%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU677^2 : 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 : n017.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 09:36:12 AM UTC 2026
% Result : Theorem 1.61s 1.37s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 113 ( 57 unt; 0 typ; 3 def)
% Number of atoms : 1071 ( 200 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 1564 ( 45 ~; 79 |; 50 &;1262 @)
% ( 3 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 25 usr; 14 con; 0-3 aty)
% ( 39 !!; 20 ??; 0 @@+; 0 @@-)
% Number of variables : 314 ( 232 ^; 71 !; 11 ?; 314 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
powerset: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_7,type,
subset: $i > $i > $o ).
thf(func_def_9,type,
kpair: $i > $i > $i ).
thf(func_def_10,type,
cartprod: $i > $i > $i ).
thf(func_def_11,type,
singleton: $i > $o ).
thf(func_def_12,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_15,type,
funcSet: $i > $i > $i ).
thf(func_def_16,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_33,type,
sK4: $i > $i ).
thf(func_def_35,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f156,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f95,f102,f139,f155]) ).
thf(f155,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f154]) ).
thf(f154,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f153]) ).
thf(f153,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[status(thm)],[f101,f149]) ).
thf(f149,plain,
( ( $false
= ( in @ sK6 @ sK2 ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f147]) ).
thf(f147,plain,
( ( $false = $true )
| ( $false
= ( in @ sK6 @ sK2 ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f105,f144]) ).
thf(f144,plain,
( ( $false
= ( in @ ( sK4 @ sK6 ) @ ( setadjoin @ ( sK4 @ sK6 ) @ emptyset ) ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(equality_resolution,[status(thm)],[f143]) ).
thf(f143,plain,
( ! [X0: $i] :
( ( ( setadjoin @ ( sK4 @ sK6 ) @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( ( in @ X0 @ ( setadjoin @ ( sK4 @ sK6 ) @ emptyset ) )
= $false ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f142]) ).
thf(f142,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ ( sK4 @ sK6 ) @ emptyset ) )
= $false )
| ( $false = $true )
| ( ( setadjoin @ ( sK4 @ sK6 ) @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[status(thm)],[f141,f101]) ).
thf(f141,plain,
( ! [X0: $i] :
( ( ( setadjoin @ ( sK4 @ sK6 ) @ emptyset )
!= ( setadjoin @ X0 @ emptyset ) )
| ( ( in @ X0 @ ( setadjoin @ ( sK4 @ sK6 ) @ emptyset ) )
= $false )
| ( $false
= ( in @ sK6 @ sK2 ) ) )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f94,f63]) ).
thf(f63,plain,
! [X1: $i] :
( ( ( setadjoin @ ( sK4 @ X1 ) @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK1 ) ) )
| ( $false
= ( in @ X1 @ sK2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK2 ) )
| ( ( ( setadjoin @ ( sK4 @ X1 ) @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK1 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: $i] :
( ( ( ( ( setadjoin @ ( sK4 @ X1 ) @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK1 ) ) )
& ( in @ ( sK4 @ X1 )
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK1 ) ) ) )
= $true )
| ( $false
= ( in @ X1 @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK2 ) )
| ( ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK1 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK1 ) ) ) )
@ ( sK4 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK2 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK1 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK1 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK1 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) ) ) ) ) )
& ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ^ [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
@ sK0
@ sK1 )
= $true ),
inference(definition_unfolding,[status(thm)],[f37,f42]) ).
thf(f42,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)],[f40,f41,f39]) ).
thf(f39,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X0: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X0 @ X4 ) ) )
= breln ),
file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',breln) ).
thf(f41,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)],[f34,f30]) ).
thf(f30,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( singleton
= ( ^ [X0: $i] :
? [X2: $i] :
( ( in @ X2 @ X0 )
& ( ( setadjoin @ X2 @ emptyset )
= X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',singleton) ).
thf(f34,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',ex1) ).
thf(f40,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)],[f14]) ).
thf(f14,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)],[f13]) ).
thf(f13,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
& ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) )
= func ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( ^ [X0: $i,X4: $i,X6: $i] :
( ( breln @ X0 @ X4 @ X6 )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X6 ) ) ) ) )
= func ),
file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',func) ).
thf(f37,plain,
( ( func @ sK2 @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) )
!= $true )
& ( ( func @ sK2 @ sK0 @ sK1 )
= $true )
& ( dsetconstrI = $true )
& ( powersetI1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f27,f28]) ).
thf(f28,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
!= $true )
& ( ( func @ X2 @ X0 @ X1 )
= $true ) )
=> ( ( ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) )
!= $true )
& ( ( func @ sK2 @ sK0 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
!= $true )
& ( ( func @ X2 @ X0 @ X1 )
= $true ) )
& ( dsetconstrI = $true )
& ( powersetI1 = $true ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
!= $true )
& ( ( func @ X2 @ X0 @ X1 )
= $true ) )
& ( powersetI1 = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
~ ( ( dsetconstrI = $true )
=> ( ( powersetI1 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X0 @ X1 )
= $true )
=> ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
~ ( dsetconstrI
=> ( powersetI1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X2 @ X0 @ X1 )
=> ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ( dsetconstrI
=> ( powersetI1
=> ! [X4: $i,X7: $i,X0: $i] :
( ( func @ X0 @ X4 @ X7 )
=> ( in @ X7 @ ( funcSet @ X0 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
( dsetconstrI
=> ( powersetI1
=> ! [X4: $i,X7: $i,X0: $i] :
( ( func @ X0 @ X4 @ X7 )
=> ( in @ X7 @ ( funcSet @ X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',funcinfuncset) ).
thf(f94,plain,
( ! [X1: $i] :
( ( ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) )
!= ( setadjoin @ X1 @ emptyset ) )
| ( $false
= ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) ) ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f93]) ).
thf(f93,definition,
( spl3_2
<=> ! [X1: $i] :
( ( ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) )
!= ( setadjoin @ X1 @ emptyset ) )
| ( $false
= ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f105,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK4 @ X0 ) @ ( setadjoin @ ( sK4 @ X0 ) @ emptyset ) ) )
| ( ( in @ X0 @ sK2 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f103]) ).
thf(f103,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK4 @ X0 ) @ ( setadjoin @ ( sK4 @ X0 ) @ emptyset ) ) )
| ( ( in @ X0 @ sK2 )
= $false )
| ( ( in @ X0 @ sK2 )
= $false ) ),
inference(superposition,[status(thm)],[f61,f63]) ).
