%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT334^21 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:48:48 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 34 unt; 0 typ; 4 def)
% Number of atoms : 494 ( 80 equ; 0 cnn)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 629 ( 30 ~; 46 |; 44 &; 465 @)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 41 usr; 16 con; 0-4 aty)
% ( 9 !!; 17 ??; 0 @@+; 0 @@-)
% Number of variables : 128 ( 0 sgn 16 !; 2 ?; 128 :)
% 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_20,type,
teach: $i > $i > mworld > $o ).
thf(func_def_21,type,
vIFF: $o > $o > $o ).
thf(func_def_22,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vAND: $o > $o > $o ).
thf(func_def_28,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
vOR: $o > $o > $o ).
thf(func_def_33,type,
vNOT: $o > $o ).
thf(func_def_34,type,
sK0: mworld > $i ).
thf(func_def_35,type,
sK1: mworld > mworld ).
thf(func_def_36,type,
sF2: $o ).
thf(func_def_37,type,
sK3: mworld ).
thf(func_def_38,type,
sK4: mworld > $i ).
thf(func_def_39,type,
sK5: mworld > $i ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f13,axiom,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f14,axiom,
( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [X0: $i] : ( teach @ X0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',db) ).
thf(f15,conjecture,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( teach @ X0 @ cs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',query) ).
thf(f16,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( teach @ X0 @ cs ) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f19,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f20,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f23,plain,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( teach @ X0 @ cs ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f24,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f32,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f33,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f42,plain,
( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [X0: $i] : ( teach @ X0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f43,plain,
( ( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f45,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(flattening,[],[f24]) ).
thf(f54,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f57,plain,
( ( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f43]) ).
thf(f58,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f59,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f62,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f64,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f69,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] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(definition_unfolding,[],[f54,f59,f58,f62]) ).
thf(f70,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( teach @ john @ math )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( teach @ mary @ psych )
@ ( teach @ sue @ psych ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f57,f59,f58,f64,f64,f62,f64]) ).
thf(f71,definition,
( sF2
= ( ^ [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] : ( teach @ Y0 @ cs ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f72,plain,
( ( ^ [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] : ( teach @ Y0 @ cs ) ) ) )
= sF2 ),
inference(reorient_equations,[],[f71]) ).
thf(f73,plain,
$true != sF2,
inference(definition_folding,[],[f69,f72]) ).
thf(f75,plain,
( ( $true = sF2 )
| ( $false
= ( ^ [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] : ( teach @ Y0 @ cs ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f72]) ).
thf(f76,plain,
( ( $true = sF2 )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
( ( $true = sF2 )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) ) )
@ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( ( $false
= ( ( mrel @ mactual @ sK3 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK3 )
& ( teach @ Y0 @ cs @ sK3 ) ) ) ) )
| ( $true = sF2 ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
( ( $true = sF2 )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK3 )
& ( teach @ Y0 @ cs @ sK3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f78]) ).
thf(f80,plain,
( ( $true = sF2 )
| ( ( mrel @ mactual @ sK3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f78]) ).
thf(f81,plain,
! [X1: $i] :
( ( $true = sF2 )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK3 )
& ( teach @ Y0 @ cs @ sK3 ) )
@ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f79]) ).
thf(f82,plain,
! [X1: $i] :
( ( $true = sF2 )
| ( $false
= ( ( eiw_di @ X1 @ sK3 )
& ( teach @ X1 @ cs @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X1: $i] :
( ( $false
= ( teach @ X1 @ cs @ sK3 ) )
| ( $true = sF2 )
| ( $false
= ( eiw_di @ X1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f82]) ).
thf(f92,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ john @ math @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) )
& ( teach @ mary @ psych @ Y0 )
& ( teach @ sue @ psych @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f93,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ john @ math @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) )
& ( teach @ mary @ psych @ Y0 )
& ( teach @ sue @ psych @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( teach @ john @ math @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) )
& ( teach @ mary @ psych @ X1 )
& ( teach @ sue @ psych @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( teach @ john @ math @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) )
& ( teach @ mary @ psych @ X1 )
& ( teach @ sue @ psych @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X1: mworld] :
( ( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) )
& ( teach @ mary @ psych @ X1 )
& ( teach @ sue @ psych @ X1 ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f95]) ).
