%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU686^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:24 AM UTC 2026
% Result : Theorem 1.72s 1.39s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 8
% Syntax : Number of formulae : 118 ( 115 unt; 0 typ; 0 def)
% Number of atoms : 1578 ( 232 equ; 0 cnn)
% Maximal formula atoms : 8 ( 13 avg)
% Number of connectives : 3655 ( 7 ~; 0 |; 105 &;2852 @)
% ( 0 <=>; 367 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 21 usr; 13 con; 0-4 aty)
% ( 265 !!; 59 ??; 0 @@+; 0 @@-)
% Number of variables : 635 ( 550 ^; 83 !; 2 ?; 635 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_10,type,
breln: $i > $i > $i > $o ).
thf(func_def_11,type,
func: $i > $i > $i > $o ).
thf(func_def_12,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_32,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f209,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f205,f141]) ).
thf(f141,plain,
( ( ap @ sK3 @ sK2 @ sK4 @ sK5 )
!= sK6 ),
inference(equality_proxy_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
( ( ( ap @ sK3 @ sK2 @ sK4 @ sK5 )
= sK6 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( ( in @ ( kpair @ sK5 @ sK6 ) @ sK4 )
=> ( ( ap @ sK3 @ sK2 @ sK4 @ sK5 )
= sK6 ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( ( in @ sK6 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ sK6 ) @ sK4 )
=> ( ( ap @ sK3 @ sK2 @ sK4 @ sK5 )
= sK6 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 ) @ sK4 )
=> ( ( ap @ sK3 @ sK2 @ sK4 @ sK5 )
= Y0 ) ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 ) @ sK4 )
=> ( ( ap @ sK3 @ sK2 @ sK4 @ sK5 )
= Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
( ( ( in @ sK5 @ sK3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 ) @ sK4 )
=> ( ( ap @ sK3 @ sK2 @ sK4 @ sK5 )
= Y0 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f90]) ).
thf(f90,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ sK4 )
=> ( ( ap @ sK3 @ sK2 @ sK4 @ Y0 )
= Y1 ) ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ sK4 )
=> ( ( ap @ sK3 @ sK2 @ sK4 @ Y0 )
= Y1 ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ sK4 )
=> ( ( ap @ sK3 @ sK2 @ sK4 @ Y0 )
= Y1 ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f85,f87]) ).
thf(f87,plain,
( $true
= ( ( subset @ sK4 @ ( cartprod @ sK3 @ sK2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK4 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK4 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
( ( ( ( subset @ sK4 @ ( cartprod @ sK3 @ sK2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK4 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK4 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ sK4 )
=> ( ( ap @ sK3 @ sK2 @ sK4 @ Y0 )
= Y1 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,plain,
( ( ^ [Y0: $i] :
( ( ( subset @ Y0 @ ( cartprod @ sK3 @ sK2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ sK2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 )
=> ( ( ap @ sK3 @ sK2 @ Y0 @ Y1 )
= Y2 ) ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( subset @ Y0 @ ( cartprod @ sK3 @ sK2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ sK2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 )
=> ( ( ap @ sK3 @ sK2 @ Y0 @ Y1 )
= Y2 ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ Y1 @ ( cartprod @ Y0 @ sK2 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ sK2
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ sK2 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 )
=> ( ( ap @ Y0 @ sK2 @ Y1 @ Y2 )
= Y3 ) ) ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ Y1 @ ( cartprod @ Y0 @ sK2 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ sK2
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ sK2 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 )
=> ( ( ap @ Y0 @ sK2 @ Y1 @ Y2 )
= Y3 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y1 @ Y0 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y1 @ Y0 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y1 @ Y0 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y1 @ Y0 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y1 @ Y0 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y1 @ Y0 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y1 @ Y0 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y1 @ Y0 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f42,f46]) ).
thf(f46,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y1 @ ( cartprod @ Y0 @ Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y2
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y2
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y1 @ ( cartprod @ Y0 @ Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y2
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y2
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y1 @ Y0 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y1 @ Y0 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y1 @ ( cartprod @ Y0 @ Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y2
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y2
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y1 @ Y0 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y1 @ Y0 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y0
@ Y2
@ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ^ [Y2: $i,Y3: $i > $o] :
( ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y4 )
& ( ( setadjoin @ Y5 @ emptyset )
= Y4 ) ) )
@ ( dsetconstr @ Y2
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
@ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y1
@ Y0
@ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y1 @ Y0 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y1
@ Y0
@ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y1 @ Y0 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f30,f37,f38,f39,f36]) ).
thf(f36,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( in @ Y7 @ Y6 )
& ( ( setadjoin @ Y7 @ emptyset )
= Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f28,f32,f35]) ).
thf(f35,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( setadjoin @ Y3 @ emptyset )
= Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f27,f33]) ).
thf(f33,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= X0 )
& ( in @ X1 @ X0 ) ) )
= singleton ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= X0 )
& ( in @ X1 @ X0 ) ) )
= singleton ),
file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',singleton) ).
thf(f27,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ex1
= ( ^ [X0: $i,X2: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X1: $i] : ( X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',ex1) ).
thf(f32,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i,X3: $i,X4: $i] : ( subset @ X4 @ ( cartprod @ X0 @ X3 ) ) )
= breln ),
file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',breln) ).
thf(f28,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( func
= ( ^ [X0: $i,X3: $i,X5: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( ex1 @ X3
@ ^ [X6: $i] : ( in @ ( kpair @ X1 @ X6 ) @ X5 ) ) )
& ( breln @ X0 @ X3 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',func) ).
thf(f39,plain,
( funcGraphProp1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y1
@ Y0
@ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y1 @ Y0 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f31,f36]) ).
thf(f31,plain,
( funcGraphProp1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y1 @ Y0 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( funcGraphProp1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y1 @ Y0 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X3 @ ( ap @ X1 @ X2 @ X0 @ X3 ) ) @ X0 ) ) )
= funcGraphProp1 ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X7: $i,X0: $i,X3: $i] :
( ( ( func @ X0 @ X3 @ X7 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( kpair @ X1 @ ( ap @ X0 @ X3 @ X7 @ X1 ) ) @ X7 ) ) )
= funcGraphProp1 ),
file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',funcGraphProp1) ).
thf(f38,plain,
( ex1E2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ^ [Y2: $i,Y3: $i > $o] :
( ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y4 )
& ( ( setadjoin @ Y5 @ emptyset )
= Y4 ) ) )
@ ( dsetconstr @ Y2
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
@ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f34,f35]) ).
thf(f34,plain,
( ex1E2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ex1 @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ex1E2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ex1 @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
( ex1E2
= ( ! [X0: $i > $o,X1: $i] :
( ( ex1 @ X1
@ ^ [X2: $i] : ( X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X0 @ X3 )
=> ( ( X0 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ex1E2
= ( ! [X2: $i > $o,X0: $i] :
( ( ex1 @ X0
@ ^ [X1: $i] : ( X2 @ X1 ) )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( X2 @ X1 )
=> ( ( X2 @ X6 )
=> ( X1 = X6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',ex1E2) ).
thf(f37,plain,
( app
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y0
@ Y2
@ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f29,f36]) ).
thf(f29,plain,
( app
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( app
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( app
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X2 @ X0 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( ap @ X2 @ X0 @ X1 @ X3 ) @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( app
= ( ! [X3: $i,X7: $i,X0: $i] :
( ( func @ X0 @ X3 @ X7 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( ap @ X0 @ X3 @ X7 @ X1 ) @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',app) ).
thf(f30,plain,
( ( ~ ( app
=> ( ex1E2
=> ( funcGraphProp1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y1 @ Y0 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ~ ( app
=> ( ex1E2
=> ( funcGraphProp1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y1 @ Y0 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( app
=> ( ex1E2
=> ( funcGraphProp1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X1 @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
=> ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ( app
=> ( ex1E2
=> ( funcGraphProp1
=> ! [X7: $i,X0: $i,X3: $i] :
( ( func @ X0 @ X3 @ X7 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X6 ) @ X7 )
=> ( ( ap @ X0 @ X3 @ X7 @ X1 )
= X6 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
( app
=> ( ex1E2
=> ( funcGraphProp1
=> ! [X7: $i,X0: $i,X3: $i] :
( ( func @ X0 @ X3 @ X7 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X6 ) @ X7 )
=> ( ( ap @ X0 @ X3 @ X7 @ X1 )
= X6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',funcGraphProp2) ).
thf(f205,plain,
( ( ap @ sK3 @ sK2 @ sK4 @ sK5 )
= sK6 ),
inference(equality_proxy_clausification,[status(thm)],[f202]) ).
thf(f202,plain,
( ( sK6
= ( ap @ sK3 @ sK2 @ sK4 @ sK5 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f201]) ).
