%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU996^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 09:37:55 AM UTC 2026
% Result : Theorem 1.46s 1.26s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 1
% Syntax : Number of formulae : 48 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 601 ( 244 equ; 0 cnn)
% Maximal formula atoms : 12 ( 12 avg)
% Number of connectives : 2309 ( 8 ~; 0 |; 134 &;1820 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 6 con; 0-2 aty)
% ( 320 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 435 ( 330 ^; 105 !; 0 ?; 435 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK2: a > a > a ).
thf(func_def_18,type,
sK3: a > a > a ).
thf(func_def_19,type,
sK4: a ).
thf(func_def_20,type,
sK5: a ).
thf(func_def_21,type,
sK6: a ).
thf(f109,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ( sK2 @ sK5 @ ( sK3 @ sK4 @ sK6 ) )
!= ( sK2 @ sK5 @ ( sK3 @ sK4 @ sK6 ) ) ),
inference(forward_demodulation,[status(thm)],[f107,f75]) ).
thf(f75,plain,
! [X2: a,X1: a] :
( ( sK3 @ X2 @ X1 )
= ( sK3 @ X1 @ X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X1 @ X2 )
= ( sK3 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
= ( sK3 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
= ( sK3 @ Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK3 @ Y2 @ Y0 ) )
= ( sK3 @ ( sK3 @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK3 @ Y2 @ Y0 ) )
= ( sK3 @ ( sK3 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK3 @ Y2 @ Y0 ) )
= ( sK3 @ ( sK3 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK3 @ Y1 @ Y2 ) @ ( sK3 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK3 @ Y2 @ Y0 ) )
= ( sK3 @ ( sK3 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK3 @ Y1 @ Y2 ) @ ( sK3 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK3 @ Y2 @ Y0 ) )
= ( sK3 @ ( sK3 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK3 @ Y1 @ Y2 ) @ ( sK3 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK3 @ Y2 @ Y0 ) )
= ( sK3 @ ( sK3 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK3 @ Y1 @ Y2 ) @ ( sK3 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK3 @ Y2 @ Y0 ) )
= ( sK3 @ ( sK3 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK3 @ Y1 @ Y2 ) @ ( sK3 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) )
= ( sK2 @ Y2 @ ( sK3 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
= ( sK3 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK3 @ Y2 @ Y0 ) )
= ( sK3 @ ( sK3 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ ( sK2 @ Y2 @ Y0 ) )
= ( sK2 @ ( sK3 @ Y1 @ Y2 ) @ ( sK3 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ ( sK3 @ Y1 @ Y0 ) @ Y0 )
= Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
= Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) )
= ( sK2 @ Y2 @ ( sK3 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y1 @ ( sK3 @ Y2 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > a > a] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 @ Y1 )
= Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ ( sK2 @ Y3 @ Y1 ) )
= ( sK2 @ ( sK2 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
= ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y1 ) )
= ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( sK2 @ Y2 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ ( sK2 @ Y3 @ Y1 ) )
= ( sK2 @ ( Y0 @ Y2 @ Y3 ) @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( Y0 @ Y2 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( sK2 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y1 )
= Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( sK2 @ Y3 @ Y1 ) @ ( sK2 @ Y3 @ Y2 ) )
= ( sK2 @ Y3 @ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y1 )
= Y1 )
=> ( ( sK2 @ Y2 @ ( Y0 @ Y3 @ Y1 ) )
= ( Y0 @ ( sK2 @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( $false
= ( !! @ ( a > a > a )
@ ^ [Y0: a > a > a] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 @ Y1 )
= Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ ( sK2 @ Y3 @ Y1 ) )
= ( sK2 @ ( sK2 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
= ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y1 ) )
= ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ ( sK2 @ Y2 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ ( sK2 @ Y3 @ Y1 ) )
= ( sK2 @ ( Y0 @ Y2 @ Y3 ) @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ ( Y0 @ Y2 @ Y1 ) @ Y1 )
= Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( sK2 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y1 )
= Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( sK2 @ Y3 @ Y1 ) @ ( sK2 @ Y3 @ Y2 ) )
= ( sK2 @ Y3 @ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y1 )
= Y1 )
=> ( ( sK2 @ Y2 @ ( Y0 @ Y3 @ Y1 ) )
= ( Y0 @ ( sK2 @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( $false
= ( ^ [Y0: a > a > a] :
( !! @ ( a > a > a )
@ ^ [Y1: a > a > a] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ ( Y0 @ Y4 @ Y2 ) )
= ( Y0 @ ( Y0 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
= ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ ( Y1 @ Y4 @ Y2 ) )
= ( Y1 @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( Y0 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ ( Y0 @ Y4 @ Y2 ) )
= ( Y0 @ ( Y1 @ Y3 @ Y4 ) @ ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
= ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ ( Y0 @ Y4 @ Y2 ) @ ( Y0 @ Y4 @ Y3 ) )
= ( Y0 @ Y4 @ ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
= Y2 )
=> ( ( Y0 @ Y3 @ ( Y1 @ Y4 @ Y2 ) )
= ( Y1 @ ( Y0 @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > a > a )
@ ^ [Y0: a > a > a] :
( !! @ ( a > a > a )
