%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU682^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:22 AM UTC 2026
% Result : Theorem 0.32s 1.36s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 8
% Syntax : Number of formulae : 76 ( 24 unt; 0 typ; 2 def)
% Number of atoms : 1084 ( 255 equ; 0 cnn)
% Maximal formula atoms : 14 ( 14 avg)
% Number of connectives : 1774 ( 60 ~; 166 |; 24 &;1294 @)
% ( 2 <=>; 149 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 17 usr; 10 con; 0-4 aty)
% ( 79 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 327 ( 101 ^; 205 !; 21 ?; 327 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
kpair: $i > $i > $i ).
thf(func_def_3,type,
cartprod: $i > $i > $i ).
thf(func_def_4,type,
breln: $i > $i > $i > $o ).
thf(func_def_7,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_21,type,
sK3: $i > $o ).
thf(func_def_24,type,
sK6: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_25,type,
sK7: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
ph8:
!>[X0: $tType] : X0 ).
thf(f120,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f94,f116,f119]) ).
thf(f119,plain,
~ spl5_4,
inference(avatar_contradiction_clause,[status(thm)],[f118]) ).
thf(f118,plain,
( $false
| ~ spl5_4 ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ( $false = $true )
| ~ spl5_4 ),
inference(backward_demodulation,[status(thm)],[f51,f91]) ).
thf(f91,plain,
( ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f89,definition,
( spl5_4
<=> ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f51,plain,
( $true
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
@ sK2
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[status(thm)],[f21,f23]) ).
thf(f23,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
file('/export/starexec/sandbox/tmp/tmp.PXOoiD20QP/DTF2THF_6243.p',breln) ).
thf(f21,plain,
( $true
= ( breln @ sK2 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true
= ( breln @ sK2 @ sK0 @ sK1 ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK2 ) )
| ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK1 ) )
| ( ( sK3 @ ( kpair @ X4 @ X5 ) )
= $true )
| ( $true
!= ( in @ X5 @ sK0 ) ) ) )
& ( $true
!= ( sK3 @ sK4 ) )
& ( ( in @ sK4 @ sK1 )
= $true )
& ( brelnall1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f12,f15,f14,f13]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X2 @ X0 @ X1 ) )
& ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X2 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
!= $true )
| ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ X5 @ X0 )
!= $true ) ) )
& ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( ( in @ X6 @ X1 )
= $true ) ) ) )
=> ( ( $true
= ( breln @ sK2 @ sK0 @ sK1 ) )
& ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK2 ) )
| ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK1 ) )
| ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X5 @ sK0 ) ) ) )
& ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( $true
= ( in @ X6 @ sK1 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK2 ) )
| ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK1 ) )
| ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X5 @ sK0 ) ) ) )
& ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( $true
= ( in @ X6 @ sK1 ) ) ) )
=> ( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK2 ) )
| ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK1 ) )
| ( ( sK3 @ ( kpair @ X4 @ X5 ) )
= $true )
| ( $true
!= ( in @ X5 @ sK0 ) ) ) )
& ? [X6: $i] :
( ( $true
!= ( sK3 @ X6 ) )
& ( $true
= ( in @ X6 @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X6: $i] :
( ( $true
!= ( sK3 @ X6 ) )
& ( $true
= ( in @ X6 @ sK1 ) ) )
=> ( ( $true
!= ( sK3 @ sK4 ) )
& ( ( in @ sK4 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X2 @ X0 @ X1 ) )
& ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X2 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
!= $true )
| ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ X5 @ X0 )
!= $true ) ) )
& ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( ( in @ X6 @ X1 )
= $true ) ) ) )
& ( brelnall1 = $true ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i > $o] :
( ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( ( in @ X6 @ X1 )
= $true ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
!= $true )
| ( ( in @ X5 @ X0 )
!= $true ) )
| ( $true
!= ( in @ X4 @ X2 ) ) ) )
& ( $true
= ( breln @ X2 @ X0 @ X1 ) ) )
& ( brelnall1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( brelnall1 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X2 @ X0 @ X1 ) )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
=> ! [X5: $i] :
( ( ( in @ X5 @ X0 )
= $true )
=> ( ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
= $true )
=> ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) ) )
=> ! [X6: $i] :
( ( ( in @ X6 @ X1 )
= $true )
=> ( $true
= ( X3 @ X6 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( brelnall1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X2 @ X0 @ X1 )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
=> ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X3 @ X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( brelnall1
=> ! [X1: $i,X3: $i,X0: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ! [X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( X4 @ ( kpair @ X5 @ X6 ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( brelnall1
=> ! [X1: $i,X3: $i,X0: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ! [X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( X4 @ ( kpair @ X5 @ X6 ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PXOoiD20QP/DTF2THF_6243.p',brelnall2) ).
thf(f116,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[status(thm)],[f115]) ).
thf(f115,plain,
( $false
| ~ spl5_3 ),
inference(trivial_inequality_removal,[status(thm)],[f114]) ).
thf(f114,plain,
( ( $true != $true )
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f19,f105]) ).
thf(f105,plain,
( ( $true
= ( sK3 @ sK4 ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
( ( $false = $true )
| ( $true
= ( sK3 @ sK4 ) )
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f18,f86]) ).
thf(f86,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f85]) ).