thf(f61,plain,
! [X1: $i] :
( ( ( in @ ( sK4 @ X1 )
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK1 ) ) )
= $true )
| ( $false
= ( in @ X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f101,plain,
( ( ( in @ sK6 @ sK2 )
= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f99,definition,
( spl3_3
<=> ( ( in @ sK6 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f139,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[status(thm)],[f138]) ).
thf(f138,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f137]) ).
thf(f137,plain,
( ( $false = $true )
| ~ spl3_1 ),
inference(backward_demodulation,[status(thm)],[f54,f135]) ).
thf(f135,plain,
( ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f133]) ).
thf(f133,plain,
( ( $false = $true )
| ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f91,f52]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
| ( $false
= ( subset @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
=> ( in @ X2 @ ( powerset @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( in @ Y0 @ ( powerset @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( in @ Y0 @ ( powerset @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f35,f32]) ).
thf(f32,plain,
( powersetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( powersetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) )
= powersetI1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X4: $i,X0: $i] :
( ( ( subset @ X4 @ X0 )
=> ( in @ X4 @ ( powerset @ X0 ) ) )
= powersetI1 ),
file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',powersetI1) ).
thf(f35,plain,
powersetI1 = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f91,plain,
( ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f89,definition,
( spl3_1
<=> ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f54,plain,
( ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f102,plain,
( spl3_3
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f97,f89,f99]) ).
thf(f97,plain,
( ( ( in @ sK6 @ sK2 )
= $true )
| ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ( ( in @ sK6 @ sK2 )
= $true )
| ( $false = $true )
| ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f81,f54]) ).
thf(f81,plain,
( ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) )
| ( ( in @ sK6 @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ( ( in @ sK6 @ sK2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ sK6 @ Y1 ) @ sK1 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ sK6 @ Y1 ) @ sK1 ) ) ) ) ) )
= $false )
| ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) ) ) ) )
@ sK6 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) ) ) ) ) ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK0
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 ) ) ) ) ) ) )
& ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( in @ Y2
@ ( dsetconstr @ sK0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ sK2 @ sK0 ) ) )
@ sK1 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) )
| ( $true != $true )
| ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( in @ Y2
@ ( dsetconstr @ sK0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ sK2 @ sK0 ) ) )
@ sK1 ) ) ),
inference(superposition,[status(thm)],[f64,f73]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) )
= $true )
| ( $false
= ( in @ X2 @ X3 ) )
| ( ( X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) )
= $true )
| ( $false
= ( in @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X2 @ X3 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f36,f31]) ).
thf(f31,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
( dsetconstrI
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X1 @ X0 )
=> ( ( X2 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',dsetconstrI) ).
thf(f36,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f64,plain,
( ( in @ sK1
@ ( dsetconstr @ ( powerset @ ( cartprod @ sK2 @ sK0 ) )
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( in @ Y2
@ ( dsetconstr @ sK0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ sK2 @ sK0 ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
( ( in @ sK1
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( ( setadjoin @ Y10 @ emptyset )
= Y9 )
& ( in @ Y10 @ Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) )
& ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y0
@ Y1
@ Y2 ) )
@ sK2
@ sK0 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f38,f43]) ).
thf(f43,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( ( setadjoin @ Y10 @ emptyset )
= Y9 )
& ( in @ Y10 @ Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) )
& ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y0
@ Y1
@ Y2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f33,f42]) ).
thf(f33,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] : ( func @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] : ( func @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( funcSet
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X1 ) )
@ ^ [X2: $i] : ( func @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( funcSet
= ( ^ [X0: $i,X4: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X4 ) )
@ ^ [X7: $i] : ( func @ X0 @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',funcSet) ).
thf(f38,plain,
( ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f95,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f87,f93,f89]) ).
thf(f87,plain,
! [X1: $i] :
( ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) )
| ( ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) )
!= ( setadjoin @ X1 @ emptyset ) )
| ( $false
= ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) ) ) )
| ( $false = $true )
| ( ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) )
!= ( setadjoin @ X1 @ emptyset ) )
| ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f85,f54]) ).
thf(f85,plain,
! [X1: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) ) ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) )
| ( ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) )
!= ( setadjoin @ X1 @ emptyset ) )
| ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
! [X1: $i] :
( ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) )
| ( $false
= ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) ) ) )
| ( $false
= ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X1: $i] :
( ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) )
| ( $false
= ( ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) ) )
& ( in @ X1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ ( kpair @ sK6 @ Y0 ) @ sK1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
! [X1: $i] :
( ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ sK6 @ Y1 ) @ sK1 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ sK6 @ Y1 ) @ sK1 ) ) ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $false
= ( in @ sK1 @ ( powerset @ ( cartprod @ sK2 @ sK0 ) ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ sK6 @ Y1 ) @ sK1 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( in @ ( kpair @ sK6 @ Y1 ) @ sK1 ) ) ) ) )
= $false )
| ( $false
= ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU677^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n017.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 12:29:26 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.38 ---- Original DTF file ---
% 0.17/0.38 thf(spec,logic,$$dhol).
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 % File : SEU677^2 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.38 % Domain : Set Theory
% 0.17/0.38 % Problem : Functions - Lambda Abstraction
% 0.17/0.38 % Version : Especial > Reduced > Especial.
