%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 03:53:24 PM UTC 2026
% Result : Theorem 0.16s 5.42s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 37 ( 17 ~; 12 |; 5 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 46 ( 40 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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') ).
fof(f2,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') ).
fof(f3,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') ).
fof(f4,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') ).
fof(f5,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)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2] : 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(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1,X2,X3] : 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(thm)],[f2]) ).
fof(f8,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(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [B] :
( a_locally_compact_top_space(B)
| ! [A] :
( ~ a_locally_compact_top_space(A)
| ! [F] :
( ~ a_continuous_function_from_onto(F,A,B)
| ~ an_open_function_from_onto(F,A,B) ) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2] :
( 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(thm)],[f9]) ).
fof(f11,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(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
? [X1] :
( ? [A] : ~ a_locally_compact_top_space(apply(X1,A))
& ? [A1] : a_locally_compact_top_space(the_product_top_space_over(X1,A1)) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f13,plain,
( ~ a_locally_compact_top_space(apply(sK0_skl,sK2_skl))
& a_locally_compact_top_space(the_product_top_space_over(sK0_skl,sK1_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X1,sK0_skl),skolemize(A1,sK1_skl),skolemize(A,sK2_skl)],[f12]) ).
fof(f14,plain,
a_locally_compact_top_space(the_product_top_space_over(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
~ a_locally_compact_top_space(apply(sK0_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( a_locally_compact_top_space(apply(X3,X0))
| ~ a_locally_compact_top_space(the_product_top_space_over(X3,X2))
| ~ a_continuous_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X3,X2),apply(X3,X0)) ),
inference(resolution,[status(thm)],[f10,f7]) ).
fof(f17,plain,
! [X0,X1,X2] :
( a_locally_compact_top_space(apply(X0,X2))
| ~ a_locally_compact_top_space(the_product_top_space_over(X0,X1)) ),
inference(resolution,[status(thm)],[f16,f6]) ).
fof(f18,plain,
! [X0] : a_locally_compact_top_space(apply(sK0_skl,X0)),
inference(resolution,[status(thm)],[f17,f14]) ).
fof(f20,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f15,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n004.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Mon Sep 21 12:38:40 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 0.16/5.42 % Refutation found
% 0.16/5.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/5.45 % Elapsed time: 0.053443 seconds
% 0.16/5.45 % CPU time: 0.157960 seconds
% 0.16/5.45 % Total memory used: 55.357 MB
% 0.16/5.45 % Net memory used: 54.781 MB
%------------------------------------------------------------------------------