thf(f85,definition,
( spl5_3
<=> ! [X0: $i] :
( ( $true
= ( sK3 @ X0 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f18,plain,
( ( in @ sK4 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f19,plain,
( $true
!= ( sK3 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f94,plain,
( spl5_3
| spl5_3
| spl5_3
| spl5_3
| spl5_4 ),
inference(avatar_split_clause,[status(thm)],[f72,f89,f85,f85,f85,f85]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( sK3 @ X3 )
= $true )
| ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) )
| ( $true
= ( sK3 @ X0 ) )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $true
= ( sK3 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ X3 @ sK1 ) )
| ( $true
= ( sK3 @ X1 ) )
| ( $false = $true )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $true
= ( sK3 @ X0 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( sK3 @ X3 )
= $true )
| ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) ) ),
inference(superposition,[status(thm)],[f65,f49]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( X4 @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ ( sK7 @ X1 @ X2 @ X3 @ X4 ) ) ) )
| ( ( X4 @ X5 )
= $true )
| ( ( in @ X5 @ X3 )
= $false )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X5 @ X3 )
= $false )
| ( $false
= ( ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ ( sK7 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
=> ( X4 @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ ( sK7 @ X1 @ X2 @ X3 @ X4 ) ) ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) )
| ( ( X4 @ X5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X5 )
= $true )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) )
| ( ( in @ X5 @ X3 )
= $false )
| ( $false
= ( ( in @ ( sK7 @ X1 @ X2 @ X3 @ X4 ) @ X1 )
=> ( ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ ( sK7 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
=> ( X4 @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ ( sK7 @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X5 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X3 )
=> ( X4 @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) ) ) )
@ ( sK7 @ X1 @ X2 @ X3 @ X4 ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) )
| ( ( in @ X5 @ X3 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X3 )
=> ( X4 @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) ) ) ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) )
| ( ( in @ X5 @ X3 )
= $false )
| ( ( X4 @ X5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X3 )
=> ( X4 @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) )
| ( $false
= ( ( in @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X3 )
=> ( X4 @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( X4 @ ( kpair @ Y0 @ Y1 ) ) ) ) ) )
@ ( sK6 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $true
= ( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( X4 @ ( kpair @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) )
| ( $true
= ( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X4 @ Y0 ) )
@ X5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( X4 @ ( kpair @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) ) ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X4 @ Y0 ) ) )
= $true )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( X4 @ ( kpair @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( X4 @ ( kpair @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( X4 @ Y0 ) ) ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o] :
( ( $true
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X3 )
=> ( Y0 @ ( kpair @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( Y0 @ Y1 ) ) ) )
@ X4 ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) ) ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) )
| ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X3 )
=> ( Y0 @ ( kpair @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X3 @ ( cartprod @ X2 @ X1 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X3 )
=> ( Y0 @ ( kpair @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X2 @ X1 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( Y1 @ ( kpair @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X2 @ X1 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( Y1 @ ( kpair @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ Y0 @ X1 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ X1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( Y2 @ ( kpair @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( Y2 @ Y3 ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ Y0 @ X1 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ X1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( Y2 @ ( kpair @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( Y3 @ ( kpair @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( Y3 @ Y4 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
=> ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( Y3 @ ( kpair @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( Y3 @ Y4 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y1
@ Y0
@ Y2 )
=> ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( Y3 @ ( kpair @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f22,f17,f23]) ).
thf(f17,plain,
brelnall1 = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f22,plain,
( brelnall1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( breln @ Y1 @ Y0 @ Y2 )
=> ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( Y3 @ ( kpair @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( brelnall1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( breln @ Y1 @ Y0 @ Y2 )
=> ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( Y3 @ ( kpair @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( brelnall1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X1 @ X2 @ X0 )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X0 )
=> ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( X3 @ X6 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( brelnall1
= ( ! [X3: $i,X0: $i,X1: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ! [X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( X4 @ ( kpair @ X5 @ X6 ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PXOoiD20QP/DTF2THF_6243.p',brelnall1) ).
thf(f65,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( sK3 @ ( kpair @ ( sK6 @ sK1 @ sK0 @ X0 @ sK2 ) @ ( sK7 @ sK0 @ sK2 @ sK1 @ X0 ) ) ) )
| ( $true
= ( X0 @ X2 ) )
| ( $true
= ( X0 @ X3 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $true
= ( X0 @ X1 ) )
| ( $false
= ( in @ X3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false = $true )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $true
= ( X0 @ X2 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $true
= ( X0 @ X1 ) )
| ( $true
= ( X0 @ X3 ) )
| ( $true
= ( sK3 @ ( kpair @ ( sK6 @ sK1 @ sK0 @ X0 @ sK2 ) @ ( sK7 @ sK0 @ sK2 @ sK1 @ X0 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f63,f51]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) )
| ( $true
= ( X0 @ X3 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $true
= ( sK3 @ ( kpair @ ( sK6 @ sK1 @ sK0 @ X0 @ sK2 ) @ ( sK7 @ sK0 @ sK2 @ sK1 @ X0 ) ) ) )
| ( $true
= ( X0 @ X1 ) )
| ( $true
= ( X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( in @ X1 @ sK1 ) )
| ( $true
= ( X0 @ X2 ) )
| ( $true
= ( X0 @ X3 ) )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $true != $true )
| ( $true
= ( sK3 @ ( kpair @ ( sK6 @ sK1 @ sK0 @ X0 @ sK2 ) @ ( sK7 @ sK0 @ sK2 @ sK1 @ X0 ) ) ) )
| ( $true
= ( X0 @ X1 ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( X0 @ X2 ) )
| ( $true
= ( X0 @ X1 ) )
| ( $true
= ( X0 @ X3 ) )
| ( $true != $true )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $true
= ( sK3 @ ( kpair @ ( sK6 @ sK1 @ sK0 @ X0 @ sK2 ) @ ( sK7 @ sK0 @ sK2 @ sK1 @ X0 ) ) ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) ) ),
