%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET064-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 05:23:25 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 7 unt; 4 nHn; 16 RR)
% Number of literals : 26 ( 0 equ; 10 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(null_class,z__dfg),
file('SET064-6.p',unknown),
[] ).
cnf(2,axiom,
~ member(not_subclass_element(z__dfg,null_class),z__dfg),
file('SET064-6.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET064-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET064-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET064-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET064-6.p',unknown),
[] ).
cnf(69,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET064-6.p',unknown),
[] ).
cnf(97,plain,
( ~ subclass(null_class,z__dfg)
| ~ subclass(z__dfg,null_class) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.2,1.0')] ).
cnf(100,plain,
equal(intersection(z__dfg,regular(z__dfg)),null_class),
inference(res,[status(thm),theory(equality)],[69,1]),
[iquote('0:Res:69.0,1.0')] ).
cnf(105,plain,
subclass(z__dfg,null_class),
inference(res,[status(thm),theory(equality)],[4,2]),
[iquote('0:Res:4.0,2.0')] ).
cnf(113,plain,
~ subclass(null_class,z__dfg),
inference(mrr,[status(thm)],[97,105]),
[iquote('0:MRR:97.1,105.0')] ).
cnf(181,plain,
( ~ member(u,null_class)
| member(u,z__dfg) ),
inference(spl,[status(thm),theory(equality)],[100,23]),
[iquote('0:SpL:100.0,23.0')] ).
cnf(189,plain,
( subclass(null_class,u)
| member(not_subclass_element(null_class,u),z__dfg) ),
inference(res,[status(thm),theory(equality)],[4,181]),
[iquote('0:Res:4.1,181.0')] ).
cnf(192,plain,
( subclass(null_class,z__dfg)
| subclass(null_class,z__dfg) ),
inference(res,[status(thm),theory(equality)],[189,5]),
[iquote('0:Res:189.1,5.0')] ).
cnf(193,plain,
subclass(null_class,z__dfg),
inference(obv,[status(thm),theory(equality)],[192]),
[iquote('0:Obv:192.0')] ).
cnf(194,plain,
$false,
inference(mrr,[status(thm)],[193,113]),
[iquote('0:MRR:193.0,113.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET064-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 20:39:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 87 clauses, backtracked 0 clauses, performed 0 splits and kept 148 clauses.
% 0.20/0.44 SPASS allocated 75840 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.44 0:00:00.04 for the input.
% 0.20/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.01 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 4, length 16 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : prove_null_class_is_unique_1 prove_null_class_is_unique_2 not_subclass_members1 not_subclass_members2 subclass_implies_equal intersection1 regularity2
% 0.20/0.44
%------------------------------------------------------------------------------