%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC402-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 22:03:50 EDT 2022
% Result : Unsatisfiable 6.62s 6.88s
% Output : Refutation 6.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of clauses : 40 ( 17 unt; 1 nHn; 40 RR)
% Number of literals : 106 ( 0 equ; 74 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC402-1.p',unknown),
[] ).
cnf(5,axiom,
equal(sk4,sk2),
file('SWC402-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC402-1.p',unknown),
[] ).
cnf(7,axiom,
ssList(sk5),
file('SWC402-1.p',unknown),
[] ).
cnf(8,axiom,
ssList(sk6),
file('SWC402-1.p',unknown),
[] ).
cnf(9,axiom,
equal(app(app(sk5,sk3),sk6),sk4),
file('SWC402-1.p',unknown),
[] ).
cnf(10,axiom,
totalorderedP(sk3),
file('SWC402-1.p',unknown),
[] ).
cnf(14,axiom,
memberP(sk1,sk7),
file('SWC402-1.p',unknown),
[] ).
cnf(15,axiom,
~ memberP(sk2,sk7),
file('SWC402-1.p',unknown),
[] ).
cnf(63,axiom,
ssItem(skaf44(u)),
file('SWC402-1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC402-1.p',unknown),
[] ).
cnf(101,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC402-1.p',unknown),
[] ).
cnf(102,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC402-1.p',unknown),
[] ).
cnf(156,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ memberP(v,u)
| memberP(app(v,w),u) ),
file('SWC402-1.p',unknown),
[] ).
cnf(157,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ memberP(w,u)
| memberP(app(v,w),u) ),
file('SWC402-1.p',unknown),
[] ).
cnf(173,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC402-1.p',unknown),
[] ).
cnf(195,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('SWC402-1.p',unknown),
[] ).
cnf(202,plain,
totalorderedP(sk1),
inference(rew,[status(thm),theory(equality)],[6,10]),
[iquote('0:Rew:6.0,10.0')] ).
cnf(206,plain,
equal(app(app(sk5,sk1),sk6),sk2),
inference(rew,[status(thm),theory(equality)],[6,9,5]),
[iquote('0:Rew:6.0,9.0,5.0,9.0')] ).
cnf(458,plain,
( ~ ssItem(u)
| ssList(cons(u,sk6)) ),
inference(res,[status(thm),theory(equality)],[8,102]),
[iquote('0:Res:8.0,102.1')] ).
cnf(496,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[88]),
[iquote('1:Spt:88.1')] ).
cnf(593,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ memberP(v,w)
| memberP(app(u,v),w) ),
inference(mrr,[status(thm)],[157,496]),
[iquote('1:MRR:157.0,496.0')] ).
cnf(594,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ memberP(u,w)
| memberP(app(u,v),w) ),
inference(mrr,[status(thm)],[156,496]),
[iquote('1:MRR:156.0,496.0')] ).
cnf(2427,plain,
( ~ ssList(app(sk5,sk1))
| ~ ssList(sk6)
| ~ memberP(app(sk5,sk1),u)
| memberP(sk2,u) ),
inference(spr,[status(thm),theory(equality)],[206,594]),
[iquote('1:SpR:206.0,594.3')] ).
cnf(3212,plain,
( ~ memberP(app(sk5,sk1),u)
| memberP(sk2,u) ),
inference(ssi,[status(thm)],[2427,8,101,7,202,1]),
[iquote('1:SSi:2427.1,2427.0,8.0,101.0,7.0,202.2,1.0')] ).
cnf(3409,plain,
( ~ ssList(sk5)
| ~ ssList(sk1)
| ~ memberP(sk1,u)
| memberP(sk2,u) ),
inference(res,[status(thm),theory(equality)],[593,3212]),
[iquote('1:Res:593.3,3212.0')] ).
cnf(3411,plain,
( ~ memberP(sk1,u)
| memberP(sk2,u) ),
inference(ssi,[status(thm)],[3409,202,1,7]),
[iquote('1:SSi:3409.1,3409.0,202.0,1.0,7.0')] ).
cnf(3412,plain,
~ memberP(sk1,sk7),
inference(res,[status(thm),theory(equality)],[3411,15]),
[iquote('1:Res:3411.1,15.0')] ).
cnf(3413,plain,
$false,
inference(mrr,[status(thm)],[3412,14]),
[iquote('1:MRR:3412.0,14.0')] ).
cnf(3414,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[88]),
[iquote('1:Spt:3413.0,88.0,88.2')] ).
cnf(3430,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)],[195,3414]),
[iquote('1:MRR:195.1,3414.1')] ).
cnf(16483,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)],[173,101]),
[iquote('0:SpR:173.3,101.2')] ).
cnf(16510,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[16483]),
[iquote('0:Obv:16483.0')] ).
cnf(16511,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[16510,102]),
[iquote('0:SSi:16510.2,102.2')] ).
cnf(17580,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)],[3430]),
[iquote('1:EqR:3430.5')] ).
cnf(17606,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[17580,101,102]),
[iquote('1:SSi:17580.0,101.2,101.2,102.2,102.2')] ).
cnf(17607,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[16511,17606]),
[iquote('1:MRR:16511.3,17606.1')] ).
cnf(17610,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[17607]),
[iquote('1:Con:17607.2')] ).
cnf(17611,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[458,17610]),
[iquote('1:MRR:458.1,17610.0')] ).
cnf(17612,plain,
$false,
inference(unc,[status(thm)],[17611,63]),
[iquote('1:UnC:17611.0,63.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC402-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 12 21:19:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 6.62/6.88
% 6.62/6.88 SPASS V 3.9
% 6.62/6.88 SPASS beiseite: Proof found.
% 6.62/6.88 % SZS status Theorem
% 6.62/6.88 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.62/6.88 SPASS derived 11835 clauses, backtracked 5106 clauses, performed 68 splits and kept 10090 clauses.
% 6.62/6.88 SPASS allocated 88660 KBytes.
% 6.62/6.88 SPASS spent 0:00:05.40 on the problem.
% 6.62/6.88 0:00:00.04 for the input.
% 6.62/6.88 0:00:00.00 for the FLOTTER CNF translation.
% 6.62/6.88 0:00:00.11 for inferences.
% 6.62/6.88 0:00:00.14 for the backtracking.
% 6.62/6.88 0:00:04.90 for the reduction.
% 6.62/6.88
% 6.62/6.88
% 6.62/6.88 Here is a proof with depth 3, length 40 :
% 6.62/6.88 % SZS output start Refutation
% See solution above
% 6.62/6.88 Formulae used in the proof : co1_1 co1_5 co1_6 co1_7 co1_8 co1_9 co1_10 co1_14 co1_15 clause47 clause72 clause85 clause86 clause140 clause141 clause157 clause179
% 6.62/6.88
%------------------------------------------------------------------------------