%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL959^24 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 10:31:10 AM UTC 2026
% Result : Theorem 0.08s 0.31s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 147 ( 92 unt; 0 typ; 10 def)
% Number of atoms : 966 ( 210 equ; 0 cnn)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 1855 ( 399 ~; 271 |; 16 &;1097 @)
% ( 1 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 7 con; 0-3 aty)
% Number of variables : 422 ( 31 ^; 377 !; 14 ?; 422 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(tp_f,type,
f: $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_sK10_SY209,type,
sK10_SY209: $i ).
thf(tp_sK11_SY224,type,
sK11_SY224: mworld > mworld ).
thf(tp_sK1_SX0,type,
sK1_SX0: mworld ).
thf(tp_sK2_SY184,type,
sK2_SY184: mworld > $i ).
thf(tp_sK3_SY195,type,
sK3_SY195: mworld > mworld ).
thf(tp_sK4_SY200,type,
sK4_SY200: mworld > $i ).
thf(tp_sK5_SY198,type,
sK5_SY198: $i > mworld ).
thf(tp_sK6_SY202,type,
sK6_SY202: mworld > mworld ).
thf(tp_sK7_SX0,type,
sK7_SX0: mworld ).
thf(tp_sK8_SY205,type,
sK8_SY205: mworld > $i ).
thf(tp_sK9_SY212,type,
sK9_SY212: mworld ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_def) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def) ).
thf(1,axiom,
! [W: mworld,V: mworld,X: $i] :
( ( ( eiw_di @ X @ W )
& ( mrel @ V @ W ) )
=> ( eiw_di @ X @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_decr) ).
thf(2,axiom,
! [W: mworld] :
? [X: $i] : ( eiw_di @ X @ W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(3,axiom,
! [W: mworld,V: mworld] : ( mrel @ W @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
thf(4,conjecture,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X: $i] : ( mbox @ ( f @ X ) ) ) ) ) )
@ ( mexists_di
@ ^ [Y: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ Y ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [Y: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ Y ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X: $i] : ( mbox @ ( f @ X ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish203) ).
thf(5,negated_conjecture,
( ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X: $i] : ( mbox @ ( f @ X ) ) ) ) ) )
@ ( mexists_di
@ ^ [Y: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ Y ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [Y: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ Y ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X: $i] : ( mbox @ ( f @ X ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ! [SY144: mworld] :
( ( mrel @ mactual @ SY144 )
=> ( ! [SY52: mworld] :
( ( mrel @ SY144 @ SY52 )
=> ~ ! [SY18: mworld] :
( ( mrel @ SY52 @ SY18 )
=> ! [SY10: $i] :
( ( eiw_di @ SY10 @ SY18 )
=> ! [SY11: mworld] :
( ( mrel @ SY18 @ SY11 )
=> ( f @ SY10 @ SY11 ) ) ) ) )
=> ? [SY56: $i] :
( ( eiw_di @ SY56 @ SY144 )
& ! [SY57: mworld] :
( ( mrel @ SY144 @ SY57 )
=> ~ ! [SY39: mworld] :
( ( mrel @ SY57 @ SY39 )
=> ( f @ SY56 @ SY39 ) ) ) ) ) )
& ! [SY152: mworld] :
( ( mrel @ mactual @ SY152 )
=> ( ? [SY120: $i] :
( ( eiw_di @ SY120 @ SY152 )
& ! [SY121: mworld] :
( ( mrel @ SY152 @ SY121 )
=> ~ ! [SY81: mworld] :
( ( mrel @ SY121 @ SY81 )
=> ( f @ SY120 @ SY81 ) ) ) )
=> ! [SY123: mworld] :
( ( mrel @ SY152 @ SY123 )
=> ~ ! [SY107: mworld] :
( ( mrel @ SY123 @ SY107 )
=> ! [SY99: $i] :
( ( eiw_di @ SY99 @ SY107 )
=> ! [SY100: mworld] :
( ( mrel @ SY107 @ SY100 )
=> ( f @ SY99 @ SY100 ) ) ) ) ) ) ) )
= $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 @ V @ W ) )
=> ( 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,
( ( ! [SY144: mworld] :
( ( mrel @ mactual @ SY144 )
=> ( ! [SY52: mworld] :
( ( mrel @ SY144 @ SY52 )
=> ~ ! [SY18: mworld] :
( ( mrel @ SY52 @ SY18 )
=> ! [SY10: $i] :
( ( eiw_di @ SY10 @ SY18 )
=> ! [SY11: mworld] :
( ( mrel @ SY18 @ SY11 )
=> ( f @ SY10 @ SY11 ) ) ) ) )
