%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU643^2 : 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 : n031.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 09:35:54 AM UTC 2026
% Result : Theorem 1.69s 1.38s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 7
% Syntax : Number of formulae : 88 ( 85 unt; 0 typ; 0 def)
% Number of atoms : 981 ( 180 equ; 0 cnn)
% Maximal formula atoms : 7 ( 11 avg)
% Number of connectives : 2016 ( 11 ~; 0 |; 67 &;1590 @)
% ( 0 <=>; 181 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 16 usr; 12 con; 0-2 aty)
% ( 112 !!; 55 ??; 0 @@+; 0 @@-)
% Number of variables : 308 ( 247 ^; 55 !; 6 ?; 308 :)
% 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,
iskpair: $i > $o ).
thf(func_def_8,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_26,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f185,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f184]) ).
thf(f184,plain,
$false = $true,
inference(boolean_simplification,[status(thm)],[f183]) ).
thf(f183,plain,
( ( ( in @ sK5 @ ( setunion @ sK2 ) )
=> $true )
= $false ),
inference(forward_demodulation,[status(thm)],[f182,f140]) ).
thf(f140,plain,
! [X0: $i] :
( ( ( in @ ( setadjoin @ X0 @ emptyset ) @ sK2 )
=> ( sK3 = X0 ) )
= $true ),
inference(superposition,[status(thm)],[f74,f131]) ).
thf(f131,plain,
( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) )
= sK2 ),
inference(equality_proxy_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
( $true
= ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) )
= sK2 ) ),
inference(boolean_simplification,[status(thm)],[f123]) ).
thf(f123,plain,
( $true
= ( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) )
= sK2 )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f114,f121]) ).
thf(f121,plain,
( $true
= ( in @ sK4 @ ( setunion @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) )
= sK2 )
& ( in @ sK4 @ ( setunion @ sK2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f113]) ).
thf(f113,plain,
( ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 )
& ( in @ Y0 @ ( setunion @ sK2 ) ) )
@ sK4 )
= $true ),
inference(sigma_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 )
& ( in @ Y0 @ ( setunion @ sK2 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f111]) ).
thf(f111,plain,
( ( $true
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 )
& ( in @ Y0 @ ( setunion @ sK2 ) ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f108,f110]) ).
thf(f110,plain,
( ( in @ sK3 @ ( setunion @ sK2 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
( ( ( in @ sK3 @ ( setunion @ sK2 ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 )
& ( in @ Y0 @ ( setunion @ sK2 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f107]) ).
thf(f107,plain,
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK2 )
& ( in @ Y1 @ ( setunion @ sK2 ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK2 )
& ( in @ Y1 @ ( setunion @ sK2 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK2 )
& ( in @ Y1 @ ( setunion @ sK2 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ sK2 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ sK2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ ( setunion @ sK2 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ sK2 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f95]) ).
thf(f95,plain,
( $false
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f35,f39]) ).
thf(f39,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] : ( in @ ( setadjoin @ Y2 @ emptyset ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ^ [Y3: $i,Y4: $i > $o] :
( ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( ( setadjoin @ Y6 @ emptyset )
= Y5 )
& ( in @ Y6 @ Y5 ) ) )
@ ( dsetconstr @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y1 ) )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
= Y1 )
& ( in @ Y3 @ ( setunion @ Y1 ) ) ) ) ) )
@ Y0 )
=> ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= Y1 )
& ( in @ Y2 @ Y1 ) ) )
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f27,f26,f32,f28,f24,f30]) ).
thf(f30,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) )
= singleton ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X2: $i] :
? [X0: $i] :
( ( in @ X0 @ X2 )
& ( ( setadjoin @ X0 @ emptyset )
= X2 ) ) )
= singleton ),
file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',singleton) ).
thf(f24,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ? [X2: $i] :
( ( in @ X2 @ ( setunion @ X0 ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= X0 ) )
& ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( iskpair
= ( ^ [X2: $i] :
? [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ ( setunion @ X2 ) )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= X2 ) )
& ( in @ X0 @ ( setunion @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',iskpair) ).
thf(f28,plain,
( setukpairinjL1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( setukpairinjL1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( setukpairinjL1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( setukpairinjL1
= ( ! [X0: $i,X1: $i,X4: $i] :
( ( in @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',setukpairinjL1) ).
thf(f32,plain,
( ex1I
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ^ [Y3: $i,Y4: $i > $o] :
( ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( ( setadjoin @ Y6 @ emptyset )
= Y5 )
& ( in @ Y6 @ Y5 ) ) )
@ ( dsetconstr @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f25,f31]) ).
thf(f31,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)],[f29,f30]) ).
thf(f29,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) )
= ex1 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X2: $i,X3: $i > $o] :
( singleton
@ ( dsetconstr @ X2
@ ^ [X0: $i] : ( X3 @ X0 ) ) ) )
= ex1 ),
file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',ex1) ).
thf(f25,plain,
( ex1I
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ex1 @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ex1I
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ex1 @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
( ex1I
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( X0 @ X1 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ( X0 @ X3 )
=> ( X1 = X3 ) ) )
=> ( ex1 @ X2
@ ^ [X4: $i] : ( X0 @ X4 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ex1I
= ( ! [X3: $i > $o,X0: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ( ( X3 @ X0 )
=> ( ! [X1: $i] :
( ( in @ X1 @ X2 )
=> ( ( X3 @ X1 )
=> ( X0 = X1 ) ) )
=> ( ex1 @ X2
@ ^ [X1: $i] : ( X3 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',ex1I) ).
thf(f26,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',setadjoinIL) ).
thf(f27,plain,
( ( ~ ( setadjoinIL
=> ( ex1I
=> ( setukpairinjL1
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( iskpair @ Y0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ~ ( setadjoinIL
=> ( ex1I
=> ( setukpairinjL1
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( iskpair @ Y0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
~ ( setadjoinIL
=> ( ex1I
=> ( setukpairinjL1
=> ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( setadjoinIL
=> ( ex1I
=> ( setukpairinjL1
=> ! [X5: $i] :
( ( iskpair @ X5 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X5 )
@ ^ [X0: $i] : ( in @ ( setadjoin @ X0 @ emptyset ) @ X5 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( setadjoinIL
=> ( ex1I
=> ( setukpairinjL1
=> ! [X5: $i] :
( ( iskpair @ X5 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X5 )
@ ^ [X0: $i] : ( in @ ( setadjoin @ X0 @ emptyset ) @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',kfstsingleton) ).
