%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU695^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 09:36:28 AM UTC 2026
% Result : Theorem 1.69s 1.36s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 13
% Syntax : Number of formulae : 156 ( 51 unt; 0 typ; 6 def)
% Number of atoms : 1522 ( 501 equ; 42 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 2816 ( 270 ~; 321 |; 26 &;1923 @)
% ( 6 <=>; 162 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 126 ( 126 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 25 usr; 16 con; 0-4 aty)
% ( 108 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 598 ( 280 ^; 300 !; 18 ?; 598 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
kpair: $i > $i > $i ).
thf(func_def_2,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_5,type,
func: $i > $i > $i > $o ).
thf(func_def_6,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_7,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_23,type,
sK2: $i > $i ).
thf(func_def_26,type,
sK5: ( $i > $i ) > $i > $i > $i ).
thf(func_def_28,type,
ph6:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
sK7: ( $i > $i ) > $i ).
thf(func_def_30,type,
sK8: ( $i > $i ) > $i ).
thf(func_def_31,type,
sK9: ( $i > $i ) > $i ).
thf(func_def_32,type,
sK10: ( $i > $i ) > $i ).
thf(f440,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f96,f113,f119,f127,f342,f365,f439]) ).
thf(f439,plain,
( ~ spl4_3
| ~ spl4_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f438]) ).
thf(f438,plain,
( $false
| ~ spl4_3
| ~ spl4_15 ),
inference(subsumption_resolution,[status(thm)],[f433,f437]) ).
thf(f437,plain,
( ( ( sK8 @ sK2 )
= ( sK2 @ ( sK7 @ sK2 ) ) )
| ~ spl4_3
| ~ spl4_15 ),
inference(trivial_inequality_removal,[status(thm)],[f436]) ).
thf(f436,plain,
( ( $true != $true )
| ( sK0 != sK0 )
| ( ( sK8 @ sK2 )
= ( sK2 @ ( sK7 @ sK2 ) ) )
| ( sK1 != sK1 )
| ~ spl4_3
| ~ spl4_15 ),
inference(duplicate_literal_removal,[status(thm)],[f428]) ).
thf(f428,plain,
( ( sK0 != sK0 )
| ( ( sK8 @ sK2 )
= ( sK2 @ ( sK7 @ sK2 ) ) )
| ( sK1 != sK1 )
| ( sK0 != sK0 )
| ( ( sK8 @ sK2 )
= ( sK2 @ ( sK7 @ sK2 ) ) )
| ( $true != $true )
| ~ spl4_3
| ~ spl4_15 ),
inference(superposition,[status(thm)],[f427,f143]) ).
thf(f143,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( in @ ( sK5 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( sK8 @ X2 )
= ( X2 @ ( sK7 @ X2 ) ) )
| ( ( sK8 @ X2 )
= ( sK2 @ ( sK7 @ X2 ) ) )
| ( sK1 != X1 )
| ( sK0 != X0 ) )
| ~ spl4_3 ),
inference(equality_proxy_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( sK8 @ X2 )
= ( X2 @ ( sK7 @ X2 ) ) )
| ( sK1 != X1 )
| ( sK0 != X0 )
| ( ( in @ ( sK5 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( ( sK2 @ ( sK7 @ X2 ) )
= ( sK8 @ X2 ) )
= $true ) )
| ~ spl4_3 ),
inference(equality_proxy_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( ( X2 @ ( sK7 @ X2 ) )
= ( sK8 @ X2 ) )
= $true )
| ( ( in @ ( sK5 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( sK1 != X1 )
| ( ( ( sK2 @ ( sK7 @ X2 ) )
= ( sK8 @ X2 ) )
= $true )
| ( sK0 != X0 ) )
| ~ spl4_3 ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( sK1 != X1 )
| ( ( ( sK2 @ ( sK7 @ X2 ) )
= ( sK8 @ X2 ) )
!= ( ( X2 @ ( sK7 @ X2 ) )
= ( sK8 @ X2 ) ) )
| ( ( in @ ( sK5 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( sK0 != X0 ) )
| ~ spl4_3 ),
inference(negative_extensionality,[status(thm)],[f135]) ).
thf(f135,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( (=) @ ( X2 @ ( sK7 @ X2 ) ) )
!= ( (=) @ ( sK2 @ ( sK7 @ X2 ) ) ) )
| ( sK0 != X0 )
| ( sK1 != X1 )
| ( ( in @ ( sK5 @ X2 @ X1 @ X0 ) @ X0 )
= $true ) )
| ~ spl4_3 ),
inference(beta_eta_normalization,[status(thm)],[f134]) ).
thf(f134,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) )
@ ( sK7 @ X2 ) )
!= ( ^ [Y0: $i] : ( (=) @ ( X2 @ Y0 ) )
@ ( sK7 @ X2 ) ) )
| ( sK0 != X0 )
| ( sK1 != X1 )
| ( ( in @ ( sK5 @ X2 @ X1 @ X0 ) @ X0 )
= $true ) )
| ~ spl4_3 ),
inference(negative_extensionality,[status(thm)],[f133]) ).
thf(f133,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: $i] : ( (=) @ ( X2 @ Y0 ) ) ) )
| ( ( in @ ( sK5 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( sK1 != X1 )
| ( sK0 != X0 ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: $i] : ( (=) @ ( X2 @ Y0 ) ) ) )
| ( sK0 != X0 )
| ( ( in @ ( sK5 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( sK1 != X1 )
| ( $false = $true ) )
| ~ spl4_3 ),
inference(duplicate_literal_removal,[status(thm)],[f128]) ).
thf(f128,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: $i] : ( (=) @ ( X2 @ Y0 ) ) ) )
| ( sK1 != X1 )
| ( sK1 != X1 )
| ( ( in @ ( sK5 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( sK0 != X0 )
| ( sK0 != X0 ) )
| ~ spl4_3 ),
inference(constrained_superposition,[status(thm)],[f95,f79]) ).
thf(f79,plain,
! [X2: $i,X3: $i > $i,X1: $i] :
( ( ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i] : ( (=) @ ( X3 @ Y0 ) ) ) )
= $true )
| ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: $i,X3: $i > $i,X1: $i] :
( ( ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( X3 @ ( sK5 @ X3 @ X1 @ X2 ) ) @ X1 ) )
= $false )
| ( ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i] : ( (=) @ ( X3 @ Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X3: $i > $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( X3 @ Y0 ) @ X1 ) )
@ ( sK5 @ X3 @ X1 @ X2 ) )
= $false )
| ( ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i] : ( (=) @ ( X3 @ Y0 ) ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i,X3: $i > $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( X3 @ Y0 ) @ X1 ) ) )
= $false )
| ( ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i] : ( (=) @ ( X3 @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X3: $i > $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( X3 @ Y0 ) @ X1 ) ) )
=> ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i] : ( (=) @ ( X3 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X3: $i > $i,X1: $i] :
( ( ^ [Y0: $i > $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( Y0 @ Y1 ) @ X1 ) ) )
=> ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y1: $i] : ( (=) @ ( Y0 @ Y1 ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( Y0 @ Y1 ) @ X1 ) ) )
=> ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y1: $i] : ( (=) @ ( Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( Y1 @ Y2 ) @ X1 ) ) )
=> ( func @ Y0 @ X1
@ ( dpsetconstr @ Y0 @ X1
@ ^ [Y2: $i] : ( (=) @ ( Y1 @ Y2 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( Y1 @ Y2 ) @ X1 ) ) )
=> ( func @ Y0 @ X1
@ ( dpsetconstr @ Y0 @ X1
@ ^ [Y2: $i] : ( (=) @ ( Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( func @ Y1 @ Y0
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y3: $i] : ( (=) @ ( Y2 @ Y3 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( func @ Y1 @ Y0
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y3: $i] : ( (=) @ ( Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( func @ Y1 @ Y0
@ ( ^ [Y3: $i,Y4: $i,Y5: $i > $i] :
( dpsetconstr @ Y3 @ Y4
@ ^ [Y6: $i,Y7: $i] :
( ( Y5 @ Y6 )
= Y7 ) )
@ Y1
@ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f31,f30,f33]) ).
thf(f33,plain,
( lam
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( lam
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [X0: $i,X1: $i,X2: $i > $i] :
( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] :
( ( X2 @ X3 )
= X4 ) ) )
= lam ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i,X1: $i,X7: $i > $i] :
( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] :
( ( X7 @ X3 )
= X4 ) ) )
= lam ),
file('/export/starexec/sandbox2/tmp/tmp.6ZDpTMNeLo/DTF2THF_1563.p',lam) ).
thf(f30,plain,
lamp = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( lamp = $true )
& ( ( sK2 @ sK3 )
!= ( ap @ sK0 @ sK1
@ ( lam @ sK0 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
@ sK3 ) )
& ( ( in @ sK3 @ sK0 )
= $true )
& ! [X4: $i] :
( ( ( in @ ( sK2 @ X4 ) @ sK1 )
= $true )
| ( ( in @ X4 @ sK0 )
!= $true ) )
& ( funcGraphProp2 = $true )
& ( dpsetconstrI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f22,f21]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ? [X3: $i] :
( ( ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X3 )
!= ( X2 @ X3 ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ! [X4: $i] :
( ( ( in @ ( X2 @ X4 ) @ X1 )
= $true )
| ( ( in @ X4 @ X0 )
!= $true ) ) )
=> ( ? [X3: $i] :
( ( ( sK2 @ X3 )
!= ( ap @ sK0 @ sK1
@ ( lam @ sK0 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
@ X3 ) )
& ( ( in @ X3 @ sK0 )
= $true ) )
& ! [X4: $i] :
( ( ( in @ ( sK2 @ X4 ) @ sK1 )
= $true )
| ( ( in @ X4 @ sK0 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X3: $i] :
( ( ( sK2 @ X3 )
!= ( ap @ sK0 @ sK1
@ ( lam @ sK0 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
@ X3 ) )
& ( ( in @ X3 @ sK0 )
= $true ) )
=> ( ( ( sK2 @ sK3 )
!= ( ap @ sK0 @ sK1
@ ( lam @ sK0 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
@ sK3 ) )
& ( ( in @ sK3 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ( lamp = $true )
& ? [X0: $i,X1: $i,X2: $i > $i] :
( ? [X3: $i] :
( ( ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X3 )
!= ( X2 @ X3 ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ! [X4: $i] :
( ( ( in @ ( X2 @ X4 ) @ X1 )
= $true )
| ( ( in @ X4 @ X0 )
!= $true ) ) )
& ( funcGraphProp2 = $true )
& ( dpsetconstrI = $true ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
( ( lamp = $true )
& ? [X0: $i,X1: $i,X2: $i > $i] :
( ? [X4: $i] :
( ( ( X2 @ X4 )
!= ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X4 ) )
& ( ( in @ X4 @ X0 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ ( X2 @ X3 ) @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( funcGraphProp2 = $true )
& ( dpsetconstrI = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ? [X4: $i] :
( ( ( X2 @ X4 )
!= ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X4 ) )
& ( ( in @ X4 @ X0 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ ( X2 @ X3 ) @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( funcGraphProp2 = $true )
& ( lamp = $true )
& ( dpsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( dpsetconstrI = $true )
=> ( ( lamp = $true )
=> ( ( funcGraphProp2 = $true )
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( X2 @ X3 ) @ X1 )
= $true ) )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( X2 @ X4 )
= ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X4 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( dpsetconstrI
=> ( lamp
=> ( funcGraphProp2
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [X5: $i] : ( X2 @ X5 ) )
@ X4 )
= ( X2 @ X4 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dpsetconstrI
=> ( lamp
=> ( funcGraphProp2
=> ! [X0: $i,X1: $i,X7: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X7 @ X3 ) @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [X4: $i] : ( X7 @ X4 ) )
@ X3 )
= ( X7 @ X3 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( dpsetconstrI
=> ( lamp
=> ( funcGraphProp2
=> ! [X0: $i,X1: $i,X7: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X7 @ X3 ) @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [X4: $i] : ( X7 @ X4 ) )
@ X3 )
= ( X7 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6ZDpTMNeLo/DTF2THF_1563.p',beta1) ).
thf(f31,plain,
( lamp
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( func @ Y1 @ Y0
@ ( lam @ Y1 @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( lamp
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( func @ Y1 @ Y0
@ ( lam @ Y1 @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( lamp
= ( ! [X0: $i > $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( X0 @ X3 ) @ X2 ) )
=> ( func @ X1 @ X2
@ ( lam @ X1 @ X2
@ ^ [X4: $i] : ( X0 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( lamp
= ( ! [X7: $i > $i,X0: $i,X1: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X7 @ X3 ) @ X1 ) )
=> ( func @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X7 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6ZDpTMNeLo/DTF2THF_1563.p',lamp) ).
thf(f95,plain,
( ( $false
= ( func @ sK0 @ sK1
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f93]) ).
thf(f93,definition,
( spl4_3
<=> ( $false
= ( func @ sK0 @ sK1
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f427,plain,
( ! [X0: $i] :
( ( ( in @ ( sK5 @ sK2 @ sK1 @ X0 ) @ sK0 )
!= $true )
| ( sK0 != X0 ) )
| ~ spl4_15 ),
inference(equality_resolution,[status(thm)],[f341]) ).
thf(f341,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK5 @ sK2 @ sK1 @ X0 )
!= X1 )
| ( sK0 != X0 )
| ( ( in @ X1 @ sK0 )
!= $true ) )
| ~ spl4_15 ),
inference(avatar_component_clause,[status(thm)],[f340]) ).
thf(f340,definition,
( spl4_15
<=> ! [X0: $i,X1: $i] :
( ( sK0 != X0 )
| ( ( in @ X1 @ sK0 )
!= $true )
| ( ( sK5 @ sK2 @ sK1 @ X0 )
!= X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_15])],[avatar_definition]) ).