% 0.17/0.38 % English : (! A:i.! B:i.! f:i.func A B f -> in f (funcSet A B))
% 0.17/0.38
% 0.17/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.38 % Source : [Bro08]
% 0.17/0.38 % Names : ZFC179l [Bro08]
% 0.17/0.38
% 0.17/0.38 % Status : Theorem
% 0.17/0.38 % Rating : 0.22 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 v7.3.0, 0.33 v7.2.0, 0.38 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.1.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.17/0.38 % Syntax : Number of formulae : 23 ( 7 unt; 15 typ; 7 def)
% 0.17/0.38 % Number of atoms : 30 ( 8 equ; 0 cnn)
% 0.17/0.38 % Maximal formula atoms : 4 ( 3 avg)
% 0.17/0.38 % Number of connectives : 60 ( 0 ~; 0 |; 2 &; 51 @)
% 0.17/0.38 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.17/0.38 % Maximal formula depth : 10 ( 2 avg)
% 0.17/0.38 % Number of types : 2 ( 0 usr)
% 0.17/0.38 % Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% 0.17/0.38 % Number of symbols : 16 ( 15 usr; 3 con; 0-3 aty)
% 0.17/0.38 % Number of variables : 25 ( 15 ^; 9 !; 1 ?; 25 :)
% 0.17/0.38 % SPC : TH0_THM_EQU_NAR
% 0.17/0.38
% 0.17/0.38 % Comments : http://mathgate.info/detsetitem.php?id=231
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 thf(in_type,type,
% 0.17/0.38 in: $i > $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(emptyset_type,type,
% 0.17/0.38 emptyset: $i ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoin_type,type,
% 0.17/0.38 setadjoin: $i > $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(powerset_type,type,
% 0.17/0.38 powerset: $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstr_type,type,
% 0.17/0.38 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstrI_type,type,
% 0.17/0.38 dsetconstrI: $o ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstrI,definition,
% 0.17/0.38 ( dsetconstrI
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( ( Xphi @ Xx )
% 0.17/0.38 => ( in @ Xx
% 0.17/0.38 @ ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(subset_type,type,
% 0.17/0.38 subset: $i > $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(powersetI1_type,type,
% 0.17/0.38 powersetI1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(powersetI1,definition,
% 0.17/0.38 ( powersetI1
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( subset @ B @ A )
% 0.17/0.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(kpair_type,type,
% 0.17/0.38 kpair: $i > $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(cartprod_type,type,
% 0.17/0.38 cartprod: $i > $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(singleton_type,type,
% 0.17/0.38 singleton: $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(singleton,definition,
% 0.17/0.38 ( singleton
% 0.17/0.38 = ( ^ [A: $i] :
% 0.17/0.38 ? [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 & ( A
% 0.17/0.38 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(ex1_type,type,
% 0.17/0.38 ex1: $i > ( $i > $o ) > $o ).
% 0.17/0.38
% 0.17/0.38 thf(ex1,definition,
% 0.17/0.38 ( ex1
% 0.17/0.38 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.17/0.38 ( singleton
% 0.17/0.38 @ ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(breln_type,type,
% 0.17/0.38 breln: $i > $i > $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(breln,definition,
% 0.17/0.38 ( breln
% 0.17/0.38 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(func_type,type,
% 0.17/0.38 func: $i > $i > $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(func,definition,
% 0.17/0.38 ( func
% 0.17/0.38 = ( ^ [A: $i,B: $i,R: $i] :
% 0.17/0.38 ( ( breln @ A @ B @ R )
% 0.17/0.38 & ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( ex1 @ B
% 0.17/0.38 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(funcSet_type,type,
% 0.17/0.38 funcSet: $i > $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(funcSet,definition,
% 0.17/0.38 ( funcSet
% 0.17/0.38 = ( ^ [A: $i,B: $i] :
% 0.17/0.38 ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
% 0.17/0.38 @ ^ [Xf: $i] : ( func @ A @ B @ Xf ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(funcinfuncset,conjecture,
% 0.17/0.38 ( dsetconstrI
% 0.17/0.38 => ( powersetI1
% 0.17/0.38 => ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.38 ( ( func @ A @ B @ Xf )
% 0.17/0.38 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 ------------------------
% 1.61/1.32 ---- Embedded in THF ---
% 1.61/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.32 %%% Generated on Tue Feb 24 12:29:26 EST 2026
% 1.61/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.32 %%% Logic specification used:
% 1.61/1.32 %%% thf(spec, logic, $$dhol).
% 1.61/1.32
% 1.61/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2DTF23048.p
% See solution above
% 1.61/1.32 ------------------------
% 1.61/1.33 ---- Cleaned THF ---
% 1.61/1.33 thf(in_type,type,
% 1.61/1.33 in: $i > $i > $o ).
% 1.61/1.33
% 1.61/1.33 thf(emptyset_type,type,
% 1.61/1.33 emptyset: $i ).
% 1.61/1.33
% 1.61/1.33 thf(setadjoin_type,type,
% 1.61/1.33 setadjoin: $i > $i > $i ).
% 1.61/1.33
% 1.61/1.33 thf(powerset_type,type,
% 1.61/1.33 powerset: $i > $i ).
% 1.61/1.33
% 1.61/1.33 thf(dsetconstr_type,type,
% 1.61/1.33 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.61/1.33
% 1.61/1.33 thf(dsetconstrI_type,type,
% 1.61/1.33 dsetconstrI: $o ).
% 1.61/1.33
% 1.61/1.33 thf(dsetconstrI,definition,
% 1.61/1.33 ( dsetconstrI
% 1.61/1.33 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.61/1.33 ( ( in @ Xx @ A )
% 1.61/1.33 => ( ( Xphi @ Xx )
% 1.61/1.33 => ( in @ Xx
% 1.61/1.33 @ ( dsetconstr @ A
% 1.61/1.33 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.61/1.33
% 1.61/1.33 thf(subset_type,type,
% 1.61/1.33 subset: $i > $i > $o ).
% 1.61/1.33
% 1.61/1.33 thf(powersetI1_type,type,
% 1.61/1.33 powersetI1: $o ).
% 1.61/1.33
% 1.61/1.33 thf(powersetI1,definition,
% 1.61/1.33 ( powersetI1
% 1.61/1.33 = ( ! [A: $i,B: $i] :
% 1.61/1.33 ( ( subset @ B @ A )
% 1.61/1.33 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.61/1.33
% 1.61/1.33 thf(kpair_type,type,
% 1.61/1.33 kpair: $i > $i > $i ).
% 1.61/1.33
% 1.61/1.33 thf(cartprod_type,type,
% 1.61/1.33 cartprod: $i > $i > $i ).
% 1.61/1.33
% 1.61/1.33 thf(singleton_type,type,
% 1.61/1.33 singleton: $i > $o ).
% 1.61/1.33
% 1.61/1.33 thf(singleton,definition,
% 1.61/1.33 ( singleton
% 1.61/1.33 = ( ^ [A: $i] :
% 1.61/1.33 ? [Xx: $i] :
% 1.61/1.33 ( ( in @ Xx @ A )
% 1.61/1.33 & ( A
% 1.61/1.33 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.61/1.33
% 1.61/1.33 thf(ex1_type,type,
% 1.61/1.33 ex1: $i > ( $i > $o ) > $o ).
% 1.61/1.33
% 1.61/1.33 thf(ex1,definition,
% 1.61/1.33 ( ex1
% 1.61/1.33 = ( ^ [A: $i,Xphi: $i > $o] :
% 1.61/1.33 ( singleton
% 1.61/1.33 @ ( dsetconstr @ A
% 1.61/1.33 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.61/1.33
% 1.61/1.33 thf(breln_type,type,
% 1.61/1.33 breln: $i > $i > $i > $o ).
