%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU493^1 : 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 : n002.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 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 12
% Syntax : Number of formulae : 154 ( 50 unt; 0 typ; 6 def)
% Number of atoms : 1257 ( 250 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 1286 ( 63 ~; 154 |; 88 &; 823 @)
% ( 6 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 15 con; 0-4 aty)
% ( 89 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 202 ( 0 sgn 50 !; 1 ?; 202 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_2,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_3,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_4,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_5,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_6,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_7,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(func_def_8,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_9,type,
symm: ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(func_def_11,type,
asymm: ( $i > $i > $o ) > $o ).
thf(func_def_12,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_13,type,
trans: ( $i > $i > $o ) > $o ).
thf(func_def_14,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_15,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_17,type,
po: ( $i > $i > $o ) > $o ).
thf(func_def_18,type,
so: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
total: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
term: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
ind: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(func_def_23,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_24,type,
norm: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
confl: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
cr: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_39,type,
vOR: $o > $o > $o ).
thf(func_def_40,type,
vAND: $o > $o > $o ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
sK0: $i > $i > $o ).
thf(f2,axiom,
( inv
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',inverse) ).
thf(f6,axiom,
( refl
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',reflexive) ).
thf(f10,axiom,
( antisymm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',antisymmetric) ).
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(f17,axiom,
( po
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( antisymm @ X0 )
& ( refl @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',partial_order) ).
thf(f30,conjecture,
! [X0: $i > $i > $o] :
( ( po @ X0 )
=> ( po @ ( inv @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_of_partial_order_is_partial_order) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( po @ X0 )
=> ( po @ ( inv @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f34,plain,
( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(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(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(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(f86,plain,
~ ! [X0: $i > $i > $o] :
( ( po @ X0 )
=> ( po @ ( inv @ X0 ) ) ),
inference(rectify,[],[f31]) ).
thf(f87,plain,
~ ! [X0: $i > $i > $o] :
( ( ( po @ X0 )
= $true )
=> ( ( po @ ( inv @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( po @ ( inv @ X0 ) )
!= $true )
& ( ( po @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f87]) ).
thf(f89,plain,
( ( $true
!= ( po @ ( inv @ sK0 ) ) )
& ( $true
= ( po @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
thf(f91,plain,
( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f95,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
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(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(f119,plain,
( $true
= ( po @ sK0 ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f120,plain,
( $true
!= ( po @ ( inv @ 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(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] : ( Y0 @ Y2 @ Y1 )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f120,f128,f91]) ).
thf(f139,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 ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f119,f128]) ).
thf(f140,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ $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] : ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f140]) ).
thf(f143,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f145,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X1: $i] :
( $true
= ( sK0 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f143]) ).
thf(f148,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X1 @ X2 ) )
=> ( X2 = X1 ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X1 @ X2 ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( X2 = X1 ) )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f152]) ).
thf(f154,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(f155,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,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,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X2 @ X1 ) ) )
| ( $true
= ( sK0 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $true
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( $true
!= ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f163,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ sK1 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( Y1 = Y0 ) ) )
@ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( Y1 = Y0 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ sK1 @ Y0 ) )
=> ( sK0 @ sK1 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK2 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( Y0 = sK2 ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ sK1 @ Y0 ) )
=> ( sK0 @ sK1 @ Y1 ) ) )
@ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK2 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( Y0 = sK2 ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ sK1 @ Y0 ) )
=> ( sK0 @ sK1 @ Y1 ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK2 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( Y0 = sK2 ) )
@ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK1 @ sK4 ) )
=> ( sK0 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK2 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK5 = sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK1 @ sK4 ) )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK6 ) )
| ( $false
= ( ( ( sK0 @ sK2 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK5 = sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK1 @ sK4 ) )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK6 ) )
| ( $false
= ( sK5 = sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK1 @ sK4 ) )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK6 ) )
| ( $true
= ( ( sK0 @ sK2 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK1 @ sK4 ) )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK6 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK1 @ sK4 ) )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK6 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f174]) ).
thf(f177,plain,
( ( $false
= ( ( ( sK0 @ sK4 @ sK6 )
& ( sK0 @ sK1 @ sK4 ) )
=> ( sK0 @ sK1 @ sK6 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
( ( $false
= ( sK0 @ sK1 @ sK6 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( $true
= ( ( sK0 @ sK4 @ sK6 )
& ( sK0 @ sK1 @ sK4 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f177]) ).
thf(f180,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( $false
= ( ( ( sK0 @ sK4 @ sK6 )
& ( sK0 @ sK1 @ sK4 ) )
=> ( sK0 @ sK1 @ sK6 ) ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f183,plain,
( ( $false
= ( sK0 @ sK1 @ sK6 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( $true
= ( ( sK0 @ sK4 @ sK6 )
& ( sK0 @ sK1 @ sK4 ) ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f182]) ).
