%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NLP266^4 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:16:35 AM UTC 2026
% Result : Theorem 4.51s 0.87s
% Output : Refutation 4.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 14
% Syntax : Number of formulae : 197 ( 70 unt; 0 typ; 2 def)
% Number of atoms : 2293 ( 474 equ; 0 cnn)
% Maximal formula atoms : 20 ( 11 avg)
% Number of connectives : 4012 ( 38 ~; 322 |; 95 &;3231 @)
% ( 2 <=>; 148 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 93 ( 93 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 46 usr; 11 con; 0-4 aty)
% ( 122 !!; 54 ??; 0 @@+; 0 @@-)
% Number of variables : 710 ( 0 sgn 315 !; 2 ?; 710 :)
% 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,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_15,type,
number: $i > $i > mworld > $o ).
thf(func_def_16,type,
string: $i > mworld > $o ).
thf(func_def_17,type,
in: $i > $i > $i > mworld > $o ).
thf(func_def_18,type,
do: $i > $i > $i > mworld > $o ).
thf(func_def_19,type,
entry_box: $i > mworld > $o ).
thf(func_def_20,type,
userid: $i > $i > mworld > $o ).
thf(func_def_21,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_23,type,
vNOT: $o > $o ).
thf(func_def_24,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vAND: $o > $o > $o ).
thf(func_def_26,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vOR: $o > $o > $o ).
thf(func_def_28,type,
vIMP: $o > $o > $o ).
thf(func_def_29,type,
vIFF: $o > $o > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
sK0: mworld ).
thf(func_def_40,type,
sK1: $i > $i > $i > $i > mworld ).
thf(func_def_41,type,
sK2: $i > $i > mworld ).
thf(func_def_42,type,
sK3: $i > $i > $i > $i > $i ).
thf(func_def_43,type,
sK4: mworld > $i > $i > $i > $i ).
thf(func_def_45,type,
sK6: mworld > $i ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f10,axiom,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X1 @ X2 )
& ( mrel @ X0 @ X1 ) )
=> ( mrel @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
thf(f11,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f12,axiom,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f13,axiom,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( mand @ ( userid @ u @ X0 ) @ ( string @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(f14,axiom,
( mlocal
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( mand @ ( entry_box @ X0 ) @ ( number @ X0 @ one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(f15,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] :
( mimplies @ ( mand @ ( string @ X1 ) @ ( entry_box @ X2 ) )
@ ( mexists_di
@ ^ [X3: $i] :
( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mimplies @ ( do @ X0 @ X3 @ X4 ) @ ( in @ X1 @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(f16,conjecture,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X2: $i] :
( mexists_di
@ ^ [X3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ X0 ) @ ( mand @ ( entry_box @ X1 ) @ ( number @ X1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mimplies @ ( do @ X3 @ X2 @ X4 ) @ ( in @ X0 @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f17,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X2: $i] :
( mexists_di
@ ^ [X3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ X0 ) @ ( mand @ ( entry_box @ X1 ) @ ( number @ X1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mimplies @ ( do @ X3 @ X2 @ X4 ) @ ( in @ X0 @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f18,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f21,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f22,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f25,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f26,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f29,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f30,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f33,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f34,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f33]) ).
thf(f35,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X1 @ X2 )
& ( mrel @ X0 @ X1 ) )
=> ( mrel @ X0 @ X2 ) ),
inference(rectify,[],[f10]) ).
thf(f36,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( ( mrel @ X1 @ X2 )
= $true )
& ( ( mrel @ X0 @ X1 )
= $true ) )
=> ( ( mrel @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f35]) ).
thf(f37,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f38,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f39,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f40,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( mand @ ( userid @ u @ X0 ) @ ( string @ X0 ) ) ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f42,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( string @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( mlocal
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( mand @ ( entry_box @ X0 ) @ ( number @ X0 @ one ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f44,plain,
( $true
= ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( entry_box @ Y0 ) @ ( number @ Y0 @ one ) ) ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f45,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] :
( mimplies @ ( mand @ ( string @ X1 ) @ ( entry_box @ X2 ) )
@ ( mexists_di
@ ^ [X3: $i] :
( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mimplies @ ( do @ X0 @ X3 @ X4 ) @ ( in @ X1 @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f46,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] :
( mimplies @ ( mand @ ( string @ Y1 ) @ ( entry_box @ Y2 ) )
@ ( mexists_di
@ ^ [Y3: $i] :
( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y0 @ Y3 @ Y4 ) @ ( in @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X2: $i] :
( mexists_di
@ ^ [X3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ X0 ) @ ( mand @ ( entry_box @ X1 ) @ ( number @ X1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mimplies @ ( do @ X3 @ X2 @ X4 ) @ ( in @ X0 @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f48,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mexists_di
@ ^ [Y2: $i] :
( mexists_di
@ ^ [Y3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( mand @ ( entry_box @ Y1 ) @ ( number @ Y1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y3 @ Y2 @ Y4 ) @ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mexists_di
@ ^ [Y2: $i] :
( mexists_di
@ ^ [Y3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( mand @ ( entry_box @ Y1 ) @ ( number @ Y1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y3 @ Y2 @ Y4 ) @ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f48]) ).
thf(f50,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X2 )
= $true )
| ( ( mrel @ X1 @ X2 )
!= $true )
| ( ( mrel @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f36]) ).
thf(f51,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X2 )
= $true )
| ( ( mrel @ X1 @ X2 )
!= $true )
| ( ( mrel @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f50]) ).
thf(f52,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f54,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f56,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f58,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f60,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f34]) ).
thf(f61,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
!= $true )
| ( ( mrel @ X0 @ X2 )
= $true )
| ( ( mrel @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f62,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f63,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f64,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( string @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f65,plain,
( $true
= ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( entry_box @ Y0 ) @ ( number @ Y0 @ one ) ) ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f66,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] :
( mimplies @ ( mand @ ( string @ Y1 ) @ ( entry_box @ Y2 ) )
@ ( mexists_di
@ ^ [Y3: $i] :
( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y0 @ Y3 @ Y4 ) @ ( in @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f67,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mexists_di
@ ^ [Y2: $i] :
( mexists_di
@ ^ [Y3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( mand @ ( entry_box @ Y1 ) @ ( number @ Y1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y3 @ Y2 @ Y4 ) @ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f70,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) )
@ ( userid @ u @ Y0 )
@ ( string @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f64,f52,f58,f63,f58,f54]) ).
