%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU789^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:33:25 AM UTC 2026
% Result : Theorem 0.56s 0.38s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 6
% Syntax : Number of formulae : 144 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 1874 ( 524 equ; 0 cnn)
% Maximal formula atoms : 13 ( 13 avg)
% Number of connectives : 3703 ( 12 ~; 346 |; 18 &;2969 @)
% ( 0 <=>; 245 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 25 usr; 10 con; 0-4 aty)
% ( 113 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 442 ( 130 ^; 308 !; 4 ?; 442 :)
% 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,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
sK2: $i > $i > $i > $i ).
thf(func_def_26,type,
sK3: $i > $i > $i > $i ).
thf(f1,axiom,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(f2,axiom,
( subbreln1
= ( ! [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 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln1) ).
thf(f3,axiom,
( breln1invprop
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',breln1invI) ).
thf(f5,axiom,
( breln1invE
= ( ! [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 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invE) ).
thf(f6,conjecture,
( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( X1
= ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz2Ex) ).
thf(f7,negated_conjecture,
~ ( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( X1
= ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( subbreln1
= ( ! [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 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f11,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,[],[f10]) ).
thf(f12,plain,
( breln1invprop
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( breln1invprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,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(f15,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,[],[f14]) ).
thf(f16,plain,
( breln1invE
= ( ! [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 ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f17,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,[],[f16]) ).
thf(f18,plain,
~ ( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( X1
= ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
~ ( ( setextsub = $true )
=> ( ( subbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ( ( breln1invE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i] :
( ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
!= X1 )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( subbreln1 = $true )
& ( setextsub = $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i] :
( ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
!= X1 )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( subbreln1 = $true )
& ( setextsub = $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ( sK1
!= ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK1 ) ) )
& ( $true
= ( breln1 @ sK0 @ sK1 ) )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( subbreln1 = $true )
& ( setextsub = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f21]) ).
thf(f23,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f24,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,[],[f11]) ).
thf(f25,plain,
( breln1invprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f26,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,[],[f15]) ).
thf(f27,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,[],[f17]) ).
thf(f28,plain,
setextsub = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f29,plain,
subbreln1 = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f30,plain,
breln1invprop = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f31,plain,
breln1invI = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f32,plain,
breln1invE = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f33,plain,
( $true
= ( breln1 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f34,plain,
( sK1
!= ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f37,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f23,f28]) ).
thf(f38,plain,
( ( !! @ $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 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f24,f29]) ).
thf(f39,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f25,f30]) ).
thf(f40,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,[],[f26,f31]) ).
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 @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f27,f32]) ).
thf(f42,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 @ Y3 @ Y2 ) @ ( breln1invset @ Y1 @ Y0 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X1: $i] :
( $true
= ( !! @ $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 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [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 ) ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( $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,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( !! @ $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(imp_proxy_clausification,[],[f45]) ).
thf(f47,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 @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f48,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 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $true
= ( ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) )
=> ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f54,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 ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f55,plain,
! [X1: $i] :
( $true
= ( !! @ $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 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [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 ) ),
inference(pi_proxy_clausification,[],[f55]) ).
thf(f57,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 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f59,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 ) ) ),
inference(pi_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ( in @ X3 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X3 @ Y0 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X3 @ Y0 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X3 @ Y0 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $true
= ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X2 @ X1 ) ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $false )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f64]) ).
thf(f66,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( breln1 @ Y1 @ ( breln1invset @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f67,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( breln1 @ X2 @ X1 )
=> ( breln1 @ X2 @ ( breln1invset @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( breln1 @ X2 @ ( breln1invset @ X2 @ X1 ) ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X1: $i] :
( $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,[],[f38]) ).
thf(f72,plain,
! [X1: $i] :
( $true
= ( !! @ $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 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f73,plain,
! [X2: $i,X1: $i] :
( $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,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( $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,[],[f73]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( !! @ $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(imp_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ^ [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 ) ) ),
inference(pi_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ( 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 ) ) ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $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,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X3 ) ) ) ) )
@ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( ( in @ ( sK2 @ X3 @ X1 @ X2 ) @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK2 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 )
=> ( in @ ( kpair @ ( sK2 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK2 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 )
=> ( in @ ( kpair @ ( sK2 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f81]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK2 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 )
=> ( in @ ( kpair @ ( sK2 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) )
@ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f82]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( kpair @ ( sK2 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) @ X1 )
=> ( in @ ( kpair @ ( sK2 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) @ X3 ) ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( ( in @ ( kpair @ ( sK2 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) @ X1 )
=> ( in @ ( kpair @ ( sK2 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) @ X3 ) ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ ( sK2 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ ( sK2 @ X3 @ X1 @ X2 ) @ ( sK3 @ X3 @ X1 @ X2 ) ) @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( subset @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f90,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f91,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( subset @ X2 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( $true
= ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( ( subset @ X1 @ X2 )
= $false )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( ( subset @ X1 @ X2 )
= $false )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f95]) ).
