%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU789^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:23 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 39
% Syntax : Number of formulae : 327 ( 85 unt; 0 typ; 33 def)
% Number of atoms : 3437 ( 674 equ; 0 cnn)
% Maximal formula atoms : 15 ( 10 avg)
% Number of connectives : 4404 ( 473 ~; 865 |; 18 &;2590 @)
% ( 25 <=>; 282 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 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 : 61 ( 57 usr; 43 con; 0-4 aty)
% ( 151 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 452 ( 0 sgn 280 !; 4 ?; 452 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
setextsub: $o ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
breln1: $i > $i > $o ).
thf(func_def_6,type,
subbreln1: $o ).
thf(func_def_7,type,
breln1invset: $i > $i > $i ).
thf(func_def_8,type,
breln1invprop: $o ).
thf(func_def_9,type,
breln1invI: $o ).
thf(func_def_10,type,
breln1invE: $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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_21,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
sF4: $o ).
thf(func_def_27,type,
sF5: $o ).
thf(func_def_28,type,
sF6: $o ).
thf(func_def_29,type,
sF7: $o ).
thf(func_def_30,type,
sF8: $o ).
thf(func_def_31,type,
sF9: $o ).
thf(func_def_40,type,
sK18: $i > $i > $i > $i ).
thf(func_def_41,type,
sK19: $i > $i > $i > $i ).
thf(f1,axiom,
( setextsub
= ( ! [X1: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(f2,axiom,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) )
=> ( subset @ X1 @ X2 ) ) ) )
= subbreln1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln1) ).
thf(f3,axiom,
( breln1invprop
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invprop) ).
thf(f4,axiom,
( breln1invI
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invI) ).
thf(f5,axiom,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) )
=> ( in @ ( kpair @ X2 @ X3 ) @ X1 ) ) ) ) )
= breln1invE ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invE) ).
thf(f6,conjecture,
( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [X1: $i,X0: $i] :
( ( breln1 @ X0 @ X1 )
=> ( X1
= ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2Ex) ).
thf(f7,negated_conjecture,
~ ( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [X1: $i,X0: $i] :
( ( breln1 @ X0 @ X1 )
=> ( X1
= ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( breln1invI
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f9,plain,
( breln1invI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
= X0 ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f11,plain,
~ ( ( setextsub = $true )
=> ( ( subbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ( ( breln1invE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
=> ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
= X0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) )
=> ( in @ ( kpair @ X2 @ X3 ) @ X1 ) ) ) ) )
= breln1invE ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
( breln1invE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( ( subset @ X0 @ X1 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f15,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( breln1invprop
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f17,plain,
( breln1invprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) )
=> ( subset @ X1 @ X2 ) ) ) )
= subbreln1 ),
inference(rectify,[],[f2]) ).
thf(f19,plain,
( subbreln1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i] :
( ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
!= X0 )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( subbreln1 = $true )
& ( setextsub = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f21,plain,
( ( breln1invE = $true )
& ( subbreln1 = $true )
& ? [X0: $i,X1: $i] :
( ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
!= X0 )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
& ( breln1invprop = $true )
& ( breln1invI = $true )
& ( setextsub = $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ( breln1invE = $true )
& ( subbreln1 = $true )
& ( sK0
!= ( breln1invset @ sK1 @ ( breln1invset @ sK1 @ sK0 ) ) )
& ( ( breln1 @ sK1 @ sK0 )
= $true )
& ( breln1invprop = $true )
& ( breln1invI = $true )
& ( setextsub = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f21]) ).
thf(f23,plain,
setextsub = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f24,plain,
breln1invI = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f25,plain,
breln1invprop = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f26,plain,
( ( breln1 @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f27,plain,
( sK0
!= ( breln1invset @ sK1 @ ( breln1invset @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f28,plain,
subbreln1 = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f29,plain,
breln1invE = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f30,plain,
( subbreln1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f31,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f32,plain,
( breln1invprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f33,plain,
( breln1invE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f34,plain,
( breln1invI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f37,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f30,f28]) ).
thf(f38,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f31,f23]) ).
thf(f39,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f32,f25]) ).
thf(f40,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f33,f29]) ).
thf(f41,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f34,f24]) ).
thf(f42,definition,
( sF2
= ( breln1invset @ sK1 @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f43,plain,
( ( breln1invset @ sK1 @ sK0 )
= sF2 ),
inference(reorient_equations,[],[f42]) ).
thf(f44,definition,
( sF3
= ( breln1invset @ sK1 @ sF2 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f45,plain,
( ( breln1invset @ sK1 @ sF2 )
= sF3 ),
inference(reorient_equations,[],[f44]) ).
thf(f46,plain,
sK0 != sF3,
inference(definition_folding,[],[f27,f45,f43]) ).
thf(f47,definition,
( sF4
= ( breln1 @ sK1 @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f48,plain,
( ( breln1 @ sK1 @ sK0 )
= sF4 ),
inference(reorient_equations,[],[f47]) ).
thf(f49,plain,
sF4 = $true,
inference(definition_folding,[],[f26,f48]) ).
thf(f50,definition,
( sF5
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f51,plain,
$true = sF5,
inference(definition_folding,[],[f37,f50]) ).
thf(f52,definition,
( sF6
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f53,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) )
= sF6 ),
inference(reorient_equations,[],[f52]) ).
thf(f54,plain,
sF6 = $true,
inference(definition_folding,[],[f38,f53]) ).
thf(f55,definition,
( sF7
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f56,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) )
= sF7 ),
inference(reorient_equations,[],[f55]) ).
thf(f57,plain,
$true = sF7,
inference(definition_folding,[],[f39,f56]) ).
thf(f58,definition,
( sF8
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f59,plain,
$true = sF8,
inference(definition_folding,[],[f40,f58]) ).
thf(f60,definition,
( sF9
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f61,plain,
sF9 = $true,
inference(definition_folding,[],[f41,f60]) ).
thf(f62,plain,
( ( $false = sF7 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f56]) ).
thf(f70,plain,
! [X1: $i] :
( ( $false = sF7 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f62]) ).
thf(f71,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ X1 ) ) ) ) )
| ( $false = sF7 ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
! [X2: $i,X1: $i] :
( ( $false = sF7 )
| ( ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ X1 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X2: $i,X1: $i] :
( ( $false = sF7 )
| ( $true
= ( ( breln1 @ X2 @ X1 )
=> ( breln1 @ X2 @ ( breln1invset @ X2 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( ( $false = sF7 )
| ( ( breln1 @ X2 @ ( breln1invset @ X2 @ X1 ) )
= $true )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f73]) ).
thf(f76,plain,
( ( sF9 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f60]) ).
thf(f77,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
@ X1 ) )
| ( sF9 = $false ) ),
inference(pi_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X1: $i] :
( ( sF9 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( in @ ( kpair @ Y2 @ Y1 ) @ ( breln1invset @ Y0 @ X1 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( in @ ( kpair @ Y2 @ Y1 ) @ ( breln1invset @ Y0 @ X1 ) ) ) ) ) ) ) )
@ X2 )
= $true )
| ( sF9 = $false ) ),
inference(pi_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) ) ) ) )
| ( sF9 = $false ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) ) )
= $true )
| ( sF9 = $false )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) )
@ X3 ) )
| ( sF9 = $false ) ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF9 = $false )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( ( ( in @ X3 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X3 @ Y0 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X3 @ Y0 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) )
= $true )
| ( sF9 = $false ) ),
inference(imp_proxy_clausification,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X3 @ X2 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( sF9 = $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X3 @ Y0 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( sF9 = $false )
| ( ( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) )
= $true )
| ( $false
= ( in @ X3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) )
= $true )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( sF9 = $false )
| ( $false
= ( in @ X3 @ X2 ) )
| ( ( in @ X4 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( sF9 = $false )
| ( $true
= ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $false )
| ( ( in @ X4 @ X2 )
= $false )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f87]) ).
