%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET063-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 05:23:24 EDT 2022
% Result : Unsatisfiable 0.22s 0.46s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 6 unt; 4 nHn; 15 RR)
% Number of literals : 25 ( 0 equ; 8 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,
subclass(x__dfg,null_class),
file('SET063-6.p',unknown),
[] ).
cnf(2,axiom,
~ equal(null_class,x__dfg),
file('SET063-6.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET063-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET063-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET063-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET063-6.p',unknown),
[] ).
cnf(69,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET063-6.p',unknown),
[] ).
cnf(97,plain,
( ~ subclass(null_class,x__dfg)
| equal(null_class,x__dfg) ),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.0')] ).
cnf(103,plain,
equal(intersection(x__dfg,regular(x__dfg)),null_class),
inference(res,[status(thm),theory(equality)],[69,2]),
[iquote('0:Res:69.0,2.0')] ).
cnf(108,plain,
~ subclass(null_class,x__dfg),
inference(mrr,[status(thm)],[97,2]),
[iquote('0:MRR:97.1,2.0')] ).
cnf(176,plain,
( ~ member(u,null_class)
| member(u,x__dfg) ),
inference(spl,[status(thm),theory(equality)],[103,23]),
[iquote('0:SpL:103.0,23.0')] ).
cnf(183,plain,
( subclass(null_class,u)
| member(not_subclass_element(null_class,u),x__dfg) ),
inference(res,[status(thm),theory(equality)],[4,176]),
[iquote('0:Res:4.1,176.0')] ).
cnf(186,plain,
( subclass(null_class,x__dfg)
| subclass(null_class,x__dfg) ),
inference(res,[status(thm),theory(equality)],[183,5]),
[iquote('0:Res:183.1,5.0')] ).
cnf(187,plain,
subclass(null_class,x__dfg),
inference(obv,[status(thm),theory(equality)],[186]),
[iquote('0:Obv:186.0')] ).
cnf(188,plain,
$false,
inference(mrr,[status(thm)],[187,108]),
[iquote('0:MRR:187.0,108.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET063-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n012.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jul 10 20:48:28 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.22/0.46
% 0.22/0.46 SPASS V 3.9
% 0.22/0.46 SPASS beiseite: Proof found.
% 0.22/0.46 % SZS status Theorem
% 0.22/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.46 SPASS derived 84 clauses, backtracked 0 clauses, performed 0 splits and kept 144 clauses.
% 0.22/0.46 SPASS allocated 75836 KBytes.
% 0.22/0.46 SPASS spent 0:00:00.08 on the problem.
% 0.22/0.46 0:00:00.04 for the input.
% 0.22/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.46 0:00:00.00 for inferences.
% 0.22/0.46 0:00:00.00 for the backtracking.
% 0.22/0.46 0:00:00.01 for the reduction.
% 0.22/0.46
% 0.22/0.46
% 0.22/0.46 Here is a proof with depth 4, length 15 :
% 0.22/0.46 % SZS output start Refutation
% See solution above
% 0.22/0.46 Formulae used in the proof : prove_corollary_of_null_class_is_subclass_1 prove_corollary_of_null_class_is_subclass_2 not_subclass_members1 not_subclass_members2 subclass_implies_equal intersection1 regularity2
% 0.22/0.46
%------------------------------------------------------------------------------