=> ? [SY56: $i] :
( ( eiw_di @ SY56 @ SY144 )
& ! [SY57: mworld] :
( ( mrel @ SY144 @ SY57 )
=> ~ ! [SY39: mworld] :
( ( mrel @ SY57 @ SY39 )
=> ( f @ SY56 @ SY39 ) ) ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(11,plain,
( ( ! [SY152: mworld] :
( ( mrel @ mactual @ SY152 )
=> ( ? [SY120: $i] :
( ( eiw_di @ SY120 @ SY152 )
& ! [SY121: mworld] :
( ( mrel @ SY152 @ SY121 )
=> ~ ! [SY81: mworld] :
( ( mrel @ SY121 @ SY81 )
=> ( f @ SY120 @ SY81 ) ) ) )
=> ! [SY123: mworld] :
( ( mrel @ SY152 @ SY123 )
=> ~ ! [SY107: mworld] :
( ( mrel @ SY123 @ SY107 )
=> ! [SY99: $i] :
( ( eiw_di @ SY99 @ SY107 )
=> ! [SY100: mworld] :
( ( mrel @ SY107 @ SY100 )
=> ( f @ SY99 @ SY100 ) ) ) ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(12,plain,
( ( ~ ! [SY144: mworld] :
( ( mrel @ mactual @ SY144 )
=> ( ! [SY52: mworld] :
( ( mrel @ SY144 @ SY52 )
=> ~ ! [SY18: mworld] :
( ( mrel @ SY52 @ SY18 )
=> ! [SY10: $i] :
( ( eiw_di @ SY10 @ SY18 )
=> ! [SY11: mworld] :
( ( mrel @ SY18 @ SY11 )
=> ( f @ SY10 @ SY11 ) ) ) ) )
=> ? [SY56: $i] :
( ( eiw_di @ SY56 @ SY144 )
& ! [SY57: mworld] :
( ( mrel @ SY144 @ SY57 )
=> ~ ! [SY39: mworld] :
( ( mrel @ SY57 @ SY39 )
=> ( f @ SY56 @ SY39 ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ! [SY152: mworld] :
( ( mrel @ mactual @ SY152 )
=> ( ? [SY120: $i] :
( ( eiw_di @ SY120 @ SY152 )
& ! [SY121: mworld] :
( ( mrel @ SY152 @ SY121 )
=> ~ ! [SY81: mworld] :
( ( mrel @ SY121 @ SY81 )
=> ( f @ SY120 @ SY81 ) ) ) )
=> ! [SY123: mworld] :
( ( mrel @ SY152 @ SY123 )
=> ~ ! [SY107: mworld] :
( ( mrel @ SY123 @ SY107 )
=> ! [SY99: $i] :
( ( eiw_di @ SY99 @ SY107 )
=> ! [SY100: mworld] :
( ( mrel @ SY107 @ SY100 )
=> ( f @ SY99 @ SY100 ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [W: mworld,V: mworld] : ( mrel @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
( ( ! [W: mworld] :
? [X: $i] : ( eiw_di @ X @ W ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(16,plain,
( ( ! [W: mworld,V: mworld,X: $i] :
( ( ( eiw_di @ X @ W )
& ( mrel @ V @ W ) )
=> ( eiw_di @ X @ V ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(17,plain,
( ( ~ ! [SY144: mworld] :
( ( mrel @ mactual @ SY144 )
=> ( ! [SY52: mworld] :
( ( mrel @ SY144 @ SY52 )
=> ~ ! [SY18: mworld] :
( ( mrel @ SY52 @ SY18 )
=> ! [SY10: $i] :
( ( eiw_di @ SY10 @ SY18 )
=> ! [SY11: mworld] :
( ( mrel @ SY18 @ SY11 )
=> ( f @ SY10 @ SY11 ) ) ) ) )
=> ? [SY56: $i] :
( ( eiw_di @ SY56 @ SY144 )
& ! [SY57: mworld] :
( ( mrel @ SY144 @ SY57 )
=> ~ ! [SY39: mworld] :
( ( mrel @ SY57 @ SY39 )
=> ( f @ SY56 @ SY39 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [SX0: mworld] :
~ ! [SX1: $i] :
~ ( eiw_di @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[15,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(19,plain,
( ( ! [SX0: mworld,SX1: mworld,SX2: $i] :
( ~ ~ ( ~ ( eiw_di @ SX2 @ SX0 )
| ~ ( mrel @ SX1 @ SX0 ) )
| ( eiw_di @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(20,plain,
( ( ~ ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ~ ! [SX3: mworld] :
( ~ ( mrel @ SX2 @ SX3 )
| ( f @ SX1 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(21,plain,
! [SV1: mworld] :
( ( ! [SY183: mworld] : ( mrel @ SV1 @ SY183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(22,plain,
! [SV2: mworld] :
( ( ~ ! [SY184: $i] :
~ ( eiw_di @ SY184 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV3: mworld] :
( ( ! [SY185: mworld,SY186: $i] :
( ~ ~ ( ~ ( eiw_di @ SY186 @ SV3 )
| ~ ( mrel @ SY185 @ SV3 ) )
| ( eiw_di @ SY186 @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ~ ! [SX3: mworld] :
( ~ ( mrel @ SX2 @ SX3 )
| ( f @ SX1 @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV4: mworld,SV1: mworld] :
( ( mrel @ SV1 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: mworld] :
( ( ! [SY184: $i] :