thf(f433,plain,
( ( ( sK8 @ sK2 )
!= ( sK2 @ ( sK7 @ sK2 ) ) )
| ~ spl4_3
| ~ spl4_15 ),
inference(trivial_inequality_removal,[status(thm)],[f432]) ).
thf(f432,plain,
( ( sK0 != sK0 )
| ( ( sK8 @ sK2 )
!= ( sK2 @ ( sK7 @ sK2 ) ) )
| ( sK1 != sK1 )
| ( $true != $true )
| ~ spl4_3
| ~ spl4_15 ),
inference(duplicate_literal_removal,[status(thm)],[f429]) ).
thf(f429,plain,
( ( sK0 != sK0 )
| ( sK0 != sK0 )
| ( ( sK8 @ sK2 )
!= ( sK2 @ ( sK7 @ sK2 ) ) )
| ( sK1 != sK1 )
| ( $true != $true )
| ( ( sK8 @ sK2 )
!= ( sK2 @ ( sK7 @ sK2 ) ) )
| ~ spl4_3
| ~ spl4_15 ),
inference(superposition,[status(thm)],[f427,f141]) ).
thf(f141,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( in @ ( sK5 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( sK8 @ X2 )
!= ( X2 @ ( sK7 @ X2 ) ) )
| ( ( sK8 @ X2 )
!= ( sK2 @ ( sK7 @ X2 ) ) )
| ( sK1 != X1 )
| ( sK0 != X0 ) )
| ~ spl4_3 ),
inference(equality_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( sK8 @ X2 )
!= ( X2 @ ( sK7 @ X2 ) ) )
| ( ( in @ ( sK5 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( ( sK2 @ ( sK7 @ X2 ) )
= ( sK8 @ X2 ) )
= $false )
| ( sK0 != X0 )
| ( sK1 != X1 ) )
| ~ spl4_3 ),
inference(equality_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( ( X2 @ ( sK7 @ X2 ) )
= ( sK8 @ X2 ) )
= $false )
| ( sK1 != X1 )
| ( ( ( sK2 @ ( sK7 @ X2 ) )
= ( sK8 @ X2 ) )
= $false )
| ( ( in @ ( sK5 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( sK0 != X0 ) )
| ~ spl4_3 ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f365,plain,
( spl4_15
| ~ spl4_3
| ~ spl4_14 ),
inference(avatar_split_clause,[status(thm)],[f364,f336,f93,f340]) ).
thf(f336,definition,
( spl4_14
<=> ( ( sK10 @ sK2 )
= ( sK2 @ ( sK9 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_14])],[avatar_definition]) ).
thf(f364,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ sK0 )
!= $true )
| ( ( sK5 @ sK2 @ sK1 @ X1 )
!= X0 )
| ( sK0 != X1 ) )
| ~ spl4_3
| ~ spl4_14 ),
inference(subsumption_resolution,[status(thm)],[f363,f338]) ).
thf(f338,plain,
( ( ( sK10 @ sK2 )
= ( sK2 @ ( sK9 @ sK2 ) ) )
| ~ spl4_14 ),
inference(avatar_component_clause,[status(thm)],[f336]) ).
thf(f363,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK10 @ sK2 )
!= ( sK2 @ ( sK9 @ sK2 ) ) )
| ( ( in @ X0 @ sK0 )
!= $true )
| ( ( sK5 @ sK2 @ sK1 @ X1 )
!= X0 )
| ( sK0 != X1 ) )
| ~ spl4_3
| ~ spl4_14 ),
inference(trivial_inequality_removal,[status(thm)],[f362]) ).
thf(f362,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK10 @ sK2 )
!= ( sK2 @ ( sK9 @ sK2 ) ) )
| ( ( sK5 @ sK2 @ sK1 @ X1 )
!= X0 )
| ( ( in @ X0 @ sK0 )
!= $true )
| ( sK0 != X1 )
| ( ( sK10 @ sK2 )
!= ( sK10 @ sK2 ) ) )
| ~ spl4_3
| ~ spl4_14 ),
inference(beta_eta_normalization,[status(thm)],[f347]) ).
thf(f347,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ sK0 )
!= $true )
| ( ( sK2
@ ( sK9
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
!= ( sK10
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
| ( ( ^ [Y0: $i] : Y0
@ ( sK5
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ sK1
@ X1 ) )
!= X0 )
| ( sK0 != X1 )
| ( ( sK10 @ sK2 )
!= ( sK10
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) )
| ~ spl4_3
| ~ spl4_14 ),
inference(superposition,[status(thm)],[f200,f338]) ).
thf(f200,plain,
( ! [X2: $i,X0: $i > $i,X1: $i] :
( ( ( sK2
@ ( X0
@ ( sK9
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) ) )
!= ( sK10
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) )
| ( ( in @ X2 @ sK0 )
!= $true )
| ( ( sK10
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) )
!= ( sK2
@ ( sK9
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) ) )
| ( sK0 != X1 )
| ( ( X0
@ ( sK5
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) )
@ sK1
@ X1 ) )
!= X2 ) )
| ~ spl4_3 ),
inference(beta_eta_normalization,[status(thm)],[f199]) ).
thf(f199,plain,
( ! [X2: $i,X0: $i > $i,X1: $i] :
( ( ( sK10
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) )
!= ( sK2
@ ( sK9
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) ) )
| ( ( X0
@ ( sK5
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) )
@ sK1
@ X1 ) )
!= X2 )
| ( ( in @ X2 @ sK0 )
!= $true )
| ( sK0 != X1 )
| ( ( ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) )
@ ( sK9
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) )
!= ( sK10
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f171]) ).
thf(f171,plain,
( ! [X2: $i,X0: $i > $i,X1: $i] :
( ( ( ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) )
@ ( sK9
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) )
!= ( sK10
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) )
| ( sK0 != X1 )
| ( ( in @ X2 @ sK0 )
!= $true )
| ( ( X0
@ ( sK5
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) )
@ sK1
@ X1 ) )
!= X2 )
| ( $false = $true )
| ( ( sK10
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) )
!= ( sK2
@ ( sK9
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) ) )
| ( sK1 != sK1 ) )
| ~ spl4_3 ),
inference(constrained_superposition,[status(thm)],[f165,f27]) ).
thf(f27,plain,
! [X4: $i] :
( ( ( in @ ( sK2 @ X4 ) @ sK1 )
= $true )
| ( ( in @ X4 @ sK0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f165,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( in @ ( X2 @ ( sK5 @ X2 @ X1 @ X0 ) ) @ X1 )
= $false )
| ( ( sK10 @ X2 )
!= ( X2 @ ( sK9 @ X2 ) ) )
| ( sK0 != X0 )
| ( ( sK10 @ X2 )
!= ( sK2 @ ( sK9 @ X2 ) ) )
| ( sK1 != X1 ) )
| ~ spl4_3 ),
inference(equality_proxy_clausification,[status(thm)],[f164]) ).
thf(f164,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( in @ ( X2 @ ( sK5 @ X2 @ X1 @ X0 ) ) @ X1 )
= $false )
| ( ( sK10 @ X2 )
!= ( X2 @ ( sK9 @ X2 ) ) )
| ( ( ( sK2 @ ( sK9 @ X2 ) )
= ( sK10 @ X2 ) )
= $false )
| ( sK0 != X0 )
| ( sK1 != X1 ) )
| ~ spl4_3 ),
inference(equality_proxy_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( sK1 != X1 )
| ( $false
= ( ( X2 @ ( sK9 @ X2 ) )
= ( sK10 @ X2 ) ) )
| ( sK0 != X0 )
| ( ( ( sK2 @ ( sK9 @ X2 ) )
= ( sK10 @ X2 ) )
= $false )
| ( ( in @ ( X2 @ ( sK5 @ X2 @ X1 @ X0 ) ) @ X1 )
= $false ) )
| ~ spl4_3 ),
inference(binary_proxy_clausification,[status(thm)],[f160]) ).
thf(f160,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( sK0 != X0 )
| ( ( in @ ( X2 @ ( sK5 @ X2 @ X1 @ X0 ) ) @ X1 )
= $false )
| ( ( ( sK2 @ ( sK9 @ X2 ) )
= ( sK10 @ X2 ) )
!= ( ( X2 @ ( sK9 @ X2 ) )
= ( sK10 @ X2 ) ) )
| ( sK1 != X1 ) )
| ~ spl4_3 ),
inference(negative_extensionality,[status(thm)],[f151]) ).
thf(f151,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( (=) @ ( sK2 @ ( sK9 @ X2 ) ) )
!= ( (=) @ ( X2 @ ( sK9 @ X2 ) ) ) )
| ( sK1 != X1 )
| ( ( in @ ( X2 @ ( sK5 @ X2 @ X1 @ X0 ) ) @ X1 )
= $false )
| ( sK0 != X0 ) )
| ~ spl4_3 ),
inference(beta_eta_normalization,[status(thm)],[f150]) ).
thf(f150,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( sK1 != X1 )
| ( ( in @ ( X2 @ ( sK5 @ X2 @ X1 @ X0 ) ) @ X1 )
= $false )
| ( sK0 != X0 )
| ( ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) )
@ ( sK9 @ X2 ) )
!= ( ^ [Y0: $i] : ( (=) @ ( X2 @ Y0 ) )
@ ( sK9 @ X2 ) ) ) )
| ~ spl4_3 ),
inference(negative_extensionality,[status(thm)],[f149]) ).
thf(f149,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: $i] : ( (=) @ ( X2 @ Y0 ) ) ) )
| ( sK1 != X1 )
| ( ( in @ ( X2 @ ( sK5 @ X2 @ X1 @ X0 ) ) @ X1 )
= $false )
| ( sK0 != X0 ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f148]) ).
thf(f148,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( sK1 != X1 )
| ( sK0 != X0 )
| ( ( in @ ( X2 @ ( sK5 @ X2 @ X1 @ X0 ) ) @ X1 )
= $false )
| ( ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: $i] : ( (=) @ ( X2 @ Y0 ) ) ) )
| ( $false = $true ) )
| ~ spl4_3 ),
inference(duplicate_literal_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( sK1 != X1 )
| ( $false = $true )
| ( sK0 != X0 )
| ( ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: $i] : ( (=) @ ( X2 @ Y0 ) ) ) )
| ( sK1 != X1 )
| ( ( in @ ( X2 @ ( sK5 @ X2 @ X1 @ X0 ) ) @ X1 )
= $false )
| ( sK0 != X0 ) )
| ~ spl4_3 ),
inference(constrained_superposition,[status(thm)],[f78,f95]) ).
thf(f78,plain,
! [X2: $i,X3: $i > $i,X1: $i] :
( ( ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i] : ( (=) @ ( X3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( in @ ( X3 @ ( sK5 @ X3 @ X1 @ X2 ) ) @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f342,plain,
( spl4_14
| spl4_15
| ~ spl4_3 ),
inference(avatar_split_clause,[status(thm)],[f334,f93,f340,f336]) ).
thf(f334,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK10 @ sK2 )
= ( sK2 @ ( sK9 @ sK2 ) ) )
| ( sK0 != X0 )
| ( ( sK5 @ sK2 @ sK1 @ X0 )
!= X1 )
| ( ( in @ X1 @ sK0 )
!= $true ) )
| ~ spl4_3 ),
inference(beta_eta_normalization,[status(thm)],[f333]) ).
thf(f333,plain,
( ! [X0: $i,X1: $i] :
( ( sK0 != X0 )
| ( ( in @ X1 @ sK0 )
!= $true )
| ( ( sK2
@ ( sK9
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= ( sK10
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
| ( ( ^ [Y0: $i] : Y0
@ ( sK5
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ sK1
@ X0 ) )
!= X1 ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f325]) ).
thf(f325,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ sK0 )
!= $true )
| ( ( sK10
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) )
!= ( sK10
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
| ( sK0 != X0 )
| ( ( ^ [Y0: $i] : Y0
@ ( sK5
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ sK1
@ X0 ) )
!= X1 )
| ( ( sK2
@ ( sK9
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= ( sK10
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) )
| ~ spl4_3 ),
inference(equality_factoring,[status(thm)],[f271]) ).
thf(f271,plain,
( ! [X2: $i,X0: $i > $i,X1: $i] :
( ( ( sK2
@ ( X0
@ ( sK9
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) ) )
= ( sK10
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) )
| ( ( sK10
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) )
= ( sK2
@ ( sK9
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) ) )
| ( sK0 != X1 )
| ( ( in @ X2 @ sK0 )
!= $true )
| ( ( X0
@ ( sK5
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) )
@ sK1
@ X1 ) )
!= X2 ) )
| ~ spl4_3 ),
inference(beta_eta_normalization,[status(thm)],[f270]) ).
thf(f270,plain,
( ! [X2: $i,X0: $i > $i,X1: $i] :
( ( ( X0
@ ( sK5
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) )
@ sK1
@ X1 ) )
!= X2 )
| ( ( sK10
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) )
= ( sK2
@ ( sK9
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) ) )
| ( sK0 != X1 )
| ( ( ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) )
@ ( sK9
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) )
= ( sK10
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) )
| ( ( in @ X2 @ sK0 )
!= $true ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f251]) ).
thf(f251,plain,
( ! [X2: $i,X0: $i > $i,X1: $i] :
( ( ( sK10
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) )
= ( sK2
@ ( sK9
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) ) )
| ( $false = $true )
| ( sK1 != sK1 )
| ( ( ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) )
@ ( sK9
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) )
= ( sK10
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) ) ) )
| ( ( X0
@ ( sK5
@ ^ [Y0: $i] : ( sK2 @ ( X0 @ Y0 ) )
@ sK1
@ X1 ) )
!= X2 )
| ( ( in @ X2 @ sK0 )
!= $true )
| ( sK0 != X1 ) )
| ~ spl4_3 ),
inference(constrained_superposition,[status(thm)],[f167,f27]) ).
