%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU684^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 09:36:23 AM UTC 2026
% Result : Theorem 1.78s 1.43s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 12
% Syntax : Number of formulae : 103 ( 55 unt; 0 typ; 2 def)
% Number of atoms : 859 ( 196 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 1223 ( 45 ~; 63 |; 49 &; 969 @)
% ( 2 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 28 usr; 14 con; 0-4 aty)
% ( 28 !!; 15 ??; 0 @@+; 0 @@-)
% Number of variables : 273 ( 181 ^; 76 !; 16 ?; 273 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_7,type,
subset: $i > $i > $o ).
thf(func_def_8,type,
kpair: $i > $i > $i ).
thf(func_def_9,type,
cartprod: $i > $i > $i ).
thf(func_def_10,type,
singleton: $i > $o ).
thf(func_def_11,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_13,type,
breln: $i > $i > $i > $o ).
thf(func_def_14,type,
func: $i > $i > $i > $o ).
thf(func_def_16,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_35,type,
sK5: $i > $i ).
thf(func_def_38,type,
sK6: $i > $i > $i > $i ).
thf(func_def_39,type,
sK7: $i > $i > $i > $i ).
thf(func_def_40,type,
sK8: $i > $i > $i > $i ).
thf(func_def_42,type,
ph9:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
sK10: $i > $i ).
thf(f196,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f172,f178,f194]) ).
thf(f194,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f193]) ).
thf(f193,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(subsumption_resolution,[status(thm)],[f192,f170]) ).
thf(f170,plain,
( ( ( in @ sK3 @ sK2 )
!= $false )
| spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f169]) ).
thf(f169,definition,
( spl4_2
<=> ( ( in @ sK3 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f192,plain,
( ( ( in @ sK3 @ sK2 )
= $false )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f191]) ).
thf(f191,plain,
( ( sK3 != sK3 )
| ( $true = $false )
| ( ( in @ sK3 @ sK2 )
= $false )
| ~ spl4_1 ),
inference(duplicate_literal_removal,[status(thm)],[f181]) ).
thf(f181,plain,
( ( $true = $false )
| ( $true = $false )
| ( sK3 != sK3 )
| ( ( in @ sK3 @ sK2 )
= $false )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f161,f167]) ).
thf(f167,plain,
( ( ( in @ ( kpair @ sK3 @ ( sK10 @ sK3 ) ) @ sK0 )
= $true )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f165]) ).
thf(f165,definition,
( spl4_1
<=> ( ( in @ ( kpair @ sK3 @ ( sK10 @ sK3 ) ) @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f161,plain,
! [X0: $i] :
( ( ( in @ ( kpair @ sK3 @ ( sK10 @ X0 ) ) @ sK0 )
= $false )
| ( sK3 != X0 )
| ( ( in @ ( kpair @ X0 @ ( sK10 @ X0 ) ) @ sK0 )
= $false )
| ( ( in @ X0 @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f159]) ).
thf(f159,plain,
! [X0: $i] :
( ( sK3 != X0 )
| ( ( in @ ( kpair @ X0 @ ( sK10 @ X0 ) ) @ sK0 )
!= ( in @ ( kpair @ sK3 @ ( sK10 @ X0 ) ) @ sK0 ) )
| ( ( in @ X0 @ sK2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f158]) ).
thf(f158,plain,
! [X0: $i] :
( ( sK3 != X0 )
| ( ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK0 )
@ ( sK10 @ X0 ) )
!= ( ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK0 )
@ ( sK10 @ X0 ) ) )
| ( ( in @ X0 @ sK2 )
= $false ) ),
inference(negative_extensionality,[status(thm)],[f157]) ).
thf(f157,plain,
! [X0: $i] :
( ( ( ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK0 ) )
!= ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK0 ) ) )
| ( ( in @ X0 @ sK2 )
= $false )
| ( sK3 != X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f156]) ).
thf(f156,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ X0 @ sK2 )
= $false )
| ( ( ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK0 ) )
!= ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK0 ) ) )
| ( sK3 != X0 ) ),
inference(constrained_superposition,[status(thm)],[f56,f154]) ).
thf(f154,plain,
! [X0: $i] :
( ( $true
= ( in
@ ( kpair @ X0
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK0 ) ) ) )
@ sK0 ) )
| ( ( in @ X0 @ sK2 )
= $false ) ),
inference(subsumption_resolution,[status(thm)],[f150,f67]) ).
thf(f67,plain,
! [X1: $i] :
( ( ( setadjoin @ ( sK5 @ X1 ) @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK0 ) ) )
| ( ( in @ X1 @ sK2 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: $i] :
( ( $true
= ( ( setadjoin @ ( sK5 @ X1 ) @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK0 ) ) ) )
| ( ( in @ X1 @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X1: $i] :
( ( $true
= ( ( ( setadjoin @ ( sK5 @ X1 ) @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK0 ) ) )
& ( in @ ( sK5 @ X1 )
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK0 ) ) ) ) )
| ( ( in @ X1 @ sK2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK0 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK0 ) ) ) )
@ ( sK5 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
= $false )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK0 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK0 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK1
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 ) ) ) ) ) ) )
& ( subset @ sK0 @ ( cartprod @ sK2 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
( $true
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 ) )
@ sK2
@ sK1
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f42,f49]) ).
thf(f49,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f45,f48,f47]) ).
thf(f47,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X0: $i,X5: $i,X6: $i] : ( subset @ X6 @ ( cartprod @ X0 @ X5 ) ) )
= breln ),
file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',breln) ).
thf(f48,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f35,f37]) ).
thf(f37,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) )
= singleton ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i] :
? [X2: $i] :
( ( in @ X2 @ X0 )
& ( ( setadjoin @ X2 @ emptyset )
= X0 ) ) )
= singleton ),
file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',singleton) ).
thf(f35,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f3]) ).
thf(f3,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',ex1) ).
thf(f45,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( breln @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( breln @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
& ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( func
= ( ^ [X0: $i,X5: $i,X7: $i] :
( ( breln @ X0 @ X5 @ X7 )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ex1 @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X7 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',func) ).
thf(f42,plain,
( $true
= ( func @ sK2 @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( theprop = $true )
& ( dsetconstrER = $true )
& ( $true
= ( func @ sK2 @ sK1 @ sK0 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ ( ap @ sK2 @ sK1 @ sK0 @ sK3 ) ) @ sK0 ) )
& ( $true
= ( in @ sK3 @ sK2 ) )
& ( funcImageSingleton = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f30,f32,f31]) ).
thf(f31,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
& ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 ) )
& ( $true
= ( in @ X3 @ X2 ) ) ) )
=> ( ( $true
= ( func @ sK2 @ sK1 @ sK0 ) )
& ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ sK2 @ sK1 @ sK0 @ X3 ) ) @ sK0 ) )
& ( ( in @ X3 @ sK2 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ sK2 @ sK1 @ sK0 @ X3 ) ) @ sK0 ) )
& ( ( in @ X3 @ sK2 )
= $true ) )
=> ( ( $true
!= ( in @ ( kpair @ sK3 @ ( ap @ sK2 @ sK1 @ sK0 @ sK3 ) ) @ sK0 ) )
& ( $true
= ( in @ sK3 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ( theprop = $true )
& ( dsetconstrER = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
& ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 ) )
& ( $true
= ( in @ X3 @ X2 ) ) ) )
& ( funcImageSingleton = $true ) ),
inference(flattening,[status(thm)],[f29]) ).
thf(f29,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
& ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 ) )
& ( $true
= ( in @ X3 @ X2 ) ) ) )
& ( funcImageSingleton = $true )
& ( theprop = $true )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
~ ( ( dsetconstrER = $true )
=> ( ( theprop = $true )
=> ( ( funcImageSingleton = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
~ ( dsetconstrER
=> ( theprop
=> ( funcImageSingleton
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X2 @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,negated_conjecture,
~ ( dsetconstrER
=> ( theprop
=> ( funcImageSingleton
=> ! [X8: $i,X5: $i,X0: $i] :
( ( func @ X0 @ X5 @ X8 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ ( kpair @ X2 @ ( ap @ X0 @ X5 @ X8 @ X2 ) ) @ X8 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f9,conjecture,
( dsetconstrER
=> ( theprop
=> ( funcImageSingleton
=> ! [X8: $i,X5: $i,X0: $i] :
( ( func @ X0 @ X5 @ X8 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ ( kpair @ X2 @ ( ap @ X0 @ X5 @ X8 @ X2 ) ) @ X8 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',funcGraphProp1) ).
