%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU323-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:45:48 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.56s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 13
% Syntax : Number of formulae : 141 ( 141 unt; 0 def)
% Number of atoms : 141 ( 140 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-4 aty)
% Number of variables : 188 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ifeq_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq2(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c_1,plain,
ifeq2(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom]) ).
fof(ifeq_axiom_001,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom_001) ).
cnf(c_2,plain,
ifeq(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom_001]) ).
fof(fc3_tops_1,axiom,
! [VAR_0,VAR_1] : ifeq(element(VAR_0,powerset(the_carrier(VAR_1))),true,ifeq(closed_subset(VAR_0,VAR_1),true,ifeq(topological_space(VAR_1),true,ifeq(top_str(VAR_1),true,open_subset(subset_complement(the_carrier(VAR_1),VAR_0),VAR_1),true),true),true),true) = true,
file('theBenchmark.p',fc3_tops_1) ).
cnf(c_3,plain,
ifeq(element(A,powerset(the_carrier(B))),true,ifeq(closed_subset(A,B),true,ifeq(topological_space(B),true,ifeq(top_str(B),true,open_subset(subset_complement(the_carrier(B),A),B),true),true),true),true) = true,
inference(clausify,[status(thm)],[fc3_tops_1]) ).
fof(existence_l1_struct_0,axiom,
one_sorted_str(sK6_existence_l1_struct_0_A) = true,
file('theBenchmark.p',existence_l1_struct_0) ).
cnf(c_8,plain,
one_sorted_str(sK6_existence_l1_struct_0_A) = true,
inference(clausify,[status(thm)],[existence_l1_struct_0]) ).
cnf(c_9,plain,
true = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(copy,[status(thm)],[c_8]) ).
fof(dt_k3_subset_1,axiom,
! [VAR_0,VAR_1] : ifeq(element(VAR_0,powerset(VAR_1)),true,element(subset_complement(VAR_1,VAR_0),powerset(VAR_1)),true) = true,
file('theBenchmark.p',dt_k3_subset_1) ).
cnf(c_10,plain,
ifeq(element(A,powerset(B)),true,element(subset_complement(B,A),powerset(B)),true) = true,
inference(clausify,[status(thm)],[dt_k3_subset_1]) ).
cnf(c_264,plain,
ifeq(element(A,powerset(B)),one_sorted_str(sK6_existence_l1_struct_0_A),element(subset_complement(B,A),powerset(B)),true) = true,
inference(paramod,[status(thm)],[c_9,c_10]) ).
cnf(c_265,plain,
ifeq(element(A,powerset(B)),one_sorted_str(sK6_existence_l1_struct_0_A),element(subset_complement(B,A),powerset(B)),one_sorted_str(sK6_existence_l1_struct_0_A)) = true,
inference(paramod,[status(thm)],[c_9,c_264]) ).
cnf(c_11,plain,
ifeq(element(A,powerset(B)),one_sorted_str(sK6_existence_l1_struct_0_A),element(subset_complement(B,A),powerset(B)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_9,c_265]) ).
fof(dt_k6_pre_topc,axiom,
! [VAR_0,VAR_1] : ifeq(element(VAR_0,powerset(the_carrier(VAR_1))),true,ifeq(top_str(VAR_1),true,element(topstr_closure(VAR_1,VAR_0),powerset(the_carrier(VAR_1))),true),true) = true,
file('theBenchmark.p',dt_k6_pre_topc) ).
cnf(c_12,plain,
ifeq(element(A,powerset(the_carrier(B))),true,ifeq(top_str(B),true,element(topstr_closure(B,A),powerset(the_carrier(B))),true),true) = true,
inference(clausify,[status(thm)],[dt_k6_pre_topc]) ).
cnf(c_266,plain,
ifeq(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),true,element(topstr_closure(B,A),powerset(the_carrier(B))),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_12]) ).
cnf(c_267,plain,
ifeq(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(B,A),powerset(the_carrier(B))),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_266]) ).
cnf(c_268,plain,
ifeq(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(B,A),powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A)),true) = true,
inference(paramod,[status(thm)],[c_9,c_267]) ).
cnf(c_269,plain,
ifeq(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(B,A),powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = true,
inference(paramod,[status(thm)],[c_9,c_268]) ).
cnf(c_13,plain,
ifeq(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(B,A),powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_9,c_269]) ).
fof(fc2_tops_1,axiom,
! [VAR_0,VAR_1] : ifeq(element(VAR_0,powerset(the_carrier(VAR_1))),true,ifeq(topological_space(VAR_1),true,ifeq(top_str(VAR_1),true,closed_subset(topstr_closure(VAR_1,VAR_0),VAR_1),true),true),true) = true,
file('theBenchmark.p',fc2_tops_1) ).
