%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO893^11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:48:35 AM UTC 2026
% Result : Theorem 0.20s 0.33s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 29
% Syntax : Number of formulae : 330 ( 37 unt; 0 typ; 21 def)
% Number of atoms : 2766 ( 612 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 3446 ( 522 ~; 816 |; 101 &;1755 @)
% ( 22 <=>; 100 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 62 usr; 30 con; 0-4 aty)
% ( 70 !!; 60 ??; 0 @@+; 0 @@-)
% Number of variables : 488 ( 0 sgn 227 !; 2 ?; 488 :)
% 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_14,type,
vNOT: $o > $o ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vIFF: $o > $o > $o ).
thf(func_def_21,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_22,type,
vIMP: $o > $o > $o ).
thf(func_def_23,type,
vOR: $o > $o > $o ).
thf(func_def_24,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
sF0: $o ).
thf(func_def_26,type,
sK1: mworld ).
thf(func_def_27,type,
sK2: mworld > mworld ).
thf(func_def_28,type,
sK3: mworld > mworld ).
thf(func_def_29,type,
sK4: mworld > mworld ).
thf(func_def_30,type,
sK5: mworld > mworld ).
thf(func_def_31,type,
sK6: mworld ).
thf(func_def_32,type,
sK7: mworld > mworld ).
thf(func_def_33,type,
sK8: mworld > mworld ).
thf(func_def_34,type,
sK9: mworld > mworld ).
thf(func_def_35,type,
sK10: mworld > mworld ).
thf(func_def_36,type,
sK11: mworld > mworld ).
thf(func_def_37,type,
sK12: mworld > mworld ).
thf(func_def_38,type,
sK13: mworld ).
thf(func_def_39,type,
sK14: mworld ).
thf(func_def_40,type,
sK15: mworld > mworld ).
thf(func_def_41,type,
sK16: mworld > mworld ).
thf(func_def_42,type,
sK17: mworld > mworld ).
thf(func_def_43,type,
sK18: mworld > mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(f6,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f10,axiom,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X1 )
& ( mrel @ X0 @ X2 ) )
=> ( mrel @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_euclidean) ).
thf(f11,conjecture,
mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f12,negated_conjecture,
~ ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f13,plain,
~ ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f16,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f19,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f22,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f24,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f28,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X1 @ X2 )
& ( mrel @ X1 @ X0 ) )
=> ( mrel @ X0 @ X2 ) ),
inference(rectify,[],[f10]) ).
thf(f29,plain,
! [X2: mworld,X1: mworld,X0: mworld] :
( ( ( ( mrel @ X1 @ X2 )
= $true )
& ( ( mrel @ X1 @ X0 )
= $true ) )
=> ( ( mrel @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f31,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f34,plain,
( ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f14]) ).
thf(f35,plain,
! [X2: mworld,X1: mworld,X0: mworld] :
( ( ( mrel @ X0 @ X2 )
= $true )
| ( ( mrel @ X1 @ X2 )
!= $true )
| ( ( mrel @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f29]) ).
thf(f36,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
!= $true )
| ( ( mrel @ X1 @ X0 )
!= $true )
| ( ( mrel @ X0 @ X2 )
= $true ) ),
inference(flattening,[],[f35]) ).
thf(f37,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( $true
!= ( mrel @ X2 @ X0 ) )
| ( ( mrel @ X2 @ X1 )
!= $true )
| ( ( mrel @ X1 @ X0 )
= $true ) ),
inference(rectify,[],[f36]) ).
thf(f38,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f40,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f41,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f42,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X0 )
= $true )
| ( ( mrel @ X2 @ X1 )
!= $true )
| ( $true
!= ( mrel @ X2 @ X0 ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f43,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f44,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f45,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f48,plain,
( ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f34]) ).
thf(f51,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ p ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f48,f43,f40,f45,f44,f38,f44,f38,f44,f38,f45]) ).
thf(f52,definition,
( sF0
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ p ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f53,plain,
sF0 != $true,
inference(definition_folding,[],[f51,f52]) ).
thf(f54,plain,
( ( $false
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ p ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f52]) ).
thf(f130,plain,
( ( $false
= ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( p @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( mrel @ mactual @ Y0 ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f131,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( p @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( mrel @ mactual @ Y0 ) ) )
!= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f130]) ).
thf(f132,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( p @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( mrel @ mactual @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(xor_proxy_clausification,[],[f131]) ).
thf(f133,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( p @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( mrel @ mactual @ Y0 ) ) )
= $false )
| ( sF0 = $true )
| ( $false
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(xor_proxy_clausification,[],[f131]) ).
thf(f134,plain,
! [X1: mworld] :
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( p @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( mrel @ mactual @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( p @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( mrel @ mactual @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f134]) ).
thf(f136,plain,
! [X2: mworld,X1: mworld] :
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( p @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( mrel @ mactual @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
& ( mrel @ Y0 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
& ( mrel @ mactual @ X1 ) ) )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( mrel @ X2 @ Y0 ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( sF0 = $true )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( mrel @ X2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( mrel @ X2 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) )
@ ( sK11 @ X1 ) )
= $false )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( sF0 = $true )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) )
@ ( sK11 @ X1 ) )
= $false )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( mrel @ X2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: mworld,X1: mworld] :
( ( sF0 = $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( mrel @ X2 @ Y0 ) )
@ ( sK12 @ X2 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) )
@ ( sK11 @ X1 ) )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( mrel @ X1 @ ( sK11 @ X1 ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ ( sK11 @ X1 ) @ Y0 ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ X2 ) @ Y0 )
=> ( p @ Y0 ) ) )
& ( mrel @ X2 @ ( sK12 @ X2 ) ) )
= $true )
| ( sF0 = $true )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ ( sK11 @ X1 ) @ Y0 ) ) ) )
| ( sF0 = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ X2 ) @ Y0 )
=> ( p @ Y0 ) ) )
& ( mrel @ X2 @ ( sK12 @ X2 ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X2 ) )
| ( sF0 = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ X2 ) @ Y0 )
=> ( p @ Y0 ) ) )
& ( mrel @ X2 @ ( sK12 @ X2 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f145,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( mrel @ X2 @ ( sK12 @ X2 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( sF0 = $true )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(and_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ X2 ) @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( sF0 = $true )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f144]) ).
thf(f147,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( sF0 = $true )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ X2 ) @ Y0 )
=> ( p @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ ( sK12 @ X2 ) @ X3 )
=> ( p @ X3 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( sF0 = $true )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ ( sK12 @ X2 ) @ X3 ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( sF0 = $true )
| ( $true
= ( p @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ ( sK11 @ X1 ) @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ X2 ) @ Y0 )
=> ( p @ Y0 ) ) )
& ( mrel @ X2 @ ( sK12 @ X2 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f143]) ).
thf(f151,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( mrel @ X2 @ ( sK12 @ X2 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ ( sK11 @ X1 ) @ Y0 ) )
@ X3 ) )
| ( sF0 = $true ) ),
inference(and_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X2 ) )
| ( sF0 = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ ( sK11 @ X1 ) @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ X2 ) @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f150]) ).
thf(f153,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ X2 ) @ Y0 )
=> ( p @ Y0 ) )
@ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ ( sK11 @ X1 ) @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ~ ( p @ X3 )
& ( mrel @ ( sK11 @ X1 ) @ X3 ) )
= $false )
| ( sF0 = $true )
| ( ( ( mrel @ ( sK12 @ X2 ) @ X4 )
=> ( p @ X4 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ ( sK12 @ X2 ) @ X4 )
=> ( p @ X4 ) )
= $true )
| ( sF0 = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ~ ( p @ X3 ) ) )
| ( $false
= ( mrel @ ( sK11 @ X1 ) @ X3 ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(and_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ ( sK12 @ X2 ) @ X4 ) )
| ( sF0 = $true )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( ~ ( p @ X3 ) ) )
| ( $false
= ( mrel @ ( sK11 @ X1 ) @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( p @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( mrel @ ( sK11 @ X1 ) @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( sF0 = $true )
| ( $false
= ( mrel @ ( sK12 @ X2 ) @ X4 ) ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ~ ( p @ X3 )
& ( mrel @ ( sK11 @ X1 ) @ X3 ) )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( sF0 = $true )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $true
= ( mrel @ X2 @ ( sK12 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f159,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( sF0 = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ ( sK11 @ X1 ) @ X3 ) )
| ( $true
= ( mrel @ X2 @ ( sK12 @ X2 ) ) )
| ( $false
= ( ~ ( p @ X3 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(and_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( mrel @ X2 @ ( sK12 @ X2 ) ) )
| ( sF0 = $true )
| ( $false
= ( mrel @ ( sK11 @ X1 ) @ X3 ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( sF0 = $true )
| ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( p @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( mrel @ mactual @ Y0 ) )
@ sK13 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f132]) ).
