TSTP Solution File: SET244-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET244-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 05:25:14 EDT 2022
% Result : Unsatisfiable 11.04s 11.21s
% Output : Refutation 11.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 9 unt; 6 nHn; 26 RR)
% Number of literals : 51 ( 0 equ; 22 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(restrict(universal_class,x__dfg,y__dfg),cross_product(x__dfg,y__dfg)),
file('SET244-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET244-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET244-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET244-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET244-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET244-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET244-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET244-6.p',unknown),
[] ).
cnf(29,axiom,
equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
file('SET244-6.p',unknown),
[] ).
cnf(117,plain,
( ~ subclass(cross_product(x__dfg,y__dfg),restrict(universal_class,x__dfg,y__dfg))
| ~ subclass(restrict(universal_class,x__dfg,y__dfg),cross_product(x__dfg,y__dfg)) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.2,1.0')] ).
cnf(163,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[3,23]),
[iquote('0:Res:3.1,23.0')] ).
cnf(786,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[24,2]),
[iquote('0:Res:24.2,2.0')] ).
cnf(789,plain,
( ~ member(not_subclass_element(u,intersection(v,w)),w)
| ~ member(not_subclass_element(u,intersection(v,w)),v)
| subclass(u,intersection(v,w)) ),
inference(res,[status(thm),theory(equality)],[24,4]),
[iquote('0:Res:24.2,4.0')] ).
cnf(2768,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[163,4]),
[iquote('0:Res:163.1,4.0')] ).
cnf(2770,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[2768]),
[iquote('0:Obv:2768.0')] ).
cnf(2789,plain,
subclass(restrict(u,v,w),cross_product(v,w)),
inference(spr,[status(thm),theory(equality)],[29,2770]),
[iquote('0:SpR:29.0,2770.0')] ).
cnf(2974,plain,
~ subclass(cross_product(x__dfg,y__dfg),restrict(universal_class,x__dfg,y__dfg)),
inference(mrr,[status(thm)],[117,2789]),
[iquote('0:MRR:117.1,2789.0')] ).
cnf(8796,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[5,786]),
[iquote('0:Res:5.0,786.2')] ).
cnf(8806,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[8796]),
[iquote('0:Con:8796.1')] ).
cnf(8858,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[3,8806]),
[iquote('0:Res:3.1,8806.0')] ).
cnf(10985,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u))
| subclass(u,intersection(v,u)) ),
inference(res,[status(thm),theory(equality)],[3,789]),
[iquote('0:Res:3.1,789.0')] ).
cnf(11002,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u)) ),
inference(obv,[status(thm),theory(equality)],[10985]),
[iquote('0:Obv:10985.1')] ).
cnf(24047,plain,
( subclass(u,intersection(universal_class,u))
| subclass(u,intersection(universal_class,u)) ),
inference(res,[status(thm),theory(equality)],[8858,11002]),
[iquote('0:Res:8858.1,11002.0')] ).
cnf(24074,plain,
subclass(u,intersection(universal_class,u)),
inference(obv,[status(thm),theory(equality)],[24047]),
[iquote('0:Obv:24047.0')] ).
cnf(24122,plain,
subclass(cross_product(u,v),restrict(universal_class,u,v)),
inference(spr,[status(thm),theory(equality)],[29,24074]),
[iquote('0:SpR:29.0,24074.0')] ).
cnf(24172,plain,
$false,
inference(unc,[status(thm)],[24122,2974]),
[iquote('0:UnC:24122.0,2974.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET244-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 03:44:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 11.04/11.21
% 11.04/11.21 SPASS V 3.9
% 11.04/11.21 SPASS beiseite: Proof found.
% 11.04/11.21 % SZS status Theorem
% 11.04/11.21 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.04/11.21 SPASS derived 20226 clauses, backtracked 208 clauses, performed 5 splits and kept 9343 clauses.
% 11.04/11.21 SPASS allocated 98903 KBytes.
% 11.04/11.21 SPASS spent 0:0:10.67 on the problem.
% 11.04/11.21 0:00:00.04 for the input.
% 11.04/11.21 0:00:00.00 for the FLOTTER CNF translation.
% 11.04/11.21 0:00:00.21 for inferences.
% 11.04/11.21 0:00:00.83 for the backtracking.
% 11.04/11.21 0:00:09.41 for the reduction.
% 11.04/11.21
% 11.04/11.21
% 11.04/11.21 Here is a proof with depth 5, length 26 :
% 11.04/11.21 % SZS output start Refutation
% See solution above
% 11.04/11.21 Formulae used in the proof : prove_restriction_with_universal_class_1 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets subclass_implies_equal intersection2 intersection3 restriction1
% 11.04/11.21
%------------------------------------------------------------------------------