%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG294^5 : 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 : n014.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 08:37:51 AM UTC 2026
% Result : Theorem 22.87s 4.54s
% Output : Refutation 22.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 20
% Syntax : Number of formulae : 204 ( 7 unt; 0 typ; 16 def)
% Number of atoms : 3595 (1328 equ; 0 cnn)
% Maximal formula atoms : 27 ( 17 avg)
% Number of connectives : 10210 ( 255 ~; 650 |;1029 &;6252 @)
% ( 42 <=>; 746 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 734 ( 734 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 48 usr; 33 con; 0-4 aty)
% ( 664 !!; 572 ??; 0 @@+; 0 @@-)
% Number of variables : 1994 (1629 ^; 286 !; 79 ?;1994 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cR: a > a ).
thf(func_def_2,type,
cL: a > a ).
thf(func_def_3,type,
cPSI: ( a > $o ) > a > $o ).
thf(func_def_4,type,
cP: a > a > a ).
thf(func_def_5,type,
cZ: a ).
thf(func_def_6,type,
cPHI: ( a > $o ) > a > $o ).
thf(func_def_21,type,
sP0: a > ( a > $o ) > $o ).
thf(func_def_22,type,
sP1: a > ( a > $o ) > $o ).
thf(func_def_23,type,
sK2: a > ( a > $o ) > a ).
thf(func_def_24,type,
sK3: ( a > $o ) > a ).
thf(func_def_25,type,
sK4: ( a > $o ) > a > ( a > $o ) > a ).
thf(func_def_26,type,
sK5: a > ( a > $o ) > a ).
thf(func_def_27,type,
sK6: a > a > ( a > $o ) > a > $o ).
thf(func_def_28,type,
sK7: a > ( a > $o ) > a ).
thf(func_def_29,type,
sK8: ( a > $o ) > a ).
thf(func_def_30,type,
sK9: ( a > $o ) > a > ( a > $o ) > a ).
thf(func_def_31,type,
sK10: a > ( a > $o ) > a ).
thf(func_def_32,type,
sK11: a > a > ( a > $o ) > a > $o ).
thf(func_def_33,type,
sK12: ( a > $o ) > a ).
thf(func_def_36,type,
ph14:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
sK15: a ).
thf(func_def_38,type,
sK16: a ).
thf(func_def_39,type,
sK17: a ).
thf(func_def_40,type,
sK18: a ).
thf(func_def_41,type,
sK19: a ).
thf(func_def_42,type,
sK20: a ).
thf(func_def_43,type,
sK21: a ).
thf(func_def_44,type,
sK22: a ).
thf(func_def_45,type,
sK23: a ).
thf(func_def_46,type,
sK24: a ).
thf(func_def_47,type,
sK25: a ).
thf(func_def_48,type,
sK26: a ).
thf(f2900,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f290,f295,f304,f309,f318,f323,f328,f333,f343,f347,f349,f1375,f1469,f1893,f2272,f2439,f2823,f2895]) ).
thf(f2895,plain,
( ~ spl13_11
| ~ spl13_15
| ~ spl13_16
| ~ spl13_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f2894]) ).
thf(f2894,plain,
( $false
| ~ spl13_11
| ~ spl13_15
| ~ spl13_16
| ~ spl13_20 ),
inference(trivial_inequality_removal,[status(thm)],[f2879]) ).
thf(f2879,plain,
( ( $true = $false )
| ~ spl13_11
| ~ spl13_15
| ~ spl13_16
| ~ spl13_20 ),
inference(backward_demodulation,[status(thm)],[f2674,f2630]) ).
thf(f2630,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK22 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK18 )
= $false )
| ~ spl13_11
| ~ spl13_15
| ~ spl13_20 ),
inference(trivial_inequality_removal,[status(thm)],[f2624]) ).
thf(f2624,plain,
( ( sK15 != sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK22 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK18 )
= $false )
| ~ spl13_11
| ~ spl13_15
| ~ spl13_20 ),
inference(superposition,[status(thm)],[f341,f2616]) ).
thf(f2616,plain,
( ( sK15
= ( cP @ sK22 @ sK18 ) )
| ~ spl13_11
| ~ spl13_15 ),
inference(backward_demodulation,[status(thm)],[f317,f2614]) ).
thf(f2614,plain,
( ( sK23 = sK18 )
| ~ spl13_11
| ~ spl13_15 ),
inference(forward_demodulation,[status(thm)],[f2610,f2467]) ).
thf(f2467,plain,
( ( ( cR @ sK15 )
= sK18 )
| ~ spl13_11 ),
inference(superposition,[status(thm)],[f56,f299]) ).
thf(f299,plain,
( ( sK15
= ( cP @ sK19 @ sK18 ) )
| ~ spl13_11 ),
inference(avatar_component_clause,[status(thm)],[f297]) ).
thf(f297,definition,
( spl13_11
<=> ( sK15
= ( cP @ sK19 @ sK18 ) ) ),
introduced(definition,[new_symbols(naming,[spl13_11])],[avatar_definition]) ).
thf(f56,plain,
! [X6: a,X5: a] :
( ( cR @ ( cP @ X6 @ X5 ) )
= X5 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ! [X0: a > $o] :
( ( ( X0 @ cZ )
= $true )
| ! [X1: a] :
( ( ( X0 @ X1 )
!= $true )
| ( ( ( X0 @ ( cL @ ( sK12 @ X0 ) ) )
!= $true )
& ( $true
= ( X0 @ ( sK12 @ X0 ) ) ) ) ) )
& ! [X3: a,X4: a > $o] :
( ( ( ( sP1 @ X3 @ X4 )
= $true )
| ( $true
!= ( cPSI @ X4 @ X3 ) ) )
& ( ( $true
= ( cPSI @ X4 @ X3 ) )
| ( ( sP1 @ X3 @ X4 )
!= $true ) ) )
& ( ( ^ [Y0: a] :
( ( cZ = Y0 )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 )
& ( ( cP @ Y1 @ Y2 )
= Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y2 @ Y1 )
= Y0 )
& ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y2 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y1 ) ) ) )
| ( cZ = Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y1 @ Y2 )
= Y0 )
& ( ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y2 )
| ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 ) ) ) ) )
| ( cZ = Y0 ) ) ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X5: a,X6: a] :
( ( cR @ ( cP @ X6 @ X5 ) )
= X5 )
& ! [X7: a] :
( ( ( ( cP @ ( cL @ X7 ) @ ( cR @ X7 ) )
= X7 )
| ( cZ = X7 ) )
& ( ( cZ != X7 )
| ( ( cP @ ( cL @ X7 ) @ ( cR @ X7 ) )
!= X7 ) ) )
& ! [X8: a,X9: a] :
( ( cL @ ( cP @ X9 @ X8 ) )
= X9 )
& ! [X10: a,X11: a > $o] :
( ( ( $true
= ( cPHI @ X11 @ X10 ) )
| ( $true
!= ( sP0 @ X10 @ X11 ) ) )
& ( ( $true
= ( sP0 @ X10 @ X11 ) )
| ( $true
!= ( cPHI @ X11 @ X10 ) ) ) )
& ( cZ
= ( cL @ cZ ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f29,f30]) ).
thf(f30,plain,
! [X0: a > $o] :
( ? [X2: a] :
( ( $true
!= ( X0 @ ( cL @ X2 ) ) )
& ( ( X0 @ X2 )
= $true ) )
=> ( ( ( X0 @ ( cL @ ( sK12 @ X0 ) ) )
!= $true )
& ( $true
= ( X0 @ ( sK12 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ! [X0: a > $o] :
( ( ( X0 @ cZ )
= $true )
| ! [X1: a] :
( ( ( X0 @ X1 )
!= $true )
| ? [X2: a] :
( ( $true
!= ( X0 @ ( cL @ X2 ) ) )
& ( ( X0 @ X2 )
= $true ) ) ) )
& ! [X3: a,X4: a > $o] :
( ( ( ( sP1 @ X3 @ X4 )
= $true )
| ( $true
!= ( cPSI @ X4 @ X3 ) ) )
& ( ( $true
= ( cPSI @ X4 @ X3 ) )
| ( ( sP1 @ X3 @ X4 )
!= $true ) ) )
& ( ( ^ [Y0: a] :
( ( cZ = Y0 )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 )
& ( ( cP @ Y1 @ Y2 )
= Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y2 @ Y1 )
= Y0 )
& ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y2 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y1 ) ) ) )
| ( cZ = Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y1 @ Y2 )
= Y0 )
& ( ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y2 )
| ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 ) ) ) ) )
| ( cZ = Y0 ) ) ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X5: a,X6: a] :
( ( cR @ ( cP @ X6 @ X5 ) )
= X5 )
& ! [X7: a] :
( ( ( ( cP @ ( cL @ X7 ) @ ( cR @ X7 ) )
= X7 )
| ( cZ = X7 ) )
& ( ( cZ != X7 )
| ( ( cP @ ( cL @ X7 ) @ ( cR @ X7 ) )
!= X7 ) ) )
& ! [X8: a,X9: a] :
( ( cL @ ( cP @ X9 @ X8 ) )
= X9 )
& ! [X10: a,X11: a > $o] :
( ( ( $true
= ( cPHI @ X11 @ X10 ) )
| ( $true
!= ( sP0 @ X10 @ X11 ) ) )
& ( ( $true
= ( sP0 @ X10 @ X11 ) )
| ( $true
!= ( cPHI @ X11 @ X10 ) ) ) )
& ( cZ
= ( cL @ cZ ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,plain,
( ! [X19: a > $o] :
( ( $true
= ( X19 @ cZ ) )
| ! [X20: a] :
( ( $true
!= ( X19 @ X20 ) )
| ? [X21: a] :
( ( ( X19 @ ( cL @ X21 ) )
!= $true )
& ( $true
= ( X19 @ X21 ) ) ) ) )
& ! [X2: a,X3: a > $o] :
( ( ( ( sP1 @ X2 @ X3 )
= $true )
| ( $true
!= ( cPSI @ X3 @ X2 ) ) )
& ( ( $true
= ( cPSI @ X3 @ X2 ) )
| ( ( sP1 @ X2 @ X3 )
!= $true ) ) )
& ( ( ^ [Y0: a] :
( ( cZ = Y0 )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 )
& ( ( cP @ Y1 @ Y2 )
= Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y2 @ Y1 )
= Y0 )
& ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y2 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y1 ) ) ) )
| ( cZ = Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y1 @ Y2 )
= Y0 )
& ( ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y2 )
| ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 ) ) ) ) )
| ( cZ = Y0 ) ) ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X16: a,X17: a] :
( ( cR @ ( cP @ X17 @ X16 ) )
= X16 )
& ! [X18: a] :
( ( ( ( cP @ ( cL @ X18 ) @ ( cR @ X18 ) )
= X18 )
| ( cZ = X18 ) )
& ( ( cZ != X18 )
| ( ( cP @ ( cL @ X18 ) @ ( cR @ X18 ) )
!= X18 ) ) )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X1 @ X0 ) )
= X1 )
& ! [X9: a,X10: a > $o] :
( ( ( $true
= ( cPHI @ X10 @ X9 ) )
| ( ( sP0 @ X9 @ X10 )
!= $true ) )
& ( ( ( sP0 @ X9 @ X10 )
= $true )
| ( $true
!= ( cPHI @ X10 @ X9 ) ) ) )
& ( cZ
= ( cL @ cZ ) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X19: a > $o] :
( ( $true
= ( X19 @ cZ ) )
| ! [X20: a] :
( ( $true
!= ( X19 @ X20 ) )
| ? [X21: a] :
( ( ( X19 @ ( cL @ X21 ) )
!= $true )
& ( $true
= ( X19 @ X21 ) ) ) ) )
& ! [X2: a,X3: a > $o] :
( ( ( sP1 @ X2 @ X3 )
= $true )
<=> ( $true
= ( cPSI @ X3 @ X2 ) ) )
& ( ( ^ [Y0: a] :
( ( cZ = Y0 )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 )
& ( ( cP @ Y1 @ Y2 )
= Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y2 @ Y1 )
= Y0 )
& ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y2 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y1 ) ) ) )
| ( cZ = Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y1 @ Y2 )
= Y0 )
& ( ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y2 )
| ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 ) ) ) ) )
| ( cZ = Y0 ) ) ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X16: a,X17: a] :
( ( cR @ ( cP @ X17 @ X16 ) )
= X16 )
& ! [X18: a] :
( ( ( cP @ ( cL @ X18 ) @ ( cR @ X18 ) )
= X18 )
<=> ( cZ != X18 ) )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X1 @ X0 ) )
= X1 )
& ! [X9: a,X10: a > $o] :
( ( $true
= ( cPHI @ X10 @ X9 ) )
<=> ( ( sP0 @ X9 @ X10 )
= $true ) )
& ( cZ
= ( cL @ cZ ) ) ),
inference(definition_folding,[status(thm)],[f8,f10,f9]) ).
thf(f9,plain,
! [X10: a > $o,X9: a] :
( ( ( sP0 @ X9 @ X10 )
= $true )
<=> ? [X11: a] :
( ! [X12: a] :
( ( $true
= ( X10 @ X12 ) )
| ? [X13: a > $o] :
( ! [X14: a] :
( ( ( X13 @ ( cL @ X14 ) )
= $true )
| ( ( X13 @ X14 )
!= $true ) )
& ( ( X13 @ X11 )
= $true )
& ! [X15: a] :
( ( ( cR @ X15 )
!= X12 )
| ( ( X13 @ X15 )
!= $true ) ) ) )
& ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X11 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X9 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f10,plain,
! [X3: a > $o,X2: a] :
( ( ( sP1 @ X2 @ X3 )
= $true )
<=> ? [X4: a] :
( ! [X5: a] :
( ( ( X3 @ X5 )
= $true )
| ? [X6: a > $o] :
( ! [X7: a] :
( ( $true
!= ( X6 @ X7 ) )
| ( ( X6 @ ( cL @ X7 ) )
= $true ) )
& ( $true
= ( X6 @ X4 ) )
& ! [X8: a] :
( ( ( cR @ X8 )
!= X5 )
| ( ( X6 @ X8 )
!= $true ) ) ) )
& ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X4 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f8,plain,
( ! [X19: a > $o] :
( ( $true
= ( X19 @ cZ ) )
| ! [X20: a] :
( ( $true
!= ( X19 @ X20 ) )
| ? [X21: a] :
( ( ( X19 @ ( cL @ X21 ) )
!= $true )
& ( $true
= ( X19 @ X21 ) ) ) ) )
& ! [X2: a,X3: a > $o] :
( ? [X4: a] :
( ! [X5: a] :
( ( ( X3 @ X5 )
= $true )
| ? [X6: a > $o] :
( ! [X7: a] :
( ( $true
!= ( X6 @ X7 ) )
| ( ( X6 @ ( cL @ X7 ) )
= $true ) )
& ( $true
= ( X6 @ X4 ) )
& ! [X8: a] :
( ( ( cR @ X8 )
!= X5 )
| ( ( X6 @ X8 )
!= $true ) ) ) )
& ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X4 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 ) ) )
<=> ( $true
= ( cPSI @ X3 @ X2 ) ) )
& ( ( ^ [Y0: a] :
( ( cZ = Y0 )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 )
& ( ( cP @ Y1 @ Y2 )
= Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y2 @ Y1 )
= Y0 )
& ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y2 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y1 ) ) ) )
| ( cZ = Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y1 @ Y2 )
= Y0 )
& ( ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y2 )
| ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 ) ) ) ) )
| ( cZ = Y0 ) ) ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X16: a,X17: a] :
( ( cR @ ( cP @ X17 @ X16 ) )
= X16 )
& ! [X18: a] :
( ( ( cP @ ( cL @ X18 ) @ ( cR @ X18 ) )
= X18 )
<=> ( cZ != X18 ) )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X1 @ X0 ) )
= X1 )
& ! [X9: a,X10: a > $o] :
( ( $true
= ( cPHI @ X10 @ X9 ) )
<=> ? [X11: a] :
( ! [X12: a] :
( ( $true
= ( X10 @ X12 ) )
| ? [X13: a > $o] :
( ! [X14: a] :
( ( ( X13 @ ( cL @ X14 ) )
= $true )
| ( ( X13 @ X14 )
!= $true ) )
& ( ( X13 @ X11 )
= $true )
& ! [X15: a] :
( ( ( cR @ X15 )
!= X12 )
| ( ( X13 @ X15 )
!= $true ) ) ) )
& ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X11 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X9 )
= $true ) ) )
& ( cZ
= ( cL @ cZ ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ^ [Y0: a] :
( ( cZ = Y0 )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 )
& ( ( cP @ Y1 @ Y2 )
= Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y2 @ Y1 )
= Y0 )
& ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y2 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y1 ) ) ) )
| ( cZ = Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y1 @ Y2 )
= Y0 )
& ( ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y2 )
| ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 ) ) ) ) )
| ( cZ = Y0 ) ) ) )
& ! [X2: a,X3: a > $o] :
( ? [X4: a] :
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X4 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 ) )
& ! [X5: a] :
( ( ( X3 @ X5 )
= $true )
| ? [X6: a > $o] :
( ! [X8: a] :
( ( ( cR @ X8 )
!= X5 )
| ( ( X6 @ X8 )
!= $true ) )
& ! [X7: a] :
( ( $true
!= ( X6 @ X7 ) )
| ( ( X6 @ ( cL @ X7 ) )
= $true ) )
& ( $true
= ( X6 @ X4 ) ) ) ) )
<=> ( $true
= ( cPSI @ X3 @ X2 ) ) )
& ! [X18: a] :
( ( ( cP @ ( cL @ X18 ) @ ( cR @ X18 ) )
= X18 )
<=> ( cZ != X18 ) )
& ! [X9: a,X10: a > $o] :
( ? [X11: a] :
( ! [X12: a] :
( ( $true
= ( X10 @ X12 ) )
| ? [X13: a > $o] :
( ! [X15: a] :
( ( ( cR @ X15 )
!= X12 )
| ( ( X13 @ X15 )
!= $true ) )
& ! [X14: a] :
( ( ( X13 @ ( cL @ X14 ) )
= $true )
| ( ( X13 @ X14 )
!= $true ) )
& ( ( X13 @ X11 )
= $true ) ) )
& ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X11 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X9 )
= $true ) )
<=> ( $true
= ( cPHI @ X10 @ X9 ) ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X16: a,X17: a] :
( ( cR @ ( cP @ X17 @ X16 ) )
= X16 )
& ! [X19: a > $o] :
( ( $true
= ( X19 @ cZ ) )
| ! [X20: a] :
( ( $true
!= ( X19 @ X20 ) )
| ? [X21: a] :
( ( ( X19 @ ( cL @ X21 ) )
!= $true )
& ( $true
= ( X19 @ X21 ) ) ) ) )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X1 @ X0 ) )
= X1 )
& ( cZ
= ( cR @ cZ ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X2: a,X3: a > $o] :
( ? [X4: a] :
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X4 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 ) )
& ! [X5: a] :
( ! [X6: a > $o] :
( ( ! [X7: a] :
( ( $true
= ( X6 @ X7 ) )
=> ( ( X6 @ ( cL @ X7 ) )
= $true ) )
& ( $true
= ( X6 @ X4 ) ) )