thf(f99,plain,
! [X1: mworld] :
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f96]) ).
thf(f100,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) )
@ ( sK5 @ X1 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( eiw_di @ ( sK5 @ X1 ) @ X1 )
& ( teach @ ( sK5 @ X1 ) @ cs @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f102,plain,
! [X1: mworld] :
( ( $true
= ( teach @ ( sK5 @ X1 ) @ cs @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X1: mworld] :
( ( $true
= ( eiw_di @ ( sK5 @ X1 ) @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f101]) ).
thf(f107,definition,
( spl6_1
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f111,definition,
( spl6_2
<=> ( ( mrel @ mactual @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f113,plain,
( ( ( mrel @ mactual @ sK3 )
= $true )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f111]) ).
thf(f114,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f80,f111,f107]) ).
thf(f116,definition,
( spl6_3
<=> ! [X1: $i] :
( ( $false
= ( teach @ X1 @ cs @ sK3 ) )
| ( $false
= ( eiw_di @ X1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f117,plain,
( ! [X1: $i] :
( ( $false
= ( teach @ X1 @ cs @ sK3 ) )
| ( $false
= ( eiw_di @ X1 @ sK3 ) ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f116]) ).
thf(f118,plain,
( spl6_1
| spl6_3 ),
inference(avatar_split_clause,[],[f83,f116,f107]) ).
thf(f131,plain,
~ spl6_1,
inference(avatar_split_clause,[],[f73,f107]) ).
thf(f147,plain,
( ( ( mrel @ mactual @ sK3 )
= $false )
| ( $false
= ( eiw_di @ ( sK5 @ sK3 ) @ sK3 ) )
| ( $false = $true )
| ~ spl6_3 ),
inference(constrained_superposition,[],[f117,f102]) ).
thf(f148,plain,
( ( ( mrel @ mactual @ sK3 )
= $false )
| ( $false
= ( eiw_di @ ( sK5 @ sK3 ) @ sK3 ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f147]) ).
thf(f150,plain,
( ( $false
= ( eiw_di @ ( sK5 @ sK3 ) @ sK3 ) )
| ( $false = $true )
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[],[f148,f113]) ).
thf(f151,plain,
( ( $false
= ( eiw_di @ ( sK5 @ sK3 ) @ sK3 ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f150]) ).
thf(f154,plain,
( ( ( mrel @ mactual @ sK3 )
= $false )
| ( $false = $true )
| ~ spl6_2
| ~ spl6_3 ),
inference(constrained_superposition,[],[f151,f103]) ).
thf(f163,plain,
( ( ( mrel @ mactual @ sK3 )
= $false )
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f167,plain,
( ( $false = $true )
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[],[f163,f113]) ).
thf(f168,plain,
( $false
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f167]) ).
thf(f169,plain,
( ~ spl6_2
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f168]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f114]) ).
cnf(s2,plain,
( spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f118]) ).
cnf(s5,plain,
~ spl6_1,
inference(sat_conversion,[],[f131]) ).
cnf(s7,plain,
( ~ spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f169]) ).
cnf(s8,plain,
spl6_3,
inference(rat,[],[s2,s5]) ).
cnf(s9,plain,
~ spl6_2,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9,s5]) ).
thf(f170,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT334^21 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n010.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 18:28:48 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.29 % (3245223)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (3245234)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (3245234)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.29 % (3245234)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=3160447211:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.29 % (3245234) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3245223-3245234"...
% 0.22/0.29 % (3245234)...printing done.
% 0.22/0.29 % (3245228)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2783925868:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (3245234)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (3245234)------------------------------
% 0.22/0.29 % (3245234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (3245234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (3245234)CaDiCaL version: 2.1.3
% 0.22/0.29 % (3245234)Termination reason: Refutation
% 0.22/0.29 % (3245234)Time elapsed: 0.004 s
% 0.22/0.29 % (3245234)Peak memory usage: 13 MB
% 0.22/0.29 % (3245234)Instructions burned: 12 (million)
% 0.22/0.29 % (3245223)Success in time 0.038 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------