%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 03:54:40 PM UTC 2026
% Result : Theorem 3.25s 0.82s
% Output : Proof 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 19 unt; 0 def)
% Number of atoms : 43 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 15 ~; 9 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 61 ( 4 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [F,A,B] :
( ( a_locally_compact_top_space(A)
& a_continuous_function_from_onto(F,A,B)
& an_open_function_from_onto(F,A,B) )
=> a_locally_compact_top_space(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kelley_p_147e) ).
fof(f2_nnf,plain,
! [F,A,B] :
( a_locally_compact_top_space(B)
| ~ a_locally_compact_top_space(A)
| ~ a_continuous_function_from_onto(F,A,B)
| ~ an_open_function_from_onto(F,A,B) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [F,A,B] :
( a_locally_compact_top_space(B)
| ~ a_locally_compact_top_space(A)
| ~ a_continuous_function_from_onto(F,A,B)
| ~ an_open_function_from_onto(F,A,B) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( a_locally_compact_top_space(X2)
| ~ a_locally_compact_top_space(X1)
| ~ a_continuous_function_from_onto(X0,X1,X2)
| ~ an_open_function_from_onto(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(an_open_function_from_onto(X0,X1,X2),true,ifeq(a_continuous_function_from_onto(X0,X1,X2),true,ifeq(a_locally_compact_top_space(X1),true,a_locally_compact_top_space(X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
fof(f1,axiom,
! [A,X,A1,X1] : an_open_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kelley_3_2) ).
fof(f1_nnf,plain,
! [A,X,A1,X1] : an_open_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,X,A1,X1] : an_open_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
an_open_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X3,X2),apply(X3,X0)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
an_open_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X3,X2),apply(X3,X0)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
fof(f0,axiom,
! [A,X,A1] : a_continuous_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X,A1),apply(X,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kelley_p90a) ).
fof(f0_nnf,plain,
! [A,X,A1] : a_continuous_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X,A1),apply(X,A)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,X,A1] : a_continuous_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X,A1),apply(X,A)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
a_continuous_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X1,X2),apply(X1,X0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
a_continuous_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X1,X2),apply(X1,X0)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f3,conjecture,
! [X1,A1] :
( a_locally_compact_top_space(the_product_top_space_over(X1,A1))
=> ! [A] : a_locally_compact_top_space(apply(X1,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kelley_5_19a) ).
fof(f3_neg,negated_conjecture,
~ ! [X1,A1] :
( a_locally_compact_top_space(the_product_top_space_over(X1,A1))
=> ! [A] : a_locally_compact_top_space(apply(X1,A)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f3_nnf,plain,
? [X1,A1] :
( ? [A] : ~ a_locally_compact_top_space(apply(X1,A))
& a_locally_compact_top_space(the_product_top_space_over(X1,A1)) ),
inference(nnf_transformation,[status(thm)],[f3_neg]) ).
fof(f3_sk,plain,
( ~ a_locally_compact_top_space(apply(sk0,sk2))
& a_locally_compact_top_space(the_product_top_space_over(sk0,sk1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f3_nnf]) ).
cnf(c3,plain,
a_locally_compact_top_space(the_product_top_space_over(sk0,sk1)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,negated_conjecture,
a_locally_compact_top_space(the_product_top_space_over(sk0,sk1)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t0,plain,
a_locally_compact_top_space(apply(sk0,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi1,hi0,hi3]) ).
cnf(t8,plain,
a_locally_compact_top_space(apply(sk0,X1)) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(c4,plain,
~ a_locally_compact_top_space(apply(sk0,sk2)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
a_locally_compact_top_space(apply(sk0,sk2)) != true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t8]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 04:07:08 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.25/0.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.25/0.82 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------