=> ? [X8: a] :
( ( ( X6 @ X8 )
= $true )
& ( ( cR @ X8 )
= X5 ) ) )
=> ( ( X3 @ X5 )
= $true ) ) )
<=> ( $true
= ( cPSI @ X3 @ X2 ) ) )
& ! [X18: a] :
( ( ( cP @ ( cL @ X18 ) @ ( cR @ X18 ) )
= X18 )
<=> ( cZ != X18 ) )
& ! [X9: a,X10: a > $o] :
( ? [X11: a] :
( ! [X12: a] :
( ! [X13: a > $o] :
( ( ! [X14: a] :
( ( ( X13 @ X14 )
= $true )
=> ( ( X13 @ ( cL @ X14 ) )
= $true ) )
& ( ( X13 @ X11 )
= $true ) )
=> ? [X15: a] :
( ( ( X13 @ X15 )
= $true )
& ( ( cR @ X15 )
= X12 ) ) )
=> ( $true
= ( X10 @ X12 ) ) )
& ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X11 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X9 )
= $true ) )
<=> ( $true
= ( cPHI @ X10 @ X9 ) ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X16: a,X17: a] :
( ( cR @ ( cP @ X17 @ X16 ) )
= X16 )
& ! [X19: a > $o] :
( ? [X20: a] :
( ! [X21: a] :
( ( $true
= ( X19 @ X21 ) )
=> ( ( X19 @ ( cL @ X21 ) )
= $true ) )
& ( $true
= ( X19 @ X20 ) ) )
=> ( $true
= ( X19 @ cZ ) ) )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X1 @ X0 ) )
= X1 )
& ( cZ
= ( cR @ cZ ) ) )
=> ( ( ^ [Y0: a] :
( ( cZ = Y0 )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 )
& ( ( cP @ Y1 @ Y2 )
= Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y2 @ Y1 )
= Y0 )
& ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y2 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y1 ) ) ) )
| ( cZ = Y0 ) ) )
= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y1 @ Y2 )
= Y0 )
& ( ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y2 )
| ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 ) ) ) ) )
| ( cZ = Y0 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: a,X1: a] :
( ( cL @ ( cP @ X1 @ X0 ) )
= X1 )
& ! [X2: a,X3: a > $o] :
( ? [X4: a] :
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X4 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 ) )
& ! [X9: a] :
( ! [X10: a > $o] :
( ( ! [X11: a] :
( ( ( X10 @ X11 )
= $true )
=> ( ( X10 @ ( cL @ X11 ) )
= $true ) )
& ( $true
= ( X10 @ X4 ) ) )
=> ? [X12: a] :
( ( $true
= ( X10 @ X12 ) )
& ( ( cR @ X12 )
= X9 ) ) )
=> ( ( X3 @ X9 )
= $true ) ) )
<=> ( $true
= ( cPSI @ X3 @ X2 ) ) )
& ( cZ
= ( cR @ cZ ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X13: a,X14: a > $o] :
( ? [X15: a] :
( ! [X16: a] :
( ! [X17: a > $o] :
( ( ! [X18: a] :
( ( ( X17 @ X18 )
= $true )
=> ( $true
= ( X17 @ ( cL @ X18 ) ) ) )
& ( $true
= ( X17 @ X15 ) ) )
=> ? [X19: a] :
( ( ( X17 @ X19 )
= $true )
& ( ( cR @ X19 )
= X16 ) ) )
=> ( ( X14 @ X16 )
= $true ) )
& ( $true
= ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X15 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X13 ) ) )
<=> ( $true
= ( cPHI @ X14 @ X13 ) ) )
& ! [X24: a,X25: a] :
( ( cR @ ( cP @ X25 @ X24 ) )
= X24 )
& ! [X26: a] :
( ( ( cP @ ( cL @ X26 ) @ ( cR @ X26 ) )
= X26 )
<=> ( cZ != X26 ) )
& ! [X27: a > $o] :
( ? [X28: a] :
( ( ( X27 @ X28 )
= $true )
& ! [X29: a] :
( ( ( X27 @ X29 )
= $true )
=> ( ( X27 @ ( cL @ X29 ) )
= $true ) ) )
=> ( ( X27 @ cZ )
= $true ) ) )
=> ( ( ^ [Y0: a] :
( ( cZ = Y0 )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 )
& ( ( cP @ Y1 @ Y2 )
= Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y2 @ Y1 )
= Y0 )
& ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y2 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y1 ) ) ) )
| ( cZ = Y0 ) ) )
= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y1 @ Y2 )
= Y0 )
& ( ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y2 )
| ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 ) ) ) ) )
| ( cZ = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a,X1: a] :
( ( cL @ ( cP @ X1 @ X0 ) )
= X1 )
& ! [X2: a,X3: a > $o] :
( ? [X4: a] :
( ( cPSI
@ ^ [X5: a] :
! [X6: a > $o] :
( ( ( X6 @ X4 )
& ! [X7: a] :
( ( X6 @ X7 )
=> ( X6 @ ( cL @ X7 ) ) ) )
=> ? [X8: a] :
( ( X6 @ X8 )
& ( ( cR @ X8 )
= X5 ) ) )
@ X2 )
& ! [X9: a] :
( ! [X10: a > $o] :
( ( ! [X11: a] :
( ( X10 @ X11 )
=> ( X10 @ ( cL @ X11 ) ) )
& ( X10 @ X4 ) )
=> ? [X12: a] :
( ( X10 @ X12 )
& ( ( cR @ X12 )
= X9 ) ) )
=> ( X3 @ X9 ) ) )
<=> ( cPSI @ X3 @ X2 ) )
& ( cZ
= ( cR @ cZ ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X13: a,X14: a > $o] :
( ? [X15: a] :
( ! [X16: a] :
( ! [X17: a > $o] :
( ( ! [X18: a] :
( ( X17 @ X18 )
=> ( X17 @ ( cL @ X18 ) ) )
& ( X17 @ X15 ) )
=> ? [X19: a] :
( ( X17 @ X19 )
& ( ( cR @ X19 )
= X16 ) ) )
=> ( X14 @ X16 ) )
& ( cPHI
@ ^ [X20: a] :
! [X21: a > $o] :
( ( ! [X22: a] :
( ( X21 @ X22 )
=> ( X21 @ ( cL @ X22 ) ) )
& ( X21 @ X15 ) )
=> ? [X23: a] :
( ( X21 @ X23 )
& ( ( cR @ X23 )
= X20 ) ) )
@ X13 ) )
<=> ( cPHI @ X14 @ X13 ) )
& ! [X24: a,X25: a] :
( ( cR @ ( cP @ X25 @ X24 ) )
= X24 )
& ! [X26: a] :
( ( ( cP @ ( cL @ X26 ) @ ( cR @ X26 ) )
= X26 )
<=> ( cZ != X26 ) )
& ! [X27: a > $o] :
( ? [X28: a] :
( ( X27 @ X28 )
& ! [X29: a] :
( ( X27 @ X29 )
=> ( X27 @ ( cL @ X29 ) ) ) )
=> ( X27 @ cZ ) ) )
=> ( ( ^ [X30: a] :
( ( cZ = X30 )
| ? [X31: a,X32: a] :
( ( ( cPHI
@ ^ [X33: a] :
! [X34: a > $o] :
( ( ! [X35: a] :
( ( X34 @ X35 )
=> ( X34 @ ( cL @ X35 ) ) )
& ( X34 @ X32 ) )
=> ? [X36: a] :
( ( ( cR @ X36 )
= X33 )
& ( X34 @ X36 ) ) )
@ X31 )
| ( cPSI
@ ^ [X37: a] :
! [X38: a > $o] :
( ( ( X38 @ X32 )
& ! [X39: a] :
( ( X38 @ X39 )
=> ( X38 @ ( cL @ X39 ) ) ) )
=> ? [X40: a] :
( ( X38 @ X40 )
& ( ( cR @ X40 )
= X37 ) ) )
@ X31 ) )
& ( ( cP @ X32 @ X31 )
= X30 ) ) ) )
= ( ^ [X41: a] :
( ( cZ = X41 )
| ? [X42: a,X43: a] :
( ( cPSI
@ ^ [X44: a] :
! [X45: a > $o] :
( ( ( X45 @ X42 )
& ! [X46: a] :
( ( X45 @ X46 )
=> ( X45 @ ( cL @ X46 ) ) ) )
=> ? [X47: a] :
( ( X45 @ X47 )
& ( ( cR @ X47 )
= X44 ) ) )
@ X43 )
& ( ( cP @ X42 @ X43 )
= X41 ) )
| ? [X48: a,X49: a] :
( ( ( cP @ X49 @ X48 )
= X41 )
& ( cPHI
@ ^ [X50: a] :
! [X51: a > $o] :
( ( ! [X52: a] :
( ( X51 @ X52 )
=> ( X51 @ ( cL @ X52 ) ) )
& ( X51 @ X49 ) )
=> ? [X53: a] :
( ( ( cR @ X53 )
= X50 )
& ( X51 @ X53 ) ) )
@ X48 ) )
| ( cZ = X41 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: a,X0: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ! [X5: a,X3: a > $o] :
( ? [X0: a] :
( ( cPSI
@ ^ [X1: a] :
! [X7: a > $o] :
( ( ( X7 @ X0 )
& ! [X8: a] :
( ( X7 @ X8 )
=> ( X7 @ ( cL @ X8 ) ) ) )
=> ? [X9: a] :
( ( X7 @ X9 )
& ( ( cR @ X9 )
= X1 ) ) )
@ X5 )
& ! [X10: a] :
( ! [X7: a > $o] :
( ( ! [X8: a] :
( ( X7 @ X8 )
=> ( X7 @ ( cL @ X8 ) ) )
& ( X7 @ X0 ) )
=> ? [X9: a] :
( ( X7 @ X9 )
& ( ( cR @ X9 )
= X10 ) ) )
=> ( X3 @ X10 ) ) )
<=> ( cPSI @ X3 @ X5 ) )
& ( cZ
= ( cR @ cZ ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X5: a,X3: a > $o] :
( ? [X0: a] :
( ! [X6: a] :
( ! [X7: a > $o] :
( ( ! [X8: a] :
( ( X7 @ X8 )
=> ( X7 @ ( cL @ X8 ) ) )
& ( X7 @ X0 ) )
=> ? [X9: a] :
( ( X7 @ X9 )
& ( ( cR @ X9 )
= X6 ) ) )
=> ( X3 @ X6 ) )
& ( cPHI
@ ^ [X1: a] :
! [X7: a > $o] :
( ( ! [X8: a] :
( ( X7 @ X8 )
=> ( X7 @ ( cL @ X8 ) ) )
& ( X7 @ X0 ) )
=> ? [X9: a] :
( ( X7 @ X9 )
& ( ( cR @ X9 )
= X1 ) ) )
@ X5 ) )
<=> ( cPHI @ X3 @ X5 ) )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X2: a] :
( ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 )
<=> ( cZ != X2 ) )
& ! [X3: a > $o] :
( ? [X2: a] :
( ( X3 @ X2 )
& ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ( X3 @ cZ ) ) )
=> ( ( ^ [X4: a] :
( ( cZ = X4 )
| ? [X1: a,X0: a] :
( ( ( cPHI
@ ^ [X11: a] :
! [X3: a > $o] :
( ( ! [X5: a] :
( ( X3 @ X5 )
=> ( X3 @ ( cL @ X5 ) ) )
& ( X3 @ X0 ) )
=> ? [X9: a] :
( ( ( cR @ X9 )
= X11 )
& ( X3 @ X9 ) ) )
@ X1 )
| ( cPSI
@ ^ [X11: a] :
! [X3: a > $o] :
( ( ( X3 @ X0 )
& ! [X5: a] :
( ( X3 @ X5 )
=> ( X3 @ ( cL @ X5 ) ) ) )
=> ? [X9: a] :
( ( X3 @ X9 )
& ( ( cR @ X9 )
= X11 ) ) )
@ X1 ) )
& ( ( cP @ X0 @ X1 )
= X4 ) ) ) )
= ( ^ [X5: a] :
( ( cZ = X5 )
| ? [X0: a,X1: a] :
( ( cPSI
@ ^ [X11: a] :
! [X3: a > $o] :
( ( ( X3 @ X0 )
& ! [X8: a] :
( ( X3 @ X8 )
=> ( X3 @ ( cL @ X8 ) ) ) )
=> ? [X9: a] :
( ( X3 @ X9 )
& ( ( cR @ X9 )
= X11 ) ) )
@ X1 )
& ( ( cP @ X0 @ X1 )
= X5 ) )
| ? [X1: a,X0: a] :
( ( ( cP @ X0 @ X1 )
= X5 )
& ( cPHI
@ ^ [X11: a] :
! [X3: a > $o] :
( ( ! [X8: a] :
( ( X3 @ X8 )
=> ( X3 @ ( cL @ X8 ) ) )
& ( X3 @ X0 ) )
=> ? [X9: a] :
( ( ( cR @ X9 )
= X11 )
& ( X3 @ X9 ) ) )
@ X1 ) )
| ( cZ = X5 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: a,X0: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ! [X5: a,X3: a > $o] :
( ? [X0: a] :
( ( cPSI
@ ^ [X1: a] :
! [X7: a > $o] :
( ( ( X7 @ X0 )
& ! [X8: a] :
( ( X7 @ X8 )
=> ( X7 @ ( cL @ X8 ) ) ) )
=> ? [X9: a] :
( ( X7 @ X9 )
& ( ( cR @ X9 )
= X1 ) ) )
@ X5 )
& ! [X10: a] :
( ! [X7: a > $o] :
( ( ! [X8: a] :
( ( X7 @ X8 )
=> ( X7 @ ( cL @ X8 ) ) )
& ( X7 @ X0 ) )
=> ? [X9: a] :
( ( X7 @ X9 )
& ( ( cR @ X9 )
= X10 ) ) )
=> ( X3 @ X10 ) ) )
<=> ( cPSI @ X3 @ X5 ) )
& ( cZ
= ( cR @ cZ ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X5: a,X3: a > $o] :
( ? [X0: a] :
( ! [X6: a] :
( ! [X7: a > $o] :
( ( ! [X8: a] :
( ( X7 @ X8 )
=> ( X7 @ ( cL @ X8 ) ) )
& ( X7 @ X0 ) )
=> ? [X9: a] :
( ( X7 @ X9 )
& ( ( cR @ X9 )
= X6 ) ) )
=> ( X3 @ X6 ) )
& ( cPHI
@ ^ [X1: a] :
! [X7: a > $o] :
( ( ! [X8: a] :
( ( X7 @ X8 )
=> ( X7 @ ( cL @ X8 ) ) )
& ( X7 @ X0 ) )
=> ? [X9: a] :
( ( X7 @ X9 )
& ( ( cR @ X9 )
= X1 ) ) )
@ X5 ) )
<=> ( cPHI @ X3 @ X5 ) )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X2: a] :
( ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 )
<=> ( cZ != X2 ) )
& ! [X3: a > $o] :
( ? [X2: a] :
( ( X3 @ X2 )
& ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ( X3 @ cZ ) ) )
=> ( ( ^ [X4: a] :
( ( cZ = X4 )
| ? [X1: a,X0: a] :
( ( ( cPHI
@ ^ [X11: a] :
! [X3: a > $o] :
( ( ! [X5: a] :
( ( X3 @ X5 )
=> ( X3 @ ( cL @ X5 ) ) )
& ( X3 @ X0 ) )
=> ? [X9: a] :
( ( ( cR @ X9 )
= X11 )
& ( X3 @ X9 ) ) )
@ X1 )
| ( cPSI
@ ^ [X11: a] :
! [X3: a > $o] :
( ( ( X3 @ X0 )
& ! [X5: a] :
( ( X3 @ X5 )
=> ( X3 @ ( cL @ X5 ) ) ) )
=> ? [X9: a] :
( ( X3 @ X9 )
& ( ( cR @ X9 )
= X11 ) ) )
@ X1 ) )
& ( ( cP @ X0 @ X1 )
= X4 ) ) ) )
= ( ^ [X5: a] :
( ( cZ = X5 )
| ? [X0: a,X1: a] :
( ( cPSI
@ ^ [X11: a] :
! [X3: a > $o] :
( ( ( X3 @ X0 )
& ! [X8: a] :
( ( X3 @ X8 )
=> ( X3 @ ( cL @ X8 ) ) ) )
=> ? [X9: a] :
( ( X3 @ X9 )
& ( ( cR @ X9 )
= X11 ) ) )
@ X1 )
& ( ( cP @ X0 @ X1 )
= X5 ) )
| ? [X1: a,X0: a] :
( ( ( cP @ X0 @ X1 )
= X5 )
& ( cPHI
@ ^ [X11: a] :
! [X3: a > $o] :
( ( ! [X8: a] :
( ( X3 @ X8 )
=> ( X3 @ ( cL @ X8 ) ) )
& ( X3 @ X0 ) )
=> ? [X9: a] :
( ( ( cR @ X9 )
= X11 )
& ( X3 @ X9 ) ) )
@ X1 ) )
| ( cZ = X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uDBwpsOxhs/DTF2THF_2178.p',cPU_X2310B_pme) ).
thf(f2610,plain,
( ( sK23
= ( cR @ sK15 ) )
| ~ spl13_15 ),
inference(superposition,[status(thm)],[f56,f317]) ).
thf(f317,plain,
( ( ( cP @ sK22 @ sK23 )
= sK15 )
| ~ spl13_15 ),
inference(avatar_component_clause,[status(thm)],[f315]) ).
thf(f315,definition,
( spl13_15
<=> ( ( cP @ sK22 @ sK23 )
= sK15 ) ),
introduced(definition,[new_symbols(naming,[spl13_15])],[avatar_definition]) ).
thf(f341,plain,
( ! [X2: a,X1: a] :
( ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 )
= $false ) )
| ~ spl13_20 ),
inference(avatar_component_clause,[status(thm)],[f340]) ).
thf(f340,definition,
( spl13_20
<=> ! [X2: a,X1: a] :
( ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl13_20])],[avatar_definition]) ).
thf(f2674,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK22 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK18 )
= $true )
| ~ spl13_11
| ~ spl13_15
| ~ spl13_16 ),
inference(forward_demodulation,[status(thm)],[f322,f2614]) ).
thf(f322,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK22 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK23 )
= $true )
| ~ spl13_16 ),
inference(avatar_component_clause,[status(thm)],[f320]) ).
thf(f320,definition,
( spl13_16
<=> ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK22 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK23 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_16])],[avatar_definition]) ).
thf(f2823,plain,
( ~ spl13_9
| ~ spl13_10
| ~ spl13_11
| ~ spl13_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f2822]) ).
thf(f2822,plain,
( $false
| ~ spl13_9
| ~ spl13_10
| ~ spl13_11
| ~ spl13_20 ),
inference(trivial_inequality_removal,[status(thm)],[f2807]) ).
thf(f2807,plain,
( ( $true = $false )
| ~ spl13_9
| ~ spl13_10
| ~ spl13_11
| ~ spl13_20 ),
inference(backward_demodulation,[status(thm)],[f2673,f2623]) ).
thf(f2623,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK18 )
= $false )
| ~ spl13_9
| ~ spl13_11
| ~ spl13_20 ),
inference(trivial_inequality_removal,[status(thm)],[f2617]) ).
thf(f2617,plain,
( ( sK15 != sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK18 )
= $false )
| ~ spl13_9
| ~ spl13_11
| ~ spl13_20 ),
inference(superposition,[status(thm)],[f341,f2606]) ).
thf(f2606,plain,
( ( ( cP @ sK24 @ sK18 )
= sK15 )
| ~ spl13_9
| ~ spl13_11 ),
inference(backward_demodulation,[status(thm)],[f289,f2602]) ).
thf(f2602,plain,
( ( sK26 = sK18 )
| ~ spl13_9
| ~ spl13_11 ),
inference(backward_demodulation,[status(thm)],[f2454,f2467]) ).
thf(f2454,plain,
( ( ( cR @ sK15 )
= sK26 )
| ~ spl13_9 ),
inference(superposition,[status(thm)],[f56,f289]) ).
thf(f289,plain,
( ( ( cP @ sK24 @ sK26 )
= sK15 )
| ~ spl13_9 ),
inference(avatar_component_clause,[status(thm)],[f287]) ).
thf(f287,definition,
( spl13_9
<=> ( ( cP @ sK24 @ sK26 )
= sK15 ) ),
introduced(definition,[new_symbols(naming,[spl13_9])],[avatar_definition]) ).
thf(f2673,plain,
( ( $true
= ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK18 ) )
| ~ spl13_9
| ~ spl13_10
| ~ spl13_11 ),
inference(forward_demodulation,[status(thm)],[f294,f2602]) ).
thf(f294,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK26 )
= $true )
| ~ spl13_10 ),
inference(avatar_component_clause,[status(thm)],[f292]) ).
thf(f292,definition,
( spl13_10
<=> ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK26 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_10])],[avatar_definition]) ).
thf(f2439,plain,
( ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f2438]) ).
thf(f2438,plain,
( $false
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_20 ),
inference(trivial_inequality_removal,[status(thm)],[f2428]) ).
thf(f2428,plain,
( ( $true = $false )
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_20 ),
inference(backward_demodulation,[status(thm)],[f2382,f2425]) ).
thf(f2425,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $false )
| ~ spl13_12
| ~ spl13_14
| ~ spl13_20 ),
inference(forward_demodulation,[status(thm)],[f1917,f2380]) ).
thf(f2380,plain,
( ( sK17 = sK25 )
| ~ spl13_12
| ~ spl13_14 ),
inference(forward_demodulation,[status(thm)],[f1915,f1924]) ).
thf(f1924,plain,
( ( sK17
= ( cR @ sK15 ) )
| ~ spl13_14 ),
inference(superposition,[status(thm)],[f56,f313]) ).
thf(f313,plain,
( ( ( cP @ sK16 @ sK17 )
= sK15 )
| ~ spl13_14 ),
inference(avatar_component_clause,[status(thm)],[f311]) ).
thf(f311,definition,
( spl13_14
<=> ( ( cP @ sK16 @ sK17 )
= sK15 ) ),
introduced(definition,[new_symbols(naming,[spl13_14])],[avatar_definition]) ).
