%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL943^24 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 Sep 30 08:14:53 AM UTC 2026
% Result : Theorem 0.22s 0.34s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 116 ( 36 unt; 0 typ; 8 def)
% Number of atoms : 1113 ( 193 equ; 0 cnn)
% Maximal formula atoms : 24 ( 9 avg)
% Number of connectives : 1609 ( 54 ~; 195 |; 0 &;1059 @)
% ( 7 <=>; 178 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 43 usr; 16 con; 0-4 aty)
% ( 116 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 361 ( 0 sgn 79 !; 0 ?; 361 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
p: mworld > $o ).
thf(func_def_12,type,
q: mworld > $o ).
thf(func_def_13,type,
r: mworld > $o ).
thf(func_def_14,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_15,type,
vIMP: $o > $o > $o ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vAND: $o > $o > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
vOR: $o > $o > $o ).
thf(func_def_26,type,
vIFF: $o > $o > $o ).
thf(func_def_27,type,
sF0: $o ).
thf(func_def_28,type,
sK1: mworld > mworld ).
thf(func_def_29,type,
sK2: mworld > mworld ).
thf(func_def_30,type,
sK3: mworld > mworld ).
thf(func_def_31,type,
sK4: mworld > mworld ).
thf(func_def_32,type,
sK5: mworld ).
thf(func_def_33,type,
sK6: mworld > mworld ).
thf(func_def_34,type,
sK7: mworld > mworld ).
thf(func_def_35,type,
sK8: mworld ).
thf(func_def_36,type,
sK9: mworld ).
thf(func_def_37,type,
sK10: mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f4,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def) ).
thf(f5,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
thf(f10,conjecture,
mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel5) ).
thf(f11,negated_conjecture,
~ ( mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f12,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f13,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
~ ( mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f15,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
inference(rectify,[],[f9]) ).
thf(f17,plain,
! [X1: mworld,X0: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(fool_elimination,[],[f16]) ).
thf(f22,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f5]) ).
thf(f23,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f24,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f25,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f26,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f31,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f15]) ).
thf(f32,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( mrel @ X1 @ X0 ) ),
inference(rectify,[],[f17]) ).
thf(f33,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f34,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f35,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f37,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( mrel @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f40,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f41,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f45,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ r ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ r ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f40,f33,f34,f35,f34,f35,f41,f34,f34,f41,f34,f34,f41,f34,f34,f35,f34,f34]) ).
thf(f46,definition,
( sF0
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ r ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ r ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f47,plain,
sF0 != $true,
inference(definition_folding,[],[f45,f46]) ).
thf(f48,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ r ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ r ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f46]) ).
thf(f108,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f109,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) ) ) )
@ sK5 )
= $false )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f108]) ).
thf(f110,plain,
( ( $false
= ( ( mrel @ mactual @ sK5 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f111,plain,
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f113,plain,
( ( sF0 = $true )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f111]) ).
thf(f114,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f111]) ).
thf(f115,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) )
@ X1 ) )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X1: mworld] :
( ( sF0 = $true )
| ( $true
= ( ( mrel @ sK5 @ X1 )
=> ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f115]) ).
thf(f117,plain,
! [X1: mworld] :
( ( ( mrel @ sK5 @ X1 )
= $false )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) )
= $true )
| ( sF0 = $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) ) ) )
= $false )
| ( ( mrel @ sK5 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( sF0 = $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) )
| ( ( mrel @ sK5 @ X1 )
= $false )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK5 @ X1 )
= $false )
| ( sF0 = $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) ) ) )
= $false )
| ( sF0 = $true )
| ( ( mrel @ sK5 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X2 ) )
| ( ( mrel @ sK5 @ X1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) )
@ X3 ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f121]) ).
thf(f130,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( q @ Y0 ) )
@ ( sK7 @ X1 ) ) )
| ( ( mrel @ sK5 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( r @ Y0 ) )
@ X3 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f122]) ).