thf(f150,plain,
! [X0: $i] :
( ( ( setadjoin @ ( sK5 @ X0 ) @ emptyset )
!= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK0 ) ) )
| ( $true
= ( in
@ ( kpair @ X0
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK0 ) ) ) )
@ sK0 ) )
| ( ( in @ X0 @ sK2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f149]) ).
thf(f149,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK2 )
= $false )
| ( ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK0 )
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK0 ) ) ) )
= $true )
| ( ( setadjoin @ ( sK5 @ X0 ) @ emptyset )
!= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f143]) ).
thf(f143,plain,
! [X0: $i] :
( ( ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK0 )
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK0 ) ) ) )
= $true )
| ( ( in @ X0 @ sK2 )
= $false )
| ( $true = $false )
| ( ( setadjoin @ ( sK5 @ X0 ) @ emptyset )
!= ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK0 ) ) ) ),
inference(superposition,[status(thm)],[f65,f124]) ).
thf(f124,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2 @ ( dsetconstr @ X0 @ X1 ) )
= $false )
| ( ( X1 @ ( setunion @ ( dsetconstr @ X0 @ X1 ) ) )
= $true )
| ( ( setadjoin @ X2 @ emptyset )
!= ( dsetconstr @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( setadjoin @ X2 @ emptyset )
!= ( dsetconstr @ X0 @ X1 ) )
| ( ( X1 @ ( setunion @ ( dsetconstr @ X0 @ X1 ) ) )
= $true )
| ( $true = $false )
| ( ( in @ X2 @ ( dsetconstr @ X0 @ X1 ) )
= $false ) ),
inference(superposition,[status(thm)],[f75,f117]) ).
thf(f117,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
= $false )
| ( $true
= ( X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
=> ( X3 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f115]) ).
thf(f115,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f113]) ).
thf(f113,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f111]) ).
thf(f111,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f43,f36]) ).
thf(f36,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X2 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',dsetconstrER) ).
thf(f43,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( setunion @ X1 ) @ X1 )
= $true )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( setadjoin @ X2 @ emptyset )
!= X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( setunion @ X1 ) @ X1 )
= $true )
| ( $false
= ( ( setadjoin @ X2 @ emptyset )
= X1 ) )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X1: $i] :
( ( ( ( ( setadjoin @ X2 @ emptyset )
= X1 )
& ( in @ X2 @ X1 ) )
= $false )
| ( ( in @ ( setunion @ X1 ) @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( setunion @ X1 ) @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= X1 )
& ( in @ Y0 @ X1 ) )
@ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= X1 )
& ( in @ Y0 @ X1 ) ) )
= $false )
| ( ( in @ ( setunion @ X1 ) @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: $i] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= X1 )
& ( in @ Y0 @ X1 ) ) )
=> ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= Y1 )
& ( in @ Y2 @ Y1 ) ) )
@ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f46,f44,f37]) ).
thf(f44,plain,
theprop = $true,
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f46,plain,
( theprop
= ( !! @ $i
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( theprop
= ( !! @ $i
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( theprop
= ( ! [X0: $i] :
( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( theprop
= ( ! [X4: $i] :
( ( singleton @ X4 )
=> ( in @ ( setunion @ X4 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',theprop) ).
thf(f65,plain,
! [X1: $i] :
( ( ( in @ ( sK5 @ X1 )
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK0 ) ) )
= $true )
| ( ( in @ X1 @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f56,plain,
( ( in
@ ( kpair @ sK3
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK0 ) ) ) )
@ sK0 )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
( ( in
@ ( kpair @ sK3
@ ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) )
@ sK2
@ sK1
@ sK0
@ sK3 ) )
@ sK0 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f41,f38]) ).
thf(f38,plain,
( ap
= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ap
= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
( ap
= ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( ap
= ( ^ [X0: $i,X5: $i,X8: $i,X2: $i] :
( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X8 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',ap) ).
thf(f41,plain,
( $true
!= ( in @ ( kpair @ sK3 @ ( ap @ sK2 @ sK1 @ sK0 @ sK3 ) ) @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f178,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[status(thm)],[f177]) ).
thf(f177,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f174]) ).
thf(f174,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f40,f171]) ).
thf(f171,plain,
( ( ( in @ sK3 @ sK2 )
= $false )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f169]) ).
thf(f40,plain,
( $true
= ( in @ sK3 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f172,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f163,f169,f165]) ).
thf(f163,plain,
( ( ( in @ ( kpair @ sK3 @ ( sK10 @ sK3 ) ) @ sK0 )
= $true )
| ( ( in @ sK3 @ sK2 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f162]) ).
thf(f162,plain,
( ( $true != $true )
| ( ( in @ sK3 @ sK2 )
= $false )
| ( ( in @ ( kpair @ sK3 @ ( sK10 @ sK3 ) ) @ sK0 )
= $true )
| ( sK3 != sK3 ) ),
inference(equality_factoring,[status(thm)],[f160]) ).
thf(f160,plain,
! [X0: $i] :
( ( $true
= ( in @ ( kpair @ sK3 @ ( sK10 @ X0 ) ) @ sK0 ) )
| ( ( in @ X0 @ sK2 )
= $false )
| ( $true
= ( in @ ( kpair @ X0 @ ( sK10 @ X0 ) ) @ sK0 ) )
| ( sK3 != X0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU684^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.30 % Computer : n020.cluster.edu
% 0.13/0.30 % Model : x86_64 x86_64
% 0.13/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30 % Memory : 8042.1875MB
% 0.13/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30 % CPULimit : 300
% 0.13/0.30 % WCLimit : 300
% 0.13/0.30 % DateTime : Tue Feb 24 12:30:57 EST 2026
% 0.13/0.30 % CPUTime :
% 0.13/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.40 ---- Original DTF file ---
% 0.18/0.40 thf(spec,logic,$$dhol).
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 % File : SEU684^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.40 % Domain : Set Theory
% 0.18/0.40 % Problem : Functions - Extensionality and Beta Reduction
% 0.18/0.40 % Version : Especial > Reduced > Especial.
% 0.18/0.40 % English : (! A:i.! B:i.! f:i.func A B f -> (! x:i.in x A ->
% 0.18/0.40 % in (kpair x (ap A B f x)) f))
% 0.18/0.40
% 0.18/0.40 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.40 % Source : [Bro08]
% 0.18/0.40 % Names : ZFC186l [Bro08]
% 0.18/0.40
% 0.18/0.40 % Status : Theorem
% 0.18/0.40 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v3.7.0
% 0.18/0.40 % Syntax : Number of formulae : 25 ( 8 unt; 16 typ; 8 def)
% 0.18/0.40 % Number of atoms : 37 ( 9 equ; 0 cnn)
% 0.18/0.40 % Maximal formula atoms : 6 ( 4 avg)
% 0.18/0.40 % Number of connectives : 77 ( 0 ~; 0 |; 2 &; 65 @)
% 0.18/0.40 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.18/0.40 % Maximal formula depth : 17 ( 3 avg)
% 0.18/0.40 % Number of types : 2 ( 0 usr)
% 0.18/0.40 % Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% 0.18/0.40 % Number of symbols : 17 ( 16 usr; 4 con; 0-4 aty)
% 0.18/0.40 % Number of variables : 32 ( 18 ^; 13 !; 1 ?; 32 :)
% 0.18/0.40 % SPC : TH0_THM_EQU_NAR
% 0.18/0.40
% 0.18/0.40 % Comments : http://mathgate.info/detsetitem.php?id=241
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 thf(in_type,type,
% 0.18/0.40 in: $i > $i > $o ).
% 0.18/0.40
% 0.18/0.40 thf(emptyset_type,type,
% 0.18/0.40 emptyset: $i ).
% 0.18/0.40
% 0.18/0.40 thf(setadjoin_type,type,
% 0.18/0.40 setadjoin: $i > $i > $i ).
% 0.18/0.40
% 0.18/0.40 thf(setunion_type,type,
% 0.18/0.40 setunion: $i > $i ).
