%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET061-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 05:23:19 EDT 2022
% Result : Unsatisfiable 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 14 ( 4 unt; 3 nHn; 14 RR)
% Number of literals : 26 ( 0 equ; 11 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,
member(z__dfg,null_class),
file('SET061-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET061-6.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET061-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET061-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET061-6.p',unknown),
[] ).
cnf(68,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET061-6.p',unknown),
[] ).
cnf(95,plain,
( ~ subclass(null_class,u)
| member(z__dfg,u) ),
inference(res,[status(thm),theory(equality)],[1,2]),
[iquote('0:Res:1.0,2.1')] ).
cnf(99,plain,
~ member(z__dfg,complement(null_class)),
inference(res,[status(thm),theory(equality)],[1,25]),
[iquote('0:Res:1.0,25.1')] ).
cnf(112,plain,
( ~ equal(u,null_class)
| member(z__dfg,u) ),
inference(res,[status(thm),theory(equality)],[7,95]),
[iquote('0:Res:7.1,95.0')] ).
cnf(178,plain,
( ~ equal(intersection(u,v),null_class)
| member(z__dfg,u) ),
inference(res,[status(thm),theory(equality)],[112,22]),
[iquote('0:Res:112.1,22.0')] ).
cnf(207,plain,
( ~ equal(null_class,null_class)
| equal(u,null_class)
| member(z__dfg,u) ),
inference(spl,[status(thm),theory(equality)],[68,178]),
[iquote('0:SpL:68.1,178.0')] ).
cnf(208,plain,
( equal(u,null_class)
| member(z__dfg,u) ),
inference(obv,[status(thm),theory(equality)],[207]),
[iquote('0:Obv:207.0')] ).
cnf(209,plain,
member(z__dfg,u),
inference(mrr,[status(thm)],[208,112]),
[iquote('0:MRR:208.0,112.0')] ).
cnf(210,plain,
$false,
inference(unc,[status(thm)],[209,99]),
[iquote('0:UnC:209.0,99.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET061-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jul 11 03:02:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.45
% 0.21/0.45 SPASS V 3.9
% 0.21/0.45 SPASS beiseite: Proof found.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.45 SPASS derived 106 clauses, backtracked 0 clauses, performed 0 splits and kept 168 clauses.
% 0.21/0.45 SPASS allocated 75873 KBytes.
% 0.21/0.45 SPASS spent 0:00:00.08 on the problem.
% 0.21/0.45 0:00:00.04 for the input.
% 0.21/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.45 0:00:00.00 for inferences.
% 0.21/0.45 0:00:00.00 for the backtracking.
% 0.21/0.45 0:00:00.02 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 Here is a proof with depth 4, length 14 :
% 0.21/0.45 % SZS output start Refutation
% See solution above
% 0.21/0.45 Formulae used in the proof : prove_existence_of_null_class_1 subclass_members equal_implies_subclass2 intersection1 complement1 regularity2
% 0.21/0.45
%------------------------------------------------------------------------------