%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO891^16 : 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 : n007.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 11:09:16 AM UTC 2026
% Result : Theorem 0.07s 0.23s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 136 ( 75 unt; 0 typ; 10 def)
% Number of atoms : 952 ( 238 equ; 0 cnn)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 1610 ( 218 ~; 256 |; 27 &;1084 @)
% ( 1 <=>; 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 : 22 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 284 ( 39 ^; 229 !; 16 ?; 284 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
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_p,type,
p: $i > mworld > $o ).
thf(tp_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(tp_sK1_SY11,type,
sK1_SY11: mworld > $i > $i ).
thf(tp_sK2_SY53,type,
sK2_SY53: $i ).
thf(tp_sK3_SY145,type,
sK3_SY145: mworld ).
thf(tp_sK4_X,type,
sK4_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
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( p @ A ) ) @ ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_substitution_1) ).
thf(2,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] :
( mforall_di
@ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(3,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(4,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(5,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(6,axiom,
! [W: mworld] :
? [X: $i] : ( eiw_di @ X @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(7,axiom,
! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ V )
& ( mrel @ V @ U ) )
=> ( mrel @ W @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
thf(8,axiom,
! [W: mworld] : ( mrel @ W @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(9,conjecture,
( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X: $i] :
( mbox
@ ( mexists_di
@ ^ [Y: $i] : ( qmltpeq @ X @ Y ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [X: $i] : ( mdia @ ( p @ X ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X: $i] : ( p @ X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(10,negated_conjecture,
( ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X: $i] :
( mbox
@ ( mexists_di
@ ^ [Y: $i] : ( qmltpeq @ X @ Y ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [X: $i] : ( mdia @ ( p @ X ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X: $i] : ( p @ X ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,plain,
( ( ! [SY50: $i] :
( ( eiw_di @ SY50 @ mactual )
=> ! [SY51: mworld] :
( ( mrel @ mactual @ SY51 )
=> ? [SY11: $i] :
( ( eiw_di @ SY11 @ SY51 )
& ( qmltpeq @ SY50 @ SY11 @ SY51 ) ) ) )
=> ( ? [SY53: $i] :
( ( eiw_di @ SY53 @ mactual )
& ? [SY54: mworld] :
( ( mrel @ mactual @ SY54 )
& ( p @ SY53 @ SY54 ) ) )
=> ? [SY55: mworld] :
( ( mrel @ mactual @ SY55 )
& ? [SY36: $i] :
( ( eiw_di @ SY36 @ SY55 )
& ( p @ SY36 @ SY55 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(12,plain,
( ( ! [SY80: $i] :
( ( eiw_di @ SY80 @ mactual )
=> ! [SY81: $i] :
( ( eiw_di @ SY81 @ mactual )
=> ( ( ( qmltpeq @ SY80 @ SY81 @ mactual )
& ( p @ SY80 @ mactual ) )
=> ( p @ SY81 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(13,plain,
( ( ! [SY108: $i] :
( ( eiw_di @ SY108 @ mactual )
=> ! [SY109: $i] :
( ( eiw_di @ SY109 @ mactual )
=> ! [SY110: $i] :
( ( eiw_di @ SY110 @ mactual )
=> ( ( ( qmltpeq @ SY108 @ SY109 @ mactual )