thf(f201,plain,
( $true
= ( $true
=> ( sK6
= ( ap @ sK3 @ sK2 @ sK4 @ sK5 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f200,f134]) ).
thf(f134,plain,
( ( in @ ( ap @ sK3 @ sK2 @ sK4 @ sK5 ) @ sK2 )
= $true ),
inference(boolean_simplification,[status(thm)],[f133]) ).
thf(f133,plain,
( $true
= ( $true
=> ( in @ ( ap @ sK3 @ sK2 @ sK4 @ sK5 ) @ sK2 ) ) ),
inference(superposition,[status(thm)],[f131,f93]) ).
thf(f93,plain,
( ( in @ sK5 @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f131,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK3 )
=> ( in @ ( ap @ sK3 @ sK2 @ sK4 @ X1 ) @ sK2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f128]) ).
thf(f128,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in @ ( ap @ sK3 @ sK2 @ sK4 @ Y0 ) @ sK2 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in @ ( ap @ sK3 @ sK2 @ sK4 @ Y0 ) @ sK2 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f109]) ).
thf(f109,plain,
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in @ ( ap @ sK3 @ sK2 @ sK4 @ Y0 ) @ sK2 ) ) ) ) ),
inference(superposition,[status(thm)],[f65,f87]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( subset @ X2 @ ( cartprod @ X1 @ X3 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X3
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X3
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ ( ap @ X1 @ X3 @ X2 @ Y0 ) @ X3 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( subset @ X2 @ ( cartprod @ X1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X2 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ ( ap @ X1 @ Y0 @ X2 @ Y1 ) @ Y0 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( subset @ X2 @ ( cartprod @ X1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X2 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ ( ap @ X1 @ Y0 @ X2 @ Y1 ) @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ Y0 @ ( cartprod @ X1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y0 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( in @ ( ap @ X1 @ Y1 @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ Y0 @ ( cartprod @ X1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y0 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( in @ ( ap @ X1 @ Y1 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y1 @ ( cartprod @ Y0 @ Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y2
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y2
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y2 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f46]) ).
thf(f200,plain,
( ( ( in @ ( ap @ sK3 @ sK2 @ sK4 @ sK5 ) @ sK2 )
=> ( sK6
= ( ap @ sK3 @ sK2 @ sK4 @ sK5 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f190]) ).
thf(f190,plain,
( ( ( in @ ( ap @ sK3 @ sK2 @ sK4 @ sK5 ) @ sK2 )
=> ( $true
=> ( sK6
= ( ap @ sK3 @ sK2 @ sK4 @ sK5 ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f187,f144]) ).
thf(f144,plain,
( ( in @ ( kpair @ sK5 @ ( ap @ sK3 @ sK2 @ sK4 @ sK5 ) ) @ sK4 )
= $true ),
inference(boolean_simplification,[status(thm)],[f143]) ).
thf(f143,plain,
( $true
= ( $true
=> ( in @ ( kpair @ sK5 @ ( ap @ sK3 @ sK2 @ sK4 @ sK5 ) ) @ sK4 ) ) ),
inference(superposition,[status(thm)],[f139,f93]) ).
thf(f139,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK3 )
=> ( in @ ( kpair @ X1 @ ( ap @ sK3 @ sK2 @ sK4 @ X1 ) ) @ sK4 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f137]) ).
thf(f137,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in @ ( kpair @ Y0 @ ( ap @ sK3 @ sK2 @ sK4 @ Y0 ) ) @ sK4 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in @ ( kpair @ Y0 @ ( ap @ sK3 @ sK2 @ sK4 @ Y0 ) ) @ sK4 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f108]) ).
thf(f108,plain,
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in @ ( kpair @ Y0 @ ( ap @ sK3 @ sK2 @ sK4 @ Y0 ) ) @ sK4 ) ) ) ) ),
inference(superposition,[status(thm)],[f78,f87]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( subset @ X3 @ ( cartprod @ X2 @ X1 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X3 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X1 @ X3 @ Y0 ) ) @ X3 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( subset @ Y0 @ ( cartprod @ X2 @ X1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X1
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( kpair @ Y1 @ ( ap @ X2 @ X1 @ Y0 @ Y1 ) ) @ Y0 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( subset @ Y0 @ ( cartprod @ X2 @ X1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X1
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( kpair @ Y1 @ ( ap @ X2 @ X1 @ Y0 @ Y1 ) ) @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ Y1 @ ( cartprod @ Y0 @ X1 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ X1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( kpair @ Y2 @ ( ap @ Y0 @ X1 @ Y1 @ Y2 ) ) @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ Y1 @ ( cartprod @ Y0 @ X1 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ X1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( kpair @ Y2 @ ( ap @ Y0 @ X1 @ Y1 @ Y2 ) ) @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y1 @ Y0 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y1 @ Y0 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f187,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ X1 ) @ sK4 )
=> ( sK6 = X1 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f186]) ).
thf(f186,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK2 )
=> ( $true
=> ( ( in @ ( kpair @ sK5 @ X1 ) @ sK4 )
=> ( sK6 = X1 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f185,f123]) ).
thf(f123,plain,
( ( in @ ( kpair @ sK5 @ sK6 ) @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f185,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ sK6 ) @ sK4 )
=> ( ( in @ ( kpair @ sK5 @ X1 ) @ sK4 )
=> ( sK6 = X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f182]) ).
thf(f182,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ sK6 ) @ sK4 )
=> ( ( in @ ( kpair @ sK5 @ Y0 ) @ sK4 )
=> ( sK6 = Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f180]) ).
thf(f180,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ sK6 ) @ sK4 )
=> ( ( in @ ( kpair @ sK5 @ Y0 ) @ sK4 )
=> ( sK6 = Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f178]) ).
thf(f178,plain,
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ sK6 ) @ sK4 )
=> ( ( in @ ( kpair @ sK5 @ Y0 ) @ sK4 )
=> ( sK6 = Y0 ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f176,f101]) ).
thf(f101,plain,
( ( in @ sK6 @ sK2 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f176,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ X1 ) @ sK4 )
=> ( ( in @ ( kpair @ sK5 @ Y0 ) @ sK4 )
=> ( X1 = Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f175]) ).
thf(f175,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 ) @ sK4 )
=> ( ( in @ ( kpair @ sK5 @ Y1 ) @ sK4 )
=> ( Y0 = Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f165]) ).
thf(f165,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 ) @ sK4 )
=> ( ( in @ ( kpair @ sK5 @ Y1 ) @ sK4 )
=> ( Y0 = Y1 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f164]) ).
thf(f164,plain,
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 ) @ sK4 )
=> ( ( in @ ( kpair @ sK5 @ Y1 ) @ sK4 )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f162]) ).
thf(f162,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( ^ [Y2: $i] : ( in @ ( kpair @ sK5 @ Y2 ) @ sK4 )
@ Y0 )
=> ( ( ^ [Y2: $i] : ( in @ ( kpair @ sK5 @ Y2 ) @ sK4 )
@ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f58,f159]) ).
thf(f159,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ sK5 @ Y1 ) @ sK4 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ sK5 @ Y1 ) @ sK4 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f158]) ).
thf(f158,plain,
( ( $true
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ sK5 @ Y1 ) @ sK4 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ sK5 @ Y1 ) @ sK4 ) ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f150,f93]) ).
thf(f150,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK3 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK4 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK4 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f145]) ).
thf(f145,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK4 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK4 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK4 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK4 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f58,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1 @ X2 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( X2 @ Y0 )
=> ( ( X2 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1 @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1 @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU686^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n008.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:30:54 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU686^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : Functions - Extensionality and Beta Reduction
% 0.20/0.46 % Version : Especial > Reduced > Especial.