thf(f120,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) @ X0 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) @ X0 ) )
| ( $false
= ( in @ ( kpair @ ( sK3 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) @ ( sK2 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) ) @ X1 ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( breln1 @ X3 @ X2 ) )
| ( $true
= ( subset @ X2 @ ( breln1invset @ X0 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f65,f88]) ).
thf(f121,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ ( sK3 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) @ ( sK2 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) ) @ X1 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) @ X0 ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ X1 ) @ X2 @ X3 ) @ X0 ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X0 @ X1 ) ) )
| ( $false
= ( breln1 @ X3 @ X2 ) )
| ( $true
= ( subset @ X2 @ ( breln1invset @ X0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f120]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) @ X1 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $true
= ( in @ ( kpair @ ( sK3 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) @ ( sK2 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) ) @ X2 ) )
| ( $false
= ( breln1 @ X3 @ X0 ) )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X1 @ X2 ) ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ X2 ) @ X0 ) ) ),
inference(constrained_superposition,[],[f53,f89]) ).
thf(f130,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ ( sK3 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) @ ( sK2 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) ) @ X2 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ X2 ) @ X3 ) @ X1 ) )
| ( $false
= ( breln1 @ X3 @ X0 ) )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X1 @ X2 ) ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ X2 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f146,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X1 ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X1 ) )
| ( $false
= ( in @ ( kpair @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) ) @ X2 ) )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X0 ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X0 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
| ( $false
= ( breln1 @ X4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) )
| ( $false
= ( breln1 @ X4 @ X3 ) )
| ( $true
= ( subset @ X3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) ) ),
inference(constrained_superposition,[],[f65,f121]) ).
thf(f147,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ ( kpair @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) ) @ X2 ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X1 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X0 ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X3 @ X4 ) @ X0 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
| ( $false
= ( breln1 @ X4 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) )
| ( $false
= ( breln1 @ X4 @ X3 ) )
| ( $true
= ( subset @ X3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f146]) ).
thf(f153,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X2 ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X2 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $true
= ( in @ ( kpair @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) ) @ X3 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X2 @ X3 ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( breln1 @ X4 @ X0 ) )
| ( $false
= ( breln1 @ X4 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X0 ) ) ),
inference(constrained_superposition,[],[f53,f130]) ).
thf(f154,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( kpair @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) ) @ X3 ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X2 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X2 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X2 @ X3 ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X4 ) @ X1 ) )
| ( $false
= ( breln1 @ X4 @ X0 ) )
| ( $false
= ( breln1 @ X4 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f153]) ).
thf(f239,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) )
| ( $false
= ( breln1 @ X3 @ X2 ) )
| ( $true
= ( subset @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X1 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X0 ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X0 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X1 @ X2 ) ) )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) )
| ( $false
= ( breln1 @ X3 @ X2 ) )
| ( $true
= ( subset @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) ) ),
inference(constrained_superposition,[],[f89,f147]) ).
thf(f242,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) )
| ( $false
= ( breln1 @ X3 @ X2 ) )
| ( $true
= ( subset @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X1 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X0 ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X0 ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) ),
inference(duplicate_literal_removal,[],[f239]) ).
thf(f243,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X1 ) )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X0 ) )
| ( $true
= ( subset @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) )
| ( $false
= ( breln1 @ X3 @ X2 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) @ X2 @ X3 ) @ X0 ) )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X1 @ X2 ) ) ) ),
inference(trivial_inequality_removal,[],[f242]) ).
thf(f255,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 ) )
| ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 ) )
| ( $false
= ( breln1 @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false ) ),
inference(equality_factoring,[],[f243]) ).
thf(f256,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 ) )
| ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( $false
= ( breln1 @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false ) ),
inference(duplicate_literal_removal,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 ) )
| ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X2 ) @ X0 ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( $false
= ( breln1 @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f256]) ).
