TSTP Solution File: SEU323-10 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU323-10 : TPTP v8.1.0. Released v7.3.0.
% 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 : Unsatisfiable 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 24 RR)
% Number of literals : 24 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ifeq2(u,u,v,w),v),
file('SEU323-10.p',unknown),
[] ).
cnf(2,axiom,
equal(ifeq(u,u,v,w),v),
file('SEU323-10.p',unknown),
[] ).
cnf(3,axiom,
equal(ifeq(element(u,powerset(the_carrier(v))),true__dfg,ifeq(closed_subset(u,v),true__dfg,ifeq(topological_space(v),true__dfg,ifeq(top_str(v),true__dfg,open_subset(subset_complement(the_carrier(v),u),v),true__dfg),true__dfg),true__dfg),true__dfg),true__dfg),
file('SEU323-10.p',unknown),
[] ).
cnf(9,axiom,
equal(ifeq(element(u,powerset(v)),true__dfg,element(subset_complement(v,u),powerset(v)),true__dfg),true__dfg),
file('SEU323-10.p',unknown),
[] ).
cnf(10,axiom,
equal(ifeq(element(u,powerset(the_carrier(v))),true__dfg,ifeq(top_str(v),true__dfg,element(topstr_closure(v,u),powerset(the_carrier(v))),true__dfg),true__dfg),true__dfg),
file('SEU323-10.p',unknown),
[] ).
cnf(11,axiom,
equal(ifeq(element(u,powerset(the_carrier(v))),true__dfg,ifeq(topological_space(v),true__dfg,ifeq(top_str(v),true__dfg,closed_subset(topstr_closure(v,u),v),true__dfg),true__dfg),true__dfg),true__dfg),
file('SEU323-10.p',unknown),
[] ).
cnf(21,axiom,
equal(ifeq2(element(u,powerset(the_carrier(v))),true__dfg,ifeq2(top_str(v),true__dfg,subset_complement(the_carrier(v),topstr_closure(v,subset_complement(the_carrier(v),u))),interior(v,u)),interior(v,u)),interior(v,u)),
file('SEU323-10.p',unknown),
[] ).
cnf(22,axiom,
equal(top_str(sK2_t51_tops_1_A),true__dfg),
file('SEU323-10.p',unknown),
[] ).
cnf(23,axiom,
equal(topological_space(sK2_t51_tops_1_A),true__dfg),
file('SEU323-10.p',unknown),
[] ).
cnf(24,axiom,
equal(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),true__dfg),
file('SEU323-10.p',unknown),
[] ).
cnf(25,axiom,
~ equal(open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true__dfg),
file('SEU323-10.p',unknown),
[] ).
cnf(102,plain,
equal(ifeq(true__dfg,true__dfg,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[24,9]),
[iquote('0:SpR:24.0,9.0')] ).
cnf(108,plain,
equal(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,102]),
[iquote('0:Rew:2.0,102.0')] ).
cnf(315,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(top_str(sK2_t51_tops_1_A),true__dfg,element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[108,10]),
[iquote('0:SpR:108.0,10.0')] ).
cnf(323,plain,
equal(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,315,22]),
[iquote('0:Rew:2.0,315.0,2.0,315.0,22.0,315.0')] ).
cnf(385,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(topological_space(sK2_t51_tops_1_A),true__dfg,ifeq(top_str(sK2_t51_tops_1_A),true__dfg,closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true__dfg),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[108,11]),
[iquote('0:SpR:108.0,11.0')] ).
cnf(394,plain,
equal(closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,385,23,22]),
[iquote('0:Rew:2.0,385.0,2.0,385.0,23.0,385.0,2.0,385.0,22.0,385.0')] ).
cnf(425,plain,
equal(ifeq2(true__dfg,true__dfg,ifeq2(top_str(sK2_t51_tops_1_A),true__dfg,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),
inference(spr,[status(thm),theory(equality)],[24,21]),
[iquote('0:SpR:24.0,21.0')] ).
cnf(437,plain,
equal(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),
inference(rew,[status(thm),theory(equality)],[1,425,22]),
[iquote('0:Rew:1.0,425.0,1.0,425.0,22.0,425.0')] ).
cnf(580,plain,
equal(ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true__dfg,ifeq(true__dfg,true__dfg,ifeq(topological_space(sK2_t51_tops_1_A),true__dfg,ifeq(top_str(sK2_t51_tops_1_A),true__dfg,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),true__dfg),true__dfg),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[394,3]),
[iquote('0:SpR:394.0,3.0')] ).
cnf(582,plain,
equal(ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true__dfg,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,580,23,22]),
[iquote('0:Rew:2.0,580.0,2.0,580.0,23.0,580.0,2.0,580.0,22.0,580.0')] ).
cnf(583,plain,
equal(ifeq(true__dfg,true__dfg,open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[323,582,437]),
[iquote('0:Rew:323.0,582.0,437.0,582.0')] ).
cnf(584,plain,
equal(open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,583]),
[iquote('0:Rew:2.0,583.0')] ).
cnf(585,plain,
$false,
inference(mrr,[status(thm)],[584,25]),
[iquote('0:MRR:584.0,25.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU323-10 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.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 : Sun Jun 19 18:48:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50
% 0.19/0.50 SPASS V 3.9
% 0.19/0.50 SPASS beiseite: Proof found.
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.50 SPASS derived 311 clauses, backtracked 0 clauses, performed 0 splits and kept 165 clauses.
% 0.19/0.50 SPASS allocated 63986 KBytes.
% 0.19/0.50 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.50 0:00:00.03 for the input.
% 0.19/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.50 0:00:00.01 for inferences.
% 0.19/0.50 0:00:00.00 for the backtracking.
% 0.19/0.50 0:00:00.08 for the reduction.
% 0.19/0.50
% 0.19/0.50
% 0.19/0.50 Here is a proof with depth 3, length 24 :
% 0.19/0.50 % SZS output start Refutation
% See solution above
% 0.19/0.50 Formulae used in the proof : ifeq_axiom ifeq_axiom_001 fc3_tops_1 dt_k3_subset_1 dt_k6_pre_topc fc2_tops_1 d1_tops_1 t51_tops_1 t51_tops_1_1 t51_tops_1_2 t51_tops_1_3
% 0.19/0.50
%------------------------------------------------------------------------------