%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU792^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:33:26 AM UTC 2026
% Result : Theorem 0.20s 0.36s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 12
% Syntax : Number of formulae : 164 ( 77 unt; 0 typ; 5 def)
% Number of atoms : 1414 ( 311 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 2309 ( 52 ~; 123 |; 27 &;1858 @)
% ( 5 <=>; 153 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 29 usr; 18 con; 0-4 aty)
% ( 91 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 279 ( 0 sgn 163 !; 8 ?; 279 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
binunion: $i > $i > $i ).
thf(func_def_1,type,
breln1: $i > $i > $o ).
thf(func_def_2,type,
breln1invset: $i > $i > $i ).
thf(func_def_3,type,
breln1invprop: $o ).
thf(func_def_5,type,
breln1compset: $i > $i > $i > $i ).
thf(func_def_6,type,
breln1compprop: $o ).
thf(func_def_7,type,
breln1unionCommutes: $o ).
thf(func_def_8,type,
woz2Ex: $o ).
thf(func_def_9,type,
woz2W: $o ).
thf(func_def_10,type,
woz2A: $o ).
thf(func_def_11,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
vIMP: $o > $o > $o ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_18,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(f1,axiom,
( breln1invprop
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invprop) ).
thf(f2,axiom,
( breln1compprop
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compprop) ).
thf(f3,axiom,
( breln1unionCommutes
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ( binunion @ X1 @ X2 )
= ( binunion @ X2 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionCommutes) ).
thf(f4,axiom,
( woz2Ex
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( X1
= ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2Ex) ).
thf(f5,axiom,
( woz2W
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ( breln1invset @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) )
= ( breln1compset @ X0 @ ( breln1invset @ X0 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2W) ).
thf(f6,axiom,
( woz2A
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1compset @ X0 @ X1 @ X3 ) @ ( breln1compset @ X0 @ X2 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2A) ).
thf(f7,conjecture,
( breln1invprop
=> ( breln1compprop
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2B) ).
thf(f8,negated_conjecture,
~ ( breln1invprop
=> ( breln1compprop
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
( breln1invprop
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( breln1invprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( breln1compprop
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f12,plain,
( breln1compprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( breln1 @ Y1 @ ( breln1compset @ Y1 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( breln1unionCommutes
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ( binunion @ X1 @ X2 )
= ( binunion @ X2 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f14,plain,
( breln1unionCommutes
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( binunion @ Y0 @ Y2 )
= ( binunion @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( woz2Ex
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( X1
= ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( woz2Ex
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( ( breln1invset @ Y1 @ ( breln1invset @ Y1 @ Y0 ) )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( woz2W
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ( breln1invset @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) )
= ( breln1compset @ X0 @ ( breln1invset @ X0 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f18,plain,
( woz2W
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( breln1invset @ Y1 @ ( breln1compset @ Y1 @ Y0 @ Y2 ) )
= ( breln1compset @ Y1 @ ( breln1invset @ Y1 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( woz2A
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1compset @ X0 @ X1 @ X3 ) @ ( breln1compset @ X0 @ X2 @ X3 ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
( woz2A
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( breln1 @ Y1 @ Y3 )
=> ( ( breln1compset @ Y1 @ ( binunion @ Y0 @ Y2 ) @ Y3 )
= ( binunion @ ( breln1compset @ Y1 @ Y0 @ Y3 ) @ ( breln1compset @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
~ ( breln1invprop
=> ( breln1compprop
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f22,plain,
~ ( ( breln1invprop = $true )
=> ( ( breln1compprop = $true )
=> ( ( breln1unionCommutes = $true )
=> ( ( woz2Ex = $true )
=> ( ( woz2W = $true )
=> ( ( woz2A = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( breln1 @ X0 @ X3 )
= $true )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
!= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) )
& ( ( breln1 @ X0 @ X3 )
= $true ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( woz2A = $true )
& ( woz2W = $true )
& ( woz2Ex = $true )
& ( breln1unionCommutes = $true )
& ( breln1compprop = $true )
& ( breln1invprop = $true ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
!= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) )
& ( ( breln1 @ X0 @ X3 )
= $true ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( woz2A = $true )
& ( woz2W = $true )
& ( woz2Ex = $true )
& ( breln1unionCommutes = $true )
& ( breln1compprop = $true )
& ( breln1invprop = $true ) ),
inference(flattening,[],[f23]) ).
