%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL958^18 : TPTP v9.3.1. Released v8.1.0.
% 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 : n008.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 10:31:09 AM UTC 2026
% Result : Theorem 0.09s 0.20s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 80 ( 41 unt; 0 typ; 10 def)
% Number of atoms : 545 ( 117 equ; 0 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 1071 ( 176 ~; 184 |; 9 &; 674 @)
% ( 1 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 3 con; 0-3 aty)
% Number of variables : 239 ( 27 ^; 204 !; 8 ?; 239 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_big_p,type,
big_p: $i > mworld > $o ).
thf(tp_big_q,type,
big_q: $i > mworld > $o ).
thf(tp_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(tp_mactual,type,
mactual: mworld ).
thf(tp_mand,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mbox,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(tp_mdia,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(tp_mequiv,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mexists_di,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(tp_mforall_di,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(tp_mimplies,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mlocal,type,
mlocal: ( mworld > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(tp_mor,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mrel,type,
mrel: mworld > mworld > $o ).
thf(tp_sK1_SY83,type,
sK1_SY83: mworld > $i ).
thf(tp_sK2_SY85,type,
sK2_SY85: $i > mworld ).
thf(tp_sK3_SY91,type,
sK3_SY91: $i > $i ).
thf(tp_sK4_SY96,type,
sK4_SY96: $i > mworld ).
thf(tp_sK5_SY101,type,
sK5_SY101: $i > mworld ).
thf(tp_sK6_SY102,type,
sK6_SY102: $i > mworld ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).
thf(mexists_di,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] :
( ( eiw_di @ X @ W )
& ( A @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(mforall_di,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] :
( ( eiw_di @ X @ W )
=> ( A @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(mimplies,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor_def) ).
thf(1,axiom,
! [W: mworld,V: mworld,X: $i] :
( ( ( eiw_di @ X @ W )
& ( mrel @ W @ V ) )
=> ( eiw_di @ X @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_cumul) ).
thf(2,axiom,
! [W: mworld] :
? [X: $i] : ( eiw_di @ X @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(3,axiom,
! [W: mworld,V: mworld] : ( mrel @ W @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
thf(4,conjecture,
( mlocal
@ ( mexists_di
@ ^ [X: $i] :
( mbox
@ ( mforall_di
@ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_p @ X ) ) @ ( mor @ ( mbox @ ( big_q @ X ) ) @ ( mbox @ ( big_p @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2137) ).
thf(5,negated_conjecture,
( ( mlocal
@ ( mexists_di
@ ^ [X: $i] :
( mbox
@ ( mforall_di
@ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_p @ X ) ) @ ( mor @ ( mbox @ ( big_q @ X ) ) @ ( mbox @ ( big_p @ Y ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ? [SY59: $i] :
( ( eiw_di @ SY59 @ mactual )
& ! [SY60: mworld] :
( ( mrel @ mactual @ SY60 )
=> ! [SY48: $i] :
( ( eiw_di @ SY48 @ SY60 )
=> ! [SY49: mworld] :
( ( mrel @ SY60 @ SY49 )
=> ( ! [SY50: mworld] :
( ( mrel @ SY49 @ SY50 )
=> ( big_p @ SY59 @ SY50 ) )
=> ( ! [SY51: mworld] :
( ( mrel @ SY49 @ SY51 )
=> ( big_q @ SY59 @ SY51 ) )
| ! [SY32: mworld] :
( ( mrel @ SY49 @ SY32 )
=> ( big_p @ SY48 @ SY32 ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(7,plain,
( ( ! [W: mworld,V: mworld,X: $i] :
( ( ( eiw_di @ X @ W )
& ( mrel @ W @ V ) )
=> ( eiw_di @ X @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(8,plain,
( ( ! [W: mworld] :
? [X: $i] : ( eiw_di @ X @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(9,plain,
( ( ! [W: mworld,V: mworld] : ( mrel @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(10,plain,
( ( ~ ? [SY59: $i] :
( ( eiw_di @ SY59 @ mactual )
& ! [SY60: mworld] :
( ( mrel @ mactual @ SY60 )
=> ! [SY48: $i] :
( ( eiw_di @ SY48 @ SY60 )
=> ! [SY49: mworld] :
( ( mrel @ SY60 @ SY49 )
=> ( ! [SY50: mworld] :
( ( mrel @ SY49 @ SY50 )
=> ( big_p @ SY59 @ SY50 ) )
=> ( ! [SY51: mworld] :
( ( mrel @ SY49 @ SY51 )
=> ( big_q @ SY59 @ SY51 ) )
| ! [SY32: mworld] :
( ( mrel @ SY49 @ SY32 )
=> ( big_p @ SY48 @ SY32 ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( ! [W: mworld,V: mworld] : ( mrel @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [W: mworld] :
? [X: $i] : ( eiw_di @ X @ W ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ! [W: mworld,V: mworld,X: $i] :
( ( ( eiw_di @ X @ W )
& ( mrel @ W @ V ) )
=> ( eiw_di @ X @ V ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ ? [SY59: $i] :
( ( eiw_di @ SY59 @ mactual )
& ! [SY60: mworld] :
( ( mrel @ mactual @ SY60 )
=> ! [SY48: $i] :
( ( eiw_di @ SY48 @ SY60 )
=> ! [SY49: mworld] :
( ( mrel @ SY60 @ SY49 )
=> ( ! [SY50: mworld] :
( ( mrel @ SY49 @ SY50 )
=> ( big_p @ SY59 @ SY50 ) )
=> ( ! [SY51: mworld] :
( ( mrel @ SY49 @ SY51 )
=> ( big_q @ SY59 @ SY51 ) )
| ! [SY32: mworld] :
( ( mrel @ SY49 @ SY32 )
=> ( big_p @ SY48 @ SY32 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( eiw_di @ SX0 @ mactual )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ mactual @ SX1 )
| ! [SX2: $i] :
( ~ ( eiw_di @ SX2 @ SX1 )
| ! [SX3: mworld] :
( ~ ( mrel @ SX1 @ SX3 )
| ~ ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_p @ SX0 @ SX4 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_q @ SX0 @ SX4 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_p @ SX2 @ SX4 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(16,plain,
( ( ! [SX0: mworld,SX1: mworld,SX2: $i] :
( ~ ~ ( ~ ( eiw_di @ SX2 @ SX0 )
| ~ ( mrel @ SX0 @ SX1 ) )
| ( eiw_di @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(17,plain,
( ( ! [SX0: mworld] :
~ ! [SX1: $i] :
~ ( eiw_di @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(18,plain,
