%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU483^1 : TPTP v9.3.1. Bugfixed v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:29:46 AM UTC 2026
% Result : Theorem 1.02s 0.56s
% Output : Refutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 3
% Syntax : Number of formulae : 50 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 299 ( 46 equ; 0 cnn)
% Maximal formula atoms : 2 ( 5 avg)
% Number of connectives : 709 ( 42 ~; 0 |; 19 &; 457 @)
% ( 0 <=>; 77 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 45 usr; 6 con; 0-4 aty)
% ( 53 !!; 61 ??; 0 @@+; 0 @@-)
% Number of variables : 158 ( 125 ^; 23 !; 10 ?; 158 :)
% 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,
vAND: $o > $o > $o ).
thf(func_def_33,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_39,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vOR: $o > $o > $o ).
thf(func_def_41,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_44,type,
sK0: $i > $i > $o ).
thf(f9,axiom,
( symm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',symmetric) ).
thf(f20,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( X0 @ X2 @ X3 ) )
& ( X1 @ X2 ) ) ) )
= term ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',terminating) ).
thf(f30,conjecture,
! [X0: $i > $i > $o] :
( ? [X1: $i,X2: $i] : ( X0 @ X1 @ X2 )
=> ( ( symm @ X0 )
=> ~ ( term @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_implies_non_terminating) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ? [X1: $i,X2: $i] : ( X0 @ X1 @ X2 )
=> ( ( symm @ X0 )
=> ~ ( term @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f36,plain,
( symm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f37,plain,
( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ? [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X4 )
=> ~ ( X0 @ X3 @ X4 ) )
& ( X1 @ X3 ) ) ) )
= term ),
inference(rectify,[],[f20]) ).
thf(f39,plain,
( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f74,plain,
~ ! [X0: $i > $i > $o] :
( ? [X1: $i,X2: $i] : ( X0 @ X1 @ X2 )
=> ( ( symm @ X0 )
=> ~ ( term @ X0 ) ) ),
inference(rectify,[],[f31]) ).
thf(f75,plain,
( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( ( symm @ Y0 )
=> ~ ( term @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f74]) ).
thf(f104,plain,
( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f105,plain,
( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f107,plain,
( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( ( symm @ Y0 )
=> ~ ( term @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f75]) ).
thf(f135,plain,
( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
@ Y0 )
=> ~ ( ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ?? @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
=> ~ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) )
@ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f107,f105,f104]) ).
thf(f136,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
=> ~ ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f137,plain,
( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
=> ~ ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f136]) ).
thf(f138,plain,
( $false
= ( ^ [Y0: $i > $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
=> ~ ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f141,plain,
( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
=> ~ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f142,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
=> ~ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f148,plain,
( $false
= ( ~ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f149,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f150,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
=> ( sK0 @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f163,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f164,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i > $o] :
( $true
= ( ( ?? @ $i @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f167,plain,
( $true
= ( $true
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( sK0 @ Y2 @ Y1 ) )
@ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] : ( sK0 @ Y3 @ Y2 ) )
@ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(constrained_superposition,[],[f165,f143]) ).
thf(f171,plain,
( $true
= ( $true
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( sK0 @ Y2 @ Y1 ) )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f172,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( sK0 @ Y2 @ Y1 ) )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(boolean_simplification,[],[f171]) ).
thf(f240,plain,
( ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( sK0 @ Y2 @ Y1 ) )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK4 )
= $true ),
inference(sigma_proxy_clausification,[],[f172]) ).
thf(f242,plain,
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ sK4 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) )
=> ~ ( sK0 @ sK4 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f240]) ).
thf(f245,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) )
=> ~ ( sK0 @ sK4 @ Y0 ) ) )
= $true ),
inference(and_proxy_clausification,[],[f242]) ).
thf(f246,plain,
( ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ sK4 ) )
= $true ),
inference(and_proxy_clausification,[],[f242]) ).
thf(f247,plain,
( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ sK4 )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f246]) ).
thf(f251,plain,
( $true
= ( sK0 @ sK5 @ sK4 ) ),
inference(beta-eta_normalization,[],[f247]) ).