thf(f74,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f182,plain,
( ( ( in @ sK5 @ ( setunion @ sK2 ) )
=> ( ( in @ ( setadjoin @ sK5 @ emptyset ) @ sK2 )
=> ( sK3 = sK5 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f177]) ).
thf(f177,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK2 )
=> ( sK3 = Y0 ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f167]) ).
thf(f167,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK2 )
=> ( sK3 = Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK2 )
=> ( sK3 = Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f149]) ).
thf(f149,plain,
( ( $true
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK2 )
=> ( sK3 = Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f148,f143]) ).
thf(f143,plain,
( ( in @ ( setadjoin @ sK3 @ emptyset ) @ sK2 )
= $true ),
inference(superposition,[status(thm)],[f51,f131]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f148,plain,
( $true
= ( ( in @ ( setadjoin @ sK3 @ emptyset ) @ sK2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK2 )
=> ( sK3 = Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f145]) ).
thf(f145,plain,
( ( $true
=> ( ( in @ ( setadjoin @ sK3 @ emptyset ) @ sK2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK2 )
=> ( sK3 = Y0 ) ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f104,f110]) ).
thf(f104,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setunion @ sK2 ) )
=> ( ( in @ ( setadjoin @ X0 @ emptyset ) @ sK2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK2 )
=> ( X0 = Y0 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setunion @ sK2 ) )
=> ( ( in @ ( setadjoin @ X0 @ emptyset ) @ sK2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK2 )
=> ( X0 = Y0 ) ) ) )
=> $false ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f102]) ).
thf(f102,plain,
! [X0: $i] :
( $true
= ( ( in @ X0 @ ( setunion @ sK2 ) )
=> ( ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK2 )
@ X0 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ sK2 )
@ Y0 )
=> ( X0 = Y0 ) ) ) )
=> $false ) ) ) ),
inference(superposition,[status(thm)],[f57,f100]) ).
thf(f100,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ sK2 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ sK2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ ( setunion @ sK2 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ sK2 ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $true
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ sK2 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ sK2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ ( setunion @ sK2 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ sK2 ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f96,f98]) ).
thf(f57,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ X1 )
=> ( ( X3 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X3 @ Y0 )
=> ( X2 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X3 ) )
& ( in @ Y0 @ ( dsetconstr @ X1 @ X3 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( Y0 @ Y1 )
=> ( X2 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1 @ Y0 ) )
& ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( Y0 @ Y1 )
=> ( X2 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1 @ Y0 ) )
& ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y1 @ Y2 )
=> ( Y0 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X1 @ Y1 ) )
& ( in @ Y2 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y1 @ Y2 )
=> ( Y0 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X1 @ Y1 ) )
& ( in @ Y2 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU643^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n031.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:30:48 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEU643^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : Ordered Pairs - Properties of Pairs
% 0.19/0.45 % Version : Especial > Reduced > Especial.
% 0.19/0.45 % English : (! u:i.iskpair u -> singleton (dsetconstr (setunion u) (^ x:i.in
% 0.19/0.45 % (setadjoin x emptyset) u)))
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.45 % Source : [Bro08]
% 0.19/0.45 % Names : ZFC145l [Bro08]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.54 v8.1.0, 0.55 v7.5.0, 0.43 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.71 v6.1.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.19/0.45 % Syntax : Number of formulae : 18 ( 6 unt; 11 typ; 6 def)
% 0.19/0.45 % Number of atoms : 31 ( 10 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 6 ( 4 avg)
% 0.19/0.45 % Number of connectives : 73 ( 0 ~; 0 |; 3 &; 60 @)
% 0.19/0.45 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 13 ( 3 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 12 ( 11 usr; 4 con; 0-2 aty)
% 0.19/0.45 % Number of variables : 20 ( 7 ^; 10 !; 3 ?; 20 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : http://mathgate.info/detsetitem.php?id=199
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(in_type,type,
% 0.19/0.45 in: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(emptyset_type,type,
% 0.19/0.45 emptyset: $i ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoin_type,type,
% 0.19/0.45 setadjoin: $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(setunion_type,type,
% 0.19/0.45 setunion: $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(dsetconstr_type,type,
% 0.19/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoinIL_type,type,
% 0.19/0.45 setadjoinIL: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoinIL,definition,
% 0.19/0.45 ( setadjoinIL
% 0.19/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(iskpair_type,type,
% 0.19/0.45 iskpair: $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(iskpair,definition,
% 0.19/0.45 ( iskpair
% 0.19/0.45 = ( ^ [A: $i] :
% 0.19/0.45 ? [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.45 & ? [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ ( setunion @ A ) )
% 0.19/0.45 & ( A
% 0.19/0.45 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(singleton_type,type,
% 0.19/0.45 singleton: $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(singleton,definition,
% 0.19/0.45 ( singleton
% 0.19/0.45 = ( ^ [A: $i] :
% 0.19/0.45 ? [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 & ( A
% 0.19/0.45 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(ex1_type,type,
% 0.19/0.45 ex1: $i > ( $i > $o ) > $o ).
% 0.19/0.45
% 0.19/0.45 thf(ex1,definition,
% 0.19/0.45 ( ex1
% 0.19/0.45 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.19/0.45 ( singleton
% 0.19/0.45 @ ( dsetconstr @ A
% 0.19/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(ex1I_type,type,
% 0.19/0.45 ex1I: $o ).
% 0.19/0.45
% 0.19/0.45 thf(ex1I,definition,
% 0.19/0.45 ( ex1I
% 0.19/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( Xphi @ Xx )
% 0.19/0.45 => ( ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 => ( ( Xphi @ Xy )
% 0.19/0.45 => ( Xy = Xx ) ) )
% 0.19/0.45 => ( ex1 @ A
% 0.19/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setukpairinjL1_type,type,
% 0.19/0.45 setukpairinjL1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setukpairinjL1,definition,
% 0.19/0.45 ( setukpairinjL1
% 0.19/0.45 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.19/0.45 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.19/0.45 => ( Xx = Xz ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(kfstsingleton,conjecture,
% 0.19/0.45 ( setadjoinIL
% 0.19/0.45 => ( ex1I
% 0.19/0.45 => ( setukpairinjL1
% 0.19/0.45 => ! [Xu: $i] :
% 0.19/0.45 ( ( iskpair @ Xu )
% 0.19/0.45 => ( singleton
% 0.19/0.45 @ ( dsetconstr @ ( setunion @ Xu )
% 0.19/0.45 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.50/1.29 ---- Embedded in THF ---
% 1.50/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.29 %%% Generated on Tue Feb 24 12:30:49 EST 2026
% 1.50/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.29 %%% Logic specification used:
% 1.50/1.29 %%% thf(spec, logic, $$dhol).
