%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ093^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 09:28:27 AM UTC 2026
% Result : Theorem 1.62s 1.48s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 1
% Syntax : Number of formulae : 51 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 1410 (1160 equ; 0 cnn)
% Maximal formula atoms : 32 ( 27 avg)
% Number of connectives : 7040 ( 426 ~; 193 |; 632 &;5363 @)
% ( 0 <=>; 231 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 11 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 1 usr; 4 con; 0-13 aty)
% ( 27 !!; 168 ??; 0 @@+; 0 @@-)
% Number of variables : 639 ( 208 ^; 395 !; 36 ?; 639 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_25,type,
sK1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(f308,plain,
$false,
inference(equality_resolution,[status(thm)],[f279]) ).
thf(f279,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X5 @ X7 @ X8 @ X9 @ X0 )
!= ( sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X5 @ X7 @ X8 @ X9 @ X1 ) ),
inference(equality_resolution,[status(thm)],[f208]) ).
thf(f208,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ( sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X7 )
!= ( sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X5 ) )
| ( ( sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X0 )
!= ( sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X1 ) ) ),
inference(subsumption_resolution,[status(thm)],[f123,f103]) ).
thf(f103,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) ),
inference(equality_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
= $true ),
inference(not_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( $false
= ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( $false
= ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( $false
= ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( ( ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10 ) ) )
=> ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6 ) ) )
& ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6 ) ) )
=> ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10 ) ) )
& ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) ) )
=> ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3 ) ) )
& ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) ) )
=> ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6 ) ) )
& ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3 ) ) )
=> ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) ) )
& ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) ) )
=> ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) ) ) )
=> ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( ^ [Y0: $i > $i] :
( ( ( ( ( ( Y0 @ X12 )
= ( Y0 @ X4 ) )
& ( ( Y0 @ X12 )
= ( Y0 @ X3 ) )
& ( ( Y0 @ X4 )
= ( Y0 @ X2 ) )
& ( ( Y0 @ X11 )
!= ( Y0 @ X10 ) ) )
=> ( ( Y0 @ X7 )
!= ( Y0 @ X6 ) ) )
& ( ( ( ( Y0 @ X2 )
= ( Y0 @ X3 ) )
& ( ( Y0 @ X1 )
= ( Y0 @ X7 ) )
& ( ( Y0 @ X9 )
= ( Y0 @ X6 ) ) )
=> ( ( Y0 @ X11 )
!= ( Y0 @ X10 ) ) )
& ( ( ( ( Y0 @ X7 )
= ( Y0 @ X6 ) )
& ( ( Y0 @ X11 )
= ( Y0 @ X8 ) )
& ( ( Y0 @ X10 )
= ( Y0 @ X5 ) ) )
=> ( ( Y0 @ X2 )
= ( Y0 @ X3 ) ) )
& ( ( ( ( Y0 @ X4 )
= ( Y0 @ X2 ) )
& ( ( Y0 @ X12 )
!= ( Y0 @ X5 ) )
& ( ( Y0 @ X11 )
= ( Y0 @ X8 ) ) )
=> ( ( Y0 @ X7 )
= ( Y0 @ X6 ) ) )
& ( ( ( ( Y0 @ X10 )
= ( Y0 @ X5 ) )
& ( ( Y0 @ X10 )
= ( Y0 @ X3 ) )
& ( ( Y0 @ X7 )
!= ( Y0 @ X6 ) )
& ( ( Y0 @ X12 )
= ( Y0 @ X3 ) ) )
=> ( ( Y0 @ X9 )
= ( Y0 @ X4 ) ) )
& ( ( ( ( Y0 @ X1 )
= ( Y0 @ X7 ) )
& ( ( Y0 @ X11 )
= ( Y0 @ X8 ) )
& ( ( Y0 @ X12 )
= ( Y0 @ X5 ) ) )
=> ( ( Y0 @ X9 )
!= ( Y0 @ X4 ) ) ) )
=> ( ( ( Y0 @ X10 )
!= ( Y0 @ X5 ) )
| ( ( Y0 @ X11 )
!= ( Y0 @ X8 ) )
| ( ( Y0 @ X12 )
!= ( Y0 @ X3 ) )
| ( ( Y0 @ X9 )
!= ( Y0 @ X6 ) )
| ( ( Y0 @ X1 )
!= ( Y0 @ X7 ) )
| ( ( Y0 @ X4 )
!= ( Y0 @ X2 ) ) ) )
@ ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 ) )
= $false ),
inference(sigma_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( $false
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( ( ( ( ( Y0 @ X12 )
= ( Y0 @ X4 ) )
& ( ( Y0 @ X12 )
= ( Y0 @ X3 ) )
& ( ( Y0 @ X4 )
= ( Y0 @ X2 ) )
& ( ( Y0 @ X11 )
!= ( Y0 @ X10 ) ) )
=> ( ( Y0 @ X7 )
!= ( Y0 @ X6 ) ) )
& ( ( ( ( Y0 @ X2 )
= ( Y0 @ X3 ) )
& ( ( Y0 @ X1 )
= ( Y0 @ X7 ) )
& ( ( Y0 @ X9 )
= ( Y0 @ X6 ) ) )
=> ( ( Y0 @ X11 )
!= ( Y0 @ X10 ) ) )
& ( ( ( ( Y0 @ X7 )
= ( Y0 @ X6 ) )
& ( ( Y0 @ X11 )
= ( Y0 @ X8 ) )
& ( ( Y0 @ X10 )
= ( Y0 @ X5 ) ) )
=> ( ( Y0 @ X2 )
= ( Y0 @ X3 ) ) )
& ( ( ( ( Y0 @ X4 )
= ( Y0 @ X2 ) )
& ( ( Y0 @ X12 )
!= ( Y0 @ X5 ) )
& ( ( Y0 @ X11 )
= ( Y0 @ X8 ) ) )
=> ( ( Y0 @ X7 )
= ( Y0 @ X6 ) ) )
& ( ( ( ( Y0 @ X10 )
= ( Y0 @ X5 ) )
& ( ( Y0 @ X10 )
= ( Y0 @ X3 ) )
& ( ( Y0 @ X7 )
!= ( Y0 @ X6 ) )
& ( ( Y0 @ X12 )
= ( Y0 @ X3 ) ) )
=> ( ( Y0 @ X9 )
= ( Y0 @ X4 ) ) )
& ( ( ( ( Y0 @ X1 )
= ( Y0 @ X7 ) )
& ( ( Y0 @ X11 )
= ( Y0 @ X8 ) )
& ( ( Y0 @ X12 )
= ( Y0 @ X5 ) ) )
=> ( ( Y0 @ X9 )
!= ( Y0 @ X4 ) ) ) )
=> ( ( ( Y0 @ X10 )
!= ( Y0 @ X5 ) )
| ( ( Y0 @ X11 )
!= ( Y0 @ X8 ) )
| ( ( Y0 @ X12 )
!= ( Y0 @ X3 ) )
| ( ( Y0 @ X9 )
!= ( Y0 @ X6 ) )
| ( ( Y0 @ X1 )
!= ( Y0 @ X7 ) )
| ( ( Y0 @ X4 )
!= ( Y0 @ X2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( ( ( ( ( Y1 @ Y0 )
= ( Y1 @ X4 ) )
& ( ( Y1 @ Y0 )
= ( Y1 @ X3 ) )
& ( ( Y1 @ X4 )
= ( Y1 @ X2 ) )
& ( ( Y1 @ X11 )
!= ( Y1 @ X10 ) ) )
=> ( ( Y1 @ X7 )
!= ( Y1 @ X6 ) ) )
& ( ( ( ( Y1 @ X2 )
= ( Y1 @ X3 ) )
& ( ( Y1 @ X1 )
= ( Y1 @ X7 ) )
& ( ( Y1 @ X9 )
= ( Y1 @ X6 ) ) )
=> ( ( Y1 @ X11 )
!= ( Y1 @ X10 ) ) )
& ( ( ( ( Y1 @ X7 )
= ( Y1 @ X6 ) )
& ( ( Y1 @ X11 )
= ( Y1 @ X8 ) )
& ( ( Y1 @ X10 )
= ( Y1 @ X5 ) ) )
=> ( ( Y1 @ X2 )
= ( Y1 @ X3 ) ) )
& ( ( ( ( Y1 @ X4 )
= ( Y1 @ X2 ) )
& ( ( Y1 @ Y0 )
!= ( Y1 @ X5 ) )
& ( ( Y1 @ X11 )
= ( Y1 @ X8 ) ) )
=> ( ( Y1 @ X7 )
= ( Y1 @ X6 ) ) )
& ( ( ( ( Y1 @ X10 )
= ( Y1 @ X5 ) )
& ( ( Y1 @ X10 )
= ( Y1 @ X3 ) )
& ( ( Y1 @ X7 )
!= ( Y1 @ X6 ) )
& ( ( Y1 @ Y0 )
= ( Y1 @ X3 ) ) )
=> ( ( Y1 @ X9 )
= ( Y1 @ X4 ) ) )
& ( ( ( ( Y1 @ X1 )
= ( Y1 @ X7 ) )
& ( ( Y1 @ X11 )
= ( Y1 @ X8 ) )
& ( ( Y1 @ Y0 )
= ( Y1 @ X5 ) ) )
=> ( ( Y1 @ X9 )
!= ( Y1 @ X4 ) ) ) )
=> ( ( ( Y1 @ X10 )
!= ( Y1 @ X5 ) )
| ( ( Y1 @ X11 )
!= ( Y1 @ X8 ) )
| ( ( Y1 @ Y0 )
!= ( Y1 @ X3 ) )
| ( ( Y1 @ X9 )
!= ( Y1 @ X6 ) )
| ( ( Y1 @ X1 )
!= ( Y1 @ X7 ) )
| ( ( Y1 @ X4 )
!= ( Y1 @ X2 ) ) ) ) )
@ X12 ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( ( ( ( ( Y1 @ Y0 )
= ( Y1 @ X4 ) )
& ( ( Y1 @ Y0 )
= ( Y1 @ X3 ) )
& ( ( Y1 @ X4 )
= ( Y1 @ X2 ) )
& ( ( Y1 @ X11 )
!= ( Y1 @ X10 ) ) )
=> ( ( Y1 @ X7 )
!= ( Y1 @ X6 ) ) )
& ( ( ( ( Y1 @ X2 )
= ( Y1 @ X3 ) )
& ( ( Y1 @ X1 )
= ( Y1 @ X7 ) )
& ( ( Y1 @ X9 )
= ( Y1 @ X6 ) ) )
=> ( ( Y1 @ X11 )
!= ( Y1 @ X10 ) ) )
& ( ( ( ( Y1 @ X7 )
= ( Y1 @ X6 ) )
& ( ( Y1 @ X11 )
= ( Y1 @ X8 ) )
& ( ( Y1 @ X10 )
= ( Y1 @ X5 ) ) )
=> ( ( Y1 @ X2 )
= ( Y1 @ X3 ) ) )
& ( ( ( ( Y1 @ X4 )
= ( Y1 @ X2 ) )
& ( ( Y1 @ Y0 )
!= ( Y1 @ X5 ) )
& ( ( Y1 @ X11 )
= ( Y1 @ X8 ) ) )
=> ( ( Y1 @ X7 )
= ( Y1 @ X6 ) ) )
& ( ( ( ( Y1 @ X10 )
= ( Y1 @ X5 ) )
& ( ( Y1 @ X10 )
= ( Y1 @ X3 ) )
& ( ( Y1 @ X7 )
!= ( Y1 @ X6 ) )
& ( ( Y1 @ Y0 )
= ( Y1 @ X3 ) ) )
=> ( ( Y1 @ X9 )
= ( Y1 @ X4 ) ) )
& ( ( ( ( Y1 @ X1 )
= ( Y1 @ X7 ) )
& ( ( Y1 @ X11 )
= ( Y1 @ X8 ) )
& ( ( Y1 @ Y0 )
= ( Y1 @ X5 ) ) )
=> ( ( Y1 @ X9 )
!= ( Y1 @ X4 ) ) ) )
=> ( ( ( Y1 @ X10 )
!= ( Y1 @ X5 ) )
| ( ( Y1 @ X11 )
!= ( Y1 @ X8 ) )
| ( ( Y1 @ Y0 )
!= ( Y1 @ X3 ) )
| ( ( Y1 @ X9 )
!= ( Y1 @ X6 ) )
| ( ( Y1 @ X1 )
!= ( Y1 @ X7 ) )
| ( ( Y1 @ X4 )
!= ( Y1 @ X2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( ( ( ( ( Y2 @ Y1 )
= ( Y2 @ X4 ) )
& ( ( Y2 @ Y1 )
= ( Y2 @ X3 ) )
& ( ( Y2 @ X4 )
= ( Y2 @ X2 ) )
& ( ( Y2 @ Y0 )
!= ( Y2 @ X10 ) ) )
=> ( ( Y2 @ X7 )
!= ( Y2 @ X6 ) ) )
& ( ( ( ( Y2 @ X2 )
= ( Y2 @ X3 ) )
& ( ( Y2 @ X1 )
= ( Y2 @ X7 ) )
& ( ( Y2 @ X9 )
= ( Y2 @ X6 ) ) )
=> ( ( Y2 @ Y0 )
!= ( Y2 @ X10 ) ) )
& ( ( ( ( Y2 @ X7 )
= ( Y2 @ X6 ) )
& ( ( Y2 @ Y0 )
= ( Y2 @ X8 ) )
& ( ( Y2 @ X10 )
= ( Y2 @ X5 ) ) )
=> ( ( Y2 @ X2 )
= ( Y2 @ X3 ) ) )
& ( ( ( ( Y2 @ X4 )
= ( Y2 @ X2 ) )
& ( ( Y2 @ Y1 )
!= ( Y2 @ X5 ) )
& ( ( Y2 @ Y0 )
= ( Y2 @ X8 ) ) )
=> ( ( Y2 @ X7 )
= ( Y2 @ X6 ) ) )
& ( ( ( ( Y2 @ X10 )
= ( Y2 @ X5 ) )
& ( ( Y2 @ X10 )
= ( Y2 @ X3 ) )
& ( ( Y2 @ X7 )
!= ( Y2 @ X6 ) )
& ( ( Y2 @ Y1 )
= ( Y2 @ X3 ) ) )
=> ( ( Y2 @ X9 )
= ( Y2 @ X4 ) ) )
& ( ( ( ( Y2 @ X1 )
= ( Y2 @ X7 ) )
& ( ( Y2 @ Y0 )
= ( Y2 @ X8 ) )
& ( ( Y2 @ Y1 )
= ( Y2 @ X5 ) ) )
=> ( ( Y2 @ X9 )
!= ( Y2 @ X4 ) ) ) )
=> ( ( ( Y2 @ X10 )
!= ( Y2 @ X5 ) )
| ( ( Y2 @ Y0 )
!= ( Y2 @ X8 ) )
| ( ( Y2 @ Y1 )
!= ( Y2 @ X3 ) )
| ( ( Y2 @ X9 )
!= ( Y2 @ X6 ) )
| ( ( Y2 @ X1 )
!= ( Y2 @ X7 ) )
| ( ( Y2 @ X4 )
!= ( Y2 @ X2 ) ) ) ) ) )
@ X11 )
= $false ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X10: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( ( ( ( ( Y2 @ Y1 )
= ( Y2 @ X4 ) )
& ( ( Y2 @ Y1 )
= ( Y2 @ X3 ) )
& ( ( Y2 @ X4 )
= ( Y2 @ X2 ) )
& ( ( Y2 @ Y0 )
!= ( Y2 @ X10 ) ) )
=> ( ( Y2 @ X7 )
!= ( Y2 @ X6 ) ) )
& ( ( ( ( Y2 @ X2 )
= ( Y2 @ X3 ) )
& ( ( Y2 @ X1 )
= ( Y2 @ X7 ) )
& ( ( Y2 @ X9 )
= ( Y2 @ X6 ) ) )
=> ( ( Y2 @ Y0 )
!= ( Y2 @ X10 ) ) )
& ( ( ( ( Y2 @ X7 )
= ( Y2 @ X6 ) )
& ( ( Y2 @ Y0 )
= ( Y2 @ X8 ) )
& ( ( Y2 @ X10 )
= ( Y2 @ X5 ) ) )
=> ( ( Y2 @ X2 )
= ( Y2 @ X3 ) ) )
& ( ( ( ( Y2 @ X4 )
= ( Y2 @ X2 ) )
& ( ( Y2 @ Y1 )
!= ( Y2 @ X5 ) )
& ( ( Y2 @ Y0 )
= ( Y2 @ X8 ) ) )
=> ( ( Y2 @ X7 )
= ( Y2 @ X6 ) ) )
& ( ( ( ( Y2 @ X10 )
= ( Y2 @ X5 ) )
& ( ( Y2 @ X10 )
= ( Y2 @ X3 ) )
& ( ( Y2 @ X7 )
!= ( Y2 @ X6 ) )
& ( ( Y2 @ Y1 )
= ( Y2 @ X3 ) ) )
=> ( ( Y2 @ X9 )
= ( Y2 @ X4 ) ) )
& ( ( ( ( Y2 @ X1 )
= ( Y2 @ X7 ) )
& ( ( Y2 @ Y0 )
= ( Y2 @ X8 ) )
& ( ( Y2 @ Y1 )
= ( Y2 @ X5 ) ) )
=> ( ( Y2 @ X9 )
!= ( Y2 @ X4 ) ) ) )
=> ( ( ( Y2 @ X10 )
!= ( Y2 @ X5 ) )
| ( ( Y2 @ Y0 )
!= ( Y2 @ X8 ) )
| ( ( Y2 @ Y1 )
!= ( Y2 @ X3 ) )
| ( ( Y2 @ X9 )
!= ( Y2 @ X6 ) )
| ( ( Y2 @ X1 )
!= ( Y2 @ X7 ) )
| ( ( Y2 @ X4 )
!= ( Y2 @ X2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X10: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( ( ( ( ( ( Y3 @ Y2 )
= ( Y3 @ X4 ) )
& ( ( Y3 @ Y2 )
= ( Y3 @ X3 ) )
& ( ( Y3 @ X4 )
= ( Y3 @ X2 ) )
& ( ( Y3 @ Y1 )
!= ( Y3 @ Y0 ) ) )
=> ( ( Y3 @ X7 )
!= ( Y3 @ X6 ) ) )
& ( ( ( ( Y3 @ X2 )
= ( Y3 @ X3 ) )
& ( ( Y3 @ X1 )
= ( Y3 @ X7 ) )
& ( ( Y3 @ X9 )
= ( Y3 @ X6 ) ) )
=> ( ( Y3 @ Y1 )
!= ( Y3 @ Y0 ) ) )
& ( ( ( ( Y3 @ X7 )
= ( Y3 @ X6 ) )
& ( ( Y3 @ Y1 )
= ( Y3 @ X8 ) )
& ( ( Y3 @ Y0 )
= ( Y3 @ X5 ) ) )
=> ( ( Y3 @ X2 )
= ( Y3 @ X3 ) ) )
& ( ( ( ( Y3 @ X4 )
= ( Y3 @ X2 ) )
& ( ( Y3 @ Y2 )
!= ( Y3 @ X5 ) )
& ( ( Y3 @ Y1 )
= ( Y3 @ X8 ) ) )
=> ( ( Y3 @ X7 )
= ( Y3 @ X6 ) ) )
& ( ( ( ( Y3 @ Y0 )
= ( Y3 @ X5 ) )
& ( ( Y3 @ Y0 )
= ( Y3 @ X3 ) )
& ( ( Y3 @ X7 )
!= ( Y3 @ X6 ) )
& ( ( Y3 @ Y2 )
= ( Y3 @ X3 ) ) )
=> ( ( Y3 @ X9 )
= ( Y3 @ X4 ) ) )
& ( ( ( ( Y3 @ X1 )
= ( Y3 @ X7 ) )
& ( ( Y3 @ Y1 )
= ( Y3 @ X8 ) )
& ( ( Y3 @ Y2 )
= ( Y3 @ X5 ) ) )
=> ( ( Y3 @ X9 )
!= ( Y3 @ X4 ) ) ) )
=> ( ( ( Y3 @ Y0 )
!= ( Y3 @ X5 ) )
| ( ( Y3 @ Y1 )
!= ( Y3 @ X8 ) )
| ( ( Y3 @ Y2 )
!= ( Y3 @ X3 ) )
| ( ( Y3 @ X9 )
!= ( Y3 @ X6 ) )
| ( ( Y3 @ X1 )
!= ( Y3 @ X7 ) )
| ( ( Y3 @ X4 )
!= ( Y3 @ X2 ) ) ) ) ) ) )
@ X10 )
= $false ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( ( ( ( ( ( Y3 @ Y2 )
= ( Y3 @ X4 ) )
& ( ( Y3 @ Y2 )
= ( Y3 @ X3 ) )
& ( ( Y3 @ X4 )
= ( Y3 @ X2 ) )
& ( ( Y3 @ Y1 )
!= ( Y3 @ Y0 ) ) )
=> ( ( Y3 @ X7 )
!= ( Y3 @ X6 ) ) )
& ( ( ( ( Y3 @ X2 )
= ( Y3 @ X3 ) )
& ( ( Y3 @ X1 )
= ( Y3 @ X7 ) )
& ( ( Y3 @ X9 )
= ( Y3 @ X6 ) ) )
=> ( ( Y3 @ Y1 )
!= ( Y3 @ Y0 ) ) )
& ( ( ( ( Y3 @ X7 )
= ( Y3 @ X6 ) )
& ( ( Y3 @ Y1 )
= ( Y3 @ X8 ) )
& ( ( Y3 @ Y0 )
= ( Y3 @ X5 ) ) )
=> ( ( Y3 @ X2 )
= ( Y3 @ X3 ) ) )
& ( ( ( ( Y3 @ X4 )
= ( Y3 @ X2 ) )
& ( ( Y3 @ Y2 )
!= ( Y3 @ X5 ) )
& ( ( Y3 @ Y1 )
= ( Y3 @ X8 ) ) )
=> ( ( Y3 @ X7 )
= ( Y3 @ X6 ) ) )
& ( ( ( ( Y3 @ Y0 )
= ( Y3 @ X5 ) )
& ( ( Y3 @ Y0 )
= ( Y3 @ X3 ) )
& ( ( Y3 @ X7 )
!= ( Y3 @ X6 ) )
& ( ( Y3 @ Y2 )
= ( Y3 @ X3 ) ) )
=> ( ( Y3 @ X9 )
= ( Y3 @ X4 ) ) )
& ( ( ( ( Y3 @ X1 )
= ( Y3 @ X7 ) )
& ( ( Y3 @ Y1 )
= ( Y3 @ X8 ) )
