%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU828^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 10:49:04 AM UTC 2026
% Result : Theorem 0.06s 0.22s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 66 ( 45 unt; 0 typ; 4 def)
% Number of atoms : 351 ( 109 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 199 ( 61 ~; 51 |; 0 &; 69 @)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 64 ( 26 ^; 38 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i > $o ).
thf(tp_powerset,type,
powerset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_sK1_SY8,type,
sK1_SY8: $i > $o ).
thf(tp_sK2_SV1,type,
sK2_SV1: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_seteq,type,
seteq: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(tp_subseteq,type,
subseteq: ( $i > $o ) > ( $i > $o ) > $o ).
thf(emptyset,definition,
( emptyset
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset) ).
thf(powerset,definition,
( powerset
= ( ^ [X: $i > $o,Y: $i > $o] : ( subseteq @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',poserset) ).
thf(seteq,definition,
( seteq
= ( ^ [X: ( $i > $o ) > $o,Y: ( $i > $o ) > $o] :
! [U: $i > $o] :
( ( X @ U )
<=> ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',seteq) ).
thf(subseteq,definition,
( subseteq
= ( ^ [X: $i > $o,Y: $i > $o] :
! [U: $i] :
( ( X @ U )
=> ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subseteq) ).
thf(1,conjecture,
( seteq @ ( powerset @ emptyset )
@ ^ [X: $i > $o] : ( X = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( seteq @ ( powerset @ emptyset )
@ ^ [X: $i > $o] : ( X = emptyset ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY8: $i > $o] :
( ! [SY6: $i] :
( ( SY8 @ SY6 )
=> $false )
<=> ( SY8
= ( ^ [X: $i] : $false ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,emptyset,powerset,seteq,subseteq]) ).
thf(4,plain,
( ( ! [SY14: $i] :
( ( sK1_SY8 @ SY14 )
=> $false )
<=> ( sK1_SY8
= ( ^ [X: $i] : $false ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY14: $i] :
( ( sK1_SY8 @ SY14 )
=> $false )
=> ( sK1_SY8
= ( ^ [X: $i] : $false ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(6,plain,
( ( ( sK1_SY8
= ( ^ [X: $i] : $false ) )
=> ! [SY14: $i] :
( ( sK1_SY8 @ SY14 )
=> $false ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(7,plain,
( ( ~ ( ! [SY14: $i] :
( ( sK1_SY8 @ SY14 )
=> $false )
=> ( sK1_SY8
= ( ^ [X: $i] : $false ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( ( sK1_SY8
= ( ^ [X: $i] : $false ) )
=> ! [SY14: $i] :
( ( sK1_SY8 @ SY14 )
=> $false ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ! [SY14: $i] :
( ( sK1_SY8 @ SY14 )
=> $false )
=> ( sK1_SY8
= ( ^ [X: $i] : $false ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY8 @ SX0 )
| $false )
| ( sK1_SY8
= ( ^ [SX0: $i] : $false ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,emptyset,powerset,seteq,subseteq]) ).
thf(11,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_SY8 @ SX0 )
| $false )
| ( sK1_SY8
= ( ^ [SX0: $i] : $false ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_SY8 @ SX0 )
| $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(13,plain,
( ( sK1_SY8
= ( ^ [SX0: $i] : $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_SY8 @ SX0 )
| $false ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SV1: $i] :
( ( sK1_SY8 @ SV1 )
= $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( sK1_SY8
= ( ^ [SX0: $i] : $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: $i] :
( ( ~ ( sK1_SY8 @ SV2 )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ( sK1_SY8 @ sK2_SV1 )
= $false )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(19,plain,
! [SV2: $i] :
( ( ( ~ ( sK1_SY8 @ SV2 ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( ( sK1_SY8 @ sK2_SV1 )
| $false )
| ~ ( ~ ( sK1_SY8 @ sK2_SV1 )
| ~ $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ( sK1_SY8 @ sK2_SV1 )
= $false )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: $i] :
( ( ( sK1_SY8 @ SV2 )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( ( sK1_SY8 @ sK2_SV1 )
| $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( ~ ( sK1_SY8 @ sK2_SV1 )
| ~ $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ( sK1_SY8 @ sK2_SV1 )
| $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(26,plain,
( ( ~ ( sK1_SY8 @ sK2_SV1 )
| ~ $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(27,plain,
( ( ( sK1_SY8 @ sK2_SV1 )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(28,plain,
( ( ( ~ ( sK1_SY8 @ sK2_SV1 ) )
= $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(29,plain,
( ( ( sK1_SY8 @ sK2_SV1 )
= $false )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(30,plain,
( ( $false = $false )
| ( ( sK1_SY8 @ sK2_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(31,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,30,27,22,21]) ).
