TSTP Solution File: SET015-4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET015-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 05:22:33 EDT 2022
% Result : Unsatisfiable 22.69s 22.93s
% Output : Refutation 22.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 41 ( 8 unt; 12 nHn; 41 RR)
% Number of literals : 100 ( 0 equ; 55 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(u,v)
| little_set(u) ),
file('SET015-4.p',unknown),
[] ).
cnf(3,axiom,
( equal(u,v)
| member(f1(u,v),v)
| member(f1(u,v),u) ),
file('SET015-4.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(f1(u,v),v)
| ~ member(f1(u,v),u)
| equal(u,v) ),
file('SET015-4.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET015-4.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET015-4.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET015-4.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET015-4.p',unknown),
[] ).
cnf(9,axiom,
( ~ little_set(u)
| member(u,v)
| member(u,complement(v)) ),
file('SET015-4.p',unknown),
[] ).
cnf(10,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET015-4.p',unknown),
[] ).
cnf(13,axiom,
equal(union(as,bs),cs),
file('SET015-4.p',unknown),
[] ).
cnf(14,axiom,
equal(union(bs,as),ds),
file('SET015-4.p',unknown),
[] ).
cnf(15,axiom,
~ equal(ds,cs),
file('SET015-4.p',unknown),
[] ).
cnf(16,plain,
( ~ member(f1(ds,cs),cs)
| ~ member(f1(ds,cs),ds) ),
inference(res,[status(thm),theory(equality)],[4,15]),
[iquote('0:Res:4.2,15.0')] ).
cnf(17,plain,
( member(f1(ds,cs),cs)
| member(f1(ds,cs),ds) ),
inference(res,[status(thm),theory(equality)],[3,15]),
[iquote('0:Res:3.2,15.0')] ).
cnf(31,plain,
( ~ member(u,intersection(complement(v),complement(w)))
| ~ member(u,union(v,w)) ),
inference(spl,[status(thm),theory(equality)],[10,8]),
[iquote('0:SpL:10.0,8.1')] ).
cnf(35,plain,
( ~ little_set(u)
| member(u,intersection(complement(v),complement(w)))
| member(u,union(v,w)) ),
inference(spr,[status(thm),theory(equality)],[10,9]),
[iquote('0:SpR:10.0,9.2')] ).
cnf(143,plain,
( ~ member(u,complement(v))
| ~ member(u,complement(w))
| ~ member(u,union(w,v)) ),
inference(res,[status(thm),theory(equality)],[7,31]),
[iquote('0:Res:7.2,31.0')] ).
cnf(466,plain,
( ~ little_set(u)
| member(u,union(v,w))
| member(u,complement(v)) ),
inference(res,[status(thm),theory(equality)],[35,5]),
[iquote('0:Res:35.1,5.0')] ).
cnf(467,plain,
( ~ little_set(u)
| member(u,union(v,w))
| member(u,complement(w)) ),
inference(res,[status(thm),theory(equality)],[35,6]),
[iquote('0:Res:35.1,6.0')] ).
cnf(2475,plain,
( ~ little_set(u)
| member(u,ds)
| member(u,complement(bs)) ),
inference(spr,[status(thm),theory(equality)],[14,466]),
[iquote('0:SpR:14.0,466.1')] ).
cnf(2476,plain,
( ~ little_set(u)
| member(u,cs)
| member(u,complement(as)) ),
inference(spr,[status(thm),theory(equality)],[13,466]),
[iquote('0:SpR:13.0,466.1')] ).
cnf(2531,plain,
( ~ little_set(u)
| member(u,ds)
| member(u,complement(as)) ),
inference(spr,[status(thm),theory(equality)],[14,467]),
[iquote('0:SpR:14.0,467.1')] ).
cnf(2532,plain,
( ~ little_set(u)
| member(u,cs)
| member(u,complement(bs)) ),
inference(spr,[status(thm),theory(equality)],[13,467]),
[iquote('0:SpR:13.0,467.1')] ).
cnf(3222,plain,
( ~ little_set(u)
| ~ member(u,as)
| member(u,ds) ),
inference(res,[status(thm),theory(equality)],[2531,8]),
[iquote('0:Res:2531.2,8.1')] ).
cnf(3231,plain,
( ~ member(u,as)
| member(u,ds) ),
inference(mrr,[status(thm)],[3222,1]),
[iquote('0:MRR:3222.0,1.1')] ).
cnf(4489,plain,
( ~ member(u,complement(bs))
| ~ member(u,complement(as))
| ~ member(u,cs) ),
inference(spl,[status(thm),theory(equality)],[13,143]),
[iquote('0:SpL:13.0,143.2')] ).
