TSTP Solution File: SET183-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET183-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 05:24:50 EDT 2022
% Result : Unsatisfiable 117.83s 117.99s
% Output : Refutation 117.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 6 unt; 6 nHn; 21 RR)
% Number of literals : 45 ( 0 equ; 22 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subclass(x__dfg,y__dfg),
file('SET183-6.p',unknown),
[] ).
cnf(2,axiom,
~ equal(intersection(x__dfg,y__dfg),x__dfg),
file('SET183-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET183-6.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET183-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET183-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET183-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET183-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET183-6.p',unknown),
[] ).
cnf(121,plain,
( ~ subclass(x__dfg,intersection(x__dfg,y__dfg))
| ~ subclass(intersection(x__dfg,y__dfg),x__dfg) ),
inference(res,[status(thm),theory(equality)],[9,2]),
[iquote('0:Res:9.2,2.0')] ).
cnf(181,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[4,23]),
[iquote('0:Res:4.1,23.0')] ).
cnf(365,plain,
( ~ subclass(u,v)
| subclass(u,w)
| member(not_subclass_element(u,w),v) ),
inference(res,[status(thm),theory(equality)],[4,3]),
[iquote('0:Res:4.1,3.0')] ).
cnf(804,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)],[25,5]),
[iquote('0:Res:25.2,5.0')] ).
cnf(7109,plain,
( subclass(intersection(u,v),u)
| subclass(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[181,5]),
[iquote('0:Res:181.1,5.0')] ).
cnf(7114,plain,
subclass(intersection(u,v),u),
inference(obv,[status(thm),theory(equality)],[7109]),
[iquote('0:Obv:7109.0')] ).
cnf(7115,plain,
~ subclass(x__dfg,intersection(x__dfg,y__dfg)),
inference(mrr,[status(thm)],[121,7114]),
[iquote('0:MRR:121.1,7114.0')] ).
cnf(13287,plain,
( ~ subclass(u,v)
| ~ member(not_subclass_element(u,intersection(w,v)),w)
| subclass(u,intersection(w,v))
| subclass(u,intersection(w,v)) ),
inference(res,[status(thm),theory(equality)],[365,804]),
[iquote('0:Res:365.2,804.0')] ).
cnf(13290,plain,
( ~ subclass(u,v)
| ~ member(not_subclass_element(u,intersection(w,v)),w)
| subclass(u,intersection(w,v)) ),
inference(obv,[status(thm),theory(equality)],[13287]),
[iquote('0:Obv:13287.2')] ).
cnf(63591,plain,
( ~ subclass(u,v)
| subclass(u,intersection(u,v))
| subclass(u,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[4,13290]),
[iquote('0:Res:4.1,13290.1')] ).
cnf(63623,plain,
( ~ subclass(u,v)
| subclass(u,intersection(u,v)) ),
inference(obv,[status(thm),theory(equality)],[63591]),
[iquote('0:Obv:63591.1')] ).
cnf(108175,plain,
~ subclass(x__dfg,y__dfg),
inference(res,[status(thm),theory(equality)],[63623,7115]),
[iquote('0:Res:63623.1,7115.0')] ).
cnf(108195,plain,
$false,
inference(mrr,[status(thm)],[108175,1]),
[iquote('0:MRR:108175.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET183-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.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 : Sat Jul 9 20:32:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 117.83/117.99
% 117.83/117.99 SPASS V 3.9
% 117.83/117.99 SPASS beiseite: Proof found.
% 117.83/117.99 % SZS status Theorem
% 117.83/117.99 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 117.83/117.99 SPASS derived 78305 clauses, backtracked 715 clauses, performed 14 splits and kept 27411 clauses.
% 117.83/117.99 SPASS allocated 165053 KBytes.
% 117.83/117.99 SPASS spent 0:1:55.90 on the problem.
% 117.83/117.99 0:00:00.04 for the input.
% 117.83/117.99 0:00:00.00 for the FLOTTER CNF translation.
% 117.83/117.99 0:00:00.93 for inferences.
% 117.83/117.99 0:0:11.45 for the backtracking.
% 117.83/117.99 0:1:42.55 for the reduction.
% 117.83/117.99
% 117.83/117.99
% 117.83/117.99 Here is a proof with depth 4, length 21 :
% 117.83/117.99 % SZS output start Refutation
% See solution above
% 117.83/117.99 Formulae used in the proof : prove_subclass_property1_1 prove_subclass_property1_2 subclass_members not_subclass_members1 not_subclass_members2 subclass_implies_equal intersection1 intersection3
% 117.83/117.99
%------------------------------------------------------------------------------