TSTP Solution File: SWC240-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC240-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 22:02:44 EDT 2022
% Result : Unsatisfiable 8.63s 8.79s
% Output : Refutation 8.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of clauses : 66 ( 27 unt; 2 nHn; 66 RR)
% Number of literals : 154 ( 0 equ; 97 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('SWC240-1.p',unknown),
[] ).
cnf(2,axiom,
ssList(sk2),
file('SWC240-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(nil,sk1),
file('SWC240-1.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('SWC240-1.p',unknown),
[] ).
cnf(15,axiom,
equalelemsP(nil),
file('SWC240-1.p',unknown),
[] ).
cnf(16,axiom,
duplicatefreeP(nil),
file('SWC240-1.p',unknown),
[] ).
cnf(17,axiom,
strictorderedP(nil),
file('SWC240-1.p',unknown),
[] ).
cnf(18,axiom,
totalorderedP(nil),
file('SWC240-1.p',unknown),
[] ).
cnf(19,axiom,
strictorderP(nil),
file('SWC240-1.p',unknown),
[] ).
cnf(20,axiom,
totalorderP(nil),
file('SWC240-1.p',unknown),
[] ).
cnf(21,axiom,
cyclefreeP(nil),
file('SWC240-1.p',unknown),
[] ).
cnf(22,axiom,
ssList(nil),
file('SWC240-1.p',unknown),
[] ).
cnf(27,axiom,
ssList(skaf82(u)),
file('SWC240-1.p',unknown),
[] ).
cnf(61,axiom,
ssItem(skaf44(u)),
file('SWC240-1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC240-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC240-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC240-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC240-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC240-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC240-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC240-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC240-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC240-1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC240-1.p',unknown),
[] ).
cnf(99,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC240-1.p',unknown),
[] ).
cnf(100,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC240-1.p',unknown),
[] ).
cnf(123,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC240-1.p',unknown),
[] ).
cnf(130,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC240-1.p',unknown),
[] ).
cnf(171,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC240-1.p',unknown),
[] ).
cnf(193,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('SWC240-1.p',unknown),
[] ).
cnf(457,plain,
( ~ ssItem(u)
| ssList(cons(u,sk2)) ),
inference(res,[status(thm),theory(equality)],[2,100]),
[iquote('0:Res:2.0,100.1')] ).
cnf(498,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[86]),
[iquote('1:Spt:86.1')] ).
cnf(502,plain,
~ memberP(nil,u),
inference(mrr,[status(thm)],[85,498]),
[iquote('1:MRR:85.0,498.0')] ).
cnf(503,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[84,498]),
[iquote('1:MRR:84.0,498.0')] ).
cnf(504,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[83,498]),
[iquote('1:MRR:83.0,498.0')] ).
cnf(505,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[82,498]),
[iquote('1:MRR:82.0,498.0')] ).
cnf(506,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[81,498]),
[iquote('1:MRR:81.0,498.0')] ).
cnf(507,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[80,498]),
[iquote('1:MRR:80.0,498.0')] ).
cnf(508,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[79,498]),
[iquote('1:MRR:79.0,498.0')] ).
cnf(509,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[78,498]),
[iquote('1:MRR:78.0,498.0')] ).
cnf(634,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[100,498]),
[iquote('1:MRR:100.1,498.0')] ).
cnf(639,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[130,498]),
[iquote('1:MRR:130.1,498.0')] ).
cnf(698,plain,
( ~ ssList(u)
| ~ ssList(v)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
inference(mrr,[status(thm)],[171,498]),
[iquote('1:MRR:171.2,498.0')] ).
cnf(703,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(v,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[9,498]),
[iquote('1:MRR:9.2,498.0')] ).
cnf(1332,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[639]),
[iquote('1:EqR:639.1')] ).
cnf(1333,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[1332,634,15,16,17,18,19,20,21,22,509,508,507,506,505,504,503]),
[iquote('1:SSi:1332.0,634.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,509.0,508.0,507.0,506.0,505.0,504.0,503.1')] ).
cnf(4671,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)],[88,703]),
[iquote('1:SpL:88.1,703.2')] ).
