%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Wed Oct 7 11:09:37 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 184 ( 50 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 359 ( 30 ~; 33 |; 4 &; 285 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 99 ( 0 ^; 99 !; 0 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_continuous_function_from_onto,type,
a_continuous_function_from_onto: $i > $i > $i > $o ).
thf(tp_a_locally_compact_top_space,type,
a_locally_compact_top_space: $i > $o ).
thf(tp_an_open_function_from_onto,type,
an_open_function_from_onto: $i > $i > $i > $o ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_sK1_X1,type,
sK1_X1: $i ).
thf(tp_sK2_SY13,type,
sK2_SY13: $i ).
thf(tp_sK3_SY14,type,
sK3_SY14: $i ).
thf(tp_the_product_top_space_over,type,
the_product_top_space_over: $i > $i > $i ).
thf(tp_the_projection_function,type,
the_projection_function: $i > $i > $i > $i ).
thf(1,axiom,
! [F: $i,A: $i,B: $i] :
( ( ( 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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_p_147e) ).
thf(2,axiom,
! [A: $i,X: $i,A1: $i,X1: $i] : ( an_open_function_from_onto @ ( the_projection_function @ A @ X @ A1 ) @ ( the_product_top_space_over @ X1 @ A1 ) @ ( apply @ X1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_3_2) ).
thf(3,axiom,
! [A: $i,X: $i,A1: $i] : ( a_continuous_function_from_onto @ ( the_projection_function @ A @ X @ A1 ) @ ( the_product_top_space_over @ X @ A1 ) @ ( apply @ X @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_p90a) ).
thf(4,conjecture,
! [X1: $i,A1: $i] :
( ( a_locally_compact_top_space @ ( the_product_top_space_over @ X1 @ A1 ) )
=> ! [A: $i] : ( a_locally_compact_top_space @ ( apply @ X1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kelley_5_19a) ).
thf(5,negated_conjecture,
( ( ! [X1: $i,A1: $i] :
( ( a_locally_compact_top_space @ ( the_product_top_space_over @ X1 @ A1 ) )
=> ! [A: $i] : ( a_locally_compact_top_space @ ( apply @ X1 @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ! [X1: $i,A1: $i] :
( ( a_locally_compact_top_space @ ( the_product_top_space_over @ X1 @ A1 ) )
=> ! [A: $i] : ( a_locally_compact_top_space @ ( apply @ X1 @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( ( 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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [A: $i,X: $i,A1: $i,X1: $i] : ( an_open_function_from_onto @ ( the_projection_function @ A @ X @ A1 ) @ ( the_product_top_space_over @ X1 @ A1 ) @ ( apply @ X1 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ! [A: $i,X: $i,A1: $i] : ( a_continuous_function_from_onto @ ( the_projection_function @ A @ X @ A1 ) @ ( the_product_top_space_over @ X @ A1 ) @ ( apply @ X @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [SY13: $i] :
( ( a_locally_compact_top_space @ ( the_product_top_space_over @ sK1_X1 @ SY13 ) )
=> ! [SY14: $i] : ( a_locally_compact_top_space @ ( apply @ sK1_X1 @ SY14 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(11,plain,
( ( ( a_locally_compact_top_space @ ( the_product_top_space_over @ sK1_X1 @ sK2_SY13 ) )
=> ! [SY14: $i] : ( a_locally_compact_top_space @ ( apply @ sK1_X1 @ SY14 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
( ( a_locally_compact_top_space @ ( the_product_top_space_over @ sK1_X1 @ sK2_SY13 ) )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SY14: $i] : ( a_locally_compact_top_space @ ( apply @ sK1_X1 @ SY14 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ! [SY14: $i] : ( a_locally_compact_top_space @ ( apply @ sK1_X1 @ SY14 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(15,plain,
( ( ~ ( a_locally_compact_top_space @ ( apply @ sK1_X1 @ sK3_SY14 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(16,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ~ ( a_continuous_function_from_onto @ F @ A @ B )
| ~ ( an_open_function_from_onto @ F @ A @ B )
| ~ ( a_locally_compact_top_space @ A )
| ( a_locally_compact_top_space @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(17,plain,
( ( ! [A: $i,X: $i,A1: $i] : ( a_continuous_function_from_onto @ ( the_projection_function @ A @ X @ A1 ) @ ( the_product_top_space_over @ X @ A1 ) @ ( apply @ X @ A ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(18,plain,
( ( ! [A: $i,X: $i,A1: $i,X1: $i] : ( an_open_function_from_onto @ ( the_projection_function @ A @ X @ A1 ) @ ( the_product_top_space_over @ X1 @ A1 ) @ ( apply @ X1 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(19,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ~ ( a_continuous_function_from_onto @ F @ A @ B )
| ~ ( an_open_function_from_onto @ F @ A @ B )
| ~ ( a_locally_compact_top_space @ A )
| ( a_locally_compact_top_space @ B ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(20,plain,
( ( a_locally_compact_top_space @ ( the_product_top_space_over @ sK1_X1 @ sK2_SY13 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ~ ( a_locally_compact_top_space @ ( apply @ sK1_X1 @ sK3_SY14 ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY16: $i,SY17: $i] : ( a_continuous_function_from_onto @ ( the_projection_function @ SV1 @ SY16 @ SY17 ) @ ( the_product_top_space_over @ SY16 @ SY17 ) @ ( apply @ SY16 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY18: $i,SY19: $i,SY20: $i] : ( an_open_function_from_onto @ ( the_projection_function @ SV2 @ SY18 @ SY19 ) @ ( the_product_top_space_over @ SY20 @ SY19 ) @ ( apply @ SY20 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV3: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ~ ( a_continuous_function_from_onto @ SV3 @ SY21 @ SY22 )