thf(f105,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) )
= $true )
| ( $false = sF6 ) ),
inference(iff_proxy_clausification,[],[f53]) ).
thf(f116,plain,
! [X1: $i] :
( ( $false = sF6 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f105]) ).
thf(f117,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( subset @ Y0 @ X1 )
=> ( Y0 = X1 ) ) ) ) )
| ( $false = sF6 ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X1: $i] :
( ( $false = sF6 )
| ( ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( subset @ Y0 @ X1 )
=> ( Y0 = X1 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X1 )
=> ( X2 = X1 ) ) ) )
| ( $false = sF6 ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( subset @ X2 @ X1 )
=> ( X2 = X1 ) ) )
| ( $false = sF6 )
| ( ( subset @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( $false = sF6 )
| ( $true
= ( X2 = X1 ) )
| ( ( subset @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( $false = sF6 )
| ( $false
= ( subset @ X2 @ X1 ) )
| ( ( subset @ X1 @ X2 )
= $false ) ),
inference(equality_proxy_clausification,[],[f121]) ).
thf(f123,plain,
( ( $false = sF4 )
| ( ( breln1 @ sK1 @ sK0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f48]) ).
thf(f126,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ( $false = sF5 ) ),
inference(iff_proxy_clausification,[],[f50]) ).
thf(f127,plain,
! [X1: $i] :
( ( $false = sF5 )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y0 @ Y2 ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X1: $i] :
( ( $false = sF5 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ X1 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( subset @ X1 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f127]) ).
thf(f129,plain,
! [X2: $i,X1: $i] :
( ( $false = sF5 )
| ( $true
= ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ X1 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( subset @ X1 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: $i,X1: $i] :
( ( $false = sF5 )
| ( $true
= ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f131,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false = sF5 ) ),
inference(imp_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X1 @ Y0 ) ) )
@ X3 )
= $true )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false = sF5 ) ),
inference(pi_proxy_clausification,[],[f131]) ).
thf(f133,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( breln1 @ X2 @ X3 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) ) )
=> ( subset @ X1 @ X3 ) ) )
= $true )
| ( $false = sF5 )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false = sF5 )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) ) )
=> ( subset @ X1 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) ) )
= $false )
| ( $false = sF5 )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $true
= ( subset @ X1 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f134]) ).
thf(f136,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) )
@ ( sK18 @ X3 @ X1 @ X2 ) ) )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $true
= ( subset @ X1 @ X3 ) )
| ( $false = sF5 )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false = sF5 )
| ( $false
= ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 )
=> ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 )
=> ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) )
= $false )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false = sF5 )
| ( $true
= ( subset @ X1 @ X3 ) )
| ( ( breln1 @ X2 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( $true
= ( subset @ X1 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false = sF5 ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 )
=> ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) )
@ ( sK19 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false = sF5 )
| ( ( breln1 @ X2 @ X3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f138]) ).
thf(f141,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ ( sK19 @ X3 @ X1 @ X2 ) ) @ X1 )
=> ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ ( sK19 @ X3 @ X1 @ X2 ) ) @ X3 ) ) ) )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false = sF5 )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF5 )
| ( ( ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ ( sK19 @ X3 @ X1 @ X2 ) ) @ X1 )
=> ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ ( sK19 @ X3 @ X1 @ X2 ) ) @ X3 ) )
= $false )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X2 @ X3 )
= $false )
| ( $true
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( subset @ X1 @ X3 ) )
| ( $false = sF5 )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f144,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false = sF5 )
| ( $false
= ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ ( sK19 @ X3 @ X1 @ X2 ) ) @ X3 ) )
| ( $true
= ( subset @ X1 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ ( sK19 @ X3 @ X1 @ X2 ) ) @ X1 )
= $true )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false = sF5 )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f166,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) )
| ( $false = sF8 ) ),
inference(iff_proxy_clausification,[],[f58]) ).
thf(f167,plain,
! [X1: $i] :
( ( $false = sF8 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y1 ) @ ( breln1invset @ Y0 @ X1 ) )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ X1 ) ) ) ) ) ) ) )
= $true )
| ( $false = sF8 ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X1: $i] :
( ( $false = sF8 )
| ( ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y1 ) @ ( breln1invset @ Y0 @ X1 ) )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ X1 ) ) ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X1: $i] :
( ( $false = sF8 )
| ( $true
= ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) ) ) ) )
= $true )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false = sF8 ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF8 )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) ) ) )
@ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ( in @ X3 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) ) ) )
| ( $false = sF8 ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF8 )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $false = sF8 )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false = sF8 )
| ( $false
= ( in @ X3 @ X2 ) )
| ( ( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) )
= $true )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false = sF8 )
| ( ( in @ X4 @ X2 )
= $false )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $false = sF8 )
| ( $false
= ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) )
| ( ( in @ X4 @ X2 )
= $false )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f177]) ).
thf(f200,definition,
( spl27_2
<=> ( $true = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
thf(f202,plain,
( ( $true = sF7 )
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f210,definition,
( spl27_4
<=> ! [X2: $i,X1: $i] :
( ( ( breln1 @ X2 @ ( breln1invset @ X2 @ X1 ) )
= $true )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl27_4])],[avatar_definition]) ).
thf(f211,plain,
( ! [X2: $i,X1: $i] :
( ( ( breln1 @ X2 @ ( breln1invset @ X2 @ X1 ) )
= $true )
| ( $false
= ( breln1 @ X2 @ X1 ) ) )
| ~ spl27_4 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f213,definition,
( spl27_5
<=> ( $false = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl27_5])],[avatar_definition]) ).
thf(f215,plain,
( ( $false = sF7 )
| ~ spl27_5 ),
inference(avatar_component_clause,[],[f213]) ).
thf(f216,plain,
( spl27_4
| spl27_5 ),
inference(avatar_split_clause,[],[f74,f213,f210]) ).
thf(f218,definition,
( spl27_6
<=> ( sF9 = $false ) ),
introduced(definition,[new_symbols(definition,[spl27_6])],[avatar_definition]) ).
thf(f220,plain,
( ( sF9 = $false )
| ~ spl27_6 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f222,definition,
( spl27_7
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( ( in @ X4 @ X2 )
= $false )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl27_7])],[avatar_definition]) ).
thf(f223,plain,
( ! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) )
| ( ( in @ X4 @ X2 )
= $false )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $false ) )
| ~ spl27_7 ),
inference(avatar_component_clause,[],[f222]) ).
thf(f224,plain,
( spl27_6
| spl27_7 ),
inference(avatar_split_clause,[],[f88,f222,f218]) ).
thf(f226,definition,
( spl27_8
<=> ( sF9 = $true ) ),
introduced(definition,[new_symbols(definition,[spl27_8])],[avatar_definition]) ).
thf(f228,plain,
( ( sF9 = $true )
| ~ spl27_8 ),
inference(avatar_component_clause,[],[f226]) ).
