%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET574^20 : 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 : n019.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 10:40:22 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 114 ( 67 unt; 0 typ; 10 def)
% Number of atoms : 869 ( 210 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1860 ( 327 ~; 269 |; 25 &;1213 @)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 214 ( 34 ^; 175 !; 5 ?; 214 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(tp_intersect,type,
intersect: $i > $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_member,type,
member: $i > $i > 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_SY24,type,
sK1_SY24: $i ).
thf(tp_sK2_SY84,type,
sK2_SY84: $i ).
thf(tp_sK3_SY86,type,
sK3_SY86: $i ).
thf(tp_sK4_SY74,type,
sK4_SY74: $i > $i > $i ).
thf(tp_sK5_X,type,
sK5_X: mworld > $i ).
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,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( intersect @ B @ C ) @ ( intersect @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(2,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mequiv @ ( intersect @ B @ C )
@ ( mexists_di
@ ^ [D: $i] : ( mand @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
thf(3,axiom,
! [W: mworld,V: mworld,X: $i] :
( ( ( eiw_di @ X @ W )
& ( mrel @ V @ W ) )
=> ( eiw_di @ X @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_decr) ).
thf(4,axiom,
! [W: mworld] :
? [X: $i] : ( eiw_di @ X @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(5,axiom,
! [W: mworld] : ( mrel @ W @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(6,conjecture,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mimplies @ ( mand @ ( member @ B @ C ) @ ( member @ B @ D ) ) @ ( intersect @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th13) ).
thf(7,negated_conjecture,
( ( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mimplies @ ( mand @ ( member @ B @ C ) @ ( member @ B @ D ) ) @ ( intersect @ C @ D ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [SY24: $i] :
( ( eiw_di @ SY24 @ mactual )
=> ! [SY25: $i] :
( ( eiw_di @ SY25 @ mactual )
=> ! [SY26: $i] :
( ( eiw_di @ SY26 @ mactual )
=> ( ( ( member @ SY24 @ SY25 @ mactual )
& ( member @ SY24 @ SY26 @ mactual ) )
=> ( intersect @ SY25 @ SY26 @ mactual ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(9,plain,
( ( ! [SY43: $i] :
( ( eiw_di @ SY43 @ mactual )
=> ! [SY44: $i] :
( ( eiw_di @ SY44 @ mactual )
=> ( ( intersect @ SY43 @ SY44 @ mactual )
=> ( intersect @ SY44 @ SY43 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(10,plain,
( ( ! [SY72: $i] :
( ( eiw_di @ SY72 @ mactual )
=> ! [SY73: $i] :
( ( eiw_di @ SY73 @ mactual )
=> ( ( intersect @ SY72 @ SY73 @ mactual )
<=> ? [SY74: $i] :
( ( eiw_di @ SY74 @ mactual )
& ( member @ SY74 @ SY72 @ mactual )
& ( member @ SY74 @ SY73 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(11,plain,
( ( ! [W: mworld,V: mworld,X: $i] :
( ( ( eiw_di @ X @ W )
& ( mrel @ V @ W ) )
=> ( eiw_di @ X @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(12,plain,
( ( ! [W: mworld] :
? [X: $i] : ( eiw_di @ X @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(13,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(14,plain,
( ( ( eiw_di @ sK1_SY24 @ mactual )
=> ! [SY84: $i] :
( ( eiw_di @ SY84 @ mactual )
=> ! [SY85: $i] :
( ( eiw_di @ SY85 @ mactual )
=> ( ( ( member @ sK1_SY24 @ SY84 @ mactual )
& ( member @ sK1_SY24 @ SY85 @ mactual ) )
=> ( intersect @ SY84 @ SY85 @ mactual ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( eiw_di @ sK1_SY24 @ mactual )
= $true ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [SY84: $i] :
