%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU655^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n025.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 09:35:59 AM UTC 2026
% Result : Theorem 1.73s 1.47s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 8
% Syntax : Number of formulae : 103 ( 100 unt; 0 typ; 0 def)
% Number of atoms : 1185 ( 271 equ; 0 cnn)
% Maximal formula atoms : 6 ( 11 avg)
% Number of connectives : 2425 ( 12 ~; 0 |; 63 &;2000 @)
% ( 0 <=>; 175 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 18 usr; 12 con; 0-2 aty)
% ( 124 !!; 51 ??; 0 @@+; 0 @@-)
% Number of variables : 347 ( 274 ^; 67 !; 6 ?; 347 :)
% 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_5,type,
iskpair: $i > $o ).
thf(func_def_7,type,
kpair: $i > $i > $i ).
thf(func_def_8,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_11,type,
kfst: $i > $i ).
thf(func_def_30,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f303,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f294,f249]) ).
thf(f249,plain,
sK5 != sK4,
inference(equality_proxy_clausification,[status(thm)],[f241]) ).
thf(f241,plain,
( ( sK4 = sK5 )
= $false ),
inference(boolean_simplification,[status(thm)],[f239]) ).
thf(f239,plain,
( ( $true
=> ( sK4 = sK5 ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f210,f237]) ).
thf(f237,plain,
( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK5 @ emptyset ) ) @ emptyset ) )
= sK2 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f210]) ).
thf(f210,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK5 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ( sK4 = sK5 ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f203]) ).
thf(f203,plain,
( ( ( in @ sK5 @ ( setunion @ sK2 ) )
=> ( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK5 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ( sK4 = sK5 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f198]) ).
thf(f198,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ( sK4 = Y0 ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f182]) ).
thf(f182,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ( sK4 = Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f149]) ).
thf(f149,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ( sK4 = Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f148]) ).
thf(f148,plain,
( $true
= ( $true
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ( sK4 = Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f147]) ).
thf(f147,plain,
( ( ( sK2 = sK2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ( sK4 = Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f146,f125]) ).
thf(f125,plain,
( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) )
= sK2 ),
inference(equality_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) )
= sK2 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
( ( ( in @ sK4 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) )
= sK2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f102]) ).
thf(f102,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 ) )
@ sK4 )
= $true ),
inference(sigma_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f97,f98]) ).
thf(f98,plain,
( ( in @ sK3 @ ( setunion @ sK2 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) )
& ( in @ sK3 @ ( setunion @ sK2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f96]) ).
thf(f96,plain,
( ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) )
& ( in @ Y0 @ ( setunion @ sK2 ) ) )
@ sK3 )
= $true ),
inference(sigma_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) )
& ( in @ Y0 @ ( setunion @ sK2 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ sK2 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) )
& ( in @ Y0 @ ( setunion @ sK2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ sK2 )
@ ^ [Y1: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ ( setunion @ sK2 )
@ ^ [Y1: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
( ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
= Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y2 @ Y0 ) )
& ( in @ Y3 @ ( dsetconstr @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
= Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ~ ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y2 @ Y0 ) )
& ( in @ Y3 @ ( dsetconstr @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
= Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ~ ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ( Y0 @ 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 ) ) )
@ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y2
@ Y3 )
= ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y0
@ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( setunion @ Y1 ) )
& ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
= Y1 ) ) )
& ( in @ Y2 @ ( setunion @ Y1 ) ) ) )
@ Y0 )
=> ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= Y1 )
& ( in @ Y2 @ Y1 ) ) )
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ ( kfst @ Y0 )
@ Y1 )
= Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f32,f37,f38,f35,f34,f27,f28]) ).
thf(f28,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( kpair
= ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( kpair
= ( ^ [X1: $i,X2: $i] : ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',kpair) ).
thf(f27,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) )
= singleton ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) )
= singleton ),
file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',singleton) ).
thf(f34,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
& ? [X2: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= X0 )
& ( in @ X2 @ ( setunion @ X0 ) ) ) ) )
= iskpair ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
& ? [X2: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= X0 )
& ( in @ X2 @ ( setunion @ X0 ) ) ) ) )
= iskpair ),
file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',iskpair) ).
thf(f35,plain,
( setukpairinjR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y2
@ Y3 )
= ( ^ [Y4: $i,Y5: $i] : ( setadjoin @ ( setadjoin @ Y4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y4 @ ( setadjoin @ Y5 @ emptyset ) ) @ emptyset ) )
@ Y0
@ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f29,f28,f28]) ).
thf(f29,plain,
( setukpairinjR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y2 @ Y3 )
= ( kpair @ Y0 @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( setukpairinjR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y2 @ Y3 )
= ( kpair @ Y0 @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
( setukpairinjR
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X1 @ X0 )
= ( kpair @ X3 @ X2 ) )
=> ( X0 = X2 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( setukpairinjR
= ( ! [X5: $i,X4: $i,X2: $i,X1: $i] :
( ( ( kpair @ X1 @ X2 )
= ( kpair @ X4 @ X5 ) )
=> ( X2 = X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',setukpairinjR) ).
thf(f38,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) )
= Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f30,f28]) ).
thf(f30,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 )
= kfstpairEq ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X1: $i,X2: $i] :
( ( ( kfst @ ( kpair @ X1 @ X2 ) )
= X1 )
= kfstpairEq ),
file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',kfstpairEq) ).
thf(f37,plain,
( ex1I
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ( Y0 @ 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 ) ) )
@ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f33,f36]) ).
thf(f36,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)],[f31,f27]) ).
thf(f31,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ex1
= ( ^ [X0: $i,X3: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X1: $i] : ( X3 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',ex1) ).
thf(f33,plain,
( ex1I
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ex1 @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ex1I
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ex1 @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
=> ( ( X2 @ X1 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X2 @ X3 )
=> ( X1 = X3 ) ) )
=> ( ex1 @ X0
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) )
= ex1I ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X0: $i,X1: $i,X3: $i > $o] :
( ( ( in @ X1 @ X0 )
=> ( ( X3 @ X1 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X3 @ X2 )
=> ( X1 = X2 ) ) )
=> ( ex1 @ X0
@ ^ [X2: $i] : ( X3 @ X2 ) ) ) ) )
= ex1I ),
file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',ex1I) ).
thf(f32,plain,
( ( ~ ( ex1I
=> ( kfstpairEq
=> ( setukpairinjR
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( iskpair @ Y0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] :
( ( kpair @ ( kfst @ Y0 ) @ Y1 )
= Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ~ ( ex1I
=> ( kfstpairEq
=> ( setukpairinjR
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( iskpair @ Y0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] :
( ( kpair @ ( kfst @ Y0 ) @ Y1 )
= Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
~ ( ex1I
=> ( kfstpairEq
=> ( setukpairinjR
=> ! [X0: $i] :
( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] :
( ( kpair @ ( kfst @ X0 ) @ X1 )
= X0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ( ex1I
=> ( kfstpairEq
=> ( setukpairinjR
=> ! [X5: $i] :
( ( iskpair @ X5 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X5 )
@ ^ [X1: $i] :
( ( kpair @ ( kfst @ X5 ) @ X1 )
= X5 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
( ex1I
=> ( kfstpairEq
=> ( setukpairinjR
=> ! [X5: $i] :
( ( iskpair @ X5 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X5 )
@ ^ [X1: $i] :
( ( kpair @ ( kfst @ X5 ) @ X1 )
= X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',ksndsingleton) ).
thf(f146,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ( sK4 = Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f145,f135]) ).
thf(f135,plain,
( sK3
= ( kfst @ sK2 ) ),
inference(superposition,[status(thm)],[f67,f125]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X2 ),
inference(equality_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( ( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X2 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= Y0 )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= Y0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
= Y1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
= Y1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f145,plain,
( ( ( ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ( sK4 = Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f144]) ).
thf(f144,plain,
( ( ( ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ( sK4 = Y0 ) ) ) )
=> $false ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f141]) ).
thf(f141,plain,
( ( ( ^ [Y0: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK2 )
@ sK4 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( ^ [Y1: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK2 )
@ Y0 )
=> ( sK4 = Y0 ) ) ) )
=> $false ) )
= $true ),
inference(superposition,[status(thm)],[f117,f90]) ).
