%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET646^3 : 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 : n012.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 10:40:43 AM UTC 2026
% Result : Theorem 0.08s 0.13s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 36
% Syntax : Number of formulae : 59 ( 56 unt; 0 typ; 35 def)
% Number of atoms : 187 ( 87 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 161 ( 12 ~; 15 |; 24 &; 95 @)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 67 ( 67 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 6 con; 0-4 aty)
% Number of variables : 125 ( 84 ^; 33 !; 8 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product,type,
cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
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_equiv_classes,type,
equiv_classes: ( $i > $i > $o ) > ( $i > $o ) > $o ).
thf(tp_equiv_rel,type,
equiv_rel: ( $i > $i > $o ) > $o ).
thf(tp_excl_union,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_id_rel,type,
id_rel: ( $i > $o ) > $i > $i > $o ).
thf(tp_in,type,
in: $i > ( $i > $o ) > $o ).
thf(tp_intersection,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_irreflexive,type,
irreflexive: ( $i > $i > $o ) > $o ).
thf(tp_is_a,type,
is_a: $i > ( $i > $o ) > $o ).
thf(tp_is_rel_on,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $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_pair_rel,type,
pair_rel: $i > $i > $i > $i > $o ).
thf(tp_reflexive,type,
reflexive: ( $i > $i > $o ) > $o ).
thf(tp_rel_codomain,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(tp_rel_composition,type,
rel_composition: ( $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_rel_diagonal,type,
rel_diagonal: $i > $i > $o ).
thf(tp_rel_domain,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(tp_rel_field,type,
rel_field: ( $i > $i > $o ) > $i > $o ).
thf(tp_rel_inverse,type,
rel_inverse: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_restrict_rel_codomain,type,
restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(tp_restrict_rel_domain,type,
restrict_rel_domain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY25,type,
sK2_SY25: $i ).
thf(tp_sK3_SY28,type,
sK3_SY28: $i ).
thf(tp_sK4_SY30,type,
sK4_SY30: $i ).
thf(tp_setminus,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_singleton,type,
singleton: $i > $i > $o ).
thf(tp_sub_rel,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(tp_subset,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_symmetric,type,
symmetric: ( $i > $i > $o ) > $o ).
thf(tp_transitive,type,
transitive: ( $i > $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(tp_upwards_well_founded,type,
upwards_well_founded: ( $i > $i > $o ) > $o ).
thf(tp_well_founded,type,
well_founded: ( $i > $i > $o ) > $o ).
thf(cartesian_product,definition,
( cartesian_product
= ( ^ [X: $i > $o,Y: $i > $o,U: $i,V: $i] :
( ( X @ U )
& ( Y @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product) ).
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(equiv_classes,definition,
( equiv_classes
= ( ^ [R: $i > $i > $o,S1: $i > $o] :
? [X: $i] :
( ( S1 @ X )
& ! [Y: $i] :
( ( S1 @ Y )
<=> ( R @ X @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equiv_classes) ).
thf(equiv_rel,definition,
( equiv_rel
= ( ^ [R: $i > $i > $o] :
( ( reflexive @ R )
& ( symmetric @ R )
& ( transitive @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equiv_rel) ).
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(id_rel,definition,
( id_rel
= ( ^ [S: $i > $o,X: $i,Y: $i] :
( ( S @ X )
& ( X = Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_rel) ).
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(irreflexive,definition,
( irreflexive
= ( ^ [R: $i > $i > $o] :
! [X: $i] :
~ ( R @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexive) ).
thf(is_a,definition,
( is_a
= ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',is_a) ).
thf(is_rel_on,definition,
( is_rel_on
= ( ^ [R: $i > $i > $o,A: $i > $o,B: $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ( ( A @ X )
& ( B @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',is_rel_on) ).
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(pair_rel,definition,
( pair_rel
= ( ^ [X: $i,Y: $i,U: $i,V: $i] :
( ( U = X )
| ( V = Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pair_rel) ).
thf(reflexive,definition,
( reflexive
= ( ^ [R: $i > $i > $o] :
! [X: $i] : ( R @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexive) ).
thf(rel_codomain,definition,
( rel_codomain
= ( ^ [R: $i > $i > $o,Y: $i] :
? [X: $i] : ( R @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rel_codomain) ).
thf(rel_composition,definition,
( rel_composition
= ( ^ [R1: $i > $i > $o,R2: $i > $i > $o,X: $i,Z: $i] :
? [Y: $i] :
( ( R1 @ X @ Y )
& ( R2 @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rel_composition) ).
thf(rel_diagonal,definition,
( rel_diagonal
= ( ^ [X: $i,Y: $i] : ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rel_diagonal) ).
thf(rel_domain,definition,
( rel_domain
= ( ^ [R: $i > $i > $o,X: $i] :
? [Y: $i] : ( R @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rel_domain) ).
thf(rel_field,definition,
( rel_field
= ( ^ [R: $i > $i > $o,X: $i] :
( ( rel_domain @ R @ X )
| ( rel_codomain @ R @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rel_field) ).
thf(rel_inverse,definition,
( rel_inverse
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rel_inverse) ).
thf(restrict_rel_codomain,definition,
( restrict_rel_codomain
= ( ^ [R: $i > $i > $o,S: $i > $o,X: $i,Y: $i] :
( ( S @ Y )
& ( R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_rel_codomain) ).
thf(restrict_rel_domain,definition,
( restrict_rel_domain
= ( ^ [R: $i > $i > $o,S: $i > $o,X: $i,Y: $i] :
( ( S @ X )
& ( R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_rel_domain) ).
