%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 02:33:52 PM UTC 2026
% Result : Theorem 2.61s 1.05s
% Output : Refutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 36 ( 17 ~; 12 |; 4 &)
% ( 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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,
( ~ a_locally_compact_top_space(apply(sK0,sK2))
& a_locally_compact_top_space(the_product_top_space_over(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
fof(f10,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(f11,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(f12,plain,
! [X2,X0,X1] :
( ~ an_open_function_from_onto(X0,X1,X2)
| a_locally_compact_top_space(X2)
| ~ a_continuous_function_from_onto(X0,X1,X2)
| ~ a_locally_compact_top_space(X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
a_locally_compact_top_space(the_product_top_space_over(sK0,sK1)),
inference(cnf_transformation,[],[f9]) ).
fof(f14,plain,
~ a_locally_compact_top_space(apply(sK0,sK2)),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
! [X2,X3,X0,X1] :
( ~ a_continuous_function_from_onto(the_projection_function(X1,X2,X3),the_product_top_space_over(X0,X3),apply(X0,X1))
| a_locally_compact_top_space(apply(X0,X1))
| ~ a_locally_compact_top_space(the_product_top_space_over(X0,X3)) ),
inference(resolution,[],[f12,f11]) ).
fof(f16,plain,
! [X2,X0,X1] :
( a_locally_compact_top_space(apply(X0,X1))
| ~ a_locally_compact_top_space(the_product_top_space_over(X0,X2)) ),
inference(resolution,[],[f15,f10]) ).
fof(f17,plain,
! [X0] : ~ a_locally_compact_top_space(the_product_top_space_over(sK0,X0)),
inference(resolution,[],[f16,f14]) ).
fof(f18,plain,
$false,
inference(resolution,[],[f17,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n010.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 18:49:03 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.61/1.05 % (2189143)Detected formulas, will run a generic FOF schedule.
% 2.61/1.05 % (2189154)dis-21_1_sil=8000:lcm=predicate:random_seed=3966567884:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.61/1.05 % (2189154)First to succeed.
% 2.61/1.05 % (2189154)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2189143"
% 2.61/1.05 % (2189149)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=4267196112:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.61/1.05 % (2189148)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1941749144:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.61/1.05 % (2189150)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2316499863:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.61/1.05 % (2189153)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4199665919:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.61/1.05 % (2189152)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4276396984:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.61/1.05 % (2189151)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=830315477:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.61/1.05 % (2189151)Refutation not found, incomplete strategy
% 2.61/1.05 % (2189151)------------------------------
% 2.61/1.05 % (2189151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.05 % (2189151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.05 % (2189151)CaDiCaL version: 2.1.3
% 2.61/1.05 % (2189151)Termination reason: Refutation not found, incomplete strategy
% 2.61/1.05 % (2189151)Time elapsed: 0.001 s
% 2.61/1.05 % (2189151)Peak memory usage: 87 MB
% 2.61/1.05 % (2189152)Also succeeded, but the first one will report.
% 2.61/1.05 % (2189153)Also succeeded, but the first one will report.
% 2.61/1.05 % (2189154)Refutation found. Thanks to Tanya!
% 2.61/1.05 % SZS status Theorem for theBenchmark
% 2.61/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 2.61/1.05 % (2189154)------------------------------
% 2.61/1.05 % (2189154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.05 % (2189154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.05 % (2189154)CaDiCaL version: 2.1.3
% 2.61/1.05 % (2189154)Termination reason: Refutation
% 2.61/1.05 % (2189154)Time elapsed: 0.001 s
% 2.61/1.05 % (2189154)Peak memory usage: 88 MB
% 2.61/1.05 % (2189154)------------------------------
% 2.61/1.05 % (2189154)------------------------------
% 2.61/1.05 % (2189143)Success in time 0.287 s
% 2.61/1.05 % Vampire exiting
%------------------------------------------------------------------------------