%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL619^1 : 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 : n003.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 10:29:31 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 17
% Syntax : Number of formulae : 84 ( 57 unt; 0 typ; 15 def)
% Number of atoms : 408 ( 122 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 989 ( 218 ~; 161 |; 12 &; 570 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 119 ( 119 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 6 con; 0-3 aty)
% Number of variables : 232 ( 28 ^; 200 !; 4 ?; 232 :)
% 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_SY0,type,
sK1_SY0: $i > $i > $o ).
thf(tp_sK2_SY108,type,
sK2_SY108: $i > $o ).
thf(tp_sK3_SY115,type,
sK3_SY115: $i > $o ).
thf(tp_sK4_SY121,type,
sK4_SY121: $i ).
thf(tp_sK5_SY128,type,
sK5_SY128: $i ).
thf(tp_sK6_SY130,type,
sK6_SY130: $i ).
thf(tp_sK7_SY99,type,
sK7_SY99: $i > ( $i > $o ) > ( $i > $i > $o ) > $i ).
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(1,axiom,
! [R: $i > $i > $o,X: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ R @ X ) @ ( mbox @ R @ ( mbox @ R @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k4) ).
thf(2,conjecture,
! [R: $i > $i > $o,X: $i > $o,Y: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ R @ ( mimpl @ X @ Y ) ) @ ( mimpl @ ( mbox @ R @ X ) @ ( mbox @ R @ ( mbox @ R @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(3,negated_conjecture,
( ( ! [R: $i > $i > $o,X: $i > $o,Y: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ R @ ( mimpl @ X @ Y ) ) @ ( mimpl @ ( mbox @ R @ X ) @ ( mbox @ R @ ( mbox @ R @ Y ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ! [SY0: $i > $i > $o,SY1: $i > $o,SY2: $i > $o,SY55: $i] :
( ~ ! [SY56: $i] :
( ( SY0 @ SY55 @ SY56 )
=> ( ~ ( SY1 @ SY56 )
| ( SY2 @ SY56 ) ) )
| ~ ! [SY57: $i] :
( ( SY0 @ SY55 @ SY57 )
=> ( SY1 @ SY57 ) )
| ! [SY58: $i] :
( ( SY0 @ SY55 @ SY58 )
=> ! [SY45: $i] :
( ( SY0 @ SY58 @ SY45 )
=> ( SY2 @ SY45 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(5,plain,
( ( ! [SY68: $i > $i > $o,SY69: $i > $o,SY98: $i] :
( ~ ! [SY99: $i] :
( ( SY68 @ SY98 @ SY99 )
=> ( SY69 @ SY99 ) )
| ! [SY100: $i] :
( ( SY68 @ SY98 @ SY100 )
=> ! [SY93: $i] :
( ( SY68 @ SY100 @ SY93 )
=> ( SY69 @ SY93 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(6,plain,
( ( ! [SY108: $i > $o,SY109: $i > $o,SY110: $i] :
( ~ ! [SY111: $i] :
( ( sK1_SY0 @ SY110 @ SY111 )
=> ( ~ ( SY108 @ SY111 )
| ( SY109 @ SY111 ) ) )
| ~ ! [SY112: $i] :
( ( sK1_SY0 @ SY110 @ SY112 )
=> ( SY108 @ SY112 ) )
| ! [SY113: $i] :
( ( sK1_SY0 @ SY110 @ SY113 )
=> ! [SY114: $i] :
( ( sK1_SY0 @ SY113 @ SY114 )
=> ( SY109 @ SY114 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(7,plain,
( ( ! [SY115: $i > $o,SY116: $i] :
( ~ ! [SY117: $i] :
( ( sK1_SY0 @ SY116 @ SY117 )
=> ( ~ ( sK2_SY108 @ SY117 )
| ( SY115 @ SY117 ) ) )
| ~ ! [SY118: $i] :
( ( sK1_SY0 @ SY116 @ SY118 )
=> ( sK2_SY108 @ SY118 ) )
| ! [SY113: $i] :
( ( sK1_SY0 @ SY116 @ SY113 )
=> ! [SY114: $i] :
( ( sK1_SY0 @ SY113 @ SY114 )
=> ( SY115 @ SY114 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY121: $i] :
( ~ ! [SY122: $i] :
( ( sK1_SY0 @ SY121 @ SY122 )
=> ( ~ ( sK2_SY108 @ SY122 )
| ( sK3_SY115 @ SY122 ) ) )
| ~ ! [SY118: $i] :
( ( sK1_SY0 @ SY121 @ SY118 )
=> ( sK2_SY108 @ SY118 ) )
| ! [SY124: $i] :
( ( sK1_SY0 @ SY121 @ SY124 )
=> ! [SY125: $i] :
( ( sK1_SY0 @ SY124 @ SY125 )
=> ( sK3_SY115 @ SY125 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(9,plain,