thf(f162,plain,
( ( ( ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( p @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( mrel @ mactual @ Y0 ) )
@ sK13 )
= $true )
| ( sF0 = $true )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( ( ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( p @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( mrel @ mactual @ Y0 ) )
@ sK13 )
= $true )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
& ( mrel @ Y0 @ Y1 ) ) ) )
@ sK14 ) ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( sF0 = $true )
| ( $false
= ( ( mrel @ mactual @ sK14 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( mrel @ sK14 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK13 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
& ( mrel @ mactual @ sK13 ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( mrel @ sK14 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK13 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
& ( mrel @ mactual @ sK13 ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK13 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
& ( mrel @ mactual @ sK13 ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( ( sF0 = $true )
| ( $true
= ( mrel @ mactual @ sK14 ) )
| ( ( mrel @ mactual @ sK13 )
= $true ) ),
inference(and_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $true
= ( mrel @ mactual @ sK14 ) )
| ( sF0 = $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK13 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f166]) ).
thf(f169,plain,
! [X1: mworld] :
( ( sF0 = $true )
| ( $true
= ( mrel @ mactual @ sK14 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK13 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: mworld] :
( ( sF0 = $true )
| ( $true
= ( ( mrel @ sK13 @ X1 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ X1 @ Y0 ) ) ) ) )
| ( $true
= ( mrel @ mactual @ sK14 ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $false
= ( mrel @ sK13 @ X1 ) )
| ( sF0 = $true )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK13 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ X1 @ Y0 ) )
@ ( sK15 @ X1 ) ) )
| ( sF0 = $true )
| ( $true
= ( mrel @ mactual @ sK14 ) ) ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: mworld] :
( ( $true
= ( ~ ( p @ ( sK15 @ X1 ) )
& ( mrel @ X1 @ ( sK15 @ X1 ) ) ) )
| ( $false
= ( mrel @ sK13 @ X1 ) )
| ( sF0 = $true )
| ( $true
= ( mrel @ mactual @ sK14 ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ mactual @ sK14 ) )
| ( sF0 = $true )
| ( $false
= ( mrel @ sK13 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: mworld] :
( ( $true
= ( ~ ( p @ ( sK15 @ X1 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK14 ) )
| ( sF0 = $true )
| ( $false
= ( mrel @ sK13 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f173]) ).
thf(f176,plain,
! [X1: mworld] :
( ( sF0 = $true )
| ( $false
= ( mrel @ sK13 @ X1 ) )
| ( $false
= ( p @ ( sK15 @ X1 ) ) )
| ( $true
= ( mrel @ mactual @ sK14 ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: mworld] :
( ( sF0 = $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK13 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
& ( mrel @ mactual @ sK13 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( mrel @ sK14 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f178,plain,
! [X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( mrel @ sK14 @ Y0 ) )
@ X1 ) )
| ( sF0 = $true )
| ( ( mrel @ mactual @ sK13 )
= $true ) ),
inference(and_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( mrel @ sK14 @ Y0 ) )
@ X1 ) )
| ( sF0 = $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK13 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f177]) ).
thf(f180,plain,
! [X2: mworld,X1: mworld] :
( ( sF0 = $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK13 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( mrel @ sK14 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: mworld,X1: mworld] :
( ( sF0 = $true )
| ( $true
= ( ( mrel @ sK13 @ X2 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ X2 @ Y0 ) ) ) ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( mrel @ sK14 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X2: mworld,X1: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ X2 @ Y0 ) ) )
= $true )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( mrel @ sK14 @ X1 ) ) )
| ( $false
= ( mrel @ sK13 @ X2 ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK13 @ X2 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( mrel @ sK14 @ X1 ) ) )
| ( sF0 = $true )
| ( ( ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ X2 @ Y0 ) )
@ ( sK16 @ X2 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK14 @ X1 )
= $false )
| ( sF0 = $true )
| ( ( ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ X2 @ Y0 ) )
@ ( sK16 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK13 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK14 @ X1 )
= $false )
| ( sF0 = $true )
| ( $false
= ( mrel @ sK13 @ X2 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ ( sK17 @ X1 ) ) )
| ( ( ^ [Y0: mworld] :
( ~ ( p @ Y0 )
& ( mrel @ X2 @ Y0 ) )
@ ( sK16 @ X2 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK14 @ X1 )
= $false )
| ( $false
= ( mrel @ sK13 @ X2 ) )
| ( $true
= ( ~ ( p @ ( sK16 @ X2 ) )
& ( mrel @ X2 @ ( sK16 @ X2 ) ) ) )
| ( sF0 = $true )
| ( $false
= ( ( mrel @ X1 @ ( sK17 @ X1 ) )
=> ( p @ ( sK17 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK14 @ X1 )
= $false )
| ( $false
= ( ( mrel @ X1 @ ( sK17 @ X1 ) )
=> ( p @ ( sK17 @ X1 ) ) ) )
| ( sF0 = $true )
| ( $true
= ( mrel @ X2 @ ( sK16 @ X2 ) ) )
| ( $false
= ( mrel @ sK13 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK14 @ X1 )
= $false )
| ( $false
= ( mrel @ sK13 @ X2 ) )
| ( $false
= ( ( mrel @ X1 @ ( sK17 @ X1 ) )
=> ( p @ ( sK17 @ X1 ) ) ) )
| ( $true
= ( ~ ( p @ ( sK16 @ X2 ) ) ) )
| ( sF0 = $true ) ),
inference(and_proxy_clausification,[],[f186]) ).
thf(f189,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( p @ ( sK17 @ X1 ) ) )
| ( ( mrel @ sK14 @ X1 )
= $false )
| ( $true
= ( ~ ( p @ ( sK16 @ X2 ) ) ) )
| ( sF0 = $true )
| ( $false
= ( mrel @ sK13 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK17 @ X1 ) ) )
| ( $true
= ( ~ ( p @ ( sK16 @ X2 ) ) ) )
| ( ( mrel @ sK14 @ X1 )
= $false )
| ( $false
= ( mrel @ sK13 @ X2 ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f191,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK14 @ X1 )
= $false )
| ( sF0 = $true )
| ( $true
= ( mrel @ X1 @ ( sK17 @ X1 ) ) )
| ( $false
= ( mrel @ sK13 @ X2 ) )
| ( ( p @ ( sK16 @ X2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: mworld,X1: mworld] :
( ( sF0 = $true )
| ( ( mrel @ sK14 @ X1 )
= $false )
| ( $false
= ( p @ ( sK17 @ X1 ) ) )
| ( $false
= ( mrel @ sK13 @ X2 ) )
| ( ( p @ ( sK16 @ X2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f193,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( mrel @ X2 @ ( sK16 @ X2 ) ) )
| ( sF0 = $true )
| ( ( mrel @ sK14 @ X1 )
= $false )
| ( $false
= ( mrel @ sK13 @ X2 ) )
| ( $false
= ( p @ ( sK17 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f187]) ).
thf(f194,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK13 @ X2 ) )
| ( $true
= ( mrel @ X1 @ ( sK17 @ X1 ) ) )
| ( sF0 = $true )
| ( ( mrel @ sK14 @ X1 )
= $false )
| ( $true
= ( mrel @ X2 @ ( sK16 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f187]) ).
thf(f195,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ sK13 )
= $true )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( mrel @ sK14 @ X1 ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f196,plain,
! [X1: mworld] :
( ( ( mrel @ sK14 @ X1 )
= $false )
| ( ( mrel @ mactual @ sK13 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
= $false )
| ( sF0 = $true ) ),
inference(and_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ sK13 )
= $true )
| ( ( mrel @ sK14 @ X1 )
= $false )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ ( sK18 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: mworld] :
( ( sF0 = $true )
| ( ( mrel @ mactual @ sK13 )
= $true )
| ( ( mrel @ sK14 @ X1 )
= $false )
| ( $false
= ( ( mrel @ X1 @ ( sK18 @ X1 ) )
=> ( p @ ( sK18 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X1: mworld] :
( ( sF0 = $true )
| ( ( mrel @ mactual @ sK13 )
= $true )
| ( ( p @ ( sK18 @ X1 ) )
= $false )
| ( ( mrel @ sK14 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: mworld] :
( ( sF0 = $true )
| ( $true
= ( mrel @ X1 @ ( sK18 @ X1 ) ) )
| ( ( mrel @ sK14 @ X1 )
= $false )
| ( ( mrel @ mactual @ sK13 )
= $true ) ),
inference(imp_proxy_clausification,[],[f198]) ).