@ ^ [Y1: a > a > a] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ ( Y0 @ Y4 @ Y2 ) )
= ( Y0 @ ( Y0 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
= ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ ( Y1 @ Y4 @ Y2 ) )
= ( Y1 @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( Y0 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ ( Y0 @ Y4 @ Y2 ) )
= ( Y0 @ ( Y1 @ Y3 @ Y4 ) @ ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
= ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ ( Y0 @ Y4 @ Y2 ) @ ( Y0 @ Y4 @ Y3 ) )
= ( Y0 @ Y4 @ ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
= Y2 )
=> ( ( Y0 @ Y3 @ ( Y1 @ Y4 @ Y2 ) )
= ( Y1 @ ( Y0 @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ ( a > a > a )
@ ^ [Y0: a > a > a] :
( !! @ ( a > a > a )
@ ^ [Y1: a > a > a] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ ( Y0 @ Y4 @ Y2 ) )
= ( Y0 @ ( Y0 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
= ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ ( Y1 @ Y4 @ Y2 ) )
= ( Y1 @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( Y0 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ ( Y0 @ Y4 @ Y2 ) )
= ( Y0 @ ( Y1 @ Y3 @ Y4 ) @ ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
= ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ ( Y0 @ Y4 @ Y2 ) @ ( Y0 @ Y4 @ Y3 ) )
= ( Y0 @ Y4 @ ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
= Y2 )
=> ( ( Y0 @ Y3 @ ( Y1 @ Y4 @ Y2 ) )
= ( Y1 @ ( Y0 @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ ( a > a > a )
@ ^ [Y0: a > a > a] :
( !! @ ( a > a > a )
@ ^ [Y1: a > a > a] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ ( Y0 @ Y4 @ Y2 ) )
= ( Y0 @ ( Y0 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
= ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ ( Y1 @ Y4 @ Y2 ) )
= ( Y1 @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ ( Y0 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ ( Y0 @ Y4 @ Y2 ) )
= ( Y0 @ ( Y1 @ Y3 @ Y4 ) @ ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ ( Y1 @ Y3 @ Y2 ) @ Y2 )
= Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
= ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
= Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ ( Y0 @ Y4 @ Y2 ) @ ( Y0 @ Y4 @ Y3 ) )
= ( Y0 @ Y4 @ ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
= Y2 )
=> ( ( Y0 @ Y3 @ ( Y1 @ Y4 @ Y2 ) )
= ( Y1 @ ( Y0 @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > a,X1: a > a > a] :
( ( ! [X2: a,X3: a,X4: a] :
( ( X0 @ ( X1 @ X2 @ X4 ) @ ( X1 @ X2 @ X3 ) )
= ( X1 @ X2 @ ( X0 @ X4 @ X3 ) ) )
& ! [X5: a] :
( ( X1 @ X5 @ X5 )
= X5 )
& ! [X6: a,X7: a] :
( ( X1 @ X7 @ X6 )
= ( X1 @ X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( X1 @ ( X0 @ X8 @ X9 ) @ X9 )
= X9 )
& ! [X10: a,X11: a,X12: a] :
( ( X0 @ X11 @ ( X1 @ X10 @ X12 ) )
= ( X1 @ ( X0 @ X11 @ X10 ) @ ( X0 @ X11 @ X12 ) ) )
& ! [X13: a,X14: a] :
( ( X0 @ ( X1 @ X13 @ X14 ) @ X14 )
= X14 )
& ! [X15: a,X16: a,X17: a] :
( ( X0 @ X16 @ ( X0 @ X15 @ X17 ) )
= ( X0 @ ( X0 @ X16 @ X15 ) @ X17 ) )
& ! [X18: a,X19: a] :
( ( X0 @ X19 @ X18 )
= ( X0 @ X18 @ X19 ) )
& ! [X20: a,X21: a,X22: a] :
( ( X1 @ X21 @ ( X1 @ X20 @ X22 ) )
= ( X1 @ ( X1 @ X21 @ X20 ) @ X22 ) )
& ! [X23: a] :
( ( X0 @ X23 @ X23 )
= X23 ) )
=> ! [X24: a,X25: a,X26: a] :
( ( ( X1 @ X25 @ X26 )
= X26 )
=> ( ( X1 @ X25 @ ( X0 @ X24 @ X26 ) )
= ( X0 @ ( X1 @ X25 @ X24 ) @ X26 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > a > a,X0: a > a > a] :
( ( ! [X2: a,X4: a,X3: a] :
( ( X0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ ( X0 @ X2 @ X4 ) ) )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
= X2 )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
= ( X0 @ X3 @ X2 ) )
& ! [X2: a,X3: a] :
( ( X0 @ ( X1 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X3: a,X2: a,X4: a] :
( ( X1 @ X2 @ ( X0 @ X3 @ X4 ) )
= ( X0 @ ( X1 @ X2 @ X3 ) @ ( X1 @ X2 @ X4 ) ) )
& ! [X2: a,X3: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X3: a,X2: a,X4: a] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) )
& ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) )
& ! [X3: a,X2: a,X4: a] :
( ( X0 @ ( X0 @ X2 @ X3 ) @ X4 )
= ( X0 @ X2 @ ( X0 @ X3 @ X4 ) ) )
& ! [X2: a] :
( ( X1 @ X2 @ X2 )
= X2 ) )
=> ! [X3: a,X2: a,X4: a] :
( ( ( X0 @ X2 @ X4 )
= X4 )
=> ( ( X0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > a > a,X0: a > a > a] :
( ( ! [X2: a,X4: a,X3: a] :
( ( X0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ ( X0 @ X2 @ X4 ) ) )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
= X2 )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
= ( X0 @ X3 @ X2 ) )
& ! [X2: a,X3: a] :
( ( X0 @ ( X1 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X3: a,X2: a,X4: a] :
( ( X1 @ X2 @ ( X0 @ X3 @ X4 ) )
= ( X0 @ ( X1 @ X2 @ X3 ) @ ( X1 @ X2 @ X4 ) ) )
& ! [X2: a,X3: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X3: a,X2: a,X4: a] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) )
& ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) )
& ! [X3: a,X2: a,X4: a] :
( ( X0 @ ( X0 @ X2 @ X3 ) @ X4 )
= ( X0 @ X2 @ ( X0 @ X3 @ X4 ) ) )
& ! [X2: a] :
( ( X1 @ X2 @ X2 )
= X2 ) )
=> ! [X3: a,X2: a,X4: a] :
( ( ( X0 @ X2 @ X4 )
= X4 )
=> ( ( X0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.clWWoTZ4Bi/DTF2THF_32249.p',cMODULAR_THM_pme) ).
thf(f107,plain,
( ( sK2 @ sK5 @ ( sK3 @ sK4 @ sK6 ) )
!= ( sK2 @ sK5 @ ( sK3 @ sK6 @ sK4 ) ) ),
inference(superposition,[status(thm)],[f76,f98]) ).
thf(f98,plain,
! [X0: a] :
( ( sK2 @ sK5 @ ( sK3 @ X0 @ sK4 ) )
= ( sK3 @ ( sK2 @ sK5 @ X0 ) @ sK4 ) ),
inference(superposition,[status(thm)],[f32,f23]) ).
