%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU494^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 08:32:11 AM UTC 2026
% Result : Theorem 0.33s 0.41s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 10
% Syntax : Number of formulae : 108 ( 41 unt; 0 typ; 5 def)
% Number of atoms : 693 ( 114 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 867 ( 66 ~; 72 |; 43 &; 559 @)
% ( 5 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 53 usr; 13 con; 0-4 aty)
% ( 67 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 160 ( 0 sgn 44 !; 1 ?; 160 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_2,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_3,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_4,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_5,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_6,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_7,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(func_def_8,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_9,type,
symm: ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(func_def_11,type,
asymm: ( $i > $i > $o ) > $o ).
thf(func_def_12,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_13,type,
trans: ( $i > $i > $o ) > $o ).
thf(func_def_14,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_15,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_17,type,
po: ( $i > $i > $o ) > $o ).
thf(func_def_18,type,
so: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
total: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
term: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
ind: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(func_def_23,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_24,type,
norm: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
confl: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
cr: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_39,type,
vOR: $o > $o > $o ).
thf(func_def_40,type,
vAND: $o > $o > $o ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
sK0: $i > $i > $o ).
thf(f2,axiom,
( inv
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',inverse) ).
thf(f11,axiom,
( asymm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ~ ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',asymmetric) ).
thf(f13,axiom,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',transitive) ).
thf(f18,axiom,
( so
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( asymm @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',strict_order) ).
thf(f30,conjecture,
! [X0: $i > $i > $o] :
( ( so @ X0 )
=> ( so @ ( inv @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_of_strict_order_is_strict_order) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( so @ X0 )
=> ( so @ ( inv @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f34,plain,
( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f50,plain,
( asymm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ~ ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f51,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f54,plain,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f55,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f62,plain,
( so
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( asymm @ X0 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f63,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( asymm @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f86,plain,
~ ! [X0: $i > $i > $o] :
( ( so @ X0 )
=> ( so @ ( inv @ X0 ) ) ),
inference(rectify,[],[f31]) ).
thf(f87,plain,
~ ! [X0: $i > $i > $o] :
( ( ( so @ X0 )
= $true )
=> ( ( so @ ( inv @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( so @ ( inv @ X0 ) )
!= $true )
& ( ( so @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f87]) ).
thf(f89,plain,
( ( $true
!= ( so @ ( inv @ sK0 ) ) )
& ( $true
= ( so @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
thf(f91,plain,
( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f100,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f102,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f107,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( asymm @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f119,plain,
( $true
= ( so @ sK0 ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f120,plain,
( $true
!= ( so @ ( inv @ sK0 ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f129,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ~ ( Y1 @ Y2 @ Y3 ) ) ) )
@ Y0 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f107,f100,f102]) ).
thf(f138,plain,
( $true
!= ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ~ ( Y1 @ Y2 @ Y3 ) ) ) )
@ Y0 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f120,f129,f91]) ).
thf(f139,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ~ ( Y1 @ Y2 @ Y3 ) ) ) )
@ Y0 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
@ Y0 ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f119,f129]) ).
thf(f140,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f140]) ).
thf(f143,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ~ ( sK0 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ~ ( sK0 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK0 @ X2 @ X1 )
=> ~ ( sK0 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f141]) ).
thf(f150,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X2 @ X1 ) ) )
| ( $true
= ( sK0 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $true
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( $true
!= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK0 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f158,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK0 @ Y1 @ Y0 ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ sK1 @ Y0 ) )
=> ( sK0 @ sK1 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK0 @ Y0 @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ sK1 @ Y0 ) )
=> ( sK0 @ sK1 @ Y1 ) ) )
@ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK0 @ Y0 @ sK2 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ sK1 @ Y0 ) )
=> ( sK0 @ sK1 @ Y1 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ~ ( sK0 @ Y0 @ sK2 ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK3 @ Y0 )
& ( sK0 @ sK1 @ sK3 ) )
=> ( sK0 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( ( sK0 @ sK2 @ sK4 )
=> ~ ( sK0 @ sK4 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK3 @ Y0 )
& ( sK0 @ sK1 @ sK3 ) )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ( sK0 @ sK2 @ sK4 )
=> ~ ( sK0 @ sK4 @ sK2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK3 @ Y0 )
& ( sK0 @ sK1 @ sK3 ) )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ~ ( sK0 @ sK4 @ sK2 ) ) ) ),
inference(imp_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK3 @ Y0 )
& ( sK0 @ sK1 @ sK3 ) )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK5 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( ( $false
= ( ( ( sK0 @ sK3 @ sK5 )
& ( sK0 @ sK1 @ sK3 ) )
=> ( sK0 @ sK1 @ sK5 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $true
= ( ( sK0 @ sK3 @ sK5 )
& ( sK0 @ sK1 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f171,plain,
( ( $true
= ( sK0 @ sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $true
= ( sK0 @ sK3 @ sK5 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK3 @ Y0 )
& ( sK0 @ sK1 @ sK3 ) )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK5 ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f174,plain,
( ( $false
= ( ( ( sK0 @ sK3 @ sK5 )
& ( sK0 @ sK1 @ sK3 ) )
=> ( sK0 @ sK1 @ sK5 ) ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $true
= ( ( sK0 @ sK3 @ sK5 )
& ( sK0 @ sK1 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f177,plain,
( ( $true
= ( sK0 @ sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( $true
= ( sK0 @ sK3 @ sK5 ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f176]) ).
thf(f180,definition,
( spl6_1
<=> ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f182,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f180]) ).
