%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL952^12 : 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 : n008.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 08:15:27 AM UTC 2026
% Result : Theorem 0.72s 0.42s
% Output : Refutation 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 10
% Syntax : Number of formulae : 113 ( 63 unt; 0 typ; 3 def)
% Number of atoms : 1224 ( 212 equ; 0 cnn)
% Maximal formula atoms : 11 ( 10 avg)
% Number of connectives : 2303 ( 22 ~; 132 |; 0 &;1760 @)
% ( 3 <=>; 229 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 62 usr; 13 con; 0-4 aty)
% ( 157 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 419 ( 0 sgn 156 !; 0 ?; 419 :)
% 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,
eiw_di: $i > mworld > $o ).
thf(func_def_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_15,type,
in: $i > $i > mworld > $o ).
thf(func_def_16,type,
empty: $i > mworld > $o ).
thf(func_def_17,type,
set_intersection2: $i > $i > $i ).
thf(func_def_18,type,
singleton: $i > $i ).
thf(func_def_19,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_22,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vAND: $o > $o > $o ).
thf(func_def_24,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vOR: $o > $o > $o ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
vIFF: $o > $o > $o ).
thf(func_def_28,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
sK0: mworld > $i ).
thf(func_def_33,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
sK1: $i > mworld > $i > mworld ).
thf(func_def_37,type,
sK2: mworld ).
thf(func_def_39,type,
sK4: mworld ).
thf(func_def_41,type,
sK6: mworld ).
thf(func_def_42,type,
sK7: mworld ).
thf(func_def_44,type,
sK9: mworld > mworld ).
thf(func_def_46,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK11: $i > mworld > $i > mworld ).
thf(func_def_48,type,
sK12: $i > $i > mworld > mworld ).
thf(func_def_49,type,
sK13: $i > $i > mworld > mworld ).
thf(func_def_50,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
sK14: mworld > $i > $i > mworld ).
thf(func_def_52,type,
sK15: $i > mworld > $i > mworld ).
thf(func_def_53,type,
sK16: mworld > $i > $i > mworld ).
thf(func_def_54,type,
sK17: $i > mworld > $i > mworld ).
thf(func_def_55,type,
sK18: mworld > $i > mworld ).
thf(func_def_56,type,
sK19: $i > mworld > $i > mworld ).
thf(func_def_57,type,
sK20: $i > mworld > $i > mworld ).
thf(func_def_58,type,
sK21: $i > mworld > $i > mworld ).
thf(func_def_59,type,
sK22: $i > mworld > $i > mworld ).
thf(func_def_60,type,
sK23: mworld > $i > $i > mworld ).
thf(func_def_61,type,
sK24: $i > mworld > $i > mworld ).
thf(func_def_62,type,
sK25: $i > mworld > $i > mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_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,X1: mworld] : ( mrel @ X0 @ X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
thf(f11,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f27,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ X0 @ ( singleton @ X1 ) ) @ ( singleton @ X1 ) ) ) @ ( mbox @ ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(f28,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ X0 @ ( singleton @ X1 ) ) @ ( singleton @ X1 ) ) ) @ ( mbox @ ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
thf(f29,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ X0 @ ( singleton @ X1 ) ) @ ( singleton @ X1 ) ) ) @ ( mbox @ ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l30_zfmisc_1) ).
thf(f30,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f37,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f38,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f41,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f42,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f45,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
inference(rectify,[],[f9]) ).
thf(f46,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f49,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f50,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f81,plain,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ X0 @ ( singleton @ X1 ) ) @ ( singleton @ X1 ) ) ) @ ( mbox @ ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f28]) ).
thf(f82,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) ) ) @ ( mbox @ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f83,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ X0 @ ( singleton @ X1 ) ) @ ( singleton @ X1 ) ) ) @ ( mbox @ ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f84,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) ) ) @ ( mbox @ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f85,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) ) ) @ ( mbox @ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f82]) ).
thf(f87,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f91,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f93,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f95,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f97,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f113,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) ) ) @ ( mbox @ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f114,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) ) ) @ ( mbox @ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f131,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] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f113,f87,f93,f97,f93,f97,f93,f91,f93,f93]) ).
thf(f132,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] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f114,f87,f93,f97,f93,f97,f93,f91,f93,f93]) ).