( ( eiw_di @ SY84 @ mactual )
=> ! [SY85: $i] :
( ( eiw_di @ SY85 @ mactual )
=> ( ( ( member @ sK1_SY24 @ SY84 @ mactual )
& ( member @ sK1_SY24 @ SY85 @ mactual ) )
=> ( intersect @ SY84 @ SY85 @ mactual ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ! [SY84: $i] :
( ( eiw_di @ SY84 @ mactual )
=> ! [SY85: $i] :
( ( eiw_di @ SY85 @ mactual )
=> ( ( ( member @ sK1_SY24 @ SY84 @ mactual )
& ( member @ sK1_SY24 @ SY85 @ mactual ) )
=> ( intersect @ SY84 @ SY85 @ mactual ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(18,plain,
( ( ( eiw_di @ sK2_SY84 @ mactual )
& ( eiw_di @ sK3_SY86 @ mactual )
& ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
& ( member @ sK1_SY24 @ sK3_SY86 @ mactual )
& ~ ( intersect @ sK2_SY84 @ sK3_SY86 @ mactual ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(19,plain,
( ( ! [SY43: $i] :
( ~ ( eiw_di @ SY43 @ mactual )
| ! [SY44: $i] :
( ~ ( eiw_di @ SY44 @ mactual )
| ~ ( intersect @ SY43 @ SY44 @ mactual )
| ( intersect @ SY44 @ SY43 @ mactual ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(20,plain,
( ( ! [SY72: $i] :
( ~ ( eiw_di @ SY72 @ mactual )
| ( ! [SY73: $i] :
( ~ ( eiw_di @ SY73 @ mactual )
| ! [SY74: $i] :
( ~ ( member @ SY74 @ SY72 @ mactual )
| ~ ( member @ SY74 @ SY73 @ mactual )
| ~ ( eiw_di @ SY74 @ mactual ) )
| ( intersect @ SY72 @ SY73 @ mactual ) )
& ! [SY73: $i] :
( ~ ( eiw_di @ SY73 @ mactual )
| ~ ( intersect @ SY72 @ SY73 @ mactual )
| ( ( member @ ( sK4_SY74 @ SY73 @ SY72 ) @ SY72 @ mactual )
& ( member @ ( sK4_SY74 @ SY73 @ SY72 ) @ SY73 @ mactual )
& ( eiw_di @ ( sK4_SY74 @ SY73 @ SY72 ) @ mactual ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(21,plain,
( ( ! [W: mworld,V: mworld,X: $i] :
( ~ ( eiw_di @ X @ W )
| ~ ( mrel @ V @ W )
| ( eiw_di @ X @ V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(22,plain,
( ( ! [W: mworld] : ( eiw_di @ ( sK5_X @ W ) @ W ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(23,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(24,plain,
( ( ! [W: mworld] : ( eiw_di @ ( sK5_X @ W ) @ W ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(25,plain,
( ( ! [W: mworld,V: mworld,X: $i] :
( ~ ( eiw_di @ X @ W )
| ~ ( mrel @ V @ W )
| ( eiw_di @ X @ V ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(26,plain,
( ( ! [SY72: $i] :
( ~ ( eiw_di @ SY72 @ mactual )
| ( ! [SY73: $i] :
( ~ ( eiw_di @ SY73 @ mactual )
| ! [SY74: $i] :
( ~ ( member @ SY74 @ SY72 @ mactual )
| ~ ( member @ SY74 @ SY73 @ mactual )
| ~ ( eiw_di @ SY74 @ mactual ) )
| ( intersect @ SY72 @ SY73 @ mactual ) )
& ! [SY73: $i] :
( ~ ( eiw_di @ SY73 @ mactual )
| ~ ( intersect @ SY72 @ SY73 @ mactual )
| ( ( member @ ( sK4_SY74 @ SY73 @ SY72 ) @ SY72 @ mactual )
& ( member @ ( sK4_SY74 @ SY73 @ SY72 ) @ SY73 @ mactual )
& ( eiw_di @ ( sK4_SY74 @ SY73 @ SY72 ) @ mactual ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(27,plain,
( ( ! [SY43: $i] :
( ~ ( eiw_di @ SY43 @ mactual )
| ! [SY44: $i] :
( ~ ( eiw_di @ SY44 @ mactual )
| ~ ( intersect @ SY43 @ SY44 @ mactual )
| ( intersect @ SY44 @ SY43 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(28,plain,
( ( eiw_di @ sK1_SY24 @ mactual )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(29,plain,
( ( ( eiw_di @ sK2_SY84 @ mactual )
& ( eiw_di @ sK3_SY86 @ mactual )
& ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
& ( member @ sK1_SY24 @ sK3_SY86 @ mactual )
& ~ ( intersect @ sK2_SY84 @ sK3_SY86 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(30,plain,
( ( ~ ( ~ ( eiw_di @ sK2_SY84 @ mactual )
| ~ ~ ( ~ ( eiw_di @ sK3_SY86 @ mactual )
| ~ ~ ( ~ ~ ( ~ ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