thf(f167,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( in @ ( X2 @ ( sK5 @ X2 @ X1 @ X0 ) ) @ X1 )
= $false )
| ( ( sK10 @ X2 )
= ( sK2 @ ( sK9 @ X2 ) ) )
| ( sK0 != X0 )
| ( sK1 != X1 )
| ( ( sK10 @ X2 )
= ( X2 @ ( sK9 @ X2 ) ) ) )
| ~ spl4_3 ),
inference(equality_proxy_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( ( in @ ( X2 @ ( sK5 @ X2 @ X1 @ X0 ) ) @ X1 )
= $false )
| ( ( ( X2 @ ( sK9 @ X2 ) )
= ( sK10 @ X2 ) )
= $true )
| ( sK1 != X1 )
| ( ( sK10 @ X2 )
= ( sK2 @ ( sK9 @ X2 ) ) )
| ( sK0 != X0 ) )
| ~ spl4_3 ),
inference(equality_proxy_clausification,[status(thm)],[f162]) ).
thf(f162,plain,
( ! [X2: $i > $i,X0: $i,X1: $i] :
( ( sK0 != X0 )
| ( sK1 != X1 )
| ( ( ( sK2 @ ( sK9 @ X2 ) )
= ( sK10 @ X2 ) )
= $true )
| ( ( in @ ( X2 @ ( sK5 @ X2 @ X1 @ X0 ) ) @ X1 )
= $false )
| ( ( ( X2 @ ( sK9 @ X2 ) )
= ( sK10 @ X2 ) )
= $true ) )
| ~ spl4_3 ),
inference(binary_proxy_clausification,[status(thm)],[f160]) ).
thf(f127,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[status(thm)],[f126]) ).
thf(f126,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ( ( sK2 @ sK3 )
!= ( sK2 @ sK3 ) )
| ( $true != $true )
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f124,f28]) ).
thf(f28,plain,
( ( in @ sK3 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f124,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK0 )
!= $true )
| ( ( sK2 @ X0 )
!= ( sK2 @ sK3 ) ) )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( sK2 @ X0 )
!= ( sK2 @ sK3 ) )
| ( ( in @ X0 @ sK0 )
!= $true ) )
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f111,f27]) ).
thf(f111,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK1 )
= $false )
| ( ( sK2 @ sK3 )
!= X0 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f110]) ).
thf(f110,definition,
( spl4_4
<=> ! [X0: $i] :
( ( ( in @ X0 @ sK1 )
= $false )
| ( ( sK2 @ sK3 )
!= X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f119,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[status(thm)],[f118]) ).
thf(f118,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
( ( $false = $true )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f28,f88]) ).
thf(f88,plain,
( ( $false
= ( in @ sK3 @ sK0 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f86]) ).
thf(f86,definition,
( spl4_1
<=> ( $false
= ( in @ sK3 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f113,plain,
( spl4_1
| spl4_4
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f103,f90,f110,f86]) ).
thf(f90,definition,
( spl4_2
<=> ! [X0: $i] :
( ( ( sK2 @ sK3 )
!= X0 )
| ( ( in @ ( kpair @ sK3 @ X0 )
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) )
= $false )
| ( ( in @ X0 @ sK1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f103,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK1 )
= $false )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ( ( sK2 @ sK3 )
!= X0 ) )
| ~ spl4_2 ),
inference(duplicate_literal_removal,[status(thm)],[f102]) ).
thf(f102,plain,
( ! [X0: $i] :
( ( ( sK2 @ sK3 )
!= X0 )
| ( ( in @ X0 @ sK1 )
= $false )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ( ( sK2 @ sK3 )
!= X0 ) )
| ~ spl4_2 ),
inference(equality_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
( ! [X0: $i] :
( ( ( sK2 @ sK3 )
!= X0 )
| ( $false
= ( ( sK2 @ sK3 )
= X0 ) )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ( ( in @ X0 @ sK1 )
= $false ) )
| ~ spl4_2 ),
inference(beta_eta_normalization,[status(thm)],[f100]) ).
thf(f100,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK1 )
= $false )
| ( ( sK2 @ sK3 )
!= X0 )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ( ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) )
@ sK3
@ X0 )
= $false ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ! [X0: $i] :
( ( ( sK2 @ sK3 )
!= X0 )
| ( ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) )
@ sK3
@ X0 )
= $false )
| ( ( in @ X0 @ sK1 )
= $false )
| ( $false = $true )
| ( $false
= ( in @ sK3 @ sK0 ) ) )
| ~ spl4_2 ),
inference(duplicate_literal_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ! [X0: $i] :
( ( $false
= ( in @ sK3 @ sK0 ) )
| ( ( sK2 @ sK3 )
!= X0 )
| ( ( in @ X0 @ sK1 )
= $false )
| ( ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) )
@ sK3
@ X0 )
= $false )
| ( ( in @ X0 @ sK1 )
= $false )
| ( $false = $true ) )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f91,f51]) ).
thf(f51,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) )
= $true )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X5 @ X1 ) )
| ( $false
= ( X3 @ X4 @ X5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( in @ X5 @ X1 ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( ( ( X3 @ X4 @ X5 )
=> ( in @ ( kpair @ X4 @ X5 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( ( in @ X5 @ X1 )
=> ( ( X3 @ X4 @ X5 )
=> ( in @ ( kpair @ X4 @ X5 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) ) )
= $true )
| ( $false
= ( in @ X4 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ X4 @ Y0 )
=> ( in @ ( kpair @ X4 @ Y0 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) ) )
@ X5 )
= $true )
| ( $false
= ( in @ X4 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ X4 @ Y0 )
=> ( in @ ( kpair @ X4 @ Y0 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) ) ) )
= $true )
| ( $false
= ( in @ X4 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i] :
( ( ( in @ X4 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ X4 @ Y0 )
=> ( in @ ( kpair @ X4 @ Y0 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( X3 @ Y0 @ Y1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( X3 @ Y0 @ Y1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ ( dpsetconstr @ X2 @ X1 @ X3 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i] :
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y0 @ Y1 @ Y2 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ ( dpsetconstr @ X2 @ X1 @ Y0 ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y0 @ Y1 @ Y2 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ ( dpsetconstr @ X2 @ X1 @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( ( Y1 @ Y2 @ Y3 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ ( dpsetconstr @ Y0 @ X1 @ Y1 ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( ( Y1 @ Y2 @ Y3 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ ( dpsetconstr @ Y0 @ X1 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( Y2 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y1 @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( Y2 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y1 @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( Y2 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y5: $i,Y6: $i] : ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f25,f24]) ).
thf(f24,plain,
( dpsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( Y2 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y5: $i,Y6: $i] : ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( dpsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( Y2 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y5: $i,Y6: $i] : ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( dpsetconstrI
= ( ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ X0 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ( ( X1 @ X0 @ X4 )
=> ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X2 @ X3
@ ^ [X5: $i,X6: $i] : ( X1 @ X5 @ X6 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dpsetconstrI
= ( ! [X3: $i,X2: $i > $i > $o,X0: $i,X1: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 @ X4 )
=> ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6ZDpTMNeLo/DTF2THF_1563.p',dpsetconstrI) ).
thf(f25,plain,
dpsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f91,plain,
( ! [X0: $i] :
( ( ( in @ ( kpair @ sK3 @ X0 )
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) )
= $false )
| ( ( sK2 @ sK3 )
!= X0 )
| ( ( in @ X0 @ sK1 )
= $false ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f96,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[status(thm)],[f83,f93,f90,f86]) ).
thf(f83,plain,
! [X0: $i] :
( ( ( sK2 @ sK3 )
!= X0 )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ( ( in @ X0 @ sK1 )
= $false )
| ( ( in @ ( kpair @ sK3 @ X0 )
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) )
= $false )
| ( $false
= ( func @ sK0 @ sK1
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f67,f66]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ap @ X3 @ X1 @ X2 @ X4 )
= X5 )
| ( $false
= ( func @ X3 @ X1 @ X2 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $false )
| ( $false
= ( in @ X5 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( func @ X3 @ X1 @ X2 ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $false )
| ( ( ( ap @ X3 @ X1 @ X2 @ X4 )
= X5 )
= $true )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( in @ X5 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( ( ap @ X3 @ X1 @ X2 @ X4 )
= X5 ) )
= $true )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( in @ X5 @ X1 ) )
| ( $false
= ( func @ X3 @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( ( ap @ X3 @ X1 @ X2 @ X4 )
= X5 ) ) )
= $true )
| ( $false
= ( func @ X3 @ X1 @ X2 ) )
| ( $false
= ( in @ X4 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( func @ X3 @ X1 @ X2 ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X2 )
=> ( ( ap @ X3 @ X1 @ X2 @ X4 )
= Y0 ) ) )
@ X5 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( func @ X3 @ X1 @ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X2 )
=> ( ( ap @ X3 @ X1 @ X2 @ X4 )
= Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( in @ X4 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X2 )
=> ( ( ap @ X3 @ X1 @ X2 @ X4 )
= Y0 ) ) ) ) )
= $true )
| ( $false
= ( func @ X3 @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X2 )
=> ( ( ap @ X3 @ X1 @ X2 @ Y0 )
= Y1 ) ) ) ) )
@ X4 )
= $true )
| ( $false
= ( func @ X3 @ X1 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( func @ X3 @ X1 @ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X2 )
=> ( ( ap @ X3 @ X1 @ X2 @ Y0 )
= Y1 ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( func @ X3 @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X2 )
=> ( ( ap @ X3 @ X1 @ X2 @ Y0 )
= Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( func @ Y0 @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X2 )
=> ( ( ap @ Y0 @ X1 @ X2 @ Y1 )
= Y2 ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ Y0 @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X2 )
=> ( ( ap @ Y0 @ X1 @ X2 @ Y1 )
= Y2 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y1 @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( ( ap @ Y1 @ X1 @ Y0 @ Y2 )
= Y3 ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y1 @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( ( ap @ Y1 @ X1 @ Y0 @ Y2 )
= Y3 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( ( ap @ Y2 @ Y0 @ Y1 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( ( ap @ Y2 @ Y0 @ Y1 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f32,f26]) ).
thf(f26,plain,
funcGraphProp2 = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f32,plain,
( funcGraphProp2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( ( ap @ Y2 @ Y0 @ Y1 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( funcGraphProp2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( ( ap @ Y2 @ Y0 @ Y1 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( funcGraphProp2
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( ( ap @ X0 @ X2 @ X1 @ X3 )
= X4 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( funcGraphProp2
= ( ! [X0: $i,X7: $i,X1: $i] :
( ( func @ X0 @ X1 @ X7 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X7 )
=> ( ( ap @ X0 @ X1 @ X7 @ X3 )
= X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6ZDpTMNeLo/DTF2THF_1563.p',funcGraphProp2) ).
thf(f67,plain,
( ( sK2 @ sK3 )
!= ( ap @ sK0 @ sK1
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) )
@ sK3 ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
( ( sK2 @ sK3 )
!= ( ap @ sK0 @ sK1
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) )
@ sK0
@ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
@ sK3 ) ),
inference(definition_unfolding,[status(thm)],[f29,f33]) ).
thf(f29,plain,
( ( sK2 @ sK3 )
!= ( ap @ sK0 @ sK1
@ ( lam @ sK0 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
@ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU695^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:31:01 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : SEU695^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.44 % Domain : Set Theory
% 0.19/0.44 % Problem : Functions - Extensionality and Beta Reduction
% 0.19/0.44 % Version : Especial > Reduced > Especial.
% 0.19/0.44 % English : (! A:i.! B:i.! f:i>i.(! x:i.in x A -> in (f x) B) ->
% 0.19/0.44 % (! x:i.in x A -> ap A B (lam A B (^ y:i.f y)) x = f x))
% 0.19/0.44
% 0.19/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.44 % Source : [Bro08]
% 0.19/0.44 % Names : ZFC197l [Bro08]
% 0.19/0.44 % : ZFC200l [Bro08]
% 0.19/0.44
% 0.19/0.44 % Status : Theorem
% 0.19/0.44 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.43 v6.1.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 0.67 v3.7.0
% 0.19/0.44 % Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 4 def)
% 0.19/0.44 % Number of atoms : 26 ( 7 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 7 ( 5 avg)
% 0.19/0.44 % Number of connectives : 77 ( 0 ~; 0 |; 0 &; 62 @)
% 0.19/0.44 % ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 13 ( 3 avg)
% 0.19/0.44 % Number of types : 2 ( 0 usr)
% 0.19/0.44 % Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 10 ( 9 usr; 3 con; 0-4 aty)
% 0.19/0.44 % Number of variables : 28 ( 9 ^; 19 !; 0 ?; 28 :)
% 0.19/0.44 % SPC : TH0_THM_EQU_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : http://mathgate.info/detsetitem.php?id=248
% 0.19/0.44 % : http://mathgate.info/detsetitem.php?id=250
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 thf(in_type,type,
% 0.19/0.44 in: $i > $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(kpair_type,type,
% 0.19/0.44 kpair: $i > $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstr_type,type,
% 0.19/0.44 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstrI_type,type,
% 0.19/0.44 dpsetconstrI: $o ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstrI,definition,
% 0.19/0.44 ( dpsetconstrI
% 0.19/0.44 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( ( Xphi @ Xx @ Xy )
% 0.19/0.44 => ( in @ ( kpair @ Xx @ Xy )
% 0.19/0.44 @ ( dpsetconstr @ A @ B
% 0.19/0.44 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(func_type,type,
% 0.19/0.44 func: $i > $i > $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(ap_type,type,
% 0.19/0.44 ap: $i > $i > $i > $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(lam_type,type,
% 0.19/0.44 lam: $i > $i > ( $i > $i ) > $i ).
% 0.19/0.44
% 0.19/0.44 thf(lam,definition,
% 0.19/0.44 ( lam
% 0.19/0.44 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.44 ( dpsetconstr @ A @ B
% 0.19/0.44 @ ^ [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( Xf @ Xx )
% 0.19/0.44 = Xy ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(lamp_type,type,
% 0.19/0.44 lamp: $o ).