thf(f255,definition,
( spl27_14
<=> ( sF6 = $true ) ),
introduced(definition,[new_symbols(definition,[spl27_14])],[avatar_definition]) ).
thf(f257,plain,
( ( sF6 = $true )
| ~ spl27_14 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f274,definition,
( spl27_18
<=> ( $false = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl27_18])],[avatar_definition]) ).
thf(f276,plain,
( ( $false = sF6 )
| ~ spl27_18 ),
inference(avatar_component_clause,[],[f274]) ).
thf(f278,definition,
( spl27_19
<=> ! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( ( subset @ X1 @ X2 )
= $false )
| ( $false
= ( subset @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl27_19])],[avatar_definition]) ).
thf(f279,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( X1 = X2 )
| ( ( subset @ X1 @ X2 )
= $false ) )
| ~ spl27_19 ),
inference(avatar_component_clause,[],[f278]) ).
thf(f280,plain,
( spl27_18
| spl27_19 ),
inference(avatar_split_clause,[],[f122,f278,f274]) ).
thf(f282,definition,
( spl27_20
<=> ( sF4 = $true ) ),
introduced(definition,[new_symbols(definition,[spl27_20])],[avatar_definition]) ).
thf(f284,plain,
( ( sF4 = $true )
| ~ spl27_20 ),
inference(avatar_component_clause,[],[f282]) ).
thf(f291,definition,
( spl27_22
<=> ( $false = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl27_22])],[avatar_definition]) ).
thf(f293,plain,
( ( $false = sF4 )
| ~ spl27_22 ),
inference(avatar_component_clause,[],[f291]) ).
thf(f295,definition,
( spl27_23
<=> ( ( breln1 @ sK1 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl27_23])],[avatar_definition]) ).
thf(f297,plain,
( ( ( breln1 @ sK1 @ sK0 )
= $true )
| ~ spl27_23 ),
inference(avatar_component_clause,[],[f295]) ).
thf(f298,plain,
( spl27_22
| spl27_23 ),
inference(avatar_split_clause,[],[f123,f295,f291]) ).
thf(f300,definition,
( spl27_24
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl27_24])],[avatar_definition]) ).
thf(f301,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( $true
= ( subset @ X1 @ X3 ) )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false
= ( breln1 @ X2 @ X1 ) ) )
| ~ spl27_24 ),
inference(avatar_component_clause,[],[f300]) ).
thf(f303,definition,
( spl27_25
<=> ( $false = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl27_25])],[avatar_definition]) ).
thf(f305,plain,
( ( $false = sF5 )
| ~ spl27_25 ),
inference(avatar_component_clause,[],[f303]) ).
thf(f306,plain,
( spl27_24
| spl27_25 ),
inference(avatar_split_clause,[],[f139,f303,f300]) ).
thf(f308,definition,
( spl27_26
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( subset @ X1 @ X3 ) )
| ( $true
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl27_26])],[avatar_definition]) ).
thf(f309,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $true
= ( subset @ X1 @ X3 ) ) )
| ~ spl27_26 ),
inference(avatar_component_clause,[],[f308]) ).
thf(f310,plain,
( spl27_26
| spl27_25 ),
inference(avatar_split_clause,[],[f143,f303,f308]) ).
thf(f312,definition,
( spl27_27
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ ( sK19 @ X3 @ X1 @ X2 ) ) @ X1 )
= $true )
| ( $true
= ( subset @ X1 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( ( breln1 @ X2 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl27_27])],[avatar_definition]) ).
thf(f313,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ ( sK19 @ X3 @ X1 @ X2 ) ) @ X1 )
= $true )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $true
= ( subset @ X1 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) )
| ~ spl27_27 ),
inference(avatar_component_clause,[],[f312]) ).
thf(f314,plain,
( spl27_27
| spl27_25 ),
inference(avatar_split_clause,[],[f145,f303,f312]) ).
thf(f316,definition,
( spl27_28
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( subset @ X1 @ X3 ) )
| ( $false
= ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ ( sK19 @ X3 @ X1 @ X2 ) ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl27_28])],[avatar_definition]) ).
thf(f317,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ ( sK18 @ X3 @ X1 @ X2 ) @ ( sK19 @ X3 @ X1 @ X2 ) ) @ X3 ) )
| ( $true
= ( subset @ X1 @ X3 ) )
| ( ( breln1 @ X2 @ X3 )
= $false )
| ( $false
= ( breln1 @ X2 @ X1 ) ) )
| ~ spl27_28 ),
inference(avatar_component_clause,[],[f316]) ).
thf(f318,plain,
( spl27_28
| spl27_25 ),
inference(avatar_split_clause,[],[f144,f303,f316]) ).
thf(f320,definition,
( spl27_29
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl27_29])],[avatar_definition]) ).
thf(f322,plain,
( ( $true = sF5 )
| ~ spl27_29 ),
inference(avatar_component_clause,[],[f320]) ).
thf(f342,plain,
spl27_8,
inference(avatar_split_clause,[],[f61,f226]) ).
thf(f343,plain,
spl27_20,
inference(avatar_split_clause,[],[f49,f282]) ).
thf(f344,plain,
spl27_14,
inference(avatar_split_clause,[],[f54,f255]) ).
thf(f345,plain,
spl27_2,
inference(avatar_split_clause,[],[f57,f200]) ).
thf(f347,definition,
( spl27_34
<=> ( $false = sF8 ) ),
introduced(definition,[new_symbols(definition,[spl27_34])],[avatar_definition]) ).
thf(f349,plain,
( ( $false = sF8 )
| ~ spl27_34 ),
inference(avatar_component_clause,[],[f347]) ).
thf(f351,definition,
( spl27_35
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
| ( ( in @ X4 @ X2 )
= $false )
| ( $false
= ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) )
| ( $false
= ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl27_35])],[avatar_definition]) ).
thf(f352,plain,
( ! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) )
| ( ( in @ X4 @ X2 )
= $false )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
| ( $false
= ( in @ X3 @ X2 ) ) )
| ~ spl27_35 ),
inference(avatar_component_clause,[],[f351]) ).
thf(f353,plain,
( spl27_34
| spl27_35 ),
inference(avatar_split_clause,[],[f178,f351,f347]) ).
thf(f359,definition,
( spl27_37
<=> ( $true = sF8 ) ),
introduced(definition,[new_symbols(definition,[spl27_37])],[avatar_definition]) ).
thf(f361,plain,
( ( $true = sF8 )
| ~ spl27_37 ),
inference(avatar_component_clause,[],[f359]) ).
thf(f383,plain,
spl27_29,
inference(avatar_split_clause,[],[f51,f320]) ).
thf(f384,plain,
spl27_37,
inference(avatar_split_clause,[],[f59,f359]) ).
thf(f385,plain,
( ( $false = $true )
| ~ spl27_20
| ~ spl27_22 ),
inference(forward_demodulation,[],[f293,f284]) ).
thf(f386,plain,
( $false
| ~ spl27_20
| ~ spl27_22 ),
inference(trivial_inequality_removal,[],[f385]) ).
thf(f387,plain,
( ~ spl27_20
| ~ spl27_22 ),
inference(avatar_contradiction_clause,[],[f386]) ).
thf(f389,plain,
( ( $false = $true )
| ~ spl27_6
| ~ spl27_8 ),
inference(forward_demodulation,[],[f228,f220]) ).
thf(f390,plain,
( $false
| ~ spl27_6
| ~ spl27_8 ),
inference(trivial_inequality_removal,[],[f389]) ).