% 0.20/0.46 % English : (! A:i.! B:i.! f:i.func A B f -> (! x:i.in x A ->
% 0.20/0.46 % (! y:i.in y B -> in (kpair x y) f -> ap A B f x = y)))
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.46 % Source : [Bro08]
% 0.20/0.46 % Names : ZFC188l [Bro08]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0, 0.67 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 23 ( 7 unt; 15 typ; 7 def)
% 0.20/0.46 % Number of atoms : 40 ( 10 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 8 ( 5 avg)
% 0.20/0.46 % Number of connectives : 90 ( 0 ~; 0 |; 2 &; 71 @)
% 0.20/0.46 % ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 17 ( 3 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 16 ( 15 usr; 4 con; 0-4 aty)
% 0.20/0.46 % Number of variables : 31 ( 12 ^; 18 !; 1 ?; 31 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : http://mathgate.info/detsetitem.php?id=242
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(in_type,type,
% 0.20/0.46 in: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset_type,type,
% 0.20/0.46 emptyset: $i ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin_type,type,
% 0.20/0.46 setadjoin: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr_type,type,
% 0.20/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(subset_type,type,
% 0.20/0.46 subset: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(kpair_type,type,
% 0.20/0.46 kpair: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(cartprod_type,type,
% 0.20/0.46 cartprod: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(singleton_type,type,
% 0.20/0.46 singleton: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(singleton,definition,
% 0.20/0.46 ( singleton
% 0.20/0.46 = ( ^ [A: $i] :
% 0.20/0.46 ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( A
% 0.20/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1_type,type,
% 0.20/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1,definition,
% 0.20/0.46 ( ex1
% 0.20/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( singleton
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(breln_type,type,
% 0.20/0.46 breln: $i > $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(breln,definition,
% 0.20/0.46 ( breln
% 0.20/0.46 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(func_type,type,
% 0.20/0.46 func: $i > $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(func,definition,
% 0.20/0.46 ( func
% 0.20/0.46 = ( ^ [A: $i,B: $i,R: $i] :
% 0.20/0.46 ( ( breln @ A @ B @ R )
% 0.20/0.46 & ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ex1 @ B
% 0.20/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ap_type,type,
% 0.20/0.46 ap: $i > $i > $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(app_type,type,
% 0.20/0.46 app: $o ).
% 0.20/0.46
% 0.20/0.46 thf(app,definition,
% 0.20/0.46 ( app
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1E2_type,type,
% 0.20/0.46 ex1E2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1E2,definition,
% 0.20/0.46 ( ex1E2
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ( ex1 @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp1_type,type,
% 0.20/0.46 funcGraphProp1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp1,definition,
% 0.20/0.46 ( funcGraphProp1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp2,conjecture,
% 0.20/0.46 ( app
% 0.20/0.46 => ( ex1E2
% 0.20/0.46 => ( funcGraphProp1
% 0.20/0.46 => ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = Xy ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.52/1.29 ---- Embedded in THF ---
% 1.52/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.29 %%% Generated on Tue Feb 24 12:30:55 EST 2026
% 1.52/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.29 %%% Logic specification used:
% 1.52/1.29 %%% thf(spec, logic, $$dhol).
% 1.52/1.29
% 1.52/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2DTF3314.p
% See solution above
% 1.52/1.29 ------------------------
% 1.72/1.30 ---- Cleaned THF ---
% 1.72/1.30 thf(in_type,type,
% 1.72/1.30 in: $i > $i > $o ).
% 1.72/1.30
% 1.72/1.30 thf(emptyset_type,type,
% 1.72/1.30 emptyset: $i ).
% 1.72/1.30
% 1.72/1.30 thf(setadjoin_type,type,
% 1.72/1.30 setadjoin: $i > $i > $i ).
% 1.72/1.30
% 1.72/1.30 thf(dsetconstr_type,type,
% 1.72/1.30 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.72/1.30
% 1.72/1.30 thf(subset_type,type,
% 1.72/1.30 subset: $i > $i > $o ).
% 1.72/1.30
% 1.72/1.30 thf(kpair_type,type,
% 1.72/1.30 kpair: $i > $i > $i ).
% 1.72/1.30
% 1.72/1.30 thf(cartprod_type,type,
% 1.72/1.30 cartprod: $i > $i > $i ).
% 1.72/1.30
% 1.72/1.30 thf(singleton_type,type,
% 1.72/1.30 singleton: $i > $o ).
% 1.72/1.30
% 1.72/1.30 thf(singleton,definition,
% 1.72/1.30 ( singleton
% 1.72/1.30 = ( ^ [A: $i] :
% 1.72/1.30 ? [Xx: $i] :
% 1.72/1.30 ( ( in @ Xx @ A )
% 1.72/1.30 & ( A
% 1.72/1.30 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.72/1.30
% 1.72/1.30 thf(ex1_type,type,
% 1.72/1.30 ex1: $i > ( $i > $o ) > $o ).
% 1.72/1.30
% 1.72/1.30 thf(ex1,definition,
% 1.72/1.30 ( ex1
% 1.72/1.30 = ( ^ [A: $i,Xphi: $i > $o] :
% 1.72/1.30 ( singleton
% 1.72/1.30 @ ( dsetconstr @ A
% 1.72/1.30 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.72/1.30
% 1.72/1.30 thf(breln_type,type,
% 1.72/1.30 breln: $i > $i > $i > $o ).
% 1.72/1.30
% 1.72/1.30 thf(breln,definition,
% 1.72/1.30 ( breln
% 1.72/1.30 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.72/1.30
% 1.72/1.30 thf(func_type,type,
% 1.72/1.30 func: $i > $i > $i > $o ).
% 1.72/1.30
% 1.72/1.30 thf(func,definition,
% 1.72/1.30 ( func
% 1.72/1.30 = ( ^ [A: $i,B: $i,R: $i] :
% 1.72/1.30 ( ( breln @ A @ B @ R )
% 1.72/1.30 & ! [Xx: $i] :
% 1.72/1.30 ( ( in @ Xx @ A )
% 1.72/1.30 => ( ex1 @ B
% 1.72/1.30 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 1.72/1.30
% 1.72/1.30 thf(ap_type,type,
% 1.72/1.30 ap: $i > $i > $i > $i > $i ).
% 1.72/1.30
% 1.72/1.30 thf(app_type,type,
% 1.72/1.30 app: $o ).
% 1.72/1.30
% 1.72/1.30 thf(app,definition,
% 1.72/1.30 ( app
% 1.72/1.30 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.72/1.30 ( ( func @ A @ B @ Xf )
% 1.72/1.30 => ! [Xx: $i] :
% 1.72/1.30 ( ( in @ Xx @ A )
% 1.72/1.30 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 1.72/1.30
% 1.72/1.30 thf(ex1E2_type,type,
% 1.72/1.30 ex1E2: $o ).
% 1.72/1.30
% 1.72/1.30 thf(ex1E2,definition,
% 1.72/1.30 ( ex1E2
% 1.72/1.30 = ( ! [A: $i,Xphi: $i > $o] :
% 1.72/1.30 ( ( ex1 @ A
% 1.72/1.30 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.72/1.30 => ! [Xx: $i] :
% 1.72/1.30 ( ( in @ Xx @ A )
% 1.72/1.30 => ! [Xy: $i] :
% 1.72/1.30 ( ( in @ Xy @ A )
% 1.72/1.30 => ( ( Xphi @ Xx )
% 1.72/1.30 => ( ( Xphi @ Xy )
% 1.72/1.30 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 1.72/1.30
% 1.72/1.30 thf(funcGraphProp1_type,type,
% 1.72/1.30 funcGraphProp1: $o ).
% 1.72/1.30
% 1.72/1.30 thf(funcGraphProp1,definition,
% 1.72/1.30 ( funcGraphProp1
% 1.72/1.30 = ( ! [A: $i,B: $i,Xf: $i] :
% 1.72/1.30 ( ( func @ A @ B @ Xf )
% 1.72/1.30 => ! [Xx: $i] :
% 1.72/1.30 ( ( in @ Xx @ A )
% 1.72/1.30 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 1.72/1.30
% 1.72/1.30 thf(funcGraphProp2,conjecture,
% 1.72/1.30 ( app
% 1.72/1.30 => ( ex1E2
% 1.72/1.30 => ( funcGraphProp1
% 1.72/1.30 => ! [A: $i,B: $i,Xf: $i] :
% 1.72/1.30 ( ( func @ A @ B @ Xf )
% 1.72/1.30 => ! [Xx: $i] :
% 1.72/1.30 ( ( in @ Xx @ A )
% 1.72/1.30 => ! [Xy: $i] :
% 1.72/1.30 ( ( in @ Xy @ B )
% 1.72/1.30 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 1.72/1.30 => ( ( ap @ A @ B @ Xf @ Xx )
% 1.72/1.30 = Xy ) ) ) ) ) ) ) ) ).
% 1.72/1.30 ------------------------
% 1.72/1.32 % (3508)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_3314 for (2999ds/2Mi)
% 1.72/1.32 % (3508)Instruction limit reached!
% 1.72/1.32 % (3508)------------------------------
% 1.72/1.32 % (3508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.32 % (3508)Termination reason: Unknown
% 1.72/1.32 % (3508)Termination phase: Property scanning
% 1.72/1.32
% 1.72/1.32 % (3508)Memory used [KB]: 1023
% 1.72/1.32 % (3508)Time elapsed: 0.002 s
% 1.72/1.32 % (3508)Instructions burned: 3 (million)
% 1.72/1.32 % (3508)------------------------------
% 1.72/1.32 % (3508)------------------------------
% 1.72/1.32 % (3507)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3314 for (2999ds/2Mi)
% 1.72/1.32 % (3507)Instruction limit reached!