% 0.19/0.44
% 0.19/0.44 thf(lamp,definition,
% 0.19/0.44 ( lamp
% 0.19/0.44 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.44 => ( func @ A @ B
% 0.19/0.44 @ ( lam @ A @ B
% 0.19/0.44 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(funcGraphProp2_type,type,
% 0.19/0.44 funcGraphProp2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(funcGraphProp2,definition,
% 0.19/0.44 ( funcGraphProp2
% 0.19/0.44 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.44 ( ( func @ A @ B @ Xf )
% 0.19/0.44 => ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.19/0.44 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.44 = Xy ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(beta1,conjecture,
% 0.19/0.44 ( dpsetconstrI
% 0.19/0.44 => ( lamp
% 0.19/0.44 => ( funcGraphProp2
% 0.19/0.44 => ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.44 => ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( ( ap @ A @ B
% 0.19/0.44 @ ( lam @ A @ B
% 0.19/0.44 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.19/0.44 @ Xx )
% 0.19/0.44 = ( Xf @ Xx ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 ------------------------
% 1.53/1.27 ---- Embedded in THF ---
% 1.53/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.28 %%% Generated on Tue Feb 24 12:31:02 EST 2026
% 1.53/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.28 %%% Logic specification used:
% 1.53/1.28 %%% thf(spec, logic, $$dhol).
% 1.53/1.28
% 1.53/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6ZDpTMNeLo/DTF2DTF1563.p
% See solution above
% 1.53/1.28 ------------------------
% 1.53/1.29 ---- Cleaned THF ---
% 1.53/1.29 thf(in_type,type,
% 1.53/1.29 in: $i > $i > $o ).
% 1.53/1.29
% 1.53/1.29 thf(kpair_type,type,
% 1.53/1.29 kpair: $i > $i > $i ).
% 1.53/1.29
% 1.53/1.29 thf(dpsetconstr_type,type,
% 1.53/1.29 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.53/1.29
% 1.53/1.29 thf(dpsetconstrI_type,type,
% 1.53/1.29 dpsetconstrI: $o ).
% 1.53/1.29
% 1.53/1.29 thf(dpsetconstrI,definition,
% 1.53/1.29 ( dpsetconstrI
% 1.53/1.29 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 1.53/1.29 ( ( in @ Xx @ A )
% 1.53/1.29 => ! [Xy: $i] :
% 1.53/1.29 ( ( in @ Xy @ B )
% 1.53/1.29 => ( ( Xphi @ Xx @ Xy )
% 1.53/1.29 => ( in @ ( kpair @ Xx @ Xy )
% 1.53/1.29 @ ( dpsetconstr @ A @ B
% 1.53/1.29 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 1.53/1.29
% 1.53/1.29 thf(func_type,type,
% 1.53/1.29 func: $i > $i > $i > $o ).
% 1.53/1.29
% 1.53/1.29 thf(ap_type,type,
% 1.53/1.29 ap: $i > $i > $i > $i > $i ).
% 1.53/1.29
% 1.53/1.29 thf(lam_type,type,
% 1.53/1.29 lam: $i > $i > ( $i > $i ) > $i ).
% 1.53/1.29
% 1.53/1.29 thf(lam,definition,
% 1.53/1.29 ( lam
% 1.53/1.29 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 1.53/1.29 ( dpsetconstr @ A @ B
% 1.53/1.29 @ ^ [Xx: $i,Xy: $i] :
% 1.53/1.29 ( ( Xf @ Xx )
% 1.53/1.29 = Xy ) ) ) ) ).
% 1.53/1.29
% 1.53/1.29 thf(lamp_type,type,
% 1.53/1.29 lamp: $o ).
% 1.53/1.29
% 1.53/1.29 thf(lamp,definition,
% 1.53/1.29 ( lamp
% 1.53/1.29 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 1.53/1.29 ( ! [Xx: $i] :
% 1.53/1.29 ( ( in @ Xx @ A )
% 1.53/1.29 => ( in @ ( Xf @ Xx ) @ B ) )
% 1.53/1.29 => ( func @ A @ B
% 1.53/1.29 @ ( lam @ A @ B
% 1.53/1.29 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 1.53/1.29
% 1.53/1.29 thf(funcGraphProp2_type,type,
% 1.53/1.29 funcGraphProp2: $o ).
% 1.53/1.29
% 1.53/1.29 thf(funcGraphProp2,definition,
% 1.53/1.29 ( funcGraphProp2
% 1.53/1.29 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.53/1.29 ( ( func @ A @ B @ Xf )
% 1.53/1.29 => ! [Xx: $i] :
% 1.53/1.29 ( ( in @ Xx @ A )
% 1.53/1.29 => ! [Xy: $i] :
% 1.53/1.29 ( ( in @ Xy @ B )
% 1.53/1.29 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 1.53/1.29 => ( ( ap @ A @ B @ Xf @ Xx )
% 1.53/1.29 = Xy ) ) ) ) ) ) ) ).
% 1.53/1.29
% 1.53/1.29 thf(beta1,conjecture,
% 1.53/1.29 ( dpsetconstrI
% 1.53/1.29 => ( lamp
% 1.53/1.29 => ( funcGraphProp2
% 1.53/1.29 => ! [A: $i,B: $i,Xf: $i > $i] :
% 1.53/1.29 ( ! [Xx: $i] :
% 1.53/1.29 ( ( in @ Xx @ A )
% 1.53/1.29 => ( in @ ( Xf @ Xx ) @ B ) )
% 1.53/1.29 => ! [Xx: $i] :
% 1.53/1.29 ( ( in @ Xx @ A )
% 1.53/1.29 => ( ( ap @ A @ B
% 1.53/1.29 @ ( lam @ A @ B
% 1.53/1.29 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 1.53/1.29 @ Xx )
% 1.53/1.29 = ( Xf @ Xx ) ) ) ) ) ) ) ).
% 1.53/1.29 ------------------------
% 1.69/1.30 % (1796)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_1563 for (2999ds/2Mi)
% 1.69/1.30 % (1795)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/2Mi)
% 1.69/1.30 % (1795)Instruction limit reached!
% 1.69/1.30 % (1795)------------------------------
% 1.69/1.30 % (1795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.30 % (1795)Termination reason: Unknown
% 1.69/1.30 % (1795)Termination phase: Property scanning
% 1.69/1.30
% 1.69/1.30 % (1795)Memory used [KB]: 1023
% 1.69/1.30 % (1795)Time elapsed: 0.002 s
% 1.69/1.30 % (1795)Instructions burned: 3 (million)
% 1.69/1.30 % (1795)------------------------------
% 1.69/1.30 % (1795)------------------------------
% 1.69/1.30 % (1796)Instruction limit reached!
% 1.69/1.30 % (1796)------------------------------
% 1.69/1.30 % (1796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.30 % (1796)Termination reason: Unknown
% 1.69/1.30 % (1796)Termination phase: Function definition elimination
% 1.69/1.30
% 1.69/1.30 % (1796)Memory used [KB]: 1023
% 1.69/1.30 % (1796)Time elapsed: 0.003 s
% 1.69/1.30 % (1796)Instructions burned: 4 (million)
% 1.69/1.30 % (1796)------------------------------
% 1.69/1.30 % (1796)------------------------------
% 1.69/1.31 % (1792)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/183Mi)
% 1.69/1.31 % (1794)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_1563 for (2999ds/27Mi)
% 1.69/1.31 % (1797)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_1563 for (2999ds/275Mi)
% 1.69/1.31 % (1798)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/18Mi)
% 1.69/1.31 % (1793)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_1563 for (2999ds/4Mi)
% 1.69/1.31 % (1793)Instruction limit reached!
% 1.69/1.31 % (1793)------------------------------
% 1.69/1.31 % (1793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.31 % (1793)Termination reason: Unknown
% 1.69/1.31 % (1793)Termination phase: Property scanning
% 1.69/1.31
% 1.69/1.31 % (1793)Memory used [KB]: 1023
% 1.69/1.31 % (1793)Time elapsed: 0.004 s
% 1.69/1.31 % (1793)Instructions burned: 4 (million)
% 1.69/1.31 % (1793)------------------------------
% 1.69/1.31 % (1793)------------------------------
% 1.69/1.31 % (1800)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_1563 for (2999ds/37Mi)
% 1.69/1.31 % (1799)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/3Mi)
% 1.69/1.32 % (1799)Instruction limit reached!
% 1.69/1.32 % (1799)------------------------------
% 1.69/1.32 % (1799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (1799)Termination reason: Unknown
% 1.69/1.32 % (1799)Termination phase: Function definition elimination
% 1.69/1.32
% 1.69/1.32 % (1799)Memory used [KB]: 1023
% 1.69/1.32 % (1799)Time elapsed: 0.003 s
% 1.69/1.32 % (1799)Instructions burned: 4 (million)
% 1.69/1.32 % (1799)------------------------------
% 1.69/1.32 % (1799)------------------------------
% 1.69/1.32 % (1797)Refutation not found, incomplete strategy
% 1.69/1.32 % (1797)------------------------------
% 1.69/1.32 % (1797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (1797)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.32
% 1.69/1.32
% 1.69/1.32 % (1797)Memory used [KB]: 5628
% 1.69/1.32 % (1797)Time elapsed: 0.012 s
% 1.69/1.32 % (1797)Instructions burned: 15 (million)
% 1.69/1.32 % (1797)------------------------------
% 1.69/1.32 % (1797)------------------------------
% 1.69/1.32 % (1798)Instruction limit reached!
% 1.69/1.32 % (1798)------------------------------
% 1.69/1.32 % (1798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (1798)Termination reason: Unknown
% 1.69/1.32 % (1798)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (1798)Memory used [KB]: 5756
% 1.69/1.32 % (1798)Time elapsed: 0.014 s
% 1.69/1.32 % (1798)Instructions burned: 19 (million)
% 1.69/1.32 % (1798)------------------------------
% 1.69/1.32 % (1798)------------------------------
% 1.69/1.33 % (1800)Instruction limit reached!
% 1.69/1.33 % (1800)------------------------------
% 1.69/1.33 % (1800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (1800)Termination reason: Unknown
% 1.69/1.33 % (1800)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (1800)Memory used [KB]: 5756
% 1.69/1.33 % (1800)Time elapsed: 0.013 s
% 1.69/1.33 % (1800)Instructions burned: 39 (million)
% 1.69/1.33 % (1800)------------------------------
% 1.69/1.33 % (1800)------------------------------
% 1.69/1.33 % (1802)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/3Mi)
% 1.69/1.33 % (1802)Instruction limit reached!
% 1.69/1.33 % (1802)------------------------------
% 1.69/1.33 % (1802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (1802)Termination reason: Unknown
% 1.69/1.33 % (1802)Termination phase: Property scanning
% 1.69/1.33
% 1.69/1.33 % (1802)Memory used [KB]: 1023
% 1.69/1.33 % (1802)Time elapsed: 0.003 s
% 1.69/1.33 % (1802)Instructions burned: 4 (million)
% 1.69/1.33 % (1802)------------------------------
% 1.69/1.33 % (1802)------------------------------
% 1.69/1.33 % (1794)Instruction limit reached!
% 1.69/1.33 % (1794)------------------------------
% 1.69/1.33 % (1794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (1794)Termination reason: Unknown
% 1.69/1.33 % (1794)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (1794)Memory used [KB]: 5756
% 1.69/1.33 % (1794)Time elapsed: 0.020 s
% 1.69/1.33 % (1794)Instructions burned: 28 (million)
% 1.69/1.33 % (1794)------------------------------
% 1.69/1.33 % (1794)------------------------------
% 1.69/1.33 % (1801)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/15Mi)
% 1.69/1.33 % (1805)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/16Mi)
% 1.69/1.34 % (1806)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/3Mi)
% 1.69/1.34 % (1806)Instruction limit reached!
% 1.69/1.34 % (1806)------------------------------
% 1.69/1.34 % (1806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (1806)Termination reason: Unknown
% 1.69/1.34 % (1806)Termination phase: Function definition elimination
% 1.69/1.34
% 1.69/1.34 % (1806)Memory used [KB]: 1023
% 1.69/1.34 % (1806)Time elapsed: 0.003 s
% 1.69/1.34 % (1806)Instructions burned: 4 (million)
% 1.69/1.34 % (1806)------------------------------
% 1.69/1.34 % (1806)------------------------------
% 1.69/1.34 % (1803)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/1041Mi)
% 1.69/1.34 % (1804)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/7Mi)
% 1.69/1.34 % (1801)Instruction limit reached!
% 1.69/1.34 % (1801)------------------------------
% 1.69/1.34 % (1801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (1801)Termination reason: Unknown
% 1.69/1.34 % (1801)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (1801)Memory used [KB]: 5628
% 1.69/1.34 % (1801)Time elapsed: 0.012 s
% 1.69/1.34 % (1801)Instructions burned: 16 (million)
% 1.69/1.34 % (1801)------------------------------
% 1.69/1.34 % (1801)------------------------------
% 1.69/1.34 % (1805)Instruction limit reached!
% 1.69/1.34 % (1805)------------------------------
% 1.69/1.34 % (1805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (1805)Termination reason: Unknown
% 1.69/1.34 % (1805)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (1805)Memory used [KB]: 5884
% 1.69/1.34 % (1805)Time elapsed: 0.007 s
% 1.69/1.34 % (1805)Instructions burned: 17 (million)
% 1.69/1.34 % (1805)------------------------------
% 1.69/1.34 % (1805)------------------------------
% 1.69/1.34 % (1804)Instruction limit reached!
% 1.69/1.34 % (1804)------------------------------
% 1.69/1.34 % (1804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (1804)Termination reason: Unknown
% 1.69/1.34 % (1804)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (1804)Memory used [KB]: 1023
% 1.69/1.34 % (1804)Time elapsed: 0.006 s
% 1.69/1.34 % (1804)Instructions burned: 7 (million)
% 1.69/1.34 % (1804)------------------------------
% 1.69/1.34 % (1804)------------------------------
% 1.69/1.35 % (1807)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/3Mi)
% 1.69/1.35 % (1807)Instruction limit reached!