| ~ ( an_open_function_from_onto @ SV3 @ SY21 @ SY22 )
| ~ ( a_locally_compact_top_space @ SY21 )
| ( a_locally_compact_top_space @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
( ( a_locally_compact_top_space @ ( apply @ sK1_X1 @ sK3_SY14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY23: $i] : ( a_continuous_function_from_onto @ ( the_projection_function @ SV1 @ SV4 @ SY23 ) @ ( the_product_top_space_over @ SV4 @ SY23 ) @ ( apply @ SV4 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY24: $i,SY25: $i] : ( an_open_function_from_onto @ ( the_projection_function @ SV2 @ SV5 @ SY24 ) @ ( the_product_top_space_over @ SY25 @ SY24 ) @ ( apply @ SY25 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY26: $i] :
( ~ ( a_continuous_function_from_onto @ SV3 @ SV6 @ SY26 )
| ~ ( an_open_function_from_onto @ SV3 @ SV6 @ SY26 )
| ~ ( a_locally_compact_top_space @ SV6 )
| ( a_locally_compact_top_space @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( a_continuous_function_from_onto @ ( the_projection_function @ SV1 @ SV4 @ SV7 ) @ ( the_product_top_space_over @ SV4 @ SV7 ) @ ( apply @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV8: $i,SV5: $i,SV2: $i] :
( ( ! [SY27: $i] : ( an_open_function_from_onto @ ( the_projection_function @ SV2 @ SV5 @ SV8 ) @ ( the_product_top_space_over @ SY27 @ SV8 ) @ ( apply @ SY27 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ~ ( a_continuous_function_from_onto @ SV3 @ SV6 @ SV9 )
| ~ ( an_open_function_from_onto @ SV3 @ SV6 @ SV9 )
| ~ ( a_locally_compact_top_space @ SV6 )
| ( a_locally_compact_top_space @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV10: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( an_open_function_from_onto @ ( the_projection_function @ SV2 @ SV5 @ SV8 ) @ ( the_product_top_space_over @ SV10 @ SV8 ) @ ( apply @ SV10 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( a_continuous_function_from_onto @ SV3 @ SV6 @ SV9 )
| ~ ( an_open_function_from_onto @ SV3 @ SV6 @ SV9 )
| ~ ( a_locally_compact_top_space @ SV6 ) )
= $true )
| ( ( a_locally_compact_top_space @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( a_continuous_function_from_onto @ SV3 @ SV6 @ SV9 )
| ~ ( an_open_function_from_onto @ SV3 @ SV6 @ SV9 ) )
= $true )
| ( ( ~ ( a_locally_compact_top_space @ SV6 ) )
= $true )
| ( ( a_locally_compact_top_space @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(35,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( a_continuous_function_from_onto @ SV3 @ SV6 @ SV9 ) )
= $true )
| ( ( ~ ( an_open_function_from_onto @ SV3 @ SV6 @ SV9 ) )
= $true )
| ( ( ~ ( a_locally_compact_top_space @ SV6 ) )
= $true )
| ( ( a_locally_compact_top_space @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(36,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ( a_continuous_function_from_onto @ SV3 @ SV6 @ SV9 )
= $false )
| ( ( ~ ( an_open_function_from_onto @ SV3 @ SV6 @ SV9 ) )
= $true )
| ( ( ~ ( a_locally_compact_top_space @ SV6 ) )
= $true )
| ( ( a_locally_compact_top_space @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(37,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ( an_open_function_from_onto @ SV3 @ SV6 @ SV9 )
= $false )
| ( ( a_continuous_function_from_onto @ SV3 @ SV6 @ SV9 )
= $false )
| ( ( ~ ( a_locally_compact_top_space @ SV6 ) )
= $true )
| ( ( a_locally_compact_top_space @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(38,plain,
! [SV9: $i,SV3: $i,SV6: $i] :
( ( ( a_locally_compact_top_space @ SV6 )
= $false )
| ( ( a_continuous_function_from_onto @ SV3 @ SV6 @ SV9 )
= $false )
| ( ( an_open_function_from_onto @ SV3 @ SV6 @ SV9 )
= $false )
| ( ( a_locally_compact_top_space @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(39,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,38,32,29,25]) ).
thf(40,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.22 % Computer : n003.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Oct 6 17:57:25 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.26
% 0.10/0.26 No.of.Axioms: 3
% 0.10/0.26
% 0.10/0.26 Length.of.Defs: 0
% 0.10/0.26
% 0.10/0.26 Contains.Choice.Funs: false
% 0.10/0.26 .
% 0.10/0.26
% 0.10/0.26 ********************************
% 0.10/0.26 * All subproblems solved! *
% 0.10/0.26 ********************************
% 0.10/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:39,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.26
% 0.10/0.26 %**** Beginning of derivation protocol ****
% 0.10/0.26 % SZS output start CNFRefutation
% See solution above
% 0.10/0.26
% 0.10/0.26 %**** End of derivation protocol ****
% 0.10/0.26 %**** no. of clauses in derivation: 40 ****
% 0.10/0.26 %**** clause counter: 39 ****
% 0.10/0.26
% 0.10/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:39,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------