% 1.72/1.32 % (3507)------------------------------
% 1.72/1.32 % (3507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.32 % (3507)Termination reason: Unknown
% 1.72/1.32 % (3507)Termination phase: Property scanning
% 1.72/1.32
% 1.72/1.32 % (3507)Memory used [KB]: 1023
% 1.72/1.32 % (3507)Time elapsed: 0.002 s
% 1.72/1.32 % (3507)Instructions burned: 4 (million)
% 1.72/1.32 % (3507)------------------------------
% 1.72/1.32 % (3507)------------------------------
% 1.72/1.32 % (3506)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_3314 for (2999ds/27Mi)
% 1.72/1.32 % (3510)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3314 for (2999ds/18Mi)
% 1.72/1.32 % (3504)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3314 for (2999ds/183Mi)
% 1.72/1.32 % (3509)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_3314 for (2999ds/275Mi)
% 1.72/1.33 % (3511)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3314 for (2999ds/3Mi)
% 1.72/1.33 % (3509)Refutation not found, incomplete strategy
% 1.72/1.33 % (3509)------------------------------
% 1.72/1.33 % (3509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.33 % (3509)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.33
% 1.72/1.33
% 1.72/1.33 % (3509)Memory used [KB]: 5628
% 1.72/1.33 % (3509)Time elapsed: 0.006 s
% 1.72/1.33 % (3509)Instructions burned: 7 (million)
% 1.72/1.33 % (3509)------------------------------
% 1.72/1.33 % (3509)------------------------------
% 1.72/1.33 % (3511)Instruction limit reached!
% 1.72/1.33 % (3511)------------------------------
% 1.72/1.33 % (3511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.33 % (3511)Termination reason: Unknown
% 1.72/1.33 % (3511)Termination phase: Function definition elimination
% 1.72/1.33
% 1.72/1.33 % (3511)Memory used [KB]: 1023
% 1.72/1.33 % (3511)Time elapsed: 0.003 s
% 1.72/1.33 % (3511)Instructions burned: 4 (million)
% 1.72/1.33 % (3511)------------------------------
% 1.72/1.33 % (3511)------------------------------
% 1.72/1.33 % (3512)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_3314 for (2999ds/37Mi)
% 1.72/1.33 % (3510)Instruction limit reached!
% 1.72/1.33 % (3510)------------------------------
% 1.72/1.33 % (3510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.33 % (3510)Termination reason: Unknown
% 1.72/1.33 % (3510)Termination phase: Saturation
% 1.72/1.33
% 1.72/1.33 % (3510)Memory used [KB]: 5756
% 1.72/1.33 % (3510)Time elapsed: 0.012 s
% 1.72/1.33 % (3510)Instructions burned: 19 (million)
% 1.72/1.33 % (3510)------------------------------
% 1.72/1.33 % (3510)------------------------------
% 1.72/1.33 % (3505)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_3314 for (2999ds/4Mi)
% 1.72/1.34 % (3506)Instruction limit reached!
% 1.72/1.34 % (3506)------------------------------
% 1.72/1.34 % (3506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.34 % (3506)Termination reason: Unknown
% 1.72/1.34 % (3506)Termination phase: Saturation
% 1.72/1.34
% 1.72/1.34 % (3506)Memory used [KB]: 5756
% 1.72/1.34 % (3506)Time elapsed: 0.016 s
% 1.72/1.34 % (3506)Instructions burned: 28 (million)
% 1.72/1.34 % (3506)------------------------------
% 1.72/1.34 % (3506)------------------------------
% 1.72/1.34 % (3505)Instruction limit reached!
% 1.72/1.34 % (3505)------------------------------
% 1.72/1.34 % (3505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.34 % (3505)Termination reason: Unknown
% 1.72/1.34 % (3505)Termination phase: Property scanning
% 1.72/1.34
% 1.72/1.34 % (3505)Memory used [KB]: 1023
% 1.72/1.34 % (3505)Time elapsed: 0.006 s
% 1.72/1.34 % (3505)Instructions burned: 4 (million)
% 1.72/1.34 % (3505)------------------------------
% 1.72/1.34 % (3505)------------------------------
% 1.72/1.34 % (3514)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_3314 for (2999ds/3Mi)
% 1.72/1.34 % (3514)Instruction limit reached!
% 1.72/1.34 % (3514)------------------------------
% 1.72/1.34 % (3514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.34 % (3514)Termination reason: Unknown
% 1.72/1.34 % (3514)Termination phase: Property scanning
% 1.72/1.34
% 1.72/1.34 % (3514)Memory used [KB]: 1023
% 1.72/1.34 % (3514)Time elapsed: 0.003 s
% 1.72/1.34 % (3514)Instructions burned: 4 (million)
% 1.72/1.34 % (3514)------------------------------
% 1.72/1.34 % (3514)------------------------------
% 1.72/1.34 % (3512)Instruction limit reached!
% 1.72/1.34 % (3512)------------------------------
% 1.72/1.34 % (3512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.34 % (3512)Termination reason: Unknown
% 1.72/1.34 % (3512)Termination phase: Saturation
% 1.72/1.34
% 1.72/1.34 % (3512)Memory used [KB]: 5756
% 1.72/1.34 % (3512)Time elapsed: 0.012 s
% 1.72/1.34 % (3512)Instructions burned: 39 (million)
% 1.72/1.34 % (3512)------------------------------
% 1.72/1.34 % (3512)------------------------------
% 1.72/1.35 % (3515)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_3314 for (2999ds/1041Mi)
% 1.72/1.35 % (3519)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_3314 for (2999ds/3Mi)
% 1.72/1.35 % (3518)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_3314 for (2999ds/3Mi)
% 1.72/1.35 % (3519)Instruction limit reached!
% 1.72/1.35 % (3519)------------------------------
% 1.72/1.35 % (3519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.35 % (3519)Termination reason: Unknown
% 1.72/1.35 % (3519)Termination phase: Property scanning
% 1.72/1.35
% 1.72/1.35 % (3519)Memory used [KB]: 1023
% 1.72/1.35 % (3519)Time elapsed: 0.002 s
% 1.72/1.35 % (3519)Instructions burned: 4 (million)
% 1.72/1.35 % (3519)------------------------------
% 1.72/1.35 % (3519)------------------------------
% 1.72/1.35 % (3518)Instruction limit reached!
% 1.72/1.35 % (3518)------------------------------
% 1.72/1.35 % (3518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.35 % (3518)Termination reason: Unknown
% 1.72/1.35 % (3518)Termination phase: Property scanning
% 1.72/1.35
% 1.72/1.35 % (3518)Memory used [KB]: 1023
% 1.72/1.35 % (3518)Time elapsed: 0.003 s
% 1.72/1.35 % (3518)Instructions burned: 4 (million)
% 1.72/1.35 % (3518)------------------------------
% 1.72/1.35 % (3518)------------------------------
% 1.72/1.35 % (3517)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3314 for (2999ds/16Mi)
% 1.72/1.36 % (3513)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_3314 for (2999ds/15Mi)
% 1.72/1.36 % (3520)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3314 for (2999ds/7Mi)
% 1.72/1.36 % (3521)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3314 for (2999ds/3Mi)
% 1.72/1.36 % (3517)Instruction limit reached!
% 1.72/1.36 % (3517)------------------------------
% 1.72/1.36 % (3517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.36 % (3517)Termination reason: Unknown
% 1.72/1.36 % (3517)Termination phase: Saturation
% 1.72/1.36
% 1.72/1.36 % (3517)Memory used [KB]: 6140
% 1.72/1.36 % (3517)Time elapsed: 0.011 s
% 1.72/1.36 % (3517)Instructions burned: 17 (million)
% 1.72/1.36 % (3517)------------------------------
% 1.72/1.36 % (3517)------------------------------
% 1.72/1.36 % (3520)Instruction limit reached!
% 1.72/1.36 % (3520)------------------------------
% 1.72/1.36 % (3520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.36 % (3520)Termination reason: Unknown
% 1.72/1.36 % (3520)Termination phase: Saturation
% 1.72/1.36
% 1.72/1.36 % (3520)Memory used [KB]: 5500
% 1.72/1.36 % (3520)Time elapsed: 0.003 s
% 1.72/1.36 % (3520)Instructions burned: 7 (million)
% 1.72/1.36 % (3520)------------------------------
% 1.72/1.36 % (3520)------------------------------
% 1.72/1.36 % (3521)Instruction limit reached!