% 1.69/1.35 % (1807)------------------------------
% 1.69/1.35 % (1807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (1807)Termination reason: Unknown
% 1.69/1.35 % (1807)Termination phase: Property scanning
% 1.69/1.35
% 1.69/1.35 % (1807)Memory used [KB]: 1023
% 1.69/1.35 % (1807)Time elapsed: 0.004 s
% 1.69/1.35 % (1807)Instructions burned: 4 (million)
% 1.69/1.35 % (1807)------------------------------
% 1.69/1.35 % (1807)------------------------------
% 1.69/1.35 % (1808)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/7Mi)
% 1.69/1.35 % (1808)Refutation not found, incomplete strategy
% 1.69/1.35 % (1808)------------------------------
% 1.69/1.35 % (1808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (1810)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/4Mi)
% 1.69/1.35 % (1808)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.35
% 1.69/1.35
% 1.69/1.35 % (1808)Memory used [KB]: 5500
% 1.69/1.35 % (1808)Time elapsed: 0.003 s
% 1.69/1.35 % (1808)Instructions burned: 4 (million)
% 1.69/1.35 % (1808)------------------------------
% 1.69/1.35 % (1808)------------------------------
% 1.69/1.35 % (1810)Instruction limit reached!
% 1.69/1.35 % (1810)------------------------------
% 1.69/1.35 % (1810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (1810)Termination reason: Unknown
% 1.69/1.35 % (1810)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (1810)Memory used [KB]: 5500
% 1.69/1.35 % (1810)Time elapsed: 0.003 s
% 1.69/1.35 % (1810)Instructions burned: 7 (million)
% 1.69/1.35 % (1810)------------------------------
% 1.69/1.35 % (1810)------------------------------
% 1.69/1.35 % (1792)First to succeed.
% 1.69/1.36 % (1809)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/3Mi)
% 1.69/1.36 % (1811)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1563 for (2999ds/18Mi)
% 1.69/1.36 % (1792)Refutation found. Thanks to Tanya!
% 1.69/1.36 % SZS status Theorem for DTF2THF_1563
% 1.69/1.36 % SZS output start Proof for DTF2THF_1563
% 1.69/1.36 thf(func_def_0, type, in: $i > $i > $o).
% 1.69/1.36 thf(func_def_1, type, kpair: $i > $i > $i).
% 1.69/1.36 thf(func_def_2, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.69/1.36 thf(func_def_5, type, func: $i > $i > $i > $o).
% 1.69/1.36 thf(func_def_6, type, ap: $i > $i > $i > $i > $i).
% 1.69/1.36 thf(func_def_7, type, lam: $i > $i > ($i > $i) > $i).
% 1.69/1.36 thf(func_def_23, type, sK2: $i > $i).
% 1.69/1.36 thf(func_def_26, type, sK5: ($i > $i) > $i > $i > $i).
% 1.69/1.36 thf(func_def_28, type, ph6: !>[X0: $tType]:(X0)).
% 1.69/1.36 thf(func_def_29, type, sK7: ($i > $i) > $i).
% 1.69/1.36 thf(func_def_30, type, sK8: ($i > $i) > $i).
% 1.69/1.36 thf(func_def_31, type, sK9: ($i > $i) > $i).
% 1.69/1.36 thf(func_def_32, type, sK10: ($i > $i) > $i).
% 1.69/1.36 thf(f440,plain,(
% 1.69/1.36 $false),
% 1.69/1.36 inference(avatar_sat_refutation,[status(thm)],[f96,f113,f119,f127,f342,f365,f439])).
% 1.69/1.36 thf(f439,plain,(
% 1.69/1.36 ~spl4_3 | ~spl4_15),
% 1.69/1.36 inference(avatar_contradiction_clause,[status(thm)],[f438])).
% 1.69/1.36 thf(f438,plain,(
% 1.69/1.36 $false | (~spl4_3 | ~spl4_15)),
% 1.69/1.36 inference(subsumption_resolution,[status(thm)],[f433,f437])).
% 1.69/1.36 thf(f437,plain,(
% 1.69/1.36 ((sK8 @ sK2) = (sK2 @ (sK7 @ sK2))) | (~spl4_3 | ~spl4_15)),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f436])).
% 1.69/1.36 thf(f436,plain,(
% 1.69/1.36 ($true != $true) | (sK0 != sK0) | ((sK8 @ sK2) = (sK2 @ (sK7 @ sK2))) | (sK1 != sK1) | (~spl4_3 | ~spl4_15)),
% 1.69/1.36 inference(duplicate_literal_removal,[status(thm)],[f428])).
% 1.69/1.36 thf(f428,plain,(
% 1.69/1.36 (sK0 != sK0) | ((sK8 @ sK2) = (sK2 @ (sK7 @ sK2))) | (sK1 != sK1) | (sK0 != sK0) | ((sK8 @ sK2) = (sK2 @ (sK7 @ sK2))) | ($true != $true) | (~spl4_3 | ~spl4_15)),
% 1.69/1.36 inference(superposition,[status(thm)],[f427,f143])).
% 1.69/1.36 thf(f143,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (((in @ (sK5 @ X2 @ X1 @ X0) @ X0) = $true) | ((sK8 @ X2) = (X2 @ (sK7 @ X2))) | ((sK8 @ X2) = (sK2 @ (sK7 @ X2))) | (sK1 != X1) | (sK0 != X0)) ) | ~spl4_3),
% 1.69/1.36 inference(equality_proxy_clausification,[status(thm)],[f142])).
% 1.69/1.36 thf(f142,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (((sK8 @ X2) = (X2 @ (sK7 @ X2))) | (sK1 != X1) | (sK0 != X0) | ((in @ (sK5 @ X2 @ X1 @ X0) @ X0) = $true) | (((sK2 @ (sK7 @ X2)) = (sK8 @ X2)) = $true)) ) | ~spl4_3),
% 1.69/1.36 inference(equality_proxy_clausification,[status(thm)],[f138])).
% 1.69/1.36 thf(f138,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : ((((X2 @ (sK7 @ X2)) = (sK8 @ X2)) = $true) | ((in @ (sK5 @ X2 @ X1 @ X0) @ X0) = $true) | (sK1 != X1) | (((sK2 @ (sK7 @ X2)) = (sK8 @ X2)) = $true) | (sK0 != X0)) ) | ~spl4_3),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.69/1.36 thf(f136,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : ((sK1 != X1) | (((sK2 @ (sK7 @ X2)) = (sK8 @ X2)) != ((X2 @ (sK7 @ X2)) = (sK8 @ X2))) | ((in @ (sK5 @ X2 @ X1 @ X0) @ X0) = $true) | (sK0 != X0)) ) | ~spl4_3),
% 1.69/1.36 inference(negative_extensionality,[status(thm)],[f135])).
% 1.69/1.36 thf(f135,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (((= @ (X2 @ (sK7 @ X2))) != (= @ (sK2 @ (sK7 @ X2)))) | (sK0 != X0) | (sK1 != X1) | ((in @ (sK5 @ X2 @ X1 @ X0) @ X0) = $true)) ) | ~spl4_3),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f134])).
% 1.69/1.36 thf(f134,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : ((((^[Y0 : $i]: (= @ (sK2 @ Y0))) @ (sK7 @ X2)) != ((^[Y0 : $i]: (= @ (X2 @ Y0))) @ (sK7 @ X2))) | (sK0 != X0) | (sK1 != X1) | ((in @ (sK5 @ X2 @ X1 @ X0) @ X0) = $true)) ) | ~spl4_3),
% 1.69/1.36 inference(negative_extensionality,[status(thm)],[f133])).
% 1.69/1.36 thf(f133,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (((^[Y0 : $i]: (= @ (sK2 @ Y0))) != (^[Y0 : $i]: (= @ (X2 @ Y0)))) | ((in @ (sK5 @ X2 @ X1 @ X0) @ X0) = $true) | (sK1 != X1) | (sK0 != X0)) ) | ~spl4_3),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.69/1.36 thf(f132,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (((^[Y0 : $i]: (= @ (sK2 @ Y0))) != (^[Y0 : $i]: (= @ (X2 @ Y0)))) | (sK0 != X0) | ((in @ (sK5 @ X2 @ X1 @ X0) @ X0) = $true) | (sK1 != X1) | ($false = $true)) ) | ~spl4_3),
% 1.69/1.36 inference(duplicate_literal_removal,[status(thm)],[f128])).
% 1.69/1.36 thf(f128,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (($false = $true) | ((^[Y0 : $i]: (= @ (sK2 @ Y0))) != (^[Y0 : $i]: (= @ (X2 @ Y0)))) | (sK1 != X1) | (sK1 != X1) | ((in @ (sK5 @ X2 @ X1 @ X0) @ X0) = $true) | (sK0 != X0) | (sK0 != X0)) ) | ~spl4_3),
% 1.69/1.36 inference(constrained_superposition,[status(thm)],[f95,f79])).
% 1.69/1.36 thf(f79,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i,X1 : $i] : (((func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y0 : $i]: (= @ (X3 @ Y0))))) = $true) | ((in @ (sK5 @ X3 @ X1 @ X2) @ X2) = $true)) )),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.69/1.36 thf(f77,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i,X1 : $i] : ((((in @ (sK5 @ X3 @ X1 @ X2) @ X2) => (in @ (X3 @ (sK5 @ X3 @ X1 @ X2)) @ X1)) = $false) | ((func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y0 : $i]: (= @ (X3 @ Y0))))) = $true)) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f76])).
% 1.69/1.36 thf(f76,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (X3 @ Y0) @ X1))) @ (sK5 @ X3 @ X1 @ X2)) = $false) | ((func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y0 : $i]: (= @ (X3 @ Y0))))) = $true)) )),
% 1.69/1.36 inference(sigma_clausification,[status(thm)],[f75])).
% 1.69/1.36 thf(f75,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (X3 @ Y0) @ X1)))) = $false) | ((func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y0 : $i]: (= @ (X3 @ Y0))))) = $true)) )),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.69/1.36 thf(f74,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (X3 @ Y0) @ X1)))) => (func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y0 : $i]: (= @ (X3 @ Y0)))))) = $true)) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.69/1.36 thf(f73,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i,X1 : $i] : ((((^[Y0 : $i > $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (Y0 @ Y1) @ X1)))) => (func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y1 : $i]: (= @ (Y0 @ Y1))))))) @ X3) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f72])).
% 1.69/1.36 thf(f72,plain,(
% 1.69/1.36 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $i) @ (^[Y0 : $i > $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (Y0 @ Y1) @ X1)))) => (func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y1 : $i]: (= @ (Y0 @ Y1)))))))) = $true)) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.69/1.36 thf(f71,plain,(
% 1.69/1.36 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (Y1 @ Y2) @ X1)))) => (func @ Y0 @ X1 @ (dpsetconstr @ Y0 @ X1 @ (^[Y2 : $i]: (= @ (Y1 @ Y2))))))))) @ X2) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f70])).
% 1.69/1.36 thf(f70,plain,(
% 1.69/1.36 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (Y1 @ Y2) @ X1)))) => (func @ Y0 @ X1 @ (dpsetconstr @ Y0 @ X1 @ (^[Y2 : $i]: (= @ (Y1 @ Y2)))))))))) = $true)) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.69/1.36 thf(f69,plain,(
% 1.69/1.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (func @ Y1 @ Y0 @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: (= @ (Y2 @ Y3))))))))))) @ X1) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f68])).
% 1.69/1.36 thf(f68,plain,(
% 1.69/1.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (func @ Y1 @ Y0 @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: (= @ (Y2 @ Y3)))))))))))) = $true)),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.69/1.36 thf(f36,plain,(
% 1.69/1.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (func @ Y1 @ Y0 @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y1 @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3))))))))))) = $true)),
% 1.69/1.36 inference(definition_unfolding,[status(thm)],[f31,f30,f33])).
% 1.69/1.36 thf(f33,plain,(
% 1.69/1.36 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f15])).
% 1.69/1.36 thf(f15,plain,(
% 1.69/1.36 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 1.69/1.36 inference(fool_elimination,[status(thm)],[f14])).
% 1.69/1.36 thf(f14,plain,(
% 1.69/1.36 ((^[X0 : $i, X1 : $i, X2 : $i > $i] : (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : (((X2 @ X3) = X4))))) = lam)),
% 1.69/1.36 inference(rectify,[status(thm)],[f2])).
% 1.69/1.36 thf(f2,axiom,(
% 1.69/1.36 ((^[X0 : $i, X1 : $i, X7 : $i > $i] : (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : (((X7 @ X3) = X4))))) = lam)),
% 1.69/1.36 file('/export/starexec/sandbox2/tmp/tmp.6ZDpTMNeLo/DTF2THF_1563.p',lam)).
% 1.69/1.36 thf(f30,plain,(
% 1.69/1.36 (lamp = $true)),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f23])).
% 1.69/1.36 thf(f23,plain,(
% 1.69/1.36 (lamp = $true) & ((((sK2 @ sK3) != (ap @ sK0 @ sK1 @ (lam @ sK0 @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0))) @ sK3)) & ((in @ sK3 @ sK0) = $true)) & ! [X4 : $i] : (((in @ (sK2 @ X4) @ sK1) = $true) | ((in @ X4 @ sK0) != $true))) & (funcGraphProp2 = $true) & (dpsetconstrI = $true)),
% 1.69/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f22,f21])).
