%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET096^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n001.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 10:39:33 AM UTC 2026
% Result : Theorem 0.09s 0.20s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 65 ( 54 unt; 0 typ; 14 def)
% Number of atoms : 318 ( 148 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 176 ( 55 ~; 39 |; 8 &; 64 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 79 ( 58 ^; 19 !; 2 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_complement,type,
complement: ( $i > $o ) > $i > $o ).
thf(tp_disjoint,type,
disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_emptyset,type,
emptyset: $i > $o ).
thf(tp_excl_union,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_in,type,
in: $i > ( $i > $o ) > $o ).
thf(tp_intersection,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_is_a,type,
is_a: $i > ( $i > $o ) > $o ).
thf(tp_meets,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_misses,type,
misses: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $o ).
thf(tp_sK2_SY12,type,
sK2_SY12: $i ).
thf(tp_sK3_SV2,type,
sK3_SV2: $i ).
thf(tp_sK4_SV3,type,
sK4_SV3: $i ).
thf(tp_setminus,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_singleton,type,
singleton: $i > $i > $o ).
thf(tp_subset,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_union,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_unord_pair,type,
unord_pair: $i > $i > $i > $o ).
thf(complement,definition,
( complement
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
thf(disjoint,definition,
( disjoint
= ( ^ [X: $i > $o,Y: $i > $o] :
( ( intersection @ X @ Y )
= emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint) ).
thf(emptyset,definition,
( emptyset
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset) ).
thf(excl_union,definition,
( excl_union
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( ( X @ U )
& ~ ( Y @ U ) )
| ( ~ ( X @ U )
& ( Y @ U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',excl_union) ).
thf(in,definition,
( in
= ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in) ).
thf(intersection,definition,
( intersection
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(is_a,definition,
( is_a
= ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',is_a) ).
thf(meets,definition,
( meets
= ( ^ [X: $i > $o,Y: $i > $o] :
? [U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meets) ).
thf(misses,definition,
( misses
= ( ^ [X: $i > $o,Y: $i > $o] :
~ ? [U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',misses) ).
thf(setminus,definition,
( setminus
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ~ ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminus) ).
thf(singleton,definition,
( singleton
= ( ^ [X: $i,U: $i] : ( U = X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(subset,definition,
( subset
= ( ^ [X: $i > $o,Y: $i > $o] :
! [U: $i] :
( ( X @ U )
=> ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(union,definition,
( union
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(unord_pair,definition,
( unord_pair
= ( ^ [X: $i,Y: $i,U: $i] :
( ( U = X )
| ( U = Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unord_pair) ).
thf(1,conjecture,
! [X: $i > $o,Y: $i] :
( ( subset @ X @ ( singleton @ Y ) )
=> ( ( X = emptyset )
| ( X
= ( singleton @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( ! [X: $i > $o,Y: $i] :
( ( subset @ X @ ( singleton @ Y ) )
=> ( ( X = emptyset )
| ( X
= ( singleton @ Y ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $o,SY1: $i] :
( ! [SY5: $i] :
( ( SY0 @ SY5 )
=> ( SY5 = SY1 ) )
=> ( ( SY0
= ( ^ [X: $i] : $false ) )
| ( SY0
= ( ^ [SY6: $i] : ( SY6 = SY1 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair]) ).
thf(4,plain,
( ( ! [SY12: $i] :
( ! [SY13: $i] :
( ( sK1_SY0 @ SY13 )
=> ( SY13 = SY12 ) )
=> ( ( sK1_SY0
= ( ^ [X: $i] : $false ) )
| ( sK1_SY0
= ( ^ [SY6: $i] : ( SY6 = SY12 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY16: $i] :
( ( sK1_SY0 @ SY16 )
=> ( SY16 = sK2_SY12 ) )
=> ( ( sK1_SY0
= ( ^ [X: $i] : $false ) )
| ( sK1_SY0
= ( ^ [SY18: $i] : ( SY18 = sK2_SY12 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY16: $i] :
( ( sK1_SY0 @ SY16 )
=> ( SY16 = sK2_SY12 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ( sK1_SY0
= ( ^ [X: $i] : $false ) )
| ( sK1_SY0
= ( ^ [SY18: $i] : ( SY18 = sK2_SY12 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( ( sK1_SY0
= ( ^ [X: $i] : $false ) )
| ( sK1_SY0
= ( ^ [SY18: $i] : ( SY18 = sK2_SY12 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( sK1_SY0
!= ( ^ [X: $i] : $false ) )
& ( sK1_SY0
!= ( ^ [SY18: $i] : ( SY18 = sK2_SY12 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [SY16: $i] :
( ~ ( sK1_SY0 @ SY16 )
| ( SY16 = sK2_SY12 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(11,plain,
( ( ! [SY16: $i] :
( ~ ( sK1_SY0 @ SY16 )
| ( SY16 = sK2_SY12 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ( sK1_SY0
!= ( ^ [X: $i] : $false ) )
& ( sK1_SY0
!= ( ^ [SY18: $i] : ( SY18 = sK2_SY12 ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ( ~ ( ( sK1_SY0
!= ( ^ [SX0: $i] : $false ) ) )
| ~ ( ( sK1_SY0
!= ( ^ [SX0: $i] : ( SX0 = sK2_SY12 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair]) ).