thf(f90,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ sK2 )
@ ^ [Y1: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ ( setunion @ sK2 )
@ ^ [Y1: $i] :
( ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ sK2 ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK2 ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f117,plain,
! [X0: $i > $o] :
( ( ( X0 @ sK4 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( X0 @ Y0 )
=> ( sK4 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ sK2 ) @ X0 ) )
& ( in @ Y0 @ ( dsetconstr @ ( setunion @ sK2 ) @ X0 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f115]) ).
thf(f115,plain,
! [X0: $i > $o] :
( ( $true
=> ( ( X0 @ sK4 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK2 ) )
=> ( ( X0 @ Y0 )
=> ( sK4 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ ( setunion @ sK2 ) @ X0 ) )
& ( in @ Y0 @ ( dsetconstr @ ( setunion @ sK2 ) @ X0 ) ) ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f55,f113]) ).
thf(f113,plain,
( ( in @ sK4 @ ( setunion @ sK2 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f112]) ).
thf(f112,plain,
( ( ( in @ sK4 @ ( setunion @ sK2 ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f103,f110]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X2 @ X3 )
=> ( ( X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( X1 @ Y0 )
=> ( X2 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X3 @ X1 ) )
& ( in @ Y0 @ ( dsetconstr @ X3 @ X1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( ( X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( X2 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ Y0 @ X1 ) )
& ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( ( X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( X2 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ Y0 @ X1 ) )
& ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( X1 @ Y2 )
=> ( Y0 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y1 @ X1 ) )
& ( in @ Y2 @ ( dsetconstr @ Y1 @ X1 ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( X1 @ Y2 )
=> ( Y0 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y1 @ X1 ) )
& ( in @ Y2 @ ( dsetconstr @ Y1 @ X1 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y2 @ Y0 ) )
& ( in @ Y3 @ ( dsetconstr @ Y2 @ Y0 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y1 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y2 @ Y0 ) )
& ( in @ Y3 @ ( dsetconstr @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f294,plain,
sK5 = sK4,
inference(equality_proxy_clausification,[status(thm)],[f282]) ).
thf(f282,plain,
( ( sK5 = sK4 )
= $true ),
inference(boolean_simplification,[status(thm)],[f277]) ).
thf(f277,plain,
( ( $true
=> ( sK5 = sK4 ) )
= $true ),
inference(superposition,[status(thm)],[f134,f237]) ).
thf(f134,plain,
! [X0: $i,X1: $i] :
( ( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= sK2 )
=> ( X1 = sK4 ) )
= $true ),
inference(superposition,[status(thm)],[f86,f125]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( X4 = X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X2 ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f83]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = X2 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = X2 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f79]) ).
thf(f79,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y3 = Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y3 = Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU655^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n025.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 12:29:42 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.46 thf(spec,logic,$$dhol).
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % File : SEU655^2 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.46 % Domain : Set Theory
% 0.21/0.46 % Problem : Ordered Pairs - Properties of Pairs
% 0.21/0.46 % Version : Especial > Reduced > Especial.
% 0.21/0.46 % English : (! u:i.iskpair u -> singleton (dsetconstr (setunion u)
% 0.21/0.46 % (^ x:i.u = kpair (kfst u) x)))
% 0.21/0.46
% 0.21/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.46 % Source : [Bro08]
% 0.21/0.46 % Names : ZFC157l [Bro08]
% 0.21/0.46
% 0.21/0.46 % Status : Theorem
% 0.21/0.46 % Rating : 0.44 v9.1.0, 0.50 v9.0.0, 0.70 v8.2.0, 0.69 v8.1.0, 0.64 v7.5.0, 0.57 v7.4.0, 0.67 v7.3.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.71 v6.1.0, 0.57 v5.5.0, 0.67 v5.4.0, 1.00 v5.2.0, 0.80 v5.0.0, 1.00 v3.7.0
% 0.21/0.46 % Syntax : Number of formulae : 21 ( 7 unt; 13 typ; 7 def)
% 0.21/0.46 % Number of atoms : 32 ( 14 equ; 0 cnn)
% 0.21/0.46 % Maximal formula atoms : 6 ( 4 avg)
% 0.21/0.46 % Number of connectives : 71 ( 0 ~; 0 |; 3 &; 58 @)
% 0.21/0.46 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.21/0.46 % Maximal formula depth : 10 ( 2 avg)
% 0.21/0.46 % Number of types : 2 ( 0 usr)
% 0.21/0.46 % Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% 0.21/0.46 % Number of symbols : 14 ( 13 usr; 4 con; 0-2 aty)
% 0.21/0.46 % Number of variables : 23 ( 9 ^; 11 !; 3 ?; 23 :)
% 0.21/0.46 % SPC : TH0_THM_EQU_NAR
% 0.21/0.46
% 0.21/0.46 % Comments : http://mathgate.info/detsetitem.php?id=211
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 thf(in_type,type,
% 0.21/0.46 in: $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyset_type,type,
% 0.21/0.46 emptyset: $i ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoin_type,type,
% 0.21/0.46 setadjoin: $i > $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(setunion_type,type,
% 0.21/0.46 setunion: $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstr_type,type,
% 0.21/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.21/0.46
% 0.21/0.46 thf(iskpair_type,type,
% 0.21/0.46 iskpair: $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(iskpair,definition,
% 0.21/0.46 ( iskpair
% 0.21/0.46 = ( ^ [A: $i] :
% 0.21/0.46 ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.21/0.46 & ? [Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ ( setunion @ A ) )
% 0.21/0.46 & ( A
% 0.21/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(kpair_type,type,
% 0.21/0.46 kpair: $i > $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(kpair,definition,
% 0.21/0.46 ( kpair
% 0.21/0.46 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(singleton_type,type,
% 0.21/0.46 singleton: $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(singleton,definition,
% 0.21/0.46 ( singleton
% 0.21/0.46 = ( ^ [A: $i] :
% 0.21/0.46 ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ( A
% 0.21/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(ex1_type,type,
% 0.21/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(ex1,definition,
% 0.21/0.46 ( ex1
% 0.21/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( singleton
% 0.21/0.46 @ ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(ex1I_type,type,
% 0.21/0.46 ex1I: $o ).
% 0.21/0.46
% 0.21/0.46 thf(ex1I,definition,
% 0.21/0.46 ( ex1I
% 0.21/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( ( Xphi @ Xx )
% 0.21/0.47 => ( ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ A )
% 0.21/0.47 => ( ( Xphi @ Xy )
% 0.21/0.47 => ( Xy = Xx ) ) )
% 0.21/0.47 => ( ex1 @ A
% 0.21/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(kfst_type,type,
% 0.21/0.47 kfst: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(kfstpairEq_type,type,
% 0.21/0.47 kfstpairEq: $o ).
% 0.21/0.47
% 0.21/0.47 thf(kfstpairEq,definition,
% 0.21/0.47 ( kfstpairEq
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.21/0.47 = Xx ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjR_type,type,
% 0.21/0.47 setukpairinjR: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjR,definition,
% 0.21/0.47 ( setukpairinjR
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.21/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.21/0.47 = ( kpair @ Xz @ Xu ) )
% 0.21/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ksndsingleton,conjecture,
% 0.21/0.47 ( ex1I
% 0.21/0.47 => ( kfstpairEq
% 0.21/0.47 => ( setukpairinjR
% 0.21/0.47 => ! [Xu: $i] :
% 0.21/0.47 ( ( iskpair @ Xu )
% 0.21/0.47 => ( singleton
% 0.21/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.21/0.47 @ ^ [Xx: $i] :
% 0.21/0.47 ( Xu
% 0.21/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 1.68/1.33 ---- Embedded in THF ---
% 1.68/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.33 %%% Generated on Tue Feb 24 12:29:43 EST 2026
% 1.68/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.33 %%% Logic specification used:
% 1.68/1.33 %%% thf(spec, logic, $$dhol).
% 1.68/1.33
% 1.68/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2DTF18052.p
% See solution above
% 1.68/1.33 ------------------------
% 1.68/1.34 ---- Cleaned THF ---
% 1.68/1.34 thf(in_type,type,
% 1.68/1.34 in: $i > $i > $o ).
% 1.68/1.34
% 1.68/1.34 thf(emptyset_type,type,
% 1.68/1.34 emptyset: $i ).