thf(f391,plain,
( ~ spl27_6
| ~ spl27_8 ),
inference(avatar_contradiction_clause,[],[f390]) ).
thf(f405,plain,
( ( $false = $true )
| ~ spl27_14
| ~ spl27_18 ),
inference(forward_demodulation,[],[f257,f276]) ).
thf(f406,plain,
( $false
| ~ spl27_14
| ~ spl27_18 ),
inference(trivial_inequality_removal,[],[f405]) ).
thf(f407,plain,
( ~ spl27_14
| ~ spl27_18 ),
inference(avatar_contradiction_clause,[],[f406]) ).
thf(f412,plain,
( ( $false = $true )
| ~ spl27_25
| ~ spl27_29 ),
inference(forward_demodulation,[],[f322,f305]) ).
thf(f413,plain,
( $false
| ~ spl27_25
| ~ spl27_29 ),
inference(trivial_inequality_removal,[],[f412]) ).
thf(f414,plain,
( ~ spl27_25
| ~ spl27_29 ),
inference(avatar_contradiction_clause,[],[f413]) ).
thf(f417,plain,
( ( $false = $true )
| ~ spl27_34
| ~ spl27_37 ),
inference(forward_demodulation,[],[f361,f349]) ).
thf(f418,plain,
( $false
| ~ spl27_34
| ~ spl27_37 ),
inference(trivial_inequality_removal,[],[f417]) ).
thf(f419,plain,
( ~ spl27_34
| ~ spl27_37 ),
inference(avatar_contradiction_clause,[],[f418]) ).
thf(f428,definition,
( spl27_42
<=> ( ( breln1 @ sK1 @ sF3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl27_42])],[avatar_definition]) ).
thf(f430,plain,
( ( ( breln1 @ sK1 @ sF3 )
= $true )
| ~ spl27_42 ),
inference(avatar_component_clause,[],[f428]) ).
thf(f432,definition,
( spl27_43
<=> ( $false
= ( breln1 @ sK1 @ sF2 ) ) ),
introduced(definition,[new_symbols(definition,[spl27_43])],[avatar_definition]) ).
thf(f434,plain,
( ( $false
= ( breln1 @ sK1 @ sF2 ) )
| ~ spl27_43 ),
inference(avatar_component_clause,[],[f432]) ).
thf(f438,plain,
( ( $false = $true )
| ~ spl27_2
| ~ spl27_5 ),
inference(forward_demodulation,[],[f215,f202]) ).
thf(f439,plain,
( $false
| ~ spl27_2
| ~ spl27_5 ),
inference(trivial_inequality_removal,[],[f438]) ).
thf(f440,plain,
( ~ spl27_2
| ~ spl27_5 ),
inference(avatar_contradiction_clause,[],[f439]) ).
thf(f442,plain,
( ( $true
= ( breln1 @ sK1 @ sF2 ) )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ~ spl27_4 ),
inference(constrained_superposition,[],[f211,f43]) ).
thf(f443,plain,
( ( ( breln1 @ sK1 @ sF3 )
= $true )
| ( $false
= ( breln1 @ sK1 @ sF2 ) )
| ~ spl27_4 ),
inference(constrained_superposition,[],[f211,f45]) ).
thf(f444,plain,
( ( $true
= ( breln1 @ sK1 @ sF2 ) )
| ( $false = $true )
| ~ spl27_4
| ~ spl27_23 ),
inference(forward_demodulation,[],[f442,f297]) ).
thf(f445,plain,
( ( $true
= ( breln1 @ sK1 @ sF2 ) )
| ~ spl27_4
| ~ spl27_23 ),
inference(trivial_inequality_removal,[],[f444]) ).
thf(f446,plain,
( spl27_43
| spl27_42
| ~ spl27_4 ),
inference(avatar_split_clause,[],[f443,f210,f428,f432]) ).
thf(f447,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ sF2 ) )
| ( ( in @ ( kpair @ X1 @ X0 ) @ sK0 )
= $false )
| ( ( breln1 @ sK1 @ sK0 )
= $false ) )
| ~ spl27_7 ),
inference(constrained_superposition,[],[f223,f43]) ).
thf(f448,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ sK1 @ sF2 ) )
| ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ sF3 ) )
| ( $false
= ( in @ ( kpair @ X1 @ X0 ) @ sF2 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) )
| ~ spl27_7 ),
inference(constrained_superposition,[],[f223,f45]) ).
thf(f449,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false = $true )
| ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ sF2 ) )
| ( ( in @ ( kpair @ X1 @ X0 ) @ sK0 )
= $false ) )
| ~ spl27_7
| ~ spl27_23 ),
inference(forward_demodulation,[],[f447,f297]) ).
thf(f450,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ sF2 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( ( in @ ( kpair @ X1 @ X0 ) @ sK0 )
= $false )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl27_7
| ~ spl27_23 ),
inference(trivial_inequality_removal,[],[f449]) ).
thf(f451,plain,
( ! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( in @ ( kpair @ X1 @ X0 ) @ sF2 ) )
| ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ sF3 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_23 ),
inference(forward_demodulation,[],[f448,f445]) ).
thf(f452,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ sF3 ) )
| ( $false
= ( in @ ( kpair @ X1 @ X0 ) @ sF2 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_23 ),
inference(trivial_inequality_removal,[],[f451]) ).
thf(f453,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sF2 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ( ( in @ ( kpair @ X1 @ X0 ) @ sK0 )
= $true )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl27_35 ),
inference(constrained_superposition,[],[f352,f43]) ).
thf(f454,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ sK1 @ sF2 ) )
| ( $true
= ( in @ ( kpair @ X1 @ X0 ) @ sF2 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sF3 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) )
| ~ spl27_35 ),
inference(constrained_superposition,[],[f352,f45]) ).
thf(f463,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( $false = $true )
| ( $true
= ( in @ ( kpair @ X1 @ X0 ) @ sF2 ) )
| ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sF3 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) )
| ~ spl27_4
| ~ spl27_23
| ~ spl27_35 ),
inference(forward_demodulation,[],[f454,f445]) ).
thf(f464,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ X1 @ X0 ) @ sF2 ) )
| ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sF3 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl27_4
| ~ spl27_23
| ~ spl27_35 ),
inference(trivial_inequality_removal,[],[f463]) ).
thf(f465,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sF2 ) )
| ( ( in @ ( kpair @ X1 @ X0 ) @ sK0 )
= $true )
| ( $false = $true )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) )
| ~ spl27_23
| ~ spl27_35 ),
inference(forward_demodulation,[],[f453,f297]) ).
thf(f466,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sF2 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( ( in @ ( kpair @ X1 @ X0 ) @ sK0 )
= $true ) )
| ~ spl27_23
| ~ spl27_35 ),
inference(trivial_inequality_removal,[],[f465]) ).
thf(f470,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ ( kpair @ X1 @ X0 ) @ sK0 )
= $true )
| ( $false
= ( in @ ( kpair @ X1 @ X0 ) @ sF3 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false = $true )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl27_4
| ~ spl27_23
| ~ spl27_35 ),
inference(constrained_superposition,[],[f464,f466]) ).
thf(f475,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( ( in @ ( kpair @ X1 @ X0 ) @ sK0 )
= $true )
| ( $false
= ( in @ ( kpair @ X1 @ X0 ) @ sF3 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false = $true ) )
| ~ spl27_4
| ~ spl27_23
| ~ spl27_35 ),
inference(duplicate_literal_removal,[],[f470]) ).