| ~ ( member @ sK1_SY24 @ sK3_SY86 @ mactual ) )
| ~ ~ ( intersect @ sK2_SY84 @ sK3_SY86 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(31,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ~ ( ~ ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ~ ( member @ SX2 @ SX1 @ mactual )
| ~ ( eiw_di @ SX2 @ mactual ) )
| ( intersect @ SX0 @ SX1 @ mactual ) )
| ~ ! [SX1: $i] :
( ~ ( eiw_di @ SX1 @ mactual )
| ~ ( intersect @ SX0 @ SX1 @ mactual )
| ~ ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SX1 @ SX0 ) @ SX0 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SX1 @ SX0 ) @ SX1 @ mactual ) )
| ~ ( eiw_di @ ( sK4_SY74 @ SX1 @ SX0 ) @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(32,plain,
! [SV1: mworld] :
( ( mrel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(33,plain,
! [SV2: mworld] :
( ( eiw_di @ ( sK5_X @ SV2 ) @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(34,plain,
! [SV3: mworld] :
( ( ! [SY87: mworld,SY88: $i] :
( ~ ( eiw_di @ SY88 @ SV3 )
| ~ ( mrel @ SY87 @ SV3 )
| ( eiw_di @ SY88 @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(35,plain,
! [SV4: $i] :
( ( ~ ( eiw_di @ SV4 @ mactual )
| ! [SY89: $i] :
( ~ ( eiw_di @ SY89 @ mactual )
| ~ ( intersect @ SV4 @ SY89 @ mactual )
| ( intersect @ SY89 @ SV4 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(36,plain,
( ( ~ ( eiw_di @ sK2_SY84 @ mactual )
| ~ ~ ( ~ ( eiw_di @ sK3_SY86 @ mactual )
| ~ ~ ( ~ ~ ( ~ ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
| ~ ( member @ sK1_SY24 @ sK3_SY86 @ mactual ) )
| ~ ~ ( intersect @ sK2_SY84 @ sK3_SY86 @ mactual ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV5: $i] :
( ( ~ ( eiw_di @ SV5 @ mactual )
| ~ ( ~ ! [SY90: $i] :
( ~ ( eiw_di @ SY90 @ mactual )
| ! [SY91: $i] :
( ~ ( member @ SY91 @ SV5 @ mactual )
| ~ ( member @ SY91 @ SY90 @ mactual )
| ~ ( eiw_di @ SY91 @ mactual ) )
| ( intersect @ SV5 @ SY90 @ mactual ) )
| ~ ! [SY92: $i] :
( ~ ( eiw_di @ SY92 @ mactual )
| ~ ( intersect @ SV5 @ SY92 @ mactual )
| ~ ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SY92 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SY92 @ SV5 ) @ SY92 @ mactual ) )
| ~ ( eiw_di @ ( sK4_SY74 @ SY92 @ SV5 ) @ mactual ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV6: mworld,SV3: mworld] :
( ( ! [SY93: $i] :
( ~ ( eiw_di @ SY93 @ SV3 )
| ~ ( mrel @ SV6 @ SV3 )
| ( eiw_di @ SY93 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV4: $i] :
( ( ( ~ ( eiw_di @ SV4 @ mactual ) )
= $true )
| ( ( ! [SY89: $i] :
( ~ ( eiw_di @ SY89 @ mactual )
| ~ ( intersect @ SV4 @ SY89 @ mactual )
| ( intersect @ SY89 @ SV4 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ( eiw_di @ sK2_SY84 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(41,plain,
( ( ~ ~ ( ~ ( eiw_di @ sK3_SY86 @ mactual )
| ~ ~ ( ~ ~ ( ~ ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
| ~ ( member @ sK1_SY24 @ sK3_SY86 @ mactual ) )
| ~ ~ ( intersect @ sK2_SY84 @ sK3_SY86 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(42,plain,
! [SV5: $i] :
( ( ( ~ ( eiw_di @ SV5 @ mactual ) )
= $true )
| ( ( ~ ( ~ ! [SY90: $i] :
( ~ ( eiw_di @ SY90 @ mactual )
| ! [SY91: $i] :
( ~ ( member @ SY91 @ SV5 @ mactual )
| ~ ( member @ SY91 @ SY90 @ mactual )
| ~ ( eiw_di @ SY91 @ mactual ) )
| ( intersect @ SV5 @ SY90 @ mactual ) )
| ~ ! [SY92: $i] :
( ~ ( eiw_di @ SY92 @ mactual )
| ~ ( intersect @ SV5 @ SY92 @ mactual )
| ~ ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SY92 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SY92 @ SV5 ) @ SY92 @ mactual ) )
| ~ ( eiw_di @ ( sK4_SY74 @ SY92 @ SV5 ) @ mactual ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV6: mworld,SV3: mworld,SV7: $i] :