~ ( eiw_di @ SY184 @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV5: mworld,SV3: mworld] :
( ( ! [SY187: $i] :
( ~ ~ ( ~ ( eiw_di @ SY187 @ SV3 )
| ~ ( mrel @ SV5 @ SV3 ) )
| ( eiw_di @ SY187 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ( mrel @ mactual @ sK1_SX0 )
| ~ ! [SY188: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY188 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY188 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
| ~ ! [SY192: $i] :
~ ~ ( ~ ( eiw_di @ SY192 @ sK1_SX0 )
| ~ ! [SY193: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY193 )
| ~ ! [SX3: mworld] :
( ~ ( mrel @ SY193 @ SX3 )
| ( f @ SY192 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(29,plain,
! [SV2: mworld] :
( ( ~ ( eiw_di @ ( sK2_SY184 @ SV2 ) @ SV2 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(30,plain,
! [SV5: mworld,SV3: mworld,SV6: $i] :
( ( ~ ~ ( ~ ( eiw_di @ SV6 @ SV3 )
| ~ ( mrel @ SV5 @ SV3 ) )
| ( eiw_di @ SV6 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ~ ( mrel @ mactual @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ! [SY188: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY188 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY188 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
| ~ ! [SY192: $i] :
~ ~ ( ~ ( eiw_di @ SY192 @ sK1_SX0 )
| ~ ! [SY193: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY193 )
| ~ ! [SX3: mworld] :
( ~ ( mrel @ SY193 @ SX3 )
| ( f @ SY192 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(33,plain,
! [SV2: mworld] :
( ( eiw_di @ ( sK2_SY184 @ SV2 ) @ SV2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV5: mworld,SV3: mworld,SV6: $i] :
( ( ( ~ ~ ( ~ ( eiw_di @ SV6 @ SV3 )
| ~ ( mrel @ SV5 @ SV3 ) ) )
= $true )
| ( ( eiw_di @ SV6 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(35,plain,
( ( mrel @ mactual @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ ! [SY188: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY188 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY188 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(37,plain,
( ( ~ ! [SY192: $i] :
~ ~ ( ~ ( eiw_di @ SY192 @ sK1_SX0 )
| ~ ! [SY193: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY193 )
| ~ ! [SX3: mworld] :
( ~ ( mrel @ SY193 @ SX3 )
| ( f @ SY192 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(38,plain,
! [SV5: mworld,SV3: mworld,SV6: $i] :
( ( ( ~ ( ~ ( eiw_di @ SV6 @ SV3 )
| ~ ( mrel @ SV5 @ SV3 ) ) )
= $false )
| ( ( eiw_di @ SV6 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(39,plain,
( ( ! [SY188: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY188 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY188 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(40,plain,
( ( ! [SY192: $i] :
~ ~ ( ~ ( eiw_di @ SY192 @ sK1_SX0 )
| ~ ! [SY193: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY193 )
| ~ ! [SX3: mworld] :
( ~ ( mrel @ SY193 @ SX3 )
| ( f @ SY192 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(41,plain,
! [SV5: mworld,SV3: mworld,SV6: $i] :
( ( ( ~ ( eiw_di @ SV6 @ SV3 )
| ~ ( mrel @ SV5 @ SV3 ) )
= $true )
| ( ( eiw_di @ SV6 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV7: mworld] :
( ( ~ ( mrel @ sK1_SX0 @ SV7 )
| ~ ! [SY195: mworld] :
( ~ ( mrel @ SV7 @ SY195 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY195 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY195 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV8: $i] :
( ( ~ ~ ( ~ ( eiw_di @ SV8 @ sK1_SX0 )
| ~ ! [SY198: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY198 )
| ~ ! [SY199: mworld] :
( ~ ( mrel @ SY198 @ SY199 )
| ( f @ SV8 @ SY199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV5: mworld,SV3: mworld,SV6: $i] :
( ( ( ~ ( eiw_di @ SV6 @ SV3 ) )
= $true )
| ( ( ~ ( mrel @ SV5 @ SV3 ) )
= $true )
| ( ( eiw_di @ SV6 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV7: mworld] :
