%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL603^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 10:29:30 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 37
% Syntax : Number of formulae : 134 ( 85 unt; 0 typ; 36 def)
% Number of atoms : 671 ( 212 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 1326 ( 216 ~; 236 |; 32 &; 802 @)
% ( 1 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 150 ( 150 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 7 con; 0-4 aty)
% Number of variables : 448 ( 76 ^; 362 !; 10 ?; 448 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_individuals,type,
individuals: $tType ).
thf(tp_cartesian_product,type,
cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(tp_current_world,type,
current_world: $i ).
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_id_rel,type,
id_rel: ( $i > $o ) > $i > $i > $o ).
thf(tp_irreflexive,type,
irreflexive: ( $i > $i > $o ) > $o ).
thf(tp_is_rel_on,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(tp_mall,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mcountersatisfiable,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(tp_mdia,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mexists,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_miff,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimpl,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_pair_rel,type,
pair_rel: $i > $i > $i > $i > $o ).
thf(tp_prop_a,type,
prop_a: $i > $o ).
thf(tp_prop_b,type,
prop_b: $i > $o ).
thf(tp_prop_c,type,
prop_c: $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 > $i > $o ).
thf(tp_sK2_SY74,type,
sK2_SY74: $i ).
thf(tp_sK3_SY84,type,
sK3_SY84: ( $i > $o ) > $i > $i ).
thf(tp_sK4_SY87,type,
sK4_SY87: ( $i > $o ) > $i > $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SY96,type,
sK6_SY96: $i ).
thf(tp_sK7_SY98,type,
sK7_SY98: $i ).
thf(tp_sK8_SY99,type,
sK8_SY99: ( $i > $o ) > $i > $i ).
thf(tp_sK9_SY102,type,
sK9_SY102: ( $i > $o ) > $i > $i ).
thf(tp_sub_rel,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(tp_symmetric,type,
symmetric: ( $i > $i > $o ) > $o ).
thf(tp_transitive,type,
transitive: ( $i > $i > $o ) > $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/sandbox/benchmark/theBenchmark.p',cartesian_product) ).
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/sandbox/benchmark/theBenchmark.p',equiv_classes) ).
thf(equiv_rel,definition,
( equiv_rel
= ( ^ [R: $i > $i > $o] :
( ( reflexive @ R )
& ( symmetric @ R )
& ( transitive @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equiv_rel) ).
thf(id_rel,definition,
( id_rel
= ( ^ [S: $i > $o,X: $i,Y: $i] :
( ( S @ X )
& ( X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id_rel) ).
thf(irreflexive,definition,
( irreflexive
= ( ^ [R: $i > $i > $o] :
! [X: $i] :
~ ( R @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexive) ).
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/sandbox/benchmark/theBenchmark.p',is_rel_on) ).
thf(mall,definition,
( mall
= ( ^ [P: individuals > $i > $o,W: $i] :
! [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mall) ).
thf(mand,definition,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
! [Y: $i] :
( ( R @ X @ Y )
=> ( P @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
? [Y: $i] :
( ( R @ X @ Y )
& ( P @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',individuals_decl) ).
thf(mexists,definition,
( mexists
= ( ^ [P: individuals > $i > $o,W: $i] :
? [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists) ).
thf(mfalse,definition,
( mfalse
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).
thf(miff,definition,
( miff
= ( ^ [U: $i > $o,V: $i > $o] : ( mand @ ( mimpl @ U @ V ) @ ( mimpl @ V @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',miff) ).
thf(mimpl,definition,
( mimpl
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimpl) ).
thf(minvalid,definition,
( minvalid
= ( ^ [P: $i > $o] :
! [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).
thf(mtrue,definition,
( mtrue
= ( ^ [X: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [P: $i > $o] :
! [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid) ).
thf(pair_rel,definition,
( pair_rel
= ( ^ [X: $i,Y: $i,U: $i,V: $i] :
( ( U = X )
| ( V = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pair_rel) ).
thf(reflexive,definition,
( reflexive
= ( ^ [R: $i > $i > $o] :
! [X: $i] : ( R @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexive) ).
thf(rel_codomain,definition,
( rel_codomain
= ( ^ [R: $i > $i > $o,Y: $i] :
? [X: $i] : ( R @ X @ Y ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',rel_composition) ).
thf(rel_diagonal,definition,
( rel_diagonal
= ( ^ [X: $i,Y: $i] : ( X = Y ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',restrict_rel_domain) ).
