%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET082-6 : 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 05:23:44 EDT 2022
% Result : Unsatisfiable 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 7 unt; 6 nHn; 16 RR)
% Number of literals : 29 ( 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ member(x__dfg,universal_class),
file('SET082-6.p',unknown),
[] ).
cnf(2,axiom,
~ equal(singleton(x__dfg),null_class),
file('SET082-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET082-6.p',unknown),
[] ).
cnf(6,axiom,
subclass(u,universal_class),
file('SET082-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET082-6.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET082-6.p',unknown),
[] ).
cnf(68,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET082-6.p',unknown),
[] ).
cnf(101,plain,
( ~ subclass(u,universal_class)
| ~ member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.2,1.0')] ).
cnf(112,plain,
~ member(x__dfg,u),
inference(mrr,[status(thm)],[101,6]),
[iquote('0:MRR:101.0,6.0')] ).
cnf(449,plain,
( ~ member(u,singleton(v))
| equal(u,v)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[14,10]),
[iquote('0:SpL:14.0,10.0')] ).
cnf(460,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[449]),
[iquote('0:Obv:449.1')] ).
cnf(465,plain,
( equal(singleton(u),null_class)
| equal(regular(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[68,460]),
[iquote('0:Res:68.1,460.0')] ).
cnf(528,plain,
( equal(singleton(u),null_class)
| equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[465,68]),
[iquote('0:SpR:465.1,68.1')] ).
cnf(532,plain,
( equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[528]),
[iquote('0:Obv:528.0')] ).
cnf(535,plain,
equal(singleton(x__dfg),null_class),
inference(res,[status(thm),theory(equality)],[532,112]),
[iquote('0:Res:532.1,112.0')] ).
cnf(539,plain,
$false,
inference(mrr,[status(thm)],[535,2]),
[iquote('0:MRR:535.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET082-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 10:09:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.49
% 0.18/0.49 SPASS V 3.9
% 0.18/0.49 SPASS beiseite: Proof found.
% 0.18/0.49 % SZS status Theorem
% 0.18/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.49 SPASS derived 388 clauses, backtracked 0 clauses, performed 0 splits and kept 370 clauses.
% 0.18/0.49 SPASS allocated 76267 KBytes.
% 0.18/0.49 SPASS spent 0:00:00.15 on the problem.
% 0.18/0.49 0:00:00.04 for the input.
% 0.18/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.49 0:00:00.01 for inferences.
% 0.18/0.49 0:00:00.00 for the backtracking.
% 0.18/0.49 0:00:00.07 for the reduction.
% 0.18/0.49
% 0.18/0.49
% 0.18/0.49 Here is a proof with depth 4, length 16 :
% 0.18/0.49 % SZS output start Refutation
% See solution above
% 0.18/0.49 Formulae used in the proof : prove_singleton_is_null_class_1 prove_singleton_is_null_class_2 subclass_members class_elements_are_sets unordered_pair_member singleton_set regularity1
% 0.18/0.49
%------------------------------------------------------------------------------