% 1.72/1.36 % (3521)------------------------------
% 1.72/1.36 % (3521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.36 % (3521)Termination reason: Unknown
% 1.72/1.36 % (3521)Termination phase: Function definition elimination
% 1.72/1.36
% 1.72/1.36 % (3521)Memory used [KB]: 1023
% 1.72/1.36 % (3521)Time elapsed: 0.003 s
% 1.72/1.36 % (3521)Instructions burned: 4 (million)
% 1.72/1.36 % (3521)------------------------------
% 1.72/1.36 % (3521)------------------------------
% 1.72/1.37 % (3516)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3314 for (2999ds/7Mi)
% 1.72/1.37 % (3523)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3314 for (2999ds/18Mi)
% 1.72/1.37 % (3513)Instruction limit reached!
% 1.72/1.37 % (3513)------------------------------
% 1.72/1.37 % (3513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.37 % (3513)Termination reason: Unknown
% 1.72/1.37 % (3513)Termination phase: Saturation
% 1.72/1.37
% 1.72/1.37 % (3513)Memory used [KB]: 5756
% 1.72/1.37 % (3513)Time elapsed: 0.017 s
% 1.72/1.37 % (3524)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3314 for (2999ds/710Mi)
% 1.72/1.37 % (3513)Instructions burned: 15 (million)
% 1.72/1.37 % (3513)------------------------------
% 1.72/1.37 % (3513)------------------------------
% 1.72/1.37 % (3516)Instruction limit reached!
% 1.72/1.37 % (3516)------------------------------
% 1.72/1.37 % (3516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.37 % (3516)Termination reason: Unknown
% 1.72/1.37 % (3516)Termination phase: Saturation
% 1.72/1.37
% 1.72/1.37 % (3516)Memory used [KB]: 1023
% 1.72/1.37 % (3516)Time elapsed: 0.009 s
% 1.72/1.37 % (3516)Instructions burned: 7 (million)
% 1.72/1.37 % (3516)------------------------------
% 1.72/1.37 % (3516)------------------------------
% 1.72/1.38 % (3522)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3314 for (2999ds/4Mi)
% 1.72/1.38 % (3523)Instruction limit reached!
% 1.72/1.38 % (3523)------------------------------
% 1.72/1.38 % (3523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.38 % (3523)Termination reason: Unknown
% 1.72/1.38 % (3523)Termination phase: Saturation
% 1.72/1.38
% 1.72/1.38 % (3523)Memory used [KB]: 5756
% 1.72/1.38 % (3523)Time elapsed: 0.007 s
% 1.72/1.38 % (3523)Instructions burned: 19 (million)
% 1.72/1.38 % (3523)------------------------------
% 1.72/1.38 % (3523)------------------------------
% 1.72/1.38 % (3522)Instruction limit reached!
% 1.72/1.38 % (3522)------------------------------
% 1.72/1.38 % (3522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.38 % (3522)Termination reason: Unknown
% 1.72/1.38 % (3522)Termination phase: Property scanning
% 1.72/1.38
% 1.72/1.38 % (3522)Memory used [KB]: 1023
% 1.72/1.38 % (3522)Time elapsed: 0.004 s
% 1.72/1.38 % (3522)Instructions burned: 5 (million)
% 1.72/1.38 % (3522)------------------------------
% 1.72/1.38 % (3522)------------------------------
% 1.72/1.38 % (3515)First to succeed.
% 1.72/1.39 % (3527)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_3314 for (2999ds/21Mi)
% 1.72/1.39 % (3525)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3314 for (2999ds/6Mi)
% 1.72/1.39 % (3515)Refutation found. Thanks to Tanya!
% 1.72/1.39 % SZS status Theorem for DTF2THF_3314
% 1.72/1.39 % SZS output start Proof for DTF2THF_3314
% 1.72/1.39 thf(func_def_0, type, in: $i > $i > $o).
% 1.72/1.39 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.72/1.39 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 1.72/1.39 thf(func_def_4, type, subset: $i > $i > $o).
% 1.72/1.39 thf(func_def_5, type, kpair: $i > $i > $i).
% 1.72/1.39 thf(func_def_6, type, cartprod: $i > $i > $i).
% 1.72/1.39 thf(func_def_7, type, singleton: $i > $o).
% 1.72/1.39 thf(func_def_9, type, ex1: $i > ($i > $o) > $o).
% 1.72/1.39 thf(func_def_10, type, breln: $i > $i > $i > $o).
% 1.72/1.39 thf(func_def_11, type, func: $i > $i > $i > $o).
% 1.72/1.39 thf(func_def_12, type, ap: $i > $i > $i > $i > $i).
% 1.72/1.39 thf(func_def_32, type, ph1: !>[X0: $tType]:(X0)).
% 1.72/1.39 thf(f209,plain,(
% 1.72/1.39 $false),
% 1.72/1.39 inference(subsumption_resolution,[status(thm)],[f205,f141])).
% 1.72/1.39 thf(f141,plain,(
% 1.72/1.39 ((ap @ sK3 @ sK2 @ sK4 @ sK5) != sK6)),
% 1.72/1.39 inference(equality_proxy_clausification,[status(thm)],[f122])).
% 1.72/1.39 thf(f122,plain,(
% 1.72/1.39 (((ap @ sK3 @ sK2 @ sK4 @ sK5) = sK6) = $false)),
% 1.72/1.39 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.72/1.39 thf(f100,plain,(
% 1.72/1.39 (((in @ (kpair @ sK5 @ sK6) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ sK5) = sK6)) = $false)),
% 1.72/1.39 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.72/1.39 thf(f99,plain,(
% 1.72/1.39 (((in @ sK6 @ sK2) => ((in @ (kpair @ sK5 @ sK6) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ sK5) = sK6))) = $false)),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f98])).
% 1.72/1.39 thf(f98,plain,(
% 1.72/1.39 (((^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ sK5) = Y0)))) @ sK6) = $false)),
% 1.72/1.39 inference(sigma_clausification,[status(thm)],[f92])).
% 1.72/1.39 thf(f92,plain,(
% 1.72/1.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ sK5) = Y0))))))),
% 1.72/1.39 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 1.72/1.39 thf(f91,plain,(
% 1.72/1.39 (((in @ sK5 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ sK5) = Y0)))))) = $false)),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f90])).
% 1.72/1.39 thf(f90,plain,(
% 1.72/1.39 (((^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ (kpair @ Y0 @ Y1) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ Y0) = Y1))))))) @ sK5) = $false)),
% 1.72/1.39 inference(sigma_clausification,[status(thm)],[f89])).
% 1.72/1.39 thf(f89,plain,(
% 1.72/1.39 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ (kpair @ Y0 @ Y1) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ Y0) = Y1)))))))) = $false)),
% 1.72/1.39 inference(boolean_simplification,[status(thm)],[f88])).
% 1.72/1.39 thf(f88,plain,(
% 1.72/1.39 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ (kpair @ Y0 @ Y1) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ Y0) = Y1))))))))) = $false)),
% 1.72/1.39 inference(backward_demodulation,[status(thm)],[f85,f87])).
% 1.72/1.39 thf(f87,plain,(
% 1.72/1.39 ($true = ((subset @ sK4 @ (cartprod @ sK3 @ sK2)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4))))))))))))),
% 1.72/1.39 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 1.72/1.39 thf(f85,plain,(
% 1.72/1.39 ((((subset @ sK4 @ (cartprod @ sK3 @ sK2)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4))))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ (kpair @ Y0 @ Y1) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ Y0) = Y1))))))))) = $false)),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f84])).
% 1.72/1.39 thf(f84,plain,(
% 1.72/1.39 (((^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ sK3 @ sK2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => ((ap @ sK3 @ sK2 @ Y0 @ Y1) = Y2)))))))))) @ sK4) = $false)),
% 1.72/1.39 inference(sigma_clausification,[status(thm)],[f83])).
% 1.72/1.39 thf(f83,plain,(
% 1.72/1.39 ((!! @ $i @ (^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ sK3 @ sK2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => ((ap @ sK3 @ sK2 @ Y0 @ Y1) = Y2))))))))))) = $false)),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.72/1.39 thf(f82,plain,(
% 1.72/1.39 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ sK2)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ sK2 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ sK2 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK2) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => ((ap @ Y0 @ sK2 @ Y1 @ Y2) = Y3)))))))))))) @ sK3) = $false)),
% 1.72/1.39 inference(sigma_clausification,[status(thm)],[f81])).
% 1.72/1.39 thf(f81,plain,(
% 1.72/1.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ sK2)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ sK2 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ sK2 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK2) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => ((ap @ Y0 @ sK2 @ Y1 @ Y2) = Y3))))))))))))) = $false)),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f80])).