! [SV1: mworld] :
( ( ! [SY80: mworld] : ( mrel @ SV1 @ SY80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(19,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( eiw_di @ SX0 @ mactual )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ mactual @ SX1 )
| ! [SX2: $i] :
( ~ ( eiw_di @ SX2 @ SX1 )
| ! [SX3: mworld] :
( ~ ( mrel @ SX1 @ SX3 )
| ~ ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_p @ SX0 @ SX4 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_q @ SX0 @ SX4 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_p @ SX2 @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV2: mworld] :
( ( ! [SY81: mworld,SY82: $i] :
( ~ ~ ( ~ ( eiw_di @ SY82 @ SV2 )
| ~ ( mrel @ SV2 @ SY81 ) )
| ( eiw_di @ SY82 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV3: mworld] :
( ( ~ ! [SY83: $i] :
~ ( eiw_di @ SY83 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV4: mworld,SV1: mworld] :
( ( mrel @ SV1 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( eiw_di @ SX0 @ mactual )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ mactual @ SX1 )
| ! [SX2: $i] :
( ~ ( eiw_di @ SX2 @ SX1 )
| ! [SX3: mworld] :
( ~ ( mrel @ SX1 @ SX3 )
| ~ ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_p @ SX0 @ SX4 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_q @ SX0 @ SX4 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SX3 @ SX4 )
| ( big_p @ SX2 @ SX4 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
! [SV5: mworld,SV2: mworld] :
( ( ! [SY84: $i] :
( ~ ~ ( ~ ( eiw_di @ SY84 @ SV2 )
| ~ ( mrel @ SV2 @ SV5 ) )
| ( eiw_di @ SY84 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV3: mworld] :
( ( ! [SY83: $i] :
~ ( eiw_di @ SY83 @ SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ( eiw_di @ SV6 @ mactual )
| ~ ! [SY85: mworld] :
( ~ ( mrel @ mactual @ SY85 )
| ! [SY86: $i] :
( ~ ( eiw_di @ SY86 @ SY85 )
| ! [SY87: mworld] :
( ~ ( mrel @ SY85 @ SY87 )
| ~ ! [SY88: mworld] :
( ~ ( mrel @ SY87 @ SY88 )
| ( big_p @ SV6 @ SY88 ) )
| ! [SY89: mworld] :
( ~ ( mrel @ SY87 @ SY89 )
| ( big_q @ SV6 @ SY89 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SY87 @ SX4 )
| ( big_p @ SY86 @ SX4 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV5: mworld,SV2: mworld,SV7: $i] :
( ( ~ ~ ( ~ ( eiw_di @ SV7 @ SV2 )
| ~ ( mrel @ SV2 @ SV5 ) )
| ( eiw_di @ SV7 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV3: mworld] :
( ( ~ ( eiw_di @ ( sK1_SY83 @ SV3 ) @ SV3 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(29,plain,
! [SV6: $i] :
( ( ~ ( ~ ( eiw_di @ SV6 @ mactual )
| ~ ! [SY85: mworld] :
( ~ ( mrel @ mactual @ SY85 )
| ! [SY86: $i] :
( ~ ( eiw_di @ SY86 @ SY85 )
| ! [SY87: mworld] :
( ~ ( mrel @ SY85 @ SY87 )
| ~ ! [SY88: mworld] :
( ~ ( mrel @ SY87 @ SY88 )
| ( big_p @ SV6 @ SY88 ) )
| ! [SY89: mworld] :
( ~ ( mrel @ SY87 @ SY89 )
| ( big_q @ SV6 @ SY89 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SY87 @ SX4 )
