TSTP Solution File: SET096-6 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET096-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 05:23:58 EDT 2022
% Result : Unsatisfiable 1.36s 1.53s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 24 ( 10 unt; 6 nHn; 24 RR)
% Number of literals : 43 ( 0 equ; 17 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subclass(x__dfg,singleton(y__dfg)),
file('SET096-6.p',unknown),
[] ).
cnf(2,axiom,
~ equal(null_class,x__dfg),
file('SET096-6.p',unknown),
[] ).
cnf(3,axiom,
~ equal(singleton(y__dfg),x__dfg),
file('SET096-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET096-6.p',unknown),
[] ).
cnf(5,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET096-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET096-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET096-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET096-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET096-6.p',unknown),
[] ).
cnf(69,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET096-6.p',unknown),
[] ).
cnf(102,plain,
member(regular(x__dfg),x__dfg),
inference(res,[status(thm),theory(equality)],[69,2]),
[iquote('0:Res:69.0,2.0')] ).
cnf(106,plain,
( ~ member(u,x__dfg)
| member(u,singleton(y__dfg)) ),
inference(res,[status(thm),theory(equality)],[1,4]),
[iquote('0:Res:1.0,4.0')] ).
cnf(107,plain,
( ~ subclass(singleton(y__dfg),x__dfg)
| equal(singleton(y__dfg),x__dfg) ),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(115,plain,
~ subclass(singleton(y__dfg),x__dfg),
inference(mrr,[status(thm)],[107,3]),
[iquote('0:MRR:107.1,3.0')] ).
cnf(477,plain,
( ~ member(u,singleton(v))
| equal(u,v)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[15,11]),
[iquote('0:SpL:15.0,11.0')] ).
cnf(489,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[477]),
[iquote('0:Obv:477.1')] ).
cnf(491,plain,
( ~ member(u,x__dfg)
| equal(u,y__dfg) ),
inference(res,[status(thm),theory(equality)],[106,489]),
[iquote('0:Res:106.1,489.0')] ).
cnf(497,plain,
( subclass(singleton(u),v)
| equal(not_subclass_element(singleton(u),v),u) ),
inference(res,[status(thm),theory(equality)],[5,489]),
[iquote('0:Res:5.1,489.0')] ).
cnf(503,plain,
equal(regular(x__dfg),y__dfg),
inference(res,[status(thm),theory(equality)],[102,491]),
[iquote('0:Res:102.0,491.0')] ).
cnf(517,plain,
member(y__dfg,x__dfg),
inference(rew,[status(thm),theory(equality)],[503,102]),
[iquote('0:Rew:503.0,102.0')] ).
cnf(5253,plain,
( ~ member(u,v)
| subclass(singleton(u),v)
| subclass(singleton(u),v) ),
inference(spl,[status(thm),theory(equality)],[497,6]),
[iquote('0:SpL:497.1,6.0')] ).
cnf(5257,plain,
( ~ member(u,v)
| subclass(singleton(u),v) ),
inference(obv,[status(thm),theory(equality)],[5253]),
[iquote('0:Obv:5253.1')] ).
cnf(5268,plain,
~ member(y__dfg,x__dfg),
inference(res,[status(thm),theory(equality)],[5257,115]),
[iquote('0:Res:5257.1,115.0')] ).
cnf(5269,plain,
$false,
inference(mrr,[status(thm)],[5268,517]),
[iquote('0:MRR:5268.0,517.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET096-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jul 9 23:24:28 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.36/1.53
% 1.36/1.53 SPASS V 3.9
% 1.36/1.53 SPASS beiseite: Proof found.
% 1.36/1.53 % SZS status Theorem
% 1.36/1.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.36/1.53 SPASS derived 4421 clauses, backtracked 0 clauses, performed 2 splits and kept 2588 clauses.
% 1.36/1.53 SPASS allocated 80763 KBytes.
% 1.36/1.53 SPASS spent 0:00:01.15 on the problem.
% 1.36/1.53 0:00:00.04 for the input.
% 1.36/1.53 0:00:00.00 for the FLOTTER CNF translation.
% 1.36/1.53 0:00:00.06 for inferences.
% 1.36/1.53 0:00:00.01 for the backtracking.
% 1.36/1.53 0:00:00.98 for the reduction.
% 1.36/1.53
% 1.36/1.53
% 1.36/1.53 Here is a proof with depth 4, length 24 :
% 1.36/1.53 % SZS output start Refutation
% See solution above
% 1.36/1.53 Formulae used in the proof : prove_two_subsets_of_singleton_1 prove_two_subsets_of_singleton_2 prove_two_subsets_of_singleton_3 subclass_members not_subclass_members1 not_subclass_members2 subclass_implies_equal unordered_pair_member singleton_set regularity1
% 1.36/1.53
%------------------------------------------------------------------------------