%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU497^1 : 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 : n013.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 0.24s 0.26s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 17
% Syntax : Number of formulae : 197 ( 56 unt; 0 typ; 9 def)
% Number of atoms : 1786 ( 434 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 1654 ( 125 ~; 376 |; 92 &; 879 @)
% ( 9 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 96 ( 96 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 58 usr; 18 con; 0-4 aty)
% ( 95 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 230 ( 0 sgn 50 !; 1 ?; 230 :)
% 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(f6,axiom,
( refl
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',reflexive) ).
thf(f8,axiom,
( rc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
| ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',reflexive_closure) ).
thf(f10,axiom,
( antisymm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',antisymmetric) ).
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(f17,axiom,
( po
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( antisymm @ X0 )
& ( refl @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',partial_order) ).
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 )
=> ( po @ ( rc @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strict_order_induces_partial_order) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( so @ X0 )
=> ( po @ ( rc @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f40,plain,
( refl
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f6]) ).
thf(f41,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f44,plain,
( rc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
| ( X1 = X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f45,plain,
( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f48,plain,
( antisymm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f10]) ).
thf(f49,plain,
( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f48]) ).
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(f60,plain,
( po
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( antisymm @ X0 )
& ( refl @ X0 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f61,plain,
( po
= ( ^ [Y0: $i > $i > $o] :
( ( refl @ Y0 )
& ( antisymm @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(fool_elimination,[],[f60]) ).
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 )
=> ( po @ ( rc @ X0 ) ) ),
inference(rectify,[],[f31]) ).
thf(f87,plain,
~ ! [X0: $i > $i > $o] :
( ( ( so @ X0 )
= $true )
=> ( ( po @ ( rc @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( po @ ( rc @ X0 ) )
!= $true )
& ( ( so @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f87]) ).
thf(f89,plain,
( ( $true
!= ( po @ ( rc @ sK0 ) ) )
& ( $true
= ( so @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
thf(f95,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f97,plain,
( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f99,plain,
( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
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(f106,plain,
( po
= ( ^ [Y0: $i > $i > $o] :
( ( refl @ Y0 )
& ( antisymm @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
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
!= ( po @ ( rc @ sK0 ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f128,plain,
( po
= ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
@ Y0 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y3 = Y2 ) ) ) )
@ 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,[],[f106,f95,f99,f102]) ).
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] : ( Y1 @ Y2 @ Y2 ) )
@ Y0 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y3 = Y2 ) ) ) )
@ 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] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f120,f128,f97]) ).
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] :
( ( Y0 = Y0 )
| ( sK0 @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) )
& ( ( Y0 = Y1 )
| ( sK0 @ Y0 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( Y2 = Y1 )
| ( sK0 @ Y2 @ Y1 ) )
& ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) ) )
=> ( ( Y2 = Y0 )
| ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f158,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( Y2 = Y1 )
| ( sK0 @ Y2 @ Y1 ) )
& ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) ) )
=> ( ( Y2 = Y0 )
| ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = Y0 )
| ( sK0 @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) )
& ( ( Y0 = Y1 )
| ( sK0 @ Y0 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( Y2 = Y1 )
| ( sK0 @ Y2 @ Y1 ) )
& ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) ) )
=> ( ( Y2 = Y0 )
| ( sK0 @ Y2 @ Y0 ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = Y0 )
| ( sK0 @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) )
& ( ( Y0 = Y1 )
| ( sK0 @ Y0 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( Y2 = Y1 )
| ( sK0 @ Y2 @ Y1 ) )
& ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) ) )
=> ( ( Y2 = Y0 )
| ( sK0 @ Y2 @ Y0 ) ) ) ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) )
& ( ( Y0 = Y1 )
| ( sK0 @ Y0 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = Y0 )
| ( sK0 @ Y0 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( Y2 = Y1 )
| ( sK0 @ Y2 @ Y1 ) )
& ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) ) )
=> ( ( Y2 = Y0 )
| ( sK0 @ Y2 @ Y0 ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) )
& ( ( Y0 = Y1 )
| ( sK0 @ Y0 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) )
@ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = Y0 )
| ( sK0 @ Y0 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( Y2 = Y1 )
| ( sK0 @ Y2 @ Y1 ) )
& ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) ) )
=> ( ( Y2 = Y0 )
| ( sK0 @ Y2 @ Y0 ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) )
& ( ( Y0 = Y1 )
| ( sK0 @ Y0 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( Y0 = Y0 )
| ( sK0 @ Y0 @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) )
& ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
=> ( ( Y1 = sK1 )
| ( sK0 @ Y1 @ sK1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( Y0 = sK2 )
| ( sK0 @ Y0 @ sK2 ) )
& ( ( sK2 = Y0 )
| ( sK0 @ sK2 @ Y0 ) ) )
=> ( Y0 = sK2 ) ) ) )
| ( $false
= ( ( sK3 = sK3 )
| ( sK0 @ sK3 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) )
& ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
=> ( ( Y1 = sK1 )
| ( sK0 @ Y1 @ sK1 ) ) ) )
@ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( Y0 = sK2 )
| ( sK0 @ Y0 @ sK2 ) )
& ( ( sK2 = Y0 )
| ( sK0 @ sK2 @ Y0 ) ) )
=> ( Y0 = sK2 ) ) ) )
| ( $false
= ( ( sK3 = sK3 )
| ( sK0 @ sK3 @ sK3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) )
& ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
=> ( ( Y1 = sK1 )
| ( sK0 @ Y1 @ sK1 ) ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK2 )
| ( sK0 @ Y0 @ sK2 ) )
& ( ( sK2 = Y0 )
| ( sK0 @ sK2 @ Y0 ) ) )
=> ( Y0 = sK2 ) )
@ sK5 ) )
| ( $false
= ( ( sK3 = sK3 )
| ( sK0 @ sK3 @ sK3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) )
& ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
=> ( ( Y1 = sK1 )
| ( sK0 @ Y1 @ sK1 ) ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK2 )
| ( sK0 @ Y0 @ sK2 ) )
& ( ( sK2 = Y0 )
| ( sK0 @ sK2 @ Y0 ) ) )
=> ( Y0 = sK2 ) )
@ sK5 ) )
| ( $false
= ( sK3 = sK3 ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) )
& ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
=> ( ( Y1 = sK1 )
| ( sK0 @ Y1 @ sK1 ) ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK2 )
| ( sK0 @ Y0 @ sK2 ) )
& ( ( sK2 = Y0 )
| ( sK0 @ sK2 @ Y0 ) ) )
=> ( Y0 = sK2 ) )
@ sK5 ) )
| ( sK3 != sK3 ) ),
inference(equality_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) )
& ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
=> ( ( Y1 = sK1 )
| ( sK0 @ Y1 @ sK1 ) ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK2 )
| ( sK0 @ Y0 @ sK2 ) )
& ( ( sK2 = Y0 )
| ( sK0 @ sK2 @ Y0 ) ) )
=> ( Y0 = sK2 ) )
@ sK5 ) ) ),
inference(trivial_inequality_removal,[],[f168]) ).
thf(f170,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( Y0 = sK4 )
| ( sK0 @ Y0 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) ) ) )
| ( $false
= ( ( ( ( sK5 = sK2 )
| ( sK0 @ sK5 @ sK2 ) )
& ( ( sK2 = sK5 )
| ( sK0 @ sK2 @ sK5 ) ) )
=> ( sK5 = sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK4 )
| ( sK0 @ Y0 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 ) )
| ( $false
= ( ( ( ( sK5 = sK2 )
| ( sK0 @ sK5 @ sK2 ) )
& ( ( sK2 = sK5 )
| ( sK0 @ sK2 @ sK5 ) ) )
=> ( sK5 = sK2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK4 )
| ( sK0 @ Y0 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 ) )
| ( $false
= ( sK5 = sK2 ) ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK4 )
| ( sK0 @ Y0 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 ) )
| ( $true
= ( ( ( sK5 = sK2 )
| ( sK0 @ sK5 @ sK2 ) )
& ( ( sK2 = sK5 )
| ( sK0 @ sK2 @ sK5 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK4 )
| ( sK0 @ Y0 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 ) )
| ( $true
= ( ( sK2 = sK5 )
| ( sK0 @ sK2 @ sK5 ) ) ) ),
inference(and_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK4 )
| ( sK0 @ Y0 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 ) )
| ( $true
= ( ( sK5 = sK2 )
| ( sK0 @ sK5 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f173]) ).
