%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU341+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 : Fri Sep 25 02:51:46 PM UTC 2026
% Result : Theorem 25.62s 3.87s
% Output : Proof 25.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 108 ( 37 ~; 35 |; 24 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(f16_nnf,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ~ in(B,interior(A,C))
| point_neighbourhood(C,A,B) )
& ( 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(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B,C] :
( ( ( ~ in(B,interior(A,C))
| point_neighbourhood(C,A,B) )
& ( 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(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c41,plain,
( ~ in(X1,interior(X0,X2))
| point_neighbourhood(X2,X0,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f40,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(f40_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(negated_conjecture,[status(cth)],[f40]) ).
fof(f40_nnf,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(nnf_transformation,[status(thm)],[f40_neg]) ).
fof(f40_sk,plain,
( ~ point_neighbourhood(sk8,sk7,sk9)
& in(sk9,sk8)
& open_subset(sk8,sk7)
& element(sk9,the_carrier(sk7))
& element(sk8,powerset(the_carrier(sk7)))
& top_str(sk7)
& topological_space(sk7)
& ~ empty_carrier(sk7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8,sk9])],[f40_nnf]) ).
cnf(c80,plain,
topological_space(sk7),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p202,plain,
( ~ in(X0,interior(sk7,X1))
| point_neighbourhood(X1,sk7,X0)
| ~ element(X1,powerset(the_carrier(sk7)))
| ~ element(X0,the_carrier(sk7))
| ~ top_str(sk7)
| empty_carrier(sk7) ),
inference(resolution,[status(thm)],[c41,c80]) ).
cnf(c81,plain,
top_str(sk7),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p448,plain,
( ~ in(X0,interior(sk7,X1))
| point_neighbourhood(X1,sk7,X0)
| ~ element(X1,powerset(the_carrier(sk7)))
| ~ element(X0,the_carrier(sk7))
| empty_carrier(sk7) ),
inference(resolution,[status(thm)],[p202,c81]) ).
cnf(c83,plain,
element(sk9,the_carrier(sk7)),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p815,plain,
( ~ in(sk9,interior(sk7,X0))
| point_neighbourhood(X0,sk7,sk9)
| ~ element(X0,powerset(the_carrier(sk7)))
| empty_carrier(sk7) ),
inference(resolution,[status(thm)],[p448,c83]) ).
cnf(c82,plain,
element(sk8,powerset(the_carrier(sk7))),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p817,plain,
( ~ in(sk9,sk8)
| point_neighbourhood(sk8,sk7,sk9)
| empty_carrier(sk7) ),
inference(resolution,[status(thm)],[p815,c82]) ).
cnf(c85,plain,
in(sk9,sk8),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p864,plain,
( point_neighbourhood(sk8,sk7,sk9)
| empty_carrier(sk7) ),
inference(resolution,[status(thm)],[p817,c85]) ).
cnf(c86,plain,
~ point_neighbourhood(sk8,sk7,sk9),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p865,plain,
empty_carrier(sk7),
inference(resolution,[status(thm)],[p864,c86]) ).
cnf(c79,plain,
~ empty_carrier(sk7),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p866,plain,
$false,
inference(resolution,[status(thm)],[p865,c79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU341+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:45:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.62/3.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.62/3.87 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------