( ( ~ ( eiw_di @ SV7 @ SV3 )
| ~ ( mrel @ SV6 @ SV3 )
| ( eiw_di @ SV7 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV4: $i] :
( ( ( eiw_di @ SV4 @ mactual )
= $false )
| ( ( ! [SY89: $i] :
( ~ ( eiw_di @ SY89 @ mactual )
| ~ ( intersect @ SV4 @ SY89 @ mactual )
| ( intersect @ SY89 @ SV4 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(45,plain,
( ( eiw_di @ sK2_SY84 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
( ( ~ ( ~ ( eiw_di @ sK3_SY86 @ mactual )
| ~ ~ ( ~ ~ ( ~ ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
| ~ ( member @ sK1_SY24 @ sK3_SY86 @ mactual ) )
| ~ ~ ( intersect @ sK2_SY84 @ sK3_SY86 @ mactual ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV5: $i] :
( ( ( eiw_di @ SV5 @ mactual )
= $false )
| ( ( ~ ( ~ ! [SY90: $i] :
( ~ ( eiw_di @ SY90 @ mactual )
| ! [SY91: $i] :
( ~ ( member @ SY91 @ SV5 @ mactual )
| ~ ( member @ SY91 @ SY90 @ mactual )
| ~ ( eiw_di @ SY91 @ mactual ) )
| ( intersect @ SV5 @ SY90 @ mactual ) )
| ~ ! [SY92: $i] :
( ~ ( eiw_di @ SY92 @ mactual )
| ~ ( intersect @ SV5 @ SY92 @ mactual )
| ~ ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SY92 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SY92 @ SV5 ) @ SY92 @ mactual ) )
| ~ ( eiw_di @ ( sK4_SY74 @ SY92 @ SV5 ) @ mactual ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV6: mworld,SV3: mworld,SV7: $i] :
( ( ( ~ ( eiw_di @ SV7 @ SV3 )
| ~ ( mrel @ SV6 @ SV3 ) )
= $true )
| ( ( eiw_di @ SV7 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( eiw_di @ SV8 @ mactual )
| ~ ( intersect @ SV4 @ SV8 @ mactual )
| ( intersect @ SV8 @ SV4 @ mactual ) )
= $true )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(50,plain,
( ( ~ ( eiw_di @ sK3_SY86 @ mactual )
| ~ ~ ( ~ ~ ( ~ ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
| ~ ( member @ sK1_SY24 @ sK3_SY86 @ mactual ) )
| ~ ~ ( intersect @ sK2_SY84 @ sK3_SY86 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV5: $i] :
( ( ( ~ ! [SY90: $i] :
( ~ ( eiw_di @ SY90 @ mactual )
| ! [SY91: $i] :
( ~ ( member @ SY91 @ SV5 @ mactual )
| ~ ( member @ SY91 @ SY90 @ mactual )
| ~ ( eiw_di @ SY91 @ mactual ) )
| ( intersect @ SV5 @ SY90 @ mactual ) )
| ~ ! [SY92: $i] :
( ~ ( eiw_di @ SY92 @ mactual )
| ~ ( intersect @ SV5 @ SY92 @ mactual )
| ~ ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SY92 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SY92 @ SV5 ) @ SY92 @ mactual ) )
| ~ ( eiw_di @ ( sK4_SY74 @ SY92 @ SV5 ) @ mactual ) ) ) )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV6: mworld,SV3: mworld,SV7: $i] :
( ( ( ~ ( eiw_di @ SV7 @ SV3 ) )
= $true )
| ( ( ~ ( mrel @ SV6 @ SV3 ) )
= $true )
| ( ( eiw_di @ SV7 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( eiw_di @ SV8 @ mactual ) )
= $true )
| ( ( ~ ( intersect @ SV4 @ SV8 @ mactual )
| ( intersect @ SV8 @ SV4 @ mactual ) )
= $true )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(54,plain,
( ( ~ ( eiw_di @ sK3_SY86 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(55,plain,
( ( ~ ~ ( ~ ~ ( ~ ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
| ~ ( member @ sK1_SY24 @ sK3_SY86 @ mactual ) )
| ~ ~ ( intersect @ sK2_SY84 @ sK3_SY86 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(56,plain,
! [SV5: $i] :
( ( ( ~ ! [SY90: $i] :
( ~ ( eiw_di @ SY90 @ mactual )
| ! [SY91: $i] :
( ~ ( member @ SY91 @ SV5 @ mactual )
| ~ ( member @ SY91 @ SY90 @ mactual )
| ~ ( eiw_di @ SY91 @ mactual ) )
| ( intersect @ SV5 @ SY90 @ mactual ) ) )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV5: $i] :
( ( ( ~ ! [SY92: $i] :
( ~ ( eiw_di @ SY92 @ mactual )
| ~ ( intersect @ SV5 @ SY92 @ mactual )
