TSTP Solution File: SET261-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET261-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 05:25:20 EDT 2022
% Result : Unsatisfiable 1.10s 1.33s
% Output : Refutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 9 unt; 5 nHn; 24 RR)
% Number of literals : 43 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(domain_of(null_class),null_class),
file('SET261-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET261-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET261-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET261-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET261-6.p',unknown),
[] ).
cnf(29,axiom,
equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
file('SET261-6.p',unknown),
[] ).
cnf(31,axiom,
( ~ member(u,domain_of(v))
| ~ equal(restrict(v,singleton(u),universal_class),null_class) ),
file('SET261-6.p',unknown),
[] ).
cnf(67,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET261-6.p',unknown),
[] ).
cnf(163,plain,
( ~ member(regular(complement(u)),u)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[67,25]),
[iquote('0:Res:67.1,25.1')] ).
cnf(181,plain,
( equal(intersection(u,v),null_class)
| member(regular(intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[67,22]),
[iquote('0:Res:67.1,22.0')] ).
cnf(356,plain,
( ~ subclass(u,v)
| equal(u,null_class)
| member(regular(u),v) ),
inference(res,[status(thm),theory(equality)],[67,2]),
[iquote('0:Res:67.1,2.0')] ).
cnf(3079,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[356,163]),
[iquote('0:Res:356.2,163.0')] ).
cnf(3093,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class) ),
inference(obv,[status(thm),theory(equality)],[3079]),
[iquote('0:Obv:3079.1')] ).
cnf(3719,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[5,3093]),
[iquote('0:Res:5.0,3093.0')] ).
cnf(3744,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[3719,25]),
[iquote('0:SpL:3719.0,25.1')] ).
cnf(3780,plain,
( ~ subclass(u,universal_class)
| ~ member(regular(u),null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[356,3744]),
[iquote('0:Res:356.2,3744.0')] ).
cnf(3793,plain,
( ~ member(regular(u),null_class)
| equal(u,null_class) ),
inference(mrr,[status(thm)],[3780,5]),
[iquote('0:MRR:3780.0,5.0')] ).
cnf(3812,plain,
( equal(intersection(null_class,u),null_class)
| equal(intersection(null_class,u),null_class) ),
inference(res,[status(thm),theory(equality)],[181,3793]),
[iquote('0:Res:181.1,3793.0')] ).
cnf(3815,plain,
equal(intersection(null_class,u),null_class),
inference(obv,[status(thm),theory(equality)],[3812]),
[iquote('0:Obv:3812.0')] ).
cnf(3896,plain,
equal(restrict(null_class,u,v),null_class),
inference(spr,[status(thm),theory(equality)],[3815,29]),
[iquote('0:SpR:3815.0,29.0')] ).
cnf(4015,plain,
( ~ member(u,domain_of(null_class))
| ~ equal(null_class,null_class) ),
inference(spl,[status(thm),theory(equality)],[3896,31]),
[iquote('0:SpL:3896.0,31.1')] ).
cnf(4016,plain,
~ member(u,domain_of(null_class)),
inference(obv,[status(thm),theory(equality)],[4015]),
[iquote('0:Obv:4015.1')] ).
cnf(4024,plain,
equal(domain_of(null_class),null_class),
inference(res,[status(thm),theory(equality)],[67,4016]),
[iquote('0:Res:67.1,4016.0')] ).
cnf(4039,plain,
$false,
inference(mrr,[status(thm)],[4024,1]),
[iquote('0:MRR:4024.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : SET261-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.09 % Command : run_spass %d %s
% 0.08/0.28 % Computer : n011.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Sun Jul 10 17:23:11 EDT 2022
% 0.08/0.28 % CPUTime :
% 1.10/1.33
% 1.10/1.33 SPASS V 3.9
% 1.10/1.33 SPASS beiseite: Proof found.
% 1.10/1.33 % SZS status Theorem
% 1.10/1.33 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.10/1.33 SPASS derived 3283 clauses, backtracked 290 clauses, performed 3 splits and kept 2216 clauses.
% 1.10/1.33 SPASS allocated 79070 KBytes.
% 1.10/1.33 SPASS spent 0:00:01.01 on the problem.
% 1.10/1.33 0:00:00.03 for the input.
% 1.10/1.33 0:00:00.00 for the FLOTTER CNF translation.
% 1.10/1.33 0:00:00.05 for inferences.
% 1.10/1.33 0:00:00.03 for the backtracking.
% 1.10/1.33 0:00:00.85 for the reduction.
% 1.10/1.33
% 1.10/1.33
% 1.10/1.33 Here is a proof with depth 9, length 24 :
% 1.10/1.33 % SZS output start Refutation
% See solution above
% 1.10/1.33 Formulae used in the proof : prove_domain_of_null_class_1 subclass_members class_elements_are_sets intersection1 complement1 restriction1 domain1 regularity1
% 1.10/1.33
%------------------------------------------------------------------------------