% 1.69/1.36 thf(f21,plain,(
% 1.69/1.36 ? [X0 : $i,X1 : $i,X2 : $i > $i] : (? [X3 : $i] : (((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ X3) != (X2 @ X3)) & ((in @ X3 @ X0) = $true)) & ! [X4 : $i] : (((in @ (X2 @ X4) @ X1) = $true) | ((in @ X4 @ X0) != $true))) => (? [X3 : $i] : (((sK2 @ X3) != (ap @ sK0 @ sK1 @ (lam @ sK0 @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0))) @ X3)) & ((in @ X3 @ sK0) = $true)) & ! [X4 : $i] : (((in @ (sK2 @ X4) @ sK1) = $true) | ((in @ X4 @ sK0) != $true)))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f22,plain,(
% 1.69/1.36 ? [X3 : $i] : (((sK2 @ X3) != (ap @ sK0 @ sK1 @ (lam @ sK0 @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0))) @ X3)) & ((in @ X3 @ sK0) = $true)) => (((sK2 @ sK3) != (ap @ sK0 @ sK1 @ (lam @ sK0 @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0))) @ sK3)) & ((in @ sK3 @ sK0) = $true))),
% 1.69/1.36 introduced(definition,[],[choice_axiom])).
% 1.69/1.36 thf(f20,plain,(
% 1.69/1.36 (lamp = $true) & ? [X0 : $i,X1 : $i,X2 : $i > $i] : (? [X3 : $i] : (((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ X3) != (X2 @ X3)) & ((in @ X3 @ X0) = $true)) & ! [X4 : $i] : (((in @ (X2 @ X4) @ X1) = $true) | ((in @ X4 @ X0) != $true))) & (funcGraphProp2 = $true) & (dpsetconstrI = $true)),
% 1.69/1.36 inference(rectify,[status(thm)],[f19])).
% 1.69/1.36 thf(f19,plain,(
% 1.69/1.36 (lamp = $true) & ? [X0 : $i,X1 : $i,X2 : $i > $i] : (? [X4 : $i] : (((X2 @ X4) != (ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4)) & ((in @ X4 @ X0) = $true)) & ! [X3 : $i] : (((in @ (X2 @ X3) @ X1) = $true) | ((in @ X3 @ X0) != $true))) & (funcGraphProp2 = $true) & (dpsetconstrI = $true)),
% 1.69/1.36 inference(flattening,[status(thm)],[f18])).
% 1.69/1.36 thf(f18,plain,(
% 1.69/1.36 ((? [X0 : $i,X1 : $i,X2 : $i > $i] : (? [X4 : $i] : (((X2 @ X4) != (ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4)) & ((in @ X4 @ X0) = $true)) & ! [X3 : $i] : (((in @ (X2 @ X3) @ X1) = $true) | ((in @ X3 @ X0) != $true))) & (funcGraphProp2 = $true)) & (lamp = $true)) & (dpsetconstrI = $true)),
% 1.69/1.36 inference(ennf_transformation,[status(thm)],[f9])).
% 1.69/1.36 thf(f9,plain,(
% 1.69/1.36 ~((dpsetconstrI = $true) => ((lamp = $true) => ((funcGraphProp2 = $true) => ! [X0 : $i,X1 : $i,X2 : $i > $i] : (! [X3 : $i] : (((in @ X3 @ X0) = $true) => ((in @ (X2 @ X3) @ X1) = $true)) => ! [X4 : $i] : (((in @ X4 @ X0) = $true) => ((X2 @ X4) = (ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4)))))))),
% 1.69/1.36 inference(fool_elimination,[status(thm)],[f8])).
% 1.69/1.36 thf(f8,plain,(
% 1.69/1.36 ~(dpsetconstrI => (lamp => (funcGraphProp2 => ! [X0 : $i,X1 : $i,X2 : $i > $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X5 : $i] : (X2 @ X5))) @ X4) = (X2 @ X4)))))))),
% 1.69/1.36 inference(rectify,[status(thm)],[f6])).
% 1.69/1.36 thf(f6,negated_conjecture,(
% 1.69/1.36 ~(dpsetconstrI => (lamp => (funcGraphProp2 => ! [X0 : $i,X1 : $i,X7 : $i > $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X7 @ X3) @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : (X7 @ X4))) @ X3) = (X7 @ X3)))))))),
% 1.69/1.36 inference(negated_conjecture,[status(cth)],[f5])).
% 1.69/1.36 thf(f5,conjecture,(
% 1.69/1.36 dpsetconstrI => (lamp => (funcGraphProp2 => ! [X0 : $i,X1 : $i,X7 : $i > $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X7 @ X3) @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : (X7 @ X4))) @ X3) = (X7 @ X3))))))),
% 1.69/1.36 file('/export/starexec/sandbox2/tmp/tmp.6ZDpTMNeLo/DTF2THF_1563.p',beta1)).
% 1.69/1.36 thf(f31,plain,(
% 1.69/1.36 (lamp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (func @ Y1 @ Y0 @ (lam @ Y1 @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3))))))))))))),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.36 thf(f17,plain,(
% 1.69/1.36 (lamp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (func @ Y1 @ Y0 @ (lam @ Y1 @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3))))))))))))),
% 1.69/1.36 inference(fool_elimination,[status(thm)],[f16])).
% 1.69/1.36 thf(f16,plain,(
% 1.69/1.36 (lamp = ! [X0 : $i > $i,X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X1) => (in @ (X0 @ X3) @ X2)) => (func @ X1 @ X2 @ (lam @ X1 @ X2 @ (^[X4 : $i] : (X0 @ X4))))))),
% 1.69/1.36 inference(rectify,[status(thm)],[f3])).
% 1.69/1.36 thf(f3,axiom,(
% 1.69/1.36 (lamp = ! [X7 : $i > $i,X0 : $i,X1 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X7 @ X3) @ X1)) => (func @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X3 : $i] : (X7 @ X3))))))),
% 1.69/1.36 file('/export/starexec/sandbox2/tmp/tmp.6ZDpTMNeLo/DTF2THF_1563.p',lamp)).
% 1.69/1.36 thf(f95,plain,(
% 1.69/1.36 ($false = (func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (^[Y0 : $i]: (= @ (sK2 @ Y0)))))) | ~spl4_3),
% 1.69/1.36 inference(avatar_component_clause,[status(thm)],[f93])).
% 1.69/1.36 thf(f93,definition,(
% 1.69/1.36 spl4_3 <=> ($false = (func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (^[Y0 : $i]: (= @ (sK2 @ Y0))))))),
% 1.69/1.36 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.69/1.36 thf(f427,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((in @ (sK5 @ sK2 @ sK1 @ X0) @ sK0) != $true) | (sK0 != X0)) ) | ~spl4_15),
% 1.69/1.36 inference(equality_resolution,[status(thm)],[f341])).
% 1.69/1.36 thf(f341,plain,(
% 1.69/1.36 ( ! [X0 : $i,X1 : $i] : (((sK5 @ sK2 @ sK1 @ X0) != X1) | (sK0 != X0) | ((in @ X1 @ sK0) != $true)) ) | ~spl4_15),
% 1.69/1.36 inference(avatar_component_clause,[status(thm)],[f340])).
% 1.69/1.36 thf(f340,definition,(
% 1.69/1.36 spl4_15 <=> ! [X0 : $i,X1 : $i] : ((sK0 != X0) | ((in @ X1 @ sK0) != $true) | ((sK5 @ sK2 @ sK1 @ X0) != X1))),
% 1.69/1.36 introduced(definition,[new_symbols(naming,[spl4_15])],[avatar_definition])).
% 1.69/1.36 thf(f433,plain,(
% 1.69/1.36 ((sK8 @ sK2) != (sK2 @ (sK7 @ sK2))) | (~spl4_3 | ~spl4_15)),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f432])).
% 1.69/1.36 thf(f432,plain,(
% 1.69/1.36 (sK0 != sK0) | ((sK8 @ sK2) != (sK2 @ (sK7 @ sK2))) | (sK1 != sK1) | ($true != $true) | (~spl4_3 | ~spl4_15)),
% 1.69/1.36 inference(duplicate_literal_removal,[status(thm)],[f429])).
% 1.69/1.36 thf(f429,plain,(
% 1.69/1.36 (sK0 != sK0) | (sK0 != sK0) | ((sK8 @ sK2) != (sK2 @ (sK7 @ sK2))) | (sK1 != sK1) | ($true != $true) | ((sK8 @ sK2) != (sK2 @ (sK7 @ sK2))) | (~spl4_3 | ~spl4_15)),
% 1.69/1.36 inference(superposition,[status(thm)],[f427,f141])).
% 1.69/1.36 thf(f141,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (((in @ (sK5 @ X2 @ X1 @ X0) @ X0) = $true) | ((sK8 @ X2) != (X2 @ (sK7 @ X2))) | ((sK8 @ X2) != (sK2 @ (sK7 @ X2))) | (sK1 != X1) | (sK0 != X0)) ) | ~spl4_3),
% 1.69/1.36 inference(equality_proxy_clausification,[status(thm)],[f140])).
% 1.69/1.36 thf(f140,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (((sK8 @ X2) != (X2 @ (sK7 @ X2))) | ((in @ (sK5 @ X2 @ X1 @ X0) @ X0) = $true) | (((sK2 @ (sK7 @ X2)) = (sK8 @ X2)) = $false) | (sK0 != X0) | (sK1 != X1)) ) | ~spl4_3),
% 1.69/1.36 inference(equality_proxy_clausification,[status(thm)],[f139])).
% 1.69/1.36 thf(f139,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : ((((X2 @ (sK7 @ X2)) = (sK8 @ X2)) = $false) | (sK1 != X1) | (((sK2 @ (sK7 @ X2)) = (sK8 @ X2)) = $false) | ((in @ (sK5 @ X2 @ X1 @ X0) @ X0) = $true) | (sK0 != X0)) ) | ~spl4_3),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.69/1.36 thf(f365,plain,(
% 1.69/1.36 spl4_15 | ~spl4_3 | ~spl4_14),
% 1.69/1.36 inference(avatar_split_clause,[status(thm)],[f364,f336,f93,f340])).
% 1.69/1.36 thf(f336,definition,(
% 1.69/1.36 spl4_14 <=> ((sK10 @ sK2) = (sK2 @ (sK9 @ sK2)))),
% 1.69/1.36 introduced(definition,[new_symbols(naming,[spl4_14])],[avatar_definition])).
% 1.69/1.36 thf(f364,plain,(
% 1.69/1.36 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ sK0) != $true) | ((sK5 @ sK2 @ sK1 @ X1) != X0) | (sK0 != X1)) ) | (~spl4_3 | ~spl4_14)),
% 1.69/1.36 inference(subsumption_resolution,[status(thm)],[f363,f338])).
% 1.69/1.36 thf(f338,plain,(
% 1.69/1.36 ((sK10 @ sK2) = (sK2 @ (sK9 @ sK2))) | ~spl4_14),
% 1.69/1.36 inference(avatar_component_clause,[status(thm)],[f336])).
% 1.69/1.36 thf(f363,plain,(
% 1.69/1.36 ( ! [X0 : $i,X1 : $i] : (((sK10 @ sK2) != (sK2 @ (sK9 @ sK2))) | ((in @ X0 @ sK0) != $true) | ((sK5 @ sK2 @ sK1 @ X1) != X0) | (sK0 != X1)) ) | (~spl4_3 | ~spl4_14)),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f362])).
% 1.69/1.36 thf(f362,plain,(
% 1.69/1.36 ( ! [X0 : $i,X1 : $i] : (((sK10 @ sK2) != (sK2 @ (sK9 @ sK2))) | ((sK5 @ sK2 @ sK1 @ X1) != X0) | ((in @ X0 @ sK0) != $true) | (sK0 != X1) | ((sK10 @ sK2) != (sK10 @ sK2))) ) | (~spl4_3 | ~spl4_14)),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f347])).
% 1.69/1.36 thf(f347,plain,(
% 1.69/1.36 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ sK0) != $true) | ((sK2 @ (sK9 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) != (sK10 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) | (((^[Y0 : $i]: (Y0)) @ (sK5 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK1 @ X1)) != X0) | (sK0 != X1) | ((sK10 @ sK2) != (sK10 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0)))))) ) | (~spl4_3 | ~spl4_14)),
% 1.69/1.36 inference(superposition,[status(thm)],[f200,f338])).
% 1.69/1.36 thf(f200,plain,(
% 1.69/1.36 ( ! [X2 : $i,X0 : $i > $i,X1 : $i] : (((sK2 @ (X0 @ (sK9 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))))) != (sK10 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))))) | ((in @ X2 @ sK0) != $true) | ((sK10 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))) != (sK2 @ (sK9 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))))) | (sK0 != X1) | ((X0 @ (sK5 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))) @ sK1 @ X1)) != X2)) ) | ~spl4_3),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f199])).
% 1.69/1.36 thf(f199,plain,(
% 1.69/1.36 ( ! [X2 : $i,X0 : $i > $i,X1 : $i] : (((sK10 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))) != (sK2 @ (sK9 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))))) | ((X0 @ (sK5 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))) @ sK1 @ X1)) != X2) | ((in @ X2 @ sK0) != $true) | (sK0 != X1) | (((^[Y0 : $i]: (sK2 @ (X0 @ Y0))) @ (sK9 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))))) != (sK10 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))))) ) | ~spl4_3),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f171])).
% 1.69/1.36 thf(f171,plain,(
% 1.69/1.36 ( ! [X2 : $i,X0 : $i > $i,X1 : $i] : ((((^[Y0 : $i]: (sK2 @ (X0 @ Y0))) @ (sK9 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))))) != (sK10 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))))) | (sK0 != X1) | ((in @ X2 @ sK0) != $true) | ((X0 @ (sK5 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))) @ sK1 @ X1)) != X2) | ($false = $true) | ((sK10 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))) != (sK2 @ (sK9 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))))) | (sK1 != sK1)) ) | ~spl4_3),
% 1.69/1.36 inference(constrained_superposition,[status(thm)],[f165,f27])).
% 1.69/1.36 thf(f27,plain,(
% 1.69/1.36 ( ! [X4 : $i] : (((in @ (sK2 @ X4) @ sK1) = $true) | ((in @ X4 @ sK0) != $true)) )),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f23])).