thf(f176,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK4 )
| ( sK0 @ Y0 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $true
= ( sK5 = sK2 ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK4 )
| ( sK0 @ Y0 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( sK2 = sK5 ) ),
inference(equality_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( $false
= ( ( ( ( sK6 = sK4 )
| ( sK0 @ sK6 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( sK6 = sK1 )
| ( sK0 @ sK6 @ sK1 ) ) ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( sK2 = sK5 ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
( ( $false
= ( ( sK6 = sK1 )
| ( sK0 @ sK6 @ sK1 ) ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( sK2 = sK5 ) ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $true
= ( ( ( sK6 = sK4 )
| ( sK0 @ sK6 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( sK2 = sK5 ) ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f181,plain,
( ( $true
= ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( sK2 = sK5 ) ),
inference(and_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( ( $true
= ( ( sK6 = sK4 )
| ( sK0 @ sK6 @ sK4 ) ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( sK2 = sK5 ) ),
inference(and_proxy_clausification,[],[f180]) ).
thf(f183,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( sK2 = sK5 )
| ( $true
= ( sK6 = sK4 ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( sK2 = sK5 )
| ( sK4 = sK6 ) ),
inference(equality_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( sK2 = sK5 )
| ( $true
= ( sK4 = sK1 ) ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f186,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( sK2 = sK5 )
| ( sK1 = sK4 ) ),
inference(equality_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( sK2 = sK5 ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f188,plain,
( ( $false
= ( sK6 = sK1 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( sK2 = sK5 ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f189,plain,
( ( sK1 != sK6 )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( sK2 = sK5 ) ),
inference(equality_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK4 )
| ( sK0 @ Y0 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( $true
= ( sK2 = sK5 ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f191,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK4 )
| ( sK0 @ Y0 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 ) ),
inference(equality_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( $false
= ( ( ( ( sK6 = sK4 )
| ( sK0 @ sK6 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( sK6 = sK1 )
| ( sK0 @ sK6 @ sK1 ) ) ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
( ( $false
= ( ( sK6 = sK1 )
| ( sK0 @ sK6 @ sK1 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ( $true
= ( ( ( sK6 = sK4 )
| ( sK0 @ sK6 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f195,plain,
( ( $true
= ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 ) ),
inference(and_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( ( $true
= ( ( sK6 = sK4 )
| ( sK0 @ sK6 @ sK4 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 ) ),
inference(and_proxy_clausification,[],[f194]) ).
thf(f197,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 )
| ( $true
= ( sK6 = sK4 ) ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 )
| ( sK4 = sK6 ) ),
inference(equality_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 )
| ( $true
= ( sK4 = sK1 ) ) ),
inference(or_proxy_clausification,[],[f195]) ).
thf(f200,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 )
| ( sK1 = sK4 ) ),
inference(equality_proxy_clausification,[],[f199]) ).
thf(f201,plain,
( ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f202,plain,
( ( $false
= ( sK6 = sK1 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f203,plain,
( ( sK1 != sK6 )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 ) ),
inference(equality_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( Y0 = sK4 )
| ( sK0 @ Y0 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 ) )
| ( sK2 != sK5 ) ),
inference(equality_proxy_clausification,[],[f172]) ).
thf(f205,plain,
( ( $false
= ( ( ( ( sK6 = sK4 )
| ( sK0 @ sK6 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
=> ( ( sK6 = sK1 )
| ( sK0 @ sK6 @ sK1 ) ) ) )
| ( sK2 != sK5 ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f206,plain,
( ( $false
= ( ( sK6 = sK1 )
| ( sK0 @ sK6 @ sK1 ) ) )
| ( sK2 != sK5 ) ),
inference(imp_proxy_clausification,[],[f205]) ).
thf(f207,plain,
( ( $true
= ( ( ( sK6 = sK4 )
| ( sK0 @ sK6 @ sK4 ) )
& ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) ) )
| ( sK2 != sK5 ) ),
inference(imp_proxy_clausification,[],[f205]) ).
thf(f208,plain,
( ( $true
= ( ( sK4 = sK1 )
| ( sK0 @ sK4 @ sK1 ) ) )
| ( sK2 != sK5 ) ),
inference(and_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( ( $true
= ( ( sK6 = sK4 )
| ( sK0 @ sK6 @ sK4 ) ) )
| ( sK2 != sK5 ) ),
inference(and_proxy_clausification,[],[f207]) ).
thf(f210,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( sK2 != sK5 )
| ( $true
= ( sK6 = sK4 ) ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f211,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( sK2 != sK5 )
| ( sK4 = sK6 ) ),
inference(equality_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( sK2 != sK5 )
| ( $true
= ( sK4 = sK1 ) ) ),
inference(or_proxy_clausification,[],[f208]) ).