& ( ( Y3 @ Y2 )
= ( Y3 @ X5 ) ) )
=> ( ( Y3 @ X9 )
!= ( Y3 @ X4 ) ) ) )
=> ( ( ( Y3 @ Y0 )
!= ( Y3 @ X5 ) )
| ( ( Y3 @ Y1 )
!= ( Y3 @ X8 ) )
| ( ( Y3 @ Y2 )
!= ( Y3 @ X3 ) )
| ( ( Y3 @ X9 )
!= ( Y3 @ X6 ) )
| ( ( Y3 @ X1 )
!= ( Y3 @ X7 ) )
| ( ( Y3 @ X4 )
!= ( Y3 @ X2 ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( ( ( ( ( ( Y4 @ Y3 )
= ( Y4 @ X4 ) )
& ( ( Y4 @ Y3 )
= ( Y4 @ X3 ) )
& ( ( Y4 @ X4 )
= ( Y4 @ X2 ) )
& ( ( Y4 @ Y2 )
!= ( Y4 @ Y1 ) ) )
=> ( ( Y4 @ X7 )
!= ( Y4 @ X6 ) ) )
& ( ( ( ( Y4 @ X2 )
= ( Y4 @ X3 ) )
& ( ( Y4 @ X1 )
= ( Y4 @ X7 ) )
& ( ( Y4 @ Y0 )
= ( Y4 @ X6 ) ) )
=> ( ( Y4 @ Y2 )
!= ( Y4 @ Y1 ) ) )
& ( ( ( ( Y4 @ X7 )
= ( Y4 @ X6 ) )
& ( ( Y4 @ Y2 )
= ( Y4 @ X8 ) )
& ( ( Y4 @ Y1 )
= ( Y4 @ X5 ) ) )
=> ( ( Y4 @ X2 )
= ( Y4 @ X3 ) ) )
& ( ( ( ( Y4 @ X4 )
= ( Y4 @ X2 ) )
& ( ( Y4 @ Y3 )
!= ( Y4 @ X5 ) )
& ( ( Y4 @ Y2 )
= ( Y4 @ X8 ) ) )
=> ( ( Y4 @ X7 )
= ( Y4 @ X6 ) ) )
& ( ( ( ( Y4 @ Y1 )
= ( Y4 @ X5 ) )
& ( ( Y4 @ Y1 )
= ( Y4 @ X3 ) )
& ( ( Y4 @ X7 )
!= ( Y4 @ X6 ) )
& ( ( Y4 @ Y3 )
= ( Y4 @ X3 ) ) )
=> ( ( Y4 @ Y0 )
= ( Y4 @ X4 ) ) )
& ( ( ( ( Y4 @ X1 )
= ( Y4 @ X7 ) )
& ( ( Y4 @ Y2 )
= ( Y4 @ X8 ) )
& ( ( Y4 @ Y3 )
= ( Y4 @ X5 ) ) )
=> ( ( Y4 @ Y0 )
!= ( Y4 @ X4 ) ) ) )
=> ( ( ( Y4 @ Y1 )
!= ( Y4 @ X5 ) )
| ( ( Y4 @ Y2 )
!= ( Y4 @ X8 ) )
| ( ( Y4 @ Y3 )
!= ( Y4 @ X3 ) )
| ( ( Y4 @ Y0 )
!= ( Y4 @ X6 ) )
| ( ( Y4 @ X1 )
!= ( Y4 @ X7 ) )
| ( ( Y4 @ X4 )
!= ( Y4 @ X2 ) ) ) ) ) ) ) )
@ X9 ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i )
@ ^ [Y4: $i > $i] :
( ( ( ( ( ( Y4 @ Y3 )
= ( Y4 @ X4 ) )
& ( ( Y4 @ Y3 )
= ( Y4 @ X3 ) )
& ( ( Y4 @ X4 )
= ( Y4 @ X2 ) )
& ( ( Y4 @ Y2 )
!= ( Y4 @ Y1 ) ) )
=> ( ( Y4 @ X7 )
!= ( Y4 @ X6 ) ) )
& ( ( ( ( Y4 @ X2 )
= ( Y4 @ X3 ) )
& ( ( Y4 @ X1 )
= ( Y4 @ X7 ) )
& ( ( Y4 @ Y0 )
= ( Y4 @ X6 ) ) )
=> ( ( Y4 @ Y2 )
!= ( Y4 @ Y1 ) ) )
& ( ( ( ( Y4 @ X7 )
= ( Y4 @ X6 ) )
& ( ( Y4 @ Y2 )
= ( Y4 @ X8 ) )
& ( ( Y4 @ Y1 )
= ( Y4 @ X5 ) ) )
=> ( ( Y4 @ X2 )
= ( Y4 @ X3 ) ) )
& ( ( ( ( Y4 @ X4 )
= ( Y4 @ X2 ) )
& ( ( Y4 @ Y3 )
!= ( Y4 @ X5 ) )
& ( ( Y4 @ Y2 )
= ( Y4 @ X8 ) ) )
=> ( ( Y4 @ X7 )
= ( Y4 @ X6 ) ) )
& ( ( ( ( Y4 @ Y1 )
= ( Y4 @ X5 ) )
& ( ( Y4 @ Y1 )
= ( Y4 @ X3 ) )
& ( ( Y4 @ X7 )
!= ( Y4 @ X6 ) )
& ( ( Y4 @ Y3 )
= ( Y4 @ X3 ) ) )
=> ( ( Y4 @ Y0 )
= ( Y4 @ X4 ) ) )
& ( ( ( ( Y4 @ X1 )
= ( Y4 @ X7 ) )
& ( ( Y4 @ Y2 )
= ( Y4 @ X8 ) )
& ( ( Y4 @ Y3 )
= ( Y4 @ X5 ) ) )
=> ( ( Y4 @ Y0 )
!= ( Y4 @ X4 ) ) ) )
=> ( ( ( Y4 @ Y1 )
!= ( Y4 @ X5 ) )
| ( ( Y4 @ Y2 )
!= ( Y4 @ X8 ) )
| ( ( Y4 @ Y3 )
!= ( Y4 @ X3 ) )
| ( ( Y4 @ Y0 )
!= ( Y4 @ X6 ) )
| ( ( Y4 @ X1 )
!= ( Y4 @ X7 ) )
| ( ( Y4 @ X4 )
!= ( Y4 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( ( ( ( ( ( Y5 @ Y4 )
= ( Y5 @ X4 ) )
& ( ( Y5 @ Y4 )
= ( Y5 @ X3 ) )
& ( ( Y5 @ X4 )
= ( Y5 @ X2 ) )
& ( ( Y5 @ Y3 )
!= ( Y5 @ Y2 ) ) )
=> ( ( Y5 @ X7 )
!= ( Y5 @ X6 ) ) )
& ( ( ( ( Y5 @ X2 )
= ( Y5 @ X3 ) )
& ( ( Y5 @ X1 )
= ( Y5 @ X7 ) )
& ( ( Y5 @ Y1 )
= ( Y5 @ X6 ) ) )
=> ( ( Y5 @ Y3 )
!= ( Y5 @ Y2 ) ) )
& ( ( ( ( Y5 @ X7 )
= ( Y5 @ X6 ) )
& ( ( Y5 @ Y3 )
= ( Y5 @ Y0 ) )
& ( ( Y5 @ Y2 )
= ( Y5 @ X5 ) ) )
=> ( ( Y5 @ X2 )
= ( Y5 @ X3 ) ) )
& ( ( ( ( Y5 @ X4 )
= ( Y5 @ X2 ) )
& ( ( Y5 @ Y4 )
!= ( Y5 @ X5 ) )
& ( ( Y5 @ Y3 )
= ( Y5 @ Y0 ) ) )
=> ( ( Y5 @ X7 )
= ( Y5 @ X6 ) ) )
& ( ( ( ( Y5 @ Y2 )
= ( Y5 @ X5 ) )
& ( ( Y5 @ Y2 )
= ( Y5 @ X3 ) )
& ( ( Y5 @ X7 )
!= ( Y5 @ X6 ) )
& ( ( Y5 @ Y4 )
= ( Y5 @ X3 ) ) )
=> ( ( Y5 @ Y1 )
= ( Y5 @ X4 ) ) )
& ( ( ( ( Y5 @ X1 )
= ( Y5 @ X7 ) )
& ( ( Y5 @ Y3 )
= ( Y5 @ Y0 ) )
& ( ( Y5 @ Y4 )
= ( Y5 @ X5 ) ) )
=> ( ( Y5 @ Y1 )
!= ( Y5 @ X4 ) ) ) )
=> ( ( ( Y5 @ Y2 )
!= ( Y5 @ X5 ) )
| ( ( Y5 @ Y3 )
!= ( Y5 @ Y0 ) )
| ( ( Y5 @ Y4 )
!= ( Y5 @ X3 ) )
| ( ( Y5 @ Y1 )
!= ( Y5 @ X6 ) )
| ( ( Y5 @ X1 )
!= ( Y5 @ X7 ) )
| ( ( Y5 @ X4 )
!= ( Y5 @ X2 ) ) ) ) ) ) ) ) )
@ X8 ) ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i )
@ ^ [Y5: $i > $i] :
( ( ( ( ( ( Y5 @ Y4 )
= ( Y5 @ X4 ) )
& ( ( Y5 @ Y4 )
= ( Y5 @ X3 ) )
& ( ( Y5 @ X4 )
= ( Y5 @ X2 ) )
& ( ( Y5 @ Y3 )
!= ( Y5 @ Y2 ) ) )
=> ( ( Y5 @ X7 )
!= ( Y5 @ X6 ) ) )
& ( ( ( ( Y5 @ X2 )
= ( Y5 @ X3 ) )
& ( ( Y5 @ X1 )
= ( Y5 @ X7 ) )
& ( ( Y5 @ Y1 )
= ( Y5 @ X6 ) ) )
=> ( ( Y5 @ Y3 )
!= ( Y5 @ Y2 ) ) )
& ( ( ( ( Y5 @ X7 )
= ( Y5 @ X6 ) )
& ( ( Y5 @ Y3 )
= ( Y5 @ Y0 ) )
& ( ( Y5 @ Y2 )
= ( Y5 @ X5 ) ) )
=> ( ( Y5 @ X2 )
= ( Y5 @ X3 ) ) )
& ( ( ( ( Y5 @ X4 )
= ( Y5 @ X2 ) )
& ( ( Y5 @ Y4 )
!= ( Y5 @ X5 ) )
& ( ( Y5 @ Y3 )
= ( Y5 @ Y0 ) ) )
=> ( ( Y5 @ X7 )
= ( Y5 @ X6 ) ) )
& ( ( ( ( Y5 @ Y2 )
= ( Y5 @ X5 ) )
& ( ( Y5 @ Y2 )
= ( Y5 @ X3 ) )
& ( ( Y5 @ X7 )
!= ( Y5 @ X6 ) )
& ( ( Y5 @ Y4 )
= ( Y5 @ X3 ) ) )
=> ( ( Y5 @ Y1 )
= ( Y5 @ X4 ) ) )
& ( ( ( ( Y5 @ X1 )
= ( Y5 @ X7 ) )
& ( ( Y5 @ Y3 )
= ( Y5 @ Y0 ) )
& ( ( Y5 @ Y4 )
= ( Y5 @ X5 ) ) )
=> ( ( Y5 @ Y1 )
!= ( Y5 @ X4 ) ) ) )
=> ( ( ( Y5 @ Y2 )
!= ( Y5 @ X5 ) )
| ( ( Y5 @ Y3 )
!= ( Y5 @ Y0 ) )
| ( ( Y5 @ Y4 )
!= ( Y5 @ X3 ) )
| ( ( Y5 @ Y1 )
!= ( Y5 @ X6 ) )
| ( ( Y5 @ X1 )
!= ( Y5 @ X7 ) )
| ( ( Y5 @ X4 )
!= ( Y5 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( !! @ ( $i > $i )
@ ^ [Y6: $i > $i] :
( ( ( ( ( ( Y6 @ Y5 )
= ( Y6 @ X4 ) )
& ( ( Y6 @ Y5 )
= ( Y6 @ X3 ) )
& ( ( Y6 @ X4 )
= ( Y6 @ X2 ) )
& ( ( Y6 @ Y4 )
!= ( Y6 @ Y3 ) ) )
=> ( ( Y6 @ Y0 )
!= ( Y6 @ X6 ) ) )
& ( ( ( ( Y6 @ X2 )
= ( Y6 @ X3 ) )
& ( ( Y6 @ X1 )
= ( Y6 @ Y0 ) )
& ( ( Y6 @ Y2 )
= ( Y6 @ X6 ) ) )
=> ( ( Y6 @ Y4 )
!= ( Y6 @ Y3 ) ) )
& ( ( ( ( Y6 @ Y0 )
= ( Y6 @ X6 ) )
& ( ( Y6 @ Y4 )
= ( Y6 @ Y1 ) )
& ( ( Y6 @ Y3 )
= ( Y6 @ X5 ) ) )
=> ( ( Y6 @ X2 )
= ( Y6 @ X3 ) ) )
& ( ( ( ( Y6 @ X4 )
= ( Y6 @ X2 ) )
& ( ( Y6 @ Y5 )
!= ( Y6 @ X5 ) )
& ( ( Y6 @ Y4 )
= ( Y6 @ Y1 ) ) )
=> ( ( Y6 @ Y0 )
= ( Y6 @ X6 ) ) )
& ( ( ( ( Y6 @ Y3 )
= ( Y6 @ X5 ) )
& ( ( Y6 @ Y3 )
= ( Y6 @ X3 ) )
& ( ( Y6 @ Y0 )
!= ( Y6 @ X6 ) )
& ( ( Y6 @ Y5 )
= ( Y6 @ X3 ) ) )
=> ( ( Y6 @ Y2 )
= ( Y6 @ X4 ) ) )
& ( ( ( ( Y6 @ X1 )
= ( Y6 @ Y0 ) )
& ( ( Y6 @ Y4 )
= ( Y6 @ Y1 ) )
& ( ( Y6 @ Y5 )
= ( Y6 @ X5 ) ) )
=> ( ( Y6 @ Y2 )
!= ( Y6 @ X4 ) ) ) )
=> ( ( ( Y6 @ Y3 )
!= ( Y6 @ X5 ) )
| ( ( Y6 @ Y4 )
!= ( Y6 @ Y1 ) )
| ( ( Y6 @ Y5 )
!= ( Y6 @ X3 ) )
| ( ( Y6 @ Y2 )
!= ( Y6 @ X6 ) )
| ( ( Y6 @ X1 )
!= ( Y6 @ Y0 ) )
| ( ( Y6 @ X4 )
!= ( Y6 @ X2 ) ) ) ) ) ) ) ) ) )
@ X7 ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( !! @ ( $i > $i )
@ ^ [Y6: $i > $i] :
( ( ( ( ( ( Y6 @ Y5 )
= ( Y6 @ X4 ) )
& ( ( Y6 @ Y5 )
= ( Y6 @ X3 ) )
& ( ( Y6 @ X4 )
= ( Y6 @ X2 ) )
& ( ( Y6 @ Y4 )
!= ( Y6 @ Y3 ) ) )
=> ( ( Y6 @ Y0 )
!= ( Y6 @ X6 ) ) )
& ( ( ( ( Y6 @ X2 )
= ( Y6 @ X3 ) )
& ( ( Y6 @ X1 )
= ( Y6 @ Y0 ) )
& ( ( Y6 @ Y2 )
= ( Y6 @ X6 ) ) )
=> ( ( Y6 @ Y4 )
!= ( Y6 @ Y3 ) ) )
& ( ( ( ( Y6 @ Y0 )
= ( Y6 @ X6 ) )
& ( ( Y6 @ Y4 )
= ( Y6 @ Y1 ) )
& ( ( Y6 @ Y3 )
= ( Y6 @ X5 ) ) )
=> ( ( Y6 @ X2 )
= ( Y6 @ X3 ) ) )
& ( ( ( ( Y6 @ X4 )
= ( Y6 @ X2 ) )
& ( ( Y6 @ Y5 )
!= ( Y6 @ X5 ) )
& ( ( Y6 @ Y4 )
= ( Y6 @ Y1 ) ) )
=> ( ( Y6 @ Y0 )
= ( Y6 @ X6 ) ) )
& ( ( ( ( Y6 @ Y3 )
= ( Y6 @ X5 ) )
& ( ( Y6 @ Y3 )
= ( Y6 @ X3 ) )
& ( ( Y6 @ Y0 )
!= ( Y6 @ X6 ) )
& ( ( Y6 @ Y5 )
= ( Y6 @ X3 ) ) )
=> ( ( Y6 @ Y2 )
= ( Y6 @ X4 ) ) )
& ( ( ( ( Y6 @ X1 )
= ( Y6 @ Y0 ) )
& ( ( Y6 @ Y4 )
= ( Y6 @ Y1 ) )
& ( ( Y6 @ Y5 )
= ( Y6 @ X5 ) ) )
=> ( ( Y6 @ Y2 )
!= ( Y6 @ X4 ) ) ) )
=> ( ( ( Y6 @ Y3 )
!= ( Y6 @ X5 ) )
| ( ( Y6 @ Y4 )
!= ( Y6 @ Y1 ) )
| ( ( Y6 @ Y5 )
!= ( Y6 @ X3 ) )
| ( ( Y6 @ Y2 )
!= ( Y6 @ X6 ) )
| ( ( Y6 @ X1 )
!= ( Y6 @ Y0 ) )
| ( ( Y6 @ X4 )
!= ( Y6 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( !! @ ( $i > $i )
@ ^ [Y7: $i > $i] :
( ( ( ( ( ( Y7 @ Y6 )
= ( Y7 @ X4 ) )
& ( ( Y7 @ Y6 )
= ( Y7 @ X3 ) )
& ( ( Y7 @ X4 )
= ( Y7 @ X2 ) )
& ( ( Y7 @ Y5 )
!= ( Y7 @ Y4 ) ) )
=> ( ( Y7 @ Y1 )
!= ( Y7 @ Y0 ) ) )
& ( ( ( ( Y7 @ X2 )
= ( Y7 @ X3 ) )
& ( ( Y7 @ X1 )
= ( Y7 @ Y1 ) )
& ( ( Y7 @ Y3 )
= ( Y7 @ Y0 ) ) )
=> ( ( Y7 @ Y5 )
!= ( Y7 @ Y4 ) ) )
& ( ( ( ( Y7 @ Y1 )
= ( Y7 @ Y0 ) )
& ( ( Y7 @ Y5 )
= ( Y7 @ Y2 ) )
& ( ( Y7 @ Y4 )
= ( Y7 @ X5 ) ) )
=> ( ( Y7 @ X2 )
= ( Y7 @ X3 ) ) )
& ( ( ( ( Y7 @ X4 )
= ( Y7 @ X2 ) )
& ( ( Y7 @ Y6 )
!= ( Y7 @ X5 ) )
& ( ( Y7 @ Y5 )
= ( Y7 @ Y2 ) ) )
=> ( ( Y7 @ Y1 )
= ( Y7 @ Y0 ) ) )
& ( ( ( ( Y7 @ Y4 )
= ( Y7 @ X5 ) )
& ( ( Y7 @ Y4 )
= ( Y7 @ X3 ) )
& ( ( Y7 @ Y1 )
!= ( Y7 @ Y0 ) )
& ( ( Y7 @ Y6 )
= ( Y7 @ X3 ) ) )
=> ( ( Y7 @ Y3 )
= ( Y7 @ X4 ) ) )
& ( ( ( ( Y7 @ X1 )
= ( Y7 @ Y1 ) )
& ( ( Y7 @ Y5 )
= ( Y7 @ Y2 ) )
& ( ( Y7 @ Y6 )
= ( Y7 @ X5 ) ) )
=> ( ( Y7 @ Y3 )
!= ( Y7 @ X4 ) ) ) )
=> ( ( ( Y7 @ Y4 )
!= ( Y7 @ X5 ) )
| ( ( Y7 @ Y5 )
!= ( Y7 @ Y2 ) )
| ( ( Y7 @ Y6 )
!= ( Y7 @ X3 ) )
| ( ( Y7 @ Y3 )
!= ( Y7 @ Y0 ) )
| ( ( Y7 @ X1 )
!= ( Y7 @ Y1 ) )
| ( ( Y7 @ X4 )
!= ( Y7 @ X2 ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $false ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( !! @ ( $i > $i )
@ ^ [Y7: $i > $i] :
( ( ( ( ( ( Y7 @ Y6 )
= ( Y7 @ X4 ) )
& ( ( Y7 @ Y6 )
= ( Y7 @ X3 ) )
& ( ( Y7 @ X4 )
= ( Y7 @ X2 ) )
& ( ( Y7 @ Y5 )
!= ( Y7 @ Y4 ) ) )
=> ( ( Y7 @ Y1 )
!= ( Y7 @ Y0 ) ) )
& ( ( ( ( Y7 @ X2 )
= ( Y7 @ X3 ) )
& ( ( Y7 @ X1 )
= ( Y7 @ Y1 ) )
& ( ( Y7 @ Y3 )
= ( Y7 @ Y0 ) ) )
=> ( ( Y7 @ Y5 )
!= ( Y7 @ Y4 ) ) )
& ( ( ( ( Y7 @ Y1 )
= ( Y7 @ Y0 ) )
& ( ( Y7 @ Y5 )
= ( Y7 @ Y2 ) )
& ( ( Y7 @ Y4 )
= ( Y7 @ X5 ) ) )
=> ( ( Y7 @ X2 )
= ( Y7 @ X3 ) ) )
& ( ( ( ( Y7 @ X4 )
= ( Y7 @ X2 ) )
& ( ( Y7 @ Y6 )
!= ( Y7 @ X5 ) )
& ( ( Y7 @ Y5 )
= ( Y7 @ Y2 ) ) )
=> ( ( Y7 @ Y1 )
= ( Y7 @ Y0 ) ) )
& ( ( ( ( Y7 @ Y4 )
= ( Y7 @ X5 ) )
& ( ( Y7 @ Y4 )
= ( Y7 @ X3 ) )
& ( ( Y7 @ Y1 )
!= ( Y7 @ Y0 ) )
& ( ( Y7 @ Y6 )
= ( Y7 @ X3 ) ) )
=> ( ( Y7 @ Y3 )
= ( Y7 @ X4 ) ) )
& ( ( ( ( Y7 @ X1 )
= ( Y7 @ Y1 ) )
& ( ( Y7 @ Y5 )
= ( Y7 @ Y2 ) )
& ( ( Y7 @ Y6 )
= ( Y7 @ X5 ) ) )
=> ( ( Y7 @ Y3 )
!= ( Y7 @ X4 ) ) ) )
=> ( ( ( Y7 @ Y4 )
!= ( Y7 @ X5 ) )
| ( ( Y7 @ Y5 )
!= ( Y7 @ Y2 ) )
| ( ( Y7 @ Y6 )
!= ( Y7 @ X3 ) )
| ( ( Y7 @ Y3 )
!= ( Y7 @ Y0 ) )
| ( ( Y7 @ X1 )
!= ( Y7 @ Y1 ) )
| ( ( Y7 @ X4 )
!= ( Y7 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( !! @ ( $i > $i )
@ ^ [Y8: $i > $i] :
( ( ( ( ( ( Y8 @ Y7 )
= ( Y8 @ X4 ) )
& ( ( Y8 @ Y7 )
= ( Y8 @ X3 ) )
& ( ( Y8 @ X4 )
= ( Y8 @ X2 ) )
& ( ( Y8 @ Y6 )
!= ( Y8 @ Y5 ) ) )
=> ( ( Y8 @ Y2 )
!= ( Y8 @ Y1 ) ) )
& ( ( ( ( Y8 @ X2 )
= ( Y8 @ X3 ) )
& ( ( Y8 @ X1 )
= ( Y8 @ Y2 ) )
& ( ( Y8 @ Y4 )
= ( Y8 @ Y1 ) ) )
=> ( ( Y8 @ Y6 )
!= ( Y8 @ Y5 ) ) )
& ( ( ( ( Y8 @ Y2 )
= ( Y8 @ Y1 ) )
& ( ( Y8 @ Y6 )
= ( Y8 @ Y3 ) )
& ( ( Y8 @ Y5 )
= ( Y8 @ Y0 ) ) )
=> ( ( Y8 @ X2 )
= ( Y8 @ X3 ) ) )
& ( ( ( ( Y8 @ X4 )
= ( Y8 @ X2 ) )
& ( ( Y8 @ Y7 )
!= ( Y8 @ Y0 ) )
& ( ( Y8 @ Y6 )
= ( Y8 @ Y3 ) ) )
=> ( ( Y8 @ Y2 )
= ( Y8 @ Y1 ) ) )
& ( ( ( ( Y8 @ Y5 )
= ( Y8 @ Y0 ) )
& ( ( Y8 @ Y5 )
= ( Y8 @ X3 ) )
& ( ( Y8 @ Y2 )
!= ( Y8 @ Y1 ) )
& ( ( Y8 @ Y7 )
= ( Y8 @ X3 ) ) )
=> ( ( Y8 @ Y4 )
= ( Y8 @ X4 ) ) )
& ( ( ( ( Y8 @ X1 )
= ( Y8 @ Y2 ) )
& ( ( Y8 @ Y6 )
= ( Y8 @ Y3 ) )
& ( ( Y8 @ Y7 )
= ( Y8 @ Y0 ) ) )
=> ( ( Y8 @ Y4 )
!= ( Y8 @ X4 ) ) ) )
=> ( ( ( Y8 @ Y5 )
!= ( Y8 @ Y0 ) )
| ( ( Y8 @ Y6 )
!= ( Y8 @ Y3 ) )
| ( ( Y8 @ Y7 )
!= ( Y8 @ X3 ) )
| ( ( Y8 @ Y4 )
!= ( Y8 @ Y1 ) )
| ( ( Y8 @ X1 )
!= ( Y8 @ Y2 ) )
| ( ( Y8 @ X4 )
!= ( Y8 @ X2 ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ),
inference(pi_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( !! @ ( $i > $i )
@ ^ [Y8: $i > $i] :
( ( ( ( ( ( Y8 @ Y7 )
= ( Y8 @ X4 ) )
& ( ( Y8 @ Y7 )
= ( Y8 @ X3 ) )
& ( ( Y8 @ X4 )
= ( Y8 @ X2 ) )
& ( ( Y8 @ Y6 )
!= ( Y8 @ Y5 ) ) )
=> ( ( Y8 @ Y2 )
!= ( Y8 @ Y1 ) ) )
& ( ( ( ( Y8 @ X2 )
= ( Y8 @ X3 ) )
& ( ( Y8 @ X1 )
= ( Y8 @ Y2 ) )
& ( ( Y8 @ Y4 )
= ( Y8 @ Y1 ) ) )
=> ( ( Y8 @ Y6 )
!= ( Y8 @ Y5 ) ) )
& ( ( ( ( Y8 @ Y2 )
= ( Y8 @ Y1 ) )
& ( ( Y8 @ Y6 )
= ( Y8 @ Y3 ) )
& ( ( Y8 @ Y5 )
= ( Y8 @ Y0 ) ) )
=> ( ( Y8 @ X2 )
= ( Y8 @ X3 ) ) )
& ( ( ( ( Y8 @ X4 )
= ( Y8 @ X2 ) )
& ( ( Y8 @ Y7 )
!= ( Y8 @ Y0 ) )
& ( ( Y8 @ Y6 )
= ( Y8 @ Y3 ) ) )
=> ( ( Y8 @ Y2 )
= ( Y8 @ Y1 ) ) )
& ( ( ( ( Y8 @ Y5 )
= ( Y8 @ Y0 ) )
& ( ( Y8 @ Y5 )
= ( Y8 @ X3 ) )
& ( ( Y8 @ Y2 )
!= ( Y8 @ Y1 ) )
& ( ( Y8 @ Y7 )
= ( Y8 @ X3 ) ) )
=> ( ( Y8 @ Y4 )
= ( Y8 @ X4 ) ) )
& ( ( ( ( Y8 @ X1 )
= ( Y8 @ Y2 ) )
& ( ( Y8 @ Y6 )
= ( Y8 @ Y3 ) )
& ( ( Y8 @ Y7 )
= ( Y8 @ Y0 ) ) )
=> ( ( Y8 @ Y4 )
!= ( Y8 @ X4 ) ) ) )
