%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : TOP002-2 : TPTP v9.3.1. Released v1.0.0.
% 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 : n026.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 11:09:35 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 19 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 79 ( 9 ~; 6 |; 0 &; 64 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element_of_collection,type,
element_of_collection: $i > $i > $o ).
thf(tp_element_of_set,type,
element_of_set: $i > $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_f,type,
f: $i ).
thf(tp_f11,type,
f11: $i > $i > $i ).
thf(tp_top_of_basis,type,
top_of_basis: $i > $i ).
thf(1,axiom,
! [X: $i] :
~ ( element_of_set @ X @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_6) ).
thf(2,axiom,
! [U: $i,Vf: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ( element_of_set @ ( f11 @ Vf @ U ) @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_40) ).
thf(3,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(4,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,negated_conjecture,
~ ( element_of_collection @ empty_set @ ( top_of_basis @ f ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1b_2) ).
thf(6,plain,
$false = $false,
inference(unfold_def,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [X: $i] :
~ ( element_of_set @ X @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ( element_of_set @ ( f11 @ Vf @ U ) @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ~ ( element_of_collection @ empty_set @ ( top_of_basis @ f ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(10,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( ~ ( element_of_collection @ empty_set @ ( top_of_basis @ f ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ( element_of_set @ ( f11 @ Vf @ U ) @ U ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ! [X: $i] :
~ ( element_of_set @ X @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( element_of_collection @ empty_set @ ( top_of_basis @ f ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(16,plain,
! [SV1: $i] :
( ( ! [SY3: $i] :
( ( element_of_collection @ SV1 @ ( top_of_basis @ SY3 ) )
| ( element_of_set @ ( f11 @ SY3 @ SV1 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
! [SV2: $i] :
( ( ~ ( element_of_set @ SV2 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(18,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV3: $i,SV1: $i] :
( ( ( element_of_collection @ SV1 @ ( top_of_basis @ SV3 ) )
| ( element_of_set @ ( f11 @ SV3 @ SV1 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: $i] :
( ( element_of_set @ SV2 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV3: $i,SV1: $i] :
( ( ( element_of_collection @ SV1 @ ( top_of_basis @ SV3 ) )
= $true )
| ( ( element_of_set @ ( f11 @ SV3 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(22,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,21,20,18]) ).
thf(23,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP002-2 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.07/0.18 % Computer : n026.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 17:57:47 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 3
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 0
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:22,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22
% 0.07/0.22 %**** End of derivation protocol ****
% 0.07/0.22 %**** no. of clauses in derivation: 23 ****
% 0.07/0.22 %**** clause counter: 22 ****
% 0.07/0.22
% 0.07/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:22,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------