thf(f1915,plain,
( ( sK25
= ( cR @ sK15 ) )
| ~ spl13_12 ),
inference(superposition,[status(thm)],[f56,f303]) ).
thf(f303,plain,
( ( ( cP @ sK24 @ sK25 )
= sK15 )
| ~ spl13_12 ),
inference(avatar_component_clause,[status(thm)],[f301]) ).
thf(f301,definition,
( spl13_12
<=> ( ( cP @ sK24 @ sK25 )
= sK15 ) ),
introduced(definition,[new_symbols(naming,[spl13_12])],[avatar_definition]) ).
thf(f1917,plain,
( ( $false
= ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK25 ) )
| ~ spl13_12
| ~ spl13_20 ),
inference(trivial_inequality_removal,[status(thm)],[f1912]) ).
thf(f1912,plain,
( ( sK15 != sK15 )
| ( $false
= ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK25 ) )
| ~ spl13_12
| ~ spl13_20 ),
inference(superposition,[status(thm)],[f341,f303]) ).
thf(f2382,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14 ),
inference(forward_demodulation,[status(thm)],[f308,f2380]) ).
thf(f308,plain,
( ( $true
= ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK25 ) )
| ~ spl13_13 ),
inference(avatar_component_clause,[status(thm)],[f306]) ).
thf(f306,definition,
( spl13_13
<=> ( $true
= ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK25 ) ) ),
introduced(definition,[new_symbols(naming,[spl13_13])],[avatar_definition]) ).
thf(f2272,plain,
( ~ spl13_8
| ~ spl13_14
| ~ spl13_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f2271]) ).
thf(f2271,plain,
( $false
| ~ spl13_8
| ~ spl13_14
| ~ spl13_20 ),
inference(trivial_inequality_removal,[status(thm)],[f2270]) ).
thf(f2270,plain,
( ( $true = $false )
| ~ spl13_8
| ~ spl13_14
| ~ spl13_20 ),
inference(forward_demodulation,[status(thm)],[f285,f1926]) ).
thf(f1926,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $false )
| ~ spl13_14
| ~ spl13_20 ),
inference(trivial_inequality_removal,[status(thm)],[f1921]) ).
thf(f1921,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $false )
| ( sK15 != sK15 )
| ~ spl13_14
| ~ spl13_20 ),
inference(superposition,[status(thm)],[f341,f313]) ).
thf(f285,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ~ spl13_8 ),
inference(avatar_component_clause,[status(thm)],[f283]) ).
thf(f283,definition,
( spl13_8
<=> ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_8])],[avatar_definition]) ).
thf(f1893,plain,
( ~ spl13_17
| ~ spl13_18
| ~ spl13_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f1892]) ).
thf(f1892,plain,
( $false
| ~ spl13_17
| ~ spl13_18
| ~ spl13_20 ),
inference(trivial_inequality_removal,[status(thm)],[f1883]) ).
thf(f1883,plain,
( ( $true = $false )
| ~ spl13_17
| ~ spl13_18
| ~ spl13_20 ),
inference(backward_demodulation,[status(thm)],[f332,f1677]) ).
thf(f1677,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK20 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK21 )
= $false )
| ~ spl13_17
| ~ spl13_20 ),
inference(trivial_inequality_removal,[status(thm)],[f1672]) ).
thf(f1672,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK20 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK21 )
= $false )
| ( sK15 != sK15 )
| ~ spl13_17
| ~ spl13_20 ),
inference(superposition,[status(thm)],[f341,f327]) ).
thf(f327,plain,
( ( ( cP @ sK20 @ sK21 )
= sK15 )
| ~ spl13_17 ),
inference(avatar_component_clause,[status(thm)],[f325]) ).
thf(f325,definition,
( spl13_17
<=> ( ( cP @ sK20 @ sK21 )
= sK15 ) ),
introduced(definition,[new_symbols(naming,[spl13_17])],[avatar_definition]) ).
thf(f332,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK20 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK21 )
= $true )
| ~ spl13_18 ),
inference(avatar_component_clause,[status(thm)],[f330]) ).
thf(f330,definition,
( spl13_18
<=> ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK20 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK21 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_18])],[avatar_definition]) ).
thf(f1469,plain,
( ~ spl13_6
| ~ spl13_11
| ~ spl13_19 ),
inference(avatar_contradiction_clause,[status(thm)],[f1468]) ).
thf(f1468,plain,
( $false
| ~ spl13_6
| ~ spl13_11
| ~ spl13_19 ),
inference(trivial_inequality_removal,[status(thm)],[f1458]) ).
thf(f1458,plain,
( ( $true = $false )
| ~ spl13_6
| ~ spl13_11
| ~ spl13_19 ),
inference(backward_demodulation,[status(thm)],[f277,f1422]) ).
thf(f1422,plain,
( ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 )
= $false )
| ~ spl13_11
| ~ spl13_19 ),
inference(trivial_inequality_removal,[status(thm)],[f1417]) ).
thf(f1417,plain,
( ( sK15 != sK15 )
| ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 )
= $false )
| ~ spl13_11
| ~ spl13_19 ),
inference(superposition,[status(thm)],[f337,f299]) ).
thf(f337,plain,
( ! [X2: a,X1: a] :
( ( ( cP @ X2 @ X1 )
!= sK15 )
| ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X2 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X1 )
= $false ) )
| ~ spl13_19 ),
inference(avatar_component_clause,[status(thm)],[f336]) ).
thf(f336,definition,
( spl13_19
<=> ! [X2: a,X1: a] :
( ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X2 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X1 )
= $false )
| ( ( cP @ X2 @ X1 )
!= sK15 ) ) ),
introduced(definition,[new_symbols(naming,[spl13_19])],[avatar_definition]) ).
thf(f277,plain,
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ~ spl13_6 ),
inference(avatar_component_clause,[status(thm)],[f275]) ).
thf(f275,definition,
( spl13_6
<=> ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) ) ),
introduced(definition,[new_symbols(naming,[spl13_6])],[avatar_definition]) ).
thf(f1375,plain,
( ~ spl13_7
| ~ spl13_14
| ~ spl13_19 ),
inference(avatar_contradiction_clause,[status(thm)],[f1374]) ).
thf(f1374,plain,
( $false
| ~ spl13_7
| ~ spl13_14
| ~ spl13_19 ),
inference(trivial_inequality_removal,[status(thm)],[f1361]) ).
thf(f1361,plain,
( ( $true = $false )
| ~ spl13_7
| ~ spl13_14
| ~ spl13_19 ),
inference(backward_demodulation,[status(thm)],[f281,f1327]) ).
thf(f1327,plain,
( ( $false
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ~ spl13_14
| ~ spl13_19 ),
inference(trivial_inequality_removal,[status(thm)],[f1326]) ).
thf(f1326,plain,
( ( $false
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( sK15 != sK15 )
| ~ spl13_14
| ~ spl13_19 ),
inference(superposition,[status(thm)],[f337,f313]) ).
thf(f281,plain,
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ~ spl13_7 ),
inference(avatar_component_clause,[status(thm)],[f279]) ).
thf(f279,definition,
( spl13_7
<=> ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) ) ),
introduced(definition,[new_symbols(naming,[spl13_7])],[avatar_definition]) ).
thf(f349,plain,
( spl13_19
| spl13_19 ),
inference(avatar_split_clause,[status(thm)],[f159,f336,f336]) ).
thf(f159,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( cP @ X4 @ X3 )
!= sK15 )
| ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X4 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X3 )
= $false )
| ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X1 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f158]) ).
thf(f158,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( $false
= ( ( cP @ X4 @ X3 )
= sK15 ) )
| ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X4 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X3 )
= $false )
| ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X1 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f157]) ).
thf(f157,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X1 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 )
= $false )
| ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( ( ( cP @ X4 @ X3 )
= sK15 )
& ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X4 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X3 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f156]) ).
thf(f156,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( ( cP @ X1 @ X2 )
!= sK15 )
| ( $false
= ( ^ [Y0: a] :
( ( ( cP @ Y0 @ X3 )
= sK15 )
& ( cPSI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
@ X3 ) )
@ X4 ) )
| ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X1 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f155]) ).
thf(f155,plain,
! [X2: a,X3: a,X1: a] :
( ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X1 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 )
= $false )
| ( $false
= ( ?? @ a
@ ^ [Y0: a] :
( ( ( cP @ Y0 @ X3 )
= sK15 )
& ( cPSI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
@ X3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f154]) ).
thf(f154,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) )
@ X3 )
= $false )
| ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X1 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 )
= $false )
| ( ( cP @ X1 @ X2 )
!= sK15 ) ),
inference(pi_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
! [X2: a,X1: a] :
( ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X1 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 )
= $false )
| ( $false
= ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
| ( ( cP @ X1 @ X2 )
!= sK15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
! [X2: a,X1: a] :
( ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $false )
| ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X1 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 )
= $false )
| ( ( cP @ X1 @ X2 )
!= sK15 ) ),
inference(equality_proxy_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
! [X2: a,X1: a] :
( ( ( ( cP @ X1 @ X2 )
= sK15 )
= $false )
| ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X1 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 )
= $false )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
! [X2: a,X1: a] :
( ( $false
= ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X1 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 ) ) )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $false )
| ( ( ( cP @ X1 @ X2 )
= sK15 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
! [X2: a,X1: a] :
( ( $false
= ( ( ( cP @ X1 @ X2 )
= sK15 )
& ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ X1 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ X2 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 ) ) ) )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f137]) ).
thf(f137,plain,
! [X2: a,X1: a] :
( ( ( ^ [Y0: a] :
( ( ( cP @ X1 @ Y0 )
= sK15 )
& ( ( cPSI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ X1 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
@ Y0 )
| ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ X1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 ) ) )
@ X2 )
= $false )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
! [X1: a] :
( ( ( ?? @ a
@ ^ [Y0: a] :
( ( ( cP @ X1 @ Y0 )
= sK15 )
& ( ( cPSI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ X1 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
@ Y0 )
| ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ X1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 ) ) ) )
= $false )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f135]) ).
thf(f135,plain,
! [X1: a] :
( ( $false
= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y0 @ Y1 )
= sK15 )
& ( ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y1 )
| ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 ) ) ) )
@ X1 ) )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y0 @ Y1 )
= sK15 )
& ( ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y1 )
| ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 ) ) ) ) )
= $false )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
( ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) )
| ( cZ = sK15 ) )
= $false )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y0 @ Y1 )
= sK15 )
& ( ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y1 )
| ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
( ( $false
= ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y0 @ Y1 )
= sK15 )
& ( ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y1 )
| ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 ) ) ) ) )
| ( cZ = sK15 ) ) )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) )
| ( cZ = sK15 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) )
| ( cZ = sK15 ) )
!= ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y0 @ Y1 )
= sK15 )
& ( ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y1 )
| ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 ) ) ) ) )
| ( cZ = sK15 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f127]) ).
thf(f127,plain,
( ( ^ [Y0: a] :
( ( cZ = Y0 )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 )
& ( ( cP @ Y1 @ Y2 )
= Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y2 @ Y1 )
= Y0 )
& ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y2 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y1 ) ) ) )
| ( cZ = Y0 ) )
@ sK15 )
!= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y1 @ Y2 )
= Y0 )
& ( ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y2 )
| ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 ) ) ) ) )
| ( cZ = Y0 ) )
@ sK15 ) ),
inference(negative_extensionality,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ^ [Y0: a] :
( ( cZ = Y0 )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 )
& ( ( cP @ Y1 @ Y2 )
= Y0 ) ) ) )
| ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y2 @ Y1 )
= Y0 )
& ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y2 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y1 ) ) ) )
| ( cZ = Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ a
@ ^ [Y1: a] :
( ?? @ a
@ ^ [Y2: a] :
( ( ( cP @ Y1 @ Y2 )
= Y0 )
& ( ( cPSI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) )
& ( Y4 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( ( cR @ Y5 )
= Y3 )
& ( Y4 @ Y5 ) ) ) ) )
@ Y2 )
| ( cPHI
@ ^ [Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( Y4 @ Y1 )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( cL @ Y5 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y5: a] :
( ( Y4 @ Y5 )
& ( ( cR @ Y5 )
= Y3 ) ) ) ) )
@ Y2 ) ) ) ) )
| ( cZ = Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f347,plain,
( spl13_20
| spl13_20 ),
inference(avatar_split_clause,[status(thm)],[f171,f340,f340]) ).
thf(f171,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( $false
= ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X3 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X4 ) )
| ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( cP @ X3 @ X4 )
!= sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f170]) ).
thf(f170,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 )
= $false )
| ( $false
= ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X3 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X4 ) )
| ( ( ( cP @ X3 @ X4 )
= sK15 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f169]) ).
thf(f169,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 )
= $false )
| ( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X3 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X4 )
& ( ( cP @ X3 @ X4 )
= sK15 ) )
= $false )
| ( ( cP @ X1 @ X2 )
!= sK15 ) ),
inference(beta_eta_normalization,[status(thm)],[f168]) ).
thf(f168,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 )
= $false )
| ( $false
= ( ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ X3 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ X3 @ Y0 )
= sK15 ) )
@ X4 ) ) ),
inference(pi_clausification,[status(thm)],[f167]) ).
thf(f167,plain,
! [X2: a,X3: a,X1: a] :
( ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 )
= $false )
| ( $false
= ( ?? @ a
@ ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ X3 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ X3 @ Y0 )
= sK15 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f166]) ).
thf(f166,plain,
! [X2: a,X3: a,X1: a] :
( ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 )
= $false )
| ( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) )
@ X3 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
! [X2: a,X1: a] :
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 )
= $false )
| ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f162]) ).
thf(f162,plain,
! [X2: a,X1: a] :
( ( $false
= ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) ) ) )
| ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f160]) ).
thf(f160,plain,
! [X2: a,X1: a] :
( ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $false )
| ( ( cP @ X1 @ X2 )
!= sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
! [X2: a,X1: a] :
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ X1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ X2 )
= $false )
| ( ( ( cP @ X1 @ X2 )
= sK15 )
= $false )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f343,plain,
~ spl13_5,
inference(avatar_split_clause,[status(thm)],[f196,f271]) ).
thf(f271,definition,
( spl13_5
<=> ( cZ = sK15 ) ),
introduced(definition,[new_symbols(naming,[spl13_5])],[avatar_definition]) ).
thf(f196,plain,
cZ != sK15,
inference(duplicate_literal_removal,[status(thm)],[f195]) ).
thf(f195,plain,
( ( cZ != sK15 )
| ( cZ != sK15 ) ),
inference(equality_proxy_clausification,[status(thm)],[f194]) ).
thf(f194,plain,
( ( ( cZ = sK15 )
= $false )
| ( cZ != sK15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f192]) ).
thf(f192,plain,
( ( cZ != sK15 )
| ( $false
= ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f190]) ).
thf(f190,plain,
( ( cZ != sK15 )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f188]) ).
thf(f188,plain,
( ( cZ != sK15 )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) )
| ( cZ = sK15 ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
( ( ( cZ = sK15 )
= $false )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) )
| ( cZ = sK15 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f333,plain,
( spl13_14
| spl13_18
| spl13_11
| spl13_5 ),
inference(avatar_split_clause,[status(thm)],[f239,f271,f297,f330,f311]) ).
thf(f239,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK20 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK21 )
= $true )
| ( cZ = sK15 )
| ( sK15
= ( cP @ sK19 @ sK18 ) )
| ( ( cP @ sK16 @ sK17 )
= sK15 ) ),
inference(equality_proxy_clausification,[status(thm)],[f238]) ).
thf(f238,plain,
( ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) )
| ( cZ = sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK20 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK21 )
= $true )
| ( sK15
= ( cP @ sK19 @ sK18 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f236]) ).
thf(f236,plain,
( ( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK20 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK21 )
& ( ( cP @ sK20 @ sK21 )
= sK15 ) )
= $true )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) )
| ( sK15
= ( cP @ sK19 @ sK18 ) )
| ( cZ = sK15 ) ),
inference(equality_proxy_clausification,[status(thm)],[f235]) ).
thf(f235,plain,
( ( ( ( cP @ sK19 @ sK18 )
= sK15 )
= $true )
| ( cZ = sK15 )
| ( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK20 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK21 )
& ( ( cP @ sK20 @ sK21 )
= sK15 ) )
= $true )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f234]) ).
thf(f234,plain,
( ( cZ = sK15 )
| ( ( ( cP @ sK19 @ sK18 )
= sK15 )
= $true )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) )
| ( $true
= ( ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK20 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ sK20 @ Y0 )
= sK15 ) )
@ sK21 ) ) ),
inference(sigma_clausification,[status(thm)],[f233]) ).
thf(f233,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK20 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ sK20 @ Y0 )
= sK15 ) ) )
= $true )
| ( cZ = sK15 )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) )
| ( ( ( cP @ sK19 @ sK18 )
= sK15 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f232]) ).
thf(f232,plain,
( ( ( ( cP @ sK19 @ sK18 )
= sK15 )
= $true )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) )
| ( $true
= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) )
@ sK20 ) )
| ( cZ = sK15 ) ),
inference(sigma_clausification,[status(thm)],[f231]) ).
thf(f231,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
= $true )
| ( cZ = sK15 )
| ( ( ( cP @ sK19 @ sK18 )
= sK15 )
= $true )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f230]) ).
thf(f230,plain,
( ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
= $true )
| ( cZ = sK15 )
| ( cZ = sK15 )
| ( ( ( cP @ sK19 @ sK18 )
= sK15 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f229]) ).
thf(f229,plain,
( ( ( cZ = sK15 )
= $true )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
= $true )
| ( ( ( cP @ sK19 @ sK18 )
= sK15 )
= $true )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) )
| ( cZ = sK15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f227]) ).
thf(f227,plain,
( ( $true
= ( ( ( cP @ sK19 @ sK18 )
= sK15 )
& ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) ) )
| ( ( cZ = sK15 )
= $true )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
= $true )
| ( cZ = sK15 )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f225]) ).
thf(f225,plain,
( ( $true
= ( ( ( cP @ sK16 @ sK17 )
= sK15 )
& ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 ) ) ) )
| ( $true
= ( ( ( cP @ sK19 @ sK18 )
= sK15 )
& ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) ) )
| ( ( cZ = sK15 )
= $true )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
= $true )
| ( cZ = sK15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f224]) ).
thf(f224,plain,
( ( cZ = sK15 )
| ( $true
= ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) ) ) )
| ( $true
= ( ( ( cP @ sK19 @ sK18 )
= sK15 )
& ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) ) )
| ( $true
= ( ( ( cP @ sK16 @ sK17 )
= sK15 )
& ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f223]) ).
thf(f223,plain,
( ( $true
= ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) ) ) )
| ( cZ = sK15 )
| ( ( ^ [Y0: a] :
( ( ( cP @ Y0 @ sK18 )
= sK15 )
& ( cPSI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
@ sK18 ) )
@ sK19 )
= $true )
| ( $true
= ( ( ( cP @ sK16 @ sK17 )
= sK15 )
& ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f222]) ).
thf(f222,plain,
( ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ( ( cP @ Y0 @ sK18 )
= sK15 )
& ( cPSI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
@ sK18 ) ) ) )
| ( $true
= ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) ) ) )
| ( cZ = sK15 )
| ( $true
= ( ( ( cP @ sK16 @ sK17 )
= sK15 )
& ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f221]) ).
thf(f221,plain,
( ( $true
= ( ( ( cP @ sK16 @ sK17 )
= sK15 )
& ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 ) ) ) )
| ( $true
= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) )
@ sK18 ) )
| ( $true
= ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) ) ) )
| ( cZ = sK15 ) ),
inference(sigma_clausification,[status(thm)],[f220]) ).
thf(f220,plain,
( ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
| ( $true
= ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) ) ) )
| ( cZ = sK15 )
| ( $true
= ( ( ( cP @ sK16 @ sK17 )
= sK15 )
& ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f219]) ).
thf(f219,plain,
( ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
| ( $true
= ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) ) ) )
| ( cZ = sK15 )
| ( cZ = sK15 )
| ( $true
= ( ( ( cP @ sK16 @ sK17 )
= sK15 )
& ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f218]) ).
thf(f218,plain,
( ( cZ = sK15 )
| ( ( cZ = sK15 )
= $true )
| ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
| ( $true
= ( ( ( cP @ sK16 @ sK17 )
= sK15 )
& ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 ) ) ) )
| ( $true
= ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f217]) ).
thf(f217,plain,
( ( cZ = sK15 )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $true )
| ( $true
= ( ( ( cP @ sK16 @ sK17 )
= sK15 )
& ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 ) ) ) )
| ( ( cZ = sK15 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f216]) ).
thf(f216,plain,
( ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $true )
| ( ( cZ = sK15 )
= $true )
| ( cZ = sK15 )
| ( ( ^ [Y0: a] :
( ( ( cP @ sK16 @ Y0 )
= sK15 )
& ( ( cPSI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
@ Y0 )
| ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK16 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 ) ) )
@ sK17 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f215]) ).