thf(f476,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ X1 @ X0 ) @ sF3 ) )
| ( ( in @ ( kpair @ X1 @ X0 ) @ sK0 )
= $true )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) )
| ~ spl27_4
| ~ spl27_23
| ~ spl27_35 ),
inference(trivial_inequality_removal,[],[f475]) ).
thf(f491,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK19 @ X0 @ sF3 @ X1 ) @ sK1 ) )
| ( $false
= ( breln1 @ X1 @ sF3 ) )
| ( ( in @ ( sK18 @ X0 @ sF3 @ X1 ) @ sK1 )
= $false )
| ( $false = $true )
| ( ( subset @ sF3 @ X0 )
= $true )
| ( ( breln1 @ X1 @ X0 )
= $false )
| ( $true
= ( in @ ( kpair @ ( sK18 @ X0 @ sF3 @ X1 ) @ ( sK19 @ X0 @ sF3 @ X1 ) ) @ sK0 ) ) )
| ~ spl27_4
| ~ spl27_23
| ~ spl27_27
| ~ spl27_35 ),
inference(constrained_superposition,[],[f313,f476]) ).
thf(f496,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ ( sK18 @ X0 @ sF3 @ X1 ) @ ( sK19 @ X0 @ sF3 @ X1 ) ) @ sK0 ) )
| ( ( breln1 @ X1 @ X0 )
= $false )
| ( $false
= ( in @ ( sK19 @ X0 @ sF3 @ X1 ) @ sK1 ) )
| ( ( in @ ( sK18 @ X0 @ sF3 @ X1 ) @ sK1 )
= $false )
| ( $false
= ( breln1 @ X1 @ sF3 ) )
| ( ( subset @ sF3 @ X0 )
= $true ) )
| ~ spl27_4
| ~ spl27_23
| ~ spl27_27
| ~ spl27_35 ),
inference(trivial_inequality_removal,[],[f491]) ).
thf(f511,plain,
( ! [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $false )
| ( $false = $true )
| ( $false
= ( breln1 @ X1 @ sF3 ) )
| ( $false
= ( in @ ( kpair @ ( sK19 @ sF3 @ X0 @ X1 ) @ ( sK18 @ sF3 @ X0 @ X1 ) ) @ sF2 ) )
| ( ( subset @ X0 @ sF3 )
= $true )
| ( ( in @ ( sK18 @ sF3 @ X0 @ X1 ) @ sK1 )
= $false )
| ( $false
= ( in @ ( sK19 @ sF3 @ X0 @ X1 ) @ sK1 ) ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_23
| ~ spl27_28 ),
inference(constrained_superposition,[],[f452,f317]) ).
thf(f512,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ ( sK19 @ sF3 @ X0 @ X1 ) @ ( sK18 @ sF3 @ X0 @ X1 ) ) @ sF2 ) )
| ( ( in @ ( sK18 @ sF3 @ X0 @ X1 ) @ sK1 )
= $false )
| ( $false
= ( breln1 @ X1 @ sF3 ) )
| ( ( breln1 @ X1 @ X0 )
= $false )
| ( $false
= ( in @ ( sK19 @ sF3 @ X0 @ X1 ) @ sK1 ) )
| ( ( subset @ X0 @ sF3 )
= $true ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_23
| ~ spl27_28 ),
inference(trivial_inequality_removal,[],[f511]) ).
thf(f526,plain,
( ! [X0: $i] :
( ( ( breln1 @ X0 @ sF3 )
= $false )
| ( $true
= ( subset @ sF3 @ sK0 ) )
| ( ( in @ ( sK18 @ sK0 @ sF3 @ X0 ) @ sK1 )
= $false )
| ( $false
= ( breln1 @ X0 @ sK0 ) )
| ( $false
= ( in @ ( sK19 @ sK0 @ sF3 @ X0 ) @ sK1 ) )
| ( ( breln1 @ X0 @ sF3 )
= $false )
| ( $false = $true )
| ( $false
= ( breln1 @ X0 @ sK0 ) )
| ( $true
= ( subset @ sF3 @ sK0 ) ) )
| ~ spl27_4
| ~ spl27_23
| ~ spl27_27
| ~ spl27_28
| ~ spl27_35 ),
inference(constrained_superposition,[],[f317,f496]) ).
thf(f529,plain,
( ! [X0: $i] :
( ( $false
= ( breln1 @ X0 @ sK0 ) )
| ( $false
= ( in @ ( sK19 @ sK0 @ sF3 @ X0 ) @ sK1 ) )
| ( $true
= ( subset @ sF3 @ sK0 ) )
| ( $false = $true )
| ( ( breln1 @ X0 @ sF3 )
= $false )
| ( ( in @ ( sK18 @ sK0 @ sF3 @ X0 ) @ sK1 )
= $false ) )
| ~ spl27_4
| ~ spl27_23
| ~ spl27_27
| ~ spl27_28
| ~ spl27_35 ),
inference(duplicate_literal_removal,[],[f526]) ).
thf(f530,plain,
( ! [X0: $i] :
( ( $false
= ( breln1 @ X0 @ sK0 ) )
| ( ( in @ ( sK18 @ sK0 @ sF3 @ X0 ) @ sK1 )
= $false )
| ( ( breln1 @ X0 @ sF3 )
= $false )
| ( $true
= ( subset @ sF3 @ sK0 ) )
| ( $false
= ( in @ ( sK19 @ sK0 @ sF3 @ X0 ) @ sK1 ) ) )
| ~ spl27_4
| ~ spl27_23
| ~ spl27_27
| ~ spl27_28
| ~ spl27_35 ),
inference(trivial_inequality_removal,[],[f529]) ).
thf(f532,definition,
( spl27_44
<=> ( $true
= ( subset @ sF3 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl27_44])],[avatar_definition]) ).
thf(f533,plain,
( ( $true
!= ( subset @ sF3 @ sK0 ) )
| spl27_44 ),
inference(avatar_component_clause,[],[f532]) ).
thf(f534,plain,
( ( $true
= ( subset @ sF3 @ sK0 ) )
| ~ spl27_44 ),
inference(avatar_component_clause,[],[f532]) ).
thf(f536,definition,
( spl27_45
<=> ! [X0: $i] :
( ( ( breln1 @ X0 @ sF3 )
= $false )
| ( $false
= ( in @ ( sK19 @ sK0 @ sF3 @ X0 ) @ sK1 ) )
| ( ( in @ ( sK18 @ sK0 @ sF3 @ X0 ) @ sK1 )
= $false )
| ( $false
= ( breln1 @ X0 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl27_45])],[avatar_definition]) ).
thf(f537,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK19 @ sK0 @ sF3 @ X0 ) @ sK1 ) )
| ( ( breln1 @ X0 @ sF3 )
= $false )
| ( ( in @ ( sK18 @ sK0 @ sF3 @ X0 ) @ sK1 )
= $false )
| ( $false
= ( breln1 @ X0 @ sK0 ) ) )
| ~ spl27_45 ),
inference(avatar_component_clause,[],[f536]) ).
thf(f539,plain,
( spl27_45
| spl27_44
| ~ spl27_4
| ~ spl27_23
| ~ spl27_27
| ~ spl27_28
| ~ spl27_35 ),
inference(avatar_split_clause,[],[f530,f351,f316,f312,f295,f210,f532,f536]) ).
