%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 : Tue Sep 29 02:34:21 PM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 34 ( 16 ~; 12 |; 3 &)
% ( 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 : 43 ( 40 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : a_continuous_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X1,X2),apply(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_p90a) ).
fof(f2,axiom,
! [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)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_3_2) ).
fof(f3,axiom,
! [X0,X1,X2] :
( ( an_open_function_from_onto(X0,X1,X2)
& a_continuous_function_from_onto(X0,X1,X2)
& a_locally_compact_top_space(X1) )
=> a_locally_compact_top_space(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_p_147e) ).
fof(f4,conjecture,
! [X0,X1] :
( a_locally_compact_top_space(the_product_top_space_over(X0,X1))
=> ! [X2] : a_locally_compact_top_space(apply(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_5_19a) ).
fof(f5,negated_conjecture,
~ ! [X0,X1] :
( a_locally_compact_top_space(the_product_top_space_over(X0,X1))
=> ! [X2] : a_locally_compact_top_space(apply(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2] :
( a_locally_compact_top_space(X2)
| ~ an_open_function_from_onto(X0,X1,X2)
| ~ a_continuous_function_from_onto(X0,X1,X2)
| ~ a_locally_compact_top_space(X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f7,plain,
! [X0,X1,X2] :
( a_locally_compact_top_space(X2)
| ~ an_open_function_from_onto(X0,X1,X2)
| ~ a_continuous_function_from_onto(X0,X1,X2)
| ~ a_locally_compact_top_space(X1) ),
inference(flattening,[],[f6]) ).
fof(f8,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(ennf_transformation,[],[f5]) ).
fof(f9,plain,
! [X2,X0,X1] : a_continuous_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X1,X2),apply(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f10,plain,
! [X2,X3,X0,X1] : an_open_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X3,X2),apply(X3,X0)),
inference(cnf_transformation,[],[f2]) ).
fof(f11,plain,
! [X2,X0,X1] :
( ~ an_open_function_from_onto(X0,X1,X2)
| ~ a_continuous_function_from_onto(X0,X1,X2)
| ~ a_locally_compact_top_space(X1)
| a_locally_compact_top_space(X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
a_locally_compact_top_space(the_product_top_space_over(sK0,sK1)),
inference(cnf_transformation,[],[f8]) ).
fof(f13,plain,
~ a_locally_compact_top_space(apply(sK0,sK2)),
inference(cnf_transformation,[],[f8]) ).
fof(f14,plain,
! [X2,X3,X0,X1] :
( ~ a_continuous_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X3,X2),apply(X3,X0))
| ~ a_locally_compact_top_space(the_product_top_space_over(X3,X2))
| a_locally_compact_top_space(apply(X3,X0)) ),
inference(resolution,[],[f11,f10]) ).
fof(f15,plain,
! [X2,X0,X1] :
( ~ a_locally_compact_top_space(the_product_top_space_over(X0,X1))
| a_locally_compact_top_space(apply(X0,X2)) ),
inference(resolution,[],[f14,f9]) ).
fof(f16,plain,
! [X0] : ~ a_locally_compact_top_space(the_product_top_space_over(sK0,X0)),
inference(resolution,[],[f15,f13]) ).
fof(f17,plain,
$false,
inference(resolution,[],[f16,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n006.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 18:48:25 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.26 % (51087)Will run a generic schedule for satisfiability detection.
% 0.19/0.26 % (51096)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3196248337:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.26 % (51096) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-51087-51096"...
% 0.19/0.26 % (51096)...printing done.
% 0.19/0.26 % (51096)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.26 % (51096)------------------------------
% 0.19/0.26 % (51096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (51096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (51096)CaDiCaL version: 2.1.3
% 0.19/0.26 % (51096)Termination reason: Refutation
% 0.19/0.26 % (51096)Time elapsed: 0.001 s
% 0.19/0.26 % (51096)Peak memory usage: 11 MB
% 0.19/0.26 % (51096)Instructions burned: 1 (million)
% 0.19/0.26 % (51087)Success in time 0.03 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------