%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU465^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 08:32:08 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 11
% Syntax : Number of formulae : 122 ( 34 unt; 0 typ; 8 def)
% Number of atoms : 934 ( 162 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 983 ( 76 ~; 142 |; 50 &; 601 @)
% ( 8 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 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 : 64 ( 60 usr; 19 con; 0-4 aty)
% ( 54 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 149 ( 0 sgn 56 !; 8 ?; 149 :)
% 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(func_def_47,type,
sK3: $i > $i > $o ).
thf(f1,axiom,
( subrel
= ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',subrel) ).
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/sandbox/benchmark/Axioms/SET009^0.ax',transitive) ).
thf(f30,conjecture,
! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i > $i > $o] :
( ( ( ( ( subrel @ X0 @ X3 )
& ( trans @ X3 ) )
=> ( X3 @ X1 @ X2 ) )
& ( subrel @ X0 @ X3 )
& ( trans @ X3 ) )
=> ( X3 @ X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_is_transitive5) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i > $i > $o] :
( ( ( ( ( subrel @ X0 @ X3 )
& ( trans @ X3 ) )
=> ( X3 @ X1 @ X2 ) )
& ( subrel @ X0 @ X3 )
& ( trans @ X3 ) )
=> ( X3 @ X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f32,plain,
( subrel
= ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f33,plain,
( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
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(f86,plain,
~ ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i > $i > $o] :
( ( ( ( ( subrel @ X0 @ X3 )
& ( trans @ X3 ) )
=> ( X3 @ X1 @ X2 ) )
& ( subrel @ X0 @ X3 )
& ( trans @ X3 ) )
=> ( X3 @ X1 @ X2 ) ),
inference(rectify,[],[f31]) ).
thf(f87,plain,
~ ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i > $i > $o] :
( ( ( ( ( ( subrel @ X0 @ X3 )
= $true )
& ( ( trans @ X3 )
= $true ) )
=> ( ( X3 @ X1 @ X2 )
= $true ) )
& ( ( subrel @ X0 @ X3 )
= $true )
& ( ( trans @ X3 )
= $true ) )
=> ( ( X3 @ X1 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
? [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i > $i > $o] :
( ( ( X3 @ X1 @ X2 )
!= $true )
& ( ( ( X3 @ X1 @ X2 )
= $true )
| ( ( subrel @ X0 @ X3 )
!= $true )
| ( ( trans @ X3 )
!= $true ) )
& ( ( subrel @ X0 @ X3 )
= $true )
& ( ( trans @ X3 )
= $true ) ),
inference(ennf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i > $i > $o] :
( ( ( X3 @ X1 @ X2 )
!= $true )
& ( ( ( X3 @ X1 @ X2 )
= $true )
| ( ( subrel @ X0 @ X3 )
!= $true )
| ( ( trans @ X3 )
!= $true ) )
& ( ( subrel @ X0 @ X3 )
= $true )
& ( ( trans @ X3 )
= $true ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( $true
!= ( sK3 @ sK1 @ sK2 ) )
& ( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $true
!= ( subrel @ sK0 @ sK3 ) )
| ( $true
!= ( trans @ sK3 ) ) )
& ( $true
= ( subrel @ sK0 @ sK3 ) )
& ( $true
= ( trans @ sK3 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f89]) ).
thf(f91,plain,
( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f103,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(f120,plain,
( $true
= ( trans @ sK3 ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f121,plain,
( $true
= ( subrel @ sK0 @ sK3 ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f122,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $true
!= ( subrel @ sK0 @ sK3 ) )
| ( $true
!= ( trans @ sK3 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f123,plain,
( $true
!= ( sK3 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f141,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
@ sK0
@ sK3 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK3 ) ) ),
inference(definition_unfolding,[],[f122,f91,f103]) ).
thf(f142,plain,
( $true
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
@ sK0
@ sK3 ) ),
inference(definition_unfolding,[],[f121,f91]) ).
thf(f143,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK3 ) ),
inference(definition_unfolding,[],[f120,f103]) ).