% 1.72/1.39 thf(f80,plain,(
% 1.72/1.39 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4)))))))))))))) @ sK2) = $false)),
% 1.72/1.39 inference(sigma_clausification,[status(thm)],[f67])).
% 1.72/1.39 thf(f67,plain,(
% 1.72/1.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))) = $false)),
% 1.72/1.39 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.72/1.39 thf(f49,plain,(
% 1.72/1.39 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y0 @ Y2 @ Y3)) @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4)))))))))))))))) = $false)),
% 1.72/1.39 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.72/1.39 thf(f48,plain,(
% 1.72/1.39 (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y0 @ Y2 @ Y3)) @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))) = $false)),
% 1.72/1.39 inference(boolean_simplification,[status(thm)],[f47])).
% 1.72/1.39 thf(f47,plain,(
% 1.72/1.39 (($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y0 @ Y2 @ Y3)) @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4)))))))))))))))))) = $false)),
% 1.72/1.39 inference(backward_demodulation,[status(thm)],[f42,f46])).
% 1.72/1.39 thf(f46,plain,(
% 1.72/1.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))) = $true)),
% 1.72/1.39 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.72/1.39 thf(f42,plain,(
% 1.72/1.39 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y0 @ Y2 @ Y3)) @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4)))))))))))))))))))),
% 1.72/1.39 inference(not_proxy_clausification,[status(thm)],[f41])).
% 1.72/1.39 thf(f41,plain,(
% 1.72/1.39 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y0 @ Y2 @ Y3)) @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))))) = $true)),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.72/1.39 thf(f40,plain,(
% 1.72/1.39 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & ((setadjoin @ Y5 @ emptyset) = Y4))))) @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y0 @ Y2 @ Y3)) @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))))) = $true)),
% 1.72/1.39 inference(definition_unfolding,[status(thm)],[f30,f37,f38,f39,f36])).
% 1.72/1.39 thf(f36,plain,(
% 1.72/1.39 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y6) & ((setadjoin @ Y7 @ emptyset) = Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 1.72/1.39 inference(definition_unfolding,[status(thm)],[f28,f32,f35])).
% 1.72/1.39 thf(f35,plain,(
% 1.72/1.39 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.72/1.39 inference(definition_unfolding,[status(thm)],[f27,f33])).
% 1.72/1.39 thf(f33,plain,(
% 1.72/1.39 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 1.72/1.39 inference(cnf_transformation,[status(thm)],[f22])).
% 1.72/1.39 thf(f22,plain,(
% 1.72/1.39 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 1.72/1.39 inference(fool_elimination,[status(thm)],[f21])).
% 1.72/1.39 thf(f21,plain,(
% 1.72/1.39 ((^[X0 : $i] : (? [X1 : $i] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))) = singleton)),
% 1.72/1.39 inference(rectify,[status(thm)],[f1])).
% 1.72/1.39 thf(f1,axiom,(
% 1.72/1.39 ((^[X0 : $i] : (? [X1 : $i] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))) = singleton)),
% 1.72/1.39 file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',singleton)).
% 1.72/1.39 thf(f27,plain,(
% 1.72/1.39 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.72/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.72/1.39 thf(f12,plain,(
% 1.72/1.39 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.72/1.39 inference(fool_elimination,[status(thm)],[f11])).
% 1.72/1.39 thf(f11,plain,(
% 1.72/1.39 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 1.72/1.39 inference(rectify,[status(thm)],[f2])).
% 1.72/1.39 thf(f2,axiom,(
% 1.72/1.39 (ex1 = (^[X0 : $i, X2 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X1 : $i] : (X2 @ X1))))))),
% 1.72/1.39 file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',ex1)).
% 1.72/1.39 thf(f32,plain,(
% 1.72/1.39 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.72/1.39 inference(cnf_transformation,[status(thm)],[f20])).
% 1.72/1.39 thf(f20,plain,(
% 1.72/1.39 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.72/1.39 inference(fool_elimination,[status(thm)],[f19])).
% 1.72/1.39 thf(f19,plain,(
% 1.72/1.39 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 1.72/1.39 inference(rectify,[status(thm)],[f3])).
% 1.72/1.39 thf(f3,axiom,(
% 1.72/1.39 ((^[X0 : $i, X3 : $i, X4 : $i] : (subset @ X4 @ (cartprod @ X0 @ X3))) = breln)),
% 1.72/1.39 file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',breln)).
% 1.72/1.39 thf(f28,plain,(
% 1.72/1.39 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 1.72/1.39 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.39 thf(f24,plain,(
% 1.72/1.39 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 1.72/1.39 inference(fool_elimination,[status(thm)],[f23])).
% 1.72/1.39 thf(f23,plain,(
% 1.72/1.39 (func = (^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))) & (breln @ X0 @ X1 @ X2))))),
% 1.72/1.39 inference(rectify,[status(thm)],[f4])).
% 1.72/1.39 thf(f4,axiom,(
% 1.72/1.39 (func = (^[X0 : $i, X3 : $i, X5 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (ex1 @ X3 @ (^[X6 : $i] : (in @ (kpair @ X1 @ X6) @ X5)))) & (breln @ X0 @ X3 @ X5))))),
% 1.72/1.39 file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',func)).
% 1.72/1.39 thf(f39,plain,(
% 1.72/1.39 (funcGraphProp1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y0 @ Y2 @ Y3)) @ Y2))))))))))))),
% 1.72/1.39 inference(definition_unfolding,[status(thm)],[f31,f36])).
% 1.72/1.39 thf(f31,plain,(
% 1.72/1.39 (funcGraphProp1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y0 @ Y2 @ Y3)) @ Y2))))))))))))),
% 1.72/1.39 inference(cnf_transformation,[status(thm)],[f14])).
% 1.72/1.39 thf(f14,plain,(
% 1.72/1.39 (funcGraphProp1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y0 @ Y2 @ Y3)) @ Y2))))))))))))),
% 1.72/1.39 inference(fool_elimination,[status(thm)],[f13])).
% 1.72/1.39 thf(f13,plain,(
% 1.72/1.39 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X1 @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X3 @ (ap @ X1 @ X2 @ X0 @ X3)) @ X0))) = funcGraphProp1)),
% 1.72/1.39 inference(rectify,[status(thm)],[f7])).
% 1.72/1.39 thf(f7,axiom,(
% 1.72/1.39 (! [X7 : $i,X0 : $i,X3 : $i] : ((func @ X0 @ X3 @ X7) => ! [X1 : $i] : ((in @ X1 @ X0) => (in @ (kpair @ X1 @ (ap @ X0 @ X3 @ X7 @ X1)) @ X7))) = funcGraphProp1)),
% 1.72/1.39 file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',funcGraphProp1)).
% 1.72/1.39 thf(f38,plain,(
% 1.72/1.39 (ex1E2 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & ((setadjoin @ Y5 @ emptyset) = Y4))))) @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))))),
% 1.72/1.39 inference(definition_unfolding,[status(thm)],[f34,f35])).
% 1.72/1.39 thf(f34,plain,(
% 1.72/1.39 (ex1E2 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))))),
% 1.72/1.39 inference(cnf_transformation,[status(thm)],[f26])).
% 1.72/1.39 thf(f26,plain,(
% 1.72/1.39 (ex1E2 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))))),
% 1.72/1.39 inference(fool_elimination,[status(thm)],[f25])).
% 1.72/1.39 thf(f25,plain,(
% 1.72/1.39 (ex1E2 = ! [X0 : $i > $o,X1 : $i] : ((ex1 @ X1 @ (^[X2 : $i] : (X0 @ X2))) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((X0 @ X3) => ((X0 @ X4) => (X3 = X4)))))))),
% 1.72/1.39 inference(rectify,[status(thm)],[f6])).
% 1.72/1.39 thf(f6,axiom,(
% 1.72/1.39 (ex1E2 = ! [X2 : $i > $o,X0 : $i] : ((ex1 @ X0 @ (^[X1 : $i] : (X2 @ X1))) => ! [X1 : $i] : ((in @ X1 @ X0) => ! [X6 : $i] : ((in @ X6 @ X0) => ((X2 @ X1) => ((X2 @ X6) => (X1 = X6)))))))),
% 1.72/1.39 file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',ex1E2)).
% 1.72/1.39 thf(f37,plain,(
% 1.72/1.39 (app = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))))),
% 1.72/1.39 inference(definition_unfolding,[status(thm)],[f29,f36])).
% 1.72/1.39 thf(f29,plain,(
% 1.72/1.39 (app = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))))),
% 1.72/1.39 inference(cnf_transformation,[status(thm)],[f18])).