inference(superposition,[status(thm)],[f60,f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( ( in @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ X2 )
= $true )
| ( ( X4 @ X5 )
= $true )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) )
| ( ( in @ X5 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( ( in @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ X2 )
= $true )
| ( $true
= ( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( $true
!= ( in @ ( sK6 @ sK1 @ sK0 @ X1 @ X0 ) @ sK2 ) )
| ( ( sK3 @ ( kpair @ ( sK6 @ sK1 @ sK0 @ X1 @ X0 ) @ ( sK7 @ sK0 @ X0 @ sK1 @ X1 ) ) )
= $true )
| ( $true
= ( X1 @ X3 ) )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ X0 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( $true
= ( X1 @ X2 ) )
| ( $true
= ( X1 @ X3 ) )
| ( $true != $true )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $true
!= ( in @ ( sK6 @ sK1 @ sK0 @ X1 @ X0 ) @ sK2 ) )
| ( ( sK3 @ ( kpair @ ( sK6 @ sK1 @ sK0 @ X1 @ X0 ) @ ( sK7 @ sK0 @ X0 @ sK1 @ X1 ) ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( ( sK3 @ ( kpair @ ( sK6 @ sK1 @ sK0 @ X1 @ X0 ) @ ( sK7 @ sK0 @ X0 @ sK1 @ X1 ) ) )
= $true )
| ( $true
!= ( in @ ( sK6 @ sK1 @ sK0 @ X1 @ X0 ) @ sK2 ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $true != $true )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $false
= ( in @ X2 @ sK1 ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $true
= ( X1 @ X3 ) )
| ( $true
= ( X1 @ X2 ) ) ),
inference(superposition,[status(thm)],[f57,f48]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( in @ ( sK7 @ X1 @ X2 @ X3 @ X4 ) @ X1 ) )
| ( ( X4 @ X5 )
= $true )
| ( ( in @ X5 @ X3 )
= $false )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( $true
!= ( in @ ( sK7 @ X0 @ X2 @ sK1 @ X1 ) @ sK0 ) )
| ( $true
= ( X1 @ X3 ) )
| ( ( subset @ sK1 @ ( cartprod @ X2 @ X0 ) )
= $false )
| ( $true
= ( sK3 @ ( kpair @ ( sK6 @ sK1 @ X0 @ X1 @ X2 ) @ ( sK7 @ X0 @ X2 @ sK1 @ X1 ) ) ) )
| ( ( in @ ( sK6 @ sK1 @ X0 @ X1 @ X2 ) @ sK2 )
!= $true )
| ( $false
= ( in @ X3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( ( in @ ( sK6 @ sK1 @ X0 @ X1 @ X2 ) @ sK2 )
!= $true )
| ( $false
= ( in @ X3 @ sK1 ) )
| ( $true
= ( sK3 @ ( kpair @ ( sK6 @ sK1 @ X0 @ X1 @ X2 ) @ ( sK7 @ X0 @ X2 @ sK1 @ X1 ) ) ) )
| ( $true
!= ( in @ ( sK7 @ X0 @ X2 @ sK1 @ X1 ) @ sK0 ) )
| ( $true
= ( X1 @ X3 ) )
| ( ( subset @ sK1 @ ( cartprod @ X2 @ X0 ) )
= $false )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f20,f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( in @ ( kpair @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ ( sK7 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 ) )
| ( ( X4 @ X5 )
= $true )
| ( ( in @ X5 @ X3 )
= $false )
| ( $false
= ( subset @ X3 @ ( cartprod @ X2 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f20,plain,
! [X4: $i,X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK1 ) )
| ( ( sK3 @ ( kpair @ X4 @ X5 ) )
= $true )
| ( $true
!= ( in @ X5 @ sK0 ) )
| ( $true
!= ( in @ X4 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEU682^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n015.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Feb 24 12:30:31 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SEU682^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.47 % Domain : Set Theory
% 0.31/0.47 % Problem : Functions - Extensionality and Beta Reduction
% 0.31/0.47 % Version : Especial > Reduced > Especial.
% 0.31/0.47 % English : (! A:i.! B:i.! R:i.breln A B R -> (! phi:i>o.(! x:i.in x A ->
% 0.31/0.47 % (! y:i.in y B -> in (kpair x y) R -> phi (kpair x y))) ->
% 0.31/0.47 % (! x:i.in x R -> phi x)))
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.47 % Source : [Bro08]
% 0.31/0.47 % Names : ZFC184l [Bro08]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.31/0.47 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.31/0.47 % Number of atoms : 16 ( 2 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 6 ( 5 avg)
% 0.31/0.47 % Number of connectives : 51 ( 0 ~; 0 |; 0 &; 38 @)
% 0.31/0.47 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 17 ( 6 avg)
% 0.31/0.47 % Number of types : 2 ( 0 usr)
% 0.31/0.47 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 7 ( 6 usr; 1 con; 0-3 aty)
% 0.31/0.47 % Number of variables : 17 ( 3 ^; 14 !; 0 ?; 17 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : http://mathgate.info/detsetitem.php?id=377
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(in_type,type,
% 0.31/0.47 in: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(subset_type,type,
% 0.31/0.47 subset: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(kpair_type,type,
% 0.31/0.47 kpair: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(cartprod_type,type,
% 0.31/0.47 cartprod: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(breln_type,type,
% 0.31/0.47 breln: $i > $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(breln,definition,
% 0.31/0.47 ( breln
% 0.31/0.47 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(brelnall1_type,type,
% 0.31/0.47 brelnall1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(brelnall1,definition,
% 0.31/0.47 ( brelnall1
% 0.31/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.31/0.47 ( ( breln @ A @ B @ R )
% 0.31/0.47 => ! [Xphi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ R )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(brelnall2,conjecture,
% 0.31/0.47 ( brelnall1
% 0.31/0.47 => ! [A: $i,B: $i,R: $i] :
% 0.31/0.47 ( ( breln @ A @ B @ R )
% 0.31/0.47 => ! [Xphi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ R )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 0.32/1.30 ---- Embedded in THF ---
% 0.32/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.30 %%% Generated on Tue Feb 24 12:30:32 EST 2026
% 0.32/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.30 %%% Logic specification used:
% 0.32/1.30 %%% thf(spec, logic, $$dhol).
% 0.32/1.30
% 0.32/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.PXOoiD20QP/DTF2DTF6243.p
% See solution above
% 0.32/1.30 ------------------------
% 0.32/1.31 ---- Cleaned THF ---
% 0.32/1.32 thf(in_type,type,
% 0.32/1.32 in: $i > $i > $o ).
% 0.32/1.32
% 0.32/1.32 thf(subset_type,type,
% 0.32/1.32 subset: $i > $i > $o ).
% 0.32/1.32
% 0.32/1.32 thf(kpair_type,type,
% 0.32/1.32 kpair: $i > $i > $i ).
% 0.32/1.32
% 0.32/1.32 thf(cartprod_type,type,
% 0.32/1.32 cartprod: $i > $i > $i ).
% 0.32/1.32
% 0.32/1.32 thf(breln_type,type,
% 0.32/1.32 breln: $i > $i > $i > $o ).
% 0.32/1.32
% 0.32/1.32 thf(breln,definition,
% 0.32/1.32 ( breln
% 0.32/1.32 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.32/1.32
% 0.32/1.32 thf(brelnall1_type,type,
% 0.32/1.32 brelnall1: $o ).
% 0.32/1.32
% 0.32/1.32 thf(brelnall1,definition,
% 0.32/1.32 ( brelnall1
% 0.32/1.32 = ( ! [A: $i,B: $i,R: $i] :
% 0.32/1.32 ( ( breln @ A @ B @ R )
% 0.32/1.32 => ! [Xphi: $i > $o] :
% 0.32/1.32 ( ! [Xx: $i] :
% 0.32/1.32 ( ( in @ Xx @ A )
% 0.32/1.32 => ! [Xy: $i] :
% 0.32/1.32 ( ( in @ Xy @ B )
% 0.32/1.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/1.32 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.32/1.32 => ! [Xx: $i] :
% 0.32/1.32 ( ( in @ Xx @ R )
% 0.32/1.32 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/1.32
% 0.32/1.32 thf(brelnall2,conjecture,
% 0.32/1.32 ( brelnall1
% 0.32/1.32 => ! [A: $i,B: $i,R: $i] :
% 0.32/1.32 ( ( breln @ A @ B @ R )
% 0.32/1.32 => ! [Xphi: $i > $o] :
% 0.32/1.32 ( ! [Xx: $i] :
% 0.32/1.32 ( ( in @ Xx @ A )
% 0.32/1.32 => ! [Xy: $i] :
% 0.32/1.32 ( ( in @ Xy @ B )
% 0.32/1.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/1.32 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.32/1.32 => ! [Xx: $i] :
% 0.32/1.32 ( ( in @ Xx @ R )
% 0.32/1.32 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.32 ------------------------
% 0.32/1.33 % (6434)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6243 for (2999ds/183Mi)
% 0.32/1.34 % (6437)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6243 for (2999ds/2Mi)
% 0.32/1.34 % (6437)Instruction limit reached!