% 0.18/0.40
% 0.18/0.40 thf(dsetconstr_type,type,
% 0.18/0.40 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.18/0.40
% 0.18/0.40 thf(dsetconstrER_type,type,
% 0.18/0.40 dsetconstrER: $o ).
% 0.18/0.40
% 0.18/0.40 thf(dsetconstrER,definition,
% 0.18/0.40 ( dsetconstrER
% 0.18/0.40 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.40 ( ( in @ Xx
% 0.18/0.40 @ ( dsetconstr @ A
% 0.18/0.40 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.40 => ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.40
% 0.18/0.40 thf(subset_type,type,
% 0.18/0.40 subset: $i > $i > $o ).
% 0.18/0.40
% 0.18/0.40 thf(kpair_type,type,
% 0.18/0.40 kpair: $i > $i > $i ).
% 0.18/0.40
% 0.18/0.40 thf(cartprod_type,type,
% 0.18/0.40 cartprod: $i > $i > $i ).
% 0.18/0.40
% 0.18/0.40 thf(singleton_type,type,
% 0.18/0.40 singleton: $i > $o ).
% 0.18/0.40
% 0.18/0.40 thf(singleton,definition,
% 0.18/0.40 ( singleton
% 0.18/0.40 = ( ^ [A: $i] :
% 0.18/0.40 ? [Xx: $i] :
% 0.18/0.40 ( ( in @ Xx @ A )
% 0.18/0.40 & ( A
% 0.18/0.40 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.40
% 0.18/0.40 thf(ex1_type,type,
% 0.18/0.40 ex1: $i > ( $i > $o ) > $o ).
% 0.18/0.40
% 0.18/0.40 thf(ex1,definition,
% 0.18/0.40 ( ex1
% 0.18/0.40 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.18/0.40 ( singleton
% 0.18/0.40 @ ( dsetconstr @ A
% 0.18/0.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.40
% 0.18/0.40 thf(theprop_type,type,
% 0.18/0.40 theprop: $o ).
% 0.18/0.40
% 0.18/0.40 thf(theprop,definition,
% 0.18/0.40 ( theprop
% 0.18/0.40 = ( ! [X: $i] :
% 0.18/0.40 ( ( singleton @ X )
% 0.18/0.40 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.18/0.40
% 0.18/0.40 thf(breln_type,type,
% 0.18/0.40 breln: $i > $i > $i > $o ).
% 0.18/0.40
% 0.18/0.40 thf(breln,definition,
% 0.18/0.40 ( breln
% 0.18/0.40 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.18/0.40
% 0.18/0.40 thf(func_type,type,
% 0.18/0.40 func: $i > $i > $i > $o ).
% 0.18/0.40
% 0.18/0.40 thf(func,definition,
% 0.18/0.40 ( func
% 0.18/0.40 = ( ^ [A: $i,B: $i,R: $i] :
% 0.18/0.40 ( ( breln @ A @ B @ R )
% 0.18/0.40 & ! [Xx: $i] :
% 0.18/0.40 ( ( in @ Xx @ A )
% 0.18/0.40 => ( ex1 @ B
% 0.18/0.40 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.18/0.40
% 0.18/0.40 thf(funcImageSingleton_type,type,
% 0.18/0.40 funcImageSingleton: $o ).
% 0.18/0.40
% 0.18/0.40 thf(funcImageSingleton,definition,
% 0.18/0.40 ( funcImageSingleton
% 0.18/0.40 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.40 ( ( func @ A @ B @ Xf )
% 0.18/0.40 => ! [Xx: $i] :
% 0.18/0.40 ( ( in @ Xx @ A )
% 0.18/0.40 => ( singleton
% 0.18/0.40 @ ( dsetconstr @ B
% 0.18/0.40 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.18/0.40
% 0.18/0.40 thf(ap_type,type,
% 0.18/0.40 ap: $i > $i > $i > $i > $i ).
% 0.18/0.40
% 0.18/0.40 thf(ap,definition,
% 0.18/0.40 ( ap
% 0.18/0.40 = ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
% 0.18/0.40 ( setunion
% 0.18/0.40 @ ( dsetconstr @ B
% 0.18/0.40 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ).
% 0.18/0.40
% 0.18/0.40 thf(funcGraphProp1,conjecture,
% 0.18/0.40 ( dsetconstrER
% 0.18/0.40 => ( theprop
% 0.18/0.40 => ( funcImageSingleton
% 0.18/0.40 => ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.40 ( ( func @ A @ B @ Xf )
% 0.18/0.40 => ! [Xx: $i] :
% 0.18/0.40 ( ( in @ Xx @ A )
% 0.18/0.40 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ) ).
% 0.18/0.40
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 ------------------------
% 1.64/1.36 ---- Embedded in THF ---
% 1.64/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.36 %%% Generated on Tue Feb 24 12:30:58 EST 2026
% 1.64/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.36 %%% Logic specification used:
% 1.64/1.36 %%% thf(spec, logic, $$dhol).
% 1.64/1.36
% 1.64/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2DTF2030.p
% See solution above
% 1.64/1.36 ------------------------
% 1.64/1.37 ---- Cleaned THF ---
% 1.64/1.37 thf(in_type,type,
% 1.64/1.37 in: $i > $i > $o ).
% 1.64/1.37
% 1.64/1.37 thf(emptyset_type,type,
% 1.64/1.37 emptyset: $i ).
% 1.64/1.37
% 1.64/1.37 thf(setadjoin_type,type,
% 1.64/1.37 setadjoin: $i > $i > $i ).
% 1.64/1.37
% 1.64/1.37 thf(setunion_type,type,
% 1.64/1.37 setunion: $i > $i ).
% 1.64/1.37
% 1.64/1.37 thf(dsetconstr_type,type,
% 1.64/1.37 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.64/1.37
% 1.64/1.37 thf(dsetconstrER_type,type,
% 1.64/1.37 dsetconstrER: $o ).
% 1.64/1.37
% 1.64/1.37 thf(dsetconstrER,definition,
% 1.64/1.37 ( dsetconstrER
% 1.64/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.64/1.37 ( ( in @ Xx
% 1.64/1.37 @ ( dsetconstr @ A
% 1.64/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.64/1.37 => ( Xphi @ Xx ) ) ) ) ).
% 1.64/1.37
% 1.64/1.37 thf(subset_type,type,
% 1.64/1.37 subset: $i > $i > $o ).
% 1.64/1.37
% 1.64/1.37 thf(kpair_type,type,
% 1.64/1.37 kpair: $i > $i > $i ).
% 1.64/1.37
% 1.64/1.37 thf(cartprod_type,type,
% 1.64/1.37 cartprod: $i > $i > $i ).
% 1.64/1.37
% 1.64/1.37 thf(singleton_type,type,
% 1.64/1.37 singleton: $i > $o ).
% 1.64/1.37
% 1.64/1.37 thf(singleton,definition,
% 1.64/1.37 ( singleton
% 1.64/1.37 = ( ^ [A: $i] :
% 1.64/1.37 ? [Xx: $i] :
% 1.64/1.37 ( ( in @ Xx @ A )
% 1.64/1.37 & ( A
% 1.64/1.37 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.64/1.37
% 1.64/1.37 thf(ex1_type,type,
% 1.64/1.37 ex1: $i > ( $i > $o ) > $o ).
% 1.64/1.37
% 1.64/1.37 thf(ex1,definition,
% 1.64/1.37 ( ex1
% 1.64/1.37 = ( ^ [A: $i,Xphi: $i > $o] :
% 1.64/1.37 ( singleton
% 1.64/1.37 @ ( dsetconstr @ A
% 1.64/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.64/1.37
% 1.64/1.37 thf(theprop_type,type,
% 1.64/1.37 theprop: $o ).
% 1.64/1.37
% 1.64/1.37 thf(theprop,definition,
% 1.64/1.37 ( theprop
% 1.64/1.37 = ( ! [X: $i] :
% 1.64/1.37 ( ( singleton @ X )
% 1.64/1.37 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 1.64/1.37
% 1.64/1.37 thf(breln_type,type,
% 1.64/1.37 breln: $i > $i > $i > $o ).
% 1.64/1.37
% 1.64/1.37 thf(breln,definition,
% 1.64/1.37 ( breln
% 1.64/1.37 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.64/1.37
% 1.64/1.37 thf(func_type,type,
% 1.64/1.37 func: $i > $i > $i > $o ).