( ( ( ~ ( mrel @ sK1_SX0 @ SV7 ) )
= $true )
| ( ( ~ ! [SY195: mworld] :
( ~ ( mrel @ SV7 @ SY195 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY195 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY195 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV8: $i] :
( ( ~ ( ~ ( eiw_di @ SV8 @ sK1_SX0 )
| ~ ! [SY198: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY198 )
| ~ ! [SY199: mworld] :
( ~ ( mrel @ SY198 @ SY199 )
| ( f @ SV8 @ SY199 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV5: mworld,SV3: mworld,SV6: $i] :
( ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( ~ ( mrel @ SV5 @ SV3 ) )
= $true )
| ( ( eiw_di @ SV6 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV7: mworld] :
( ( ( mrel @ sK1_SX0 @ SV7 )
= $false )
| ( ( ~ ! [SY195: mworld] :
( ~ ( mrel @ SV7 @ SY195 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY195 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY195 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV8: $i] :
( ( ~ ( eiw_di @ SV8 @ sK1_SX0 )
| ~ ! [SY198: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY198 )
| ~ ! [SY199: mworld] :
( ~ ( mrel @ SY198 @ SY199 )
| ( f @ SV8 @ SY199 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV6: $i,SV3: mworld,SV5: mworld] :
( ( ( mrel @ SV5 @ SV3 )
= $false )
| ( ( eiw_di @ SV6 @ SV3 )
= $false )
| ( ( eiw_di @ SV6 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV7: mworld] :
( ( ( ! [SY195: mworld] :
( ~ ( mrel @ SV7 @ SY195 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY195 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY195 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV8: $i] :
( ( ( ~ ( eiw_di @ SV8 @ sK1_SX0 ) )
= $true )
| ( ( ~ ! [SY198: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY198 )
| ~ ! [SY199: mworld] :
( ~ ( mrel @ SY198 @ SY199 )
| ( f @ SV8 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV7: mworld] :
( ( ( ~ ( mrel @ SV7 @ ( sK3_SY195 @ SV7 ) )
| ! [SY200: $i] :
( ~ ( eiw_di @ SY200 @ ( sK3_SY195 @ SV7 ) )
| ! [SY201: mworld] :
( ~ ( mrel @ ( sK3_SY195 @ SV7 ) @ SY201 )
| ( f @ SY200 @ SY201 ) ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV7 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(54,plain,
! [SV8: $i] :
( ( ( eiw_di @ SV8 @ sK1_SX0 )
= $false )
| ( ( ~ ! [SY198: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY198 )
| ~ ! [SY199: mworld] :
( ~ ( mrel @ SY198 @ SY199 )
| ( f @ SV8 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV7: mworld] :
( ( ( ~ ( mrel @ SV7 @ ( sK3_SY195 @ SV7 ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV7: mworld] :
( ( ( ! [SY200: $i] :
( ~ ( eiw_di @ SY200 @ ( sK3_SY195 @ SV7 ) )
| ! [SY201: mworld] :
( ~ ( mrel @ ( sK3_SY195 @ SV7 ) @ SY201 )
| ( f @ SY200 @ SY201 ) ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(57,plain,
! [SV8: $i] :
( ( ( ! [SY198: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY198 )
| ~ ! [SY199: mworld] :
( ~ ( mrel @ SY198 @ SY199 )
| ( f @ SV8 @ SY199 ) ) ) )
= $false )
| ( ( eiw_di @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV7: mworld] :
( ( ( mrel @ SV7 @ ( sK3_SY195 @ SV7 ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(59,plain,
! [SV7: mworld] :
( ( ( ~ ( eiw_di @ ( sK4_SY200 @ SV7 ) @ ( sK3_SY195 @ SV7 ) )
| ! [SY202: mworld] :
( ~ ( mrel @ ( sK3_SY195 @ SV7 ) @ SY202 )
| ( f @ ( sK4_SY200 @ SV7 ) @ SY202 ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV7 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(60,plain,
! [SV8: $i] :
( ( ( ~ ( mrel @ sK1_SX0 @ ( sK5_SY198 @ SV8 ) )
| ~ ! [SY203: mworld] :
( ~ ( mrel @ ( sK5_SY198 @ SV8 ) @ SY203 )
| ( f @ SV8 @ SY203 ) ) )
= $false )
| ( ( eiw_di @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(61,plain,
! [SV7: mworld] :
( ( ( ~ ( eiw_di @ ( sK4_SY200 @ SV7 ) @ ( sK3_SY195 @ SV7 ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(62,plain,