=> ( ( ( Y8 @ Y5 )
!= ( Y8 @ Y0 ) )
| ( ( Y8 @ Y6 )
!= ( Y8 @ Y3 ) )
| ( ( Y8 @ Y7 )
!= ( Y8 @ X3 ) )
| ( ( Y8 @ Y4 )
!= ( Y8 @ Y1 ) )
| ( ( Y8 @ X1 )
!= ( Y8 @ Y2 ) )
| ( ( Y8 @ X4 )
!= ( Y8 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ?? @ $i
@ ^ [Y8: $i] :
( !! @ ( $i > $i )
@ ^ [Y9: $i > $i] :
( ( ( ( ( ( Y9 @ Y8 )
= ( Y9 @ Y0 ) )
& ( ( Y9 @ Y8 )
= ( Y9 @ X3 ) )
& ( ( Y9 @ Y0 )
= ( Y9 @ X2 ) )
& ( ( Y9 @ Y7 )
!= ( Y9 @ Y6 ) ) )
=> ( ( Y9 @ Y3 )
!= ( Y9 @ Y2 ) ) )
& ( ( ( ( Y9 @ X2 )
= ( Y9 @ X3 ) )
& ( ( Y9 @ X1 )
= ( Y9 @ Y3 ) )
& ( ( Y9 @ Y5 )
= ( Y9 @ Y2 ) ) )
=> ( ( Y9 @ Y7 )
!= ( Y9 @ Y6 ) ) )
& ( ( ( ( Y9 @ Y3 )
= ( Y9 @ Y2 ) )
& ( ( Y9 @ Y7 )
= ( Y9 @ Y4 ) )
& ( ( Y9 @ Y6 )
= ( Y9 @ Y1 ) ) )
=> ( ( Y9 @ X2 )
= ( Y9 @ X3 ) ) )
& ( ( ( ( Y9 @ Y0 )
= ( Y9 @ X2 ) )
& ( ( Y9 @ Y8 )
!= ( Y9 @ Y1 ) )
& ( ( Y9 @ Y7 )
= ( Y9 @ Y4 ) ) )
=> ( ( Y9 @ Y3 )
= ( Y9 @ Y2 ) ) )
& ( ( ( ( Y9 @ Y6 )
= ( Y9 @ Y1 ) )
& ( ( Y9 @ Y6 )
= ( Y9 @ X3 ) )
& ( ( Y9 @ Y3 )
!= ( Y9 @ Y2 ) )
& ( ( Y9 @ Y8 )
= ( Y9 @ X3 ) ) )
=> ( ( Y9 @ Y5 )
= ( Y9 @ Y0 ) ) )
& ( ( ( ( Y9 @ X1 )
= ( Y9 @ Y3 ) )
& ( ( Y9 @ Y7 )
= ( Y9 @ Y4 ) )
& ( ( Y9 @ Y8 )
= ( Y9 @ Y1 ) ) )
=> ( ( Y9 @ Y5 )
!= ( Y9 @ Y0 ) ) ) )
=> ( ( ( Y9 @ Y6 )
!= ( Y9 @ Y1 ) )
| ( ( Y9 @ Y7 )
!= ( Y9 @ Y4 ) )
| ( ( Y9 @ Y8 )
!= ( Y9 @ X3 ) )
| ( ( Y9 @ Y5 )
!= ( Y9 @ Y2 ) )
| ( ( Y9 @ X1 )
!= ( Y9 @ Y3 ) )
| ( ( Y9 @ Y0 )
!= ( Y9 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: $i,X3: $i,X1: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ?? @ $i
@ ^ [Y8: $i] :
( !! @ ( $i > $i )
@ ^ [Y9: $i > $i] :
( ( ( ( ( ( Y9 @ Y8 )
= ( Y9 @ Y0 ) )
& ( ( Y9 @ Y8 )
= ( Y9 @ X3 ) )
& ( ( Y9 @ Y0 )
= ( Y9 @ X2 ) )
& ( ( Y9 @ Y7 )
!= ( Y9 @ Y6 ) ) )
=> ( ( Y9 @ Y3 )
!= ( Y9 @ Y2 ) ) )
& ( ( ( ( Y9 @ X2 )
= ( Y9 @ X3 ) )
& ( ( Y9 @ X1 )
= ( Y9 @ Y3 ) )
& ( ( Y9 @ Y5 )
= ( Y9 @ Y2 ) ) )
=> ( ( Y9 @ Y7 )
!= ( Y9 @ Y6 ) ) )
& ( ( ( ( Y9 @ Y3 )
= ( Y9 @ Y2 ) )
& ( ( Y9 @ Y7 )
= ( Y9 @ Y4 ) )
& ( ( Y9 @ Y6 )
= ( Y9 @ Y1 ) ) )
=> ( ( Y9 @ X2 )
= ( Y9 @ X3 ) ) )
& ( ( ( ( Y9 @ Y0 )
= ( Y9 @ X2 ) )
& ( ( Y9 @ Y8 )
!= ( Y9 @ Y1 ) )
& ( ( Y9 @ Y7 )
= ( Y9 @ Y4 ) ) )
=> ( ( Y9 @ Y3 )
= ( Y9 @ Y2 ) ) )
& ( ( ( ( Y9 @ Y6 )
= ( Y9 @ Y1 ) )
& ( ( Y9 @ Y6 )
= ( Y9 @ X3 ) )
& ( ( Y9 @ Y3 )
!= ( Y9 @ Y2 ) )
& ( ( Y9 @ Y8 )
= ( Y9 @ X3 ) ) )
=> ( ( Y9 @ Y5 )
= ( Y9 @ Y0 ) ) )
& ( ( ( ( Y9 @ X1 )
= ( Y9 @ Y3 ) )
& ( ( Y9 @ Y7 )
= ( Y9 @ Y4 ) )
& ( ( Y9 @ Y8 )
= ( Y9 @ Y1 ) ) )
=> ( ( Y9 @ Y5 )
!= ( Y9 @ Y0 ) ) ) )
=> ( ( ( Y9 @ Y6 )
!= ( Y9 @ Y1 ) )
| ( ( Y9 @ Y7 )
!= ( Y9 @ Y4 ) )
| ( ( Y9 @ Y8 )
!= ( Y9 @ X3 ) )
| ( ( Y9 @ Y5 )
!= ( Y9 @ Y2 ) )
| ( ( Y9 @ X1 )
!= ( Y9 @ Y3 ) )
| ( ( Y9 @ Y0 )
!= ( Y9 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X2: $i,X3: $i,X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ?? @ $i
@ ^ [Y8: $i] :
( ?? @ $i
@ ^ [Y9: $i] :
( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( ( ( ( ( ( Y10 @ Y9 )
= ( Y10 @ Y1 ) )
& ( ( Y10 @ Y9 )
= ( Y10 @ Y0 ) )
& ( ( Y10 @ Y1 )
= ( Y10 @ X2 ) )
& ( ( Y10 @ Y8 )
!= ( Y10 @ Y7 ) ) )
=> ( ( Y10 @ Y4 )
!= ( Y10 @ Y3 ) ) )
& ( ( ( ( Y10 @ X2 )
= ( Y10 @ Y0 ) )
& ( ( Y10 @ X1 )
= ( Y10 @ Y4 ) )
& ( ( Y10 @ Y6 )
= ( Y10 @ Y3 ) ) )
=> ( ( Y10 @ Y8 )
!= ( Y10 @ Y7 ) ) )
& ( ( ( ( Y10 @ Y4 )
= ( Y10 @ Y3 ) )
& ( ( Y10 @ Y8 )
= ( Y10 @ Y5 ) )
& ( ( Y10 @ Y7 )
= ( Y10 @ Y2 ) ) )
=> ( ( Y10 @ X2 )
= ( Y10 @ Y0 ) ) )
& ( ( ( ( Y10 @ Y1 )
= ( Y10 @ X2 ) )
& ( ( Y10 @ Y9 )
!= ( Y10 @ Y2 ) )
& ( ( Y10 @ Y8 )
= ( Y10 @ Y5 ) ) )
=> ( ( Y10 @ Y4 )
= ( Y10 @ Y3 ) ) )
& ( ( ( ( Y10 @ Y7 )
= ( Y10 @ Y2 ) )
& ( ( Y10 @ Y7 )
= ( Y10 @ Y0 ) )
& ( ( Y10 @ Y4 )
!= ( Y10 @ Y3 ) )
& ( ( Y10 @ Y9 )
= ( Y10 @ Y0 ) ) )
=> ( ( Y10 @ Y6 )
= ( Y10 @ Y1 ) ) )
& ( ( ( ( Y10 @ X1 )
= ( Y10 @ Y4 ) )
& ( ( Y10 @ Y8 )
= ( Y10 @ Y5 ) )
& ( ( Y10 @ Y9 )
= ( Y10 @ Y2 ) ) )
=> ( ( Y10 @ Y6 )
!= ( Y10 @ Y1 ) ) ) )
=> ( ( ( Y10 @ Y7 )
!= ( Y10 @ Y2 ) )
| ( ( Y10 @ Y8 )
!= ( Y10 @ Y5 ) )
| ( ( Y10 @ Y9 )
!= ( Y10 @ Y0 ) )
| ( ( Y10 @ Y6 )
!= ( Y10 @ Y3 ) )
| ( ( Y10 @ X1 )
!= ( Y10 @ Y4 ) )
| ( ( Y10 @ Y1 )
!= ( Y10 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X2: $i,X1: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ?? @ $i
@ ^ [Y8: $i] :
( ?? @ $i
@ ^ [Y9: $i] :
( !! @ ( $i > $i )
@ ^ [Y10: $i > $i] :
( ( ( ( ( ( Y10 @ Y9 )
= ( Y10 @ Y1 ) )
& ( ( Y10 @ Y9 )
= ( Y10 @ Y0 ) )
& ( ( Y10 @ Y1 )
= ( Y10 @ X2 ) )
& ( ( Y10 @ Y8 )
!= ( Y10 @ Y7 ) ) )
=> ( ( Y10 @ Y4 )
!= ( Y10 @ Y3 ) ) )
& ( ( ( ( Y10 @ X2 )
= ( Y10 @ Y0 ) )
& ( ( Y10 @ X1 )
= ( Y10 @ Y4 ) )
& ( ( Y10 @ Y6 )
= ( Y10 @ Y3 ) ) )
=> ( ( Y10 @ Y8 )
!= ( Y10 @ Y7 ) ) )
& ( ( ( ( Y10 @ Y4 )
= ( Y10 @ Y3 ) )
& ( ( Y10 @ Y8 )
= ( Y10 @ Y5 ) )
& ( ( Y10 @ Y7 )
= ( Y10 @ Y2 ) ) )
=> ( ( Y10 @ X2 )
= ( Y10 @ Y0 ) ) )
& ( ( ( ( Y10 @ Y1 )
= ( Y10 @ X2 ) )
& ( ( Y10 @ Y9 )
!= ( Y10 @ Y2 ) )
& ( ( Y10 @ Y8 )
= ( Y10 @ Y5 ) ) )
=> ( ( Y10 @ Y4 )
= ( Y10 @ Y3 ) ) )
& ( ( ( ( Y10 @ Y7 )
= ( Y10 @ Y2 ) )
& ( ( Y10 @ Y7 )
= ( Y10 @ Y0 ) )
& ( ( Y10 @ Y4 )
!= ( Y10 @ Y3 ) )
& ( ( Y10 @ Y9 )
= ( Y10 @ Y0 ) ) )
=> ( ( Y10 @ Y6 )
= ( Y10 @ Y1 ) ) )
& ( ( ( ( Y10 @ X1 )
= ( Y10 @ Y4 ) )
& ( ( Y10 @ Y8 )
= ( Y10 @ Y5 ) )
& ( ( Y10 @ Y9 )
= ( Y10 @ Y2 ) ) )
=> ( ( Y10 @ Y6 )
!= ( Y10 @ Y1 ) ) ) )
=> ( ( ( Y10 @ Y7 )
!= ( Y10 @ Y2 ) )
| ( ( Y10 @ Y8 )
!= ( Y10 @ Y5 ) )
| ( ( Y10 @ Y9 )
!= ( Y10 @ Y0 ) )
| ( ( Y10 @ Y6 )
!= ( Y10 @ Y3 ) )
| ( ( Y10 @ X1 )
!= ( Y10 @ Y4 ) )
| ( ( Y10 @ Y1 )
!= ( Y10 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ?? @ $i
@ ^ [Y8: $i] :
( ?? @ $i
@ ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( !! @ ( $i > $i )
@ ^ [Y11: $i > $i] :
( ( ( ( ( ( Y11 @ Y10 )
= ( Y11 @ Y2 ) )
& ( ( Y11 @ Y10 )
= ( Y11 @ Y1 ) )
& ( ( Y11 @ Y2 )
= ( Y11 @ Y0 ) )
& ( ( Y11 @ Y9 )
!= ( Y11 @ Y8 ) ) )
=> ( ( Y11 @ Y5 )
!= ( Y11 @ Y4 ) ) )
& ( ( ( ( Y11 @ Y0 )
= ( Y11 @ Y1 ) )
& ( ( Y11 @ X1 )
= ( Y11 @ Y5 ) )
& ( ( Y11 @ Y7 )
= ( Y11 @ Y4 ) ) )
=> ( ( Y11 @ Y9 )
!= ( Y11 @ Y8 ) ) )
& ( ( ( ( Y11 @ Y5 )
= ( Y11 @ Y4 ) )
& ( ( Y11 @ Y9 )
= ( Y11 @ Y6 ) )
& ( ( Y11 @ Y8 )
= ( Y11 @ Y3 ) ) )
=> ( ( Y11 @ Y0 )
= ( Y11 @ Y1 ) ) )
& ( ( ( ( Y11 @ Y2 )
= ( Y11 @ Y0 ) )
& ( ( Y11 @ Y10 )
!= ( Y11 @ Y3 ) )
& ( ( Y11 @ Y9 )
= ( Y11 @ Y6 ) ) )
=> ( ( Y11 @ Y5 )
= ( Y11 @ Y4 ) ) )
& ( ( ( ( Y11 @ Y8 )
= ( Y11 @ Y3 ) )
& ( ( Y11 @ Y8 )
= ( Y11 @ Y1 ) )
& ( ( Y11 @ Y5 )
!= ( Y11 @ Y4 ) )
& ( ( Y11 @ Y10 )
= ( Y11 @ Y1 ) ) )
=> ( ( Y11 @ Y7 )
= ( Y11 @ Y2 ) ) )
& ( ( ( ( Y11 @ X1 )
= ( Y11 @ Y5 ) )
& ( ( Y11 @ Y9 )
= ( Y11 @ Y6 ) )
& ( ( Y11 @ Y10 )
= ( Y11 @ Y3 ) ) )
=> ( ( Y11 @ Y7 )
!= ( Y11 @ Y2 ) ) ) )
=> ( ( ( Y11 @ Y8 )
!= ( Y11 @ Y3 ) )
| ( ( Y11 @ Y9 )
!= ( Y11 @ Y6 ) )
| ( ( Y11 @ Y10 )
!= ( Y11 @ Y1 ) )
| ( ( Y11 @ Y7 )
!= ( Y11 @ Y4 ) )
| ( ( Y11 @ X1 )
!= ( Y11 @ Y5 ) )
| ( ( Y11 @ Y2 )
!= ( Y11 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $false ),
inference(pi_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
! [X1: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ?? @ $i
@ ^ [Y8: $i] :
( ?? @ $i
@ ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( !! @ ( $i > $i )
@ ^ [Y11: $i > $i] :
( ( ( ( ( ( Y11 @ Y10 )
= ( Y11 @ Y2 ) )
& ( ( Y11 @ Y10 )
= ( Y11 @ Y1 ) )
& ( ( Y11 @ Y2 )
= ( Y11 @ Y0 ) )
& ( ( Y11 @ Y9 )
!= ( Y11 @ Y8 ) ) )
=> ( ( Y11 @ Y5 )
!= ( Y11 @ Y4 ) ) )
& ( ( ( ( Y11 @ Y0 )
= ( Y11 @ Y1 ) )
& ( ( Y11 @ X1 )
= ( Y11 @ Y5 ) )
& ( ( Y11 @ Y7 )
= ( Y11 @ Y4 ) ) )
=> ( ( Y11 @ Y9 )
!= ( Y11 @ Y8 ) ) )
& ( ( ( ( Y11 @ Y5 )
= ( Y11 @ Y4 ) )
& ( ( Y11 @ Y9 )
= ( Y11 @ Y6 ) )
& ( ( Y11 @ Y8 )
= ( Y11 @ Y3 ) ) )
=> ( ( Y11 @ Y0 )
= ( Y11 @ Y1 ) ) )
& ( ( ( ( Y11 @ Y2 )
= ( Y11 @ Y0 ) )
& ( ( Y11 @ Y10 )
!= ( Y11 @ Y3 ) )
& ( ( Y11 @ Y9 )
= ( Y11 @ Y6 ) ) )
=> ( ( Y11 @ Y5 )
= ( Y11 @ Y4 ) ) )
& ( ( ( ( Y11 @ Y8 )
= ( Y11 @ Y3 ) )
& ( ( Y11 @ Y8 )
= ( Y11 @ Y1 ) )
& ( ( Y11 @ Y5 )
!= ( Y11 @ Y4 ) )
& ( ( Y11 @ Y10 )
= ( Y11 @ Y1 ) ) )
=> ( ( Y11 @ Y7 )
= ( Y11 @ Y2 ) ) )
& ( ( ( ( Y11 @ X1 )
= ( Y11 @ Y5 ) )
& ( ( Y11 @ Y9 )
= ( Y11 @ Y6 ) )
& ( ( Y11 @ Y10 )
= ( Y11 @ Y3 ) ) )
=> ( ( Y11 @ Y7 )
!= ( Y11 @ Y2 ) ) ) )
=> ( ( ( Y11 @ Y8 )
!= ( Y11 @ Y3 ) )
| ( ( Y11 @ Y9 )
!= ( Y11 @ Y6 ) )
| ( ( Y11 @ Y10 )
!= ( Y11 @ Y1 ) )
| ( ( Y11 @ Y7 )
!= ( Y11 @ Y4 ) )
| ( ( Y11 @ X1 )
!= ( Y11 @ Y5 ) )
| ( ( Y11 @ Y2 )
!= ( Y11 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ?? @ $i
@ ^ [Y8: $i] :
( ?? @ $i
@ ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ?? @ $i
@ ^ [Y11: $i] :
( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( ( ( ( ( ( Y12 @ Y11 )
= ( Y12 @ Y3 ) )
& ( ( Y12 @ Y11 )
= ( Y12 @ Y2 ) )
& ( ( Y12 @ Y3 )
= ( Y12 @ Y1 ) )
& ( ( Y12 @ Y10 )
!= ( Y12 @ Y9 ) ) )
=> ( ( Y12 @ Y6 )
!= ( Y12 @ Y5 ) ) )
& ( ( ( ( Y12 @ Y1 )
= ( Y12 @ Y2 ) )
& ( ( Y12 @ Y0 )
= ( Y12 @ Y6 ) )
& ( ( Y12 @ Y8 )
= ( Y12 @ Y5 ) ) )
=> ( ( Y12 @ Y10 )
!= ( Y12 @ Y9 ) ) )
& ( ( ( ( Y12 @ Y6 )
= ( Y12 @ Y5 ) )
& ( ( Y12 @ Y10 )
= ( Y12 @ Y7 ) )
& ( ( Y12 @ Y9 )
= ( Y12 @ Y4 ) ) )
=> ( ( Y12 @ Y1 )
= ( Y12 @ Y2 ) ) )
& ( ( ( ( Y12 @ Y3 )
= ( Y12 @ Y1 ) )
& ( ( Y12 @ Y11 )
!= ( Y12 @ Y4 ) )
& ( ( Y12 @ Y10 )
= ( Y12 @ Y7 ) ) )
=> ( ( Y12 @ Y6 )
= ( Y12 @ Y5 ) ) )
& ( ( ( ( Y12 @ Y9 )
= ( Y12 @ Y4 ) )
& ( ( Y12 @ Y9 )
= ( Y12 @ Y2 ) )
& ( ( Y12 @ Y6 )
!= ( Y12 @ Y5 ) )
& ( ( Y12 @ Y11 )
= ( Y12 @ Y2 ) ) )
=> ( ( Y12 @ Y8 )
= ( Y12 @ Y3 ) ) )
& ( ( ( ( Y12 @ Y0 )
= ( Y12 @ Y6 ) )
& ( ( Y12 @ Y10 )
= ( Y12 @ Y7 ) )
& ( ( Y12 @ Y11 )
= ( Y12 @ Y4 ) ) )
=> ( ( Y12 @ Y8 )
!= ( Y12 @ Y3 ) ) ) )
=> ( ( ( Y12 @ Y9 )
!= ( Y12 @ Y4 ) )
| ( ( Y12 @ Y10 )
!= ( Y12 @ Y7 ) )
| ( ( Y12 @ Y11 )
!= ( Y12 @ Y2 ) )
| ( ( Y12 @ Y8 )
!= ( Y12 @ Y5 ) )
| ( ( Y12 @ Y0 )
!= ( Y12 @ Y6 ) )
| ( ( Y12 @ Y3 )
!= ( Y12 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ?? @ $i
@ ^ [Y8: $i] :
( ?? @ $i
@ ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ?? @ $i
@ ^ [Y11: $i] :
( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( ( ( ( ( ( Y12 @ Y11 )
= ( Y12 @ Y3 ) )
& ( ( Y12 @ Y11 )
= ( Y12 @ Y2 ) )
& ( ( Y12 @ Y3 )
= ( Y12 @ Y1 ) )
& ( ( Y12 @ Y10 )
!= ( Y12 @ Y9 ) ) )
=> ( ( Y12 @ Y6 )
!= ( Y12 @ Y5 ) ) )
& ( ( ( ( Y12 @ Y1 )
= ( Y12 @ Y2 ) )
& ( ( Y12 @ Y0 )
= ( Y12 @ Y6 ) )
& ( ( Y12 @ Y8 )
= ( Y12 @ Y5 ) ) )
=> ( ( Y12 @ Y10 )
!= ( Y12 @ Y9 ) ) )
& ( ( ( ( Y12 @ Y6 )
= ( Y12 @ Y5 ) )
& ( ( Y12 @ Y10 )
= ( Y12 @ Y7 ) )
& ( ( Y12 @ Y9 )
= ( Y12 @ Y4 ) ) )
=> ( ( Y12 @ Y1 )
= ( Y12 @ Y2 ) ) )
& ( ( ( ( Y12 @ Y3 )
= ( Y12 @ Y1 ) )
& ( ( Y12 @ Y11 )
!= ( Y12 @ Y4 ) )
& ( ( Y12 @ Y10 )
= ( Y12 @ Y7 ) ) )
=> ( ( Y12 @ Y6 )
= ( Y12 @ Y5 ) ) )
& ( ( ( ( Y12 @ Y9 )
= ( Y12 @ Y4 ) )
& ( ( Y12 @ Y9 )
= ( Y12 @ Y2 ) )
& ( ( Y12 @ Y6 )
!= ( Y12 @ Y5 ) )
& ( ( Y12 @ Y11 )
= ( Y12 @ Y2 ) ) )
=> ( ( Y12 @ Y8 )
= ( Y12 @ Y3 ) ) )
& ( ( ( ( Y12 @ Y0 )
= ( Y12 @ Y6 ) )
& ( ( Y12 @ Y10 )
= ( Y12 @ Y7 ) )
& ( ( Y12 @ Y11 )
= ( Y12 @ Y4 ) ) )
=> ( ( Y12 @ Y8 )
!= ( Y12 @ Y3 ) ) ) )
=> ( ( ( Y12 @ Y9 )
!= ( Y12 @ Y4 ) )
| ( ( Y12 @ Y10 )
!= ( Y12 @ Y7 ) )
| ( ( Y12 @ Y11 )
!= ( Y12 @ Y2 ) )
| ( ( Y12 @ Y8 )
!= ( Y12 @ Y5 ) )
| ( ( Y12 @ Y0 )
!= ( Y12 @ Y6 ) )
| ( ( Y12 @ Y3 )
!= ( Y12 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ?? @ $i
@ ^ [Y8: $i] :
( ?? @ $i
@ ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ?? @ $i
@ ^ [Y11: $i] :
( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( ( ( ( ( ( Y12 @ Y11 )
= ( Y12 @ Y3 ) )
& ( ( Y12 @ Y11 )
= ( Y12 @ Y2 ) )
& ( ( Y12 @ Y3 )
= ( Y12 @ Y1 ) )
& ( ( Y12 @ Y10 )
!= ( Y12 @ Y9 ) ) )
=> ( ( Y12 @ Y6 )
!= ( Y12 @ Y5 ) ) )
& ( ( ( ( Y12 @ Y1 )
= ( Y12 @ Y2 ) )
& ( ( Y12 @ Y0 )
= ( Y12 @ Y6 ) )
& ( ( Y12 @ Y8 )
= ( Y12 @ Y5 ) ) )
=> ( ( Y12 @ Y10 )
!= ( Y12 @ Y9 ) ) )
& ( ( ( ( Y12 @ Y6 )
= ( Y12 @ Y5 ) )
& ( ( Y12 @ Y10 )
= ( Y12 @ Y7 ) )
& ( ( Y12 @ Y9 )
= ( Y12 @ Y4 ) ) )
=> ( ( Y12 @ Y1 )
= ( Y12 @ Y2 ) ) )
& ( ( ( ( Y12 @ Y3 )
= ( Y12 @ Y1 ) )
& ( ( Y12 @ Y11 )
!= ( Y12 @ Y4 ) )
& ( ( Y12 @ Y10 )
= ( Y12 @ Y7 ) ) )
=> ( ( Y12 @ Y6 )
= ( Y12 @ Y5 ) ) )
& ( ( ( ( Y12 @ Y9 )
= ( Y12 @ Y4 ) )
& ( ( Y12 @ Y9 )
= ( Y12 @ Y2 ) )
& ( ( Y12 @ Y6 )
!= ( Y12 @ Y5 ) )
& ( ( Y12 @ Y11 )
= ( Y12 @ Y2 ) ) )