% 0.32/1.34 % (6437)------------------------------
% 0.32/1.34 % (6437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.34 % (6437)Termination reason: Unknown
% 0.32/1.34 % (6437)Termination phase: Property scanning
% 0.32/1.34
% 0.32/1.34 % (6437)Memory used [KB]: 895
% 0.32/1.34 % (6437)Time elapsed: 0.003 s
% 0.32/1.34 % (6437)Instructions burned: 2 (million)
% 0.32/1.34 % (6437)------------------------------
% 0.32/1.34 % (6437)------------------------------
% 0.32/1.34 % (6438)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_6243 for (2999ds/2Mi)
% 0.32/1.34 % (6436)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_6243 for (2999ds/27Mi)
% 0.32/1.34 % (6435)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_6243 for (2999ds/4Mi)
% 0.32/1.34 % (6438)Instruction limit reached!
% 0.32/1.34 % (6438)------------------------------
% 0.32/1.34 % (6438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.34 % (6438)Termination reason: Unknown
% 0.32/1.34 % (6438)Termination phase: Function definition elimination
% 0.32/1.34
% 0.32/1.34 % (6438)Memory used [KB]: 1023
% 0.32/1.34 % (6438)Time elapsed: 0.003 s
% 0.32/1.34 % (6438)Instructions burned: 3 (million)
% 0.32/1.34 % (6438)------------------------------
% 0.32/1.34 % (6438)------------------------------
% 0.32/1.34 % (6440)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6243 for (2999ds/18Mi)
% 0.32/1.34 % (6435)Instruction limit reached!
% 0.32/1.34 % (6435)------------------------------
% 0.32/1.34 % (6435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.34 % (6435)Termination reason: Unknown
% 0.32/1.34 % (6435)Termination phase: Saturation
% 0.32/1.34
% 0.32/1.34 % (6435)Memory used [KB]: 5500
% 0.32/1.34 % (6435)Time elapsed: 0.005 s
% 0.32/1.34 % (6435)Instructions burned: 5 (million)
% 0.32/1.34 % (6435)------------------------------
% 0.32/1.34 % (6435)------------------------------
% 0.32/1.35 % (6442)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_6243 for (2999ds/37Mi)
% 0.32/1.35 % (6439)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_6243 for (2999ds/275Mi)
% 0.32/1.35 % (6440)Instruction limit reached!
% 0.32/1.35 % (6440)------------------------------
% 0.32/1.35 % (6440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.35 % (6440)Termination reason: Unknown
% 0.32/1.35 % (6440)Termination phase: Saturation
% 0.32/1.35
% 0.32/1.35 % (6440)Memory used [KB]: 5628
% 0.32/1.35 % (6440)Time elapsed: 0.014 s
% 0.32/1.35 % (6440)Instructions burned: 18 (million)
% 0.32/1.35 % (6440)------------------------------
% 0.32/1.35 % (6440)------------------------------
% 0.32/1.35 % (6436)First to succeed.
% 0.32/1.35 % (6441)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6243 for (2999ds/3Mi)
% 0.32/1.36 % (6441)Instruction limit reached!
% 0.32/1.36 % (6441)------------------------------
% 0.32/1.36 % (6441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.36 % (6441)Termination reason: Unknown
% 0.32/1.36 % (6441)Termination phase: Saturation
% 0.32/1.36
% 0.32/1.36 % (6441)Memory used [KB]: 5500
% 0.32/1.36 % (6441)Time elapsed: 0.003 s
% 0.32/1.36 % (6441)Instructions burned: 3 (million)
% 0.32/1.36 % (6441)------------------------------
% 0.32/1.36 % (6441)------------------------------
% 0.32/1.36 % (6436)Refutation found. Thanks to Tanya!
% 0.32/1.36 % SZS status Theorem for DTF2THF_6243
% 0.32/1.36 % SZS output start Proof for DTF2THF_6243
% 0.32/1.36 thf(func_def_0, type, in: $i > $i > $o).
% 0.32/1.36 thf(func_def_1, type, subset: $i > $i > $o).
% 0.32/1.36 thf(func_def_2, type, kpair: $i > $i > $i).
% 0.32/1.36 thf(func_def_3, type, cartprod: $i > $i > $i).
% 0.32/1.36 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 0.32/1.36 thf(func_def_7, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.32/1.36 thf(func_def_21, type, sK3: $i > $o).
% 0.32/1.36 thf(func_def_24, type, sK6: $i > $i > ($i > $o) > $i > $i).
% 0.32/1.36 thf(func_def_25, type, sK7: $i > $i > $i > ($i > $o) > $i).
% 0.32/1.36 thf(func_def_26, type, ph8: !>[X0: $tType]:(X0)).
% 0.32/1.36 thf(f120,plain,(
% 0.32/1.36 $false),
% 0.32/1.36 inference(avatar_sat_refutation,[status(thm)],[f94,f116,f119])).
% 0.32/1.36 thf(f119,plain,(
% 0.32/1.36 ~spl5_4),
% 0.32/1.36 inference(avatar_contradiction_clause,[status(thm)],[f118])).
% 0.32/1.36 thf(f118,plain,(
% 0.32/1.36 $false | ~spl5_4),
% 0.32/1.36 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 0.32/1.36 thf(f117,plain,(
% 0.32/1.36 ($false = $true) | ~spl5_4),
% 0.32/1.36 inference(backward_demodulation,[status(thm)],[f51,f91])).
% 0.32/1.36 thf(f91,plain,(
% 0.32/1.36 ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0))) | ~spl5_4),
% 0.32/1.36 inference(avatar_component_clause,[status(thm)],[f89])).