| ~ ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SY92 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SY92 @ SV5 ) @ SY92 @ mactual ) )
| ~ ( eiw_di @ ( sK4_SY74 @ SY92 @ SV5 ) @ mactual ) ) ) )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(58,plain,
! [SV6: mworld,SV3: mworld,SV7: $i] :
( ( ( eiw_di @ SV7 @ SV3 )
= $false )
| ( ( ~ ( mrel @ SV6 @ SV3 ) )
= $true )
| ( ( eiw_di @ SV7 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV4: $i,SV8: $i] :
( ( ( eiw_di @ SV8 @ mactual )
= $false )
| ( ( ~ ( intersect @ SV4 @ SV8 @ mactual )
| ( intersect @ SV8 @ SV4 @ mactual ) )
= $true )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(60,plain,
( ( eiw_di @ sK3_SY86 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(61,plain,
( ( ~ ( ~ ~ ( ~ ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
| ~ ( member @ sK1_SY24 @ sK3_SY86 @ mactual ) )
| ~ ~ ( intersect @ sK2_SY84 @ sK3_SY86 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(62,plain,
! [SV5: $i] :
( ( ( ! [SY90: $i] :
( ~ ( eiw_di @ SY90 @ mactual )
| ! [SY91: $i] :
( ~ ( member @ SY91 @ SV5 @ mactual )
| ~ ( member @ SY91 @ SY90 @ mactual )
| ~ ( eiw_di @ SY91 @ mactual ) )
| ( intersect @ SV5 @ SY90 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(63,plain,
! [SV5: $i] :
( ( ( ! [SY92: $i] :
( ~ ( eiw_di @ SY92 @ mactual )
| ~ ( intersect @ SV5 @ SY92 @ mactual )
| ~ ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SY92 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SY92 @ SV5 ) @ SY92 @ mactual ) )
| ~ ( eiw_di @ ( sK4_SY74 @ SY92 @ SV5 ) @ mactual ) ) ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(64,plain,
! [SV7: $i,SV3: mworld,SV6: mworld] :
( ( ( mrel @ SV6 @ SV3 )
= $false )
| ( ( eiw_di @ SV7 @ SV3 )
= $false )
| ( ( eiw_di @ SV7 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( intersect @ SV4 @ SV8 @ mactual ) )
= $true )
| ( ( intersect @ SV8 @ SV4 @ mactual )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(66,plain,
( ( ~ ~ ( ~ ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
| ~ ( member @ sK1_SY24 @ sK3_SY86 @ mactual ) )
| ~ ~ ( intersect @ sK2_SY84 @ sK3_SY86 @ mactual ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ( eiw_di @ SV9 @ mactual )
| ! [SY94: $i] :
( ~ ( member @ SY94 @ SV5 @ mactual )
| ~ ( member @ SY94 @ SV9 @ mactual )
| ~ ( eiw_di @ SY94 @ mactual ) )
| ( intersect @ SV5 @ SV9 @ mactual ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( eiw_di @ SV10 @ mactual )
| ~ ( intersect @ SV5 @ SV10 @ mactual )
| ~ ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV10 @ mactual ) )
| ~ ( eiw_di @ ( sK4_SY74 @ SV10 @ SV5 ) @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(69,plain,
! [SV8: $i,SV4: $i] :
( ( ( intersect @ SV4 @ SV8 @ mactual )
= $false )
| ( ( intersect @ SV8 @ SV4 @ mactual )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false )
| ( ( eiw_di @ SV4 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
( ( ~ ~ ( ~ ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
| ~ ( member @ sK1_SY24 @ sK3_SY86 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(71,plain,
( ( ~ ~ ( intersect @ sK2_SY84 @ sK3_SY86 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(72,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ( eiw_di @ SV9 @ mactual ) )
= $true )
| ( ( ! [SY94: $i] :
( ~ ( member @ SY94 @ SV5 @ mactual )
| ~ ( member @ SY94 @ SV9 @ mactual )
| ~ ( eiw_di @ SY94 @ mactual ) )
| ( intersect @ SV5 @ SV9 @ mactual ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( eiw_di @ SV10 @ mactual ) )
= $true )
| ( ( ~ ( intersect @ SV5 @ SV10 @ mactual )
| ~ ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV10 @ mactual ) )
