%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET574^20 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : 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 08:23:16 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 122 ( 48 unt; 0 typ; 9 def)
% Number of atoms : 947 ( 178 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1342 ( 85 ~; 163 |; 48 &; 928 @)
% ( 10 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 43 usr; 17 con; 0-4 aty)
% ( 33 !!; 12 ??; 0 @@+; 0 @@-)
% Number of variables : 257 ( 0 sgn 39 !; 2 ?; 257 :)
% 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,
intersect: $i > $i > mworld > $o ).
thf(func_def_15,type,
member: $i > $i > mworld > $o ).
thf(func_def_18,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_19,type,
vIMP: $o > $o > $o ).
thf(func_def_20,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_24,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
vAND: $o > $o > $o ).
thf(func_def_26,type,
vOR: $o > $o > $o ).
thf(func_def_27,type,
vIFF: $o > $o > $o ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_29,type,
sK0: mworld > $i ).
thf(func_def_30,type,
sF1: $o ).
thf(func_def_31,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
sK2: $i > $i > $i ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
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,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f6,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).
thf(f12,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(f13,axiom,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f14,axiom,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mequiv @ ( intersect @ X0 @ X1 )
@ ( mexists_di
@ ^ [X2: $i] : ( mand @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
thf(f16,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( mand @ ( member @ X0 @ X1 ) @ ( member @ X0 @ X2 ) ) @ ( intersect @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th13) ).
thf(f17,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( mand @ ( member @ X0 @ X1 ) @ ( member @ X0 @ X2 ) ) @ ( intersect @ X1 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f22,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f23,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f26,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f27,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f32,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f5]) ).
thf(f33,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f36,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
inference(rectify,[],[f6]) ).
thf(f37,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f40,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( mand @ ( member @ X0 @ X1 ) @ ( member @ X0 @ X2 ) ) @ ( intersect @ X1 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f41,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) @ ( intersect @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f43,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f45,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mequiv @ ( intersect @ X0 @ X1 )
@ ( mexists_di
@ ^ [X2: $i] : ( mand @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f46,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( intersect @ Y0 @ Y1 )
@ ( mexists_di
@ ^ [Y2: $i] : ( mand @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f49,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) @ ( intersect @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(flattening,[],[f41]) ).
thf(f55,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f56,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f57,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f58,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f62,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( intersect @ Y0 @ Y1 )
@ ( mexists_di
@ ^ [Y2: $i] : ( mand @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f63,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f66,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f69,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) @ ( intersect @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f73,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( intersect @ Y0 @ Y1 )
@ ( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
& ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( member @ Y2 @ Y0 )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f62,f56,f57,f57,f55,f63,f66]) ).
thf(f74,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( 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 ) )
@ ( member @ Y0 @ Y1 )
@ ( member @ Y0 @ Y2 ) )
@ ( intersect @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f69,f56,f57,f57,f57,f58,f66]) ).
thf(f75,definition,
( sF1
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( 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 ) )
@ ( member @ Y0 @ Y1 )
@ ( member @ Y0 @ Y2 ) )
@ ( intersect @ Y1 @ Y2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f76,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( 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 ) )
@ ( member @ Y0 @ Y1 )
@ ( member @ Y0 @ Y2 ) )
@ ( intersect @ Y1 @ Y2 ) ) ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f75]) ).
thf(f77,plain,
$true != sF1,
inference(definition_folding,[],[f74,f76]) ).