thf(f215,plain,
( ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ( ( cP @ sK16 @ Y0 )
= sK15 )
& ( ( cPSI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
@ Y0 )
| ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK16 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 ) ) ) ) )
| ( cZ = sK15 )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) ) )
= $true )
| ( ( cZ = sK15 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f214]) ).
thf(f214,plain,
( ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) )
| ( cZ = sK15 ) )
= $true )
| ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ( ( cP @ sK16 @ Y0 )
= sK15 )
& ( ( cPSI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
@ Y0 )
| ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK16 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 ) ) ) ) )
| ( cZ = sK15 ) ),
inference(equality_proxy_clausification,[status(thm)],[f213]) ).
thf(f213,plain,
( ( ( cZ = sK15 )
= $true )
| ( $true
= ( ?? @ a
@ ^ [Y0: a] :
( ( ( cP @ sK16 @ Y0 )
= sK15 )
& ( ( cPSI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) )
& ( Y2 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( ( cR @ Y3 )
= Y1 )
& ( Y2 @ Y3 ) ) ) ) )
@ Y0 )
| ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK16 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 ) ) ) ) )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) )
| ( cZ = sK15 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f212]) ).
thf(f212,plain,
( ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) )
| ( cZ = sK15 ) )
= $true )
| ( $true
= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y0 @ Y1 )
= sK15 )
& ( ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y1 )
| ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 ) ) ) )
@ sK16 ) )
| ( ( cZ = sK15 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f211]) ).
thf(f211,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y0 @ Y1 )
= sK15 )
& ( ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y1 )
| ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 ) ) ) ) )
= $true )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) )
| ( cZ = sK15 ) )
= $true )
| ( ( cZ = sK15 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f129]) ).
thf(f129,plain,
( ( $true
= ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y0 @ Y1 )
= sK15 )
& ( ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y0 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y1 )
| ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 ) ) ) ) )
| ( cZ = sK15 ) ) )
| ( ( ( cZ = sK15 )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
| ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( ( cP @ Y1 @ Y0 )
= sK15 )
& ( cPSI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( ( cR @ Y4 )
= Y2 )
& ( Y3 @ Y4 ) ) ) ) )
@ Y0 ) ) ) )
| ( cZ = sK15 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f328,plain,
( spl13_11
| spl13_5
| spl13_17
| spl13_14 ),
inference(avatar_split_clause,[status(thm)],[f241,f311,f325,f271,f297]) ).
thf(f241,plain,
( ( sK15
= ( cP @ sK19 @ sK18 ) )
| ( ( cP @ sK20 @ sK21 )
= sK15 )
| ( cZ = sK15 )
| ( ( cP @ sK16 @ sK17 )
= sK15 ) ),
inference(equality_proxy_clausification,[status(thm)],[f240]) ).
thf(f240,plain,
( ( ( cP @ sK20 @ sK21 )
= sK15 )
| ( cZ = sK15 )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) )
| ( sK15
= ( cP @ sK19 @ sK18 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f237]) ).
thf(f237,plain,
( ( sK15
= ( cP @ sK19 @ sK18 ) )
| ( cZ = sK15 )
| ( $true
= ( ( cP @ sK20 @ sK21 )
= sK15 ) )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f236]) ).
thf(f323,plain,
( spl13_16
| spl13_14
| spl13_5
| spl13_6 ),
inference(avatar_split_clause,[status(thm)],[f250,f275,f271,f311,f320]) ).
thf(f250,plain,
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( ( cP @ sK16 @ sK17 )
= sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK22 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK23 )
= $true )
| ( cZ = sK15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f248]) ).
thf(f248,plain,
( ( $true
= ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK22 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK23 )
& ( ( cP @ sK22 @ sK23 )
= sK15 ) ) )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( ( cP @ sK16 @ sK17 )
= sK15 )
| ( cZ = sK15 ) ),
inference(beta_eta_normalization,[status(thm)],[f247]) ).
thf(f247,plain,
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( ( cP @ sK16 @ sK17 )
= sK15 )
| ( cZ = sK15 )
| ( ( ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK22 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ sK22 @ Y0 )
= sK15 ) )
@ sK23 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f246]) ).
thf(f246,plain,
( ( cZ = sK15 )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK22 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ sK22 @ Y0 )
= sK15 ) ) )
= $true )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( ( cP @ sK16 @ sK17 )
= sK15 ) ),
inference(equality_proxy_clausification,[status(thm)],[f245]) ).
thf(f245,plain,
( ( cZ = sK15 )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK22 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ sK22 @ Y0 )
= sK15 ) ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f244]) ).
thf(f244,plain,
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( cZ = sK15 )
| ( cZ = sK15 )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK22 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ sK22 @ Y0 )
= sK15 ) ) )
= $true )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f243]) ).
thf(f243,plain,
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( ( cZ = sK15 )
= $true )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK22 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ sK22 @ Y0 )
= sK15 ) ) )
= $true )
| ( cZ = sK15 ) ),
inference(beta_eta_normalization,[status(thm)],[f242]) ).
thf(f242,plain,
( ( cZ = sK15 )
| ( $true
= ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) )
@ sK22 ) )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( ( cZ = sK15 )
= $true )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) ) ),
inference(sigma_clausification,[status(thm)],[f228]) ).
thf(f228,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
= $true )
| ( $true
= ( ( cP @ sK16 @ sK17 )
= sK15 ) )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( ( cZ = sK15 )
= $true )
| ( cZ = sK15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f227]) ).
thf(f318,plain,
( spl13_5
| spl13_14
| spl13_15
| spl13_6 ),
inference(avatar_split_clause,[status(thm)],[f251,f275,f315,f311,f271]) ).
thf(f251,plain,
( ( ( cP @ sK16 @ sK17 )
= sK15 )
| ( cZ = sK15 )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( ( cP @ sK22 @ sK23 )
= sK15 ) ),
inference(equality_proxy_clausification,[status(thm)],[f249]) ).
thf(f249,plain,
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( ( cP @ sK16 @ sK17 )
= sK15 )
| ( cZ = sK15 )
| ( ( ( cP @ sK22 @ sK23 )
= sK15 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f248]) ).
thf(f309,plain,
( spl13_7
| spl13_8
| spl13_5
| spl13_11
| spl13_13 ),
inference(avatar_split_clause,[status(thm)],[f263,f306,f297,f271,f283,f279]) ).
thf(f263,plain,
( ( sK15
= ( cP @ sK19 @ sK18 ) )
| ( $true
= ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK25 ) )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( cZ = sK15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f261]) ).
thf(f261,plain,
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( sK15
= ( cP @ sK19 @ sK18 ) )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( cZ = sK15 )
| ( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK25 )
& ( ( cP @ sK24 @ sK25 )
= sK15 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f260]) ).
thf(f260,plain,
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( cZ = sK15 )
| ( sK15
= ( cP @ sK19 @ sK18 ) )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( ( ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK24 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ sK24 @ Y0 )
= sK15 ) )
@ sK25 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f259]) ).
thf(f259,plain,
( ( sK15
= ( cP @ sK19 @ sK18 ) )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK24 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ sK24 @ Y0 )
= sK15 ) ) )
= $true )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( cZ = sK15 ) ),
inference(equality_proxy_clausification,[status(thm)],[f258]) ).
thf(f258,plain,
( ( ( ( cP @ sK19 @ sK18 )
= sK15 )
= $true )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( cZ = sK15 )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK24 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ sK24 @ Y0 )
= sK15 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f256]) ).
thf(f256,plain,
( ( cZ = sK15 )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( $true
= ( ( ( cP @ sK19 @ sK18 )
= sK15 )
& ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) ) )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK24 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ sK24 @ Y0 )
= sK15 ) ) )
= $true )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f255]) ).
thf(f255,plain,
( ( cZ = sK15 )
| ( $true
= ( ( ( cP @ sK19 @ sK18 )
= sK15 )
& ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) ) )
| ( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) )
@ sK24 )
= $true )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) ) ),
inference(sigma_clausification,[status(thm)],[f254]) ).
thf(f254,plain,
( ( cZ = sK15 )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
= $true )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( $true
= ( ( ( cP @ sK19 @ sK18 )
= sK15 )
& ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f253]) ).
thf(f253,plain,
( ( cZ = sK15 )
| ( $true
= ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 ) ) )
| ( $true
= ( ( ( cP @ sK19 @ sK18 )
= sK15 )
& ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) ) )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f252]) ).
thf(f252,plain,
( ( cZ = sK15 )
| ( $true
= ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 ) ) )
| ( $true
= ( ( ( cP @ sK19 @ sK18 )
= sK15 )
& ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) ) )
| ( cZ = sK15 )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f226]) ).
thf(f226,plain,
( ( ( cZ = sK15 )
= $true )
| ( cZ = sK15 )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( cPHI
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( cL @ Y4 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
& ( ( cR @ Y4 )
= Y2 ) ) ) ) )
@ Y1 )
& ( ( cP @ Y0 @ Y1 )
= sK15 ) ) ) )
= $true )
| ( $true
= ( ( ( cP @ sK19 @ sK18 )
= sK15 )
& ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) ) )
| ( $true
= ( ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 )
| ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f225]) ).
thf(f304,plain,
( spl13_7
| spl13_5
| spl13_11
| spl13_8
| spl13_12 ),
inference(avatar_split_clause,[status(thm)],[f264,f301,f283,f297,f271,f279]) ).
thf(f264,plain,
( ( ( cP @ sK24 @ sK25 )
= sK15 )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( sK15
= ( cP @ sK19 @ sK18 ) )
| ( cZ = sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f262]) ).
thf(f262,plain,
( ( ( ( cP @ sK24 @ sK25 )
= sK15 )
= $true )
| ( cZ = sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( sK15
= ( cP @ sK19 @ sK18 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f261]) ).
thf(f295,plain,
( spl13_10
| spl13_7
| spl13_6
| spl13_8
| spl13_5 ),
inference(avatar_split_clause,[status(thm)],[f268,f271,f283,f275,f279,f292]) ).
thf(f268,plain,
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK26 )
= $true )
| ( cZ = sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f266]) ).
thf(f266,plain,
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( cZ = sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( $true
= ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK24 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK26 )
& ( ( cP @ sK24 @ sK26 )
= sK15 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f265]) ).
thf(f265,plain,
( ( $true
= ( ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK24 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ sK24 @ Y0 )
= sK15 ) )
@ sK26 ) )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( cZ = sK15 ) ),
inference(sigma_clausification,[status(thm)],[f257]) ).
thf(f257,plain,
( ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( cZ = sK15 )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ( cPHI
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ sK24 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cL @ Y3 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( ( cR @ Y3 )
= Y1 ) ) ) ) )
@ Y0 )
& ( ( cP @ sK24 @ Y0 )
= sK15 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f256]) ).
thf(f290,plain,
( spl13_5
| spl13_6
| spl13_7
| spl13_8
| spl13_9 ),
inference(avatar_split_clause,[status(thm)],[f269,f287,f283,f279,f275,f271]) ).
thf(f269,plain,
( ( cZ = sK15 )
| ( ( cP @ sK24 @ sK26 )
= sK15 )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f267]) ).
thf(f267,plain,
( ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK19 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK18 ) )
| ( $true
= ( cPSI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) )
& ( Y1 @ sK16 ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( ( cR @ Y2 )
= Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK17 ) )
| ( ( cPHI
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK16 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cL @ Y2 ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( ( cR @ Y2 )
= Y0 ) ) ) ) )
@ sK17 )
= $true )
| ( $true
= ( ( cP @ sK24 @ sK26 )
= sK15 ) )
| ( cZ = sK15 ) ),
inference(binary_proxy_clausification,[status(thm)],[f266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ALG294^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n014.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 03:43:12 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.38 ---- Original DTF file ---
% 0.16/0.38 thf(spec,logic,$$dhol).
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 % File : ALG294^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.38 % Domain : General Algebra (Domain theory)
% 0.16/0.38 % Problem : TPS problem from PU-LAMBDA-MODEL-THMS
% 0.16/0.38 % Version : Especial.
% 0.16/0.38 % English :
% 0.16/0.38
% 0.16/0.38 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.38 % Source : [Bro09]
% 0.16/0.38 % Names : tps_1238 [Bro09]
% 0.16/0.38
% 0.16/0.38 % Status : Theorem
% 0.16/0.38 % Rating : 0.44 v9.1.0, 0.25 v9.0.0, 0.50 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.71 v7.4.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v4.1.0, 1.00 v4.0.0
% 0.16/0.38 % Syntax : Number of formulae : 8 ( 0 unt; 7 typ; 0 def)
% 0.16/0.38 % Number of atoms : 29 ( 21 equ; 0 cnn)
% 0.16/0.38 % Maximal formula atoms : 15 ( 29 avg)
% 0.16/0.38 % Number of connectives : 148 ( 1 ~; 5 |; 29 &; 89 @)
% 0.16/0.38 % ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% 0.16/0.38 % Maximal formula depth : 24 ( 24 avg)
% 0.16/0.38 % Number of types : 2 ( 1 usr)
% 0.16/0.38 % Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% 0.16/0.38 % Number of symbols : 7 ( 6 usr; 1 con; 0-2 aty)
% 0.16/0.38 % Number of variables : 54 ( 8 ^; 29 !; 17 ?; 54 :)
% 0.16/0.38 % SPC : TH0_THM_EQU_NAR
% 0.16/0.38
% 0.16/0.38 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.38 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.38 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.38 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 thf(a_type,type,
% 0.16/0.38 a: $tType ).
% 0.16/0.38
% 0.16/0.38 thf(cR,type,
% 0.16/0.38 cR: a > a ).
% 0.16/0.38
% 0.16/0.38 thf(cL,type,
% 0.16/0.38 cL: a > a ).
% 0.16/0.38
% 0.16/0.38 thf(cPSI,type,
% 0.16/0.38 cPSI: ( a > $o ) > a > $o ).
% 0.16/0.38
% 0.16/0.38 thf(cP,type,
% 0.16/0.38 cP: a > a > a ).
% 0.16/0.38
% 0.16/0.38 thf(cZ,type,
% 0.16/0.38 cZ: a ).
% 0.16/0.38
% 0.16/0.38 thf(cPHI,type,
% 0.16/0.38 cPHI: ( a > $o ) > a > $o ).
% 0.16/0.38
% 0.16/0.38 thf(cPU_X2310B_pme,conjecture,
% 0.16/0.38 ( ( ( ( cL @ cZ )
% 0.16/0.38 = cZ )
% 0.16/0.38 & ( ( cR @ cZ )
% 0.16/0.38 = cZ )
% 0.16/0.38 & ! [Xx: a,Xy: a] :
% 0.16/0.38 ( ( cL @ ( cP @ Xx @ Xy ) )
% 0.16/0.38 = Xx )
% 0.16/0.38 & ! [Xx: a,Xy: a] :
% 0.16/0.38 ( ( cR @ ( cP @ Xx @ Xy ) )
% 0.16/0.38 = Xy )
% 0.16/0.38 & ! [Xt: a] :
% 0.16/0.38 ( ( Xt != cZ )
% 0.16/0.38 <=> ( Xt
% 0.16/0.38 = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
% 0.16/0.38 & ! [X: a > $o] :
% 0.16/0.38 ( ? [Xt: a] :
% 0.16/0.38 ( ( X @ Xt )
% 0.16/0.38 & ! [Xu: a] :
% 0.16/0.38 ( ( X @ Xu )
% 0.16/0.38 => ( X @ ( cL @ Xu ) ) ) )
% 0.16/0.38 => ( X @ cZ ) )
% 0.16/0.38 & ! [X: a > $o,Xz: a] :
% 0.16/0.38 ( ( cPHI @ X @ Xz )
% 0.16/0.38 <=> ? [Xx: a] :
% 0.16/0.38 ( ! [Xx_14: a] :
% 0.16/0.38 ( ! [X0: a > $o] :
% 0.16/0.38 ( ( ( X0 @ Xx )
% 0.16/0.38 & ! [Xz0: a] :
% 0.16/0.38 ( ( X0 @ Xz0 )
% 0.16/0.38 => ( X0 @ ( cL @ Xz0 ) ) ) )
% 0.16/0.38 => ? [Xv: a] :
% 0.16/0.38 ( ( X0 @ Xv )
% 0.16/0.38 & ( ( cR @ Xv )
% 0.16/0.38 = Xx_14 ) ) )
% 0.16/0.38 => ( X @ Xx_14 ) )
% 0.16/0.38 & ( cPHI
% 0.16/0.38 @ ^ [Xy: a] :
% 0.16/0.38 ! [X0: a > $o] :
% 0.16/0.38 ( ( ( X0 @ Xx )
% 0.16/0.38 & ! [Xz0: a] :
% 0.16/0.38 ( ( X0 @ Xz0 )
% 0.16/0.38 => ( X0 @ ( cL @ Xz0 ) ) ) )
% 0.16/0.38 => ? [Xv: a] :
% 0.16/0.38 ( ( X0 @ Xv )
% 0.16/0.38 & ( ( cR @ Xv )
% 0.16/0.38 = Xy ) ) )
% 0.16/0.38 @ Xz ) ) )
% 0.16/0.38 & ! [X: a > $o,Xz: a] :
% 0.16/0.38 ( ( cPSI @ X @ Xz )
% 0.16/0.38 <=> ? [Xx: a] :
% 0.16/0.38 ( ! [Xx_15: a] :
% 0.16/0.38 ( ! [X0: a > $o] :
% 0.16/0.38 ( ( ( X0 @ Xx )
% 0.16/0.38 & ! [Xz0: a] :
% 0.16/0.38 ( ( X0 @ Xz0 )
% 0.16/0.38 => ( X0 @ ( cL @ Xz0 ) ) ) )
% 0.16/0.38 => ? [Xv: a] :
% 0.16/0.38 ( ( X0 @ Xv )
% 0.16/0.38 & ( ( cR @ Xv )
% 0.16/0.38 = Xx_15 ) ) )
% 0.16/0.38 => ( X @ Xx_15 ) )
% 0.16/0.38 & ( cPSI
% 0.16/0.38 @ ^ [Xy: a] :
% 0.16/0.38 ! [X0: a > $o] :
% 0.16/0.38 ( ( ( X0 @ Xx )
% 0.16/0.38 & ! [Xz0: a] :
% 0.16/0.38 ( ( X0 @ Xz0 )
% 0.16/0.38 => ( X0 @ ( cL @ Xz0 ) ) ) )
% 0.16/0.38 => ? [Xv: a] :
% 0.16/0.38 ( ( X0 @ Xv )
% 0.16/0.38 & ( ( cR @ Xv )
% 0.16/0.38 = Xy ) ) )
% 0.16/0.38 @ Xz ) ) ) )
% 0.16/0.38 => ( ( ^ [Xu: a] :
% 0.16/0.38 ( ( Xu = cZ )
% 0.16/0.38 | ? [Xx: a,Xy: a] :
% 0.16/0.38 ( ( Xu
% 0.16/0.38 = ( cP @ Xx @ Xy ) )
% 0.16/0.38 & ( ( cPHI
% 0.16/0.38 @ ^ [Xy0: a] :
% 0.16/0.38 ! [X: a > $o] :
% 0.16/0.38 ( ( ( X @ Xx )
% 0.16/0.38 & ! [Xz: a] :
% 0.16/0.38 ( ( X @ Xz )
% 0.16/0.38 => ( X @ ( cL @ Xz ) ) ) )
% 0.16/0.38 => ? [Xv: a] :
% 0.16/0.38 ( ( X @ Xv )
% 0.16/0.38 & ( ( cR @ Xv )
% 0.16/0.38 = Xy0 ) ) )
% 0.16/0.38 @ Xy )
% 0.16/0.38 | ( cPSI
% 0.16/0.38 @ ^ [Xy0: a] :
% 0.16/0.38 ! [X: a > $o] :
% 0.16/0.38 ( ( ( X @ Xx )
% 0.16/0.38 & ! [Xz: a] :
% 0.16/0.38 ( ( X @ Xz )
% 0.16/0.38 => ( X @ ( cL @ Xz ) ) ) )
% 0.16/0.38 => ? [Xv: a] :
% 0.16/0.38 ( ( X @ Xv )
% 0.16/0.38 & ( ( cR @ Xv )
% 0.16/0.38 = Xy0 ) ) )
% 0.16/0.38 @ Xy ) ) ) ) )
% 0.16/0.38 = ( ^ [Xz: a] :
% 0.16/0.38 ( ( Xz = cZ )
% 0.16/0.38 | ? [Xx: a,Xy: a] :
% 0.16/0.38 ( ( Xz
% 0.16/0.38 = ( cP @ Xx @ Xy ) )
% 0.16/0.38 & ( cPHI
% 0.16/0.38 @ ^ [Xy0: a] :
% 0.16/0.38 ! [X: a > $o] :
% 0.16/0.38 ( ( ( X @ Xx )
% 0.16/0.38 & ! [Xz0: a] :
% 0.16/0.38 ( ( X @ Xz0 )
% 0.16/0.38 => ( X @ ( cL @ Xz0 ) ) ) )
% 0.16/0.38 => ? [Xv: a] :
% 0.16/0.38 ( ( X @ Xv )
% 0.16/0.38 & ( ( cR @ Xv )
% 0.16/0.38 = Xy0 ) ) )
% 0.16/0.38 @ Xy ) )
% 0.16/0.38 | ( Xz = cZ )
% 0.16/0.38 | ? [Xx: a,Xy: a] :
% 0.16/0.38 ( ( Xz
% 0.16/0.38 = ( cP @ Xx @ Xy ) )
% 0.16/0.38 & ( cPSI
% 0.16/0.38 @ ^ [Xy0: a] :
% 0.16/0.38 ! [X: a > $o] :
% 0.16/0.38 ( ( ( X @ Xx )
% 0.16/0.38 & ! [Xz0: a] :
% 0.16/0.38 ( ( X @ Xz0 )
% 0.16/0.38 => ( X @ ( cL @ Xz0 ) ) ) )
% 0.16/0.38 => ? [Xv: a] :
% 0.16/0.38 ( ( X @ Xv )
% 0.16/0.38 & ( ( cR @ Xv )
% 0.16/0.38 = Xy0 ) ) )
% 0.16/0.38 @ Xy ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 ------------------------
% 1.65/1.33 ---- Embedded in THF ---
% 1.65/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.33 %%% Generated on Tue Feb 24 03:43:13 EST 2026
% 1.65/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.33 %%% Logic specification used:
% 1.65/1.33 %%% thf(spec, logic, $$dhol).