% 1.61/1.33
% 1.61/1.33 thf(breln,definition,
% 1.61/1.33 ( breln
% 1.61/1.33 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.61/1.33
% 1.61/1.33 thf(func_type,type,
% 1.61/1.33 func: $i > $i > $i > $o ).
% 1.61/1.33
% 1.61/1.33 thf(func,definition,
% 1.61/1.33 ( func
% 1.61/1.33 = ( ^ [A: $i,B: $i,R: $i] :
% 1.61/1.33 ( ( breln @ A @ B @ R )
% 1.61/1.33 & ! [Xx: $i] :
% 1.61/1.33 ( ( in @ Xx @ A )
% 1.61/1.33 => ( ex1 @ B
% 1.61/1.33 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 1.61/1.33
% 1.61/1.33 thf(funcSet_type,type,
% 1.61/1.33 funcSet: $i > $i > $i ).
% 1.61/1.33
% 1.61/1.33 thf(funcSet,definition,
% 1.61/1.33 ( funcSet
% 1.61/1.33 = ( ^ [A: $i,B: $i] :
% 1.61/1.33 ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
% 1.61/1.33 @ ^ [Xf: $i] : ( func @ A @ B @ Xf ) ) ) ) ).
% 1.61/1.33
% 1.61/1.33 thf(funcinfuncset,conjecture,
% 1.61/1.33 ( dsetconstrI
% 1.61/1.33 => ( powersetI1
% 1.61/1.33 => ! [A: $i,B: $i,Xf: $i] :
% 1.61/1.33 ( ( func @ A @ B @ Xf )
% 1.61/1.33 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 1.61/1.33 ------------------------
% 1.61/1.35 % (23151)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23048 for (2999ds/18Mi)
% 1.61/1.35 % (23148)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23048 for (2999ds/2Mi)
% 1.61/1.35 % (23149)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_23048 for (2999ds/2Mi)
% 1.61/1.35 % (23146)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_23048 for (2999ds/4Mi)
% 1.61/1.35 % (23147)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_23048 for (2999ds/27Mi)
% 1.61/1.35 % (23145)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23048 for (2999ds/183Mi)
% 1.61/1.35 % (23150)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_23048 for (2999ds/275Mi)
% 1.61/1.35 % (23148)Instruction limit reached!
% 1.61/1.35 % (23148)------------------------------
% 1.61/1.35 % (23148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (23148)Termination reason: Unknown
% 1.61/1.35 % (23149)Instruction limit reached!
% 1.61/1.35 % (23149)------------------------------
% 1.61/1.35 % (23149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (23148)Termination phase: Property scanning
% 1.61/1.35
% 1.61/1.35 % (23148)Memory used [KB]: 1023
% 1.61/1.35 % (23148)Time elapsed: 0.003 s
% 1.61/1.35 % (23148)Instructions burned: 3 (million)
% 1.61/1.35 % (23148)------------------------------
% 1.61/1.35 % (23148)------------------------------
% 1.61/1.35 % (23149)Termination reason: Unknown
% 1.61/1.35 % (23149)Termination phase: Property scanning
% 1.61/1.35
% 1.61/1.35 % (23149)Memory used [KB]: 1023
% 1.61/1.35 % (23149)Time elapsed: 0.003 s
% 1.61/1.35 % (23149)Instructions burned: 3 (million)
% 1.61/1.35 % (23149)------------------------------
% 1.61/1.35 % (23149)------------------------------
% 1.61/1.35 % (23146)Instruction limit reached!
% 1.61/1.35 % (23146)------------------------------
% 1.61/1.35 % (23146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (23146)Termination reason: Unknown
% 1.61/1.35 % (23146)Termination phase: Saturation
% 1.61/1.35
% 1.61/1.35 % (23146)Memory used [KB]: 5500
% 1.61/1.35 % (23146)Time elapsed: 0.004 s
% 1.61/1.35 % (23146)Instructions burned: 4 (million)
% 1.61/1.35 % (23146)------------------------------
% 1.61/1.35 % (23146)------------------------------
% 1.61/1.35 % (23150)Refutation not found, incomplete strategy
% 1.61/1.35 % (23150)------------------------------
% 1.61/1.35 % (23150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (23150)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.35
% 1.61/1.35
% 1.61/1.35 % (23150)Memory used [KB]: 5500
% 1.61/1.35 % (23150)Time elapsed: 0.005 s
% 1.61/1.35 % (23150)Instructions burned: 4 (million)
% 1.61/1.35 % (23150)------------------------------
% 1.61/1.35 % (23150)------------------------------
% 1.61/1.36 % (23151)Instruction limit reached!
% 1.61/1.36 % (23151)------------------------------
% 1.61/1.36 % (23151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.36 % (23151)Termination reason: Unknown
% 1.61/1.36 % (23151)Termination phase: Saturation
% 1.61/1.36
% 1.61/1.36 % (23151)Memory used [KB]: 5628
% 1.61/1.36 % (23151)Time elapsed: 0.011 s
% 1.61/1.36 % (23151)Instructions burned: 18 (million)
% 1.61/1.36 % (23151)------------------------------
% 1.61/1.36 % (23151)------------------------------
% 1.61/1.36 % (23147)First to succeed.
% 1.61/1.37 % (23147)Refutation found. Thanks to Tanya!
% 1.61/1.37 % SZS status Theorem for DTF2THF_23048
% 1.61/1.37 % SZS output start Proof for DTF2THF_23048
% 1.61/1.37 thf(func_def_0, type, in: $i > $i > $o).
% 1.61/1.37 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.61/1.37 thf(func_def_3, type, powerset: $i > $i).
% 1.61/1.37 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 1.61/1.37 thf(func_def_7, type, subset: $i > $i > $o).
% 1.61/1.37 thf(func_def_9, type, kpair: $i > $i > $i).
% 1.61/1.37 thf(func_def_10, type, cartprod: $i > $i > $i).
% 1.61/1.37 thf(func_def_11, type, singleton: $i > $o).
% 1.61/1.37 thf(func_def_12, type, ex1: $i > ($i > $o) > $o).
% 1.61/1.37 thf(func_def_13, type, breln: $i > $i > $i > $o).
% 1.61/1.37 thf(func_def_14, type, func: $i > $i > $i > $o).
% 1.61/1.37 thf(func_def_15, type, funcSet: $i > $i > $i).
% 1.61/1.37 thf(func_def_16, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.61/1.37 thf(func_def_33, type, sK4: $i > $i).
% 1.61/1.37 thf(func_def_35, type, ph5: !>[X0: $tType]:(X0)).