thf(f272,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X0 ) @ X0 ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false ) ),
inference(constrained_superposition,[],[f87,f257]) ).
thf(f273,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X0 ) @ X0 ) )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false ) ),
inference(duplicate_literal_removal,[],[f272]) ).
thf(f274,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 @ X0 ) @ X0 ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f273]) ).
thf(f280,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false ) ),
inference(constrained_superposition,[],[f83,f274]) ).
thf(f281,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false ) ),
inference(duplicate_literal_removal,[],[f280]) ).
thf(f282,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( $false
= ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f281]) ).
thf(f292,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false )
| ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false ) ),
inference(constrained_superposition,[],[f70,f282]) ).
thf(f293,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false )
| ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ X1 )
= $false ) ),
inference(duplicate_literal_removal,[],[f292]) ).
thf(f294,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false )
| ( ( breln1 @ X0 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f293]) ).
thf(f305,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) )
| ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
= X0 )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false
= ( breln1 @ X1 @ X0 ) ) ),
inference(constrained_superposition,[],[f96,f294]) ).
thf(f306,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) )
| ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
= X0 )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false
= ( breln1 @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f305]) ).
thf(f368,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ X3 @ X0 ) )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X0 ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X2 ) )
| ( $false
= ( breln1 @ X2 @ X0 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X2 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X2 @ X0 ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X1 ) )
| ( $false
= ( breln1 @ X3 @ X0 ) )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X0 ) ) ),
inference(constrained_superposition,[],[f88,f154]) ).
thf(f374,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ X3 @ X0 ) )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X0 ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X2 ) )
| ( $false
= ( breln1 @ X2 @ X0 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X2 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X2 @ X0 ) ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X1 ) ) ),
inference(duplicate_literal_removal,[],[f368]) ).
thf(f375,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X2 ) )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X1 ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X0 ) )
| ( $false
= ( breln1 @ X3 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) ) )
| ( $false
= ( breln1 @ X2 @ X0 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X2 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X0 ) ) @ X3 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X2 @ X0 ) ) )
| ( $false
= ( breln1 @ X3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f374]) ).
thf(f388,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) )
| ( $false
= ( breln1 @ X2 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false
= ( breln1 @ X2 @ X0 ) ) ),
inference(equality_factoring,[],[f375]) ).
thf(f389,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) )
| ( $false
= ( breln1 @ X2 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false
= ( breln1 @ X2 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f388]) ).
thf(f390,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) )
| ( $false
= ( breln1 @ X2 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false
= ( breln1 @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f389]) ).
thf(f405,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X1 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ( $false
= ( breln1 @ X1 @ X0 ) ) ),
inference(constrained_superposition,[],[f87,f390]) ).
thf(f406,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X1 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[],[f405]) ).
thf(f407,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK2 @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X1 ) @ X1 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f406]) ).
thf(f413,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f83,f407]) ).
thf(f414,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[],[f413]) ).
thf(f415,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) )
| ( $false
= ( breln1 @ X1 @ X0 ) )
| ( $false
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f414]) ).
thf(f427,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false )
| ( $true
= ( subset @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false ) ),
inference(constrained_superposition,[],[f70,f415]) ).
thf(f428,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false )
| ( $true
= ( subset @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) )
| ( ( breln1 @ X0 @ X1 )
= $false ) ),
inference(duplicate_literal_removal,[],[f427]) ).
thf(f429,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false )
| ( ( breln1 @ X0 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f428]) ).
thf(f446,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false )
| ( ( breln1 @ X0 @ X1 )
= $false ) ),
inference(constrained_superposition,[],[f306,f429]) ).
thf(f447,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false )
| ( ( breln1 @ X0 @ X1 )
= $false ) ),
inference(duplicate_literal_removal,[],[f446]) ).
thf(f448,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false )
| ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 )
| ( ( breln1 @ X0 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f447]) ).
thf(f457,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 )
| ( ( breln1 @ X0 @ X1 )
= $false ) ),
inference(constrained_superposition,[],[f70,f448]) ).
thf(f458,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( breln1 @ X0 @ X1 )
= $false )
| ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 ) ),
inference(duplicate_literal_removal,[],[f457]) ).
thf(f459,plain,
! [X0: $i,X1: $i] :
( ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 )
| ( ( breln1 @ X0 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f458]) ).