% 1.68/1.34
% 1.68/1.34 thf(setadjoin_type,type,
% 1.68/1.34 setadjoin: $i > $i > $i ).
% 1.68/1.34
% 1.68/1.34 thf(setunion_type,type,
% 1.68/1.34 setunion: $i > $i ).
% 1.68/1.34
% 1.68/1.34 thf(dsetconstr_type,type,
% 1.68/1.34 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.68/1.34
% 1.68/1.34 thf(iskpair_type,type,
% 1.68/1.34 iskpair: $i > $o ).
% 1.68/1.34
% 1.68/1.34 thf(iskpair,definition,
% 1.68/1.34 ( iskpair
% 1.68/1.34 = ( ^ [A: $i] :
% 1.68/1.34 ? [Xx: $i] :
% 1.68/1.34 ( ( in @ Xx @ ( setunion @ A ) )
% 1.68/1.34 & ? [Xy: $i] :
% 1.68/1.34 ( ( in @ Xy @ ( setunion @ A ) )
% 1.68/1.34 & ( A
% 1.68/1.34 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 1.68/1.34
% 1.68/1.34 thf(kpair_type,type,
% 1.68/1.34 kpair: $i > $i > $i ).
% 1.68/1.34
% 1.68/1.34 thf(kpair,definition,
% 1.68/1.34 ( kpair
% 1.68/1.34 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 1.68/1.34
% 1.68/1.34 thf(singleton_type,type,
% 1.68/1.34 singleton: $i > $o ).
% 1.68/1.34
% 1.68/1.34 thf(singleton,definition,
% 1.68/1.34 ( singleton
% 1.68/1.34 = ( ^ [A: $i] :
% 1.68/1.34 ? [Xx: $i] :
% 1.68/1.34 ( ( in @ Xx @ A )
% 1.68/1.34 & ( A
% 1.68/1.34 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.68/1.34
% 1.68/1.34 thf(ex1_type,type,
% 1.68/1.34 ex1: $i > ( $i > $o ) > $o ).
% 1.68/1.34
% 1.68/1.34 thf(ex1,definition,
% 1.68/1.34 ( ex1
% 1.68/1.34 = ( ^ [A: $i,Xphi: $i > $o] :
% 1.68/1.34 ( singleton
% 1.68/1.34 @ ( dsetconstr @ A
% 1.68/1.34 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.68/1.34
% 1.68/1.34 thf(ex1I_type,type,
% 1.68/1.34 ex1I: $o ).
% 1.68/1.34
% 1.68/1.34 thf(ex1I,definition,
% 1.68/1.34 ( ex1I
% 1.68/1.34 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.68/1.34 ( ( in @ Xx @ A )
% 1.68/1.34 => ( ( Xphi @ Xx )
% 1.68/1.34 => ( ! [Xy: $i] :
% 1.68/1.34 ( ( in @ Xy @ A )
% 1.68/1.34 => ( ( Xphi @ Xy )
% 1.68/1.34 => ( Xy = Xx ) ) )
% 1.68/1.34 => ( ex1 @ A
% 1.68/1.34 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.68/1.34
% 1.68/1.34 thf(kfst_type,type,
% 1.68/1.34 kfst: $i > $i ).
% 1.68/1.34
% 1.68/1.34 thf(kfstpairEq_type,type,
% 1.68/1.34 kfstpairEq: $o ).
% 1.68/1.34
% 1.68/1.34 thf(kfstpairEq,definition,
% 1.68/1.34 ( kfstpairEq
% 1.68/1.34 = ( ! [Xx: $i,Xy: $i] :
% 1.68/1.34 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 1.68/1.34 = Xx ) ) ) ).
% 1.68/1.34
% 1.68/1.34 thf(setukpairinjR_type,type,
% 1.68/1.34 setukpairinjR: $o ).
% 1.68/1.34
% 1.68/1.34 thf(setukpairinjR,definition,
% 1.68/1.34 ( setukpairinjR
% 1.68/1.34 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 1.68/1.34 ( ( ( kpair @ Xx @ Xy )
% 1.68/1.34 = ( kpair @ Xz @ Xu ) )
% 1.68/1.34 => ( Xy = Xu ) ) ) ) ).
% 1.68/1.34
% 1.68/1.34 thf(ksndsingleton,conjecture,
% 1.68/1.34 ( ex1I
% 1.68/1.34 => ( kfstpairEq
% 1.68/1.34 => ( setukpairinjR
% 1.68/1.34 => ! [Xu: $i] :
% 1.68/1.34 ( ( iskpair @ Xu )
% 1.68/1.34 => ( singleton
% 1.68/1.34 @ ( dsetconstr @ ( setunion @ Xu )
% 1.68/1.34 @ ^ [Xx: $i] :
% 1.68/1.34 ( Xu
% 1.68/1.34 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ) ).
% 1.68/1.34 ------------------------
% 1.68/1.35 % (18199)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18052 for (3000ds/183Mi)
% 1.68/1.35 % (18205)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18052 for (3000ds/18Mi)
% 1.68/1.36 % (18205)Instruction limit reached!
% 1.68/1.36 % (18205)------------------------------
% 1.68/1.36 % (18205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.36 % (18205)Termination reason: Unknown
% 1.68/1.36 % (18205)Termination phase: Saturation
% 1.68/1.36
% 1.68/1.36 % (18205)Memory used [KB]: 5628
% 1.68/1.36 % (18205)Time elapsed: 0.009 s
% 1.68/1.36 % (18205)Instructions burned: 18 (million)
% 1.68/1.36 % (18205)------------------------------
% 1.68/1.36 % (18205)------------------------------
% 1.68/1.36 % (18200)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_18052 for (3000ds/4Mi)
% 1.68/1.36 % (18201)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_18052 for (3000ds/27Mi)
% 1.68/1.36 % (18203)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_18052 for (3000ds/2Mi)
% 1.68/1.36 % (18204)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_18052 for (3000ds/275Mi)
% 1.68/1.36 % (18202)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18052 for (3000ds/2Mi)
% 1.68/1.36 % (18203)Instruction limit reached!
% 1.68/1.36 % (18203)------------------------------
% 1.68/1.36 % (18203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.36 % (18203)Termination reason: Unknown
% 1.68/1.36 % (18203)Termination phase: shuffling
% 1.68/1.36
% 1.68/1.36 % (18203)Memory used [KB]: 1023
% 1.68/1.36 % (18203)Time elapsed: 0.003 s
% 1.68/1.36 % (18203)Instructions burned: 2 (million)
% 1.68/1.36 % (18203)------------------------------
% 1.68/1.36 % (18203)------------------------------
% 1.68/1.36 % (18202)Instruction limit reached!
% 1.68/1.36 % (18202)------------------------------
% 1.68/1.36 % (18202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.36 % (18202)Termination reason: Unknown
% 1.68/1.36 % (18202)Termination phase: Preprocessing 3
% 1.68/1.36
% 1.68/1.36 % (18202)Memory used [KB]: 1023
% 1.68/1.36 % (18202)Time elapsed: 0.004 s
% 1.68/1.36 % (18202)Instructions burned: 3 (million)
% 1.68/1.36 % (18202)------------------------------
% 1.68/1.36 % (18202)------------------------------
% 1.68/1.36 % (18200)Instruction limit reached!
% 1.68/1.36 % (18200)------------------------------
% 1.68/1.36 % (18200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.36 % (18200)Termination reason: Unknown
% 1.68/1.36 % (18200)Termination phase: Saturation
% 1.68/1.36
% 1.68/1.36 % (18200)Memory used [KB]: 5500
% 1.68/1.36 % (18200)Time elapsed: 0.005 s
% 1.68/1.36 % (18200)Instructions burned: 5 (million)
% 1.68/1.36 % (18200)------------------------------
% 1.68/1.36 % (18200)------------------------------
% 1.68/1.37 % (18204)Refutation not found, incomplete strategy
% 1.68/1.37 % (18204)------------------------------
% 1.68/1.37 % (18204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (18204)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.37
% 1.68/1.37
% 1.68/1.37 % (18204)Memory used [KB]: 5628
% 1.68/1.37 % (18204)Time elapsed: 0.010 s
% 1.68/1.37 % (18204)Instructions burned: 12 (million)
% 1.68/1.37 % (18204)------------------------------
% 1.68/1.37 % (18204)------------------------------
% 1.68/1.37 % (18207)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/3Mi)
% 1.68/1.37 % (18207)Instruction limit reached!