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(sub_rel,definition,
( sub_rel
= ( ^ [R1: $i > $i > $o,R2: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R1 @ X @ Y )
=> ( R2 @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sub_rel) ).
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(symmetric,definition,
( symmetric
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ( R @ Y @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric) ).
thf(transitive,definition,
( transitive
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Y )
& ( R @ Y @ Z ) )
=> ( R @ X @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive) ).
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(upwards_well_founded,definition,
( upwards_well_founded
= ( ^ [R: $i > $i > $o] :
! [X: $i > $o,Z: $i] :
( ( X @ Z )
=> ? [Y: $i] :
( ( X @ Y )
& ! [W: $i] :
( ( R @ Y @ Y )
=> ~ ( X @ W ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upwards_well_founded) ).
thf(well_founded,definition,
( well_founded
= ( ^ [R: $i > $i > $o] :
! [X: $i > $o,Z: $i] :
( ( X @ Z )
=> ? [Y: $i] :
( ( X @ Y )
& ! [W: $i] :
( ( R @ Y @ W )
=> ~ ( X @ W ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_founded) ).
thf(1,conjecture,
! [X: $i,Y: $i] :
( sub_rel @ ( pair_rel @ X @ Y )
@ ( cartesian_product
@ ^ [X: $i] : $true
@ ^ [X: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( ! [X: $i,Y: $i] :
( sub_rel @ ( pair_rel @ X @ Y )
@ ( cartesian_product
@ ^ [X: $i] : $true
@ ^ [X: $i] : $true ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i,SY1: $i,SY18: $i,SY19: $i] :
( ( ( SY18 = SY0 )
| ( SY19 = SY1 ) )
=> ( $true
& $true ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cartesian_product,complement,disjoint,emptyset,equiv_classes,equiv_rel,excl_union,id_rel,in,intersection,irreflexive,is_a,is_rel_on,meets,misses,pair_rel,reflexive,rel_codomain,rel_composition,rel_diagonal,rel_domain,rel_field,rel_inverse,restrict_rel_codomain,restrict_rel_domain,setminus,singleton,sub_rel,subset,symmetric,transitive,union,unord_pair,upwards_well_founded,well_founded]) ).
thf(4,plain,
( ( ! [SY25: $i,SY26: $i,SY27: $i] :
( ( ( SY26 = sK1_SY0 )
| ( SY27 = SY25 ) )
=> ( $true
& $true ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY28: $i,SY29: $i] :
( ( ( SY28 = sK1_SY0 )
| ( SY29 = sK2_SY25 ) )
=> ( $true
& $true ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY30: $i] :
( ( ( sK3_SY28 = sK1_SY0 )
| ( SY30 = sK2_SY25 ) )
=> ( $true
& $true ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ( ( sK3_SY28 = sK1_SY0 )
| ( sK4_SY30 = sK2_SY25 ) )
=> ( $true
& $true ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ( sK3_SY28 = sK1_SY0 )
| ( sK4_SY30 = sK2_SY25 ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(9,plain,
( ( $true
& $true )
= $false ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(10,plain,
$true = $false,
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(11,plain,
$true = $false,
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(12,plain,
( ( ~ $true ) = $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ $true ) = $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(14,plain,
( ( ( sK3_SY28 = sK1_SY0 )
| ( sK4_SY30 = sK2_SY25 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(15,plain,
( ( ~ $true ) = $true ),
inference(copy,[status(thm)],[12]) ).
thf(16,plain,
( ( ( sK3_SY28 = sK1_SY0 )
= $true )
| ( ( sK4_SY30 = sK2_SY25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(17,plain,
$true = $false,
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,17]) ).
thf(19,plain,
( ( ( sK3_SY28 = sK1_SY0 )
| ( sK4_SY30 = sK2_SY25 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(20,plain,
( ( ~ $true ) = $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ( sK3_SY28 = sK1_SY0 )
= $true )
| ( ( sK4_SY30 = sK2_SY25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(22,plain,
$true = $false,
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,22]) ).
thf(24,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[23,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET646^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 14:47:31 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.13
% 0.08/0.13 No.of.Axioms: 0
% 0.08/0.13
% 0.08/0.13 Length.of.Defs: 5966
% 0.08/0.13
% 0.08/0.13 Contains.Choice.Funs: false
% 0.08/0.13
% 0.08/0.13 ********************************
% 0.08/0.13 * All subproblems solved! *
% 0.08/0.13 ********************************
% 0.08/0.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,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:23,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.13
% 0.08/0.13 %**** Beginning of derivation protocol ****
% 0.08/0.13 % SZS output start CNFRefutation
% See solution above
% 0.08/0.13
% 0.08/0.13 %**** End of derivation protocol ****
% 0.08/0.13 %**** no. of clauses in derivation: 24 ****
% 0.08/0.13 %**** clause counter: 23 ****
% 0.08/0.13
% 0.08/0.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,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:23,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------