%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU320+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 : n007.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 0.22s 0.49s
% Output : Proof 0.22s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_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_l1_pre_topc,axiom,
! [A] :
( top_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_pre_topc) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(existence_l1_pre_topc,axiom,
? [A] : top_str(A),
file('theBenchmark.p',existence_l1_pre_topc) ).
fof(existence_l1_struct_0,axiom,
? [A] : one_sorted_str(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t29_tops_1,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('theBenchmark.p',t29_tops_1) ).
fof(t30_tops_1,conjecture,
! [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(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(f_1_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_1_2,plain,
$true,
inference(clausify,[status(thm)],[f_1_1]) ).
fof(f_2_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_2_2,plain,
! [U_1,U_0] :
( element(subset_complement(U_1,U_0),powerset(U_1))
| ~ element(U_0,powerset(U_1)) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( element(subset_complement(U_1,U_0),powerset(U_1))
| ~ element(U_0,powerset(U_1)) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( one_sorted_str(A)
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_pre_topc]) ).
fof(f_3_2,plain,
! [U_2] :
( one_sorted_str(U_2)
| ~ top_str(U_2) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( one_sorted_str(U_2)
| ~ top_str(U_2) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_4_2,plain,
$true,
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_6_2,plain,
$true,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
? [A] : top_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_pre_topc]) ).
fof(f_7_2,plain,
? [U_3] : top_str(U_3),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
top_str(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1)],[f_7_2]) ).
cnf(f_7_4,plain,
top_str(sK1),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_8_2,plain,
? [U_4] : one_sorted_str(U_4),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
one_sorted_str(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_4,sK2)],[f_8_2]) ).
cnf(f_8_4,plain,
one_sorted_str(sK2),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_9_2,plain,
! [U_6] :
? [U_5] : element(U_5,U_6),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_6] : element(sK3(U_6),U_6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_5,sK3(U_6))],[f_9_2]) ).
cnf(f_9_4,plain,
element(sK3(U_6),U_6),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_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_10_2,plain,
! [U_8,U_7] :
( subset_complement(U_8,subset_complement(U_8,U_7)) = U_7
| ~ element(U_7,powerset(U_8)) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( subset_complement(U_8,subset_complement(U_8,U_7)) = U_7
| ~ element(U_7,powerset(U_8)) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_11_2,plain,
! [U_10,U_9] : subset(U_10,U_10),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_10] : subset(U_10,U_10),
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
subset(U_10,U_10),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A] :
( ! [B] :
( ( ( closed_subset(B,A)
| ~ open_subset(subset_complement(the_carrier(A),B),A) )
& ( open_subset(subset_complement(the_carrier(A),B),A)
| ~ closed_subset(B,A) ) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[t29_tops_1]) ).
fof(f_12_2,plain,
! [U_12] :
( ! [U_11] :
( ( ( closed_subset(U_11,U_12)
| ~ open_subset(subset_complement(the_carrier(U_12),U_11),U_12) )
& ( open_subset(subset_complement(the_carrier(U_12),U_11),U_12)
| ~ closed_subset(U_11,U_12) ) )
| ~ element(U_11,powerset(the_carrier(U_12))) )
| ~ top_str(U_12) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( open_subset(subset_complement(the_carrier(U_12),U_11),U_12)
| ~ closed_subset(U_11,U_12)
| ~ element(U_11,powerset(the_carrier(U_12)))
| ~ top_str(U_12) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( closed_subset(U_11,U_12)
| ~ open_subset(subset_complement(the_carrier(U_12),U_11),U_12)
| ~ element(U_11,powerset(the_carrier(U_12)))
| ~ top_str(U_12) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,negated_conjecture,
~ ! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( open_subset(B,A)
<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
inference(negate,[status(cth)],[t30_tops_1]) ).
fof(f_13_2,negated_conjecture,
? [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)],[f_13_1]) ).
fof(f_13_3,negated_conjecture,
? [U_14] :
( ? [U_13] :
( ( ( ~ open_subset(U_13,U_14)
& closed_subset(subset_complement(the_carrier(U_14),U_13),U_14) )
| ( ~ closed_subset(subset_complement(the_carrier(U_14),U_13),U_14)
& open_subset(U_13,U_14) ) )
& element(U_13,powerset(the_carrier(U_14))) )
& top_str(U_14) ),
inference(variable_rename,[status(thm)],[f_13_2]) ).
fof(f_13_4,negated_conjecture,
( ? [U_13] :
( ( ( ~ open_subset(U_13,sK4)
& closed_subset(subset_complement(the_carrier(sK4),U_13),sK4) )
| ( ~ closed_subset(subset_complement(the_carrier(sK4),U_13),sK4)
& open_subset(U_13,sK4) ) )
& element(U_13,powerset(the_carrier(sK4))) )
& top_str(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_14,sK4)],[f_13_3]) ).
fof(f_13_5,negated_conjecture,
( ( ( ~ open_subset(sK5,sK4)
& closed_subset(subset_complement(the_carrier(sK4),sK5),sK4) )
| ( ~ closed_subset(subset_complement(the_carrier(sK4),sK5),sK4)
& open_subset(sK5,sK4) ) )
& element(sK5,powerset(the_carrier(sK4)))
& top_str(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_13,sK5)],[f_13_4]) ).
fof(f_13_6,negated_conjecture,
( ( ~ open_subset(sK5,sK4)
| ~ sP1 )
& ( closed_subset(subset_complement(the_carrier(sK4),sK5),sK4)
| ~ sP1 )
& ( ~ closed_subset(subset_complement(the_carrier(sK4),sK5),sK4)
| ~ sP0 )
& ( open_subset(sK5,sK4)
| ~ sP0 )
& ( sP1
| sP0 )
& element(sK5,powerset(the_carrier(sK4)))
& top_str(sK4) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_13_5]) ).
cnf(f_13_7,negated_conjecture,
top_str(sK4),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_8,negated_conjecture,
element(sK5,powerset(the_carrier(sK4))),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_9,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_10,negated_conjecture,
( open_subset(sK5,sK4)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_11,negated_conjecture,
( ~ closed_subset(subset_complement(the_carrier(sK4),sK5),sK4)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_12,negated_conjecture,
( closed_subset(subset_complement(the_carrier(sK4),sK5),sK4)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_13,negated_conjecture,
( ~ open_subset(sK5,sK4)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_13_6]) ).
fof(f_14_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_14_2,plain,
! [U_16,U_15] :
( ( element(U_16,powerset(U_15))
| ~ subset(U_16,U_15) )
& ( subset(U_16,U_15)
| ~ element(U_16,powerset(U_15)) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_20,U_18] :
( element(U_20,powerset(U_18))
| ~ subset(U_20,U_18) )
& ! [U_19,U_17] :
( subset(U_19,U_17)
| ~ element(U_19,powerset(U_17)) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( subset(U_19,U_17)
| ~ element(U_19,powerset(U_17)) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( element(U_20,powerset(U_18))
| ~ subset(U_20,U_18) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_1_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_2]) ).
cnf(f_4_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_2]) ).
cnf(f_5_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_2]) ).
cnf(f_6_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_2]) ).
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,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,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_6,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,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_9,axiom,
( top_str(Eq_y_0)
| ~ top_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_10,axiom,
( one_sorted_str(Eq_y_0)
| ~ one_sorted_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( closed_subset(Eq_y_0,Eq_y_1)
| ~ closed_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU320+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:52:19 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.22/0.49 % SZS status Theorem for theBenchmark
% 0.22/0.49 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------