thf(f540,plain,
( ( sK0 = sF3 )
| ( $false
= ( subset @ sK0 @ sF3 ) )
| ( $false = $true )
| ~ spl27_19
| ~ spl27_44 ),
inference(constrained_superposition,[],[f534,f279]) ).
thf(f542,plain,
( ( $false
= ( subset @ sK0 @ sF3 ) )
| ( sK0 = sF3 )
| ~ spl27_19
| ~ spl27_44 ),
inference(trivial_inequality_removal,[],[f540]) ).
thf(f544,plain,
( ( $false
= ( subset @ sK0 @ sF3 ) )
| ~ spl27_19
| ~ spl27_44 ),
inference(forward_subsumption_resolution,[],[f542,f46]) ).
thf(f552,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ sF3 )
= $true )
| ( ( in @ ( sK18 @ sF3 @ X0 @ X1 ) @ sK1 )
= $false )
| ( ( breln1 @ X1 @ X0 )
= $false )
| ( $false
= ( breln1 @ X1 @ sF3 ) )
| ( ( in @ ( sK18 @ sF3 @ X0 @ X1 ) @ sK1 )
= $false )
| ( $false
= ( in @ ( kpair @ ( sK18 @ sF3 @ X0 @ X1 ) @ ( sK19 @ sF3 @ X0 @ X1 ) ) @ sK0 ) )
| ( $false = $true )
| ( $false
= ( in @ ( sK19 @ sF3 @ X0 @ X1 ) @ sK1 ) )
| ( $false
= ( in @ ( sK19 @ sF3 @ X0 @ X1 ) @ sK1 ) ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_23
| ~ spl27_28 ),
inference(constrained_superposition,[],[f450,f512]) ).
thf(f556,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( breln1 @ X1 @ sF3 ) )
| ( $false
= ( in @ ( sK19 @ sF3 @ X0 @ X1 ) @ sK1 ) )
| ( ( breln1 @ X1 @ X0 )
= $false )
| ( $false
= ( in @ ( kpair @ ( sK18 @ sF3 @ X0 @ X1 ) @ ( sK19 @ sF3 @ X0 @ X1 ) ) @ sK0 ) )
| ( ( subset @ X0 @ sF3 )
= $true )
| ( $false = $true )
| ( ( in @ ( sK18 @ sF3 @ X0 @ X1 ) @ sK1 )
= $false ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_23
| ~ spl27_28 ),
inference(duplicate_literal_removal,[],[f552]) ).
thf(f557,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ ( sK18 @ sF3 @ X0 @ X1 ) @ ( sK19 @ sF3 @ X0 @ X1 ) ) @ sK0 ) )
| ( $false
= ( breln1 @ X1 @ sF3 ) )
| ( ( subset @ X0 @ sF3 )
= $true )
| ( $false
= ( in @ ( sK19 @ sF3 @ X0 @ X1 ) @ sK1 ) )
| ( ( in @ ( sK18 @ sF3 @ X0 @ X1 ) @ sK1 )
= $false )
| ( ( breln1 @ X1 @ X0 )
= $false ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_23
| ~ spl27_28 ),
inference(trivial_inequality_removal,[],[f556]) ).
thf(f581,plain,
( ! [X0: $i] :
( ( $false
= ( breln1 @ X0 @ sK0 ) )
| ( ( breln1 @ X0 @ sF3 )
= $false )
| ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ X0 ) @ sK1 ) )
| ( $false
= ( breln1 @ X0 @ sK0 ) )
| ( $true
= ( subset @ sK0 @ sF3 ) )
| ( ( breln1 @ X0 @ sF3 )
= $false )
| ( $false = $true )
| ( $true
= ( subset @ sK0 @ sF3 ) )
| ( $false
= ( in @ ( sK19 @ sF3 @ sK0 @ X0 ) @ sK1 ) ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_23
| ~ spl27_27
| ~ spl27_28 ),
inference(constrained_superposition,[],[f313,f557]) ).
thf(f583,plain,
( ! [X0: $i] :
( ( $false
= ( breln1 @ X0 @ sK0 ) )
| ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ X0 ) @ sK1 ) )
| ( $false = $true )
| ( $false
= ( in @ ( sK19 @ sF3 @ sK0 @ X0 ) @ sK1 ) )
| ( $true
= ( subset @ sK0 @ sF3 ) )
| ( ( breln1 @ X0 @ sF3 )
= $false ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_23
| ~ spl27_27
| ~ spl27_28 ),
inference(duplicate_literal_removal,[],[f581]) ).
thf(f584,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK19 @ sF3 @ sK0 @ X0 ) @ sK1 ) )
| ( ( breln1 @ X0 @ sF3 )
= $false )
| ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ X0 ) @ sK1 ) )
| ( $false
= ( breln1 @ X0 @ sK0 ) )
| ( $true
= ( subset @ sK0 @ sF3 ) ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_23
| ~ spl27_27
| ~ spl27_28 ),
inference(trivial_inequality_removal,[],[f583]) ).
thf(f592,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK19 @ sF3 @ sK0 @ X0 ) @ sK1 ) )
| ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ X0 ) @ sK1 ) )
| ( $false = $true )
| ( $false
= ( breln1 @ X0 @ sK0 ) )
| ( ( breln1 @ X0 @ sF3 )
= $false ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_27
| ~ spl27_28
| ~ spl27_44 ),
inference(forward_demodulation,[],[f584,f544]) ).
thf(f593,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK19 @ sF3 @ sK0 @ X0 ) @ sK1 ) )
| ( ( breln1 @ X0 @ sF3 )
= $false )
| ( $false
= ( breln1 @ X0 @ sK0 ) )
| ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ X0 ) @ sK1 ) ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_27
| ~ spl27_28
| ~ spl27_44 ),
inference(trivial_inequality_removal,[],[f592]) ).
thf(f598,plain,
( ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ sK1 ) @ sK1 ) )
| ( $false = $true )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( $true
= ( subset @ sK0 @ sF3 ) )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_44 ),
inference(constrained_superposition,[],[f309,f593]) ).
thf(f599,plain,
( ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ sK1 ) @ sK1 ) )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( $false = $true )
| ( $true
= ( subset @ sK0 @ sF3 ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_44 ),
inference(duplicate_literal_removal,[],[f598]) ).
thf(f600,plain,
( ( $true
= ( subset @ sK0 @ sF3 ) )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ sK1 ) @ sK1 ) )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_44 ),
inference(trivial_inequality_removal,[],[f599]) ).
thf(f604,plain,
( ( ( breln1 @ sK1 @ sK0 )
= $false )
| ( $false = $true )
| ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ sK1 ) @ sK1 ) )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_44 ),
inference(forward_demodulation,[],[f600,f544]) ).
thf(f605,plain,
( ( ( breln1 @ sK1 @ sK0 )
= $false )
| ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ sK1 ) @ sK1 ) )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_44 ),
inference(trivial_inequality_removal,[],[f604]) ).
thf(f608,plain,
( ( $false = $true )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ sK1 ) @ sK1 ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_44 ),
inference(forward_demodulation,[],[f605,f297]) ).
thf(f609,plain,
( ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ sK1 ) @ sK1 ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_44 ),
inference(trivial_inequality_removal,[],[f608]) ).
thf(f612,plain,
( ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ sK1 ) @ sK1 ) )
| ( $false = $true )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_42
| ~ spl27_44 ),
inference(forward_demodulation,[],[f609,f430]) ).
