%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO534^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:48:22 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 11
% Syntax : Number of formulae : 94 ( 30 unt; 0 typ; 6 def)
% Number of atoms : 363 ( 101 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 739 ( 91 ~; 83 |; 2 &; 510 @)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 153 ( 153 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 29 usr; 12 con; 0-4 aty)
% ( 0 !!; 40 ??; 0 @@+; 0 @@-)
% Number of variables : 206 ( 0 sgn 83 !; 25 ?; 206 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
epsa: ( $i > $i > $i > $o ) > $i ).
thf(func_def_3,type,
epsb: ( $i > $i > $i > $o ) > $i ).
thf(func_def_4,type,
epsc: ( $i > $i > $i > $o ) > $i ).
thf(func_def_5,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
sK0: $i > $i > $i > $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_20,type,
sK5: ( $i > $i > $i > $o ) > $i ).
thf(func_def_21,type,
sK6: ( $i > $i > $i > $o ) > $i ).
thf(func_def_22,type,
sK7: ( $i > $i > $i > $o ) > $i ).
thf(func_def_23,type,
sK8: ( $i > $i > $i > $o ) > $i ).
thf(func_def_24,type,
sK9: ( $i > $i > $i > $o ) > $i ).
thf(func_def_25,type,
sK10: ( $i > $i > $i > $o ) > $i ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceax) ).
thf(f2,axiom,
( ( ^ [X0: $i > $i > $i > $o] :
( eps
@ ^ [X1: $i] :
? [X2: $i,X3: $i] : ( X0 @ X1 @ X2 @ X3 ) ) )
= epsa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',epsad) ).
thf(f3,axiom,
( ( ^ [X0: $i > $i > $i > $o] :
( eps
@ ^ [X1: $i] :
? [X2: $i] : ( X0 @ ( epsa @ X0 ) @ X1 @ X2 ) ) )
= epsb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',epsbd) ).
thf(f4,axiom,
( epsc
= ( ^ [X0: $i > $i > $i > $o] :
( eps
@ ^ [X1: $i] : ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',epscd) ).
thf(f5,conjecture,
! [X0: $i > $i > $i > $o] :
( ? [X1: $i,X3: $i,X2: $i] : ( X0 @ X1 @ X2 @ X3 )
=> ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) @ ( epsc @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f6,negated_conjecture,
~ ! [X0: $i > $i > $i > $o] :
( ? [X1: $i,X3: $i,X2: $i] : ( X0 @ X1 @ X2 @ X3 )
=> ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) @ ( epsc @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( ( ^ [X0: $i > $i > $i > $o] :
( eps
@ ^ [X1: $i] :
? [X2: $i,X3: $i] : ( X0 @ X1 @ X2 @ X3 ) ) )
= epsa ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( epsa
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: $i > $i > $i > $o] :
( ? [X1: $i,X2: $i,X3: $i] : ( X0 @ X1 @ X3 @ X2 )
=> ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) @ ( epsc @ X0 ) ) ),
inference(rectify,[],[f6]) ).
thf(f10,plain,
~ ! [X0: $i > $i > $i > $o] :
( ? [X1: $i,X2: $i,X3: $i] :
( ( X0 @ X1 @ X3 @ X2 )
= $true )
=> ( ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) @ ( epsc @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
inference(rectify,[],[f1]) ).
thf(f12,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ( ^ [X0: $i > $i > $i > $o] :
( eps
@ ^ [X1: $i] :
? [X2: $i] : ( X0 @ ( epsa @ X0 ) @ X1 @ X2 ) ) )
= epsb ),
inference(rectify,[],[f3]) ).
thf(f14,plain,
( epsb
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ ( epsa @ Y0 ) @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( epsc
= ( ^ [X0: $i > $i > $i > $o] :
( eps
@ ^ [X1: $i] : ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) @ X1 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( epsc
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] : ( Y0 @ ( epsa @ Y0 ) @ ( epsb @ Y0 ) @ Y1 ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
? [X0: $i > $i > $i > $o] :
( ( ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) @ ( epsc @ X0 ) )
!= $true )
& ? [X1: $i,X2: $i,X3: $i] :
( ( X0 @ X1 @ X3 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f18,plain,
! [X0: $i > $o] :
( ( ( X0 @ ( eps @ X0 ) )
= $true )
| ! [X1: $i] :
( ( X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f19,plain,
( ( ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) @ ( epsc @ sK0 ) )
!= $true )
& ( ( sK0 @ sK1 @ sK3 @ sK2 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f17]) ).