thf(f213,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( sK2 != sK5 )
| ( sK1 = sK4 ) ),
inference(equality_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( sK2 != sK5 ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f215,plain,
( ( $false
= ( sK6 = sK1 ) )
| ( sK2 != sK5 ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f216,plain,
( ( sK1 != sK6 )
| ( sK2 != sK5 ) ),
inference(equality_proxy_clausification,[],[f215]) ).
thf(f265,definition,
( spl8_1
<=> ( sK4 = sK6 ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f267,plain,
( ( sK4 = sK6 )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f269,definition,
( spl8_2
<=> ( sK2 = sK5 ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f273,definition,
( spl8_3
<=> ( $true
= ( sK0 @ sK5 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f275,plain,
( ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f273]) ).
thf(f277,definition,
( spl8_4
<=> ( $true
= ( sK0 @ sK6 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f279,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f277]) ).
thf(f280,plain,
( spl8_1
| spl8_2
| spl8_3
| spl8_4 ),
inference(avatar_split_clause,[],[f184,f277,f273,f269,f265]) ).
thf(f282,definition,
( spl8_5
<=> ( sK1 = sK4 ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f284,plain,
( ( sK1 = sK4 )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f282]) ).
thf(f286,definition,
( spl8_6
<=> ( $true
= ( sK0 @ sK4 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
thf(f288,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f286]) ).
thf(f289,plain,
( spl8_5
| spl8_2
| spl8_3
| spl8_6 ),
inference(avatar_split_clause,[],[f186,f286,f273,f269,f282]) ).
thf(f291,definition,
( spl8_7
<=> ( sK1 = sK6 ) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
thf(f293,plain,
( ( sK1 != sK6 )
| spl8_7 ),
inference(avatar_component_clause,[],[f291]) ).
thf(f294,plain,
( spl8_2
| spl8_3
| ~ spl8_7 ),
inference(avatar_split_clause,[],[f189,f291,f273,f269]) ).
thf(f296,definition,
( spl8_8
<=> ( $false
= ( sK0 @ sK6 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
thf(f298,plain,
( ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f296]) ).
thf(f299,plain,
( spl8_2
| spl8_3
| spl8_8 ),
inference(avatar_split_clause,[],[f187,f296,f273,f269]) ).
thf(f301,definition,
( spl8_9
<=> ( $true
= ( sK0 @ sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
thf(f303,plain,
( ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f301]) ).
thf(f304,plain,
( spl8_1
| spl8_2
| spl8_9
| spl8_4 ),
inference(avatar_split_clause,[],[f198,f277,f301,f269,f265]) ).
thf(f305,plain,
( spl8_5
| spl8_2
| spl8_9
| spl8_6 ),
inference(avatar_split_clause,[],[f200,f286,f301,f269,f282]) ).
thf(f306,plain,
( spl8_2
| spl8_9
| ~ spl8_7 ),
inference(avatar_split_clause,[],[f203,f291,f301,f269]) ).
thf(f307,plain,
( spl8_2
| spl8_9
| spl8_8 ),
inference(avatar_split_clause,[],[f201,f296,f301,f269]) ).
thf(f308,plain,
( spl8_1
| ~ spl8_2
| spl8_4 ),
inference(avatar_split_clause,[],[f211,f277,f269,f265]) ).
thf(f309,plain,
( spl8_5
| ~ spl8_2
| spl8_6 ),
inference(avatar_split_clause,[],[f213,f286,f269,f282]) ).
thf(f310,plain,
( ~ spl8_2
| ~ spl8_7 ),
inference(avatar_split_clause,[],[f216,f291,f269]) ).
thf(f311,plain,
( ~ spl8_2
| spl8_8 ),
inference(avatar_split_clause,[],[f214,f296,f269]) ).
thf(f353,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK2 @ sK5 ) )
| ~ spl8_3 ),
inference(constrained_superposition,[],[f275,f148]) ).
thf(f364,plain,
( ( $false
= ( sK0 @ sK2 @ sK5 ) )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f353]) ).
thf(f398,plain,
( ( $true = $false )
| ~ spl8_3
| ~ spl8_9 ),
inference(constrained_superposition,[],[f364,f303]) ).
thf(f404,plain,
( $false
| ~ spl8_3
| ~ spl8_9 ),
inference(trivial_inequality_removal,[],[f398]) ).
thf(f405,plain,
( ~ spl8_3
| ~ spl8_9 ),
inference(avatar_contradiction_clause,[],[f404]) ).
thf(f407,plain,
( ( sK1 != sK4 )
| ~ spl8_1
| spl8_7 ),
inference(constrained_superposition,[],[f293,f267]) ).