thf(f144,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK3 @ Y2 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK3 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK3 @ Y2 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK3 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK3 @ Y0 @ X1 ) )
=> ( sK3 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK3 @ Y0 @ X1 ) )
=> ( sK3 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK3 @ Y0 @ X2 )
& ( sK3 @ X2 @ X1 ) )
=> ( sK3 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK3 @ Y0 @ X2 )
& ( sK3 @ X2 @ X1 ) )
=> ( sK3 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK3 @ X3 @ X2 )
& ( sK3 @ X2 @ X1 ) )
=> ( sK3 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK3 @ X3 @ X2 )
& ( sK3 @ X2 @ X1 ) ) )
| ( $true
= ( sK3 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK3 @ X2 @ X1 ) )
| ( $true
= ( sK3 @ X3 @ X1 ) )
| ( $false
= ( sK3 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f154,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK3 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK3 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK0 @ X2 @ X1 )
=> ( sK3 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK3 @ Y2 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK3 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f160,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ Y0 ) ) )
@ sK4 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK3 @ Y2 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK3 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ Y0 ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK3 @ Y2 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK3 @ Y2 @ Y0 ) ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK4 )
=> ( sK3 @ Y0 @ sK4 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK3 @ Y0 @ sK5 ) )
=> ( sK3 @ Y1 @ sK5 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK4 )
=> ( sK3 @ Y0 @ sK4 ) )
@ sK6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK3 @ Y0 @ sK5 ) )
=> ( sK3 @ Y1 @ sK5 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK4 )
=> ( sK3 @ Y0 @ sK4 ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK3 @ Y0 @ sK5 ) )
=> ( sK3 @ Y1 @ sK5 ) ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK6 @ sK4 )
=> ( sK3 @ sK6 @ sK4 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK3 @ Y0 @ sK7 )
& ( sK3 @ sK7 @ sK5 ) )
=> ( sK3 @ Y0 @ sK5 ) ) ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( sK3 @ sK6 @ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK3 @ Y0 @ sK7 )
& ( sK3 @ sK7 @ sK5 ) )
=> ( sK3 @ Y0 @ sK5 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK3 @ Y0 @ sK7 )
& ( sK3 @ sK7 @ sK5 ) )
=> ( sK3 @ Y0 @ sK5 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK3 @ Y0 @ sK7 )
& ( sK3 @ sK7 @ sK5 ) )
=> ( sK3 @ Y0 @ sK5 ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $false
= ( ( ( sK3 @ sK8 @ sK7 )
& ( sK3 @ sK7 @ sK5 ) )
=> ( sK3 @ sK8 @ sK5 ) ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $false
= ( sK3 @ sK8 @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $true
= ( ( sK3 @ sK8 @ sK7 )
& ( sK3 @ sK7 @ sK5 ) ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f172,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $true
= ( sK3 @ sK7 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $true
= ( sK3 @ sK8 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( sK3 @ sK6 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK3 @ Y0 @ sK7 )
& ( sK3 @ sK7 @ sK5 ) )
=> ( sK3 @ Y0 @ sK5 ) )
@ sK9 ) ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f175,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( sK3 @ sK6 @ sK4 ) )
| ( $false
= ( ( ( sK3 @ sK9 @ sK7 )
& ( sK3 @ sK7 @ sK5 ) )
=> ( sK3 @ sK9 @ sK5 ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( sK3 @ sK6 @ sK4 ) )
| ( $false
= ( sK3 @ sK9 @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( sK3 @ sK6 @ sK4 ) )
| ( $true
= ( ( sK3 @ sK9 @ sK7 )
& ( sK3 @ sK7 @ sK5 ) ) ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( sK3 @ sK6 @ sK4 ) )
| ( $true
= ( sK3 @ sK7 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( $true
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( sK3 @ sK6 @ sK4 ) )
| ( $true
= ( sK3 @ sK9 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f177]) ).
thf(f181,definition,
( spl10_1
<=> ( $true
= ( sK3 @ sK8 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
thf(f183,plain,
( ( $true
= ( sK3 @ sK8 @ sK7 ) )
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f181]) ).
thf(f185,definition,
( spl10_2
<=> ( $true
= ( sK0 @ sK6 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f187,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f185]) ).
thf(f189,definition,
( spl10_3
<=> ( $true
= ( sK3 @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f192,plain,
( spl10_1
| spl10_2
| spl10_3 ),
inference(avatar_split_clause,[],[f173,f189,f185,f181]) ).
thf(f194,definition,
( spl10_4
<=> ( $true
= ( sK3 @ sK7 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f196,plain,
( ( $true
= ( sK3 @ sK7 @ sK5 ) )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f194]) ).
thf(f197,plain,
( spl10_4
| spl10_2
| spl10_3 ),
inference(avatar_split_clause,[],[f172,f189,f185,f194]) ).