thf(f274,definition,
( spl19_20
<=> ! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_20])],[avatar_definition]) ).
thf(f275,plain,
( ! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl19_20 ),
inference(avatar_component_clause,[],[f274]) ).
thf(f277,definition,
( spl19_21
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl19_21])],[avatar_definition]) ).
thf(f281,definition,
( spl19_22
<=> ! [X2: mworld,X3: mworld] :
( ( $false
= ( mrel @ ( sK12 @ X2 ) @ X3 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $true
= ( p @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_22])],[avatar_definition]) ).
thf(f282,plain,
( ! [X2: mworld,X3: mworld] :
( ( $false
= ( mrel @ ( sK12 @ X2 ) @ X3 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $true
= ( p @ X3 ) ) )
| ~ spl19_22 ),
inference(avatar_component_clause,[],[f281]) ).
thf(f283,plain,
( spl19_20
| spl19_21
| spl19_22 ),
inference(avatar_split_clause,[],[f149,f281,f277,f274]) ).
thf(f285,definition,
( spl19_23
<=> ! [X2: mworld] :
( ( $true
= ( mrel @ X2 @ ( sK12 @ X2 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_23])],[avatar_definition]) ).
thf(f286,plain,
( ! [X2: mworld] :
( ( $true
= ( mrel @ X2 @ ( sK12 @ X2 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) )
| ~ spl19_23 ),
inference(avatar_component_clause,[],[f285]) ).
thf(f287,plain,
( spl19_23
| spl19_20
| spl19_21 ),
inference(avatar_split_clause,[],[f145,f277,f274,f285]) ).
thf(f289,definition,
( spl19_24
<=> ! [X1: mworld,X3: mworld] :
( ( $true
= ( p @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ ( sK11 @ X1 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_24])],[avatar_definition]) ).
thf(f290,plain,
( ! [X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ ( sK11 @ X1 ) @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( p @ X3 ) ) )
| ~ spl19_24 ),
inference(avatar_component_clause,[],[f289]) ).
thf(f291,plain,
( spl19_24
| spl19_22
| spl19_21 ),
inference(avatar_split_clause,[],[f157,f277,f281,f289]) ).
thf(f292,plain,
( spl19_21
| spl19_24
| spl19_23 ),
inference(avatar_split_clause,[],[f160,f285,f289,f277]) ).
thf(f294,definition,
( spl19_25
<=> ( $true
= ( mrel @ mactual @ sK14 ) ) ),
introduced(definition,[new_symbols(definition,[spl19_25])],[avatar_definition]) ).
thf(f296,plain,
( ( $true
= ( mrel @ mactual @ sK14 ) )
| ~ spl19_25 ),
inference(avatar_component_clause,[],[f294]) ).
thf(f298,definition,
( spl19_26
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK13 @ X1 ) )
| ( $false
= ( p @ ( sK15 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_26])],[avatar_definition]) ).
thf(f299,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ sK13 @ X1 ) )
| ( $false
= ( p @ ( sK15 @ X1 ) ) ) )
| ~ spl19_26 ),
inference(avatar_component_clause,[],[f298]) ).
thf(f300,plain,
( spl19_21
| spl19_25
| spl19_26 ),
inference(avatar_split_clause,[],[f176,f298,f294,f277]) ).
thf(f302,definition,
( spl19_27
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK13 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_27])],[avatar_definition]) ).
thf(f303,plain,
( ! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) )
| ( $false
= ( mrel @ sK13 @ X1 ) ) )
| ~ spl19_27 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f304,plain,
( spl19_25
| spl19_27
| spl19_21 ),
inference(avatar_split_clause,[],[f174,f277,f302,f294]) ).
thf(f306,definition,
( spl19_28
<=> ( ( mrel @ mactual @ sK13 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl19_28])],[avatar_definition]) ).
thf(f308,plain,
( ( ( mrel @ mactual @ sK13 )
= $true )
| ~ spl19_28 ),
inference(avatar_component_clause,[],[f306]) ).
thf(f309,plain,
( spl19_25
| spl19_21
| spl19_28 ),
inference(avatar_split_clause,[],[f167,f306,f277,f294]) ).
thf(f311,definition,
( spl19_29
<=> ! [X1: mworld] :
( ( ( mrel @ sK14 @ X1 )
= $false )
| ( $true
= ( mrel @ X1 @ ( sK17 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_29])],[avatar_definition]) ).
thf(f312,plain,
( ! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK17 @ X1 ) ) )
| ( ( mrel @ sK14 @ X1 )
= $false ) )
| ~ spl19_29 ),
inference(avatar_component_clause,[],[f311]) ).
thf(f314,definition,
( spl19_30
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ sK13 @ X2 ) )
| ( ( p @ ( sK16 @ X2 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl19_30])],[avatar_definition]) ).
thf(f315,plain,
( ! [X2: mworld] :
( ( $false
= ( mrel @ sK13 @ X2 ) )
| ( ( p @ ( sK16 @ X2 ) )
= $false ) )
| ~ spl19_30 ),
inference(avatar_component_clause,[],[f314]) ).
thf(f316,plain,
( spl19_21
| spl19_29
| spl19_30 ),
inference(avatar_split_clause,[],[f191,f314,f311,f277]) ).
thf(f318,definition,
( spl19_31
<=> ! [X1: mworld] :
( ( ( mrel @ sK14 @ X1 )
= $false )
| ( $false
= ( p @ ( sK17 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_31])],[avatar_definition]) ).
thf(f319,plain,
( ! [X1: mworld] :
( ( ( mrel @ sK14 @ X1 )
= $false )
| ( $false
= ( p @ ( sK17 @ X1 ) ) ) )
| ~ spl19_31 ),
inference(avatar_component_clause,[],[f318]) ).
thf(f320,plain,
( spl19_31
| spl19_21
| spl19_30 ),
inference(avatar_split_clause,[],[f192,f314,f277,f318]) ).
thf(f322,definition,
( spl19_32
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ sK13 @ X2 ) )
| ( $true
= ( mrel @ X2 @ ( sK16 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_32])],[avatar_definition]) ).
thf(f323,plain,
( ! [X2: mworld] :
( ( $true
= ( mrel @ X2 @ ( sK16 @ X2 ) ) )
| ( $false
= ( mrel @ sK13 @ X2 ) ) )
| ~ spl19_32 ),
inference(avatar_component_clause,[],[f322]) ).
thf(f324,plain,
( spl19_21
| spl19_29
| spl19_32 ),
inference(avatar_split_clause,[],[f194,f322,f311,f277]) ).
thf(f325,plain,
( spl19_21
| spl19_32
| spl19_31 ),
inference(avatar_split_clause,[],[f193,f318,f322,f277]) ).
thf(f327,definition,
( spl19_33
<=> ! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK18 @ X1 ) ) )
| ( ( mrel @ sK14 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl19_33])],[avatar_definition]) ).
thf(f328,plain,
( ! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK18 @ X1 ) ) )
| ( ( mrel @ sK14 @ X1 )
= $false ) )
| ~ spl19_33 ),
inference(avatar_component_clause,[],[f327]) ).
thf(f329,plain,
( spl19_21
| spl19_33
| spl19_28 ),
inference(avatar_split_clause,[],[f200,f306,f327,f277]) ).
thf(f331,definition,
( spl19_34
<=> ! [X1: mworld] :
( ( ( p @ ( sK18 @ X1 ) )
= $false )
| ( ( mrel @ sK14 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl19_34])],[avatar_definition]) ).
thf(f332,plain,
( ! [X1: mworld] :
( ( ( mrel @ sK14 @ X1 )
= $false )
| ( ( p @ ( sK18 @ X1 ) )
= $false ) )
| ~ spl19_34 ),
inference(avatar_component_clause,[],[f331]) ).
thf(f333,plain,
( spl19_21
| spl19_28
| spl19_34 ),
inference(avatar_split_clause,[],[f199,f331,f306,f277]) ).
thf(f334,plain,
~ spl19_21,
inference(avatar_split_clause,[],[f53,f277]) ).
thf(f347,plain,
( ( $false = $true )
| ( $false
= ( p @ ( sK17 @ sK14 ) ) )
| ~ spl19_31 ),
inference(constrained_superposition,[],[f41,f319]) ).
thf(f348,plain,
( ( $false
= ( p @ ( sK17 @ sK14 ) ) )
| ~ spl19_31 ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f424,definition,
( spl19_35
<=> ( $false
= ( mrel @ sK14 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl19_35])],[avatar_definition]) ).