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/sandbox/benchmark/theBenchmark.p',sub_rel) ).
thf(symmetric,definition,
( symmetric
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ( R @ Y @ X ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',transitive) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',well_founded) ).
thf(1,conjecture,
! [R: $i > $i > $o] :
( ! [A: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ R @ A ) @ ( mbox @ R @ ( mbox @ R @ A ) ) ) )
& ( mvalid @ ( mimpl @ ( mbox @ R @ A ) @ A ) ) )
=> ( ( reflexive @ R )
& ( transitive @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( ! [R: $i > $i > $o] :
( ! [A: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ R @ A ) @ ( mbox @ R @ ( mbox @ R @ A ) ) ) )
& ( mvalid @ ( mimpl @ ( mbox @ R @ A ) @ A ) ) )
=> ( ( reflexive @ R )
& ( transitive @ R ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i > $o] :
( ! [SY1: $i > $o] :
( ! [SY30: $i] :
( ~ ! [SY31: $i] :
( ( SY0 @ SY30 @ SY31 )
=> ( SY1 @ SY31 ) )
| ! [SY32: $i] :
( ( SY0 @ SY30 @ SY32 )
=> ! [SY25: $i] :
( ( SY0 @ SY32 @ SY25 )
=> ( SY1 @ SY25 ) ) ) )
& ! [SY49: $i] :
( ~ ! [SY50: $i] :
( ( SY0 @ SY49 @ SY50 )
=> ( SY1 @ SY50 ) )
| ( SY1 @ SY49 ) ) )
=> ( ! [SY51: $i] : ( SY0 @ SY51 @ SY51 )
& ! [SY52: $i,SY53: $i,SY54: $i] :
( ( ( SY0 @ SY52 @ SY53 )
& ( SY0 @ SY53 @ SY54 ) )
=> ( SY0 @ SY52 @ SY54 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cartesian_product,equiv_classes,equiv_rel,id_rel,irreflexive,is_rel_on,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid,pair_rel,reflexive,rel_codomain,rel_composition,rel_diagonal,rel_domain,rel_field,rel_inverse,restrict_rel_codomain,restrict_rel_domain,sub_rel,symmetric,transitive,upwards_well_founded,well_founded]) ).
thf(4,plain,
( ( ! [SY67: $i > $o] :
( ! [SY68: $i] :
( ~ ! [SY69: $i] :
( ( sK1_SY0 @ SY68 @ SY69 )
=> ( SY67 @ SY69 ) )
| ! [SY70: $i] :
( ( sK1_SY0 @ SY68 @ SY70 )
=> ! [SY71: $i] :
( ( sK1_SY0 @ SY70 @ SY71 )
=> ( SY67 @ SY71 ) ) ) )
& ! [SY72: $i] :
( ~ ! [SY73: $i] :
( ( sK1_SY0 @ SY72 @ SY73 )
=> ( SY67 @ SY73 ) )
| ( SY67 @ SY72 ) ) )
=> ( ! [SY74: $i] : ( sK1_SY0 @ SY74 @ SY74 )
& ! [SY75: $i,SY76: $i,SY77: $i] :
( ( ( sK1_SY0 @ SY75 @ SY76 )
& ( sK1_SY0 @ SY76 @ SY77 ) )
=> ( sK1_SY0 @ SY75 @ SY77 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY67: $i > $o] :
( ! [SY68: $i] :
( ~ ! [SY69: $i] :
( ( sK1_SY0 @ SY68 @ SY69 )
=> ( SY67 @ SY69 ) )
| ! [SY70: $i] :
( ( sK1_SY0 @ SY68 @ SY70 )
=> ! [SY71: $i] :
( ( sK1_SY0 @ SY70 @ SY71 )
=> ( SY67 @ SY71 ) ) ) )
& ! [SY72: $i] :
( ~ ! [SY73: $i] :
( ( sK1_SY0 @ SY72 @ SY73 )
=> ( SY67 @ SY73 ) )
| ( SY67 @ SY72 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY74: $i] : ( sK1_SY0 @ SY74 @ SY74 )
& ! [SY75: $i,SY76: $i,SY77: $i] :
( ( ( sK1_SY0 @ SY75 @ SY76 )
& ( sK1_SY0 @ SY76 @ SY77 ) )
=> ( sK1_SY0 @ SY75 @ SY77 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [SY74: $i] : ( sK1_SY0 @ SY74 @ SY74 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(8,plain,
( ( ! [SY75: $i,SY76: $i,SY77: $i] :
( ( ( sK1_SY0 @ SY75 @ SY76 )
& ( sK1_SY0 @ SY76 @ SY77 ) )
=> ( sK1_SY0 @ SY75 @ SY77 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(9,plain,
( ( ~ ! [SY74: $i] : ( sK1_SY0 @ SY74 @ SY74 ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ! [SY75: $i,SY76: $i,SY77: $i] :
( ( ( sK1_SY0 @ SY75 @ SY76 )
& ( sK1_SY0 @ SY76 @ SY77 ) )
=> ( sK1_SY0 @ SY75 @ SY77 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [SY67: $i > $o] :
( ! [SY68: $i] :
( ~ ! [SY69: $i] :
( ( sK1_SY0 @ SY68 @ SY69 )
=> ( SY67 @ SY69 ) )
| ! [SY70: $i] :
( ( sK1_SY0 @ SY68 @ SY70 )
=> ! [SY71: $i] :
( ( sK1_SY0 @ SY70 @ SY71 )
=> ( SY67 @ SY71 ) ) ) )
& ! [SY72: $i] :
( ~ ! [SY73: $i] :
( ( sK1_SY0 @ SY72 @ SY73 )
=> ( SY67 @ SY73 ) )
| ( SY67 @ SY72 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(12,plain,
( ( ~ ! [SY74: $i] : ( sK1_SY0 @ SY74 @ SY74 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ! [SX0: $i > $o] :
~ ( ~ ! [SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( SX0 @ SX3 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ( SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,cartesian_product,equiv_classes,equiv_rel,id_rel,irreflexive,is_rel_on,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid,pair_rel,reflexive,rel_codomain,rel_composition,rel_diagonal,rel_domain,rel_field,rel_inverse,restrict_rel_codomain,restrict_rel_domain,sub_rel,symmetric,transitive,upwards_well_founded,well_founded]) ).
