%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU324+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 : Theorem 0.90s 0.58s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 18 unt; 0 def)
% Number of atoms : 152 ( 47 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 143 ( 45 ~; 44 |; 30 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 20 !; 4 ?)
% 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(t55_tops_1_neg,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(assume_negation,[status(cth)],[t55_tops_1]) ).
cnf(c_30,plain,
( subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) = interior(A,B)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(clausify,[status(thm)],[d1_tops_1]) ).
cnf(c_34,plain,
( open_subset(interior(A,B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(clausify,[status(thm)],[fc6_tops_1]) ).
cnf(c_42,plain,
( closed_subset(subset_complement(the_carrier(A),B),A)
| ~ open_subset(B,A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(clausify,[status(thm)],[t30_tops_1]) ).
cnf(c_44,plain,
( topstr_closure(A,B) = B
| ~ closed_subset(B,A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(clausify,[status(thm)],[t52_pre_topc]) ).
fof(nnf_25,plain,
? [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)],[t55_tops_1_neg]) ).
fof(sk_t55_tops_1_neg_sk,plain,
( ( ( ~ open_subset(sK3,sK0)
& interior(sK0,sK3) = sK3 )
| ( interior(sK1,sK2) != sK2
& open_subset(sK2,sK1) ) )
& element(sK2,powerset(the_carrier(sK1)))
& element(sK3,powerset(the_carrier(sK0)))
& top_str(sK1)
& top_str(sK0)
& topological_space(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK3),skolemize(D,sK2)],[nnf_25]) ).
fof(sk_t55_tops_1_neg,plain,
( ( ~ open_subset(sK3,sK0)
| interior(sK1,sK2) != sK2 )
& ( interior(sK0,sK3) = sK3
| interior(sK1,sK2) != sK2 )
& ( ~ open_subset(sK3,sK0)
| open_subset(sK2,sK1) )
& ( interior(sK0,sK3) = sK3
| open_subset(sK2,sK1) )
& element(sK2,powerset(the_carrier(sK1)))
& element(sK3,powerset(the_carrier(sK0)))
& top_str(sK1)
& top_str(sK0)
& topological_space(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_t55_tops_1_neg_sk]) ).
cnf(c_46,negated_conjecture,
top_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t55_tops_1_neg]) ).
cnf(c_47,negated_conjecture,
top_str(sK1),
inference(split_conjunct,[status(thm)],[sk_t55_tops_1_neg]) ).
cnf(c_52,negated_conjecture,
( subset_complement(the_carrier(sK1),topstr_closure(sK1,subset_complement(the_carrier(sK1),A))) = interior(sK1,A)
| ~ element(A,powerset(the_carrier(sK1))) ),
inference(resolve,[status(thm)],[c_47,c_30]) ).
cnf(c_53,negated_conjecture,
( interior(sK1,A) = subset_complement(the_carrier(sK1),topstr_closure(sK1,subset_complement(the_carrier(sK1),A)))
| ~ element(A,powerset(the_carrier(sK1))) ),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_66,negated_conjecture,
( closed_subset(subset_complement(the_carrier(sK1),A),sK1)
| ~ open_subset(A,sK1)
| ~ element(A,powerset(the_carrier(sK1))) ),
inference(resolve,[status(thm)],[c_47,c_42]) ).
cnf(c_68,negated_conjecture,
( topstr_closure(sK1,A) = A
| ~ closed_subset(A,sK1)
| ~ element(A,powerset(the_carrier(sK1))) ),
inference(resolve,[status(thm)],[c_47,c_44]) ).
cnf(c_76,negated_conjecture,
( open_subset(interior(sK0,A),sK0)
| ~ element(A,powerset(the_carrier(sK0)))
| ~ topological_space(sK0) ),
inference(resolve,[status(thm)],[c_46,c_34]) ).
cnf(c_106,negated_conjecture,
( ~ open_subset(sK3,sK0)
| interior(sK1,sK2) != sK2 ),
inference(split_conjunct,[status(thm)],[sk_t55_tops_1_neg]) ).
cnf(c_107,negated_conjecture,
( interior(sK0,sK3) = sK3
| interior(sK1,sK2) != sK2 ),
inference(split_conjunct,[status(thm)],[sk_t55_tops_1_neg]) ).
cnf(c_108,negated_conjecture,
( ~ open_subset(sK3,sK0)
| open_subset(sK2,sK1) ),
inference(split_conjunct,[status(thm)],[sk_t55_tops_1_neg]) ).
cnf(c_109,negated_conjecture,
( interior(sK0,sK3) = sK3
| open_subset(sK2,sK1) ),
inference(split_conjunct,[status(thm)],[sk_t55_tops_1_neg]) ).
cnf(c_110,negated_conjecture,
element(sK2,powerset(the_carrier(sK1))),
inference(split_conjunct,[status(thm)],[sk_t55_tops_1_neg]) ).
cnf(c_111,negated_conjecture,
element(sK3,powerset(the_carrier(sK0))),
inference(split_conjunct,[status(thm)],[sk_t55_tops_1_neg]) ).
cnf(c_112,negated_conjecture,
topological_space(sK0),
inference(split_conjunct,[status(thm)],[sk_t55_tops_1_neg]) ).
cnf(c_113,plain,
( subset_complement(B,subset_complement(B,A)) = A
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[involutiveness_k3_subset_1]) ).
cnf(c_115,plain,
( element(subset_complement(B,A),powerset(B))
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[dt_k3_subset_1]) ).
cnf(c_124,negated_conjecture,
( open_subset(interior(sK0,A),sK0)
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_112,c_76]) ).