thf(f613,plain,
( ( $false
= ( in @ ( sK18 @ sF3 @ sK0 @ sK1 ) @ sK1 ) )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_42
| ~ spl27_44 ),
inference(trivial_inequality_removal,[],[f612]) ).
thf(f616,plain,
( ( $false = $true )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ( $true
= ( subset @ sK0 @ sF3 ) )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_42
| ~ spl27_44 ),
inference(constrained_superposition,[],[f613,f301]) ).
thf(f621,plain,
( ( $true
= ( subset @ sK0 @ sF3 ) )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_42
| ~ spl27_44 ),
inference(trivial_inequality_removal,[],[f616]) ).
thf(f624,plain,
( ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( $false = $true )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_42
| ~ spl27_44 ),
inference(forward_demodulation,[],[f621,f544]) ).
thf(f625,plain,
( ( ( breln1 @ sK1 @ sK0 )
= $false )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_42
| ~ spl27_44 ),
inference(trivial_inequality_removal,[],[f624]) ).
thf(f628,plain,
( ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( $false = $true )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_42
| ~ spl27_44 ),
inference(forward_demodulation,[],[f625,f297]) ).
thf(f629,plain,
( ( ( breln1 @ sK1 @ sF3 )
= $false )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_42
| ~ spl27_44 ),
inference(trivial_inequality_removal,[],[f628]) ).
thf(f633,plain,
( ( $false = $true )
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_42
| ~ spl27_44 ),
inference(forward_demodulation,[],[f629,f430]) ).
thf(f634,plain,
( $false
| ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_42
| ~ spl27_44 ),
inference(trivial_inequality_removal,[],[f633]) ).
thf(f635,plain,
( ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_42
| ~ spl27_44 ),
inference(avatar_contradiction_clause,[],[f634]) ).
thf(f638,plain,
( ( $false = $true )
| ~ spl27_4
| ~ spl27_23
| ~ spl27_43 ),
inference(forward_demodulation,[],[f434,f445]) ).
thf(f639,plain,
( $false
| ~ spl27_4
| ~ spl27_23
| ~ spl27_43 ),
inference(trivial_inequality_removal,[],[f638]) ).
thf(f640,plain,
( ~ spl27_4
| ~ spl27_23
| ~ spl27_43 ),
inference(avatar_contradiction_clause,[],[f639]) ).
thf(f703,plain,
( ( ( in @ ( sK18 @ sK0 @ sF3 @ sK1 ) @ sK1 )
= $false )
| ( $true
= ( subset @ sF3 @ sK0 ) )
| ( $false = $true )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ~ spl27_26
| ~ spl27_45 ),
inference(constrained_superposition,[],[f537,f309]) ).
thf(f706,plain,
( ( $false = $true )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( ( in @ ( sK18 @ sK0 @ sF3 @ sK1 ) @ sK1 )
= $false )
| ( $true
= ( subset @ sF3 @ sK0 ) )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ~ spl27_26
| ~ spl27_45 ),
inference(duplicate_literal_removal,[],[f703]) ).
thf(f707,plain,
( ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( $true
= ( subset @ sF3 @ sK0 ) )
| ( ( in @ ( sK18 @ sK0 @ sF3 @ sK1 ) @ sK1 )
= $false )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ~ spl27_26
| ~ spl27_45 ),
inference(trivial_inequality_removal,[],[f706]) ).
thf(f711,plain,
( ( ( in @ ( sK18 @ sK0 @ sF3 @ sK1 ) @ sK1 )
= $false )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ~ spl27_26
| spl27_44
| ~ spl27_45 ),
inference(forward_subsumption_resolution,[],[f707,f533]) ).
thf(f713,plain,
( ( ( in @ ( sK18 @ sK0 @ sF3 @ sK1 ) @ sK1 )
= $false )
| ( $false = $true )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ~ spl27_23
| ~ spl27_26
| spl27_44
| ~ spl27_45 ),
inference(forward_demodulation,[],[f711,f297]) ).
thf(f714,plain,
( ( ( in @ ( sK18 @ sK0 @ sF3 @ sK1 ) @ sK1 )
= $false )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ~ spl27_23
| ~ spl27_26
| spl27_44
| ~ spl27_45 ),
inference(trivial_inequality_removal,[],[f713]) ).
thf(f717,plain,
( ( ( in @ ( sK18 @ sK0 @ sF3 @ sK1 ) @ sK1 )
= $false )
| ( $false = $true )
| ~ spl27_23
| ~ spl27_26
| ~ spl27_42
| spl27_44
| ~ spl27_45 ),
inference(forward_demodulation,[],[f714,f430]) ).
thf(f718,plain,
( ( ( in @ ( sK18 @ sK0 @ sF3 @ sK1 ) @ sK1 )
= $false )
| ~ spl27_23
| ~ spl27_26
| ~ spl27_42
| spl27_44
| ~ spl27_45 ),
inference(trivial_inequality_removal,[],[f717]) ).
thf(f723,plain,
( ( $true
= ( subset @ sF3 @ sK0 ) )
| ( $false = $true )
| ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_42
| spl27_44
| ~ spl27_45 ),
inference(constrained_superposition,[],[f301,f718]) ).
thf(f726,plain,
( ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ( $true
= ( subset @ sF3 @ sK0 ) )
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_42
| spl27_44
| ~ spl27_45 ),
inference(trivial_inequality_removal,[],[f723]) ).
thf(f728,plain,
( ( ( breln1 @ sK1 @ sF3 )
= $false )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_42
| spl27_44
| ~ spl27_45 ),
inference(forward_subsumption_resolution,[],[f726,f533]) ).
thf(f731,plain,
( ( $false = $true )
| ( ( breln1 @ sK1 @ sK0 )
= $false )
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_42
| spl27_44
| ~ spl27_45 ),
inference(forward_demodulation,[],[f728,f430]) ).
thf(f732,plain,
( ( ( breln1 @ sK1 @ sK0 )
= $false )
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_42
| spl27_44
| ~ spl27_45 ),
inference(trivial_inequality_removal,[],[f731]) ).
thf(f736,plain,
( ( $false = $true )
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_42
| spl27_44
| ~ spl27_45 ),
inference(forward_demodulation,[],[f732,f297]) ).
thf(f737,plain,
( $false
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_42
| spl27_44
| ~ spl27_45 ),
inference(trivial_inequality_removal,[],[f736]) ).
thf(f738,plain,
( ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_42
| spl27_44
| ~ spl27_45 ),
inference(avatar_contradiction_clause,[],[f737]) ).
cnf(s3,plain,
( spl27_4
| spl27_5 ),
inference(sat_conversion,[],[f216]) ).
cnf(s4,plain,
( spl27_6
| spl27_7 ),
inference(sat_conversion,[],[f224]) ).
cnf(s13,plain,
( spl27_18
| spl27_19 ),
inference(sat_conversion,[],[f280]) ).
cnf(s15,plain,
( spl27_22
| spl27_23 ),
inference(sat_conversion,[],[f298]) ).
cnf(s16,plain,
( spl27_24
| spl27_25 ),
inference(sat_conversion,[],[f306]) ).
cnf(s17,plain,
( spl27_25
| spl27_26 ),
inference(sat_conversion,[],[f310]) ).
cnf(s18,plain,
( spl27_25
| spl27_27 ),
inference(sat_conversion,[],[f314]) ).
