference(spl,[status(thm),theory(equality)],[581,4476]),
[iquote('1:SpL:581.0,4476.1')] ).
cnf(5212,plain,
~ ssList(skaf82(sk1)),
inference(obv,[status(thm),theory(equality)],[5014]),
[iquote('1:Obv:5014.1')] ).
cnf(5213,plain,
$false,
inference(ssi,[status(thm)],[5212,28,201,1]),
[iquote('1:SSi:5212.0,28.0,201.0,1.0')] ).
cnf(5293,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[87]),
[iquote('1:Spt:5213.0,87.0,87.2')] ).
cnf(5307,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)],[194,5293]),
[iquote('1:MRR:194.1,5293.1')] ).
cnf(15779,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)],[172,100]),
[iquote('0:SpR:172.3,100.2')] ).
cnf(15830,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[15779]),
[iquote('0:Obv:15779.0')] ).
cnf(15831,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[15830,101]),
[iquote('0:SSi:15830.2,101.2')] ).
cnf(17946,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)],[5307]),
[iquote('1:EqR:5307.5')] ).
cnf(17974,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[17946,100,101]),
[iquote('1:SSi:17946.0,100.2,100.2,101.2,101.2')] ).
cnf(17976,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[15831,17974]),
[iquote('1:MRR:15831.3,17974.1')] ).
cnf(17979,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[17976]),
[iquote('1:Con:17976.2')] ).
cnf(17980,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[536,17979]),
[iquote('1:MRR:536.1,17979.0')] ).
cnf(17982,plain,
$false,
inference(unc,[status(thm)],[17980,27]),
[iquote('1:UnC:17980.0,27.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC249-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 13:55:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 8.26/8.42
% 8.26/8.42 SPASS V 3.9
% 8.26/8.42 SPASS beiseite: Proof found.
% 8.26/8.42 % SZS status Theorem
% 8.26/8.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.26/8.42 SPASS derived 11672 clauses, backtracked 2704 clauses, performed 52 splits and kept 7501 clauses.
% 8.26/8.42 SPASS allocated 89627 KBytes.
% 8.26/8.42 SPASS spent 0:00:06.84 on the problem.
% 8.26/8.42 0:00:00.04 for the input.
% 8.26/8.42 0:00:00.00 for the FLOTTER CNF translation.
% 8.26/8.42 0:00:00.13 for inferences.
% 8.26/8.42 0:00:00.16 for the backtracking.
% 8.26/8.42 0:00:06.26 for the reduction.
% 8.26/8.42
% 8.26/8.42
% 8.26/8.42 Here is a proof with depth 2, length 68 :
% 8.26/8.42 % SZS output start Refutation
% See solution above
% 8.26/8.42 Formulae used in the proof : co1_1 co1_6 co1_8 co1_9 co1_12 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause12 clause13 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause74 clause85 clause86 clause109 clause116 clause157 clause179
% 8.26/8.42
%------------------------------------------------------------------------------