% 1.50/1.29
% 1.50/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2DTF17750.p
% See solution above
% 1.50/1.29 ------------------------
% 1.69/1.30 ---- Cleaned THF ---
% 1.69/1.30 thf(in_type,type,
% 1.69/1.30 in: $i > $i > $o ).
% 1.69/1.30
% 1.69/1.30 thf(emptyset_type,type,
% 1.69/1.30 emptyset: $i ).
% 1.69/1.30
% 1.69/1.30 thf(setadjoin_type,type,
% 1.69/1.30 setadjoin: $i > $i > $i ).
% 1.69/1.30
% 1.69/1.30 thf(setunion_type,type,
% 1.69/1.30 setunion: $i > $i ).
% 1.69/1.30
% 1.69/1.30 thf(dsetconstr_type,type,
% 1.69/1.30 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.69/1.30
% 1.69/1.30 thf(setadjoinIL_type,type,
% 1.69/1.30 setadjoinIL: $o ).
% 1.69/1.30
% 1.69/1.30 thf(setadjoinIL,definition,
% 1.69/1.30 ( setadjoinIL
% 1.69/1.30 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(iskpair_type,type,
% 1.69/1.30 iskpair: $i > $o ).
% 1.69/1.30
% 1.69/1.30 thf(iskpair,definition,
% 1.69/1.30 ( iskpair
% 1.69/1.30 = ( ^ [A: $i] :
% 1.69/1.30 ? [Xx: $i] :
% 1.69/1.30 ( ( in @ Xx @ ( setunion @ A ) )
% 1.69/1.30 & ? [Xy: $i] :
% 1.69/1.30 ( ( in @ Xy @ ( setunion @ A ) )
% 1.69/1.30 & ( A
% 1.69/1.30 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(singleton_type,type,
% 1.69/1.30 singleton: $i > $o ).
% 1.69/1.30
% 1.69/1.30 thf(singleton,definition,
% 1.69/1.30 ( singleton
% 1.69/1.30 = ( ^ [A: $i] :
% 1.69/1.30 ? [Xx: $i] :
% 1.69/1.30 ( ( in @ Xx @ A )
% 1.69/1.30 & ( A
% 1.69/1.30 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(ex1_type,type,
% 1.69/1.30 ex1: $i > ( $i > $o ) > $o ).
% 1.69/1.30
% 1.69/1.30 thf(ex1,definition,
% 1.69/1.30 ( ex1
% 1.69/1.30 = ( ^ [A: $i,Xphi: $i > $o] :
% 1.69/1.30 ( singleton
% 1.69/1.30 @ ( dsetconstr @ A
% 1.69/1.30 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(ex1I_type,type,
% 1.69/1.30 ex1I: $o ).
% 1.69/1.30
% 1.69/1.30 thf(ex1I,definition,
% 1.69/1.30 ( ex1I
% 1.69/1.30 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.69/1.30 ( ( in @ Xx @ A )
% 1.69/1.30 => ( ( Xphi @ Xx )
% 1.69/1.30 => ( ! [Xy: $i] :
% 1.69/1.30 ( ( in @ Xy @ A )
% 1.69/1.30 => ( ( Xphi @ Xy )
% 1.69/1.30 => ( Xy = Xx ) ) )
% 1.69/1.30 => ( ex1 @ A
% 1.69/1.30 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(setukpairinjL1_type,type,
% 1.69/1.30 setukpairinjL1: $o ).
% 1.69/1.30
% 1.69/1.30 thf(setukpairinjL1,definition,
% 1.69/1.30 ( setukpairinjL1
% 1.69/1.30 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.69/1.30 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 1.69/1.30 => ( Xx = Xz ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(kfstsingleton,conjecture,
% 1.69/1.30 ( setadjoinIL
% 1.69/1.30 => ( ex1I
% 1.69/1.30 => ( setukpairinjL1
% 1.69/1.30 => ! [Xu: $i] :
% 1.69/1.30 ( ( iskpair @ Xu )
% 1.69/1.30 => ( singleton
% 1.69/1.30 @ ( dsetconstr @ ( setunion @ Xu )
% 1.69/1.30 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ) ).
% 1.69/1.30 ------------------------
% 1.69/1.32 % (17851)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_17750 for (2999ds/2Mi)
% 1.69/1.32 % (17851)Instruction limit reached!
% 1.69/1.32 % (17851)------------------------------
% 1.69/1.32 % (17851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (17851)Termination reason: Unknown
% 1.69/1.32 % (17851)Termination phase: Property scanning
% 1.69/1.32
% 1.69/1.32 % (17851)Memory used [KB]: 1023
% 1.69/1.32 % (17851)Time elapsed: 0.002 s
% 1.69/1.32 % (17851)Instructions burned: 3 (million)
% 1.69/1.32 % (17851)------------------------------
% 1.69/1.32 % (17851)------------------------------
% 1.69/1.33 % (17847)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17750 for (2999ds/183Mi)
% 1.69/1.33 % (17848)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_17750 for (2999ds/4Mi)
% 1.69/1.33 % (17849)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_17750 for (2999ds/27Mi)
% 1.69/1.33 % (17850)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17750 for (2999ds/2Mi)
% 1.69/1.33 % (17852)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_17750 for (2999ds/275Mi)
% 1.69/1.33 % (17850)Instruction limit reached!
% 1.69/1.33 % (17850)------------------------------
% 1.69/1.33 % (17850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (17850)Termination reason: Unknown
% 1.69/1.33 % (17850)Termination phase: shuffling
% 1.69/1.33
% 1.69/1.33 % (17850)Memory used [KB]: 1023
% 1.69/1.33 % (17850)Time elapsed: 0.003 s
% 1.69/1.33 % (17850)Instructions burned: 2 (million)
% 1.69/1.33 % (17850)------------------------------
% 1.69/1.33 % (17850)------------------------------
% 1.69/1.33 % (17848)Instruction limit reached!