( ( ~ ! [SY126: $i] :
( ( sK1_SY0 @ sK4_SY121 @ SY126 )
=> ( ~ ( sK2_SY108 @ SY126 )
| ( sK3_SY115 @ SY126 ) ) )
| ~ ! [SY127: $i] :
( ( sK1_SY0 @ sK4_SY121 @ SY127 )
=> ( sK2_SY108 @ SY127 ) )
| ! [SY128: $i] :
( ( sK1_SY0 @ sK4_SY121 @ SY128 )
=> ! [SY125: $i] :
( ( sK1_SY0 @ SY128 @ SY125 )
=> ( sK3_SY115 @ SY125 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(10,plain,
( ( ~ ( ~ ! [SY126: $i] :
( ( sK1_SY0 @ sK4_SY121 @ SY126 )
=> ( ~ ( sK2_SY108 @ SY126 )
| ( sK3_SY115 @ SY126 ) ) )
| ~ ! [SY127: $i] :
( ( sK1_SY0 @ sK4_SY121 @ SY127 )
=> ( sK2_SY108 @ SY127 ) )
| ! [SY128: $i] :
( ( sK1_SY0 @ sK4_SY121 @ SY128 )
=> ! [SY125: $i] :
( ( sK1_SY0 @ SY128 @ SY125 )
=> ( sK3_SY115 @ SY125 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [SY126: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SY126 )
| ~ ( sK2_SY108 @ SY126 )
| ( sK3_SY115 @ SY126 ) )
& ! [SY127: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SY127 )
| ( sK2_SY108 @ SY127 ) )
& ( sK1_SY0 @ sK4_SY121 @ sK5_SY128 )
& ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
& ~ ( sK3_SY115 @ sK6_SY130 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(12,plain,
( ( ! [SY68: $i > $i > $o,SY69: $i > $o,SY98: $i] :
( ( ( SY68 @ SY98 @ ( sK7_SY99 @ SY98 @ SY69 @ SY68 ) )
& ~ ( SY69 @ ( sK7_SY99 @ SY98 @ SY69 @ SY68 ) ) )
| ! [SY100: $i] :
( ~ ( SY68 @ SY98 @ SY100 )
| ! [SY93: $i] :
( ~ ( SY68 @ SY100 @ SY93 )
| ( SY69 @ SY93 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(13,plain,
( ( ! [SY68: $i > $i > $o,SY69: $i > $o,SY98: $i] :
( ( ( SY68 @ SY98 @ ( sK7_SY99 @ SY98 @ SY69 @ SY68 ) )
& ~ ( SY69 @ ( sK7_SY99 @ SY98 @ SY69 @ SY68 ) ) )
| ! [SY100: $i] :
( ~ ( SY68 @ SY98 @ SY100 )
| ! [SY93: $i] :
( ~ ( SY68 @ SY100 @ SY93 )
| ( SY69 @ SY93 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [SY126: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SY126 )
| ~ ( sK2_SY108 @ SY126 )
| ( sK3_SY115 @ SY126 ) )
& ! [SY127: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SY127 )
| ( sK2_SY108 @ SY127 ) )
& ( sK1_SY0 @ sK4_SY121 @ sK5_SY128 )
& ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
& ~ ( sK3_SY115 @ sK6_SY130 ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SX0 )
| ~ ( sK2_SY108 @ SX0 )
| ( sK3_SY115 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SX0 )
| ( sK2_SY108 @ SX0 ) )
| ~ ~ ( ~ ( sK1_SY0 @ sK4_SY121 @ sK5_SY128 )
| ~ ~ ( ~ ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
| ~ ~ ( sK3_SY115 @ sK6_SY130 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(16,plain,
( ( ! [SX0: $i > $i > $o,SX1: $i > $o,SX2: $i] :
( ~ ( ~ ( SX0 @ SX2 @ ( sK7_SY99 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK7_SY99 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( SX0 @ SX2 @ SX3 )
| ! [SX4: $i] :
( ~ ( SX0 @ SX3 @ SX4 )
| ( SX1 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(17,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SX0 )
| ~ ( sK2_SY108 @ SX0 )
| ( sK3_SY115 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SX0 )
| ( sK2_SY108 @ SX0 ) )
| ~ ~ ( ~ ( sK1_SY0 @ sK4_SY121 @ sK5_SY128 )
| ~ ~ ( ~ ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
| ~ ~ ( sK3_SY115 @ sK6_SY130 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: $i > $i > $o] :
( ( ! [SY131: $i > $o,SY132: $i] :
( ~ ( ~ ( SV1 @ SY132 @ ( sK7_SY99 @ SY132 @ SY131 @ SV1 ) )
| ~ ~ ( SY131 @ ( sK7_SY99 @ SY132 @ SY131 @ SV1 ) ) )
| ! [SY133: $i] :
( ~ ( SV1 @ SY132 @ SY133 )
| ! [SY134: $i] :
( ~ ( SV1 @ SY133 @ SY134 )
| ( SY131 @ SY134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SX0 )