| ( big_p @ SY86 @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV5: mworld,SV2: mworld,SV7: $i] :
( ( ( ~ ~ ( ~ ( eiw_di @ SV7 @ SV2 )
| ~ ( mrel @ SV2 @ SV5 ) ) )
= $true )
| ( ( eiw_di @ SV7 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV3: mworld] :
( ( eiw_di @ ( sK1_SY83 @ SV3 ) @ SV3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV6: $i] :
( ( ~ ( eiw_di @ SV6 @ mactual )
| ~ ! [SY85: mworld] :
( ~ ( mrel @ mactual @ SY85 )
| ! [SY86: $i] :
( ~ ( eiw_di @ SY86 @ SY85 )
| ! [SY87: mworld] :
( ~ ( mrel @ SY85 @ SY87 )
| ~ ! [SY88: mworld] :
( ~ ( mrel @ SY87 @ SY88 )
| ( big_p @ SV6 @ SY88 ) )
| ! [SY89: mworld] :
( ~ ( mrel @ SY87 @ SY89 )
| ( big_q @ SV6 @ SY89 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SY87 @ SX4 )
| ( big_p @ SY86 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV5: mworld,SV2: mworld,SV7: $i] :
( ( ( ~ ( ~ ( eiw_di @ SV7 @ SV2 )
| ~ ( mrel @ SV2 @ SV5 ) ) )
= $false )
| ( ( eiw_di @ SV7 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV6: $i] :
( ( ( ~ ( eiw_di @ SV6 @ mactual ) )
= $true )
| ( ( ~ ! [SY85: mworld] :
( ~ ( mrel @ mactual @ SY85 )
| ! [SY86: $i] :
( ~ ( eiw_di @ SY86 @ SY85 )
| ! [SY87: mworld] :
( ~ ( mrel @ SY85 @ SY87 )
| ~ ! [SY88: mworld] :
( ~ ( mrel @ SY87 @ SY88 )
| ( big_p @ SV6 @ SY88 ) )
| ! [SY89: mworld] :
( ~ ( mrel @ SY87 @ SY89 )
| ( big_q @ SV6 @ SY89 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SY87 @ SX4 )
| ( big_p @ SY86 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV5: mworld,SV2: mworld,SV7: $i] :
( ( ( ~ ( eiw_di @ SV7 @ SV2 )
| ~ ( mrel @ SV2 @ SV5 ) )
= $true )
| ( ( eiw_di @ SV7 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(36,plain,
! [SV6: $i] :
( ( ( eiw_di @ SV6 @ mactual )
= $false )
| ( ( ~ ! [SY85: mworld] :
( ~ ( mrel @ mactual @ SY85 )
| ! [SY86: $i] :
( ~ ( eiw_di @ SY86 @ SY85 )
| ! [SY87: mworld] :
( ~ ( mrel @ SY85 @ SY87 )
| ~ ! [SY88: mworld] :
( ~ ( mrel @ SY87 @ SY88 )
| ( big_p @ SV6 @ SY88 ) )
| ! [SY89: mworld] :
( ~ ( mrel @ SY87 @ SY89 )
| ( big_q @ SV6 @ SY89 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SY87 @ SX4 )
| ( big_p @ SY86 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV5: mworld,SV2: mworld,SV7: $i] :
( ( ( ~ ( eiw_di @ SV7 @ SV2 ) )
= $true )
| ( ( ~ ( mrel @ SV2 @ SV5 ) )
= $true )
| ( ( eiw_di @ SV7 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV6: $i] :
( ( ( ! [SY85: mworld] :
( ~ ( mrel @ mactual @ SY85 )
| ! [SY86: $i] :
( ~ ( eiw_di @ SY86 @ SY85 )
| ! [SY87: mworld] :
( ~ ( mrel @ SY85 @ SY87 )
| ~ ! [SY88: mworld] :
( ~ ( mrel @ SY87 @ SY88 )
| ( big_p @ SV6 @ SY88 ) )
| ! [SY89: mworld] :
( ~ ( mrel @ SY87 @ SY89 )
| ( big_q @ SV6 @ SY89 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SY87 @ SX4 )
| ( big_p @ SY86 @ SX4 ) ) ) ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV5: mworld,SV2: mworld,SV7: $i] :
( ( ( eiw_di @ SV7 @ SV2 )
= $false )
| ( ( ~ ( mrel @ SV2 @ SV5 ) )
= $true )