% 1.65/1.33
% 1.65/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.uDBwpsOxhs/DTF2DTF2178.p
% See solution above
% 1.65/1.33 ------------------------
% 1.65/1.34 ---- Cleaned THF ---
% 1.65/1.34 thf(a_type,type,
% 1.65/1.34 a: $tType ).
% 1.65/1.34
% 1.65/1.34 thf(cR,type,
% 1.65/1.34 cR: a > a ).
% 1.65/1.34
% 1.65/1.34 thf(cL,type,
% 1.65/1.34 cL: a > a ).
% 1.65/1.34
% 1.65/1.34 thf(cPSI,type,
% 1.65/1.34 cPSI: ( a > $o ) > a > $o ).
% 1.65/1.34
% 1.65/1.34 thf(cP,type,
% 1.65/1.34 cP: a > a > a ).
% 1.65/1.34
% 1.65/1.34 thf(cZ,type,
% 1.65/1.34 cZ: a ).
% 1.65/1.34
% 1.65/1.34 thf(cPHI,type,
% 1.65/1.34 cPHI: ( a > $o ) > a > $o ).
% 1.65/1.34
% 1.65/1.34 thf(cPU_X2310B_pme,conjecture,
% 1.65/1.34 ( ( ( ( cL @ cZ )
% 1.65/1.34 = cZ )
% 1.65/1.34 & ( ( cR @ cZ )
% 1.65/1.34 = cZ )
% 1.65/1.34 & ! [Xx: a,Xy: a] :
% 1.65/1.34 ( ( cL @ ( cP @ Xx @ Xy ) )
% 1.65/1.34 = Xx )
% 1.65/1.34 & ! [Xx: a,Xy: a] :
% 1.65/1.34 ( ( cR @ ( cP @ Xx @ Xy ) )
% 1.65/1.34 = Xy )
% 1.65/1.34 & ! [Xt: a] :
% 1.65/1.34 ( ( Xt != cZ )
% 1.65/1.34 <=> ( Xt
% 1.65/1.34 = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
% 1.65/1.34 & ! [X: a > $o] :
% 1.65/1.34 ( ? [Xt: a] :
% 1.65/1.34 ( ( X @ Xt )
% 1.65/1.34 & ! [Xu: a] :
% 1.65/1.34 ( ( X @ Xu )
% 1.65/1.34 => ( X @ ( cL @ Xu ) ) ) )
% 1.65/1.34 => ( X @ cZ ) )
% 1.65/1.34 & ! [X: a > $o,Xz: a] :
% 1.65/1.34 ( ( cPHI @ X @ Xz )
% 1.65/1.34 <=> ? [Xx: a] :
% 1.65/1.34 ( ! [Xx_14: a] :
% 1.65/1.34 ( ! [X0: a > $o] :
% 1.65/1.34 ( ( ( X0 @ Xx )
% 1.65/1.34 & ! [Xz0: a] :
% 1.65/1.34 ( ( X0 @ Xz0 )
% 1.65/1.34 => ( X0 @ ( cL @ Xz0 ) ) ) )
% 1.65/1.34 => ? [Xv: a] :
% 1.65/1.34 ( ( X0 @ Xv )
% 1.65/1.34 & ( ( cR @ Xv )
% 1.65/1.34 = Xx_14 ) ) )
% 1.65/1.34 => ( X @ Xx_14 ) )
% 1.65/1.34 & ( cPHI
% 1.65/1.34 @ ^ [Xy: a] :
% 1.65/1.34 ! [X0: a > $o] :
% 1.65/1.34 ( ( ( X0 @ Xx )
% 1.65/1.34 & ! [Xz0: a] :
% 1.65/1.34 ( ( X0 @ Xz0 )
% 1.65/1.34 => ( X0 @ ( cL @ Xz0 ) ) ) )
% 1.65/1.34 => ? [Xv: a] :
% 1.65/1.34 ( ( X0 @ Xv )
% 1.65/1.34 & ( ( cR @ Xv )
% 1.65/1.34 = Xy ) ) )
% 1.65/1.34 @ Xz ) ) )
% 1.65/1.34 & ! [X: a > $o,Xz: a] :
% 1.65/1.34 ( ( cPSI @ X @ Xz )
% 1.65/1.34 <=> ? [Xx: a] :
% 1.65/1.34 ( ! [Xx_15: a] :
% 1.65/1.34 ( ! [X0: a > $o] :
% 1.65/1.34 ( ( ( X0 @ Xx )
% 1.65/1.34 & ! [Xz0: a] :
% 1.65/1.34 ( ( X0 @ Xz0 )
% 1.65/1.34 => ( X0 @ ( cL @ Xz0 ) ) ) )
% 1.65/1.34 => ? [Xv: a] :
% 1.65/1.34 ( ( X0 @ Xv )
% 1.65/1.34 & ( ( cR @ Xv )
% 1.65/1.34 = Xx_15 ) ) )
% 1.65/1.34 => ( X @ Xx_15 ) )
% 1.65/1.34 & ( cPSI
% 1.65/1.34 @ ^ [Xy: a] :
% 1.65/1.34 ! [X0: a > $o] :
% 1.65/1.34 ( ( ( X0 @ Xx )
% 1.65/1.34 & ! [Xz0: a] :
% 1.65/1.34 ( ( X0 @ Xz0 )
% 1.65/1.34 => ( X0 @ ( cL @ Xz0 ) ) ) )
% 1.65/1.34 => ? [Xv: a] :
% 1.65/1.34 ( ( X0 @ Xv )
% 1.65/1.34 & ( ( cR @ Xv )
% 1.65/1.34 = Xy ) ) )
% 1.65/1.34 @ Xz ) ) ) )
% 1.65/1.34 => ( ( ^ [Xu: a] :
% 1.65/1.34 ( ( Xu = cZ )
% 1.65/1.34 | ? [Xx: a,Xy: a] :
% 1.65/1.34 ( ( Xu
% 1.65/1.34 = ( cP @ Xx @ Xy ) )
% 1.65/1.34 & ( ( cPHI
% 1.65/1.34 @ ^ [Xy0: a] :
% 1.65/1.34 ! [X: a > $o] :
% 1.65/1.34 ( ( ( X @ Xx )
% 1.65/1.34 & ! [Xz: a] :
% 1.65/1.34 ( ( X @ Xz )
% 1.65/1.34 => ( X @ ( cL @ Xz ) ) ) )
% 1.65/1.34 => ? [Xv: a] :
% 1.65/1.34 ( ( X @ Xv )
% 1.65/1.34 & ( ( cR @ Xv )
% 1.65/1.34 = Xy0 ) ) )
% 1.65/1.34 @ Xy )
% 1.65/1.34 | ( cPSI
% 1.65/1.34 @ ^ [Xy0: a] :
% 1.65/1.34 ! [X: a > $o] :
% 1.65/1.34 ( ( ( X @ Xx )
% 1.65/1.34 & ! [Xz: a] :
% 1.65/1.34 ( ( X @ Xz )
% 1.65/1.34 => ( X @ ( cL @ Xz ) ) ) )
% 1.65/1.34 => ? [Xv: a] :
% 1.65/1.34 ( ( X @ Xv )
% 1.65/1.34 & ( ( cR @ Xv )
% 1.65/1.34 = Xy0 ) ) )
% 1.65/1.34 @ Xy ) ) ) ) )
% 1.65/1.34 = ( ^ [Xz: a] :
% 1.65/1.34 ( ( Xz = cZ )
% 1.65/1.34 | ? [Xx: a,Xy: a] :
% 1.65/1.34 ( ( Xz
% 1.65/1.34 = ( cP @ Xx @ Xy ) )
% 1.65/1.34 & ( cPHI
% 1.65/1.34 @ ^ [Xy0: a] :
% 1.65/1.34 ! [X: a > $o] :
% 1.65/1.34 ( ( ( X @ Xx )
% 1.65/1.34 & ! [Xz0: a] :
% 1.65/1.34 ( ( X @ Xz0 )
% 1.65/1.34 => ( X @ ( cL @ Xz0 ) ) ) )
% 1.65/1.34 => ? [Xv: a] :
% 1.65/1.34 ( ( X @ Xv )
% 1.65/1.34 & ( ( cR @ Xv )
% 1.65/1.34 = Xy0 ) ) )
% 1.65/1.34 @ Xy ) )
% 1.65/1.34 | ( Xz = cZ )
% 1.65/1.34 | ? [Xx: a,Xy: a] :
% 1.65/1.34 ( ( Xz
% 1.65/1.34 = ( cP @ Xx @ Xy ) )
% 1.65/1.34 & ( cPSI
% 1.65/1.34 @ ^ [Xy0: a] :
% 1.65/1.34 ! [X: a > $o] :
% 1.65/1.34 ( ( ( X @ Xx )
% 1.65/1.34 & ! [Xz0: a] :
% 1.65/1.34 ( ( X @ Xz0 )
% 1.65/1.34 => ( X @ ( cL @ Xz0 ) ) ) )
% 1.65/1.34 => ? [Xv: a] :
% 1.65/1.34 ( ( X @ Xv )
% 1.65/1.34 & ( ( cR @ Xv )
% 1.65/1.34 = Xy0 ) ) )
% 1.65/1.34 @ Xy ) ) ) ) ) ) ).
% 1.65/1.34 ------------------------
% 1.65/1.36 % (2276)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2178 for (2999ds/183Mi)
% 1.65/1.36 % (2279)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2178 for (2999ds/2Mi)
% 1.65/1.36 % (2277)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_2178 for (2999ds/4Mi)
% 1.65/1.36 % (2280)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_2178 for (2999ds/2Mi)
% 1.65/1.36 % (2278)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_2178 for (2999ds/27Mi)
% 1.65/1.36 % (2281)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_2178 for (2999ds/275Mi)
% 1.65/1.36 % (2282)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2178 for (2999ds/18Mi)
% 1.65/1.36 % (2279)Instruction limit reached!
% 1.65/1.36 % (2279)------------------------------
% 1.65/1.36 % (2279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.36 % (2279)Termination reason: Unknown
% 1.65/1.36 % (2280)Instruction limit reached!
% 1.65/1.36 % (2280)------------------------------
% 1.65/1.36 % (2280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.36 % (2280)Termination reason: Unknown
% 1.65/1.36 % (2280)Termination phase: shuffling
% 1.65/1.36
% 1.65/1.36 % (2280)Memory used [KB]: 1023
% 1.65/1.36 % (2280)Time elapsed: 0.003 s
% 1.65/1.36 % (2280)Instructions burned: 4 (million)
% 1.65/1.36 % (2280)------------------------------
% 1.65/1.36 % (2280)------------------------------
% 1.65/1.36 % (2279)Termination phase: Property scanning
% 1.65/1.36
% 1.65/1.36 % (2279)Memory used [KB]: 1023
% 1.65/1.36 % (2279)Time elapsed: 0.003 s
% 1.65/1.36 % (2279)Instructions burned: 3 (million)
% 1.65/1.36 % (2279)------------------------------
% 1.65/1.36 % (2279)------------------------------
% 1.65/1.36 % (2277)Instruction limit reached!
% 1.65/1.36 % (2277)------------------------------
% 1.65/1.36 % (2277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.36 % (2277)Termination reason: Unknown
% 1.65/1.36 % (2277)Termination phase: Preprocessing 3
% 1.65/1.36
% 1.65/1.36 % (2277)Memory used [KB]: 1023
% 1.65/1.36 % (2277)Time elapsed: 0.004 s
% 1.65/1.36 % (2277)Instructions burned: 5 (million)
% 1.65/1.36 % (2277)------------------------------
% 1.65/1.36 % (2277)------------------------------
% 1.65/1.37 % (2282)Instruction limit reached!
% 1.65/1.37 % (2282)------------------------------
% 1.65/1.37 % (2282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.37 % (2282)Termination reason: Unknown
% 1.65/1.37 % (2282)Termination phase: Saturation
% 1.65/1.37
% 1.65/1.37 % (2282)Memory used [KB]: 5628
% 1.65/1.37 % (2282)Time elapsed: 0.010 s
% 1.65/1.37 % (2282)Instructions burned: 18 (million)
% 1.65/1.37 % (2282)------------------------------
% 1.65/1.37 % (2282)------------------------------
% 1.65/1.37 % (2278)Instruction limit reached!
% 1.65/1.37 % (2278)------------------------------
% 1.65/1.37 % (2278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.37 % (2278)Termination reason: Unknown
% 1.65/1.37 % (2278)Termination phase: Saturation
% 1.65/1.37
% 1.65/1.37 % (2278)Memory used [KB]: 5756
% 1.65/1.37 % (2278)Time elapsed: 0.016 s
% 1.65/1.37 % (2278)Instructions burned: 28 (million)
% 1.65/1.37 % (2278)------------------------------
% 1.65/1.37 % (2278)------------------------------
% 1.65/1.38 % (2283)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2178 for (2999ds/3Mi)
% 1.65/1.38 % (2284)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_2178 for (2999ds/37Mi)
% 1.65/1.38 % (2285)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_2178 for (2999ds/15Mi)
% 1.65/1.38 % (2283)Instruction limit reached!
% 1.65/1.38 % (2283)------------------------------
% 1.65/1.38 % (2283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.38 % (2283)Termination reason: Unknown
% 1.65/1.38 % (2283)Termination phase: Property scanning
% 1.65/1.38
% 1.65/1.38 % (2283)Memory used [KB]: 1023
% 1.65/1.38 % (2283)Time elapsed: 0.003 s
% 1.65/1.38 % (2283)Instructions burned: 4 (million)
% 1.65/1.38 % (2283)------------------------------
% 1.65/1.38 % (2283)------------------------------
% 1.65/1.38 % (2286)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_2178 for (2999ds/3Mi)
% 1.65/1.39 % (2285)Instruction limit reached!
% 1.65/1.39 % (2285)------------------------------
% 1.65/1.39 % (2285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.39 % (2285)Termination reason: Unknown
% 1.65/1.39 % (2285)Termination phase: Saturation
% 1.65/1.39
% 1.65/1.39 % (2285)Memory used [KB]: 5628
% 1.65/1.39 % (2285)Time elapsed: 0.009 s
% 1.65/1.39 % (2285)Instructions burned: 16 (million)
% 1.65/1.39 % (2285)------------------------------
% 1.65/1.39 % (2285)------------------------------
% 1.65/1.39 % (2286)Instruction limit reached!
% 1.65/1.39 % (2286)------------------------------
% 1.65/1.39 % (2286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.39 % (2286)Termination reason: Unknown
% 1.65/1.39 % (2286)Termination phase: Property scanning
% 1.65/1.39
% 1.65/1.39 % (2286)Memory used [KB]: 1023
% 1.65/1.39 % (2286)Time elapsed: 0.003 s
% 1.65/1.39 % (2286)Instructions burned: 4 (million)
% 1.65/1.39 % (2286)------------------------------
% 1.65/1.39 % (2286)------------------------------
% 1.65/1.39 % (2287)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_2178 for (2999ds/1041Mi)
% 1.65/1.39 % (2284)Instruction limit reached!
% 1.65/1.39 % (2284)------------------------------
% 1.65/1.39 % (2284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.39 % (2284)Termination reason: Unknown
% 1.65/1.39 % (2284)Termination phase: Saturation
% 1.65/1.39
% 1.65/1.39 % (2284)Memory used [KB]: 5628
% 1.65/1.39 % (2284)Time elapsed: 0.018 s
% 1.65/1.39 % (2284)Instructions burned: 38 (million)
% 1.65/1.39 % (2284)------------------------------
% 1.65/1.39 % (2284)------------------------------
% 1.65/1.39 % (2288)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2178 for (2999ds/7Mi)
% 1.72/1.40 % (2288)Instruction limit reached!
% 1.72/1.40 % (2288)------------------------------
% 1.72/1.40 % (2288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.40 % (2288)Termination reason: Unknown
% 1.72/1.40 % (2288)Termination phase: Property scanning
% 1.72/1.40
% 1.72/1.40 % (2288)Memory used [KB]: 1151
% 1.72/1.40 % (2288)Time elapsed: 0.005 s
% 1.72/1.40 % (2288)Instructions burned: 8 (million)
% 1.72/1.40 % (2288)------------------------------
% 1.72/1.40 % (2288)------------------------------
% 1.72/1.40 % (2289)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2178 for (2999ds/16Mi)
% 1.72/1.40 % (2290)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_2178 for (2999ds/3Mi)
% 1.72/1.40 % (2290)Instruction limit reached!
% 1.72/1.40 % (2290)------------------------------
% 1.72/1.40 % (2290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.40 % (2290)Termination reason: Unknown
% 1.72/1.40 % (2290)Termination phase: Property scanning
% 1.72/1.40
% 1.72/1.40 % (2290)Memory used [KB]: 1023
% 1.72/1.40 % (2290)Time elapsed: 0.003 s
% 1.72/1.40 % (2290)Instructions burned: 4 (million)
% 1.72/1.40 % (2290)------------------------------
% 1.72/1.40 % (2290)------------------------------
% 1.72/1.41 % (2289)Instruction limit reached!
% 1.72/1.41 % (2289)------------------------------
% 1.72/1.41 % (2289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.41 % (2289)Termination reason: Unknown
% 1.72/1.41 % (2289)Termination phase: Saturation
% 1.72/1.41
% 1.72/1.41 % (2289)Memory used [KB]: 5628
% 1.72/1.41 % (2289)Time elapsed: 0.009 s
% 1.72/1.41 % (2289)Instructions burned: 16 (million)
% 1.72/1.41 % (2289)------------------------------
% 1.72/1.41 % (2289)------------------------------
% 1.72/1.41 % (2291)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_2178 for (2999ds/3Mi)
% 1.72/1.41 % (2291)Instruction limit reached!
% 1.72/1.41 % (2291)------------------------------
% 1.72/1.41 % (2291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.41 % (2291)Termination reason: Unknown
% 1.72/1.41 % (2291)Termination phase: Property scanning
% 1.72/1.41
% 1.72/1.41 % (2291)Memory used [KB]: 1023
% 1.72/1.41 % (2291)Time elapsed: 0.003 s
% 1.72/1.41 % (2291)Instructions burned: 4 (million)
% 1.72/1.41 % (2291)------------------------------
% 1.72/1.41 % (2291)------------------------------
% 1.72/1.41 % (2292)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2178 for (2999ds/7Mi)
% 1.72/1.42 % (2292)Instruction limit reached!
% 1.72/1.42 % (2292)------------------------------
% 1.72/1.42 % (2292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (2292)Termination reason: Unknown
% 1.72/1.42 % (2292)Termination phase: Property scanning
% 1.72/1.42
% 1.72/1.42 % (2292)Memory used [KB]: 1151
% 1.72/1.42 % (2292)Time elapsed: 0.005 s
% 1.72/1.42 % (2292)Instructions burned: 8 (million)
% 1.72/1.42 % (2292)------------------------------
% 1.72/1.42 % (2292)------------------------------
% 1.72/1.42 % (2293)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2178 for (2999ds/3Mi)
% 1.72/1.42 % (2293)Instruction limit reached!