thf(f199,definition,
( spl10_5
<=> ( $false
= ( sK3 @ sK8 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
thf(f201,plain,
( ( $false
= ( sK3 @ sK8 @ sK5 ) )
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f202,plain,
( spl10_5
| spl10_2
| spl10_3 ),
inference(avatar_split_clause,[],[f170,f189,f185,f199]) ).
thf(f204,definition,
( spl10_6
<=> ( $true
= ( sK3 @ sK9 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
thf(f206,plain,
( ( $true
= ( sK3 @ sK9 @ sK7 ) )
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f204]) ).
thf(f208,definition,
( spl10_7
<=> ( $false
= ( sK3 @ sK6 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f210,plain,
( ( $false
= ( sK3 @ sK6 @ sK4 ) )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f208]) ).
thf(f211,plain,
( spl10_6
| spl10_7
| spl10_3 ),
inference(avatar_split_clause,[],[f179,f189,f208,f204]) ).
thf(f212,plain,
( spl10_4
| spl10_7
| spl10_3 ),
inference(avatar_split_clause,[],[f178,f189,f208,f194]) ).
thf(f214,definition,
( spl10_8
<=> ( $false
= ( sK3 @ sK9 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
thf(f216,plain,
( ( $false
= ( sK3 @ sK9 @ sK5 ) )
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f214]) ).
thf(f217,plain,
( spl10_8
| spl10_7
| spl10_3 ),
inference(avatar_split_clause,[],[f176,f189,f208,f214]) ).
thf(f218,plain,
~ spl10_3,
inference(avatar_split_clause,[],[f123,f189]) ).
thf(f230,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK6 @ sK4 ) )
| ~ spl10_7 ),
inference(constrained_superposition,[],[f158,f210]) ).
thf(f231,plain,
( ( $false
= ( sK0 @ sK6 @ sK4 ) )
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f230]) ).
thf(f233,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_7 ),
inference(constrained_superposition,[],[f231,f187]) ).
thf(f237,plain,
( $false
| ~ spl10_2
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f233]) ).
thf(f238,plain,
( ~ spl10_2
| ~ spl10_7 ),
inference(avatar_contradiction_clause,[],[f237]) ).
thf(f266,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK3 @ X0 @ sK5 ) )
| ( $false
= ( sK3 @ sK9 @ X0 ) ) )
| ~ spl10_8 ),
inference(constrained_superposition,[],[f216,f152]) ).
thf(f280,plain,
( ! [X0: $i] :
( ( $false
= ( sK3 @ X0 @ sK5 ) )
| ( $false
= ( sK3 @ sK9 @ X0 ) ) )
| ~ spl10_8 ),
inference(trivial_inequality_removal,[],[f266]) ).
thf(f327,plain,
( ( $true = $false )
| ( $false
= ( sK3 @ sK7 @ sK5 ) )
| ~ spl10_6
| ~ spl10_8 ),
inference(constrained_superposition,[],[f206,f280]) ).
thf(f328,plain,
( ( $false
= ( sK3 @ sK7 @ sK5 ) )
| ~ spl10_6
| ~ spl10_8 ),
inference(trivial_inequality_removal,[],[f327]) ).
thf(f340,plain,
( ( $true = $false )
| ~ spl10_4
| ~ spl10_6
| ~ spl10_8 ),
inference(constrained_superposition,[],[f328,f196]) ).
thf(f348,plain,
( $false
| ~ spl10_4
| ~ spl10_6
| ~ spl10_8 ),
inference(trivial_inequality_removal,[],[f340]) ).
thf(f349,plain,
( ~ spl10_4
| ~ spl10_6
| ~ spl10_8 ),
inference(avatar_contradiction_clause,[],[f348]) ).
thf(f354,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK3 @ X0 @ sK5 ) )
| ( $false
= ( sK3 @ sK8 @ X0 ) ) )
| ~ spl10_5 ),
inference(constrained_superposition,[],[f152,f201]) ).
thf(f357,plain,
( ! [X0: $i] :
( ( $false
= ( sK3 @ X0 @ sK5 ) )
| ( $false
= ( sK3 @ sK8 @ X0 ) ) )
| ~ spl10_5 ),
inference(trivial_inequality_removal,[],[f354]) ).
thf(f393,plain,
( ( $true = $false )
| ( $false
= ( sK3 @ sK7 @ sK5 ) )
| ~ spl10_1
| ~ spl10_5 ),
inference(constrained_superposition,[],[f183,f357]) ).