thf(f425,plain,
( ( $false
!= ( mrel @ sK14 @ mactual ) )
| spl19_35 ),
inference(avatar_component_clause,[],[f424]) ).
thf(f426,plain,
( ( $false
= ( mrel @ sK14 @ mactual ) )
| ~ spl19_35 ),
inference(avatar_component_clause,[],[f424]) ).
thf(f446,plain,
( ! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X2 @ X1 )
!= $true )
| ( $false = $true )
| ( $true
= ( p @ X1 ) )
| ( ( mrel @ X2 @ ( sK11 @ X0 ) )
!= $true )
| ( $false
= ( mrel @ mactual @ X0 ) ) )
| ~ spl19_24 ),
inference(constrained_superposition,[],[f290,f42]) ).
thf(f462,plain,
( ! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X2 @ ( sK11 @ X0 ) )
!= $true )
| ( ( mrel @ X2 @ X1 )
!= $true )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl19_24 ),
inference(trivial_inequality_removal,[],[f446]) ).
thf(f587,definition,
( spl19_40
<=> ( ( mrel @ sK13 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl19_40])],[avatar_definition]) ).
thf(f588,plain,
( ( ( mrel @ sK13 @ mactual )
!= $false )
| spl19_40 ),
inference(avatar_component_clause,[],[f587]) ).
thf(f589,plain,
( ( ( mrel @ sK13 @ mactual )
= $false )
| ~ spl19_40 ),
inference(avatar_component_clause,[],[f587]) ).
thf(f607,plain,
( ! [X0: mworld] :
( ( $false = $true )
| ( $true
!= ( mrel @ X0 @ sK13 ) )
| ( $true
!= ( mrel @ X0 @ mactual ) ) )
| ~ spl19_40 ),
inference(constrained_superposition,[],[f42,f589]) ).
thf(f608,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ X0 @ sK13 ) )
| ( $true
!= ( mrel @ X0 @ mactual ) ) )
| ~ spl19_40 ),
inference(trivial_inequality_removal,[],[f607]) ).
thf(f638,plain,
( ( $true != $true )
| ( $true
!= ( mrel @ mactual @ mactual ) )
| ~ spl19_28
| ~ spl19_40 ),
inference(constrained_superposition,[],[f608,f308]) ).
thf(f644,plain,
( ( $true
!= ( mrel @ mactual @ mactual ) )
| ~ spl19_28
| ~ spl19_40 ),
inference(trivial_inequality_removal,[],[f638]) ).
thf(f648,plain,
( $false
| ~ spl19_28
| ~ spl19_40 ),
inference(forward_subsumption_resolution,[],[f644,f41]) ).
thf(f649,plain,
( ~ spl19_28
| ~ spl19_40 ),
inference(avatar_contradiction_clause,[],[f648]) ).
thf(f684,plain,
( ! [X0: mworld,X1: mworld] :
( ( $false = $true )
| ( $false
= ( p @ ( sK18 @ X0 ) ) )
| ( $true
!= ( mrel @ X1 @ sK14 ) )
| ( ( mrel @ X1 @ X0 )
!= $true ) )
| ~ spl19_34 ),
inference(constrained_superposition,[],[f332,f42]) ).
thf(f688,plain,
( ( $false = $true )
| ( $false
= ( p @ ( sK18 @ sK14 ) ) )
| ~ spl19_34 ),
inference(constrained_superposition,[],[f41,f332]) ).
thf(f695,plain,
( ( $false
= ( p @ ( sK18 @ sK14 ) ) )
| ~ spl19_34 ),
inference(trivial_inequality_removal,[],[f688]) ).
thf(f698,plain,
( ! [X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X1 @ sK14 ) )
| ( ( mrel @ X1 @ X0 )
!= $true )
| ( $false
= ( p @ ( sK18 @ X0 ) ) ) )
| ~ spl19_34 ),
inference(trivial_inequality_removal,[],[f684]) ).
thf(f822,plain,
( ! [X0: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true != $true )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ X0 @ X1 )
!= $true )
| ( $true
= ( p @ X1 ) ) )
| ~ spl19_20
| ~ spl19_24 ),
inference(constrained_superposition,[],[f462,f275]) ).
thf(f831,plain,
( ! [X0: mworld,X1: mworld] :
( ( $true != $true )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ X0 @ X1 )
!= $true )
| ( $true
= ( p @ X1 ) ) )
| ~ spl19_20
| ~ spl19_24 ),
inference(duplicate_literal_removal,[],[f822]) ).
thf(f832,plain,
( ! [X0: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( p @ X1 ) )
| ( ( mrel @ X0 @ X1 )
!= $true ) )
| ~ spl19_20
| ~ spl19_24 ),
inference(trivial_inequality_removal,[],[f831]) ).
thf(f926,plain,
( ! [X0: mworld] :
( ( ( mrel @ sK14 @ X0 )
!= $true )
| ( ( p @ X0 )
= $true )
| ( $false = $true ) )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25 ),
inference(constrained_superposition,[],[f296,f832]) ).
thf(f927,plain,
( ! [X0: mworld] :
( ( ( mrel @ mactual @ X0 )
!= $true )
| ( $false = $true )
| ( ( p @ X0 )
= $true ) )
| ~ spl19_20
| ~ spl19_24 ),
inference(constrained_superposition,[],[f41,f832]) ).
thf(f937,plain,
( ! [X0: mworld] :
( ( ( mrel @ mactual @ X0 )
!= $true )
| ( ( p @ X0 )
= $true ) )
| ~ spl19_20
| ~ spl19_24 ),
inference(trivial_inequality_removal,[],[f927]) ).
thf(f940,plain,
( ! [X0: mworld] :
( ( ( mrel @ sK14 @ X0 )
!= $true )
| ( ( p @ X0 )
= $true ) )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25 ),
inference(trivial_inequality_removal,[],[f926]) ).
thf(f954,definition,
( spl19_49
<=> ! [X0: mworld] :
( ( $true
!= ( mrel @ ( sK18 @ mactual ) @ X0 ) )
| ( ( p @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl19_49])],[avatar_definition]) ).
thf(f955,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ ( sK18 @ mactual ) @ X0 ) )
| ( ( p @ X0 )
= $true ) )
| ~ spl19_49 ),
inference(avatar_component_clause,[],[f954]) ).
thf(f965,plain,
( ( $true != $true )
| ( $true
= ( p @ ( sK16 @ mactual ) ) )
| ( ( mrel @ sK13 @ mactual )
= $false )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_32 ),
inference(constrained_superposition,[],[f937,f323]) ).
thf(f971,plain,
( ( $true
= ( p @ ( sK16 @ mactual ) ) )
| ( ( mrel @ sK13 @ mactual )
= $false )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_32 ),
inference(trivial_inequality_removal,[],[f965]) ).
thf(f989,definition,
( spl19_51
<=> ! [X0: mworld] :
( ( $true
!= ( mrel @ ( sK16 @ mactual ) @ X0 ) )
| ( ( p @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl19_51])],[avatar_definition]) ).
thf(f990,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ ( sK16 @ mactual ) @ X0 ) )
| ( ( p @ X0 )
= $true ) )
| ~ spl19_51 ),
inference(avatar_component_clause,[],[f989]) ).
thf(f996,definition,
( spl19_52
<=> ( $true
= ( p @ ( sK16 @ mactual ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_52])],[avatar_definition]) ).
thf(f997,plain,
( ( $true
!= ( p @ ( sK16 @ mactual ) ) )
| spl19_52 ),
inference(avatar_component_clause,[],[f996]) ).
thf(f998,plain,
( ( $true
= ( p @ ( sK16 @ mactual ) ) )
| ~ spl19_52 ),
inference(avatar_component_clause,[],[f996]) ).
thf(f999,plain,
( spl19_40
| spl19_52
| ~ spl19_20
| ~ spl19_24
| ~ spl19_32 ),
inference(avatar_split_clause,[],[f971,f322,f289,f274,f996,f587]) ).
thf(f1021,plain,
( ( $false != $false )
| ( $false
= ( p @ ( sK16 @ mactual ) ) )
| ~ spl19_30
| spl19_40 ),
inference(constrained_superposition,[],[f588,f315]) ).
thf(f1024,plain,
( ( $false
= ( p @ ( sK16 @ mactual ) ) )
| ~ spl19_30
| spl19_40 ),
inference(trivial_inequality_removal,[],[f1021]) ).
thf(f1025,plain,
( ( $false = $true )
| ~ spl19_30
| spl19_40
| ~ spl19_52 ),
inference(forward_demodulation,[],[f1024,f998]) ).