thf(f131,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( sF0 = $true )
| ( ( mrel @ sK5 @ X1 )
= $false )
| ( $true
= ( ( mrel @ X1 @ X3 )
=> ( r @ X3 ) ) )
| ( ( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
= $true )
| ( ( ( mrel @ X1 @ ( sK7 @ X1 ) )
=> ( q @ ( sK7 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f130]) ).
thf(f132,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ X1 @ ( sK7 @ X1 ) )
=> ( q @ ( sK7 @ X1 ) ) )
= $false )
| ( sF0 = $true )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
= $true )
| ( $true
= ( r @ X3 ) )
| ( ( mrel @ sK5 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f131]) ).
thf(f133,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( r @ X3 ) )
| ( sF0 = $true )
| ( ( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
= $true )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( mrel @ sK5 @ X1 )
= $false )
| ( $false
= ( q @ ( sK7 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f132]) ).
thf(f136,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( p @ X2 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ sK5 @ X1 )
= $false )
| ( sF0 = $true )
| ( $true
= ( r @ X3 ) )
| ( $false
= ( q @ ( sK7 @ X1 ) ) )
| ( $false
= ( mrel @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f137,plain,
( ( sF0 = $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f113]) ).
thf(f138,plain,
( ( sF0 = $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( p @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f113]) ).
thf(f139,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( p @ Y0 ) )
@ sK8 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f138]) ).
thf(f140,plain,
( ( sF0 = $true )
| ( ( ( mrel @ sK5 @ sK8 )
=> ( p @ sK8 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( ( $false
= ( p @ sK8 ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f143,plain,
( ( sF0 = $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) )
@ sK9 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f144,plain,
( ( $false
= ( ( mrel @ sK5 @ sK9 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( q @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
( ( sF0 = $true )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( q @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f147,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( r @ Y0 ) ) )
= $false )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( q @ Y0 ) ) )
= $true )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f145]) ).
thf(f149,plain,
! [X1: mworld] :
( ( sF0 = $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( q @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X1: mworld] :
( ( sF0 = $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( q @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( sF0 = $true )
| ( $true
= ( q @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( r @ Y0 ) )
@ sK10 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f147]) ).
thf(f153,plain,
( ( ( ( mrel @ sK9 @ sK10 )
=> ( r @ sK10 ) )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
( ( sF0 = $true )
| ( ( r @ sK10 )
= $false ) ),
inference(imp_proxy_clausification,[],[f153]) ).
thf(f213,definition,
( spl11_15
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
thf(f230,definition,
( spl11_19
<=> ! [X2: mworld,X1: mworld,X3: mworld] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( q @ ( sK7 @ X1 ) ) )
| ( $true
= ( r @ X3 ) )
| ( ( mrel @ sK5 @ X1 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_19])],[avatar_definition]) ).
thf(f231,plain,
( ! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( r @ X3 ) )
| ( ( mrel @ sK5 @ X1 )
= $false )
| ( $false
= ( q @ ( sK7 @ X1 ) ) ) )
| ~ spl11_19 ),
inference(avatar_component_clause,[],[f230]) ).
thf(f232,plain,
( spl11_15
| spl11_19 ),
inference(avatar_split_clause,[],[f136,f230,f213]) ).
thf(f239,definition,
( spl11_21
<=> ( $false
= ( p @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_21])],[avatar_definition]) ).
thf(f241,plain,
( ( $false
= ( p @ sK8 ) )
| ~ spl11_21 ),
inference(avatar_component_clause,[],[f239]) ).
thf(f242,plain,
( spl11_21
| spl11_15 ),
inference(avatar_split_clause,[],[f141,f213,f239]) ).
thf(f249,definition,
( spl11_23
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( q @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_23])],[avatar_definition]) ).
thf(f250,plain,
( ! [X1: mworld] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) )
| ~ spl11_23 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f251,plain,
( spl11_15
| spl11_23 ),
inference(avatar_split_clause,[],[f151,f249,f213]) ).