thf(f71,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) )
@ ( entry_box @ Y0 )
@ ( number @ Y0 @ one ) ) ) ) ) ),
inference(definition_unfolding,[],[f65,f52,f63,f58,f54]) ).
thf(f72,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( string @ Y1 )
@ ( entry_box @ Y2 ) )
@ ( ^ [Y3: $i > mworld > $o,Y4: mworld] :
( ?? @ $i
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) )
@ ^ [Y3: $i] :
( ^ [Y4: mworld > $o,Y5: mworld] :
( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ ( ^ [Y4: $i > mworld > $o,Y5: mworld] :
( !! @ $i
@ ^ [Y6: $i] : ( Y4 @ Y6 @ Y5 ) )
@ ^ [Y4: $i] :
( ^ [Y5: mworld > $o,Y6: mworld > $o,Y7: mworld] :
( ( Y5 @ Y7 )
=> ( Y6 @ Y7 ) )
@ ( do @ Y0 @ Y3 @ Y4 )
@ ( in @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f66,f52,f58,f62,f62,f62,f56,f54,f63,f58,f62,f56]) ).
thf(f73,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: $i > mworld > $o,Y4: mworld] :
( ?? @ $i
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) )
@ ^ [Y3: $i] :
( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ ( ^ [Y4: mworld > $o,Y5: mworld] :
( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ ( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ ( userid @ u @ Y0 )
@ ( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ ( entry_box @ Y1 )
@ ( number @ Y1 @ one ) ) ) )
@ ( ^ [Y4: mworld > $o,Y5: mworld] :
( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ ( ^ [Y4: $i > mworld > $o,Y5: mworld] :
( !! @ $i
@ ^ [Y6: $i] : ( Y4 @ Y6 @ Y5 ) )
@ ^ [Y4: $i] :
( ^ [Y5: mworld > $o,Y6: mworld > $o,Y7: mworld] :
( ( Y5 @ Y7 )
=> ( Y6 @ Y7 ) )
@ ( do @ Y3 @ Y2 @ Y4 )
@ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f67,f52,f58,f63,f63,f63,f63,f54,f58,f54,f54,f58,f62,f56]) ).
thf(f74,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( ( userid @ u @ Y1 @ Y5 )
& ( entry_box @ Y2 @ Y5 )
& ( number @ Y2 @ one @ Y5 ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( do @ Y4 @ Y3 @ Y6 @ Y5 )
=> ( in @ Y1 @ Y2 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( ( userid @ u @ Y1 @ Y5 )
& ( entry_box @ Y2 @ Y5 )
& ( number @ Y2 @ one @ Y5 ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( do @ Y4 @ Y3 @ Y6 @ Y5 )
=> ( in @ Y1 @ Y2 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( $false
= ( ( mrel @ mactual @ sK0 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK0 @ Y4 )
=> ( ( userid @ u @ Y0 @ Y4 )
& ( entry_box @ Y1 @ Y4 )
& ( number @ Y1 @ one @ Y4 ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK0 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y3 @ Y2 @ Y5 @ Y4 )
=> ( in @ Y0 @ Y1 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK0 @ Y4 )
=> ( ( userid @ u @ Y0 @ Y4 )
& ( entry_box @ Y1 @ Y4 )
& ( number @ Y1 @ one @ Y4 ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK0 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y3 @ Y2 @ Y5 @ Y4 )
=> ( in @ Y0 @ Y1 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( $true
= ( mrel @ mactual @ sK0 ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f79,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK0 @ Y4 )
=> ( ( userid @ u @ Y0 @ Y4 )
& ( entry_box @ Y1 @ Y4 )
& ( number @ Y1 @ one @ Y4 ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK0 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y3 @ Y2 @ Y5 @ Y4 )
=> ( in @ Y0 @ Y1 @ Y5 @ Y4 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f80,plain,
! [X1: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK0 @ Y3 )
=> ( ( userid @ u @ X1 @ Y3 )
& ( entry_box @ Y0 @ Y3 )
& ( number @ Y0 @ one @ Y3 ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK0 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( do @ Y2 @ Y1 @ Y4 @ Y3 )
=> ( in @ X1 @ Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK0 @ Y3 )
=> ( ( userid @ u @ X1 @ Y3 )
& ( entry_box @ Y0 @ Y3 )
& ( number @ Y0 @ one @ Y3 ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK0 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( do @ Y2 @ Y1 @ Y4 @ Y3 )
=> ( in @ X1 @ Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK0 @ Y2 )
=> ( ( userid @ u @ X1 @ Y2 )
& ( entry_box @ X2 @ Y2 )
& ( number @ X2 @ one @ Y2 ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( do @ Y1 @ Y0 @ Y3 @ Y2 )
=> ( in @ X1 @ X2 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK0 @ Y2 )
=> ( ( userid @ u @ X1 @ Y2 )
& ( entry_box @ X2 @ Y2 )
& ( number @ X2 @ one @ Y2 ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( do @ Y1 @ Y0 @ Y3 @ Y2 )
=> ( in @ X1 @ X2 @ Y3 @ Y2 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X1: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK0 @ Y1 )
=> ( ( userid @ u @ X1 @ Y1 )
& ( entry_box @ X2 @ Y1 )
& ( number @ X2 @ one @ Y1 ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ Y0 @ X3 @ Y2 @ Y1 )
=> ( in @ X1 @ X2 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $false
= ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK0 @ Y1 )
=> ( ( userid @ u @ X1 @ Y1 )
& ( entry_box @ X2 @ Y1 )
& ( number @ X2 @ one @ Y1 ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ Y0 @ X3 @ Y2 @ Y1 )
=> ( in @ X1 @ X2 @ Y2 @ Y1 ) ) ) ) ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( userid @ u @ X1 @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( number @ X2 @ one @ Y0 ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( userid @ u @ X1 @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( number @ X2 @ one @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) )
@ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( userid @ u @ X1 @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( number @ X2 @ one @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) )
@ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( userid @ u @ X1 @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( number @ X2 @ one @ Y0 ) ) )
@ ( sK2 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( mrel @ sK0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) ) ) ) )
| ( $false
= ( ( mrel @ sK0 @ ( sK2 @ X1 @ X2 ) )
=> ( ( userid @ u @ X1 @ ( sK2 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK2 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK2 @ X1 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) ) ) )
| ( $false
= ( ( mrel @ sK0 @ ( sK2 @ X1 @ X2 ) )
=> ( ( userid @ u @ X1 @ ( sK2 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK2 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK2 @ X1 @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( mrel @ sK0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( ( mrel @ sK0 @ ( sK2 @ X1 @ X2 ) )
=> ( ( userid @ u @ X1 @ ( sK2 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK2 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK2 @ X1 @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f90]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( mrel @ sK0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( ( userid @ u @ X1 @ ( sK2 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK2 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK2 @ X1 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( mrel @ sK0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f92]) ).