thf(14,plain,
( ( ! [SY74: $i] : ( sK1_SY0 @ SY74 @ SY74 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i > $o] :
( ( ~ ( ~ ! [SY78: $i] :
( ~ ! [SY79: $i] :
( ~ ( sK1_SY0 @ SY78 @ SY79 )
| ( SV1 @ SY79 ) )
| ! [SY80: $i] :
( ~ ( sK1_SY0 @ SY78 @ SY80 )
| ! [SY81: $i] :
( ~ ( sK1_SY0 @ SY80 @ SY81 )
| ( SV1 @ SY81 ) ) ) )
| ~ ! [SY82: $i] :
( ~ ! [SY83: $i] :
( ~ ( sK1_SY0 @ SY82 @ SY83 )
| ( SV1 @ SY83 ) )
| ( SV1 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( sK1_SY0 @ sK2_SY74 @ sK2_SY74 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(17,plain,
! [SV1: $i > $o] :
( ( ~ ! [SY78: $i] :
( ~ ! [SY79: $i] :
( ~ ( sK1_SY0 @ SY78 @ SY79 )
| ( SV1 @ SY79 ) )
| ! [SY80: $i] :
( ~ ( sK1_SY0 @ SY78 @ SY80 )
| ! [SY81: $i] :
( ~ ( sK1_SY0 @ SY80 @ SY81 )
| ( SV1 @ SY81 ) ) ) )
| ~ ! [SY82: $i] :
( ~ ! [SY83: $i] :
( ~ ( sK1_SY0 @ SY82 @ SY83 )
| ( SV1 @ SY83 ) )
| ( SV1 @ SY82 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: $i > $o] :
( ( ~ ! [SY78: $i] :
( ~ ! [SY79: $i] :
( ~ ( sK1_SY0 @ SY78 @ SY79 )
| ( SV1 @ SY79 ) )
| ! [SY80: $i] :
( ~ ( sK1_SY0 @ SY78 @ SY80 )
| ! [SY81: $i] :
( ~ ( sK1_SY0 @ SY80 @ SY81 )
| ( SV1 @ SY81 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(19,plain,
! [SV1: $i > $o] :
( ( ~ ! [SY82: $i] :
( ~ ! [SY83: $i] :
( ~ ( sK1_SY0 @ SY82 @ SY83 )
| ( SV1 @ SY83 ) )
| ( SV1 @ SY82 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
! [SV1: $i > $o] :
( ( ! [SY78: $i] :
( ~ ! [SY79: $i] :
( ~ ( sK1_SY0 @ SY78 @ SY79 )
| ( SV1 @ SY79 ) )
| ! [SY80: $i] :
( ~ ( sK1_SY0 @ SY78 @ SY80 )
| ! [SY81: $i] :
( ~ ( sK1_SY0 @ SY80 @ SY81 )
| ( SV1 @ SY81 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(21,plain,
! [SV1: $i > $o] :
( ( ! [SY82: $i] :
( ~ ! [SY83: $i] :
( ~ ( sK1_SY0 @ SY82 @ SY83 )
| ( SV1 @ SY83 ) )
| ( SV1 @ SY82 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(22,plain,
! [SV1: $i > $o,SV2: $i] :
( ( ~ ! [SY84: $i] :
( ~ ( sK1_SY0 @ SV2 @ SY84 )
| ( SV1 @ SY84 ) )
| ! [SY85: $i] :
( ~ ( sK1_SY0 @ SV2 @ SY85 )
| ! [SY81: $i] :
( ~ ( sK1_SY0 @ SY85 @ SY81 )
| ( SV1 @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ~ ! [SY87: $i] :
( ~ ( sK1_SY0 @ SV3 @ SY87 )
| ( SV1 @ SY87 ) )
| ( SV1 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: $i > $o,SV2: $i] :
( ( ( ~ ! [SY84: $i] :
( ~ ( sK1_SY0 @ SV2 @ SY84 )
| ( SV1 @ SY84 ) ) )
= $true )
| ( ( ! [SY85: $i] :
( ~ ( sK1_SY0 @ SV2 @ SY85 )
| ! [SY81: $i] :
( ~ ( sK1_SY0 @ SY85 @ SY81 )
| ( SV1 @ SY81 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ! [SY87: $i] :
( ~ ( sK1_SY0 @ SV3 @ SY87 )
| ( SV1 @ SY87 ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV1: $i > $o,SV2: $i] :
( ( ( ! [SY84: $i] :
( ~ ( sK1_SY0 @ SV2 @ SY84 )
| ( SV1 @ SY84 ) ) )
= $false )
| ( ( ! [SY85: $i] :
( ~ ( sK1_SY0 @ SV2 @ SY85 )
| ! [SY81: $i] :
( ~ ( sK1_SY0 @ SY85 @ SY81 )
| ( SV1 @ SY81 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ! [SY87: $i] :
( ~ ( sK1_SY0 @ SV3 @ SY87 )