& ( qmltpeq @ SY109 @ SY110 @ mactual ) )
=> ( qmltpeq @ SY108 @ SY110 @ mactual ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(14,plain,
( ( ! [SY127: $i] :
( ( eiw_di @ SY127 @ mactual )
=> ! [SY128: $i] :
( ( eiw_di @ SY128 @ mactual )
=> ( ( qmltpeq @ SY127 @ SY128 @ mactual )
=> ( qmltpeq @ SY128 @ SY127 @ mactual ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(15,plain,
( ( ! [SY134: $i] :
( ( eiw_di @ SY134 @ mactual )
=> ( qmltpeq @ SY134 @ SY134 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(16,plain,
( ( ! [W: mworld,V: mworld,X: $i] :
( ( ( eiw_di @ X @ W )
& ( mrel @ W @ V ) )
=> ( eiw_di @ X @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(17,plain,
( ( ! [W: mworld] :
? [X: $i] : ( eiw_di @ X @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(18,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ V )
& ( mrel @ V @ U ) )
=> ( mrel @ W @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(19,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[8,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(20,plain,
( ( ! [SY50: $i] :
( ( eiw_di @ SY50 @ mactual )
=> ! [SY51: mworld] :
( ( mrel @ mactual @ SY51 )
=> ? [SY11: $i] :
( ( eiw_di @ SY11 @ SY51 )
& ( qmltpeq @ SY50 @ SY11 @ SY51 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(21,plain,
( ( ? [SY53: $i] :
( ( eiw_di @ SY53 @ mactual )
& ? [SY54: mworld] :
( ( mrel @ mactual @ SY54 )
& ( p @ SY53 @ SY54 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(22,plain,
( ( ? [SY55: mworld] :
( ( mrel @ mactual @ SY55 )
& ? [SY36: $i] :
( ( eiw_di @ SY36 @ SY55 )
& ( p @ SY36 @ SY55 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(23,plain,
( ( ~ ? [SY55: mworld] :
( ( mrel @ mactual @ SY55 )
& ? [SY36: $i] :
( ( eiw_di @ SY36 @ SY55 )
& ( p @ SY36 @ SY55 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [SY55: mworld] :
( ! [SY36: $i] :
( ~ ( eiw_di @ SY36 @ SY55 )
| ~ ( p @ SY36 @ SY55 ) )
| ~ ( mrel @ mactual @ SY55 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(25,plain,
( ( ! [SY50: $i] :
( ~ ( eiw_di @ SY50 @ mactual )
| ! [SY51: mworld] :
( ~ ( mrel @ mactual @ SY51 )
| ( ( eiw_di @ ( sK1_SY11 @ SY51 @ SY50 ) @ SY51 )
& ( qmltpeq @ SY50 @ ( sK1_SY11 @ SY51 @ SY50 ) @ SY51 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(26,plain,
( ( ( mrel @ mactual @ sK3_SY145 )
& ( p @ sK2_SY53 @ sK3_SY145 )
& ( eiw_di @ sK2_SY53 @ mactual ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(27,plain,
( ( ! [SY80: $i] :
( ~ ( eiw_di @ SY80 @ mactual )
| ! [SY81: $i] :
( ~ ( eiw_di @ SY81 @ mactual )
| ~ ( p @ SY80 @ mactual )
| ~ ( qmltpeq @ SY80 @ SY81 @ mactual )
| ( p @ SY81 @ mactual ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(28,plain,
( ( ! [SY108: $i] :
( ~ ( eiw_di @ SY108 @ mactual )
| ! [SY109: $i] :
( ~ ( eiw_di @ SY109 @ mactual )
| ! [SY110: $i] :
( ~ ( eiw_di @ SY110 @ mactual )
| ~ ( qmltpeq @ SY108 @ SY109 @ mactual )
| ~ ( qmltpeq @ SY109 @ SY110 @ mactual )
| ( qmltpeq @ SY108 @ SY110 @ mactual ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(29,plain,
( ( ! [SY127: $i] :
( ~ ( eiw_di @ SY127 @ mactual )
| ! [SY128: $i] :
( ~ ( eiw_di @ SY128 @ mactual )
| ~ ( qmltpeq @ SY127 @ SY128 @ mactual )
| ( qmltpeq @ SY128 @ SY127 @ mactual ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(30,plain,
( ( ! [SY134: $i] :
( ~ ( eiw_di @ SY134 @ mactual )