=> ( ( Y12 @ Y8 )
= ( Y12 @ Y3 ) ) )
& ( ( ( ( Y12 @ Y0 )
= ( Y12 @ Y6 ) )
& ( ( Y12 @ Y10 )
= ( Y12 @ Y7 ) )
& ( ( Y12 @ Y11 )
= ( Y12 @ Y4 ) ) )
=> ( ( Y12 @ Y8 )
!= ( Y12 @ Y3 ) ) ) )
=> ( ( ( Y12 @ Y9 )
!= ( Y12 @ Y4 ) )
| ( ( Y12 @ Y10 )
!= ( Y12 @ Y7 ) )
| ( ( Y12 @ Y11 )
!= ( Y12 @ Y2 ) )
| ( ( Y12 @ Y8 )
!= ( Y12 @ Y5 ) )
| ( ( Y12 @ Y0 )
!= ( Y12 @ Y6 ) )
| ( ( Y12 @ Y3 )
!= ( Y12 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ?? @ $i
@ ^ [Y8: $i] :
( ?? @ $i
@ ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ?? @ $i
@ ^ [Y11: $i] :
( !! @ ( $i > $i )
@ ^ [Y12: $i > $i] :
( ( ( ( ( ( Y12 @ Y11 )
= ( Y12 @ Y3 ) )
& ( ( Y12 @ Y11 )
= ( Y12 @ Y2 ) )
& ( ( Y12 @ Y3 )
= ( Y12 @ Y1 ) )
& ( ( Y12 @ Y10 )
!= ( Y12 @ Y9 ) ) )
=> ( ( Y12 @ Y6 )
!= ( Y12 @ Y5 ) ) )
& ( ( ( ( Y12 @ Y1 )
= ( Y12 @ Y2 ) )
& ( ( Y12 @ Y0 )
= ( Y12 @ Y6 ) )
& ( ( Y12 @ Y8 )
= ( Y12 @ Y5 ) ) )
=> ( ( Y12 @ Y10 )
!= ( Y12 @ Y9 ) ) )
& ( ( ( ( Y12 @ Y6 )
= ( Y12 @ Y5 ) )
& ( ( Y12 @ Y10 )
= ( Y12 @ Y7 ) )
& ( ( Y12 @ Y9 )
= ( Y12 @ Y4 ) ) )
=> ( ( Y12 @ Y1 )
= ( Y12 @ Y2 ) ) )
& ( ( ( ( Y12 @ Y3 )
= ( Y12 @ Y1 ) )
& ( ( Y12 @ Y11 )
!= ( Y12 @ Y4 ) )
& ( ( Y12 @ Y10 )
= ( Y12 @ Y7 ) ) )
=> ( ( Y12 @ Y6 )
= ( Y12 @ Y5 ) ) )
& ( ( ( ( Y12 @ Y9 )
= ( Y12 @ Y4 ) )
& ( ( Y12 @ Y9 )
= ( Y12 @ Y2 ) )
& ( ( Y12 @ Y6 )
!= ( Y12 @ Y5 ) )
& ( ( Y12 @ Y11 )
= ( Y12 @ Y2 ) ) )
=> ( ( Y12 @ Y8 )
= ( Y12 @ Y3 ) ) )
& ( ( ( ( Y12 @ Y0 )
= ( Y12 @ Y6 ) )
& ( ( Y12 @ Y10 )
= ( Y12 @ Y7 ) )
& ( ( Y12 @ Y11 )
= ( Y12 @ Y4 ) ) )
=> ( ( Y12 @ Y8 )
!= ( Y12 @ Y3 ) ) ) )
=> ( ( ( Y12 @ Y9 )
!= ( Y12 @ Y4 ) )
| ( ( Y12 @ Y10 )
!= ( Y12 @ Y7 ) )
| ( ( Y12 @ Y11 )
!= ( Y12 @ Y2 ) )
| ( ( Y12 @ Y8 )
!= ( Y12 @ Y5 ) )
| ( ( Y12 @ Y0 )
!= ( Y12 @ Y6 ) )
| ( ( Y12 @ Y3 )
!= ( Y12 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i,X11: $i] :
! [X12: $i > $i] :
( ( ( ( ( ( X12 @ X0 )
= ( X12 @ X7 ) )
& ( ( X12 @ X1 )
= ( X12 @ X4 ) )
& ( ( X12 @ X11 )
= ( X12 @ X5 ) ) )
=> ( ( X12 @ X3 )
!= ( X12 @ X8 ) ) )
& ( ( ( ( X12 @ X0 )
= ( X12 @ X9 ) )
& ( ( X12 @ X5 )
!= ( X12 @ X6 ) )
& ( ( X12 @ X2 )
= ( X12 @ X9 ) )
& ( ( X12 @ X2 )
= ( X12 @ X7 ) ) )
=> ( ( X12 @ X3 )
= ( X12 @ X8 ) ) )
& ( ( ( ( X12 @ X1 )
= ( X12 @ X4 ) )
& ( ( X12 @ X0 )
!= ( X12 @ X7 ) )
& ( ( X12 @ X8 )
= ( X12 @ X10 ) ) )
=> ( ( X12 @ X5 )
= ( X12 @ X6 ) ) )
& ( ( ( ( X12 @ X2 )
= ( X12 @ X7 ) )
& ( ( X12 @ X1 )
= ( X12 @ X4 ) )
& ( ( X12 @ X5 )
= ( X12 @ X6 ) ) )
=> ( ( X12 @ X10 )
= ( X12 @ X9 ) ) )
& ( ( ( ( X12 @ X3 )
= ( X12 @ X6 ) )
& ( ( X12 @ X11 )
= ( X12 @ X5 ) )
& ( ( X12 @ X10 )
= ( X12 @ X9 ) ) )
=> ( ( X12 @ X1 )
!= ( X12 @ X2 ) ) )
& ( ( ( ( X12 @ X1 )
!= ( X12 @ X2 ) )
& ( ( X12 @ X8 )
= ( X12 @ X10 ) )
& ( ( X12 @ X0 )
= ( X12 @ X9 ) )
& ( ( X12 @ X0 )
= ( X12 @ X8 ) ) )
=> ( ( X12 @ X5 )
!= ( X12 @ X6 ) ) ) )
=> ( ( ( X12 @ X8 )
!= ( X12 @ X10 ) )
| ( ( X12 @ X11 )
!= ( X12 @ X5 ) )
| ( ( X12 @ X3 )
!= ( X12 @ X6 ) )
| ( ( X12 @ X0 )
!= ( X12 @ X9 ) )
| ( ( X12 @ X1 )
!= ( X12 @ X4 ) )
| ( ( X12 @ X2 )
!= ( X12 @ X7 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X5: $i,X0: $i,X3: $i,X9: $i,X1: $i,X11: $i,X8: $i,X2: $i,X6: $i,X4: $i,X7: $i,X10: $i] :
! [X12: $i > $i] :
( ( ( ( ( ( X12 @ X2 )
= ( X12 @ X5 ) )
& ( ( X12 @ X0 )
= ( X12 @ X1 ) )
& ( ( X12 @ X11 )
= ( X12 @ X10 ) ) )
=> ( ( X12 @ X6 )
!= ( X12 @ X9 ) ) )
& ( ( ( ( X12 @ X4 )
= ( X12 @ X5 ) )
& ( ( X12 @ X8 )
!= ( X12 @ X11 ) )
& ( ( X12 @ X3 )
= ( X12 @ X4 ) )
& ( ( X12 @ X2 )
= ( X12 @ X3 ) ) )
=> ( ( X12 @ X6 )
= ( X12 @ X9 ) ) )
& ( ( ( ( X12 @ X0 )
= ( X12 @ X1 ) )
& ( ( X12 @ X2 )
!= ( X12 @ X5 ) )
& ( ( X12 @ X7 )
= ( X12 @ X6 ) ) )
=> ( ( X12 @ X8 )
= ( X12 @ X11 ) ) )
& ( ( ( ( X12 @ X2 )
= ( X12 @ X3 ) )
& ( ( X12 @ X0 )
= ( X12 @ X1 ) )
& ( ( X12 @ X8 )
= ( X12 @ X11 ) ) )
=> ( ( X12 @ X4 )
= ( X12 @ X7 ) ) )
& ( ( ( ( X12 @ X8 )
= ( X12 @ X9 ) )
& ( ( X12 @ X11 )
= ( X12 @ X10 ) )
& ( ( X12 @ X4 )
= ( X12 @ X7 ) ) )
=> ( ( X12 @ X0 )
!= ( X12 @ X3 ) ) )
& ( ( ( ( X12 @ X0 )
!= ( X12 @ X3 ) )
& ( ( X12 @ X7 )
= ( X12 @ X6 ) )
& ( ( X12 @ X4 )
= ( X12 @ X5 ) )
& ( ( X12 @ X5 )
= ( X12 @ X6 ) ) )
=> ( ( X12 @ X8 )
!= ( X12 @ X11 ) ) ) )
=> ( ( ( X12 @ X7 )
!= ( X12 @ X6 ) )
| ( ( X12 @ X11 )
!= ( X12 @ X10 ) )
| ( ( X12 @ X8 )
!= ( X12 @ X9 ) )
| ( ( X12 @ X4 )
!= ( X12 @ X5 ) )
| ( ( X12 @ X0 )
!= ( X12 @ X1 ) )
| ( ( X12 @ X2 )
!= ( X12 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X5: $i,X0: $i,X3: $i,X9: $i,X1: $i,X11: $i,X8: $i,X2: $i,X6: $i,X4: $i,X7: $i,X10: $i] :
! [X12: $i > $i] :
( ( ( ( ( ( X12 @ X2 )
= ( X12 @ X5 ) )
& ( ( X12 @ X0 )
= ( X12 @ X1 ) )
& ( ( X12 @ X11 )
= ( X12 @ X10 ) ) )
=> ( ( X12 @ X6 )
!= ( X12 @ X9 ) ) )
& ( ( ( ( X12 @ X4 )
= ( X12 @ X5 ) )
& ( ( X12 @ X8 )
!= ( X12 @ X11 ) )
& ( ( X12 @ X3 )
= ( X12 @ X4 ) )
& ( ( X12 @ X2 )
= ( X12 @ X3 ) ) )
=> ( ( X12 @ X6 )
= ( X12 @ X9 ) ) )
& ( ( ( ( X12 @ X0 )
= ( X12 @ X1 ) )
& ( ( X12 @ X2 )
!= ( X12 @ X5 ) )
& ( ( X12 @ X7 )
= ( X12 @ X6 ) ) )
=> ( ( X12 @ X8 )
= ( X12 @ X11 ) ) )
& ( ( ( ( X12 @ X2 )
= ( X12 @ X3 ) )
& ( ( X12 @ X0 )
= ( X12 @ X1 ) )
& ( ( X12 @ X8 )
= ( X12 @ X11 ) ) )
=> ( ( X12 @ X4 )
= ( X12 @ X7 ) ) )
& ( ( ( ( X12 @ X8 )
= ( X12 @ X9 ) )
& ( ( X12 @ X11 )
= ( X12 @ X10 ) )
& ( ( X12 @ X4 )
= ( X12 @ X7 ) ) )
=> ( ( X12 @ X0 )
!= ( X12 @ X3 ) ) )
& ( ( ( ( X12 @ X0 )
!= ( X12 @ X3 ) )
& ( ( X12 @ X7 )
= ( X12 @ X6 ) )
& ( ( X12 @ X4 )
= ( X12 @ X5 ) )
& ( ( X12 @ X5 )
= ( X12 @ X6 ) ) )
=> ( ( X12 @ X8 )
!= ( X12 @ X11 ) ) ) )
=> ( ( ( X12 @ X7 )
!= ( X12 @ X6 ) )
| ( ( X12 @ X11 )
!= ( X12 @ X10 ) )
| ( ( X12 @ X8 )
!= ( X12 @ X9 ) )
| ( ( X12 @ X4 )
!= ( X12 @ X5 ) )
| ( ( X12 @ X0 )
!= ( X12 @ X1 ) )
| ( ( X12 @ X2 )
!= ( X12 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aP8Kuc7Iur/DTF2THF_15784.p',cSIXFRIENDS_PTH) ).
thf(f123,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ( sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X6 )
!= ( sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X3 ) )
| ( ( sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X7 )
!= ( sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X5 ) )
| ( ( sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X0 )
!= ( sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X1 ) ) ),
inference(equality_resolution,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 ) )
| ( $false
= ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
| ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) )
= $false )
| ( $false
= ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) ) )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
= $false )
| ( $false
= ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) ) )
| ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) )
= $false )
| ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( $false
= ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) ) )
| ( $false
= ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) ) )
| ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
= $false )
| ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) )
= $true )
| ( $false
= ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) ) )
| ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) )
= $false )
| ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) ) )
= $false )
| ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) )
= $true )
| ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( $false
= ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) ) ) )
| ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) ) )
=> ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X10: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i,X12: $i] :
( ( ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10 ) ) )
=> ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6 ) ) )
& ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6 ) ) )
=> ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10 ) ) )
& ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) ) )
=> ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3 ) ) )
& ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) ) )
=> ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6 ) ) )
& ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3 ) ) )
=> ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) ) )
& ( ( ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8 ) )
& ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12 )
= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5 ) ) )
=> ( ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9 )
!= ( sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ093^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n011.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 11:32:02 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : PUZ093^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Puzzles
% 0.30/0.46 % Problem : TPS problem from BASIC-HO-EQ-THMS
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_1207 [Bro09]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v7.4.0, 0.22 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 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
% 0.30/0.46 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.30/0.46 % Number of atoms : 32 ( 32 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 32 ( 32 avg)
% 0.30/0.46 % Number of connectives : 107 ( 12 ~; 5 |; 19 &; 64 @)
% 0.30/0.46 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 25 ( 25 avg)
% 0.30/0.46 % Number of types : 1 ( 0 usr)
% 0.30/0.46 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.46 % Number of variables : 13 ( 0 ^; 1 !; 12 ?; 13 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(cSIXFRIENDS_PTH,conjecture,
% 0.30/0.46 ? [Xa: $i,Xaa: $i,Xb: $i,Xbb: $i,Xc: $i,Xcc: $i,Xd: $i,Xdd: $i,Xe: $i,Xee: $i,Xh: $i,Xhh: $i] :
% 0.30/0.46 ! [P: $i > $i] :
% 0.30/0.46 ( ( ( ( ( ( P @ Xa )
% 0.30/0.46 = ( P @ Xaa ) )
% 0.30/0.46 & ( ( P @ Xb )
% 0.30/0.46 = ( P @ Xbb ) )
% 0.30/0.46 & ( ( P @ Xe )
% 0.30/0.46 = ( P @ Xhh ) ) )
% 0.30/0.46 => ( ( P @ Xc )
% 0.30/0.46 = ( P @ Xdd ) ) )
% 0.30/0.46 & ( ( ( ( P @ Xa )
% 0.30/0.46 = ( P @ Xaa ) )
% 0.30/0.46 & ( ( P @ Xh )
% 0.30/0.46 = ( P @ Xhh ) )
% 0.30/0.46 & ( ( P @ Xb )
% 0.30/0.46 = ( P @ Xcc ) ) )
% 0.30/0.46 => ( ( P @ Xd )
% 0.30/0.46 != ( P @ Xee ) ) )
% 0.30/0.46 & ( ( ( ( P @ Xc )
% 0.30/0.46 = ( P @ Xcc ) )
% 0.30/0.46 & ( ( P @ Xcc )
% 0.30/0.46 = ( P @ Xd ) )
% 0.30/0.46 & ( ( P @ Xd )
% 0.30/0.46 = ( P @ Xdd ) )
% 0.30/0.46 & ( ( P @ Xa )
% 0.30/0.46 != ( P @ Xbb ) ) )
% 0.30/0.46 => ( ( P @ Xe )
% 0.30/0.46 != ( P @ Xhh ) ) )
% 0.30/0.46 & ( ( ( ( P @ Xa )
% 0.30/0.46 = ( P @ Xaa ) )
% 0.30/0.46 & ( ( P @ Xd )
% 0.30/0.46 = ( P @ Xdd ) )
% 0.30/0.46 & ( ( P @ Xb )
% 0.30/0.46 != ( P @ Xcc ) ) )
% 0.30/0.46 => ( ( P @ Xe )
% 0.30/0.46 = ( P @ Xhh ) ) )
% 0.30/0.46 & ( ( ( ( P @ Xe )
% 0.30/0.46 = ( P @ Xee ) )
% 0.30/0.46 & ( ( P @ Xh )
% 0.30/0.46 = ( P @ Xhh ) )
% 0.30/0.46 & ( ( P @ Xc )
% 0.30/0.46 = ( P @ Xdd ) ) )
% 0.30/0.46 => ( ( P @ Xa )
% 0.30/0.46 != ( P @ Xbb ) ) )
% 0.30/0.46 & ( ( ( ( P @ Xb )
% 0.30/0.46 = ( P @ Xbb ) )
% 0.30/0.46 & ( ( P @ Xbb )
% 0.30/0.46 = ( P @ Xc ) )
% 0.30/0.46 & ( ( P @ Xc )
% 0.30/0.46 = ( P @ Xcc ) )
% 0.30/0.46 & ( ( P @ Xe )
% 0.30/0.46 != ( P @ Xhh ) ) )
% 0.30/0.46 => ( ( P @ Xd )
% 0.30/0.46 = ( P @ Xee ) ) ) )
% 0.30/0.46 => ( ( ( P @ Xa )
% 0.30/0.46 != ( P @ Xaa ) )
% 0.30/0.46 | ( ( P @ Xb )
% 0.30/0.46 != ( P @ Xbb ) )
% 0.30/0.46 | ( ( P @ Xc )
% 0.30/0.46 != ( P @ Xcc ) )
% 0.30/0.46 | ( ( P @ Xd )
% 0.30/0.46 != ( P @ Xdd ) )
% 0.30/0.46 | ( ( P @ Xe )
% 0.30/0.46 != ( P @ Xee ) )
% 0.30/0.46 | ( ( P @ Xh )
% 0.30/0.46 != ( P @ Xhh ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.52/1.24 ---- Embedded in THF ---
% 1.52/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.24 %%% Generated on Tue Feb 24 11:32:03 EST 2026
% 1.52/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.24 %%% Logic specification used:
% 1.52/1.24 %%% thf(spec, logic, $$dhol).