thf(f1026,plain,
( $false
| ~ spl19_30
| spl19_40
| ~ spl19_52 ),
inference(trivial_inequality_removal,[],[f1025]) ).
thf(f1027,plain,
( ~ spl19_30
| spl19_40
| ~ spl19_52 ),
inference(avatar_contradiction_clause,[],[f1026]) ).
thf(f1057,plain,
( ( $true != $true )
| ( $true
= ( p @ ( sK17 @ sK14 ) ) )
| ( $false
= ( mrel @ sK14 @ sK14 ) )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_29 ),
inference(constrained_superposition,[],[f940,f312]) ).
thf(f1073,plain,
( ( $true
= ( p @ ( sK17 @ sK14 ) ) )
| ( $false
= ( mrel @ sK14 @ sK14 ) )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_29 ),
inference(trivial_inequality_removal,[],[f1057]) ).
thf(f1102,plain,
( ( $false = $true )
| ( $false
= ( mrel @ sK14 @ sK14 ) )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_29
| ~ spl19_31 ),
inference(forward_demodulation,[],[f1073,f348]) ).
thf(f1103,plain,
( ( $false
= ( mrel @ sK14 @ sK14 ) )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_29
| ~ spl19_31 ),
inference(trivial_inequality_removal,[],[f1102]) ).
thf(f1107,plain,
( ( $false = $true )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_29
| ~ spl19_31 ),
inference(forward_demodulation,[],[f1103,f41]) ).
thf(f1108,plain,
( $false
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_29
| ~ spl19_31 ),
inference(trivial_inequality_removal,[],[f1107]) ).
thf(f1109,plain,
( ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_29
| ~ spl19_31 ),
inference(avatar_contradiction_clause,[],[f1108]) ).
thf(f1148,plain,
( ( $false = $true )
| ( $false
= ( p @ ( sK15 @ sK13 ) ) )
| ~ spl19_26 ),
inference(constrained_superposition,[],[f299,f41]) ).
thf(f1154,plain,
( ( $false != $false )
| ( $false
= ( p @ ( sK15 @ mactual ) ) )
| ~ spl19_26
| spl19_40 ),
inference(constrained_superposition,[],[f588,f299]) ).
thf(f1165,plain,
( ( $false
= ( p @ ( sK15 @ mactual ) ) )
| ~ spl19_26
| spl19_40 ),
inference(trivial_inequality_removal,[],[f1154]) ).
thf(f1166,plain,
( ( $false
= ( p @ ( sK15 @ sK13 ) ) )
| ~ spl19_26 ),
inference(trivial_inequality_removal,[],[f1148]) ).
thf(f1209,plain,
( ( $true
= ( p @ ( sK15 @ mactual ) ) )
| ( $true != $true )
| ( ( mrel @ sK13 @ mactual )
= $false )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_27 ),
inference(constrained_superposition,[],[f937,f303]) ).
thf(f1226,plain,
( ( $true
= ( p @ ( sK15 @ mactual ) ) )
| ( ( mrel @ sK13 @ mactual )
= $false )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_27 ),
inference(trivial_inequality_removal,[],[f1209]) ).
thf(f1240,plain,
( ( $true
= ( p @ ( sK15 @ mactual ) ) )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_27
| spl19_40 ),
inference(forward_subsumption_resolution,[],[f1226,f588]) ).
thf(f1248,plain,
( ( $false = $true )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_26
| ~ spl19_27
| spl19_40 ),
inference(forward_demodulation,[],[f1240,f1165]) ).
thf(f1249,plain,
( $false
| ~ spl19_20
| ~ spl19_24
| ~ spl19_26
| ~ spl19_27
| spl19_40 ),
inference(trivial_inequality_removal,[],[f1248]) ).
thf(f1250,plain,
( ~ spl19_20
| ~ spl19_24
| ~ spl19_26
| ~ spl19_27
| spl19_40 ),
inference(avatar_contradiction_clause,[],[f1249]) ).
thf(f1283,plain,
( ! [X0: mworld] :
( ( ( p @ X0 )
= $true )
| ( ( mrel @ sK14 @ X0 )
!= $true )
| ( $false = $true ) )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25 ),
inference(constrained_superposition,[],[f296,f832]) ).
thf(f1289,plain,
( ! [X0: mworld] :
( ( ( mrel @ mactual @ X0 )
!= $true )
| ( $false
= ( p @ ( sK18 @ X0 ) ) )
| ( $true != $true ) )
| ~ spl19_25
| ~ spl19_34 ),
inference(constrained_superposition,[],[f698,f296]) ).
thf(f1291,plain,
( ! [X0: mworld] :
( ( ( mrel @ sK14 @ X0 )
!= $true )
| ( ( p @ X0 )
= $true ) )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25 ),
inference(trivial_inequality_removal,[],[f1283]) ).
thf(f1293,plain,
( ! [X0: mworld] :
( ( ( mrel @ mactual @ X0 )
!= $true )
| ( $false
= ( p @ ( sK18 @ X0 ) ) ) )
| ~ spl19_25
| ~ spl19_34 ),
inference(trivial_inequality_removal,[],[f1289]) ).
thf(f1298,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ X0 @ sK14 ) )
| ( $false = $true )
| ( $true
!= ( mrel @ X0 @ mactual ) ) )
| ~ spl19_35 ),
inference(constrained_superposition,[],[f426,f42]) ).
thf(f1304,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ X0 @ sK14 ) )
| ( $true
!= ( mrel @ X0 @ mactual ) ) )
| ~ spl19_35 ),
inference(trivial_inequality_removal,[],[f1298]) ).
thf(f1397,plain,
( ( $false
= ( mrel @ sK14 @ sK14 ) )
| ( $true != $true )
| ( $true
= ( p @ ( sK18 @ sK14 ) ) )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_33 ),
inference(constrained_superposition,[],[f1291,f328]) ).
thf(f1402,plain,
( ( $false
= ( mrel @ sK14 @ sK14 ) )
| ( $true
= ( p @ ( sK18 @ sK14 ) ) )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_33 ),
inference(trivial_inequality_removal,[],[f1397]) ).
thf(f1407,plain,
( ( $true
= ( p @ ( sK18 @ sK14 ) ) )
| ( $false = $true )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_33 ),
inference(forward_demodulation,[],[f1402,f41]) ).
thf(f1408,plain,
( ( $true
= ( p @ ( sK18 @ sK14 ) ) )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_33 ),
inference(trivial_inequality_removal,[],[f1407]) ).
thf(f1413,plain,
( ( $false = $true )
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_33
| ~ spl19_34 ),
inference(forward_demodulation,[],[f1408,f695]) ).
thf(f1414,plain,
( $false
| ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_33
| ~ spl19_34 ),
inference(trivial_inequality_removal,[],[f1413]) ).
thf(f1415,plain,
( ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_33
| ~ spl19_34 ),
inference(avatar_contradiction_clause,[],[f1414]) ).
thf(f1487,plain,
( ! [X2: mworld,X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X2 @ ( sK12 @ X0 ) ) )
| ( $true
= ( p @ X1 ) )
| ( ( mrel @ X2 @ X1 )
!= $true )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false = $true ) )
| ~ spl19_22 ),
inference(constrained_superposition,[],[f42,f282]) ).
thf(f1498,plain,
( ! [X2: mworld,X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X2 @ ( sK12 @ X0 ) ) )
| ( ( mrel @ X2 @ X1 )
!= $true )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl19_22 ),
inference(trivial_inequality_removal,[],[f1487]) ).
thf(f1603,plain,
( ( $true != $true )
| ( ( p @ ( sK18 @ mactual ) )
= $true )
| ~ spl19_49 ),
inference(constrained_superposition,[],[f955,f41]) ).
thf(f1610,plain,
( ( ( p @ ( sK18 @ mactual ) )
= $true )
| ~ spl19_49 ),
inference(trivial_inequality_removal,[],[f1603]) ).
thf(f1640,plain,
( ( $true != $true )
| ( $true
= ( p @ ( sK16 @ mactual ) ) )
| ~ spl19_51 ),
inference(constrained_superposition,[],[f990,f41]) ).
thf(f1653,plain,
( ( $true
= ( p @ ( sK16 @ mactual ) ) )
| ~ spl19_51 ),
inference(trivial_inequality_removal,[],[f1640]) ).
thf(f1670,plain,
( $false
| ~ spl19_51
| spl19_52 ),
inference(forward_subsumption_resolution,[],[f1653,f997]) ).
thf(f1671,plain,
( ~ spl19_51
| spl19_52 ),
inference(avatar_contradiction_clause,[],[f1670]) ).