thf(f78,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( intersect @ Y0 @ Y1 @ mactual )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
& ( member @ Y2 @ Y0 @ mactual )
& ( member @ Y2 @ Y1 @ mactual ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f79,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( intersect @ Y0 @ Y1 @ mactual )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
& ( member @ Y2 @ Y0 @ mactual )
& ( member @ Y2 @ Y1 @ mactual ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( intersect @ X1 @ Y0 @ mactual )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
& ( member @ Y1 @ X1 @ mactual )
& ( member @ Y1 @ Y0 @ mactual ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( intersect @ X1 @ Y0 @ mactual )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
& ( member @ Y1 @ X1 @ mactual )
& ( member @ Y1 @ Y0 @ mactual ) ) ) ) ) )
= $true )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( intersect @ X1 @ Y0 @ mactual )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
& ( member @ Y1 @ X1 @ mactual )
& ( member @ Y1 @ Y0 @ mactual ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( intersect @ X1 @ X2 @ mactual )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X1 @ mactual )
& ( member @ Y0 @ X2 @ mactual ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( ( ( intersect @ X1 @ X2 @ mactual )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X1 @ mactual )
& ( member @ Y0 @ X2 @ mactual ) ) ) )
= $true )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X1 @ mactual )
& ( member @ Y0 @ X2 @ mactual ) ) )
= ( intersect @ X1 @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f84]) ).
thf(f87,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X1 @ mactual )
& ( member @ Y0 @ X2 @ mactual ) ) ) )
| ( ( intersect @ X1 @ X2 @ mactual )
= $true )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f85]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X1 @ mactual )
& ( member @ Y0 @ X2 @ mactual ) )
@ X3 ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( intersect @ X1 @ X2 @ mactual )
= $true )
| ( $false
= ( eiw_di @ X2 @ mactual ) ) ),
inference(pi_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( ( intersect @ X1 @ X2 @ mactual )
= $true )
| ( $false
= ( ( eiw_di @ X3 @ mactual )
& ( member @ X3 @ X1 @ mactual )
& ( member @ X3 @ X2 @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( member @ X3 @ X1 @ mactual )
& ( member @ X3 @ X2 @ mactual ) ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( ( intersect @ X1 @ X2 @ mactual )
= $true )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X3 @ mactual ) ) ),
inference(and_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( intersect @ X1 @ X2 @ mactual )
= $true )
| ( $false
= ( eiw_di @ X3 @ mactual ) )
| ( $false
= ( member @ X3 @ X2 @ mactual ) )
| ( $false
= ( member @ X3 @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(and_proxy_clausification,[],[f90]) ).
thf(f107,plain,
( ( $false
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( 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 ) )
@ ( member @ Y0 @ Y1 )
@ ( member @ Y0 @ Y2 ) )
@ ( intersect @ Y1 @ Y2 ) ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(iff_proxy_clausification,[],[f76]) ).
thf(f108,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( ( member @ Y0 @ Y1 @ mactual )
& ( member @ Y0 @ Y2 @ mactual ) )
=> ( intersect @ Y1 @ Y2 @ mactual ) ) ) ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
( ( $true = sF1 )
| ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( ( member @ Y0 @ Y1 @ mactual )
& ( member @ Y0 @ Y2 @ mactual ) )
=> ( intersect @ Y1 @ Y2 @ mactual ) ) ) ) ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f108]) ).
thf(f110,plain,
( ( $false
= ( ( eiw_di @ sK3 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( member @ sK3 @ Y0 @ mactual )
& ( member @ sK3 @ Y1 @ mactual ) )
=> ( intersect @ Y0 @ Y1 @ mactual ) ) ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f111,plain,
( ( $true = sF1 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( member @ sK3 @ Y0 @ mactual )
& ( member @ sK3 @ Y1 @ mactual ) )
=> ( intersect @ Y0 @ Y1 @ mactual ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f112,plain,
( ( ( eiw_di @ sK3 @ mactual )
= $true )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f113,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( member @ sK3 @ Y0 @ mactual )
& ( member @ sK3 @ Y1 @ mactual ) )
=> ( intersect @ Y0 @ Y1 @ mactual ) ) ) ) )
@ sK4 ) )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f111]) ).