thf(f184,definition,
( spl6_2
<=> ( $true
= ( sK0 @ sK3 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f186,plain,
( ( $true
= ( sK0 @ sK3 @ sK5 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f184]) ).
thf(f187,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f172,f184,f180]) ).
thf(f189,definition,
( spl6_3
<=> ( $true
= ( sK0 @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f191,plain,
( ( $true
= ( sK0 @ sK1 @ sK3 ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f189]) ).
thf(f192,plain,
( spl6_1
| spl6_3 ),
inference(avatar_split_clause,[],[f171,f189,f180]) ).
thf(f194,definition,
( spl6_4
<=> ( $false
= ( sK0 @ sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f196,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f194]) ).
thf(f197,plain,
( spl6_1
| spl6_4 ),
inference(avatar_split_clause,[],[f169,f194,f180]) ).
thf(f199,definition,
( spl6_5
<=> ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f201,plain,
( ( $true
= ( sK0 @ sK4 @ sK2 ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f202,plain,
( spl6_5
| spl6_2 ),
inference(avatar_split_clause,[],[f178,f184,f199]) ).
thf(f203,plain,
( spl6_5
| spl6_3 ),
inference(avatar_split_clause,[],[f177,f189,f199]) ).
thf(f204,plain,
( spl6_5
| spl6_4 ),
inference(avatar_split_clause,[],[f175,f194,f199]) ).
thf(f241,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK5 ) )
| ( $false
= ( sK0 @ sK1 @ X0 ) ) )
| ~ spl6_4 ),
inference(constrained_superposition,[],[f196,f156]) ).
thf(f244,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK5 ) )
| ( $false
= ( sK0 @ sK1 @ X0 ) ) )
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f241]) ).
thf(f304,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK1 @ sK3 ) )
| ~ spl6_2
| ~ spl6_4 ),
inference(constrained_superposition,[],[f186,f244]) ).
thf(f307,plain,
( ( $false
= ( sK0 @ sK1 @ sK3 ) )
| ~ spl6_2
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f304]) ).
thf(f315,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(constrained_superposition,[],[f307,f191]) ).
thf(f323,plain,
( $false
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f315]) ).
thf(f324,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(avatar_contradiction_clause,[],[f323]) ).
thf(f443,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK2 @ sK4 ) )
| ~ spl6_5 ),
inference(constrained_superposition,[],[f148,f201]) ).
thf(f460,plain,
( ( $false
= ( sK0 @ sK2 @ sK4 ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f443]) ).
thf(f485,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_5 ),
inference(constrained_superposition,[],[f460,f182]) ).
thf(f495,plain,
( $false
| ~ spl6_1
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f485]) ).
thf(f496,plain,
( ~ spl6_1
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f495]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f187]) ).
cnf(s2,plain,
( spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f192]) ).
cnf(s3,plain,
( spl6_1
| spl6_4 ),
inference(sat_conversion,[],[f197]) ).
cnf(s4,plain,
( spl6_2
| spl6_5 ),
inference(sat_conversion,[],[f202]) ).
cnf(s5,plain,
( spl6_3
| spl6_5 ),
inference(sat_conversion,[],[f203]) ).
cnf(s6,plain,
( spl6_4
| spl6_5 ),
inference(sat_conversion,[],[f204]) ).
cnf(s8,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f324]) ).
cnf(s10,plain,
( ~ spl6_1
| ~ spl6_5 ),
inference(sat_conversion,[],[f496]) ).
cnf(s11,plain,
spl6_1,
inference(rat,[],[s8,s1,s2,s3]) ).
cnf(s12,plain,
~ spl6_5,
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
spl6_4,
inference(rat,[],[s6,s12]) ).
cnf(s14,plain,
spl6_3,
inference(rat,[],[s5,s12]) ).
cnf(s15,plain,
spl6_2,
inference(rat,[],[s4,s12]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s8,s13,s14,s15]) ).
thf(f499,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU494^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.29 % Computer : n018.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8046.5625MB
% 0.12/0.29 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Sep 29 13:48:11 UTC 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.28/0.34 Running first-order model finding
% 0.28/0.34 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
% 0.33/0.41 % (89872)Will run a generic schedule for satisfiability detection.
% 0.33/0.41 % (89880)dis+10_1_sil=32000:sp=arity:random_seed=114857809:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.33/0.41 % (89878)% WARNING: option uhcvi not known.
% 0.33/0.41 % (89877)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=505502167_2999 on theBenchmark for (2999ds/0Mi)
% 0.33/0.41 % (89879)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4208947267:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.33/0.41 % (89878)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3098539836:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.33/0.41 % (89881)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3114827066:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.33/0.41 % (89883)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=661103974:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.33/0.41 % (89882)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=608667777:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.33/0.41 % (89880) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-89872-89880"...
% 0.33/0.41 % (89878)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.33/0.41 % (89881)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.33/0.41 % (89880)...printing done.
% 0.33/0.41 % (89880)Refutation found. Thanks to Tanya!
% 0.33/0.41 % SZS status Theorem for theBenchmark
% 0.33/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.33/0.41 % (89880)------------------------------
% 0.33/0.41 % (89880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.41 % (89880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.41 % (89880)CaDiCaL version: 2.1.3
% 0.33/0.41 % (89880)Termination reason: Refutation
% 0.33/0.41 % (89880)Time elapsed: 0.018 s
% 0.33/0.41 % (89880)Peak memory usage: 13 MB
% 0.33/0.41 % (89880)Instructions burned: 38 (million)
% 0.33/0.41 % (89872)Success in time 0.054 s
% 0.33/0.41 % Vampire exiting
%------------------------------------------------------------------------------