% 1.52/1.24
% 1.52/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.aP8Kuc7Iur/DTF2DTF15784.p
% See solution above
% 1.52/1.24 ------------------------
% 1.52/1.25 ---- Cleaned THF ---
% 1.52/1.25 thf(cSIXFRIENDS_PTH,conjecture,
% 1.52/1.25 ? [Xa: $i,Xaa: $i,Xb: $i,Xbb: $i,Xc: $i,Xcc: $i,Xd: $i,Xdd: $i,Xe: $i,Xee: $i,Xh: $i,Xhh: $i] :
% 1.52/1.25 ! [P: $i > $i] :
% 1.52/1.25 ( ( ( ( ( ( P @ Xa )
% 1.52/1.25 = ( P @ Xaa ) )
% 1.52/1.25 & ( ( P @ Xb )
% 1.52/1.25 = ( P @ Xbb ) )
% 1.52/1.25 & ( ( P @ Xe )
% 1.52/1.25 = ( P @ Xhh ) ) )
% 1.52/1.25 => ( ( P @ Xc )
% 1.52/1.25 = ( P @ Xdd ) ) )
% 1.52/1.25 & ( ( ( ( P @ Xa )
% 1.52/1.25 = ( P @ Xaa ) )
% 1.52/1.25 & ( ( P @ Xh )
% 1.52/1.25 = ( P @ Xhh ) )
% 1.52/1.25 & ( ( P @ Xb )
% 1.52/1.25 = ( P @ Xcc ) ) )
% 1.52/1.25 => ( ( P @ Xd )
% 1.52/1.25 != ( P @ Xee ) ) )
% 1.52/1.25 & ( ( ( ( P @ Xc )
% 1.52/1.25 = ( P @ Xcc ) )
% 1.52/1.25 & ( ( P @ Xcc )
% 1.52/1.25 = ( P @ Xd ) )
% 1.52/1.25 & ( ( P @ Xd )
% 1.52/1.25 = ( P @ Xdd ) )
% 1.52/1.25 & ( ( P @ Xa )
% 1.52/1.25 != ( P @ Xbb ) ) )
% 1.52/1.25 => ( ( P @ Xe )
% 1.52/1.25 != ( P @ Xhh ) ) )
% 1.52/1.25 & ( ( ( ( P @ Xa )
% 1.52/1.25 = ( P @ Xaa ) )
% 1.52/1.25 & ( ( P @ Xd )
% 1.52/1.25 = ( P @ Xdd ) )
% 1.52/1.25 & ( ( P @ Xb )
% 1.52/1.25 != ( P @ Xcc ) ) )
% 1.52/1.25 => ( ( P @ Xe )
% 1.52/1.25 = ( P @ Xhh ) ) )
% 1.52/1.25 & ( ( ( ( P @ Xe )
% 1.52/1.25 = ( P @ Xee ) )
% 1.52/1.25 & ( ( P @ Xh )
% 1.52/1.25 = ( P @ Xhh ) )
% 1.52/1.25 & ( ( P @ Xc )
% 1.52/1.25 = ( P @ Xdd ) ) )
% 1.52/1.25 => ( ( P @ Xa )
% 1.52/1.25 != ( P @ Xbb ) ) )
% 1.52/1.25 & ( ( ( ( P @ Xb )
% 1.52/1.25 = ( P @ Xbb ) )
% 1.52/1.25 & ( ( P @ Xbb )
% 1.52/1.25 = ( P @ Xc ) )
% 1.52/1.25 & ( ( P @ Xc )
% 1.52/1.25 = ( P @ Xcc ) )
% 1.52/1.25 & ( ( P @ Xe )
% 1.52/1.25 != ( P @ Xhh ) ) )
% 1.52/1.25 => ( ( P @ Xd )
% 1.52/1.25 = ( P @ Xee ) ) ) )
% 1.52/1.25 => ( ( ( P @ Xa )
% 1.52/1.25 != ( P @ Xaa ) )
% 1.52/1.25 | ( ( P @ Xb )
% 1.52/1.25 != ( P @ Xbb ) )
% 1.52/1.25 | ( ( P @ Xc )
% 1.52/1.25 != ( P @ Xcc ) )
% 1.52/1.25 | ( ( P @ Xd )
% 1.52/1.25 != ( P @ Xdd ) )
% 1.52/1.25 | ( ( P @ Xe )
% 1.52/1.25 != ( P @ Xee ) )
% 1.52/1.25 | ( ( P @ Xh )
% 1.52/1.25 != ( P @ Xhh ) ) ) ) ).
% 1.52/1.25 ------------------------
% 1.52/1.27 % (16063)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/183Mi)
% 1.52/1.27 % (16064)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_15784 for (2999ds/4Mi)
% 1.52/1.27 % (16064)Instruction limit reached!
% 1.52/1.27 % (16064)------------------------------
% 1.52/1.27 % (16064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.27 % (16064)Termination reason: Unknown
% 1.52/1.27 % (16064)Termination phase: Property scanning
% 1.52/1.27
% 1.52/1.27 % (16064)Memory used [KB]: 1023
% 1.52/1.27 % (16064)Time elapsed: 0.002 s
% 1.52/1.27 % (16064)Instructions burned: 4 (million)
% 1.52/1.27 % (16064)------------------------------
% 1.52/1.27 % (16064)------------------------------
% 1.52/1.28 % (16065)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_15784 for (2999ds/27Mi)
% 1.52/1.28 % (16066)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/2Mi)
% 1.52/1.28 % (16067)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_15784 for (2999ds/2Mi)
% 1.52/1.28 % (16068)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_15784 for (2999ds/275Mi)
% 1.52/1.28 % (16069)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/18Mi)
% 1.52/1.28 % (16066)Instruction limit reached!
% 1.52/1.28 % (16066)------------------------------
% 1.52/1.28 % (16066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (16066)Termination reason: Unknown
% 1.52/1.28 % (16066)Termination phase: Preprocessing 3
% 1.52/1.28
% 1.52/1.28 % (16066)Memory used [KB]: 895
% 1.52/1.28 % (16066)Time elapsed: 0.003 s
% 1.52/1.28 % (16066)Instructions burned: 2 (million)
% 1.52/1.28 % (16066)------------------------------
% 1.52/1.28 % (16066)------------------------------
% 1.52/1.28 % (16067)Instruction limit reached!
% 1.52/1.28 % (16067)------------------------------
% 1.52/1.28 % (16067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (16067)Termination reason: Unknown
% 1.52/1.28 % (16067)Termination phase: shuffling
% 1.52/1.28
% 1.52/1.28 % (16067)Memory used [KB]: 895
% 1.52/1.28 % (16067)Time elapsed: 0.003 s
% 1.52/1.28 % (16067)Instructions burned: 2 (million)
% 1.52/1.28 % (16067)------------------------------
% 1.52/1.28 % (16067)------------------------------
% 1.52/1.28 % (16070)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/3Mi)
% 1.52/1.28 % (16070)Instruction limit reached!
% 1.52/1.28 % (16070)------------------------------
% 1.52/1.28 % (16070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (16070)Termination reason: Unknown
% 1.52/1.28 % (16070)Termination phase: Property scanning
% 1.52/1.28
% 1.52/1.28 % (16070)Memory used [KB]: 1023
% 1.52/1.28 % (16070)Time elapsed: 0.003 s
% 1.52/1.28 % (16070)Instructions burned: 5 (million)
% 1.52/1.28 % (16070)------------------------------
% 1.52/1.28 % (16070)------------------------------
% 1.52/1.28 % (16069)Instruction limit reached!
% 1.52/1.28 % (16069)------------------------------
% 1.52/1.28 % (16069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (16069)Termination reason: Unknown
% 1.52/1.28 % (16069)Termination phase: Saturation
% 1.52/1.28
% 1.52/1.28 % (16069)Memory used [KB]: 5500
% 1.52/1.28 % (16069)Time elapsed: 0.011 s
% 1.52/1.28 % (16069)Instructions burned: 18 (million)
% 1.52/1.28 % (16069)------------------------------
% 1.52/1.28 % (16069)------------------------------
% 1.52/1.29 % (16065)Instruction limit reached!
% 1.52/1.29 % (16065)------------------------------
% 1.52/1.29 % (16065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (16065)Termination reason: Unknown
% 1.52/1.29 % (16065)Termination phase: Saturation
% 1.52/1.29
% 1.52/1.29 % (16065)Memory used [KB]: 5500
% 1.52/1.29 % (16065)Time elapsed: 0.016 s
% 1.52/1.29 % (16065)Instructions burned: 27 (million)
% 1.52/1.29 % (16065)------------------------------
% 1.52/1.29 % (16065)------------------------------
% 1.52/1.29 % (16073)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_15784 for (2999ds/3Mi)
% 1.52/1.29 % (16073)Instruction limit reached!
% 1.52/1.29 % (16073)------------------------------
% 1.52/1.29 % (16073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (16073)Termination reason: Unknown
% 1.52/1.29 % (16073)Termination phase: Property scanning
% 1.52/1.29
% 1.52/1.29 % (16073)Memory used [KB]: 1023
% 1.52/1.29 % (16073)Time elapsed: 0.003 s
% 1.52/1.29 % (16073)Instructions burned: 5 (million)
% 1.52/1.29 % (16073)------------------------------
% 1.52/1.29 % (16073)------------------------------
% 1.52/1.29 % (16071)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_15784 for (2999ds/37Mi)
% 1.52/1.29 % (16072)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_15784 for (2999ds/15Mi)
% 1.62/1.30 % (16072)Instruction limit reached!
% 1.62/1.30 % (16072)------------------------------
% 1.62/1.30 % (16072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (16072)Termination reason: Unknown
% 1.62/1.30 % (16072)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (16072)Memory used [KB]: 5500
% 1.62/1.30 % (16072)Time elapsed: 0.010 s
% 1.62/1.30 % (16072)Instructions burned: 16 (million)
% 1.62/1.30 % (16072)------------------------------
% 1.62/1.30 % (16072)------------------------------
% 1.62/1.30 % (16077)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/16Mi)
% 1.62/1.30 % (16074)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_15784 for (2999ds/1041Mi)
% 1.62/1.31 % (16077)Instruction limit reached!
% 1.62/1.31 % (16077)------------------------------
% 1.62/1.31 % (16077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (16077)Termination reason: Unknown
% 1.62/1.31 % (16077)Termination phase: Twee Goal Transformation
% 1.62/1.31
% 1.62/1.31 % (16077)Memory used [KB]: 1023
% 1.62/1.31 % (16077)Time elapsed: 0.006 s
% 1.62/1.31 % (16077)Instructions burned: 16 (million)
% 1.62/1.31 % (16077)------------------------------
% 1.62/1.31 % (16077)------------------------------
% 1.62/1.31 % (16075)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/7Mi)
% 1.62/1.31 % (16075)Instruction limit reached!
% 1.62/1.31 % (16075)------------------------------
% 1.62/1.31 % (16075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (16075)Termination reason: Unknown
% 1.62/1.31 % (16075)Termination phase: Property scanning
% 1.62/1.31
% 1.62/1.31 % (16075)Memory used [KB]: 1023
% 1.62/1.31 % (16075)Time elapsed: 0.005 s
% 1.62/1.31 % (16075)Instructions burned: 7 (million)
% 1.62/1.31 % (16075)------------------------------
% 1.62/1.31 % (16075)------------------------------
% 1.62/1.31 % (16071)Instruction limit reached!
% 1.62/1.31 % (16071)------------------------------
% 1.62/1.31 % (16071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (16071)Termination reason: Unknown
% 1.62/1.31 % (16071)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (16071)Memory used [KB]: 5628
% 1.62/1.31 % (16071)Time elapsed: 0.020 s
% 1.62/1.31 % (16071)Instructions burned: 38 (million)
% 1.62/1.31 % (16071)------------------------------
% 1.62/1.31 % (16071)------------------------------
% 1.62/1.32 % (16079)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_15784 for (2999ds/3Mi)
% 1.62/1.32 % (16079)Instruction limit reached!
% 1.62/1.32 % (16079)------------------------------
% 1.62/1.32 % (16079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (16079)Termination reason: Unknown
% 1.62/1.32 % (16079)Termination phase: Property scanning
% 1.62/1.32
% 1.62/1.32 % (16079)Memory used [KB]: 1023
% 1.62/1.32 % (16079)Time elapsed: 0.003 s
% 1.62/1.32 % (16079)Instructions burned: 5 (million)
% 1.62/1.32 % (16079)------------------------------
% 1.62/1.32 % (16079)------------------------------
% 1.62/1.32 % (16063)Instruction limit reached!
% 1.62/1.32 % (16063)------------------------------
% 1.62/1.32 % (16063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (16063)Termination reason: Unknown
% 1.62/1.32 % (16063)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (16063)Memory used [KB]: 6012
% 1.62/1.32 % (16063)Time elapsed: 0.053 s
% 1.62/1.32 % (16063)Instructions burned: 185 (million)
% 1.62/1.32 % (16063)------------------------------
% 1.62/1.32 % (16063)------------------------------
% 1.62/1.32 % (16078)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_15784 for (2999ds/3Mi)
% 1.62/1.32 % (16078)Instruction limit reached!
% 1.62/1.32 % (16078)------------------------------
% 1.62/1.32 % (16078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (16078)Termination reason: Unknown
% 1.62/1.32 % (16078)Termination phase: Property scanning
% 1.62/1.32
% 1.62/1.32 % (16078)Memory used [KB]: 1023
% 1.62/1.32 % (16078)Time elapsed: 0.004 s
% 1.62/1.32 % (16078)Instructions burned: 4 (million)
% 1.62/1.32 % (16078)------------------------------
% 1.62/1.32 % (16078)------------------------------
% 1.62/1.33 % (16080)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/7Mi)
% 1.62/1.33 % (16082)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/4Mi)
% 1.62/1.33 % (16083)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/18Mi)
% 1.62/1.33 % (16082)Instruction limit reached!
% 1.62/1.33 % (16082)------------------------------
% 1.62/1.33 % (16082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (16082)Termination reason: Unknown
% 1.62/1.33 % (16082)Termination phase: Property scanning
% 1.62/1.33
% 1.62/1.33 % (16082)Memory used [KB]: 1023
% 1.62/1.33 % (16082)Time elapsed: 0.003 s
% 1.62/1.33 % (16082)Instructions burned: 5 (million)
% 1.62/1.33 % (16082)------------------------------
% 1.62/1.33 % (16082)------------------------------
% 1.62/1.33 % (16081)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/3Mi)
% 1.62/1.33 % (16080)Instruction limit reached!
% 1.62/1.33 % (16080)------------------------------
% 1.62/1.33 % (16080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (16080)Termination reason: Unknown
% 1.62/1.33 % (16080)Termination phase: Property scanning
% 1.62/1.33
% 1.62/1.33 % (16080)Memory used [KB]: 1023
% 1.62/1.33 % (16080)Time elapsed: 0.005 s
% 1.62/1.33 % (16080)Instructions burned: 7 (million)
% 1.62/1.33 % (16080)------------------------------
% 1.62/1.33 % (16080)------------------------------
% 1.62/1.33 % (16081)Instruction limit reached!
% 1.62/1.33 % (16081)------------------------------
% 1.62/1.33 % (16081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (16081)Termination reason: Unknown
% 1.62/1.33 % (16081)Termination phase: shuffling
% 1.62/1.33
% 1.62/1.33 % (16081)Memory used [KB]: 1023
% 1.62/1.33 % (16081)Time elapsed: 0.003 s
% 1.62/1.33 % (16081)Instructions burned: 3 (million)
% 1.62/1.33 % (16081)------------------------------
% 1.62/1.33 % (16081)------------------------------
% 1.62/1.33 % (16083)Instruction limit reached!
% 1.62/1.33 % (16083)------------------------------
% 1.62/1.33 % (16083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (16083)Termination reason: Unknown
% 1.62/1.33 % (16083)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (16083)Memory used [KB]: 5500
% 1.62/1.33 % (16083)Time elapsed: 0.006 s
% 1.62/1.33 % (16083)Instructions burned: 19 (million)
% 1.62/1.33 % (16083)------------------------------
% 1.62/1.33 % (16083)------------------------------
% 1.62/1.34 % (16084)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/710Mi)
% 1.62/1.34 % (16085)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/6Mi)
% 1.62/1.34 % (16085)Instruction limit reached!
% 1.62/1.34 % (16085)------------------------------
% 1.62/1.34 % (16085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (16085)Termination reason: Unknown
% 1.62/1.34 % (16085)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (16085)Memory used [KB]: 5500
% 1.62/1.34 % (16085)Time elapsed: 0.004 s
% 1.62/1.34 % (16085)Instructions burned: 8 (million)
% 1.62/1.34 % (16085)------------------------------
% 1.62/1.34 % (16085)------------------------------
% 1.62/1.34 % (16088)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/5Mi)
% 1.62/1.34 % (16088)Instruction limit reached!
% 1.62/1.34 % (16088)------------------------------
% 1.62/1.34 % (16088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (16088)Termination reason: Unknown
% 1.62/1.34 % (16088)Termination phase: Property scanning
% 1.62/1.34
% 1.62/1.34 % (16088)Memory used [KB]: 1023
% 1.62/1.34 % (16088)Time elapsed: 0.002 s
% 1.62/1.34 % (16088)Instructions burned: 5 (million)
% 1.62/1.34 % (16088)------------------------------
% 1.62/1.34 % (16088)------------------------------
% 1.62/1.34 % (16086)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/902Mi)
% 1.62/1.35 % (16087)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_15784 for (2999ds/21Mi)
% 1.62/1.35 % (16089)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/6Mi)
% 1.62/1.35 % (16090)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/377Mi)
% 1.62/1.35 % (16089)Instruction limit reached!
% 1.62/1.35 % (16089)------------------------------
% 1.62/1.35 % (16089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (16089)Termination reason: Unknown
% 1.62/1.35 % (16089)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (16089)Memory used [KB]: 5500
% 1.62/1.35 % (16089)Time elapsed: 0.004 s
% 1.62/1.35 % (16089)Instructions burned: 8 (million)
% 1.62/1.35 % (16089)------------------------------
% 1.62/1.35 % (16089)------------------------------
% 1.62/1.36 % (16087)Instruction limit reached!
% 1.62/1.36 % (16087)------------------------------
% 1.62/1.36 % (16087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (16087)Termination reason: Unknown
% 1.62/1.36 % (16087)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (16087)Memory used [KB]: 5628
% 1.62/1.36 % (16087)Time elapsed: 0.014 s
% 1.62/1.36 % (16087)Instructions burned: 22 (million)
% 1.62/1.36 % (16087)------------------------------
% 1.62/1.36 % (16087)------------------------------
% 1.62/1.36 % (16091)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/779Mi)
% 1.62/1.37 % (16092)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_15784 for (2999ds/19Mi)
% 1.62/1.38 % (16092)Instruction limit reached!
% 1.62/1.38 % (16092)------------------------------
% 1.62/1.38 % (16092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.38 % (16092)Termination reason: Unknown
% 1.62/1.38 % (16092)Termination phase: Saturation
% 1.62/1.38
% 1.62/1.38 % (16092)Memory used [KB]: 5500
% 1.62/1.38 % (16092)Time elapsed: 0.008 s
% 1.62/1.38 % (16092)Instructions burned: 22 (million)
% 1.62/1.38 % (16092)------------------------------
% 1.62/1.38 % (16092)------------------------------
% 1.62/1.39 % (16093)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_15784 for (2998ds/879Mi)
% 1.62/1.40 % (16068)Instruction limit reached!
% 1.62/1.40 % (16068)------------------------------
% 1.62/1.40 % (16068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.40 % (16068)Termination reason: Unknown
% 1.62/1.40 % (16068)Termination phase: Saturation
% 1.62/1.40
% 1.62/1.40 % (16068)Memory used [KB]: 5884
% 1.62/1.40 % (16068)Time elapsed: 0.125 s
% 1.62/1.40 % (16068)Instructions burned: 275 (million)
% 1.62/1.40 % (16068)------------------------------
% 1.62/1.40 % (16068)------------------------------
% 1.62/1.41 % (16094)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_15784 for (2998ds/17Mi)
% 1.62/1.41 % (16094)Instruction limit reached!
% 1.62/1.41 % (16094)------------------------------
% 1.62/1.41 % (16094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.41 % (16094)Termination reason: Unknown
% 1.62/1.41 % (16094)Termination phase: Saturation
% 1.62/1.41
% 1.62/1.41 % (16094)Memory used [KB]: 5500
% 1.62/1.41 % (16094)Time elapsed: 0.007 s
% 1.62/1.41 % (16094)Instructions burned: 18 (million)
% 1.62/1.41 % (16094)------------------------------
% 1.62/1.41 % (16094)------------------------------
% 1.62/1.42 % (16095)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15784 for (2998ds/3Mi)
% 1.62/1.42 % (16095)Instruction limit reached!
% 1.62/1.42 % (16095)------------------------------
% 1.62/1.42 % (16095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.42 % (16095)Termination reason: Unknown
% 1.62/1.42 % (16095)Termination phase: Property scanning
% 1.62/1.42
% 1.62/1.42 % (16095)Memory used [KB]: 1023
% 1.62/1.42 % (16095)Time elapsed: 0.003 s
% 1.62/1.42 % (16095)Instructions burned: 5 (million)
% 1.62/1.42 % (16095)------------------------------
% 1.62/1.42 % (16095)------------------------------
% 1.62/1.43 % (16096)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_15784 for (2998ds/30Mi)
% 1.62/1.44 % (16096)Instruction limit reached!
% 1.62/1.44 % (16096)------------------------------
% 1.62/1.44 % (16096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.44 % (16096)Termination reason: Unknown
% 1.62/1.44 % (16096)Termination phase: Saturation
% 1.62/1.44
% 1.62/1.44 % (16096)Memory used [KB]: 5500
% 1.62/1.44 % (16096)Time elapsed: 0.010 s
% 1.62/1.44 % (16096)Instructions burned: 30 (million)
% 1.62/1.44 % (16096)------------------------------
% 1.62/1.44 % (16096)------------------------------
% 1.62/1.45 % (16097)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_15784 for (2998ds/127Mi)
% 1.62/1.46 % (16090)Instruction limit reached!
% 1.62/1.46 % (16090)------------------------------
% 1.62/1.46 % (16090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.46 % (16090)Termination reason: Unknown
% 1.62/1.46 % (16090)Termination phase: Saturation
% 1.62/1.46
% 1.62/1.46 % (16090)Memory used [KB]: 6012
% 1.62/1.46 % (16090)Time elapsed: 0.106 s
% 1.62/1.46 % (16090)Instructions burned: 379 (million)
% 1.62/1.46 % (16090)------------------------------
% 1.62/1.46 % (16090)------------------------------
% 1.62/1.47 % (16098)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_15784 for (2998ds/100Mi)
% 1.62/1.47 % (16091)First to succeed.
% 1.62/1.48 % (16091)Refutation found. Thanks to Tanya!
% 1.62/1.48 % SZS status Theorem for DTF2THF_15784
% 1.62/1.48 % SZS output start Proof for DTF2THF_15784
% 1.62/1.48 thf(func_def_25, type, sK1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i).
% 1.62/1.48 thf(f308,plain,(
% 1.62/1.48 $false),
% 1.62/1.48 inference(equality_resolution,[status(thm)],[f279])).
% 1.62/1.48 thf(f279,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X5 @ X7 @ X8 @ X9 @ X0) != (sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X5 @ X7 @ X8 @ X9 @ X1))) )),
% 1.62/1.48 inference(equality_resolution,[status(thm)],[f208])).
% 1.62/1.48 thf(f208,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X7) != (sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X5)) | ((sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X0) != (sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X1))) )),
% 1.62/1.48 inference(subsumption_resolution,[status(thm)],[f123,f103])).
% 1.62/1.48 thf(f103,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7))) )),
% 1.62/1.48 inference(equality_proxy_clausification,[status(thm)],[f102])).
% 1.62/1.48 thf(f102,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : ((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)) = $true)) )),
% 1.62/1.48 inference(not_proxy_clausification,[status(thm)],[f100])).
% 1.62/1.48 thf(f100,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (($false = (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7))))) )),
% 1.62/1.48 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.62/1.48 thf(f99,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (($false = (((((~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8)))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3)))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6)))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)))))) )),
% 1.62/1.48 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.62/1.48 thf(f34,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (($false = ((((((~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8)))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3)))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6)))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2)))))) )),
% 1.62/1.48 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.62/1.48 thf(f33,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : ((((((((((((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4)) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2))) & (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10)))) => (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6)))) & (((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3)) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6))) => (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10))))) & (((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6)) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5))) => ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3)))) & (((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2)) & (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5)))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8))) => ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6)))) & ((((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5)) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3))) & (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6)))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3))) => ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4)))) & (((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5))) => (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4))))) => ((((((~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8)))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3)))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6)))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)))) | (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2))))) = $false)) )),
% 1.62/1.48 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.62/1.48 thf(f32,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : ((((^[Y0 : $i > $i]: ((((((((((((Y0 @ X12) = (Y0 @ X4)) & ((Y0 @ X12) = (Y0 @ X3))) & ((Y0 @ X4) = (Y0 @ X2))) & (~ ((Y0 @ X11) = (Y0 @ X10)))) => (~ ((Y0 @ X7) = (Y0 @ X6)))) & (((((Y0 @ X2) = (Y0 @ X3)) & ((Y0 @ X1) = (Y0 @ X7))) & ((Y0 @ X9) = (Y0 @ X6))) => (~ ((Y0 @ X11) = (Y0 @ X10))))) & (((((Y0 @ X7) = (Y0 @ X6)) & ((Y0 @ X11) = (Y0 @ X8))) & ((Y0 @ X10) = (Y0 @ X5))) => ((Y0 @ X2) = (Y0 @ X3)))) & (((((Y0 @ X4) = (Y0 @ X2)) & (~ ((Y0 @ X12) = (Y0 @ X5)))) & ((Y0 @ X11) = (Y0 @ X8))) => ((Y0 @ X7) = (Y0 @ X6)))) & ((((((Y0 @ X10) = (Y0 @ X5)) & ((Y0 @ X10) = (Y0 @ X3))) & (~ ((Y0 @ X7) = (Y0 @ X6)))) & ((Y0 @ X12) = (Y0 @ X3))) => ((Y0 @ X9) = (Y0 @ X4)))) & (((((Y0 @ X1) = (Y0 @ X7)) & ((Y0 @ X11) = (Y0 @ X8))) & ((Y0 @ X12) = (Y0 @ X5))) => (~ ((Y0 @ X9) = (Y0 @ X4))))) => ((((((~ ((Y0 @ X10) = (Y0 @ X5))) | (~ ((Y0 @ X11) = (Y0 @ X8)))) | (~ ((Y0 @ X12) = (Y0 @ X3)))) | (~ ((Y0 @ X9) = (Y0 @ X6)))) | (~ ((Y0 @ X1) = (Y0 @ X7)))) | (~ ((Y0 @ X4) = (Y0 @ X2)))))) @ (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2)) = $false)) )),
% 1.62/1.48 inference(sigma_clausification,[status(thm)],[f31])).