thf(f529,plain,
( ( sK1 != sK1 )
| ( ( breln1 @ sK0 @ sK1 )
= $false ) ),
inference(constrained_superposition,[],[f34,f459]) ).
thf(f530,plain,
( ( breln1 @ sK0 @ sK1 )
= $false ),
inference(trivial_inequality_removal,[],[f529]) ).
thf(f571,plain,
$true = $false,
inference(constrained_superposition,[],[f33,f530]) ).
thf(f572,plain,
$false,
inference(trivial_inequality_removal,[],[f571]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n013.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 14:28:21 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.38 % (2196638)Will run a generic schedule for satisfiability detection.
% 0.20/0.38 % (2196643)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1053035481_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.38 % Exception at run slice level
% 0.20/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.38 % (2196644)% WARNING: option uhcvi not known.
% 0.20/0.38 % (2196647)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2465958805:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.38 % (2196647)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.38 % (2196644)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2239239207:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.38 % (2196648)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=275070344:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.38 % (2196644)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.38 % (2196644)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.56/0.38 % (2196645)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2964659725:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.56/0.38 % (2196649)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4109238183:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.56/0.38 % (2196646)dis+10_1_sil=32000:sp=arity:random_seed=3810987803:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.56/0.38 % (2196651)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=378772686:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.56/0.38 % Exception at run slice level
% 0.56/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.56/0.38 % (2196659)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2191382929:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.56/0.38 % (2196647)Instruction limit reached!
% 0.56/0.38 % (2196647)------------------------------
% 0.56/0.38 % (2196647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.38 % (2196647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.38 % (2196647)CaDiCaL version: 2.1.3
% 0.56/0.38 % (2196647)Termination reason: Instruction limit
% 0.56/0.38 % (2196647)Termination phase: Saturation
% 0.56/0.38 % (2196647)Time elapsed: 0.050 s
% 0.56/0.38 % (2196647)Peak memory usage: 12 MB
% 0.56/0.38 % (2196647)Instructions burned: 118 (million)
% 0.56/0.38 % (2196661)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=3286132899:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.56/0.38 % (2196661)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.56/0.38 % (2196661)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.56/0.38 % (2196646)Instruction limit reached!
% 0.56/0.38 % (2196646)------------------------------
% 0.56/0.38 % (2196646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.38 % (2196646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.38 % (2196646)CaDiCaL version: 2.1.3
% 0.56/0.38 % (2196646)Termination reason: Instruction limit
% 0.56/0.38 % (2196646)Termination phase: Saturation
% 0.56/0.38 % (2196646)Time elapsed: 0.085 s
% 0.56/0.38 % (2196646)Peak memory usage: 12 MB
% 0.56/0.38 % (2196646)Instructions burned: 103 (million)
% 0.56/0.38 % (2196659)Instruction limit reached!
% 0.56/0.38 % (2196659)------------------------------
% 0.56/0.38 % (2196659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.38 % (2196659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.38 % (2196659)CaDiCaL version: 2.1.3
% 0.56/0.38 % (2196659)Termination reason: Instruction limit
% 0.56/0.38 % (2196659)Termination phase: Saturation
% 0.56/0.38 % (2196659)Time elapsed: 0.064 s
% 0.56/0.38 % (2196659)Peak memory usage: 12 MB
% 0.56/0.38 % (2196659)Instructions burned: 133 (million)
% 0.56/0.38 % (2196661) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2196638-2196661"...
% 0.56/0.38 % (2196661)...printing done.
% 0.56/0.38 % (2196661)Refutation found. Thanks to Tanya!
% 0.56/0.38 % SZS status Theorem for theBenchmark
% 0.56/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.56/0.38 % (2196661)------------------------------
% 0.56/0.38 % (2196661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.38 % (2196661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.38 % (2196661)CaDiCaL version: 2.1.3
% 0.56/0.38 % (2196661)Termination reason: Refutation
% 0.56/0.38 % (2196661)Time elapsed: 0.040 s
% 0.56/0.38 % (2196661)Peak memory usage: 13 MB
% 0.56/0.38 % (2196661)Instructions burned: 132 (million)
% 0.56/0.38 % (2196638)Success in time 0.16 s
% 0.56/0.38 % Vampire exiting
%------------------------------------------------------------------------------