thf(f252,plain,
( $true
= ( $true
=> ( sK0 @ sK4 @ sK5 ) ) ),
inference(constrained_superposition,[],[f153,f251]) ).
thf(f255,plain,
( ( sK0 @ sK4 @ sK5 )
= $true ),
inference(boolean_simplification,[],[f252]) ).
thf(f260,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) )
=> ~ ( sK0 @ sK4 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f245]) ).
thf(f261,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ X1 ) )
=> ~ ( sK0 @ sK4 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f300,plain,
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ sK5 ) )
=> ~ $true ) ),
inference(constrained_superposition,[],[f261,f255]) ).
thf(f303,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ sK5 ) )
=> $false )
= $true ),
inference(boolean_simplification,[],[f300]) ).
thf(f304,plain,
( $true
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ sK5 ) ) ) ),
inference(boolean_simplification,[],[f303]) ).
thf(f305,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ sK5 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f305]) ).
thf(f310,plain,
! [X1: $i] :
( $false
= ( sK0 @ X1 @ sK5 ) ),
inference(beta-eta_normalization,[],[f306]) ).
thf(f313,plain,
$false = $true,
inference(constrained_superposition,[],[f255,f310]) ).
thf(f321,plain,
$false,
inference(trivial_inequality_removal,[],[f313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU483^1 : TPTP v9.3.1. Bugfixed v3.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.30 % Computer : n006.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8046.5625MB
% 0.12/0.30 % OS : Linux 6.8.0-71-generic
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Sep 29 13:43:09 UTC 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.36 Running higher-order theorem proving
% 0.28/0.38 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
% 1.02/0.55 % (733881)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.02/0.55 % (733888)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1522989404:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.02/0.55 % (733888)Instruction limit reached!
% 1.02/0.55 % (733888)------------------------------
% 1.02/0.55 % (733888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.55 % (733888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.55 % (733888)CaDiCaL version: 2.1.3
% 1.02/0.55 % (733888)Termination reason: Instruction limit
% 1.02/0.55 % (733888)Termination phase: Property scanning
% 1.02/0.55 % (733888)Time elapsed: 0.002 s
% 1.02/0.55 % (733888)Peak memory usage: 10 MB
% 1.02/0.55 % (733888)Instructions burned: 4 (million)
% 1.02/0.55 % (733892)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.02/0.55 % (733892)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
% 1.02/0.55 % (733886)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=541749603:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.02/0.55 % (733887)lrs+10_16_si=on:nwc=1.5:random_seed=1267669785:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.02/0.55 % (733890)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2384158516:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.02/0.55 % (733889)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=2790416680: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)
% 1.02/0.55 % (733892)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=3809914738:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.02/0.55 % (733891)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3879702958:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.02/0.55 % (733887)Instruction limit reached!
% 1.02/0.55 % (733887)------------------------------
% 1.02/0.55 % (733887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.55 % (733887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.55 % (733887)CaDiCaL version: 2.1.3
% 1.02/0.55 % (733887)Termination reason: Instruction limit
% 1.02/0.55 % (733887)Termination phase: Saturation
% 1.02/0.55 % (733887)Time elapsed: 0.017 s
% 1.02/0.55 % (733887)Peak memory usage: 12 MB
% 1.02/0.55 % (733887)Instructions burned: 18 (million)
% 1.02/0.55 % (733892)Refutation not found, incomplete strategy
% 1.02/0.55 % (733892)------------------------------
% 1.02/0.55 % (733892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.55 % (733892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.55 % (733892)CaDiCaL version: 2.1.3
% 1.02/0.55 % (733892)Termination reason: Refutation not found, incomplete strategy
% 1.02/0.55 % (733892)Time elapsed: 0.016 s
% 1.02/0.55 % (733892)Peak memory usage: 12 MB
% 1.02/0.55 % (733892)Instructions burned: 17 (million)
% 1.02/0.55 % (733892)------------------------------
% 1.02/0.55 % (733892)------------------------------
% 1.02/0.55 % (733890)Instruction limit reached!