cnf(4683,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)],[88,4671,698]),
[iquote('1:Rew:88.1,4671.3,698.2,4671.3')] ).
cnf(5355,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1)
| memberP(nil,sk5(u,nil,v)) ),
inference(ssi,[status(thm)],[4683,15,16,17,18,19,20,21,22,634,509,508,507,506,505,504,503,1333]),
[iquote('1:SSi:4683.2,4683.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,634.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.1,509.0,508.0,507.0,506.0,505.0,504.0,503.0,1333.0')] ).
cnf(5356,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1) ),
inference(mrr,[status(thm)],[5355,502]),
[iquote('1:MRR:5355.2,502.0')] ).
cnf(5766,plain,
( ~ ssList(u)
| ~ ssList(skaf82(u))
| ~ equal(u,sk1)
| equal(nil,u) ),
inference(spl,[status(thm),theory(equality)],[123,5356]),
[iquote('1:SpL:123.2,5356.1')] ).
cnf(5771,plain,
( ~ ssList(u)
| ~ equal(u,sk1)
| equal(nil,u) ),
inference(ssi,[status(thm)],[5766,27]),
[iquote('1:SSi:5766.1,27.0')] ).
cnf(6379,plain,
( ~ equal(sk1,sk1)
| equal(nil,sk1) ),
inference(ems,[status(thm)],[5771,1]),
[iquote('1:EmS:5771.0,1.0')] ).
cnf(6381,plain,
equal(nil,sk1),
inference(obv,[status(thm),theory(equality)],[6379]),
[iquote('1:Obv:6379.0')] ).
cnf(6382,plain,
$false,
inference(mrr,[status(thm)],[6381,7]),
[iquote('1:MRR:6381.0,7.0')] ).
cnf(6414,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[86]),
[iquote('1:Spt:6382.0,86.0,86.2')] ).
cnf(6426,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)],[193,6414]),
[iquote('1:MRR:193.1,6414.1')] ).
cnf(16154,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)],[171,99]),
[iquote('0:SpR:171.3,99.2')] ).
cnf(16200,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[16154]),
[iquote('0:Obv:16154.0')] ).
cnf(16201,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[16200,100]),
[iquote('0:SSi:16200.2,100.2')] ).
cnf(18215,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)],[6426]),
[iquote('1:EqR:6426.5')] ).
cnf(18248,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[18215,99,100]),
[iquote('1:SSi:18215.0,99.2,99.2,100.2,100.2')] ).
cnf(18251,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[16201,18248]),
[iquote('1:MRR:16201.3,18248.1')] ).
cnf(18257,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[18251]),
[iquote('1:Con:18251.2')] ).
cnf(18258,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[457,18257]),
[iquote('1:MRR:457.1,18257.0')] ).
cnf(18264,plain,
$false,
inference(unc,[status(thm)],[18258,61]),
[iquote('1:UnC:18258.0,61.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWC240-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 12 19:30:26 EDT 2022
% 0.14/0.35 % CPUTime :
% 8.63/8.79
% 8.63/8.79 SPASS V 3.9
% 8.63/8.79 SPASS beiseite: Proof found.
% 8.63/8.79 % SZS status Theorem
% 8.63/8.79 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.63/8.79 SPASS derived 11801 clauses, backtracked 2802 clauses, performed 29 splits and kept 7340 clauses.
% 8.63/8.79 SPASS allocated 90599 KBytes.
% 8.63/8.79 SPASS spent 0:00:06.85 on the problem.
% 8.63/8.79 0:00:00.04 for the input.
% 8.63/8.79 0:00:00.00 for the FLOTTER CNF translation.
% 8.63/8.79 0:00:00.13 for inferences.
% 8.63/8.79 0:00:00.18 for the backtracking.
% 8.63/8.79 0:00:06.29 for the reduction.
% 8.63/8.79
% 8.63/8.79
% 8.63/8.79 Here is a proof with depth 3, length 66 :
% 8.63/8.79 % SZS output start Refutation
% See solution above
% 8.63/8.79 Formulae used in the proof : co1_1 co1_2 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
% 8.63/8.79
%------------------------------------------------------------------------------