| ( qmltpeq @ SY134 @ SY134 @ mactual ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(31,plain,
( ( ! [W: mworld,V: mworld,X: $i] :
( ~ ( eiw_di @ X @ W )
| ~ ( mrel @ W @ V )
| ( eiw_di @ X @ V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(32,plain,
( ( ! [W: mworld] : ( eiw_di @ ( sK4_X @ W ) @ W ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(33,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ~ ( mrel @ W @ V )
| ~ ( mrel @ V @ U )
| ( mrel @ W @ U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(34,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(35,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ~ ( mrel @ W @ V )
| ~ ( mrel @ V @ U )
| ( mrel @ W @ U ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(36,plain,
( ( ! [W: mworld] : ( eiw_di @ ( sK4_X @ W ) @ W ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(37,plain,
( ( ! [W: mworld,V: mworld,X: $i] :
( ~ ( eiw_di @ X @ W )
| ~ ( mrel @ W @ V )
| ( eiw_di @ X @ V ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(38,plain,
( ( ! [SY134: $i] :
( ~ ( eiw_di @ SY134 @ mactual )
| ( qmltpeq @ SY134 @ SY134 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(39,plain,
( ( ! [SY127: $i] :
( ~ ( eiw_di @ SY127 @ mactual )
| ! [SY128: $i] :
( ~ ( eiw_di @ SY128 @ mactual )
| ~ ( qmltpeq @ SY127 @ SY128 @ mactual )
| ( qmltpeq @ SY128 @ SY127 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(40,plain,
( ( ! [SY108: $i] :
( ~ ( eiw_di @ SY108 @ mactual )
| ! [SY109: $i] :
( ~ ( eiw_di @ SY109 @ mactual )
| ! [SY110: $i] :
( ~ ( eiw_di @ SY110 @ mactual )
| ~ ( qmltpeq @ SY108 @ SY109 @ mactual )
| ~ ( qmltpeq @ SY109 @ SY110 @ mactual )
| ( qmltpeq @ SY108 @ SY110 @ mactual ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(41,plain,
( ( ! [SY80: $i] :
( ~ ( eiw_di @ SY80 @ mactual )
| ! [SY81: $i] :
( ~ ( eiw_di @ SY81 @ mactual )
| ~ ( p @ SY80 @ mactual )
| ~ ( qmltpeq @ SY80 @ SY81 @ mactual )
| ( p @ SY81 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(42,plain,
( ( ( mrel @ mactual @ sK3_SY145 )
& ( p @ sK2_SY53 @ sK3_SY145 )
& ( eiw_di @ sK2_SY53 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(43,plain,
( ( ! [SY50: $i] :
( ~ ( eiw_di @ SY50 @ mactual )
| ! [SY51: mworld] :
( ~ ( mrel @ mactual @ SY51 )
| ( ( eiw_di @ ( sK1_SY11 @ SY51 @ SY50 ) @ SY51 )
& ( qmltpeq @ SY50 @ ( sK1_SY11 @ SY51 @ SY50 ) @ SY51 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(44,plain,
( ( ! [SY55: mworld] :
( ! [SY36: $i] :
( ~ ( eiw_di @ SY36 @ SY55 )
| ~ ( p @ SY36 @ SY55 ) )
| ~ ( mrel @ mactual @ SY55 ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(45,plain,
( ( ! [SX0: $i] :
( ~ ( eiw_di @ SX0 @ mactual )
| ! [SX1: mworld] :
( ~ ( mrel @ mactual @ SX1 )
| ~ ( ~ ( eiw_di @ ( sK1_SY11 @ SX1 @ SX0 ) @ SX1 )
| ~ ( qmltpeq @ SX0 @ ( sK1_SY11 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(46,plain,
( ( ~ ( ~ ~ ( ~ ( mrel @ mactual @ sK3_SY145 )
| ~ ( p @ sK2_SY53 @ sK3_SY145 ) )
| ~ ( eiw_di @ sK2_SY53 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(47,plain,
! [SV1: mworld] :
( ( mrel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(48,plain,
! [SV2: mworld] :
( ( ! [SY146: mworld,SY147: mworld] :
( ~ ( mrel @ SV2 @ SY146 )
| ~ ( mrel @ SY146 @ SY147 )
| ( mrel @ SV2 @ SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(49,plain,
! [SV3: mworld] :
( ( eiw_di @ ( sK4_X @ SV3 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(50,plain,