! [SV7: mworld] :
( ( ( ! [SY202: mworld] :
( ~ ( mrel @ ( sK3_SY195 @ SV7 ) @ SY202 )
| ( f @ ( sK4_SY200 @ SV7 ) @ SY202 ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(63,plain,
! [SV8: $i] :
( ( ( ~ ( mrel @ sK1_SX0 @ ( sK5_SY198 @ SV8 ) ) )
= $false )
| ( ( eiw_di @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(64,plain,
! [SV8: $i] :
( ( ( ~ ! [SY203: mworld] :
( ~ ( mrel @ ( sK5_SY198 @ SV8 ) @ SY203 )
| ( f @ SV8 @ SY203 ) ) )
= $false )
| ( ( eiw_di @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(65,plain,
! [SV7: mworld] :
( ( ( eiw_di @ ( sK4_SY200 @ SV7 ) @ ( sK3_SY195 @ SV7 ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(66,plain,
! [SV7: mworld] :
( ( ( ~ ( mrel @ ( sK3_SY195 @ SV7 ) @ ( sK6_SY202 @ SV7 ) )
| ( f @ ( sK4_SY200 @ SV7 ) @ ( sK6_SY202 @ SV7 ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV7 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(67,plain,
! [SV8: $i] :
( ( ( mrel @ sK1_SX0 @ ( sK5_SY198 @ SV8 ) )
= $true )
| ( ( eiw_di @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV8: $i] :
( ( ( ! [SY203: mworld] :
( ~ ( mrel @ ( sK5_SY198 @ SV8 ) @ SY203 )
| ( f @ SV8 @ SY203 ) ) )
= $true )
| ( ( eiw_di @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(69,plain,
! [SV7: mworld] :
( ( ( ~ ( mrel @ ( sK3_SY195 @ SV7 ) @ ( sK6_SY202 @ SV7 ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(70,plain,
! [SV7: mworld] :
( ( ( f @ ( sK4_SY200 @ SV7 ) @ ( sK6_SY202 @ SV7 ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(71,plain,
! [SV9: mworld,SV8: $i] :
( ( ( ~ ( mrel @ ( sK5_SY198 @ SV8 ) @ SV9 )
| ( f @ SV8 @ SV9 ) )
= $true )
| ( ( eiw_di @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV7: mworld] :
( ( ( mrel @ ( sK3_SY195 @ SV7 ) @ ( sK6_SY202 @ SV7 ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(73,plain,
! [SV9: mworld,SV8: $i] :
( ( ( ~ ( mrel @ ( sK5_SY198 @ SV8 ) @ SV9 ) )
= $true )
| ( ( f @ SV8 @ SV9 )
= $true )
| ( ( eiw_di @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(74,plain,
! [SV9: mworld,SV8: $i] :
( ( ( mrel @ ( sK5_SY198 @ SV8 ) @ SV9 )
= $false )
| ( ( f @ SV8 @ SV9 )
= $true )
| ( ( eiw_di @ SV8 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(75,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,74,72,70,67,65,58,50,35,33]) ).
thf(76,plain,
( ( ! [W: mworld,V: mworld] : ( mrel @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(77,plain,
( ( ! [W: mworld] :
? [X: $i] : ( eiw_di @ X @ W ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(78,plain,
( ( ! [W: mworld,V: mworld,X: $i] :
( ( ( eiw_di @ X @ W )
& ( mrel @ V @ W ) )
=> ( eiw_di @ X @ V ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(79,plain,
( ( ~ ! [SY152: mworld] :
( ( mrel @ mactual @ SY152 )
=> ( ? [SY120: $i] :
( ( eiw_di @ SY120 @ SY152 )
& ! [SY121: mworld] :
( ( mrel @ SY152 @ SY121 )
=> ~ ! [SY81: mworld] :
( ( mrel @ SY121 @ SY81 )
=> ( f @ SY120 @ SY81 ) ) ) )
=> ! [SY123: mworld] :
( ( mrel @ SY152 @ SY123 )
=> ~ ! [SY107: mworld] :
( ( mrel @ SY123 @ SY107 )
=> ! [SY99: $i] :
( ( eiw_di @ SY99 @ SY107 )
=> ! [SY100: mworld] :
( ( mrel @ SY107 @ SY100 )
=> ( f @ SY99 @ SY100 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(80,plain,
( ( ! [SX0: mworld] :
~ ! [SX1: $i] :
~ ( eiw_di @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[77,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(81,plain,
( ( ! [SX0: mworld,SX1: mworld,SX2: $i] :
( ~ ~ ( ~ ( eiw_di @ SX2 @ SX0 )
| ~ ( mrel @ SX1 @ SX0 ) )
| ( eiw_di @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(82,plain,
( ( ~ ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ~ ! [SX3: mworld] :
( ~ ( mrel @ SX2 @ SX3 )
| ( f @ SX1 @ SX3 ) ) ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(83,plain,
! [SV10: mworld] :
