TSTP Solution File: SET103-6 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET103-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 05:24:05 EDT 2022
% Result : Unsatisfiable 0.22s 0.52s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 9 unt; 6 nHn; 18 RR)
% Number of literals : 31 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(unordered_pair(singleton(x__dfg),unordered_pair(x__dfg,null_class)),ordered_pair(x__dfg,y__dfg)),
file('SET103-6.p',unknown),
[] ).
cnf(2,axiom,
~ member(y__dfg,universal_class),
file('SET103-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET103-6.p',unknown),
[] ).
cnf(6,axiom,
subclass(u,universal_class),
file('SET103-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET103-6.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET103-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
file('SET103-6.p',unknown),
[] ).
cnf(68,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET103-6.p',unknown),
[] ).
cnf(101,plain,
( ~ subclass(u,universal_class)
| ~ member(y__dfg,u) ),
inference(res,[status(thm),theory(equality)],[3,2]),
[iquote('0:Res:3.2,2.0')] ).
cnf(109,plain,
~ member(y__dfg,u),
inference(mrr,[status(thm)],[101,6]),
[iquote('0:MRR:101.0,6.0')] ).
cnf(463,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(474,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[463]),
[iquote('0:Obv:463.1')] ).
cnf(477,plain,
( equal(singleton(u),null_class)
| equal(regular(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[68,474]),
[iquote('0:Res:68.1,474.0')] ).
cnf(555,plain,
( equal(singleton(u),null_class)
| equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[477,68]),
[iquote('0:SpR:477.1,68.1')] ).
cnf(559,plain,
( equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[555]),
[iquote('0:Obv:555.0')] ).
cnf(562,plain,
equal(singleton(y__dfg),null_class),
inference(res,[status(thm),theory(equality)],[559,109]),
[iquote('0:Res:559.1,109.0')] ).
cnf(577,plain,
equal(unordered_pair(singleton(u),unordered_pair(u,null_class)),ordered_pair(u,y__dfg)),
inference(spr,[status(thm),theory(equality)],[562,15]),
[iquote('0:SpR:562.0,15.0')] ).
cnf(589,plain,
$false,
inference(unc,[status(thm)],[577,1]),
[iquote('0:UnC:577.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET103-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.15 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n017.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 04:03:17 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.52
% 0.22/0.52 SPASS V 3.9
% 0.22/0.52 SPASS beiseite: Proof found.
% 0.22/0.52 % SZS status Theorem
% 0.22/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.52 SPASS derived 432 clauses, backtracked 0 clauses, performed 0 splits and kept 399 clauses.
% 0.22/0.52 SPASS allocated 76337 KBytes.
% 0.22/0.52 SPASS spent 0:00:00.14 on the problem.
% 0.22/0.52 0:00:00.04 for the input.
% 0.22/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.52 0:00:00.01 for inferences.
% 0.22/0.52 0:00:00.00 for the backtracking.
% 0.22/0.52 0:00:00.07 for the reduction.
% 0.22/0.52
% 0.22/0.52
% 0.22/0.52 Here is a proof with depth 5, length 18 :
% 0.22/0.52 % SZS output start Refutation
% See solution above
% 0.22/0.52 Formulae used in the proof : prove_property_1_of_ordered_pair_1 prove_property_1_of_ordered_pair_2 subclass_members class_elements_are_sets unordered_pair_member singleton_set ordered_pair regularity1
% 0.22/0.52
%------------------------------------------------------------------------------