thf(f185,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f184]) ).
thf(f187,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK1 @ sK4 ) )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK6 ) )
| ( sK2 != sK5 )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f173]) ).
thf(f188,plain,
( ( $false
= ( ( ( sK0 @ sK4 @ sK6 )
& ( sK0 @ sK1 @ sK4 ) )
=> ( sK0 @ sK1 @ sK6 ) ) )
| ( sK2 != sK5 )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
( ( $false
= ( sK0 @ sK1 @ sK6 ) )
| ( sK2 != sK5 )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( $true
= ( ( sK0 @ sK4 @ sK6 )
& ( sK0 @ sK1 @ sK4 ) ) )
| ( sK2 != sK5 )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f191,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( sK2 != sK5 )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ( sK2 != sK5 )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f190]) ).
thf(f193,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) ) ),
inference(forward_demodulation,[],[f181,f146]) ).
thf(f194,plain,
( ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) ) ),
inference(trivial_inequality_removal,[],[f193]) ).
thf(f195,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) ) ),
inference(forward_demodulation,[],[f180,f146]) ).
thf(f196,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) ) ),
inference(trivial_inequality_removal,[],[f195]) ).
thf(f197,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK1 @ sK6 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) ) ),
inference(forward_demodulation,[],[f178,f146]) ).
thf(f198,plain,
( ( $false
= ( sK0 @ sK1 @ sK6 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) ) ),
inference(trivial_inequality_removal,[],[f197]) ).
thf(f199,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) ) ),
inference(forward_demodulation,[],[f186,f146]) ).
thf(f200,plain,
( ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f199]) ).
thf(f201,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) ) ),
inference(forward_demodulation,[],[f185,f146]) ).
thf(f202,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f201]) ).
thf(f203,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK1 @ sK6 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) ) ),
inference(forward_demodulation,[],[f183,f146]) ).
thf(f204,plain,
( ( $false
= ( sK0 @ sK1 @ sK6 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f203]) ).
thf(f205,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ( sK2 != sK5 ) ),
inference(forward_demodulation,[],[f192,f146]) ).
thf(f206,plain,
( ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ( sK2 != sK5 ) ),
inference(trivial_inequality_removal,[],[f205]) ).
thf(f207,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( sK2 != sK5 ) ),
inference(forward_demodulation,[],[f191,f146]) ).
thf(f208,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ( sK2 != sK5 ) ),
inference(trivial_inequality_removal,[],[f207]) ).
thf(f209,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK1 @ sK6 ) )
| ( sK2 != sK5 ) ),
inference(forward_demodulation,[],[f189,f146]) ).
thf(f210,plain,
( ( $false
= ( sK0 @ sK1 @ sK6 ) )
| ( sK2 != sK5 ) ),
inference(trivial_inequality_removal,[],[f209]) ).
thf(f212,definition,
( spl7_1
<=> ( $true
= ( sK0 @ sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f214,plain,
( ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f212]) ).
thf(f216,definition,
( spl7_2
<=> ( $true
= ( sK0 @ sK4 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f218,plain,
( ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f216]) ).
thf(f219,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f194,f216,f212]) ).
thf(f221,definition,
( spl7_3
<=> ( $true
= ( sK0 @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f223,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f221]) ).
thf(f224,plain,
( spl7_1
| spl7_3 ),
inference(avatar_split_clause,[],[f196,f221,f212]) ).
thf(f226,definition,
( spl7_4
<=> ( $false
= ( sK0 @ sK1 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f228,plain,
( ( $false
= ( sK0 @ sK1 @ sK6 ) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f226]) ).
thf(f229,plain,
( spl7_1
| spl7_4 ),
inference(avatar_split_clause,[],[f198,f226,f212]) ).
thf(f231,definition,
( spl7_5
<=> ( $true
= ( sK0 @ sK5 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f233,plain,
( ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f231]) ).
thf(f234,plain,
( spl7_5
| spl7_2 ),
inference(avatar_split_clause,[],[f200,f216,f231]) ).
thf(f235,plain,
( spl7_5
| spl7_3 ),
inference(avatar_split_clause,[],[f202,f221,f231]) ).
thf(f236,plain,
( spl7_5
| spl7_4 ),
inference(avatar_split_clause,[],[f204,f226,f231]) ).
thf(f238,definition,
( spl7_6
<=> ( sK2 = sK5 ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f240,plain,
( ( sK2 != sK5 )
| spl7_6 ),
inference(avatar_component_clause,[],[f238]) ).
thf(f241,plain,
( ~ spl7_6
| spl7_2 ),
inference(avatar_split_clause,[],[f206,f216,f238]) ).
thf(f242,plain,
( ~ spl7_6
| spl7_3 ),
inference(avatar_split_clause,[],[f208,f221,f238]) ).