| ( SV1 @ SY87 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV1: $i > $o,SV2: $i] :
( ( ( ~ ( sK1_SY0 @ SV2 @ ( sK3_SY84 @ SV1 @ SV2 ) )
| ( SV1 @ ( sK3_SY84 @ SV1 @ SV2 ) ) )
= $false )
| ( ( ! [SY85: $i] :
( ~ ( sK1_SY0 @ SV2 @ SY85 )
| ! [SY81: $i] :
( ~ ( sK1_SY0 @ SY85 @ SY81 )
| ( SV1 @ SY81 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(29,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ( sK1_SY0 @ SV3 @ ( sK4_SY87 @ SV1 @ SV3 ) )
| ( SV1 @ ( sK4_SY87 @ SV1 @ SV3 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(30,plain,
! [SV1: $i > $o,SV2: $i] :
( ( ( ~ ( sK1_SY0 @ SV2 @ ( sK3_SY84 @ SV1 @ SV2 ) ) )
= $false )
| ( ( ! [SY85: $i] :
( ~ ( sK1_SY0 @ SV2 @ SY85 )
| ! [SY81: $i] :
( ~ ( sK1_SY0 @ SY85 @ SY81 )
| ( SV1 @ SY81 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(31,plain,
! [SV2: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $false )
| ( ( ! [SY85: $i] :
( ~ ( sK1_SY0 @ SV2 @ SY85 )
| ! [SY81: $i] :
( ~ ( sK1_SY0 @ SY85 @ SY81 )
| ( SV1 @ SY81 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ( sK1_SY0 @ SV3 @ ( sK4_SY87 @ SV1 @ SV3 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK4_SY87 @ SV1 @ SV3 ) )
= $false )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV1: $i > $o,SV2: $i] :
( ( ( sK1_SY0 @ SV2 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $true )
| ( ( ! [SY85: $i] :
( ~ ( sK1_SY0 @ SV2 @ SY85 )
| ! [SY81: $i] :
( ~ ( sK1_SY0 @ SY85 @ SY81 )
| ( SV1 @ SY81 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV1: $i > $o,SV4: $i,SV2: $i] :
( ( ( ~ ( sK1_SY0 @ SV2 @ SV4 )
| ! [SY88: $i] :
( ~ ( sK1_SY0 @ SV4 @ SY88 )
| ( SV1 @ SY88 ) ) )
= $true )
| ( ( SV1 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( sK1_SY0 @ SV3 @ ( sK4_SY87 @ SV1 @ SV3 ) )
= $true )
| ( ( SV1 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV1: $i > $o,SV5: $i,SV2: $i] :
( ( ( ~ ( sK1_SY0 @ SV2 @ SV5 )
| ! [SY89: $i] :
( ~ ( sK1_SY0 @ SV5 @ SY89 )
| ( SV1 @ SY89 ) ) )
= $true )
| ( ( sK1_SY0 @ SV2 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV1: $i > $o,SV4: $i,SV2: $i] :
( ( ( ~ ( sK1_SY0 @ SV2 @ SV4 ) )
= $true )
| ( ( ! [SY88: $i] :
( ~ ( sK1_SY0 @ SV4 @ SY88 )
| ( SV1 @ SY88 ) ) )
= $true )
| ( ( SV1 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV1: $i > $o,SV5: $i,SV2: $i] :
( ( ( ~ ( sK1_SY0 @ SV2 @ SV5 ) )
= $true )
| ( ( ! [SY89: $i] :
( ~ ( sK1_SY0 @ SV5 @ SY89 )
| ( SV1 @ SY89 ) ) )
= $true )
| ( ( sK1_SY0 @ SV2 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV1: $i > $o,SV4: $i,SV2: $i] :
( ( ( sK1_SY0 @ SV2 @ SV4 )
= $false )
| ( ( ! [SY88: $i] :
( ~ ( sK1_SY0 @ SV4 @ SY88 )
| ( SV1 @ SY88 ) ) )
= $true )
| ( ( SV1 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV1: $i > $o,SV5: $i,SV2: $i] :
( ( ( sK1_SY0 @ SV2 @ SV5 )
= $false )
| ( ( ! [SY89: $i] :
( ~ ( sK1_SY0 @ SV5 @ SY89 )
| ( SV1 @ SY89 ) ) )
= $true )
| ( ( sK1_SY0 @ SV2 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV2: $i,SV1: $i > $o,SV6: $i,SV4: $i] :