| ( ( eiw_di @ SV7 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV6: $i] :
( ( ( ~ ( mrel @ mactual @ ( sK2_SY85 @ SV6 ) )
| ! [SY91: $i] :
( ~ ( eiw_di @ SY91 @ ( sK2_SY85 @ SV6 ) )
| ! [SY92: mworld] :
( ~ ( mrel @ ( sK2_SY85 @ SV6 ) @ SY92 )
| ~ ! [SY88: mworld] :
( ~ ( mrel @ SY92 @ SY88 )
| ( big_p @ SV6 @ SY88 ) )
| ! [SY89: mworld] :
( ~ ( mrel @ SY92 @ SY89 )
| ( big_q @ SV6 @ SY89 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SY92 @ SX4 )
| ( big_p @ SY91 @ SX4 ) ) ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(41,plain,
! [SV7: $i,SV5: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV5 )
= $false )
| ( ( eiw_di @ SV7 @ SV2 )
= $false )
| ( ( eiw_di @ SV7 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV6: $i] :
( ( ( ~ ( mrel @ mactual @ ( sK2_SY85 @ SV6 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(43,plain,
! [SV6: $i] :
( ( ( ! [SY91: $i] :
( ~ ( eiw_di @ SY91 @ ( sK2_SY85 @ SV6 ) )
| ! [SY92: mworld] :
( ~ ( mrel @ ( sK2_SY85 @ SV6 ) @ SY92 )
| ~ ! [SY88: mworld] :
( ~ ( mrel @ SY92 @ SY88 )
| ( big_p @ SV6 @ SY88 ) )
| ! [SY89: mworld] :
( ~ ( mrel @ SY92 @ SY89 )
| ( big_q @ SV6 @ SY89 ) )
| ! [SX4: mworld] :
( ~ ( mrel @ SY92 @ SX4 )
| ( big_p @ SY91 @ SX4 ) ) ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
! [SV6: $i] :
( ( ( mrel @ mactual @ ( sK2_SY85 @ SV6 ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(45,plain,
! [SV6: $i] :
( ( ( ~ ( eiw_di @ ( sK3_SY91 @ SV6 ) @ ( sK2_SY85 @ SV6 ) )
| ! [SY96: mworld] :
( ~ ( mrel @ ( sK2_SY85 @ SV6 ) @ SY96 )
| ~ ! [SY88: mworld] :
( ~ ( mrel @ SY96 @ SY88 )
| ( big_p @ SV6 @ SY88 ) )
| ! [SY89: mworld] :
( ~ ( mrel @ SY96 @ SY89 )
| ( big_q @ SV6 @ SY89 ) )
| ! [SY99: mworld] :
( ~ ( mrel @ SY96 @ SY99 )
| ( big_p @ ( sK3_SY91 @ SV6 ) @ SY99 ) ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[43]) ).
thf(46,plain,
! [SV6: $i] :
( ( ( ~ ( eiw_di @ ( sK3_SY91 @ SV6 ) @ ( sK2_SY85 @ SV6 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(47,plain,
! [SV6: $i] :
( ( ( ! [SY96: mworld] :
( ~ ( mrel @ ( sK2_SY85 @ SV6 ) @ SY96 )
| ~ ! [SY88: mworld] :
( ~ ( mrel @ SY96 @ SY88 )
| ( big_p @ SV6 @ SY88 ) )
| ! [SY89: mworld] :
( ~ ( mrel @ SY96 @ SY89 )
| ( big_q @ SV6 @ SY89 ) )
| ! [SY99: mworld] :
( ~ ( mrel @ SY96 @ SY99 )
| ( big_p @ ( sK3_SY91 @ SV6 ) @ SY99 ) ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(48,plain,
! [SV6: $i] :
( ( ( eiw_di @ ( sK3_SY91 @ SV6 ) @ ( sK2_SY85 @ SV6 ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(49,plain,
! [SV6: $i] :
( ( ( ~ ( mrel @ ( sK2_SY85 @ SV6 ) @ ( sK4_SY96 @ SV6 ) )
| ~ ! [SY100: mworld] :
( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SY100 )
| ( big_p @ SV6 @ SY100 ) )
| ! [SY101: mworld] :
( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SY101 )
| ( big_q @ SV6 @ SY101 ) )
| ! [SY102: mworld] :
( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SY102 )
| ( big_p @ ( sK3_SY91 @ SV6 ) @ SY102 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[47]) ).
