TSTP Solution File: SET012-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET012-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 05:22:27 EDT 2022
% Result : Unsatisfiable 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 27 ( 14 unt; 6 nHn; 27 RR)
% Number of literals : 45 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(complement(as),bs),
file('SET012-3.p',unknown),
[] ).
cnf(2,axiom,
equal(complement(bs),cs),
file('SET012-3.p',unknown),
[] ).
cnf(3,axiom,
~ equal(cs,as),
file('SET012-3.p',unknown),
[] ).
cnf(5,axiom,
( little_set(f1(u,v))
| equal(u,v) ),
file('SET012-3.p',unknown),
[] ).
cnf(6,axiom,
( equal(u,v)
| member(f1(u,v),v)
| member(f1(u,v),u) ),
file('SET012-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(f1(u,v),v)
| ~ member(f1(u,v),u)
| equal(u,v) ),
file('SET012-3.p',unknown),
[] ).
cnf(34,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET012-3.p',unknown),
[] ).
cnf(35,axiom,
( ~ little_set(u)
| member(u,v)
| member(u,complement(v)) ),
file('SET012-3.p',unknown),
[] ).
cnf(152,plain,
( ~ member(f1(as,cs),cs)
| ~ member(f1(as,cs),as) ),
inference(res,[status(thm),theory(equality)],[7,3]),
[iquote('0:Res:7.2,3.0')] ).
cnf(153,plain,
( member(f1(as,cs),cs)
| member(f1(as,cs),as) ),
inference(res,[status(thm),theory(equality)],[6,3]),
[iquote('0:Res:6.2,3.0')] ).
cnf(156,plain,
little_set(f1(as,cs)),
inference(res,[status(thm),theory(equality)],[5,3]),
[iquote('0:Res:5.1,3.0')] ).
cnf(273,plain,
( ~ member(u,bs)
| ~ member(u,cs) ),
inference(spl,[status(thm),theory(equality)],[2,34]),
[iquote('0:SpL:2.0,34.1')] ).
cnf(274,plain,
( ~ member(u,as)
| ~ member(u,bs) ),
inference(spl,[status(thm),theory(equality)],[1,34]),
[iquote('0:SpL:1.0,34.1')] ).
cnf(521,plain,
member(f1(as,cs),cs),
inference(spt,[spt(split,[position(s1)])],[153]),
[iquote('1:Spt:153.0')] ).
cnf(522,plain,
~ member(f1(as,cs),as),
inference(mrr,[status(thm)],[152,521]),
[iquote('1:MRR:152.0,521.0')] ).
cnf(524,plain,
~ member(f1(as,cs),bs),
inference(res,[status(thm),theory(equality)],[521,273]),
[iquote('1:Res:521.0,273.1')] ).
cnf(548,plain,
( ~ little_set(u)
| member(u,bs)
| member(u,cs) ),
inference(spr,[status(thm),theory(equality)],[2,35]),
[iquote('0:SpR:2.0,35.2')] ).
cnf(549,plain,
( ~ little_set(u)
| member(u,as)
| member(u,bs) ),
inference(spr,[status(thm),theory(equality)],[1,35]),
[iquote('0:SpR:1.0,35.2')] ).
cnf(715,plain,
( ~ little_set(f1(as,cs))
| member(f1(as,cs),as) ),
inference(res,[status(thm),theory(equality)],[549,524]),
[iquote('1:Res:549.2,524.0')] ).
cnf(718,plain,
member(f1(as,cs),as),
inference(ssi,[status(thm)],[715,156]),
[iquote('1:SSi:715.0,156.0')] ).
cnf(719,plain,
$false,
inference(mrr,[status(thm)],[718,522]),
[iquote('1:MRR:718.0,522.0')] ).
cnf(728,plain,
~ member(f1(as,cs),cs),
inference(spt,[spt(split,[position(sa)])],[719,521]),
[iquote('1:Spt:719.0,153.0,521.0')] ).
cnf(729,plain,
member(f1(as,cs),as),
inference(spt,[spt(split,[position(s2)])],[153]),
[iquote('1:Spt:719.0,153.1')] ).
cnf(732,plain,
( ~ little_set(f1(as,cs))
| member(f1(as,cs),bs) ),
inference(res,[status(thm),theory(equality)],[548,728]),
[iquote('1:Res:548.2,728.0')] ).
cnf(733,plain,
member(f1(as,cs),bs),
inference(ssi,[status(thm)],[732,156]),
[iquote('1:SSi:732.0,156.0')] ).
cnf(735,plain,
~ member(f1(as,cs),as),
inference(res,[status(thm),theory(equality)],[733,274]),
[iquote('1:Res:733.0,274.1')] ).
cnf(737,plain,
$false,
inference(mrr,[status(thm)],[735,729]),
[iquote('1:MRR:735.0,729.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET012-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Sun Jul 10 16:45:18 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.52
% 0.20/0.52 SPASS V 3.9
% 0.20/0.52 SPASS beiseite: Proof found.
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.52 SPASS derived 466 clauses, backtracked 8 clauses, performed 4 splits and kept 461 clauses.
% 0.20/0.52 SPASS allocated 76433 KBytes.
% 0.20/0.52 SPASS spent 0:00:00.17 on the problem.
% 0.20/0.52 0:00:00.04 for the input.
% 0.20/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.52 0:00:00.01 for inferences.
% 0.20/0.52 0:00:00.00 for the backtracking.
% 0.20/0.52 0:00:00.08 for the reduction.
% 0.20/0.52
% 0.20/0.52
% 0.20/0.52 Here is a proof with depth 4, length 27 :
% 0.20/0.52 % SZS output start Refutation
% See solution above
% 0.20/0.52 Formulae used in the proof : complement_of_a_is_b complement_of_b_is_c prove_a_equals_c extensionality1 extensionality2 extensionality3 complement1 complement2
% 0.20/0.52
%------------------------------------------------------------------------------