%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /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 : Thu Sep 24 08:58:59 AM UTC 2026
% Result : Theorem 8.25s 8.55s
% Output : Proof 8.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 82 ( 41 unt; 0 def)
% Number of atoms : 180 ( 29 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 171 ( 73 ~; 65 |; 23 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 34 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc3_tops_1,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& closed_subset(B,A)
& top_str(A)
& topological_space(A) )
=> open_subset(subset_complement(the_carrier(A),B),A) ),
file('theBenchmark.p',fc3_tops_1) ).
fof(dt_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k3_subset_1) ).
fof(dt_k6_pre_topc,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A) )
=> element(topstr_closure(A,B),powerset(the_carrier(A))) ),
file('theBenchmark.p',dt_k6_pre_topc) ).
fof(fc2_tops_1,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A)
& topological_space(A) )
=> closed_subset(topstr_closure(A,B),A) ),
file('theBenchmark.p',fc2_tops_1) ).
fof(d1_tops_1,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) ) ),
file('theBenchmark.p',d1_tops_1) ).
fof(t51_tops_1,conjecture,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> open_subset(interior(A,B),A) ) ),
file('theBenchmark.p',t51_tops_1) ).
fof(f_1_1,plain,
! [A,B] :
( open_subset(subset_complement(the_carrier(A),B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ closed_subset(B,A)
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[fc3_tops_1]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( open_subset(subset_complement(the_carrier(U_1),U_0),U_1)
| ~ element(U_0,powerset(the_carrier(U_1)))
| ~ closed_subset(U_0,U_1)
| ~ top_str(U_1)
| ~ topological_space(U_1) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( open_subset(subset_complement(the_carrier(U_1),U_0),U_1)
| ~ element(U_0,powerset(the_carrier(U_1)))
| ~ closed_subset(U_0,U_1)
| ~ top_str(U_1)
| ~ topological_space(U_1) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_6_1,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k3_subset_1]) ).
fof(f_6_2,plain,
! [U_10,U_9] :
( element(subset_complement(U_10,U_9),powerset(U_10))
| ~ element(U_9,powerset(U_10)) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( element(subset_complement(U_10,U_9),powerset(U_10))
| ~ element(U_9,powerset(U_10)) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B] :
( element(topstr_closure(A,B),powerset(the_carrier(A)))
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[dt_k6_pre_topc]) ).
fof(f_7_2,plain,
! [U_12,U_11] :
( element(topstr_closure(U_12,U_11),powerset(the_carrier(U_12)))
| ~ element(U_11,powerset(the_carrier(U_12)))
| ~ top_str(U_12) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( element(topstr_closure(U_12,U_11),powerset(the_carrier(U_12)))
| ~ element(U_11,powerset(the_carrier(U_12)))
| ~ top_str(U_12) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_9_1,plain,
! [A,B] :
( closed_subset(topstr_closure(A,B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[fc2_tops_1]) ).
fof(f_9_2,plain,
! [U_14,U_13] :
( closed_subset(topstr_closure(U_14,U_13),U_14)
| ~ element(U_13,powerset(the_carrier(U_14)))
| ~ top_str(U_14)
| ~ topological_space(U_14) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( closed_subset(topstr_closure(U_14,U_13),U_14)
| ~ element(U_13,powerset(the_carrier(U_14)))
| ~ top_str(U_14)
| ~ topological_space(U_14) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_20_1,plain,
! [A] :
( ! [B] :
( interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B)))
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[d1_tops_1]) ).
fof(f_20_2,plain,
! [U_32] :
( ! [U_31] :
( interior(U_32,U_31) = subset_complement(the_carrier(U_32),topstr_closure(U_32,subset_complement(the_carrier(U_32),U_31)))
| ~ element(U_31,powerset(the_carrier(U_32))) )
| ~ top_str(U_32) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( interior(U_32,U_31) = subset_complement(the_carrier(U_32),topstr_closure(U_32,subset_complement(the_carrier(U_32),U_31)))
| ~ element(U_31,powerset(the_carrier(U_32)))
| ~ top_str(U_32) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,negated_conjecture,
~ ! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> open_subset(interior(A,B),A) ) ),
inference(negate,[status(cth)],[t51_tops_1]) ).
fof(f_21_2,negated_conjecture,
? [A] :
( ? [B] :
( ~ open_subset(interior(A,B),A)
& element(B,powerset(the_carrier(A))) )
& top_str(A)
& topological_space(A) ),
inference(fof_nnf,[status(thm)],[f_21_1]) ).
fof(f_21_3,negated_conjecture,
? [U_34] :
( ? [U_33] :
( ~ open_subset(interior(U_34,U_33),U_34)
& element(U_33,powerset(the_carrier(U_34))) )
& top_str(U_34)
& topological_space(U_34) ),
inference(variable_rename,[status(thm)],[f_21_2]) ).
fof(f_21_4,negated_conjecture,
( ? [U_33] :
( ~ open_subset(interior(sK6,U_33),sK6)
& element(U_33,powerset(the_carrier(sK6))) )
& top_str(sK6)
& topological_space(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_34,sK6)],[f_21_3]) ).
fof(f_21_5,negated_conjecture,
( ~ open_subset(interior(sK6,sK7),sK6)
& element(sK7,powerset(the_carrier(sK6)))
& top_str(sK6)
& topological_space(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_33,sK7)],[f_21_4]) ).
fof(f_21_6,negated_conjecture,
( ~ open_subset(interior(sK6,sK7),sK6)
& element(sK7,powerset(the_carrier(sK6)))
& top_str(sK6)
& topological_space(sK6) ),
inference(definitional_conversion,[status(esa)],[f_21_5]) ).
