TSTP Solution File: SEU323+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU323+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 14:36:15 EDT 2022
% Result : Theorem 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 28 ( 9 unt; 0 nHn; 28 RR)
% Number of literals : 60 ( 0 equ; 36 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
topological_space(skc4),
file('SEU323+1.p',unknown),
[] ).
cnf(2,axiom,
top_str(skc4),
file('SEU323+1.p',unknown),
[] ).
cnf(7,axiom,
element(skc5,powerset(the_carrier(skc4))),
file('SEU323+1.p',unknown),
[] ).
cnf(9,axiom,
~ open_subset(interior(skc4,skc5),skc4),
file('SEU323+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ element(u,powerset(v))
| element(subset_complement(v,u),powerset(v)) ),
file('SEU323+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ element(u,powerset(v))
| equal(subset_complement(v,subset_complement(v,u)),u) ),
file('SEU323+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ top_str(u)
| ~ element(v,powerset(the_carrier(u)))
| element(topstr_closure(u,v),powerset(the_carrier(u))) ),
file('SEU323+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ topological_space(u)
| ~ top_str(u)
| ~ element(v,powerset(the_carrier(u)))
| closed_subset(topstr_closure(u,v),u) ),
file('SEU323+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ top_str(u)
| ~ element(v,powerset(the_carrier(u)))
| equal(subset_complement(the_carrier(u),topstr_closure(u,subset_complement(the_carrier(u),v))),interior(u,v)) ),
file('SEU323+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ topological_space(u)
| ~ top_str(u)
| ~ closed_subset(v,u)
| ~ element(v,powerset(the_carrier(u)))
| open_subset(subset_complement(the_carrier(u),v),u) ),
file('SEU323+1.p',unknown),
[] ).
cnf(24,plain,
( ~ topological_space(skc4)
| ~ closed_subset(u,skc4)
| ~ element(u,powerset(the_carrier(skc4)))
| open_subset(subset_complement(the_carrier(skc4),u),skc4) ),
inference(res,[status(thm),theory(equality)],[2,23]),
[iquote('0:Res:2.0,23.0')] ).
cnf(27,plain,
( ~ topological_space(skc4)
| ~ element(u,powerset(the_carrier(skc4)))
| closed_subset(topstr_closure(skc4,u),skc4) ),
inference(res,[status(thm),theory(equality)],[2,20]),
[iquote('0:Res:2.0,20.0')] ).
cnf(28,plain,
( ~ element(u,powerset(the_carrier(skc4)))
| element(topstr_closure(skc4,u),powerset(the_carrier(skc4))) ),
inference(res,[status(thm),theory(equality)],[2,18]),
[iquote('0:Res:2.0,18.0')] ).
cnf(40,plain,
( ~ top_str(skc4)
| equal(subset_complement(the_carrier(skc4),topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5))),interior(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[7,21]),
[iquote('0:Res:7.0,21.1')] ).
cnf(45,plain,
element(subset_complement(the_carrier(skc4),skc5),powerset(the_carrier(skc4))),
inference(res,[status(thm),theory(equality)],[7,16]),
[iquote('0:Res:7.0,16.0')] ).
cnf(52,plain,
( ~ element(u,powerset(the_carrier(skc4)))
| closed_subset(topstr_closure(skc4,u),skc4) ),
inference(mrr,[status(thm)],[27,1]),
[iquote('0:MRR:27.0,1.0')] ).
cnf(55,plain,
equal(subset_complement(the_carrier(skc4),topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5))),interior(skc4,skc5)),
inference(mrr,[status(thm)],[40,2]),
[iquote('0:MRR:40.0,2.0')] ).
cnf(56,plain,
( ~ closed_subset(u,skc4)
| ~ element(u,powerset(the_carrier(skc4)))
| open_subset(subset_complement(the_carrier(skc4),u),skc4) ),
inference(mrr,[status(thm)],[24,1]),
[iquote('0:MRR:24.0,1.0')] ).