thf(f394,plain,
( ( $false
= ( sK3 @ sK7 @ sK5 ) )
| ~ spl10_1
| ~ spl10_5 ),
inference(trivial_inequality_removal,[],[f393]) ).
thf(f407,plain,
( ( $true = $false )
| ~ spl10_1
| ~ spl10_4
| ~ spl10_5 ),
inference(constrained_superposition,[],[f394,f196]) ).
thf(f415,plain,
( $false
| ~ spl10_1
| ~ spl10_4
| ~ spl10_5 ),
inference(trivial_inequality_removal,[],[f407]) ).
thf(f416,plain,
( ~ spl10_1
| ~ spl10_4
| ~ spl10_5 ),
inference(avatar_contradiction_clause,[],[f415]) ).
cnf(s1,plain,
( spl10_1
| spl10_2
| spl10_3 ),
inference(sat_conversion,[],[f192]) ).
cnf(s2,plain,
( spl10_2
| spl10_3
| spl10_4 ),
inference(sat_conversion,[],[f197]) ).
cnf(s3,plain,
( spl10_2
| spl10_3
| spl10_5 ),
inference(sat_conversion,[],[f202]) ).
cnf(s4,plain,
( spl10_3
| spl10_6
| spl10_7 ),
inference(sat_conversion,[],[f211]) ).
cnf(s5,plain,
( spl10_3
| spl10_4
| spl10_7 ),
inference(sat_conversion,[],[f212]) ).
cnf(s6,plain,
( spl10_3
| spl10_7
| spl10_8 ),
inference(sat_conversion,[],[f217]) ).
cnf(s7,plain,
~ spl10_3,
inference(sat_conversion,[],[f218]) ).
cnf(s9,plain,
( ~ spl10_2
| ~ spl10_7 ),
inference(sat_conversion,[],[f238]) ).
cnf(s11,plain,
( ~ spl10_4
| ~ spl10_6
| ~ spl10_8 ),
inference(sat_conversion,[],[f349]) ).
cnf(s13,plain,
( ~ spl10_1
| ~ spl10_4
| ~ spl10_5 ),
inference(sat_conversion,[],[f416]) ).
cnf(s14,plain,
( spl10_7
| spl10_8 ),
inference(rat,[],[s6,s7]) ).
cnf(s15,plain,
( spl10_4
| spl10_7 ),
inference(rat,[],[s5,s7]) ).
cnf(s16,plain,
( spl10_6
| spl10_7 ),
inference(rat,[],[s4,s7]) ).
cnf(s17,plain,
( spl10_2
| spl10_5 ),
inference(rat,[],[s3,s7]) ).
cnf(s18,plain,
( spl10_2
| spl10_4 ),
inference(rat,[],[s2,s7]) ).
cnf(s19,plain,
( spl10_1
| spl10_2 ),
inference(rat,[],[s1,s7]) ).
cnf(s20,plain,
spl10_7,
inference(rat,[],[s11,s16,s15,s14]) ).
cnf(s21,plain,
~ spl10_2,
inference(rat,[],[s9,s20]) ).
cnf(s22,plain,
spl10_5,
inference(rat,[],[s17,s21]) ).
cnf(s23,plain,
spl10_4,
inference(rat,[],[s18,s21]) ).
cnf(s24,plain,
spl10_1,
inference(rat,[],[s19,s21]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s13,s24,s22,s23]) ).
thf(f419,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU465^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n026.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 13:44:43 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.25 % (612290)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (612301)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1061036109:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.25 % (612296)% WARNING: option uhcvi not known.
% 0.09/0.25 % (612295)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=415585119_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.25 % (612296)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=422427021:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.25 % (612299)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3052915703:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.25 % (612297)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2307088749:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.25 % (612298)dis+10_1_sil=32000:sp=arity:random_seed=2734870782:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.25 % (612301) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-612290-612301"...
% 0.09/0.25 % (612300)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3819297105:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.25 % (612296)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (612301)...printing done.
% 0.09/0.25 % (612299)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (612301)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (612301)------------------------------
% 0.09/0.26 % (612301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (612301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (612301)CaDiCaL version: 2.1.3
% 0.09/0.26 % (612301)Termination reason: Refutation
% 0.09/0.26 % (612301)Time elapsed: 0.009 s
% 0.09/0.26 % (612301)Peak memory usage: 13 MB
% 0.09/0.26 % (612301)Instructions burned: 30 (million)
% 0.09/0.26 % (612290)Success in time 0.039 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------