thf(f95,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( mrel @ sK0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( ( entry_box @ X2 @ ( sK2 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK2 @ X1 @ X2 ) ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f93]) ).
thf(f96,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( mrel @ sK0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
@ ( sK3 @ X1 @ X2 @ X3 @ X4 ) ) )
| ( $false
= ( ( mrel @ sK0 @ ( sK2 @ X1 @ X2 ) )
=> ( ( userid @ u @ X1 @ ( sK2 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK2 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK2 @ X1 @ X2 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f91]) ).
thf(f98,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
@ ( sK3 @ X1 @ X2 @ X3 @ X4 ) ) )
| ( $false
= ( ( userid @ u @ X1 @ ( sK2 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK2 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK2 @ X1 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f97]) ).
thf(f99,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
@ ( sK3 @ X1 @ X2 @ X3 @ X4 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f97]) ).
thf(f100,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( do @ X4 @ X3 @ ( sK3 @ X1 @ X2 @ X3 @ X4 ) @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ ( sK3 @ X1 @ X2 @ X3 @ X4 ) @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f99]) ).
thf(f101,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X2 @ ( sK3 @ X1 @ X2 @ X3 @ X4 ) @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( do @ X4 @ X3 @ ( sK3 @ X1 @ X2 @ X3 @ X4 ) @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f100]) ).
thf(f103,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
@ ( sK3 @ X1 @ X2 @ X3 @ X4 ) ) )
| ( $false
= ( ( entry_box @ X2 @ ( sK2 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK2 @ X1 @ X2 ) ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f98]) ).
thf(f104,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
@ ( sK3 @ X1 @ X2 @ X3 @ X4 ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( do @ X4 @ X3 @ ( sK3 @ X1 @ X2 @ X3 @ X4 ) @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ ( sK3 @ X1 @ X2 @ X3 @ X4 ) @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X2 @ ( sK3 @ X1 @ X2 @ X3 @ X4 ) @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( do @ X4 @ X3 @ ( sK3 @ X1 @ X2 @ X3 @ X4 ) @ ( sK1 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f108,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( string @ Y2 @ Y0 )
& ( entry_box @ Y3 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( do @ Y1 @ Y4 @ Y6 @ Y5 )
=> ( in @ Y2 @ Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f109,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( string @ Y2 @ Y0 )
& ( entry_box @ Y3 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( do @ Y1 @ Y4 @ Y6 @ Y5 )
=> ( in @ Y2 @ Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f108]) ).
thf(f110,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( string @ Y1 @ X1 )
& ( entry_box @ Y2 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ X1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y0 @ Y3 @ Y5 @ Y4 )
=> ( in @ Y1 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f111,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( string @ Y1 @ X1 )
& ( entry_box @ Y2 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ X1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y0 @ Y3 @ Y5 @ Y4 )
=> ( in @ Y1 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f112,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( string @ Y1 @ X1 )
& ( entry_box @ Y2 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ X1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y0 @ Y3 @ Y5 @ Y4 )
=> ( in @ Y1 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( string @ Y0 @ X1 )
& ( entry_box @ Y1 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( do @ X2 @ Y2 @ Y4 @ Y3 )
=> ( in @ Y0 @ Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( string @ Y0 @ X1 )
& ( entry_box @ Y1 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( do @ X2 @ Y2 @ Y4 @ Y3 )
=> ( in @ Y0 @ Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( string @ X3 @ X1 )
& ( entry_box @ Y0 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( do @ X2 @ Y1 @ Y3 @ Y2 )
=> ( in @ X3 @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( ( string @ X3 @ X1 )
& ( entry_box @ Y0 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( do @ X2 @ Y1 @ Y3 @ Y2 )
=> ( in @ X3 @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( ( string @ X3 @ X1 )
& ( entry_box @ X4 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( string @ X3 @ X1 )
& ( entry_box @ X4 @ X1 ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( string @ X3 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) )
@ ( sK4 @ X1 @ X3 @ X4 @ X2 ) ) )
| ( $false
= ( string @ X3 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X2 @ ( sK4 @ X1 @ X3 @ X4 @ X2 ) @ Y1 @ Y0 )
=> ( in @ X3 @ X4 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( string @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X2 @ ( sK4 @ X1 @ X3 @ X4 @ X2 ) @ Y1 @ Y0 )
=> ( in @ X3 @ X4 @ Y1 @ Y0 ) ) ) )
@ X5 ) )
| ( $false
= ( string @ X3 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X5 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X2 @ ( sK4 @ X1 @ X3 @ X4 @ X2 ) @ Y0 @ X5 )
=> ( in @ X3 @ X4 @ Y0 @ X5 ) ) ) ) )
| ( $false
= ( string @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f122]) ).