thf(f25,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK2 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) ) )
& ( $true
= ( breln1 @ sK0 @ sK3 ) )
& ( $true
= ( breln1 @ sK0 @ sK2 ) )
& ( $true
= ( breln1 @ sK0 @ sK1 ) )
& ( woz2A = $true )
& ( woz2W = $true )
& ( woz2Ex = $true )
& ( breln1unionCommutes = $true )
& ( breln1compprop = $true )
& ( breln1invprop = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f24]) ).
thf(f26,plain,
( breln1invprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f27,plain,
( breln1compprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( breln1 @ Y1 @ ( breln1compset @ Y1 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f28,plain,
( breln1unionCommutes
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( binunion @ Y0 @ Y2 )
= ( binunion @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f29,plain,
( woz2Ex
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( ( breln1invset @ Y1 @ ( breln1invset @ Y1 @ Y0 ) )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f30,plain,
( woz2W
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( breln1invset @ Y1 @ ( breln1compset @ Y1 @ Y0 @ Y2 ) )
= ( breln1compset @ Y1 @ ( breln1invset @ Y1 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f31,plain,
( woz2A
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( breln1 @ Y1 @ Y3 )
=> ( ( breln1compset @ Y1 @ ( binunion @ Y0 @ Y2 ) @ Y3 )
= ( binunion @ ( breln1compset @ Y1 @ Y0 @ Y3 ) @ ( breln1compset @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f32,plain,
breln1invprop = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f33,plain,
breln1compprop = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f34,plain,
breln1unionCommutes = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f35,plain,
woz2Ex = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f36,plain,
woz2W = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f37,plain,
woz2A = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f38,plain,
( $true
= ( breln1 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f39,plain,
( $true
= ( breln1 @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f40,plain,
( $true
= ( breln1 @ sK0 @ sK3 ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f41,plain,
( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK2 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f44,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f26,f32]) ).
thf(f45,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( breln1 @ Y1 @ ( breln1compset @ Y1 @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f27,f33]) ).
thf(f46,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( binunion @ Y0 @ Y2 )
= ( binunion @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f28,f34]) ).
thf(f47,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( ( breln1invset @ Y1 @ ( breln1invset @ Y1 @ Y0 ) )
= Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f29,f35]) ).
thf(f48,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( breln1invset @ Y1 @ ( breln1compset @ Y1 @ Y0 @ Y2 ) )
= ( breln1compset @ Y1 @ ( breln1invset @ Y1 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f30,f36]) ).
thf(f49,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( breln1 @ Y1 @ Y3 )
=> ( ( breln1compset @ Y1 @ ( binunion @ Y0 @ Y2 ) @ Y3 )
= ( binunion @ ( breln1compset @ Y1 @ Y0 @ Y3 ) @ ( breln1compset @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f31,f37]) ).