% 1.69/1.33 % (17848)------------------------------
% 1.69/1.33 % (17848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (17848)Termination reason: Unknown
% 1.69/1.33 % (17848)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (17848)Memory used [KB]: 1023
% 1.69/1.33 % (17848)Time elapsed: 0.004 s
% 1.69/1.33 % (17848)Instructions burned: 4 (million)
% 1.69/1.33 % (17848)------------------------------
% 1.69/1.33 % (17848)------------------------------
% 1.69/1.33 % (17854)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17750 for (2999ds/3Mi)
% 1.69/1.33 % (17854)Instruction limit reached!
% 1.69/1.33 % (17854)------------------------------
% 1.69/1.33 % (17854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (17854)Termination reason: Unknown
% 1.69/1.33 % (17854)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (17854)Memory used [KB]: 1023
% 1.69/1.33 % (17854)Time elapsed: 0.003 s
% 1.69/1.33 % (17854)Instructions burned: 5 (million)
% 1.69/1.33 % (17854)------------------------------
% 1.69/1.33 % (17854)------------------------------
% 1.69/1.34 % (17852)Refutation not found, incomplete strategy
% 1.69/1.34 % (17852)------------------------------
% 1.69/1.34 % (17852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (17852)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.34
% 1.69/1.34
% 1.69/1.34 % (17852)Memory used [KB]: 5628
% 1.69/1.34 % (17852)Time elapsed: 0.010 s
% 1.69/1.34 % (17852)Instructions burned: 12 (million)
% 1.69/1.34 % (17852)------------------------------
% 1.69/1.34 % (17852)------------------------------
% 1.69/1.34 % (17853)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17750 for (2999ds/18Mi)
% 1.69/1.34 % (17855)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_17750 for (2999ds/37Mi)
% 1.69/1.34 % (17857)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_17750 for (2999ds/3Mi)
% 1.69/1.34 % (17849)Instruction limit reached!
% 1.69/1.34 % (17849)------------------------------
% 1.69/1.34 % (17849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (17849)Termination reason: Unknown
% 1.69/1.34 % (17849)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (17849)Memory used [KB]: 5628
% 1.69/1.34 % (17849)Time elapsed: 0.018 s
% 1.69/1.34 % (17849)Instructions burned: 27 (million)
% 1.69/1.34 % (17849)------------------------------
% 1.69/1.34 % (17849)------------------------------
% 1.69/1.34 % (17857)Instruction limit reached!
% 1.69/1.34 % (17857)------------------------------
% 1.69/1.34 % (17857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (17857)Termination reason: Unknown
% 1.69/1.34 % (17857)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (17857)Memory used [KB]: 1023
% 1.69/1.34 % (17857)Time elapsed: 0.003 s
% 1.69/1.34 % (17857)Instructions burned: 5 (million)
% 1.69/1.34 % (17857)------------------------------
% 1.69/1.34 % (17857)------------------------------
% 1.69/1.35 % (17856)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_17750 for (2999ds/15Mi)
% 1.69/1.35 % (17858)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_17750 for (2999ds/1041Mi)
% 1.69/1.35 % (17855)Instruction limit reached!
% 1.69/1.35 % (17855)------------------------------
% 1.69/1.35 % (17855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (17855)Termination reason: Unknown
% 1.69/1.35 % (17855)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (17855)Memory used [KB]: 5756
% 1.69/1.35 % (17855)Time elapsed: 0.013 s
% 1.69/1.35 % (17855)Instructions burned: 38 (million)
% 1.69/1.35 % (17855)------------------------------
% 1.69/1.35 % (17855)------------------------------
% 1.69/1.35 % (17860)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17750 for (2999ds/16Mi)
% 1.69/1.35 % (17853)Instruction limit reached!
% 1.69/1.35 % (17853)------------------------------
% 1.69/1.35 % (17853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (17853)Termination reason: Unknown
% 1.69/1.35 % (17853)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (17853)Memory used [KB]: 5628
% 1.69/1.35 % (17853)Time elapsed: 0.020 s
% 1.69/1.35 % (17853)Instructions burned: 18 (million)
% 1.69/1.35 % (17853)------------------------------
% 1.69/1.35 % (17853)------------------------------
% 1.69/1.35 % (17856)Instruction limit reached!
% 1.69/1.35 % (17856)------------------------------
% 1.69/1.35 % (17856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (17856)Termination reason: Unknown
% 1.69/1.35 % (17856)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (17856)Memory used [KB]: 5628
% 1.69/1.35 % (17856)Time elapsed: 0.011 s
% 1.69/1.35 % (17856)Instructions burned: 15 (million)
% 1.69/1.35 % (17856)------------------------------
% 1.69/1.35 % (17856)------------------------------
% 1.69/1.36 % (17860)Instruction limit reached!
% 1.69/1.36 % (17860)------------------------------
% 1.69/1.36 % (17860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (17860)Termination reason: Unknown
% 1.69/1.36 % (17860)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (17860)Memory used [KB]: 5884
% 1.69/1.36 % (17860)Time elapsed: 0.008 s
% 1.69/1.36 % (17860)Instructions burned: 17 (million)
% 1.69/1.36 % (17860)------------------------------
% 1.69/1.36 % (17860)------------------------------
% 1.69/1.36 % (17859)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17750 for (2999ds/7Mi)
% 1.69/1.36 % (17861)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_17750 for (2999ds/3Mi)
% 1.69/1.36 % (17859)Instruction limit reached!
% 1.69/1.36 % (17859)------------------------------
% 1.69/1.36 % (17859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (17859)Termination reason: Unknown
% 1.69/1.36 % (17859)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (17859)Memory used [KB]: 1023
% 1.69/1.36 % (17859)Time elapsed: 0.006 s
% 1.69/1.36 % (17859)Instructions burned: 8 (million)
% 1.69/1.36 % (17859)------------------------------
% 1.69/1.36 % (17859)------------------------------
% 1.69/1.36 % (17861)Instruction limit reached!