thf(f124,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( $false
= ( string @ X3 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X2 @ ( sK4 @ X1 @ X3 @ X4 @ X2 ) @ Y0 @ X5 )
=> ( in @ X3 @ X4 @ Y0 @ X5 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: mworld,X6: $i,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( $false
= ( string @ X3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( do @ X2 @ ( sK4 @ X1 @ X3 @ X4 @ X2 ) @ Y0 @ X5 )
=> ( in @ X3 @ X4 @ Y0 @ X5 ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X1: mworld,X6: $i,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( $false
= ( string @ X3 @ X1 ) )
| ( $true
= ( ( do @ X2 @ ( sK4 @ X1 @ X3 @ X4 @ X2 ) @ X6 @ X5 )
=> ( in @ X3 @ X4 @ X6 @ X5 ) ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X1: mworld,X6: $i,X4: $i,X5: mworld] :
( ( $false
= ( do @ X2 @ ( sK4 @ X1 @ X3 @ X4 @ X2 ) @ X6 @ X5 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( $false
= ( string @ X3 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( in @ X3 @ X4 @ X6 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f128,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( ( entry_box @ Y0 @ Y1 )
& ( number @ Y0 @ one @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f129,plain,
( $true
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( ( entry_box @ Y0 @ Y1 )
& ( number @ Y0 @ one @ Y1 ) ) ) )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f128]) ).
thf(f130,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( entry_box @ sK5 @ Y0 )
& ( number @ sK5 @ one @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f131,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( entry_box @ sK5 @ Y0 )
& ( number @ sK5 @ one @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( entry_box @ sK5 @ X1 )
& ( number @ sK5 @ one @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f133,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( entry_box @ sK5 @ X1 )
& ( number @ sK5 @ one @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X1: mworld] :
( ( $true
= ( number @ sK5 @ one @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( entry_box @ sK5 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f133]) ).
thf(f136,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( userid @ u @ Y1 @ Y2 )
& ( string @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f137,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( userid @ u @ Y1 @ Y2 )
& ( string @ Y1 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( userid @ u @ Y0 @ Y1 )
& ( string @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( userid @ u @ Y0 @ Y1 )
& ( string @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( userid @ u @ Y0 @ Y1 )
& ( string @ Y0 @ Y1 ) ) ) )
@ ( sK6 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( userid @ u @ ( sK6 @ X1 ) @ Y0 )
& ( string @ ( sK6 @ X1 ) @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( userid @ u @ ( sK6 @ X1 ) @ Y0 )
& ( string @ ( sK6 @ X1 ) @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( ( userid @ u @ ( sK6 @ X1 ) @ X2 )
& ( string @ ( sK6 @ X1 ) @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( userid @ u @ ( sK6 @ X1 ) @ X2 )
& ( string @ ( sK6 @ X1 ) @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( string @ ( sK6 @ X1 ) @ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( userid @ u @ ( sK6 @ X1 ) @ X2 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f144]) ).
thf(f168,plain,
( ( $true = $false )
| ( $true
= ( entry_box @ sK5 @ sK0 ) ) ),
inference(constrained_superposition,[],[f78,f135]) ).
thf(f173,plain,
( $true
= ( entry_box @ sK5 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f168]) ).
thf(f190,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( string @ ( sK6 @ mactual ) @ X0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) ),
inference(constrained_superposition,[],[f60,f145]) ).
thf(f193,plain,
! [X0: mworld] :
( ( $true
= ( string @ ( sK6 @ mactual ) @ X0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f190]) ).
thf(f204,plain,
! [X2: $i,X3: $i,X0: mworld,X1: $i] :
( ( $true = $false )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ X2 @ ( sK6 @ X0 ) @ X3 @ X1 ) ) )
| ( $false
= ( number @ X1 @ one @ ( sK2 @ ( sK6 @ X0 ) @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ ( sK2 @ ( sK6 @ X0 ) @ X1 ) ) ) ),
inference(constrained_superposition,[],[f146,f96]) ).
thf(f205,plain,
! [X2: $i,X3: $i,X0: mworld,X1: $i] :
( ( $true
= ( mrel @ sK0 @ ( sK1 @ X2 @ ( sK6 @ X0 ) @ X3 @ X1 ) ) )
| ( $false
= ( number @ X1 @ one @ ( sK2 @ ( sK6 @ X0 ) @ X1 ) ) )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( entry_box @ X1 @ ( sK2 @ ( sK6 @ X0 ) @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f204]) ).
thf(f238,plain,
! [X2: $i,X3: $i,X0: $i,X1: mworld,X4: $i,X5: $i] :
( ( $true = $false )
| ( $false
= ( entry_box @ X3 @ X1 ) )
| ( $false
= ( mrel @ X1 @ ( sK1 @ ( sK4 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( string @ X2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( in @ X2 @ X3 @ ( sK3 @ X4 @ X5 @ ( sK4 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK1 @ ( sK4 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X4 @ X5 ) ) ) ),
inference(constrained_superposition,[],[f127,f102]) ).
thf(f239,plain,
! [X2: $i,X3: $i,X0: $i,X1: mworld,X4: $i,X5: $i] :
( ( $true
= ( in @ X2 @ X3 @ ( sK3 @ X4 @ X5 @ ( sK4 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK1 @ ( sK4 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( mrel @ X1 @ ( sK1 @ ( sK4 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( string @ X2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X3 @ X1 ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X4 @ X5 ) ) ) ),
inference(trivial_inequality_removal,[],[f238]) ).
thf(f273,plain,
! [X2: $i,X0: mworld,X1: $i] :
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ X1 @ ( sK6 @ X0 ) @ X2 @ sK5 ) ) )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( entry_box @ sK5 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) ) ),
inference(constrained_superposition,[],[f134,f205]) ).
thf(f275,plain,
! [X2: $i,X0: mworld,X1: $i] :
( ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ X1 @ ( sK6 @ X0 ) @ X2 @ sK5 ) ) )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( entry_box @ sK5 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[],[f273]) ).
thf(f280,plain,
! [X2: $i,X0: mworld,X1: $i] :
( ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ X1 @ ( sK6 @ X0 ) @ X2 @ sK5 ) ) )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true = $false ) ),
inference(forward_subsumption_demodulation,[],[f275,f135]) ).