thf(f50,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( breln1 @ Y1 @ Y3 )
=> ( ( breln1compset @ Y1 @ ( binunion @ Y0 @ Y2 ) @ Y3 )
= ( binunion @ ( breln1compset @ Y1 @ Y0 @ Y3 ) @ ( breln1compset @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y0 @ Y2 )
=> ( ( breln1compset @ Y0 @ ( binunion @ X1 @ Y1 ) @ Y2 )
= ( binunion @ ( breln1compset @ Y0 @ X1 @ Y2 ) @ ( breln1compset @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y0 @ Y2 )
=> ( ( breln1compset @ Y0 @ ( binunion @ X1 @ Y1 ) @ Y2 )
= ( binunion @ ( breln1compset @ Y0 @ X1 @ Y2 ) @ ( breln1compset @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ X2 @ Y1 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ Y0 ) @ Y1 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ Y1 ) @ ( breln1compset @ X2 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ X2 @ Y1 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ Y0 ) @ Y1 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ Y1 ) @ ( breln1compset @ X2 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ X2 @ Y1 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ Y0 ) @ Y1 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ Y1 ) @ ( breln1compset @ X2 @ Y0 @ Y1 ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ( breln1 @ X2 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ X3 ) @ Y0 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ Y0 ) @ ( breln1compset @ X2 @ X3 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ X3 ) @ Y0 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ Y0 ) @ ( breln1compset @ X2 @ X3 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ X3 ) @ Y0 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ Y0 ) @ ( breln1compset @ X2 @ X3 @ Y0 ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $true
= ( ( breln1 @ X2 @ X4 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ X3 ) @ X4 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ X4 ) @ ( breln1compset @ X2 @ X3 @ X4 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X4 ) )
| ( $true
= ( ( breln1compset @ X2 @ ( binunion @ X1 @ X3 ) @ X4 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ X4 ) @ ( breln1compset @ X2 @ X3 @ X4 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( breln1compset @ X2 @ ( binunion @ X1 @ X3 ) @ X4 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ X4 ) @ ( breln1compset @ X2 @ X3 @ X4 ) ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X4 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( breln1invset @ Y1 @ ( breln1compset @ Y1 @ Y0 @ Y2 ) )
= ( breln1compset @ Y1 @ ( breln1invset @ Y1 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f63,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( breln1invset @ Y0 @ ( breln1compset @ Y0 @ X1 @ Y1 ) )
= ( breln1compset @ Y0 @ ( breln1invset @ Y0 @ Y1 ) @ ( breln1invset @ Y0 @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( breln1invset @ Y0 @ ( breln1compset @ Y0 @ X1 @ Y1 ) )
= ( breln1compset @ Y0 @ ( breln1invset @ Y0 @ Y1 ) @ ( breln1invset @ Y0 @ X1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( breln1invset @ X2 @ ( breln1compset @ X2 @ X1 @ Y0 ) )
= ( breln1compset @ X2 @ ( breln1invset @ X2 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( breln1invset @ X2 @ ( breln1compset @ X2 @ X1 @ Y0 ) )
= ( breln1compset @ X2 @ ( breln1invset @ X2 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( breln1invset @ X2 @ ( breln1compset @ X2 @ X1 @ Y0 ) )
= ( breln1compset @ X2 @ ( breln1invset @ X2 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ( breln1 @ X2 @ X3 )
=> ( ( breln1invset @ X2 @ ( breln1compset @ X2 @ X1 @ X3 ) )
= ( breln1compset @ X2 @ ( breln1invset @ X2 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $true
= ( ( breln1invset @ X2 @ ( breln1compset @ X2 @ X1 @ X3 ) )
= ( breln1compset @ X2 @ ( breln1invset @ X2 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1invset @ X2 @ ( breln1compset @ X2 @ X1 @ X3 ) )
= ( breln1compset @ X2 @ ( breln1invset @ X2 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( ( breln1invset @ Y1 @ ( breln1invset @ Y1 @ Y0 ) )
= Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f47]) ).
thf(f72,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( ( breln1invset @ Y0 @ ( breln1invset @ Y0 @ X1 ) )
= X1 ) ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f73,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( ( breln1invset @ Y0 @ ( breln1invset @ Y0 @ X1 ) )
= X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( breln1 @ X2 @ X1 )
=> ( ( breln1invset @ X2 @ ( breln1invset @ X2 @ X1 ) )
= X1 ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ( breln1invset @ X2 @ ( breln1invset @ X2 @ X1 ) )
= X1 ) ) ),
inference(imp_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X1: $i] :
( ( ( breln1invset @ X2 @ ( breln1invset @ X2 @ X1 ) )
= X1 )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( binunion @ Y0 @ Y2 )
= ( binunion @ Y2 @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f78,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( binunion @ X1 @ Y1 )
= ( binunion @ Y1 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( binunion @ X1 @ Y1 )
= ( binunion @ Y1 @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( binunion @ X1 @ Y0 )
= ( binunion @ Y0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( binunion @ X1 @ Y0 )
= ( binunion @ Y0 @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( binunion @ X1 @ Y0 )
= ( binunion @ Y0 @ X1 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ( breln1 @ X2 @ X3 )
=> ( ( binunion @ X1 @ X3 )
= ( binunion @ X3 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $true
= ( ( binunion @ X1 @ X3 )
= ( binunion @ X3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( ( binunion @ X1 @ X3 )
= ( binunion @ X3 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( breln1 @ Y1 @ ( breln1compset @ Y1 @ Y0 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f45]) ).
