TSTP Solution File: SWC251-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC251-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 22:02:49 EDT 2022
% Result : Unsatisfiable 32.95s 33.18s
% Output : Refutation 32.95s
% 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 : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC251-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(nil,sk1),
file('SWC251-1.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('SWC251-1.p',unknown),
[] ).
cnf(14,axiom,
ssList(sk7),
file('SWC251-1.p',unknown),
[] ).
cnf(20,axiom,
equalelemsP(nil),
file('SWC251-1.p',unknown),
[] ).
cnf(21,axiom,
duplicatefreeP(nil),
file('SWC251-1.p',unknown),
[] ).
cnf(22,axiom,
strictorderedP(nil),
file('SWC251-1.p',unknown),
[] ).
cnf(23,axiom,
totalorderedP(nil),
file('SWC251-1.p',unknown),
[] ).
cnf(24,axiom,
strictorderP(nil),
file('SWC251-1.p',unknown),
[] ).
cnf(25,axiom,
totalorderP(nil),
file('SWC251-1.p',unknown),
[] ).
cnf(26,axiom,
cyclefreeP(nil),
file('SWC251-1.p',unknown),
[] ).
cnf(27,axiom,
ssList(nil),
file('SWC251-1.p',unknown),
[] ).
cnf(31,axiom,
ssItem(skaf83(u)),
file('SWC251-1.p',unknown),
[] ).
cnf(32,axiom,
ssList(skaf82(u)),
file('SWC251-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC251-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC251-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC251-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC251-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC251-1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC251-1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC251-1.p',unknown),
[] ).
cnf(90,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC251-1.p',unknown),
[] ).
cnf(91,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC251-1.p',unknown),
[] ).
cnf(93,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC251-1.p',unknown),
[] ).
cnf(104,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC251-1.p',unknown),
[] ).
cnf(105,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC251-1.p',unknown),
[] ).
cnf(128,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC251-1.p',unknown),
[] ).
cnf(135,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC251-1.p',unknown),
[] ).
cnf(176,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC251-1.p',unknown),
[] ).
cnf(198,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('SWC251-1.p',unknown),
[] ).
cnf(360,plain,
( ~ ssItem(u)
| ssList(cons(u,sk7)) ),
inference(res,[status(thm),theory(equality)],[14,105]),
[iquote('0:Res:14.0,105.1')] ).
cnf(586,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[91]),
[iquote('1:Spt:91.1')] ).
cnf(591,plain,
~ memberP(nil,u),
inference(mrr,[status(thm)],[90,586]),
[iquote('1:MRR:90.0,586.0')] ).
cnf(592,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[89,586]),
[iquote('1:MRR:89.0,586.0')] ).
cnf(593,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[88,586]),
[iquote('1:MRR:88.0,586.0')] ).
cnf(594,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[87,586]),
[iquote('1:MRR:87.0,586.0')] ).
cnf(595,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[86,586]),
[iquote('1:MRR:86.0,586.0')] ).
cnf(596,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[85,586]),
[iquote('1:MRR:85.0,586.0')] ).
cnf(597,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[84,586]),
[iquote('1:MRR:84.0,586.0')] ).
cnf(598,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[83,586]),
[iquote('1:MRR:83.0,586.0')] ).
cnf(715,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[105,586]),
[iquote('1:MRR:105.1,586.0')] ).
cnf(720,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[135,586]),
[iquote('1:MRR:135.1,586.0')] ).
cnf(804,plain,
( ~ ssList(u)
| ~ ssList(v)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
inference(mrr,[status(thm)],[176,586]),
[iquote('1:MRR:176.2,586.0')] ).
cnf(809,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(v,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[9,586]),
[iquote('1:MRR:9.2,586.0')] ).
cnf(2796,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[720]),
[iquote('1:EqR:720.1')] ).
cnf(2797,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[2796,715,20,21,26,25,24,23,22,27,592,593,594,595,596,597,598]),
[iquote('1:SSi:2796.0,715.0,20.0,21.0,26.0,25.0,24.0,23.0,22.0,27.0,592.0,593.0,594.0,595.0,596.0,597.0,598.1')] ).
cnf(5627,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)],[93,809]),
[iquote('1:SpL:93.1,809.2')] ).