cnf(80,plain,
( ~ element(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),powerset(the_carrier(skc4)))
| equal(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),subset_complement(the_carrier(skc4),interior(skc4,skc5))) ),
inference(spr,[status(thm),theory(equality)],[55,17]),
[iquote('0:SpR:55.0,17.1')] ).
cnf(84,plain,
( ~ closed_subset(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),skc4)
| ~ element(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),powerset(the_carrier(skc4)))
| open_subset(interior(skc4,skc5),skc4) ),
inference(spr,[status(thm),theory(equality)],[55,56]),
[iquote('0:SpR:55.0,56.2')] ).
cnf(87,plain,
( ~ closed_subset(subset_complement(the_carrier(skc4),interior(skc4,skc5)),skc4)
| ~ element(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),powerset(the_carrier(skc4)))
| open_subset(interior(skc4,skc5),skc4) ),
inference(rew,[status(thm),theory(equality)],[80,84]),
[iquote('0:Rew:80.1,84.0')] ).
cnf(88,plain,
( ~ closed_subset(subset_complement(the_carrier(skc4),interior(skc4,skc5)),skc4)
| ~ element(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),powerset(the_carrier(skc4))) ),
inference(mrr,[status(thm)],[87,9]),
[iquote('0:MRR:87.2,9.0')] ).
cnf(183,plain,
( ~ element(subset_complement(the_carrier(skc4),skc5),powerset(the_carrier(skc4)))
| ~ closed_subset(subset_complement(the_carrier(skc4),interior(skc4,skc5)),skc4) ),
inference(res,[status(thm),theory(equality)],[28,88]),
[iquote('0:Res:28.1,88.1')] ).
cnf(186,plain,
~ closed_subset(subset_complement(the_carrier(skc4),interior(skc4,skc5)),skc4),
inference(mrr,[status(thm)],[183,45]),
[iquote('0:MRR:183.0,45.0')] ).
cnf(247,plain,
( ~ element(subset_complement(the_carrier(skc4),skc5),powerset(the_carrier(skc4)))
| equal(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),subset_complement(the_carrier(skc4),interior(skc4,skc5))) ),
inference(res,[status(thm),theory(equality)],[28,80]),
[iquote('0:Res:28.1,80.0')] ).
cnf(250,plain,
equal(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),subset_complement(the_carrier(skc4),interior(skc4,skc5))),
inference(mrr,[status(thm)],[247,45]),
[iquote('0:MRR:247.0,45.0')] ).
cnf(273,plain,
( ~ element(subset_complement(the_carrier(skc4),skc5),powerset(the_carrier(skc4)))
| closed_subset(subset_complement(the_carrier(skc4),interior(skc4,skc5)),skc4) ),
inference(spr,[status(thm),theory(equality)],[250,52]),
[iquote('0:SpR:250.0,52.1')] ).
cnf(286,plain,
$false,
inference(mrr,[status(thm)],[273,45,186]),
[iquote('0:MRR:273.0,273.1,45.0,186.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU323+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.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 : Mon Jun 20 12:20:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.46
% 0.18/0.46 SPASS V 3.9
% 0.18/0.46 SPASS beiseite: Proof found.
% 0.18/0.46 % SZS status Theorem
% 0.18/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 SPASS derived 192 clauses, backtracked 0 clauses, performed 0 splits and kept 96 clauses.
% 0.18/0.46 SPASS allocated 97849 KBytes.
% 0.18/0.46 SPASS spent 0:00:00.12 on the problem.
% 0.18/0.46 0:00:00.04 for the input.
% 0.18/0.46 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.46 0:00:00.00 for inferences.
% 0.18/0.46 0:00:00.00 for the backtracking.
% 0.18/0.46 0:00:00.02 for the reduction.
% 0.18/0.46
% 0.18/0.46
% 0.18/0.46 Here is a proof with depth 4, length 28 :
% 0.18/0.46 % SZS output start Refutation
% See solution above
% 0.18/0.46 Formulae used in the proof : t51_tops_1 dt_k3_subset_1 involutiveness_k3_subset_1 dt_k6_pre_topc fc2_tops_1 d1_tops_1 fc3_tops_1
% 0.18/0.46
%------------------------------------------------------------------------------