TSTP Solution File: SET553-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET553-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 05:26:54 EDT 2022
% Result : Unsatisfiable 1.69s 1.88s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 5 unt; 3 nHn; 10 RR)
% Number of literals : 15 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ subclass(cantor(x__dfg),domain_of(x__dfg)),
file('SET553-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET553-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET553-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET553-6.p',unknown),
[] ).
cnf(78,axiom,
equal(intersection(domain_of(u),diagonalise(compose(inverse(element_relation),u))),cantor(u)),
file('SET553-6.p',unknown),
[] ).
cnf(184,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[3,22]),
[iquote('0:Res:3.1,22.0')] ).
cnf(8720,plain,
( subclass(intersection(u,v),u)
| subclass(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[184,4]),
[iquote('0:Res:184.1,4.0')] ).
cnf(8724,plain,
subclass(intersection(u,v),u),
inference(obv,[status(thm),theory(equality)],[8720]),
[iquote('0:Obv:8720.0')] ).
cnf(8959,plain,
subclass(cantor(u),domain_of(u)),
inference(spr,[status(thm),theory(equality)],[78,8724]),
[iquote('0:SpR:78.0,8724.0')] ).
cnf(8981,plain,
$false,
inference(unc,[status(thm)],[8959,1]),
[iquote('0:UnC:8959.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET553-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.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 00:07:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.88
% 1.69/1.88 SPASS V 3.9
% 1.69/1.88 SPASS beiseite: Proof found.
% 1.69/1.88 % SZS status Theorem
% 1.69/1.88 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.69/1.88 SPASS derived 7474 clauses, backtracked 842 clauses, performed 5 splits and kept 4016 clauses.
% 1.69/1.88 SPASS allocated 82571 KBytes.
% 1.69/1.88 SPASS spent 0:00:01.50 on the problem.
% 1.69/1.88 0:00:00.04 for the input.
% 1.69/1.88 0:00:00.00 for the FLOTTER CNF translation.
% 1.69/1.88 0:00:00.08 for inferences.
% 1.69/1.88 0:00:00.07 for the backtracking.
% 1.69/1.88 0:00:01.26 for the reduction.
% 1.69/1.88
% 1.69/1.88
% 1.69/1.88 Here is a proof with depth 3, length 10 :
% 1.69/1.88 % SZS output start Refutation
% See solution above
% 1.69/1.88 Formulae used in the proof : prove_cantor_class_alternate_defn_1 not_subclass_members1 not_subclass_members2 intersection1 cantor_class
% 1.69/1.88
%------------------------------------------------------------------------------