% 1.62/1.48 thf(f31,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (($false = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: ((((((((((((Y0 @ X12) = (Y0 @ X4)) & ((Y0 @ X12) = (Y0 @ X3))) & ((Y0 @ X4) = (Y0 @ X2))) & (~ ((Y0 @ X11) = (Y0 @ X10)))) => (~ ((Y0 @ X7) = (Y0 @ X6)))) & (((((Y0 @ X2) = (Y0 @ X3)) & ((Y0 @ X1) = (Y0 @ X7))) & ((Y0 @ X9) = (Y0 @ X6))) => (~ ((Y0 @ X11) = (Y0 @ X10))))) & (((((Y0 @ X7) = (Y0 @ X6)) & ((Y0 @ X11) = (Y0 @ X8))) & ((Y0 @ X10) = (Y0 @ X5))) => ((Y0 @ X2) = (Y0 @ X3)))) & (((((Y0 @ X4) = (Y0 @ X2)) & (~ ((Y0 @ X12) = (Y0 @ X5)))) & ((Y0 @ X11) = (Y0 @ X8))) => ((Y0 @ X7) = (Y0 @ X6)))) & ((((((Y0 @ X10) = (Y0 @ X5)) & ((Y0 @ X10) = (Y0 @ X3))) & (~ ((Y0 @ X7) = (Y0 @ X6)))) & ((Y0 @ X12) = (Y0 @ X3))) => ((Y0 @ X9) = (Y0 @ X4)))) & (((((Y0 @ X1) = (Y0 @ X7)) & ((Y0 @ X11) = (Y0 @ X8))) & ((Y0 @ X12) = (Y0 @ X5))) => (~ ((Y0 @ X9) = (Y0 @ X4))))) => ((((((~ ((Y0 @ X10) = (Y0 @ X5))) | (~ ((Y0 @ X11) = (Y0 @ X8)))) | (~ ((Y0 @ X12) = (Y0 @ X3)))) | (~ ((Y0 @ X9) = (Y0 @ X6)))) | (~ ((Y0 @ X1) = (Y0 @ X7)))) | (~ ((Y0 @ X4) = (Y0 @ X2))))))))) )),
% 1.62/1.48 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.62/1.48 thf(f30,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (($false = ((^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((((((((((((Y1 @ Y0) = (Y1 @ X4)) & ((Y1 @ Y0) = (Y1 @ X3))) & ((Y1 @ X4) = (Y1 @ X2))) & (~ ((Y1 @ X11) = (Y1 @ X10)))) => (~ ((Y1 @ X7) = (Y1 @ X6)))) & (((((Y1 @ X2) = (Y1 @ X3)) & ((Y1 @ X1) = (Y1 @ X7))) & ((Y1 @ X9) = (Y1 @ X6))) => (~ ((Y1 @ X11) = (Y1 @ X10))))) & (((((Y1 @ X7) = (Y1 @ X6)) & ((Y1 @ X11) = (Y1 @ X8))) & ((Y1 @ X10) = (Y1 @ X5))) => ((Y1 @ X2) = (Y1 @ X3)))) & (((((Y1 @ X4) = (Y1 @ X2)) & (~ ((Y1 @ Y0) = (Y1 @ X5)))) & ((Y1 @ X11) = (Y1 @ X8))) => ((Y1 @ X7) = (Y1 @ X6)))) & ((((((Y1 @ X10) = (Y1 @ X5)) & ((Y1 @ X10) = (Y1 @ X3))) & (~ ((Y1 @ X7) = (Y1 @ X6)))) & ((Y1 @ Y0) = (Y1 @ X3))) => ((Y1 @ X9) = (Y1 @ X4)))) & (((((Y1 @ X1) = (Y1 @ X7)) & ((Y1 @ X11) = (Y1 @ X8))) & ((Y1 @ Y0) = (Y1 @ X5))) => (~ ((Y1 @ X9) = (Y1 @ X4))))) => ((((((~ ((Y1 @ X10) = (Y1 @ X5))) | (~ ((Y1 @ X11) = (Y1 @ X8)))) | (~ ((Y1 @ Y0) = (Y1 @ X3)))) | (~ ((Y1 @ X9) = (Y1 @ X6)))) | (~ ((Y1 @ X1) = (Y1 @ X7)))) | (~ ((Y1 @ X4) = (Y1 @ X2)))))))) @ X12))) )),
% 1.62/1.48 inference(pi_clausification,[status(thm)],[f29])).
% 1.62/1.48 thf(f29,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((((((((((((Y1 @ Y0) = (Y1 @ X4)) & ((Y1 @ Y0) = (Y1 @ X3))) & ((Y1 @ X4) = (Y1 @ X2))) & (~ ((Y1 @ X11) = (Y1 @ X10)))) => (~ ((Y1 @ X7) = (Y1 @ X6)))) & (((((Y1 @ X2) = (Y1 @ X3)) & ((Y1 @ X1) = (Y1 @ X7))) & ((Y1 @ X9) = (Y1 @ X6))) => (~ ((Y1 @ X11) = (Y1 @ X10))))) & (((((Y1 @ X7) = (Y1 @ X6)) & ((Y1 @ X11) = (Y1 @ X8))) & ((Y1 @ X10) = (Y1 @ X5))) => ((Y1 @ X2) = (Y1 @ X3)))) & (((((Y1 @ X4) = (Y1 @ X2)) & (~ ((Y1 @ Y0) = (Y1 @ X5)))) & ((Y1 @ X11) = (Y1 @ X8))) => ((Y1 @ X7) = (Y1 @ X6)))) & ((((((Y1 @ X10) = (Y1 @ X5)) & ((Y1 @ X10) = (Y1 @ X3))) & (~ ((Y1 @ X7) = (Y1 @ X6)))) & ((Y1 @ Y0) = (Y1 @ X3))) => ((Y1 @ X9) = (Y1 @ X4)))) & (((((Y1 @ X1) = (Y1 @ X7)) & ((Y1 @ X11) = (Y1 @ X8))) & ((Y1 @ Y0) = (Y1 @ X5))) => (~ ((Y1 @ X9) = (Y1 @ X4))))) => ((((((~ ((Y1 @ X10) = (Y1 @ X5))) | (~ ((Y1 @ X11) = (Y1 @ X8)))) | (~ ((Y1 @ Y0) = (Y1 @ X3)))) | (~ ((Y1 @ X9) = (Y1 @ X6)))) | (~ ((Y1 @ X1) = (Y1 @ X7)))) | (~ ((Y1 @ X4) = (Y1 @ X2))))))))))) )),
% 1.62/1.48 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.62/1.48 thf(f28,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((((((((((((Y2 @ Y1) = (Y2 @ X4)) & ((Y2 @ Y1) = (Y2 @ X3))) & ((Y2 @ X4) = (Y2 @ X2))) & (~ ((Y2 @ Y0) = (Y2 @ X10)))) => (~ ((Y2 @ X7) = (Y2 @ X6)))) & (((((Y2 @ X2) = (Y2 @ X3)) & ((Y2 @ X1) = (Y2 @ X7))) & ((Y2 @ X9) = (Y2 @ X6))) => (~ ((Y2 @ Y0) = (Y2 @ X10))))) & (((((Y2 @ X7) = (Y2 @ X6)) & ((Y2 @ Y0) = (Y2 @ X8))) & ((Y2 @ X10) = (Y2 @ X5))) => ((Y2 @ X2) = (Y2 @ X3)))) & (((((Y2 @ X4) = (Y2 @ X2)) & (~ ((Y2 @ Y1) = (Y2 @ X5)))) & ((Y2 @ Y0) = (Y2 @ X8))) => ((Y2 @ X7) = (Y2 @ X6)))) & ((((((Y2 @ X10) = (Y2 @ X5)) & ((Y2 @ X10) = (Y2 @ X3))) & (~ ((Y2 @ X7) = (Y2 @ X6)))) & ((Y2 @ Y1) = (Y2 @ X3))) => ((Y2 @ X9) = (Y2 @ X4)))) & (((((Y2 @ X1) = (Y2 @ X7)) & ((Y2 @ Y0) = (Y2 @ X8))) & ((Y2 @ Y1) = (Y2 @ X5))) => (~ ((Y2 @ X9) = (Y2 @ X4))))) => ((((((~ ((Y2 @ X10) = (Y2 @ X5))) | (~ ((Y2 @ Y0) = (Y2 @ X8)))) | (~ ((Y2 @ Y1) = (Y2 @ X3)))) | (~ ((Y2 @ X9) = (Y2 @ X6)))) | (~ ((Y2 @ X1) = (Y2 @ X7)))) | (~ ((Y2 @ X4) = (Y2 @ X2)))))))))) @ X11) = $false)) )),
% 1.62/1.48 inference(pi_clausification,[status(thm)],[f27])).
% 1.62/1.48 thf(f27,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((((((((((((Y2 @ Y1) = (Y2 @ X4)) & ((Y2 @ Y1) = (Y2 @ X3))) & ((Y2 @ X4) = (Y2 @ X2))) & (~ ((Y2 @ Y0) = (Y2 @ X10)))) => (~ ((Y2 @ X7) = (Y2 @ X6)))) & (((((Y2 @ X2) = (Y2 @ X3)) & ((Y2 @ X1) = (Y2 @ X7))) & ((Y2 @ X9) = (Y2 @ X6))) => (~ ((Y2 @ Y0) = (Y2 @ X10))))) & (((((Y2 @ X7) = (Y2 @ X6)) & ((Y2 @ Y0) = (Y2 @ X8))) & ((Y2 @ X10) = (Y2 @ X5))) => ((Y2 @ X2) = (Y2 @ X3)))) & (((((Y2 @ X4) = (Y2 @ X2)) & (~ ((Y2 @ Y1) = (Y2 @ X5)))) & ((Y2 @ Y0) = (Y2 @ X8))) => ((Y2 @ X7) = (Y2 @ X6)))) & ((((((Y2 @ X10) = (Y2 @ X5)) & ((Y2 @ X10) = (Y2 @ X3))) & (~ ((Y2 @ X7) = (Y2 @ X6)))) & ((Y2 @ Y1) = (Y2 @ X3))) => ((Y2 @ X9) = (Y2 @ X4)))) & (((((Y2 @ X1) = (Y2 @ X7)) & ((Y2 @ Y0) = (Y2 @ X8))) & ((Y2 @ Y1) = (Y2 @ X5))) => (~ ((Y2 @ X9) = (Y2 @ X4))))) => ((((((~ ((Y2 @ X10) = (Y2 @ X5))) | (~ ((Y2 @ Y0) = (Y2 @ X8)))) | (~ ((Y2 @ Y1) = (Y2 @ X3)))) | (~ ((Y2 @ X9) = (Y2 @ X6)))) | (~ ((Y2 @ X1) = (Y2 @ X7)))) | (~ ((Y2 @ X4) = (Y2 @ X2))))))))))))) )),
% 1.62/1.48 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.62/1.48 thf(f26,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ ($i > $i) @ (^[Y3 : $i > $i]: ((((((((((((Y3 @ Y2) = (Y3 @ X4)) & ((Y3 @ Y2) = (Y3 @ X3))) & ((Y3 @ X4) = (Y3 @ X2))) & (~ ((Y3 @ Y1) = (Y3 @ Y0)))) => (~ ((Y3 @ X7) = (Y3 @ X6)))) & (((((Y3 @ X2) = (Y3 @ X3)) & ((Y3 @ X1) = (Y3 @ X7))) & ((Y3 @ X9) = (Y3 @ X6))) => (~ ((Y3 @ Y1) = (Y3 @ Y0))))) & (((((Y3 @ X7) = (Y3 @ X6)) & ((Y3 @ Y1) = (Y3 @ X8))) & ((Y3 @ Y0) = (Y3 @ X5))) => ((Y3 @ X2) = (Y3 @ X3)))) & (((((Y3 @ X4) = (Y3 @ X2)) & (~ ((Y3 @ Y2) = (Y3 @ X5)))) & ((Y3 @ Y1) = (Y3 @ X8))) => ((Y3 @ X7) = (Y3 @ X6)))) & ((((((Y3 @ Y0) = (Y3 @ X5)) & ((Y3 @ Y0) = (Y3 @ X3))) & (~ ((Y3 @ X7) = (Y3 @ X6)))) & ((Y3 @ Y2) = (Y3 @ X3))) => ((Y3 @ X9) = (Y3 @ X4)))) & (((((Y3 @ X1) = (Y3 @ X7)) & ((Y3 @ Y1) = (Y3 @ X8))) & ((Y3 @ Y2) = (Y3 @ X5))) => (~ ((Y3 @ X9) = (Y3 @ X4))))) => ((((((~ ((Y3 @ Y0) = (Y3 @ X5))) | (~ ((Y3 @ Y1) = (Y3 @ X8)))) | (~ ((Y3 @ Y2) = (Y3 @ X3)))) | (~ ((Y3 @ X9) = (Y3 @ X6)))) | (~ ((Y3 @ X1) = (Y3 @ X7)))) | (~ ((Y3 @ X4) = (Y3 @ X2)))))))))))) @ X10) = $false)) )),
% 1.62/1.48 inference(pi_clausification,[status(thm)],[f25])).
% 1.62/1.48 thf(f25,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ ($i > $i) @ (^[Y3 : $i > $i]: ((((((((((((Y3 @ Y2) = (Y3 @ X4)) & ((Y3 @ Y2) = (Y3 @ X3))) & ((Y3 @ X4) = (Y3 @ X2))) & (~ ((Y3 @ Y1) = (Y3 @ Y0)))) => (~ ((Y3 @ X7) = (Y3 @ X6)))) & (((((Y3 @ X2) = (Y3 @ X3)) & ((Y3 @ X1) = (Y3 @ X7))) & ((Y3 @ X9) = (Y3 @ X6))) => (~ ((Y3 @ Y1) = (Y3 @ Y0))))) & (((((Y3 @ X7) = (Y3 @ X6)) & ((Y3 @ Y1) = (Y3 @ X8))) & ((Y3 @ Y0) = (Y3 @ X5))) => ((Y3 @ X2) = (Y3 @ X3)))) & (((((Y3 @ X4) = (Y3 @ X2)) & (~ ((Y3 @ Y2) = (Y3 @ X5)))) & ((Y3 @ Y1) = (Y3 @ X8))) => ((Y3 @ X7) = (Y3 @ X6)))) & ((((((Y3 @ Y0) = (Y3 @ X5)) & ((Y3 @ Y0) = (Y3 @ X3))) & (~ ((Y3 @ X7) = (Y3 @ X6)))) & ((Y3 @ Y2) = (Y3 @ X3))) => ((Y3 @ X9) = (Y3 @ X4)))) & (((((Y3 @ X1) = (Y3 @ X7)) & ((Y3 @ Y1) = (Y3 @ X8))) & ((Y3 @ Y2) = (Y3 @ X5))) => (~ ((Y3 @ X9) = (Y3 @ X4))))) => ((((((~ ((Y3 @ Y0) = (Y3 @ X5))) | (~ ((Y3 @ Y1) = (Y3 @ X8)))) | (~ ((Y3 @ Y2) = (Y3 @ X3)))) | (~ ((Y3 @ X9) = (Y3 @ X6)))) | (~ ((Y3 @ X1) = (Y3 @ X7)))) | (~ ((Y3 @ X4) = (Y3 @ X2))))))))))))) = $false)) )),
% 1.62/1.48 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.62/1.48 thf(f24,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (!! @ ($i > $i) @ (^[Y4 : $i > $i]: ((((((((((((Y4 @ Y3) = (Y4 @ X4)) & ((Y4 @ Y3) = (Y4 @ X3))) & ((Y4 @ X4) = (Y4 @ X2))) & (~ ((Y4 @ Y2) = (Y4 @ Y1)))) => (~ ((Y4 @ X7) = (Y4 @ X6)))) & (((((Y4 @ X2) = (Y4 @ X3)) & ((Y4 @ X1) = (Y4 @ X7))) & ((Y4 @ Y0) = (Y4 @ X6))) => (~ ((Y4 @ Y2) = (Y4 @ Y1))))) & (((((Y4 @ X7) = (Y4 @ X6)) & ((Y4 @ Y2) = (Y4 @ X8))) & ((Y4 @ Y1) = (Y4 @ X5))) => ((Y4 @ X2) = (Y4 @ X3)))) & (((((Y4 @ X4) = (Y4 @ X2)) & (~ ((Y4 @ Y3) = (Y4 @ X5)))) & ((Y4 @ Y2) = (Y4 @ X8))) => ((Y4 @ X7) = (Y4 @ X6)))) & ((((((Y4 @ Y1) = (Y4 @ X5)) & ((Y4 @ Y1) = (Y4 @ X3))) & (~ ((Y4 @ X7) = (Y4 @ X6)))) & ((Y4 @ Y3) = (Y4 @ X3))) => ((Y4 @ Y0) = (Y4 @ X4)))) & (((((Y4 @ X1) = (Y4 @ X7)) & ((Y4 @ Y2) = (Y4 @ X8))) & ((Y4 @ Y3) = (Y4 @ X5))) => (~ ((Y4 @ Y0) = (Y4 @ X4))))) => ((((((~ ((Y4 @ Y1) = (Y4 @ X5))) | (~ ((Y4 @ Y2) = (Y4 @ X8)))) | (~ ((Y4 @ Y3) = (Y4 @ X3)))) | (~ ((Y4 @ Y0) = (Y4 @ X6)))) | (~ ((Y4 @ X1) = (Y4 @ X7)))) | (~ ((Y4 @ X4) = (Y4 @ X2)))))))))))))) @ X9))) )),
% 1.62/1.48 inference(pi_clausification,[status(thm)],[f23])).
% 1.62/1.48 thf(f23,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (!! @ ($i > $i) @ (^[Y4 : $i > $i]: ((((((((((((Y4 @ Y3) = (Y4 @ X4)) & ((Y4 @ Y3) = (Y4 @ X3))) & ((Y4 @ X4) = (Y4 @ X2))) & (~ ((Y4 @ Y2) = (Y4 @ Y1)))) => (~ ((Y4 @ X7) = (Y4 @ X6)))) & (((((Y4 @ X2) = (Y4 @ X3)) & ((Y4 @ X1) = (Y4 @ X7))) & ((Y4 @ Y0) = (Y4 @ X6))) => (~ ((Y4 @ Y2) = (Y4 @ Y1))))) & (((((Y4 @ X7) = (Y4 @ X6)) & ((Y4 @ Y2) = (Y4 @ X8))) & ((Y4 @ Y1) = (Y4 @ X5))) => ((Y4 @ X2) = (Y4 @ X3)))) & (((((Y4 @ X4) = (Y4 @ X2)) & (~ ((Y4 @ Y3) = (Y4 @ X5)))) & ((Y4 @ Y2) = (Y4 @ X8))) => ((Y4 @ X7) = (Y4 @ X6)))) & ((((((Y4 @ Y1) = (Y4 @ X5)) & ((Y4 @ Y1) = (Y4 @ X3))) & (~ ((Y4 @ X7) = (Y4 @ X6)))) & ((Y4 @ Y3) = (Y4 @ X3))) => ((Y4 @ Y0) = (Y4 @ X4)))) & (((((Y4 @ X1) = (Y4 @ X7)) & ((Y4 @ Y2) = (Y4 @ X8))) & ((Y4 @ Y3) = (Y4 @ X5))) => (~ ((Y4 @ Y0) = (Y4 @ X4))))) => ((((((~ ((Y4 @ Y1) = (Y4 @ X5))) | (~ ((Y4 @ Y2) = (Y4 @ X8)))) | (~ ((Y4 @ Y3) = (Y4 @ X3)))) | (~ ((Y4 @ Y0) = (Y4 @ X6)))) | (~ ((Y4 @ X1) = (Y4 @ X7)))) | (~ ((Y4 @ X4) = (Y4 @ X2))))))))))))))))) )),
% 1.62/1.48 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.62/1.48 thf(f22,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (!! @ ($i > $i) @ (^[Y5 : $i > $i]: ((((((((((((Y5 @ Y4) = (Y5 @ X4)) & ((Y5 @ Y4) = (Y5 @ X3))) & ((Y5 @ X4) = (Y5 @ X2))) & (~ ((Y5 @ Y3) = (Y5 @ Y2)))) => (~ ((Y5 @ X7) = (Y5 @ X6)))) & (((((Y5 @ X2) = (Y5 @ X3)) & ((Y5 @ X1) = (Y5 @ X7))) & ((Y5 @ Y1) = (Y5 @ X6))) => (~ ((Y5 @ Y3) = (Y5 @ Y2))))) & (((((Y5 @ X7) = (Y5 @ X6)) & ((Y5 @ Y3) = (Y5 @ Y0))) & ((Y5 @ Y2) = (Y5 @ X5))) => ((Y5 @ X2) = (Y5 @ X3)))) & (((((Y5 @ X4) = (Y5 @ X2)) & (~ ((Y5 @ Y4) = (Y5 @ X5)))) & ((Y5 @ Y3) = (Y5 @ Y0))) => ((Y5 @ X7) = (Y5 @ X6)))) & ((((((Y5 @ Y2) = (Y5 @ X5)) & ((Y5 @ Y2) = (Y5 @ X3))) & (~ ((Y5 @ X7) = (Y5 @ X6)))) & ((Y5 @ Y4) = (Y5 @ X3))) => ((Y5 @ Y1) = (Y5 @ X4)))) & (((((Y5 @ X1) = (Y5 @ X7)) & ((Y5 @ Y3) = (Y5 @ Y0))) & ((Y5 @ Y4) = (Y5 @ X5))) => (~ ((Y5 @ Y1) = (Y5 @ X4))))) => ((((((~ ((Y5 @ Y2) = (Y5 @ X5))) | (~ ((Y5 @ Y3) = (Y5 @ Y0)))) | (~ ((Y5 @ Y4) = (Y5 @ X3)))) | (~ ((Y5 @ Y1) = (Y5 @ X6)))) | (~ ((Y5 @ X1) = (Y5 @ X7)))) | (~ ((Y5 @ X4) = (Y5 @ X2)))))))))))))))) @ X8))) )),
% 1.62/1.48 inference(pi_clausification,[status(thm)],[f21])).