( ( ( ~ ( sK1_SY0 @ SV4 @ SV6 )
| ( SV1 @ SV6 ) )
= $true )
| ( ( sK1_SY0 @ SV2 @ SV4 )
= $false )
| ( ( SV1 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV2: $i,SV1: $i > $o,SV7: $i,SV5: $i] :
( ( ( ~ ( sK1_SY0 @ SV5 @ SV7 )
| ( SV1 @ SV7 ) )
= $true )
| ( ( sK1_SY0 @ SV2 @ SV5 )
= $false )
| ( ( sK1_SY0 @ SV2 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV2: $i,SV1: $i > $o,SV6: $i,SV4: $i] :
( ( ( ~ ( sK1_SY0 @ SV4 @ SV6 ) )
= $true )
| ( ( SV1 @ SV6 )
= $true )
| ( ( sK1_SY0 @ SV2 @ SV4 )
= $false )
| ( ( SV1 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV2: $i,SV1: $i > $o,SV7: $i,SV5: $i] :
( ( ( ~ ( sK1_SY0 @ SV5 @ SV7 ) )
= $true )
| ( ( SV1 @ SV7 )
= $true )
| ( ( sK1_SY0 @ SV2 @ SV5 )
= $false )
| ( ( sK1_SY0 @ SV2 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV2: $i,SV1: $i > $o,SV6: $i,SV4: $i] :
( ( ( sK1_SY0 @ SV4 @ SV6 )
= $false )
| ( ( SV1 @ SV6 )
= $true )
| ( ( sK1_SY0 @ SV2 @ SV4 )
= $false )
| ( ( SV1 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV2: $i,SV1: $i > $o,SV7: $i,SV5: $i] :
( ( ( sK1_SY0 @ SV5 @ SV7 )
= $false )
| ( ( SV1 @ SV7 )
= $true )
| ( ( sK1_SY0 @ SV2 @ SV5 )
= $false )
| ( ( sK1_SY0 @ SV2 @ ( sK3_SY84 @ SV1 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(48,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,47,46,36,33]) ).
thf(49,plain,
( ( ! [SY67: $i > $o] :
( ! [SY68: $i] :
( ~ ! [SY69: $i] :
( ( sK1_SY0 @ SY68 @ SY69 )
=> ( SY67 @ SY69 ) )
| ! [SY70: $i] :
( ( sK1_SY0 @ SY68 @ SY70 )
=> ! [SY71: $i] :
( ( sK1_SY0 @ SY70 @ SY71 )
=> ( SY67 @ SY71 ) ) ) )
& ! [SY72: $i] :
( ~ ! [SY73: $i] :
( ( sK1_SY0 @ SY72 @ SY73 )
=> ( SY67 @ SY73 ) )
| ( SY67 @ SY72 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(50,plain,
( ( ~ ! [SY75: $i,SY76: $i,SY77: $i] :
( ( ( sK1_SY0 @ SY75 @ SY76 )
& ( sK1_SY0 @ SY76 @ SY77 ) )
=> ( sK1_SY0 @ SY75 @ SY77 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(51,plain,
( ( ! [SX0: $i > $o] :
~ ( ~ ! [SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( SX0 @ SX3 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ( SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49,cartesian_product,equiv_classes,equiv_rel,id_rel,irreflexive,is_rel_on,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid,pair_rel,reflexive,rel_codomain,rel_composition,rel_diagonal,rel_domain,rel_field,rel_inverse,restrict_rel_codomain,restrict_rel_domain,sub_rel,symmetric,transitive,upwards_well_founded,well_founded]) ).
thf(52,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( sK1_SY0 @ SX0 @ SX1 )
| ~ ( sK1_SY0 @ SX1 @ SX2 ) )
| ( sK1_SY0 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50,cartesian_product,equiv_classes,equiv_rel,id_rel,irreflexive,is_rel_on,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid,pair_rel,reflexive,rel_codomain,rel_composition,rel_diagonal,rel_domain,rel_field,rel_inverse,restrict_rel_codomain,restrict_rel_domain,sub_rel,symmetric,transitive,upwards_well_founded,well_founded]) ).