% 1.64/1.37
% 1.64/1.37 thf(func,definition,
% 1.64/1.37 ( func
% 1.64/1.37 = ( ^ [A: $i,B: $i,R: $i] :
% 1.64/1.37 ( ( breln @ A @ B @ R )
% 1.64/1.37 & ! [Xx: $i] :
% 1.64/1.37 ( ( in @ Xx @ A )
% 1.64/1.37 => ( ex1 @ B
% 1.64/1.37 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 1.64/1.37
% 1.64/1.37 thf(funcImageSingleton_type,type,
% 1.64/1.37 funcImageSingleton: $o ).
% 1.64/1.37
% 1.64/1.37 thf(funcImageSingleton,definition,
% 1.64/1.37 ( funcImageSingleton
% 1.64/1.37 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.64/1.37 ( ( func @ A @ B @ Xf )
% 1.64/1.37 => ! [Xx: $i] :
% 1.64/1.37 ( ( in @ Xx @ A )
% 1.64/1.37 => ( singleton
% 1.64/1.37 @ ( dsetconstr @ B
% 1.64/1.37 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 1.64/1.37
% 1.64/1.37 thf(ap_type,type,
% 1.64/1.37 ap: $i > $i > $i > $i > $i ).
% 1.64/1.37
% 1.64/1.37 thf(ap,definition,
% 1.64/1.37 ( ap
% 1.64/1.37 = ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
% 1.64/1.37 ( setunion
% 1.64/1.37 @ ( dsetconstr @ B
% 1.64/1.37 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ).
% 1.64/1.37
% 1.64/1.37 thf(funcGraphProp1,conjecture,
% 1.64/1.37 ( dsetconstrER
% 1.64/1.37 => ( theprop
% 1.64/1.37 => ( funcImageSingleton
% 1.64/1.37 => ! [A: $i,B: $i,Xf: $i] :
% 1.64/1.37 ( ( func @ A @ B @ Xf )
% 1.64/1.37 => ! [Xx: $i] :
% 1.64/1.37 ( ( in @ Xx @ A )
% 1.64/1.37 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ) ).
% 1.64/1.37 ------------------------
% 1.64/1.39 % (2129)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_2030 for (2999ds/27Mi)
% 1.64/1.39 % (2130)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2030 for (2999ds/2Mi)
% 1.64/1.39 % (2127)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2030 for (2999ds/183Mi)
% 1.64/1.39 % (2131)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_2030 for (2999ds/2Mi)
% 1.64/1.39 % (2132)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_2030 for (2999ds/275Mi)
% 1.64/1.39 % (2133)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2030 for (2999ds/18Mi)
% 1.64/1.39 % (2130)Instruction limit reached!
% 1.64/1.39 % (2130)------------------------------
% 1.64/1.39 % (2130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (2130)Termination reason: Unknown
% 1.64/1.39 % (2131)Instruction limit reached!
% 1.64/1.39 % (2131)------------------------------
% 1.64/1.39 % (2131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (2130)Termination phase: Property scanning
% 1.64/1.39
% 1.64/1.39 % (2130)Memory used [KB]: 1023
% 1.64/1.39 % (2130)Time elapsed: 0.003 s
% 1.64/1.39 % (2130)Instructions burned: 2 (million)
% 1.64/1.39 % (2130)------------------------------
% 1.64/1.39 % (2130)------------------------------
% 1.64/1.39 % (2131)Termination reason: Unknown
% 1.64/1.39 % (2131)Termination phase: Property scanning
% 1.64/1.39
% 1.64/1.39 % (2131)Memory used [KB]: 1023
% 1.64/1.39 % (2131)Time elapsed: 0.003 s
% 1.64/1.39 % (2131)Instructions burned: 3 (million)
% 1.64/1.39 % (2131)------------------------------
% 1.64/1.39 % (2131)------------------------------
% 1.78/1.40 % (2128)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_2030 for (2999ds/4Mi)
% 1.78/1.40 % (2132)Refutation not found, incomplete strategy
% 1.78/1.40 % (2132)------------------------------
% 1.78/1.40 % (2132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.40 % (2132)Termination reason: Refutation not found, incomplete strategy
% 1.78/1.40
% 1.78/1.40
% 1.78/1.40 % (2132)Memory used [KB]: 5628
% 1.78/1.40 % (2132)Time elapsed: 0.007 s
% 1.78/1.40 % (2132)Instructions burned: 9 (million)
% 1.78/1.40 % (2132)------------------------------
% 1.78/1.40 % (2132)------------------------------
% 1.78/1.40 % (2128)Instruction limit reached!
% 1.78/1.40 % (2128)------------------------------
% 1.78/1.40 % (2128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.40 % (2128)Termination reason: Unknown
% 1.78/1.40 % (2128)Termination phase: Property scanning
% 1.78/1.40
% 1.78/1.40 % (2128)Memory used [KB]: 1023
% 1.78/1.40 % (2128)Time elapsed: 0.004 s
% 1.78/1.40 % (2128)Instructions burned: 4 (million)
% 1.78/1.40 % (2128)------------------------------
% 1.78/1.40 % (2128)------------------------------
% 1.78/1.40 % (2133)Instruction limit reached!
% 1.78/1.40 % (2133)------------------------------
% 1.78/1.40 % (2133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.40 % (2133)Termination reason: Unknown
% 1.78/1.40 % (2133)Termination phase: Saturation
% 1.78/1.40
% 1.78/1.40 % (2133)Memory used [KB]: 5756
% 1.78/1.40 % (2133)Time elapsed: 0.011 s
% 1.78/1.40 % (2133)Instructions burned: 18 (million)
% 1.78/1.40 % (2133)------------------------------
% 1.78/1.40 % (2133)------------------------------
% 1.78/1.41 % (2129)Instruction limit reached!
% 1.78/1.41 % (2129)------------------------------
% 1.78/1.41 % (2129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.41 % (2129)Termination reason: Unknown
% 1.78/1.41 % (2129)Termination phase: Saturation
% 1.78/1.41
% 1.78/1.41 % (2129)Memory used [KB]: 5756
% 1.78/1.41 % (2129)Time elapsed: 0.016 s
% 1.78/1.41 % (2129)Instructions burned: 28 (million)
% 1.78/1.41 % (2129)------------------------------
% 1.78/1.41 % (2129)------------------------------
% 1.78/1.41 % (2134)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2030 for (2999ds/3Mi)
% 1.78/1.41 % (2135)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_2030 for (2999ds/37Mi)
% 1.78/1.41 % (2134)Instruction limit reached!
% 1.78/1.41 % (2134)------------------------------
% 1.78/1.41 % (2134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.41 % (2134)Termination reason: Unknown
% 1.78/1.41 % (2134)Termination phase: Preprocessing 3
% 1.78/1.41
% 1.78/1.41 % (2134)Memory used [KB]: 1023
% 1.78/1.41 % (2134)Time elapsed: 0.003 s
% 1.78/1.41 % (2134)Instructions burned: 3 (million)
% 1.78/1.41 % (2134)------------------------------
% 1.78/1.41 % (2134)------------------------------
% 1.78/1.41 % (2136)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_2030 for (2999ds/15Mi)
% 1.78/1.42 % (2137)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_2030 for (2999ds/3Mi)
% 1.78/1.42 % (2137)Instruction limit reached!
% 1.78/1.42 % (2137)------------------------------
% 1.78/1.42 % (2137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.42 % (2137)Termination reason: Unknown
% 1.78/1.42 % (2137)Termination phase: Preprocessing 2
% 1.78/1.42
% 1.78/1.42 % (2137)Memory used [KB]: 1023
% 1.78/1.42 % (2137)Time elapsed: 0.003 s
% 1.78/1.42 % (2137)Instructions burned: 3 (million)
% 1.78/1.42 % (2137)------------------------------
% 1.78/1.42 % (2137)------------------------------
% 1.78/1.42 % (2138)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_2030 for (2999ds/1041Mi)
% 1.78/1.42 % (2136)Instruction limit reached!
