TSTP Solution File: SET080-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET080-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 05:23:42 EDT 2022
% Result : Unsatisfiable 0.18s 0.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 8 unt; 6 nHn; 17 RR)
% Number of literals : 29 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 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(null_class,singleton(null_class)),
file('SET080-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET080-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET080-6.p',unknown),
[] ).
cnf(12,axiom,
member(unordered_pair(u,v),universal_class),
file('SET080-6.p',unknown),
[] ).
cnf(13,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET080-6.p',unknown),
[] ).
cnf(67,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET080-6.p',unknown),
[] ).
cnf(106,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[13,12]),
[iquote('0:SpR:13.0,12.0')] ).
cnf(135,plain,
( ~ member(u,universal_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[13,11]),
[iquote('0:SpR:13.0,11.1')] ).
cnf(137,plain,
~ member(null_class,universal_class),
inference(res,[status(thm),theory(equality)],[135,1]),
[iquote('0:Res:135.1,1.0')] ).
cnf(461,plain,
( ~ member(u,singleton(v))
| equal(u,v)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[13,9]),
[iquote('0:SpL:13.0,9.0')] ).
cnf(473,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[461]),
[iquote('0:Obv:461.1')] ).
cnf(632,plain,
( equal(singleton(u),null_class)
| equal(regular(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[67,473]),
[iquote('0:Res:67.1,473.0')] ).
cnf(656,plain,
( equal(singleton(u),null_class)
| equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[632,67]),
[iquote('0:SpR:632.1,67.1')] ).
cnf(660,plain,
( equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[656]),
[iquote('0:Obv:656.0')] ).
cnf(663,plain,
equal(singleton(null_class),null_class),
inference(res,[status(thm),theory(equality)],[660,1]),
[iquote('0:Res:660.1,1.0')] ).
cnf(680,plain,
member(null_class,universal_class),
inference(spr,[status(thm),theory(equality)],[663,106]),
[iquote('0:SpR:663.0,106.0')] ).
cnf(697,plain,
$false,
inference(mrr,[status(thm)],[680,137]),
[iquote('0:MRR:680.0,137.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET080-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.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 11:11:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.50
% 0.18/0.50 SPASS V 3.9
% 0.18/0.50 SPASS beiseite: Proof found.
% 0.18/0.50 % SZS status Theorem
% 0.18/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.50 SPASS derived 548 clauses, backtracked 0 clauses, performed 0 splits and kept 443 clauses.
% 0.18/0.50 SPASS allocated 76383 KBytes.
% 0.18/0.50 SPASS spent 0:00:00.16 on the problem.
% 0.18/0.50 0:00:00.04 for the input.
% 0.18/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.50 0:00:00.01 for inferences.
% 0.18/0.50 0:00:00.00 for the backtracking.
% 0.18/0.50 0:00:00.08 for the reduction.
% 0.18/0.50
% 0.18/0.50
% 0.18/0.50 Here is a proof with depth 5, length 17 :
% 0.18/0.50 % SZS output start Refutation
% See solution above
% 0.18/0.50 Formulae used in the proof : prove_null_class_in_its_singleton_1 unordered_pair_member unordered_pair3 unordered_pairs_in_universal singleton_set regularity1
% 0.18/0.50
%------------------------------------------------------------------------------