thf(f281,plain,
! [X2: $i,X0: mworld,X1: $i] :
( ( $true
= ( mrel @ sK0 @ ( sK1 @ X1 @ ( sK6 @ X0 ) @ X2 @ sK5 ) ) )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f331,plain,
! [X2: $i,X3: $i,X0: $i,X1: mworld,X4: $i,X5: $i] :
( ( $true = $false )
| ( $false
= ( entry_box @ X3 @ X1 ) )
| ( $false
= ( mrel @ X1 @ ( sK1 @ ( sK4 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( string @ X2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( in @ X2 @ X3 @ ( sK3 @ X4 @ X5 @ ( sK4 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK1 @ ( sK4 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( number @ X5 @ one @ ( sK2 @ X4 @ X5 ) ) )
| ( $false
= ( userid @ u @ X4 @ ( sK2 @ X4 @ X5 ) ) )
| ( $false
= ( entry_box @ X5 @ ( sK2 @ X4 @ X5 ) ) ) ),
inference(constrained_superposition,[],[f127,f107]) ).
thf(f332,plain,
! [X2: $i,X3: $i,X0: $i,X1: mworld,X4: $i,X5: $i] :
( ( $true
= ( in @ X2 @ X3 @ ( sK3 @ X4 @ X5 @ ( sK4 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK1 @ ( sK4 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( mrel @ X1 @ ( sK1 @ ( sK4 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( string @ X2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X3 @ X1 ) )
| ( $false
= ( number @ X5 @ one @ ( sK2 @ X4 @ X5 ) ) )
| ( $false
= ( userid @ u @ X4 @ ( sK2 @ X4 @ X5 ) ) )
| ( $false
= ( entry_box @ X5 @ ( sK2 @ X4 @ X5 ) ) ) ),
inference(trivial_inequality_removal,[],[f331]) ).
thf(f557,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( mrel @ X2 @ ( sK1 @ ( sK4 @ X2 @ X0 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( string @ X0 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( entry_box @ X1 @ X2 ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X0 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f101,f239]) ).
thf(f558,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( mrel @ X2 @ ( sK1 @ ( sK4 @ X2 @ X0 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( string @ X0 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( entry_box @ X1 @ X2 ) ) ),
inference(duplicate_literal_removal,[],[f557]) ).
thf(f559,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( mrel @ X2 @ ( sK1 @ ( sK4 @ X2 @ X0 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( string @ X0 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( entry_box @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f558]) ).
thf(f700,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( number @ X1 @ one @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( mrel @ X2 @ ( sK1 @ ( sK4 @ X2 @ X0 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( string @ X0 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( entry_box @ X1 @ X2 ) )
| ( $false
= ( number @ X1 @ one @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ ( sK2 @ X0 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f106,f332]) ).
thf(f703,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( number @ X1 @ one @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( mrel @ X2 @ ( sK1 @ ( sK4 @ X2 @ X0 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( string @ X0 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( entry_box @ X1 @ X2 ) ) ),
inference(duplicate_literal_removal,[],[f700]) ).
thf(f704,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( mrel @ X2 @ ( sK1 @ ( sK4 @ X2 @ X0 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( number @ X1 @ one @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( string @ X0 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( entry_box @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f703]) ).
thf(f1006,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X0 @ X1 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( string @ X0 @ sK0 ) )
| ( $false
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) ) ),
inference(constrained_superposition,[],[f94,f559]) ).
thf(f1011,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( string @ X0 @ sK0 ) )
| ( $false
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f1006]) ).
thf(f1012,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( mrel @ sK0 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( string @ X0 @ sK0 ) )
| ( $false
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f1011]) ).
thf(f1056,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( string @ X0 @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) ) ),
inference(forward_demodulation,[],[f1012,f78]) ).
thf(f1057,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( mrel @ sK0 @ ( sK2 @ X0 @ X1 ) ) )
| ( $false
= ( string @ X0 @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f1056]) ).
thf(f1266,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( userid @ u @ ( sK6 @ X0 ) @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( entry_box @ sK5 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( number @ sK5 @ one @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) )
| ( $false
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( entry_box @ sK5 @ sK0 ) ) ),
inference(constrained_superposition,[],[f281,f704]) ).
thf(f1267,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( userid @ u @ ( sK6 @ X0 ) @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( entry_box @ sK5 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( number @ sK5 @ one @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) )
| ( $false
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( entry_box @ sK5 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f1266]) ).
thf(f1304,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( userid @ u @ ( sK6 @ X0 ) @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( entry_box @ sK5 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( number @ sK5 @ one @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) )
| ( $false
= ( entry_box @ sK5 @ sK0 ) ) ),
inference(forward_demodulation,[],[f1267,f78]) ).
thf(f1305,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( userid @ u @ ( sK6 @ X0 ) @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( entry_box @ sK5 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( number @ sK5 @ one @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) )
| ( $false
= ( entry_box @ sK5 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f1304]) ).
thf(f1328,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( userid @ u @ ( sK6 @ X0 ) @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( entry_box @ sK5 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( number @ sK5 @ one @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) ) ),
inference(forward_demodulation,[],[f1305,f173]) ).
thf(f1329,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( userid @ u @ ( sK6 @ X0 ) @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( entry_box @ sK5 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( number @ sK5 @ one @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f1328]) ).
thf(f1330,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( userid @ u @ ( sK6 @ X0 ) @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( entry_box @ sK5 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $true = $false )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) ) ),
inference(forward_subsumption_demodulation,[],[f1329,f134]) ).
thf(f1331,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( userid @ u @ ( sK6 @ X0 ) @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( entry_box @ sK5 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f1330]) ).
thf(f1332,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( userid @ u @ ( sK6 @ X0 ) @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $true = $false )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) ) ),
inference(forward_subsumption_demodulation,[],[f1331,f135]) ).
thf(f1333,plain,
! [X0: mworld] :
( ( $false
= ( userid @ u @ ( sK6 @ X0 ) @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f1332]) ).
thf(f1371,definition,
( spl7_7
<=> ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f1373,plain,
( ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f1371]) ).