% 1.62/1.48 thf(f21,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (!! @ ($i > $i) @ (^[Y5 : $i > $i]: ((((((((((((Y5 @ Y4) = (Y5 @ X4)) & ((Y5 @ Y4) = (Y5 @ X3))) & ((Y5 @ X4) = (Y5 @ X2))) & (~ ((Y5 @ Y3) = (Y5 @ Y2)))) => (~ ((Y5 @ X7) = (Y5 @ X6)))) & (((((Y5 @ X2) = (Y5 @ X3)) & ((Y5 @ X1) = (Y5 @ X7))) & ((Y5 @ Y1) = (Y5 @ X6))) => (~ ((Y5 @ Y3) = (Y5 @ Y2))))) & (((((Y5 @ X7) = (Y5 @ X6)) & ((Y5 @ Y3) = (Y5 @ Y0))) & ((Y5 @ Y2) = (Y5 @ X5))) => ((Y5 @ X2) = (Y5 @ X3)))) & (((((Y5 @ X4) = (Y5 @ X2)) & (~ ((Y5 @ Y4) = (Y5 @ X5)))) & ((Y5 @ Y3) = (Y5 @ Y0))) => ((Y5 @ X7) = (Y5 @ X6)))) & ((((((Y5 @ Y2) = (Y5 @ X5)) & ((Y5 @ Y2) = (Y5 @ X3))) & (~ ((Y5 @ X7) = (Y5 @ X6)))) & ((Y5 @ Y4) = (Y5 @ X3))) => ((Y5 @ Y1) = (Y5 @ X4)))) & (((((Y5 @ X1) = (Y5 @ X7)) & ((Y5 @ Y3) = (Y5 @ Y0))) & ((Y5 @ Y4) = (Y5 @ X5))) => (~ ((Y5 @ Y1) = (Y5 @ X4))))) => ((((((~ ((Y5 @ Y2) = (Y5 @ X5))) | (~ ((Y5 @ Y3) = (Y5 @ Y0)))) | (~ ((Y5 @ Y4) = (Y5 @ X3)))) | (~ ((Y5 @ Y1) = (Y5 @ X6)))) | (~ ((Y5 @ X1) = (Y5 @ X7)))) | (~ ((Y5 @ X4) = (Y5 @ X2))))))))))))))))))) )),
% 1.62/1.48 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.62/1.48 thf(f20,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (!! @ ($i > $i) @ (^[Y6 : $i > $i]: ((((((((((((Y6 @ Y5) = (Y6 @ X4)) & ((Y6 @ Y5) = (Y6 @ X3))) & ((Y6 @ X4) = (Y6 @ X2))) & (~ ((Y6 @ Y4) = (Y6 @ Y3)))) => (~ ((Y6 @ Y0) = (Y6 @ X6)))) & (((((Y6 @ X2) = (Y6 @ X3)) & ((Y6 @ X1) = (Y6 @ Y0))) & ((Y6 @ Y2) = (Y6 @ X6))) => (~ ((Y6 @ Y4) = (Y6 @ Y3))))) & (((((Y6 @ Y0) = (Y6 @ X6)) & ((Y6 @ Y4) = (Y6 @ Y1))) & ((Y6 @ Y3) = (Y6 @ X5))) => ((Y6 @ X2) = (Y6 @ X3)))) & (((((Y6 @ X4) = (Y6 @ X2)) & (~ ((Y6 @ Y5) = (Y6 @ X5)))) & ((Y6 @ Y4) = (Y6 @ Y1))) => ((Y6 @ Y0) = (Y6 @ X6)))) & ((((((Y6 @ Y3) = (Y6 @ X5)) & ((Y6 @ Y3) = (Y6 @ X3))) & (~ ((Y6 @ Y0) = (Y6 @ X6)))) & ((Y6 @ Y5) = (Y6 @ X3))) => ((Y6 @ Y2) = (Y6 @ X4)))) & (((((Y6 @ X1) = (Y6 @ Y0)) & ((Y6 @ Y4) = (Y6 @ Y1))) & ((Y6 @ Y5) = (Y6 @ X5))) => (~ ((Y6 @ Y2) = (Y6 @ X4))))) => ((((((~ ((Y6 @ Y3) = (Y6 @ X5))) | (~ ((Y6 @ Y4) = (Y6 @ Y1)))) | (~ ((Y6 @ Y5) = (Y6 @ X3)))) | (~ ((Y6 @ Y2) = (Y6 @ X6)))) | (~ ((Y6 @ X1) = (Y6 @ Y0)))) | (~ ((Y6 @ X4) = (Y6 @ X2)))))))))))))))))) @ X7))) )),
% 1.62/1.48 inference(pi_clausification,[status(thm)],[f19])).
% 1.62/1.48 thf(f19,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (!! @ ($i > $i) @ (^[Y6 : $i > $i]: ((((((((((((Y6 @ Y5) = (Y6 @ X4)) & ((Y6 @ Y5) = (Y6 @ X3))) & ((Y6 @ X4) = (Y6 @ X2))) & (~ ((Y6 @ Y4) = (Y6 @ Y3)))) => (~ ((Y6 @ Y0) = (Y6 @ X6)))) & (((((Y6 @ X2) = (Y6 @ X3)) & ((Y6 @ X1) = (Y6 @ Y0))) & ((Y6 @ Y2) = (Y6 @ X6))) => (~ ((Y6 @ Y4) = (Y6 @ Y3))))) & (((((Y6 @ Y0) = (Y6 @ X6)) & ((Y6 @ Y4) = (Y6 @ Y1))) & ((Y6 @ Y3) = (Y6 @ X5))) => ((Y6 @ X2) = (Y6 @ X3)))) & (((((Y6 @ X4) = (Y6 @ X2)) & (~ ((Y6 @ Y5) = (Y6 @ X5)))) & ((Y6 @ Y4) = (Y6 @ Y1))) => ((Y6 @ Y0) = (Y6 @ X6)))) & ((((((Y6 @ Y3) = (Y6 @ X5)) & ((Y6 @ Y3) = (Y6 @ X3))) & (~ ((Y6 @ Y0) = (Y6 @ X6)))) & ((Y6 @ Y5) = (Y6 @ X3))) => ((Y6 @ Y2) = (Y6 @ X4)))) & (((((Y6 @ X1) = (Y6 @ Y0)) & ((Y6 @ Y4) = (Y6 @ Y1))) & ((Y6 @ Y5) = (Y6 @ X5))) => (~ ((Y6 @ Y2) = (Y6 @ X4))))) => ((((((~ ((Y6 @ Y3) = (Y6 @ X5))) | (~ ((Y6 @ Y4) = (Y6 @ Y1)))) | (~ ((Y6 @ Y5) = (Y6 @ X3)))) | (~ ((Y6 @ Y2) = (Y6 @ X6)))) | (~ ((Y6 @ X1) = (Y6 @ Y0)))) | (~ ((Y6 @ X4) = (Y6 @ X2))))))))))))))))))))) )),
% 1.62/1.48 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.62/1.48 thf(f18,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : ((((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (!! @ ($i > $i) @ (^[Y7 : $i > $i]: ((((((((((((Y7 @ Y6) = (Y7 @ X4)) & ((Y7 @ Y6) = (Y7 @ X3))) & ((Y7 @ X4) = (Y7 @ X2))) & (~ ((Y7 @ Y5) = (Y7 @ Y4)))) => (~ ((Y7 @ Y1) = (Y7 @ Y0)))) & (((((Y7 @ X2) = (Y7 @ X3)) & ((Y7 @ X1) = (Y7 @ Y1))) & ((Y7 @ Y3) = (Y7 @ Y0))) => (~ ((Y7 @ Y5) = (Y7 @ Y4))))) & (((((Y7 @ Y1) = (Y7 @ Y0)) & ((Y7 @ Y5) = (Y7 @ Y2))) & ((Y7 @ Y4) = (Y7 @ X5))) => ((Y7 @ X2) = (Y7 @ X3)))) & (((((Y7 @ X4) = (Y7 @ X2)) & (~ ((Y7 @ Y6) = (Y7 @ X5)))) & ((Y7 @ Y5) = (Y7 @ Y2))) => ((Y7 @ Y1) = (Y7 @ Y0)))) & ((((((Y7 @ Y4) = (Y7 @ X5)) & ((Y7 @ Y4) = (Y7 @ X3))) & (~ ((Y7 @ Y1) = (Y7 @ Y0)))) & ((Y7 @ Y6) = (Y7 @ X3))) => ((Y7 @ Y3) = (Y7 @ X4)))) & (((((Y7 @ X1) = (Y7 @ Y1)) & ((Y7 @ Y5) = (Y7 @ Y2))) & ((Y7 @ Y6) = (Y7 @ X5))) => (~ ((Y7 @ Y3) = (Y7 @ X4))))) => ((((((~ ((Y7 @ Y4) = (Y7 @ X5))) | (~ ((Y7 @ Y5) = (Y7 @ Y2)))) | (~ ((Y7 @ Y6) = (Y7 @ X3)))) | (~ ((Y7 @ Y3) = (Y7 @ Y0)))) | (~ ((Y7 @ X1) = (Y7 @ Y1)))) | (~ ((Y7 @ X4) = (Y7 @ X2)))))))))))))))))))) @ X6) = $false)) )),
% 1.62/1.48 inference(pi_clausification,[status(thm)],[f17])).
% 1.62/1.48 thf(f17,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (!! @ ($i > $i) @ (^[Y7 : $i > $i]: ((((((((((((Y7 @ Y6) = (Y7 @ X4)) & ((Y7 @ Y6) = (Y7 @ X3))) & ((Y7 @ X4) = (Y7 @ X2))) & (~ ((Y7 @ Y5) = (Y7 @ Y4)))) => (~ ((Y7 @ Y1) = (Y7 @ Y0)))) & (((((Y7 @ X2) = (Y7 @ X3)) & ((Y7 @ X1) = (Y7 @ Y1))) & ((Y7 @ Y3) = (Y7 @ Y0))) => (~ ((Y7 @ Y5) = (Y7 @ Y4))))) & (((((Y7 @ Y1) = (Y7 @ Y0)) & ((Y7 @ Y5) = (Y7 @ Y2))) & ((Y7 @ Y4) = (Y7 @ X5))) => ((Y7 @ X2) = (Y7 @ X3)))) & (((((Y7 @ X4) = (Y7 @ X2)) & (~ ((Y7 @ Y6) = (Y7 @ X5)))) & ((Y7 @ Y5) = (Y7 @ Y2))) => ((Y7 @ Y1) = (Y7 @ Y0)))) & ((((((Y7 @ Y4) = (Y7 @ X5)) & ((Y7 @ Y4) = (Y7 @ X3))) & (~ ((Y7 @ Y1) = (Y7 @ Y0)))) & ((Y7 @ Y6) = (Y7 @ X3))) => ((Y7 @ Y3) = (Y7 @ X4)))) & (((((Y7 @ X1) = (Y7 @ Y1)) & ((Y7 @ Y5) = (Y7 @ Y2))) & ((Y7 @ Y6) = (Y7 @ X5))) => (~ ((Y7 @ Y3) = (Y7 @ X4))))) => ((((((~ ((Y7 @ Y4) = (Y7 @ X5))) | (~ ((Y7 @ Y5) = (Y7 @ Y2)))) | (~ ((Y7 @ Y6) = (Y7 @ X3)))) | (~ ((Y7 @ Y3) = (Y7 @ Y0)))) | (~ ((Y7 @ X1) = (Y7 @ Y1)))) | (~ ((Y7 @ X4) = (Y7 @ X2))))))))))))))))))))))) )),
% 1.62/1.48 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.62/1.48 thf(f16,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (!! @ ($i > $i) @ (^[Y8 : $i > $i]: ((((((((((((Y8 @ Y7) = (Y8 @ X4)) & ((Y8 @ Y7) = (Y8 @ X3))) & ((Y8 @ X4) = (Y8 @ X2))) & (~ ((Y8 @ Y6) = (Y8 @ Y5)))) => (~ ((Y8 @ Y2) = (Y8 @ Y1)))) & (((((Y8 @ X2) = (Y8 @ X3)) & ((Y8 @ X1) = (Y8 @ Y2))) & ((Y8 @ Y4) = (Y8 @ Y1))) => (~ ((Y8 @ Y6) = (Y8 @ Y5))))) & (((((Y8 @ Y2) = (Y8 @ Y1)) & ((Y8 @ Y6) = (Y8 @ Y3))) & ((Y8 @ Y5) = (Y8 @ Y0))) => ((Y8 @ X2) = (Y8 @ X3)))) & (((((Y8 @ X4) = (Y8 @ X2)) & (~ ((Y8 @ Y7) = (Y8 @ Y0)))) & ((Y8 @ Y6) = (Y8 @ Y3))) => ((Y8 @ Y2) = (Y8 @ Y1)))) & ((((((Y8 @ Y5) = (Y8 @ Y0)) & ((Y8 @ Y5) = (Y8 @ X3))) & (~ ((Y8 @ Y2) = (Y8 @ Y1)))) & ((Y8 @ Y7) = (Y8 @ X3))) => ((Y8 @ Y4) = (Y8 @ X4)))) & (((((Y8 @ X1) = (Y8 @ Y2)) & ((Y8 @ Y6) = (Y8 @ Y3))) & ((Y8 @ Y7) = (Y8 @ Y0))) => (~ ((Y8 @ Y4) = (Y8 @ X4))))) => ((((((~ ((Y8 @ Y5) = (Y8 @ Y0))) | (~ ((Y8 @ Y6) = (Y8 @ Y3)))) | (~ ((Y8 @ Y7) = (Y8 @ X3)))) | (~ ((Y8 @ Y4) = (Y8 @ Y1)))) | (~ ((Y8 @ X1) = (Y8 @ Y2)))) | (~ ((Y8 @ X4) = (Y8 @ X2)))))))))))))))))))))) @ X5))) )),
% 1.62/1.48 inference(pi_clausification,[status(thm)],[f15])).
% 1.62/1.48 thf(f15,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (!! @ ($i > $i) @ (^[Y8 : $i > $i]: ((((((((((((Y8 @ Y7) = (Y8 @ X4)) & ((Y8 @ Y7) = (Y8 @ X3))) & ((Y8 @ X4) = (Y8 @ X2))) & (~ ((Y8 @ Y6) = (Y8 @ Y5)))) => (~ ((Y8 @ Y2) = (Y8 @ Y1)))) & (((((Y8 @ X2) = (Y8 @ X3)) & ((Y8 @ X1) = (Y8 @ Y2))) & ((Y8 @ Y4) = (Y8 @ Y1))) => (~ ((Y8 @ Y6) = (Y8 @ Y5))))) & (((((Y8 @ Y2) = (Y8 @ Y1)) & ((Y8 @ Y6) = (Y8 @ Y3))) & ((Y8 @ Y5) = (Y8 @ Y0))) => ((Y8 @ X2) = (Y8 @ X3)))) & (((((Y8 @ X4) = (Y8 @ X2)) & (~ ((Y8 @ Y7) = (Y8 @ Y0)))) & ((Y8 @ Y6) = (Y8 @ Y3))) => ((Y8 @ Y2) = (Y8 @ Y1)))) & ((((((Y8 @ Y5) = (Y8 @ Y0)) & ((Y8 @ Y5) = (Y8 @ X3))) & (~ ((Y8 @ Y2) = (Y8 @ Y1)))) & ((Y8 @ Y7) = (Y8 @ X3))) => ((Y8 @ Y4) = (Y8 @ X4)))) & (((((Y8 @ X1) = (Y8 @ Y2)) & ((Y8 @ Y6) = (Y8 @ Y3))) & ((Y8 @ Y7) = (Y8 @ Y0))) => (~ ((Y8 @ Y4) = (Y8 @ X4))))) => ((((((~ ((Y8 @ Y5) = (Y8 @ Y0))) | (~ ((Y8 @ Y6) = (Y8 @ Y3)))) | (~ ((Y8 @ Y7) = (Y8 @ X3)))) | (~ ((Y8 @ Y4) = (Y8 @ Y1)))) | (~ ((Y8 @ X1) = (Y8 @ Y2)))) | (~ ((Y8 @ X4) = (Y8 @ X2))))))))))))))))))))))))) )),
% 1.62/1.48 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.62/1.48 thf(f14,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (!! @ ($i > $i) @ (^[Y9 : $i > $i]: ((((((((((((Y9 @ Y8) = (Y9 @ Y0)) & ((Y9 @ Y8) = (Y9 @ X3))) & ((Y9 @ Y0) = (Y9 @ X2))) & (~ ((Y9 @ Y7) = (Y9 @ Y6)))) => (~ ((Y9 @ Y3) = (Y9 @ Y2)))) & (((((Y9 @ X2) = (Y9 @ X3)) & ((Y9 @ X1) = (Y9 @ Y3))) & ((Y9 @ Y5) = (Y9 @ Y2))) => (~ ((Y9 @ Y7) = (Y9 @ Y6))))) & (((((Y9 @ Y3) = (Y9 @ Y2)) & ((Y9 @ Y7) = (Y9 @ Y4))) & ((Y9 @ Y6) = (Y9 @ Y1))) => ((Y9 @ X2) = (Y9 @ X3)))) & (((((Y9 @ Y0) = (Y9 @ X2)) & (~ ((Y9 @ Y8) = (Y9 @ Y1)))) & ((Y9 @ Y7) = (Y9 @ Y4))) => ((Y9 @ Y3) = (Y9 @ Y2)))) & ((((((Y9 @ Y6) = (Y9 @ Y1)) & ((Y9 @ Y6) = (Y9 @ X3))) & (~ ((Y9 @ Y3) = (Y9 @ Y2)))) & ((Y9 @ Y8) = (Y9 @ X3))) => ((Y9 @ Y5) = (Y9 @ Y0)))) & (((((Y9 @ X1) = (Y9 @ Y3)) & ((Y9 @ Y7) = (Y9 @ Y4))) & ((Y9 @ Y8) = (Y9 @ Y1))) => (~ ((Y9 @ Y5) = (Y9 @ Y0))))) => ((((((~ ((Y9 @ Y6) = (Y9 @ Y1))) | (~ ((Y9 @ Y7) = (Y9 @ Y4)))) | (~ ((Y9 @ Y8) = (Y9 @ X3)))) | (~ ((Y9 @ Y5) = (Y9 @ Y2)))) | (~ ((Y9 @ X1) = (Y9 @ Y3)))) | (~ ((Y9 @ Y0) = (Y9 @ X2)))))))))))))))))))))))) @ X4))) )),
% 1.62/1.48 inference(pi_clausification,[status(thm)],[f13])).
% 1.62/1.48 thf(f13,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (!! @ ($i > $i) @ (^[Y9 : $i > $i]: ((((((((((((Y9 @ Y8) = (Y9 @ Y0)) & ((Y9 @ Y8) = (Y9 @ X3))) & ((Y9 @ Y0) = (Y9 @ X2))) & (~ ((Y9 @ Y7) = (Y9 @ Y6)))) => (~ ((Y9 @ Y3) = (Y9 @ Y2)))) & (((((Y9 @ X2) = (Y9 @ X3)) & ((Y9 @ X1) = (Y9 @ Y3))) & ((Y9 @ Y5) = (Y9 @ Y2))) => (~ ((Y9 @ Y7) = (Y9 @ Y6))))) & (((((Y9 @ Y3) = (Y9 @ Y2)) & ((Y9 @ Y7) = (Y9 @ Y4))) & ((Y9 @ Y6) = (Y9 @ Y1))) => ((Y9 @ X2) = (Y9 @ X3)))) & (((((Y9 @ Y0) = (Y9 @ X2)) & (~ ((Y9 @ Y8) = (Y9 @ Y1)))) & ((Y9 @ Y7) = (Y9 @ Y4))) => ((Y9 @ Y3) = (Y9 @ Y2)))) & ((((((Y9 @ Y6) = (Y9 @ Y1)) & ((Y9 @ Y6) = (Y9 @ X3))) & (~ ((Y9 @ Y3) = (Y9 @ Y2)))) & ((Y9 @ Y8) = (Y9 @ X3))) => ((Y9 @ Y5) = (Y9 @ Y0)))) & (((((Y9 @ X1) = (Y9 @ Y3)) & ((Y9 @ Y7) = (Y9 @ Y4))) & ((Y9 @ Y8) = (Y9 @ Y1))) => (~ ((Y9 @ Y5) = (Y9 @ Y0))))) => ((((((~ ((Y9 @ Y6) = (Y9 @ Y1))) | (~ ((Y9 @ Y7) = (Y9 @ Y4)))) | (~ ((Y9 @ Y8) = (Y9 @ X3)))) | (~ ((Y9 @ Y5) = (Y9 @ Y2)))) | (~ ((Y9 @ X1) = (Y9 @ Y3)))) | (~ ((Y9 @ Y0) = (Y9 @ X2))))))))))))))))))))))))))) )),
% 1.62/1.48 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.62/1.48 thf(f12,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: (!! @ ($i > $i) @ (^[Y10 : $i > $i]: ((((((((((((Y10 @ Y9) = (Y10 @ Y1)) & ((Y10 @ Y9) = (Y10 @ Y0))) & ((Y10 @ Y1) = (Y10 @ X2))) & (~ ((Y10 @ Y8) = (Y10 @ Y7)))) => (~ ((Y10 @ Y4) = (Y10 @ Y3)))) & (((((Y10 @ X2) = (Y10 @ Y0)) & ((Y10 @ X1) = (Y10 @ Y4))) & ((Y10 @ Y6) = (Y10 @ Y3))) => (~ ((Y10 @ Y8) = (Y10 @ Y7))))) & (((((Y10 @ Y4) = (Y10 @ Y3)) & ((Y10 @ Y8) = (Y10 @ Y5))) & ((Y10 @ Y7) = (Y10 @ Y2))) => ((Y10 @ X2) = (Y10 @ Y0)))) & (((((Y10 @ Y1) = (Y10 @ X2)) & (~ ((Y10 @ Y9) = (Y10 @ Y2)))) & ((Y10 @ Y8) = (Y10 @ Y5))) => ((Y10 @ Y4) = (Y10 @ Y3)))) & ((((((Y10 @ Y7) = (Y10 @ Y2)) & ((Y10 @ Y7) = (Y10 @ Y0))) & (~ ((Y10 @ Y4) = (Y10 @ Y3)))) & ((Y10 @ Y9) = (Y10 @ Y0))) => ((Y10 @ Y6) = (Y10 @ Y1)))) & (((((Y10 @ X1) = (Y10 @ Y4)) & ((Y10 @ Y8) = (Y10 @ Y5))) & ((Y10 @ Y9) = (Y10 @ Y2))) => (~ ((Y10 @ Y6) = (Y10 @ Y1))))) => ((((((~ ((Y10 @ Y7) = (Y10 @ Y2))) | (~ ((Y10 @ Y8) = (Y10 @ Y5)))) | (~ ((Y10 @ Y9) = (Y10 @ Y0)))) | (~ ((Y10 @ Y6) = (Y10 @ Y3)))) | (~ ((Y10 @ X1) = (Y10 @ Y4)))) | (~ ((Y10 @ Y1) = (Y10 @ X2)))))))))))))))))))))))))) @ X3))) )),
% 1.62/1.48 inference(pi_clausification,[status(thm)],[f11])).
% 1.62/1.48 thf(f11,plain,(
% 1.62/1.48 ( ! [X2 : $i,X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: (!! @ ($i > $i) @ (^[Y10 : $i > $i]: ((((((((((((Y10 @ Y9) = (Y10 @ Y1)) & ((Y10 @ Y9) = (Y10 @ Y0))) & ((Y10 @ Y1) = (Y10 @ X2))) & (~ ((Y10 @ Y8) = (Y10 @ Y7)))) => (~ ((Y10 @ Y4) = (Y10 @ Y3)))) & (((((Y10 @ X2) = (Y10 @ Y0)) & ((Y10 @ X1) = (Y10 @ Y4))) & ((Y10 @ Y6) = (Y10 @ Y3))) => (~ ((Y10 @ Y8) = (Y10 @ Y7))))) & (((((Y10 @ Y4) = (Y10 @ Y3)) & ((Y10 @ Y8) = (Y10 @ Y5))) & ((Y10 @ Y7) = (Y10 @ Y2))) => ((Y10 @ X2) = (Y10 @ Y0)))) & (((((Y10 @ Y1) = (Y10 @ X2)) & (~ ((Y10 @ Y9) = (Y10 @ Y2)))) & ((Y10 @ Y8) = (Y10 @ Y5))) => ((Y10 @ Y4) = (Y10 @ Y3)))) & ((((((Y10 @ Y7) = (Y10 @ Y2)) & ((Y10 @ Y7) = (Y10 @ Y0))) & (~ ((Y10 @ Y4) = (Y10 @ Y3)))) & ((Y10 @ Y9) = (Y10 @ Y0))) => ((Y10 @ Y6) = (Y10 @ Y1)))) & (((((Y10 @ X1) = (Y10 @ Y4)) & ((Y10 @ Y8) = (Y10 @ Y5))) & ((Y10 @ Y9) = (Y10 @ Y2))) => (~ ((Y10 @ Y6) = (Y10 @ Y1))))) => ((((((~ ((Y10 @ Y7) = (Y10 @ Y2))) | (~ ((Y10 @ Y8) = (Y10 @ Y5)))) | (~ ((Y10 @ Y9) = (Y10 @ Y0)))) | (~ ((Y10 @ Y6) = (Y10 @ Y3)))) | (~ ((Y10 @ X1) = (Y10 @ Y4)))) | (~ ((Y10 @ Y1) = (Y10 @ X2))))))))))))))))))))))))))))) )),
% 1.62/1.48 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.62/1.48 thf(f10,plain,(
% 1.62/1.48 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (!! @ ($i > $i) @ (^[Y11 : $i > $i]: ((((((((((((Y11 @ Y10) = (Y11 @ Y2)) & ((Y11 @ Y10) = (Y11 @ Y1))) & ((Y11 @ Y2) = (Y11 @ Y0))) & (~ ((Y11 @ Y9) = (Y11 @ Y8)))) => (~ ((Y11 @ Y5) = (Y11 @ Y4)))) & (((((Y11 @ Y0) = (Y11 @ Y1)) & ((Y11 @ X1) = (Y11 @ Y5))) & ((Y11 @ Y7) = (Y11 @ Y4))) => (~ ((Y11 @ Y9) = (Y11 @ Y8))))) & (((((Y11 @ Y5) = (Y11 @ Y4)) & ((Y11 @ Y9) = (Y11 @ Y6))) & ((Y11 @ Y8) = (Y11 @ Y3))) => ((Y11 @ Y0) = (Y11 @ Y1)))) & (((((Y11 @ Y2) = (Y11 @ Y0)) & (~ ((Y11 @ Y10) = (Y11 @ Y3)))) & ((Y11 @ Y9) = (Y11 @ Y6))) => ((Y11 @ Y5) = (Y11 @ Y4)))) & ((((((Y11 @ Y8) = (Y11 @ Y3)) & ((Y11 @ Y8) = (Y11 @ Y1))) & (~ ((Y11 @ Y5) = (Y11 @ Y4)))) & ((Y11 @ Y10) = (Y11 @ Y1))) => ((Y11 @ Y7) = (Y11 @ Y2)))) & (((((Y11 @ X1) = (Y11 @ Y5)) & ((Y11 @ Y9) = (Y11 @ Y6))) & ((Y11 @ Y10) = (Y11 @ Y3))) => (~ ((Y11 @ Y7) = (Y11 @ Y2))))) => ((((((~ ((Y11 @ Y8) = (Y11 @ Y3))) | (~ ((Y11 @ Y9) = (Y11 @ Y6)))) | (~ ((Y11 @ Y10) = (Y11 @ Y1)))) | (~ ((Y11 @ Y7) = (Y11 @ Y4)))) | (~ ((Y11 @ X1) = (Y11 @ Y5)))) | (~ ((Y11 @ Y2) = (Y11 @ Y0)))))))))))))))))))))))))))) @ X2) = $false)) )),
% 1.62/1.48 inference(pi_clausification,[status(thm)],[f9])).