thf(f20,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( eps @ X0 ) )
= $true )
| ( ( X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f21,plain,
( epsb
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ ( epsa @ Y0 ) @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f22,plain,
( ( sK0 @ sK1 @ sK3 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f19]) ).
thf(f23,plain,
( ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) @ ( epsc @ sK0 ) )
!= $true ),
inference(cnf_transformation,[],[f19]) ).
thf(f24,plain,
( epsa
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f25,plain,
( epsc
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] : ( Y0 @ ( epsa @ Y0 ) @ ( epsb @ Y0 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,plain,
( epsb
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] : ( ?? @ $i @ ( Y0 @ ( epsa @ Y0 ) @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f28,plain,
( epsc
= ( ^ [Y0: $i > $i > $i > $o] : ( eps @ ( Y0 @ ( epsa @ Y0 ) @ ( epsb @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f30,definition,
( spl4_1
<=> ( epsa
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f32,plain,
( ( epsa
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,plain,
spl4_1,
inference(avatar_split_clause,[],[f24,f30]) ).
thf(f35,definition,
( spl4_2
<=> ( ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) @ ( epsc @ sK0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f37,plain,
( ( ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) @ ( epsc @ sK0 ) )
!= $true )
| spl4_2 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f38,plain,
~ spl4_2,
inference(avatar_split_clause,[],[f23,f35]) ).
thf(f40,definition,
( spl4_3
<=> ( ( sK0 @ sK1 @ sK3 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f42,plain,
( ( ( sK0 @ sK1 @ sK3 @ sK2 )
= $true )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
spl4_3,
inference(avatar_split_clause,[],[f22,f40]) ).
thf(f45,definition,
( spl4_4
<=> ( epsb
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] : ( ?? @ $i @ ( Y0 @ ( epsa @ Y0 ) @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f47,plain,
( ( epsb
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] : ( ?? @ $i @ ( Y0 @ ( epsa @ Y0 ) @ Y1 ) ) ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f48,plain,
spl4_4,
inference(avatar_split_clause,[],[f27,f45]) ).
thf(f50,definition,
( spl4_5
<=> ( epsc
= ( ^ [Y0: $i > $i > $i > $o] : ( eps @ ( Y0 @ ( epsa @ Y0 ) @ ( epsb @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f52,plain,
( ( epsc
= ( ^ [Y0: $i > $i > $i > $o] : ( eps @ ( Y0 @ ( epsa @ Y0 ) @ ( epsb @ Y0 ) ) ) ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f53,plain,
spl4_5,
inference(avatar_split_clause,[],[f28,f50]) ).
thf(f57,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
~ ( X2 @ Y0 )
@ X1 )
!= $true )
| ( ( ^ [Y0: $i] :
~ ( X2 @ Y0 )
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) )
= $true ) ),
inference(primitive_instantiation,[],[f20]) ).
thf(f60,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) )
= $true )
| ( ( ~ ( X2 @ X1 ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f61,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) )
| ( ( ~ ( X2 @ X1 ) )
!= $true ) ),
inference(not_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) )
| ( ( X2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f61]) ).
thf(f69,plain,
! [X3: $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
~ ( X3 @ Y0 )
@ ( eps
@ ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
~ ( X3 @ Y1 )
@ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
~ ( X3 @ Y0 )
@ X1 )
= $true ) ),
inference(primitive_instantiation,[],[f62]) ).
thf(f75,plain,
! [X3: $i > $o,X1: $i] :
( ( ( ~ ( X3 @ X1 ) )
= $true )
| ( ( ~ ( X3
@ ( eps
@ ^ [Y0: $i] :
~ ~ ( X3 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f76,plain,
! [X3: $i > $o,X1: $i] :
( ( ( X3 @ X1 )
= $false )
| ( ( ~ ( X3
@ ( eps
@ ^ [Y0: $i] :
~ ~ ( X3 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X3: $i > $o,X1: $i] :
( ( ( X3
@ ( eps
@ ^ [Y0: $i] :
~ ~ ( X3 @ Y0 ) ) )
= $true )
| ( ( X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X3: $i > $o,X1: $i] :
( ( ( X3 @ X1 )
= $false )
| ( ( X3
@ ( eps
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true ) ),
inference(boolean_simplification,[],[f77]) ).