% 1.02/0.55 % (733890)------------------------------
% 1.02/0.55 % (733890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.55 % (733890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.55 % (733890)CaDiCaL version: 2.1.3
% 1.02/0.55 % (733890)Termination reason: Instruction limit
% 1.02/0.55 % (733890)Termination phase: Saturation
% 1.02/0.55 % (733890)Time elapsed: 0.023 s
% 1.02/0.55 % (733890)Peak memory usage: 12 MB
% 1.02/0.55 % (733890)Instructions burned: 24 (million)
% 1.02/0.55 % (733894)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4067564412:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.02/0.55 % (733894)Instruction limit reached!
% 1.02/0.55 % (733894)------------------------------
% 1.02/0.55 % (733894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.55 % (733894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.55 % (733894)CaDiCaL version: 2.1.3
% 1.02/0.55 % (733894)Termination reason: Instruction limit
% 1.02/0.55 % (733894)Termination phase: shuffling
% 1.02/0.55 % (733894)Time elapsed: 0.002 s
% 1.02/0.55 % (733894)Peak memory usage: 9 MB
% 1.02/0.55 % (733894)Instructions burned: 2 (million)
% 1.02/0.55 % (733902)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.02/0.55 % (733901)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=14646592:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.02/0.55 % (733902)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1740874623:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.02/0.55 % (733905)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
% 1.02/0.55 % (733905)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.02/0.55 % (733905)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1990598905:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.02/0.55 % (733901)Instruction limit reached!
% 1.02/0.55 % (733901)------------------------------
% 1.02/0.55 % (733901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.55 % (733901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.55 % (733901)CaDiCaL version: 2.1.3
% 1.02/0.55 % (733901)Termination reason: Instruction limit
% 1.02/0.55 % (733901)Termination phase: Property scanning
% 1.02/0.55 % (733901)Time elapsed: 0.005 s
% 1.02/0.55 % (733901)Peak memory usage: 10 MB
% 1.02/0.55 % (733901)Instructions burned: 5 (million)
% 1.02/0.55 % (733903)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2644047839:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.02/0.55 % (733902)Instruction limit reached!
% 1.02/0.55 % (733902)------------------------------
% 1.02/0.55 % (733902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.55 % (733902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.55 % (733902)CaDiCaL version: 2.1.3
% 1.02/0.55 % (733902)Termination reason: Instruction limit
% 1.02/0.55 % (733902)Termination phase: Function definition elimination
% 1.02/0.55 % (733902)Time elapsed: 0.007 s
% 1.02/0.55 % (733902)Peak memory usage: 10 MB
% 1.02/0.55 % (733902)Instructions burned: 8 (million)
% 1.02/0.55 % (733903)Instruction limit reached!
% 1.02/0.55 % (733903)------------------------------
% 1.02/0.55 % (733903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.55 % (733903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.55 % (733903)CaDiCaL version: 2.1.3
% 1.02/0.55 % (733903)Termination reason: Instruction limit
% 1.02/0.55 % (733903)Termination phase: Saturation
% 1.02/0.55 % (733903)Time elapsed: 0.010 s
% 1.02/0.55 % (733903)Peak memory usage: 12 MB
% 1.02/0.55 % (733903)Instructions burned: 12 (million)
% 1.02/0.55 % (733905)Instruction limit reached!
% 1.02/0.55 % (733905)------------------------------
% 1.02/0.55 % (733905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.55 % (733905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.55 % (733905)CaDiCaL version: 2.1.3
% 1.02/0.55 % (733905)Termination reason: Instruction limit
% 1.02/0.55 % (733905)Termination phase: Saturation
% 1.02/0.55 % (733905)Time elapsed: 0.014 s
% 1.02/0.55 % (733905)Peak memory usage: 12 MB
% 1.02/0.55 % (733905)Instructions burned: 29 (million)
% 1.02/0.55 % (733891)Instruction limit reached!