% 1.68/1.37 % (18207)------------------------------
% 1.68/1.37 % (18207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (18207)Termination reason: Unknown
% 1.68/1.37 % (18207)Termination phase: Property scanning
% 1.68/1.37
% 1.68/1.37 % (18207)Memory used [KB]: 1023
% 1.68/1.37 % (18207)Time elapsed: 0.003 s
% 1.68/1.37 % (18207)Instructions burned: 5 (million)
% 1.68/1.37 % (18207)------------------------------
% 1.68/1.37 % (18207)------------------------------
% 1.68/1.38 % (18201)Instruction limit reached!
% 1.68/1.38 % (18201)------------------------------
% 1.68/1.38 % (18201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (18201)Termination reason: Unknown
% 1.68/1.38 % (18201)Termination phase: Saturation
% 1.68/1.38
% 1.68/1.38 % (18201)Memory used [KB]: 5628
% 1.68/1.38 % (18201)Time elapsed: 0.019 s
% 1.68/1.38 % (18201)Instructions burned: 28 (million)
% 1.68/1.38 % (18201)------------------------------
% 1.68/1.38 % (18201)------------------------------
% 1.68/1.38 % (18208)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_18052 for (2999ds/37Mi)
% 1.68/1.38 % (18209)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_18052 for (2999ds/15Mi)
% 1.68/1.38 % (18211)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_18052 for (2999ds/3Mi)
% 1.68/1.38 % (18211)Instruction limit reached!
% 1.68/1.38 % (18211)------------------------------
% 1.68/1.38 % (18211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (18211)Termination reason: Unknown
% 1.68/1.38 % (18211)Termination phase: Property scanning
% 1.68/1.38
% 1.68/1.38 % (18211)Memory used [KB]: 1023
% 1.68/1.38 % (18211)Time elapsed: 0.004 s
% 1.68/1.38 % (18211)Instructions burned: 3 (million)
% 1.68/1.38 % (18211)------------------------------
% 1.68/1.38 % (18211)------------------------------
% 1.68/1.38 % (18216)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/7Mi)
% 1.68/1.39 % (18216)Instruction limit reached!
% 1.68/1.39 % (18216)------------------------------
% 1.68/1.39 % (18216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.39 % (18216)Termination reason: Unknown
% 1.68/1.39 % (18216)Termination phase: Saturation
% 1.68/1.39
% 1.68/1.39 % (18216)Memory used [KB]: 1023
% 1.68/1.39 % (18216)Time elapsed: 0.004 s
% 1.68/1.39 % (18216)Instructions burned: 10 (million)
% 1.68/1.39 % (18216)------------------------------
% 1.68/1.39 % (18216)------------------------------
% 1.68/1.39 % (18213)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_18052 for (2999ds/1041Mi)
% 1.68/1.39 % (18209)Instruction limit reached!
% 1.68/1.39 % (18209)------------------------------
% 1.68/1.39 % (18209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.39 % (18209)Termination reason: Unknown
% 1.68/1.39 % (18209)Termination phase: Saturation
% 1.68/1.39
% 1.68/1.39 % (18209)Memory used [KB]: 5628
% 1.68/1.39 % (18209)Time elapsed: 0.037 s
% 1.68/1.39 % (18209)Instructions burned: 16 (million)
% 1.68/1.39 % (18209)------------------------------
% 1.68/1.39 % (18209)------------------------------
% 1.68/1.39 % (18219)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/16Mi)
% 1.68/1.40 % (18224)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_18052 for (2999ds/3Mi)
% 1.68/1.40 % (18224)Instruction limit reached!
% 1.68/1.40 % (18224)------------------------------
% 1.68/1.40 % (18224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.40 % (18224)Termination reason: Unknown
% 1.68/1.40 % (18224)Termination phase: Property scanning
% 1.68/1.40
% 1.68/1.40 % (18224)Memory used [KB]: 1023
% 1.68/1.40 % (18224)Time elapsed: 0.002 s
% 1.68/1.40 % (18224)Instructions burned: 3 (million)
% 1.68/1.40 % (18224)------------------------------
% 1.68/1.40 % (18224)------------------------------
% 1.73/1.40 % (18208)Instruction limit reached!
% 1.73/1.40 % (18208)------------------------------
% 1.73/1.40 % (18208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.40 % (18208)Termination reason: Unknown
% 1.73/1.40 % (18208)Termination phase: Saturation
% 1.73/1.40
% 1.73/1.40 % (18208)Memory used [KB]: 5756
% 1.73/1.40 % (18208)Time elapsed: 0.023 s
% 1.73/1.40 % (18208)Instructions burned: 37 (million)
% 1.73/1.40 % (18208)------------------------------
% 1.73/1.40 % (18208)------------------------------
% 1.73/1.40 % (18222)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_18052 for (2999ds/3Mi)
% 1.73/1.40 % (18222)Instruction limit reached!
% 1.73/1.40 % (18222)------------------------------
% 1.73/1.40 % (18222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.40 % (18222)Termination reason: Unknown
% 1.73/1.40 % (18222)Termination phase: Property scanning
% 1.73/1.40
% 1.73/1.40 % (18222)Memory used [KB]: 1023
% 1.73/1.40 % (18222)Time elapsed: 0.004 s
% 1.73/1.40 % (18222)Instructions burned: 4 (million)
% 1.73/1.40 % (18222)------------------------------
% 1.73/1.40 % (18222)------------------------------
% 1.73/1.40 % (18219)Instruction limit reached!
% 1.73/1.40 % (18219)------------------------------
% 1.73/1.40 % (18219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.40 % (18219)Termination reason: Unknown
% 1.73/1.40 % (18219)Termination phase: Saturation
% 1.73/1.40
% 1.73/1.40 % (18219)Memory used [KB]: 5884
% 1.73/1.40 % (18219)Time elapsed: 0.010 s
% 1.73/1.40 % (18219)Instructions burned: 17 (million)
% 1.73/1.40 % (18219)------------------------------
% 1.73/1.40 % (18219)------------------------------
% 1.73/1.41 % (18230)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/3Mi)
% 1.73/1.41 % (18199)Instruction limit reached!
% 1.73/1.41 % (18199)------------------------------
% 1.73/1.41 % (18199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.41 % (18199)Termination reason: Unknown
% 1.73/1.41 % (18199)Termination phase: Saturation
% 1.73/1.41
% 1.73/1.41 % (18199)Memory used [KB]: 6268
% 1.73/1.41 % (18199)Time elapsed: 0.055 s
% 1.73/1.41 % (18199)Instructions burned: 185 (million)
% 1.73/1.41 % (18199)------------------------------
% 1.73/1.41 % (18199)------------------------------
% 1.73/1.41 % (18230)Instruction limit reached!
% 1.73/1.41 % (18230)------------------------------
% 1.73/1.41 % (18230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.41 % (18230)Termination reason: Unknown
% 1.73/1.41 % (18230)Termination phase: Function definition elimination
% 1.73/1.41
% 1.73/1.41 % (18230)Memory used [KB]: 1023
% 1.73/1.41 % (18230)Time elapsed: 0.002 s
% 1.73/1.41 % (18230)Instructions burned: 4 (million)
% 1.73/1.41 % (18230)------------------------------
% 1.73/1.41 % (18230)------------------------------
% 1.73/1.41 % (18226)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/7Mi)
% 1.73/1.41 % (18226)Instruction limit reached!
% 1.73/1.41 % (18226)------------------------------
% 1.73/1.41 % (18226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.41 % (18226)Termination reason: Unknown
% 1.73/1.41 % (18226)Termination phase: Saturation
% 1.73/1.41
% 1.73/1.41 % (18226)Memory used [KB]: 5500
% 1.73/1.41 % (18226)Time elapsed: 0.006 s
% 1.73/1.41 % (18226)Instructions burned: 7 (million)
% 1.73/1.41 % (18226)------------------------------
% 1.73/1.41 % (18226)------------------------------
% 1.73/1.41 % (18236)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/710Mi)
% 1.73/1.42 % (18238)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/6Mi)
% 1.73/1.42 % (18239)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/902Mi)
% 1.73/1.42 % (18235)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/18Mi)
% 1.73/1.42 % (18232)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/4Mi)
% 1.73/1.42 % (18238)Instruction limit reached!