thf(f23,plain,
( sK4
= ( sK2 @ sK5 @ sK4 ) ),
inference(equality_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( sK2 @ sK5 @ sK4 )
= sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $false
= ( ( ( sK2 @ sK5 @ sK4 )
= sK4 )
=> ( ( sK2 @ sK5 @ ( sK3 @ sK6 @ sK4 ) )
= ( sK3 @ ( sK2 @ sK5 @ sK6 ) @ sK4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ sK5 @ sK4 )
= sK4 )
=> ( ( sK2 @ sK5 @ ( sK3 @ Y0 @ sK4 ) )
= ( sK3 @ ( sK2 @ sK5 @ Y0 ) @ sK4 ) ) )
@ sK6 ) ),
inference(sigma_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK5 @ sK4 )
= sK4 )
=> ( ( sK2 @ sK5 @ ( sK3 @ Y0 @ sK4 ) )
= ( sK3 @ ( sK2 @ sK5 @ Y0 ) @ sK4 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ sK4 )
= sK4 )
=> ( ( sK2 @ Y0 @ ( sK3 @ Y1 @ sK4 ) )
= ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ sK4 ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ sK4 )
= sK4 )
=> ( ( sK2 @ Y0 @ ( sK3 @ Y1 @ sK4 ) )
= ( sK3 @ ( sK2 @ Y0 @ Y1 ) @ sK4 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y1 @ ( sK3 @ Y2 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y0 )
= Y0 )
=> ( ( sK2 @ Y1 @ ( sK3 @ Y2 @ Y0 ) )
= ( sK3 @ ( sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f32,plain,
! [X2: a,X3: a,X1: a] :
( ( sK3 @ ( sK2 @ X3 @ X1 ) @ ( sK2 @ X3 @ X2 ) )
= ( sK2 @ X3 @ ( sK3 @ X1 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: a,X3: a,X1: a] :
( ( ( sK3 @ ( sK2 @ X3 @ X1 ) @ ( sK2 @ X3 @ X2 ) )
= ( sK2 @ X3 @ ( sK3 @ X1 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ ( sK2 @ Y0 @ X1 ) @ ( sK2 @ Y0 @ X2 ) )
= ( sK2 @ Y0 @ ( sK3 @ X1 @ X2 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ ( sK2 @ Y0 @ X1 ) @ ( sK2 @ Y0 @ X2 ) )
= ( sK2 @ Y0 @ ( sK3 @ X1 @ X2 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y1 @ X1 ) @ ( sK2 @ Y1 @ Y0 ) )
= ( sK2 @ Y1 @ ( sK3 @ X1 @ Y0 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ ( sK2 @ Y1 @ X1 ) @ ( sK2 @ Y1 @ Y0 ) )
= ( sK2 @ Y1 @ ( sK3 @ X1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) )
= ( sK2 @ Y2 @ ( sK3 @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ ( sK2 @ Y2 @ Y0 ) @ ( sK2 @ Y2 @ Y1 ) )
= ( sK2 @ Y2 @ ( sK3 @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f76,plain,
( ( sK3 @ ( sK2 @ sK5 @ sK6 ) @ sK4 )
!= ( sK2 @ sK5 @ ( sK3 @ sK4 @ sK6 ) ) ),
inference(backward_demodulation,[status(thm)],[f22,f75]) ).
thf(f22,plain,
( ( sK3 @ ( sK2 @ sK5 @ sK6 ) @ sK4 )
!= ( sK2 @ sK5 @ ( sK3 @ sK6 @ sK4 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( $false
= ( ( sK2 @ sK5 @ ( sK3 @ sK6 @ sK4 ) )
= ( sK3 @ ( sK2 @ sK5 @ sK6 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEU996^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.36 % Computer : n007.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Tue Feb 24 12:37:53 EST 2026
% 0.16/0.36 % CPUTime :
% 0.16/0.36 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.48 ---- Original DTF file ---
% 0.27/0.48 thf(spec,logic,$$dhol).
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 % File : SEU996^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.48 % Domain : Set Theory (Relations)
% 0.27/0.48 % Problem : TPS problem MODULAR-THM
% 0.27/0.48 % Version : Especial.
% 0.27/0.48 % English : Every distributive lattice is modular.
% 0.27/0.48
% 0.27/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.48 % Source : [Bro09]
% 0.27/0.48 % Names : tps_0373 [Bro09]
% 0.27/0.48 % : MODULAR-THM [TPS]
% 0.27/0.48
% 0.27/0.48 % Status : Theorem
% 0.27/0.48 % Rating : 0.00 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.27/0.48 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.27/0.48 % Number of atoms : 12 ( 12 equ; 0 cnn)
% 0.27/0.48 % Maximal formula atoms : 12 ( 12 avg)
% 0.27/0.48 % Number of connectives : 77 ( 0 ~; 0 |; 9 &; 66 @)
% 0.27/0.48 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.48 % Maximal formula depth : 16 ( 16 avg)
% 0.27/0.48 % Number of types : 1 ( 1 usr)
% 0.27/0.48 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.27/0.48 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.27/0.48 % Number of variables : 27 ( 0 ^; 27 !; 0 ?; 27 :)
% 0.27/0.48 % SPC : TH0_THM_EQU_NAR
% 0.27/0.48
% 0.27/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.48 % : Polymorphic definitions expanded.
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 thf(a_type,type,
% 0.27/0.48 a: $tType ).
% 0.27/0.48
% 0.27/0.48 thf(cMODULAR_THM_pme,conjecture,
% 0.27/0.48 ! [JOIN: a > a > a,MEET: a > a > a] :
% 0.27/0.48 ( ( ! [Xx: a] :
% 0.27/0.48 ( ( JOIN @ Xx @ Xx )
% 0.27/0.48 = Xx )
% 0.27/0.48 & ! [Xx: a] :
% 0.27/0.48 ( ( MEET @ Xx @ Xx )
% 0.27/0.48 = Xx )
% 0.27/0.48 & ! [Xx: a,Xy: a,Xz: a] :
% 0.27/0.48 ( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
% 0.27/0.48 = ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
% 0.27/0.48 & ! [Xx: a,Xy: a,Xz: a] :
% 0.27/0.48 ( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
% 0.27/0.48 = ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
% 0.27/0.48 & ! [Xx: a,Xy: a] :
% 0.27/0.48 ( ( JOIN @ Xx @ Xy )
% 0.27/0.48 = ( JOIN @ Xy @ Xx ) )
% 0.27/0.48 & ! [Xx: a,Xy: a] :
% 0.27/0.48 ( ( MEET @ Xx @ Xy )
% 0.27/0.48 = ( MEET @ Xy @ Xx ) )
% 0.27/0.48 & ! [Xx: a,Xy: a] :
% 0.27/0.48 ( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
% 0.27/0.48 = Xy )
% 0.27/0.48 & ! [Xx: a,Xy: a] :
% 0.27/0.48 ( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
% 0.27/0.48 = Xy )
% 0.27/0.48 & ! [Xx: a,Xy: a,Xz: a] :
% 0.27/0.48 ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
% 0.27/0.48 = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) )
% 0.27/0.48 & ! [Xx: a,Xy: a,Xz: a] :
% 0.27/0.48 ( ( MEET @ Xx @ ( JOIN @ Xy @ Xz ) )
% 0.27/0.48 = ( JOIN @ ( MEET @ Xx @ Xy ) @ ( MEET @ Xx @ Xz ) ) ) )
% 0.27/0.48 => ! [Xx: a,Xy: a,Xz: a] :
% 0.27/0.48 ( ( ( JOIN @ Xx @ Xz )
% 0.27/0.48 = Xz )
% 0.27/0.48 => ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
% 0.27/0.48 = ( MEET @ ( JOIN @ Xx @ Xy ) @ Xz ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 ------------------------
% 1.46/1.21 ---- Embedded in THF ---
% 1.46/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.21 %%% Generated on Tue Feb 24 12:37:54 EST 2026
% 1.46/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.21 %%% Logic specification used:
% 1.46/1.21 %%% thf(spec, logic, $$dhol).