thf(f1375,definition,
( spl7_8
<=> ( $true
= ( mrel @ sK0 @ ( sK2 @ ( sK6 @ mactual ) @ sK5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f1376,plain,
( ( $true
!= ( mrel @ sK0 @ ( sK2 @ ( sK6 @ mactual ) @ sK5 ) ) )
| spl7_8 ),
inference(avatar_component_clause,[],[f1375]) ).
thf(f1377,plain,
( ( $true
= ( mrel @ sK0 @ ( sK2 @ ( sK6 @ mactual ) @ sK5 ) ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f1375]) ).
thf(f1386,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK0 ) )
| ~ spl7_7 ),
inference(constrained_superposition,[],[f193,f1373]) ).
thf(f1387,plain,
( ( $false
= ( mrel @ mactual @ sK0 ) )
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f1386]) ).
thf(f1398,plain,
( ( $true = $false )
| ~ spl7_7 ),
inference(constrained_superposition,[],[f1387,f78]) ).
thf(f1414,plain,
( $false
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f1398]) ).
thf(f1415,plain,
~ spl7_7,
inference(avatar_contradiction_clause,[],[f1414]) ).
thf(f1428,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) ) ),
inference(constrained_superposition,[],[f146,f1333]) ).
thf(f1429,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f1428]) ).
thf(f1430,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f1429]) ).
thf(f1434,plain,
( ! [X0: mworld] :
( ( $true != $true )
| ( $true
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ mactual ) @ sK5 ) ) )
| ( $true
!= ( mrel @ X0 @ sK0 ) ) )
| ~ spl7_8 ),
inference(constrained_superposition,[],[f61,f1377]) ).
thf(f1445,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ X0 @ sK0 ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ ( sK6 @ mactual ) @ sK5 ) ) ) )
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f1434]) ).
thf(f1460,plain,
( ( $true != $true )
| ( $true
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ mactual ) @ sK5 ) ) )
| ~ spl7_8 ),
inference(constrained_superposition,[],[f1445,f78]) ).
thf(f1471,plain,
( ( $true
= ( mrel @ mactual @ ( sK2 @ ( sK6 @ mactual ) @ sK5 ) ) )
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f1460]) ).
thf(f1754,plain,
( ( $true = $false )
| ( $true = $false )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ~ spl7_8 ),
inference(constrained_superposition,[],[f1430,f1471]) ).
thf(f1773,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ~ spl7_8 ),
inference(duplicate_literal_removal,[],[f1754]) ).
thf(f1774,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f1773]) ).
thf(f1782,plain,
( ( $true = $false )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ~ spl7_8 ),
inference(forward_demodulation,[],[f1774,f60]) ).
thf(f1783,plain,
( ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f1782]) ).
thf(f1790,plain,
( spl7_7
| ~ spl7_8 ),
inference(avatar_split_clause,[],[f1783,f1375,f1371]) ).
thf(f1791,plain,
( ( $true != $true )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ( $false
= ( entry_box @ sK5 @ sK0 ) )
| spl7_8 ),
inference(constrained_superposition,[],[f1376,f1057]) ).
thf(f1796,plain,
( ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ( $false
= ( entry_box @ sK5 @ sK0 ) )
| spl7_8 ),
inference(trivial_inequality_removal,[],[f1791]) ).
thf(f1797,plain,
( ( $true = $false )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| spl7_8 ),
inference(forward_demodulation,[],[f1796,f173]) ).
thf(f1798,plain,
( ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| spl7_8 ),
inference(trivial_inequality_removal,[],[f1797]) ).
thf(f1799,plain,
( spl7_7
| spl7_8 ),
inference(avatar_split_clause,[],[f1798,f1375,f1371]) ).
cnf(s118,plain,
~ spl7_7,
inference(sat_conversion,[],[f1415]) ).
cnf(s149,plain,
( spl7_7
| ~ spl7_8 ),
inference(sat_conversion,[],[f1790]) ).
cnf(s161,plain,
( spl7_7
| spl7_8 ),
inference(sat_conversion,[],[f1799]) ).
cnf(s162,plain,
spl7_8,
inference(rat,[],[s161,s118]) ).
cnf(s163,plain,
$false,
inference(rat,[],[s149,s162,s118]) ).
thf(f1800,plain,
$false,
inference(avatar_sat_refutation,[],[s163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NLP266^4 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 11:46:49 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.12 Running first-order model finding
% 0.08/0.12 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.16/0.48 % (4183388)Will run a generic schedule for satisfiability detection.
% 2.16/0.48 % (4183396)% WARNING: option uhcvi not known.
% 2.16/0.48 % (4183398)dis+10_1_sil=32000:sp=arity:random_seed=1230336870:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 2.16/0.48 % (4183396)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=274242117:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 2.16/0.48 % (4183397)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3704743397:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 2.16/0.48 % (4183401)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1371440174:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 2.16/0.48 % (4183395)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2663075055_3000 on theBenchmark for (3000ds/0Mi)
% 2.16/0.48 % (4183400)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1961867689:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 2.16/0.48 % (4183402)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3846724732:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 2.16/0.48 % (4183396)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.16/0.48 % (4183400)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.16/0.48 % (4183396)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.16/0.48 % Exception at run slice level
% 2.16/0.48 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.16/0.48 % (4183415)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1364058218:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.16/0.48 % Exception at run slice level
% 2.16/0.48 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.16/0.48 % (4183424)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2960717551:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.16/0.48 % (4183398)Instruction limit reached!
% 2.16/0.48 % (4183398)------------------------------
% 2.16/0.48 % (4183398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.16/0.48 % (4183398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.16/0.48 % (4183398)CaDiCaL version: 2.1.3
% 2.16/0.48 % (4183398)Termination reason: Instruction limit
% 2.16/0.48 % (4183398)Termination phase: Saturation
% 2.16/0.48 % (4183398)Time elapsed: 0.026 s
% 2.16/0.48 % (4183398)Peak memory usage: 12 MB
% 2.16/0.48 % (4183398)Instructions burned: 104 (million)
% 2.16/0.48 % (4183400)Instruction limit reached!
