TSTP Solution File: SET507-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET507-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 05:26:40 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 10 unt; 5 nHn; 21 RR)
% Number of literals : 34 ( 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subclass(universal_class,null_class),
file('SET507-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET507-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET507-6.p',unknown),
[] ).
cnf(12,axiom,
member(unordered_pair(u,v),universal_class),
file('SET507-6.p',unknown),
[] ).
cnf(13,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET507-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET507-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET507-6.p',unknown),
[] ).
cnf(53,axiom,
member(omega,universal_class),
file('SET507-6.p',unknown),
[] ).
cnf(68,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET507-6.p',unknown),
[] ).
cnf(117,plain,
( ~ subclass(null_class,universal_class)
| equal(null_class,universal_class) ),
inference(res,[status(thm),theory(equality)],[1,8]),
[iquote('0:Res:1.0,8.0')] ).
cnf(119,plain,
equal(null_class,universal_class),
inference(mrr,[status(thm)],[117,5]),
[iquote('0:MRR:117.0,5.0')] ).
cnf(124,plain,
( equal(u,universal_class)
| equal(intersection(u,regular(u)),null_class) ),
inference(rew,[status(thm),theory(equality)],[119,68]),
[iquote('0:Rew:119.0,68.0')] ).
cnf(131,plain,
( equal(u,universal_class)
| equal(intersection(u,regular(u)),universal_class) ),
inference(rew,[status(thm),theory(equality)],[119,124]),
[iquote('0:Rew:119.0,124.1')] ).
cnf(135,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[13,12]),
[iquote('0:SpR:13.0,12.0')] ).
cnf(176,plain,
( ~ member(u,universal_class)
| equal(v,universal_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[131,22]),
[iquote('0:SpL:131.1,22.0')] ).
cnf(228,plain,
( equal(u,universal_class)
| member(omega,u) ),
inference(res,[status(thm),theory(equality)],[53,176]),
[iquote('0:Res:53.0,176.0')] ).
cnf(237,plain,
( ~ member(omega,u)
| equal(complement(u),universal_class) ),
inference(res,[status(thm),theory(equality)],[228,25]),
[iquote('0:Res:228.1,25.1')] ).
cnf(244,plain,
equal(complement(universal_class),universal_class),
inference(res,[status(thm),theory(equality)],[53,237]),
[iquote('0:Res:53.0,237.0')] ).
cnf(272,plain,
( ~ member(u,universal_class)
| ~ member(u,universal_class) ),
inference(spl,[status(thm),theory(equality)],[244,25]),
[iquote('0:SpL:244.0,25.1')] ).
cnf(273,plain,
~ member(u,universal_class),
inference(obv,[status(thm),theory(equality)],[272]),
[iquote('0:Obv:272.0')] ).
cnf(274,plain,
$false,
inference(unc,[status(thm)],[273,135]),
[iquote('0:UnC:273.0,135.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET507-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n016.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 11:49:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 140 clauses, backtracked 0 clauses, performed 1 splits and kept 217 clauses.
% 0.19/0.45 SPASS allocated 75962 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.45 0:00:00.04 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.03 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 5, length 21 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : prove_universal_class_not_subclass_of_null_class_1 class_elements_are_sets subclass_implies_equal unordered_pairs_in_universal singleton_set intersection1 complement1 omega_in_universal regularity2
% 0.19/0.45
%------------------------------------------------------------------------------