%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU324+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 : n006.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 08:59:00 AM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 111 ( 51 unt; 0 def)
% Number of atoms : 297 ( 70 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 295 ( 109 ~; 99 |; 63 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 44 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(fc6_tops_1,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A)
& topological_space(A) )
=> open_subset(interior(A,B),A) ),
file('theBenchmark.p',fc6_tops_1) ).
fof(involutiveness_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('theBenchmark.p',involutiveness_k3_subset_1) ).
fof(t30_tops_1,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( open_subset(B,A)
<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('theBenchmark.p',t30_tops_1) ).
fof(t52_pre_topc,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( ( ( topstr_closure(A,B) = B
& topological_space(A) )
=> closed_subset(B,A) )
& ( closed_subset(B,A)
=> topstr_closure(A,B) = B ) ) ) ),
file('theBenchmark.p',t52_pre_topc) ).
fof(t55_tops_1,conjecture,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( top_str(B)
=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ! [D] :
( element(D,powerset(the_carrier(B)))
=> ( ( interior(A,C) = C
=> open_subset(C,A) )
& ( open_subset(D,B)
=> interior(B,D) = D ) ) ) ) ) ),
file('theBenchmark.p',t55_tops_1) ).
fof(f_1_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_1_2,plain,
! [U_1] :
( ! [U_0] :
( interior(U_1,U_0) = subset_complement(the_carrier(U_1),topstr_closure(U_1,subset_complement(the_carrier(U_1),U_0)))
| ~ element(U_0,powerset(the_carrier(U_1))) )
| ~ top_str(U_1) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( interior(U_1,U_0) = subset_complement(the_carrier(U_1),topstr_closure(U_1,subset_complement(the_carrier(U_1),U_0)))
| ~ element(U_0,powerset(the_carrier(U_1)))
| ~ top_str(U_1) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_4_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_4_2,plain,
! [U_5,U_4] :
( element(subset_complement(U_5,U_4),powerset(U_5))
| ~ element(U_4,powerset(U_5)) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( element(subset_complement(U_5,U_4),powerset(U_5))
| ~ element(U_4,powerset(U_5)) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_16_1,plain,
! [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)],[fc6_tops_1]) ).
fof(f_16_2,plain,
! [U_20,U_19] :
( open_subset(interior(U_20,U_19),U_20)
| ~ element(U_19,powerset(the_carrier(U_20)))
| ~ top_str(U_20)
| ~ topological_space(U_20) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( open_subset(interior(U_20,U_19),U_20)
| ~ element(U_19,powerset(the_carrier(U_20)))
| ~ top_str(U_20)
| ~ topological_space(U_20) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A,B] :
( subset_complement(A,subset_complement(A,B)) = B
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1]) ).
fof(f_17_2,plain,
! [U_22,U_21] :
( subset_complement(U_22,subset_complement(U_22,U_21)) = U_21
| ~ element(U_21,powerset(U_22)) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( subset_complement(U_22,subset_complement(U_22,U_21)) = U_21
| ~ element(U_21,powerset(U_22)) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_22_1,plain,
! [A] :
( ! [B] :
( ( ( open_subset(B,A)
| ~ closed_subset(subset_complement(the_carrier(A),B),A) )
& ( closed_subset(subset_complement(the_carrier(A),B),A)
| ~ open_subset(B,A) ) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[t30_tops_1]) ).
fof(f_22_2,plain,
! [U_32] :
( ! [U_31] :
( ( ( open_subset(U_31,U_32)
| ~ closed_subset(subset_complement(the_carrier(U_32),U_31),U_32) )
& ( closed_subset(subset_complement(the_carrier(U_32),U_31),U_32)
| ~ open_subset(U_31,U_32) ) )
| ~ element(U_31,powerset(the_carrier(U_32))) )
| ~ top_str(U_32) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( closed_subset(subset_complement(the_carrier(U_32),U_31),U_32)
| ~ open_subset(U_31,U_32)
| ~ element(U_31,powerset(the_carrier(U_32)))
| ~ top_str(U_32) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_24_1,plain,
! [A] :
( ! [B] :
( ( ( closed_subset(B,A)
| topstr_closure(A,B) != B
| ~ topological_space(A) )
& ( topstr_closure(A,B) = B
| ~ closed_subset(B,A) ) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[t52_pre_topc]) ).