% 1.72/1.39 thf(f18,plain,(
% 1.72/1.39 (app = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))))),
% 1.72/1.39 inference(fool_elimination,[status(thm)],[f17])).
% 1.72/1.39 thf(f17,plain,(
% 1.72/1.39 (app = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (ap @ X2 @ X0 @ X1 @ X3) @ X0))))),
% 1.72/1.39 inference(rectify,[status(thm)],[f5])).
% 1.72/1.39 thf(f5,axiom,(
% 1.72/1.39 (app = ! [X3 : $i,X7 : $i,X0 : $i] : ((func @ X0 @ X3 @ X7) => ! [X1 : $i] : ((in @ X1 @ X0) => (in @ (ap @ X0 @ X3 @ X7 @ X1) @ X3))))),
% 1.72/1.39 file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',app)).
% 1.72/1.39 thf(f30,plain,(
% 1.72/1.39 ((~ (app => (ex1E2 => (funcGraphProp1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))))) = $true)),
% 1.72/1.39 inference(cnf_transformation,[status(thm)],[f16])).
% 1.72/1.39 thf(f16,plain,(
% 1.72/1.39 ((~ (app => (ex1E2 => (funcGraphProp1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))))) = $true)),
% 1.72/1.39 inference(fool_elimination,[status(thm)],[f15])).
% 1.72/1.39 thf(f15,plain,(
% 1.72/1.39 ~(app => (ex1E2 => (funcGraphProp1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X1 @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X2) => ((in @ (kpair @ X3 @ X4) @ X0) => ((ap @ X1 @ X2 @ X0 @ X3) = X4))))))))),
% 1.72/1.39 inference(rectify,[status(thm)],[f9])).
% 1.72/1.39 thf(f9,negated_conjecture,(
% 1.72/1.39 ~(app => (ex1E2 => (funcGraphProp1 => ! [X7 : $i,X0 : $i,X3 : $i] : ((func @ X0 @ X3 @ X7) => ! [X1 : $i] : ((in @ X1 @ X0) => ! [X6 : $i] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X7) => ((ap @ X0 @ X3 @ X7 @ X1) = X6))))))))),
% 1.72/1.39 inference(negated_conjecture,[status(cth)],[f8])).
% 1.72/1.39 thf(f8,conjecture,(
% 1.72/1.39 app => (ex1E2 => (funcGraphProp1 => ! [X7 : $i,X0 : $i,X3 : $i] : ((func @ X0 @ X3 @ X7) => ! [X1 : $i] : ((in @ X1 @ X0) => ! [X6 : $i] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X7) => ((ap @ X0 @ X3 @ X7 @ X1) = X6)))))))),
% 1.72/1.39 file('/export/starexec/sandbox/tmp/tmp.fNYJKl6XLB/DTF2THF_3314.p',funcGraphProp2)).
% 1.72/1.39 thf(f205,plain,(
% 1.72/1.39 ((ap @ sK3 @ sK2 @ sK4 @ sK5) = sK6)),
% 1.72/1.39 inference(equality_proxy_clausification,[status(thm)],[f202])).
% 1.72/1.39 thf(f202,plain,(
% 1.72/1.39 ((sK6 = (ap @ sK3 @ sK2 @ sK4 @ sK5)) = $true)),
% 1.72/1.39 inference(boolean_simplification,[status(thm)],[f201])).
% 1.72/1.39 thf(f201,plain,(
% 1.72/1.39 ($true = ($true => (sK6 = (ap @ sK3 @ sK2 @ sK4 @ sK5))))),
% 1.72/1.39 inference(forward_demodulation,[status(thm)],[f200,f134])).
% 1.72/1.39 thf(f134,plain,(
% 1.72/1.39 ((in @ (ap @ sK3 @ sK2 @ sK4 @ sK5) @ sK2) = $true)),
% 1.72/1.39 inference(boolean_simplification,[status(thm)],[f133])).
% 1.72/1.39 thf(f133,plain,(
% 1.72/1.39 ($true = ($true => (in @ (ap @ sK3 @ sK2 @ sK4 @ sK5) @ sK2)))),
% 1.72/1.39 inference(superposition,[status(thm)],[f131,f93])).
% 1.72/1.39 thf(f93,plain,(
% 1.72/1.39 ((in @ sK5 @ sK3) = $true)),
% 1.72/1.39 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 1.72/1.39 thf(f131,plain,(
% 1.72/1.39 ( ! [X1 : $i] : ((((in @ X1 @ sK3) => (in @ (ap @ sK3 @ sK2 @ sK4 @ X1) @ sK2)) = $true)) )),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f128])).
% 1.72/1.39 thf(f128,plain,(
% 1.72/1.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (ap @ sK3 @ sK2 @ sK4 @ Y0) @ sK2))) @ X1))) )),
% 1.72/1.39 inference(pi_clausification,[status(thm)],[f111])).
% 1.72/1.39 thf(f111,plain,(
% 1.72/1.39 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (ap @ sK3 @ sK2 @ sK4 @ Y0) @ sK2)))) = $true)),
% 1.72/1.39 inference(boolean_simplification,[status(thm)],[f109])).
% 1.72/1.39 thf(f109,plain,(
% 1.72/1.39 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (ap @ sK3 @ sK2 @ sK4 @ Y0) @ sK2))))))),
% 1.72/1.39 inference(superposition,[status(thm)],[f65,f87])).
% 1.72/1.39 thf(f65,plain,(
% 1.72/1.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((subset @ X2 @ (cartprod @ X1 @ X3)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X3 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X2)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X3 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X2))))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (ap @ X1 @ X3 @ X2 @ Y0) @ X3))))) = $true)) )),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.72/1.39 thf(f64,plain,(
% 1.72/1.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((subset @ X2 @ (cartprod @ X1 @ Y0)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X2)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X2))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (ap @ X1 @ Y0 @ X2 @ Y1) @ Y0)))))) @ X3) = $true)) )),
% 1.72/1.39 inference(pi_clausification,[status(thm)],[f63])).
% 1.72/1.39 thf(f63,plain,(
% 1.72/1.39 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((subset @ X2 @ (cartprod @ X1 @ Y0)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X2)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X2))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (ap @ X1 @ Y0 @ X2 @ Y1) @ Y0))))))))) )),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.72/1.39 thf(f62,plain,(
% 1.72/1.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y0 @ (cartprod @ X1 @ Y1)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y0)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y0))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (ap @ X1 @ Y1 @ Y0 @ Y2) @ Y1)))))))) @ X2) = $true)) )),
% 1.72/1.39 inference(pi_clausification,[status(thm)],[f61])).
% 1.72/1.39 thf(f61,plain,(
% 1.72/1.39 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y0 @ (cartprod @ X1 @ Y1)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y0)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y0))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (ap @ X1 @ Y1 @ Y0 @ Y2) @ Y1))))))))))) )),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.72/1.39 thf(f60,plain,(
% 1.72/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2)))))))))) @ X1) = $true)) )),
% 1.72/1.39 inference(pi_clausification,[status(thm)],[f46])).
% 1.72/1.39 thf(f200,plain,(
% 1.72/1.39 (((in @ (ap @ sK3 @ sK2 @ sK4 @ sK5) @ sK2) => (sK6 = (ap @ sK3 @ sK2 @ sK4 @ sK5))) = $true)),
% 1.72/1.39 inference(boolean_simplification,[status(thm)],[f190])).
% 1.72/1.39 thf(f190,plain,(
% 1.72/1.39 (((in @ (ap @ sK3 @ sK2 @ sK4 @ sK5) @ sK2) => ($true => (sK6 = (ap @ sK3 @ sK2 @ sK4 @ sK5)))) = $true)),
% 1.72/1.39 inference(superposition,[status(thm)],[f187,f144])).
% 1.72/1.39 thf(f144,plain,(
% 1.72/1.39 ((in @ (kpair @ sK5 @ (ap @ sK3 @ sK2 @ sK4 @ sK5)) @ sK4) = $true)),
% 1.72/1.39 inference(boolean_simplification,[status(thm)],[f143])).
% 1.72/1.39 thf(f143,plain,(
% 1.72/1.39 ($true = ($true => (in @ (kpair @ sK5 @ (ap @ sK3 @ sK2 @ sK4 @ sK5)) @ sK4)))),
% 1.72/1.39 inference(superposition,[status(thm)],[f139,f93])).
% 1.72/1.39 thf(f139,plain,(
% 1.72/1.39 ( ! [X1 : $i] : ((((in @ X1 @ sK3) => (in @ (kpair @ X1 @ (ap @ sK3 @ sK2 @ sK4 @ X1)) @ sK4)) = $true)) )),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f137])).