thf(32,plain,
( ( ~ ( ( sK1_SY8
= ( ^ [X: $i] : $false ) )
=> ! [SY14: $i] :
( ( sK1_SY8 @ SY14 )
=> $false ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(33,plain,
( ( ~ ( ( sK1_SY8
!= ( ^ [SX0: $i] : $false ) )
| ! [SX0: $i] :
( ~ ( sK1_SY8 @ SX0 )
| $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32,emptyset,powerset,seteq,subseteq]) ).
thf(34,plain,
( ( ( sK1_SY8
!= ( ^ [SX0: $i] : $false ) )
| ! [SX0: $i] :
( ~ ( sK1_SY8 @ SX0 )
| $false ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(35,plain,
( ( sK1_SY8
!= ( ^ [SX0: $i] : $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(36,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_SY8 @ SX0 )
| $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(37,plain,
( ( sK1_SY8
= ( ^ [SX0: $i] : $false ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(38,plain,
( ( ~ ( sK1_SY8 @ sK3_SX0 )
| $false )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(39,plain,
( ( ! [SV3: $i] :
( ( sK1_SY8 @ SV3 )
= $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[37]) ).
thf(40,plain,
( ( sK1_SY8
= ( ^ [SX0: $i] : $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[37]) ).
thf(41,plain,
( ( ~ ( sK1_SY8 @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
$false = $false,
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV4: $i] :
( ( ( sK1_SY8 @ SV4 )
= $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(44,plain,
( ( sK1_SY8 @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV4: $i] :
( ( ~ ( ( sK1_SY8 @ SV4 )
| $false )
| ~ ( ~ ( sK1_SY8 @ SV4 )
| ~ $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV4: $i] :
( ( ( sK1_SY8 @ SV4 )
= $false )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV4: $i] :
( ( ( ~ ( ( sK1_SY8 @ SV4 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( sK1_SY8 @ SV4 )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV4: $i] :
( ( ( ( sK1_SY8 @ SV4 )
| $false )
= $false )
| ( ( ~ ( ~ ( sK1_SY8 @ SV4 )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV4: $i] :
( ( ( sK1_SY8 @ SV4 )
= $false )
| ( ( ~ ( ~ ( sK1_SY8 @ SV4 )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(50,plain,
! [SV4: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( sK1_SY8 @ SV4 )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(51,plain,
! [SV4: $i] :
( ( ( ~ ( sK1_SY8 @ SV4 )
| ~ $false )
= $false )
| ( ( sK1_SY8 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV4: $i] :
( ( ( ~ ( sK1_SY8 @ SV4 )
| ~ $false )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV4: $i] :
( ( ( ~ ( sK1_SY8 @ SV4 ) )
= $false )
| ( ( sK1_SY8 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(54,plain,
! [SV4: $i] :
( ( ( ~ $false ) = $false )
| ( ( sK1_SY8 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV4: $i] :
( ( ( ~ ( sK1_SY8 @ SV4 ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(56,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(57,plain,
! [SV4: $i] :
( ( ( sK1_SY8 @ SV4 )
= $true )
| ( ( sK1_SY8 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(58,plain,
! [SV4: $i] :
( ( $false = $true )
| ( ( sK1_SY8 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV4: $i] :
( ( ( sK1_SY8 @ SV4 )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(60,plain,
( ( $false = $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(61,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[40,60,59,58,57,46,44,42]) ).
thf(62,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[61,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU828^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n015.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Oct 6 15:40:28 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.22
% 0.06/0.22 No.of.Axioms: 0
% 0.06/0.22
% 0.06/0.22 Length.of.Defs: 604
% 0.06/0.22
% 0.06/0.22 Contains.Choice.Funs: false
% 0.06/0.22
% 0.06/0.22 ********************************
% 0.06/0.22 * All subproblems solved! *
% 0.06/0.22 ********************************
% 0.06/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:61,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.22
% 0.06/0.22 %**** Beginning of derivation protocol ****
% 0.06/0.22 % SZS output start CNFRefutation
% See solution above
% 0.06/0.22
% 0.06/0.22 %**** End of derivation protocol ****
% 0.06/0.22 %**** no. of clauses in derivation: 62 ****
% 0.06/0.22 %**** clause counter: 61 ****
% 0.06/0.22
% 0.06/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:61,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------