% 1.46/1.21
% 1.46/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.clWWoTZ4Bi/DTF2DTF32249.p
% See solution above
% 1.46/1.21 ------------------------
% 1.46/1.22 ---- Cleaned THF ---
% 1.46/1.22 thf(a_type,type,
% 1.46/1.22 a: $tType ).
% 1.46/1.22
% 1.46/1.22 thf(cMODULAR_THM_pme,conjecture,
% 1.46/1.22 ! [JOIN: a > a > a,MEET: a > a > a] :
% 1.46/1.22 ( ( ! [Xx: a] :
% 1.46/1.22 ( ( JOIN @ Xx @ Xx )
% 1.46/1.22 = Xx )
% 1.46/1.22 & ! [Xx: a] :
% 1.46/1.22 ( ( MEET @ Xx @ Xx )
% 1.46/1.22 = Xx )
% 1.46/1.22 & ! [Xx: a,Xy: a,Xz: a] :
% 1.46/1.22 ( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
% 1.46/1.22 = ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
% 1.46/1.22 & ! [Xx: a,Xy: a,Xz: a] :
% 1.46/1.22 ( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
% 1.46/1.22 = ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
% 1.46/1.22 & ! [Xx: a,Xy: a] :
% 1.46/1.22 ( ( JOIN @ Xx @ Xy )
% 1.46/1.22 = ( JOIN @ Xy @ Xx ) )
% 1.46/1.22 & ! [Xx: a,Xy: a] :
% 1.46/1.22 ( ( MEET @ Xx @ Xy )
% 1.46/1.22 = ( MEET @ Xy @ Xx ) )
% 1.46/1.22 & ! [Xx: a,Xy: a] :
% 1.46/1.22 ( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
% 1.46/1.22 = Xy )
% 1.46/1.22 & ! [Xx: a,Xy: a] :
% 1.46/1.22 ( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
% 1.46/1.22 = Xy )
% 1.46/1.22 & ! [Xx: a,Xy: a,Xz: a] :
% 1.46/1.22 ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
% 1.46/1.22 = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) )
% 1.46/1.22 & ! [Xx: a,Xy: a,Xz: a] :
% 1.46/1.22 ( ( MEET @ Xx @ ( JOIN @ Xy @ Xz ) )
% 1.46/1.22 = ( JOIN @ ( MEET @ Xx @ Xy ) @ ( MEET @ Xx @ Xz ) ) ) )
% 1.46/1.22 => ! [Xx: a,Xy: a,Xz: a] :
% 1.46/1.22 ( ( ( JOIN @ Xx @ Xz )
% 1.46/1.22 = Xz )
% 1.46/1.22 => ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
% 1.46/1.22 = ( MEET @ ( JOIN @ Xx @ Xy ) @ Xz ) ) ) ) ).
% 1.46/1.22 ------------------------
% 1.46/1.23 % (32348)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_32249 for (3000ds/27Mi)
% 1.46/1.24 % (32350)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_32249 for (3000ds/2Mi)
% 1.46/1.24 % (32350)Instruction limit reached!
% 1.46/1.24 % (32350)------------------------------
% 1.46/1.24 % (32350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.24 % (32350)Termination reason: Unknown
% 1.46/1.24 % (32350)Termination phase: shuffling
% 1.46/1.24
% 1.46/1.24 % (32350)Memory used [KB]: 1023
% 1.46/1.24 % (32350)Time elapsed: 0.003 s
% 1.46/1.24 % (32350)Instructions burned: 3 (million)
% 1.46/1.24 % (32350)------------------------------
% 1.46/1.24 % (32350)------------------------------
% 1.46/1.24 % (32346)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32249 for (3000ds/183Mi)
% 1.46/1.24 % (32349)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32249 for (3000ds/2Mi)
% 1.46/1.24 % (32352)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32249 for (3000ds/18Mi)
% 1.46/1.24 % (32351)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_32249 for (3000ds/275Mi)
% 1.46/1.24 % (32349)Instruction limit reached!
% 1.46/1.24 % (32349)------------------------------
% 1.46/1.24 % (32349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.24 % (32349)Termination reason: Unknown
% 1.46/1.24 % (32349)Termination phase: Preprocessing 3
% 1.46/1.24
% 1.46/1.24 % (32349)Memory used [KB]: 1023
% 1.46/1.24 % (32349)Time elapsed: 0.003 s
% 1.46/1.24 % (32349)Instructions burned: 2 (million)
% 1.46/1.24 % (32349)------------------------------
% 1.46/1.24 % (32349)------------------------------
% 1.46/1.24 % (32348)Instruction limit reached!
% 1.46/1.24 % (32348)------------------------------
% 1.46/1.24 % (32348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.24 % (32348)Termination reason: Unknown
% 1.46/1.24 % (32348)Termination phase: Saturation
% 1.46/1.24
% 1.46/1.24 % (32348)Memory used [KB]: 5628
% 1.46/1.24 % (32348)Time elapsed: 0.011 s
% 1.46/1.24 % (32348)Instructions burned: 28 (million)
% 1.46/1.24 % (32348)------------------------------
% 1.46/1.24 % (32348)------------------------------
% 1.46/1.25 % (32347)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_32249 for (3000ds/4Mi)
% 1.46/1.25 % (32347)Instruction limit reached!
% 1.46/1.25 % (32347)------------------------------
% 1.46/1.25 % (32347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.25 % (32347)Termination reason: Unknown
% 1.46/1.25 % (32347)Termination phase: Saturation
% 1.46/1.25
% 1.46/1.25 % (32347)Memory used [KB]: 5500
% 1.46/1.25 % (32347)Time elapsed: 0.004 s
% 1.46/1.25 % (32347)Instructions burned: 4 (million)
% 1.46/1.25 % (32347)------------------------------
% 1.46/1.25 % (32347)------------------------------
% 1.46/1.25 % (32354)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_32249 for (2999ds/37Mi)
% 1.46/1.25 % (32352)Instruction limit reached!