( ( ! [SY204: mworld] : ( mrel @ SV10 @ SY204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV11: mworld] :
( ( ~ ! [SY205: $i] :
~ ( eiw_di @ SY205 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV12: mworld] :
( ( ! [SY206: mworld,SY207: $i] :
( ~ ~ ( ~ ( eiw_di @ SY207 @ SV12 )
| ~ ( mrel @ SY206 @ SV12 ) )
| ( eiw_di @ SY207 @ SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(86,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX0 @ SX2 )
| ~ ! [SX3: mworld] :
( ~ ( mrel @ SX2 @ SX3 )
| ( f @ SX1 @ SX3 ) ) ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV13: mworld,SV10: mworld] :
( ( mrel @ SV10 @ SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV11: mworld] :
( ( ! [SY205: $i] :
~ ( eiw_di @ SY205 @ SV11 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV14: mworld,SV12: mworld] :
( ( ! [SY208: $i] :
( ~ ~ ( ~ ( eiw_di @ SY208 @ SV12 )
| ~ ( mrel @ SV14 @ SV12 ) )
| ( eiw_di @ SY208 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(90,plain,
( ( ~ ( mrel @ mactual @ sK7_SX0 )
| ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( eiw_di @ SY209 @ sK7_SX0 )
| ~ ! [SY210: mworld] :
( ~ ( mrel @ sK7_SX0 @ SY210 )
| ~ ! [SX3: mworld] :
( ~ ( mrel @ SY210 @ SX3 )
| ( f @ SY209 @ SX3 ) ) ) )
| ! [SY212: mworld] :
( ~ ( mrel @ sK7_SX0 @ SY212 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY212 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(91,plain,
! [SV11: mworld] :
( ( ~ ( eiw_di @ ( sK8_SY205 @ SV11 ) @ SV11 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(92,plain,
! [SV14: mworld,SV12: mworld,SV15: $i] :
( ( ~ ~ ( ~ ( eiw_di @ SV15 @ SV12 )
| ~ ( mrel @ SV14 @ SV12 ) )
| ( eiw_di @ SV15 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(93,plain,
( ( ~ ( mrel @ mactual @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(94,plain,
( ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( eiw_di @ SY209 @ sK7_SX0 )
| ~ ! [SY210: mworld] :
( ~ ( mrel @ sK7_SX0 @ SY210 )
| ~ ! [SX3: mworld] :
( ~ ( mrel @ SY210 @ SX3 )
| ( f @ SY209 @ SX3 ) ) ) )
| ! [SY212: mworld] :
( ~ ( mrel @ sK7_SX0 @ SY212 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY212 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(95,plain,
! [SV11: mworld] :
( ( eiw_di @ ( sK8_SY205 @ SV11 ) @ SV11 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(96,plain,
! [SV14: mworld,SV12: mworld,SV15: $i] :
( ( ( ~ ~ ( ~ ( eiw_di @ SV15 @ SV12 )
| ~ ( mrel @ SV14 @ SV12 ) ) )
= $true )
| ( ( eiw_di @ SV15 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(97,plain,
( ( mrel @ mactual @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(98,plain,
( ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( eiw_di @ SY209 @ sK7_SX0 )
| ~ ! [SY210: mworld] :
( ~ ( mrel @ sK7_SX0 @ SY210 )
| ~ ! [SX3: mworld] :
( ~ ( mrel @ SY210 @ SX3 )
| ( f @ SY209 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(99,plain,
( ( ! [SY212: mworld] :
( ~ ( mrel @ sK7_SX0 @ SY212 )
| ~ ! [SX2: mworld] :
( ~ ( mrel @ SY212 @ SX2 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SX2 )
| ! [SX4: mworld] :
( ~ ( mrel @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(100,plain,
! [SV14: mworld,SV12: mworld,SV15: $i] :
( ( ( ~ ( ~ ( eiw_di @ SV15 @ SV12 )
| ~ ( mrel @ SV14 @ SV12 ) ) )
= $false )
| ( ( eiw_di @ SV15 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(101,plain,
( ( ~ ! [SY209: $i] :
~ ~ ( ~ ( eiw_di @ SY209 @ sK7_SX0 )
| ~ ! [SY210: mworld] :
( ~ ( mrel @ sK7_SX0 @ SY210 )
| ~ ! [SX3: mworld] :
( ~ ( mrel @ SY210 @ SX3 )
| ( f @ SY209 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(102,plain,
( ( ~ ( mrel @ sK7_SX0 @ sK9_SY212 )
| ~ ! [SY216: mworld] :
( ~ ( mrel @ sK9_SY212 @ SY216 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY216 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY216 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[99]) ).
