TSTP Solution File: LCL626^1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL626^1 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:24:31 EDT 2022
% Result : Theorem 0.21s 0.45s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 86
% Syntax : Number of formulae : 145 ( 73 unt; 48 typ; 36 def)
% Number of atoms : 436 ( 126 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 774 ( 186 ~; 113 |; 16 &; 449 @)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 249 ( 249 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 47 usr; 7 con; 0-4 aty)
% Number of variables : 244 ( 76 ^ 158 !; 10 ?; 244 :)
% 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_r,type,
r: $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_X,type,
sK1_X: $i > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY1,type,
sK3_SY1: $i ).
thf(tp_sK4_SY9,type,
sK4_SY9: $i ).
thf(tp_sK5_SY14,type,
sK5_SY14: $i ).
thf(tp_sK6_SY7,type,
sK6_SY7: $i > ( $i > $o ) > $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/sandbox2/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/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(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(irreflexive,definition,
( irreflexive
= ( ^ [R: $i > $i > $o] :
! [X: $i] :
~ ( R @ X @ X ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',is_rel_on) ).
thf(mall,definition,
( mall
= ( ^ [P: individuals > $i > $o,W: $i] :
! [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mall) ).
thf(mand,definition,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(mexists,definition,
( mexists
= ( ^ [P: individuals > $i > $o,W: $i] :
? [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists) ).
thf(mfalse,definition,
( mfalse
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(miff,definition,
( miff
= ( ^ [U: $i > $o,V: $i > $o] : ( mand @ ( mimpl @ U @ V ) @ ( mimpl @ V @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',miff) ).
thf(mimpl,definition,
( mimpl
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimpl) ).
thf(minvalid,definition,
( minvalid
= ( ^ [P: $i > $o] :
! [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mtrue,definition,
( mtrue
= ( ^ [X: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [P: $i > $o] :
! [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox2/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/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(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(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(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,axiom,
( ( transitive @ r )
& ( upwards_well_founded @ r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upwf_trans) ).
thf(2,conjecture,
! [X: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k4) ).
thf(3,negated_conjecture,
( ( ! [X: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( mvalid @ ( mimpl @ ( mbox @ r @ sK1_X ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ sK1_X ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ~ ( mvalid @ ( mimpl @ ( mbox @ r @ sK1_X ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ sK1_X ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( ( transitive @ r )
& ( upwards_well_founded @ r ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(7,plain,
( ( ~ ( mvalid @ ( mimpl @ ( mbox @ r @ sK1_X ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ sK1_X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( r @ SX0 @ SX1 )
| ~ ( r @ SX1 @ SX2 ) )
| ( r @ SX0 @ SX2 ) )
| ~ ! [SX0: $i > $o,SX1: $i] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( r @ SX2 @ SX2 )
| ~ ( SX0 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,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(9,plain,
( ( ~ ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( sK1_X @ SX1 ) )
| ! [SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( r @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( r @ SX2 @ SX3 )
| ( sK1_X @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,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(10,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( r @ SX0 @ SX1 )
| ~ ( r @ SX1 @ SX2 ) )
| ( r @ SX0 @ SX2 ) )
| ~ ! [SX0: $i > $o,SX1: $i] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( r @ SX2 @ SX2 )
| ~ ( SX0 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( sK1_X @ SX1 ) )