% 1.46/1.25 % (32352)------------------------------
% 1.46/1.25 % (32352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.25 % (32352)Termination reason: Unknown
% 1.46/1.25 % (32352)Termination phase: Saturation
% 1.46/1.25
% 1.46/1.25 % (32352)Memory used [KB]: 5628
% 1.46/1.25 % (32352)Time elapsed: 0.013 s
% 1.46/1.25 % (32352)Instructions burned: 19 (million)
% 1.46/1.25 % (32352)------------------------------
% 1.46/1.25 % (32352)------------------------------
% 1.46/1.26 % (32355)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_32249 for (2999ds/15Mi)
% 1.46/1.26 % (32354)First to succeed.
% 1.46/1.26 % (32353)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32249 for (2999ds/3Mi)
% 1.46/1.26 % (32353)Instruction limit reached!
% 1.46/1.26 % (32353)------------------------------
% 1.46/1.26 % (32353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (32353)Termination reason: Unknown
% 1.46/1.26 % (32353)Termination phase: Property scanning
% 1.46/1.26
% 1.46/1.26 % (32353)Memory used [KB]: 1023
% 1.46/1.26 % (32353)Time elapsed: 0.004 s
% 1.46/1.26 % (32353)Instructions burned: 3 (million)
% 1.46/1.26 % (32353)------------------------------
% 1.46/1.26 % (32353)------------------------------
% 1.46/1.26 % (32354)Refutation found. Thanks to Tanya!
% 1.46/1.26 % SZS status Theorem for DTF2THF_32249
% 1.46/1.26 % SZS output start Proof for DTF2THF_32249
% 1.46/1.26 thf(type_def_5, type, a: $tType).
% 1.46/1.26 thf(func_def_0, type, a: $tType).
% 1.46/1.26 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 1.46/1.26 thf(func_def_17, type, sK2: a > a > a).
% 1.46/1.26 thf(func_def_18, type, sK3: a > a > a).
% 1.46/1.26 thf(func_def_19, type, sK4: a).
% 1.46/1.26 thf(func_def_20, type, sK5: a).
% 1.46/1.26 thf(func_def_21, type, sK6: a).
% 1.46/1.26 thf(f109,plain,(
% 1.46/1.26 $false),
% 1.46/1.26 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.46/1.26 thf(f108,plain,(
% 1.46/1.26 ((sK2 @ sK5 @ (sK3 @ sK4 @ sK6)) != (sK2 @ sK5 @ (sK3 @ sK4 @ sK6)))),
% 1.46/1.26 inference(forward_demodulation,[status(thm)],[f107,f75])).
% 1.46/1.26 thf(f75,plain,(
% 1.46/1.26 ( ! [X2 : a,X1 : a] : (((sK3 @ X2 @ X1) = (sK3 @ X1 @ X2))) )),
% 1.46/1.26 inference(equality_proxy_clausification,[status(thm)],[f74])).
% 1.46/1.26 thf(f74,plain,(
% 1.46/1.26 ( ! [X2 : a,X1 : a] : (($true = ((sK3 @ X1 @ X2) = (sK3 @ X2 @ X1)))) )),
% 1.46/1.26 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.46/1.26 thf(f73,plain,(
% 1.46/1.26 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK3 @ X1 @ Y0) = (sK3 @ Y0 @ X1))) @ X2) = $true)) )),
% 1.46/1.26 inference(pi_clausification,[status(thm)],[f72])).
% 1.46/1.26 thf(f72,plain,(
% 1.46/1.26 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK3 @ X1 @ Y0) = (sK3 @ Y0 @ X1)))) = $true)) )),
% 1.46/1.26 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.46/1.26 thf(f71,plain,(
% 1.46/1.26 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))) @ X1))) )),
% 1.46/1.26 inference(pi_clausification,[status(thm)],[f69])).
% 1.46/1.26 thf(f69,plain,(
% 1.46/1.26 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0)))))))),
% 1.46/1.26 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.46/1.26 thf(f61,plain,(
% 1.46/1.26 ($true = (((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK2 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))))),
% 1.46/1.26 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.46/1.26 thf(f54,plain,(
% 1.46/1.26 (((((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK2 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK3 @ Y2 @ Y0)) = (sK3 @ (sK3 @ Y1 @ Y2) @ Y0))))))))) = $true)),
% 1.46/1.26 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.46/1.26 thf(f45,plain,(
% 1.46/1.26 ($true = (((((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK2 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK3 @ Y2 @ Y0)) = (sK3 @ (sK3 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y1 @ Y0) @ Y0) = Y0)))))))),
% 1.46/1.26 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.46/1.26 thf(f43,plain,(
% 1.46/1.26 (((((((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK2 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK3 @ Y2 @ Y0)) = (sK3 @ (sK3 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK3 @ Y1 @ Y2) @ (sK3 @ Y1 @ Y0)))))))))) = $true)),
% 1.46/1.26 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.46/1.26 thf(f36,plain,(
% 1.46/1.26 ((((((((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK2 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK3 @ Y2 @ Y0)) = (sK3 @ (sK3 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK3 @ Y1 @ Y2) @ (sK3 @ Y1 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) = $true)),
% 1.46/1.26 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.46/1.26 thf(f34,plain,(
% 1.46/1.26 (((((((((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK2 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK3 @ Y2 @ Y0)) = (sK3 @ (sK3 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK3 @ Y1 @ Y2) @ (sK3 @ Y1 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ Y1 @ Y0))))))) = $true)),
% 1.46/1.26 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.46/1.26 thf(f25,plain,(
% 1.46/1.26 ((((((((((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK2 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK3 @ Y2 @ Y0)) = (sK3 @ (sK3 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK3 @ Y1 @ Y2) @ (sK3 @ Y1 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0)))) = $true)),
% 1.46/1.26 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.46/1.26 thf(f13,plain,(
% 1.46/1.26 ($true = ((((((((((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK2 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK3 @ Y2 @ Y0)) = (sK3 @ (sK3 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK3 @ Y1 @ Y2) @ (sK3 @ Y1 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1)) = (sK2 @ Y2 @ (sK3 @ Y0 @ Y1)))))))))))),
% 1.46/1.26 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.46/1.26 thf(f11,plain,(
% 1.46/1.26 ($false = (((((((((((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ Y0) = Y0))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK2 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) = (sK3 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK3 @ Y2 @ Y0)) = (sK3 @ (sK3 @ Y1 @ Y2) @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ (sK2 @ Y2 @ Y0)) = (sK2 @ (sK3 @ Y1 @ Y2) @ (sK3 @ Y1 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ (sK3 @ Y1 @ Y0) @ Y0) = Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ Y0) = Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1)) = (sK2 @ Y2 @ (sK3 @ Y0 @ Y1)))))))))) => (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y0) = Y0) => ((sK2 @ Y1 @ (sK3 @ Y2 @ Y0)) = (sK3 @ (sK2 @ Y1 @ Y2) @ Y0)))))))))))),
% 1.46/1.26 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.46/1.26 thf(f10,plain,(
% 1.46/1.26 ($false = ((^[Y0 : a > a > a]: (((((((((((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1 @ Y1) = Y1))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ (sK2 @ Y3 @ Y1)) = (sK2 @ (sK2 @ Y2 @ Y3) @ Y1))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) = (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ (Y0 @ Y3 @ Y1)) = (Y0 @ (Y0 @ Y2 @ Y3) @ Y1))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (sK2 @ Y2 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ (sK2 @ Y3 @ Y1)) = (sK2 @ (Y0 @ Y2 @ Y3) @ (Y0 @ Y2 @ Y1)))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (Y0 @ Y2 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (sK2 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y1) = Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (sK2 @ Y3 @ Y1) @ (sK2 @ Y3 @ Y2)) = (sK2 @ Y3 @ (Y0 @ Y1 @ Y2)))))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y1) = Y1) => ((sK2 @ Y2 @ (Y0 @ Y3 @ Y1)) = (Y0 @ (sK2 @ Y2 @ Y3) @ Y1))))))))))) @ sK3))),
% 1.46/1.26 inference(sigma_clausification,[status(thm)],[f9])).