% 0.32/1.36 thf(f89,definition,(
% 0.32/1.36 spl5_4 <=> ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0)))),
% 0.32/1.36 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 0.32/1.36 thf(f51,plain,(
% 0.32/1.36 ($true = (subset @ sK1 @ (cartprod @ sK2 @ sK0)))),
% 0.32/1.36 inference(beta_eta_normalization,[status(thm)],[f24])).
% 0.32/1.36 thf(f24,plain,(
% 0.32/1.36 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ sK2 @ sK0 @ sK1))),
% 0.32/1.36 inference(definition_unfolding,[status(thm)],[f21,f23])).
% 0.32/1.36 thf(f23,plain,(
% 0.32/1.36 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.32/1.36 inference(cnf_transformation,[status(thm)],[f10])).
% 0.32/1.36 thf(f10,plain,(
% 0.32/1.36 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.32/1.36 inference(fool_elimination,[status(thm)],[f1])).
% 0.32/1.36 thf(f1,axiom,(
% 0.32/1.36 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 0.32/1.36 file('/export/starexec/sandbox/tmp/tmp.PXOoiD20QP/DTF2THF_6243.p',breln)).
% 0.32/1.36 thf(f21,plain,(
% 0.32/1.36 ($true = (breln @ sK2 @ sK0 @ sK1))),
% 0.32/1.36 inference(cnf_transformation,[status(thm)],[f16])).
% 0.32/1.36 thf(f16,plain,(
% 0.32/1.36 (($true = (breln @ sK2 @ sK0 @ sK1)) & (! [X4 : $i] : (($true != (in @ X4 @ sK2)) | ! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ sK1)) | ((sK3 @ (kpair @ X4 @ X5)) = $true) | ($true != (in @ X5 @ sK0)))) & (($true != (sK3 @ sK4)) & ((in @ sK4 @ sK1) = $true)))) & (brelnall1 = $true)),
% 0.32/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f12,f15,f14,f13])).
% 0.32/1.36 thf(f13,plain,(
% 0.32/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X2 @ X0 @ X1)) & ? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ X2)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ X1) != $true) | ($true = (X3 @ (kpair @ X4 @ X5))) | ((in @ X5 @ X0) != $true))) & ? [X6 : $i] : (($true != (X3 @ X6)) & ((in @ X6 @ X1) = $true)))) => (($true = (breln @ sK2 @ sK0 @ sK1)) & ? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ sK2)) | ! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ sK1)) | ($true = (X3 @ (kpair @ X4 @ X5))) | ($true != (in @ X5 @ sK0)))) & ? [X6 : $i] : (($true != (X3 @ X6)) & ($true = (in @ X6 @ sK1)))))),
% 0.32/1.36 introduced(definition,[],[choice_axiom])).
% 0.32/1.36 thf(f14,plain,(
% 0.32/1.36 ? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ sK2)) | ! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ sK1)) | ($true = (X3 @ (kpair @ X4 @ X5))) | ($true != (in @ X5 @ sK0)))) & ? [X6 : $i] : (($true != (X3 @ X6)) & ($true = (in @ X6 @ sK1)))) => (! [X4 : $i] : (($true != (in @ X4 @ sK2)) | ! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ sK1)) | ((sK3 @ (kpair @ X4 @ X5)) = $true) | ($true != (in @ X5 @ sK0)))) & ? [X6 : $i] : (($true != (sK3 @ X6)) & ($true = (in @ X6 @ sK1))))),
% 0.32/1.36 introduced(definition,[],[choice_axiom])).
% 0.32/1.36 thf(f15,plain,(
% 0.32/1.36 ? [X6 : $i] : (($true != (sK3 @ X6)) & ($true = (in @ X6 @ sK1))) => (($true != (sK3 @ sK4)) & ((in @ sK4 @ sK1) = $true))),
% 0.32/1.36 introduced(definition,[],[choice_axiom])).
% 0.32/1.36 thf(f12,plain,(
% 0.32/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X2 @ X0 @ X1)) & ? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ X2)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ X1) != $true) | ($true = (X3 @ (kpair @ X4 @ X5))) | ((in @ X5 @ X0) != $true))) & ? [X6 : $i] : (($true != (X3 @ X6)) & ((in @ X6 @ X1) = $true)))) & (brelnall1 = $true)),
% 0.32/1.36 inference(flattening,[status(thm)],[f11])).
% 0.32/1.36 thf(f11,plain,(
% 0.32/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i > $o] : (? [X6 : $i] : (($true != (X3 @ X6)) & ((in @ X6 @ X1) = $true)) & ! [X4 : $i] : (! [X5 : $i] : ((($true = (X3 @ (kpair @ X4 @ X5))) | ((in @ (kpair @ X4 @ X5) @ X1) != $true)) | ((in @ X5 @ X0) != $true)) | ($true != (in @ X4 @ X2)))) & ($true = (breln @ X2 @ X0 @ X1))) & (brelnall1 = $true)),
% 0.32/1.36 inference(ennf_transformation,[status(thm)],[f9])).
% 0.32/1.36 thf(f9,plain,(
% 0.32/1.36 ~((brelnall1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X2 @ X0 @ X1)) => ! [X3 : $i > $o] : (! [X4 : $i] : (($true = (in @ X4 @ X2)) => ! [X5 : $i] : (((in @ X5 @ X0) = $true) => (((in @ (kpair @ X4 @ X5) @ X1) = $true) => ($true = (X3 @ (kpair @ X4 @ X5)))))) => ! [X6 : $i] : (((in @ X6 @ X1) = $true) => ($true = (X3 @ X6))))))),
% 0.32/1.36 inference(fool_elimination,[status(thm)],[f8])).
% 0.32/1.36 thf(f8,plain,(
% 0.32/1.36 ~(brelnall1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X2 @ X0 @ X1) => ! [X3 : $i > $o] : (! [X4 : $i] : ((in @ X4 @ X2) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X1) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X1) => (X3 @ X6)))))),
% 0.32/1.36 inference(rectify,[status(thm)],[f4])).
% 0.32/1.36 thf(f4,negated_conjecture,(
% 0.32/1.36 ~(brelnall1 => ! [X1 : $i,X3 : $i,X0 : $i] : ((breln @ X0 @ X1 @ X3) => ! [X4 : $i > $o] : (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X5 @ X6) @ X3) => (X4 @ (kpair @ X5 @ X6))))) => ! [X5 : $i] : ((in @ X5 @ X3) => (X4 @ X5)))))),
% 0.32/1.36 inference(negated_conjecture,[status(cth)],[f3])).