thf(f87,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( breln1 @ Y0 @ ( breln1compset @ Y0 @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( breln1 @ Y0 @ ( breln1compset @ Y0 @ X1 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( breln1 @ X2 @ ( breln1compset @ X2 @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( breln1 @ X2 @ ( breln1compset @ X2 @ X1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( breln1 @ X2 @ ( breln1compset @ X2 @ X1 @ Y0 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ( breln1 @ X2 @ X3 )
=> ( breln1 @ X2 @ ( breln1compset @ X2 @ X1 @ X3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( breln1 @ X2 @ ( breln1compset @ X2 @ X1 @ X3 ) ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f95,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( breln1 @ X2 @ X1 )
=> ( breln1 @ X2 @ ( breln1invset @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f96]) ).
thf(f98,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( breln1 @ X2 @ ( breln1invset @ X2 @ X1 ) ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f97]) ).
thf(f113,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ sK0 @ X0 ) )
| ( ( binunion @ sK2 @ X0 )
= ( binunion @ X0 @ sK2 ) ) ),
inference(constrained_superposition,[],[f39,f85]) ).
thf(f120,plain,
! [X0: $i] :
( ( $false
= ( breln1 @ sK0 @ X0 ) )
| ( ( binunion @ sK2 @ X0 )
= ( binunion @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f113]) ).
thf(f172,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( breln1invset @ X1 @ ( breln1compset @ X1 @ X2 @ ( breln1invset @ X1 @ X0 ) ) )
= ( breln1compset @ X1 @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $false
= ( breln1 @ X1 @ X0 ) ) ),
inference(constrained_superposition,[],[f70,f76]) ).
thf(f181,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) ) )
| ( ( breln1 @ sK0 @ sK3 )
= $false )
| ( ( breln1 @ sK0 @ sK2 )
= $false ) ),
inference(constrained_superposition,[],[f41,f70]) ).
thf(f193,plain,
( ( $true = $false )
| ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) ) )
| ( ( breln1 @ sK0 @ sK2 )
= $false ) ),
inference(forward_demodulation,[],[f181,f40]) ).
thf(f194,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) ) )
| ( ( breln1 @ sK0 @ sK2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f193]) ).
thf(f197,plain,
( ( $true = $false )
| ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) ) ) ),
inference(forward_demodulation,[],[f194,f39]) ).
thf(f198,plain,
( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f197]) ).
thf(f206,plain,
( ( $true = $false )
| ( ( binunion @ sK1 @ sK2 )
= ( binunion @ sK2 @ sK1 ) ) ),
inference(constrained_superposition,[],[f38,f120]) ).
thf(f213,plain,
( ( binunion @ sK1 @ sK2 )
= ( binunion @ sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f206]) ).
thf(f311,definition,
( spl4_7
<=> ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f313,plain,
( ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f311]) ).
thf(f324,definition,
( spl4_10
<=> ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
thf(f326,plain,
( ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK1 ) ) )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f324]) ).
thf(f370,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) ) @ ( breln1compset @ sK0 @ sK1 @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) ) ) )
| ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK1 ) ) )
| ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) )
| ( ( breln1 @ sK0 @ sK1 )
= $false ) ),
inference(constrained_superposition,[],[f198,f172]) ).
thf(f373,definition,
( spl4_14
<=> ( $false
= ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_14])],[avatar_definition]) ).
thf(f374,plain,
( ( $false
!= ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) )
| spl4_14 ),
inference(avatar_component_clause,[],[f373]) ).
thf(f375,plain,
( ( $false
= ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) )
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f373]) ).
thf(f381,plain,
( ( $true = $false )
| ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) ) @ ( breln1compset @ sK0 @ sK1 @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) ) ) )
| ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK1 ) ) )
| ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) ) ),
inference(forward_demodulation,[],[f370,f38]) ).
thf(f382,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) ) @ ( breln1compset @ sK0 @ sK1 @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) ) ) )
| ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK1 ) ) )
| ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) ) ),
inference(trivial_inequality_removal,[],[f381]) ).