fof(f_24_2,plain,
! [U_40] :
( ! [U_39] :
( ( ( closed_subset(U_39,U_40)
| topstr_closure(U_40,U_39) != U_39
| ~ topological_space(U_40) )
& ( topstr_closure(U_40,U_39) = U_39
| ~ closed_subset(U_39,U_40) ) )
| ~ element(U_39,powerset(the_carrier(U_40))) )
| ~ top_str(U_40) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( topstr_closure(U_40,U_39) = U_39
| ~ closed_subset(U_39,U_40)
| ~ element(U_39,powerset(the_carrier(U_40)))
| ~ top_str(U_40) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,negated_conjecture,
~ ! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( top_str(B)
=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ! [D] :
( element(D,powerset(the_carrier(B)))
=> ( ( interior(A,C) = C
=> open_subset(C,A) )
& ( open_subset(D,B)
=> interior(B,D) = D ) ) ) ) ) ),
inference(negate,[status(cth)],[t55_tops_1]) ).
fof(f_25_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ( ( ~ open_subset(C,A)
& interior(A,C) = C )
| ( interior(B,D) != D
& open_subset(D,B) ) )
& element(D,powerset(the_carrier(B))) )
& element(C,powerset(the_carrier(A))) )
& top_str(B) )
& top_str(A)
& topological_space(A) ),
inference(fof_nnf,[status(thm)],[f_25_1]) ).
fof(f_25_3,negated_conjecture,
? [U_44] :
( ? [U_43] :
( ? [U_42] :
( ? [U_41] :
( ( ( ~ open_subset(U_42,U_44)
& interior(U_44,U_42) = U_42 )
| ( interior(U_43,U_41) != U_41
& open_subset(U_41,U_43) ) )
& element(U_41,powerset(the_carrier(U_43))) )
& element(U_42,powerset(the_carrier(U_44))) )
& top_str(U_43) )
& top_str(U_44)
& topological_space(U_44) ),
inference(variable_rename,[status(thm)],[f_25_2]) ).
fof(f_25_4,negated_conjecture,
( ? [U_43] :
( ? [U_42] :
( ? [U_41] :
( ( ( ~ open_subset(U_42,sK7)
& interior(sK7,U_42) = U_42 )
| ( interior(U_43,U_41) != U_41
& open_subset(U_41,U_43) ) )
& element(U_41,powerset(the_carrier(U_43))) )
& element(U_42,powerset(the_carrier(sK7))) )
& top_str(U_43) )
& top_str(sK7)
& topological_space(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_44,sK7)],[f_25_3]) ).
fof(f_25_5,negated_conjecture,
( ? [U_42] :
( ? [U_41] :
( ( ( ~ open_subset(U_42,sK7)
& interior(sK7,U_42) = U_42 )
| ( interior(sK8,U_41) != U_41
& open_subset(U_41,sK8) ) )
& element(U_41,powerset(the_carrier(sK8))) )
& element(U_42,powerset(the_carrier(sK7))) )
& top_str(sK8)
& top_str(sK7)
& topological_space(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_43,sK8)],[f_25_4]) ).
fof(f_25_6,negated_conjecture,
( ? [U_41] :
( ( ( ~ open_subset(sK9,sK7)
& interior(sK7,sK9) = sK9 )
| ( interior(sK8,U_41) != U_41
& open_subset(U_41,sK8) ) )
& element(U_41,powerset(the_carrier(sK8))) )
& element(sK9,powerset(the_carrier(sK7)))
& top_str(sK8)
& top_str(sK7)
& topological_space(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_42,sK9)],[f_25_5]) ).
fof(f_25_7,negated_conjecture,
( ( ( ~ open_subset(sK9,sK7)
& interior(sK7,sK9) = sK9 )
| ( interior(sK8,sK10) != sK10
& open_subset(sK10,sK8) ) )
& element(sK10,powerset(the_carrier(sK8)))
& element(sK9,powerset(the_carrier(sK7)))
& top_str(sK8)
& top_str(sK7)
& topological_space(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_41,sK10)],[f_25_6]) ).
fof(f_25_8,negated_conjecture,
( ( ~ open_subset(sK9,sK7)
| ~ sP1 )
& ( interior(sK7,sK9) = sK9
| ~ sP1 )
& ( interior(sK8,sK10) != sK10
| ~ sP0 )
& ( open_subset(sK10,sK8)
| ~ sP0 )
& ( sP1
| sP0 )
& element(sK10,powerset(the_carrier(sK8)))
& element(sK9,powerset(the_carrier(sK7)))
& top_str(sK8)
& top_str(sK7)
& topological_space(sK7) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_25_7]) ).
cnf(f_25_9,negated_conjecture,
topological_space(sK7),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_10,negated_conjecture,
top_str(sK7),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_11,negated_conjecture,
top_str(sK8),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_12,negated_conjecture,
element(sK9,powerset(the_carrier(sK7))),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_13,negated_conjecture,
element(sK10,powerset(the_carrier(sK8))),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_14,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_15,negated_conjecture,
( open_subset(sK10,sK8)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_16,negated_conjecture,
( interior(sK8,sK10) != sK10
| ~ sP0 ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_17,negated_conjecture,
( interior(sK7,sK9) = sK9
| ~ sP1 ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_18,negated_conjecture,
( ~ open_subset(sK9,sK7)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_25_8]) ).