% 1.61/1.37 thf(f156,plain,(
% 1.61/1.37 $false),
% 1.61/1.37 inference(avatar_sat_refutation,[status(thm)],[f95,f102,f139,f155])).
% 1.61/1.37 thf(f155,plain,(
% 1.61/1.37 ~spl3_2 | ~spl3_3),
% 1.61/1.37 inference(avatar_contradiction_clause,[status(thm)],[f154])).
% 1.61/1.37 thf(f154,plain,(
% 1.61/1.37 $false | (~spl3_2 | ~spl3_3)),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f153])).
% 1.61/1.37 thf(f153,plain,(
% 1.61/1.37 ($false = $true) | (~spl3_2 | ~spl3_3)),
% 1.61/1.37 inference(backward_demodulation,[status(thm)],[f101,f149])).
% 1.61/1.37 thf(f149,plain,(
% 1.61/1.37 ($false = (in @ sK6 @ sK2)) | (~spl3_2 | ~spl3_3)),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f147])).
% 1.61/1.37 thf(f147,plain,(
% 1.61/1.37 ($false = $true) | ($false = (in @ sK6 @ sK2)) | (~spl3_2 | ~spl3_3)),
% 1.61/1.37 inference(superposition,[status(thm)],[f105,f144])).
% 1.61/1.37 thf(f144,plain,(
% 1.61/1.37 ($false = (in @ (sK4 @ sK6) @ (setadjoin @ (sK4 @ sK6) @ emptyset))) | (~spl3_2 | ~spl3_3)),
% 1.61/1.37 inference(equality_resolution,[status(thm)],[f143])).
% 1.61/1.37 thf(f143,plain,(
% 1.61/1.37 ( ! [X0 : $i] : (((setadjoin @ (sK4 @ sK6) @ emptyset) != (setadjoin @ X0 @ emptyset)) | ((in @ X0 @ (setadjoin @ (sK4 @ sK6) @ emptyset)) = $false)) ) | (~spl3_2 | ~spl3_3)),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f142])).
% 1.61/1.37 thf(f142,plain,(
% 1.61/1.37 ( ! [X0 : $i] : (((in @ X0 @ (setadjoin @ (sK4 @ sK6) @ emptyset)) = $false) | ($false = $true) | ((setadjoin @ (sK4 @ sK6) @ emptyset) != (setadjoin @ X0 @ emptyset))) ) | (~spl3_2 | ~spl3_3)),
% 1.61/1.37 inference(forward_demodulation,[status(thm)],[f141,f101])).
% 1.61/1.37 thf(f141,plain,(
% 1.61/1.37 ( ! [X0 : $i] : (((setadjoin @ (sK4 @ sK6) @ emptyset) != (setadjoin @ X0 @ emptyset)) | ((in @ X0 @ (setadjoin @ (sK4 @ sK6) @ emptyset)) = $false) | ($false = (in @ sK6 @ sK2))) ) | ~spl3_2),
% 1.61/1.37 inference(superposition,[status(thm)],[f94,f63])).
% 1.61/1.37 thf(f63,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (((setadjoin @ (sK4 @ X1) @ emptyset) = (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK1)))) | ($false = (in @ X1 @ sK2))) )),
% 1.61/1.37 inference(equality_proxy_clausification,[status(thm)],[f62])).
% 1.61/1.37 thf(f62,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (($false = (in @ X1 @ sK2)) | (((setadjoin @ (sK4 @ X1) @ emptyset) = (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK1)))) = $true)) )),
% 1.61/1.37 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.61/1.37 thf(f60,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (((((setadjoin @ (sK4 @ X1) @ emptyset) = (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK1)))) & (in @ (sK4 @ X1) @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK1))))) = $true) | ($false = (in @ X1 @ sK2))) )),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.61/1.37 thf(f59,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (($false = (in @ X1 @ sK2)) | (((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK1)))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK1)))))) @ (sK4 @ X1)) = $true)) )),
% 1.61/1.37 inference(sigma_clausification,[status(thm)],[f58])).
% 1.61/1.37 thf(f58,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (($false = (in @ X1 @ sK2)) | ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK1)))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK1))))))) = $true)) )),
% 1.61/1.37 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.61/1.37 thf(f57,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK2) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK1)))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK1)))))))))) )),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.61/1.37 thf(f56,plain,(
% 1.61/1.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK1)))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK1))))))))) @ X1) = $true)) )),
% 1.61/1.37 inference(pi_clausification,[status(thm)],[f55])).
% 1.61/1.37 thf(f55,plain,(
% 1.61/1.37 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK1)))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK1)))))))))) = $true)),
% 1.61/1.37 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.61/1.37 thf(f53,plain,(
% 1.61/1.37 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK1)))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK1)))))))))) & (subset @ sK1 @ (cartprod @ sK2 @ sK0))) = $true)),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.61/1.37 thf(f45,plain,(
% 1.61/1.37 (((^[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 @ sK0 @ sK1) = $true)),
% 1.61/1.37 inference(definition_unfolding,[status(thm)],[f37,f42])).
% 1.61/1.37 thf(f42,plain,(
% 1.61/1.37 (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))))))))),
% 1.61/1.37 inference(definition_unfolding,[status(thm)],[f40,f41,f39])).
% 1.61/1.37 thf(f39,plain,(
% 1.61/1.37 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f21])).
% 1.61/1.37 thf(f21,plain,(
% 1.61/1.37 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f20])).
% 1.61/1.37 thf(f20,plain,(
% 1.61/1.37 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 1.61/1.37 inference(rectify,[status(thm)],[f5])).
% 1.61/1.37 thf(f5,axiom,(
% 1.61/1.37 ((^[X0 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X0 @ X4))) = breln)),
% 1.61/1.37 file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',breln)).
% 1.61/1.37 thf(f41,plain,(
% 1.61/1.37 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.61/1.37 inference(definition_unfolding,[status(thm)],[f34,f30])).
% 1.61/1.37 thf(f30,plain,(
% 1.61/1.37 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f12])).
% 1.61/1.37 thf(f12,plain,(
% 1.61/1.37 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f11])).
% 1.61/1.37 thf(f11,plain,(
% 1.61/1.37 (singleton = (^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))))),
% 1.61/1.37 inference(rectify,[status(thm)],[f3])).
% 1.61/1.37 thf(f3,axiom,(
% 1.61/1.37 (singleton = (^[X0 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) & ((setadjoin @ X2 @ emptyset) = X0)))))),
% 1.61/1.37 file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',singleton)).