thf(53,plain,
! [SV8: $i > $o] :
( ( ~ ( ~ ! [SY90: $i] :
( ~ ! [SY91: $i] :
( ~ ( sK1_SY0 @ SY90 @ SY91 )
| ( SV8 @ SY91 ) )
| ! [SY92: $i] :
( ~ ( sK1_SY0 @ SY90 @ SY92 )
| ! [SY93: $i] :
( ~ ( sK1_SY0 @ SY92 @ SY93 )
| ( SV8 @ SY93 ) ) ) )
| ~ ! [SY94: $i] :
( ~ ! [SY95: $i] :
( ~ ( sK1_SY0 @ SY94 @ SY95 )
| ( SV8 @ SY95 ) )
| ( SV8 @ SY94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(54,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( sK1_SY0 @ SX0 @ SX1 )
| ~ ( sK1_SY0 @ SX1 @ SX2 ) )
| ( sK1_SY0 @ SX0 @ SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV8: $i > $o] :
( ( ~ ! [SY90: $i] :
( ~ ! [SY91: $i] :
( ~ ( sK1_SY0 @ SY90 @ SY91 )
| ( SV8 @ SY91 ) )
| ! [SY92: $i] :
( ~ ( sK1_SY0 @ SY90 @ SY92 )
| ! [SY93: $i] :
( ~ ( sK1_SY0 @ SY92 @ SY93 )
| ( SV8 @ SY93 ) ) ) )
| ~ ! [SY94: $i] :
( ~ ! [SY95: $i] :
( ~ ( sK1_SY0 @ SY94 @ SY95 )
| ( SV8 @ SY95 ) )
| ( SV8 @ SY94 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
( ( ! [SY96: $i,SY97: $i] :
( ~ ~ ( ~ ( sK1_SY0 @ sK5_SX0 @ SY96 )
| ~ ( sK1_SY0 @ SY96 @ SY97 ) )
| ( sK1_SY0 @ sK5_SX0 @ SY97 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[54]) ).
thf(57,plain,
! [SV8: $i > $o] :
( ( ~ ! [SY90: $i] :
( ~ ! [SY91: $i] :
( ~ ( sK1_SY0 @ SY90 @ SY91 )
| ( SV8 @ SY91 ) )
| ! [SY92: $i] :
( ~ ( sK1_SY0 @ SY90 @ SY92 )
| ! [SY93: $i] :
( ~ ( sK1_SY0 @ SY92 @ SY93 )
| ( SV8 @ SY93 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(58,plain,
! [SV8: $i > $o] :
( ( ~ ! [SY94: $i] :
( ~ ! [SY95: $i] :
( ~ ( sK1_SY0 @ SY94 @ SY95 )
| ( SV8 @ SY95 ) )
| ( SV8 @ SY94 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(59,plain,
( ( ! [SY98: $i] :
( ~ ~ ( ~ ( sK1_SY0 @ sK5_SX0 @ sK6_SY96 )
| ~ ( sK1_SY0 @ sK6_SY96 @ SY98 ) )
| ( sK1_SY0 @ sK5_SX0 @ SY98 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(60,plain,
! [SV8: $i > $o] :
( ( ! [SY90: $i] :
( ~ ! [SY91: $i] :
( ~ ( sK1_SY0 @ SY90 @ SY91 )
| ( SV8 @ SY91 ) )
| ! [SY92: $i] :
( ~ ( sK1_SY0 @ SY90 @ SY92 )
| ! [SY93: $i] :
( ~ ( sK1_SY0 @ SY92 @ SY93 )
| ( SV8 @ SY93 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(61,plain,
! [SV8: $i > $o] :
( ( ! [SY94: $i] :
( ~ ! [SY95: $i] :
( ~ ( sK1_SY0 @ SY94 @ SY95 )
| ( SV8 @ SY95 ) )
| ( SV8 @ SY94 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
( ( ~ ~ ( ~ ( sK1_SY0 @ sK5_SX0 @ sK6_SY96 )
| ~ ( sK1_SY0 @ sK6_SY96 @ sK7_SY98 ) )
| ( sK1_SY0 @ sK5_SX0 @ sK7_SY98 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(63,plain,
! [SV8: $i > $o,SV9: $i] :
( ( ~ ! [SY99: $i] :
( ~ ( sK1_SY0 @ SV9 @ SY99 )
| ( SV8 @ SY99 ) )
| ! [SY100: $i] :
( ~ ( sK1_SY0 @ SV9 @ SY100 )
| ! [SY93: $i] :
( ~ ( sK1_SY0 @ SY100 @ SY93 )
| ( SV8 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV8: $i > $o,SV10: $i] :
( ( ~ ! [SY102: $i] :
( ~ ( sK1_SY0 @ SV10 @ SY102 )
| ( SV8 @ SY102 ) )
| ( SV8 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(65,plain,
( ( ~ ~ ( ~ ( sK1_SY0 @ sK5_SX0 @ sK6_SY96 )
| ~ ( sK1_SY0 @ sK6_SY96 @ sK7_SY98 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(66,plain,
( ( sK1_SY0 @ sK5_SX0 @ sK7_SY98 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(67,plain,
! [SV8: $i > $o,SV9: $i] :
( ( ( ~ ! [SY99: $i] :
( ~ ( sK1_SY0 @ SV9 @ SY99 )
| ( SV8 @ SY99 ) ) )
= $true )
| ( ( ! [SY100: $i] :
( ~ ( sK1_SY0 @ SV9 @ SY100 )
| ! [SY93: $i] :
( ~ ( sK1_SY0 @ SY100 @ SY93 )
| ( SV8 @ SY93 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV8: $i > $o,SV10: $i] :
( ( ( ~ ! [SY102: $i] :
( ~ ( sK1_SY0 @ SV10 @ SY102 )
| ( SV8 @ SY102 ) ) )
= $true )
| ( ( SV8 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(69,plain,
