TSTP Solution File: SWC189-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC189-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 22:02:21 EDT 2022
% Result : Unsatisfiable 13.58s 13.82s
% Output : Refutation 13.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 31 ( 12 unt; 1 nHn; 31 RR)
% Number of literals : 88 ( 0 equ; 64 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 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(6,axiom,
equal(sk1,sk3),
file('SWC189-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ ssItem(x)
| ~ equal(app(app(app(v,cons(x,nil)),cons(w,nil)),u),sk3)
| equal(x,w) ),
file('SWC189-1.p',unknown),
[] ).
cnf(10,axiom,
ssList(sk7),
file('SWC189-1.p',unknown),
[] ).
cnf(11,axiom,
ssList(sk8),
file('SWC189-1.p',unknown),
[] ).
cnf(12,axiom,
equal(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),sk1),
file('SWC189-1.p',unknown),
[] ).
cnf(13,axiom,
~ equal(sk6,sk5),
file('SWC189-1.p',unknown),
[] ).
cnf(25,axiom,
ssItem(skaf83(u)),
file('SWC189-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC189-1.p',unknown),
[] ).
cnf(98,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC189-1.p',unknown),
[] ).
cnf(99,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC189-1.p',unknown),
[] ).
cnf(170,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC189-1.p',unknown),
[] ).
cnf(192,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('SWC189-1.p',unknown),
[] ).
cnf(201,plain,
equal(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),sk3),
inference(rew,[status(thm),theory(equality)],[6,12]),
[iquote('0:Rew:6.0,12.0')] ).
cnf(516,plain,
( ~ ssItem(u)
| ssList(cons(u,sk7)) ),
inference(res,[status(thm),theory(equality)],[10,99]),
[iquote('0:Res:10.0,99.1')] ).
cnf(552,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[85]),
[iquote('1:Spt:85.1')] ).
cnf(752,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(app(v,cons(w,nil)),cons(x,nil)),u),sk3)
| equal(w,x) ),
inference(mrr,[status(thm)],[7,552]),
[iquote('1:MRR:7.3,7.2,552.0')] ).
cnf(5647,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(sk3,sk3)
| equal(sk6,sk5) ),
inference(spl,[status(thm),theory(equality)],[201,752]),
[iquote('1:SpL:201.0,752.2')] ).
cnf(6370,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| equal(sk6,sk5) ),
inference(obv,[status(thm),theory(equality)],[5647]),
[iquote('1:Obv:5647.2')] ).
cnf(6371,plain,
equal(sk6,sk5),
inference(ssi,[status(thm)],[6370,10,11]),
[iquote('1:SSi:6370.1,6370.0,10.0,11.0')] ).
cnf(6372,plain,
$false,
inference(mrr,[status(thm)],[6371,13]),
[iquote('1:MRR:6371.0,13.0')] ).
cnf(6394,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[85]),
[iquote('1:Spt:6372.0,85.0,85.2')] ).
cnf(6412,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)],[192,6394]),
[iquote('1:MRR:192.1,6394.1')] ).
cnf(25708,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)],[170,98]),
[iquote('0:SpR:170.3,98.2')] ).
cnf(25760,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[25708]),
[iquote('0:Obv:25708.0')] ).
cnf(25761,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[25760,99]),
[iquote('0:SSi:25760.2,99.2')] ).
cnf(27532,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)],[6412]),
[iquote('1:EqR:6412.5')] ).
cnf(27570,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[27532,98,99]),
[iquote('1:SSi:27532.0,98.2,98.2,99.2,99.2')] ).
cnf(27571,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[25761,27570]),
[iquote('1:MRR:25761.3,27570.1')] ).
cnf(27574,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[27571]),
[iquote('1:Con:27571.2')] ).
cnf(27576,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[516,27574]),
[iquote('1:MRR:516.1,27574.0')] ).
cnf(27578,plain,
$false,
inference(unc,[status(thm)],[27576,25]),
[iquote('1:UnC:27576.0,25.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC189-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.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 23:00:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 13.58/13.82
% 13.58/13.82 SPASS V 3.9
% 13.58/13.82 SPASS beiseite: Proof found.
% 13.58/13.82 % SZS status Theorem
% 13.58/13.82 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.58/13.82 SPASS derived 16840 clauses, backtracked 7840 clauses, performed 92 splits and kept 14681 clauses.
% 13.58/13.82 SPASS allocated 95471 KBytes.
% 13.58/13.82 SPASS spent 0:0:10.49 on the problem.
% 13.58/13.82 0:00:00.04 for the input.
% 13.58/13.82 0:00:00.00 for the FLOTTER CNF translation.
% 13.58/13.82 0:00:00.14 for inferences.
% 13.58/13.82 0:00:00.33 for the backtracking.
% 13.58/13.82 0:00:09.73 for the reduction.
% 13.58/13.82
% 13.58/13.82
% 13.58/13.82 Here is a proof with depth 1, length 31 :
% 13.58/13.82 % SZS output start Refutation
% See solution above
% 13.58/13.82 Formulae used in the proof : co1_6 co1_7 co1_10 co1_11 co1_12 co1_13 clause12 clause72 clause85 clause86 clause157 clause179
% 13.58/13.82
%------------------------------------------------------------------------------