% 1.61/1.37 thf(f34,plain,(
% 1.61/1.37 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f19])).
% 1.61/1.37 thf(f19,plain,(
% 1.61/1.37 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f4])).
% 1.61/1.37 thf(f4,axiom,(
% 1.61/1.37 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 1.61/1.37 file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',ex1)).
% 1.61/1.37 thf(f40,plain,(
% 1.61/1.37 (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))))))))),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.61/1.37 thf(f14,plain,(
% 1.61/1.37 (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))))))))),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f13])).
% 1.61/1.37 thf(f13,plain,(
% 1.61/1.37 ((^[X0 : $i, X1 : $i, X2 : $i] : ((breln @ X0 @ X1 @ X2) & ! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))))) = func)),
% 1.61/1.37 inference(rectify,[status(thm)],[f6])).
% 1.61/1.37 thf(f6,axiom,(
% 1.61/1.37 ((^[X0 : $i, X4 : $i, X6 : $i] : ((breln @ X0 @ X4 @ X6) & ! [X2 : $i] : ((in @ X2 @ X0) => (ex1 @ X4 @ (^[X3 : $i] : (in @ (kpair @ X2 @ X3) @ X6)))))) = func)),
% 1.61/1.37 file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',func)).
% 1.61/1.37 thf(f37,plain,(
% 1.61/1.37 ((func @ sK2 @ sK0 @ sK1) = $true)),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f29])).
% 1.61/1.37 thf(f29,plain,(
% 1.61/1.37 (((in @ sK1 @ (funcSet @ sK2 @ sK0)) != $true) & ((func @ sK2 @ sK0 @ sK1) = $true)) & (dsetconstrI = $true) & (powersetI1 = $true)),
% 1.61/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f27,f28])).
% 1.61/1.37 thf(f28,plain,(
% 1.61/1.37 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (funcSet @ X2 @ X0)) != $true) & ((func @ X2 @ X0 @ X1) = $true)) => (((in @ sK1 @ (funcSet @ sK2 @ sK0)) != $true) & ((func @ sK2 @ sK0 @ sK1) = $true))),
% 1.61/1.37 introduced(definition,[],[choice_axiom])).
% 1.61/1.37 thf(f27,plain,(
% 1.61/1.37 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (funcSet @ X2 @ X0)) != $true) & ((func @ X2 @ X0 @ X1) = $true)) & (dsetconstrI = $true) & (powersetI1 = $true)),
% 1.61/1.37 inference(flattening,[status(thm)],[f26])).
% 1.61/1.37 thf(f26,plain,(
% 1.61/1.37 (? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (funcSet @ X2 @ X0)) != $true) & ((func @ X2 @ X0 @ X1) = $true)) & (powersetI1 = $true)) & (dsetconstrI = $true)),
% 1.61/1.37 inference(ennf_transformation,[status(thm)],[f25])).
% 1.61/1.37 thf(f25,plain,(
% 1.61/1.37 ~((dsetconstrI = $true) => ((powersetI1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((func @ X2 @ X0 @ X1) = $true) => ((in @ X1 @ (funcSet @ X2 @ X0)) = $true))))),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f24])).
% 1.61/1.37 thf(f24,plain,(
% 1.61/1.37 ~(dsetconstrI => (powersetI1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X0 @ X1) => (in @ X1 @ (funcSet @ X2 @ X0)))))),
% 1.61/1.37 inference(rectify,[status(thm)],[f9])).
% 1.61/1.37 thf(f9,negated_conjecture,(
% 1.61/1.37 ~(dsetconstrI => (powersetI1 => ! [X4 : $i,X7 : $i,X0 : $i] : ((func @ X0 @ X4 @ X7) => (in @ X7 @ (funcSet @ X0 @ X4)))))),
% 1.61/1.37 inference(negated_conjecture,[status(cth)],[f8])).
% 1.61/1.37 thf(f8,conjecture,(
% 1.61/1.37 dsetconstrI => (powersetI1 => ! [X4 : $i,X7 : $i,X0 : $i] : ((func @ X0 @ X4 @ X7) => (in @ X7 @ (funcSet @ X0 @ X4))))),
% 1.61/1.37 file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',funcinfuncset)).
% 1.61/1.37 thf(f94,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1))) != (setadjoin @ X1 @ emptyset)) | ($false = (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1)))))) ) | ~spl3_2),
% 1.61/1.37 inference(avatar_component_clause,[status(thm)],[f93])).
% 1.61/1.37 thf(f93,definition,(
% 1.61/1.37 spl3_2 <=> ! [X1 : $i] : (((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1))) != (setadjoin @ X1 @ emptyset)) | ($false = (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1))))))),
% 1.61/1.37 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.61/1.37 thf(f105,plain,(
% 1.61/1.37 ( ! [X0 : $i] : (($true = (in @ (sK4 @ X0) @ (setadjoin @ (sK4 @ X0) @ emptyset))) | ((in @ X0 @ sK2) = $false)) )),
% 1.61/1.37 inference(duplicate_literal_removal,[status(thm)],[f103])).
% 1.61/1.37 thf(f103,plain,(
% 1.61/1.37 ( ! [X0 : $i] : (($true = (in @ (sK4 @ X0) @ (setadjoin @ (sK4 @ X0) @ emptyset))) | ((in @ X0 @ sK2) = $false) | ((in @ X0 @ sK2) = $false)) )),
% 1.61/1.37 inference(superposition,[status(thm)],[f61,f63])).
% 1.61/1.37 thf(f61,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (((in @ (sK4 @ X1) @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK1)))) = $true) | ($false = (in @ X1 @ sK2))) )),
% 1.61/1.37 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.61/1.37 thf(f101,plain,(
% 1.61/1.37 ((in @ sK6 @ sK2) = $true) | ~spl3_3),
% 1.61/1.37 inference(avatar_component_clause,[status(thm)],[f99])).
% 1.61/1.37 thf(f99,definition,(
% 1.61/1.37 spl3_3 <=> ((in @ sK6 @ sK2) = $true)),
% 1.61/1.37 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.61/1.37 thf(f139,plain,(
% 1.61/1.37 ~spl3_1),
% 1.61/1.37 inference(avatar_contradiction_clause,[status(thm)],[f138])).
% 1.61/1.37 thf(f138,plain,(
% 1.61/1.37 $false | ~spl3_1),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f137])).
