%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL594^1 : 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 : n011.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 10:29:28 AM UTC 2026
% Result : Theorem 0.57s 0.31s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 16
% Syntax : Number of formulae : 65 ( 38 unt; 0 typ; 15 def)
% Number of atoms : 305 ( 116 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 607 ( 101 ~; 55 |; 4 &; 444 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 115 ( 115 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 3 con; 0-4 aty)
% Number of variables : 222 ( 130 ^; 84 !; 8 ?; 222 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_individuals,type,
individuals: $tType ).
thf(tp_current_world,type,
current_world: $i ).
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_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_sK1_SY1,type,
sK1_SY1: ( $i > $i > $o ) > $i > $o ).
thf(tp_sK2_SY23,type,
sK2_SY23: ( $i > $i > $o ) > $i ).
thf(tp_sK3_E,type,
sK3_E: $i > ( $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK4_E,type,
sK4_E: $i > ( $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK5_E,type,
sK5_E: $i > ( $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK6_E,type,
sK6_E: $i > ( $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $o ) > $i ).
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',individuals_decl) ).
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(1,conjecture,
? [R: $i > $i > $o] :
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ R @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( ? [R: $i > $i > $o] :
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ R @ A ) @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [SY0: $i > $i > $o] :
! [SY1: $i > $o,SY17: $i] :
( ~ ! [SY18: $i] :
( ( SY0 @ SY17 @ SY18 )
=> ( SY1 @ SY18 ) )
| ( SY1 @ SY17 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(4,plain,
( ( ~ ? [SY0: $i > $i > $o] :
! [SY1: $i > $o,SY17: $i] :
( ~ ! [SY18: $i] :
( ( SY0 @ SY17 @ SY18 )
=> ( SY1 @ SY18 ) )
| ( SY1 @ SY17 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i > $i > $o] :
( ! [SY25: $i] :
( ~ ( SY0 @ ( sK2_SY23 @ SY0 ) @ SY25 )
| ( sK1_SY1 @ SY0 @ SY25 ) )
& ~ ( sK1_SY1 @ SY0 @ ( sK2_SY23 @ SY0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY0: $i > $i > $o] :
( ! [SY25: $i] :
( ~ ( SY0 @ ( sK2_SY23 @ SY0 ) @ SY25 )
| ( sK1_SY1 @ SY0 @ SY25 ) )
& ~ ( sK1_SY1 @ SY0 @ ( sK2_SY23 @ SY0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: $i > $i > $o] :
~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ ( sK2_SY23 @ SX0 ) @ SX1 )
| ( sK1_SY1 @ SX0 @ SX1 ) )
| ~ ~ ( sK1_SY1 @ SX0 @ ( sK2_SY23 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(8,plain,
! [SV1: $i > $i > $o] :
( ( ~ ( ~ ! [SY26: $i] :
( ~ ( SV1 @ ( sK2_SY23 @ SV1 ) @ SY26 )
| ( sK1_SY1 @ SV1 @ SY26 ) )
| ~ ~ ( sK1_SY1 @ SV1 @ ( sK2_SY23 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: $i > $i > $o] :
( ( ~ ! [SY26: $i] :
( ~ ( SV1 @ ( sK2_SY23 @ SV1 ) @ SY26 )
| ( sK1_SY1 @ SV1 @ SY26 ) )
| ~ ~ ( sK1_SY1 @ SV1 @ ( sK2_SY23 @ SV1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i > $i > $o] :
( ( ~ ! [SY26: $i] :
( ~ ( SV1 @ ( sK2_SY23 @ SV1 ) @ SY26 )
| ( sK1_SY1 @ SV1 @ SY26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: $i > $i > $o] :
( ( ~ ~ ( sK1_SY1 @ SV1 @ ( sK2_SY23 @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i > $i > $o] :
( ( ! [SY26: $i] :
( ~ ( SV1 @ ( sK2_SY23 @ SV1 ) @ SY26 )
| ( sK1_SY1 @ SV1 @ SY26 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: $i > $i > $o] :
( ( ~ ( sK1_SY1 @ SV1 @ ( sK2_SY23 @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i > $i > $o] :
( ( ~ ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
| ( sK1_SY1 @ SV1 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i > $i > $o] :
( ( sK1_SY1 @ SV1 @ ( sK2_SY23 @ SV1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV2: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 ) )
= $true )
| ( ( sK1_SY1 @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV2: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false )
| ( ( sK1_SY1 @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(18,plain,
( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] : $true
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] : $true ) )
= $false ),
inference(prim_subst,[status(thm)],[15:[bind(SV1,$thf( ^ [SV10: $i] : ^ [SV11: $i] : $true ))]]) ).
thf(19,plain,
( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] : $false
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] : $false ) )
= $false ),
inference(prim_subst,[status(thm)],[15:[bind(SV1,$thf( ^ [SV8: $i] : ^ [SV9: $i] : $false ))]]) ).