( ( ~ ( ~ ( sK1_SY0 @ sK5_SX0 @ sK6_SY96 )
| ~ ( sK1_SY0 @ sK6_SY96 @ sK7_SY98 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(70,plain,
! [SV8: $i > $o,SV9: $i] :
( ( ( ! [SY99: $i] :
( ~ ( sK1_SY0 @ SV9 @ SY99 )
| ( SV8 @ SY99 ) ) )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( sK1_SY0 @ SV9 @ SY100 )
| ! [SY93: $i] :
( ~ ( sK1_SY0 @ SY100 @ SY93 )
| ( SV8 @ SY93 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV8: $i > $o,SV10: $i] :
( ( ( ! [SY102: $i] :
( ~ ( sK1_SY0 @ SV10 @ SY102 )
| ( SV8 @ SY102 ) ) )
= $false )
| ( ( SV8 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(72,plain,
( ( ~ ( sK1_SY0 @ sK5_SX0 @ sK6_SY96 )
| ~ ( sK1_SY0 @ sK6_SY96 @ sK7_SY98 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(73,plain,
! [SV8: $i > $o,SV9: $i] :
( ( ( ~ ( sK1_SY0 @ SV9 @ ( sK8_SY99 @ SV8 @ SV9 ) )
| ( SV8 @ ( sK8_SY99 @ SV8 @ SV9 ) ) )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( sK1_SY0 @ SV9 @ SY100 )
| ! [SY93: $i] :
( ~ ( sK1_SY0 @ SY100 @ SY93 )
| ( SV8 @ SY93 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[70]) ).
thf(74,plain,
! [SV8: $i > $o,SV10: $i] :
( ( ( ~ ( sK1_SY0 @ SV10 @ ( sK9_SY102 @ SV8 @ SV10 ) )
| ( SV8 @ ( sK9_SY102 @ SV8 @ SV10 ) ) )
= $false )
| ( ( SV8 @ SV10 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[71]) ).
thf(75,plain,
( ( ~ ( sK1_SY0 @ sK5_SX0 @ sK6_SY96 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(76,plain,
( ( ~ ( sK1_SY0 @ sK6_SY96 @ sK7_SY98 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(77,plain,
! [SV8: $i > $o,SV9: $i] :
( ( ( ~ ( sK1_SY0 @ SV9 @ ( sK8_SY99 @ SV8 @ SV9 ) ) )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( sK1_SY0 @ SV9 @ SY100 )
| ! [SY93: $i] :
( ~ ( sK1_SY0 @ SY100 @ SY93 )
| ( SV8 @ SY93 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(78,plain,
! [SV9: $i,SV8: $i > $o] :
( ( ( SV8 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( sK1_SY0 @ SV9 @ SY100 )
| ! [SY93: $i] :
( ~ ( sK1_SY0 @ SY100 @ SY93 )
| ( SV8 @ SY93 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(79,plain,
! [SV8: $i > $o,SV10: $i] :
( ( ( ~ ( sK1_SY0 @ SV10 @ ( sK9_SY102 @ SV8 @ SV10 ) ) )
= $false )
| ( ( SV8 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(80,plain,
! [SV10: $i,SV8: $i > $o] :
( ( ( SV8 @ ( sK9_SY102 @ SV8 @ SV10 ) )
= $false )
| ( ( SV8 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(81,plain,
( ( sK1_SY0 @ sK5_SX0 @ sK6_SY96 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(82,plain,
( ( sK1_SY0 @ sK6_SY96 @ sK7_SY98 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(83,plain,
! [SV8: $i > $o,SV9: $i] :
( ( ( sK1_SY0 @ SV9 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $true )
| ( ( ! [SY100: $i] :
( ~ ( sK1_SY0 @ SV9 @ SY100 )
| ! [SY93: $i] :
( ~ ( sK1_SY0 @ SY100 @ SY93 )
| ( SV8 @ SY93 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(84,plain,
! [SV8: $i > $o,SV11: $i,SV9: $i] :
( ( ( ~ ( sK1_SY0 @ SV9 @ SV11 )
| ! [SY103: $i] :
( ~ ( sK1_SY0 @ SV11 @ SY103 )
| ( SV8 @ SY103 ) ) )
= $true )
| ( ( SV8 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV8: $i > $o,SV10: $i] :
( ( ( sK1_SY0 @ SV10 @ ( sK9_SY102 @ SV8 @ SV10 ) )
= $true )
| ( ( SV8 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(86,plain,
! [SV8: $i > $o,SV12: $i,SV9: $i] :
( ( ( ~ ( sK1_SY0 @ SV9 @ SV12 )
| ! [SY104: $i] :
( ~ ( sK1_SY0 @ SV12 @ SY104 )
| ( SV8 @ SY104 ) ) )
= $true )
| ( ( sK1_SY0 @ SV9 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(87,plain,
! [SV8: $i > $o,SV11: $i,SV9: $i] :
( ( ( ~ ( sK1_SY0 @ SV9 @ SV11 ) )
= $true )
| ( ( ! [SY103: $i] :