cnf(f_21_7,negated_conjecture,
topological_space(sK6),
inference(clausify,[status(thm)],[f_21_6]) ).
cnf(f_21_8,negated_conjecture,
top_str(sK6),
inference(clausify,[status(thm)],[f_21_6]) ).
cnf(f_21_9,negated_conjecture,
element(sK7,powerset(the_carrier(sK6))),
inference(clausify,[status(thm)],[f_21_6]) ).
cnf(f_21_10,negated_conjecture,
~ open_subset(interior(sK6,sK7),sK6),
inference(clausify,[status(thm)],[f_21_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_8,axiom,
( interior(Eq_x_0,Eq_x_1) = interior(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( open_subset(Eq_y_0,Eq_y_1)
| ~ open_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ open_subset(interior(sK6,sK7),sK6),
inference(start,[status(thm),parent(0:0)],[f_21_10]) ).
cnf(t2,plain,
( sK6 != sK6
| ~ open_subset(subset_complement(the_carrier(sK6),topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7))),sK6)
| subset_complement(the_carrier(sK6),topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7))) != interior(sK6,sK7)
| open_subset(interior(sK6,sK7),sK6) ),
inference(extension,[status(thm),parent(t1:1)],[equality_16]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( interior(sK6,sK7) != interior(sK6,sK7)
| subset_complement(the_carrier(sK6),topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7))) != interior(sK6,sK7)
| subset_complement(the_carrier(sK6),topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7))) = interior(sK6,sK7) ),
inference(extension,[status(thm),parent(t2:2)],[equality_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( interior(sK6,sK7) != subset_complement(the_carrier(sK6),topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7)))
| subset_complement(the_carrier(sK6),topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7))) = interior(sK6,sK7) ),
inference(extension,[status(thm),parent(t4:2)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ element(sK7,powerset(the_carrier(sK6)))
| ~ top_str(sK6)
| interior(sK6,sK7) = subset_complement(the_carrier(sK6),topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7))) ),
inference(extension,[status(thm),parent(t6:2)],[f_20_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
top_str(sK6),
inference(extension,[status(thm),parent(t8:2)],[f_21_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
element(sK7,powerset(the_carrier(sK6))),
inference(extension,[status(thm),parent(t8:3)],[f_21_9]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( sK7 != sK7
| sK6 != sK6
| interior(sK6,sK7) = interior(sK6,sK7) ),
inference(extension,[status(thm),parent(t4:3)],[equality_8]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t4:3]) ).
cnf(t16,plain,
sK6 = sK6,
inference(extension,[status(thm),parent(t14:2)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
sK7 = sK7,
inference(extension,[status(thm),parent(t14:3)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
( ~ top_str(sK6)
| ~ closed_subset(topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7)),sK6)
| ~ element(topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7)),powerset(the_carrier(sK6)))
| ~ topological_space(sK6)
| open_subset(subset_complement(the_carrier(sK6),topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7))),sK6) ),
inference(extension,[status(thm),parent(t2:3)],[f_1_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:3]) ).
cnf(t22,plain,
topological_space(sK6),
inference(extension,[status(thm),parent(t20:2)],[f_21_7]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(l11,lemma,
topological_space(sK6),
inference(lemma,[status(cth),parent(t20:2),below(t2:3)],[t20:2]) ).
cnf(t24,plain,
( ~ element(subset_complement(the_carrier(sK6),sK7),powerset(the_carrier(sK6)))
| ~ top_str(sK6)
| element(topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7)),powerset(the_carrier(sK6))) ),
inference(extension,[status(thm),parent(t20:3)],[f_7_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
top_str(sK6),
inference(extension,[status(thm),parent(t24:2)],[f_21_8]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( ~ element(sK7,powerset(the_carrier(sK6)))
| element(subset_complement(the_carrier(sK6),sK7),powerset(the_carrier(sK6))) ),
inference(extension,[status(thm),parent(t24:3)],[f_6_3]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
element(sK7,powerset(the_carrier(sK6))),
inference(extension,[status(thm),parent(t28:2)],[f_21_9]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( ~ top_str(sK6)
| ~ element(subset_complement(the_carrier(sK6),sK7),powerset(the_carrier(sK6)))
| ~ topological_space(sK6)
| closed_subset(topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7)),sK6) ),
inference(extension,[status(thm),parent(t20:4)],[f_9_3]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t20:4]) ).
cnf(t34,plain,
topological_space(sK6),
inference(lemma_extension,[status(thm),parent(t32:2)],[l11:1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( ~ element(sK7,powerset(the_carrier(sK6)))
| element(subset_complement(the_carrier(sK6),sK7),powerset(the_carrier(sK6))) ),
inference(extension,[status(thm),parent(t32:3)],[f_6_3]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t32:3]) ).
cnf(t38,plain,
element(sK7,powerset(the_carrier(sK6))),
inference(extension,[status(thm),parent(t36:2)],[f_21_9]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
top_str(sK6),
inference(extension,[status(thm),parent(t32:4)],[f_21_8]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t32:4]) ).
cnf(t42,plain,
top_str(sK6),
inference(extension,[status(thm),parent(t20:5)],[f_21_8]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t20:5]) ).
cnf(t44,plain,
sK6 = sK6,
inference(extension,[status(thm),parent(t2:4)],[equality_1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 23:57:45 UTC 2026
% 0.08/0.36 % CPUTime :
% 8.25/8.55 % SZS status Theorem for theBenchmark
% 8.25/8.55 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------