% 1.02/0.55 % (733891)------------------------------
% 1.02/0.55 % (733891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.55 % (733891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.55 % (733891)CaDiCaL version: 2.1.3
% 1.02/0.55 % (733891)Termination reason: Instruction limit
% 1.02/0.55 % (733891)Termination phase: Saturation
% 1.02/0.55 % (733891)Time elapsed: 0.070 s
% 1.02/0.55 % (733891)Peak memory usage: 12 MB
% 1.02/0.55 % (733891)Instructions burned: 75 (million)
% 1.02/0.55 % (733886)Instruction limit reached!
% 1.02/0.55 % (733886)------------------------------
% 1.02/0.55 % (733886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.55 % (733886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.55 % (733886)CaDiCaL version: 2.1.3
% 1.02/0.55 % (733886)Termination reason: Instruction limit
% 1.02/0.55 % (733886)Termination phase: Saturation
% 1.02/0.55 % (733886)Time elapsed: 0.075 s
% 1.02/0.55 % (733886)Peak memory usage: 12 MB
% 1.02/0.55 % (733886)Instructions burned: 87 (million)
% 1.02/0.55 % (733913)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=532863986:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.02/0.55 % (733910)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2230794347:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.02/0.55 % (733913)Refutation not found, incomplete strategy
% 1.02/0.55 % (733913)------------------------------
% 1.02/0.55 % (733913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.55 % (733913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.55 % (733913)CaDiCaL version: 2.1.3
% 1.02/0.55 % (733913)Termination reason: Refutation not found, incomplete strategy
% 1.02/0.55 % (733913)Time elapsed: 0.005 s
% 1.02/0.55 % (733913)Peak memory usage: 12 MB
% 1.02/0.55 % (733913)Instructions burned: 8 (million)
% 1.02/0.55 % (733913)------------------------------
% 1.02/0.55 % (733913)------------------------------
% 1.02/0.55 % (733912)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.02/0.55 % (733911)lrs+10_1_si=on:cs=on:random_seed=3265592325:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.02/0.55 % (733912)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2638993133:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.02/0.56 % (733911)Instruction limit reached!
% 1.02/0.56 % (733911)------------------------------
% 1.02/0.56 % (733911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.56 % (733911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.56 % (733911)CaDiCaL version: 2.1.3
% 1.02/0.56 % (733911)Termination reason: Instruction limit
% 1.02/0.56 % (733911)Termination phase: Function definition elimination
% 1.02/0.56 % (733911)Time elapsed: 0.007 s
% 1.02/0.56 % (733911)Peak memory usage: 10 MB
% 1.02/0.56 % (733911)Instructions burned: 8 (million)
% 1.02/0.56 % (733912)Instruction limit reached!
% 1.02/0.56 % (733912)------------------------------
% 1.02/0.56 % (733912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.56 % (733912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.56 % (733912)CaDiCaL version: 2.1.3
% 1.02/0.56 % (733912)Termination reason: Instruction limit
% 1.02/0.56 % (733912)Termination phase: shuffling
% 1.02/0.56 % (733912)Time elapsed: 0.002 s
% 1.02/0.56 % (733912)Peak memory usage: 9 MB
% 1.02/0.56 % (733912)Instructions burned: 2 (million)
% 1.02/0.56 % (733914)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2369675723:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.02/0.56 % (733915)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2463263476:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.02/0.56 % (733910) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-733881-733910"...
% 1.02/0.56 % (733910)...printing done.
% 1.02/0.56 % (733910)Refutation found. Thanks to Tanya!
% 1.02/0.56 % SZS status Theorem for theBenchmark
% 1.02/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 1.02/0.56 % (733910)------------------------------
% 1.02/0.56 % (733910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.56 % (733910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.56 % (733910)CaDiCaL version: 2.1.3
% 1.02/0.56 % (733910)Termination reason: Refutation
% 1.02/0.56 % (733910)Time elapsed: 0.027 s
% 1.02/0.56 % (733910)Peak memory usage: 13 MB
% 1.02/0.56 % (733910)Instructions burned: 27 (million)
% 1.02/0.56 % (733881)Success in time 0.165 s
% 1.02/0.56 % Vampire exiting
%------------------------------------------------------------------------------