% 1.73/1.42 % (18238)------------------------------
% 1.73/1.42 % (18238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.42 % (18238)Termination reason: Unknown
% 1.73/1.42 % (18238)Termination phase: Saturation
% 1.73/1.42
% 1.73/1.42 % (18238)Memory used [KB]: 5500
% 1.73/1.42 % (18238)Time elapsed: 0.003 s
% 1.73/1.42 % (18238)Instructions burned: 7 (million)
% 1.73/1.42 % (18238)------------------------------
% 1.73/1.42 % (18238)------------------------------
% 1.73/1.42 % (18239)Refutation not found, incomplete strategy
% 1.73/1.42 % (18239)------------------------------
% 1.73/1.42 % (18239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.42 % (18239)Termination reason: Refutation not found, incomplete strategy
% 1.73/1.42
% 1.73/1.42
% 1.73/1.42 % (18239)Memory used [KB]: 5500
% 1.73/1.42 % (18239)Time elapsed: 0.003 s
% 1.73/1.42 % (18239)Instructions burned: 5 (million)
% 1.73/1.42 % (18239)------------------------------
% 1.73/1.42 % (18239)------------------------------
% 1.73/1.42 % (18232)Instruction limit reached!
% 1.73/1.42 % (18232)------------------------------
% 1.73/1.42 % (18232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.42 % (18232)Termination reason: Unknown
% 1.73/1.42 % (18232)Termination phase: Function definition elimination
% 1.73/1.42
% 1.73/1.42 % (18232)Memory used [KB]: 1023
% 1.73/1.42 % (18232)Time elapsed: 0.004 s
% 1.73/1.42 % (18232)Instructions burned: 4 (million)
% 1.73/1.42 % (18232)------------------------------
% 1.73/1.42 % (18232)------------------------------
% 1.73/1.42 % (18235)Instruction limit reached!
% 1.73/1.42 % (18235)------------------------------
% 1.73/1.42 % (18235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.42 % (18235)Termination reason: Unknown
% 1.73/1.42 % (18235)Termination phase: Saturation
% 1.73/1.42
% 1.73/1.42 % (18235)Memory used [KB]: 5628
% 1.73/1.42 % (18235)Time elapsed: 0.009 s
% 1.73/1.42 % (18235)Instructions burned: 19 (million)
% 1.73/1.42 % (18235)------------------------------
% 1.73/1.42 % (18235)------------------------------
% 1.73/1.43 % (18245)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/5Mi)
% 1.73/1.43 % (18242)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/21Mi)
% 1.73/1.43 % (18246)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/6Mi)
% 1.73/1.43 % (18245)Instruction limit reached!
% 1.73/1.43 % (18245)------------------------------
% 1.73/1.43 % (18245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.43 % (18245)Termination reason: Unknown
% 1.73/1.43 % (18245)Termination phase: Saturation
% 1.73/1.43
% 1.73/1.43 % (18245)Memory used [KB]: 5500
% 1.73/1.43 % (18245)Time elapsed: 0.003 s
% 1.73/1.43 % (18245)Instructions burned: 7 (million)
% 1.73/1.43 % (18245)------------------------------
% 1.73/1.43 % (18245)------------------------------
% 1.73/1.43 % (18246)Instruction limit reached!
% 1.73/1.43 % (18246)------------------------------
% 1.73/1.43 % (18246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.43 % (18246)Termination reason: Unknown
% 1.73/1.43 % (18246)Termination phase: Saturation
% 1.73/1.43
% 1.73/1.43 % (18246)Memory used [KB]: 5500
% 1.73/1.43 % (18246)Time elapsed: 0.003 s
% 1.73/1.43 % (18246)Instructions burned: 7 (million)
% 1.73/1.43 % (18246)------------------------------
% 1.73/1.43 % (18246)------------------------------
% 1.73/1.44 % (18251)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/779Mi)
% 1.73/1.44 % (18242)Instruction limit reached!
% 1.73/1.44 % (18242)------------------------------
% 1.73/1.44 % (18242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.44 % (18242)Termination reason: Unknown
% 1.73/1.44 % (18242)Termination phase: Saturation
% 1.73/1.44
% 1.73/1.44 % (18242)Memory used [KB]: 5628
% 1.73/1.44 % (18242)Time elapsed: 0.011 s
% 1.73/1.44 % (18242)Instructions burned: 23 (million)
% 1.73/1.44 % (18242)------------------------------
% 1.73/1.44 % (18242)------------------------------
% 1.73/1.44 % (18248)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/377Mi)
% 1.73/1.44 % (18253)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/19Mi)
% 1.73/1.44 % (18254)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/879Mi)
% 1.73/1.44 % (18253)Instruction limit reached!
% 1.73/1.44 % (18253)------------------------------
% 1.73/1.44 % (18253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.44 % (18253)Termination reason: Unknown
% 1.73/1.44 % (18253)Termination phase: Saturation
% 1.73/1.44
% 1.73/1.44 % (18253)Memory used [KB]: 5628
% 1.73/1.44 % (18253)Time elapsed: 0.007 s
% 1.73/1.44 % (18253)Instructions burned: 21 (million)
% 1.73/1.44 % (18253)------------------------------
% 1.73/1.44 % (18253)------------------------------
% 1.73/1.45 % (18258)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/17Mi)
% 1.73/1.45 % (18258)Instruction limit reached!
% 1.73/1.45 % (18258)------------------------------
% 1.73/1.45 % (18258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.45 % (18258)Termination reason: Unknown
% 1.73/1.45 % (18258)Termination phase: Saturation
% 1.73/1.45
% 1.73/1.45 % (18258)Memory used [KB]: 5756
% 1.73/1.45 % (18258)Time elapsed: 0.008 s
% 1.73/1.45 % (18258)Instructions burned: 18 (million)
% 1.73/1.45 % (18258)------------------------------
% 1.73/1.45 % (18258)------------------------------
% 1.73/1.45 % (18264)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_18052 for (2999ds/3Mi)
% 1.73/1.45 % (18264)Instruction limit reached!
% 1.73/1.45 % (18264)------------------------------
% 1.73/1.45 % (18264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.45 % (18264)Termination reason: Unknown
% 1.73/1.45 % (18264)Termination phase: Property scanning
% 1.73/1.45
% 1.73/1.45 % (18264)Memory used [KB]: 1023
% 1.73/1.45 % (18264)Time elapsed: 0.002 s
% 1.73/1.45 % (18264)Instructions burned: 4 (million)
% 1.73/1.45 % (18264)------------------------------
% 1.73/1.45 % (18264)------------------------------
% 1.73/1.46 % (18270)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_18052 for (2998ds/30Mi)
% 1.73/1.46 % (18271)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_18052 for (2998ds/127Mi)
% 1.73/1.46 % (18213)First to succeed.
% 1.73/1.47 % (18270)Refutation not found, incomplete strategy
% 1.73/1.47 % (18270)------------------------------
% 1.73/1.47 % (18270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.47 % (18270)Termination reason: Refutation not found, incomplete strategy
% 1.73/1.47
% 1.73/1.47
% 1.73/1.47 % (18270)Memory used [KB]: 5500
% 1.73/1.47 % (18270)Time elapsed: 0.006 s
% 1.73/1.47 % (18270)Instructions burned: 10 (million)
% 1.73/1.47 % (18270)------------------------------
% 1.73/1.47 % (18270)------------------------------
% 1.73/1.47 % (18213)Refutation found. Thanks to Tanya!
% 1.73/1.47 % SZS status Theorem for DTF2THF_18052
% 1.73/1.47 % SZS output start Proof for DTF2THF_18052
% 1.73/1.47 thf(func_def_0, type, in: $i > $i > $o).
% 1.73/1.47 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.73/1.47 thf(func_def_3, type, setunion: $i > $i).
% 1.73/1.47 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 1.73/1.47 thf(func_def_5, type, iskpair: $i > $o).