| ~ ( eiw_di @ ( sK4_SY74 @ SV10 @ SV5 ) @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(74,plain,
( ( ~ ( ~ ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
| ~ ( member @ sK1_SY24 @ sK3_SY86 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(75,plain,
( ( ~ ( intersect @ sK2_SY84 @ sK3_SY86 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(76,plain,
! [SV5: $i,SV9: $i] :
( ( ( eiw_di @ SV9 @ mactual )
= $false )
| ( ( ! [SY94: $i] :
( ~ ( member @ SY94 @ SV5 @ mactual )
| ~ ( member @ SY94 @ SV9 @ mactual )
| ~ ( eiw_di @ SY94 @ mactual ) )
| ( intersect @ SV5 @ SV9 @ mactual ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV5: $i,SV10: $i] :
( ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( ~ ( intersect @ SV5 @ SV10 @ mactual )
| ~ ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV10 @ mactual ) )
| ~ ( eiw_di @ ( sK4_SY74 @ SV10 @ SV5 ) @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(78,plain,
( ( ~ ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
| ~ ( member @ sK1_SY24 @ sK3_SY86 @ mactual ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(79,plain,
( ( intersect @ sK2_SY84 @ sK3_SY86 @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV9: $i,SV5: $i] :
( ( ( ! [SY94: $i] :
( ~ ( member @ SY94 @ SV5 @ mactual )
| ~ ( member @ SY94 @ SV9 @ mactual )
| ~ ( eiw_di @ SY94 @ mactual ) ) )
= $true )
| ( ( intersect @ SV5 @ SV9 @ mactual )
= $true )
| ( ( eiw_di @ SV9 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( intersect @ SV5 @ SV10 @ mactual ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV10 @ mactual ) )
| ~ ( eiw_di @ ( sK4_SY74 @ SV10 @ SV5 ) @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(82,plain,
( ( ~ ( member @ sK1_SY24 @ sK2_SY84 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(83,plain,
( ( ~ ( member @ sK1_SY24 @ sK3_SY86 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(84,plain,
! [SV9: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( member @ SV11 @ SV5 @ mactual )
| ~ ( member @ SV11 @ SV9 @ mactual )
| ~ ( eiw_di @ SV11 @ mactual ) )
= $true )
| ( ( intersect @ SV5 @ SV9 @ mactual )
= $true )
| ( ( eiw_di @ SV9 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV10: $i,SV5: $i] :
( ( ( intersect @ SV5 @ SV10 @ mactual )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV10 @ mactual ) )
| ~ ( eiw_di @ ( sK4_SY74 @ SV10 @ SV5 ) @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(86,plain,
( ( member @ sK1_SY24 @ sK2_SY84 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(87,plain,
( ( member @ sK1_SY24 @ sK3_SY86 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(88,plain,
! [SV9: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( member @ SV11 @ SV5 @ mactual )
| ~ ( member @ SV11 @ SV9 @ mactual ) )
= $true )
| ( ( ~ ( eiw_di @ SV11 @ mactual ) )
= $true )
| ( ( intersect @ SV5 @ SV9 @ mactual )
= $true )
| ( ( eiw_di @ SV9 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV10 @ mactual ) )
| ~ ( eiw_di @ ( sK4_SY74 @ SV10 @ SV5 ) @ mactual ) )
= $false )
| ( ( intersect @ SV5 @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(90,plain,
! [SV9: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( member @ SV11 @ SV5 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV11 @ SV9 @ mactual ) )
= $true )
| ( ( ~ ( eiw_di @ SV11 @ mactual ) )
= $true )
| ( ( intersect @ SV5 @ SV9 @ mactual )
= $true )
| ( ( eiw_di @ SV9 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(91,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV10 @ mactual ) ) )
= $false )