% 1.72/1.39 thf(f137,plain,(
% 1.72/1.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (kpair @ Y0 @ (ap @ sK3 @ sK2 @ sK4 @ Y0)) @ sK4))) @ X1))) )),
% 1.72/1.39 inference(pi_clausification,[status(thm)],[f110])).
% 1.72/1.39 thf(f110,plain,(
% 1.72/1.39 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (kpair @ Y0 @ (ap @ sK3 @ sK2 @ sK4 @ Y0)) @ sK4)))) = $true)),
% 1.72/1.39 inference(boolean_simplification,[status(thm)],[f108])).
% 1.72/1.39 thf(f108,plain,(
% 1.72/1.39 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (kpair @ Y0 @ (ap @ sK3 @ sK2 @ sK4 @ Y0)) @ sK4))))))),
% 1.72/1.39 inference(superposition,[status(thm)],[f78,f87])).
% 1.72/1.39 thf(f78,plain,(
% 1.72/1.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((subset @ X3 @ (cartprod @ X2 @ X1)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X1 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X3)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X3))))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (kpair @ Y0 @ (ap @ X2 @ X1 @ X3 @ Y0)) @ X3))))) = $true)) )),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.72/1.39 thf(f77,plain,(
% 1.72/1.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ X2 @ X1)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ X1 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X1 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (kpair @ Y1 @ (ap @ X2 @ X1 @ Y0 @ Y1)) @ Y0)))))) @ X3) = $true)) )),
% 1.72/1.39 inference(pi_clausification,[status(thm)],[f76])).
% 1.72/1.39 thf(f76,plain,(
% 1.72/1.39 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ X2 @ X1)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ X1 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X1 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (kpair @ Y1 @ (ap @ X2 @ X1 @ Y0 @ Y1)) @ Y0))))))) = $true)) )),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.72/1.39 thf(f75,plain,(
% 1.72/1.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ X1)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ X1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ X1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (kpair @ Y2 @ (ap @ Y0 @ X1 @ Y1 @ Y2)) @ Y1)))))))) @ X2) = $true)) )),
% 1.72/1.39 inference(pi_clausification,[status(thm)],[f74])).
% 1.72/1.39 thf(f74,plain,(
% 1.72/1.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ X1)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ X1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ X1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (kpair @ Y2 @ (ap @ Y0 @ X1 @ Y1 @ Y2)) @ Y1))))))))) = $true)) )),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.72/1.39 thf(f73,plain,(
% 1.72/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y0 @ Y2 @ Y3)) @ Y2)))))))))) @ X1) = $true)) )),
% 1.72/1.39 inference(pi_clausification,[status(thm)],[f68])).
% 1.72/1.39 thf(f68,plain,(
% 1.72/1.39 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y0 @ Y2 @ Y3)) @ Y2))))))))))))),
% 1.72/1.39 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.72/1.39 thf(f187,plain,(
% 1.72/1.39 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => ((in @ (kpair @ sK5 @ X1) @ sK4) => (sK6 = X1))) = $true)) )),
% 1.72/1.39 inference(boolean_simplification,[status(thm)],[f186])).
% 1.72/1.39 thf(f186,plain,(
% 1.72/1.39 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK2) => ($true => ((in @ (kpair @ sK5 @ X1) @ sK4) => (sK6 = X1)))))) )),
% 1.72/1.39 inference(forward_demodulation,[status(thm)],[f185,f123])).
% 1.72/1.39 thf(f123,plain,(
% 1.72/1.39 ((in @ (kpair @ sK5 @ sK6) @ sK4) = $true)),
% 1.72/1.39 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.72/1.39 thf(f185,plain,(
% 1.72/1.39 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => ((in @ (kpair @ sK5 @ sK6) @ sK4) => ((in @ (kpair @ sK5 @ X1) @ sK4) => (sK6 = X1)))) = $true)) )),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f182])).
% 1.72/1.39 thf(f182,plain,(
% 1.72/1.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ sK6) @ sK4) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => (sK6 = Y0))))) @ X1))) )),
% 1.72/1.39 inference(pi_clausification,[status(thm)],[f180])).
% 1.72/1.39 thf(f180,plain,(
% 1.72/1.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ sK6) @ sK4) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => (sK6 = Y0)))))))),
% 1.72/1.39 inference(boolean_simplification,[status(thm)],[f178])).
% 1.72/1.39 thf(f178,plain,(
% 1.72/1.39 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ sK6) @ sK4) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => (sK6 = Y0))))))))),
% 1.72/1.39 inference(superposition,[status(thm)],[f176,f101])).
% 1.72/1.39 thf(f101,plain,(
% 1.72/1.39 ((in @ sK6 @ sK2) = $true)),
% 1.72/1.39 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.72/1.39 thf(f176,plain,(
% 1.72/1.39 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ X1) @ sK4) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => (X1 = Y0))))))) = $true)) )),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f175])).
% 1.72/1.39 thf(f175,plain,(
% 1.72/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => ((in @ (kpair @ sK5 @ Y1) @ sK4) => (Y0 = Y1)))))))) @ X1) = $true)) )),
% 1.72/1.39 inference(pi_clausification,[status(thm)],[f165])).
% 1.72/1.39 thf(f165,plain,(
% 1.72/1.39 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => ((in @ (kpair @ sK5 @ Y1) @ sK4) => (Y0 = Y1))))))))) = $true)),
% 1.72/1.39 inference(boolean_simplification,[status(thm)],[f164])).
% 1.72/1.39 thf(f164,plain,(
% 1.72/1.39 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => ((in @ (kpair @ sK5 @ Y1) @ sK4) => (Y0 = Y1)))))))))))),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f162])).
% 1.72/1.39 thf(f162,plain,(
% 1.72/1.39 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((^[Y2 : $i]: (in @ (kpair @ sK5 @ Y2) @ sK4)) @ Y0) => (((^[Y2 : $i]: (in @ (kpair @ sK5 @ Y2) @ sK4)) @ Y1) => (Y0 = Y1)))))))))) = $true)),
% 1.72/1.39 inference(superposition,[status(thm)],[f58,f159])).
% 1.72/1.39 thf(f159,plain,(
% 1.72/1.39 ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK4)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK4))))))) = $true)),
% 1.72/1.39 inference(boolean_simplification,[status(thm)],[f158])).
% 1.72/1.39 thf(f158,plain,(
% 1.72/1.39 (($true => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK4)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK4)))))))) = $true)),
% 1.72/1.39 inference(superposition,[status(thm)],[f150,f93])).
% 1.72/1.39 thf(f150,plain,(
% 1.72/1.39 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK3) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK4)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK4)))))))))) )),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f145])).
% 1.72/1.39 thf(f145,plain,(
% 1.72/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4))))))))) @ X1) = $true)) )),
% 1.72/1.39 inference(pi_clausification,[status(thm)],[f106])).
% 1.72/1.39 thf(f106,plain,(
% 1.72/1.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4)))))))))))),
% 1.72/1.39 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.72/1.39 thf(f58,plain,(
% 1.72/1.39 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X1 @ X2)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X2))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((X2 @ Y0) => ((X2 @ Y1) => (Y0 = Y1)))))))))))) )),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.72/1.39 thf(f57,plain,(
% 1.72/1.39 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X1 @ Y0)) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y0 @ Y1) => ((Y0 @ Y2) => (Y1 = Y2))))))))))) @ X2) = $true)) )),
% 1.72/1.39 inference(pi_clausification,[status(thm)],[f56])).
% 1.72/1.39 thf(f56,plain,(
% 1.72/1.39 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X1 @ Y0)) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y0 @ Y1) => ((Y0 @ Y2) => (Y1 = Y2)))))))))))))) )),
% 1.72/1.39 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.72/1.39 thf(f55,plain,(
% 1.72/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))))))) @ X1) = $true)) )),
% 1.72/1.39 inference(pi_clausification,[status(thm)],[f50])).
% 1.72/1.39 thf(f50,plain,(
% 1.72/1.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) = $true)),
% 1.72/1.39 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.72/1.39 % SZS output end Proof for DTF2THF_3314
% 1.72/1.39 % (3515)------------------------------
% 1.72/1.39 % (3515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.39 % (3515)Termination reason: Refutation
% 1.72/1.39
% 1.72/1.39 % (3515)Memory used [KB]: 6140
% 1.72/1.39 % (3515)Time elapsed: 0.043 s
% 1.72/1.39 % (3515)Instructions burned: 85 (million)
% 1.72/1.39 % (3515)------------------------------
% 1.72/1.39 % (3515)------------------------------
% 1.72/1.39 % (3503)Success in time 0.075 s
%------------------------------------------------------------------------------