thf(f243,plain,
( ~ spl7_6
| spl7_4 ),
inference(avatar_split_clause,[],[f210,f226,f238]) ).
thf(f265,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK6 ) )
| ( $false
= ( sK0 @ sK1 @ X0 ) ) )
| ~ spl7_4 ),
inference(constrained_superposition,[],[f228,f161]) ).
thf(f270,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK6 ) )
| ( $false
= ( sK0 @ sK1 @ X0 ) ) )
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f265]) ).
thf(f309,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl7_2
| ~ spl7_4 ),
inference(constrained_superposition,[],[f218,f270]) ).
thf(f312,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl7_2
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f412,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(constrained_superposition,[],[f312,f223]) ).
thf(f422,plain,
( $false
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f412]) ).
thf(f423,plain,
( ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(avatar_contradiction_clause,[],[f422]) ).
thf(f582,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 )
| ~ spl7_5 ),
inference(constrained_superposition,[],[f153,f233]) ).
thf(f607,plain,
( ( $false
= ( sK0 @ sK2 @ sK5 ) )
| ( sK2 = sK5 )
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f582]) ).
thf(f625,plain,
( ( $false
= ( sK0 @ sK2 @ sK5 ) )
| ~ spl7_5
| spl7_6 ),
inference(forward_subsumption_resolution,[],[f607,f240]) ).
thf(f817,plain,
( ( $true = $false )
| ~ spl7_1
| ~ spl7_5
| spl7_6 ),
inference(constrained_superposition,[],[f625,f214]) ).
thf(f829,plain,
( $false
| ~ spl7_1
| ~ spl7_5
| spl7_6 ),
inference(trivial_inequality_removal,[],[f817]) ).
thf(f830,plain,
( ~ spl7_1
| ~ spl7_5
| spl7_6 ),
inference(avatar_contradiction_clause,[],[f829]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f219]) ).
cnf(s2,plain,
( spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f224]) ).
cnf(s3,plain,
( spl7_1
| spl7_4 ),
inference(sat_conversion,[],[f229]) ).
cnf(s4,plain,
( spl7_2
| spl7_5 ),
inference(sat_conversion,[],[f234]) ).
cnf(s5,plain,
( spl7_3
| spl7_5 ),
inference(sat_conversion,[],[f235]) ).
cnf(s6,plain,
( spl7_4
| spl7_5 ),
inference(sat_conversion,[],[f236]) ).
cnf(s7,plain,
( spl7_2
| ~ spl7_6 ),
inference(sat_conversion,[],[f241]) ).
cnf(s8,plain,
( spl7_3
| ~ spl7_6 ),
inference(sat_conversion,[],[f242]) ).
cnf(s9,plain,
( spl7_4
| ~ spl7_6 ),
inference(sat_conversion,[],[f243]) ).
cnf(s11,plain,
( ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(sat_conversion,[],[f423]) ).
cnf(s13,plain,
( ~ spl7_1
| ~ spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f830]) ).
cnf(s14,plain,
spl7_1,
inference(rat,[],[s11,s1,s2,s3]) ).
cnf(s15,plain,
spl7_4,
inference(rat,[],[s13,s6,s9,s14]) ).
cnf(s16,plain,
spl7_3,
inference(rat,[],[s13,s5,s8,s14]) ).
cnf(s17,plain,
~ spl7_2,
inference(rat,[],[s11,s15,s16]) ).
cnf(s18,plain,
~ spl7_6,
inference(rat,[],[s7,s17]) ).
cnf(s19,plain,
spl7_5,
inference(rat,[],[s4,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s13,s14,s18,s19]) ).
thf(f834,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU493^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n002.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:48:38 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.19/0.29 % (1307876)Will run a generic schedule for satisfiability detection.
% 0.19/0.29 % (1307891)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=619442996:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.29 % (1307891)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % (1307888)% WARNING: option uhcvi not known.
% 0.19/0.29 % (1307887)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1360525418_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.29 % (1307890)dis+10_1_sil=32000:sp=arity:random_seed=734598711:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.29 % (1307888)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1328234307:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.29 % (1307889)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3387769344:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.29 % (1307888)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % Exception at run slice level
% 0.19/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.29 % (1307892)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4099455079:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.29 % (1307888)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.29 % (1307891) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1307876-1307891"...
% 0.19/0.29 % (1307891)...printing done.
% 0.19/0.29 % (1307891)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (1307891)------------------------------
% 0.19/0.29 % (1307891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1307891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1307891)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1307891)Termination reason: Refutation
% 0.19/0.29 % (1307891)Time elapsed: 0.020 s
% 0.19/0.29 % (1307891)Peak memory usage: 13 MB
% 0.19/0.29 % (1307891)Instructions burned: 78 (million)
% 0.19/0.29 % (1307876)Success in time 0.053 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------