TSTP Solution File: SET012-4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 0.19s 0.40s
% Output : Refutation 0.19s
% 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(2,axiom,
( little_set(f1(u,v))
| equal(u,v) ),
file('SET012-4.p',unknown),
[] ).
cnf(3,axiom,
( equal(u,v)
| member(f1(u,v),v)
| member(f1(u,v),u) ),
file('SET012-4.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(f1(u,v),v)
| ~ member(f1(u,v),u)
| equal(u,v) ),
file('SET012-4.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET012-4.p',unknown),
[] ).
cnf(6,axiom,
( ~ little_set(u)
| member(u,v)
| member(u,complement(v)) ),
file('SET012-4.p',unknown),
[] ).
cnf(9,axiom,
equal(complement(as),bs),
file('SET012-4.p',unknown),
[] ).
cnf(10,axiom,
equal(complement(bs),cs),
file('SET012-4.p',unknown),
[] ).
cnf(11,axiom,
~ equal(cs,as),
file('SET012-4.p',unknown),
[] ).
cnf(15,plain,
( ~ member(f1(as,cs),cs)
| ~ member(f1(as,cs),as) ),
inference(res,[status(thm),theory(equality)],[4,11]),
[iquote('0:Res:4.2,11.0')] ).
cnf(16,plain,
( member(f1(as,cs),cs)
| member(f1(as,cs),as) ),
inference(res,[status(thm),theory(equality)],[3,11]),
[iquote('0:Res:3.2,11.0')] ).
cnf(17,plain,
little_set(f1(as,cs)),
inference(res,[status(thm),theory(equality)],[2,11]),
[iquote('0:Res:2.1,11.0')] ).
cnf(21,plain,
( ~ member(u,bs)
| ~ member(u,cs) ),
inference(spl,[status(thm),theory(equality)],[10,5]),
[iquote('0:SpL:10.0,5.1')] ).
cnf(22,plain,
( ~ member(u,as)
| ~ member(u,bs) ),
inference(spl,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpL:9.0,5.1')] ).
cnf(23,plain,
member(f1(as,cs),cs),
inference(spt,[spt(split,[position(s1)])],[16]),
[iquote('1:Spt:16.0')] ).
cnf(24,plain,
~ member(f1(as,cs),as),
inference(mrr,[status(thm)],[15,23]),
[iquote('1:MRR:15.0,23.0')] ).
cnf(26,plain,
~ member(f1(as,cs),bs),
inference(res,[status(thm),theory(equality)],[23,21]),
[iquote('1:Res:23.0,21.1')] ).
cnf(27,plain,
( ~ little_set(u)
| member(u,bs)
| member(u,cs) ),
inference(spr,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpR:10.0,6.2')] ).
cnf(28,plain,
( ~ little_set(u)
| member(u,as)
| member(u,bs) ),
inference(spr,[status(thm),theory(equality)],[9,6]),
[iquote('0:SpR:9.0,6.2')] ).
cnf(35,plain,
( ~ little_set(f1(as,cs))
| member(f1(as,cs),as) ),
inference(res,[status(thm),theory(equality)],[28,26]),
[iquote('1:Res:28.2,26.0')] ).
cnf(36,plain,
member(f1(as,cs),as),
inference(ssi,[status(thm)],[35,17]),
[iquote('1:SSi:35.0,17.0')] ).
cnf(37,plain,
$false,
inference(mrr,[status(thm)],[36,24]),
[iquote('1:MRR:36.0,24.0')] ).
cnf(38,plain,
~ member(f1(as,cs),cs),
inference(spt,[spt(split,[position(sa)])],[37,23]),
[iquote('1:Spt:37.0,16.0,23.0')] ).
cnf(39,plain,
member(f1(as,cs),as),
inference(spt,[spt(split,[position(s2)])],[16]),
[iquote('1:Spt:37.0,16.1')] ).
cnf(41,plain,
( ~ little_set(f1(as,cs))
| member(f1(as,cs),bs) ),
inference(res,[status(thm),theory(equality)],[27,38]),
[iquote('1:Res:27.2,38.0')] ).
cnf(42,plain,
member(f1(as,cs),bs),
inference(ssi,[status(thm)],[41,17]),
[iquote('1:SSi:41.0,17.0')] ).
cnf(56,plain,
~ member(f1(as,cs),as),
inference(res,[status(thm),theory(equality)],[42,22]),
[iquote('1:Res:42.0,22.1')] ).
cnf(57,plain,
$false,
inference(mrr,[status(thm)],[56,39]),
[iquote('1:MRR:56.0,39.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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 Jul 10 20:03:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.40
% 0.19/0.40 SPASS V 3.9
% 0.19/0.40 SPASS beiseite: Proof found.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40 SPASS derived 40 clauses, backtracked 3 clauses, performed 1 splits and kept 37 clauses.
% 0.19/0.40 SPASS allocated 75626 KBytes.
% 0.19/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.40 0:00:00.03 for the input.
% 0.19/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40 0:00:00.00 for inferences.
% 0.19/0.40 0:00:00.00 for the backtracking.
% 0.19/0.40 0:00:00.00 for the reduction.
% 0.19/0.40
% 0.19/0.40
% 0.19/0.40 Here is a proof with depth 4, length 27 :
% 0.19/0.40 % SZS output start Refutation
% See solution above
% 0.19/0.40 Formulae used in the proof : extensionality1 extensionality2 extensionality3 complement1 complement2 complement_of_a_is_b complement_of_b_is_c prove_a_equals_c
% 0.19/0.40
%------------------------------------------------------------------------------