%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET253-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 05:25:17 EDT 2022
% Result : Unsatisfiable 0.93s 1.12s
% Output : Refutation 0.93s
% 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 : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ subclass(restrict(x__dfg,y__dfg,z__dfg),cross_product(y__dfg,z__dfg)),
file('SET253-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET253-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET253-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET253-6.p',unknown),
[] ).
cnf(29,axiom,
equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
file('SET253-6.p',unknown),
[] ).
cnf(161,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(4074,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[161,4]),
[iquote('0:Res:161.1,4.0')] ).
cnf(4076,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[4074]),
[iquote('0:Obv:4074.0')] ).
cnf(4094,plain,
subclass(restrict(u,v,w),cross_product(v,w)),
inference(spr,[status(thm),theory(equality)],[29,4076]),
[iquote('0:SpR:29.0,4076.0')] ).
cnf(4268,plain,
$false,
inference(unc,[status(thm)],[4094,1]),
[iquote('0:UnC:4094.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET253-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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 16:08:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.93/1.12
% 0.93/1.12 SPASS V 3.9
% 0.93/1.12 SPASS beiseite: Proof found.
% 0.93/1.12 % SZS status Theorem
% 0.93/1.12 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.93/1.12 SPASS derived 3807 clauses, backtracked 204 clauses, performed 4 splits and kept 2035 clauses.
% 0.93/1.12 SPASS allocated 79709 KBytes.
% 0.93/1.12 SPASS spent 0:00:00.76 on the problem.
% 0.93/1.12 0:00:00.04 for the input.
% 0.93/1.12 0:00:00.00 for the FLOTTER CNF translation.
% 0.93/1.12 0:00:00.06 for inferences.
% 0.93/1.12 0:00:00.02 for the backtracking.
% 0.93/1.12 0:00:00.60 for the reduction.
% 0.93/1.12
% 0.93/1.12
% 0.93/1.12 Here is a proof with depth 3, length 10 :
% 0.93/1.12 % SZS output start Refutation
% See solution above
% 0.93/1.12 Formulae used in the proof : prove_restriction_property4_1 not_subclass_members1 not_subclass_members2 intersection2 restriction1
% 0.93/1.12
%------------------------------------------------------------------------------