thf(103,plain,
! [SV14: mworld,SV12: mworld,SV15: $i] :
( ( ( ~ ( eiw_di @ SV15 @ SV12 )
| ~ ( mrel @ SV14 @ SV12 ) )
= $true )
| ( ( eiw_di @ SV15 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(104,plain,
( ( ! [SY209: $i] :
~ ~ ( ~ ( eiw_di @ SY209 @ sK7_SX0 )
| ~ ! [SY210: mworld] :
( ~ ( mrel @ sK7_SX0 @ SY210 )
| ~ ! [SX3: mworld] :
( ~ ( mrel @ SY210 @ SX3 )
| ( f @ SY209 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(105,plain,
( ( ~ ( mrel @ sK7_SX0 @ sK9_SY212 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(106,plain,
( ( ~ ! [SY216: mworld] :
( ~ ( mrel @ sK9_SY212 @ SY216 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY216 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY216 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(107,plain,
! [SV14: mworld,SV12: mworld,SV15: $i] :
( ( ( ~ ( eiw_di @ SV15 @ SV12 ) )
= $true )
| ( ( ~ ( mrel @ SV14 @ SV12 ) )
= $true )
| ( ( eiw_di @ SV15 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(108,plain,
( ( ~ ~ ( ~ ( eiw_di @ sK10_SY209 @ sK7_SX0 )
| ~ ! [SY219: mworld] :
( ~ ( mrel @ sK7_SX0 @ SY219 )
| ~ ! [SY220: mworld] :
( ~ ( mrel @ SY219 @ SY220 )
| ( f @ sK10_SY209 @ SY220 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[104]) ).
thf(109,plain,
( ( mrel @ sK7_SX0 @ sK9_SY212 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(110,plain,
( ( ! [SY216: mworld] :
( ~ ( mrel @ sK9_SY212 @ SY216 )
| ! [SX3: $i] :
( ~ ( eiw_di @ SX3 @ SY216 )
| ! [SX4: mworld] :
( ~ ( mrel @ SY216 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(111,plain,
! [SV14: mworld,SV12: mworld,SV15: $i] :
( ( ( eiw_di @ SV15 @ SV12 )
= $false )
| ( ( ~ ( mrel @ SV14 @ SV12 ) )
= $true )
| ( ( eiw_di @ SV15 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
( ( ~ ( ~ ( eiw_di @ sK10_SY209 @ sK7_SX0 )
| ~ ! [SY219: mworld] :
( ~ ( mrel @ sK7_SX0 @ SY219 )
| ~ ! [SY220: mworld] :
( ~ ( mrel @ SY219 @ SY220 )
| ( f @ sK10_SY209 @ SY220 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(113,plain,
! [SV16: mworld] :
( ( ~ ( mrel @ sK9_SY212 @ SV16 )
| ! [SY221: $i] :
( ~ ( eiw_di @ SY221 @ SV16 )
| ! [SY222: mworld] :
( ~ ( mrel @ SV16 @ SY222 )
| ( f @ SY221 @ SY222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(114,plain,
! [SV15: $i,SV12: mworld,SV14: mworld] :
( ( ( mrel @ SV14 @ SV12 )
= $false )
| ( ( eiw_di @ SV15 @ SV12 )
= $false )
| ( ( eiw_di @ SV15 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(115,plain,
( ( ~ ( eiw_di @ sK10_SY209 @ sK7_SX0 )
| ~ ! [SY219: mworld] :
( ~ ( mrel @ sK7_SX0 @ SY219 )
| ~ ! [SY220: mworld] :
( ~ ( mrel @ SY219 @ SY220 )
| ( f @ sK10_SY209 @ SY220 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(116,plain,
! [SV16: mworld] :
( ( ( ~ ( mrel @ sK9_SY212 @ SV16 ) )
= $true )
| ( ( ! [SY221: $i] :
( ~ ( eiw_di @ SY221 @ SV16 )
| ! [SY222: mworld] :
( ~ ( mrel @ SV16 @ SY222 )
| ( f @ SY221 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(117,plain,
( ( ~ ( eiw_di @ sK10_SY209 @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(118,plain,
( ( ~ ! [SY219: mworld] :
( ~ ( mrel @ sK7_SX0 @ SY219 )
| ~ ! [SY220: mworld] :
( ~ ( mrel @ SY219 @ SY220 )
| ( f @ sK10_SY209 @ SY220 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(119,plain,
! [SV16: mworld] :
( ( ( mrel @ sK9_SY212 @ SV16 )
= $false )
| ( ( ! [SY221: $i] :
( ~ ( eiw_di @ SY221 @ SV16 )
| ! [SY222: mworld] :
( ~ ( mrel @ SV16 @ SY222 )
| ( f @ SY221 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(120,plain,
( ( eiw_di @ sK10_SY209 @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(121,plain,
( ( ! [SY219: mworld] :
( ~ ( mrel @ sK7_SX0 @ SY219 )
| ~ ! [SY220: mworld] :
( ~ ( mrel @ SY219 @ SY220 )
| ( f @ sK10_SY209 @ SY220 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(122,plain,
! [SV16: mworld,SV17: $i] :
( ( ( ~ ( eiw_di @ SV17 @ SV16 )
| ! [SY223: mworld] :
( ~ ( mrel @ SV16 @ SY223 )
| ( f @ SV17 @ SY223 ) ) )
= $true )
| ( ( mrel @ sK9_SY212 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(123,plain,
! [SV18: mworld] :
