%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : TOP021+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 21:32:22 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 18 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 24 ~; 18 |; 4 &)
% ( 0 <=>; 4 =>; 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 : 75 ( 6 sgn 39 !; 7 ?)
% 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)) ).
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)) ).
fof(kelley_p_147e,axiom,
! [F,A,B] :
( ( an_open_function_from_onto(F,A,B)
& a_continuous_function_from_onto(F,A,B)
& a_locally_compact_top_space(A) )
=> a_locally_compact_top_space(B) ) ).
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)) ) ).
fof(subgoal_0,plain,
! [X1,A1] :
( a_locally_compact_top_space(the_product_top_space_over(X1,A1))
=> ! [A] : a_locally_compact_top_space(apply(X1,A)) ),
inference(strip,[],[kelley_5_19a]) ).
fof(negate_0_0,plain,
~ ! [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,[],[subgoal_0]) ).
fof(normalize_0_0,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(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ? [A] : ~ a_locally_compact_top_space(apply(skolemFOFtoCNF_X1,A))
& ? [A1] : a_locally_compact_top_space(the_product_top_space_over(skolemFOFtoCNF_X1,A1)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [A] : ~ a_locally_compact_top_space(apply(skolemFOFtoCNF_X1,A)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ a_locally_compact_top_space(apply(skolemFOFtoCNF_X1,skolemFOFtoCNF_A)),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A1] : a_locally_compact_top_space(the_product_top_space_over(skolemFOFtoCNF_X1,A1)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_5,plain,
a_locally_compact_top_space(the_product_top_space_over(skolemFOFtoCNF_X1,skolemFOFtoCNF_A1)),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,A1,X] : a_continuous_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X,A1),apply(X,A)),
inference(canonicalize,[],[kelley_p90a]) ).
fof(normalize_0_7,plain,
! [A,A1,X] : a_continuous_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X,A1),apply(X,A)),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,A1,X,X1] : an_open_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A)),
inference(canonicalize,[],[kelley_3_2]) ).
fof(normalize_0_9,plain,
! [A,A1,X,X1] : an_open_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A)),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,F] :
( ~ a_continuous_function_from_onto(F,A,B)
| ~ a_locally_compact_top_space(A)
| ~ an_open_function_from_onto(F,A,B)
| a_locally_compact_top_space(B) ),
inference(canonicalize,[],[kelley_p_147e]) ).
fof(normalize_0_11,plain,
! [A,B,F] :
( ~ a_continuous_function_from_onto(F,A,B)
| ~ a_locally_compact_top_space(A)
| ~ an_open_function_from_onto(F,A,B)
| a_locally_compact_top_space(B) ),
inference(specialize,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
~ a_locally_compact_top_space(apply(skolemFOFtoCNF_X1,skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
a_locally_compact_top_space(the_product_top_space_over(skolemFOFtoCNF_X1,skolemFOFtoCNF_A1)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
a_continuous_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X,A1),apply(X,A)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
a_continuous_function_from_onto(the_projection_function(X_10,X_13,X_11),the_product_top_space_over(X_13,X_11),apply(X_13,X_10)),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_10)),bind(A1,$fot(X_11)),bind(X,$fot(X_13))]]) ).
cnf(refute_0_4,plain,
an_open_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ a_continuous_function_from_onto(F,A,B)
| ~ a_locally_compact_top_space(A)
| ~ an_open_function_from_onto(F,A,B)
| a_locally_compact_top_space(B) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
( ~ a_continuous_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A))
| ~ a_locally_compact_top_space(the_product_top_space_over(X1,A1))
| ~ an_open_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A))
| a_locally_compact_top_space(apply(X1,A)) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(the_product_top_space_over(X1,A1))),bind(B,$fot(apply(X1,A))),bind(F,$fot(the_projection_function(A,X,A1)))]]) ).
cnf(refute_0_7,plain,
( ~ a_continuous_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A))
| ~ a_locally_compact_top_space(the_product_top_space_over(X1,A1))
| a_locally_compact_top_space(apply(X1,A)) ),
inference(resolve,[$cnf( an_open_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ a_continuous_function_from_onto(the_projection_function(X_10,X_13,X_11),the_product_top_space_over(X_13,X_11),apply(X_13,X_10))
| ~ a_locally_compact_top_space(the_product_top_space_over(X_13,X_11))
| a_locally_compact_top_space(apply(X_13,X_10)) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_10)),bind(A1,$fot(X_11)),bind(X,$fot(X_13)),bind(X1,$fot(X_13))]]) ).
cnf(refute_0_9,plain,
( ~ a_locally_compact_top_space(the_product_top_space_over(X_13,X_11))
| a_locally_compact_top_space(apply(X_13,X_10)) ),
inference(resolve,[$cnf( a_continuous_function_from_onto(the_projection_function(X_10,X_13,X_11),the_product_top_space_over(X_13,X_11),apply(X_13,X_10)) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ a_locally_compact_top_space(the_product_top_space_over(skolemFOFtoCNF_X1,skolemFOFtoCNF_A1))
| a_locally_compact_top_space(apply(skolemFOFtoCNF_X1,X_14)) ),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(X_14)),bind(X_11,$fot(skolemFOFtoCNF_A1)),bind(X_13,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_11,plain,
a_locally_compact_top_space(apply(skolemFOFtoCNF_X1,X_14)),
inference(resolve,[$cnf( a_locally_compact_top_space(the_product_top_space_over(skolemFOFtoCNF_X1,skolemFOFtoCNF_A1)) )],[refute_0_1,refute_0_10]) ).
cnf(refute_0_12,plain,
a_locally_compact_top_space(apply(skolemFOFtoCNF_X1,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_11:[bind(X_14,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( a_locally_compact_top_space(apply(skolemFOFtoCNF_X1,skolemFOFtoCNF_A)) )],[refute_0_12,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : TOP021+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun May 29 04:03:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------