cnf(4496,plain,
( ~ member(u,complement(as))
| ~ member(u,complement(bs))
| ~ member(u,ds) ),
inference(spl,[status(thm),theory(equality)],[14,143]),
[iquote('0:SpL:14.0,143.2')] ).
cnf(6923,plain,
( ~ little_set(u)
| ~ member(u,bs)
| member(u,cs) ),
inference(res,[status(thm),theory(equality)],[2532,8]),
[iquote('0:Res:2532.2,8.1')] ).
cnf(6929,plain,
( ~ member(u,bs)
| member(u,cs) ),
inference(mrr,[status(thm)],[6923,1]),
[iquote('0:MRR:6923.0,1.1')] ).
cnf(15147,plain,
( ~ little_set(u)
| ~ member(u,complement(as))
| ~ member(u,ds)
| member(u,bs) ),
inference(res,[status(thm),theory(equality)],[9,4496]),
[iquote('0:Res:9.2,4496.1')] ).
cnf(15208,plain,
( ~ member(u,complement(as))
| ~ member(u,ds)
| member(u,bs) ),
inference(mrr,[status(thm)],[15147,1]),
[iquote('0:MRR:15147.0,1.1')] ).
cnf(15609,plain,
( ~ little_set(u)
| ~ member(u,complement(as))
| ~ member(u,cs)
| member(u,ds) ),
inference(res,[status(thm),theory(equality)],[2475,4489]),
[iquote('0:Res:2475.2,4489.0')] ).
cnf(15670,plain,
( ~ member(u,complement(as))
| ~ member(u,cs)
| member(u,ds) ),
inference(mrr,[status(thm)],[15609,1]),
[iquote('0:MRR:15609.0,1.1')] ).
cnf(17783,plain,
( ~ little_set(u)
| ~ member(u,ds)
| member(u,cs)
| member(u,bs) ),
inference(res,[status(thm),theory(equality)],[2476,15208]),
[iquote('0:Res:2476.2,15208.0')] ).
cnf(17854,plain,
( ~ member(u,ds)
| member(u,cs) ),
inference(mrr,[status(thm)],[17783,1,6929]),
[iquote('0:MRR:17783.0,17783.3,1.1,6929.0')] ).
cnf(17947,plain,
member(f1(ds,cs),cs),
inference(mrr,[status(thm)],[17,17854]),
[iquote('0:MRR:17.1,17854.0')] ).
cnf(17970,plain,
~ member(f1(ds,cs),ds),
inference(mrr,[status(thm)],[16,17854]),
[iquote('0:MRR:16.0,17854.1')] ).
cnf(47177,plain,
( ~ little_set(u)
| ~ member(u,cs)
| member(u,as)
| member(u,ds) ),
inference(res,[status(thm),theory(equality)],[9,15670]),
[iquote('0:Res:9.2,15670.0')] ).
cnf(47182,plain,
( ~ member(u,cs)
| member(u,ds) ),
inference(mrr,[status(thm)],[47177,1,3231]),
[iquote('0:MRR:47177.0,47177.2,1.1,3231.0')] ).
cnf(47206,plain,
~ member(f1(ds,cs),cs),
inference(res,[status(thm),theory(equality)],[47182,17970]),
[iquote('0:Res:47182.1,17970.0')] ).
cnf(47227,plain,
$false,
inference(mrr,[status(thm)],[47206,17947]),
[iquote('0:MRR:47206.0,17947.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET015-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n016.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jul 10 23:12:27 EDT 2022
% 0.12/0.32 % CPUTime :
% 22.69/22.93
% 22.69/22.93 SPASS V 3.9
% 22.69/22.93 SPASS beiseite: Proof found.
% 22.69/22.93 % SZS status Theorem
% 22.69/22.93 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.69/22.93 SPASS derived 28011 clauses, backtracked 8091 clauses, performed 33 splits and kept 13676 clauses.
% 22.69/22.93 SPASS allocated 104883 KBytes.
% 22.69/22.93 SPASS spent 0:0:22.19 on the problem.
% 22.69/22.93 0:00:00.04 for the input.
% 22.69/22.93 0:00:00.00 for the FLOTTER CNF translation.
% 22.69/22.93 0:00:00.27 for inferences.
% 22.69/22.93 0:00:00.22 for the backtracking.
% 22.69/22.93 0:0:21.55 for the reduction.
% 22.69/22.93
% 22.69/22.93
% 22.69/22.93 Here is a proof with depth 6, length 41 :
% 22.69/22.93 % SZS output start Refutation
% See solution above
% 22.69/22.93 Formulae used in the proof : a2 extensionality2 extensionality3 intersection1 intersection2 intersection3 complement1 complement2 union a_union_b_is_c b_union_a_is_d prove_c_equals_d
% 22.69/22.93
%------------------------------------------------------------------------------