% 0.32/1.36 thf(f3,conjecture,(
% 0.32/1.36 brelnall1 => ! [X1 : $i,X3 : $i,X0 : $i] : ((breln @ X0 @ X1 @ X3) => ! [X4 : $i > $o] : (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X5 @ X6) @ X3) => (X4 @ (kpair @ X5 @ X6))))) => ! [X5 : $i] : ((in @ X5 @ X3) => (X4 @ X5))))),
% 0.32/1.36 file('/export/starexec/sandbox/tmp/tmp.PXOoiD20QP/DTF2THF_6243.p',brelnall2)).
% 0.32/1.36 thf(f116,plain,(
% 0.32/1.36 ~spl5_3),
% 0.32/1.36 inference(avatar_contradiction_clause,[status(thm)],[f115])).
% 0.32/1.36 thf(f115,plain,(
% 0.32/1.36 $false | ~spl5_3),
% 0.32/1.36 inference(trivial_inequality_removal,[status(thm)],[f114])).
% 0.32/1.36 thf(f114,plain,(
% 0.32/1.36 ($true != $true) | ~spl5_3),
% 0.32/1.36 inference(superposition,[status(thm)],[f19,f105])).
% 0.32/1.36 thf(f105,plain,(
% 0.32/1.36 ($true = (sK3 @ sK4)) | ~spl5_3),
% 0.32/1.36 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 0.32/1.36 thf(f100,plain,(
% 0.32/1.36 ($false = $true) | ($true = (sK3 @ sK4)) | ~spl5_3),
% 0.32/1.36 inference(superposition,[status(thm)],[f18,f86])).
% 0.32/1.36 thf(f86,plain,(
% 0.32/1.36 ( ! [X0 : $i] : (($false = (in @ X0 @ sK1)) | ($true = (sK3 @ X0))) ) | ~spl5_3),
% 0.32/1.36 inference(avatar_component_clause,[status(thm)],[f85])).
% 0.32/1.36 thf(f85,definition,(
% 0.32/1.36 spl5_3 <=> ! [X0 : $i] : (($true = (sK3 @ X0)) | ($false = (in @ X0 @ sK1)))),
% 0.32/1.36 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 0.32/1.36 thf(f18,plain,(
% 0.32/1.36 ((in @ sK4 @ sK1) = $true)),
% 0.32/1.36 inference(cnf_transformation,[status(thm)],[f16])).
% 0.32/1.36 thf(f19,plain,(
% 0.32/1.36 ($true != (sK3 @ sK4))),
% 0.32/1.36 inference(cnf_transformation,[status(thm)],[f16])).
% 0.32/1.36 thf(f94,plain,(
% 0.32/1.36 spl5_3 | spl5_3 | spl5_3 | spl5_3 | spl5_4),
% 0.32/1.36 inference(avatar_split_clause,[status(thm)],[f72,f89,f85,f85,f85,f85])).
% 0.32/1.36 thf(f72,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((sK3 @ X3) = $true) | ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0))) | ($true = (sK3 @ X0)) | ($false = (in @ X2 @ sK1)) | ($true = (sK3 @ X2)) | ($false = (in @ X1 @ sK1)) | ($false = (in @ X3 @ sK1)) | ($false = (in @ X0 @ sK1)) | ($true = (sK3 @ X1))) )),
% 0.32/1.36 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 0.32/1.36 thf(f66,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = (in @ X3 @ sK1)) | ($true = (sK3 @ X1)) | ($false = $true) | ($false = (in @ X2 @ sK1)) | ($true = (sK3 @ X0)) | ($false = (in @ X1 @ sK1)) | ($false = (in @ X0 @ sK1)) | ($true = (sK3 @ X2)) | ((sK3 @ X3) = $true) | ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0)))) )),
% 0.32/1.36 inference(superposition,[status(thm)],[f65,f49])).
% 0.32/1.36 thf(f49,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ (sK7 @ X1 @ X2 @ X3 @ X4)))) | ((X4 @ X5) = $true) | ((in @ X5 @ X3) = $false) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1)))) )),
% 0.32/1.36 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 0.32/1.36 thf(f47,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((in @ X5 @ X3) = $false) | ($false = ((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ (sK7 @ X1 @ X2 @ X3 @ X4)) @ X3) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ (sK7 @ X1 @ X2 @ X3 @ X4))))) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1))) | ((X4 @ X5) = $true)) )),
% 0.32/1.36 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 0.32/1.36 thf(f46,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((X4 @ X5) = $true) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1))) | ((in @ X5 @ X3) = $false) | ($false = ((in @ (sK7 @ X1 @ X2 @ X3 @ X4) @ X1) => ((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ (sK7 @ X1 @ X2 @ X3 @ X4)) @ X3) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ (sK7 @ X1 @ X2 @ X3 @ X4))))))) )),
% 0.32/1.36 inference(beta_eta_normalization,[status(thm)],[f45])).
% 0.32/1.36 thf(f45,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((X4 @ X5) = $true) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0))))) @ (sK7 @ X1 @ X2 @ X3 @ X4))) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1))) | ((in @ X5 @ X3) = $false)) )),
% 0.32/1.36 inference(sigma_clausification,[status(thm)],[f44])).
% 0.32/1.36 thf(f44,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0))))))) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1))) | ((in @ X5 @ X3) = $false) | ((X4 @ X5) = $true)) )),
% 0.32/1.36 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 0.32/1.36 thf(f41,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($true = ((in @ X5 @ X3) => (X4 @ X5))) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0)))))))) )),
% 0.32/1.36 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 0.32/1.36 thf(f40,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (subset @ X3 @ (cartprod @ X2 @ X1))) | ($false = ((in @ (sK6 @ X3 @ X1 @ X4 @ X2) @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0)))))))) | ($true = ((in @ X5 @ X3) => (X4 @ X5)))) )),
% 0.32/1.36 inference(beta_eta_normalization,[status(thm)],[f39])).
% 0.32/1.36 thf(f39,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (subset @ X3 @ (cartprod @ X2 @ X1))) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1)))))))) @ (sK6 @ X3 @ X1 @ X4 @ X2))) | ($true = ((in @ X5 @ X3) => (X4 @ X5)))) )),
% 0.32/1.36 inference(sigma_clausification,[status(thm)],[f38])).
% 0.32/1.36 thf(f38,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1)))))))))) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1))) | ($true = ((in @ X5 @ X3) => (X4 @ X5)))) )),
% 0.32/1.36 inference(beta_eta_normalization,[status(thm)],[f37])).