% 1.46/1.26 thf(f9,plain,(
% 1.46/1.26 ($false = (!! @ (a > a > a) @ (^[Y0 : a > a > a]: (((((((((((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1 @ Y1) = Y1))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ (sK2 @ Y3 @ Y1)) = (sK2 @ (sK2 @ Y2 @ Y3) @ Y1))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) = (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ (Y0 @ Y3 @ Y1)) = (Y0 @ (Y0 @ Y2 @ Y3) @ Y1))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ (sK2 @ Y2 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ (sK2 @ Y3 @ Y1)) = (sK2 @ (Y0 @ Y2 @ Y3) @ (Y0 @ Y2 @ Y1)))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ (Y0 @ Y2 @ Y1) @ Y1) = Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (sK2 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y1) = Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (sK2 @ Y3 @ Y1) @ (sK2 @ Y3 @ Y2)) = (sK2 @ Y3 @ (Y0 @ Y1 @ Y2)))))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y1) = Y1) => ((sK2 @ Y2 @ (Y0 @ Y3 @ Y1)) = (Y0 @ (sK2 @ Y2 @ Y3) @ Y1)))))))))))))),
% 1.46/1.26 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.46/1.26 thf(f8,plain,(
% 1.46/1.26 ($false = ((^[Y0 : a > a > a]: (!! @ (a > a > a) @ (^[Y1 : a > a > a]: (((((((((((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) = Y2))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ (Y0 @ Y4 @ Y2)) = (Y0 @ (Y0 @ Y3 @ Y4) @ Y2))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) = (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ (Y1 @ Y4 @ Y2)) = (Y1 @ (Y1 @ Y3 @ Y4) @ Y2))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (Y0 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ (Y0 @ Y4 @ Y2)) = (Y0 @ (Y1 @ Y3 @ Y4) @ (Y1 @ Y3 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) = (Y0 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y2) = Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ (Y0 @ Y4 @ Y2) @ (Y0 @ Y4 @ Y3)) = (Y0 @ Y4 @ (Y1 @ Y2 @ Y3)))))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) = Y2) => ((Y0 @ Y3 @ (Y1 @ Y4 @ Y2)) = (Y1 @ (Y0 @ Y3 @ Y4) @ Y2))))))))))))) @ sK2))),
% 1.46/1.26 inference(sigma_clausification,[status(thm)],[f7])).
% 1.46/1.26 thf(f7,plain,(
% 1.46/1.26 ($false = (!! @ (a > a > a) @ (^[Y0 : a > a > a]: (!! @ (a > a > a) @ (^[Y1 : a > a > a]: (((((((((((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) = Y2))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ (Y0 @ Y4 @ Y2)) = (Y0 @ (Y0 @ Y3 @ Y4) @ Y2))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) = (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ (Y1 @ Y4 @ Y2)) = (Y1 @ (Y1 @ Y3 @ Y4) @ Y2))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (Y0 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ (Y0 @ Y4 @ Y2)) = (Y0 @ (Y1 @ Y3 @ Y4) @ (Y1 @ Y3 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) = (Y0 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y2) = Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ (Y0 @ Y4 @ Y2) @ (Y0 @ Y4 @ Y3)) = (Y0 @ Y4 @ (Y1 @ Y2 @ Y3)))))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) = Y2) => ((Y0 @ Y3 @ (Y1 @ Y4 @ Y2)) = (Y1 @ (Y0 @ Y3 @ Y4) @ Y2)))))))))))))))),
% 1.46/1.26 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.46/1.26 thf(f6,plain,(
% 1.46/1.26 ((~ (!! @ (a > a > a) @ (^[Y0 : a > a > a]: (!! @ (a > a > a) @ (^[Y1 : a > a > a]: (((((((((((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) = Y2))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ (Y0 @ Y4 @ Y2)) = (Y0 @ (Y0 @ Y3 @ Y4) @ Y2))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) = (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ (Y1 @ Y4 @ Y2)) = (Y1 @ (Y1 @ Y3 @ Y4) @ Y2))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (Y0 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ (Y0 @ Y4 @ Y2)) = (Y0 @ (Y1 @ Y3 @ Y4) @ (Y1 @ Y3 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) = (Y0 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y2) = Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ (Y0 @ Y4 @ Y2) @ (Y0 @ Y4 @ Y3)) = (Y0 @ Y4 @ (Y1 @ Y2 @ Y3)))))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) = Y2) => ((Y0 @ Y3 @ (Y1 @ Y4 @ Y2)) = (Y1 @ (Y0 @ Y3 @ Y4) @ Y2))))))))))))))) = $true)),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f5])).