| ~ ( sK2_SY108 @ SX0 )
| ( sK3_SY115 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SX0 )
| ( sK2_SY108 @ SX0 ) )
| ~ ~ ( ~ ( sK1_SY0 @ sK4_SY121 @ sK5_SY128 )
| ~ ~ ( ~ ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
| ~ ~ ( sK3_SY115 @ sK6_SY130 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: $i > $o,SV1: $i > $i > $o] :
( ( ! [SY135: $i] :
( ~ ( ~ ( SV1 @ SY135 @ ( sK7_SY99 @ SY135 @ SV2 @ SV1 ) )
| ~ ~ ( SV2 @ ( sK7_SY99 @ SY135 @ SV2 @ SV1 ) ) )
| ! [SY136: $i] :
( ~ ( SV1 @ SY135 @ SY136 )
| ! [SY137: $i] :
( ~ ( SV1 @ SY136 @ SY137 )
| ( SV2 @ SY137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SX0 )
| ~ ( sK2_SY108 @ SX0 )
| ( sK3_SY115 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SX0 )
| ( sK2_SY108 @ SX0 ) )
| ~ ~ ( ~ ( sK1_SY0 @ sK4_SY121 @ sK5_SY128 )
| ~ ~ ( ~ ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
| ~ ~ ( sK3_SY115 @ sK6_SY130 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: $i > $o,SV3: $i,SV1: $i > $i > $o] :
( ( ~ ( ~ ( SV1 @ SV3 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
| ~ ~ ( SV2 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) ) )
| ! [SY138: $i] :
( ~ ( SV1 @ SV3 @ SY138 )
| ! [SY137: $i] :
( ~ ( SV1 @ SY138 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV4: $i] :
( ( ~ ( sK1_SY0 @ sK4_SY121 @ SV4 )
| ~ ( sK2_SY108 @ SV4 )
| ( sK3_SY115 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SX0 )
| ( sK2_SY108 @ SX0 ) )
| ~ ~ ( ~ ( sK1_SY0 @ sK4_SY121 @ sK5_SY128 )
| ~ ~ ( ~ ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
| ~ ~ ( sK3_SY115 @ sK6_SY130 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV2: $i > $o,SV3: $i,SV1: $i > $i > $o] :
( ( ( ~ ( ~ ( SV1 @ SV3 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
| ~ ~ ( SV2 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) ) ) )
= $true )
| ( ( ! [SY138: $i] :
( ~ ( SV1 @ SV3 @ SY138 )
| ! [SY137: $i] :
( ~ ( SV1 @ SY138 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV4: $i] :
( ( ( ~ ( sK1_SY0 @ sK4_SY121 @ SV4 ) )
= $true )
| ( ( ~ ( sK2_SY108 @ SV4 )
| ( sK3_SY115 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SX0 )
| ( sK2_SY108 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ~ ( ~ ( sK1_SY0 @ sK4_SY121 @ sK5_SY128 )
| ~ ~ ( ~ ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
| ~ ~ ( sK3_SY115 @ sK6_SY130 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
! [SV2: $i > $o,SV3: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ SV3 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
| ~ ~ ( SV2 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) ) )
= $false )
| ( ( ! [SY138: $i] :
( ~ ( SV1 @ SV3 @ SY138 )
| ! [SY137: $i] :
( ~ ( SV1 @ SY138 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV4: $i] :
( ( ( sK1_SY0 @ sK4_SY121 @ SV4 )
= $false )
| ( ( ~ ( sK2_SY108 @ SV4 )
| ( sK3_SY115 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY121 @ SX0 )
| ( sK2_SY108 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ( ~ ( sK1_SY0 @ sK4_SY121 @ sK5_SY128 )
| ~ ~ ( ~ ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
| ~ ~ ( sK3_SY115 @ sK6_SY130 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV2: $i > $o,SV3: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ SV3 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) ) )
= $false )
| ( ( ! [SY138: $i] :
( ~ ( SV1 @ SV3 @ SY138 )
| ! [SY137: $i] :
( ~ ( SV1 @ SY138 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: $i > $i > $o,SV3: $i,SV2: $i > $o] :