% 2.16/0.48 % (4183400)------------------------------
% 2.16/0.48 % (4183400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.16/0.48 % (4183400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.16/0.48 % (4183400)CaDiCaL version: 2.1.3
% 2.16/0.48 % (4183400)Termination reason: Instruction limit
% 2.16/0.48 % (4183400)Termination phase: Saturation
% 2.16/0.48 % (4183400)Time elapsed: 0.029 s
% 2.16/0.48 % (4183400)Peak memory usage: 12 MB
% 2.16/0.48 % (4183400)Instructions burned: 116 (million)
% 2.16/0.48 % (4183401)Instruction limit reached!
% 2.16/0.48 % (4183401)------------------------------
% 2.16/0.48 % (4183401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.16/0.48 % (4183401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.16/0.48 % (4183401)CaDiCaL version: 2.1.3
% 2.16/0.48 % (4183401)Termination reason: Instruction limit
% 2.16/0.48 % (4183401)Termination phase: Saturation
% 2.16/0.48 % (4183401)Time elapsed: 0.034 s
% 2.16/0.48 % (4183401)Peak memory usage: 12 MB
% 2.16/0.48 % (4183401)Instructions burned: 134 (million)
% 2.16/0.48 % (4183433)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2102378065:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.16/0.48 % (4183433)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.16/0.48 % (4183433)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.16/0.48 % (4183434)ott-21_1_sil=16000:fs=off:random_seed=1056073249:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.16/0.48 % (4183402)Instruction limit reached!
% 4.51/0.87 % (4183402)------------------------------
% 4.51/0.87 % (4183402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.51/0.87 % (4183402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.51/0.87 % (4183402)CaDiCaL version: 2.1.3
% 4.51/0.87 % (4183402)Termination reason: Instruction limit
% 4.51/0.87 % (4183402)Termination phase: Saturation
% 4.51/0.87 % (4183402)Time elapsed: 0.040 s
% 4.51/0.87 % (4183402)Peak memory usage: 12 MB
% 4.51/0.87 % (4183402)Instructions burned: 160 (million)
% 4.51/0.87 % (4183435)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1011771816:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 4.51/0.87 % (4183442)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2678482133:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 4.51/0.87 % Exception at run slice level
% 4.51/0.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.51/0.87 % (4183424)Instruction limit reached!
% 4.51/0.87 % (4183424)------------------------------
% 4.51/0.87 % (4183424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.51/0.87 % (4183424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.51/0.87 % (4183424)CaDiCaL version: 2.1.3
% 4.51/0.87 % (4183424)Termination reason: Instruction limit
% 4.51/0.87 % (4183424)Termination phase: Saturation
% 4.51/0.87 % (4183424)Time elapsed: 0.034 s
% 4.51/0.87 % (4183424)Peak memory usage: 12 MB
% 4.51/0.87 % (4183424)Instructions burned: 133 (million)
% 4.51/0.87 % (4183447)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=505904133:i=1179_2999 on theBenchmark for (2999ds/1179Mi)
% 4.51/0.87 % (4183451)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2387233657:i=889:ins=1_2999 on theBenchmark for (2999ds/889Mi)
% 4.51/0.87 % Exception at run slice level
% 4.51/0.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.51/0.87 % (4183457)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3853510292:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2999 on theBenchmark for (2999ds/692Mi)
% 4.51/0.87 % (4183457)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.51/0.87 % (4183434)Instruction limit reached!
% 4.51/0.87 % (4183434)------------------------------
% 4.51/0.87 % (4183434)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.51/0.87 % (4183434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.51/0.87 % (4183434)CaDiCaL version: 2.1.3
% 4.51/0.87 % (4183434)Termination reason: Instruction limit
% 4.51/0.87 % (4183434)Termination phase: Saturation
% 4.51/0.87 % (4183434)Time elapsed: 0.044 s
% 4.51/0.87 % (4183434)Peak memory usage: 13 MB
% 4.51/0.87 % (4183434)Instructions burned: 183 (million)
% 4.51/0.87 % (4183465)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4022706522:i=879:kws=inv_precedence:fsr=off_2999 on theBenchmark for (2999ds/879Mi)
% 4.51/0.87 % (4183465)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.51/0.87 % (4183435)Instruction limit reached!
% 4.51/0.87 % (4183435)------------------------------
% 4.51/0.87 % (4183435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.51/0.87 % (4183435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.51/0.87 % (4183435)CaDiCaL version: 2.1.3
% 4.51/0.87 % (4183435)Termination reason: Instruction limit
% 4.51/0.87 % (4183435)Termination phase: Saturation
% 4.51/0.87 % (4183435)Time elapsed: 0.129 s
% 4.51/0.87 % (4183435)Peak memory usage: 13 MB
% 4.51/0.87 % (4183435)Instructions burned: 481 (million)
% 4.51/0.87 % (4183492)fmb+10_1_sil=64000:random_seed=1225531859:i=22061:nm=2:gsp=on_2998 on theBenchmark for (2998ds/22061Mi)
% 4.51/0.87 % (4183492)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.51/0.87 % Exception at run slice level
% 4.51/0.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.51/0.87 % (4183433)Instruction limit reached!
% 4.51/0.87 % (4183433)------------------------------
% 4.51/0.87 % (4183433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.51/0.87 % (4183433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.51/0.87 % (4183433)CaDiCaL version: 2.1.3
% 4.51/0.87 % (4183433)Termination reason: Instruction limit
% 4.51/0.87 % (4183433)Termination phase: Saturation
% 4.51/0.87 % (4183433)Time elapsed: 0.156 s
% 4.51/0.87 % (4183433)Peak memory usage: 14 MB
% 4.51/0.87 % (4183433)Instructions burned: 687 (million)
% 4.51/0.87 % (4183497)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2710704005:i=9515:nm=5_2998 on theBenchmark for (2998ds/9515Mi)
% 4.51/0.87 % Exception at run slice level
% 4.51/0.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.51/0.87 % (4183499)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2894705289:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 4.51/0.87 % Exception at run slice level
% 4.51/0.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.51/0.87 % (4183505)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3943131126:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 4.51/0.87 % (4183505)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.51/0.87 % (4183511)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2348401042:i=1472:ins=7:fdi=8:gsp=on_2997 on theBenchmark for (2997ds/1472Mi)
% 4.51/0.87 % (4183511)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.51/0.87 % (4183511)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.51/0.87 % (4183457)Instruction limit reached!