| ! [SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( r @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( r @ SX2 @ SX3 )
| ( sK1_X @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( r @ SX0 @ SX1 )
| ~ ( r @ SX1 @ SX2 ) )
| ( r @ SX0 @ SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ! [SX0: $i > $o,SX1: $i] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( r @ SX2 @ SX2 )
| ~ ( SX0 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ! [SY0: $i] :
( ~ ( r @ sK2_SX0 @ SY0 )
| ( sK1_X @ SY0 ) )
| ! [SY1: $i] :
( ~ ( r @ sK2_SX0 @ SY1 )
| ! [SX2: $i] :
( ~ ( r @ SY1 @ SX2 )
| ! [SX3: $i] :
( ~ ( r @ SX2 @ SX3 )
| ( sK1_X @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(15,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( r @ SX0 @ SX1 )
| ~ ( r @ SX1 @ SX2 ) )
| ( r @ SX0 @ SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( r @ SX2 @ SX2 )
| ~ ( SX0 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ! [SY0: $i] :
( ~ ( r @ sK2_SX0 @ SY0 )
| ( sK1_X @ SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ! [SY1: $i] :
( ~ ( r @ sK2_SX0 @ SY1 )
| ! [SX2: $i] :
( ~ ( r @ SY1 @ SX2 )
| ! [SX3: $i] :
( ~ ( r @ SX2 @ SX3 )
| ( sK1_X @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(19,plain,
! [SV1: $i] :
( ( ! [SY4: $i,SY5: $i] :
( ~ ~ ( ~ ( r @ SV1 @ SY4 )
| ~ ( r @ SY4 @ SY5 ) )
| ( r @ SV1 @ SY5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV2: $i > $o] :
( ( ! [SY6: $i] :
( ~ ( SV2 @ SY6 )
| ~ ! [SY7: $i] :
~ ~ ( ~ ( SV2 @ SY7 )
| ~ ! [SY8: $i] :
( ~ ( r @ SY7 @ SY7 )
| ~ ( SV2 @ SY8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ! [SY0: $i] :
( ~ ( r @ sK2_SX0 @ SY0 )
| ( sK1_X @ SY0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( ~ ( r @ sK2_SX0 @ sK3_SY1 )
| ! [SY9: $i] :
( ~ ( r @ sK3_SY1 @ SY9 )
| ! [SX3: $i] :
( ~ ( r @ SY9 @ SX3 )
| ( sK1_X @ SX3 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(23,plain,
! [SV3: $i,SV1: $i] :
( ( ! [SY11: $i] :
( ~ ~ ( ~ ( r @ SV1 @ SV3 )
| ~ ( r @ SV3 @ SY11 ) )
| ( r @ SV1 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ~ ( SV2 @ SV4 )
| ~ ! [SY7: $i] :
~ ~ ( ~ ( SV2 @ SY7 )
| ~ ! [SY8: $i] :
( ~ ( r @ SY7 @ SY7 )
| ~ ( SV2 @ SY8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV5: $i] :
( ( ~ ( r @ sK2_SX0 @ SV5 )
| ( sK1_X @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ( r @ sK2_SX0 @ sK3_SY1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ! [SY9: $i] :
( ~ ( r @ sK3_SY1 @ SY9 )
| ! [SX3: $i] :
( ~ ( r @ SY9 @ SX3 )
| ( sK1_X @ SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(28,plain,
! [SV6: $i,SV3: $i,SV1: $i] :
( ( ~ ~ ( ~ ( r @ SV1 @ SV3 )
| ~ ( r @ SV3 @ SV6 ) )
| ( r @ SV1 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( ~ ( SV2 @ SV4 ) )
= $true )
| ( ( ~ ! [SY7: $i] :
~ ~ ( ~ ( SV2 @ SY7 )
| ~ ! [SY8: $i] :
( ~ ( r @ SY7 @ SY7 )
| ~ ( SV2 @ SY8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV5: $i] :
( ( ( ~ ( r @ sK2_SX0 @ SV5 ) )
= $true )
| ( ( sK1_X @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(31,plain,
( ( r @ sK2_SX0 @ sK3_SY1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(32,plain,
( ( ~ ( r @ sK3_SY1 @ sK4_SY9 )
| ! [SY14: $i] :
( ~ ( r @ sK4_SY9 @ SY14 )
| ( sK1_X @ SY14 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(33,plain,
! [SV6: $i,SV3: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( r @ SV1 @ SV3 )
| ~ ( r @ SV3 @ SV6 ) ) )
= $true )
| ( ( r @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( SV2 @ SV4 )
= $false )
| ( ( ~ ! [SY7: $i] :
~ ~ ( ~ ( SV2 @ SY7 )
| ~ ! [SY8: $i] :
( ~ ( r @ SY7 @ SY7 )
| ~ ( SV2 @ SY8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(35,plain,
! [SV5: $i] :
( ( ( r @ sK2_SX0 @ SV5 )
= $false )
| ( ( sK1_X @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(36,plain,
( ( ~ ( r @ sK3_SY1 @ sK4_SY9 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(37,plain,
( ( ! [SY14: $i] :
( ~ ( r @ sK4_SY9 @ SY14 )
| ( sK1_X @ SY14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(38,plain,
! [SV6: $i,SV3: $i,SV1: $i] :
( ( ( ~ ( ~ ( r @ SV1 @ SV3 )
| ~ ( r @ SV3 @ SV6 ) ) )
= $false )
| ( ( r @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( ! [SY7: $i] :
~ ~ ( ~ ( SV2 @ SY7 )
| ~ ! [SY8: $i] :
( ~ ( r @ SY7 @ SY7 )
| ~ ( SV2 @ SY8 ) ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(40,plain,
( ( r @ sK3_SY1 @ sK4_SY9 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(41,plain,
