%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 09:12:54 AM UTC 2026
% Result : Theorem 0.10s 5.39s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 18 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 22 ~; 12 |; 9 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 58 ( 1 sgn 36 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(kelley_p90a,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('theBenchmark.p',kelley_p90a) ).
fof(kelley_3_2,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('theBenchmark.p',kelley_3_2) ).
fof(kelley_p_147e,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('theBenchmark.p',kelley_p_147e) ).
fof(kelley_5_19a,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('theBenchmark.p',kelley_5_19a) ).
fof(f_1_1,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(fof_nnf,[status(thm)],[kelley_p90a]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] : a_continuous_function_from_onto(the_projection_function(U_2,U_1,U_0),the_product_top_space_over(U_1,U_0),apply(U_1,U_2)),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
a_continuous_function_from_onto(the_projection_function(U_2,U_1,U_0),the_product_top_space_over(U_1,U_0),apply(U_1,U_2)),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,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(fof_nnf,[status(thm)],[kelley_3_2]) ).
fof(f_2_2,plain,
! [U_6,U_5,U_4,U_3] : an_open_function_from_onto(the_projection_function(U_6,U_5,U_4),the_product_top_space_over(U_3,U_4),apply(U_3,U_6)),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
an_open_function_from_onto(the_projection_function(U_6,U_5,U_4),the_product_top_space_over(U_3,U_4),apply(U_3,U_6)),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,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(fof_nnf,[status(thm)],[kelley_p_147e]) ).
fof(f_3_2,plain,
! [U_9,U_8,U_7] :
( a_locally_compact_top_space(U_7)
| ~ a_locally_compact_top_space(U_8)
| ~ a_continuous_function_from_onto(U_9,U_8,U_7)
| ~ an_open_function_from_onto(U_9,U_8,U_7) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( a_locally_compact_top_space(U_7)
| ~ a_locally_compact_top_space(U_8)
| ~ a_continuous_function_from_onto(U_9,U_8,U_7)
| ~ an_open_function_from_onto(U_9,U_8,U_7) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,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(negate,[status(cth)],[kelley_5_19a]) ).
fof(f_4_2,negated_conjecture,
? [X1,A1] :
( ? [A] : ~ a_locally_compact_top_space(apply(X1,A))
& a_locally_compact_top_space(the_product_top_space_over(X1,A1)) ),
inference(fof_nnf,[status(thm)],[f_4_1]) ).
fof(f_4_3,negated_conjecture,
? [U_12,U_11] :
( ? [U_10] : ~ a_locally_compact_top_space(apply(U_12,U_10))
& a_locally_compact_top_space(the_product_top_space_over(U_12,U_11)) ),
inference(variable_rename,[status(thm)],[f_4_2]) ).
fof(f_4_4,negated_conjecture,
? [U_12] :
( ? [U_11] : a_locally_compact_top_space(the_product_top_space_over(U_12,U_11))
& ? [U_10] : ~ a_locally_compact_top_space(apply(U_12,U_10)) ),
inference(miniscope,[status(thm)],[f_4_3]) ).
fof(f_4_5,negated_conjecture,
( ? [U_11] : a_locally_compact_top_space(the_product_top_space_over(sK1,U_11))
& ? [U_10] : ~ a_locally_compact_top_space(apply(sK1,U_10)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_12,sK1)],[f_4_4]) ).
fof(f_4_6,negated_conjecture,
( ? [U_11] : a_locally_compact_top_space(the_product_top_space_over(sK1,U_11))
& ~ a_locally_compact_top_space(apply(sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_10,sK2)],[f_4_5]) ).
fof(f_4_7,negated_conjecture,
( a_locally_compact_top_space(the_product_top_space_over(sK1,sK3))
& ~ a_locally_compact_top_space(apply(sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_11,sK3)],[f_4_6]) ).
fof(f_4_8,negated_conjecture,
( a_locally_compact_top_space(the_product_top_space_over(sK1,sK3))
& ~ a_locally_compact_top_space(apply(sK1,sK2)) ),
inference(definitional_conversion,[status(esa)],[f_4_7]) ).
cnf(f_4_9,negated_conjecture,
~ a_locally_compact_top_space(apply(sK1,sK2)),
inference(clausify,[status(thm)],[f_4_8]) ).
cnf(f_4_10,negated_conjecture,
a_locally_compact_top_space(the_product_top_space_over(sK1,sK3)),
inference(clausify,[status(thm)],[f_4_8]) ).
cnf(t1,plain,
~ a_locally_compact_top_space(apply(sK1,sK2)),
inference(start,[status(thm),parent(0:0)],[f_4_9]) ).
cnf(t2,plain,
( ~ a_continuous_function_from_onto(the_projection_function(sK2,sK1,sK3),the_product_top_space_over(sK1,sK3),apply(sK1,sK2))
| ~ a_locally_compact_top_space(the_product_top_space_over(sK1,sK3))
| ~ an_open_function_from_onto(the_projection_function(sK2,sK1,sK3),the_product_top_space_over(sK1,sK3),apply(sK1,sK2))
| a_locally_compact_top_space(apply(sK1,sK2)) ),
inference(extension,[status(thm),parent(t1:1)],[f_3_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
an_open_function_from_onto(the_projection_function(sK2,sK1,sK3),the_product_top_space_over(sK1,sK3),apply(sK1,sK2)),
inference(extension,[status(thm),parent(t2:2)],[f_2_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
a_locally_compact_top_space(the_product_top_space_over(sK1,sK3)),
inference(extension,[status(thm),parent(t2:3)],[f_4_10]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
a_continuous_function_from_onto(the_projection_function(sK2,sK1,sK3),the_product_top_space_over(sK1,sK3),apply(sK1,sK2)),
inference(extension,[status(thm),parent(t2:4)],[f_1_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n017.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sun Sep 20 08:12:46 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.39 % SZS status Theorem for theBenchmark
% 0.10/5.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------