cnf(c_1509,negated_conjecture,
( closed_subset(subset_complement(the_carrier(sK1),sK2),sK1)
| ~ element(sK2,powerset(the_carrier(sK1)))
| interior(sK0,sK3) = sK3 ),
inference(resolve,[status(thm)],[c_109,c_66]) ).
cnf(c_142,negated_conjecture,
( closed_subset(subset_complement(the_carrier(sK1),sK2),sK1)
| interior(sK0,sK3) = sK3 ),
inference(resolve,[status(thm)],[c_110,c_1509]) ).
cnf(c_148,plain,
interior(sK1,sK2) = subset_complement(the_carrier(sK1),topstr_closure(sK1,subset_complement(the_carrier(sK1),sK2))),
inference(resolve,[status(thm)],[c_110,c_53]) ).
cnf(c_153,plain,
subset_complement(the_carrier(sK1),subset_complement(the_carrier(sK1),sK2)) = sK2,
inference(resolve,[status(thm)],[c_113,c_110]) ).
cnf(c_173,plain,
element(subset_complement(the_carrier(sK1),sK2),powerset(the_carrier(sK1))),
inference(resolve,[status(thm)],[c_115,c_110]) ).
cnf(c_202,plain,
open_subset(interior(sK0,sK3),sK0),
inference(resolve,[status(thm)],[c_124,c_111]) ).
cnf(c_1510,negated_conjecture,
( topstr_closure(sK1,subset_complement(the_carrier(sK1),sK2)) = subset_complement(the_carrier(sK1),sK2)
| ~ element(subset_complement(the_carrier(sK1),sK2),powerset(the_carrier(sK1)))
| interior(sK0,sK3) = sK3 ),
inference(resolve,[status(thm)],[c_142,c_68]) ).
cnf(c_358,negated_conjecture,
( topstr_closure(sK1,subset_complement(the_carrier(sK1),sK2)) = subset_complement(the_carrier(sK1),sK2)
| interior(sK0,sK3) = sK3 ),
inference(resolve,[status(thm)],[c_173,c_1510]) ).
cnf(c_360,plain,
( interior(sK0,sK3) = sK3
| subset_complement(the_carrier(sK1),topstr_closure(sK1,subset_complement(the_carrier(sK1),sK2))) != sK2 ),
inference(paramod,[status(thm)],[c_148,c_107]) ).
cnf(c_1511,plain,
( interior(sK0,sK3) = sK3
| subset_complement(the_carrier(sK1),subset_complement(the_carrier(sK1),sK2)) != sK2
| interior(sK0,sK3) = sK3 ),
inference(paramod,[status(thm)],[c_358,c_360]) ).
cnf(c_1512,plain,
( subset_complement(the_carrier(sK1),subset_complement(the_carrier(sK1),sK2)) != sK2
| interior(sK0,sK3) = sK3 ),
inference(copy,[status(thm)],[c_1511]) ).
cnf(c_1456,plain,
interior(sK0,sK3) = sK3,
inference(resolve,[status(thm)],[c_153,c_1512]) ).
cnf(c_1462,plain,
open_subset(sK3,sK0),
inference(paramod,[status(thm)],[c_1456,c_202]) ).
cnf(c_1475,negated_conjecture,
open_subset(sK2,sK1),
inference(resolve,[status(thm)],[c_1462,c_108]) ).
cnf(c_1476,negated_conjecture,
interior(sK1,sK2) != sK2,
inference(resolve,[status(thm)],[c_1462,c_106]) ).
cnf(c_1513,negated_conjecture,
( closed_subset(subset_complement(the_carrier(sK1),sK2),sK1)
| ~ element(sK2,powerset(the_carrier(sK1))) ),
inference(resolve,[status(thm)],[c_1475,c_66]) ).
cnf(c_1477,negated_conjecture,
closed_subset(subset_complement(the_carrier(sK1),sK2),sK1),
inference(resolve,[status(thm)],[c_110,c_1513]) ).
cnf(c_1480,plain,
subset_complement(the_carrier(sK1),topstr_closure(sK1,subset_complement(the_carrier(sK1),sK2))) != sK2,
inference(paramod,[status(thm)],[c_148,c_1476]) ).
cnf(c_1514,negated_conjecture,
( topstr_closure(sK1,subset_complement(the_carrier(sK1),sK2)) = subset_complement(the_carrier(sK1),sK2)
| ~ element(subset_complement(the_carrier(sK1),sK2),powerset(the_carrier(sK1))) ),
inference(resolve,[status(thm)],[c_1477,c_68]) ).
cnf(c_1481,negated_conjecture,
topstr_closure(sK1,subset_complement(the_carrier(sK1),sK2)) = subset_complement(the_carrier(sK1),sK2),
inference(resolve,[status(thm)],[c_173,c_1514]) ).
cnf(c_1515,plain,
subset_complement(the_carrier(sK1),subset_complement(the_carrier(sK1),sK2)) != sK2,
inference(paramod,[status(thm)],[c_1481,c_1480]) ).
cnf(c_1508,plain,
$false,
inference(resolve,[status(thm)],[c_153,c_1515]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU324+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n003.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sat Sep 26 09:13:53 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 2530972 was started by sandbox2 on n003,
% 0.12/0.37 % Sat Sep 26 09:13:53 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.90/0.58
% 0.90/0.58 % SZS status Theorem for theBenchmark
% 0.90/0.58
% 0.90/0.58 % Proof 1 at 0.14 (+ 0.04) seconds.
% 0.90/0.58 % Length of proof is 43.
% 0.90/0.58 % Level of proof is 11.
% 0.90/0.58 % Maximum clause weight is 43.000.
% 0.90/0.58 % Given clauses 422.
% 0.90/0.58
% 0.90/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------