TSTP Solution File: SET238-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET238-6 : 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 05:25:12 EDT 2022
% Result : Unsatisfiable 1.01s 1.19s
% Output : Refutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 9 unt; 3 nHn; 17 RR)
% Number of literals : 26 ( 0 equ; 8 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 : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(z__dfg,restrict(xr,x__dfg,y__dfg)),
file('SET238-6.p',unknown),
[] ).
cnf(2,axiom,
~ member(ordered_pair(first(z__dfg),second(z__dfg)),restrict(xr,x__dfg,y__dfg)),
file('SET238-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET238-6.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET238-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET238-6.p',unknown),
[] ).
cnf(19,axiom,
( ~ member(u,cross_product(v,w))
| equal(ordered_pair(first(u),second(u)),u) ),
file('SET238-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET238-6.p',unknown),
[] ).
cnf(30,axiom,
equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
file('SET238-6.p',unknown),
[] ).
cnf(117,plain,
( ~ subclass(restrict(xr,x__dfg,y__dfg),u)
| member(z__dfg,u) ),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.0,3.1')] ).
cnf(172,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[4,24]),
[iquote('0:Res:4.1,24.0')] ).
cnf(4451,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[172,5]),
[iquote('0:Res:172.1,5.0')] ).
cnf(4453,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[4451]),
[iquote('0:Obv:4451.0')] ).
cnf(4471,plain,
subclass(restrict(u,v,w),cross_product(v,w)),
inference(spr,[status(thm),theory(equality)],[30,4453]),
[iquote('0:SpR:30.0,4453.0')] ).
cnf(5534,plain,
member(z__dfg,cross_product(x__dfg,y__dfg)),
inference(res,[status(thm),theory(equality)],[4471,117]),
[iquote('0:Res:4471.0,117.0')] ).
cnf(5567,plain,
equal(ordered_pair(first(z__dfg),second(z__dfg)),z__dfg),
inference(res,[status(thm),theory(equality)],[5534,19]),
[iquote('0:Res:5534.0,19.0')] ).
cnf(5568,plain,
~ member(z__dfg,restrict(xr,x__dfg,y__dfg)),
inference(rew,[status(thm),theory(equality)],[5567,2]),
[iquote('0:Rew:5567.0,2.0')] ).
cnf(5574,plain,
$false,
inference(mrr,[status(thm)],[5568,1]),
[iquote('0:MRR:5568.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET238-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 01:22:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.01/1.19
% 1.01/1.19 SPASS V 3.9
% 1.01/1.19 SPASS beiseite: Proof found.
% 1.01/1.19 % SZS status Theorem
% 1.01/1.19 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.01/1.19 SPASS derived 4894 clauses, backtracked 174 clauses, performed 4 splits and kept 2347 clauses.
% 1.01/1.19 SPASS allocated 80513 KBytes.
% 1.01/1.19 SPASS spent 0:00:00.82 on the problem.
% 1.01/1.19 0:00:00.04 for the input.
% 1.01/1.19 0:00:00.00 for the FLOTTER CNF translation.
% 1.01/1.19 0:00:00.06 for inferences.
% 1.01/1.19 0:00:00.02 for the backtracking.
% 1.01/1.19 0:00:00.66 for the reduction.
% 1.01/1.19
% 1.01/1.19
% 1.01/1.19 Here is a proof with depth 5, length 17 :
% 1.01/1.19 % SZS output start Refutation
% See solution above
% 1.01/1.19 Formulae used in the proof : prove_corollary_to_restriction_alternate_defn1_1 prove_corollary_to_restriction_alternate_defn1_2 subclass_members not_subclass_members1 not_subclass_members2 cartesian_product4 intersection2 restriction1
% 1.01/1.19
%------------------------------------------------------------------------------