thf(f79,plain,
! [X3: $i > $o,X1: $i] :
( ( ( X3 @ ( eps @ X3 ) )
= $true )
| ( ( X3 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
( ! [X1: $i > $i > $i > $o] :
( ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] : ( ?? @ $i @ ( Y0 @ ( epsa @ Y0 ) @ Y1 ) ) )
@ X1 )
= ( epsb @ X1 ) )
| ~ spl4_4 ),
inference(argument_congruence,[],[f47]) ).
thf(f81,plain,
( ! [X1: $i > $i > $i > $o] :
( ( epsb @ X1 )
= ( eps
@ ^ [Y0: $i] : ( ?? @ $i @ ( X1 @ ( epsa @ X1 ) @ Y0 ) ) ) )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f80]) ).
thf(f82,plain,
( ! [X1: $i > $i > $i > $o] :
( ( epsa @ X1 )
= ( ^ [Y0: $i > $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl4_1 ),
inference(argument_congruence,[],[f32]) ).
thf(f83,plain,
( ! [X1: $i > $i > $i > $o] :
( ( eps
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( X1 @ Y0 @ Y2 @ Y1 ) ) ) )
= ( epsa @ X1 ) )
| ~ spl4_1 ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
( ! [X1: $i > $i > $i > $o] :
( ( ^ [Y0: $i > $i > $i > $o] : ( eps @ ( Y0 @ ( epsa @ Y0 ) @ ( epsb @ Y0 ) ) )
@ X1 )
= ( epsc @ X1 ) )
| ~ spl4_5 ),
inference(argument_congruence,[],[f52]) ).
thf(f85,plain,
( ! [X1: $i > $i > $i > $o] :
( ( eps @ ( X1 @ ( epsa @ X1 ) @ ( epsb @ X1 ) ) )
= ( epsc @ X1 ) )
| ~ spl4_5 ),
inference(beta-eta_normalization,[],[f84]) ).
thf(f86,plain,
( ( $true
!= ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) @ ( eps @ ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) ) ) ) )
| spl4_2
| ~ spl4_5 ),
inference(superposition,[],[f37,f85]) ).
thf(f88,definition,
( spl4_6
<=> ( $true
= ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) @ ( eps @ ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f90,plain,
( ( $true
!= ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) @ ( eps @ ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) ) ) ) )
| spl4_6 ),
inference(avatar_component_clause,[],[f88]) ).
thf(f91,plain,
( ~ spl4_6
| spl4_2
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f86,f50,f35,f88]) ).
thf(f93,plain,
( ! [X0: $i > $i > $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( ?? @ $i @ ( X0 @ ( epsa @ X0 ) @ Y0 ) )
@ ( epsb @ X0 ) ) )
| ( ( ^ [Y0: $i] : ( ?? @ $i @ ( X0 @ ( epsa @ X0 ) @ Y0 ) )
@ X1 )
!= $true ) )
| ~ spl4_4 ),
inference(superposition,[],[f20,f81]) ).
thf(f94,plain,
( ! [X0: $i > $i > $i > $o,X1: $i] :
( ( ( ?? @ $i @ ( X0 @ ( epsa @ X0 ) @ X1 ) )
!= $true )
| ( ( ?? @ $i @ ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) ) )
= $true ) )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
( ! [X2: $i,X0: $i > $i > $i > $o,X1: $i] :
( ( ( ?? @ $i @ ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) ) )
= $true )
| ( ( X0 @ ( epsa @ X0 ) @ X1 @ X2 )
= $false ) )
| ~ spl4_4 ),
inference(pi_proxy_clausification,[],[f94]) ).
thf(f96,plain,
( ! [X2: $i,X0: $i > $i > $i > $o,X1: $i] :
( ( $true
= ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) @ ( sK5 @ X0 ) ) )
| ( ( X0 @ ( epsa @ X0 ) @ X1 @ X2 )
= $false ) )
| ~ spl4_4 ),
inference(sigma_proxy_clausification,[],[f95]) ).