thf(f420,plain,
( ( $false
= ( sK0 @ sK4 @ sK1 ) )
| ~ spl8_1
| ~ spl8_8 ),
inference(constrained_superposition,[],[f298,f267]) ).
thf(f438,plain,
( ( $true = $false )
| ~ spl8_1
| ~ spl8_6
| ~ spl8_8 ),
inference(constrained_superposition,[],[f420,f288]) ).
thf(f444,plain,
( $false
| ~ spl8_1
| ~ spl8_6
| ~ spl8_8 ),
inference(trivial_inequality_removal,[],[f438]) ).
thf(f445,plain,
( ~ spl8_1
| ~ spl8_6
| ~ spl8_8 ),
inference(avatar_contradiction_clause,[],[f444]) ).
thf(f446,plain,
( ~ spl8_5
| ~ spl8_1
| spl8_7 ),
inference(avatar_split_clause,[],[f407,f291,f265,f282]) ).
thf(f458,plain,
( ( $true
= ( sK0 @ sK6 @ sK1 ) )
| ~ spl8_4
| ~ spl8_5 ),
inference(constrained_superposition,[],[f279,f284]) ).
thf(f492,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ sK4 @ X0 ) )
| ( $true
= ( sK0 @ sK6 @ X0 ) ) )
| ~ spl8_4 ),
inference(constrained_superposition,[],[f279,f156]) ).
thf(f496,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ sK6 @ X0 ) )
| ( $false
= ( sK0 @ sK4 @ X0 ) ) )
| ~ spl8_4 ),
inference(trivial_inequality_removal,[],[f492]) ).
thf(f576,plain,
( ( $true = $false )
| ~ spl8_4
| ~ spl8_5
| ~ spl8_8 ),
inference(constrained_superposition,[],[f458,f298]) ).
thf(f588,plain,
( $false
| ~ spl8_4
| ~ spl8_5
| ~ spl8_8 ),
inference(trivial_inequality_removal,[],[f576]) ).
thf(f589,plain,
( ~ spl8_4
| ~ spl8_5
| ~ spl8_8 ),
inference(avatar_contradiction_clause,[],[f588]) ).
thf(f627,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK4 @ sK1 ) )
| ~ spl8_4
| ~ spl8_8 ),
inference(constrained_superposition,[],[f298,f496]) ).
thf(f628,plain,
( ( $false
= ( sK0 @ sK4 @ sK1 ) )
| ~ spl8_4
| ~ spl8_8 ),
inference(trivial_inequality_removal,[],[f627]) ).
thf(f641,plain,
( ( $true = $false )
| ~ spl8_4
| ~ spl8_6
| ~ spl8_8 ),
inference(constrained_superposition,[],[f628,f288]) ).
thf(f649,plain,
( $false
| ~ spl8_4
| ~ spl8_6
| ~ spl8_8 ),
inference(trivial_inequality_removal,[],[f641]) ).
thf(f650,plain,
( ~ spl8_4
| ~ spl8_6
| ~ spl8_8 ),
inference(avatar_contradiction_clause,[],[f649]) ).
cnf(s1,plain,
( spl8_1
| spl8_2
| spl8_3
| spl8_4 ),
inference(sat_conversion,[],[f280]) ).
cnf(s2,plain,
( spl8_2
| spl8_3
| spl8_5
| spl8_6 ),
inference(sat_conversion,[],[f289]) ).
cnf(s3,plain,
( spl8_2
| spl8_3
| ~ spl8_7 ),
inference(sat_conversion,[],[f294]) ).
cnf(s4,plain,
( spl8_2
| spl8_3
| spl8_8 ),
inference(sat_conversion,[],[f299]) ).
cnf(s5,plain,
( spl8_1
| spl8_2
| spl8_4
| spl8_9 ),
inference(sat_conversion,[],[f304]) ).
cnf(s6,plain,
( spl8_2
| spl8_5
| spl8_6
| spl8_9 ),
inference(sat_conversion,[],[f305]) ).
cnf(s7,plain,
( spl8_2
| ~ spl8_7
| spl8_9 ),
inference(sat_conversion,[],[f306]) ).
cnf(s8,plain,
( spl8_2
| spl8_8
| spl8_9 ),
inference(sat_conversion,[],[f307]) ).
cnf(s9,plain,
( spl8_1
| ~ spl8_2
| spl8_4 ),
inference(sat_conversion,[],[f308]) ).