% 1.69/1.36 % (17861)------------------------------
% 1.69/1.36 % (17861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (17861)Termination reason: Unknown
% 1.69/1.36 % (17861)Termination phase: Twee Goal Transformation
% 1.69/1.36
% 1.69/1.36 % (17861)Memory used [KB]: 1023
% 1.69/1.36 % (17861)Time elapsed: 0.003 s
% 1.69/1.36 % (17861)Instructions burned: 4 (million)
% 1.69/1.36 % (17861)------------------------------
% 1.69/1.36 % (17861)------------------------------
% 1.69/1.37 % (17864)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17750 for (2999ds/3Mi)
% 1.69/1.37 % (17864)Instruction limit reached!
% 1.69/1.37 % (17864)------------------------------
% 1.69/1.37 % (17864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (17864)Termination reason: Unknown
% 1.69/1.37 % (17864)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (17864)Memory used [KB]: 1023
% 1.69/1.37 % (17864)Time elapsed: 0.003 s
% 1.69/1.37 % (17864)Instructions burned: 5 (million)
% 1.69/1.37 % (17864)------------------------------
% 1.69/1.37 % (17864)------------------------------
% 1.69/1.37 % (17862)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17750 for (2999ds/3Mi)
% 1.69/1.37 % (17863)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17750 for (2999ds/7Mi)
% 1.69/1.37 % (17862)Instruction limit reached!
% 1.69/1.37 % (17862)------------------------------
% 1.69/1.37 % (17862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (17862)Termination reason: Unknown
% 1.69/1.37 % (17862)Termination phase: Function definition elimination
% 1.69/1.37
% 1.69/1.37 % (17862)Memory used [KB]: 1023
% 1.69/1.37 % (17862)Time elapsed: 0.004 s
% 1.69/1.37 % (17862)Instructions burned: 4 (million)
% 1.69/1.37 % (17862)------------------------------
% 1.69/1.37 % (17862)------------------------------
% 1.69/1.37 % (17868)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17750 for (2999ds/18Mi)
% 1.69/1.38 % (17863)Refutation not found, incomplete strategy
% 1.69/1.38 % (17863)------------------------------
% 1.69/1.38 % (17863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (17863)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.38
% 1.69/1.38
% 1.69/1.38 % (17863)Memory used [KB]: 5500
% 1.69/1.38 % (17863)Time elapsed: 0.005 s
% 1.69/1.38 % (17863)Instructions burned: 5 (million)
% 1.69/1.38 % (17863)------------------------------
% 1.69/1.38 % (17863)------------------------------
% 1.69/1.38 % (17858)First to succeed.
% 1.69/1.38 % (17871)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_17750 for (2999ds/710Mi)
% 1.69/1.38 % (17866)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17750 for (2999ds/4Mi)
% 1.69/1.38 % (17868)Instruction limit reached!
% 1.69/1.38 % (17868)------------------------------
% 1.69/1.38 % (17868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (17868)Termination reason: Unknown
% 1.69/1.38 % (17868)Termination phase: Saturation
% 1.69/1.38
% 1.69/1.38 % (17868)Memory used [KB]: 5628
% 1.69/1.38 % (17868)Time elapsed: 0.008 s
% 1.69/1.38 % (17868)Instructions burned: 20 (million)
% 1.69/1.38 % (17868)------------------------------
% 1.69/1.38 % (17868)------------------------------
% 1.69/1.38 % (17858)Refutation found. Thanks to Tanya!
% 1.69/1.38 % SZS status Theorem for DTF2THF_17750
% 1.69/1.38 % SZS output start Proof for DTF2THF_17750
% 1.69/1.38 thf(func_def_0, type, in: $i > $i > $o).
% 1.69/1.38 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.69/1.38 thf(func_def_3, type, setunion: $i > $i).
% 1.69/1.38 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 1.69/1.38 thf(func_def_7, type, iskpair: $i > $o).
% 1.69/1.38 thf(func_def_8, type, singleton: $i > $o).
% 1.69/1.38 thf(func_def_9, type, ex1: $i > ($i > $o) > $o).
% 1.69/1.38 thf(func_def_26, type, ph1: !>[X0: $tType]:(X0)).
% 1.69/1.38 thf(f185,plain,(
% 1.69/1.38 $false),
% 1.69/1.38 inference(trivial_inequality_removal,[status(thm)],[f184])).
% 1.69/1.38 thf(f184,plain,(
% 1.69/1.38 ($false = $true)),
% 1.69/1.38 inference(boolean_simplification,[status(thm)],[f183])).
% 1.69/1.38 thf(f183,plain,(
% 1.69/1.38 (((in @ sK5 @ (setunion @ sK2)) => $true) = $false)),
% 1.69/1.38 inference(forward_demodulation,[status(thm)],[f182,f140])).
% 1.69/1.38 thf(f140,plain,(
% 1.69/1.38 ( ! [X0 : $i] : ((((in @ (setadjoin @ X0 @ emptyset) @ sK2) => (sK3 = X0)) = $true)) )),
% 1.69/1.38 inference(superposition,[status(thm)],[f74,f131])).
% 1.69/1.38 thf(f131,plain,(
% 1.69/1.38 ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2)),
% 1.69/1.38 inference(equality_proxy_clausification,[status(thm)],[f124])).
% 1.69/1.38 thf(f124,plain,(
% 1.69/1.38 ($true = ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2))),
% 1.69/1.38 inference(boolean_simplification,[status(thm)],[f123])).
% 1.69/1.38 thf(f123,plain,(
% 1.69/1.38 ($true = (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2) & $true))),
% 1.69/1.38 inference(backward_demodulation,[status(thm)],[f114,f121])).
% 1.69/1.38 thf(f121,plain,(
% 1.69/1.38 ($true = (in @ sK4 @ (setunion @ sK2)))),
% 1.69/1.38 inference(binary_proxy_clausification,[status(thm)],[f114])).
% 1.69/1.38 thf(f114,plain,(
% 1.69/1.38 ((((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2) & (in @ sK4 @ (setunion @ sK2))) = $true)),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f113])).
% 1.69/1.38 thf(f113,plain,(
% 1.69/1.38 (((^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) & (in @ Y0 @ (setunion @ sK2)))) @ sK4) = $true)),
% 1.69/1.38 inference(sigma_clausification,[status(thm)],[f112])).
