TSTP Solution File: SWC408-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC408-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 22:03:53 EDT 2022
% Result : Unsatisfiable 4.23s 4.41s
% Output : Refutation 4.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 33 ( 13 unt; 1 nHn; 33 RR)
% Number of literals : 90 ( 0 equ; 64 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
ssList(sk2),
file('SWC408-1.p',unknown),
[] ).
cnf(5,axiom,
equal(app(sk4,sk4),sk3),
file('SWC408-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk4,sk2),
file('SWC408-1.p',unknown),
[] ).
cnf(7,axiom,
equal(sk3,sk1),
file('SWC408-1.p',unknown),
[] ).
cnf(9,axiom,
memberP(sk2,sk5),
file('SWC408-1.p',unknown),
[] ).
cnf(10,axiom,
~ memberP(sk1,sk5),
file('SWC408-1.p',unknown),
[] ).
cnf(22,axiom,
ssItem(skaf83(u)),
file('SWC408-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC408-1.p',unknown),
[] ).
cnf(95,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC408-1.p',unknown),
[] ).
cnf(96,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC408-1.p',unknown),
[] ).
cnf(151,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ memberP(w,u)
| memberP(app(v,w),u) ),
file('SWC408-1.p',unknown),
[] ).
cnf(167,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC408-1.p',unknown),
[] ).
cnf(189,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('SWC408-1.p',unknown),
[] ).
cnf(198,plain,
equal(app(sk2,sk2),sk1),
inference(rew,[status(thm),theory(equality)],[6,5,7]),
[iquote('0:Rew:6.0,5.0,7.0,5.0')] ).
cnf(442,plain,
( ~ ssItem(u)
| ssList(cons(u,sk2)) ),
inference(res,[status(thm),theory(equality)],[2,96]),
[iquote('0:Res:2.0,96.1')] ).
cnf(478,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[82]),
[iquote('1:Spt:82.1')] ).
cnf(575,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ memberP(v,w)
| memberP(app(u,v),w) ),
inference(mrr,[status(thm)],[151,478]),
[iquote('1:MRR:151.0,478.0')] ).
cnf(1796,plain,
( ~ ssList(sk2)
| ~ ssList(sk2)
| ~ memberP(sk2,u)
| memberP(sk1,u) ),
inference(spr,[status(thm),theory(equality)],[198,575]),
[iquote('1:SpR:198.0,575.3')] ).
cnf(1801,plain,
( ~ ssList(sk2)
| ~ memberP(sk2,u)
| memberP(sk1,u) ),
inference(obv,[status(thm),theory(equality)],[1796]),
[iquote('1:Obv:1796.0')] ).
cnf(2836,plain,
( ~ memberP(sk2,u)
| memberP(sk1,u) ),
inference(ssi,[status(thm)],[1801,2]),
[iquote('1:SSi:1801.0,2.0')] ).
cnf(3209,plain,
memberP(sk1,sk5),
inference(res,[status(thm),theory(equality)],[9,2836]),
[iquote('1:Res:9.0,2836.0')] ).
cnf(3210,plain,
$false,
inference(mrr,[status(thm)],[3209,10]),
[iquote('1:MRR:3209.0,10.0')] ).
cnf(3211,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[82]),
[iquote('1:Spt:3210.0,82.0,82.2')] ).
cnf(3229,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)],[189,3211]),
[iquote('1:MRR:189.1,3211.1')] ).
cnf(10052,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)],[167,95]),
[iquote('0:SpR:167.3,95.2')] ).
cnf(10084,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[10052]),
[iquote('0:Obv:10052.0')] ).
cnf(10085,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[10084,96]),
[iquote('0:SSi:10084.2,96.2')] ).
cnf(11201,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)],[3229]),
[iquote('1:EqR:3229.5')] ).
cnf(11224,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[11201,95,96]),
[iquote('1:SSi:11201.0,95.2,95.2,96.2,96.2')] ).
cnf(11225,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[10085,11224]),
[iquote('1:MRR:10085.3,11224.1')] ).
cnf(11228,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[11225]),
[iquote('1:Con:11225.2')] ).
cnf(11229,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[442,11228]),
[iquote('1:MRR:442.1,11228.0')] ).
cnf(11230,plain,
$false,
inference(unc,[status(thm)],[11229,22]),
[iquote('1:UnC:11229.0,22.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC408-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 11 20:08:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 4.23/4.41
% 4.23/4.41 SPASS V 3.9
% 4.23/4.41 SPASS beiseite: Proof found.
% 4.23/4.41 % SZS status Theorem
% 4.23/4.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.23/4.41 SPASS derived 6925 clauses, backtracked 3078 clauses, performed 57 splits and kept 6372 clauses.
% 4.23/4.41 SPASS allocated 84472 KBytes.
% 4.23/4.41 SPASS spent 0:00:03.68 on the problem.
% 4.23/4.41 0:00:00.04 for the input.
% 4.23/4.41 0:00:00.00 for the FLOTTER CNF translation.
% 4.23/4.41 0:00:00.07 for inferences.
% 4.23/4.41 0:00:00.09 for the backtracking.
% 4.23/4.41 0:00:03.25 for the reduction.
% 4.23/4.41
% 4.23/4.41
% 4.23/4.41 Here is a proof with depth 2, length 33 :
% 4.23/4.41 % SZS output start Refutation
% See solution above
% 4.23/4.41 Formulae used in the proof : co1_2 co1_5 co1_6 co1_7 co1_9 co1_10 clause12 clause72 clause85 clause86 clause141 clause157 clause179
% 4.23/4.41
%------------------------------------------------------------------------------