% 1.72/1.42 % (2293)------------------------------
% 1.72/1.42 % (2293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (2293)Termination reason: Unknown
% 1.72/1.42 % (2293)Termination phase: Property scanning
% 1.72/1.42
% 1.72/1.42 % (2293)Memory used [KB]: 1023
% 1.72/1.42 % (2293)Time elapsed: 0.003 s
% 1.72/1.42 % (2293)Instructions burned: 4 (million)
% 1.72/1.42 % (2293)------------------------------
% 1.72/1.42 % (2293)------------------------------
% 1.72/1.42 % (2294)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2178 for (2999ds/4Mi)
% 1.72/1.43 % (2294)Instruction limit reached!
% 1.72/1.43 % (2294)------------------------------
% 1.72/1.43 % (2294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.43 % (2294)Termination reason: Unknown
% 1.72/1.43 % (2294)Termination phase: Property scanning
% 1.72/1.43
% 1.72/1.43 % (2294)Memory used [KB]: 1023
% 1.72/1.43 % (2294)Time elapsed: 0.003 s
% 1.72/1.43 % (2294)Instructions burned: 4 (million)
% 1.72/1.43 % (2294)------------------------------
% 1.72/1.43 % (2294)------------------------------
% 1.72/1.43 % (2295)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2178 for (2999ds/18Mi)
% 1.72/1.43 % (2296)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2178 for (2999ds/710Mi)
% 1.72/1.44 % (2295)Instruction limit reached!
% 1.72/1.44 % (2295)------------------------------
% 1.72/1.44 % (2295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.44 % (2295)Termination reason: Unknown
% 1.72/1.44 % (2295)Termination phase: Saturation
% 1.72/1.44
% 1.72/1.44 % (2295)Memory used [KB]: 5628
% 1.72/1.44 % (2295)Time elapsed: 0.010 s
% 1.72/1.44 % (2295)Instructions burned: 18 (million)
% 1.72/1.44 % (2295)------------------------------
% 1.72/1.44 % (2295)------------------------------
% 1.72/1.44 % (2297)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2178 for (2999ds/6Mi)
% 1.72/1.44 % (2297)Instruction limit reached!
% 1.72/1.44 % (2297)------------------------------
% 1.72/1.44 % (2297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.44 % (2297)Termination reason: Unknown
% 1.72/1.44 % (2297)Termination phase: Preprocessing 3
% 1.72/1.44
% 1.72/1.44 % (2297)Memory used [KB]: 1151
% 1.72/1.44 % (2297)Time elapsed: 0.004 s
% 1.72/1.44 % (2297)Instructions burned: 6 (million)
% 1.72/1.44 % (2297)------------------------------
% 1.72/1.44 % (2297)------------------------------
% 1.72/1.44 % (2298)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_2178 for (2999ds/902Mi)
% 1.72/1.45 % (2276)Instruction limit reached!
% 1.72/1.45 % (2276)------------------------------
% 1.72/1.45 % (2276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (2276)Termination reason: Unknown
% 1.72/1.45 % (2276)Termination phase: Saturation
% 1.72/1.45
% 1.72/1.45 % (2276)Memory used [KB]: 6396
% 1.72/1.45 % (2276)Time elapsed: 0.091 s
% 1.72/1.45 % (2276)Instructions burned: 184 (million)
% 1.72/1.45 % (2276)------------------------------
% 1.72/1.45 % (2276)------------------------------
% 1.72/1.45 % (2299)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_2178 for (2999ds/21Mi)
% 1.72/1.45 % (2300)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2178 for (2999ds/5Mi)
% 1.72/1.46 % (2300)Instruction limit reached!
% 1.72/1.46 % (2300)------------------------------
% 1.72/1.46 % (2300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (2300)Termination reason: Unknown
% 1.72/1.46 % (2300)Termination phase: Property scanning
% 1.72/1.46
% 1.72/1.46 % (2300)Memory used [KB]: 1023
% 1.72/1.46 % (2300)Time elapsed: 0.004 s
% 1.72/1.46 % (2300)Instructions burned: 6 (million)
% 1.72/1.46 % (2300)------------------------------
% 1.72/1.46 % (2300)------------------------------
% 1.72/1.46 % (2299)Instruction limit reached!
% 1.72/1.46 % (2299)------------------------------
% 1.72/1.46 % (2299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (2299)Termination reason: Unknown
% 1.72/1.46 % (2299)Termination phase: Saturation
% 1.72/1.46
% 1.72/1.46 % (2299)Memory used [KB]: 5756
% 1.72/1.46 % (2299)Time elapsed: 0.012 s
% 1.72/1.46 % (2299)Instructions burned: 22 (million)
% 1.72/1.46 % (2299)------------------------------
% 1.72/1.46 % (2299)------------------------------
% 1.72/1.47 % (2301)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_2178 for (2999ds/6Mi)
% 1.72/1.47 % (2301)Instruction limit reached!
% 1.72/1.47 % (2301)------------------------------
% 1.72/1.47 % (2301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.47 % (2301)Termination reason: Unknown
% 1.72/1.47 % (2301)Termination phase: Property scanning
% 1.72/1.47
% 1.72/1.47 % (2301)Memory used [KB]: 1023
% 1.72/1.47 % (2301)Time elapsed: 0.004 s
% 1.72/1.47 % (2301)Instructions burned: 6 (million)
% 1.72/1.47 % (2301)------------------------------
% 1.72/1.47 % (2301)------------------------------
% 1.72/1.47 % (2302)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_2178 for (2998ds/377Mi)
% 1.72/1.48 % (2303)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_2178 for (2998ds/779Mi)
% 1.72/1.48 % (2304)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_2178 for (2998ds/19Mi)
% 1.72/1.49 % (2281)Instruction limit reached!
% 1.72/1.49 % (2281)------------------------------
% 1.72/1.49 % (2281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (2281)Termination reason: Unknown
% 1.72/1.49 % (2281)Termination phase: Saturation
% 1.72/1.49
% 1.72/1.49 % (2281)Memory used [KB]: 6140
% 1.72/1.49 % (2281)Time elapsed: 0.129 s
% 1.72/1.49 % (2281)Instructions burned: 275 (million)
% 1.72/1.49 % (2281)------------------------------
% 1.72/1.49 % (2281)------------------------------
% 1.72/1.49 % (2304)Instruction limit reached!
% 1.72/1.49 % (2304)------------------------------
% 1.72/1.49 % (2304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (2304)Termination reason: Unknown
% 1.72/1.49 % (2304)Termination phase: Saturation
% 1.72/1.49
% 1.72/1.49 % (2304)Memory used [KB]: 5628
% 1.72/1.49 % (2304)Time elapsed: 0.010 s
% 1.72/1.49 % (2304)Instructions burned: 19 (million)
% 1.72/1.49 % (2304)------------------------------
% 1.72/1.49 % (2304)------------------------------
% 1.72/1.50 % (2305)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_2178 for (2998ds/879Mi)
% 1.72/1.51 % (2306)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_2178 for (2998ds/17Mi)
% 1.72/1.52 % (2306)Instruction limit reached!
% 1.72/1.52 % (2306)------------------------------
% 1.72/1.52 % (2306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.52 % (2306)Termination reason: Unknown
% 1.72/1.52 % (2306)Termination phase: Saturation
% 1.72/1.52
% 1.72/1.52 % (2306)Memory used [KB]: 5628
% 1.72/1.52 % (2306)Time elapsed: 0.009 s
% 1.72/1.52 % (2306)Instructions burned: 17 (million)
% 1.72/1.52 % (2306)------------------------------
% 1.72/1.52 % (2306)------------------------------
% 1.72/1.53 % (2307)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2178 for (2998ds/3Mi)
% 1.72/1.53 % (2307)Instruction limit reached!
% 1.72/1.53 % (2307)------------------------------
% 1.72/1.53 % (2307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.53 % (2307)Termination reason: Unknown
% 1.72/1.53 % (2307)Termination phase: Property scanning
% 1.72/1.53
% 1.72/1.53 % (2307)Memory used [KB]: 1023
% 1.72/1.53 % (2307)Time elapsed: 0.003 s
% 1.72/1.53 % (2307)Instructions burned: 4 (million)
% 1.72/1.53 % (2307)------------------------------
% 1.72/1.53 % (2307)------------------------------
% 1.72/1.55 % (2308)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_2178 for (2998ds/30Mi)
% 1.72/1.56 % (2308)Instruction limit reached!
% 1.72/1.56 % (2308)------------------------------
% 1.72/1.56 % (2308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.56 % (2308)Termination reason: Unknown
% 1.72/1.56 % (2308)Termination phase: Saturation
% 1.72/1.56
% 1.72/1.56 % (2308)Memory used [KB]: 5756
% 1.72/1.56 % (2308)Time elapsed: 0.017 s
% 1.72/1.56 % (2308)Instructions burned: 31 (million)
% 1.72/1.56 % (2308)------------------------------
% 1.72/1.56 % (2308)------------------------------
% 1.72/1.58 % (2309)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_2178 for (2997ds/127Mi)
% 1.72/1.64 % (2309)Instruction limit reached!
% 1.72/1.64 % (2309)------------------------------
% 1.72/1.64 % (2309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.64 % (2309)Termination reason: Unknown
% 1.72/1.64 % (2309)Termination phase: Saturation
% 1.72/1.64
% 1.72/1.64 % (2309)Memory used [KB]: 6140
% 1.72/1.64 % (2309)Time elapsed: 0.087 s
% 1.72/1.64 % (2309)Instructions burned: 128 (million)
% 1.72/1.64 % (2309)------------------------------
% 1.72/1.64 % (2309)------------------------------
% 1.72/1.66 % (2302)Instruction limit reached!
% 1.72/1.66 % (2302)------------------------------
% 1.72/1.66 % (2302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.66 % (2302)Termination reason: Unknown
% 1.72/1.66 % (2302)Termination phase: Saturation
% 1.72/1.66
% 1.72/1.66 % (2302)Memory used [KB]: 6268
% 1.72/1.66 % (2302)Time elapsed: 0.186 s
% 1.72/1.66 % (2302)Instructions burned: 378 (million)
% 1.72/1.66 % (2302)------------------------------
% 1.72/1.66 % (2302)------------------------------
% 1.72/1.66 % (2310)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_2178 for (2997ds/100Mi)
% 1.72/1.67 % (2311)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_2178 for (2997ds/3Mi)
% 1.72/1.68 % (2311)Instruction limit reached!
% 1.72/1.68 % (2311)------------------------------
% 1.72/1.68 % (2311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.68 % (2311)Termination reason: Unknown
% 1.72/1.68 % (2311)Termination phase: Property scanning
% 1.72/1.68
% 1.72/1.68 % (2311)Memory used [KB]: 1023
% 1.72/1.68 % (2311)Time elapsed: 0.003 s
% 1.72/1.68 % (2311)Instructions burned: 4 (million)
% 1.72/1.68 % (2311)------------------------------
% 1.72/1.68 % (2311)------------------------------
% 1.72/1.69 % (2312)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_2178 for (2996ds/20Mi)
% 1.72/1.70 % (2312)Instruction limit reached!
% 1.72/1.70 % (2312)------------------------------
% 1.72/1.70 % (2312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.70 % (2312)Termination reason: Unknown
% 1.72/1.70 % (2312)Termination phase: Saturation
% 1.72/1.70
% 1.72/1.70 % (2312)Memory used [KB]: 5628
% 1.72/1.70 % (2312)Time elapsed: 0.011 s
% 1.72/1.70 % (2312)Instructions burned: 20 (million)
% 1.72/1.70 % (2312)------------------------------
% 1.72/1.70 % (2312)------------------------------
% 1.72/1.71 % (2310)Instruction limit reached!
% 1.72/1.71 % (2310)------------------------------
% 1.72/1.71 % (2310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.71 % (2310)Termination reason: Unknown
% 1.72/1.71 % (2310)Termination phase: Saturation
% 1.72/1.71
% 1.72/1.71 % (2310)Memory used [KB]: 6012
% 1.72/1.71 % (2310)Time elapsed: 0.071 s
% 1.72/1.71 % (2310)Instructions burned: 100 (million)
% 1.72/1.71 % (2310)------------------------------
% 1.72/1.71 % (2310)------------------------------
% 1.72/1.72 % (2313)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_2178 for (2996ds/86Mi)
% 1.72/1.72 % (2314)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_2178 for (2996ds/107Mi)
% 1.72/1.75 % (2313)Instruction limit reached!
% 1.72/1.75 % (2313)------------------------------
% 1.72/1.75 % (2313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.75 % (2313)Termination reason: Unknown
% 1.72/1.75 % (2313)Termination phase: Saturation
% 1.72/1.75
% 1.72/1.75 % (2313)Memory used [KB]: 6012
% 1.72/1.75 % (2313)Time elapsed: 0.035 s
% 1.72/1.75 % (2313)Instructions burned: 86 (million)
% 1.72/1.75 % (2313)------------------------------
% 1.72/1.75 % (2313)------------------------------
% 1.72/1.77 % (2315)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_2178 for (2995ds/39Mi)
% 1.72/1.77 % (2296)Instruction limit reached!
% 1.72/1.77 % (2296)------------------------------
% 1.72/1.77 % (2296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.77 % (2296)Termination reason: Unknown
% 1.72/1.77 % (2296)Termination phase: Saturation
% 1.72/1.77
% 1.72/1.77 % (2296)Memory used [KB]: 7547
% 1.72/1.77 % (2296)Time elapsed: 0.342 s
% 1.72/1.77 % (2296)Instructions burned: 710 (million)
% 1.72/1.77 % (2296)------------------------------
% 1.72/1.77 % (2296)------------------------------
% 1.72/1.78 % (2314)Instruction limit reached!
% 1.72/1.78 % (2314)------------------------------
% 1.72/1.78 % (2314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.78 % (2314)Termination reason: Unknown
% 1.72/1.78 % (2314)Termination phase: Saturation
% 1.72/1.78
% 1.72/1.78 % (2314)Memory used [KB]: 6140
% 1.72/1.78 % (2314)Time elapsed: 0.055 s
% 1.72/1.78 % (2314)Instructions burned: 108 (million)
% 1.72/1.78 % (2314)------------------------------
% 1.72/1.78 % (2314)------------------------------
% 1.72/1.78 % (2315)Instruction limit reached!
% 1.72/1.78 % (2315)------------------------------
% 1.72/1.78 % (2315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.78 % (2315)Termination reason: Unknown
% 1.72/1.78 % (2315)Termination phase: Saturation
% 1.72/1.78
% 1.72/1.78 % (2315)Memory used [KB]: 5628
% 1.72/1.78 % (2315)Time elapsed: 0.019 s
% 1.72/1.78 % (2315)Instructions burned: 39 (million)
% 1.72/1.78 % (2315)------------------------------
% 1.72/1.78 % (2315)------------------------------
% 1.72/1.79 % (2316)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_2178 for (2995ds/448Mi)
% 1.72/1.79 % (2317)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_2178 for (2995ds/46Mi)
% 1.72/1.80 % (2318)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_2178 for (2995ds/98Mi)
% 1.72/1.81 % (2317)Instruction limit reached!
% 1.72/1.81 % (2317)------------------------------
% 1.72/1.81 % (2317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.81 % (2317)Termination reason: Unknown
% 1.72/1.81 % (2317)Termination phase: Saturation
% 1.72/1.81
% 1.72/1.81 % (2317)Memory used [KB]: 6012
% 1.72/1.81 % (2317)Time elapsed: 0.024 s
% 1.72/1.81 % (2317)Instructions burned: 47 (million)
% 1.72/1.81 % (2317)------------------------------
% 1.72/1.81 % (2317)------------------------------
% 1.72/1.83 % (2319)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_2178 for (2995ds/507Mi)
% 1.72/1.84 % (2303)Instruction limit reached!
% 1.72/1.84 % (2303)------------------------------
% 1.72/1.84 % (2303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.84 % (2303)Termination reason: Unknown
% 1.72/1.84 % (2303)Termination phase: Saturation
% 1.72/1.84
% 1.72/1.84 % (2303)Memory used [KB]: 7291
% 1.72/1.84 % (2303)Time elapsed: 0.364 s
% 1.72/1.84 % (2303)Instructions burned: 779 (million)
% 1.72/1.84 % (2303)------------------------------
% 1.72/1.84 % (2303)------------------------------
% 1.72/1.84 % (2318)Instruction limit reached!
% 1.72/1.84 % (2318)------------------------------
% 1.72/1.84 % (2318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.84 % (2318)Termination reason: Unknown
% 1.72/1.84 % (2318)Termination phase: Saturation
% 1.72/1.84
% 1.72/1.84 % (2318)Memory used [KB]: 1279
% 1.72/1.84 % (2318)Time elapsed: 0.046 s
% 1.72/1.84 % (2318)Instructions burned: 98 (million)
% 1.72/1.84 % (2318)------------------------------
% 1.72/1.84 % (2318)------------------------------
% 1.72/1.85 % (2298)Instruction limit reached!
% 1.72/1.85 % (2298)------------------------------
% 1.72/1.85 % (2298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.85 % (2298)Termination reason: Unknown
% 1.72/1.85 % (2298)Termination phase: Saturation
% 1.72/1.85
% 1.72/1.85 % (2298)Memory used [KB]: 7036
% 1.72/1.85 % (2298)Time elapsed: 0.406 s
% 1.72/1.85 % (2298)Instructions burned: 903 (million)
% 1.72/1.85 % (2298)------------------------------
% 1.72/1.85 % (2298)------------------------------
% 1.72/1.86 % (2320)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_2178 for (2995ds/149Mi)
% 1.72/1.86 % (2321)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_2178 for (2995ds/39Mi)
% 1.72/1.86 % (2322)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_2178 for (2995ds/6Mi)
% 1.72/1.87 % (2322)Instruction limit reached!
% 1.72/1.87 % (2322)------------------------------
% 1.72/1.87 % (2322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.87 % (2322)Termination reason: Unknown
% 1.72/1.87 % (2322)Termination phase: Property scanning
% 1.72/1.87
% 1.72/1.87 % (2322)Memory used [KB]: 1023
% 1.72/1.87 % (2322)Time elapsed: 0.004 s
% 1.72/1.87 % (2322)Instructions burned: 6 (million)
% 1.72/1.87 % (2322)------------------------------
% 1.72/1.87 % (2322)------------------------------
% 1.72/1.88 % (2287)Instruction limit reached!
% 1.72/1.88 % (2287)------------------------------
% 1.72/1.88 % (2287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.88 % (2287)Termination reason: Unknown
% 1.72/1.88 % (2287)Termination phase: Saturation
% 1.72/1.88
% 1.72/1.88 % (2287)Memory used [KB]: 6908
% 1.72/1.88 % (2287)Time elapsed: 0.491 s
% 1.72/1.88 % (2287)Instructions burned: 1041 (million)
% 1.72/1.88 % (2287)------------------------------
% 1.72/1.88 % (2287)------------------------------
% 1.72/1.88 % (2321)Instruction limit reached!
% 1.72/1.88 % (2321)------------------------------
% 1.72/1.88 % (2321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.88 % (2321)Termination reason: Unknown
% 1.72/1.88 % (2321)Termination phase: Saturation
% 1.72/1.88
% 1.72/1.88 % (2321)Memory used [KB]: 5756
% 1.72/1.88 % (2321)Time elapsed: 0.021 s
% 1.72/1.88 % (2321)Instructions burned: 39 (million)
% 1.72/1.88 % (2321)------------------------------
% 1.72/1.88 % (2321)------------------------------
% 1.72/1.88 % (2323)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_2178 for (2994ds/1087Mi)
% 1.72/1.90 % (2324)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_2178 for (2994ds/47Mi)
% 1.72/1.90 % (2325)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_2178 for (2994ds/44Mi)
% 1.72/1.91 % (2305)Instruction limit reached!
% 1.72/1.91 % (2305)------------------------------
% 1.72/1.91 % (2305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.91 % (2305)Termination reason: Unknown
% 1.72/1.91 % (2305)Termination phase: Saturation
% 1.72/1.91
% 1.72/1.91 % (2305)Memory used [KB]: 7419
% 1.72/1.91 % (2305)Time elapsed: 0.433 s
% 1.72/1.91 % (2305)Instructions burned: 879 (million)
% 1.72/1.91 % (2305)------------------------------
% 1.72/1.91 % (2305)------------------------------
% 1.72/1.92 % (2325)Instruction limit reached!