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_4,axiom,
( the_carrier(Eq_x_0) = the_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( subset_complement(Eq_x_0,Eq_x_1) = subset_complement(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,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,
( interior(sK8,sK10) != sK10
| ~ sP0 ),
inference(start,[status(thm),parent(0:0)],[f_25_16]) ).
cnf(t2,plain,
( sP1
| sP0 ),
inference(extension,[status(thm),parent(t1:1)],[f_25_14]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ open_subset(sK9,sK7)
| ~ sP1 ),
inference(extension,[status(thm),parent(t2:2)],[f_25_18]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( sK7 != sK7
| ~ open_subset(interior(sK7,sK9),sK7)
| interior(sK7,sK9) != sK9
| open_subset(sK9,sK7) ),
inference(extension,[status(thm),parent(t4:2)],[equality_18]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ sP1
| interior(sK7,sK9) = sK9 ),
inference(extension,[status(thm),parent(t6:2)],[f_25_17]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
$false,
inference(reduction,[status(thm),parent(t8:2)],[t8:2,t2:2]) ).
cnf(t11,plain,
( ~ top_str(sK7)
| ~ element(sK9,powerset(the_carrier(sK7)))
| ~ topological_space(sK7)
| open_subset(interior(sK7,sK9),sK7) ),
inference(extension,[status(thm),parent(t6:3)],[f_16_3]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t6:3]) ).
cnf(t13,plain,
topological_space(sK7),
inference(extension,[status(thm),parent(t11:2)],[f_25_9]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t11:2]) ).
cnf(t15,plain,
element(sK9,powerset(the_carrier(sK7))),
inference(extension,[status(thm),parent(t11:3)],[f_25_12]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t11:3]) ).
cnf(t17,plain,
top_str(sK7),
inference(extension,[status(thm),parent(t11:4)],[f_25_10]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t11:4]) ).
cnf(t19,plain,
sK7 = sK7,
inference(extension,[status(thm),parent(t6:4)],[equality_1]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t6:4]) ).
cnf(l1,lemma,
sP0,
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t21,plain,
( subset_complement(the_carrier(sK8),topstr_closure(sK8,subset_complement(the_carrier(sK8),sK10))) != sK10
| interior(sK8,sK10) != subset_complement(the_carrier(sK8),topstr_closure(sK8,subset_complement(the_carrier(sK8),sK10)))
| interior(sK8,sK10) = sK10 ),
inference(extension,[status(thm),parent(t1:2)],[equality_3]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t1:2]) ).
cnf(t23,plain,
( ~ element(sK10,powerset(the_carrier(sK8)))
| ~ top_str(sK8)
| interior(sK8,sK10) = subset_complement(the_carrier(sK8),topstr_closure(sK8,subset_complement(the_carrier(sK8),sK10))) ),
inference(extension,[status(thm),parent(t21:2)],[f_1_3]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t21:2]) ).
cnf(t25,plain,
top_str(sK8),
inference(extension,[status(thm),parent(t23:2)],[f_25_11]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t23:2]) ).
cnf(t27,plain,
element(sK10,powerset(the_carrier(sK8))),
inference(extension,[status(thm),parent(t23:3)],[f_25_13]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t23:3]) ).
cnf(t29,plain,
( subset_complement(the_carrier(sK8),subset_complement(the_carrier(sK8),sK10)) != sK10
| subset_complement(the_carrier(sK8),topstr_closure(sK8,subset_complement(the_carrier(sK8),sK10))) != subset_complement(the_carrier(sK8),subset_complement(the_carrier(sK8),sK10))
| subset_complement(the_carrier(sK8),topstr_closure(sK8,subset_complement(the_carrier(sK8),sK10))) = sK10 ),
inference(extension,[status(thm),parent(t21:3)],[equality_3]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t21:3]) ).
cnf(t31,plain,
( topstr_closure(sK8,subset_complement(the_carrier(sK8),sK10)) != subset_complement(the_carrier(sK8),sK10)
| the_carrier(sK8) != the_carrier(sK8)
| subset_complement(the_carrier(sK8),topstr_closure(sK8,subset_complement(the_carrier(sK8),sK10))) = subset_complement(the_carrier(sK8),subset_complement(the_carrier(sK8),sK10)) ),
inference(extension,[status(thm),parent(t29:2)],[equality_7]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t29:2]) ).