thf(20,plain,
! [SV7: $i > $i > $o] :
( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] :
~ ( SV7 @ SX0 @ SX1 )
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( SV7 @ SX0 @ SX1 ) ) )
= $false ),
inference(prim_subst,[status(thm)],[15:[bind(SV1,$thf( ^ [SV5: $i] : ^ [SV6: $i] : ~ ( SV7 @ SV5 @ SV6 ) ))]]) ).
thf(21,plain,
( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 )
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $false ),
inference(prim_subst,[status(thm)],[15:[bind(SV1,$thf( ^ [SY27: $i] : ^ [SY28: $i] : ( SY27 != SY28 ) ))]]) ).
thf(22,plain,
( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $false ),
inference(prim_subst,[status(thm)],[15:[bind(SV1,$thf( ^ [SV4: $i] : ^ [SV3: $i] : ( SV4 = SV3 ) ))]]) ).
thf(23,plain,
! [SV2: $i] :
( ( $true = $false )
| ( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] : $true
@ SV2 )
= $true ) ),
inference(prim_subst,[status(thm)],[17:[bind(SV1,$thf( ^ [SV10: $i] : ^ [SV11: $i] : $true ))]]) ).
thf(25,plain,
! [SV2: $i,SV7: $i > $i > $o] :
( ( ( ~ ( SV7
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( SV7 @ SX0 @ SX1 ) )
@ SV2 ) )
= $false )
| ( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] :
~ ( SV7 @ SX0 @ SX1 )
@ SV2 )
= $true ) ),
inference(prim_subst,[status(thm)],[17:[bind(SV1,$thf( ^ [SV5: $i] : ^ [SV6: $i] : ~ ( SV7 @ SV5 @ SV6 ) ))]]) ).
thf(26,plain,
! [SV2: $i] :
( ( ( ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
!= SV2 )
= $false )
| ( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 )
@ SV2 )
= $true ) ),
inference(prim_subst,[status(thm)],[17:[bind(SV1,$thf( ^ [SY27: $i] : ^ [SY28: $i] : ( SY27 != SY28 ) ))]]) ).
thf(27,plain,
! [SV2: $i] :
( ( ( ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= SV2 )
= $false )
| ( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ SV2 )
= $true ) ),
inference(prim_subst,[status(thm)],[17:[bind(SV1,$thf( ^ [SV4: $i] : ^ [SV3: $i] : ( SV4 = SV3 ) ))]]) ).
thf(28,plain,
! [SV2: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false )
| ( ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= ( ~ ( sK1_SY1 @ SV1 @ SV2 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[17]) ).
thf(29,plain,
! [SV2: $i,SV1: $i > $i > $o] :
( ( ( ~ ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
| ~ ( sK1_SY1 @ SV1 @ SV2 ) )
| ~ ( ~ ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
| ~ ~ ( sK1_SY1 @ SV1 @ SV2 ) ) )
= $false )
| ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[28]) ).
thf(30,plain,
! [SV2: $i,SV1: $i > $i > $o] :
( ( ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= ( ~ ( sK1_SY1 @ SV1 @ SV2 ) ) )
= $false )
| ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: $i,SV1: $i > $i > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
| ~ ~ ( sK1_SY1 @ SV1 @ SV2 ) ) )
= $false )
| ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV2: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
| ~ ~ ( sK1_SY1 @ SV1 @ SV2 ) )
= $true )
| ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV2: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 ) )
= $true )
| ( ( ~ ~ ( sK1_SY1 @ SV1 @ SV2 ) )
= $true )
| ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV2: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false )
| ( ( ~ ~ ( sK1_SY1 @ SV1 @ SV2 ) )
= $true )
| ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV2: $i,SV1: $i > $i > $o] :
( ( ( ~ ( sK1_SY1 @ SV1 @ SV2 ) )
= $false )
| ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false )
| ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(40,plain,
! [SV2: $i,SV1: $i > $i > $o] :
( ( ( sK1_SY1 @ SV1 @ SV2 )
= $true )
| ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false )
| ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(41,plain,
! [SV2: $i,SV22: $i > $i > $i,SV21: $i > $i > $i > $i > $o] :
( ( ( ~ ( sK1_SY1
@ ( SV21
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) ) )
@ SV2 )
@ ( SV22
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) ) )
@ SV2 ) ) )
= $false )
| ( ( sK1_SY1
@ ( SV21
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) ) )
@ SV2 )
@ ( SV22
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) ) )
@ SV2 ) )
= $true )
| ( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] :
~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) )
@ SV2 )
= $true ) ),
inference(extuni,[status(esa)],[30:[bind(SV1,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) ) ))]]) ).