% 1.72/1.92 % (2325)------------------------------
% 1.72/1.92 % (2325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.92 % (2325)Termination reason: Unknown
% 1.72/1.92 % (2325)Termination phase: Saturation
% 1.72/1.92
% 1.72/1.92 % (2325)Memory used [KB]: 1279
% 1.72/1.92 % (2325)Time elapsed: 0.022 s
% 1.72/1.92 % (2325)Instructions burned: 44 (million)
% 1.72/1.92 % (2325)------------------------------
% 1.72/1.92 % (2325)------------------------------
% 1.72/1.92 % (2324)Instruction limit reached!
% 1.72/1.92 % (2324)------------------------------
% 1.72/1.92 % (2324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.92 % (2324)Termination reason: Unknown
% 1.72/1.92 % (2324)Termination phase: Saturation
% 1.72/1.92
% 1.72/1.92 % (2324)Memory used [KB]: 5884
% 1.72/1.92 % (2324)Time elapsed: 0.026 s
% 1.72/1.92 % (2324)Instructions burned: 48 (million)
% 1.72/1.92 % (2324)------------------------------
% 1.72/1.92 % (2324)------------------------------
% 1.72/1.93 % (2320)Instruction limit reached!
% 1.72/1.93 % (2320)------------------------------
% 1.72/1.93 % (2320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.93 % (2320)Termination reason: Unknown
% 1.72/1.93 % (2326)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_2178 for (2994ds/432Mi)
% 1.72/1.93 % (2320)Termination phase: Saturation
% 1.72/1.93
% 1.72/1.93 % (2320)Memory used [KB]: 6012
% 1.72/1.93 % (2320)Time elapsed: 0.075 s
% 1.72/1.93 % (2320)Instructions burned: 150 (million)
% 1.72/1.93 % (2320)------------------------------
% 1.72/1.93 % (2320)------------------------------
% 1.72/1.93 % (2327)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_2178 for (2994ds/62Mi)
% 1.72/1.94 % (2328)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_2178 for (2994ds/31Mi)
% 1.72/1.95 % (2329)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_2178 for (2994ds/96Mi)
% 1.72/1.95 % (2328)Instruction limit reached!
% 1.72/1.95 % (2328)------------------------------
% 1.72/1.95 % (2328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.95 % (2328)Termination reason: Unknown
% 1.72/1.95 % (2328)Termination phase: Saturation
% 1.72/1.95
% 1.72/1.95 % (2328)Memory used [KB]: 5756
% 1.72/1.95 % (2328)Time elapsed: 0.017 s
% 1.72/1.95 % (2328)Instructions burned: 32 (million)
% 1.72/1.95 % (2328)------------------------------
% 1.72/1.95 % (2328)------------------------------
% 1.72/1.96 % (2327)Instruction limit reached!
% 1.72/1.96 % (2327)------------------------------
% 1.72/1.96 % (2327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.96 % (2327)Termination reason: Unknown
% 1.72/1.96 % (2327)Termination phase: Saturation
% 1.72/1.96
% 1.72/1.96 % (2327)Memory used [KB]: 5756
% 1.72/1.96 % (2327)Time elapsed: 0.029 s
% 1.72/1.96 % (2327)Instructions burned: 62 (million)
% 1.72/1.96 % (2327)------------------------------
% 1.72/1.96 % (2327)------------------------------
% 1.72/1.97 % (2330)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_2178 for (2994ds/453Mi)
% 1.72/1.98 % (2331)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_2178 for (2993ds/71Mi)
% 1.72/1.99 % (2329)Instruction limit reached!
% 1.72/1.99 % (2329)------------------------------
% 1.72/1.99 % (2329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.99 % (2329)Termination reason: Unknown
% 1.72/1.99 % (2329)Termination phase: Saturation
% 1.72/1.99
% 1.72/1.99 % (2329)Memory used [KB]: 5884
% 1.72/1.99 % (2329)Time elapsed: 0.050 s
% 1.72/1.99 % (2329)Instructions burned: 97 (million)
% 1.72/1.99 % (2329)------------------------------
% 1.72/1.99 % (2329)------------------------------
% 1.72/2.00 % (2316)Instruction limit reached!
% 1.72/2.00 % (2316)------------------------------
% 1.72/2.00 % (2316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/2.00 % (2316)Termination reason: Unknown
% 1.72/2.00 % (2316)Termination phase: Saturation
% 1.72/2.00
% 1.72/2.00 % (2316)Memory used [KB]: 6524
% 1.72/2.00 % (2316)Time elapsed: 0.207 s
% 1.72/2.00 % (2316)Instructions burned: 449 (million)
% 1.72/2.00 % (2316)------------------------------
% 1.72/2.00 % (2316)------------------------------
% 1.72/2.01 % (2332)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_2178 for (2993ds/83Mi)
% 1.72/2.01 % (2333)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_2178 for (2993ds/11Mi)
% 1.72/2.01 % (2331)Instruction limit reached!
% 1.72/2.01 % (2331)------------------------------
% 1.72/2.01 % (2331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/2.01 % (2331)Termination reason: Unknown
% 1.72/2.01 % (2331)Termination phase: Saturation
% 1.72/2.01
% 1.72/2.01 % (2331)Memory used [KB]: 6012
% 1.72/2.01 % (2331)Time elapsed: 0.038 s
% 1.72/2.01 % (2331)Instructions burned: 71 (million)
% 1.72/2.01 % (2331)------------------------------
% 1.72/2.01 % (2331)------------------------------
% 1.72/2.02 % (2333)Instruction limit reached!
% 1.72/2.02 % (2333)------------------------------
% 1.72/2.02 % (2333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/2.02 % (2333)Termination reason: Unknown
% 1.72/2.02 % (2333)Termination phase: Saturation
% 1.72/2.02
% 1.72/2.02 % (2333)Memory used [KB]: 5628
% 1.72/2.02 % (2333)Time elapsed: 0.007 s
% 1.72/2.02 % (2333)Instructions burned: 12 (million)
% 1.72/2.02 % (2333)------------------------------
% 1.72/2.02 % (2333)------------------------------
% 6.41/2.03 % (2334)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_2178 for (2993ds/41Mi)
% 6.41/2.03 % (2335)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2178 for (2993ds/6Mi)
% 6.41/2.04 % (2335)Instruction limit reached!
% 6.41/2.04 % (2335)------------------------------
% 6.41/2.04 % (2335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.04 % (2335)Termination reason: Unknown
% 6.41/2.04 % (2335)Termination phase: Property scanning
% 6.41/2.04
% 6.41/2.04 % (2335)Memory used [KB]: 1151
% 6.41/2.04 % (2335)Time elapsed: 0.005 s
% 6.41/2.04 % (2335)Instructions burned: 8 (million)
% 6.41/2.04 % (2335)------------------------------
% 6.41/2.04 % (2335)------------------------------
% 6.41/2.05 % (2334)Instruction limit reached!
% 6.41/2.05 % (2334)------------------------------
% 6.41/2.05 % (2334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.05 % (2334)Termination reason: Unknown
% 6.41/2.05 % (2334)Termination phase: Saturation
% 6.41/2.05
% 6.41/2.05 % (2334)Memory used [KB]: 5628
% 6.41/2.05 % (2334)Time elapsed: 0.020 s
% 6.41/2.05 % (2334)Instructions burned: 43 (million)
% 6.41/2.05 % (2334)------------------------------
% 6.41/2.05 % (2334)------------------------------
% 6.41/2.05 % (2332)Instruction limit reached!
% 6.41/2.05 % (2332)------------------------------
% 6.41/2.05 % (2332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.05 % (2332)Termination reason: Unknown
% 6.41/2.05 % (2332)Termination phase: Saturation
% 6.41/2.05
% 6.41/2.05 % (2332)Memory used [KB]: 5884
% 6.41/2.05 % (2332)Time elapsed: 0.041 s
% 6.41/2.05 % (2332)Instructions burned: 83 (million)
% 6.41/2.05 % (2332)------------------------------
% 6.41/2.05 % (2332)------------------------------
% 6.41/2.05 % (2336)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_2178 for (2993ds/150Mi)
% 6.41/2.06 % (2319)Instruction limit reached!
% 6.41/2.06 % (2319)------------------------------
% 6.41/2.06 % (2319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.06 % (2319)Termination reason: Unknown
% 6.41/2.06 % (2319)Termination phase: Saturation
% 6.41/2.06
% 6.41/2.06 % (2319)Memory used [KB]: 6396
% 6.41/2.06 % (2319)Time elapsed: 0.234 s
% 6.41/2.06 % (2319)Instructions burned: 507 (million)
% 6.41/2.06 % (2319)------------------------------
% 6.41/2.06 % (2319)------------------------------
% 6.41/2.06 % (2337)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_2178 for (2993ds/343Mi)
% 6.41/2.07 % (2338)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_2178 for (2993ds/109Mi)
% 6.41/2.08 % (2339)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_2178 for (2992ds/253Mi)
% 6.41/2.12 % (2338)Instruction limit reached!
% 6.41/2.12 % (2338)------------------------------
% 6.41/2.12 % (2338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.12 % (2338)Termination reason: Unknown
% 6.41/2.12 % (2338)Termination phase: Saturation
% 6.41/2.12
% 6.41/2.12 % (2338)Memory used [KB]: 6012
% 6.41/2.12 % (2338)Time elapsed: 0.054 s
% 6.41/2.12 % (2338)Instructions burned: 110 (million)
% 6.41/2.12 % (2338)------------------------------
% 6.41/2.12 % (2338)------------------------------
% 6.41/2.12 % (2326)Instruction limit reached!
% 6.41/2.12 % (2326)------------------------------
% 6.41/2.12 % (2326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.12 % (2326)Termination reason: Unknown
% 6.41/2.12 % (2326)Termination phase: Saturation
% 6.41/2.12
% 6.41/2.12 % (2326)Memory used [KB]: 2046
% 6.41/2.12 % (2326)Time elapsed: 0.191 s
% 6.41/2.12 % (2326)Instructions burned: 432 (million)
% 6.41/2.12 % (2326)------------------------------
% 6.41/2.12 % (2326)------------------------------
% 6.92/2.13 % (2336)Instruction limit reached!
% 6.92/2.13 % (2336)------------------------------
% 6.92/2.13 % (2336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.13 % (2336)Termination reason: Unknown
% 6.92/2.13 % (2336)Termination phase: Saturation
% 6.92/2.13
% 6.92/2.13 % (2336)Memory used [KB]: 6396
% 6.92/2.13 % (2336)Time elapsed: 0.075 s
% 6.92/2.13 % (2336)Instructions burned: 151 (million)
% 6.92/2.13 % (2336)------------------------------
% 6.92/2.13 % (2336)------------------------------
% 6.92/2.13 % (2340)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_2178 for (2992ds/140Mi)
% 6.92/2.14 % (2341)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_2178 for (2992ds/614Mi)
% 6.92/2.14 % (2342)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_2178 for (2992ds/202Mi)
% 6.92/2.16 % (2340)Refutation not found, incomplete strategy
% 6.92/2.16 % (2340)------------------------------
% 6.92/2.16 % (2340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.16 % (2340)Termination reason: Refutation not found, incomplete strategy
% 6.92/2.16
% 6.92/2.16
% 6.92/2.16 % (2340)Memory used [KB]: 5884
% 6.92/2.16 % (2340)Time elapsed: 0.045 s
% 6.92/2.16 % (2340)Instructions burned: 44 (million)
% 6.92/2.16 % (2340)------------------------------
% 6.92/2.16 % (2340)------------------------------
% 6.92/2.17 % (2343)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_2178 for (2991ds/339Mi)
% 6.92/2.18 % (2330)Instruction limit reached!
% 6.92/2.18 % (2330)------------------------------
% 6.92/2.18 % (2330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.18 % (2330)Termination reason: Unknown
% 6.92/2.18 % (2330)Termination phase: Saturation
% 6.92/2.18
% 6.92/2.18 % (2330)Memory used [KB]: 6268
% 6.92/2.18 % (2330)Time elapsed: 0.211 s
% 6.92/2.18 % (2330)Instructions burned: 453 (million)
% 6.92/2.18 % (2330)------------------------------
% 6.92/2.18 % (2330)------------------------------
% 6.92/2.19 % (2344)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_2178 for (2991ds/283Mi)
% 7.18/2.20 % (2339)Instruction limit reached!
% 7.18/2.20 % (2339)------------------------------
% 7.18/2.20 % (2339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.20 % (2339)Termination reason: Unknown
% 7.18/2.20 % (2339)Termination phase: Saturation
% 7.18/2.20
% 7.18/2.20 % (2339)Memory used [KB]: 6268
% 7.18/2.20 % (2339)Time elapsed: 0.121 s
% 7.18/2.20 % (2339)Instructions burned: 253 (million)
% 7.18/2.20 % (2339)------------------------------
% 7.18/2.20 % (2339)------------------------------
% 7.18/2.21 % (2345)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_2178 for (2991ds/134Mi)
% 7.18/2.23 % (2337)Instruction limit reached!
% 7.18/2.23 % (2337)------------------------------
% 7.18/2.23 % (2337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.23 % (2337)Termination reason: Unknown
% 7.18/2.23 % (2337)Termination phase: Saturation
% 7.18/2.23
% 7.18/2.23 % (2337)Memory used [KB]: 6780
% 7.18/2.23 % (2337)Time elapsed: 0.165 s
% 7.18/2.23 % (2337)Instructions burned: 344 (million)
% 7.18/2.23 % (2337)------------------------------
% 7.18/2.23 % (2337)------------------------------
% 7.18/2.24 % (2342)Instruction limit reached!
% 7.18/2.24 % (2342)------------------------------
% 7.18/2.24 % (2342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.24 % (2342)Termination reason: Unknown
% 7.18/2.24 % (2342)Termination phase: Saturation
% 7.18/2.24
% 7.18/2.24 % (2342)Memory used [KB]: 6524
% 7.18/2.24 % (2342)Time elapsed: 0.119 s
% 7.18/2.24 % (2342)Instructions burned: 202 (million)
% 7.18/2.24 % (2342)------------------------------
% 7.18/2.24 % (2342)------------------------------
% 7.18/2.24 % (2346)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_2178 for (2991ds/298Mi)
% 7.18/2.25 % (2347)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_2178 for (2991ds/192Mi)
% 7.18/2.28 % (2345)Instruction limit reached!
% 7.18/2.28 % (2345)------------------------------
% 7.18/2.28 % (2345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.28 % (2345)Termination reason: Unknown
% 7.18/2.28 % (2345)Termination phase: Saturation
% 7.18/2.28
% 7.18/2.28 % (2345)Memory used [KB]: 6396
% 7.18/2.28 % (2345)Time elapsed: 0.067 s
% 7.18/2.28 % (2345)Instructions burned: 135 (million)
% 7.18/2.28 % (2345)------------------------------
% 7.18/2.28 % (2345)------------------------------
% 7.79/2.30 % (2348)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_2178 for (2990ds/258Mi)
% 7.79/2.32 % (2344)Instruction limit reached!
% 7.79/2.32 % (2344)------------------------------
% 7.79/2.32 % (2344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.32 % (2344)Termination reason: Unknown
% 7.79/2.32 % (2344)Termination phase: Saturation
% 7.79/2.32
% 7.79/2.32 % (2344)Memory used [KB]: 7547
% 7.79/2.32 % (2344)Time elapsed: 0.129 s
% 7.79/2.32 % (2344)Instructions burned: 283 (million)
% 7.79/2.32 % (2344)------------------------------
% 7.79/2.32 % (2344)------------------------------
% 7.79/2.34 % (2349)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_2178 for (2990ds/90Mi)
% 7.79/2.34 % (2343)Instruction limit reached!
% 7.79/2.34 % (2343)------------------------------
% 7.79/2.34 % (2343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.34 % (2343)Termination reason: Unknown
% 7.79/2.34 % (2343)Termination phase: Saturation
% 7.79/2.34
% 7.79/2.34 % (2343)Memory used [KB]: 6268
% 7.79/2.34 % (2343)Time elapsed: 0.165 s
% 7.79/2.34 % (2343)Instructions burned: 340 (million)
% 7.79/2.34 % (2343)------------------------------
% 7.79/2.34 % (2343)------------------------------
% 7.79/2.35 % (2347)Instruction limit reached!
% 7.79/2.35 % (2347)------------------------------
% 7.79/2.35 % (2347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.35 % (2347)Termination reason: Unknown
% 7.79/2.35 % (2347)Termination phase: Saturation
% 7.79/2.35
% 7.79/2.35 % (2347)Memory used [KB]: 6524
% 7.79/2.35 % (2347)Time elapsed: 0.093 s
% 7.79/2.35 % (2347)Instructions burned: 192 (million)
% 7.79/2.35 % (2347)------------------------------
% 7.79/2.35 % (2347)------------------------------
% 7.79/2.35 % (2350)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_2178 for (2990ds/231Mi)
% 7.79/2.36 % (2351)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_2178 for (2989ds/458Mi)
% 7.79/2.38 % (2349)Instruction limit reached!
% 7.79/2.38 % (2349)------------------------------
% 7.79/2.38 % (2349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.38 % (2349)Termination reason: Unknown
% 7.79/2.38 % (2349)Termination phase: Saturation
% 7.79/2.38
% 7.79/2.38 % (2349)Memory used [KB]: 6012
% 7.79/2.38 % (2349)Time elapsed: 0.048 s
% 7.79/2.38 % (2349)Instructions burned: 91 (million)
% 7.79/2.38 % (2349)------------------------------
% 7.79/2.38 % (2349)------------------------------
% 7.79/2.39 % (2346)Instruction limit reached!
% 7.79/2.39 % (2346)------------------------------
% 7.79/2.39 % (2346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.39 % (2346)Termination reason: Unknown
% 7.79/2.39 % (2346)Termination phase: Saturation
% 7.79/2.39
% 7.79/2.39 % (2346)Memory used [KB]: 6268
% 7.79/2.39 % (2346)Time elapsed: 0.146 s
% 7.79/2.39 % (2346)Instructions burned: 299 (million)
% 7.79/2.39 % (2346)------------------------------
% 7.79/2.39 % (2346)------------------------------
% 8.54/2.40 % (2323)Instruction limit reached!
% 8.54/2.40 % (2323)------------------------------
% 8.54/2.40 % (2323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.40 % (2323)Termination reason: Unknown
% 8.54/2.40 % (2323)Termination phase: Saturation
% 8.54/2.40
% 8.54/2.40 % (2323)Memory used [KB]: 7675
% 8.54/2.40 % (2323)Time elapsed: 0.519 s
% 8.54/2.40 % (2323)Instructions burned: 1087 (million)
% 8.54/2.40 % (2323)------------------------------
% 8.54/2.40 % (2323)------------------------------
% 8.54/2.40 % (2352)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_2178 for (2989ds/31Mi)
% 8.54/2.40 % (2353)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_2178 for (2989ds/297Mi)
% 8.54/2.42 % (2352)Instruction limit reached!
% 8.54/2.42 % (2352)------------------------------
% 8.54/2.42 % (2352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.42 % (2352)Termination reason: Unknown
% 8.54/2.42 % (2352)Termination phase: Saturation
% 8.54/2.42
% 8.54/2.42 % (2352)Memory used [KB]: 5756
% 8.54/2.42 % (2352)Time elapsed: 0.017 s
% 8.54/2.42 % (2352)Instructions burned: 31 (million)
% 8.54/2.42 % (2352)------------------------------
% 8.54/2.42 % (2352)------------------------------
% 8.54/2.42 % (2354)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_2178 for (2989ds/987Mi)
% 8.54/2.42 % (2341)Instruction limit reached!
% 8.54/2.42 % (2341)------------------------------
% 8.54/2.42 % (2341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.42 % (2341)Termination reason: Unknown
% 8.54/2.42 % (2341)Termination phase: Saturation
% 8.54/2.42
% 8.54/2.42 % (2341)Memory used [KB]: 7036
% 8.54/2.42 % (2341)Time elapsed: 0.307 s
% 8.54/2.42 % (2341)Instructions burned: 615 (million)
% 8.54/2.42 % (2341)------------------------------
% 8.54/2.42 % (2341)------------------------------
% 8.54/2.42 % (2348)Instruction limit reached!
% 8.54/2.42 % (2348)------------------------------
% 8.54/2.42 % (2348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.42 % (2348)Termination reason: Unknown
% 8.54/2.42 % (2348)Termination phase: Saturation
% 8.54/2.42
% 8.54/2.42 % (2348)Memory used [KB]: 6524
% 8.54/2.42 % (2348)Time elapsed: 0.127 s
% 8.54/2.42 % (2348)Instructions burned: 259 (million)
% 8.54/2.42 % (2348)------------------------------
% 8.54/2.42 % (2348)------------------------------
% 8.54/2.43 % (2355)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_2178 for (2989ds/182Mi)
% 8.54/2.44 % (2356)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_2178 for (2989ds/182Mi)
% 8.54/2.44 % (2357)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_2178 for (2989ds/154Mi)
% 8.54/2.48 % (2350)Instruction limit reached!