( ( ~ ( mrel @ sK7_SX0 @ SV18 )
| ~ ! [SY224: mworld] :
( ~ ( mrel @ SV18 @ SY224 )
| ( f @ sK10_SY209 @ SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(124,plain,
! [SV16: mworld,SV17: $i] :
( ( ( ~ ( eiw_di @ SV17 @ SV16 ) )
= $true )
| ( ( ! [SY223: mworld] :
( ~ ( mrel @ SV16 @ SY223 )
| ( f @ SV17 @ SY223 ) ) )
= $true )
| ( ( mrel @ sK9_SY212 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(125,plain,
! [SV18: mworld] :
( ( ( ~ ( mrel @ sK7_SX0 @ SV18 ) )
= $true )
| ( ( ~ ! [SY224: mworld] :
( ~ ( mrel @ SV18 @ SY224 )
| ( f @ sK10_SY209 @ SY224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(126,plain,
! [SV16: mworld,SV17: $i] :
( ( ( eiw_di @ SV17 @ SV16 )
= $false )
| ( ( ! [SY223: mworld] :
( ~ ( mrel @ SV16 @ SY223 )
| ( f @ SV17 @ SY223 ) ) )
= $true )
| ( ( mrel @ sK9_SY212 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(127,plain,
! [SV18: mworld] :
( ( ( mrel @ sK7_SX0 @ SV18 )
= $false )
| ( ( ~ ! [SY224: mworld] :
( ~ ( mrel @ SV18 @ SY224 )
| ( f @ sK10_SY209 @ SY224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(128,plain,
! [SV17: $i,SV19: mworld,SV16: mworld] :
( ( ( ~ ( mrel @ SV16 @ SV19 )
| ( f @ SV17 @ SV19 ) )
= $true )
| ( ( eiw_di @ SV17 @ SV16 )
= $false )
| ( ( mrel @ sK9_SY212 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(129,plain,
! [SV18: mworld] :
( ( ( ! [SY224: mworld] :
( ~ ( mrel @ SV18 @ SY224 )
| ( f @ sK10_SY209 @ SY224 ) ) )
= $false )
| ( ( mrel @ sK7_SX0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(130,plain,
! [SV17: $i,SV19: mworld,SV16: mworld] :
( ( ( ~ ( mrel @ SV16 @ SV19 ) )
= $true )
| ( ( f @ SV17 @ SV19 )
= $true )
| ( ( eiw_di @ SV17 @ SV16 )
= $false )
| ( ( mrel @ sK9_SY212 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(131,plain,
! [SV18: mworld] :
( ( ( ~ ( mrel @ SV18 @ ( sK11_SY224 @ SV18 ) )
| ( f @ sK10_SY209 @ ( sK11_SY224 @ SV18 ) ) )
= $false )
| ( ( mrel @ sK7_SX0 @ SV18 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[129]) ).
thf(132,plain,
! [SV17: $i,SV19: mworld,SV16: mworld] :
( ( ( mrel @ SV16 @ SV19 )
= $false )
| ( ( f @ SV17 @ SV19 )
= $true )
| ( ( eiw_di @ SV17 @ SV16 )
= $false )
| ( ( mrel @ sK9_SY212 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(133,plain,
! [SV18: mworld] :
( ( ( ~ ( mrel @ SV18 @ ( sK11_SY224 @ SV18 ) ) )
= $false )
| ( ( mrel @ sK7_SX0 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(134,plain,
! [SV18: mworld] :
( ( ( f @ sK10_SY209 @ ( sK11_SY224 @ SV18 ) )
= $false )
| ( ( mrel @ sK7_SX0 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(135,plain,
! [SV18: mworld] :
( ( ( mrel @ SV18 @ ( sK11_SY224 @ SV18 ) )
= $true )
| ( ( mrel @ sK7_SX0 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(136,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[87,135,134,132,120,114,109,97,95]) ).
thf(137,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[136,75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL959^24 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 12:37:06 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.31
% 0.08/0.31 No.of.Axioms: 3
% 0.08/0.31
% 0.08/0.31 Length.of.Defs: 1653
% 0.08/0.31
% 0.08/0.31 Contains.Choice.Funs: false
% 0.08/0.31 ......
% 0.08/0.31
% 0.08/0.31 ********************************
% 0.08/0.31 * All subproblems solved! *
% 0.08/0.31 ********************************
% 0.08/0.31 % SZS status Theorem for /export/starexec/sandbox/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:136,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.31
% 0.08/0.31 %**** Beginning of derivation protocol ****
% 0.08/0.31 % SZS output start CNFRefutation
% See solution above
% 0.08/0.32
% 0.08/0.32 %**** End of derivation protocol ****
% 0.08/0.32 %**** no. of clauses in derivation: 137 ****
% 0.08/0.32 %**** clause counter: 136 ****
% 0.08/0.32
% 0.08/0.32 % SZS status Theorem for /export/starexec/sandbox/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:136,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------