% 4.51/0.87 % (4183457)------------------------------
% 4.51/0.87 % (4183457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.51/0.87 % (4183457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.51/0.87 % (4183457)CaDiCaL version: 2.1.3
% 4.51/0.87 % (4183457)Termination reason: Instruction limit
% 4.51/0.87 % (4183457)Termination phase: Saturation
% 4.51/0.87 % (4183457)Time elapsed: 0.159 s
% 4.51/0.87 % (4183457)Peak memory usage: 13 MB
% 4.51/0.87 % (4183457)Instructions burned: 692 (million)
% 4.51/0.87 % (4183538)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3255372195:i=6324_2997 on theBenchmark for (2997ds/6324Mi)
% 4.51/0.87 % Exception at run slice level
% 4.51/0.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.51/0.87 % (4183542)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3932051277:fmbsr=2.30978:i=2174_2997 on theBenchmark for (2997ds/2174Mi)
% 4.51/0.87 % Exception at run slice level
% 4.51/0.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.51/0.87 % (4183548)ott-2_1_sil=16000:newcnf=on:random_seed=4084553705:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2997 on theBenchmark for (2997ds/869Mi)
% 4.51/0.87 % (4183548)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.51/0.87 % (4183465)Instruction limit reached!
% 4.51/0.87 % (4183465)------------------------------
% 4.51/0.87 % (4183465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.51/0.87 % (4183465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.51/0.87 % (4183465)CaDiCaL version: 2.1.3
% 4.51/0.87 % (4183465)Termination reason: Instruction limit
% 4.51/0.87 % (4183465)Termination phase: Saturation
% 4.51/0.87 % (4183465)Time elapsed: 0.210 s
% 4.51/0.87 % (4183465)Peak memory usage: 13 MB
% 4.51/0.87 % (4183465)Instructions burned: 883 (million)
% 4.51/0.87 % (4183550)ott+10_1_sil=32000:tgt=ground:random_seed=4022655631:i=5114:av=off_2996 on theBenchmark for (2996ds/5114Mi)
% 4.51/0.87 % (4183447)Instruction limit reached!
% 4.51/0.87 % (4183447)------------------------------
% 4.51/0.87 % (4183447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.51/0.87 % (4183447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.51/0.87 % (4183447)CaDiCaL version: 2.1.3
% 4.51/0.87 % (4183447)Termination reason: Instruction limit
% 4.51/0.87 % (4183447)Termination phase: Saturation
% 4.51/0.87 % (4183447)Time elapsed: 0.270 s
% 4.51/0.87 % (4183447)Peak memory usage: 14 MB
% 4.51/0.87 % (4183447)Instructions burned: 1180 (million)
% 4.51/0.87 % (4183552)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1423193653:i=54282_2996 on theBenchmark for (2996ds/54282Mi)
% 4.51/0.87 % Exception at run slice level
% 4.51/0.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.51/0.87 % (4183554)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3805730723:i=3512:aac=none_2996 on theBenchmark for (2996ds/3512Mi)
% 4.51/0.87 % (4183554)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.51/0.87 % (4183548)Instruction limit reached!
% 4.51/0.87 % (4183548)------------------------------
% 4.51/0.87 % (4183548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.51/0.87 % (4183548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.51/0.87 % (4183548)CaDiCaL version: 2.1.3
% 4.51/0.87 % (4183548)Termination reason: Instruction limit
% 4.51/0.87 % (4183548)Termination phase: Saturation
% 4.51/0.87 % (4183548)Time elapsed: 0.195 s
% 4.51/0.87 % (4183548)Peak memory usage: 13 MB
% 4.51/0.87 % (4183548)Instructions burned: 872 (million)
% 4.51/0.87 % (4183556)dis+21_1_sil=32000:sas=cadical:random_seed=3840119987:i=3773:amm=off_2995 on theBenchmark for (2995ds/3773Mi)
% 4.51/0.87 % (4183511)Instruction limit reached!
% 4.51/0.87 % (4183511)------------------------------
% 4.51/0.87 % (4183511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.51/0.87 % (4183511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.51/0.87 % (4183511)CaDiCaL version: 2.1.3
% 4.51/0.87 % (4183511)Termination reason: Instruction limit
% 4.51/0.87 % (4183511)Termination phase: Saturation
% 4.51/0.87 % (4183511)Time elapsed: 0.409 s
% 4.51/0.87 % (4183511)Peak memory usage: 22 MB
% 4.51/0.87 % (4183511)Instructions burned: 1475 (million)
% 4.51/0.87 % (4183558)ott+11_1_sil=16000:gs=on:random_seed=834334191:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2993 on theBenchmark for (2993ds/2251Mi)
% 4.51/0.87 % (4183558)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.51/0.87 % (4183558) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4183388-4183558"...
% 4.51/0.87 % (4183558)...printing done.
% 4.51/0.87 % (4183558)Refutation found. Thanks to Tanya!
% 4.51/0.87 % SZS status Theorem for theBenchmark
% 4.51/0.87 % SZS output start Proof for theBenchmark
% See solution above
% 4.51/0.87 % (4183558)------------------------------
% 4.51/0.87 % (4183558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.51/0.87 % (4183558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.51/0.87 % (4183558)CaDiCaL version: 2.1.3
% 4.51/0.87 % (4183558)Termination reason: Refutation
% 4.51/0.87 % (4183558)Time elapsed: 0.088 s
% 4.51/0.87 % (4183558)Peak memory usage: 13 MB
% 4.51/0.87 % (4183558)Instructions burned: 342 (million)
% 4.51/0.87 % (4183388)Success in time 0.74 s
% 4.51/0.87 % Vampire exiting
%------------------------------------------------------------------------------