cnf(s10,plain,
( ~ spl8_2
| spl8_5
| spl8_6 ),
inference(sat_conversion,[],[f309]) ).
cnf(s11,plain,
( ~ spl8_2
| ~ spl8_7 ),
inference(sat_conversion,[],[f310]) ).
cnf(s12,plain,
( ~ spl8_2
| spl8_8 ),
inference(sat_conversion,[],[f311]) ).
cnf(s27,plain,
( ~ spl8_3
| ~ spl8_9 ),
inference(sat_conversion,[],[f405]) ).
cnf(s29,plain,
( ~ spl8_1
| ~ spl8_6
| ~ spl8_8 ),
inference(sat_conversion,[],[f445]) ).
cnf(s30,plain,
( ~ spl8_1
| ~ spl8_5
| spl8_7 ),
inference(sat_conversion,[],[f446]) ).
cnf(s33,plain,
( ~ spl8_4
| ~ spl8_5
| ~ spl8_8 ),
inference(sat_conversion,[],[f589]) ).
cnf(s35,plain,
( ~ spl8_4
| ~ spl8_6
| ~ spl8_8 ),
inference(sat_conversion,[],[f650]) ).
cnf(s36,plain,
( spl8_3
| spl8_2
| spl8_1 ),
inference(rat,[],[s2,s33,s35,s4,s1]) ).
cnf(s37,plain,
( spl8_9
| spl8_2
| spl8_1 ),
inference(rat,[],[s6,s33,s35,s8,s5]) ).
cnf(s38,plain,
( spl8_2
| spl8_1 ),
inference(rat,[],[s37,s27,s36]) ).
cnf(s39,plain,
spl8_1,
inference(rat,[],[s10,s33,s35,s9,s12,s38]) ).
cnf(s40,plain,
( spl8_9
| spl8_2 ),
inference(rat,[],[s6,s30,s29,s7,s8,s39]) ).
cnf(s41,plain,
( spl8_3
| spl8_2 ),
inference(rat,[],[s2,s30,s29,s3,s4,s39]) ).
cnf(s42,plain,
spl8_2,
inference(rat,[],[s41,s27,s40]) ).
cnf(s43,plain,
spl8_8,
inference(rat,[],[s12,s42]) ).
cnf(s44,plain,
~ spl8_7,
inference(rat,[],[s11,s42]) ).
cnf(s45,plain,
~ spl8_6,
inference(rat,[],[s29,s39,s43]) ).
cnf(s46,plain,
~ spl8_5,
inference(rat,[],[s30,s39,s44]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s10,s42,s46,s45]) ).
thf(f652,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU497^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n013.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:45:46 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 0.24/0.26 % (2135378)Will run a generic schedule for satisfiability detection.
% 0.24/0.26 % (2135383)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4112298448_2999 on theBenchmark for (2999ds/0Mi)
% 0.24/0.26 % Exception at run slice level
% 0.24/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.26 % (2135384)% WARNING: option uhcvi not known.
% 0.24/0.26 % (2135384)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3790545768:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.24/0.26 % (2135385)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3881395484:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.24/0.26 % (2135388)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1808777325:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.24/0.26 % (2135386)dis+10_1_sil=32000:sp=arity:random_seed=299760384:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.24/0.26 % (2135389)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1032142785:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.24/0.26 % (2135387)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2684658917:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.24/0.26 % (2135384)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.24/0.26 % (2135387)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.24/0.26 % (2135391)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1835580181:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.24/0.26 % (2135384)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.24/0.26 % Exception at run slice level
% 0.24/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.26 % (2135389) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2135378-2135389"...
% 0.24/0.26 % (2135399)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=575971422:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.24/0.26 % (2135389)...printing done.
% 0.24/0.26 % (2135389)Refutation found. Thanks to Tanya!
% 0.24/0.26 % SZS status Theorem for theBenchmark
% 0.24/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.27 % (2135389)------------------------------
% 0.24/0.27 % (2135389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.27 % (2135389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.27 % (2135389)CaDiCaL version: 2.1.3
% 0.24/0.27 % (2135389)Termination reason: Refutation
% 0.24/0.27 % (2135389)Time elapsed: 0.020 s
% 0.24/0.27 % (2135389)Peak memory usage: 13 MB
% 0.24/0.27 % (2135389)Instructions burned: 38 (million)
% 0.24/0.27 % (2135378)Success in time 0.053 s
% 0.24/0.27 % Vampire exiting
%------------------------------------------------------------------------------