% 1.78/1.42 % (2136)------------------------------
% 1.78/1.42 % (2136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.42 % (2136)Termination reason: Unknown
% 1.78/1.42 % (2136)Termination phase: Saturation
% 1.78/1.42
% 1.78/1.42 % (2136)Memory used [KB]: 5756
% 1.78/1.42 % (2136)Time elapsed: 0.009 s
% 1.78/1.42 % (2136)Instructions burned: 15 (million)
% 1.78/1.42 % (2136)------------------------------
% 1.78/1.42 % (2136)------------------------------
% 1.78/1.42 % (2139)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2030 for (2999ds/7Mi)
% 1.78/1.43 % (2139)Instruction limit reached!
% 1.78/1.43 % (2139)------------------------------
% 1.78/1.43 % (2139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.43 % (2139)Termination reason: Unknown
% 1.78/1.43 % (2139)Termination phase: Saturation
% 1.78/1.43
% 1.78/1.43 % (2139)Memory used [KB]: 1023
% 1.78/1.43 % (2139)Time elapsed: 0.006 s
% 1.78/1.43 % (2139)Instructions burned: 9 (million)
% 1.78/1.43 % (2139)------------------------------
% 1.78/1.43 % (2139)------------------------------
% 1.78/1.43 % (2140)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2030 for (2999ds/16Mi)
% 1.78/1.43 % (2127)First to succeed.
% 1.78/1.43 % (2135)Instruction limit reached!
% 1.78/1.43 % (2135)------------------------------
% 1.78/1.43 % (2135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.43 % (2135)Termination reason: Unknown
% 1.78/1.43 % (2135)Termination phase: Saturation
% 1.78/1.43
% 1.78/1.43 % (2135)Memory used [KB]: 5756
% 1.78/1.43 % (2135)Time elapsed: 0.020 s
% 1.78/1.43 % (2135)Instructions burned: 38 (million)
% 1.78/1.43 % (2135)------------------------------
% 1.78/1.43 % (2135)------------------------------
% 1.78/1.43 % (2127)Refutation found. Thanks to Tanya!
% 1.78/1.43 % SZS status Theorem for DTF2THF_2030
% 1.78/1.43 % SZS output start Proof for DTF2THF_2030
% 1.78/1.43 thf(func_def_0, type, in: $i > $i > $o).
% 1.78/1.43 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.78/1.43 thf(func_def_3, type, setunion: $i > $i).
% 1.78/1.43 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 1.78/1.43 thf(func_def_7, type, subset: $i > $i > $o).
% 1.78/1.43 thf(func_def_8, type, kpair: $i > $i > $i).
% 1.78/1.43 thf(func_def_9, type, cartprod: $i > $i > $i).
% 1.78/1.43 thf(func_def_10, type, singleton: $i > $o).
% 1.78/1.43 thf(func_def_11, type, ex1: $i > ($i > $o) > $o).
% 1.78/1.43 thf(func_def_13, type, breln: $i > $i > $i > $o).
% 1.78/1.43 thf(func_def_14, type, func: $i > $i > $i > $o).
% 1.78/1.43 thf(func_def_16, type, ap: $i > $i > $i > $i > $i).
% 1.78/1.43 thf(func_def_35, type, sK5: $i > $i).
% 1.78/1.43 thf(func_def_38, type, sK6: $i > $i > $i > $i).
% 1.78/1.43 thf(func_def_39, type, sK7: $i > $i > $i > $i).
% 1.78/1.43 thf(func_def_40, type, sK8: $i > $i > $i > $i).
% 1.78/1.43 thf(func_def_42, type, ph9: !>[X0: $tType]:(X0)).
% 1.78/1.43 thf(func_def_45, type, sK10: $i > $i).
% 1.78/1.43 thf(f196,plain,(
% 1.78/1.43 $false),
% 1.78/1.43 inference(avatar_sat_refutation,[status(thm)],[f172,f178,f194])).
% 1.78/1.43 thf(f194,plain,(
% 1.78/1.43 ~spl4_1 | spl4_2),
% 1.78/1.43 inference(avatar_contradiction_clause,[status(thm)],[f193])).
% 1.78/1.43 thf(f193,plain,(
% 1.78/1.43 $false | (~spl4_1 | spl4_2)),
% 1.78/1.43 inference(subsumption_resolution,[status(thm)],[f192,f170])).
% 1.78/1.43 thf(f170,plain,(
% 1.78/1.43 ((in @ sK3 @ sK2) != $false) | spl4_2),
% 1.78/1.43 inference(avatar_component_clause,[status(thm)],[f169])).
% 1.78/1.43 thf(f169,definition,(
% 1.78/1.43 spl4_2 <=> ((in @ sK3 @ sK2) = $false)),
% 1.78/1.43 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.78/1.43 thf(f192,plain,(
% 1.78/1.43 ((in @ sK3 @ sK2) = $false) | ~spl4_1),
% 1.78/1.43 inference(trivial_inequality_removal,[status(thm)],[f191])).
% 1.78/1.43 thf(f191,plain,(
% 1.78/1.43 (sK3 != sK3) | ($true = $false) | ((in @ sK3 @ sK2) = $false) | ~spl4_1),
% 1.78/1.43 inference(duplicate_literal_removal,[status(thm)],[f181])).
% 1.78/1.43 thf(f181,plain,(
% 1.78/1.43 ($true = $false) | ($true = $false) | (sK3 != sK3) | ((in @ sK3 @ sK2) = $false) | ~spl4_1),
% 1.78/1.43 inference(superposition,[status(thm)],[f161,f167])).
% 1.78/1.43 thf(f167,plain,(
% 1.78/1.43 ((in @ (kpair @ sK3 @ (sK10 @ sK3)) @ sK0) = $true) | ~spl4_1),
% 1.78/1.43 inference(avatar_component_clause,[status(thm)],[f165])).
% 1.78/1.43 thf(f165,definition,(
% 1.78/1.43 spl4_1 <=> ((in @ (kpair @ sK3 @ (sK10 @ sK3)) @ sK0) = $true)),
% 1.78/1.43 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.78/1.43 thf(f161,plain,(
% 1.78/1.43 ( ! [X0 : $i] : (((in @ (kpair @ sK3 @ (sK10 @ X0)) @ sK0) = $false) | (sK3 != X0) | ((in @ (kpair @ X0 @ (sK10 @ X0)) @ sK0) = $false) | ((in @ X0 @ sK2) = $false)) )),
% 1.78/1.43 inference(binary_proxy_clausification,[status(thm)],[f159])).
% 1.78/1.43 thf(f159,plain,(
% 1.78/1.43 ( ! [X0 : $i] : ((sK3 != X0) | ((in @ (kpair @ X0 @ (sK10 @ X0)) @ sK0) != (in @ (kpair @ sK3 @ (sK10 @ X0)) @ sK0)) | ((in @ X0 @ sK2) = $false)) )),
% 1.78/1.43 inference(beta_eta_normalization,[status(thm)],[f158])).
% 1.78/1.43 thf(f158,plain,(
% 1.78/1.43 ( ! [X0 : $i] : ((sK3 != X0) | (((^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK0)) @ (sK10 @ X0)) != ((^[Y0 : $i]: (in @ (kpair @ sK3 @ Y0) @ sK0)) @ (sK10 @ X0))) | ((in @ X0 @ sK2) = $false)) )),
% 1.78/1.43 inference(negative_extensionality,[status(thm)],[f157])).
% 1.78/1.43 thf(f157,plain,(
% 1.78/1.43 ( ! [X0 : $i] : (((^[Y0 : $i]: (in @ (kpair @ sK3 @ Y0) @ sK0)) != (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK0))) | ((in @ X0 @ sK2) = $false) | (sK3 != X0)) )),
% 1.78/1.43 inference(trivial_inequality_removal,[status(thm)],[f156])).
% 1.78/1.43 thf(f156,plain,(
% 1.78/1.43 ( ! [X0 : $i] : (($true != $true) | ((in @ X0 @ sK2) = $false) | ((^[Y0 : $i]: (in @ (kpair @ sK3 @ Y0) @ sK0)) != (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK0))) | (sK3 != X0)) )),
% 1.78/1.43 inference(constrained_superposition,[status(thm)],[f56,f154])).