thf(f103,plain,
( ! [X0: $i > $i > $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( X0 @ Y0 @ Y2 @ Y1 ) ) )
@ ( epsa @ X0 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( X0 @ Y0 @ Y2 @ Y1 ) ) )
@ X1 )
!= $true ) )
| ~ spl4_1 ),
inference(superposition,[],[f20,f83]) ).
thf(f104,plain,
( ! [X0: $i > $i > $i > $o,X1: $i] :
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( X0 @ ( epsa @ X0 ) @ Y1 @ Y0 ) ) ) )
| ( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( X0 @ X1 @ Y1 @ Y0 ) ) ) ) )
| ~ spl4_1 ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f105,plain,
( ! [X0: $i > $i > $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( X0 @ ( epsa @ X0 ) @ Y1 @ Y0 ) )
@ ( sK6 @ X0 ) )
= $true )
| ( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( X0 @ X1 @ Y1 @ Y0 ) ) ) ) )
| ~ spl4_1 ),
inference(sigma_proxy_clausification,[],[f104]) ).
thf(f106,plain,
( ! [X2: $i,X0: $i > $i > $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( X0 @ X1 @ Y1 @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( X0 @ ( epsa @ X0 ) @ Y1 @ Y0 ) )
@ ( sK6 @ X0 ) )
= $true ) )
| ~ spl4_1 ),
inference(pi_proxy_clausification,[],[f105]) ).
thf(f107,plain,
( ! [X2: $i,X0: $i > $i > $i > $o,X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] : ( X0 @ X1 @ Y0 @ X2 ) )
= $false )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] : ( X0 @ ( epsa @ X0 ) @ Y0 @ ( sK6 @ X0 ) ) ) ) )
| ~ spl4_1 ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f108,plain,
( ! [X2: $i,X3: $i,X0: $i > $i > $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] : ( X0 @ X1 @ Y0 @ X2 )
@ X3 )
= $false )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] : ( X0 @ ( epsa @ X0 ) @ Y0 @ ( sK6 @ X0 ) ) ) ) )
| ~ spl4_1 ),
inference(pi_proxy_clausification,[],[f107]) ).
thf(f109,plain,
( ! [X2: $i,X3: $i,X0: $i > $i > $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] : ( X0 @ ( epsa @ X0 ) @ Y0 @ ( sK6 @ X0 ) )
@ ( sK7 @ X0 ) )
= $true )
| ( ( ^ [Y0: $i] : ( X0 @ X1 @ Y0 @ X2 )
@ X3 )
= $false ) )
| ~ spl4_1 ),
inference(sigma_proxy_clausification,[],[f108]) ).
thf(f110,plain,
( ! [X2: $i,X3: $i,X0: $i > $i > $i > $o,X1: $i] :
( ( $true
= ( X0 @ ( epsa @ X0 ) @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) ) )
| ( $false
= ( X0 @ X1 @ X3 @ X2 ) ) )
| ~ spl4_1 ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f145,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) @ X0 ) )
| ( $true != $true ) )
| spl4_6 ),
inference(superposition,[],[f90,f79]) ).
thf(f148,plain,
( ! [X0: $i] :
( $false
= ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) @ X0 ) )
| spl4_6 ),
inference(trivial_inequality_removal,[],[f145]) ).
thf(f254,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK0 @ ( epsa @ sK0 ) @ X0 @ X1 )
= $false )
| ( $false = $true ) )
| ~ spl4_4
| spl4_6 ),
inference(superposition,[],[f96,f148]) ).
thf(f257,plain,
( ! [X0: $i,X1: $i] :
( ( sK0 @ ( epsa @ sK0 ) @ X0 @ X1 )
= $false )
| ~ spl4_4
| spl4_6 ),
inference(trivial_inequality_removal,[],[f254]) ).
thf(f340,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ X1 @ X2 )
= $false )
| ( $false = $true ) )
| ~ spl4_1
| ~ spl4_4
| spl4_6 ),
inference(superposition,[],[f110,f257]) ).