cnf(t33,plain,
( sK8 != sK8
| the_carrier(sK8) = the_carrier(sK8) ),
inference(extension,[status(thm),parent(t31:2)],[equality_4]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t31:2]) ).
cnf(t35,plain,
( sK8 != sK8
| sK8 = sK8 ),
inference(extension,[status(thm),parent(t33:2)],[equality_2]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t33:2]) ).
cnf(t37,plain,
sK8 = sK8,
inference(extension,[status(thm),parent(t35:2)],[equality_1]) ).
cnf(t38,plain,
$false,
inference(connection,[status(thm),parent(t37:1)],[t37:1,t35:2]) ).
cnf(t39,plain,
( ~ element(subset_complement(the_carrier(sK8),sK10),powerset(the_carrier(sK8)))
| ~ closed_subset(subset_complement(the_carrier(sK8),sK10),sK8)
| ~ top_str(sK8)
| topstr_closure(sK8,subset_complement(the_carrier(sK8),sK10)) = subset_complement(the_carrier(sK8),sK10) ),
inference(extension,[status(thm),parent(t31:3)],[f_24_3]) ).
cnf(t40,plain,
$false,
inference(connection,[status(thm),parent(t39:1)],[t39:1,t31:3]) ).
cnf(t41,plain,
top_str(sK8),
inference(extension,[status(thm),parent(t39:2)],[f_25_11]) ).
cnf(t42,plain,
$false,
inference(connection,[status(thm),parent(t41:1)],[t41:1,t39:2]) ).
cnf(l21,lemma,
top_str(sK8),
inference(lemma,[status(cth),parent(t39:2),below(t31:3)],[t39:2]) ).
cnf(t43,plain,
( ~ element(sK10,powerset(the_carrier(sK8)))
| ~ open_subset(sK10,sK8)
| ~ top_str(sK8)
| closed_subset(subset_complement(the_carrier(sK8),sK10),sK8) ),
inference(extension,[status(thm),parent(t39:3)],[f_22_3]) ).
cnf(t44,plain,
$false,
inference(connection,[status(thm),parent(t43:1)],[t43:1,t39:3]) ).
cnf(t45,plain,
top_str(sK8),
inference(lemma_extension,[status(thm),parent(t43:2)],[l21:1]) ).
cnf(t46,plain,
$false,
inference(connection,[status(thm),parent(t45:1)],[t45:1,t43:2]) ).
cnf(t47,plain,
( ~ sP0
| open_subset(sK10,sK8) ),
inference(extension,[status(thm),parent(t43:3)],[f_25_15]) ).
cnf(t48,plain,
$false,
inference(connection,[status(thm),parent(t47:1)],[t47:1,t43:3]) ).
cnf(t49,plain,
sP0,
inference(lemma_extension,[status(thm),parent(t47:2)],[l1:1]) ).
cnf(t50,plain,
$false,
inference(connection,[status(thm),parent(t49:1)],[t49:1,t47:2]) ).
cnf(t51,plain,
element(sK10,powerset(the_carrier(sK8))),
inference(extension,[status(thm),parent(t43:4)],[f_25_13]) ).
cnf(t52,plain,
$false,
inference(connection,[status(thm),parent(t51:1)],[t51:1,t43:4]) ).
cnf(t53,plain,
( ~ element(sK10,powerset(the_carrier(sK8)))
| element(subset_complement(the_carrier(sK8),sK10),powerset(the_carrier(sK8))) ),
inference(extension,[status(thm),parent(t39:4)],[f_4_3]) ).
cnf(t54,plain,
$false,
inference(connection,[status(thm),parent(t53:1)],[t53:1,t39:4]) ).
cnf(t55,plain,
element(sK10,powerset(the_carrier(sK8))),
inference(extension,[status(thm),parent(t53:2)],[f_25_13]) ).
cnf(t56,plain,
$false,
inference(connection,[status(thm),parent(t55:1)],[t55:1,t53:2]) ).
cnf(t57,plain,
( ~ element(sK10,powerset(the_carrier(sK8)))
| subset_complement(the_carrier(sK8),subset_complement(the_carrier(sK8),sK10)) = sK10 ),
inference(extension,[status(thm),parent(t29:3)],[f_17_3]) ).
cnf(t58,plain,
$false,
inference(connection,[status(thm),parent(t57:1)],[t57:1,t29:3]) ).
cnf(t59,plain,
element(sK10,powerset(the_carrier(sK8))),
inference(extension,[status(thm),parent(t57:2)],[f_25_13]) ).
cnf(t60,plain,
$false,
inference(connection,[status(thm),parent(t59:1)],[t59:1,t57:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU324+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
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 19 23:54:57 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.44 % SZS status Theorem for theBenchmark
% 0.13/0.44 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------