% 0.32/1.36 thf(f37,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X3) => (X4 @ Y0))) @ X5)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1)))))))))) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1)))) )),
% 0.32/1.36 inference(pi_clausification,[status(thm)],[f36])).
% 0.32/1.36 thf(f36,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (X4 @ Y0)))) = $true) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1))))))))))) )),
% 0.32/1.36 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 0.32/1.36 thf(f35,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (X4 @ Y0)))))) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1)))) )),
% 0.32/1.36 inference(beta_eta_normalization,[status(thm)],[f34])).
% 0.32/1.36 thf(f34,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (($true = ((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ (kpair @ Y1 @ Y2) @ X3) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (Y0 @ Y1)))))) @ X4)) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1)))) )),
% 0.32/1.36 inference(pi_clausification,[status(thm)],[f33])).
% 0.32/1.36 thf(f33,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (subset @ X3 @ (cartprod @ X2 @ X1))) | ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ (kpair @ Y1 @ Y2) @ X3) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (Y0 @ Y1))))))))) )),
% 0.32/1.36 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 0.32/1.36 thf(f32,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X3 @ (cartprod @ X2 @ X1)) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ (kpair @ Y1 @ Y2) @ X3) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (Y0 @ Y1)))))))))) )),
% 0.32/1.36 inference(beta_eta_normalization,[status(thm)],[f31])).
% 0.32/1.36 thf(f31,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X2 @ X1)) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (Y1 @ (kpair @ Y2 @ Y3))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2))))))))) @ X3))) )),
% 0.32/1.36 inference(pi_clausification,[status(thm)],[f30])).
% 0.32/1.36 thf(f30,plain,(
% 0.32/1.36 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X2 @ X1)) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (Y1 @ (kpair @ Y2 @ Y3))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))))) )),
% 0.32/1.36 inference(beta_eta_normalization,[status(thm)],[f29])).
% 0.32/1.36 thf(f29,plain,(
% 0.32/1.36 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ X1)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ X1) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3))))))))))) @ X2) = $true)) )),
% 0.32/1.36 inference(pi_clausification,[status(thm)],[f28])).
% 0.32/1.36 thf(f28,plain,(
% 0.32/1.36 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ X1)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ X1) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3)))))))))))))) )),
% 0.32/1.36 inference(beta_eta_normalization,[status(thm)],[f27])).
% 0.32/1.36 thf(f27,plain,(
% 0.32/1.36 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y1 @ Y0)) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4))))))))))))) @ X1))) )),
% 0.32/1.36 inference(pi_clausification,[status(thm)],[f26])).
% 0.32/1.36 thf(f26,plain,(
% 0.32/1.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y1 @ Y0)) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))) = $true)),
% 0.32/1.36 inference(beta_eta_normalization,[status(thm)],[f25])).
% 0.32/1.36 thf(f25,plain,(
% 0.32/1.36 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y1 @ Y0 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))))),
% 0.32/1.36 inference(definition_unfolding,[status(thm)],[f22,f17,f23])).
% 0.32/1.36 thf(f17,plain,(
% 0.32/1.36 (brelnall1 = $true)),
% 0.32/1.36 inference(cnf_transformation,[status(thm)],[f16])).
% 0.32/1.36 thf(f22,plain,(
% 0.32/1.36 (brelnall1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y1 @ Y0 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))))),
% 0.32/1.36 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.36 thf(f7,plain,(
% 0.32/1.36 (brelnall1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y1 @ Y0 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))))),
% 0.32/1.36 inference(fool_elimination,[status(thm)],[f6])).
% 0.32/1.36 thf(f6,plain,(
% 0.32/1.36 (brelnall1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X2 @ X0) => ! [X3 : $i > $o] : (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X0) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X0) => (X3 @ X6)))))),
% 0.32/1.36 inference(rectify,[status(thm)],[f2])).
% 0.32/1.36 thf(f2,axiom,(
% 0.32/1.36 (brelnall1 = ! [X3 : $i,X0 : $i,X1 : $i] : ((breln @ X0 @ X1 @ X3) => ! [X4 : $i > $o] : (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X5 @ X6) @ X3) => (X4 @ (kpair @ X5 @ X6))))) => ! [X5 : $i] : ((in @ X5 @ X3) => (X4 @ X5)))))),
% 0.32/1.36 file('/export/starexec/sandbox/tmp/tmp.PXOoiD20QP/DTF2THF_6243.p',brelnall1)).
% 0.32/1.36 thf(f65,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($true = (sK3 @ (kpair @ (sK6 @ sK1 @ sK0 @ X0 @ sK2) @ (sK7 @ sK0 @ sK2 @ sK1 @ X0)))) | ($true = (X0 @ X2)) | ($true = (X0 @ X3)) | ($false = (in @ X1 @ sK1)) | ($false = (in @ X2 @ sK1)) | ($true = (X0 @ X1)) | ($false = (in @ X3 @ sK1))) )),
% 0.32/1.36 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 0.32/1.36 thf(f64,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($false = $true) | ($false = (in @ X2 @ sK1)) | ($false = (in @ X3 @ sK1)) | ($true = (X0 @ X2)) | ($false = (in @ X1 @ sK1)) | ($true = (X0 @ X1)) | ($true = (X0 @ X3)) | ($true = (sK3 @ (kpair @ (sK6 @ sK1 @ sK0 @ X0 @ sK2) @ (sK7 @ sK0 @ sK2 @ sK1 @ X0))))) )),
% 0.32/1.36 inference(forward_demodulation,[status(thm)],[f63,f51])).
% 0.32/1.36 thf(f63,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0))) | ($true = (X0 @ X3)) | ($false = (in @ X1 @ sK1)) | ($false = (in @ X3 @ sK1)) | ($false = (in @ X2 @ sK1)) | ($true = (sK3 @ (kpair @ (sK6 @ sK1 @ sK0 @ X0 @ sK2) @ (sK7 @ sK0 @ sK2 @ sK1 @ X0)))) | ($true = (X0 @ X1)) | ($true = (X0 @ X2))) )),
% 0.32/1.36 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 0.32/1.36 thf(f62,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($false = (in @ X1 @ sK1)) | ($true = (X0 @ X2)) | ($true = (X0 @ X3)) | ($false = (in @ X3 @ sK1)) | ($false = (in @ X2 @ sK1)) | ($true != $true) | ($true = (sK3 @ (kpair @ (sK6 @ sK1 @ sK0 @ X0 @ sK2) @ (sK7 @ sK0 @ sK2 @ sK1 @ X0)))) | ($true = (X0 @ X1)) | ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0)))) )),
% 0.32/1.36 inference(duplicate_literal_removal,[status(thm)],[f61])).