% 1.73/1.47 thf(func_def_7, type, kpair: $i > $i > $i).
% 1.73/1.47 thf(func_def_8, type, singleton: $i > $o).
% 1.73/1.47 thf(func_def_9, type, ex1: $i > ($i > $o) > $o).
% 1.73/1.47 thf(func_def_11, type, kfst: $i > $i).
% 1.73/1.47 thf(func_def_30, type, ph1: !>[X0: $tType]:(X0)).
% 1.73/1.47 thf(f303,plain,(
% 1.73/1.47 $false),
% 1.73/1.47 inference(subsumption_resolution,[status(thm)],[f294,f249])).
% 1.73/1.47 thf(f249,plain,(
% 1.73/1.47 (sK5 != sK4)),
% 1.73/1.47 inference(equality_proxy_clausification,[status(thm)],[f241])).
% 1.73/1.47 thf(f241,plain,(
% 1.73/1.47 ((sK4 = sK5) = $false)),
% 1.73/1.47 inference(boolean_simplification,[status(thm)],[f239])).
% 1.73/1.47 thf(f239,plain,(
% 1.73/1.47 (($true => (sK4 = sK5)) = $false)),
% 1.73/1.47 inference(backward_demodulation,[status(thm)],[f210,f237])).
% 1.73/1.47 thf(f237,plain,(
% 1.73/1.47 (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK5 @ emptyset)) @ emptyset)) = sK2) = $true)),
% 1.73/1.47 inference(binary_proxy_clausification,[status(thm)],[f210])).
% 1.73/1.47 thf(f210,plain,(
% 1.73/1.47 ((((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK5 @ emptyset)) @ emptyset)) = sK2) => (sK4 = sK5)) = $false)),
% 1.73/1.47 inference(binary_proxy_clausification,[status(thm)],[f203])).
% 1.73/1.47 thf(f203,plain,(
% 1.73/1.47 (((in @ sK5 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK5 @ emptyset)) @ emptyset)) = sK2) => (sK4 = sK5))) = $false)),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f198])).
% 1.73/1.47 thf(f198,plain,(
% 1.73/1.47 (((^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0)))) @ sK5) = $false)),
% 1.73/1.47 inference(sigma_clausification,[status(thm)],[f182])).
% 1.73/1.47 thf(f182,plain,(
% 1.73/1.47 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0))))))),
% 1.73/1.47 inference(not_proxy_clausification,[status(thm)],[f149])).
% 1.73/1.47 thf(f149,plain,(
% 1.73/1.47 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0)))))) = $true)),
% 1.73/1.47 inference(boolean_simplification,[status(thm)],[f148])).
% 1.73/1.47 thf(f148,plain,(
% 1.73/1.47 ($true = ($true => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0))))))))),
% 1.73/1.47 inference(boolean_simplification,[status(thm)],[f147])).
% 1.73/1.47 thf(f147,plain,(
% 1.73/1.47 (((sK2 = sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0))))))) = $true)),
% 1.73/1.47 inference(forward_demodulation,[status(thm)],[f146,f125])).
% 1.73/1.47 thf(f125,plain,(
% 1.73/1.47 ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2)),
% 1.73/1.47 inference(equality_proxy_clausification,[status(thm)],[f110])).
% 1.73/1.47 thf(f110,plain,(
% 1.73/1.47 (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2) = $true)),
% 1.73/1.47 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.73/1.47 thf(f103,plain,(
% 1.73/1.47 (((in @ sK4 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2)) = $true)),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f102])).
% 1.73/1.47 thf(f102,plain,(
% 1.73/1.47 (((^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2))) @ sK4) = $true)),
% 1.73/1.47 inference(sigma_clausification,[status(thm)],[f101])).
% 1.73/1.47 thf(f101,plain,(
% 1.73/1.47 ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2)))) = $true)),
% 1.73/1.47 inference(boolean_simplification,[status(thm)],[f100])).
% 1.73/1.47 thf(f100,plain,(
% 1.73/1.47 (((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2)))) & $true) = $true)),
% 1.73/1.47 inference(backward_demodulation,[status(thm)],[f97,f98])).
% 1.73/1.47 thf(f98,plain,(
% 1.73/1.47 ((in @ sK3 @ (setunion @ sK2)) = $true)),
% 1.73/1.47 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.73/1.47 thf(f97,plain,(
% 1.73/1.47 (((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2)))) & (in @ sK3 @ (setunion @ sK2))) = $true)),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f96])).
% 1.73/1.47 thf(f96,plain,(
% 1.73/1.47 (((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)))) & (in @ Y0 @ (setunion @ sK2)))) @ sK3) = $true)),
% 1.73/1.47 inference(sigma_clausification,[status(thm)],[f91])).
% 1.73/1.47 thf(f91,plain,(
% 1.73/1.47 ((?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)))) & (in @ Y0 @ (setunion @ sK2))))) = $true)),
% 1.73/1.47 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 1.73/1.47 thf(f89,plain,(
% 1.73/1.47 (((?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)))) & (in @ Y0 @ (setunion @ sK2))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)))) & (in @ Y0 @ (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)))))))) = $false)),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f88])).
% 1.73/1.47 thf(f88,plain,(
% 1.73/1.47 (((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))))) @ sK2) = $false)),
% 1.73/1.47 inference(sigma_clausification,[status(thm)],[f73])).
% 1.73/1.47 thf(f73,plain,(
% 1.73/1.47 ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))))))))) = $false)),
% 1.73/1.47 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.73/1.47 thf(f57,plain,(
% 1.73/1.47 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y3 = Y1)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))))))) = $false)),
% 1.73/1.47 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.73/1.47 thf(f44,plain,(
% 1.73/1.47 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y3 = Y1)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))))))))))) = $false)),
% 1.73/1.47 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.73/1.47 thf(f41,plain,(
% 1.73/1.47 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y0 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y3 = Y1)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))))))))) = $false)),
% 1.73/1.47 inference(not_proxy_clausification,[status(thm)],[f40])).
% 1.73/1.47 thf(f40,plain,(
% 1.73/1.47 ((~ ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y0 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y3 = Y1)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))))))))))))) = $true)),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.73/1.47 thf(f39,plain,(
% 1.73/1.47 ((~ ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y0 @ 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))))))) @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ ((^[Y2 : $i]: ((^[Y3 : $i]: (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))))) @ Y1 @ Y0)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y2 @ Y3) = ((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y0 @ Y1)) => (Y3 = Y1)))))))))) => (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = Y1)))) & (in @ Y2 @ (setunion @ Y1)))))) @ Y0) => ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = Y1) & (in @ Y2 @ Y1))))) @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))))) @ (kfst @ Y0) @ Y1) = Y0))))))))))) = $true)),
% 1.73/1.47 inference(definition_unfolding,[status(thm)],[f32,f37,f38,f35,f34,f27,f28])).
% 1.73/1.47 thf(f28,plain,(
% 1.73/1.47 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 1.73/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 1.73/1.47 thf(f24,plain,(
% 1.73/1.47 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 1.73/1.47 inference(fool_elimination,[status(thm)],[f23])).
% 1.73/1.47 thf(f23,plain,(
% 1.73/1.47 (kpair = (^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))),
% 1.73/1.47 inference(rectify,[status(thm)],[f2])).
% 1.73/1.47 thf(f2,axiom,(
% 1.73/1.47 (kpair = (^[X1 : $i, X2 : $i] : (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))))),
% 1.73/1.47 file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',kpair)).
% 1.73/1.47 thf(f27,plain,(
% 1.73/1.47 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.73/1.47 inference(cnf_transformation,[status(thm)],[f18])).
% 1.73/1.47 thf(f18,plain,(
% 1.73/1.47 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.73/1.47 inference(fool_elimination,[status(thm)],[f17])).
% 1.73/1.47 thf(f17,plain,(
% 1.73/1.47 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 1.73/1.47 inference(rectify,[status(thm)],[f3])).
% 1.73/1.47 thf(f3,axiom,(
% 1.73/1.47 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 1.73/1.47 file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',singleton)).
% 1.73/1.47 thf(f34,plain,(
% 1.73/1.47 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0)))))))),
% 1.73/1.47 inference(cnf_transformation,[status(thm)],[f26])).