thf(44,plain,
! [SV2: $i,SV16: $i > $i > $o] :
( ( ( ~ ( SV16
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 ) )
@ SV2 ) )
= $false )
| ( ( ~ ( SV16
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 ) )
@ SV2 ) )
= $false )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 )
@ SV2 ) )
= $false ) ),
inference(extuni,[status(esa)],[30:[bind(SV1,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ~ ( SV16 @ SX0 @ SX1 ) ))]]) ).
thf(45,plain,
! [SV2: $i,SV16: $i > $i > $o] :
( ( ( SV16
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 ) )
@ SV2 )
= $true )
| ( ( ~ ( SV16
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 ) )
@ SV2 ) )
= $false )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 )
@ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV2: $i,SV22: $i > $i > $i,SV21: $i > $i > $i > $i > $o] :
( ( ( sK1_SY1
@ ( SV21
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) ) )
@ SV2 )
@ ( SV22
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) ) )
@ SV2 ) )
= $true )
| ( ( sK1_SY1
@ ( SV21
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) ) )
@ SV2 )
@ ( SV22
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) ) )
@ SV2 ) )
= $true )
| ( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] :
~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) )
@ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(49,plain,
! [SV2: $i,SV16: $i > $i > $o] :
( ( ( SV16
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 ) )
@ SV2 )
= $true )
| ( ( SV16
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 ) )
@ SV2 )
= $true )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 )
@ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV2: $i,SV16: $i > $i > $o] :
( ( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 )
@ SV2 )
= $true )
| ( ( SV16
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 ) )
@ SV2 )
= $true )
| ( ( SV16
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 ) )
@ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(53,plain,
! [SV2: $i,SV7: $i > $i > $o] :
( ( ( SV7
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( SV7 @ SX0 @ SX1 ) )
@ SV2 )
= $true )
| ( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] :
~ ( SV7 @ SX0 @ SX1 )
@ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(54,plain,
! [SV2: $i] :
( ( ( ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
= SV2 )
= $true )
| ( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 )
@ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(55,plain,
( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 )
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true ),
inference(extuni,[status(esa)],[27:[bind(SV2,$thf( sK2_SY23 @ ^ [SX0: $i] : ^ [SX1: $i] : ( SX0 = SX1 ) ))]]) ).
thf(56,plain,
! [SV2: $i,SV1: $i > $i > $o] :
( ( ( sK1_SY1 @ SV1 @ SV2 )
= $true )
| ( ( SV1 @ ( sK2_SY23 @ SV1 ) @ SV2 )
= $false ) ),
inference(sim,[status(thm)],[40]) ).
thf(57,plain,
! [SV2: $i,SV16: $i > $i > $o] :
( ( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 )
@ SV2 )
= $true )
| ( ( SV16
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( SV16 @ SX0 @ SX1 ) )
@ SV2 )
= $true ) ),
inference(sim,[status(thm)],[51]) ).
thf(58,plain,
! [SV2: $i,SV22: $i > $i > $i,SV21: $i > $i > $i > $i > $o] :
( ( ( sK1_SY1
@ ( SV21
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) ) )
@ SV2 )
@ ( SV22
@ ( sK2_SY23
@ ^ [SX0: $i,SX1: $i] :
~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) ) )
@ SV2 ) )
= $true )
| ( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] :
~ ( sK1_SY1 @ ( SV21 @ SX0 @ SX1 ) @ ( SV22 @ SX0 @ SX1 ) )
@ SV2 )
= $true ) ),
inference(sim,[status(thm)],[48]) ).
thf(59,plain,
! [SV2: $i] :
( ( sK1_SY1
@ ^ [SX0: $i,SX1: $i] : $true
@ SV2 )
= $true ),
inference(sim,[status(thm)],[23]) ).
thf(60,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,59,58,57,56,55,54,53,22,21,20,19,18,17]) ).
thf(61,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL594^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n011.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 12:24:36 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.57/0.31
% 0.57/0.31 No.of.Axioms: 0
% 0.57/0.31
% 0.57/0.31 Length.of.Defs: 2230
% 0.57/0.31
% 0.57/0.31 Contains.Choice.Funs: false
% 0.57/0.31 ..
% 0.57/0.31
% 0.57/0.31 ********************************
% 0.57/0.31 * All subproblems solved! *
% 0.57/0.31 ********************************
% 0.57/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:60,loop_count:0,foatp_calls:2,translation:fof_experiment)
% 0.57/0.31
% 0.57/0.31 %**** Beginning of derivation protocol ****
% 0.57/0.31 % SZS output start CNFRefutation
% See solution above
% 0.57/0.31
% 0.57/0.31 %**** End of derivation protocol ****
% 0.57/0.31 %**** no. of clauses in derivation: 50 ****
% 0.57/0.31 %**** clause counter: 60 ****
% 0.57/0.31
% 0.57/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:60,loop_count:0,foatp_calls:2,translation:fof_experiment)
%------------------------------------------------------------------------------