thf(f1726,plain,
( ( $true != $true )
| ( ( p @ ( sK18 @ mactual ) )
= $false )
| ~ spl19_25
| ~ spl19_34 ),
inference(constrained_superposition,[],[f1293,f41]) ).
thf(f1734,plain,
( ( ( p @ ( sK18 @ mactual ) )
= $false )
| ~ spl19_25
| ~ spl19_34 ),
inference(trivial_inequality_removal,[],[f1726]) ).
thf(f1742,plain,
( ( $false = $true )
| ~ spl19_25
| ~ spl19_34
| ~ spl19_49 ),
inference(forward_demodulation,[],[f1734,f1610]) ).
thf(f1743,plain,
( $false
| ~ spl19_25
| ~ spl19_34
| ~ spl19_49 ),
inference(trivial_inequality_removal,[],[f1742]) ).
thf(f1744,plain,
( ~ spl19_25
| ~ spl19_34
| ~ spl19_49 ),
inference(avatar_contradiction_clause,[],[f1743]) ).
thf(f1829,plain,
( ( $true
!= ( mrel @ mactual @ mactual ) )
| ( $true != $true )
| ~ spl19_25
| ~ spl19_35 ),
inference(constrained_superposition,[],[f1304,f296]) ).
thf(f1843,plain,
( ( $true
!= ( mrel @ mactual @ mactual ) )
| ~ spl19_25
| ~ spl19_35 ),
inference(trivial_inequality_removal,[],[f1829]) ).
thf(f1845,plain,
( $false
| ~ spl19_25
| ~ spl19_35 ),
inference(forward_subsumption_resolution,[],[f1843,f41]) ).
thf(f1846,plain,
( ~ spl19_25
| ~ spl19_35 ),
inference(avatar_contradiction_clause,[],[f1845]) ).
thf(f1909,plain,
( ! [X0: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) )
| ~ spl19_22
| ~ spl19_23 ),
inference(constrained_superposition,[],[f1498,f286]) ).
thf(f1922,plain,
( ! [X0: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X1 )
!= $true )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true != $true )
| ( $true
= ( p @ X1 ) ) )
| ~ spl19_22
| ~ spl19_23 ),
inference(duplicate_literal_removal,[],[f1909]) ).
thf(f1923,plain,
( ! [X0: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( p @ X1 ) )
| ( ( mrel @ X0 @ X1 )
!= $true ) )
| ~ spl19_22
| ~ spl19_23 ),
inference(trivial_inequality_removal,[],[f1922]) ).
thf(f1970,plain,
( ! [X0: mworld] :
( ( ( p @ X0 )
= $true )
| ( $false = $true )
| ( ( mrel @ sK13 @ X0 )
!= $true ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_28 ),
inference(constrained_superposition,[],[f1923,f308]) ).
thf(f1977,plain,
( ! [X0: mworld] :
( ( ( p @ X0 )
= $true )
| ( $true
!= ( mrel @ ( sK18 @ mactual ) @ X0 ) )
| ( $false = $true )
| ( $false
= ( mrel @ sK14 @ mactual ) ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_33 ),
inference(constrained_superposition,[],[f1923,f328]) ).
thf(f1982,plain,
( ! [X0: mworld] :
( ( ( p @ X0 )
= $true )
| ( ( mrel @ sK14 @ X0 )
!= $true )
| ( $false = $true ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_25 ),
inference(constrained_superposition,[],[f296,f1923]) ).
thf(f1988,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ ( sK16 @ mactual ) @ X0 ) )
| ( ( p @ X0 )
= $true )
| ( ( mrel @ sK13 @ mactual )
= $false )
| ( $false = $true ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_32 ),
inference(constrained_superposition,[],[f323,f1923]) ).
thf(f1996,plain,
( ! [X0: mworld] :
( ( ( p @ X0 )
= $true )
| ( $true
!= ( mrel @ ( sK16 @ mactual ) @ X0 ) )
| ( ( mrel @ sK13 @ mactual )
= $false ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_32 ),
inference(trivial_inequality_removal,[],[f1988]) ).
thf(f1997,plain,
( ! [X0: mworld] :
( ( ( mrel @ sK13 @ X0 )
!= $true )
| ( ( p @ X0 )
= $true ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_28 ),
inference(trivial_inequality_removal,[],[f1970]) ).
thf(f1998,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ ( sK18 @ mactual ) @ X0 ) )
| ( ( p @ X0 )
= $true )
| ( $false
= ( mrel @ sK14 @ mactual ) ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_33 ),
inference(trivial_inequality_removal,[],[f1977]) ).
thf(f1999,plain,
( ! [X0: mworld] :
( ( ( mrel @ sK14 @ X0 )
!= $true )
| ( ( p @ X0 )
= $true ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_25 ),
inference(trivial_inequality_removal,[],[f1982]) ).
thf(f2014,plain,
( ! [X0: mworld] :
( ( ( p @ X0 )
= $true )
| ( $true
!= ( mrel @ ( sK16 @ mactual ) @ X0 ) ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_32
| spl19_40 ),
inference(forward_subsumption_resolution,[],[f1996,f588]) ).
thf(f2015,plain,
( ! [X0: mworld] :
( ( ( p @ X0 )
= $true )
| ( $true
!= ( mrel @ ( sK18 @ mactual ) @ X0 ) ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_33
| spl19_35 ),
inference(forward_subsumption_resolution,[],[f1998,f425]) ).
thf(f2022,plain,
( spl19_51
| ~ spl19_22
| ~ spl19_23
| ~ spl19_32
| spl19_40 ),
inference(avatar_split_clause,[],[f2014,f587,f322,f285,f281,f989]) ).
thf(f2023,plain,
( spl19_49
| ~ spl19_22
| ~ spl19_23
| ~ spl19_33
| spl19_35 ),
inference(avatar_split_clause,[],[f2015,f424,f327,f285,f281,f954]) ).
thf(f2031,plain,
( ( $false
= ( mrel @ sK13 @ sK13 ) )
| ( $true != $true )
| ( $true
= ( p @ ( sK15 @ sK13 ) ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_27
| ~ spl19_28 ),
inference(constrained_superposition,[],[f1997,f303]) ).
thf(f2038,plain,
( ( $true
= ( p @ ( sK15 @ sK13 ) ) )
| ( $false
= ( mrel @ sK13 @ sK13 ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_27
| ~ spl19_28 ),
inference(trivial_inequality_removal,[],[f2031]) ).
thf(f2047,plain,
( ( $false
= ( mrel @ sK13 @ sK13 ) )
| ( $false = $true )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_26
| ~ spl19_27
| ~ spl19_28 ),
inference(forward_demodulation,[],[f2038,f1166]) ).
thf(f2048,plain,
( ( $false
= ( mrel @ sK13 @ sK13 ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_26
| ~ spl19_27
| ~ spl19_28 ),
inference(trivial_inequality_removal,[],[f2047]) ).
thf(f2049,plain,
( ( $false = $true )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_26
| ~ spl19_27
| ~ spl19_28 ),
inference(forward_demodulation,[],[f2048,f41]) ).
thf(f2050,plain,
( $false
| ~ spl19_22
| ~ spl19_23
| ~ spl19_26
| ~ spl19_27
| ~ spl19_28 ),
inference(trivial_inequality_removal,[],[f2049]) ).
thf(f2051,plain,
( ~ spl19_22
| ~ spl19_23
| ~ spl19_26
| ~ spl19_27
| ~ spl19_28 ),
inference(avatar_contradiction_clause,[],[f2050]) ).
thf(f2087,plain,
( ( $false
= ( p @ ( sK17 @ sK14 ) ) )
| ( $false = $true )
| ~ spl19_31 ),
inference(constrained_superposition,[],[f41,f319]) ).
thf(f2101,plain,
( ( $false
= ( p @ ( sK17 @ sK14 ) ) )
| ~ spl19_31 ),
inference(trivial_inequality_removal,[],[f2087]) ).
thf(f2156,plain,
( ( $true
= ( p @ ( sK17 @ sK14 ) ) )
| ( $false
= ( mrel @ sK14 @ sK14 ) )
| ( $true != $true )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_25
| ~ spl19_29 ),
inference(constrained_superposition,[],[f1999,f312]) ).
thf(f2157,plain,
( ( $true
= ( p @ ( sK17 @ sK14 ) ) )
| ( $false
= ( mrel @ sK14 @ sK14 ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_25
| ~ spl19_29 ),
inference(trivial_inequality_removal,[],[f2156]) ).
thf(f2180,plain,
( ( $false
= ( mrel @ sK14 @ sK14 ) )
| ( $false = $true )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_25
| ~ spl19_29
| ~ spl19_31 ),
inference(forward_demodulation,[],[f2157,f2101]) ).