% 1.73/1.47 thf(f26,plain,(
% 1.73/1.47 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0)))))))),
% 1.73/1.47 inference(fool_elimination,[status(thm)],[f25])).
% 1.73/1.47 thf(f25,plain,(
% 1.73/1.47 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ (setunion @ X0)) & ? [X2 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0) & (in @ X2 @ (setunion @ X0)))))) = iskpair)),
% 1.73/1.47 inference(rectify,[status(thm)],[f1])).
% 1.73/1.47 thf(f1,axiom,(
% 1.73/1.47 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ (setunion @ X0)) & ? [X2 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0) & (in @ X2 @ (setunion @ X0)))))) = iskpair)),
% 1.73/1.47 file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',iskpair)).
% 1.73/1.47 thf(f35,plain,(
% 1.73/1.47 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y2 @ Y3) = ((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y0 @ Y1)) => (Y3 = Y1)))))))))))),
% 1.73/1.47 inference(definition_unfolding,[status(thm)],[f29,f28,f28])).
% 1.73/1.47 thf(f29,plain,(
% 1.73/1.47 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y3) = (kpair @ Y0 @ Y1)) => (Y3 = Y1)))))))))))),
% 1.73/1.47 inference(cnf_transformation,[status(thm)],[f16])).
% 1.73/1.47 thf(f16,plain,(
% 1.73/1.47 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y3) = (kpair @ Y0 @ Y1)) => (Y3 = Y1)))))))))))),
% 1.73/1.47 inference(fool_elimination,[status(thm)],[f15])).
% 1.73/1.47 thf(f15,plain,(
% 1.73/1.47 (setukpairinjR = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X1 @ X0) = (kpair @ X3 @ X2)) => (X0 = X2)))),
% 1.73/1.47 inference(rectify,[status(thm)],[f7])).
% 1.73/1.47 thf(f7,axiom,(
% 1.73/1.47 (setukpairinjR = ! [X5 : $i,X4 : $i,X2 : $i,X1 : $i] : (((kpair @ X1 @ X2) = (kpair @ X4 @ X5)) => (X2 = X5)))),
% 1.73/1.47 file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',setukpairinjR)).
% 1.73/1.47 thf(f38,plain,(
% 1.73/1.47 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ ((^[Y2 : $i]: ((^[Y3 : $i]: (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))))) @ Y1 @ Y0)) = Y1))))))),
% 1.73/1.47 inference(definition_unfolding,[status(thm)],[f30,f28])).
% 1.73/1.47 thf(f30,plain,(
% 1.73/1.47 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))))),
% 1.73/1.47 inference(cnf_transformation,[status(thm)],[f12])).
% 1.73/1.47 thf(f12,plain,(
% 1.73/1.47 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))))),
% 1.73/1.47 inference(fool_elimination,[status(thm)],[f11])).
% 1.73/1.47 thf(f11,plain,(
% 1.73/1.47 (! [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X0 @ X1)) = X0) = kfstpairEq)),
% 1.73/1.47 inference(rectify,[status(thm)],[f6])).
% 1.73/1.47 thf(f6,axiom,(
% 1.73/1.47 (! [X1 : $i,X2 : $i] : ((kfst @ (kpair @ X1 @ X2)) = X1) = kfstpairEq)),
% 1.73/1.47 file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',kfstpairEq)).
% 1.73/1.47 thf(f37,plain,(
% 1.73/1.47 (ex1I = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y0 @ 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))))))) @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 1.73/1.47 inference(definition_unfolding,[status(thm)],[f33,f36])).
% 1.73/1.47 thf(f36,plain,(
% 1.73/1.47 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.73/1.47 inference(definition_unfolding,[status(thm)],[f31,f27])).
% 1.73/1.47 thf(f31,plain,(
% 1.73/1.47 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.73/1.47 inference(cnf_transformation,[status(thm)],[f22])).
% 1.73/1.47 thf(f22,plain,(
% 1.73/1.47 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.73/1.47 inference(fool_elimination,[status(thm)],[f21])).
% 1.73/1.47 thf(f21,plain,(
% 1.73/1.47 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 1.73/1.47 inference(rectify,[status(thm)],[f4])).
% 1.73/1.47 thf(f4,axiom,(
% 1.73/1.47 (ex1 = (^[X0 : $i, X3 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X1 : $i] : (X3 @ X1))))))),
% 1.73/1.47 file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',ex1)).
% 1.73/1.47 thf(f33,plain,(
% 1.73/1.47 (ex1I = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y0 @ Y3) => (Y1 = Y3))))) => (ex1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 1.73/1.47 inference(cnf_transformation,[status(thm)],[f14])).
% 1.73/1.47 thf(f14,plain,(
% 1.73/1.47 (ex1I = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y0 @ Y3) => (Y1 = Y3))))) => (ex1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 1.73/1.47 inference(fool_elimination,[status(thm)],[f13])).
% 1.73/1.47 thf(f13,plain,(
% 1.73/1.47 (! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ X0) => ((X2 @ X1) => (! [X3 : $i] : ((in @ X3 @ X0) => ((X2 @ X3) => (X1 = X3))) => (ex1 @ X0 @ (^[X4 : $i] : (X2 @ X4)))))) = ex1I)),
% 1.73/1.47 inference(rectify,[status(thm)],[f5])).
% 1.73/1.47 thf(f5,axiom,(
% 1.73/1.47 (! [X0 : $i,X1 : $i,X3 : $i > $o] : ((in @ X1 @ X0) => ((X3 @ X1) => (! [X2 : $i] : ((in @ X2 @ X0) => ((X3 @ X2) => (X1 = X2))) => (ex1 @ X0 @ (^[X2 : $i] : (X3 @ X2)))))) = ex1I)),
% 1.73/1.47 file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',ex1I)).
% 1.73/1.47 thf(f32,plain,(
% 1.73/1.47 ((~ (ex1I => (kfstpairEq => (setukpairinjR => (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))))))) = $true)),
% 1.73/1.47 inference(cnf_transformation,[status(thm)],[f20])).
% 1.73/1.47 thf(f20,plain,(
% 1.73/1.47 ((~ (ex1I => (kfstpairEq => (setukpairinjR => (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))))))) = $true)),
% 1.73/1.47 inference(fool_elimination,[status(thm)],[f19])).
% 1.73/1.47 thf(f19,plain,(
% 1.73/1.47 ~(ex1I => (kfstpairEq => (setukpairinjR => ! [X0 : $i] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (((kpair @ (kfst @ X0) @ X1) = X0)))))))))),
% 1.73/1.47 inference(rectify,[status(thm)],[f9])).
% 1.73/1.47 thf(f9,negated_conjecture,(
% 1.73/1.47 ~(ex1I => (kfstpairEq => (setukpairinjR => ! [X5 : $i] : ((iskpair @ X5) => (singleton @ (dsetconstr @ (setunion @ X5) @ (^[X1 : $i] : (((kpair @ (kfst @ X5) @ X1) = X5)))))))))),
% 1.73/1.47 inference(negated_conjecture,[status(cth)],[f8])).
% 1.73/1.47 thf(f8,conjecture,(
% 1.73/1.47 ex1I => (kfstpairEq => (setukpairinjR => ! [X5 : $i] : ((iskpair @ X5) => (singleton @ (dsetconstr @ (setunion @ X5) @ (^[X1 : $i] : (((kpair @ (kfst @ X5) @ X1) = X5))))))))),
% 1.73/1.47 file('/export/starexec/sandbox2/tmp/tmp.dZVbaxsGCr/DTF2THF_18052.p',ksndsingleton)).
% 1.73/1.47 thf(f146,plain,(
% 1.73/1.47 ((((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0))))))) = $true)),
% 1.73/1.47 inference(forward_demodulation,[status(thm)],[f145,f135])).
% 1.73/1.47 thf(f135,plain,(
% 1.73/1.47 (sK3 = (kfst @ sK2))),
% 1.73/1.47 inference(superposition,[status(thm)],[f67,f125])).
% 1.73/1.47 thf(f67,plain,(
% 1.73/1.47 ( ! [X2 : $i,X1 : $i] : (((kfst @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = X2)) )),
% 1.73/1.47 inference(equality_proxy_clausification,[status(thm)],[f66])).