% 1.46/1.26 thf(f5,plain,(
% 1.46/1.26 ((~ (!! @ (a > a > a) @ (^[Y0 : a > a > a]: (!! @ (a > a > a) @ (^[Y1 : a > a > a]: (((((((((((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2 @ Y2) = Y2))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ (Y0 @ Y4 @ Y2)) = (Y0 @ (Y0 @ Y3 @ Y4) @ Y2))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) = (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ (Y1 @ Y4 @ Y2)) = (Y1 @ (Y1 @ Y3 @ Y4) @ Y2))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ (Y0 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ (Y0 @ Y4 @ Y2)) = (Y0 @ (Y1 @ Y3 @ Y4) @ (Y1 @ Y3 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ (Y1 @ Y3 @ Y2) @ Y2) = Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) = (Y0 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y2) = Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ (Y0 @ Y4 @ Y2) @ (Y0 @ Y4 @ Y3)) = (Y0 @ Y4 @ (Y1 @ Y2 @ Y3)))))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) = Y2) => ((Y0 @ Y3 @ (Y1 @ Y4 @ Y2)) = (Y1 @ (Y0 @ Y3 @ Y4) @ Y2))))))))))))))) = $true)),
% 1.46/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.26 thf(f4,plain,(
% 1.46/1.26 ~! [X0 : a > a > a,X1 : a > a > a] : ((! [X2 : a,X3 : a,X4 : a] : ((X0 @ (X1 @ X2 @ X4) @ (X1 @ X2 @ X3)) = (X1 @ X2 @ (X0 @ X4 @ X3))) & ! [X5 : a] : ((X1 @ X5 @ X5) = X5) & ! [X6 : a,X7 : a] : ((X1 @ X7 @ X6) = (X1 @ X6 @ X7)) & ! [X8 : a,X9 : a] : ((X1 @ (X0 @ X8 @ X9) @ X9) = X9) & ! [X10 : a,X11 : a,X12 : a] : ((X0 @ X11 @ (X1 @ X10 @ X12)) = (X1 @ (X0 @ X11 @ X10) @ (X0 @ X11 @ X12))) & ! [X13 : a,X14 : a] : ((X0 @ (X1 @ X13 @ X14) @ X14) = X14) & ! [X15 : a,X16 : a,X17 : a] : ((X0 @ X16 @ (X0 @ X15 @ X17)) = (X0 @ (X0 @ X16 @ X15) @ X17)) & ! [X18 : a,X19 : a] : ((X0 @ X19 @ X18) = (X0 @ X18 @ X19)) & ! [X20 : a,X21 : a,X22 : a] : ((X1 @ X21 @ (X1 @ X20 @ X22)) = (X1 @ (X1 @ X21 @ X20) @ X22)) & ! [X23 : a] : ((X0 @ X23 @ X23) = X23)) => ! [X24 : a,X25 : a,X26 : a] : (((X1 @ X25 @ X26) = X26) => ((X1 @ X25 @ (X0 @ X24 @ X26)) = (X0 @ (X1 @ X25 @ X24) @ X26))))),
% 1.46/1.26 inference(rectify,[status(thm)],[f2])).
% 1.46/1.26 thf(f2,negated_conjecture,(
% 1.46/1.26 ~! [X1 : a > a > a,X0 : a > a > a] : ((! [X2 : a,X4 : a,X3 : a] : ((X0 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X0 @ X2 @ X3) @ (X0 @ X2 @ X4))) & ! [X2 : a] : ((X0 @ X2 @ X2) = X2) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) = (X0 @ X3 @ X2)) & ! [X2 : a,X3 : a] : ((X0 @ (X1 @ X2 @ X3) @ X3) = X3) & ! [X3 : a,X2 : a,X4 : a] : ((X1 @ X2 @ (X0 @ X3 @ X4)) = (X0 @ (X1 @ X2 @ X3) @ (X1 @ X2 @ X4))) & ! [X2 : a,X3 : a] : ((X1 @ (X0 @ X2 @ X3) @ X3) = X3) & ! [X3 : a,X2 : a,X4 : a] : ((X1 @ (X1 @ X2 @ X3) @ X4) = (X1 @ X2 @ (X1 @ X3 @ X4))) & ! [X2 : a,X3 : a] : ((X1 @ X2 @ X3) = (X1 @ X3 @ X2)) & ! [X3 : a,X2 : a,X4 : a] : ((X0 @ (X0 @ X2 @ X3) @ X4) = (X0 @ X2 @ (X0 @ X3 @ X4))) & ! [X2 : a] : ((X1 @ X2 @ X2) = X2)) => ! [X3 : a,X2 : a,X4 : a] : (((X0 @ X2 @ X4) = X4) => ((X0 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X0 @ X2 @ X3) @ X4))))),
% 1.46/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.26 thf(f1,conjecture,(
% 1.46/1.26 ! [X1 : a > a > a,X0 : a > a > a] : ((! [X2 : a,X4 : a,X3 : a] : ((X0 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X0 @ X2 @ X3) @ (X0 @ X2 @ X4))) & ! [X2 : a] : ((X0 @ X2 @ X2) = X2) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) = (X0 @ X3 @ X2)) & ! [X2 : a,X3 : a] : ((X0 @ (X1 @ X2 @ X3) @ X3) = X3) & ! [X3 : a,X2 : a,X4 : a] : ((X1 @ X2 @ (X0 @ X3 @ X4)) = (X0 @ (X1 @ X2 @ X3) @ (X1 @ X2 @ X4))) & ! [X2 : a,X3 : a] : ((X1 @ (X0 @ X2 @ X3) @ X3) = X3) & ! [X3 : a,X2 : a,X4 : a] : ((X1 @ (X1 @ X2 @ X3) @ X4) = (X1 @ X2 @ (X1 @ X3 @ X4))) & ! [X2 : a,X3 : a] : ((X1 @ X2 @ X3) = (X1 @ X3 @ X2)) & ! [X3 : a,X2 : a,X4 : a] : ((X0 @ (X0 @ X2 @ X3) @ X4) = (X0 @ X2 @ (X0 @ X3 @ X4))) & ! [X2 : a] : ((X1 @ X2 @ X2) = X2)) => ! [X3 : a,X2 : a,X4 : a] : (((X0 @ X2 @ X4) = X4) => ((X0 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X0 @ X2 @ X3) @ X4))))),
% 1.46/1.26 file('/export/starexec/sandbox2/tmp/tmp.clWWoTZ4Bi/DTF2THF_32249.p',cMODULAR_THM_pme)).
% 1.46/1.26 thf(f107,plain,(
% 1.46/1.26 ((sK2 @ sK5 @ (sK3 @ sK4 @ sK6)) != (sK2 @ sK5 @ (sK3 @ sK6 @ sK4)))),
% 1.46/1.26 inference(superposition,[status(thm)],[f76,f98])).
% 1.46/1.26 thf(f98,plain,(
% 1.46/1.26 ( ! [X0 : a] : (((sK2 @ sK5 @ (sK3 @ X0 @ sK4)) = (sK3 @ (sK2 @ sK5 @ X0) @ sK4))) )),
% 1.46/1.26 inference(superposition,[status(thm)],[f32,f23])).
% 1.46/1.26 thf(f23,plain,(
% 1.46/1.26 (sK4 = (sK2 @ sK5 @ sK4))),
% 1.46/1.26 inference(equality_proxy_clausification,[status(thm)],[f21])).