cnf(c_14,plain,
ifeq(element(A,powerset(the_carrier(B))),true,ifeq(topological_space(B),true,ifeq(top_str(B),true,closed_subset(topstr_closure(B,A),B),true),true),true) = true,
inference(clausify,[status(thm)],[fc2_tops_1]) ).
cnf(c_270,plain,
ifeq(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(B),true,ifeq(top_str(B),true,closed_subset(topstr_closure(B,A),B),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_14]) ).
cnf(c_271,plain,
ifeq(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(B),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),true,closed_subset(topstr_closure(B,A),B),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_270]) ).
cnf(c_272,plain,
ifeq(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(B),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(B,A),B),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_271]) ).
cnf(c_273,plain,
ifeq(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(B),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(B,A),B),one_sorted_str(sK6_existence_l1_struct_0_A)),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_272]) ).
cnf(c_274,plain,
ifeq(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(B),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(B,A),B),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),true) = true,
inference(paramod,[status(thm)],[c_9,c_273]) ).
cnf(c_275,plain,
ifeq(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(B),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(B,A),B),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = true,
inference(paramod,[status(thm)],[c_9,c_274]) ).
cnf(c_15,plain,
ifeq(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(B),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(B,A),B),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_9,c_275]) ).
fof(existence_l1_pre_topc,axiom,
top_str(sK5_existence_l1_pre_topc_A) = true,
file('theBenchmark.p',existence_l1_pre_topc) ).
cnf(c_18,plain,
top_str(sK5_existence_l1_pre_topc_A) = true,
inference(clausify,[status(thm)],[existence_l1_pre_topc]) ).
cnf(c_276,plain,
top_str(sK5_existence_l1_pre_topc_A) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_9,c_18]) ).
cnf(c_19,plain,
one_sorted_str(sK6_existence_l1_struct_0_A) = top_str(sK5_existence_l1_pre_topc_A),
inference(copy,[status(thm)],[c_276]) ).
fof(d1_tops_1,axiom,
! [VAR_0,VAR_1] : ifeq2(element(VAR_0,powerset(the_carrier(VAR_1))),true,ifeq2(top_str(VAR_1),true,subset_complement(the_carrier(VAR_1),topstr_closure(VAR_1,subset_complement(the_carrier(VAR_1),VAR_0))),interior(VAR_1,VAR_0)),interior(VAR_1,VAR_0)) = interior(VAR_1,VAR_0),
file('theBenchmark.p',d1_tops_1) ).
cnf(c_34,plain,
ifeq2(element(A,powerset(the_carrier(B))),true,ifeq2(top_str(B),true,subset_complement(the_carrier(B),topstr_closure(B,subset_complement(the_carrier(B),A))),interior(B,A)),interior(B,A)) = interior(B,A),
inference(clausify,[status(thm)],[d1_tops_1]) ).
cnf(c_277,plain,
ifeq2(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq2(top_str(B),true,subset_complement(the_carrier(B),topstr_closure(B,subset_complement(the_carrier(B),A))),interior(B,A)),interior(B,A)) = interior(B,A),
inference(paramod,[status(thm)],[c_9,c_34]) ).
cnf(c_278,plain,
ifeq2(element(A,powerset(the_carrier(B))),top_str(sK5_existence_l1_pre_topc_A),ifeq2(top_str(B),true,subset_complement(the_carrier(B),topstr_closure(B,subset_complement(the_carrier(B),A))),interior(B,A)),interior(B,A)) = interior(B,A),
inference(paramod,[status(thm)],[c_19,c_277]) ).
cnf(c_279,plain,
ifeq2(element(A,powerset(the_carrier(B))),top_str(sK5_existence_l1_pre_topc_A),ifeq2(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),subset_complement(the_carrier(B),topstr_closure(B,subset_complement(the_carrier(B),A))),interior(B,A)),interior(B,A)) = interior(B,A),
inference(paramod,[status(thm)],[c_9,c_278]) ).
cnf(c_35,plain,
ifeq2(element(A,powerset(the_carrier(B))),top_str(sK5_existence_l1_pre_topc_A),ifeq2(top_str(B),top_str(sK5_existence_l1_pre_topc_A),subset_complement(the_carrier(B),topstr_closure(B,subset_complement(the_carrier(B),A))),interior(B,A)),interior(B,A)) = interior(B,A),
inference(paramod,[status(thm)],[c_19,c_279]) ).