% 1.73/1.47 thf(f66,plain,(
% 1.73/1.47 ( ! [X2 : $i,X1 : $i] : ((((kfst @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = X2) = $true)) )),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f65])).
% 1.73/1.47 thf(f65,plain,(
% 1.73/1.47 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = Y0)) @ X2) = $true)) )),
% 1.73/1.47 inference(pi_clausification,[status(thm)],[f64])).
% 1.73/1.47 thf(f64,plain,(
% 1.73/1.47 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = Y0))) = $true)) )),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.73/1.47 thf(f63,plain,(
% 1.73/1.47 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y1)))) @ X1) = $true)) )),
% 1.73/1.47 inference(pi_clausification,[status(thm)],[f58])).
% 1.73/1.47 thf(f58,plain,(
% 1.73/1.47 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y1))))))),
% 1.73/1.47 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.73/1.47 thf(f145,plain,(
% 1.73/1.47 ((((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0))))))) = $true)),
% 1.73/1.47 inference(boolean_simplification,[status(thm)],[f144])).
% 1.73/1.47 thf(f144,plain,(
% 1.73/1.47 ((((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0))))) => $false)) = $true)),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f141])).
% 1.73/1.47 thf(f141,plain,(
% 1.73/1.47 ((((^[Y0 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2)) @ sK4) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((^[Y1 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)) @ Y0) => (sK4 = Y0))))) => $false)) = $true)),
% 1.73/1.47 inference(superposition,[status(thm)],[f117,f90])).
% 1.73/1.47 thf(f90,plain,(
% 1.73/1.47 ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)))) & (in @ Y0 @ (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2))))))) = $false)),
% 1.73/1.47 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 1.73/1.47 thf(f117,plain,(
% 1.73/1.47 ( ! [X0 : $i > $o] : ((((X0 @ sK4) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((X0 @ Y0) => (sK4 = Y0))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ (setunion @ sK2) @ X0)) & (in @ Y0 @ (dsetconstr @ (setunion @ sK2) @ X0))))))) = $true)) )),
% 1.73/1.47 inference(boolean_simplification,[status(thm)],[f115])).
% 1.73/1.47 thf(f115,plain,(
% 1.73/1.47 ( ! [X0 : $i > $o] : ((($true => ((X0 @ sK4) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((X0 @ Y0) => (sK4 = Y0))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ (setunion @ sK2) @ X0)) & (in @ Y0 @ (dsetconstr @ (setunion @ sK2) @ X0)))))))) = $true)) )),
% 1.73/1.47 inference(superposition,[status(thm)],[f55,f113])).
% 1.73/1.47 thf(f113,plain,(
% 1.73/1.47 ((in @ sK4 @ (setunion @ sK2)) = $true)),
% 1.73/1.47 inference(boolean_simplification,[status(thm)],[f112])).
% 1.73/1.47 thf(f112,plain,(
% 1.73/1.47 (((in @ sK4 @ (setunion @ sK2)) & $true) = $true)),
% 1.73/1.47 inference(backward_demodulation,[status(thm)],[f103,f110])).
% 1.73/1.47 thf(f55,plain,(
% 1.73/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((in @ X2 @ X3) => ((X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => ((X1 @ Y0) => (X2 = Y0))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X3 @ X1)) & (in @ Y0 @ (dsetconstr @ X3 @ X1)))))))) = $true)) )),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.73/1.47 thf(f54,plain,(
% 1.73/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((in @ X2 @ Y0) => ((X1 @ X2) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ Y1) => (X2 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ Y0 @ X1)) & (in @ Y1 @ (dsetconstr @ Y0 @ X1))))))))) @ X3) = $true)) )),
% 1.73/1.47 inference(pi_clausification,[status(thm)],[f53])).
% 1.73/1.47 thf(f53,plain,(
% 1.73/1.47 ( ! [X2 : $i,X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ Y0) => ((X1 @ X2) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ Y1) => (X2 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ Y0 @ X1)) & (in @ Y1 @ (dsetconstr @ Y0 @ X1)))))))))) = $true)) )),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.73/1.47 thf(f52,plain,(
% 1.73/1.47 ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((X1 @ Y0) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((X1 @ Y2) => (Y0 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ X1)) & (in @ Y2 @ (dsetconstr @ Y1 @ X1))))))))))) @ X2) = $true)) )),
% 1.73/1.47 inference(pi_clausification,[status(thm)],[f51])).
% 1.73/1.47 thf(f51,plain,(
% 1.73/1.47 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((X1 @ Y0) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((X1 @ Y2) => (Y0 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ X1)) & (in @ Y2 @ (dsetconstr @ Y1 @ X1)))))))))))) = $true)) )),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.73/1.47 thf(f50,plain,(
% 1.73/1.47 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y0 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y2 @ Y0))))))))))))) @ X1) = $true)) )),
% 1.73/1.47 inference(pi_clausification,[status(thm)],[f45])).
% 1.73/1.47 thf(f45,plain,(
% 1.73/1.47 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y0 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y2 @ Y0)))))))))))))) = $true)),
% 1.73/1.47 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.73/1.47 thf(f294,plain,(
% 1.73/1.47 (sK5 = sK4)),
% 1.73/1.47 inference(equality_proxy_clausification,[status(thm)],[f282])).
% 1.73/1.47 thf(f282,plain,(
% 1.73/1.47 ((sK5 = sK4) = $true)),
% 1.73/1.47 inference(boolean_simplification,[status(thm)],[f277])).
% 1.73/1.47 thf(f277,plain,(
% 1.73/1.47 (($true => (sK5 = sK4)) = $true)),
% 1.73/1.47 inference(superposition,[status(thm)],[f134,f237])).
% 1.73/1.47 thf(f134,plain,(
% 1.73/1.47 ( ! [X0 : $i,X1 : $i] : (((((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = sK2) => (X1 = sK4)) = $true)) )),
% 1.73/1.47 inference(superposition,[status(thm)],[f86,f125])).
% 1.73/1.47 thf(f86,plain,(
% 1.73/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (X4 = X2)) = $true)) )),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.73/1.47 thf(f85,plain,(
% 1.73/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: (((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (Y0 = X2))) @ X4) = $true)) )),
% 1.73/1.47 inference(pi_clausification,[status(thm)],[f84])).
% 1.73/1.47 thf(f84,plain,(
% 1.73/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (Y0 = X2)))) = $true)) )),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f83])).
% 1.73/1.47 thf(f83,plain,(
% 1.73/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (Y1 = X2))))) @ X3) = $true)) )),
% 1.73/1.47 inference(pi_clausification,[status(thm)],[f82])).
% 1.73/1.47 thf(f82,plain,(
% 1.73/1.47 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (Y1 = X2)))))) = $true)) )),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f81])).
% 1.73/1.47 thf(f81,plain,(
% 1.73/1.47 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y2 = Y0))))))) @ X2) = $true)) )),
% 1.73/1.47 inference(pi_clausification,[status(thm)],[f80])).
% 1.73/1.47 thf(f80,plain,(
% 1.73/1.47 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) = $true)) )),
% 1.73/1.47 inference(beta_eta_normalization,[status(thm)],[f79])).
% 1.73/1.47 thf(f79,plain,(
% 1.73/1.47 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y3 = Y1))))))))) @ X1) = $true)) )),
% 1.73/1.47 inference(pi_clausification,[status(thm)],[f74])).
% 1.73/1.47 thf(f74,plain,(
% 1.73/1.47 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y3 = Y1)))))))))) = $true)),
% 1.73/1.47 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.73/1.47 % SZS output end Proof for DTF2THF_18052
% 1.73/1.47 % (18213)------------------------------
% 1.73/1.47 % (18213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.47 % (18213)Termination reason: Refutation
% 1.73/1.47
% 1.73/1.47 % (18213)Memory used [KB]: 6268
% 1.73/1.47 % (18213)Time elapsed: 0.087 s
% 1.73/1.47 % (18213)Instructions burned: 130 (million)
% 1.73/1.47 % (18213)------------------------------
% 1.73/1.47 % (18213)------------------------------
% 1.73/1.47 % (18198)Success in time 0.122 s
%------------------------------------------------------------------------------