thf(f258,definition,
( spl11_25
<=> ( ( r @ sK10 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_25])],[avatar_definition]) ).
thf(f260,plain,
( ( ( r @ sK10 )
= $false )
| ~ spl11_25 ),
inference(avatar_component_clause,[],[f258]) ).
thf(f261,plain,
( spl11_25
| spl11_15 ),
inference(avatar_split_clause,[],[f154,f213,f258]) ).
thf(f262,plain,
~ spl11_15,
inference(avatar_split_clause,[],[f47,f213]) ).
thf(f280,plain,
( ! [X1: mworld] :
( ( $true = $false )
| ( $true
= ( q @ X1 ) ) )
| ~ spl11_23 ),
inference(forward_demodulation,[],[f250,f37]) ).
thf(f281,plain,
( ! [X1: mworld] :
( $true
= ( q @ X1 ) )
| ~ spl11_23 ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f292,definition,
( spl11_27
<=> ! [X2: mworld] :
( $true
= ( p @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_27])],[avatar_definition]) ).
thf(f293,plain,
( ! [X2: mworld] :
( $true
= ( p @ X2 ) )
| ~ spl11_27 ),
inference(avatar_component_clause,[],[f292]) ).
thf(f295,definition,
( spl11_28
<=> ! [X3: mworld] :
( $true
= ( r @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_28])],[avatar_definition]) ).
thf(f296,plain,
( ! [X3: mworld] :
( $true
= ( r @ X3 ) )
| ~ spl11_28 ),
inference(avatar_component_clause,[],[f295]) ).
thf(f300,plain,
( ! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( r @ X3 ) )
| ( $true
= ( p @ X2 ) )
| ( $true = $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( q @ ( sK7 @ X1 ) ) )
| ( ( mrel @ sK5 @ X1 )
= $false ) )
| ~ spl11_19 ),
inference(forward_demodulation,[],[f231,f37]) ).
thf(f301,plain,
( ! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( r @ X3 ) )
| ( $false
= ( q @ ( sK7 @ X1 ) ) )
| ( ( mrel @ sK5 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl11_19 ),
inference(trivial_inequality_removal,[],[f300]) ).
thf(f302,plain,
( ! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( p @ X2 ) )
| ( $true
= ( r @ X3 ) )
| ( ( mrel @ sK5 @ X1 )
= $false )
| ( $true = $false )
| ( $false
= ( mrel @ X1 @ X3 ) ) )
| ~ spl11_19
| ~ spl11_23 ),
inference(forward_demodulation,[],[f301,f281]) ).
thf(f303,plain,
( ! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( r @ X3 ) )
| ( $true
= ( p @ X2 ) )
| ( ( mrel @ sK5 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) ) )
| ~ spl11_19
| ~ spl11_23 ),
inference(trivial_inequality_removal,[],[f302]) ).
thf(f304,plain,
( ! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true = $false )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( r @ X3 ) )
| ( $false
= ( mrel @ X1 @ X3 ) ) )
| ~ spl11_19
| ~ spl11_23 ),
inference(forward_demodulation,[],[f303,f37]) ).
thf(f305,plain,
( ! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( r @ X3 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl11_19
| ~ spl11_23 ),
inference(trivial_inequality_removal,[],[f304]) ).
thf(f306,plain,
( ! [X2: mworld,X3: mworld] :
( ( $true = $false )
| ( $true
= ( r @ X3 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl11_19
| ~ spl11_23 ),
inference(forward_demodulation,[],[f305,f37]) ).
thf(f307,plain,
( ! [X2: mworld,X3: mworld] :
( ( $true
= ( p @ X2 ) )
| ( $true
= ( r @ X3 ) ) )
| ~ spl11_19
| ~ spl11_23 ),
inference(trivial_inequality_removal,[],[f306]) ).
thf(f308,plain,
( spl11_27
| spl11_28
| ~ spl11_19
| ~ spl11_23 ),
inference(avatar_split_clause,[],[f307,f249,f230,f295,f292]) ).