! [SV4: mworld] :
( ( ! [SY148: mworld,SY149: $i] :
( ~ ( eiw_di @ SY149 @ SV4 )
| ~ ( mrel @ SV4 @ SY148 )
| ( eiw_di @ SY149 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(51,plain,
! [SV5: $i] :
( ( ~ ( eiw_di @ SV5 @ mactual )
| ( qmltpeq @ SV5 @ SV5 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(52,plain,
! [SV6: $i] :
( ( ~ ( eiw_di @ SV6 @ mactual )
| ! [SY150: $i] :
( ~ ( eiw_di @ SY150 @ mactual )
| ~ ( qmltpeq @ SV6 @ SY150 @ mactual )
| ( qmltpeq @ SY150 @ SV6 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(53,plain,
! [SV7: $i] :
( ( ~ ( eiw_di @ SV7 @ mactual )
| ! [SY151: $i] :
( ~ ( eiw_di @ SY151 @ mactual )
| ! [SY152: $i] :
( ~ ( eiw_di @ SY152 @ mactual )
| ~ ( qmltpeq @ SV7 @ SY151 @ mactual )
| ~ ( qmltpeq @ SY151 @ SY152 @ mactual )
| ( qmltpeq @ SV7 @ SY152 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(54,plain,
! [SV8: $i] :
( ( ~ ( eiw_di @ SV8 @ mactual )
| ! [SY153: $i] :
( ~ ( eiw_di @ SY153 @ mactual )
| ~ ( p @ SV8 @ mactual )
| ~ ( qmltpeq @ SV8 @ SY153 @ mactual )
| ( p @ SY153 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(55,plain,
! [SV9: mworld] :
( ( ! [SY154: $i] :
( ~ ( eiw_di @ SY154 @ SV9 )
| ~ ( p @ SY154 @ SV9 ) )
| ~ ( mrel @ mactual @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(56,plain,
! [SV10: $i] :
( ( ~ ( eiw_di @ SV10 @ mactual )
| ! [SY155: mworld] :
( ~ ( mrel @ mactual @ SY155 )
| ~ ( ~ ( eiw_di @ ( sK1_SY11 @ SY155 @ SV10 ) @ SY155 )
| ~ ( qmltpeq @ SV10 @ ( sK1_SY11 @ SY155 @ SV10 ) @ SY155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(57,plain,
( ( ~ ~ ( ~ ( mrel @ mactual @ sK3_SY145 )
| ~ ( p @ sK2_SY53 @ sK3_SY145 ) )
| ~ ( eiw_di @ sK2_SY53 @ mactual ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(58,plain,
! [SV11: mworld,SV2: mworld] :
( ( ! [SY156: mworld] :
( ~ ( mrel @ SV2 @ SV11 )
| ~ ( mrel @ SV11 @ SY156 )
| ( mrel @ SV2 @ SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(59,plain,
! [SV12: mworld,SV4: mworld] :
( ( ! [SY157: $i] :
( ~ ( eiw_di @ SY157 @ SV4 )
| ~ ( mrel @ SV4 @ SV12 )
| ( eiw_di @ SY157 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV5: $i] :
( ( ( ~ ( eiw_di @ SV5 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV5 @ SV5 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(61,plain,
! [SV6: $i] :
( ( ( ~ ( eiw_di @ SV6 @ mactual ) )
= $true )
| ( ( ! [SY150: $i] :
( ~ ( eiw_di @ SY150 @ mactual )
| ~ ( qmltpeq @ SV6 @ SY150 @ mactual )
| ( qmltpeq @ SY150 @ SV6 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(62,plain,
! [SV7: $i] :
( ( ( ~ ( eiw_di @ SV7 @ mactual ) )
= $true )
| ( ( ! [SY151: $i] :
( ~ ( eiw_di @ SY151 @ mactual )
| ! [SY152: $i] :
( ~ ( eiw_di @ SY152 @ mactual )
| ~ ( qmltpeq @ SV7 @ SY151 @ mactual )
| ~ ( qmltpeq @ SY151 @ SY152 @ mactual )
| ( qmltpeq @ SV7 @ SY152 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(63,plain,
! [SV8: $i] :
( ( ( ~ ( eiw_di @ SV8 @ mactual ) )
= $true )
| ( ( ! [SY153: $i] :
( ~ ( eiw_di @ SY153 @ mactual )
| ~ ( p @ SV8 @ mactual )
| ~ ( qmltpeq @ SV8 @ SY153 @ mactual )
| ( p @ SY153 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(64,plain,
! [SV9: mworld] :
( ( ( ! [SY154: $i] :
( ~ ( eiw_di @ SY154 @ SV9 )
| ~ ( p @ SY154 @ SV9 ) ) )
= $true )
| ( ( ~ ( mrel @ mactual @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(65,plain,
! [SV10: $i] :
( ( ( ~ ( eiw_di @ SV10 @ mactual ) )
= $true )