% 1.69/1.38 thf(f112,plain,(
% 1.69/1.38 ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) & (in @ Y0 @ (setunion @ sK2))))) = $true)),
% 1.69/1.38 inference(boolean_simplification,[status(thm)],[f111])).
% 1.69/1.38 thf(f111,plain,(
% 1.69/1.38 (($true & (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) & (in @ Y0 @ (setunion @ sK2)))))) = $true)),
% 1.69/1.38 inference(backward_demodulation,[status(thm)],[f108,f110])).
% 1.69/1.38 thf(f110,plain,(
% 1.69/1.38 ((in @ sK3 @ (setunion @ sK2)) = $true)),
% 1.69/1.38 inference(binary_proxy_clausification,[status(thm)],[f108])).
% 1.69/1.38 thf(f108,plain,(
% 1.69/1.38 (((in @ sK3 @ (setunion @ sK2)) & (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) & (in @ Y0 @ (setunion @ sK2)))))) = $true)),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f107])).
% 1.69/1.38 thf(f107,plain,(
% 1.69/1.38 ($true = ((^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2) & (in @ Y1 @ (setunion @ sK2))))))) @ sK3))),
% 1.69/1.38 inference(sigma_clausification,[status(thm)],[f98])).
% 1.69/1.38 thf(f98,plain,(
% 1.69/1.38 ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2) & (in @ Y1 @ (setunion @ sK2)))))))) = $true)),
% 1.69/1.38 inference(binary_proxy_clausification,[status(thm)],[f96])).
% 1.69/1.38 thf(f96,plain,(
% 1.69/1.38 (((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2) & (in @ Y1 @ (setunion @ sK2)))))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ sK2)))) & (in @ Y0 @ (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ sK2)))))))) = $false)),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f95])).
% 1.69/1.38 thf(f95,plain,(
% 1.69/1.38 ($false = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0)))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0))))))))) @ sK2))),
% 1.69/1.38 inference(sigma_clausification,[status(thm)],[f63])).
% 1.69/1.38 thf(f63,plain,(
% 1.69/1.38 ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0)))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) = $false)),
% 1.69/1.38 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.69/1.38 thf(f42,plain,(
% 1.69/1.38 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0)))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0))))))))))) = $false)),
% 1.69/1.38 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.69/1.38 thf(f41,plain,(
% 1.69/1.38 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0)))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))))) = $false)),
% 1.69/1.38 inference(boolean_simplification,[status(thm)],[f40])).
% 1.69/1.38 thf(f40,plain,(
% 1.69/1.38 (($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0)))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0))))))))))))) = $false)),
% 1.69/1.38 inference(backward_demodulation,[status(thm)],[f35,f39])).
% 1.69/1.38 thf(f39,plain,(
% 1.69/1.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) = $true)),
% 1.69/1.38 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.69/1.38 thf(f35,plain,(
% 1.69/1.38 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0)))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0))))))))))))) = $false)),
% 1.69/1.38 inference(not_proxy_clausification,[status(thm)],[f34])).
% 1.69/1.38 thf(f34,plain,(
% 1.69/1.38 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0)))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))))))) = $true)),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.69/1.38 thf(f33,plain,(
% 1.69/1.38 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (((setadjoin @ Y6 @ emptyset) = Y5) & (in @ Y6 @ Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y1)) & (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = Y1) & (in @ Y3 @ (setunion @ Y1))))))))) @ Y0) => ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = Y1) & (in @ Y2 @ Y1))))) @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))))) = $true)),
% 1.69/1.38 inference(definition_unfolding,[status(thm)],[f27,f26,f32,f28,f24,f30])).
% 1.69/1.38 thf(f30,plain,(
% 1.69/1.38 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.69/1.38 inference(cnf_transformation,[status(thm)],[f13])).
% 1.69/1.38 thf(f13,plain,(
% 1.69/1.38 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.69/1.38 inference(fool_elimination,[status(thm)],[f12])).
% 1.69/1.38 thf(f12,plain,(
% 1.69/1.38 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 1.69/1.38 inference(rectify,[status(thm)],[f3])).
% 1.69/1.38 thf(f3,axiom,(
% 1.69/1.38 ((^[X2 : $i] : (? [X0 : $i] : ((in @ X0 @ X2) & ((setadjoin @ X0 @ emptyset) = X2)))) = singleton)),
% 1.69/1.38 file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',singleton)).
% 1.69/1.38 thf(f24,plain,(
% 1.69/1.38 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0))))))))))),
% 1.69/1.38 inference(cnf_transformation,[status(thm)],[f11])).
% 1.69/1.38 thf(f11,plain,(
% 1.69/1.38 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0))))))))))),
% 1.69/1.38 inference(fool_elimination,[status(thm)],[f10])).
% 1.69/1.38 thf(f10,plain,(
% 1.69/1.38 (iskpair = (^[X0 : $i] : (? [X1 : $i] : (? [X2 : $i] : ((in @ X2 @ (setunion @ X0)) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0)) & (in @ X1 @ (setunion @ X0))))))),
% 1.69/1.38 inference(rectify,[status(thm)],[f2])).
% 1.69/1.38 thf(f2,axiom,(
% 1.69/1.38 (iskpair = (^[X2 : $i] : (? [X0 : $i] : (? [X1 : $i] : ((in @ X1 @ (setunion @ X2)) & ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = X2)) & (in @ X0 @ (setunion @ X2))))))),
% 1.69/1.38 file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',iskpair)).
% 1.69/1.38 thf(f28,plain,(
% 1.69/1.38 (setukpairinjL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))),
% 1.69/1.38 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.38 thf(f17,plain,(
% 1.69/1.38 (setukpairinjL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))),
% 1.69/1.38 inference(fool_elimination,[status(thm)],[f16])).
% 1.69/1.38 thf(f16,plain,(
% 1.69/1.38 (setukpairinjL1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X0 = X2)))),
% 1.69/1.38 inference(rectify,[status(thm)],[f6])).
% 1.69/1.38 thf(f6,axiom,(
% 1.69/1.38 (setukpairinjL1 = ! [X0 : $i,X1 : $i,X4 : $i] : ((in @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X0 = X4)))),
% 1.69/1.38 file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',setukpairinjL1)).