thf(f114,plain,
( ( $true = sF1 )
| ( $false
= ( ( eiw_di @ sK4 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( member @ sK3 @ sK4 @ mactual )
& ( member @ sK3 @ Y0 @ mactual ) )
=> ( intersect @ sK4 @ Y0 @ mactual ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f115,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( member @ sK3 @ sK4 @ mactual )
& ( member @ sK3 @ Y0 @ mactual ) )
=> ( intersect @ sK4 @ Y0 @ mactual ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f114]) ).
thf(f116,plain,
( ( ( eiw_di @ sK4 @ mactual )
= $true )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f114]) ).
thf(f117,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( member @ sK3 @ sK4 @ mactual )
& ( member @ sK3 @ Y0 @ mactual ) )
=> ( intersect @ sK4 @ Y0 @ mactual ) ) )
@ sK5 ) )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f115]) ).
thf(f118,plain,
( ( $true = sF1 )
| ( $false
= ( ( eiw_di @ sK5 @ mactual )
=> ( ( ( member @ sK3 @ sK4 @ mactual )
& ( member @ sK3 @ sK5 @ mactual ) )
=> ( intersect @ sK4 @ sK5 @ mactual ) ) ) ) ),
inference(beta-eta_normalization,[],[f117]) ).
thf(f119,plain,
( ( $true = sF1 )
| ( $false
= ( ( ( member @ sK3 @ sK4 @ mactual )
& ( member @ sK3 @ sK5 @ mactual ) )
=> ( intersect @ sK4 @ sK5 @ mactual ) ) ) ),
inference(imp_proxy_clausification,[],[f118]) ).
thf(f120,plain,
( ( $true
= ( eiw_di @ sK5 @ mactual ) )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f118]) ).
thf(f121,plain,
( ( $false
= ( intersect @ sK4 @ sK5 @ mactual ) )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f122,plain,
( ( $true
= ( ( member @ sK3 @ sK4 @ mactual )
& ( member @ sK3 @ sK5 @ mactual ) ) )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f123,plain,
( ( $true
= ( member @ sK3 @ sK5 @ mactual ) )
| ( $true = sF1 ) ),
inference(and_proxy_clausification,[],[f122]) ).
thf(f124,plain,
( ( $true
= ( member @ sK3 @ sK4 @ mactual ) )
| ( $true = sF1 ) ),
inference(and_proxy_clausification,[],[f122]) ).
thf(f138,definition,
( spl6_1
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f142,definition,
( spl6_2
<=> ( ( eiw_di @ sK3 @ mactual )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f144,plain,
( ( ( eiw_di @ sK3 @ mactual )
= $true )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f142]) ).
thf(f145,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f112,f142,f138]) ).
thf(f147,definition,
( spl6_3
<=> ( ( eiw_di @ sK4 @ mactual )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f149,plain,
( ( ( eiw_di @ sK4 @ mactual )
= $true )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f147]) ).
thf(f150,plain,
( spl6_3
| spl6_1 ),
inference(avatar_split_clause,[],[f116,f138,f147]) ).
thf(f152,definition,
( spl6_4
<=> ( $true
= ( eiw_di @ sK5 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f154,plain,
( ( $true
= ( eiw_di @ sK5 @ mactual ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f152]) ).
thf(f155,plain,
( spl6_1
| spl6_4 ),
inference(avatar_split_clause,[],[f120,f152,f138]) ).
thf(f157,definition,
( spl6_5
<=> ( $true
= ( member @ sK3 @ sK4 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f159,plain,
( ( $true
= ( member @ sK3 @ sK4 @ mactual ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f157]) ).
thf(f160,plain,
( spl6_1
| spl6_5 ),
inference(avatar_split_clause,[],[f124,f157,f138]) ).
thf(f162,definition,
( spl6_6
<=> ( $true
= ( member @ sK3 @ sK5 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f164,plain,
( ( $true
= ( member @ sK3 @ sK5 @ mactual ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f162]) ).
thf(f165,plain,
( spl6_1
| spl6_6 ),
inference(avatar_split_clause,[],[f123,f162,f138]) ).