thf(f348,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( sK0 @ X0 @ X1 @ X2 )
= $false )
| ~ spl4_1
| ~ spl4_4
| spl4_6 ),
inference(trivial_inequality_removal,[],[f340]) ).
thf(f359,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_4
| spl4_6 ),
inference(superposition,[],[f348,f42]) ).
thf(f375,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_4
| spl4_6 ),
inference(trivial_inequality_removal,[],[f359]) ).
thf(f376,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_4
| spl4_6 ),
inference(avatar_contradiction_clause,[],[f375]) ).
cnf(s1,plain,
spl4_1,
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f38]) ).
cnf(s3,plain,
spl4_3,
inference(sat_conversion,[],[f43]) ).
cnf(s4,plain,
spl4_4,
inference(sat_conversion,[],[f48]) ).
cnf(s5,plain,
spl4_5,
inference(sat_conversion,[],[f53]) ).
cnf(s6,plain,
( spl4_2
| ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f91]) ).
cnf(s23,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f376]) ).
cnf(s29,plain,
~ spl4_6,
inference(rat,[],[s6,s5,s2]) ).
cnf(s31,plain,
~ spl4_1,
inference(rat,[],[s23,s3,s4,s29]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s1,s31]) ).
thf(f385,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO534^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n014.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 17:13:15 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.29 % (2946079)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (2946086)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3471718545:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (2946086)Refutation not found, incomplete strategy
% 0.20/0.29 % (2946086)------------------------------
% 0.20/0.29 % (2946086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2946086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2946086)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2946086)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (2946086)Time elapsed: 0.001 s
% 0.20/0.29 % (2946086)Peak memory usage: 12 MB
% 0.20/0.29 % (2946086)Instructions burned: 3 (million)
% 0.20/0.29 % (2946086)------------------------------
% 0.20/0.29 % (2946086)------------------------------
% 0.20/0.29 % (2946085)lrs+10_16_si=on:nwc=1.5:random_seed=3136754540:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (2946087)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=984455257:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.29 % (2946084)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2705515602:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (2946092)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1587024494:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.29 % (2946084)Refutation not found, incomplete strategy
% 0.20/0.29 % (2946084)------------------------------
% 0.20/0.29 % (2946084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2946084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2946084)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2946084)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (2946084)Time elapsed: 0.005 s
% 0.20/0.29 % (2946084)Peak memory usage: 12 MB
% 0.20/0.29 % (2946084)Instructions burned: 7 (million)
% 0.20/0.29 % (2946092)Instruction limit reached!
% 0.20/0.29 % (2946092)------------------------------
% 0.20/0.29 % (2946092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2946092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2946092)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2946092)Termination reason: Instruction limit
% 0.20/0.29 % (2946092)Termination phase: Saturation
% 0.20/0.29 % (2946092)Time elapsed: 0.001 s
% 0.20/0.29 % (2946092)Peak memory usage: 12 MB
% 0.20/0.29 % (2946092)Instructions burned: 2 (million)
% 0.20/0.29 % (2946084)------------------------------
% 0.20/0.29 % (2946084)------------------------------
% 0.20/0.29 % (2946088)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=201213405:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (2946090)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (2946090)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.29 % (2946085)Instruction limit reached!
% 0.20/0.29 % (2946085)------------------------------
% 0.20/0.29 % (2946085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2946085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2946085)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2946085)Termination reason: Instruction limit
% 0.20/0.29 % (2946085)Termination phase: Saturation
% 0.20/0.29 % (2946085)Time elapsed: 0.012 s
% 0.20/0.29 % (2946085)Peak memory usage: 12 MB
% 0.20/0.29 % (2946085)Instructions burned: 20 (million)
% 0.20/0.29 % (2946087) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2946079-2946087"...
% 0.20/0.29 % (2946087)...printing done.
% 0.20/0.29 % (2946087)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (2946087)------------------------------
% 0.20/0.29 % (2946087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2946087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2946087)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2946087)Termination reason: Refutation
% 0.20/0.29 % (2946087)Time elapsed: 0.014 s
% 0.20/0.29 % (2946087)Peak memory usage: 13 MB
% 0.20/0.29 % (2946087)Instructions burned: 22 (million)
% 0.20/0.29 % (2946079)Success in time 0.053 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------