( ( ~ ( r @ sK4_SY9 @ sK5_SY14 )
| ( sK1_X @ sK5_SY14 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(42,plain,
! [SV6: $i,SV3: $i,SV1: $i] :
( ( ( ~ ( r @ SV1 @ SV3 )
| ~ ( r @ SV3 @ SV6 ) )
= $true )
| ( ( r @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( ~ ~ ( ~ ( SV2 @ ( sK6_SY7 @ SV4 @ SV2 ) )
| ~ ! [SY15: $i] :
( ~ ( r @ ( sK6_SY7 @ SV4 @ SV2 ) @ ( sK6_SY7 @ SV4 @ SV2 ) )
| ~ ( SV2 @ SY15 ) ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(44,plain,
( ( ~ ( r @ sK4_SY9 @ sK5_SY14 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(45,plain,
( ( sK1_X @ sK5_SY14 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV6: $i,SV3: $i,SV1: $i] :
( ( ( ~ ( r @ SV1 @ SV3 ) )
= $true )
| ( ( ~ ( r @ SV3 @ SV6 ) )
= $true )
| ( ( r @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( ~ ( ~ ( SV2 @ ( sK6_SY7 @ SV4 @ SV2 ) )
| ~ ! [SY15: $i] :
( ~ ( r @ ( sK6_SY7 @ SV4 @ SV2 ) @ ( sK6_SY7 @ SV4 @ SV2 ) )
| ~ ( SV2 @ SY15 ) ) ) )
= $true )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(48,plain,
( ( r @ sK4_SY9 @ sK5_SY14 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV6: $i,SV3: $i,SV1: $i] :
( ( ( r @ SV1 @ SV3 )
= $false )
| ( ( ~ ( r @ SV3 @ SV6 ) )
= $true )
| ( ( r @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( sK6_SY7 @ SV4 @ SV2 ) )
| ~ ! [SY15: $i] :
( ~ ( r @ ( sK6_SY7 @ SV4 @ SV2 ) @ ( sK6_SY7 @ SV4 @ SV2 ) )
| ~ ( SV2 @ SY15 ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV1: $i,SV6: $i,SV3: $i] :
( ( ( r @ SV3 @ SV6 )
= $false )
| ( ( r @ SV1 @ SV3 )
= $false )
| ( ( r @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( sK6_SY7 @ SV4 @ SV2 ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(53,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ( ~ ! [SY15: $i] :
( ~ ( r @ ( sK6_SY7 @ SV4 @ SV2 ) @ ( sK6_SY7 @ SV4 @ SV2 ) )
| ~ ( SV2 @ SY15 ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(54,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( SV2 @ ( sK6_SY7 @ SV4 @ SV2 ) )
= $true )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(55,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ( ! [SY15: $i] :
( ~ ( r @ ( sK6_SY7 @ SV4 @ SV2 ) @ ( sK6_SY7 @ SV4 @ SV2 ) )
| ~ ( SV2 @ SY15 ) ) )
= $true )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV7: $i,SV2: $i > $o,SV4: $i] :
( ( ( ~ ( r @ ( sK6_SY7 @ SV4 @ SV2 ) @ ( sK6_SY7 @ SV4 @ SV2 ) )
| ~ ( SV2 @ SV7 ) )
= $true )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(57,plain,
! [SV7: $i,SV2: $i > $o,SV4: $i] :
( ( ( ~ ( r @ ( sK6_SY7 @ SV4 @ SV2 ) @ ( sK6_SY7 @ SV4 @ SV2 ) ) )
= $true )
| ( ( ~ ( SV2 @ SV7 ) )
= $true )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(58,plain,
! [SV7: $i,SV2: $i > $o,SV4: $i] :
( ( ( r @ ( sK6_SY7 @ SV4 @ SV2 ) @ ( sK6_SY7 @ SV4 @ SV2 ) )
= $false )
| ( ( ~ ( SV2 @ SV7 ) )
= $true )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(59,plain,
! [SV4: $i,SV7: $i,SV2: $i > $o] :
( ( ( SV2 @ SV7 )
= $false )
| ( ( r @ ( sK6_SY7 @ SV4 @ SV2 ) @ ( sK6_SY7 @ SV4 @ SV2 ) )
= $false )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(60,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,59,54,51,48,45,40,35]) ).
thf(61,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL626^1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.12/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jul 4 22:35:12 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36
% 0.14/0.36 No.of.Axioms: 1
% 0.14/0.36
% 0.14/0.36 Length.of.Defs: 6087
% 0.14/0.36
% 0.14/0.36 Contains.Choice.Funs: false
% 0.14/0.37 (rf:0,axioms:1,ps:3,u:6,ude:false,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.21/0.45
% 0.21/0.45 ********************************
% 0.21/0.45 * All subproblems solved! *
% 0.21/0.45 ********************************
% 0.21/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:false,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:60,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.45
% 0.21/0.45 %**** Beginning of derivation protocol ****
% 0.21/0.45 % SZS output start CNFRefutation
% See solution above
% 0.21/0.45
% 0.21/0.45 %**** End of derivation protocol ****
% 0.21/0.45 %**** no. of clauses in derivation: 61 ****
% 0.21/0.45 %**** clause counter: 60 ****
% 0.21/0.45
% 0.21/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:false,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:60,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------