( ( ( ~ ~ ( SV2 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) ) )
= $false )
| ( ( ! [SY138: $i] :
( ~ ( SV1 @ SV3 @ SY138 )
| ! [SY137: $i] :
( ~ ( SV1 @ SY138 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(37,plain,
! [SV4: $i] :
( ( ( ~ ( sK2_SY108 @ SV4 ) )
= $true )
| ( ( sK3_SY115 @ SV4 )
= $true )
| ( ( sK1_SY0 @ sK4_SY121 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV5: $i] :
( ( ~ ( sK1_SY0 @ sK4_SY121 @ SV5 )
| ( sK2_SY108 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(39,plain,
( ( ~ ( sK1_SY0 @ sK4_SY121 @ sK5_SY128 )
| ~ ~ ( ~ ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
| ~ ~ ( sK3_SY115 @ sK6_SY130 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV2: $i > $o,SV3: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ SV3 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $true )
| ( ( ! [SY138: $i] :
( ~ ( SV1 @ SV3 @ SY138 )
| ! [SY137: $i] :
( ~ ( SV1 @ SY138 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV1: $i > $i > $o,SV3: $i,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) ) )
= $true )
| ( ( ! [SY138: $i] :
( ~ ( SV1 @ SV3 @ SY138 )
| ! [SY137: $i] :
( ~ ( SV1 @ SY138 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(42,plain,
! [SV4: $i] :
( ( ( sK2_SY108 @ SV4 )
= $false )
| ( ( sK3_SY115 @ SV4 )
= $true )
| ( ( sK1_SY0 @ sK4_SY121 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV5: $i] :
( ( ( ~ ( sK1_SY0 @ sK4_SY121 @ SV5 ) )
= $true )
| ( ( sK2_SY108 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(44,plain,
( ( ~ ( sK1_SY0 @ sK4_SY121 @ sK5_SY128 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(45,plain,
( ( ~ ~ ( ~ ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
| ~ ~ ( sK3_SY115 @ sK6_SY130 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(46,plain,
! [SV2: $i > $o,SV6: $i,SV3: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ SV3 @ SV6 )
| ! [SY140: $i] :
( ~ ( SV1 @ SV6 @ SY140 )
| ( SV2 @ SY140 ) ) )
= $true )
| ( ( SV1 @ SV3 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV1: $i > $i > $o,SV3: $i,SV2: $i > $o] :
( ( ( SV2 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $false )
| ( ( ! [SY138: $i] :
( ~ ( SV1 @ SV3 @ SY138 )
| ! [SY137: $i] :
( ~ ( SV1 @ SY138 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV5: $i] :
( ( ( sK1_SY0 @ sK4_SY121 @ SV5 )
= $false )
| ( ( sK2_SY108 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(49,plain,
( ( sK1_SY0 @ sK4_SY121 @ sK5_SY128 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(50,plain,
( ( ~ ( ~ ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
| ~ ~ ( sK3_SY115 @ sK6_SY130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV2: $i > $o,SV6: $i,SV3: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ SV3 @ SV6 ) )
= $true )
| ( ( ! [SY140: $i] :
( ~ ( SV1 @ SV6 @ SY140 )
| ( SV2 @ SY140 ) ) )
= $true )
| ( ( SV1 @ SV3 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV2: $i > $o,SV7: $i,SV3: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ SV3 @ SV7 )
| ! [SY141: $i] :
( ~ ( SV1 @ SV7 @ SY141 )
| ( SV2 @ SY141 ) ) )
= $true )
| ( ( SV2 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(53,plain,
( ( ~ ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
| ~ ~ ( sK3_SY115 @ sK6_SY130 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV2: $i > $o,SV6: $i,SV3: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ SV3 @ SV6 )
= $false )
| ( ( ! [SY140: $i] :
( ~ ( SV1 @ SV6 @ SY140 )
| ( SV2 @ SY140 ) ) )
= $true )