thf(f2181,plain,
( ( $false
= ( mrel @ sK14 @ sK14 ) )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_25
| ~ spl19_29
| ~ spl19_31 ),
inference(trivial_inequality_removal,[],[f2180]) ).
thf(f2194,plain,
( ( $false = $true )
| ~ spl19_22
| ~ spl19_23
| ~ spl19_25
| ~ spl19_29
| ~ spl19_31 ),
inference(forward_demodulation,[],[f2181,f41]) ).
thf(f2195,plain,
( $false
| ~ spl19_22
| ~ spl19_23
| ~ spl19_25
| ~ spl19_29
| ~ spl19_31 ),
inference(trivial_inequality_removal,[],[f2194]) ).
thf(f2196,plain,
( ~ spl19_22
| ~ spl19_23
| ~ spl19_25
| ~ spl19_29
| ~ spl19_31 ),
inference(avatar_contradiction_clause,[],[f2195]) ).
cnf(s13,plain,
( spl19_20
| spl19_21
| spl19_22 ),
inference(sat_conversion,[],[f283]) ).
cnf(s14,plain,
( spl19_20
| spl19_21
| spl19_23 ),
inference(sat_conversion,[],[f287]) ).
cnf(s15,plain,
( spl19_21
| spl19_22
| spl19_24 ),
inference(sat_conversion,[],[f291]) ).
cnf(s16,plain,
( spl19_21
| spl19_23
| spl19_24 ),
inference(sat_conversion,[],[f292]) ).
cnf(s17,plain,
( spl19_21
| spl19_25
| spl19_26 ),
inference(sat_conversion,[],[f300]) ).
cnf(s18,plain,
( spl19_21
| spl19_25
| spl19_27 ),
inference(sat_conversion,[],[f304]) ).
cnf(s19,plain,
( spl19_21
| spl19_25
| spl19_28 ),
inference(sat_conversion,[],[f309]) ).
cnf(s20,plain,
( spl19_21
| spl19_29
| spl19_30 ),
inference(sat_conversion,[],[f316]) ).
cnf(s21,plain,
( spl19_21
| spl19_30
| spl19_31 ),
inference(sat_conversion,[],[f320]) ).
cnf(s22,plain,
( spl19_21
| spl19_29
| spl19_32 ),
inference(sat_conversion,[],[f324]) ).
cnf(s23,plain,
( spl19_21
| spl19_31
| spl19_32 ),
inference(sat_conversion,[],[f325]) ).
cnf(s24,plain,
( spl19_21
| spl19_28
| spl19_33 ),
inference(sat_conversion,[],[f329]) ).
cnf(s25,plain,
( spl19_21
| spl19_28
| spl19_34 ),
inference(sat_conversion,[],[f333]) ).
cnf(s26,plain,
~ spl19_21,
inference(sat_conversion,[],[f334]) ).
cnf(s36,plain,
( ~ spl19_28
| ~ spl19_40 ),
inference(sat_conversion,[],[f649]) ).
cnf(s56,plain,
( ~ spl19_20
| ~ spl19_24
| ~ spl19_32
| spl19_40
| spl19_52 ),
inference(sat_conversion,[],[f999]) ).
cnf(s58,plain,
( ~ spl19_30
| spl19_40
| ~ spl19_52 ),
inference(sat_conversion,[],[f1027]) ).
cnf(s65,plain,
( ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_29
| ~ spl19_31 ),
inference(sat_conversion,[],[f1109]) ).
cnf(s74,plain,
( ~ spl19_20
| ~ spl19_24
| ~ spl19_26
| ~ spl19_27
| spl19_40 ),
inference(sat_conversion,[],[f1250]) ).
cnf(s88,plain,
( ~ spl19_20
| ~ spl19_24
| ~ spl19_25
| ~ spl19_33
| ~ spl19_34 ),
inference(sat_conversion,[],[f1415]) ).
cnf(s94,plain,
( ~ spl19_51
| spl19_52 ),
inference(sat_conversion,[],[f1671]) ).
cnf(s98,plain,
( ~ spl19_25
| ~ spl19_34
| ~ spl19_49 ),
inference(sat_conversion,[],[f1744]) ).
cnf(s99,plain,
( ~ spl19_25
| ~ spl19_35 ),
inference(sat_conversion,[],[f1846]) ).
cnf(s102,plain,
( ~ spl19_22
| ~ spl19_23
| ~ spl19_32
| spl19_40
| spl19_51 ),
inference(sat_conversion,[],[f2022]) ).
cnf(s103,plain,
( ~ spl19_22
| ~ spl19_23
| ~ spl19_33
| spl19_35
| spl19_49 ),
inference(sat_conversion,[],[f2023]) ).
cnf(s109,plain,
( ~ spl19_22
| ~ spl19_23
| ~ spl19_26
| ~ spl19_27
| ~ spl19_28 ),
inference(sat_conversion,[],[f2051]) ).
cnf(s114,plain,
( ~ spl19_22
| ~ spl19_23
| ~ spl19_25
| ~ spl19_29
| ~ spl19_31 ),
inference(sat_conversion,[],[f2196]) ).
cnf(s123,plain,
( spl19_28
| spl19_34 ),
inference(rat,[],[s25,s26]) ).
cnf(s124,plain,
( spl19_28
| spl19_33 ),
inference(rat,[],[s24,s26]) ).
cnf(s125,plain,
( spl19_31
| spl19_32 ),
inference(rat,[],[s23,s26]) ).
cnf(s126,plain,
( spl19_29
| spl19_32 ),
inference(rat,[],[s22,s26]) ).
cnf(s127,plain,
( spl19_30
| spl19_31 ),
inference(rat,[],[s21,s26]) ).
cnf(s128,plain,
( spl19_29
| spl19_30 ),
inference(rat,[],[s20,s26]) ).
cnf(s129,plain,
( spl19_25
| spl19_28 ),
inference(rat,[],[s19,s26]) ).
cnf(s130,plain,
( spl19_25
| spl19_27 ),
inference(rat,[],[s18,s26]) ).
cnf(s131,plain,
( spl19_25
| spl19_26 ),
inference(rat,[],[s17,s26]) ).
cnf(s132,plain,
( spl19_23
| spl19_24 ),
inference(rat,[],[s16,s26]) ).
cnf(s133,plain,
( spl19_22
| spl19_24 ),
inference(rat,[],[s15,s26]) ).
cnf(s134,plain,
( spl19_20
| spl19_23 ),
inference(rat,[],[s14,s26]) ).
cnf(s135,plain,
( spl19_20
| spl19_22 ),
inference(rat,[],[s13,s26]) ).
cnf(s136,plain,
( spl19_25
| spl19_20 ),
inference(rat,[],[s109,s131,s130,s129,s134,s135]) ).
cnf(s137,plain,
( spl19_28
| spl19_20 ),
inference(rat,[],[s103,s98,s124,s123,s134,s135,s99,s136]) ).
cnf(s138,plain,
( spl19_29
| spl19_20 ),
inference(rat,[],[s94,s58,s102,s128,s126,s134,s135,s36,s137]) ).
cnf(s139,plain,
spl19_20,
inference(rat,[],[s94,s58,s102,s127,s125,s114,s138,s36,s137,s136,s135,s134]) ).
cnf(s140,plain,
( spl19_29
| spl19_40
| ~ spl19_23
| ~ spl19_22 ),
inference(rat,[],[s94,s58,s102,s128,s126]) ).
cnf(s141,plain,
( spl19_40
| ~ spl19_25
| ~ spl19_23
| ~ spl19_22 ),
inference(rat,[],[s94,s58,s102,s127,s125,s114,s140]) ).
cnf(s142,plain,
( ~ spl19_25
| ~ spl19_23
| ~ spl19_22 ),
inference(rat,[],[s103,s98,s124,s123,s36,s141,s99]) ).
cnf(s143,plain,
( ~ spl19_23
| ~ spl19_22 ),
inference(rat,[],[s109,s131,s130,s129,s142]) ).
cnf(s144,plain,
( spl19_29
| spl19_40
| ~ spl19_24 ),
inference(rat,[],[s58,s56,s128,s126,s139]) ).
cnf(s145,plain,
( spl19_31
| spl19_40
| ~ spl19_24 ),
inference(rat,[],[s58,s56,s127,s125,s139]) ).
cnf(s146,plain,
( spl19_40
| ~ spl19_24 ),
inference(rat,[],[s74,s131,s130,s65,s145,s144,s139]) ).
cnf(s147,plain,
~ spl19_24,
inference(rat,[],[s88,s129,s124,s123,s36,s146,s139]) ).
