%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU341+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 08:45:51 AM UTC 2026
% Result : Theorem 0.15s 5.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 12 unt; 0 def)
% Number of atoms : 114 ( 9 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 136 ( 52 ~; 42 |; 24 &)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 4 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_connsp_2,axiom,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ( point_neighbourhood(C,A,B)
<=> in(B,interior(A,C)) ) ) ) ),
file('theBenchmark.p',d1_connsp_2) ).
fof(t55_tops_1,axiom,
! [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(t5_connsp_2,conjecture,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( in(C,B)
& open_subset(B,A) )
=> point_neighbourhood(B,A,C) ) ) ) ),
file('theBenchmark.p',t5_connsp_2) ).
fof(t5_connsp_2_neg,negated_conjecture,
~ ! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( in(C,B)
& open_subset(B,A) )
=> point_neighbourhood(B,A,C) ) ) ) ),
inference(assume_negation,[status(cth)],[t5_connsp_2]) ).
fof(nnf_45,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ point_neighbourhood(B,A,C)
& in(C,B)
& open_subset(B,A)
& element(C,the_carrier(A)) )
& element(B,powerset(the_carrier(A))) )
& top_str(A)
& topological_space(A)
& ~ empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t5_connsp_2_neg]) ).
fof(sk_t5_connsp_2_neg,plain,
( ~ point_neighbourhood(sK1,sK0,sK2)
& in(sK2,sK1)
& open_subset(sK1,sK0)
& element(sK2,the_carrier(sK0))
& element(sK1,powerset(the_carrier(sK0)))
& top_str(sK0)
& topological_space(sK0)
& ~ empty_carrier(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_45]) ).
cnf(c_47,negated_conjecture,
topological_space(sK0),
inference(split_conjunct,[status(thm)],[sk_t5_connsp_2_neg]) ).
cnf(c_48,plain,
( 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(clausify,[status(thm)],[t55_tops_1]) ).
cnf(c_51,plain,
( ~ in(B,interior(A,C))
| point_neighbourhood(C,A,B)
| ~ element(C,powerset(the_carrier(A)))
| ~ element(B,the_carrier(A))
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[d1_connsp_2]) ).
cnf(c_57,negated_conjecture,
( interior(A,C) = C
| ~ open_subset(C,A)
| ~ element(C,powerset(the_carrier(A)))
| ~ element(B,powerset(the_carrier(sK0)))
| ~ top_str(A)
| ~ top_str(sK0) ),
inference(resolve,[status(thm)],[c_48,c_47]) ).
cnf(c_58,negated_conjecture,
open_subset(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t5_connsp_2_neg]) ).
cnf(c_59,negated_conjecture,
( interior(sK0,sK1) = sK1
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ element(A,powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ top_str(sK0) ),
inference(resolve,[status(thm)],[c_58,c_57]) ).
cnf(c_60,negated_conjecture,
( interior(sK0,sK1) = sK1
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ element(A,powerset(the_carrier(sK0)))
| ~ top_str(sK0) ),
inference(copy,[status(thm)],[c_59]) ).
cnf(c_61,negated_conjecture,
~ point_neighbourhood(sK1,sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_t5_connsp_2_neg]) ).
cnf(c_62,negated_conjecture,
in(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_t5_connsp_2_neg]) ).
cnf(c_63,negated_conjecture,
element(sK2,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t5_connsp_2_neg]) ).
cnf(c_64,negated_conjecture,
element(sK1,powerset(the_carrier(sK0))),
inference(split_conjunct,[status(thm)],[sk_t5_connsp_2_neg]) ).
cnf(c_65,negated_conjecture,
top_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t5_connsp_2_neg]) ).
cnf(c_66,negated_conjecture,
~ empty_carrier(sK0),
inference(split_conjunct,[status(thm)],[sk_t5_connsp_2_neg]) ).
cnf(c_123,negated_conjecture,
( ~ in(A,interior(sK0,B))
| point_neighbourhood(B,sK0,A)
| ~ element(B,powerset(the_carrier(sK0)))
| ~ element(A,the_carrier(sK0))
| ~ top_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_51,c_47]) ).
cnf(c_197,negated_conjecture,
( ~ in(A,interior(sK0,B))
| point_neighbourhood(B,sK0,A)
| ~ element(B,powerset(the_carrier(sK0)))
| ~ element(A,the_carrier(sK0))
| ~ top_str(sK0) ),
inference(resolve,[status(thm)],[c_66,c_123]) ).
cnf(c_124,negated_conjecture,
( ~ in(A,interior(sK0,B))
| point_neighbourhood(B,sK0,A)
| ~ element(B,powerset(the_carrier(sK0)))
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_65,c_197]) ).
cnf(c_198,plain,
( interior(sK0,sK1) = sK1
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ top_str(sK0) ),
inference(factor,[status(thm)],[c_60]) ).
cnf(c_199,negated_conjecture,
( interior(sK0,sK1) = sK1
| ~ element(sK1,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_65,c_198]) ).
cnf(c_128,negated_conjecture,
interior(sK0,sK1) = sK1,
inference(resolve,[status(thm)],[c_64,c_199]) ).
cnf(c_200,negated_conjecture,
( ~ in(sK2,interior(sK0,A))
| point_neighbourhood(A,sK0,sK2)
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_124,c_63]) ).
cnf(c_201,negated_conjecture,
( ~ in(sK2,interior(sK0,sK1))
| point_neighbourhood(sK1,sK0,sK2) ),
inference(resolve,[status(thm)],[c_200,c_64]) ).
cnf(c_202,negated_conjecture,
~ in(sK2,interior(sK0,sK1)),
inference(resolve,[status(thm)],[c_201,c_61]) ).
cnf(c_203,negated_conjecture,
~ in(sK2,sK1),
inference(paramod,[status(thm)],[c_128,c_202]) ).
cnf(c_196,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_62,c_203]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU341+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n001.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 09:21:33 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 1477621 was started by sandbox on n001,
% 0.11/5.38 % Sat Sep 26 09:21:33 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.42
% 0.15/5.42 % SZS status Theorem for theBenchmark
% 0.15/5.42
% 0.15/5.42 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/5.42 % Length of proof is 20.
% 0.15/5.42 % Level of proof is 6.
% 0.15/5.42 % Maximum clause weight is 18.000.
% 0.15/5.42 % Given clauses 60.
% 0.15/5.42
% 0.15/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------