TSTP Solution File: SET257-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET257-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 05:25:19 EDT 2022
% Result : Unsatisfiable 11.42s 11.61s
% Output : Refutation 11.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 8 unt; 5 nHn; 20 RR)
% Number of literals : 36 ( 0 equ; 14 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 : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(restrict(cross_product(x__dfg,y__dfg),x__dfg,y__dfg),cross_product(x__dfg,y__dfg)),
file('SET257-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET257-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET257-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET257-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET257-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET257-6.p',unknown),
[] ).
cnf(30,axiom,
equal(intersection(cross_product(u,v),w),restrict(w,u,v)),
file('SET257-6.p',unknown),
[] ).
cnf(120,plain,
( ~ subclass(cross_product(x__dfg,y__dfg),restrict(cross_product(x__dfg,y__dfg),x__dfg,y__dfg))
| ~ subclass(restrict(cross_product(x__dfg,y__dfg),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(167,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(793,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(2772,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[167,4]),
[iquote('0:Res:167.1,4.0')] ).
cnf(2774,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[2772]),
[iquote('0:Obv:2772.0')] ).
cnf(2794,plain,
subclass(restrict(u,v,w),u),
inference(spr,[status(thm),theory(equality)],[30,2774]),
[iquote('0:SpR:30.0,2774.0')] ).
cnf(2918,plain,
~ subclass(cross_product(x__dfg,y__dfg),restrict(cross_product(x__dfg,y__dfg),x__dfg,y__dfg)),
inference(mrr,[status(thm)],[120,2794]),
[iquote('0:MRR:120.1,2794.0')] ).
cnf(11094,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)],[3,793]),
[iquote('0:Res:3.1,793.0')] ).
cnf(11111,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u)) ),
inference(obv,[status(thm),theory(equality)],[11094]),
[iquote('0:Obv:11094.1')] ).
cnf(24220,plain,
( subclass(u,intersection(u,u))
| subclass(u,intersection(u,u)) ),
inference(res,[status(thm),theory(equality)],[3,11111]),
[iquote('0:Res:3.1,11111.0')] ).
cnf(24247,plain,
subclass(u,intersection(u,u)),
inference(obv,[status(thm),theory(equality)],[24220]),
[iquote('0:Obv:24220.0')] ).
cnf(26326,plain,
subclass(cross_product(u,v),restrict(cross_product(u,v),u,v)),
inference(spr,[status(thm),theory(equality)],[30,24247]),
[iquote('0:SpR:30.0,24247.0')] ).
cnf(26374,plain,
$false,
inference(unc,[status(thm)],[26326,2918]),
[iquote('0:UnC:26326.0,2918.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET257-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n012.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 09:22:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 11.42/11.61
% 11.42/11.61 SPASS V 3.9
% 11.42/11.61 SPASS beiseite: Proof found.
% 11.42/11.61 % SZS status Theorem
% 11.42/11.61 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.42/11.61 SPASS derived 20524 clauses, backtracked 208 clauses, performed 5 splits and kept 9444 clauses.
% 11.42/11.61 SPASS allocated 99163 KBytes.
% 11.42/11.61 SPASS spent 0:0:11.06 on the problem.
% 11.42/11.61 0:00:00.04 for the input.
% 11.42/11.61 0:00:00.00 for the FLOTTER CNF translation.
% 11.42/11.61 0:00:00.22 for inferences.
% 11.42/11.61 0:00:00.86 for the backtracking.
% 11.42/11.61 0:00:09.77 for the reduction.
% 11.42/11.61
% 11.42/11.61
% 11.42/11.61 Here is a proof with depth 4, length 20 :
% 11.42/11.61 % SZS output start Refutation
% See solution above
% 11.42/11.61 Formulae used in the proof : prove_restriction_property5_1 not_subclass_members1 not_subclass_members2 subclass_implies_equal intersection2 intersection3 restriction2
% 11.42/11.61
%------------------------------------------------------------------------------