% 1.62/1.48 thf(f9,plain,(
% 1.62/1.48 ( ! [X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (!! @ ($i > $i) @ (^[Y11 : $i > $i]: ((((((((((((Y11 @ Y10) = (Y11 @ Y2)) & ((Y11 @ Y10) = (Y11 @ Y1))) & ((Y11 @ Y2) = (Y11 @ Y0))) & (~ ((Y11 @ Y9) = (Y11 @ Y8)))) => (~ ((Y11 @ Y5) = (Y11 @ Y4)))) & (((((Y11 @ Y0) = (Y11 @ Y1)) & ((Y11 @ X1) = (Y11 @ Y5))) & ((Y11 @ Y7) = (Y11 @ Y4))) => (~ ((Y11 @ Y9) = (Y11 @ Y8))))) & (((((Y11 @ Y5) = (Y11 @ Y4)) & ((Y11 @ Y9) = (Y11 @ Y6))) & ((Y11 @ Y8) = (Y11 @ Y3))) => ((Y11 @ Y0) = (Y11 @ Y1)))) & (((((Y11 @ Y2) = (Y11 @ Y0)) & (~ ((Y11 @ Y10) = (Y11 @ Y3)))) & ((Y11 @ Y9) = (Y11 @ Y6))) => ((Y11 @ Y5) = (Y11 @ Y4)))) & ((((((Y11 @ Y8) = (Y11 @ Y3)) & ((Y11 @ Y8) = (Y11 @ Y1))) & (~ ((Y11 @ Y5) = (Y11 @ Y4)))) & ((Y11 @ Y10) = (Y11 @ Y1))) => ((Y11 @ Y7) = (Y11 @ Y2)))) & (((((Y11 @ X1) = (Y11 @ Y5)) & ((Y11 @ Y9) = (Y11 @ Y6))) & ((Y11 @ Y10) = (Y11 @ Y3))) => (~ ((Y11 @ Y7) = (Y11 @ Y2))))) => ((((((~ ((Y11 @ Y8) = (Y11 @ Y3))) | (~ ((Y11 @ Y9) = (Y11 @ Y6)))) | (~ ((Y11 @ Y10) = (Y11 @ Y1)))) | (~ ((Y11 @ Y7) = (Y11 @ Y4)))) | (~ ((Y11 @ X1) = (Y11 @ Y5)))) | (~ ((Y11 @ Y2) = (Y11 @ Y0))))))))))))))))))))))))))))))) )),
% 1.62/1.48 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.62/1.48 thf(f8,plain,(
% 1.62/1.48 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (?? @ $i @ (^[Y11 : $i]: (!! @ ($i > $i) @ (^[Y12 : $i > $i]: ((((((((((((Y12 @ Y11) = (Y12 @ Y3)) & ((Y12 @ Y11) = (Y12 @ Y2))) & ((Y12 @ Y3) = (Y12 @ Y1))) & (~ ((Y12 @ Y10) = (Y12 @ Y9)))) => (~ ((Y12 @ Y6) = (Y12 @ Y5)))) & (((((Y12 @ Y1) = (Y12 @ Y2)) & ((Y12 @ Y0) = (Y12 @ Y6))) & ((Y12 @ Y8) = (Y12 @ Y5))) => (~ ((Y12 @ Y10) = (Y12 @ Y9))))) & (((((Y12 @ Y6) = (Y12 @ Y5)) & ((Y12 @ Y10) = (Y12 @ Y7))) & ((Y12 @ Y9) = (Y12 @ Y4))) => ((Y12 @ Y1) = (Y12 @ Y2)))) & (((((Y12 @ Y3) = (Y12 @ Y1)) & (~ ((Y12 @ Y11) = (Y12 @ Y4)))) & ((Y12 @ Y10) = (Y12 @ Y7))) => ((Y12 @ Y6) = (Y12 @ Y5)))) & ((((((Y12 @ Y9) = (Y12 @ Y4)) & ((Y12 @ Y9) = (Y12 @ Y2))) & (~ ((Y12 @ Y6) = (Y12 @ Y5)))) & ((Y12 @ Y11) = (Y12 @ Y2))) => ((Y12 @ Y8) = (Y12 @ Y3)))) & (((((Y12 @ Y0) = (Y12 @ Y6)) & ((Y12 @ Y10) = (Y12 @ Y7))) & ((Y12 @ Y11) = (Y12 @ Y4))) => (~ ((Y12 @ Y8) = (Y12 @ Y3))))) => ((((((~ ((Y12 @ Y9) = (Y12 @ Y4))) | (~ ((Y12 @ Y10) = (Y12 @ Y7)))) | (~ ((Y12 @ Y11) = (Y12 @ Y2)))) | (~ ((Y12 @ Y8) = (Y12 @ Y5)))) | (~ ((Y12 @ Y0) = (Y12 @ Y6)))) | (~ ((Y12 @ Y3) = (Y12 @ Y1)))))))))))))))))))))))))))))) @ X1))) )),
% 1.62/1.48 inference(pi_clausification,[status(thm)],[f7])).
% 1.62/1.48 thf(f7,plain,(
% 1.62/1.48 ($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (?? @ $i @ (^[Y11 : $i]: (!! @ ($i > $i) @ (^[Y12 : $i > $i]: ((((((((((((Y12 @ Y11) = (Y12 @ Y3)) & ((Y12 @ Y11) = (Y12 @ Y2))) & ((Y12 @ Y3) = (Y12 @ Y1))) & (~ ((Y12 @ Y10) = (Y12 @ Y9)))) => (~ ((Y12 @ Y6) = (Y12 @ Y5)))) & (((((Y12 @ Y1) = (Y12 @ Y2)) & ((Y12 @ Y0) = (Y12 @ Y6))) & ((Y12 @ Y8) = (Y12 @ Y5))) => (~ ((Y12 @ Y10) = (Y12 @ Y9))))) & (((((Y12 @ Y6) = (Y12 @ Y5)) & ((Y12 @ Y10) = (Y12 @ Y7))) & ((Y12 @ Y9) = (Y12 @ Y4))) => ((Y12 @ Y1) = (Y12 @ Y2)))) & (((((Y12 @ Y3) = (Y12 @ Y1)) & (~ ((Y12 @ Y11) = (Y12 @ Y4)))) & ((Y12 @ Y10) = (Y12 @ Y7))) => ((Y12 @ Y6) = (Y12 @ Y5)))) & ((((((Y12 @ Y9) = (Y12 @ Y4)) & ((Y12 @ Y9) = (Y12 @ Y2))) & (~ ((Y12 @ Y6) = (Y12 @ Y5)))) & ((Y12 @ Y11) = (Y12 @ Y2))) => ((Y12 @ Y8) = (Y12 @ Y3)))) & (((((Y12 @ Y0) = (Y12 @ Y6)) & ((Y12 @ Y10) = (Y12 @ Y7))) & ((Y12 @ Y11) = (Y12 @ Y4))) => (~ ((Y12 @ Y8) = (Y12 @ Y3))))) => ((((((~ ((Y12 @ Y9) = (Y12 @ Y4))) | (~ ((Y12 @ Y10) = (Y12 @ Y7)))) | (~ ((Y12 @ Y11) = (Y12 @ Y2)))) | (~ ((Y12 @ Y8) = (Y12 @ Y5)))) | (~ ((Y12 @ Y0) = (Y12 @ Y6)))) | (~ ((Y12 @ Y3) = (Y12 @ Y1))))))))))))))))))))))))))))))))),
% 1.62/1.48 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.62/1.48 thf(f6,plain,(
% 1.62/1.48 ((~ (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (?? @ $i @ (^[Y11 : $i]: (!! @ ($i > $i) @ (^[Y12 : $i > $i]: ((((((((((((Y12 @ Y11) = (Y12 @ Y3)) & ((Y12 @ Y11) = (Y12 @ Y2))) & ((Y12 @ Y3) = (Y12 @ Y1))) & (~ ((Y12 @ Y10) = (Y12 @ Y9)))) => (~ ((Y12 @ Y6) = (Y12 @ Y5)))) & (((((Y12 @ Y1) = (Y12 @ Y2)) & ((Y12 @ Y0) = (Y12 @ Y6))) & ((Y12 @ Y8) = (Y12 @ Y5))) => (~ ((Y12 @ Y10) = (Y12 @ Y9))))) & (((((Y12 @ Y6) = (Y12 @ Y5)) & ((Y12 @ Y10) = (Y12 @ Y7))) & ((Y12 @ Y9) = (Y12 @ Y4))) => ((Y12 @ Y1) = (Y12 @ Y2)))) & (((((Y12 @ Y3) = (Y12 @ Y1)) & (~ ((Y12 @ Y11) = (Y12 @ Y4)))) & ((Y12 @ Y10) = (Y12 @ Y7))) => ((Y12 @ Y6) = (Y12 @ Y5)))) & ((((((Y12 @ Y9) = (Y12 @ Y4)) & ((Y12 @ Y9) = (Y12 @ Y2))) & (~ ((Y12 @ Y6) = (Y12 @ Y5)))) & ((Y12 @ Y11) = (Y12 @ Y2))) => ((Y12 @ Y8) = (Y12 @ Y3)))) & (((((Y12 @ Y0) = (Y12 @ Y6)) & ((Y12 @ Y10) = (Y12 @ Y7))) & ((Y12 @ Y11) = (Y12 @ Y4))) => (~ ((Y12 @ Y8) = (Y12 @ Y3))))) => ((((((~ ((Y12 @ Y9) = (Y12 @ Y4))) | (~ ((Y12 @ Y10) = (Y12 @ Y7)))) | (~ ((Y12 @ Y11) = (Y12 @ Y2)))) | (~ ((Y12 @ Y8) = (Y12 @ Y5)))) | (~ ((Y12 @ Y0) = (Y12 @ Y6)))) | (~ ((Y12 @ Y3) = (Y12 @ Y1)))))))))))))))))))))))))))))))) = $true)),
% 1.62/1.48 inference(cnf_transformation,[status(thm)],[f5])).
% 1.62/1.48 thf(f5,plain,(
% 1.62/1.48 ((~ (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (?? @ $i @ (^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (?? @ $i @ (^[Y11 : $i]: (!! @ ($i > $i) @ (^[Y12 : $i > $i]: ((((((((((((Y12 @ Y11) = (Y12 @ Y3)) & ((Y12 @ Y11) = (Y12 @ Y2))) & ((Y12 @ Y3) = (Y12 @ Y1))) & (~ ((Y12 @ Y10) = (Y12 @ Y9)))) => (~ ((Y12 @ Y6) = (Y12 @ Y5)))) & (((((Y12 @ Y1) = (Y12 @ Y2)) & ((Y12 @ Y0) = (Y12 @ Y6))) & ((Y12 @ Y8) = (Y12 @ Y5))) => (~ ((Y12 @ Y10) = (Y12 @ Y9))))) & (((((Y12 @ Y6) = (Y12 @ Y5)) & ((Y12 @ Y10) = (Y12 @ Y7))) & ((Y12 @ Y9) = (Y12 @ Y4))) => ((Y12 @ Y1) = (Y12 @ Y2)))) & (((((Y12 @ Y3) = (Y12 @ Y1)) & (~ ((Y12 @ Y11) = (Y12 @ Y4)))) & ((Y12 @ Y10) = (Y12 @ Y7))) => ((Y12 @ Y6) = (Y12 @ Y5)))) & ((((((Y12 @ Y9) = (Y12 @ Y4)) & ((Y12 @ Y9) = (Y12 @ Y2))) & (~ ((Y12 @ Y6) = (Y12 @ Y5)))) & ((Y12 @ Y11) = (Y12 @ Y2))) => ((Y12 @ Y8) = (Y12 @ Y3)))) & (((((Y12 @ Y0) = (Y12 @ Y6)) & ((Y12 @ Y10) = (Y12 @ Y7))) & ((Y12 @ Y11) = (Y12 @ Y4))) => (~ ((Y12 @ Y8) = (Y12 @ Y3))))) => ((((((~ ((Y12 @ Y9) = (Y12 @ Y4))) | (~ ((Y12 @ Y10) = (Y12 @ Y7)))) | (~ ((Y12 @ Y11) = (Y12 @ Y2)))) | (~ ((Y12 @ Y8) = (Y12 @ Y5)))) | (~ ((Y12 @ Y0) = (Y12 @ Y6)))) | (~ ((Y12 @ Y3) = (Y12 @ Y1)))))))))))))))))))))))))))))))) = $true)),
% 1.62/1.48 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.48 thf(f4,plain,(
% 1.62/1.48 ~? [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i,X9 : $i,X10 : $i,X11 : $i] : ! [X12 : $i > $i] : ((((((X12 @ X0) = (X12 @ X7)) & ((X12 @ X1) = (X12 @ X4)) & ((X12 @ X11) = (X12 @ X5))) => ((X12 @ X3) != (X12 @ X8))) & ((((X12 @ X0) = (X12 @ X9)) & ((X12 @ X5) != (X12 @ X6)) & ((X12 @ X2) = (X12 @ X9)) & ((X12 @ X2) = (X12 @ X7))) => ((X12 @ X3) = (X12 @ X8))) & ((((X12 @ X1) = (X12 @ X4)) & ((X12 @ X0) != (X12 @ X7)) & ((X12 @ X8) = (X12 @ X10))) => ((X12 @ X5) = (X12 @ X6))) & ((((X12 @ X2) = (X12 @ X7)) & ((X12 @ X1) = (X12 @ X4)) & ((X12 @ X5) = (X12 @ X6))) => ((X12 @ X10) = (X12 @ X9))) & ((((X12 @ X3) = (X12 @ X6)) & ((X12 @ X11) = (X12 @ X5)) & ((X12 @ X10) = (X12 @ X9))) => ((X12 @ X1) != (X12 @ X2))) & ((((X12 @ X1) != (X12 @ X2)) & ((X12 @ X8) = (X12 @ X10)) & ((X12 @ X0) = (X12 @ X9)) & ((X12 @ X0) = (X12 @ X8))) => ((X12 @ X5) != (X12 @ X6)))) => (((X12 @ X8) != (X12 @ X10)) | ((X12 @ X11) != (X12 @ X5)) | ((X12 @ X3) != (X12 @ X6)) | ((X12 @ X0) != (X12 @ X9)) | ((X12 @ X1) != (X12 @ X4)) | ((X12 @ X2) != (X12 @ X7))))),
% 1.62/1.48 inference(rectify,[status(thm)],[f2])).
% 1.62/1.48 thf(f2,negated_conjecture,(
% 1.62/1.48 ~? [X5 : $i,X0 : $i,X3 : $i,X9 : $i,X1 : $i,X11 : $i,X8 : $i,X2 : $i,X6 : $i,X4 : $i,X7 : $i,X10 : $i] : ! [X12 : $i > $i] : ((((((X12 @ X2) = (X12 @ X5)) & ((X12 @ X0) = (X12 @ X1)) & ((X12 @ X11) = (X12 @ X10))) => ((X12 @ X6) != (X12 @ X9))) & ((((X12 @ X4) = (X12 @ X5)) & ((X12 @ X8) != (X12 @ X11)) & ((X12 @ X3) = (X12 @ X4)) & ((X12 @ X2) = (X12 @ X3))) => ((X12 @ X6) = (X12 @ X9))) & ((((X12 @ X0) = (X12 @ X1)) & ((X12 @ X2) != (X12 @ X5)) & ((X12 @ X7) = (X12 @ X6))) => ((X12 @ X8) = (X12 @ X11))) & ((((X12 @ X2) = (X12 @ X3)) & ((X12 @ X0) = (X12 @ X1)) & ((X12 @ X8) = (X12 @ X11))) => ((X12 @ X4) = (X12 @ X7))) & ((((X12 @ X8) = (X12 @ X9)) & ((X12 @ X11) = (X12 @ X10)) & ((X12 @ X4) = (X12 @ X7))) => ((X12 @ X0) != (X12 @ X3))) & ((((X12 @ X0) != (X12 @ X3)) & ((X12 @ X7) = (X12 @ X6)) & ((X12 @ X4) = (X12 @ X5)) & ((X12 @ X5) = (X12 @ X6))) => ((X12 @ X8) != (X12 @ X11)))) => (((X12 @ X7) != (X12 @ X6)) | ((X12 @ X11) != (X12 @ X10)) | ((X12 @ X8) != (X12 @ X9)) | ((X12 @ X4) != (X12 @ X5)) | ((X12 @ X0) != (X12 @ X1)) | ((X12 @ X2) != (X12 @ X3))))),
% 1.62/1.48 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.48 thf(f1,conjecture,(
% 1.62/1.48 ? [X5 : $i,X0 : $i,X3 : $i,X9 : $i,X1 : $i,X11 : $i,X8 : $i,X2 : $i,X6 : $i,X4 : $i,X7 : $i,X10 : $i] : ! [X12 : $i > $i] : ((((((X12 @ X2) = (X12 @ X5)) & ((X12 @ X0) = (X12 @ X1)) & ((X12 @ X11) = (X12 @ X10))) => ((X12 @ X6) != (X12 @ X9))) & ((((X12 @ X4) = (X12 @ X5)) & ((X12 @ X8) != (X12 @ X11)) & ((X12 @ X3) = (X12 @ X4)) & ((X12 @ X2) = (X12 @ X3))) => ((X12 @ X6) = (X12 @ X9))) & ((((X12 @ X0) = (X12 @ X1)) & ((X12 @ X2) != (X12 @ X5)) & ((X12 @ X7) = (X12 @ X6))) => ((X12 @ X8) = (X12 @ X11))) & ((((X12 @ X2) = (X12 @ X3)) & ((X12 @ X0) = (X12 @ X1)) & ((X12 @ X8) = (X12 @ X11))) => ((X12 @ X4) = (X12 @ X7))) & ((((X12 @ X8) = (X12 @ X9)) & ((X12 @ X11) = (X12 @ X10)) & ((X12 @ X4) = (X12 @ X7))) => ((X12 @ X0) != (X12 @ X3))) & ((((X12 @ X0) != (X12 @ X3)) & ((X12 @ X7) = (X12 @ X6)) & ((X12 @ X4) = (X12 @ X5)) & ((X12 @ X5) = (X12 @ X6))) => ((X12 @ X8) != (X12 @ X11)))) => (((X12 @ X7) != (X12 @ X6)) | ((X12 @ X11) != (X12 @ X10)) | ((X12 @ X8) != (X12 @ X9)) | ((X12 @ X4) != (X12 @ X5)) | ((X12 @ X0) != (X12 @ X1)) | ((X12 @ X2) != (X12 @ X3))))),
% 1.62/1.48 file('/export/starexec/sandbox/tmp/tmp.aP8Kuc7Iur/DTF2THF_15784.p',cSIXFRIENDS_PTH)).
% 1.62/1.48 thf(f123,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X6) != (sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X3)) | ((sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X7) != (sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X5)) | ((sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X0) != (sK1 @ X0 @ X1 @ X2 @ X3 @ X2 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X1))) )),
% 1.62/1.48 inference(equality_resolution,[status(thm)],[f97])).
% 1.62/1.48 thf(f97,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) != (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4)) | ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5) != (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12)) | ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8) != (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11)) | ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) != (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7))) )),
% 1.62/1.48 inference(equality_proxy_clausification,[status(thm)],[f96])).
% 1.62/1.48 thf(f96,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5) != (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12)) | ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) != (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)) | ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8) != (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11)) | ($false = ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4)))) )),
% 1.62/1.48 inference(equality_proxy_clausification,[status(thm)],[f95])).
% 1.62/1.48 thf(f95,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) != (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)) | (((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5)) = $false) | ($false = ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4))) | ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8) != (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11))) )),
% 1.62/1.48 inference(equality_proxy_clausification,[status(thm)],[f94])).
% 1.62/1.48 thf(f94,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : ((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)) = $false) | ($false = ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4))) | (((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5)) = $false) | ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8) != (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11))) )),
% 1.62/1.48 inference(equality_proxy_clausification,[status(thm)],[f93])).
% 1.62/1.48 thf(f93,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (($false = ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8))) | ($false = ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4))) | (((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)) = $false) | (((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5)) = $false)) )),
% 1.62/1.48 inference(not_proxy_clausification,[status(thm)],[f92])).
% 1.62/1.48 thf(f92,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (((~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4))) = $true) | ($false = ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8))) | (((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5)) = $false) | (((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)) = $false)) )),
% 1.62/1.48 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 1.62/1.48 thf(f91,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8))) = $false) | ((~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4))) = $true) | (((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5)) = $false)) )),
% 1.62/1.48 inference(binary_proxy_clausification,[status(thm)],[f90])).
% 1.62/1.48 thf(f90,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (($false = ((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5)))) | ((~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4))) = $true)) )),
% 1.62/1.48 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.62/1.48 thf(f36,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (((((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5))) => (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4)))) = $true)) )),
% 1.62/1.48 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.62/1.48 thf(f35,plain,(
% 1.62/1.48 ( ! [X2 : $i,X3 : $i,X10 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i,X12 : $i] : (((((((((((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4)) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2))) & (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10)))) => (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6)))) & (((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3)) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6))) => (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10))))) & (((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6)) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5))) => ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3)))) & (((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X2)) & (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5)))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8))) => ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6)))) & ((((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5)) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X10) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3))) & (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X6)))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X3))) => ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4)))) & (((((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X1) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X7)) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X11) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X8))) & ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X12) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X5))) => (~ ((sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X9) = (sK1 @ X12 @ X5 @ X4 @ X7 @ X9 @ X6 @ X8 @ X1 @ X11 @ X10 @ X3 @ X2 @ X4))))) = $true)) )),
% 1.62/1.48 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.62/1.48 % SZS output end Proof for DTF2THF_15784
% 1.62/1.48 % (16091)------------------------------
% 1.62/1.48 % (16091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.48 % (16091)Termination reason: Refutation
% 1.62/1.48
% 1.62/1.48 % (16091)Memory used [KB]: 6524
% 1.62/1.48 % (16091)Time elapsed: 0.120 s
% 1.62/1.48 % (16091)Instructions burned: 379 (million)
% 1.62/1.48 % (16091)------------------------------
% 1.62/1.48 % (16091)------------------------------
% 1.62/1.48 % (16062)Success in time 0.212 s
%------------------------------------------------------------------------------