thf(50,plain,
! [SV6: $i] :
( ( ( ~ ( mrel @ ( sK2_SY85 @ SV6 ) @ ( sK4_SY96 @ SV6 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(51,plain,
! [SV6: $i] :
( ( ( ~ ! [SY100: mworld] :
( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SY100 )
| ( big_p @ SV6 @ SY100 ) )
| ! [SY101: mworld] :
( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SY101 )
| ( big_q @ SV6 @ SY101 ) )
| ! [SY102: mworld] :
( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SY102 )
| ( big_p @ ( sK3_SY91 @ SV6 ) @ SY102 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(52,plain,
! [SV6: $i] :
( ( ( mrel @ ( sK2_SY85 @ SV6 ) @ ( sK4_SY96 @ SV6 ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(53,plain,
! [SV6: $i] :
( ( ( ~ ! [SY100: mworld] :
( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SY100 )
| ( big_p @ SV6 @ SY100 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(54,plain,
! [SV6: $i] :
( ( ( ! [SY101: mworld] :
( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SY101 )
| ( big_q @ SV6 @ SY101 ) )
| ! [SY102: mworld] :
( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SY102 )
| ( big_p @ ( sK3_SY91 @ SV6 ) @ SY102 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV6: $i] :
( ( ( ! [SY100: mworld] :
( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SY100 )
| ( big_p @ SV6 @ SY100 ) ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV6: $i] :
( ( ( ! [SY101: mworld] :
( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SY101 )
| ( big_q @ SV6 @ SY101 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(57,plain,
! [SV6: $i] :
( ( ( ! [SY102: mworld] :
( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SY102 )
| ( big_p @ ( sK3_SY91 @ SV6 ) @ SY102 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(58,plain,
! [SV8: mworld,SV6: $i] :
( ( ( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SV8 )
| ( big_p @ SV6 @ SV8 ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV6: $i] :
( ( ( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ ( sK5_SY101 @ SV6 ) )
| ( big_q @ SV6 @ ( sK5_SY101 @ SV6 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(60,plain,
! [SV6: $i] :
( ( ( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ ( sK6_SY102 @ SV6 ) )
| ( big_p @ ( sK3_SY91 @ SV6 ) @ ( sK6_SY102 @ SV6 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(61,plain,
! [SV8: mworld,SV6: $i] :
( ( ( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ SV8 ) )
= $true )
| ( ( big_p @ SV6 @ SV8 )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV6: $i] :
( ( ( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ ( sK5_SY101 @ SV6 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(63,plain,
! [SV6: $i] :
( ( ( big_q @ SV6 @ ( sK5_SY101 @ SV6 ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(64,plain,
! [SV6: $i] :
( ( ( ~ ( mrel @ ( sK4_SY96 @ SV6 ) @ ( sK6_SY102 @ SV6 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(65,plain,
! [SV6: $i] :
( ( ( big_p @ ( sK3_SY91 @ SV6 ) @ ( sK6_SY102 @ SV6 ) )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(66,plain,
! [SV8: mworld,SV6: $i] :
( ( ( mrel @ ( sK4_SY96 @ SV6 ) @ SV8 )
= $false )
| ( ( big_p @ SV6 @ SV8 )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV6: $i] :
( ( ( mrel @ ( sK4_SY96 @ SV6 ) @ ( sK5_SY101 @ SV6 ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(68,plain,
! [SV6: $i] :
( ( ( mrel @ ( sK4_SY96 @ SV6 ) @ ( sK6_SY102 @ SV6 ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(69,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,68,67,66,65,63,52,48,44,41,31]) ).
thf(70,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL958^18 : TPTP v9.3.1. Released v8.1.0.
% 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
% 0.09/0.16 % Computer : n008.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 12:38:24 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.20
% 0.09/0.20 No.of.Axioms: 3
% 0.09/0.20
% 0.09/0.20 Length.of.Defs: 1663
% 0.09/0.20
% 0.09/0.20 Contains.Choice.Funs: false
% 0.09/0.20 ...
% 0.09/0.20
% 0.09/0.20 ********************************
% 0.09/0.20 * All subproblems solved! *
% 0.09/0.20 ********************************
% 0.09/0.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:69,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.20
% 0.09/0.20 %**** Beginning of derivation protocol ****
% 0.09/0.20 % SZS output start CNFRefutation
% See solution above
% 0.09/0.20
% 0.09/0.20 %**** End of derivation protocol ****
% 0.09/0.20 %**** no. of clauses in derivation: 70 ****
% 0.09/0.20 %**** clause counter: 69 ****
% 0.09/0.20
% 0.09/0.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:69,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------