% 1.78/1.43 thf(f154,plain,(
% 1.78/1.43 ( ! [X0 : $i] : (($true = (in @ (kpair @ X0 @ (setunion @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK0))))) @ sK0)) | ((in @ X0 @ sK2) = $false)) )),
% 1.78/1.43 inference(subsumption_resolution,[status(thm)],[f150,f67])).
% 1.78/1.43 thf(f67,plain,(
% 1.78/1.43 ( ! [X1 : $i] : (((setadjoin @ (sK5 @ X1) @ emptyset) = (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK0)))) | ((in @ X1 @ sK2) = $false)) )),
% 1.78/1.43 inference(equality_proxy_clausification,[status(thm)],[f66])).
% 1.78/1.43 thf(f66,plain,(
% 1.78/1.43 ( ! [X1 : $i] : (($true = ((setadjoin @ (sK5 @ X1) @ emptyset) = (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK0))))) | ((in @ X1 @ sK2) = $false)) )),
% 1.78/1.43 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.78/1.43 thf(f64,plain,(
% 1.78/1.43 ( ! [X1 : $i] : (($true = (((setadjoin @ (sK5 @ X1) @ emptyset) = (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK0)))) & (in @ (sK5 @ X1) @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK0)))))) | ((in @ X1 @ sK2) = $false)) )),
% 1.78/1.43 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.78/1.43 thf(f63,plain,(
% 1.78/1.43 ( ! [X1 : $i] : (((in @ X1 @ sK2) = $false) | ($true = ((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK1 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK0)))) & (in @ Y0 @ (dsetconstr @ sK1 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK0)))))) @ (sK5 @ X1)))) )),
% 1.78/1.43 inference(sigma_clausification,[status(thm)],[f62])).
% 1.78/1.43 thf(f62,plain,(
% 1.78/1.43 ( ! [X1 : $i] : (((in @ X1 @ sK2) = $false) | ($true = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK1 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK0)))) & (in @ Y0 @ (dsetconstr @ sK1 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK0))))))))) )),
% 1.78/1.43 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.78/1.43 thf(f61,plain,(
% 1.78/1.43 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK1 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK0)))) & (in @ Y0 @ (dsetconstr @ sK1 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK0)))))))) = $true)) )),
% 1.78/1.43 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.78/1.43 thf(f60,plain,(
% 1.78/1.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK1 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0)))) & (in @ Y1 @ (dsetconstr @ sK1 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0))))))))) @ X1) = $true)) )),
% 1.78/1.43 inference(pi_clausification,[status(thm)],[f59])).
% 1.78/1.43 thf(f59,plain,(
% 1.78/1.43 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK1 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0)))) & (in @ Y1 @ (dsetconstr @ sK1 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0)))))))))) = $true)),
% 1.78/1.43 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.78/1.43 thf(f57,plain,(
% 1.78/1.43 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK1 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0)))) & (in @ Y1 @ (dsetconstr @ sK1 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK0)))))))))) & (subset @ sK0 @ (cartprod @ sK2 @ sK1))))),
% 1.78/1.43 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.78/1.43 thf(f52,plain,(
% 1.78/1.43 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((setadjoin @ Y7 @ emptyset) = Y6) & (in @ Y7 @ Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2))))))) @ sK2 @ sK1 @ sK0))),
% 1.78/1.43 inference(definition_unfolding,[status(thm)],[f42,f49])).
% 1.78/1.43 thf(f49,plain,(
% 1.78/1.43 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((setadjoin @ Y7 @ emptyset) = Y6) & (in @ Y7 @ Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2))))))))),
% 1.78/1.43 inference(definition_unfolding,[status(thm)],[f45,f48,f47])).
% 1.78/1.43 thf(f47,plain,(
% 1.78/1.43 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.78/1.43 inference(cnf_transformation,[status(thm)],[f13])).
% 1.78/1.43 thf(f13,plain,(
% 1.78/1.43 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.78/1.43 inference(fool_elimination,[status(thm)],[f12])).
% 1.78/1.43 thf(f12,plain,(
% 1.78/1.43 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 1.78/1.43 inference(rectify,[status(thm)],[f5])).
% 1.78/1.43 thf(f5,axiom,(
% 1.78/1.43 ((^[X0 : $i, X5 : $i, X6 : $i] : (subset @ X6 @ (cartprod @ X0 @ X5))) = breln)),
% 1.78/1.43 file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',breln)).
% 1.78/1.43 thf(f48,plain,(
% 1.78/1.43 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.78/1.43 inference(definition_unfolding,[status(thm)],[f35,f37])).
% 1.78/1.43 thf(f37,plain,(
% 1.78/1.43 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.78/1.43 inference(cnf_transformation,[status(thm)],[f28])).
% 1.78/1.43 thf(f28,plain,(
% 1.78/1.43 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.78/1.43 inference(fool_elimination,[status(thm)],[f27])).
% 1.78/1.43 thf(f27,plain,(
% 1.78/1.43 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 1.78/1.43 inference(rectify,[status(thm)],[f2])).
% 1.78/1.43 thf(f2,axiom,(
% 1.78/1.43 ((^[X0 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) & ((setadjoin @ X2 @ emptyset) = X0)))) = singleton)),
% 1.78/1.43 file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',singleton)).
% 1.78/1.43 thf(f35,plain,(
% 1.78/1.43 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.78/1.43 inference(cnf_transformation,[status(thm)],[f16])).
% 1.78/1.43 thf(f16,plain,(
% 1.78/1.43 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.78/1.43 inference(fool_elimination,[status(thm)],[f3])).
% 1.78/1.43 thf(f3,axiom,(
% 1.78/1.43 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 1.78/1.43 file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',ex1)).
% 1.78/1.43 thf(f45,plain,(
% 1.78/1.43 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & (breln @ Y0 @ Y1 @ Y2))))))))),
% 1.78/1.43 inference(cnf_transformation,[status(thm)],[f24])).
% 1.78/1.43 thf(f24,plain,(
% 1.78/1.43 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & (breln @ Y0 @ Y1 @ Y2))))))))),
% 1.78/1.43 inference(fool_elimination,[status(thm)],[f23])).
% 1.78/1.43 thf(f23,plain,(
% 1.78/1.43 (func = (^[X0 : $i, X1 : $i, X2 : $i] : ((breln @ X0 @ X1 @ X2) & ! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))))))),
% 1.78/1.43 inference(rectify,[status(thm)],[f6])).
% 1.78/1.43 thf(f6,axiom,(
% 1.78/1.43 (func = (^[X0 : $i, X5 : $i, X7 : $i] : ((breln @ X0 @ X5 @ X7) & ! [X2 : $i] : ((in @ X2 @ X0) => (ex1 @ X5 @ (^[X3 : $i] : (in @ (kpair @ X2 @ X3) @ X7)))))))),
% 1.78/1.43 file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',func)).
% 1.78/1.43 thf(f42,plain,(
% 1.78/1.43 ($true = (func @ sK2 @ sK1 @ sK0))),
% 1.78/1.43 inference(cnf_transformation,[status(thm)],[f33])).
% 1.78/1.43 thf(f33,plain,(
% 1.78/1.43 (theprop = $true) & (dsetconstrER = $true) & (($true = (func @ sK2 @ sK1 @ sK0)) & (($true != (in @ (kpair @ sK3 @ (ap @ sK2 @ sK1 @ sK0 @ sK3)) @ sK0)) & ($true = (in @ sK3 @ sK2)))) & (funcImageSingleton = $true)),
% 1.78/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f30,f32,f31])).
% 1.78/1.43 thf(f31,plain,(
% 1.78/1.43 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X2 @ X1 @ X0)) & ? [X3 : $i] : (($true != (in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0)) & ($true = (in @ X3 @ X2)))) => (($true = (func @ sK2 @ sK1 @ sK0)) & ? [X3 : $i] : (($true != (in @ (kpair @ X3 @ (ap @ sK2 @ sK1 @ sK0 @ X3)) @ sK0)) & ((in @ X3 @ sK2) = $true)))),
% 1.78/1.43 introduced(definition,[],[choice_axiom])).
% 1.78/1.43 thf(f32,plain,(
% 1.78/1.43 ? [X3 : $i] : (($true != (in @ (kpair @ X3 @ (ap @ sK2 @ sK1 @ sK0 @ X3)) @ sK0)) & ((in @ X3 @ sK2) = $true)) => (($true != (in @ (kpair @ sK3 @ (ap @ sK2 @ sK1 @ sK0 @ sK3)) @ sK0)) & ($true = (in @ sK3 @ sK2)))),
% 1.78/1.43 introduced(definition,[],[choice_axiom])).