| ( ( ! [SY155: mworld] :
( ~ ( mrel @ mactual @ SY155 )
| ~ ( ~ ( eiw_di @ ( sK1_SY11 @ SY155 @ SV10 ) @ SY155 )
| ~ ( qmltpeq @ SV10 @ ( sK1_SY11 @ SY155 @ SV10 ) @ SY155 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(66,plain,
( ( ~ ~ ( ~ ( mrel @ mactual @ sK3_SY145 )
| ~ ( p @ sK2_SY53 @ sK3_SY145 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(67,plain,
( ( ~ ( eiw_di @ sK2_SY53 @ mactual ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(68,plain,
! [SV13: mworld,SV11: mworld,SV2: mworld] :
( ( ~ ( mrel @ SV2 @ SV11 )
| ~ ( mrel @ SV11 @ SV13 )
| ( mrel @ SV2 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(69,plain,
! [SV12: mworld,SV4: mworld,SV14: $i] :
( ( ~ ( eiw_di @ SV14 @ SV4 )
| ~ ( mrel @ SV4 @ SV12 )
| ( eiw_di @ SV14 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV5: $i] :
( ( ( eiw_di @ SV5 @ mactual )
= $false )
| ( ( qmltpeq @ SV5 @ SV5 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(71,plain,
! [SV6: $i] :
( ( ( eiw_di @ SV6 @ mactual )
= $false )
| ( ( ! [SY150: $i] :
( ~ ( eiw_di @ SY150 @ mactual )
| ~ ( qmltpeq @ SV6 @ SY150 @ mactual )
| ( qmltpeq @ SY150 @ SV6 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV7: $i] :
( ( ( eiw_di @ SV7 @ mactual )
= $false )
| ( ( ! [SY151: $i] :
( ~ ( eiw_di @ SY151 @ mactual )
| ! [SY152: $i] :
( ~ ( eiw_di @ SY152 @ mactual )
| ~ ( qmltpeq @ SV7 @ SY151 @ mactual )
| ~ ( qmltpeq @ SY151 @ SY152 @ mactual )
| ( qmltpeq @ SV7 @ SY152 @ mactual ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV8: $i] :
( ( ( eiw_di @ SV8 @ mactual )
= $false )
| ( ( ! [SY153: $i] :
( ~ ( eiw_di @ SY153 @ mactual )
| ~ ( p @ SV8 @ mactual )
| ~ ( qmltpeq @ SV8 @ SY153 @ mactual )
| ( p @ SY153 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV9: mworld,SV15: $i] :
( ( ( ~ ( eiw_di @ SV15 @ SV9 )
| ~ ( p @ SV15 @ SV9 ) )
= $true )
| ( ( ~ ( mrel @ mactual @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV10: $i] :
( ( ( eiw_di @ SV10 @ mactual )
= $false )
| ( ( ! [SY155: mworld] :
( ~ ( mrel @ mactual @ SY155 )
| ~ ( ~ ( eiw_di @ ( sK1_SY11 @ SY155 @ SV10 ) @ SY155 )
| ~ ( qmltpeq @ SV10 @ ( sK1_SY11 @ SY155 @ SV10 ) @ SY155 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(76,plain,
( ( ~ ( ~ ( mrel @ mactual @ sK3_SY145 )
| ~ ( p @ sK2_SY53 @ sK3_SY145 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(77,plain,
( ( eiw_di @ sK2_SY53 @ mactual )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(78,plain,
! [SV13: mworld,SV11: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV11 )
| ~ ( mrel @ SV11 @ SV13 ) )
= $true )
| ( ( mrel @ SV2 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV12: mworld,SV4: mworld,SV14: $i] :
( ( ( ~ ( eiw_di @ SV14 @ SV4 )
| ~ ( mrel @ SV4 @ SV12 ) )
= $true )
| ( ( eiw_di @ SV14 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV6: $i,SV16: $i] :
( ( ( ~ ( eiw_di @ SV16 @ mactual )
| ~ ( qmltpeq @ SV6 @ SV16 @ mactual )
| ( qmltpeq @ SV16 @ SV6 @ mactual ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV7: $i,SV17: $i] :
( ( ( ~ ( eiw_di @ SV17 @ mactual )
| ! [SY158: $i] :
( ~ ( eiw_di @ SY158 @ mactual )
| ~ ( qmltpeq @ SV7 @ SV17 @ mactual )
| ~ ( qmltpeq @ SV17 @ SY158 @ mactual )
| ( qmltpeq @ SV7 @ SY158 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV8: $i,SV18: $i] :
( ( ( ~ ( eiw_di @ SV18 @ mactual )
| ~ ( p @ SV8 @ mactual )
| ~ ( qmltpeq @ SV8 @ SV18 @ mactual )