thf(f388,definition,
( spl4_16
<=> ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
= ( binunion @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) ) @ ( breln1compset @ sK0 @ sK1 @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_16])],[avatar_definition]) ).
thf(f390,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) ) @ ( breln1compset @ sK0 @ sK1 @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) ) ) )
| spl4_16 ),
inference(avatar_component_clause,[],[f388]) ).
thf(f391,plain,
( spl4_7
| spl4_10
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f382,f388,f324,f311]) ).
thf(f584,definition,
( spl4_30
<=> ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
= ( binunion @ ( breln1compset @ sK0 @ sK2 @ sK3 ) @ ( breln1compset @ sK0 @ sK1 @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_30])],[avatar_definition]) ).
thf(f586,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1compset @ sK0 @ sK2 @ sK3 ) @ ( breln1compset @ sK0 @ sK1 @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) ) ) )
| spl4_30 ),
inference(avatar_component_clause,[],[f584]) ).
thf(f595,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1compset @ sK0 @ sK2 @ sK3 ) @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) )
| ( ( breln1 @ sK0 @ sK3 )
= $false )
| spl4_30 ),
inference(constrained_superposition,[],[f586,f76]) ).
thf(f596,plain,
( ( $true = $false )
| ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1compset @ sK0 @ sK2 @ sK3 ) @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) )
| spl4_30 ),
inference(forward_demodulation,[],[f595,f40]) ).
thf(f597,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1compset @ sK0 @ sK2 @ sK3 ) @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) )
| spl4_30 ),
inference(trivial_inequality_removal,[],[f596]) ).
thf(f643,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( breln1compset @ sK0 @ ( binunion @ sK2 @ sK1 ) @ sK3 ) )
| ( ( breln1 @ sK0 @ sK1 )
= $false )
| ( ( breln1 @ sK0 @ sK3 )
= $false )
| ( ( breln1 @ sK0 @ sK2 )
= $false )
| spl4_30 ),
inference(constrained_superposition,[],[f597,f61]) ).
thf(f645,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 ) )
| ( ( breln1 @ sK0 @ sK1 )
= $false )
| ( ( breln1 @ sK0 @ sK3 )
= $false )
| ( ( breln1 @ sK0 @ sK2 )
= $false )
| spl4_30 ),
inference(forward_demodulation,[],[f643,f213]) ).
thf(f646,plain,
( ( ( breln1 @ sK0 @ sK1 )
= $false )
| ( ( breln1 @ sK0 @ sK3 )
= $false )
| ( ( breln1 @ sK0 @ sK2 )
= $false )
| spl4_30 ),
inference(trivial_inequality_removal,[],[f645]) ).
thf(f662,plain,
( ( $true = $false )
| ( ( breln1 @ sK0 @ sK3 )
= $false )
| ( ( breln1 @ sK0 @ sK2 )
= $false )
| spl4_30 ),
inference(forward_demodulation,[],[f646,f38]) ).
thf(f663,plain,
( ( ( breln1 @ sK0 @ sK3 )
= $false )
| ( ( breln1 @ sK0 @ sK2 )
= $false )
| spl4_30 ),
inference(trivial_inequality_removal,[],[f662]) ).
thf(f670,plain,
( ( $true = $false )
| ( ( breln1 @ sK0 @ sK2 )
= $false )
| spl4_30 ),
inference(forward_demodulation,[],[f663,f40]) ).
thf(f671,plain,
( ( ( breln1 @ sK0 @ sK2 )
= $false )
| spl4_30 ),
inference(trivial_inequality_removal,[],[f670]) ).
thf(f679,plain,
( ( $true = $false )
| ( ( breln1 @ sK0 @ sK3 )
= $false )
| ( ( breln1 @ sK0 @ sK2 )
= $false )
| ~ spl4_14 ),
inference(constrained_superposition,[],[f93,f375]) ).
thf(f680,plain,
( ( ( breln1 @ sK0 @ sK3 )
= $false )
| ( ( breln1 @ sK0 @ sK2 )
= $false )
| ~ spl4_14 ),
inference(trivial_inequality_removal,[],[f679]) ).