% 1.78/1.43 thf(f30,plain,(
% 1.78/1.43 (theprop = $true) & (dsetconstrER = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X2 @ X1 @ X0)) & ? [X3 : $i] : (($true != (in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0)) & ($true = (in @ X3 @ X2)))) & (funcImageSingleton = $true)),
% 1.78/1.43 inference(flattening,[status(thm)],[f29])).
% 1.78/1.43 thf(f29,plain,(
% 1.78/1.43 ((? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X2 @ X1 @ X0)) & ? [X3 : $i] : (($true != (in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0)) & ($true = (in @ X3 @ X2)))) & (funcImageSingleton = $true)) & (theprop = $true)) & (dsetconstrER = $true)),
% 1.78/1.43 inference(ennf_transformation,[status(thm)],[f26])).
% 1.78/1.43 thf(f26,plain,(
% 1.78/1.43 ~((dsetconstrER = $true) => ((theprop = $true) => ((funcImageSingleton = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X2 @ X1 @ X0)) => ! [X3 : $i] : (($true = (in @ X3 @ X2)) => ($true = (in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0)))))))),
% 1.78/1.43 inference(fool_elimination,[status(thm)],[f25])).
% 1.78/1.43 thf(f25,plain,(
% 1.78/1.43 ~(dsetconstrER => (theprop => (funcImageSingleton => ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0))))))),
% 1.78/1.43 inference(rectify,[status(thm)],[f10])).
% 1.78/1.43 thf(f10,negated_conjecture,(
% 1.78/1.43 ~(dsetconstrER => (theprop => (funcImageSingleton => ! [X8 : $i,X5 : $i,X0 : $i] : ((func @ X0 @ X5 @ X8) => ! [X2 : $i] : ((in @ X2 @ X0) => (in @ (kpair @ X2 @ (ap @ X0 @ X5 @ X8 @ X2)) @ X8))))))),
% 1.78/1.43 inference(negated_conjecture,[status(cth)],[f9])).
% 1.78/1.43 thf(f9,conjecture,(
% 1.78/1.43 dsetconstrER => (theprop => (funcImageSingleton => ! [X8 : $i,X5 : $i,X0 : $i] : ((func @ X0 @ X5 @ X8) => ! [X2 : $i] : ((in @ X2 @ X0) => (in @ (kpair @ X2 @ (ap @ X0 @ X5 @ X8 @ X2)) @ X8)))))),
% 1.78/1.43 file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',funcGraphProp1)).
% 1.78/1.43 thf(f150,plain,(
% 1.78/1.43 ( ! [X0 : $i] : (((setadjoin @ (sK5 @ X0) @ emptyset) != (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK0)))) | ($true = (in @ (kpair @ X0 @ (setunion @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK0))))) @ sK0)) | ((in @ X0 @ sK2) = $false)) )),
% 1.78/1.43 inference(beta_eta_normalization,[status(thm)],[f149])).
% 1.78/1.43 thf(f149,plain,(
% 1.78/1.43 ( ! [X0 : $i] : (((in @ X0 @ sK2) = $false) | (((^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK0)) @ (setunion @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK0))))) = $true) | ((setadjoin @ (sK5 @ X0) @ emptyset) != (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK0))))) )),
% 1.78/1.43 inference(trivial_inequality_removal,[status(thm)],[f143])).
% 1.78/1.43 thf(f143,plain,(
% 1.78/1.43 ( ! [X0 : $i] : ((((^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK0)) @ (setunion @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK0))))) = $true) | ((in @ X0 @ sK2) = $false) | ($true = $false) | ((setadjoin @ (sK5 @ X0) @ emptyset) != (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK0))))) )),
% 1.78/1.43 inference(superposition,[status(thm)],[f65,f124])).
% 1.78/1.43 thf(f124,plain,(
% 1.78/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X2 @ (dsetconstr @ X0 @ X1)) = $false) | ((X1 @ (setunion @ (dsetconstr @ X0 @ X1))) = $true) | ((setadjoin @ X2 @ emptyset) != (dsetconstr @ X0 @ X1))) )),
% 1.78/1.43 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.78/1.43 thf(f120,plain,(
% 1.78/1.43 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((setadjoin @ X2 @ emptyset) != (dsetconstr @ X0 @ X1)) | ((X1 @ (setunion @ (dsetconstr @ X0 @ X1))) = $true) | ($true = $false) | ((in @ X2 @ (dsetconstr @ X0 @ X1)) = $false)) )),
% 1.78/1.43 inference(superposition,[status(thm)],[f75,f117])).
% 1.78/1.43 thf(f117,plain,(
% 1.78/1.43 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ X3)) = $false) | ($true = (X3 @ X1))) )),
% 1.78/1.43 inference(binary_proxy_clausification,[status(thm)],[f116])).
% 1.78/1.43 thf(f116,plain,(
% 1.78/1.43 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((in @ X1 @ (dsetconstr @ X2 @ X3)) => (X3 @ X1)) = $true)) )),
% 1.78/1.43 inference(beta_eta_normalization,[status(thm)],[f115])).
% 1.78/1.43 thf(f115,plain,(
% 1.78/1.43 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X1 @ (dsetconstr @ X2 @ Y0)) => (Y0 @ X1))) @ X3) = $true)) )),
% 1.78/1.43 inference(pi_clausification,[status(thm)],[f114])).
% 1.78/1.43 thf(f114,plain,(
% 1.78/1.43 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X1 @ (dsetconstr @ X2 @ Y0)) => (Y0 @ X1)))))) )),
% 1.78/1.43 inference(beta_eta_normalization,[status(thm)],[f113])).
% 1.78/1.43 thf(f113,plain,(
% 1.78/1.43 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ X1))))) @ X2))) )),
% 1.78/1.43 inference(pi_clausification,[status(thm)],[f112])).
% 1.78/1.43 thf(f112,plain,(
% 1.78/1.43 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ X1)))))))) )),
% 1.78/1.43 inference(beta_eta_normalization,[status(thm)],[f111])).
% 1.78/1.43 thf(f111,plain,(
% 1.78/1.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0))))))) @ X1) = $true)) )),
% 1.78/1.43 inference(pi_clausification,[status(thm)],[f110])).
% 1.78/1.43 thf(f110,plain,(
% 1.78/1.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))) = $true)),
% 1.78/1.43 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.78/1.43 thf(f51,plain,(
% 1.78/1.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))) = $true)),
% 1.78/1.43 inference(definition_unfolding,[status(thm)],[f43,f36])).
% 1.78/1.43 thf(f36,plain,(
% 1.78/1.43 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))))),
% 1.78/1.43 inference(cnf_transformation,[status(thm)],[f18])).
% 1.78/1.43 thf(f18,plain,(
% 1.78/1.43 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))))),
% 1.78/1.43 inference(fool_elimination,[status(thm)],[f17])).
% 1.78/1.43 thf(f17,plain,(
% 1.78/1.43 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X2)) = dsetconstrER)),
% 1.78/1.43 inference(rectify,[status(thm)],[f1])).
% 1.78/1.43 thf(f1,axiom,(
% 1.78/1.43 (! [X1 : $i > $o,X0 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.78/1.43 file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',dsetconstrER)).
% 1.78/1.43 thf(f43,plain,(
% 1.78/1.43 (dsetconstrER = $true)),
% 1.78/1.43 inference(cnf_transformation,[status(thm)],[f33])).
% 1.78/1.43 thf(f75,plain,(
% 1.78/1.43 ( ! [X2 : $i,X1 : $i] : (((in @ (setunion @ X1) @ X1) = $true) | ((in @ X2 @ X1) = $false) | ((setadjoin @ X2 @ emptyset) != X1)) )),
% 1.78/1.43 inference(equality_proxy_clausification,[status(thm)],[f74])).