| ( p @ SV18 @ mactual ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV9: mworld,SV15: $i] :
( ( ( ~ ( eiw_di @ SV15 @ SV9 ) )
= $true )
| ( ( ~ ( p @ SV15 @ SV9 ) )
= $true )
| ( ( ~ ( mrel @ mactual @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV10: $i,SV19: mworld] :
( ( ( ~ ( mrel @ mactual @ SV19 )
| ~ ( ~ ( eiw_di @ ( sK1_SY11 @ SV19 @ SV10 ) @ SV19 )
| ~ ( qmltpeq @ SV10 @ ( sK1_SY11 @ SV19 @ SV10 ) @ SV19 ) ) )
= $true )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(85,plain,
( ( ~ ( mrel @ mactual @ sK3_SY145 )
| ~ ( p @ sK2_SY53 @ sK3_SY145 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV13: mworld,SV11: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV11 ) )
= $true )
| ( ( ~ ( mrel @ SV11 @ SV13 ) )
= $true )
| ( ( mrel @ SV2 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(87,plain,
! [SV12: mworld,SV4: mworld,SV14: $i] :
( ( ( ~ ( eiw_di @ SV14 @ SV4 ) )
= $true )
| ( ( ~ ( mrel @ SV4 @ SV12 ) )
= $true )
| ( ( eiw_di @ SV14 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV6: $i,SV16: $i] :
( ( ( ~ ( eiw_di @ SV16 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV6 @ SV16 @ mactual )
| ( qmltpeq @ SV16 @ SV6 @ mactual ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV7: $i,SV17: $i] :
( ( ( ~ ( eiw_di @ SV17 @ mactual ) )
= $true )
| ( ( ! [SY158: $i] :
( ~ ( eiw_di @ SY158 @ mactual )
| ~ ( qmltpeq @ SV7 @ SV17 @ mactual )
| ~ ( qmltpeq @ SV17 @ SY158 @ mactual )
| ( qmltpeq @ SV7 @ SY158 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV8: $i,SV18: $i] :
( ( ( ~ ( eiw_di @ SV18 @ mactual ) )
= $true )
| ( ( ~ ( p @ SV8 @ mactual )
| ~ ( qmltpeq @ SV8 @ SV18 @ mactual )
| ( p @ SV18 @ mactual ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV9: mworld,SV15: $i] :
( ( ( eiw_di @ SV15 @ SV9 )
= $false )
| ( ( ~ ( p @ SV15 @ SV9 ) )
= $true )
| ( ( ~ ( mrel @ mactual @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV10: $i,SV19: mworld] :
( ( ( ~ ( mrel @ mactual @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( eiw_di @ ( sK1_SY11 @ SV19 @ SV10 ) @ SV19 )
| ~ ( qmltpeq @ SV10 @ ( sK1_SY11 @ SV19 @ SV10 ) @ SV19 ) ) )
= $true )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(93,plain,
( ( ~ ( mrel @ mactual @ sK3_SY145 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(94,plain,
( ( ~ ( p @ sK2_SY53 @ sK3_SY145 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(95,plain,
! [SV13: mworld,SV11: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV11 )
= $false )
| ( ( ~ ( mrel @ SV11 @ SV13 ) )
= $true )
| ( ( mrel @ SV2 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV12: mworld,SV4: mworld,SV14: $i] :
( ( ( eiw_di @ SV14 @ SV4 )
= $false )
| ( ( ~ ( mrel @ SV4 @ SV12 ) )
= $true )
| ( ( eiw_di @ SV14 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(97,plain,
! [SV6: $i,SV16: $i] :
( ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV6 @ SV16 @ mactual )
| ( qmltpeq @ SV16 @ SV6 @ mactual ) )
= $true )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV7: $i,SV17: $i] :
( ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( ! [SY158: $i] :
( ~ ( eiw_di @ SY158 @ mactual )
| ~ ( qmltpeq @ SV7 @ SV17 @ mactual )
| ~ ( qmltpeq @ SV17 @ SY158 @ mactual )
| ( qmltpeq @ SV7 @ SY158 @ mactual ) ) )
= $true )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(99,plain,
! [SV8: $i,SV18: $i] :
( ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( ~ ( p @ SV8 @ mactual )