thf(f683,plain,
( ( $true = $false )
| ( ( breln1 @ sK0 @ sK2 )
= $false )
| ~ spl4_14 ),
inference(forward_demodulation,[],[f680,f40]) ).
thf(f684,plain,
( ( ( breln1 @ sK0 @ sK2 )
= $false )
| ~ spl4_14 ),
inference(trivial_inequality_removal,[],[f683]) ).
thf(f687,plain,
( ( $true = $false )
| ~ spl4_14 ),
inference(constrained_superposition,[],[f684,f39]) ).
thf(f693,plain,
( $false
| ~ spl4_14 ),
inference(trivial_inequality_removal,[],[f687]) ).
thf(f694,plain,
~ spl4_14,
inference(avatar_contradiction_clause,[],[f693]) ).
thf(f707,plain,
( ( $true = $false )
| ( ( breln1 @ sK0 @ sK3 )
= $false )
| ~ spl4_7 ),
inference(constrained_superposition,[],[f98,f313]) ).
thf(f708,plain,
( ( ( breln1 @ sK0 @ sK3 )
= $false )
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f707]) ).
thf(f731,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1compset @ sK0 @ sK2 @ sK3 ) @ ( breln1compset @ sK0 @ sK1 @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) ) ) )
| ( $false
= ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK2 @ sK3 ) ) )
| spl4_16 ),
inference(constrained_superposition,[],[f390,f76]) ).
thf(f732,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1compset @ sK0 @ sK2 @ sK3 ) @ ( breln1compset @ sK0 @ sK1 @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) ) ) )
| spl4_14
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f731,f374]) ).
thf(f735,plain,
( ~ spl4_30
| spl4_14
| spl4_16 ),
inference(avatar_split_clause,[],[f732,f388,f373,f584]) ).
thf(f736,plain,
( ( $true = $false )
| ~ spl4_7 ),
inference(constrained_superposition,[],[f708,f40]) ).
thf(f742,plain,
( $false
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f736]) ).
thf(f743,plain,
~ spl4_7,
inference(avatar_contradiction_clause,[],[f742]) ).
thf(f764,plain,
( ( $true = $false )
| ( ( breln1 @ sK0 @ sK1 )
= $false )
| ~ spl4_10 ),
inference(constrained_superposition,[],[f98,f326]) ).
thf(f765,plain,
( ( ( breln1 @ sK0 @ sK1 )
= $false )
| ~ spl4_10 ),
inference(trivial_inequality_removal,[],[f764]) ).
thf(f774,plain,
( ( $true = $false )
| ~ spl4_10 ),
inference(constrained_superposition,[],[f765,f38]) ).
thf(f780,plain,
( $false
| ~ spl4_10 ),
inference(trivial_inequality_removal,[],[f774]) ).
thf(f781,plain,
~ spl4_10,
inference(avatar_contradiction_clause,[],[f780]) ).
thf(f839,plain,
( ( $true = $false )
| spl4_30 ),
inference(constrained_superposition,[],[f671,f39]) ).
thf(f845,plain,
( $false
| spl4_30 ),
inference(trivial_inequality_removal,[],[f839]) ).
thf(f846,plain,
spl4_30,
inference(avatar_contradiction_clause,[],[f845]) ).
cnf(s10,plain,
( spl4_7
| spl4_10
| ~ spl4_16 ),
inference(sat_conversion,[],[f391]) ).
cnf(s38,plain,
~ spl4_14,
inference(sat_conversion,[],[f694]) ).
cnf(s43,plain,
( spl4_14
| spl4_16
| ~ spl4_30 ),
inference(sat_conversion,[],[f735]) ).
cnf(s45,plain,
~ spl4_7,
inference(sat_conversion,[],[f743]) ).
cnf(s50,plain,
~ spl4_10,
inference(sat_conversion,[],[f781]) ).
cnf(s67,plain,
spl4_30,
inference(sat_conversion,[],[f846]) ).
cnf(s71,plain,
( spl4_14
| spl4_16 ),
inference(rat,[],[s43,s67]) ).
cnf(s72,plain,
spl4_16,
inference(rat,[],[s71,s38]) ).
cnf(s82,plain,
$false,
inference(rat,[],[s10,s72,s50,s45]) ).
thf(f847,plain,
$false,
inference(avatar_sat_refutation,[],[s82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU792^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:32:26 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.24 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
% 0.20/0.36 % (160966)Will run a generic schedule for satisfiability detection.