thf(f309,plain,
( ( $true = $false )
| ~ spl11_21
| ~ spl11_27 ),
inference(constrained_superposition,[],[f293,f241]) ).
thf(f319,plain,
( $false
| ~ spl11_21
| ~ spl11_27 ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f320,plain,
( ~ spl11_21
| ~ spl11_27 ),
inference(avatar_contradiction_clause,[],[f319]) ).
thf(f322,plain,
( ( $true = $false )
| ~ spl11_25
| ~ spl11_28 ),
inference(constrained_superposition,[],[f260,f296]) ).
thf(f325,plain,
( $false
| ~ spl11_25
| ~ spl11_28 ),
inference(trivial_inequality_removal,[],[f322]) ).
thf(f326,plain,
( ~ spl11_25
| ~ spl11_28 ),
inference(avatar_contradiction_clause,[],[f325]) ).
cnf(s17,plain,
( spl11_15
| spl11_19 ),
inference(sat_conversion,[],[f232]) ).
cnf(s19,plain,
( spl11_15
| spl11_21 ),
inference(sat_conversion,[],[f242]) ).
cnf(s21,plain,
( spl11_15
| spl11_23 ),
inference(sat_conversion,[],[f251]) ).
cnf(s23,plain,
( spl11_15
| spl11_25 ),
inference(sat_conversion,[],[f261]) ).
cnf(s24,plain,
~ spl11_15,
inference(sat_conversion,[],[f262]) ).
cnf(s27,plain,
( ~ spl11_19
| ~ spl11_23
| spl11_27
| spl11_28 ),
inference(sat_conversion,[],[f308]) ).
cnf(s31,plain,
( ~ spl11_21
| ~ spl11_27 ),
inference(sat_conversion,[],[f320]) ).
cnf(s33,plain,
( ~ spl11_25
| ~ spl11_28 ),
inference(sat_conversion,[],[f326]) ).
cnf(s35,plain,
spl11_25,
inference(rat,[],[s23,s24]) ).
cnf(s36,plain,
~ spl11_28,
inference(rat,[],[s33,s35]) ).
cnf(s38,plain,
spl11_23,
inference(rat,[],[s21,s24]) ).
cnf(s40,plain,
spl11_21,
inference(rat,[],[s19,s24]) ).
cnf(s41,plain,
~ spl11_27,
inference(rat,[],[s31,s40]) ).
cnf(s42,plain,
~ spl11_19,
inference(rat,[],[s27,s36,s38,s41]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s17,s42,s24]) ).
thf(f327,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL943^24 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n004.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 10:45:07 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.28 Running higher-order theorem proving
% 0.22/0.30 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.34 % (1133572)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.34 % (1133583)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.34 % (1133583)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.34 % (1133583)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1415762479:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.34 % (1133578)lrs+10_16_si=on:nwc=1.5:random_seed=1798081652:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.34 % (1133583) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1133572-1133583"...
% 0.22/0.34 % (1133578) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1133572-1133578"...
% 0.22/0.34 % (1133577)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=688083630:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.34 % (1133581)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=848663143:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.34 % (1133583)...printing done.
% 0.22/0.34 % (1133582)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2331814216:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.34 % (1133579)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1701952621:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.34 % (1133583)Refutation found. Thanks to Tanya!
% 0.22/0.34 % SZS status Theorem for theBenchmark
% 0.22/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.35 % (1133583)------------------------------
% 0.22/0.35 % (1133583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (1133583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (1133583)CaDiCaL version: 2.1.3
% 0.22/0.35 % (1133583)Termination reason: Refutation
% 0.22/0.35 % (1133583)Time elapsed: 0.011 s
% 0.22/0.35 % (1133583)Peak memory usage: 13 MB
% 0.22/0.35 % (1133583)Instructions burned: 23 (million)
% 0.22/0.35 % (1133572)Success in time 0.035 s
% 0.22/0.35 % Vampire exiting
%------------------------------------------------------------------------------