% 1.46/1.26 thf(f21,plain,(
% 1.46/1.26 (((sK2 @ sK5 @ sK4) = sK4) = $true)),
% 1.46/1.26 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.46/1.26 thf(f19,plain,(
% 1.46/1.26 ($false = (((sK2 @ sK5 @ sK4) = sK4) => ((sK2 @ sK5 @ (sK3 @ sK6 @ sK4)) = (sK3 @ (sK2 @ sK5 @ sK6) @ sK4))))),
% 1.46/1.26 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.46/1.26 thf(f18,plain,(
% 1.46/1.26 ($false = ((^[Y0 : a]: (((sK2 @ sK5 @ sK4) = sK4) => ((sK2 @ sK5 @ (sK3 @ Y0 @ sK4)) = (sK3 @ (sK2 @ sK5 @ Y0) @ sK4)))) @ sK6))),
% 1.46/1.26 inference(sigma_clausification,[status(thm)],[f17])).
% 1.46/1.26 thf(f17,plain,(
% 1.46/1.26 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ sK5 @ sK4) = sK4) => ((sK2 @ sK5 @ (sK3 @ Y0 @ sK4)) = (sK3 @ (sK2 @ sK5 @ Y0) @ sK4))))))),
% 1.46/1.26 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.46/1.26 thf(f16,plain,(
% 1.46/1.26 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ sK4) = sK4) => ((sK2 @ Y0 @ (sK3 @ Y1 @ sK4)) = (sK3 @ (sK2 @ Y0 @ Y1) @ sK4)))))) @ sK5))),
% 1.46/1.26 inference(sigma_clausification,[status(thm)],[f15])).
% 1.46/1.26 thf(f15,plain,(
% 1.46/1.26 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ sK4) = sK4) => ((sK2 @ Y0 @ (sK3 @ Y1 @ sK4)) = (sK3 @ (sK2 @ Y0 @ Y1) @ sK4))))))) = $false)),
% 1.46/1.26 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.46/1.26 thf(f14,plain,(
% 1.46/1.26 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y0) = Y0) => ((sK2 @ Y1 @ (sK3 @ Y2 @ Y0)) = (sK3 @ (sK2 @ Y1 @ Y2) @ Y0)))))))) @ sK4) = $false)),
% 1.46/1.26 inference(sigma_clausification,[status(thm)],[f12])).
% 1.46/1.26 thf(f12,plain,(
% 1.46/1.26 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y0) = Y0) => ((sK2 @ Y1 @ (sK3 @ Y2 @ Y0)) = (sK3 @ (sK2 @ Y1 @ Y2) @ Y0))))))))) = $false)),
% 1.46/1.26 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.46/1.26 thf(f32,plain,(
% 1.46/1.26 ( ! [X2 : a,X3 : a,X1 : a] : (((sK3 @ (sK2 @ X3 @ X1) @ (sK2 @ X3 @ X2)) = (sK2 @ X3 @ (sK3 @ X1 @ X2)))) )),
% 1.46/1.26 inference(equality_proxy_clausification,[status(thm)],[f31])).
% 1.46/1.26 thf(f31,plain,(
% 1.46/1.26 ( ! [X2 : a,X3 : a,X1 : a] : ((((sK3 @ (sK2 @ X3 @ X1) @ (sK2 @ X3 @ X2)) = (sK2 @ X3 @ (sK3 @ X1 @ X2))) = $true)) )),
% 1.46/1.26 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.46/1.26 thf(f30,plain,(
% 1.46/1.26 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ (sK2 @ Y0 @ X1) @ (sK2 @ Y0 @ X2)) = (sK2 @ Y0 @ (sK3 @ X1 @ X2)))) @ X3))) )),
% 1.46/1.26 inference(pi_clausification,[status(thm)],[f29])).
% 1.46/1.26 thf(f29,plain,(
% 1.46/1.26 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK3 @ (sK2 @ Y0 @ X1) @ (sK2 @ Y0 @ X2)) = (sK2 @ Y0 @ (sK3 @ X1 @ X2))))) = $true)) )),
% 1.46/1.26 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.46/1.26 thf(f28,plain,(
% 1.46/1.26 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y1 @ X1) @ (sK2 @ Y1 @ Y0)) = (sK2 @ Y1 @ (sK3 @ X1 @ Y0)))))) @ X2) = $true)) )),
% 1.46/1.26 inference(pi_clausification,[status(thm)],[f27])).
% 1.46/1.26 thf(f27,plain,(
% 1.46/1.26 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ (sK2 @ Y1 @ X1) @ (sK2 @ Y1 @ Y0)) = (sK2 @ Y1 @ (sK3 @ X1 @ Y0))))))) = $true)) )),
% 1.46/1.26 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.46/1.26 thf(f26,plain,(
% 1.46/1.26 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1)) = (sK2 @ Y2 @ (sK3 @ Y0 @ Y1)))))))) @ X1))) )),
% 1.46/1.26 inference(pi_clausification,[status(thm)],[f24])).
% 1.46/1.26 thf(f24,plain,(
% 1.46/1.26 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ (sK2 @ Y2 @ Y0) @ (sK2 @ Y2 @ Y1)) = (sK2 @ Y2 @ (sK3 @ Y0 @ Y1))))))))) = $true)),
% 1.46/1.26 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.46/1.26 thf(f76,plain,(
% 1.46/1.26 ((sK3 @ (sK2 @ sK5 @ sK6) @ sK4) != (sK2 @ sK5 @ (sK3 @ sK4 @ sK6)))),
% 1.46/1.26 inference(backward_demodulation,[status(thm)],[f22,f75])).
% 1.46/1.26 thf(f22,plain,(
% 1.46/1.26 ((sK3 @ (sK2 @ sK5 @ sK6) @ sK4) != (sK2 @ sK5 @ (sK3 @ sK6 @ sK4)))),
% 1.46/1.26 inference(equality_proxy_clausification,[status(thm)],[f20])).
% 1.46/1.26 thf(f20,plain,(
% 1.46/1.26 ($false = ((sK2 @ sK5 @ (sK3 @ sK6 @ sK4)) = (sK3 @ (sK2 @ sK5 @ sK6) @ sK4)))),
% 1.46/1.26 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.46/1.26 % SZS output end Proof for DTF2THF_32249
% 1.46/1.26 % (32354)------------------------------
% 1.46/1.26 % (32354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (32354)Termination reason: Refutation
% 1.46/1.26
% 1.46/1.26 % (32354)Memory used [KB]: 5756
% 1.46/1.26 % (32354)Time elapsed: 0.013 s
% 1.46/1.26 % (32354)Instructions burned: 28 (million)
% 1.46/1.26 % (32354)------------------------------
% 1.46/1.26 % (32354)------------------------------
% 1.46/1.26 % (32345)Success in time 0.037 s
%------------------------------------------------------------------------------