% 1.78/1.43 thf(f74,plain,(
% 1.78/1.43 ( ! [X2 : $i,X1 : $i] : (((in @ (setunion @ X1) @ X1) = $true) | ($false = ((setadjoin @ X2 @ emptyset) = X1)) | ((in @ X2 @ X1) = $false)) )),
% 1.78/1.43 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.78/1.43 thf(f73,plain,(
% 1.78/1.43 ( ! [X2 : $i,X1 : $i] : (((((setadjoin @ X2 @ emptyset) = X1) & (in @ X2 @ X1)) = $false) | ((in @ (setunion @ X1) @ X1) = $true)) )),
% 1.78/1.43 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.78/1.43 thf(f72,plain,(
% 1.78/1.43 ( ! [X2 : $i,X1 : $i] : (((in @ (setunion @ X1) @ X1) = $true) | (((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = X1) & (in @ Y0 @ X1))) @ X2) = $false)) )),
% 1.78/1.43 inference(pi_clausification,[status(thm)],[f71])).
% 1.78/1.43 thf(f71,plain,(
% 1.78/1.43 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = X1) & (in @ Y0 @ X1)))) = $false) | ((in @ (setunion @ X1) @ X1) = $true)) )),
% 1.78/1.43 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.78/1.43 thf(f70,plain,(
% 1.78/1.43 ( ! [X1 : $i] : (($true = ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = X1) & (in @ Y0 @ X1)))) => (in @ (setunion @ X1) @ X1)))) )),
% 1.78/1.43 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.78/1.43 thf(f69,plain,(
% 1.78/1.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0)))) => (in @ (setunion @ Y0) @ Y0))) @ X1) = $true)) )),
% 1.78/1.43 inference(pi_clausification,[status(thm)],[f68])).
% 1.78/1.43 thf(f68,plain,(
% 1.78/1.43 ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0)))) => (in @ (setunion @ Y0) @ Y0)))) = $true)),
% 1.78/1.43 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.78/1.43 thf(f55,plain,(
% 1.78/1.43 ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = Y1) & (in @ Y2 @ Y1))))) @ Y0) => (in @ (setunion @ Y0) @ Y0)))) = $true)),
% 1.78/1.43 inference(definition_unfolding,[status(thm)],[f46,f44,f37])).
% 1.78/1.43 thf(f44,plain,(
% 1.78/1.43 (theprop = $true)),
% 1.78/1.43 inference(cnf_transformation,[status(thm)],[f33])).
% 1.78/1.43 thf(f46,plain,(
% 1.78/1.43 (theprop = (!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))))),
% 1.78/1.43 inference(cnf_transformation,[status(thm)],[f15])).
% 1.78/1.43 thf(f15,plain,(
% 1.78/1.43 (theprop = (!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))))),
% 1.78/1.43 inference(fool_elimination,[status(thm)],[f14])).
% 1.78/1.43 thf(f14,plain,(
% 1.78/1.43 (theprop = ! [X0 : $i] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)))),
% 1.78/1.43 inference(rectify,[status(thm)],[f4])).
% 1.78/1.43 thf(f4,axiom,(
% 1.78/1.43 (theprop = ! [X4 : $i] : ((singleton @ X4) => (in @ (setunion @ X4) @ X4)))),
% 1.78/1.43 file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',theprop)).
% 1.78/1.43 thf(f65,plain,(
% 1.78/1.43 ( ! [X1 : $i] : (((in @ (sK5 @ X1) @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK0)))) = $true) | ((in @ X1 @ sK2) = $false)) )),
% 1.78/1.43 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.78/1.43 thf(f56,plain,(
% 1.78/1.43 ((in @ (kpair @ sK3 @ (setunion @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ (kpair @ sK3 @ Y0) @ sK0))))) @ sK0) != $true)),
% 1.78/1.43 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.78/1.43 thf(f53,plain,(
% 1.78/1.43 ((in @ (kpair @ sK3 @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))) @ sK2 @ sK1 @ sK0 @ sK3)) @ sK0) != $true)),
% 1.78/1.43 inference(definition_unfolding,[status(thm)],[f41,f38])).
% 1.78/1.43 thf(f38,plain,(
% 1.78/1.43 (ap = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))))),
% 1.78/1.43 inference(cnf_transformation,[status(thm)],[f22])).
% 1.78/1.43 thf(f22,plain,(
% 1.78/1.43 (ap = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))))),
% 1.78/1.43 inference(fool_elimination,[status(thm)],[f21])).
% 1.78/1.43 thf(f21,plain,(
% 1.78/1.43 (ap = (^[X0 : $i, X1 : $i, X2 : $i, X3 : $i] : (setunion @ (dsetconstr @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2))))))),
% 1.78/1.43 inference(rectify,[status(thm)],[f8])).
% 1.78/1.43 thf(f8,axiom,(
% 1.78/1.43 (ap = (^[X0 : $i, X5 : $i, X8 : $i, X2 : $i] : (setunion @ (dsetconstr @ X5 @ (^[X3 : $i] : (in @ (kpair @ X2 @ X3) @ X8))))))),
% 1.78/1.43 file('/export/starexec/sandbox/tmp/tmp.GuwOmzQ2sM/DTF2THF_2030.p',ap)).
% 1.78/1.43 thf(f41,plain,(
% 1.78/1.43 ($true != (in @ (kpair @ sK3 @ (ap @ sK2 @ sK1 @ sK0 @ sK3)) @ sK0))),
% 1.78/1.43 inference(cnf_transformation,[status(thm)],[f33])).
% 1.78/1.43 thf(f178,plain,(
% 1.78/1.43 ~spl4_2),
% 1.78/1.43 inference(avatar_contradiction_clause,[status(thm)],[f177])).
% 1.78/1.43 thf(f177,plain,(
% 1.78/1.43 $false | ~spl4_2),
% 1.78/1.43 inference(trivial_inequality_removal,[status(thm)],[f174])).
% 1.78/1.43 thf(f174,plain,(
% 1.78/1.43 ($true = $false) | ~spl4_2),
% 1.78/1.43 inference(superposition,[status(thm)],[f40,f171])).
% 1.78/1.43 thf(f171,plain,(
% 1.78/1.43 ((in @ sK3 @ sK2) = $false) | ~spl4_2),
% 1.78/1.43 inference(avatar_component_clause,[status(thm)],[f169])).
% 1.78/1.43 thf(f40,plain,(
% 1.78/1.43 ($true = (in @ sK3 @ sK2))),
% 1.78/1.43 inference(cnf_transformation,[status(thm)],[f33])).
% 1.78/1.43 thf(f172,plain,(
% 1.78/1.43 spl4_1 | spl4_2),
% 1.78/1.43 inference(avatar_split_clause,[status(thm)],[f163,f169,f165])).
% 1.78/1.43 thf(f163,plain,(
% 1.78/1.43 ((in @ (kpair @ sK3 @ (sK10 @ sK3)) @ sK0) = $true) | ((in @ sK3 @ sK2) = $false)),
% 1.78/1.43 inference(trivial_inequality_removal,[status(thm)],[f162])).
% 1.78/1.43 thf(f162,plain,(
% 1.78/1.43 ($true != $true) | ((in @ sK3 @ sK2) = $false) | ((in @ (kpair @ sK3 @ (sK10 @ sK3)) @ sK0) = $true) | (sK3 != sK3)),
% 1.78/1.43 inference(equality_factoring,[status(thm)],[f160])).
% 1.78/1.43 thf(f160,plain,(
% 1.78/1.43 ( ! [X0 : $i] : (($true = (in @ (kpair @ sK3 @ (sK10 @ X0)) @ sK0)) | ((in @ X0 @ sK2) = $false) | ($true = (in @ (kpair @ X0 @ (sK10 @ X0)) @ sK0)) | (sK3 != X0)) )),
% 1.78/1.43 inference(binary_proxy_clausification,[status(thm)],[f159])).
% 1.78/1.43 % SZS output end Proof for DTF2THF_2030
% 1.78/1.43 % (2127)------------------------------
% 1.78/1.43 % (2127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.43 % (2127)Termination reason: Refutation
% 1.78/1.43
% 1.78/1.43 % (2127)Memory used [KB]: 6012
% 1.78/1.43 % (2127)Time elapsed: 0.041 s
% 1.78/1.43 % (2127)Instructions burned: 79 (million)
% 1.78/1.43 % (2127)------------------------------
% 1.78/1.43 % (2127)------------------------------
% 1.78/1.43 % (2126)Success in time 0.042 s
%------------------------------------------------------------------------------