| ( ( SV1 @ SV3 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV2: $i > $o,SV7: $i,SV3: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ SV3 @ SV7 ) )
= $true )
| ( ( ! [SY141: $i] :
( ~ ( SV1 @ SV7 @ SY141 )
| ( SV2 @ SY141 ) ) )
= $true )
| ( ( SV2 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(56,plain,
( ( ~ ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(57,plain,
( ( ~ ~ ( sK3_SY115 @ sK6_SY130 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(58,plain,
! [SV3: $i,SV2: $i > $o,SV8: $i,SV6: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ SV6 @ SV8 )
| ( SV2 @ SV8 ) )
= $true )
| ( ( SV1 @ SV3 @ SV6 )
= $false )
| ( ( SV1 @ SV3 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV2: $i > $o,SV7: $i,SV3: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ SV3 @ SV7 )
= $false )
| ( ( ! [SY141: $i] :
( ~ ( SV1 @ SV7 @ SY141 )
| ( SV2 @ SY141 ) ) )
= $true )
| ( ( SV2 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(60,plain,
( ( sK1_SY0 @ sK5_SY128 @ sK6_SY130 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(61,plain,
( ( ~ ( sK3_SY115 @ sK6_SY130 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV3: $i,SV2: $i > $o,SV8: $i,SV6: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ SV6 @ SV8 ) )
= $true )
| ( ( SV2 @ SV8 )
= $true )
| ( ( SV1 @ SV3 @ SV6 )
= $false )
| ( ( SV1 @ SV3 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV3: $i,SV2: $i > $o,SV9: $i,SV7: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ SV7 @ SV9 )
| ( SV2 @ SV9 ) )
= $true )
| ( ( SV1 @ SV3 @ SV7 )
= $false )
| ( ( SV2 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(64,plain,
( ( sK3_SY115 @ sK6_SY130 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV3: $i,SV2: $i > $o,SV8: $i,SV6: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ SV6 @ SV8 )
= $false )
| ( ( SV2 @ SV8 )
= $true )
| ( ( SV1 @ SV3 @ SV6 )
= $false )
| ( ( SV1 @ SV3 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV3: $i,SV2: $i > $o,SV9: $i,SV7: $i,SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ SV7 @ SV9 ) )
= $true )
| ( ( SV2 @ SV9 )
= $true )
| ( ( SV1 @ SV3 @ SV7 )
= $false )
| ( ( SV2 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV3: $i,SV2: $i > $o,SV9: $i,SV7: $i,SV1: $i > $i > $o] :
( ( ( SV1 @ SV7 @ SV9 )
= $false )
| ( ( SV2 @ SV9 )
= $true )
| ( ( SV1 @ SV3 @ SV7 )
= $false )
| ( ( SV2 @ ( sK7_SY99 @ SV3 @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(68,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[42,67,65,64,60,49,48]) ).
thf(69,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL619^1 : 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
% 0.07/0.19 % Computer : n003.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 12:26:39 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.25
% 0.07/0.25 No.of.Axioms: 1
% 0.07/0.25
% 0.07/0.25 Length.of.Defs: 2215
% 0.07/0.25
% 0.07/0.25 Contains.Choice.Funs: false
% 0.07/0.25 ...
% 0.07/0.25
% 0.07/0.25 ********************************
% 0.07/0.25 * All subproblems solved! *
% 0.07/0.25 ********************************
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:68,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.07/0.25
% 0.07/0.25 %**** Beginning of derivation protocol ****
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25
% 0.07/0.25 %**** End of derivation protocol ****
% 0.07/0.25 %**** no. of clauses in derivation: 69 ****
% 0.07/0.25 %**** clause counter: 68 ****
% 0.07/0.25
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:68,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------