% 1.69/1.38 thf(f32,plain,(
% 1.69/1.38 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (((setadjoin @ Y6 @ emptyset) = Y5) & (in @ Y6 @ Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.69/1.38 inference(definition_unfolding,[status(thm)],[f25,f31])).
% 1.69/1.38 thf(f31,plain,(
% 1.69/1.38 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.69/1.38 inference(definition_unfolding,[status(thm)],[f29,f30])).
% 1.69/1.38 thf(f29,plain,(
% 1.69/1.38 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.69/1.38 inference(cnf_transformation,[status(thm)],[f21])).
% 1.69/1.38 thf(f21,plain,(
% 1.69/1.38 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.69/1.38 inference(fool_elimination,[status(thm)],[f20])).
% 1.69/1.38 thf(f20,plain,(
% 1.69/1.38 ((^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))) = ex1)),
% 1.69/1.38 inference(rectify,[status(thm)],[f4])).
% 1.69/1.38 thf(f4,axiom,(
% 1.69/1.38 ((^[X2 : $i, X3 : $i > $o] : (singleton @ (dsetconstr @ X2 @ (^[X0 : $i] : (X3 @ X0))))) = ex1)),
% 1.69/1.38 file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',ex1)).
% 1.69/1.38 thf(f25,plain,(
% 1.69/1.38 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (ex1 @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.69/1.38 inference(cnf_transformation,[status(thm)],[f19])).
% 1.69/1.38 thf(f19,plain,(
% 1.69/1.38 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (ex1 @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.69/1.38 inference(fool_elimination,[status(thm)],[f18])).
% 1.69/1.38 thf(f18,plain,(
% 1.69/1.38 (ex1I = ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((X0 @ X1) => (! [X3 : $i] : ((in @ X3 @ X2) => ((X0 @ X3) => (X1 = X3))) => (ex1 @ X2 @ (^[X4 : $i] : (X0 @ X4)))))))),
% 1.69/1.38 inference(rectify,[status(thm)],[f5])).
% 1.69/1.38 thf(f5,axiom,(
% 1.69/1.38 (ex1I = ! [X3 : $i > $o,X0 : $i,X2 : $i] : ((in @ X0 @ X2) => ((X3 @ X0) => (! [X1 : $i] : ((in @ X1 @ X2) => ((X3 @ X1) => (X0 = X1))) => (ex1 @ X2 @ (^[X1 : $i] : (X3 @ X1)))))))),
% 1.69/1.38 file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',ex1I)).
% 1.69/1.38 thf(f26,plain,(
% 1.69/1.38 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 1.69/1.38 inference(cnf_transformation,[status(thm)],[f15])).
% 1.69/1.38 thf(f15,plain,(
% 1.69/1.38 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 1.69/1.38 inference(fool_elimination,[status(thm)],[f14])).
% 1.69/1.38 thf(f14,plain,(
% 1.69/1.38 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 1.69/1.38 inference(rectify,[status(thm)],[f1])).
% 1.69/1.38 thf(f1,axiom,(
% 1.69/1.38 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 1.69/1.38 file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',setadjoinIL)).
% 1.69/1.38 thf(f27,plain,(
% 1.69/1.38 ((~ (setadjoinIL => (ex1I => (setukpairinjL1 => (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))))) = $true)),
% 1.69/1.38 inference(cnf_transformation,[status(thm)],[f23])).
% 1.69/1.38 thf(f23,plain,(
% 1.69/1.38 ((~ (setadjoinIL => (ex1I => (setukpairinjL1 => (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))))) = $true)),
% 1.69/1.38 inference(fool_elimination,[status(thm)],[f22])).
% 1.69/1.38 thf(f22,plain,(
% 1.69/1.38 ~(setadjoinIL => (ex1I => (setukpairinjL1 => ! [X0 : $i] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (in @ (setadjoin @ X1 @ emptyset) @ X0))))))))),
% 1.69/1.38 inference(rectify,[status(thm)],[f8])).
% 1.69/1.38 thf(f8,negated_conjecture,(
% 1.69/1.38 ~(setadjoinIL => (ex1I => (setukpairinjL1 => ! [X5 : $i] : ((iskpair @ X5) => (singleton @ (dsetconstr @ (setunion @ X5) @ (^[X0 : $i] : (in @ (setadjoin @ X0 @ emptyset) @ X5))))))))),
% 1.69/1.38 inference(negated_conjecture,[status(cth)],[f7])).
% 1.69/1.38 thf(f7,conjecture,(
% 1.69/1.38 setadjoinIL => (ex1I => (setukpairinjL1 => ! [X5 : $i] : ((iskpair @ X5) => (singleton @ (dsetconstr @ (setunion @ X5) @ (^[X0 : $i] : (in @ (setadjoin @ X0 @ emptyset) @ X5)))))))),
% 1.69/1.38 file('/export/starexec/sandbox/tmp/tmp.6yPGDUDJ3P/DTF2THF_17750.p',kfstsingleton)).
% 1.69/1.38 thf(f74,plain,(
% 1.69/1.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (X3 = X1)))) )),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.69/1.38 thf(f73,plain,(
% 1.69/1.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (Y0 = X1))) @ X3) = $true)) )),
% 1.69/1.38 inference(pi_clausification,[status(thm)],[f72])).
% 1.69/1.38 thf(f72,plain,(
% 1.69/1.38 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (Y0 = X1)))) = $true)) )),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.69/1.38 thf(f71,plain,(
% 1.69/1.38 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y1 = X1))))) @ X2) = $true)) )),
% 1.69/1.38 inference(pi_clausification,[status(thm)],[f70])).
% 1.69/1.38 thf(f70,plain,(
% 1.69/1.38 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y1 = X1)))))) = $true)) )),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.69/1.38 thf(f69,plain,(
% 1.69/1.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0))))))) @ X1) = $true)) )),
% 1.69/1.38 inference(pi_clausification,[status(thm)],[f64])).
% 1.69/1.38 thf(f64,plain,(
% 1.69/1.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) = $true)),
% 1.69/1.38 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.69/1.38 thf(f182,plain,(
% 1.69/1.38 (((in @ sK5 @ (setunion @ sK2)) => ((in @ (setadjoin @ sK5 @ emptyset) @ sK2) => (sK3 = sK5))) = $false)),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f177])).