% 0.32/1.36 thf(f61,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($true = (X0 @ X2)) | ($true = (X0 @ X1)) | ($true = (X0 @ X3)) | ($true != $true) | ($false = (in @ X2 @ sK1)) | ($false = (in @ X1 @ sK1)) | ($true = (sK3 @ (kpair @ (sK6 @ sK1 @ sK0 @ X0 @ sK2) @ (sK7 @ sK0 @ sK2 @ sK1 @ X0)))) | ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0))) | ($false = (in @ X3 @ sK1)) | ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0)))) )),
% 0.32/1.36 inference(superposition,[status(thm)],[f60,f43])).
% 0.32/1.36 thf(f43,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((in @ (sK6 @ X3 @ X1 @ X4 @ X2) @ X2) = $true) | ((X4 @ X5) = $true) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1))) | ((in @ X5 @ X3) = $false)) )),
% 0.32/1.36 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 0.32/1.36 thf(f42,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((in @ (sK6 @ X3 @ X1 @ X4 @ X2) @ X2) = $true) | ($true = ((in @ X5 @ X3) => (X4 @ X5))) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1)))) )),
% 0.32/1.36 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 0.32/1.36 thf(f60,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($true != (in @ (sK6 @ sK1 @ sK0 @ X1 @ X0) @ sK2)) | ((sK3 @ (kpair @ (sK6 @ sK1 @ sK0 @ X1 @ X0) @ (sK7 @ sK0 @ X0 @ sK1 @ X1))) = $true) | ($true = (X1 @ X3)) | ($false = (in @ X3 @ sK1)) | ($false = (in @ X2 @ sK1)) | ($true = (X1 @ X2)) | ($false = (subset @ sK1 @ (cartprod @ X0 @ sK0)))) )),
% 0.32/1.36 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 0.32/1.36 thf(f59,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($true = (X1 @ X2)) | ($true = (X1 @ X3)) | ($true != $true) | ($false = (in @ X2 @ sK1)) | ($false = (subset @ sK1 @ (cartprod @ X0 @ sK0))) | ($false = (in @ X3 @ sK1)) | ($true != (in @ (sK6 @ sK1 @ sK0 @ X1 @ X0) @ sK2)) | ((sK3 @ (kpair @ (sK6 @ sK1 @ sK0 @ X1 @ X0) @ (sK7 @ sK0 @ X0 @ sK1 @ X1))) = $true)) )),
% 0.32/1.36 inference(duplicate_literal_removal,[status(thm)],[f58])).
% 0.32/1.36 thf(f58,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (((sK3 @ (kpair @ (sK6 @ sK1 @ sK0 @ X1 @ X0) @ (sK7 @ sK0 @ X0 @ sK1 @ X1))) = $true) | ($true != (in @ (sK6 @ sK1 @ sK0 @ X1 @ X0) @ sK2)) | ($false = (subset @ sK1 @ (cartprod @ X0 @ sK0))) | ($true != $true) | ($false = (in @ X3 @ sK1)) | ($false = (in @ X2 @ sK1)) | ($false = (subset @ sK1 @ (cartprod @ X0 @ sK0))) | ($true = (X1 @ X3)) | ($true = (X1 @ X2))) )),
% 0.32/1.36 inference(superposition,[status(thm)],[f57,f48])).
% 0.32/1.36 thf(f48,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($true = (in @ (sK7 @ X1 @ X2 @ X3 @ X4) @ X1)) | ((X4 @ X5) = $true) | ((in @ X5 @ X3) = $false) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1)))) )),
% 0.32/1.36 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 0.32/1.36 thf(f57,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($true != (in @ (sK7 @ X0 @ X2 @ sK1 @ X1) @ sK0)) | ($true = (X1 @ X3)) | ((subset @ sK1 @ (cartprod @ X2 @ X0)) = $false) | ($true = (sK3 @ (kpair @ (sK6 @ sK1 @ X0 @ X1 @ X2) @ (sK7 @ X0 @ X2 @ sK1 @ X1)))) | ((in @ (sK6 @ sK1 @ X0 @ X1 @ X2) @ sK2) != $true) | ($false = (in @ X3 @ sK1))) )),
% 0.32/1.36 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 0.32/1.36 thf(f55,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (((in @ (sK6 @ sK1 @ X0 @ X1 @ X2) @ sK2) != $true) | ($false = (in @ X3 @ sK1)) | ($true = (sK3 @ (kpair @ (sK6 @ sK1 @ X0 @ X1 @ X2) @ (sK7 @ X0 @ X2 @ sK1 @ X1)))) | ($true != (in @ (sK7 @ X0 @ X2 @ sK1 @ X1) @ sK0)) | ($true = (X1 @ X3)) | ((subset @ sK1 @ (cartprod @ X2 @ X0)) = $false) | ($true != $true)) )),
% 0.32/1.36 inference(superposition,[status(thm)],[f20,f50])).
% 0.32/1.36 thf(f50,plain,(
% 0.32/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($true = (in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ (sK7 @ X1 @ X2 @ X3 @ X4)) @ X3)) | ((X4 @ X5) = $true) | ((in @ X5 @ X3) = $false) | ($false = (subset @ X3 @ (cartprod @ X2 @ X1)))) )),
% 0.32/1.36 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 0.32/1.36 thf(f20,plain,(
% 0.32/1.36 ( ! [X4 : $i,X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ sK1)) | ((sK3 @ (kpair @ X4 @ X5)) = $true) | ($true != (in @ X5 @ sK0)) | ($true != (in @ X4 @ sK2))) )),
% 0.32/1.36 inference(cnf_transformation,[status(thm)],[f16])).
% 0.32/1.36 % SZS output end Proof for DTF2THF_6243
% 0.32/1.36 % (6436)------------------------------
% 0.32/1.36 % (6436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.36 % (6436)Termination reason: Refutation
% 0.32/1.36
% 0.32/1.36 % (6436)Memory used [KB]: 5756
% 0.32/1.36 % (6436)Time elapsed: 0.020 s
% 0.32/1.36 % (6436)Instructions burned: 25 (million)
% 0.32/1.36 % (6436)------------------------------
% 0.32/1.36 % (6436)------------------------------
% 0.32/1.36 % (6433)Success in time 0.035 s
%------------------------------------------------------------------------------