thf(f167,definition,
( spl6_7
<=> ( $false
= ( intersect @ sK4 @ sK5 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f169,plain,
( ( $false
= ( intersect @ sK4 @ sK5 @ mactual ) )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f167]) ).
thf(f170,plain,
( spl6_1
| spl6_7 ),
inference(avatar_split_clause,[],[f121,f167,f138]) ).
thf(f172,definition,
( spl6_8
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( eiw_di @ X3 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( member @ X1 @ X3 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( member @ X1 @ X2 @ mactual ) )
| ( $true
= ( intersect @ X2 @ X3 @ mactual ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f173,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( intersect @ X2 @ X3 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X3 @ mactual ) )
| ( $false
= ( member @ X1 @ X3 @ mactual ) )
| ( $false
= ( member @ X1 @ X2 @ mactual ) ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f172]) ).
thf(f179,plain,
~ spl6_1,
inference(avatar_split_clause,[],[f77,f138]) ).
thf(f215,plain,
spl6_8,
inference(avatar_split_clause,[],[f91,f172]) ).
thf(f219,plain,
( ! [X0: $i] :
( ( $false
= ( eiw_di @ X0 @ mactual ) )
| ( $false
= ( eiw_di @ sK5 @ mactual ) )
| ( $false
= ( member @ X0 @ sK5 @ mactual ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ( ( member @ X0 @ sK4 @ mactual )
= $false ) )
| ~ spl6_7
| ~ spl6_8 ),
inference(constrained_superposition,[],[f169,f173]) ).
thf(f221,plain,
( ! [X0: $i] :
( ( $false
= ( eiw_di @ sK5 @ mactual ) )
| ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ( $false
= ( member @ X0 @ sK5 @ mactual ) )
| ( $false
= ( eiw_di @ X0 @ mactual ) )
| ( ( member @ X0 @ sK4 @ mactual )
= $false ) )
| ~ spl6_7
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f219]) ).
thf(f226,plain,
( ! [X0: $i] :
( ( $false
= ( eiw_di @ X0 @ mactual ) )
| ( ( member @ X0 @ sK4 @ mactual )
= $false )
| ( $false
= ( member @ X0 @ sK5 @ mactual ) )
| ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ( $false = $true ) )
| ~ spl6_4
| ~ spl6_7
| ~ spl6_8 ),
inference(forward_demodulation,[],[f221,f154]) ).
thf(f227,plain,
( ! [X0: $i] :
( ( ( member @ X0 @ sK4 @ mactual )
= $false )
| ( $false
= ( eiw_di @ X0 @ mactual ) )
| ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ( $false
= ( member @ X0 @ sK5 @ mactual ) ) )
| ~ spl6_4
| ~ spl6_7
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f226]) ).
thf(f234,plain,
( ! [X0: $i] :
( ( ( member @ X0 @ sK4 @ mactual )
= $false )
| ( $false
= ( eiw_di @ X0 @ mactual ) )
| ( $false
= ( member @ X0 @ sK5 @ mactual ) )
| ( $false = $true ) )
| ~ spl6_3
| ~ spl6_4
| ~ spl6_7
| ~ spl6_8 ),
inference(forward_demodulation,[],[f227,f149]) ).
thf(f235,plain,
( ! [X0: $i] :
( ( $false
= ( member @ X0 @ sK5 @ mactual ) )
| ( ( member @ X0 @ sK4 @ mactual )
= $false )
| ( $false
= ( eiw_di @ X0 @ mactual ) ) )
| ~ spl6_3
| ~ spl6_4
| ~ spl6_7
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f234]) ).
thf(f240,plain,
( ( $false
= ( member @ sK3 @ sK4 @ mactual ) )
| ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ( $false = $true )
| ~ spl6_3
| ~ spl6_4
| ~ spl6_6
| ~ spl6_7
| ~ spl6_8 ),
inference(constrained_superposition,[],[f235,f164]) ).