fof(t51_tops_1,axiom,
top_str(sK2_t51_tops_1_A) = true,
file('theBenchmark.p',t51_tops_1) ).
cnf(c_36,plain,
top_str(sK2_t51_tops_1_A) = true,
inference(clausify,[status(thm)],[t51_tops_1]) ).
cnf(c_280,plain,
top_str(sK2_t51_tops_1_A) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_9,c_36]) ).
cnf(c_281,plain,
top_str(sK2_t51_tops_1_A) = top_str(sK5_existence_l1_pre_topc_A),
inference(paramod,[status(thm)],[c_19,c_280]) ).
cnf(c_37,plain,
top_str(sK5_existence_l1_pre_topc_A) = top_str(sK2_t51_tops_1_A),
inference(copy,[status(thm)],[c_281]) ).
fof(t51_tops_1_1,axiom,
topological_space(sK2_t51_tops_1_A) = true,
file('theBenchmark.p',t51_tops_1_1) ).
cnf(c_38,plain,
topological_space(sK2_t51_tops_1_A) = true,
inference(clausify,[status(thm)],[t51_tops_1_1]) ).
cnf(c_282,plain,
topological_space(sK2_t51_tops_1_A) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_9,c_38]) ).
cnf(c_283,plain,
topological_space(sK2_t51_tops_1_A) = top_str(sK5_existence_l1_pre_topc_A),
inference(paramod,[status(thm)],[c_19,c_282]) ).
cnf(c_39,plain,
topological_space(sK2_t51_tops_1_A) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_37,c_283]) ).
fof(t51_tops_1_2,axiom,
element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = true,
file('theBenchmark.p',t51_tops_1_2) ).
cnf(c_40,plain,
element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = true,
inference(clausify,[status(thm)],[t51_tops_1_2]) ).
cnf(c_284,plain,
element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_9,c_40]) ).
cnf(c_285,plain,
element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = top_str(sK5_existence_l1_pre_topc_A),
inference(paramod,[status(thm)],[c_19,c_284]) ).
cnf(c_41,plain,
element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_37,c_285]) ).
fof(t51_tops_1_3,axiom,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != true,
file('theBenchmark.p',t51_tops_1_3) ).
cnf(c_42,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != true,
inference(clausify,[status(thm)],[t51_tops_1_3]) ).
cnf(c_286,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_9,c_42]) ).
cnf(c_287,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != top_str(sK5_existence_l1_pre_topc_A),
inference(paramod,[status(thm)],[c_19,c_286]) ).
cnf(c_43,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_37,c_287]) ).
cnf(c_288,plain,
ifeq(element(A,powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(closed_subset(A,B),true,ifeq(topological_space(B),true,ifeq(top_str(B),true,open_subset(subset_complement(the_carrier(B),A),B),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_289,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK5_existence_l1_pre_topc_A),ifeq(closed_subset(A,B),true,ifeq(topological_space(B),true,ifeq(top_str(B),true,open_subset(subset_complement(the_carrier(B),A),B),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_288]) ).
cnf(c_290,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),true,ifeq(topological_space(B),true,ifeq(top_str(B),true,open_subset(subset_complement(the_carrier(B),A),B),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_37,c_289]) ).
cnf(c_291,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(B),true,ifeq(top_str(B),true,open_subset(subset_complement(the_carrier(B),A),B),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_290]) ).
cnf(c_292,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK5_existence_l1_pre_topc_A),ifeq(topological_space(B),true,ifeq(top_str(B),true,open_subset(subset_complement(the_carrier(B),A),B),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_291]) ).
cnf(c_293,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),true,ifeq(top_str(B),true,open_subset(subset_complement(the_carrier(B),A),B),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_37,c_292]) ).
cnf(c_294,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),true,open_subset(subset_complement(the_carrier(B),A),B),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_293]) ).
cnf(c_295,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK5_existence_l1_pre_topc_A),ifeq(top_str(B),true,open_subset(subset_complement(the_carrier(B),A),B),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_294]) ).
cnf(c_296,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),true,open_subset(subset_complement(the_carrier(B),A),B),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_37,c_295]) ).
cnf(c_297,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),open_subset(subset_complement(the_carrier(B),A),B),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_296]) ).
cnf(c_298,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK5_existence_l1_pre_topc_A),open_subset(subset_complement(the_carrier(B),A),B),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_297]) ).
cnf(c_299,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_37,c_298]) ).
cnf(c_300,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),one_sorted_str(sK6_existence_l1_struct_0_A)),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_299]) ).