thf(14,plain,
! [SV1: $i] :
( ( ~ ( sK1_SY0 @ SV1 )
| ( SV1 = sK2_SY12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
( ( ~ ( ( sK1_SY0
!= ( ^ [SX0: $i] : $false ) ) )
| ~ ( ( sK1_SY0
!= ( ^ [SX0: $i] : ( SX0 = sK2_SY12 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: $i] :
( ( ( ~ ( sK1_SY0 @ SV1 ) )
= $true )
| ( ( SV1 = sK2_SY12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( ( sK1_SY0
!= ( ^ [SX0: $i] : $false ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( ( sK1_SY0
!= ( ^ [SX0: $i] : ( SX0 = sK2_SY12 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: $i] :
( ( ( sK1_SY0 @ SV1 )
= $false )
| ( ( SV1 = sK2_SY12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( sK1_SY0
!= ( ^ [SX0: $i] : $false ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( sK1_SY0
!= ( ^ [SX0: $i] : ( SX0 = sK2_SY12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( sK1_SY0
= ( ^ [SX0: $i] : $false ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
( ( sK1_SY0
= ( ^ [SX0: $i] : ( SX0 = sK2_SY12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
( ( ! [SV2: $i] :
( ( sK1_SY0 @ SV2 )
= $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( sK1_SY0
= ( ^ [SX0: $i] : $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( ! [SV3: $i] :
( ( sK1_SY0 @ SV3 )
= ( SV3 = sK2_SY12 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[23]) ).
thf(27,plain,
( ( sK1_SY0
= ( ^ [SX0: $i] : ( SX0 = sK2_SY12 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( ( sK1_SY0 @ sK3_SV2 )
= $false )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(29,plain,
( ( ( sK1_SY0 @ sK4_SV3 )
= ( sK4_SV3 = sK2_SY12 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(30,plain,
( ( ~ ( ( sK1_SY0 @ sK3_SV2 )
| $false )
| ~ ( ~ ( sK1_SY0 @ sK3_SV2 )
| ~ $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[28]) ).
thf(31,plain,
( ( ( sK1_SY0 @ sK3_SV2 )
= $false )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ( ( sK1_SY0 @ sK4_SV3 )
| ( sK4_SV3 = sK2_SY12 ) )
| ~ ( ~ ( sK1_SY0 @ sK4_SV3 )
| ( sK4_SV3 != sK2_SY12 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[29]) ).
thf(33,plain,
( ( ( sK1_SY0 @ sK4_SV3 )
= ( sK4_SV3 = sK2_SY12 ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ( ( sK1_SY0 @ sK3_SV2 )
| $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(35,plain,
( ( ~ ( ~ ( sK1_SY0 @ sK3_SV2 )
| ~ $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(36,plain,
( ( ~ ( ( sK1_SY0 @ sK4_SV3 )
| ( sK4_SV3 = sK2_SY12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(37,plain,
( ( ~ ( ~ ( sK1_SY0 @ sK4_SV3 )
| ( sK4_SV3 != sK2_SY12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(38,plain,
( ( ( sK1_SY0 @ sK3_SV2 )
| $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
( ( ~ ( sK1_SY0 @ sK3_SV2 )
| ~ $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ( sK1_SY0 @ sK4_SV3 )
| ( sK4_SV3 = sK2_SY12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(41,plain,
( ( ~ ( sK1_SY0 @ sK4_SV3 )
| ( sK4_SV3 != sK2_SY12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(42,plain,
( ( ( sK1_SY0 @ sK3_SV2 )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(43,plain,
( ( ( ~ ( sK1_SY0 @ sK3_SV2 ) )
= $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(44,plain,
( ( ( sK1_SY0 @ sK4_SV3 )
= $true )
| ( ( sK4_SV3 = sK2_SY12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(45,plain,
( ( ( ~ ( sK1_SY0 @ sK4_SV3 ) )
= $true )
| ( ( sK4_SV3 != sK2_SY12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(46,plain,
( ( ( sK1_SY0 @ sK3_SV2 )
= $false )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
( ( ( sK1_SY0 @ sK4_SV3 )
= $false )
| ( ( sK4_SV3 != sK2_SY12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(48,plain,
( ( $false = $false )
| ( ( sK1_SY0 @ sK3_SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(49,plain,
( ( ( sK4_SV3 = sK2_SY12 )
= $false )
| ( ( sK1_SY0 @ sK4_SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(50,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,49,48,44,42,33,31,27,25]) ).
thf(51,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET096^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n001.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 14:36:39 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.20
% 0.09/0.20 No.of.Axioms: 0
% 0.09/0.20
% 0.09/0.20 Length.of.Defs: 2097
% 0.09/0.20
% 0.09/0.20 Contains.Choice.Funs: false
% 0.09/0.20
% 0.09/0.20 ********************************
% 0.09/0.20 * All subproblems solved! *
% 0.09/0.20 ********************************
% 0.09/0.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:50,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.20
% 0.09/0.20 %**** Beginning of derivation protocol ****
% 0.09/0.20 % SZS output start CNFRefutation
% See solution above
% 0.09/0.20
% 0.09/0.20 %**** End of derivation protocol ****
% 0.09/0.20 %**** no. of clauses in derivation: 51 ****
% 0.09/0.20 %**** clause counter: 50 ****
% 0.09/0.20
% 0.09/0.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:50,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------