% 1.61/1.37 thf(f137,plain,(
% 1.61/1.37 ($false = $true) | ~spl3_1),
% 1.61/1.37 inference(backward_demodulation,[status(thm)],[f54,f135])).
% 1.61/1.37 thf(f135,plain,(
% 1.61/1.37 ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0))) | ~spl3_1),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f133])).
% 1.61/1.37 thf(f133,plain,(
% 1.61/1.37 ($false = $true) | ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0))) | ~spl3_1),
% 1.61/1.37 inference(superposition,[status(thm)],[f91,f52])).
% 1.61/1.37 thf(f52,plain,(
% 1.61/1.37 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) | ($false = (subset @ X2 @ X1))) )),
% 1.61/1.37 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.61/1.37 thf(f51,plain,(
% 1.61/1.37 ( ! [X2 : $i,X1 : $i] : ((((subset @ X2 @ X1) => (in @ X2 @ (powerset @ X1))) = $true)) )),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.61/1.37 thf(f50,plain,(
% 1.61/1.37 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ Y0 @ X1) => (in @ Y0 @ (powerset @ X1)))) @ X2))) )),
% 1.61/1.37 inference(pi_clausification,[status(thm)],[f49])).
% 1.61/1.37 thf(f49,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ X1) => (in @ Y0 @ (powerset @ X1))))) = $true)) )),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.61/1.37 thf(f48,plain,(
% 1.61/1.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0)))))) @ X1) = $true)) )),
% 1.61/1.37 inference(pi_clausification,[status(thm)],[f47])).
% 1.61/1.37 thf(f47,plain,(
% 1.61/1.37 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) = $true)),
% 1.61/1.37 inference(definition_unfolding,[status(thm)],[f35,f32])).
% 1.61/1.37 thf(f32,plain,(
% 1.61/1.37 (powersetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))))),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f23])).
% 1.61/1.37 thf(f23,plain,(
% 1.61/1.37 (powersetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))))),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f22])).
% 1.61/1.37 thf(f22,plain,(
% 1.61/1.37 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))) = powersetI1)),
% 1.61/1.37 inference(rectify,[status(thm)],[f2])).
% 1.61/1.37 thf(f2,axiom,(
% 1.61/1.37 (! [X4 : $i,X0 : $i] : ((subset @ X4 @ X0) => (in @ X4 @ (powerset @ X0))) = powersetI1)),
% 1.61/1.37 file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',powersetI1)).
% 1.61/1.37 thf(f35,plain,(
% 1.61/1.37 (powersetI1 = $true)),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f29])).
% 1.61/1.37 thf(f91,plain,(
% 1.61/1.37 ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0)))) | ~spl3_1),
% 1.61/1.37 inference(avatar_component_clause,[status(thm)],[f89])).
% 1.61/1.37 thf(f89,definition,(
% 1.61/1.37 spl3_1 <=> ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0))))),
% 1.61/1.37 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.61/1.37 thf(f54,plain,(
% 1.61/1.37 ((subset @ sK1 @ (cartprod @ sK2 @ sK0)) = $true)),
% 1.61/1.37 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.61/1.37 thf(f102,plain,(
% 1.61/1.37 spl3_3 | spl3_1),
% 1.61/1.37 inference(avatar_split_clause,[status(thm)],[f97,f89,f99])).
% 1.61/1.37 thf(f97,plain,(
% 1.61/1.37 ((in @ sK6 @ sK2) = $true) | ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0))))),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.61/1.37 thf(f96,plain,(
% 1.61/1.37 ((in @ sK6 @ sK2) = $true) | ($false = $true) | ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0))))),
% 1.61/1.37 inference(forward_demodulation,[status(thm)],[f81,f54])).
% 1.61/1.37 thf(f81,plain,(
% 1.61/1.37 ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0))) | ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0)))) | ((in @ sK6 @ sK2) = $true)),
% 1.61/1.37 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.61/1.37 thf(f79,plain,(
% 1.61/1.37 (((in @ sK6 @ sK2) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK6 @ Y1) @ sK1)))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK6 @ Y1) @ sK1)))))))) = $false) | ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0)))) | ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0)))),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.61/1.37 thf(f78,plain,(
% 1.61/1.37 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK1)))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK1))))))))) @ sK6)) | ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0)))) | ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0)))),
% 1.61/1.37 inference(sigma_clausification,[status(thm)],[f77])).
% 1.61/1.37 thf(f77,plain,(
% 1.61/1.37 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK1)))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK1))))))))))) | ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0))) | ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0))))),
% 1.61/1.37 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.61/1.37 thf(f76,plain,(
% 1.61/1.37 ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK1)))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK1)))))))))) & (subset @ sK1 @ (cartprod @ sK2 @ sK0))))),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.61/1.37 thf(f75,plain,(
% 1.61/1.37 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ sK0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))))))))) & (subset @ Y0 @ (cartprod @ sK2 @ sK0)))) @ sK1)) | ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0))))),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.61/1.37 thf(f74,plain,(
% 1.61/1.37 ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0)))) | ($true != $true) | ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ sK0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))))))))) & (subset @ Y0 @ (cartprod @ sK2 @ sK0)))) @ sK1))),
% 1.61/1.37 inference(superposition,[status(thm)],[f64,f73])).
% 1.61/1.37 thf(f73,plain,(
% 1.61/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (((in @ X2 @ (dsetconstr @ X3 @ X1)) = $true) | ($false = (in @ X2 @ X3)) | ((X1 @ X2) = $false)) )),
% 1.61/1.37 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.61/1.37 thf(f72,plain,(
% 1.61/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((X1 @ X2) => (in @ X2 @ (dsetconstr @ X3 @ X1))) = $true) | ($false = (in @ X2 @ X3))) )),
% 1.61/1.37 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.61/1.37 thf(f71,plain,(
% 1.61/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((in @ X2 @ X3) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X3 @ X1)))) = $true)) )),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.61/1.37 thf(f70,plain,(
% 1.61/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((in @ X2 @ Y0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ Y0 @ X1))))) @ X3) = $true)) )),
% 1.61/1.37 inference(pi_clausification,[status(thm)],[f69])).
% 1.61/1.37 thf(f69,plain,(
% 1.61/1.37 ( ! [X2 : $i,X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ Y0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ Y0 @ X1)))))) = $true)) )),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.61/1.37 thf(f68,plain,(
% 1.61/1.37 ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ X1))))))) @ X2) = $true)) )),
% 1.61/1.37 inference(pi_clausification,[status(thm)],[f67])).