% 1.69/1.36 thf(f165,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (((in @ (X2 @ (sK5 @ X2 @ X1 @ X0)) @ X1) = $false) | ((sK10 @ X2) != (X2 @ (sK9 @ X2))) | (sK0 != X0) | ((sK10 @ X2) != (sK2 @ (sK9 @ X2))) | (sK1 != X1)) ) | ~spl4_3),
% 1.69/1.36 inference(equality_proxy_clausification,[status(thm)],[f164])).
% 1.69/1.36 thf(f164,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (((in @ (X2 @ (sK5 @ X2 @ X1 @ X0)) @ X1) = $false) | ((sK10 @ X2) != (X2 @ (sK9 @ X2))) | (((sK2 @ (sK9 @ X2)) = (sK10 @ X2)) = $false) | (sK0 != X0) | (sK1 != X1)) ) | ~spl4_3),
% 1.69/1.36 inference(equality_proxy_clausification,[status(thm)],[f163])).
% 1.69/1.36 thf(f163,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : ((sK1 != X1) | ($false = ((X2 @ (sK9 @ X2)) = (sK10 @ X2))) | (sK0 != X0) | (((sK2 @ (sK9 @ X2)) = (sK10 @ X2)) = $false) | ((in @ (X2 @ (sK5 @ X2 @ X1 @ X0)) @ X1) = $false)) ) | ~spl4_3),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f160])).
% 1.69/1.36 thf(f160,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : ((sK0 != X0) | ((in @ (X2 @ (sK5 @ X2 @ X1 @ X0)) @ X1) = $false) | (((sK2 @ (sK9 @ X2)) = (sK10 @ X2)) != ((X2 @ (sK9 @ X2)) = (sK10 @ X2))) | (sK1 != X1)) ) | ~spl4_3),
% 1.69/1.36 inference(negative_extensionality,[status(thm)],[f151])).
% 1.69/1.36 thf(f151,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (((= @ (sK2 @ (sK9 @ X2))) != (= @ (X2 @ (sK9 @ X2)))) | (sK1 != X1) | ((in @ (X2 @ (sK5 @ X2 @ X1 @ X0)) @ X1) = $false) | (sK0 != X0)) ) | ~spl4_3),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f150])).
% 1.69/1.36 thf(f150,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : ((sK1 != X1) | ((in @ (X2 @ (sK5 @ X2 @ X1 @ X0)) @ X1) = $false) | (sK0 != X0) | (((^[Y0 : $i]: (= @ (sK2 @ Y0))) @ (sK9 @ X2)) != ((^[Y0 : $i]: (= @ (X2 @ Y0))) @ (sK9 @ X2)))) ) | ~spl4_3),
% 1.69/1.36 inference(negative_extensionality,[status(thm)],[f149])).
% 1.69/1.36 thf(f149,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (((^[Y0 : $i]: (= @ (sK2 @ Y0))) != (^[Y0 : $i]: (= @ (X2 @ Y0)))) | (sK1 != X1) | ((in @ (X2 @ (sK5 @ X2 @ X1 @ X0)) @ X1) = $false) | (sK0 != X0)) ) | ~spl4_3),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f148])).
% 1.69/1.36 thf(f148,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : ((sK1 != X1) | (sK0 != X0) | ((in @ (X2 @ (sK5 @ X2 @ X1 @ X0)) @ X1) = $false) | ((^[Y0 : $i]: (= @ (sK2 @ Y0))) != (^[Y0 : $i]: (= @ (X2 @ Y0)))) | ($false = $true)) ) | ~spl4_3),
% 1.69/1.36 inference(duplicate_literal_removal,[status(thm)],[f144])).
% 1.69/1.36 thf(f144,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : ((sK1 != X1) | ($false = $true) | (sK0 != X0) | ((^[Y0 : $i]: (= @ (sK2 @ Y0))) != (^[Y0 : $i]: (= @ (X2 @ Y0)))) | (sK1 != X1) | ((in @ (X2 @ (sK5 @ X2 @ X1 @ X0)) @ X1) = $false) | (sK0 != X0)) ) | ~spl4_3),
% 1.69/1.36 inference(constrained_superposition,[status(thm)],[f78,f95])).
% 1.69/1.36 thf(f78,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i,X1 : $i] : (((func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y0 : $i]: (= @ (X3 @ Y0))))) = $true) | ($false = (in @ (X3 @ (sK5 @ X3 @ X1 @ X2)) @ X1))) )),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.69/1.36 thf(f342,plain,(
% 1.69/1.36 spl4_14 | spl4_15 | ~spl4_3),
% 1.69/1.36 inference(avatar_split_clause,[status(thm)],[f334,f93,f340,f336])).
% 1.69/1.36 thf(f334,plain,(
% 1.69/1.36 ( ! [X0 : $i,X1 : $i] : (((sK10 @ sK2) = (sK2 @ (sK9 @ sK2))) | (sK0 != X0) | ((sK5 @ sK2 @ sK1 @ X0) != X1) | ((in @ X1 @ sK0) != $true)) ) | ~spl4_3),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f333])).
% 1.69/1.36 thf(f333,plain,(
% 1.69/1.36 ( ! [X0 : $i,X1 : $i] : ((sK0 != X0) | ((in @ X1 @ sK0) != $true) | ((sK2 @ (sK9 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = (sK10 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) | (((^[Y0 : $i]: (Y0)) @ (sK5 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK1 @ X0)) != X1)) ) | ~spl4_3),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f325])).
% 1.69/1.36 thf(f325,plain,(
% 1.69/1.36 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ sK0) != $true) | ((sK10 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0)))) != (sK10 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) | (sK0 != X0) | (((^[Y0 : $i]: (Y0)) @ (sK5 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK1 @ X0)) != X1) | ((sK2 @ (sK9 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = (sK10 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0)))))) ) | ~spl4_3),
% 1.69/1.36 inference(equality_factoring,[status(thm)],[f271])).
% 1.69/1.36 thf(f271,plain,(
% 1.69/1.36 ( ! [X2 : $i,X0 : $i > $i,X1 : $i] : (((sK2 @ (X0 @ (sK9 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))))) = (sK10 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))))) | ((sK10 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))) = (sK2 @ (sK9 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))))) | (sK0 != X1) | ((in @ X2 @ sK0) != $true) | ((X0 @ (sK5 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))) @ sK1 @ X1)) != X2)) ) | ~spl4_3),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f270])).
% 1.69/1.36 thf(f270,plain,(
% 1.69/1.36 ( ! [X2 : $i,X0 : $i > $i,X1 : $i] : (((X0 @ (sK5 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))) @ sK1 @ X1)) != X2) | ((sK10 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))) = (sK2 @ (sK9 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))))) | (sK0 != X1) | (((^[Y0 : $i]: (sK2 @ (X0 @ Y0))) @ (sK9 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))))) = (sK10 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))))) | ((in @ X2 @ sK0) != $true)) ) | ~spl4_3),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f251])).
% 1.69/1.36 thf(f251,plain,(
% 1.69/1.36 ( ! [X2 : $i,X0 : $i > $i,X1 : $i] : (((sK10 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))) = (sK2 @ (sK9 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0)))))) | ($false = $true) | (sK1 != sK1) | (((^[Y0 : $i]: (sK2 @ (X0 @ Y0))) @ (sK9 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))))) = (sK10 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))))) | ((X0 @ (sK5 @ (^[Y0 : $i]: (sK2 @ (X0 @ Y0))) @ sK1 @ X1)) != X2) | ((in @ X2 @ sK0) != $true) | (sK0 != X1)) ) | ~spl4_3),
% 1.69/1.36 inference(constrained_superposition,[status(thm)],[f167,f27])).
% 1.69/1.36 thf(f167,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (((in @ (X2 @ (sK5 @ X2 @ X1 @ X0)) @ X1) = $false) | ((sK10 @ X2) = (sK2 @ (sK9 @ X2))) | (sK0 != X0) | (sK1 != X1) | ((sK10 @ X2) = (X2 @ (sK9 @ X2)))) ) | ~spl4_3),
% 1.69/1.36 inference(equality_proxy_clausification,[status(thm)],[f166])).
% 1.69/1.36 thf(f166,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : (((in @ (X2 @ (sK5 @ X2 @ X1 @ X0)) @ X1) = $false) | (((X2 @ (sK9 @ X2)) = (sK10 @ X2)) = $true) | (sK1 != X1) | ((sK10 @ X2) = (sK2 @ (sK9 @ X2))) | (sK0 != X0)) ) | ~spl4_3),
% 1.69/1.36 inference(equality_proxy_clausification,[status(thm)],[f162])).
% 1.69/1.36 thf(f162,plain,(
% 1.69/1.36 ( ! [X2 : $i > $i,X0 : $i,X1 : $i] : ((sK0 != X0) | (sK1 != X1) | (((sK2 @ (sK9 @ X2)) = (sK10 @ X2)) = $true) | ((in @ (X2 @ (sK5 @ X2 @ X1 @ X0)) @ X1) = $false) | (((X2 @ (sK9 @ X2)) = (sK10 @ X2)) = $true)) ) | ~spl4_3),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f160])).
% 1.69/1.36 thf(f127,plain,(
% 1.69/1.36 ~spl4_4),
% 1.69/1.36 inference(avatar_contradiction_clause,[status(thm)],[f126])).
% 1.69/1.36 thf(f126,plain,(
% 1.69/1.36 $false | ~spl4_4),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.69/1.36 thf(f125,plain,(
% 1.69/1.36 ((sK2 @ sK3) != (sK2 @ sK3)) | ($true != $true) | ~spl4_4),
% 1.69/1.36 inference(superposition,[status(thm)],[f124,f28])).
% 1.69/1.36 thf(f28,plain,(
% 1.69/1.36 ((in @ sK3 @ sK0) = $true)),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f23])).
% 1.69/1.36 thf(f124,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((in @ X0 @ sK0) != $true) | ((sK2 @ X0) != (sK2 @ sK3))) ) | ~spl4_4),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.69/1.36 thf(f121,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (($false = $true) | ((sK2 @ X0) != (sK2 @ sK3)) | ((in @ X0 @ sK0) != $true)) ) | ~spl4_4),
% 1.69/1.36 inference(superposition,[status(thm)],[f111,f27])).
% 1.69/1.36 thf(f111,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((in @ X0 @ sK1) = $false) | ((sK2 @ sK3) != X0)) ) | ~spl4_4),
% 1.69/1.36 inference(avatar_component_clause,[status(thm)],[f110])).
% 1.69/1.36 thf(f110,definition,(
% 1.69/1.36 spl4_4 <=> ! [X0 : $i] : (((in @ X0 @ sK1) = $false) | ((sK2 @ sK3) != X0))),
% 1.69/1.36 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.69/1.36 thf(f119,plain,(
% 1.69/1.36 ~spl4_1),
% 1.69/1.36 inference(avatar_contradiction_clause,[status(thm)],[f118])).
% 1.69/1.36 thf(f118,plain,(
% 1.69/1.36 $false | ~spl4_1),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.69/1.36 thf(f115,plain,(
% 1.69/1.36 ($false = $true) | ~spl4_1),
% 1.69/1.36 inference(superposition,[status(thm)],[f28,f88])).
% 1.69/1.36 thf(f88,plain,(
% 1.69/1.36 ($false = (in @ sK3 @ sK0)) | ~spl4_1),
% 1.69/1.36 inference(avatar_component_clause,[status(thm)],[f86])).
% 1.69/1.36 thf(f86,definition,(
% 1.69/1.36 spl4_1 <=> ($false = (in @ sK3 @ sK0))),
% 1.69/1.36 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.69/1.36 thf(f113,plain,(
% 1.69/1.36 spl4_1 | spl4_4 | ~spl4_2),
% 1.69/1.36 inference(avatar_split_clause,[status(thm)],[f103,f90,f110,f86])).
% 1.69/1.36 thf(f90,definition,(
% 1.69/1.36 spl4_2 <=> ! [X0 : $i] : (((sK2 @ sK3) != X0) | ((in @ (kpair @ sK3 @ X0) @ (dpsetconstr @ sK0 @ sK1 @ (^[Y0 : $i]: (= @ (sK2 @ Y0))))) = $false) | ((in @ X0 @ sK1) = $false))),
% 1.69/1.36 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.69/1.36 thf(f103,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((in @ X0 @ sK1) = $false) | ($false = (in @ sK3 @ sK0)) | ((sK2 @ sK3) != X0)) ) | ~spl4_2),
% 1.69/1.36 inference(duplicate_literal_removal,[status(thm)],[f102])).
% 1.69/1.36 thf(f102,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((sK2 @ sK3) != X0) | ((in @ X0 @ sK1) = $false) | ($false = (in @ sK3 @ sK0)) | ((sK2 @ sK3) != X0)) ) | ~spl4_2),
% 1.69/1.36 inference(equality_proxy_clausification,[status(thm)],[f101])).
% 1.69/1.36 thf(f101,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((sK2 @ sK3) != X0) | ($false = ((sK2 @ sK3) = X0)) | ($false = (in @ sK3 @ sK0)) | ((in @ X0 @ sK1) = $false)) ) | ~spl4_2),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f100])).
% 1.69/1.36 thf(f100,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((in @ X0 @ sK1) = $false) | ((sK2 @ sK3) != X0) | ($false = (in @ sK3 @ sK0)) | (((^[Y0 : $i]: (= @ (sK2 @ Y0))) @ sK3 @ X0) = $false)) ) | ~spl4_2),
% 1.69/1.36 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.69/1.36 thf(f99,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((sK2 @ sK3) != X0) | (((^[Y0 : $i]: (= @ (sK2 @ Y0))) @ sK3 @ X0) = $false) | ((in @ X0 @ sK1) = $false) | ($false = $true) | ($false = (in @ sK3 @ sK0))) ) | ~spl4_2),
% 1.69/1.36 inference(duplicate_literal_removal,[status(thm)],[f97])).