| ~ ( qmltpeq @ SV8 @ SV18 @ mactual )
| ( p @ SV18 @ mactual ) )
= $true )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV9: mworld,SV15: $i] :
( ( ( p @ SV15 @ SV9 )
= $false )
| ( ( eiw_di @ SV15 @ SV9 )
= $false )
| ( ( ~ ( mrel @ mactual @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(101,plain,
! [SV10: $i,SV19: mworld] :
( ( ( mrel @ mactual @ SV19 )
= $false )
| ( ( ~ ( ~ ( eiw_di @ ( sK1_SY11 @ SV19 @ SV10 ) @ SV19 )
| ~ ( qmltpeq @ SV10 @ ( sK1_SY11 @ SV19 @ SV10 ) @ SV19 ) ) )
= $true )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(102,plain,
( ( mrel @ mactual @ sK3_SY145 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(103,plain,
( ( p @ sK2_SY53 @ sK3_SY145 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(104,plain,
! [SV2: mworld,SV13: mworld,SV11: mworld] :
( ( ( mrel @ SV11 @ SV13 )
= $false )
| ( ( mrel @ SV2 @ SV11 )
= $false )
| ( ( mrel @ SV2 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV14: $i,SV12: mworld,SV4: mworld] :
( ( ( mrel @ SV4 @ SV12 )
= $false )
| ( ( eiw_di @ SV14 @ SV4 )
= $false )
| ( ( eiw_di @ SV14 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV16: $i,SV6: $i] :
( ( ( ~ ( qmltpeq @ SV6 @ SV16 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV16 @ SV6 @ mactual )
= $true )
| ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV17: $i,SV7: $i,SV20: $i] :
( ( ( ~ ( eiw_di @ SV20 @ mactual )
| ~ ( qmltpeq @ SV7 @ SV17 @ mactual )
| ~ ( qmltpeq @ SV17 @ SV20 @ mactual )
| ( qmltpeq @ SV7 @ SV20 @ mactual ) )
= $true )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( p @ SV8 @ mactual )
| ~ ( qmltpeq @ SV8 @ SV18 @ mactual ) )
= $true )
| ( ( p @ SV18 @ mactual )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV15: $i,SV9: mworld] :
( ( ( mrel @ mactual @ SV9 )
= $false )
| ( ( eiw_di @ SV15 @ SV9 )
= $false )
| ( ( p @ SV15 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV10: $i,SV19: mworld] :
( ( ( ~ ( eiw_di @ ( sK1_SY11 @ SV19 @ SV10 ) @ SV19 )
| ~ ( qmltpeq @ SV10 @ ( sK1_SY11 @ SV19 @ SV10 ) @ SV19 ) )
= $false )
| ( ( mrel @ mactual @ SV19 )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV16: $i,SV6: $i] :
( ( ( qmltpeq @ SV6 @ SV16 @ mactual )
= $false )
| ( ( qmltpeq @ SV16 @ SV6 @ mactual )
= $true )
| ( ( eiw_di @ SV16 @ mactual )
= $false )
| ( ( eiw_di @ SV6 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(112,plain,
! [SV17: $i,SV7: $i,SV20: $i] :
( ( ( ~ ( eiw_di @ SV20 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV7 @ SV17 @ mactual )
| ~ ( qmltpeq @ SV17 @ SV20 @ mactual )
| ( qmltpeq @ SV7 @ SV20 @ mactual ) )
= $true )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(113,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( p @ SV8 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV8 @ SV18 @ mactual ) )
= $true )
| ( ( p @ SV18 @ mactual )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(114,plain,
! [SV10: $i,SV19: mworld] :
( ( ( ~ ( eiw_di @ ( sK1_SY11 @ SV19 @ SV10 ) @ SV19 ) )
= $false )
| ( ( mrel @ mactual @ SV19 )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(115,plain,
! [SV19: mworld,SV10: $i] :
( ( ( ~ ( qmltpeq @ SV10 @ ( sK1_SY11 @ SV19 @ SV10 ) @ SV19 ) )
= $false )
| ( ( mrel @ mactual @ SV19 )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(116,plain,
! [SV17: $i,SV7: $i,SV20: $i] :
( ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV7 @ SV17 @ mactual )