thf(f133,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( qmltpeq @ ( set_intersection2 @ Y1 @ ( singleton @ Y3 ) ) @ ( singleton @ Y3 ) @ Y5 ) ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( in @ Y3 @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( qmltpeq @ ( set_intersection2 @ Y1 @ ( singleton @ Y3 ) ) @ ( singleton @ Y3 ) @ Y5 ) ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( in @ Y3 @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y2 ) ) @ ( singleton @ Y2 ) @ Y4 ) ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( in @ Y2 @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y2 ) ) @ ( singleton @ Y2 ) @ Y4 ) ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( in @ Y2 @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y2 ) ) @ ( singleton @ Y2 ) @ Y4 ) ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( in @ Y2 @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( eiw_di @ X2 @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) @ Y3 ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( in @ Y1 @ X2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) @ Y3 ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( in @ Y1 @ X2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) @ Y3 ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( in @ Y1 @ X2 @ Y3 ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( ( mrel @ X1 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X3 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ Y0 ) ) @ ( singleton @ Y0 ) @ Y2 ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( in @ Y0 @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X3 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ Y0 ) ) @ ( singleton @ Y0 ) @ Y2 ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( in @ Y0 @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X3 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ Y0 ) ) @ ( singleton @ Y0 ) @ Y2 ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( in @ Y0 @ X2 @ Y2 ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( ( eiw_di @ X4 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( in @ X4 @ X2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( in @ X4 @ X2 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( in @ X4 @ X2 @ Y1 ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X5 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( in @ X4 @ X2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( in @ X4 @ X2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( in @ X4 @ X2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ Y0 ) )
@ ( sK1 @ X4 @ X5 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( in @ X4 @ X2 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ Y0 ) )
@ ( sK1 @ X4 @ X5 @ X2 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( in @ X4 @ X2 @ Y0 ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( ( mrel @ X5 @ ( sK1 @ X4 @ X5 @ X2 ) )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ ( sK1 @ X4 @ X5 @ X2 ) ) ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( in @ X4 @ X2 @ X6 ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ ( sK1 @ X4 @ X5 @ X2 ) ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( in @ X4 @ X2 @ X6 ) ) ) ),
inference(imp_proxy_clausification,[],[f152]) ).
thf(f156,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ ( sK1 @ X4 @ X5 @ X2 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( in @ X4 @ X2 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f153]) ).
thf(f157,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( qmltpeq @ ( set_intersection2 @ Y1 @ ( singleton @ Y3 ) ) @ ( singleton @ Y3 ) @ Y5 ) ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( in @ Y3 @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f158,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( qmltpeq @ ( set_intersection2 @ Y1 @ ( singleton @ Y3 ) ) @ ( singleton @ Y3 ) @ Y5 ) ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( in @ Y3 @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( $false
= ( ( mrel @ mactual @ sK2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y2 ) ) @ ( singleton @ Y2 ) @ Y4 ) ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( in @ Y2 @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y2 ) ) @ ( singleton @ Y2 ) @ Y4 ) ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( in @ Y2 @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f162,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( qmltpeq @ ( set_intersection2 @ Y0 @ ( singleton @ Y2 ) ) @ ( singleton @ Y2 ) @ Y4 ) ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( in @ Y2 @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( $false
= ( ( eiw_di @ sK3 @ sK2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) @ Y3 ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( in @ Y1 @ sK3 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) @ Y3 ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( in @ Y1 @ sK3 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( $true
= ( eiw_di @ sK3 @ sK2 ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f166,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ Y1 ) ) @ ( singleton @ Y1 ) @ Y3 ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( in @ Y1 @ sK3 @ Y3 ) ) ) ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( $false
= ( ( mrel @ sK2 @ sK4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK4 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK4 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ Y0 ) ) @ ( singleton @ Y0 ) @ Y2 ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( in @ Y0 @ sK3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK4 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK4 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ Y0 ) ) @ ( singleton @ Y0 ) @ Y2 ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( in @ Y0 @ sK3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f167]) ).
thf(f170,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK4 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK4 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ Y0 ) ) @ ( singleton @ Y0 ) @ Y2 ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( in @ Y0 @ sK3 @ Y2 ) ) ) ) ) ) )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f171,plain,
( $false
= ( ( eiw_di @ sK5 @ sK4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ sK5 ) ) @ ( singleton @ sK5 ) @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( in @ sK5 @ sK3 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ sK5 ) ) @ ( singleton @ sK5 ) @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( in @ sK5 @ sK3 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( $true
= ( eiw_di @ sK5 @ sK4 ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ sK5 ) ) @ ( singleton @ sK5 ) @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( in @ sK5 @ sK3 @ Y1 ) ) ) ) )
@ sK6 ) ),
inference(sigma_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( $false
= ( ( mrel @ sK4 @ sK6 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ sK5 ) ) @ ( singleton @ sK5 ) @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
=> ( in @ sK5 @ sK3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ sK5 ) ) @ ( singleton @ sK5 ) @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
=> ( in @ sK5 @ sK3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
=> ( in @ sK5 @ sK3 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f176]) ).
