TSTP Solution File: SWC399-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC399-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 22:03:49 EDT 2022
% Result : Unsatisfiable 7.02s 7.24s
% Output : Refutation 7.02s
% 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('SWC399-1.p',unknown),
[] ).
cnf(5,axiom,
equal(sk4,sk2),
file('SWC399-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC399-1.p',unknown),
[] ).
cnf(7,axiom,
ssList(sk5),
file('SWC399-1.p',unknown),
[] ).
cnf(8,axiom,
ssList(sk6),
file('SWC399-1.p',unknown),
[] ).
cnf(9,axiom,
equal(app(app(sk5,sk3),sk6),sk4),
file('SWC399-1.p',unknown),
[] ).
cnf(10,axiom,
equalelemsP(sk3),
file('SWC399-1.p',unknown),
[] ).
cnf(14,axiom,
memberP(sk1,sk7),
file('SWC399-1.p',unknown),
[] ).
cnf(15,axiom,
~ memberP(sk2,sk7),
file('SWC399-1.p',unknown),
[] ).
cnf(63,axiom,
ssItem(skaf44(u)),
file('SWC399-1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC399-1.p',unknown),
[] ).
cnf(101,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC399-1.p',unknown),
[] ).
cnf(102,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC399-1.p',unknown),
[] ).
cnf(156,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ memberP(v,u)
| memberP(app(v,w),u) ),
file('SWC399-1.p',unknown),
[] ).
cnf(157,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ memberP(w,u)
| memberP(app(v,w),u) ),
file('SWC399-1.p',unknown),
[] ).
cnf(173,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC399-1.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('SWC399-1.p',unknown),
[] ).
cnf(202,plain,
equalelemsP(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(456,plain,
( ~ ssItem(u)
| ssList(cons(u,sk6)) ),
inference(res,[status(thm),theory(equality)],[8,102]),
[iquote('0:Res:8.0,102.1')] ).
cnf(494,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[88]),
[iquote('1:Spt:88.1')] ).
cnf(591,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ memberP(v,w)
| memberP(app(u,v),w) ),
inference(mrr,[status(thm)],[157,494]),
[iquote('1:MRR:157.0,494.0')] ).
cnf(592,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ memberP(u,w)
| memberP(app(u,v),w) ),
inference(mrr,[status(thm)],[156,494]),
[iquote('1:MRR:156.0,494.0')] ).
cnf(2517,plain,
( ~ ssList(app(sk5,sk1))
| ~ ssList(sk6)
| ~ memberP(app(sk5,sk1),u)
| memberP(sk2,u) ),
inference(spr,[status(thm),theory(equality)],[206,592]),
[iquote('1:SpR:206.0,592.3')] ).
cnf(3275,plain,
( ~ memberP(app(sk5,sk1),u)
| memberP(sk2,u) ),
inference(ssi,[status(thm)],[2517,8,101,7,202,1]),
[iquote('1:SSi:2517.1,2517.0,8.0,101.0,7.0,202.2,1.0')] ).
cnf(3421,plain,
( ~ ssList(sk5)
| ~ ssList(sk1)
| ~ memberP(sk1,u)
| memberP(sk2,u) ),
inference(res,[status(thm),theory(equality)],[591,3275]),
[iquote('1:Res:591.3,3275.0')] ).
cnf(3423,plain,
( ~ memberP(sk1,u)
| memberP(sk2,u) ),
inference(ssi,[status(thm)],[3421,202,1,7]),
[iquote('1:SSi:3421.1,3421.0,202.0,1.0,7.0')] ).
cnf(3501,plain,
~ memberP(sk1,sk7),
inference(res,[status(thm),theory(equality)],[3423,15]),
[iquote('1:Res:3423.1,15.0')] ).
cnf(3502,plain,
$false,
inference(mrr,[status(thm)],[3501,14]),
[iquote('1:MRR:3501.0,14.0')] ).
cnf(3503,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[88]),
[iquote('1:Spt:3502.0,88.0,88.2')] ).
cnf(3520,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)],[195,3503]),
[iquote('1:MRR:195.1,3503.1')] ).
cnf(16645,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(16672,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[16645]),
[iquote('0:Obv:16645.0')] ).
cnf(16673,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[16672,102]),
[iquote('0:SSi:16672.2,102.2')] ).
cnf(17883,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)],[3520]),
[iquote('1:EqR:3520.5')] ).
cnf(17909,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[17883,101,102]),
[iquote('1:SSi:17883.0,101.2,101.2,102.2,102.2')] ).
cnf(17910,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[16673,17909]),
[iquote('1:MRR:16673.3,17909.1')] ).
cnf(17913,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[17910]),
[iquote('1:Con:17910.2')] ).
cnf(17914,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[456,17913]),
[iquote('1:MRR:456.1,17913.0')] ).
cnf(17915,plain,
$false,
inference(unc,[status(thm)],[17914,63]),
[iquote('1:UnC:17914.0,63.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC399-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 00:57:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 7.02/7.24
% 7.02/7.24 SPASS V 3.9
% 7.02/7.24 SPASS beiseite: Proof found.
% 7.02/7.24 % SZS status Theorem
% 7.02/7.24 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.02/7.24 SPASS derived 12079 clauses, backtracked 5133 clauses, performed 68 splits and kept 10238 clauses.
% 7.02/7.24 SPASS allocated 88847 KBytes.
% 7.02/7.24 SPASS spent 0:00:05.71 on the problem.
% 7.02/7.24 0:00:00.04 for the input.
% 7.02/7.24 0:00:00.00 for the FLOTTER CNF translation.
% 7.02/7.24 0:00:00.12 for inferences.
% 7.02/7.24 0:00:00.15 for the backtracking.
% 7.02/7.24 0:00:05.19 for the reduction.
% 7.02/7.24
% 7.02/7.24
% 7.02/7.24 Here is a proof with depth 3, length 40 :
% 7.02/7.24 % SZS output start Refutation
% See solution above
% 7.02/7.24 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
% 7.02/7.24
%------------------------------------------------------------------------------