% 1.69/1.36 thf(f97,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (($false = (in @ sK3 @ sK0)) | ((sK2 @ sK3) != X0) | ((in @ X0 @ sK1) = $false) | (((^[Y0 : $i]: (= @ (sK2 @ Y0))) @ sK3 @ X0) = $false) | ((in @ X0 @ sK1) = $false) | ($false = $true)) ) | ~spl4_2),
% 1.69/1.36 inference(superposition,[status(thm)],[f91,f51])).
% 1.69/1.36 thf(f51,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i,X5 : $i] : (((in @ (kpair @ X4 @ X5) @ (dpsetconstr @ X2 @ X1 @ X3)) = $true) | ($false = (in @ X4 @ X2)) | ($false = (in @ X5 @ X1)) | ($false = (X3 @ X4 @ X5))) )),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.69/1.36 thf(f50,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i,X5 : $i] : (($false = (in @ X5 @ X1)) | ($false = (in @ X4 @ X2)) | (((X3 @ X4 @ X5) => (in @ (kpair @ X4 @ X5) @ (dpsetconstr @ X2 @ X1 @ X3))) = $true)) )),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.69/1.36 thf(f49,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X1) => ((X3 @ X4 @ X5) => (in @ (kpair @ X4 @ X5) @ (dpsetconstr @ X2 @ X1 @ X3)))) = $true) | ($false = (in @ X4 @ X2))) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.69/1.36 thf(f48,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i,X5 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X1) => ((X3 @ X4 @ Y0) => (in @ (kpair @ X4 @ Y0) @ (dpsetconstr @ X2 @ X1 @ X3))))) @ X5) = $true) | ($false = (in @ X4 @ X2))) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f47])).
% 1.69/1.36 thf(f47,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X3 @ X4 @ Y0) => (in @ (kpair @ X4 @ Y0) @ (dpsetconstr @ X2 @ X1 @ X3)))))) = $true) | ($false = (in @ X4 @ X2))) )),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.69/1.36 thf(f46,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i] : ((((in @ X4 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X3 @ X4 @ Y0) => (in @ (kpair @ X4 @ Y0) @ (dpsetconstr @ X2 @ X1 @ X3))))))) = $true)) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.69/1.36 thf(f45,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((X3 @ Y0 @ Y1) => (in @ (kpair @ Y0 @ Y1) @ (dpsetconstr @ X2 @ X1 @ X3)))))))) @ X4) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f44])).
% 1.69/1.36 thf(f44,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((X3 @ Y0 @ Y1) => (in @ (kpair @ Y0 @ Y1) @ (dpsetconstr @ X2 @ X1 @ X3))))))))) = $true)) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.69/1.36 thf(f43,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i] : ((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y0 @ Y1 @ Y2) => (in @ (kpair @ Y1 @ Y2) @ (dpsetconstr @ X2 @ X1 @ Y0)))))))))) @ X3) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f42])).
% 1.69/1.36 thf(f42,plain,(
% 1.69/1.36 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y0 @ Y1 @ Y2) => (in @ (kpair @ Y1 @ Y2) @ (dpsetconstr @ X2 @ X1 @ Y0))))))))))) = $true)) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.69/1.36 thf(f41,plain,(
% 1.69/1.36 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => ((Y1 @ Y2 @ Y3) => (in @ (kpair @ Y2 @ Y3) @ (dpsetconstr @ Y0 @ X1 @ Y1)))))))))))) @ X2) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f40])).
% 1.69/1.36 thf(f40,plain,(
% 1.69/1.36 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => ((Y1 @ Y2 @ Y3) => (in @ (kpair @ Y2 @ Y3) @ (dpsetconstr @ Y0 @ X1 @ Y1))))))))))))) = $true)) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.69/1.36 thf(f39,plain,(
% 1.69/1.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((Y2 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ Y2)))))))))))))) @ X1) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f38])).
% 1.69/1.36 thf(f38,plain,(
% 1.69/1.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((Y2 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ Y2))))))))))))))) = $true)),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.69/1.36 thf(f35,plain,(
% 1.69/1.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((Y2 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6))))))))))))))))))) = $true)),
% 1.69/1.36 inference(definition_unfolding,[status(thm)],[f25,f24])).
% 1.69/1.36 thf(f24,plain,(
% 1.69/1.36 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((Y2 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6))))))))))))))))))))),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f13])).
% 1.69/1.36 thf(f13,plain,(
% 1.69/1.36 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((Y2 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6))))))))))))))))))))),
% 1.69/1.36 inference(fool_elimination,[status(thm)],[f12])).
% 1.69/1.36 thf(f12,plain,(
% 1.69/1.36 (dpsetconstrI = ! [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i] : ((in @ X0 @ X2) => ! [X4 : $i] : ((in @ X4 @ X3) => ((X1 @ X0 @ X4) => (in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X2 @ X3 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6))))))))),
% 1.69/1.36 inference(rectify,[status(thm)],[f1])).
% 1.69/1.36 thf(f1,axiom,(
% 1.69/1.36 (dpsetconstrI = ! [X3 : $i,X2 : $i > $i > $o,X0 : $i,X1 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((X2 @ X3 @ X4) => (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : (X2 @ X5 @ X6))))))))),
% 1.69/1.36 file('/export/starexec/sandbox2/tmp/tmp.6ZDpTMNeLo/DTF2THF_1563.p',dpsetconstrI)).
% 1.69/1.36 thf(f25,plain,(
% 1.69/1.36 (dpsetconstrI = $true)),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f23])).
% 1.69/1.36 thf(f91,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((in @ (kpair @ sK3 @ X0) @ (dpsetconstr @ sK0 @ sK1 @ (^[Y0 : $i]: (= @ (sK2 @ Y0))))) = $false) | ((sK2 @ sK3) != X0) | ((in @ X0 @ sK1) = $false)) ) | ~spl4_2),
% 1.69/1.36 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.69/1.36 thf(f96,plain,(
% 1.69/1.36 spl4_1 | spl4_2 | spl4_3),
% 1.69/1.36 inference(avatar_split_clause,[status(thm)],[f83,f93,f90,f86])).
% 1.69/1.36 thf(f83,plain,(
% 1.69/1.36 ( ! [X0 : $i] : (((sK2 @ sK3) != X0) | ($false = (in @ sK3 @ sK0)) | ((in @ X0 @ sK1) = $false) | ((in @ (kpair @ sK3 @ X0) @ (dpsetconstr @ sK0 @ sK1 @ (^[Y0 : $i]: (= @ (sK2 @ Y0))))) = $false) | ($false = (func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (^[Y0 : $i]: (= @ (sK2 @ Y0))))))) )),
% 1.69/1.36 inference(superposition,[status(thm)],[f67,f66])).
% 1.69/1.36 thf(f66,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (((ap @ X3 @ X1 @ X2 @ X4) = X5) | ($false = (func @ X3 @ X1 @ X2)) | ($false = (in @ X4 @ X3)) | ((in @ (kpair @ X4 @ X5) @ X2) = $false) | ($false = (in @ X5 @ X1))) )),
% 1.69/1.36 inference(equality_proxy_clausification,[status(thm)],[f65])).
% 1.69/1.36 thf(f65,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (func @ X3 @ X1 @ X2)) | ((in @ (kpair @ X4 @ X5) @ X2) = $false) | (((ap @ X3 @ X1 @ X2 @ X4) = X5) = $true) | ($false = (in @ X4 @ X3)) | ($false = (in @ X5 @ X1))) )),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.69/1.36 thf(f64,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X2) => ((ap @ X3 @ X1 @ X2 @ X4) = X5)) = $true) | ($false = (in @ X4 @ X3)) | ($false = (in @ X5 @ X1)) | ($false = (func @ X3 @ X1 @ X2))) )),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.69/1.36 thf(f63,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => ((ap @ X3 @ X1 @ X2 @ X4) = X5))) = $true) | ($false = (func @ X3 @ X1 @ X2)) | ($false = (in @ X4 @ X3))) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.69/1.36 thf(f62,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (in @ X4 @ X3)) | ($false = (func @ X3 @ X1 @ X2)) | (((^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ (kpair @ X4 @ Y0) @ X2) => ((ap @ X3 @ X1 @ X2 @ X4) = Y0)))) @ X5) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f61])).
% 1.69/1.36 thf(f61,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X4 @ X3)) | ($false = (func @ X3 @ X1 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ (kpair @ X4 @ Y0) @ X2) => ((ap @ X3 @ X1 @ X2 @ X4) = Y0))))) = $true)) )),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.69/1.36 thf(f60,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((in @ X4 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ (kpair @ X4 @ Y0) @ X2) => ((ap @ X3 @ X1 @ X2 @ X4) = Y0)))))) = $true) | ($false = (func @ X3 @ X1 @ X2))) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.69/1.36 thf(f59,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ (kpair @ Y0 @ Y1) @ X2) => ((ap @ X3 @ X1 @ X2 @ Y0) = Y1))))))) @ X4) = $true) | ($false = (func @ X3 @ X1 @ X2))) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f58])).
% 1.69/1.36 thf(f58,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (func @ X3 @ X1 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ (kpair @ Y0 @ Y1) @ X2) => ((ap @ X3 @ X1 @ X2 @ Y0) = Y1)))))))) = $true)) )),
% 1.69/1.36 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.69/1.36 thf(f57,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((func @ X3 @ X1 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ (kpair @ Y0 @ Y1) @ X2) => ((ap @ X3 @ X1 @ X2 @ Y0) = Y1))))))))) = $true)) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.69/1.36 thf(f56,plain,(
% 1.69/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((func @ Y0 @ X1 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ (kpair @ Y1 @ Y2) @ X2) => ((ap @ Y0 @ X1 @ X2 @ Y1) = Y2)))))))))) @ X3) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f55])).
% 1.69/1.36 thf(f55,plain,(
% 1.69/1.36 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((func @ Y0 @ X1 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ (kpair @ Y1 @ Y2) @ X2) => ((ap @ Y0 @ X1 @ X2 @ Y1) = Y2))))))))))) = $true)) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.69/1.36 thf(f54,plain,(
% 1.69/1.36 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ Y1 @ X1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => ((ap @ Y1 @ X1 @ Y0 @ Y2) = Y3)))))))))))) @ X2) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f53])).
% 1.69/1.36 thf(f53,plain,(
% 1.69/1.36 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ Y1 @ X1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => ((ap @ Y1 @ X1 @ Y0 @ Y2) = Y3))))))))))))) = $true)) )),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.69/1.36 thf(f52,plain,(
% 1.69/1.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => ((ap @ Y2 @ Y0 @ Y1 @ Y3) = Y4)))))))))))))) @ X1) = $true)) )),
% 1.69/1.36 inference(pi_clausification,[status(thm)],[f37])).
% 1.69/1.36 thf(f37,plain,(
% 1.69/1.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => ((ap @ Y2 @ Y0 @ Y1 @ Y3) = Y4))))))))))))))) = $true)),
% 1.69/1.36 inference(definition_unfolding,[status(thm)],[f32,f26])).
% 1.69/1.36 thf(f26,plain,(
% 1.69/1.36 (funcGraphProp2 = $true)),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f23])).
% 1.69/1.36 thf(f32,plain,(
% 1.69/1.36 (funcGraphProp2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => ((ap @ Y2 @ Y0 @ Y1 @ Y3) = Y4))))))))))))))))),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f11])).
% 1.69/1.36 thf(f11,plain,(
% 1.69/1.36 (funcGraphProp2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => ((ap @ Y2 @ Y0 @ Y1 @ Y3) = Y4))))))))))))))))),
% 1.69/1.36 inference(fool_elimination,[status(thm)],[f10])).
% 1.69/1.36 thf(f10,plain,(
% 1.69/1.36 (funcGraphProp2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X2) => ((in @ (kpair @ X3 @ X4) @ X1) => ((ap @ X0 @ X2 @ X1 @ X3) = X4))))))),
% 1.69/1.36 inference(rectify,[status(thm)],[f4])).
% 1.69/1.36 thf(f4,axiom,(
% 1.69/1.36 (funcGraphProp2 = ! [X0 : $i,X7 : $i,X1 : $i] : ((func @ X0 @ X1 @ X7) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X7) => ((ap @ X0 @ X1 @ X7 @ X3) = X4))))))),
% 1.69/1.36 file('/export/starexec/sandbox2/tmp/tmp.6ZDpTMNeLo/DTF2THF_1563.p',funcGraphProp2)).
% 1.69/1.36 thf(f67,plain,(
% 1.69/1.36 ((sK2 @ sK3) != (ap @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (^[Y0 : $i]: (= @ (sK2 @ Y0)))) @ sK3))),
% 1.69/1.36 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.69/1.36 thf(f34,plain,(
% 1.69/1.36 ((sK2 @ sK3) != (ap @ sK0 @ sK1 @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))) @ sK0 @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0))) @ sK3))),
% 1.69/1.36 inference(definition_unfolding,[status(thm)],[f29,f33])).
% 1.69/1.36 thf(f29,plain,(
% 1.69/1.36 ((sK2 @ sK3) != (ap @ sK0 @ sK1 @ (lam @ sK0 @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0))) @ sK3))),
% 1.69/1.36 inference(cnf_transformation,[status(thm)],[f23])).
% 1.69/1.36 % SZS output end Proof for DTF2THF_1563
% 1.69/1.36 % (1792)------------------------------
% 1.69/1.36 % (1792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (1792)Termination reason: Refutation
% 1.69/1.36
% 1.69/1.36 % (1792)Memory used [KB]: 6268
% 1.69/1.36 % (1792)Time elapsed: 0.050 s
% 1.69/1.36 % (1792)Instructions burned: 106 (million)
% 1.69/1.36 % (1792)------------------------------
% 1.69/1.36 % (1792)------------------------------
% 1.69/1.36 % (1791)Success in time 0.059 s
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