| ~ ( qmltpeq @ SV17 @ SV20 @ mactual )
| ( qmltpeq @ SV7 @ SV20 @ mactual ) )
= $true )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(117,plain,
! [SV18: $i,SV8: $i] :
( ( ( p @ SV8 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV8 @ SV18 @ mactual ) )
= $true )
| ( ( p @ SV18 @ mactual )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV10: $i,SV19: mworld] :
( ( ( eiw_di @ ( sK1_SY11 @ SV19 @ SV10 ) @ SV19 )
= $true )
| ( ( mrel @ mactual @ SV19 )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(119,plain,
! [SV19: mworld,SV10: $i] :
( ( ( qmltpeq @ SV10 @ ( sK1_SY11 @ SV19 @ SV10 ) @ SV19 )
= $true )
| ( ( mrel @ mactual @ SV19 )
= $false )
| ( ( eiw_di @ SV10 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(120,plain,
! [SV20: $i,SV17: $i,SV7: $i] :
( ( ( ~ ( qmltpeq @ SV7 @ SV17 @ mactual )
| ~ ( qmltpeq @ SV17 @ SV20 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV7 @ SV20 @ mactual )
= $true )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(121,plain,
! [SV18: $i,SV8: $i] :
( ( ( qmltpeq @ SV8 @ SV18 @ mactual )
= $false )
| ( ( p @ SV8 @ mactual )
= $false )
| ( ( p @ SV18 @ mactual )
= $true )
| ( ( eiw_di @ SV18 @ mactual )
= $false )
| ( ( eiw_di @ SV8 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(122,plain,
! [SV20: $i,SV17: $i,SV7: $i] :
( ( ( ~ ( qmltpeq @ SV7 @ SV17 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV17 @ SV20 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV7 @ SV20 @ mactual )
= $true )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(123,plain,
! [SV20: $i,SV17: $i,SV7: $i] :
( ( ( qmltpeq @ SV7 @ SV17 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV17 @ SV20 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV7 @ SV20 @ mactual )
= $true )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(124,plain,
! [SV7: $i,SV20: $i,SV17: $i] :
( ( ( qmltpeq @ SV17 @ SV20 @ mactual )
= $false )
| ( ( qmltpeq @ SV7 @ SV17 @ mactual )
= $false )
| ( ( qmltpeq @ SV7 @ SV20 @ mactual )
= $true )
| ( ( eiw_di @ SV20 @ mactual )
= $false )
| ( ( eiw_di @ SV17 @ mactual )
= $false )
| ( ( eiw_di @ SV7 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(125,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[47,124,121,119,118,111,109,105,104,103,102,77,70,49]) ).
thf(126,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO891^16 : 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
% 0.07/0.17 % Computer : n007.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 17:51:15 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.23
% 0.07/0.23 No.of.Axioms: 8
% 0.07/0.23
% 0.07/0.23 Length.of.Defs: 1663
% 0.07/0.23
% 0.07/0.23 Contains.Choice.Funs: false
% 0.07/0.23 .....
% 0.07/0.23
% 0.07/0.23 ********************************
% 0.07/0.23 * All subproblems solved! *
% 0.07/0.23 ********************************
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:125,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.23
% 0.07/0.23 %**** Beginning of derivation protocol ****
% 0.07/0.23 % SZS output start CNFRefutation
% See solution above
% 0.07/0.23
% 0.07/0.23 %**** End of derivation protocol ****
% 0.07/0.23 %**** no. of clauses in derivation: 126 ****
% 0.07/0.23 %**** clause counter: 125 ****
% 0.07/0.23
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:125,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------