thf(f179,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ sK5 ) ) @ ( singleton @ sK5 ) @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f176]) ).
thf(f180,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ sK5 ) ) @ ( singleton @ sK5 ) @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ sK6 @ X1 )
=> ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ sK5 ) ) @ ( singleton @ sK5 ) @ X1 ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK6 @ X1 ) )
| ( $true
= ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ sK5 ) ) @ ( singleton @ sK5 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
=> ( in @ sK5 @ sK3 @ Y0 ) )
@ sK7 ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f184,plain,
( $false
= ( ( mrel @ sK6 @ sK7 )
=> ( in @ sK5 @ sK3 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
( $false
= ( in @ sK5 @ sK3 @ sK7 ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f558,plain,
! [X1: mworld] :
( ( $true = $false )
| ( $true
= ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ sK5 ) ) @ ( singleton @ sK5 ) @ X1 ) ) ),
inference(forward_demodulation,[],[f182,f95]) ).
thf(f559,plain,
! [X1: mworld] :
( $true
= ( qmltpeq @ ( set_intersection2 @ sK3 @ ( singleton @ sK5 ) ) @ ( singleton @ sK5 ) @ X1 ) ),
inference(trivial_inequality_removal,[],[f558]) ).
thf(f708,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ ( sK1 @ X4 @ X5 @ X2 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( in @ X4 @ X2 @ X6 ) ) ),
inference(forward_demodulation,[],[f156,f95]) ).
thf(f709,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ ( sK1 @ X4 @ X5 @ X2 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( in @ X4 @ X2 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f708]) ).
thf(f710,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ ( sK1 @ X4 @ X5 @ X2 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( in @ X4 @ X2 @ X6 ) ) ),
inference(forward_demodulation,[],[f709,f95]) ).
thf(f711,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ ( sK1 @ X4 @ X5 @ X2 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( in @ X4 @ X2 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f710]) ).
thf(f712,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ ( sK1 @ X4 @ X5 @ X2 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( in @ X4 @ X2 @ X6 ) ) ),
inference(forward_demodulation,[],[f711,f95]) ).
thf(f713,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ ( sK1 @ X4 @ X5 @ X2 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( in @ X4 @ X2 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f712]) ).
thf(f714,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ ( sK1 @ X4 @ X5 @ X2 ) ) )
| ( $true
= ( in @ X4 @ X2 @ X6 ) ) ),
inference(forward_demodulation,[],[f713,f95]) ).
thf(f715,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ ( sK1 @ X4 @ X5 @ X2 ) ) )
| ( $true
= ( in @ X4 @ X2 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f714]) ).
thf(f744,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true = $false )
| ( $false
= ( eiw_di @ sK3 @ X1 ) )
| ( $false
= ( eiw_di @ sK5 @ X2 ) )
| ( $true
= ( in @ sK5 @ sK3 @ X3 ) ) ),
inference(constrained_superposition,[],[f715,f559]) ).
thf(f761,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( eiw_di @ sK3 @ X1 ) )
| ( $false
= ( eiw_di @ sK5 @ X2 ) )
| ( $true
= ( in @ sK5 @ sK3 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f744]) ).
thf(f765,definition,
( spl26_8
<=> ! [X3: mworld] :
( $true
= ( in @ sK5 @ sK3 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl26_8])],[avatar_definition]) ).
thf(f766,plain,
( ! [X3: mworld] :
( $true
= ( in @ sK5 @ sK3 @ X3 ) )
| ~ spl26_8 ),
inference(avatar_component_clause,[],[f765]) ).
thf(f768,definition,
( spl26_9
<=> ! [X2: mworld] :
( $false
= ( eiw_di @ sK5 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl26_9])],[avatar_definition]) ).
thf(f769,plain,
( ! [X2: mworld] :
( $false
= ( eiw_di @ sK5 @ X2 ) )
| ~ spl26_9 ),
inference(avatar_component_clause,[],[f768]) ).
thf(f771,definition,
( spl26_10
<=> ! [X1: mworld] :
( $false
= ( eiw_di @ sK3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl26_10])],[avatar_definition]) ).
thf(f772,plain,
( ! [X1: mworld] :
( $false
= ( eiw_di @ sK3 @ X1 ) )
| ~ spl26_10 ),
inference(avatar_component_clause,[],[f771]) ).