cnf(s19,plain,
( spl27_25
| spl27_28 ),
inference(sat_conversion,[],[f318]) ).
cnf(s24,plain,
spl27_8,
inference(sat_conversion,[],[f342]) ).
cnf(s25,plain,
spl27_20,
inference(sat_conversion,[],[f343]) ).
cnf(s26,plain,
spl27_14,
inference(sat_conversion,[],[f344]) ).
cnf(s27,plain,
spl27_2,
inference(sat_conversion,[],[f345]) ).
cnf(s28,plain,
( spl27_34
| spl27_35 ),
inference(sat_conversion,[],[f353]) ).
cnf(s34,plain,
spl27_29,
inference(sat_conversion,[],[f383]) ).
cnf(s35,plain,
spl27_37,
inference(sat_conversion,[],[f384]) ).
cnf(s36,plain,
( ~ spl27_20
| ~ spl27_22 ),
inference(sat_conversion,[],[f387]) ).
cnf(s37,plain,
( ~ spl27_6
| ~ spl27_8 ),
inference(sat_conversion,[],[f391]) ).
cnf(s38,plain,
( ~ spl27_14
| ~ spl27_18 ),
inference(sat_conversion,[],[f407]) ).
cnf(s39,plain,
( ~ spl27_25
| ~ spl27_29 ),
inference(sat_conversion,[],[f414]) ).
cnf(s40,plain,
( ~ spl27_34
| ~ spl27_37 ),
inference(sat_conversion,[],[f419]) ).
cnf(s42,plain,
( ~ spl27_2
| ~ spl27_5 ),
inference(sat_conversion,[],[f440]) ).
cnf(s43,plain,
( ~ spl27_4
| spl27_42
| spl27_43 ),
inference(sat_conversion,[],[f446]) ).
cnf(s45,plain,
( ~ spl27_4
| ~ spl27_23
| ~ spl27_27
| ~ spl27_28
| ~ spl27_35
| spl27_44
| spl27_45 ),
inference(sat_conversion,[],[f539]) ).
cnf(s47,plain,
( ~ spl27_4
| ~ spl27_7
| ~ spl27_19
| ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_27
| ~ spl27_28
| ~ spl27_42
| ~ spl27_44 ),
inference(sat_conversion,[],[f635]) ).
cnf(s48,plain,
( ~ spl27_4
| ~ spl27_23
| ~ spl27_43 ),
inference(sat_conversion,[],[f640]) ).
cnf(s54,plain,
( ~ spl27_23
| ~ spl27_24
| ~ spl27_26
| ~ spl27_42
| spl27_44
| ~ spl27_45 ),
inference(sat_conversion,[],[f738]) ).
cnf(s55,plain,
~ spl27_34,
inference(rat,[],[s40,s35]) ).
cnf(s56,plain,
~ spl27_25,
inference(rat,[],[s39,s34]) ).
cnf(s57,plain,
spl27_35,
inference(rat,[],[s28,s55]) ).
cnf(s58,plain,
~ spl27_5,
inference(rat,[],[s42,s27]) ).
cnf(s59,plain,
~ spl27_18,
inference(rat,[],[s38,s26]) ).
cnf(s60,plain,
~ spl27_22,
inference(rat,[],[s36,s25]) ).
cnf(s61,plain,
~ spl27_6,
inference(rat,[],[s37,s24]) ).
cnf(s62,plain,
spl27_28,
inference(rat,[],[s19,s56]) ).
cnf(s63,plain,
spl27_27,
inference(rat,[],[s18,s56]) ).
cnf(s64,plain,
spl27_26,
inference(rat,[],[s17,s56]) ).
cnf(s65,plain,
spl27_24,
inference(rat,[],[s16,s56]) ).
cnf(s66,plain,
spl27_23,
inference(rat,[],[s15,s60]) ).
cnf(s67,plain,
spl27_19,
inference(rat,[],[s13,s59]) ).
cnf(s68,plain,
spl27_7,
inference(rat,[],[s4,s61]) ).
cnf(s69,plain,
spl27_4,
inference(rat,[],[s3,s58]) ).
cnf(s70,plain,
~ spl27_43,
inference(rat,[],[s48,s66,s69]) ).
cnf(s71,plain,
spl27_42,
inference(rat,[],[s43,s70,s69]) ).
cnf(s72,plain,
~ spl27_44,
inference(rat,[],[s47,s69,s68,s62,s63,s64,s65,s66,s67,s71]) ).
cnf(s73,plain,
~ spl27_45,
inference(rat,[],[s54,s71,s66,s65,s64,s72]) ).
cnf(s74,plain,
$false,
inference(rat,[],[s45,s69,s66,s57,s62,s63,s73,s72]) ).
thf(f739,plain,
$false,
inference(avatar_sat_refutation,[],[s74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU789^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n026.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:31:42 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.29 % (677927)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (677945)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (677945)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.29 % (677945)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3654651562:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (677939)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2596187903:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (677940)lrs+10_16_si=on:nwc=1.5:random_seed=1786355353:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (677941)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=254807603:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (677942)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=232091416:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.29 % (677943)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1119813182:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (677944)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1055837189:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (677941)Instruction limit reached!
% 0.20/0.29 % (677941)------------------------------
% 0.20/0.29 % (677941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (677941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (677941)CaDiCaL version: 2.1.3
% 0.20/0.29 % (677941)Termination reason: Instruction limit
% 0.20/0.29 % (677941)Termination phase: Saturation
% 0.20/0.29 % (677941)Time elapsed: 0.002 s
% 0.20/0.29 % (677941)Peak memory usage: 11 MB
% 0.20/0.29 % (677941)Instructions burned: 3 (million)
% 0.20/0.29 % (677945) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-677927-677945"...
% 0.20/0.29 % (677940)Instruction limit reached!
% 0.20/0.29 % (677940)------------------------------
% 0.20/0.29 % (677940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (677940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (677940)CaDiCaL version: 2.1.3
% 0.20/0.29 % (677940)Termination reason: Instruction limit
% 0.20/0.29 % (677940)Termination phase: Saturation
% 0.20/0.29 % (677940)Time elapsed: 0.010 s
% 0.20/0.29 % (677940)Peak memory usage: 12 MB
% 0.20/0.29 % (677940)Instructions burned: 20 (million)
% 0.20/0.29 % (677943)Instruction limit reached!
% 0.20/0.29 % (677943)------------------------------
% 0.20/0.29 % (677943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (677943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (677943)CaDiCaL version: 2.1.3
% 0.20/0.29 % (677943)Termination reason: Instruction limit
% 0.20/0.29 % (677943)Termination phase: Saturation
% 0.20/0.29 % (677943)Time elapsed: 0.013 s
% 0.20/0.29 % (677943)Peak memory usage: 12 MB
% 0.20/0.29 % (677943)Instructions burned: 24 (million)
% 0.20/0.29 % (677945)...printing done.
% 0.20/0.29 % (677945)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (677945)------------------------------
% 0.20/0.29 % (677945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (677945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (677945)CaDiCaL version: 2.1.3
% 0.20/0.29 % (677945)Termination reason: Refutation
% 0.20/0.29 % (677945)Time elapsed: 0.021 s
% 0.20/0.29 % (677945)Peak memory usage: 13 MB
% 0.20/0.29 % (677945)Instructions burned: 70 (million)
% 0.20/0.29 % (677927)Success in time 0.046 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------