% 1.69/1.38 thf(f177,plain,(
% 1.69/1.38 (((^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (sK3 = Y0)))) @ sK5) = $false)),
% 1.69/1.38 inference(sigma_clausification,[status(thm)],[f167])).
% 1.69/1.38 thf(f167,plain,(
% 1.69/1.38 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (sK3 = Y0))))))),
% 1.69/1.38 inference(not_proxy_clausification,[status(thm)],[f150])).
% 1.69/1.38 thf(f150,plain,(
% 1.69/1.38 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (sK3 = Y0)))))) = $true)),
% 1.69/1.38 inference(boolean_simplification,[status(thm)],[f149])).
% 1.69/1.38 thf(f149,plain,(
% 1.69/1.38 (($true => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (sK3 = Y0))))))) = $true)),
% 1.69/1.38 inference(forward_demodulation,[status(thm)],[f148,f143])).
% 1.69/1.38 thf(f143,plain,(
% 1.69/1.38 ((in @ (setadjoin @ sK3 @ emptyset) @ sK2) = $true)),
% 1.69/1.38 inference(superposition,[status(thm)],[f51,f131])).
% 1.69/1.38 thf(f51,plain,(
% 1.69/1.38 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (setadjoin @ X2 @ X1)) = $true)) )),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.69/1.38 thf(f50,plain,(
% 1.69/1.38 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1))) @ X2) = $true)) )),
% 1.69/1.38 inference(pi_clausification,[status(thm)],[f49])).
% 1.69/1.38 thf(f49,plain,(
% 1.69/1.38 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1)))) = $true)) )),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.69/1.38 thf(f48,plain,(
% 1.69/1.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))) @ X1) = $true)) )),
% 1.69/1.38 inference(pi_clausification,[status(thm)],[f39])).
% 1.69/1.38 thf(f148,plain,(
% 1.69/1.38 ($true = ((in @ (setadjoin @ sK3 @ emptyset) @ sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (sK3 = Y0))))))))),
% 1.69/1.38 inference(boolean_simplification,[status(thm)],[f145])).
% 1.69/1.38 thf(f145,plain,(
% 1.69/1.38 (($true => ((in @ (setadjoin @ sK3 @ emptyset) @ sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (sK3 = Y0)))))))) = $true)),
% 1.69/1.38 inference(superposition,[status(thm)],[f104,f110])).
% 1.69/1.38 thf(f104,plain,(
% 1.69/1.38 ( ! [X0 : $i] : ((((in @ X0 @ (setunion @ sK2)) => ((in @ (setadjoin @ X0 @ emptyset) @ sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (X0 = Y0)))))))) = $true)) )),
% 1.69/1.38 inference(boolean_simplification,[status(thm)],[f103])).
% 1.69/1.38 thf(f103,plain,(
% 1.69/1.38 ( ! [X0 : $i] : ((((in @ X0 @ (setunion @ sK2)) => ((in @ (setadjoin @ X0 @ emptyset) @ sK2) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (X0 = Y0))))) => $false))) = $true)) )),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f102])).
% 1.69/1.38 thf(f102,plain,(
% 1.69/1.38 ( ! [X0 : $i] : (($true = ((in @ X0 @ (setunion @ sK2)) => (((^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ sK2)) @ X0) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ sK2)) @ Y0) => (X0 = Y0))))) => $false))))) )),
% 1.69/1.38 inference(superposition,[status(thm)],[f57,f100])).
% 1.69/1.38 thf(f100,plain,(
% 1.69/1.38 ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ sK2)))) & (in @ Y0 @ (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ sK2))))))) = $false)),
% 1.69/1.38 inference(boolean_simplification,[status(thm)],[f99])).
% 1.69/1.38 thf(f99,plain,(
% 1.69/1.38 (($true => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ sK2)))) & (in @ Y0 @ (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ sK2)))))))) = $false)),
% 1.69/1.38 inference(backward_demodulation,[status(thm)],[f96,f98])).
% 1.69/1.38 thf(f57,plain,(
% 1.69/1.38 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((in @ X2 @ X1) => ((X3 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X3 @ Y0) => (X2 = Y0))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X3)) & (in @ Y0 @ (dsetconstr @ X1 @ X3)))))))) = $true)) )),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.69/1.38 thf(f56,plain,(
% 1.69/1.38 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) => (X2 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ Y0)) & (in @ Y1 @ (dsetconstr @ X1 @ Y0))))))))) @ X3) = $true)) )),
% 1.69/1.38 inference(pi_clausification,[status(thm)],[f55])).
% 1.69/1.38 thf(f55,plain,(
% 1.69/1.38 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) => (X2 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ Y0)) & (in @ Y1 @ (dsetconstr @ X1 @ Y0)))))))))) = $true)) )),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.69/1.38 thf(f54,plain,(
% 1.69/1.38 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y1 @ Y2) => (Y0 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X1 @ Y1)) & (in @ Y2 @ (dsetconstr @ X1 @ Y1))))))))))) @ X2) = $true)) )),
% 1.69/1.38 inference(pi_clausification,[status(thm)],[f53])).
% 1.69/1.38 thf(f53,plain,(
% 1.69/1.38 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y1 @ Y2) => (Y0 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X1 @ Y1)) & (in @ Y2 @ (dsetconstr @ X1 @ Y1)))))))))))) = $true)) )),
% 1.69/1.38 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.69/1.38 thf(f52,plain,(
% 1.69/1.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y2))))))))))))) @ X1) = $true)) )),
% 1.69/1.38 inference(pi_clausification,[status(thm)],[f43])).
% 1.69/1.38 thf(f43,plain,(
% 1.69/1.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y2)))))))))))))) = $true)),
% 1.69/1.38 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.69/1.38 % SZS output end Proof for DTF2THF_17750
% 1.69/1.38 % (17858)------------------------------
% 1.69/1.38 % (17858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (17858)Termination reason: Refutation
% 1.69/1.38
% 1.69/1.38 % (17858)Memory used [KB]: 6140
% 1.69/1.38 % (17858)Time elapsed: 0.031 s
% 1.69/1.38 % (17858)Instructions burned: 74 (million)
% 1.69/1.38 % (17858)------------------------------
% 1.69/1.38 % (17858)------------------------------
% 1.69/1.38 % (17846)Success in time 0.064 s
%------------------------------------------------------------------------------