cnf(5641,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)],[93,5627,804]),
[iquote('1:Rew:93.1,5627.3,804.2,5627.3')] ).
cnf(5642,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1)
| memberP(nil,sk5(u,nil,v)) ),
inference(ssi,[status(thm)],[5641,20,21,26,25,24,23,22,27,715,592,593,594,595,596,597,598,2797]),
[iquote('1:SSi:5641.2,5641.0,20.0,21.0,26.0,25.0,24.0,23.0,22.0,27.0,715.0,20.0,21.0,26.0,25.0,24.0,23.0,22.0,27.1,592.0,593.0,594.0,595.0,596.0,597.0,598.0,2797.0')] ).
cnf(5643,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1) ),
inference(mrr,[status(thm)],[5642,591]),
[iquote('1:MRR:5642.2,591.0')] ).
cnf(5661,plain,
( ~ ssList(u)
| ~ ssList(skaf82(u))
| ~ equal(u,sk1)
| equal(nil,u) ),
inference(spl,[status(thm),theory(equality)],[128,5643]),
[iquote('1:SpL:128.2,5643.1')] ).
cnf(5676,plain,
( ~ ssList(u)
| ~ equal(u,sk1)
| equal(nil,u) ),
inference(ssi,[status(thm)],[5661,32]),
[iquote('1:SSi:5661.1,32.0')] ).
cnf(9859,plain,
( ~ equal(sk1,sk1)
| equal(nil,sk1) ),
inference(ems,[status(thm)],[5676,1]),
[iquote('1:EmS:5676.0,1.0')] ).
cnf(9862,plain,
equal(nil,sk1),
inference(obv,[status(thm),theory(equality)],[9859]),
[iquote('1:Obv:9859.0')] ).
cnf(9863,plain,
$false,
inference(mrr,[status(thm)],[9862,7]),
[iquote('1:MRR:9862.0,7.0')] ).
cnf(9978,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[91]),
[iquote('1:Spt:9863.0,91.0,91.2')] ).
cnf(10007,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)],[198,9978]),
[iquote('1:MRR:198.1,9978.1')] ).
cnf(46040,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)],[176,104]),
[iquote('0:SpR:176.3,104.2')] ).
cnf(46073,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[46040]),
[iquote('0:Obv:46040.0')] ).
cnf(46074,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[46073,105]),
[iquote('0:SSi:46073.2,105.2')] ).
cnf(47362,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)],[10007]),
[iquote('1:EqR:10007.5')] ).
cnf(47388,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[47362,104,105]),
[iquote('1:SSi:47362.0,104.2,104.2,105.2,105.2')] ).
cnf(47390,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[46074,47388]),
[iquote('1:MRR:46074.3,47388.1')] ).
cnf(47393,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[47390]),
[iquote('1:Con:47390.2')] ).
cnf(47395,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[360,47393]),
[iquote('1:MRR:360.1,47393.0')] ).
cnf(47399,plain,
$false,
inference(unc,[status(thm)],[47395,31]),
[iquote('1:UnC:47395.0,31.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC251-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.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 02:46:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 32.95/33.18
% 32.95/33.18 SPASS V 3.9
% 32.95/33.18 SPASS beiseite: Proof found.
% 32.95/33.18 % SZS status Theorem
% 32.95/33.18 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.95/33.18 SPASS derived 32463 clauses, backtracked 11844 clauses, performed 123 splits and kept 25786 clauses.
% 32.95/33.18 SPASS allocated 107921 KBytes.
% 32.95/33.18 SPASS spent 0:0:24.46 on the problem.
% 32.95/33.18 0:00:00.04 for the input.
% 32.95/33.18 0:00:00.00 for the FLOTTER CNF translation.
% 32.95/33.18 0:00:00.29 for inferences.
% 32.95/33.18 0:00:00.92 for the backtracking.
% 32.95/33.18 0:0:22.79 for the reduction.
% 32.95/33.18
% 32.95/33.18
% 32.95/33.18 Here is a proof with depth 3, length 66 :
% 32.95/33.18 % SZS output start Refutation
% See solution above
% 32.95/33.18 Formulae used in the proof : co1_1 co1_7 co1_9 co1_14 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
% 32.95/33.18
%------------------------------------------------------------------------------