% 0.20/0.36 % (160974)dis+10_1_sil=32000:sp=arity:random_seed=3869001736:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.36 % (160972)% WARNING: option uhcvi not known.
% 0.20/0.36 % (160971)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=634791524_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.36 % (160975)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4101731624:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.36 % (160972)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=989531575:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.36 % (160976)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3315425306:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.36 % (160973)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4017630811:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.36 % (160977)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3523842239:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.36 % (160975)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.36 % (160972)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.36 % Exception at run slice level
% 0.20/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.36 % (160972)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.36 % (160974)Instruction limit reached!
% 0.20/0.36 % (160974)------------------------------
% 0.20/0.36 % (160974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (160974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (160974)CaDiCaL version: 2.1.3
% 0.20/0.36 % (160974)Termination reason: Instruction limit
% 0.20/0.36 % (160974)Termination phase: Saturation
% 0.20/0.36 % (160974)Time elapsed: 0.028 s
% 0.20/0.36 % (160974)Peak memory usage: 12 MB
% 0.20/0.36 % (160974)Instructions burned: 106 (million)
% 0.20/0.36 % (160990)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=24391050:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.36 % Exception at run slice level
% 0.20/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.36 % (160996)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1327671065:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.36 % (160997)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1686145070:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.20/0.36 % (160997)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.36 % (160997)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.36 % (160975)Instruction limit reached!
% 0.20/0.36 % (160975)------------------------------
% 0.20/0.36 % (160975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (160975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (160975)CaDiCaL version: 2.1.3
% 0.20/0.36 % (160975)Termination reason: Instruction limit
% 0.20/0.36 % (160975)Termination phase: Saturation
% 0.20/0.36 % (160975)Time elapsed: 0.057 s
% 0.20/0.36 % (160975)Peak memory usage: 13 MB
% 0.20/0.36 % (160975)Instructions burned: 117 (million)
% 0.20/0.36 % (160996)Instruction limit reached!
% 0.20/0.36 % (160996)------------------------------
% 0.20/0.36 % (160996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (160996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (160996)CaDiCaL version: 2.1.3
% 0.20/0.36 % (160996)Termination reason: Instruction limit
% 0.20/0.36 % (160996)Termination phase: Saturation
% 0.20/0.36 % (160996)Time elapsed: 0.031 s
% 0.20/0.36 % (160996)Peak memory usage: 12 MB
% 0.20/0.36 % (160996)Instructions burned: 132 (million)
% 0.20/0.36 % (160976)Instruction limit reached!
% 0.20/0.36 % (160976)------------------------------
% 0.20/0.36 % (160976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (160976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (160976)CaDiCaL version: 2.1.3
% 0.20/0.36 % (160976)Termination reason: Instruction limit
% 0.20/0.36 % (160976)Termination phase: Saturation
% 0.20/0.36 % (160976)Time elapsed: 0.064 s
% 0.20/0.36 % (160976)Peak memory usage: 12 MB
% 0.20/0.36 % (160976)Instructions burned: 131 (million)
% 0.20/0.36 % (160972) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-160966-160972"...
% 0.20/0.36 % (160972)...printing done.
% 0.20/0.36 % (160972)Refutation found. Thanks to Tanya!
% 0.20/0.36 % SZS status Theorem for theBenchmark
% 0.20/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.36 % (160972)------------------------------
% 0.20/0.36 % (160972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.36 % (160972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.36 % (160972)CaDiCaL version: 2.1.3
% 0.75/0.36 % (160972)Termination reason: Refutation
% 0.75/0.36 % (160972)Time elapsed: 0.070 s
% 0.75/0.36 % (160972)Peak memory usage: 13 MB
% 0.75/0.36 % (160972)Instructions burned: 142 (million)
% 0.75/0.36 % (160966)Success in time 0.117 s
% 0.75/0.36 % Vampire exiting
%------------------------------------------------------------------------------