% 1.61/1.37 thf(f67,plain,(
% 1.61/1.37 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ X1)))))))) = $true)) )),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.61/1.37 thf(f66,plain,(
% 1.61/1.37 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ Y0))))))))) @ X1) = $true)) )),
% 1.61/1.37 inference(pi_clausification,[status(thm)],[f65])).
% 1.61/1.37 thf(f65,plain,(
% 1.61/1.37 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ Y0)))))))))) = $true)),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.61/1.37 thf(f46,plain,(
% 1.61/1.37 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))) = $true)),
% 1.61/1.37 inference(definition_unfolding,[status(thm)],[f36,f31])).
% 1.61/1.37 thf(f31,plain,(
% 1.61/1.37 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f16])).
% 1.61/1.37 thf(f16,plain,(
% 1.61/1.37 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f15])).
% 1.61/1.37 thf(f15,plain,(
% 1.61/1.37 (dsetconstrI = ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ X0) => ((X2 @ X1) => (in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))))))),
% 1.61/1.37 inference(rectify,[status(thm)],[f1])).
% 1.61/1.37 thf(f1,axiom,(
% 1.61/1.37 (dsetconstrI = ! [X0 : $i,X2 : $i,X1 : $i > $o] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 1.61/1.37 file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',dsetconstrI)).
% 1.61/1.37 thf(f36,plain,(
% 1.61/1.37 (dsetconstrI = $true)),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f29])).
% 1.61/1.37 thf(f64,plain,(
% 1.61/1.37 ((in @ sK1 @ (dsetconstr @ (powerset @ (cartprod @ sK2 @ sK0)) @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ sK0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))))))))) & (subset @ Y0 @ (cartprod @ sK2 @ sK0)))))) != $true)),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.61/1.37 thf(f44,plain,(
% 1.61/1.37 ((in @ sK1 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (((setadjoin @ Y10 @ emptyset) = Y9) & (in @ Y10 @ Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))) & ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5))))))) @ Y0 @ Y1 @ Y2)))))) @ sK2 @ sK0)) != $true)),
% 1.61/1.37 inference(definition_unfolding,[status(thm)],[f38,f43])).
% 1.61/1.37 thf(f43,plain,(
% 1.61/1.37 (funcSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (((setadjoin @ Y10 @ emptyset) = Y9) & (in @ Y10 @ Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))) & ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5))))))) @ Y0 @ Y1 @ Y2)))))))),
% 1.61/1.37 inference(definition_unfolding,[status(thm)],[f33,f42])).
% 1.61/1.37 thf(f33,plain,(
% 1.61/1.37 (funcSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: (func @ Y0 @ Y1 @ Y2)))))))),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f18])).
% 1.61/1.37 thf(f18,plain,(
% 1.61/1.37 (funcSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: (func @ Y0 @ Y1 @ Y2)))))))),
% 1.61/1.37 inference(fool_elimination,[status(thm)],[f17])).
% 1.61/1.37 thf(f17,plain,(
% 1.61/1.37 (funcSet = (^[X0 : $i, X1 : $i] : (dsetconstr @ (powerset @ (cartprod @ X0 @ X1)) @ (^[X2 : $i] : (func @ X0 @ X1 @ X2)))))),
% 1.61/1.37 inference(rectify,[status(thm)],[f7])).
% 1.61/1.37 thf(f7,axiom,(
% 1.61/1.37 (funcSet = (^[X0 : $i, X4 : $i] : (dsetconstr @ (powerset @ (cartprod @ X0 @ X4)) @ (^[X7 : $i] : (func @ X0 @ X4 @ X7)))))),
% 1.61/1.37 file('/export/starexec/sandbox/tmp/tmp.XXFHuGo89z/DTF2THF_23048.p',funcSet)).
% 1.61/1.37 thf(f38,plain,(
% 1.61/1.37 ((in @ sK1 @ (funcSet @ sK2 @ sK0)) != $true)),
% 1.61/1.37 inference(cnf_transformation,[status(thm)],[f29])).
% 1.61/1.37 thf(f95,plain,(
% 1.61/1.37 spl3_1 | spl3_2),
% 1.61/1.37 inference(avatar_split_clause,[status(thm)],[f87,f93,f89])).
% 1.61/1.37 thf(f87,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0)))) | ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1))) != (setadjoin @ X1 @ emptyset)) | ($false = (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1)))))) )),
% 1.61/1.37 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.61/1.37 thf(f86,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (($false = (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1))))) | ($false = $true) | ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1))) != (setadjoin @ X1 @ emptyset)) | ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0))))) )),
% 1.61/1.37 inference(forward_demodulation,[status(thm)],[f85,f54])).
% 1.61/1.37 thf(f85,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (($false = (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1))))) | ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0))) | ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1))) != (setadjoin @ X1 @ emptyset)) | ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0))))) )),
% 1.61/1.37 inference(equality_proxy_clausification,[status(thm)],[f84])).
% 1.61/1.37 thf(f84,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0))) | ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0)))) | ($false = ((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1))))) | ($false = (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1)))))) )),
% 1.61/1.37 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.61/1.37 thf(f83,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0))) | ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0)))) | ($false = (((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1)))) & (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK6 @ Y0) @ sK1))))))) )),
% 1.61/1.37 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.61/1.37 thf(f82,plain,(
% 1.61/1.37 ( ! [X1 : $i] : (($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0))) | ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0)))) | ($false = ((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK6 @ Y1) @ sK1)))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK6 @ Y1) @ sK1)))))) @ X1))) )),
% 1.61/1.37 inference(pi_clausification,[status(thm)],[f80])).
% 1.61/1.37 thf(f80,plain,(
% 1.61/1.37 ($false = (in @ sK1 @ (powerset @ (cartprod @ sK2 @ sK0)))) | ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK6 @ Y1) @ sK1)))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK6 @ Y1) @ sK1))))))) = $false) | ($false = (subset @ sK1 @ (cartprod @ sK2 @ sK0)))),
% 1.61/1.37 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.61/1.37 % SZS output end Proof for DTF2THF_23048
% 1.61/1.37 % (23147)------------------------------
% 1.61/1.37 % (23147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.37 % (23147)Termination reason: Refutation
% 1.61/1.37
% 1.61/1.37 % (23147)Memory used [KB]: 5756
% 1.61/1.37 % (23147)Time elapsed: 0.017 s
% 1.61/1.37 % (23147)Instructions burned: 21 (million)
% 1.61/1.37 % (23147)------------------------------
% 1.61/1.37 % (23147)------------------------------
% 1.61/1.37 % (23144)Success in time 0.031 s
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