thf(f774,plain,
( spl26_8
| spl26_9
| spl26_10 ),
inference(avatar_split_clause,[],[f761,f771,f768,f765]) ).
thf(f775,plain,
( ( $true = $false )
| ~ spl26_8 ),
inference(constrained_superposition,[],[f766,f185]) ).
thf(f779,plain,
( $false
| ~ spl26_8 ),
inference(trivial_inequality_removal,[],[f775]) ).
thf(f780,plain,
~ spl26_8,
inference(avatar_contradiction_clause,[],[f779]) ).
thf(f781,plain,
( ( $true = $false )
| ~ spl26_9 ),
inference(constrained_superposition,[],[f769,f173]) ).
thf(f787,plain,
( $false
| ~ spl26_9 ),
inference(trivial_inequality_removal,[],[f781]) ).
thf(f788,plain,
~ spl26_9,
inference(avatar_contradiction_clause,[],[f787]) ).
thf(f789,plain,
( ( $true = $false )
| ~ spl26_10 ),
inference(constrained_superposition,[],[f772,f165]) ).
thf(f795,plain,
( $false
| ~ spl26_10 ),
inference(trivial_inequality_removal,[],[f789]) ).
thf(f796,plain,
~ spl26_10,
inference(avatar_contradiction_clause,[],[f795]) ).
cnf(s9,plain,
( spl26_8
| spl26_9
| spl26_10 ),
inference(sat_conversion,[],[f774]) ).
cnf(s11,plain,
~ spl26_8,
inference(sat_conversion,[],[f780]) ).
cnf(s13,plain,
~ spl26_9,
inference(sat_conversion,[],[f788]) ).
cnf(s15,plain,
~ spl26_10,
inference(sat_conversion,[],[f796]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s9,s15,s13,s11]) ).
thf(f797,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL952^12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 % Computer : n008.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 10:51:54 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.28 Running first-order model finding
% 0.24/0.28 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
% 0.72/0.42 % (2992663)Will run a generic schedule for satisfiability detection.
% 0.72/0.42 % (2992669)% WARNING: option uhcvi not known.
% 0.72/0.42 % (2992669)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3001980653:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.72/0.42 % (2992669)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.72/0.42 % (2992669)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.72/0.42 % (2992671)dis+10_1_sil=32000:sp=arity:random_seed=2358985865:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.72/0.42 % (2992672)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1747841129:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.72/0.42 % (2992668)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=524647840_2999 on theBenchmark for (2999ds/0Mi)
% 0.72/0.42 % (2992674)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1050675271:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.72/0.42 % (2992670)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1956944237:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.72/0.42 % (2992673)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=129552544:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.72/0.42 % (2992672)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.72/0.42 % Exception at run slice level
% 0.72/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.72/0.42 % (2992682)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=813973441:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.72/0.42 % Exception at run slice level
% 0.72/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.72/0.42 % (2992671) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2992663-2992671"...
% 0.72/0.42 % (2992684)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1314432841:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.72/0.42 % (2992671)...printing done.
% 0.72/0.42 % (2992672)Instruction limit reached!
% 0.72/0.42 % (2992672)------------------------------
% 0.72/0.42 % (2992672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.42 % (2992672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.42 % (2992672)CaDiCaL version: 2.1.3
% 0.72/0.42 % (2992672)Termination reason: Instruction limit
% 0.72/0.42 % (2992672)Termination phase: Saturation
% 0.72/0.42 % (2992672)Time elapsed: 0.090 s
% 0.72/0.42 % (2992672)Peak memory usage: 12 MB
% 0.72/0.42 % (2992672)Instructions burned: 116 (million)
% 0.72/0.42 % (2992671)Refutation found. Thanks to Tanya!
% 0.72/0.42 % SZS status Theorem for theBenchmark
% 0.72/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.72/0.42 % (2992671)------------------------------
% 0.72/0.42 % (2992671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.42 % (2992671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.42 % (2992671)CaDiCaL version: 2.1.3
% 0.72/0.42 % (2992671)Termination reason: Refutation
% 0.72/0.42 % (2992671)Time elapsed: 0.088 s
% 0.72/0.42 % (2992671)Peak memory usage: 13 MB
% 0.72/0.42 % (2992671)Instructions burned: 108 (million)
% 0.72/0.42 % (2992663)Success in time 0.127 s
% 0.72/0.42 % Vampire exiting
%------------------------------------------------------------------------------