( ~ ( sK1_SY0 @ SV11 @ SY103 )
| ( SV8 @ SY103 ) ) )
= $true )
| ( ( SV8 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(88,plain,
! [SV8: $i > $o,SV12: $i,SV9: $i] :
( ( ( ~ ( sK1_SY0 @ SV9 @ SV12 ) )
= $true )
| ( ( ! [SY104: $i] :
( ~ ( sK1_SY0 @ SV12 @ SY104 )
| ( SV8 @ SY104 ) ) )
= $true )
| ( ( sK1_SY0 @ SV9 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(89,plain,
! [SV8: $i > $o,SV11: $i,SV9: $i] :
( ( ( sK1_SY0 @ SV9 @ SV11 )
= $false )
| ( ( ! [SY103: $i] :
( ~ ( sK1_SY0 @ SV11 @ SY103 )
| ( SV8 @ SY103 ) ) )
= $true )
| ( ( SV8 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(90,plain,
! [SV8: $i > $o,SV12: $i,SV9: $i] :
( ( ( sK1_SY0 @ SV9 @ SV12 )
= $false )
| ( ( ! [SY104: $i] :
( ~ ( sK1_SY0 @ SV12 @ SY104 )
| ( SV8 @ SY104 ) ) )
= $true )
| ( ( sK1_SY0 @ SV9 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(91,plain,
! [SV9: $i,SV8: $i > $o,SV13: $i,SV11: $i] :
( ( ( ~ ( sK1_SY0 @ SV11 @ SV13 )
| ( SV8 @ SV13 ) )
= $true )
| ( ( sK1_SY0 @ SV9 @ SV11 )
= $false )
| ( ( SV8 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(92,plain,
! [SV9: $i,SV8: $i > $o,SV14: $i,SV12: $i] :
( ( ( ~ ( sK1_SY0 @ SV12 @ SV14 )
| ( SV8 @ SV14 ) )
= $true )
| ( ( sK1_SY0 @ SV9 @ SV12 )
= $false )
| ( ( sK1_SY0 @ SV9 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(93,plain,
! [SV9: $i,SV8: $i > $o,SV13: $i,SV11: $i] :
( ( ( ~ ( sK1_SY0 @ SV11 @ SV13 ) )
= $true )
| ( ( SV8 @ SV13 )
= $true )
| ( ( sK1_SY0 @ SV9 @ SV11 )
= $false )
| ( ( SV8 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(94,plain,
! [SV9: $i,SV8: $i > $o,SV14: $i,SV12: $i] :
( ( ( ~ ( sK1_SY0 @ SV12 @ SV14 ) )
= $true )
| ( ( SV8 @ SV14 )
= $true )
| ( ( sK1_SY0 @ SV9 @ SV12 )
= $false )
| ( ( sK1_SY0 @ SV9 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(95,plain,
! [SV9: $i,SV8: $i > $o,SV13: $i,SV11: $i] :
( ( ( sK1_SY0 @ SV11 @ SV13 )
= $false )
| ( ( SV8 @ SV13 )
= $true )
| ( ( sK1_SY0 @ SV9 @ SV11 )
= $false )
| ( ( SV8 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(96,plain,
! [SV9: $i,SV8: $i > $o,SV14: $i,SV12: $i] :
( ( ( sK1_SY0 @ SV12 @ SV14 )
= $false )
| ( ( SV8 @ SV14 )
= $true )
| ( ( sK1_SY0 @ SV9 @ SV12 )
= $false )
| ( ( sK1_SY0 @ SV9 @ ( sK8_SY99 @ SV8 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(97,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[66,96,95,85,82,81,80]) ).
thf(98,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[97,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL603^1 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.09/0.17 % Computer : n007.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 12:23:00 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.24
% 0.09/0.24 No.of.Axioms: 0
% 0.09/0.24
% 0.09/0.24 Length.of.Defs: 6063
% 0.09/0.24
% 0.09/0.24 Contains.Choice.Funs: false
% 0.09/0.24 ...
% 0.09/0.24
% 0.09/0.24 ********************************
% 0.09/0.24 * All subproblems solved! *
% 0.09/0.24 ********************************
% 0.09/0.24 % SZS status Theorem for /export/starexec/sandbox/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:97,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.24
% 0.09/0.24 %**** Beginning of derivation protocol ****
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24
% 0.09/0.24 %**** End of derivation protocol ****
% 0.09/0.24 %**** no. of clauses in derivation: 98 ****
% 0.09/0.24 %**** clause counter: 97 ****
% 0.09/0.24
% 0.09/0.24 % SZS status Theorem for /export/starexec/sandbox/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:97,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------