thf(f249,plain,
( ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ( $false
= ( member @ sK3 @ sK4 @ mactual ) )
| ~ spl6_3
| ~ spl6_4
| ~ spl6_6
| ~ spl6_7
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f240]) ).
thf(f258,plain,
( ( $false
= ( member @ sK3 @ sK4 @ mactual ) )
| ( $false = $true )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_6
| ~ spl6_7
| ~ spl6_8 ),
inference(forward_demodulation,[],[f249,f144]) ).
thf(f259,plain,
( ( $false
= ( member @ sK3 @ sK4 @ mactual ) )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_6
| ~ spl6_7
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f258]) ).
thf(f269,plain,
( ( $false = $true )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6
| ~ spl6_7
| ~ spl6_8 ),
inference(forward_demodulation,[],[f259,f159]) ).
thf(f270,plain,
( $false
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6
| ~ spl6_7
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f271,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6
| ~ spl6_7
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f270]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f145]) ).
cnf(s2,plain,
( spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f150]) ).
cnf(s3,plain,
( spl6_1
| spl6_4 ),
inference(sat_conversion,[],[f155]) ).
cnf(s4,plain,
( spl6_1
| spl6_5 ),
inference(sat_conversion,[],[f160]) ).
cnf(s5,plain,
( spl6_1
| spl6_6 ),
inference(sat_conversion,[],[f165]) ).
cnf(s6,plain,
( spl6_1
| spl6_7 ),
inference(sat_conversion,[],[f170]) ).
cnf(s8,plain,
~ spl6_1,
inference(sat_conversion,[],[f179]) ).
cnf(s10,plain,
spl6_8,
inference(sat_conversion,[],[f215]) ).
cnf(s12,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6
| ~ spl6_7
| ~ spl6_8 ),
inference(sat_conversion,[],[f271]) ).
cnf(s14,plain,
spl6_7,
inference(rat,[],[s6,s8]) ).
cnf(s15,plain,
spl6_6,
inference(rat,[],[s5,s8]) ).
cnf(s16,plain,
spl6_5,
inference(rat,[],[s4,s8]) ).
cnf(s17,plain,
spl6_4,
inference(rat,[],[s3,s8]) ).
cnf(s18,plain,
spl6_3,
inference(rat,[],[s2,s8]) ).
cnf(s19,plain,
~ spl6_2,
inference(rat,[],[s12,s10,s14,s15,s16,s17,s18]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s1,s19,s8]) ).
thf(f272,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET574^20 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n008.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:38:09 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.29 % (3161047)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (3161058)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.29 % (3161058)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.29 % (3161058)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2132887988:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.29 % (3161054)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1015745953:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.29 % (3161052)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3654793518:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.29 % (3161055)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1107457078:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.29 % (3161058) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3161047-3161058"...
% 0.23/0.29 % (3161054)Instruction limit reached!
% 0.23/0.29 % (3161054)------------------------------
% 0.23/0.29 % (3161054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (3161054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (3161054)CaDiCaL version: 2.1.3
% 0.23/0.29 % (3161054)Termination reason: Instruction limit
% 0.23/0.29 % (3161054)Termination phase: Property scanning
% 0.23/0.29 % (3161054)Time elapsed: 0.002 s
% 0.23/0.29 % (3161054)Peak memory usage: 10 MB
% 0.23/0.29 % (3161054)Instructions burned: 4 (million)
% 0.23/0.29 % (3161058)...printing done.
% 0.23/0.29 % (3161058)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.30 % (3161058)------------------------------
% 0.23/0.30 % (3161058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (3161058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (3161058)CaDiCaL version: 2.1.3
% 0.23/0.30 % (3161058)Termination reason: Refutation
% 0.23/0.30 % (3161058)Time elapsed: 0.008 s
% 0.23/0.30 % (3161058)Peak memory usage: 13 MB
% 0.23/0.30 % (3161058)Instructions burned: 24 (million)
% 0.23/0.30 % (3161047)Success in time 0.04 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------