| ( ( intersect @ SV5 @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(92,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( eiw_di @ ( sK4_SY74 @ SV10 @ SV5 ) @ mactual ) )
= $false )
| ( ( intersect @ SV5 @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(93,plain,
! [SV9: $i,SV5: $i,SV11: $i] :
( ( ( member @ SV11 @ SV5 @ mactual )
= $false )
| ( ( ~ ( member @ SV11 @ SV9 @ mactual ) )
= $true )
| ( ( ~ ( eiw_di @ SV11 @ mactual ) )
= $true )
| ( ( intersect @ SV5 @ SV9 @ mactual )
= $true )
| ( ( eiw_di @ SV9 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(94,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV10 @ mactual ) ) )
= $true )
| ( ( intersect @ SV5 @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(95,plain,
! [SV5: $i,SV10: $i] :
( ( ( eiw_di @ ( sK4_SY74 @ SV10 @ SV5 ) @ mactual )
= $true )
| ( ( intersect @ SV5 @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(96,plain,
! [SV5: $i,SV9: $i,SV11: $i] :
( ( ( member @ SV11 @ SV9 @ mactual )
= $false )
| ( ( member @ SV11 @ SV5 @ mactual )
= $false )
| ( ( ~ ( eiw_di @ SV11 @ mactual ) )
= $true )
| ( ( intersect @ SV5 @ SV9 @ mactual )
= $true )
| ( ( eiw_di @ SV9 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(97,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV5 @ mactual )
| ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV10 @ mactual ) )
= $false )
| ( ( intersect @ SV5 @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(98,plain,
! [SV9: $i,SV5: $i,SV11: $i] :
( ( ( eiw_di @ SV11 @ mactual )
= $false )
| ( ( member @ SV11 @ SV5 @ mactual )
= $false )
| ( ( member @ SV11 @ SV9 @ mactual )
= $false )
| ( ( intersect @ SV5 @ SV9 @ mactual )
= $true )
| ( ( eiw_di @ SV9 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(99,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV5 @ mactual ) )
= $false )
| ( ( intersect @ SV5 @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(100,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV10 @ mactual ) )
= $false )
| ( ( intersect @ SV5 @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(101,plain,
! [SV5: $i,SV10: $i] :
( ( ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV5 @ mactual )
= $true )
| ( ( intersect @ SV5 @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(102,plain,
! [SV5: $i,SV10: $i] :
( ( ( member @ ( sK4_SY74 @ SV10 @ SV5 ) @ SV10 @ mactual )
= $true )
| ( ( intersect @ SV5 @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( eiw_di @ SV5 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(103,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,102,101,98,95,87,86,79,69,64,60,45,33,32]) ).
thf(104,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET574^20 : 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
% 0.07/0.19 % Computer : n019.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 14:46:16 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.24
% 0.07/0.24 No.of.Axioms: 5
% 0.07/0.24
% 0.07/0.24 Length.of.Defs: 1663
% 0.07/0.24
% 0.07/0.24 Contains.Choice.Funs: false
% 0.07/0.24 ....
% 0.07/0.24
% 0.07/0.24 ********************************
% 0.07/0.24 * All subproblems solved! *
% 0.07/0.24 ********************************
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:103,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.24
% 0.07/0.24 %**** Beginning of derivation protocol ****
% 0.07/0.24 % SZS output start CNFRefutation
% See solution above
% 0.07/0.24
% 0.07/0.24 %**** End of derivation protocol ****
% 0.07/0.24 %**** no. of clauses in derivation: 104 ****
% 0.07/0.24 %**** clause counter: 103 ****
% 0.07/0.24
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:103,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------