cnf(c_301,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK5_existence_l1_pre_topc_A)),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_300]) ).
cnf(c_302,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK2_t51_tops_1_A)),true),true),true) = true,
inference(paramod,[status(thm)],[c_37,c_301]) ).
cnf(c_303,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_302]) ).
cnf(c_304,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK2_t51_tops_1_A)),top_str(sK5_existence_l1_pre_topc_A)),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_303]) ).
cnf(c_305,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),true),true) = true,
inference(paramod,[status(thm)],[c_37,c_304]) ).
cnf(c_306,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),true) = true,
inference(paramod,[status(thm)],[c_9,c_305]) ).
cnf(c_307,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK5_existence_l1_pre_topc_A)),true) = true,
inference(paramod,[status(thm)],[c_19,c_306]) ).
cnf(c_308,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),true) = true,
inference(paramod,[status(thm)],[c_37,c_307]) ).
cnf(c_309,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = true,
inference(paramod,[status(thm)],[c_9,c_308]) ).
cnf(c_310,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK5_existence_l1_pre_topc_A)) = true,
inference(paramod,[status(thm)],[c_19,c_309]) ).
cnf(c_311,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = true,
inference(paramod,[status(thm)],[c_37,c_310]) ).
cnf(c_312,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_9,c_311]) ).
cnf(c_313,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK5_existence_l1_pre_topc_A),
inference(paramod,[status(thm)],[c_19,c_312]) ).
cnf(c_48,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(closed_subset(A,B),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(B),A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_37,c_313]) ).
cnf(c_314,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK5_existence_l1_pre_topc_A),ifeq(topological_space(B),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(B,A),B),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_315,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(B,A),B),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_37,c_314]) ).
cnf(c_316,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK5_existence_l1_pre_topc_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(B,A),B),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_19,c_315]) ).
cnf(c_317,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(B,A),B),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_37,c_316]) ).
cnf(c_318,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK5_existence_l1_pre_topc_A),closed_subset(topstr_closure(B,A),B),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_19,c_317]) ).
cnf(c_319,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),closed_subset(topstr_closure(B,A),B),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_37,c_318]) ).
cnf(c_320,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),closed_subset(topstr_closure(B,A),B),top_str(sK5_existence_l1_pre_topc_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_19,c_319]) ).
cnf(c_321,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),closed_subset(topstr_closure(B,A),B),top_str(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_37,c_320]) ).
cnf(c_322,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),closed_subset(topstr_closure(B,A),B),top_str(sK2_t51_tops_1_A)),top_str(sK5_existence_l1_pre_topc_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_19,c_321]) ).
cnf(c_323,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),closed_subset(topstr_closure(B,A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_37,c_322]) ).
cnf(c_324,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),closed_subset(topstr_closure(B,A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK5_existence_l1_pre_topc_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_19,c_323]) ).
cnf(c_325,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),closed_subset(topstr_closure(B,A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_37,c_324]) ).
cnf(c_326,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),closed_subset(topstr_closure(B,A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK5_existence_l1_pre_topc_A),
inference(paramod,[status(thm)],[c_19,c_325]) ).
cnf(c_50,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(topological_space(B),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),closed_subset(topstr_closure(B,A),B),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_37,c_326]) ).
cnf(c_327,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK5_existence_l1_pre_topc_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(B,A),powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_19,c_13]) ).
cnf(c_328,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(B,A),powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_37,c_327]) ).
cnf(c_329,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK5_existence_l1_pre_topc_A),element(topstr_closure(B,A),powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_19,c_328]) ).
cnf(c_330,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),element(topstr_closure(B,A),powerset(the_carrier(B))),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_37,c_329]) ).
cnf(c_331,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),element(topstr_closure(B,A),powerset(the_carrier(B))),top_str(sK5_existence_l1_pre_topc_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_19,c_330]) ).
cnf(c_332,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),element(topstr_closure(B,A),powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_37,c_331]) ).
cnf(c_333,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),element(topstr_closure(B,A),powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A)),top_str(sK5_existence_l1_pre_topc_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_19,c_332]) ).
cnf(c_334,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),element(topstr_closure(B,A),powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_37,c_333]) ).
cnf(c_335,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),element(topstr_closure(B,A),powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK5_existence_l1_pre_topc_A),
inference(paramod,[status(thm)],[c_19,c_334]) ).
cnf(c_51,plain,
ifeq(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq(top_str(B),top_str(sK2_t51_tops_1_A),element(topstr_closure(B,A),powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_37,c_335]) ).
