TSTP Solution File: SET411-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET411-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 05:26:10 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 19 ( 8 unt; 2 nHn; 19 RR)
% Number of literals : 31 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(ordered_pair(x__dfg,y__dfg),singleton_relation),
file('SET411-6.p',unknown),
[] ).
cnf(2,axiom,
~ member(x__dfg,universal_class),
file('SET411-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET411-6.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET411-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET411-6.p',unknown),
[] ).
cnf(6,axiom,
subclass(u,universal_class),
file('SET411-6.p',unknown),
[] ).
cnf(21,axiom,
( ~ member(ordered_pair(u,v),element_relation)
| member(u,v) ),
file('SET411-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET411-6.p',unknown),
[] ).
cnf(106,axiom,
equal(intersection(complement(compose(element_relation,complement(identity_relation))),element_relation),singleton_relation),
file('SET411-6.p',unknown),
[] ).
cnf(122,plain,
( ~ subclass(u,universal_class)
| ~ member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[3,2]),
[iquote('0:Res:3.2,2.0')] ).
cnf(124,plain,
( ~ subclass(singleton_relation,u)
| member(ordered_pair(x__dfg,y__dfg),u) ),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.0,3.1')] ).
cnf(131,plain,
~ member(x__dfg,u),
inference(mrr,[status(thm)],[122,6]),
[iquote('0:MRR:122.0,6.0')] ).
cnf(173,plain,
( ~ subclass(singleton_relation,element_relation)
| member(x__dfg,y__dfg) ),
inference(res,[status(thm),theory(equality)],[124,21]),
[iquote('0:Res:124.1,21.0')] ).
cnf(174,plain,
~ subclass(singleton_relation,element_relation),
inference(mrr,[status(thm)],[173,131]),
[iquote('0:MRR:173.1,131.0')] ).
cnf(186,plain,
( ~ member(u,singleton_relation)
| member(u,element_relation) ),
inference(spl,[status(thm),theory(equality)],[106,24]),
[iquote('0:SpL:106.0,24.0')] ).
cnf(197,plain,
( ~ member(not_subclass_element(u,element_relation),singleton_relation)
| subclass(u,element_relation) ),
inference(res,[status(thm),theory(equality)],[186,5]),
[iquote('0:Res:186.1,5.0')] ).
cnf(210,plain,
( subclass(singleton_relation,element_relation)
| subclass(singleton_relation,element_relation) ),
inference(res,[status(thm),theory(equality)],[4,197]),
[iquote('0:Res:4.1,197.0')] ).
cnf(211,plain,
subclass(singleton_relation,element_relation),
inference(obv,[status(thm),theory(equality)],[210]),
[iquote('0:Obv:210.0')] ).
cnf(212,plain,
$false,
inference(mrr,[status(thm)],[211,174]),
[iquote('0:MRR:211.0,174.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET411-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 9 22:52:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 86 clauses, backtracked 0 clauses, performed 0 splits and kept 174 clauses.
% 0.20/0.45 SPASS allocated 75872 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.45 0:00:00.04 for the input.
% 0.20/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.02 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 3, length 19 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : prove_compose_condition_for_singleton_membership1_1 prove_compose_condition_for_singleton_membership1_2 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets element_relation2 intersection2 compose_can_define_singleton
% 0.20/0.45
%------------------------------------------------------------------------------