%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 : Fri Sep 25 03:55:00 PM UTC 2026
% Result : Theorem 1.53s 1.28s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 17 unt; 2 def)
% Number of atoms : 58 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 45 ( 22 ~; 16 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 53 ( 0 sgn 50 !; 3 ?; 18 :)
% 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] :
( ( a_locally_compact_top_space(X1)
& a_continuous_function_from_onto(X0,X1,X2)
& an_open_function_from_onto(X0,X1,X2) )
=> 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(X1)
| ~ a_continuous_function_from_onto(X0,X1,X2)
| ~ an_open_function_from_onto(X0,X1,X2)
| a_locally_compact_top_space(X2) ),
inference(ennf_transformation,[],[f3]) ).
fof(f7,plain,
! [X0,X1,X2] :
( ~ a_locally_compact_top_space(X1)
| ~ a_continuous_function_from_onto(X0,X1,X2)
| ~ an_open_function_from_onto(X0,X1,X2)
| a_locally_compact_top_space(X2) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
? [X0,X1] :
( a_locally_compact_top_space(the_product_top_space_over(X0,X1))
& ? [X2] : ~ a_locally_compact_top_space(apply(X0,X2)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f9,plain,
( a_locally_compact_top_space(the_product_top_space_over(sK0,sK1))
& ~ a_locally_compact_top_space(apply(sK0,sK2)) ),
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] :
( ~ a_locally_compact_top_space(X1)
| ~ a_continuous_function_from_onto(X0,X1,X2)
| ~ an_open_function_from_onto(X0,X1,X2)
| a_locally_compact_top_space(X2) ),
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]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] : a_continuous_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X1,X2),apply(X1,X0)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : an_open_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X3,X2),apply(X3,X0)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( a_locally_compact_top_space(X2)
| ~ a_locally_compact_top_space(X1)
| ~ an_open_function_from_onto(X0,X1,X2)
| ~ a_continuous_function_from_onto(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_52,negated_conjecture,
~ a_locally_compact_top_space(apply(sK0,sK2)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_53,negated_conjecture,
a_locally_compact_top_space(the_product_top_space_over(sK0,sK1)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( a_locally_compact_top_space(apply(X1,X0))
| ~ a_locally_compact_top_space(the_product_top_space_over(X1,X2))
| ~ an_open_function_from_onto(the_projection_function(X0,X1,X2),the_product_top_space_over(X1,X2),apply(X1,X0)) ),
inference(resolution,[status(thm)],[c_49,c_51]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( a_locally_compact_top_space(apply(X0,X2))
| ~ a_locally_compact_top_space(the_product_top_space_over(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_72,c_50]) ).
tcf(c_94,definition,
iPr_def_10 = the_product_top_space_over(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_95,definition,
iPr_def_11 = apply(sK0,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_96,negated_conjecture,
a_locally_compact_top_space(iPr_def_10),
inference(demodulation,[status(thm)],[c_53,c_94]) ).
tcf(c_97,negated_conjecture,
~ a_locally_compact_top_space(iPr_def_11),
inference(demodulation,[status(thm)],[c_52,c_95]) ).
tcf(c_188,plain,
! [X0: $i] :
( a_locally_compact_top_space(apply(sK0,X0))
| ~ a_locally_compact_top_space(iPr_def_10) ),
inference(superposition,[status(thm)],[c_94,c_80]) ).
tcf(c_189,plain,
! [X0: $i] : a_locally_compact_top_space(apply(sK0,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_188,c_96]) ).
tcf(c_191,plain,
a_locally_compact_top_space(iPr_def_11),
inference(superposition,[status(thm)],[c_95,c_189]) ).
tcf(c_192,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_191,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 04:10:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.53/1.28 % SZS status Started for theBenchmark.p
% 1.53/1.28 % SZS status Theorem for theBenchmark.p
% 1.53/1.28
% 1.53/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.53/1.28
% 1.53/1.28 % ------ iProver source info
% 1.53/1.28
% 1.53/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.53/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.53/1.28 % git: non_committed_changes: false
% 1.53/1.28
% 1.53/1.28 % ------ Parsing...
% 1.53/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.53/1.28
% 1.53/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.53/1.28
% 1.53/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.53/1.28
% 1.53/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.53/1.28 % ------ Proving...
% 1.53/1.28 % ------ Problem Properties
% 1.53/1.28
% 1.53/1.28 %
% 1.53/1.28 % clauses 5
% 1.53/1.28 % conjectures 2
% 1.53/1.28 % EPR 2
% 1.53/1.28 % Horn 5
% 1.53/1.28 % unary 4
% 1.53/1.28 % binary 1
% 1.53/1.28 % lits 6
% 1.53/1.28 % lits eq 2
% 1.53/1.28 % fd_pure 0
% 1.53/1.28 % fd_pseudo 0
% 1.53/1.28 % fd_cond 0
% 1.53/1.28 % fd_pseudo_cond 0
% 1.53/1.28 % AC symbols 0
% 1.53/1.28
% 1.53/1.28 % ------ Schedule dynamic 5 is on
% 1.53/1.28
% 1.53/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.53/1.28
% 1.53/1.28
% 1.53/1.28 % ------
% 1.53/1.28 % Current options:
% 1.53/1.28 % ------
% 1.53/1.28
% 1.53/1.28
% 1.53/1.28 %
% 1.53/1.28
% 1.53/1.28 % ------ Proving...
% 1.53/1.28 %
% 1.53/1.28
% 1.53/1.28 % SZS status Theorem for theBenchmark.p
% 1.53/1.28
% 1.53/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.53/1.28
% 1.53/1.28
%------------------------------------------------------------------------------