cnf(c_336,plain,
ifeq(element(A,powerset(B)),top_str(sK5_existence_l1_pre_topc_A),element(subset_complement(B,A),powerset(B)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_19,c_11]) ).
cnf(c_337,plain,
ifeq(element(A,powerset(B)),top_str(sK2_t51_tops_1_A),element(subset_complement(B,A),powerset(B)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_37,c_336]) ).
cnf(c_338,plain,
ifeq(element(A,powerset(B)),top_str(sK2_t51_tops_1_A),element(subset_complement(B,A),powerset(B)),top_str(sK5_existence_l1_pre_topc_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_19,c_337]) ).
cnf(c_339,plain,
ifeq(element(A,powerset(B)),top_str(sK2_t51_tops_1_A),element(subset_complement(B,A),powerset(B)),top_str(sK2_t51_tops_1_A)) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(paramod,[status(thm)],[c_37,c_338]) ).
cnf(c_340,plain,
ifeq(element(A,powerset(B)),top_str(sK2_t51_tops_1_A),element(subset_complement(B,A),powerset(B)),top_str(sK2_t51_tops_1_A)) = top_str(sK5_existence_l1_pre_topc_A),
inference(paramod,[status(thm)],[c_19,c_339]) ).
cnf(c_52,plain,
ifeq(element(A,powerset(B)),top_str(sK2_t51_tops_1_A),element(subset_complement(B,A),powerset(B)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_37,c_340]) ).
cnf(c_341,plain,
ifeq2(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq2(top_str(B),top_str(sK5_existence_l1_pre_topc_A),subset_complement(the_carrier(B),topstr_closure(B,subset_complement(the_carrier(B),A))),interior(B,A)),interior(B,A)) = interior(B,A),
inference(paramod,[status(thm)],[c_37,c_35]) ).
cnf(c_54,plain,
ifeq2(element(A,powerset(the_carrier(B))),top_str(sK2_t51_tops_1_A),ifeq2(top_str(B),top_str(sK2_t51_tops_1_A),subset_complement(the_carrier(B),topstr_closure(B,subset_complement(the_carrier(B),A))),interior(B,A)),interior(B,A)) = interior(B,A),
inference(paramod,[status(thm)],[c_37,c_341]) ).
cnf(c_342,plain,
ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_41,c_52]) ).
cnf(c_80,plain,
element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_2,c_342]) ).
cnf(c_343,plain,
ifeq2(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq2(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),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(paramod,[status(thm)],[c_41,c_54]) ).
cnf(c_344,plain,
ifeq2(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),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),
inference(paramod,[status(thm)],[c_1,c_343]) ).
cnf(c_83,plain,
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(paramod,[status(thm)],[c_1,c_344]) ).
cnf(c_345,plain,
ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(topological_space(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),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),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_80,c_50]) ).
cnf(c_346,plain,
ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),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),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_39,c_345]) ).
cnf(c_347,plain,
ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),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),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_2,c_346]) ).
cnf(c_348,plain,
ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),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),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_2,c_347]) ).
cnf(c_166,plain,
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) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_2,c_348]) ).
cnf(c_349,plain,
ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),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))),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_80,c_51]) ).
cnf(c_350,plain,
ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),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))),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_2,c_349]) ).
cnf(c_167,plain,
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))) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_2,c_350]) ).
cnf(c_351,plain,
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))),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(topological_space(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),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),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_166,c_48]) ).
cnf(c_352,plain,
ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(topological_space(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),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),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_167,c_351]) ).
cnf(c_353,plain,
ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),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),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_39,c_352]) ).
cnf(c_354,plain,
ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_83,c_353]) ).
cnf(c_355,plain,
ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_2,c_354]) ).
cnf(c_356,plain,
ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A)),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_2,c_355]) ).
cnf(c_357,plain,
ifeq(top_str(sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A),open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),top_str(sK2_t51_tops_1_A)) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_2,c_356]) ).
cnf(c_358,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) = top_str(sK2_t51_tops_1_A),
inference(paramod,[status(thm)],[c_2,c_357]) ).
cnf(c_263,plain,
$false,
inference(resolve,[status(thm)],[c_43,c_358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU323-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n002.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 09:15:05 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 1354510 was started by sandbox on n002,
% 0.19/0.45 % Sat Sep 26 09:15:05 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.23/0.56
% 0.23/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.56
% 0.23/0.56 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.23/0.56 % Length of proof is 33.
% 0.23/0.56 % Level of proof is 7.
% 0.23/0.56 % Maximum clause weight is 81.000.
% 0.23/0.56 % Given clauses 92.
% 0.23/0.56
% 0.23/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------