cnf(s148,plain,
spl19_23,
inference(rat,[],[s132,s147]) ).
cnf(s149,plain,
spl19_22,
inference(rat,[],[s133,s147]) ).
cnf(s150,plain,
$false,
inference(rat,[],[s143,s149,s148]) ).
thf(f2210,plain,
$false,
inference(avatar_sat_refutation,[],[s150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO893^11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n010.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 17:26:18 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.33 % (3172030)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.33 % (3172038)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4286982034:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.33 % (3172037)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3705809691:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.33 % (3172035)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=78852747:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.33 % (3172039)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=433334082:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.33 % (3172036)lrs+10_16_si=on:nwc=1.5:random_seed=2098173974:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.33 % (3172037)Refutation not found, incomplete strategy
% 0.20/0.33 % (3172037)------------------------------
% 0.20/0.33 % (3172037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (3172037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (3172037)CaDiCaL version: 2.1.3
% 0.20/0.33 % (3172037)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.33 % (3172037)Time elapsed: 0.002 s
% 0.20/0.33 % (3172037)Peak memory usage: 12 MB
% 0.20/0.33 % (3172037)Instructions burned: 3 (million)
% 0.20/0.33 % (3172041)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.33 % (3172041)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
% 0.20/0.33 % (3172037)------------------------------
% 0.20/0.33 % (3172037)------------------------------
% 0.20/0.33 % (3172041)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=3014387315:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.33 % (3172036)Instruction limit reached!
% 0.20/0.33 % (3172036)------------------------------
% 0.20/0.33 % (3172036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (3172036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (3172036)CaDiCaL version: 2.1.3
% 0.20/0.33 % (3172036)Termination reason: Instruction limit
% 0.20/0.33 % (3172036)Termination phase: Saturation
% 0.20/0.33 % (3172036)Time elapsed: 0.011 s
% 0.20/0.33 % (3172036)Peak memory usage: 12 MB
% 0.20/0.33 % (3172036)Instructions burned: 19 (million)
% 0.20/0.33 % (3172039)Instruction limit reached!
% 0.20/0.33 % (3172039)------------------------------
% 0.20/0.33 % (3172039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (3172039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (3172039)CaDiCaL version: 2.1.3
% 0.20/0.33 % (3172039)Termination reason: Instruction limit
% 0.20/0.33 % (3172039)Termination phase: Saturation
% 0.20/0.33 % (3172039)Time elapsed: 0.013 s
% 0.20/0.33 % (3172039)Peak memory usage: 11 MB
% 0.20/0.33 % (3172039)Instructions burned: 26 (million)
% 0.20/0.33 % (3172040)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=589901927:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.33 % (3172047)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=876558899:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.33 % (3172047)Instruction limit reached!
% 0.20/0.33 % (3172047)------------------------------
% 0.20/0.33 % (3172047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (3172047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (3172047)CaDiCaL version: 2.1.3
% 0.20/0.33 % (3172047)Termination reason: Instruction limit
% 0.20/0.33 % (3172047)Termination phase: Saturation
% 0.20/0.33 % (3172047)Time elapsed: 0.002 s
% 0.20/0.33 % (3172047)Peak memory usage: 11 MB
% 0.20/0.33 % (3172047)Instructions burned: 3 (million)
% 0.20/0.33 % (3172051)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.33 % (3172049)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3856015134:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.33 % (3172051)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3170465071:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.33 % (3172049)Instruction limit reached!
% 0.20/0.33 % (3172049)------------------------------
% 0.20/0.33 % (3172049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (3172049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (3172049)CaDiCaL version: 2.1.3
% 0.20/0.33 % (3172049)Termination reason: Instruction limit
% 0.20/0.33 % (3172049)Termination phase: Saturation
% 0.20/0.33 % (3172049)Time elapsed: 0.003 s
% 0.20/0.33 % (3172049)Peak memory usage: 11 MB
% 0.20/0.33 % (3172049)Instructions burned: 6 (million)
% 0.20/0.33 % (3172051)Instruction limit reached!
% 0.20/0.33 % (3172051)------------------------------
% 0.20/0.33 % (3172051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (3172051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (3172051)CaDiCaL version: 2.1.3
% 0.20/0.33 % (3172051)Termination reason: Instruction limit
% 0.20/0.33 % (3172051)Termination phase: Saturation
% 0.20/0.33 % (3172051)Time elapsed: 0.005 s
% 0.20/0.33 % (3172051)Peak memory usage: 12 MB
% 0.20/0.33 % (3172051)Instructions burned: 8 (million)
% 0.20/0.33 % (3172053)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=380451578:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.33 % (3172035)Instruction limit reached!
% 0.20/0.33 % (3172035)------------------------------
% 0.20/0.33 % (3172035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (3172035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (3172035)CaDiCaL version: 2.1.3
% 0.20/0.33 % (3172035)Termination reason: Instruction limit
% 0.20/0.33 % (3172035)Termination phase: Saturation
% 0.20/0.33 % (3172035)Time elapsed: 0.048 s
% 0.20/0.33 % (3172035)Peak memory usage: 13 MB
% 0.20/0.33 % (3172035)Instructions burned: 87 (million)
% 0.20/0.33 % (3172056)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
% 0.20/0.33 % (3172056)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.33 % (3172053)Instruction limit reached!
% 0.20/0.33 % (3172053)------------------------------
% 0.20/0.33 % (3172053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (3172053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (3172053)CaDiCaL version: 2.1.3
% 0.20/0.33 % (3172053)Termination reason: Instruction limit
% 0.20/0.33 % (3172053)Termination phase: Saturation
% 0.20/0.33 % (3172053)Time elapsed: 0.007 s
% 0.20/0.33 % (3172053)Peak memory usage: 12 MB
% 0.20/0.33 % (3172053)Instructions burned: 12 (million)
% 0.20/0.33 % (3172056)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3018228600:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.33 % (3172057)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=280710422:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.33 % (3172041) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3172030-3172041"...
% 0.20/0.33 % (3172056)Instruction limit reached!
% 0.20/0.33 % (3172056)------------------------------
% 0.20/0.33 % (3172056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (3172056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (3172056)CaDiCaL version: 2.1.3
% 0.20/0.33 % (3172056)Termination reason: Instruction limit
% 0.20/0.33 % (3172056)Termination phase: Saturation
% 0.20/0.33 % (3172056)Time elapsed: 0.014 s
% 0.20/0.33 % (3172056)Peak memory usage: 12 MB
% 0.20/0.33 % (3172056)Instructions burned: 28 (million)
% 0.20/0.33 % (3172059)lrs+10_1_si=on:cs=on:random_seed=363710567:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.20/0.33 % (3172057) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3172030-3172057"...
% 0.20/0.33 % (3172060)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.20/0.33 % (3172059)Instruction limit reached!
% 0.20/0.33 % (3172059)------------------------------
% 0.20/0.33 % (3172059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (3172059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (3172059)CaDiCaL version: 2.1.3
% 0.20/0.33 % (3172059)Termination reason: Instruction limit
% 0.20/0.33 % (3172059)Termination phase: Saturation
% 0.20/0.33 % (3172059)Time elapsed: 0.004 s
% 0.20/0.33 % (3172059)Peak memory usage: 11 MB
% 0.20/0.33 % (3172059)Instructions burned: 8 (million)
% 0.20/0.33 % (3172060)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=454527074:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.33 % (3172057)...printing done.
% 0.20/0.33 % (3172041)...printing done.
% 0.20/0.33 % (3172060)Refutation not found, incomplete strategy
% 0.20/0.33 % (3172060)------------------------------
% 0.20/0.33 % (3172060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (3172060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (3172060)CaDiCaL version: 2.1.3
% 0.20/0.33 % (3172060)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.33 % (3172060)Time elapsed: 0.003 s
% 0.20/0.33 % (3172060)Peak memory usage: 12 MB
% 0.20/0.33 % (3172041)Refutation found. Thanks to Tanya!
% 0.20/0.33 % SZS status Theorem for theBenchmark
% 0.20/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.34 % (3172041)------------------------------
% 0.20/0.34 % (3172041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (3172041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (3172041)CaDiCaL version: 2.1.3
% 0.20/0.34 % (3172041)Termination reason: Refutation
% 0.20/0.34 % (3172041)Time elapsed: 0.065 s
% 0.20/0.34 % (3172041)Peak memory usage: 14 MB
% 0.20/0.34 % (3172041)Instructions burned: 119 (million)
% 0.20/0.34 % (3172030)Success in time 0.106 s
% 0.20/0.34 % Vampire exiting
%------------------------------------------------------------------------------