% 8.54/2.48 % (2350)------------------------------
% 8.54/2.48 % (2350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.48 % (2350)Termination reason: Unknown
% 8.54/2.48 % (2350)Termination phase: Saturation
% 8.54/2.48
% 8.54/2.48 % (2350)Memory used [KB]: 6780
% 8.54/2.48 % (2350)Time elapsed: 0.127 s
% 8.54/2.48 % (2350)Instructions burned: 231 (million)
% 8.54/2.48 % (2350)------------------------------
% 8.54/2.48 % (2350)------------------------------
% 8.54/2.50 % (2358)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_2178 for (2988ds/79Mi)
% 9.16/2.51 % (2357)Instruction limit reached!
% 9.16/2.51 % (2357)------------------------------
% 9.16/2.51 % (2357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.51 % (2357)Termination reason: Unknown
% 9.16/2.51 % (2357)Termination phase: Saturation
% 9.16/2.51
% 9.16/2.51 % (2357)Memory used [KB]: 6140
% 9.16/2.51 % (2357)Time elapsed: 0.074 s
% 9.16/2.51 % (2357)Instructions burned: 154 (million)
% 9.16/2.51 % (2357)------------------------------
% 9.16/2.51 % (2357)------------------------------
% 9.16/2.52 % (2355)Instruction limit reached!
% 9.16/2.52 % (2355)------------------------------
% 9.16/2.52 % (2355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.52 % (2355)Termination reason: Unknown
% 9.16/2.52 % (2355)Termination phase: Saturation
% 9.16/2.52
% 9.16/2.52 % (2355)Memory used [KB]: 6396
% 9.16/2.52 % (2355)Time elapsed: 0.091 s
% 9.16/2.52 % (2355)Instructions burned: 183 (million)
% 9.16/2.52 % (2355)------------------------------
% 9.16/2.52 % (2355)------------------------------
% 9.16/2.52 % (2356)Instruction limit reached!
% 9.16/2.52 % (2356)------------------------------
% 9.16/2.52 % (2356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.52 % (2356)Termination reason: Unknown
% 9.16/2.52 % (2356)Termination phase: Saturation
% 9.16/2.52
% 9.16/2.52 % (2356)Memory used [KB]: 6012
% 9.16/2.52 % (2356)Time elapsed: 0.088 s
% 9.16/2.52 % (2356)Instructions burned: 182 (million)
% 9.16/2.52 % (2356)------------------------------
% 9.16/2.52 % (2356)------------------------------
% 9.16/2.53 % (2359)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_2178 for (2988ds/216Mi)
% 9.16/2.53 % (2358)Instruction limit reached!
% 9.16/2.53 % (2358)------------------------------
% 9.16/2.53 % (2358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.53 % (2358)Termination reason: Unknown
% 9.16/2.53 % (2358)Termination phase: Saturation
% 9.16/2.53
% 9.16/2.53 % (2358)Memory used [KB]: 5884
% 9.16/2.53 % (2358)Time elapsed: 0.039 s
% 9.16/2.53 % (2358)Instructions burned: 80 (million)
% 9.16/2.53 % (2358)------------------------------
% 9.16/2.53 % (2358)------------------------------
% 9.16/2.54 % (2360)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_2178 for (2988ds/114Mi)
% 9.16/2.54 % (2361)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_2178 for (2988ds/922Mi)
% 9.16/2.54 % (2353)Instruction limit reached!
% 9.16/2.54 % (2353)------------------------------
% 9.16/2.54 % (2353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.54 % (2353)Termination reason: Unknown
% 9.16/2.54 % (2353)Termination phase: Saturation
% 9.16/2.54
% 9.16/2.54 % (2353)Memory used [KB]: 6012
% 9.16/2.54 % (2353)Time elapsed: 0.136 s
% 9.16/2.54 % (2353)Instructions burned: 297 (million)
% 9.16/2.54 % (2353)------------------------------
% 9.16/2.54 % (2353)------------------------------
% 9.16/2.55 % (2362)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_2178 for (2988ds/182Mi)
% 9.16/2.55 % (2363)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_2178 for (2988ds/164Mi)
% 9.16/2.58 % (2351)Instruction limit reached!
% 9.16/2.58 % (2351)------------------------------
% 9.16/2.58 % (2351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.58 % (2351)Termination reason: Unknown
% 9.16/2.58 % (2351)Termination phase: Saturation
% 9.16/2.58
% 9.16/2.58 % (2351)Memory used [KB]: 6780
% 9.16/2.58 % (2351)Time elapsed: 0.220 s
% 9.16/2.58 % (2351)Instructions burned: 458 (million)
% 9.16/2.58 % (2351)------------------------------
% 9.16/2.58 % (2351)------------------------------
% 9.16/2.59 % (2360)Instruction limit reached!
% 9.16/2.59 % (2360)------------------------------
% 9.16/2.59 % (2360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.59 % (2360)Termination reason: Unknown
% 9.16/2.59 % (2360)Termination phase: Saturation
% 9.16/2.59
% 9.16/2.59 % (2360)Memory used [KB]: 6268
% 9.16/2.59 % (2360)Time elapsed: 0.055 s
% 9.16/2.59 % (2360)Instructions burned: 114 (million)
% 9.16/2.59 % (2360)------------------------------
% 9.16/2.59 % (2360)------------------------------
% 9.97/2.60 % (2364)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_2178 for (2987ds/50Mi)
% 9.97/2.61 % (2365)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_2178 for (2987ds/368Mi)
% 9.97/2.62 % (2359)Instruction limit reached!
% 9.97/2.62 % (2359)------------------------------
% 9.97/2.62 % (2359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/2.62 % (2359)Termination reason: Unknown
% 9.97/2.62 % (2359)Termination phase: Saturation
% 9.97/2.62
% 9.97/2.62 % (2359)Memory used [KB]: 5756
% 9.97/2.62 % (2359)Time elapsed: 0.091 s
% 9.97/2.62 % (2359)Instructions burned: 216 (million)
% 9.97/2.62 % (2359)------------------------------
% 9.97/2.62 % (2359)------------------------------
% 9.97/2.62 % (2364)Instruction limit reached!
% 9.97/2.62 % (2364)------------------------------
% 9.97/2.62 % (2364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/2.62 % (2364)Termination reason: Unknown
% 9.97/2.62 % (2364)Termination phase: Saturation
% 9.97/2.62
% 9.97/2.62 % (2364)Memory used [KB]: 10234
% 9.97/2.62 % (2364)Time elapsed: 0.026 s
% 9.97/2.62 % (2364)Instructions burned: 50 (million)
% 9.97/2.62 % (2364)------------------------------
% 9.97/2.62 % (2364)------------------------------
% 9.97/2.63 % (2362)Instruction limit reached!
% 9.97/2.63 % (2362)------------------------------
% 9.97/2.63 % (2362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/2.63 % (2362)Termination reason: Unknown
% 9.97/2.63 % (2362)Termination phase: Saturation
% 9.97/2.63
% 9.97/2.63 % (2362)Memory used [KB]: 5756
% 9.97/2.63 % (2362)Time elapsed: 0.079 s
% 9.97/2.63 % (2362)Instructions burned: 183 (million)
% 9.97/2.63 % (2362)------------------------------
% 9.97/2.63 % (2362)------------------------------
% 9.97/2.63 % (2366)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_2178 for (2987ds/1021Mi)
% 9.97/2.64 % (2363)Instruction limit reached!
% 9.97/2.64 % (2363)------------------------------
% 9.97/2.64 % (2363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/2.64 % (2363)Termination reason: Unknown
% 9.97/2.64 % (2363)Termination phase: Saturation
% 9.97/2.64
% 9.97/2.64 % (2363)Memory used [KB]: 1407
% 9.97/2.64 % (2363)Time elapsed: 0.083 s
% 9.97/2.64 % (2363)Instructions burned: 165 (million)
% 9.97/2.64 % (2363)------------------------------
% 9.97/2.64 % (2363)------------------------------
% 9.97/2.64 % (2367)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_2178 for (2987ds/267Mi)
% 9.97/2.64 % (2368)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_2178 for (2987ds/204Mi)
% 9.97/2.65 % (2369)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_2178 for (2987ds/26Mi)
% 9.97/2.66 % (2369)Instruction limit reached!
% 9.97/2.66 % (2369)------------------------------
% 9.97/2.66 % (2369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/2.66 % (2369)Termination reason: Unknown
% 9.97/2.66 % (2369)Termination phase: Saturation
% 9.97/2.66
% 9.97/2.66 % (2369)Memory used [KB]: 5628
% 9.97/2.66 % (2369)Time elapsed: 0.013 s
% 9.97/2.66 % (2369)Instructions burned: 26 (million)
% 9.97/2.66 % (2369)------------------------------
% 9.97/2.66 % (2369)------------------------------
% 9.97/2.68 % (2370)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_2178 for (2986ds/53Mi)
% 10.35/2.70 % (2370)Instruction limit reached!
% 10.35/2.70 % (2370)------------------------------
% 10.35/2.70 % (2370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.70 % (2370)Termination reason: Unknown
% 10.35/2.70 % (2370)Termination phase: Saturation
% 10.35/2.70
% 10.35/2.70 % (2370)Memory used [KB]: 5628
% 10.35/2.70 % (2370)Time elapsed: 0.024 s
% 10.35/2.70 % (2370)Instructions burned: 54 (million)
% 10.35/2.70 % (2370)------------------------------
% 10.35/2.70 % (2370)------------------------------
% 10.35/2.72 % (2371)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_2178 for (2986ds/4436Mi)
% 10.35/2.74 % (2368)Instruction limit reached!
% 10.35/2.74 % (2368)------------------------------
% 10.35/2.74 % (2368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.74 % (2368)Termination reason: Unknown
% 10.35/2.74 % (2368)Termination phase: Saturation
% 10.35/2.74
% 10.35/2.74 % (2368)Memory used [KB]: 6012
% 10.35/2.74 % (2368)Time elapsed: 0.096 s
% 10.35/2.74 % (2368)Instructions burned: 204 (million)
% 10.35/2.74 % (2368)------------------------------
% 10.35/2.74 % (2368)------------------------------
% 10.35/2.75 % (2372)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_2178 for (2986ds/1539Mi)
% 10.35/2.76 % (2367)Instruction limit reached!
% 10.35/2.76 % (2367)------------------------------
% 10.35/2.76 % (2367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.76 % (2367)Termination reason: Unknown
% 10.35/2.76 % (2367)Termination phase: Saturation
% 10.35/2.76
% 10.35/2.76 % (2367)Memory used [KB]: 6012
% 10.35/2.76 % (2367)Time elapsed: 0.126 s
% 10.35/2.76 % (2367)Instructions burned: 267 (million)
% 10.35/2.76 % (2367)------------------------------
% 10.35/2.76 % (2367)------------------------------
% 10.35/2.78 % (2373)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_2178 for (2985ds/408Mi)
% 10.35/2.78 % (2365)Instruction limit reached!
% 10.35/2.78 % (2365)------------------------------
% 10.35/2.78 % (2365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.78 % (2365)Termination reason: Unknown
% 10.35/2.78 % (2365)Termination phase: Saturation
% 10.35/2.78
% 10.35/2.78 % (2365)Memory used [KB]: 6908
% 10.35/2.78 % (2365)Time elapsed: 0.180 s
% 10.35/2.78 % (2365)Instructions burned: 369 (million)
% 10.35/2.78 % (2365)------------------------------
% 10.35/2.78 % (2365)------------------------------
% 10.83/2.80 % (2374)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_2178 for (2985ds/5205Mi)
% 10.83/2.87 % (2354)Instruction limit reached!
% 10.83/2.87 % (2354)------------------------------
% 10.83/2.87 % (2354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.83/2.87 % (2354)Termination reason: Unknown
% 10.83/2.87 % (2354)Termination phase: Saturation
% 10.83/2.87
% 10.83/2.87 % (2354)Memory used [KB]: 6524
% 10.83/2.87 % (2354)Time elapsed: 0.452 s
% 10.83/2.87 % (2354)Instructions burned: 988 (million)
% 10.83/2.87 % (2354)------------------------------
% 10.83/2.87 % (2354)------------------------------
% 10.83/2.88 % (2375)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_2178 for (2984ds/1913Mi)
% 11.30/2.97 % (2361)Instruction limit reached!
% 11.30/2.97 % (2361)------------------------------
% 11.30/2.97 % (2361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.30/2.97 % (2361)Termination reason: Unknown
% 11.30/2.97 % (2361)Termination phase: Saturation
% 11.30/2.97
% 11.30/2.97 % (2361)Memory used [KB]: 7036
% 11.30/2.97 % (2361)Time elapsed: 0.429 s
% 11.30/2.97 % (2361)Instructions burned: 923 (million)
% 11.30/2.97 % (2361)------------------------------
% 11.30/2.97 % (2361)------------------------------
% 11.30/2.97 % (2373)Instruction limit reached!
% 11.30/2.97 % (2373)------------------------------
% 11.30/2.97 % (2373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.30/2.97 % (2373)Termination reason: Unknown
% 11.30/2.97 % (2373)Termination phase: Saturation
% 11.30/2.97
% 11.30/2.97 % (2373)Memory used [KB]: 7036
% 11.30/2.97 % (2373)Time elapsed: 0.196 s
% 11.30/2.97 % (2373)Instructions burned: 409 (million)
% 11.30/2.97 % (2373)------------------------------
% 11.30/2.97 % (2373)------------------------------
% 11.30/2.98 % (2376)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_2178 for (2983ds/4350Mi)
% 11.30/2.99 % (2377)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_2178 for (2983ds/68Mi)
% 11.30/3.02 % (2377)Instruction limit reached!
% 11.30/3.02 % (2377)------------------------------
% 11.30/3.02 % (2377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.30/3.02 % (2377)Termination reason: Unknown
% 11.30/3.02 % (2377)Termination phase: Saturation
% 11.30/3.02
% 11.30/3.02 % (2377)Memory used [KB]: 5884
% 11.30/3.02 % (2377)Time elapsed: 0.033 s
% 11.30/3.02 % (2377)Instructions burned: 68 (million)
% 11.30/3.02 % (2377)------------------------------
% 11.30/3.02 % (2377)------------------------------
% 13.35/3.04 % (2378)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_2178 for (2983ds/358Mi)
% 13.35/3.11 % (2366)Instruction limit reached!
% 13.35/3.11 % (2366)------------------------------
% 13.35/3.11 % (2366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.11 % (2366)Termination reason: Unknown
% 13.35/3.11 % (2366)Termination phase: Saturation
% 13.35/3.11
% 13.35/3.11 % (2366)Memory used [KB]: 6908
% 13.35/3.11 % (2366)Time elapsed: 0.479 s
% 13.35/3.11 % (2366)Instructions burned: 1021 (million)
% 13.35/3.11 % (2366)------------------------------
% 13.35/3.11 % (2366)------------------------------
% 14.01/3.13 % (2379)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_2178 for (2982ds/31Mi)
% 14.01/3.14 % (2379)Instruction limit reached!
% 14.01/3.14 % (2379)------------------------------
% 14.01/3.14 % (2379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.01/3.14 % (2379)Termination reason: Unknown
% 14.01/3.14 % (2379)Termination phase: Saturation
% 14.01/3.14
% 14.01/3.14 % (2379)Memory used [KB]: 5756
% 14.01/3.14 % (2379)Time elapsed: 0.018 s
% 14.01/3.14 % (2379)Instructions burned: 32 (million)
% 14.01/3.14 % (2379)------------------------------
% 14.01/3.14 % (2379)------------------------------
% 14.01/3.16 % (2380)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_2178 for (2981ds/279Mi)
% 14.40/3.21 % (2378)Instruction limit reached!
% 14.40/3.21 % (2378)------------------------------
% 14.40/3.21 % (2378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.40/3.21 % (2378)Termination reason: Unknown
% 14.40/3.21 % (2378)Termination phase: Saturation
% 14.40/3.21
% 14.40/3.21 % (2378)Memory used [KB]: 6012
% 14.40/3.21 % (2378)Time elapsed: 0.173 s
% 14.40/3.21 % (2378)Instructions burned: 358 (million)
% 14.40/3.21 % (2378)------------------------------
% 14.40/3.21 % (2378)------------------------------
% 14.40/3.22 % (2381)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_2178 for (2981ds/258Mi)
% 14.40/3.29 % (2380)Instruction limit reached!
% 14.40/3.29 % (2380)------------------------------
% 14.40/3.29 % (2380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.40/3.29 % (2380)Termination reason: Unknown
% 14.40/3.29 % (2380)Termination phase: Saturation
% 14.40/3.29
% 14.40/3.29 % (2380)Memory used [KB]: 6268
% 14.40/3.29 % (2380)Time elapsed: 0.129 s
% 14.40/3.29 % (2380)Instructions burned: 279 (million)
% 14.40/3.29 % (2380)------------------------------
% 14.40/3.29 % (2380)------------------------------
% 15.23/3.30 % (2382)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_2178 for (2980ds/26Mi)
% 15.23/3.31 % (2382)Instruction limit reached!
% 15.23/3.31 % (2382)------------------------------
% 15.23/3.31 % (2382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.23/3.31 % (2382)Termination reason: Unknown
% 15.23/3.31 % (2382)Termination phase: Saturation
% 15.23/3.31
% 15.23/3.31 % (2382)Memory used [KB]: 5628
% 15.23/3.31 % (2382)Time elapsed: 0.014 s
% 15.23/3.31 % (2382)Instructions burned: 27 (million)
% 15.23/3.31 % (2382)------------------------------
% 15.23/3.31 % (2382)------------------------------
% 15.23/3.33 % (2383)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_2178 for (2980ds/995Mi)
% 15.23/3.34 % (2381)Instruction limit reached!
% 15.23/3.34 % (2381)------------------------------
% 15.23/3.34 % (2381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.23/3.34 % (2381)Termination reason: Unknown
% 15.23/3.34 % (2381)Termination phase: Saturation
% 15.23/3.34
% 15.23/3.34 % (2381)Memory used [KB]: 6268
% 15.23/3.34 % (2381)Time elapsed: 0.123 s
% 15.23/3.34 % (2381)Instructions burned: 258 (million)
% 15.23/3.34 % (2381)------------------------------
% 15.23/3.34 % (2381)------------------------------
% 15.23/3.36 % (2384)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_2178 for (2979ds/373Mi)
% 16.39/3.50 % (2372)Instruction limit reached!
% 16.39/3.50 % (2372)------------------------------
% 16.39/3.50 % (2372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.39/3.50 % (2372)Termination reason: Unknown
% 16.39/3.50 % (2372)Termination phase: Saturation
% 16.39/3.50
% 16.39/3.50 % (2372)Memory used [KB]: 8955
% 16.39/3.50 % (2372)Time elapsed: 0.752 s
% 16.39/3.50 % (2372)Instructions burned: 1540 (million)
% 16.39/3.50 % (2372)------------------------------
% 16.39/3.50 % (2372)------------------------------
% 16.39/3.52 % (2385)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_2178 for (2978ds/253Mi)
% 16.39/3.54 % (2384)Instruction limit reached!
% 16.39/3.54 % (2384)------------------------------
% 16.39/3.54 % (2384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.39/3.54 % (2384)Termination reason: Unknown
% 16.39/3.54 % (2384)Termination phase: Saturation
% 16.39/3.54
% 16.39/3.54 % (2384)Memory used [KB]: 7164
% 16.39/3.54 % (2384)Time elapsed: 0.182 s
% 16.39/3.54 % (2384)Instructions burned: 374 (million)
% 16.39/3.54 % (2384)------------------------------
% 16.39/3.54 % (2384)------------------------------
% 16.39/3.56 % (2386)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_2178 for (2978ds/832Mi)
% 17.00/3.64 % (2385)Instruction limit reached!
% 17.00/3.64 % (2385)------------------------------
% 17.00/3.64 % (2385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.00/3.64 % (2385)Termination reason: Unknown
% 17.00/3.64 % (2385)Termination phase: Saturation
% 17.00/3.64
% 17.00/3.64 % (2385)Memory used [KB]: 6140
% 17.00/3.64 % (2385)Time elapsed: 0.122 s
% 17.00/3.64 % (2385)Instructions burned: 254 (million)
% 17.00/3.64 % (2385)------------------------------
% 17.00/3.64 % (2385)------------------------------
% 17.00/3.66 % (2387)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_2178 for (2977ds/668Mi)
% 17.54/3.72 % (2375)Instruction limit reached!
% 17.54/3.72 % (2375)------------------------------
% 17.54/3.72 % (2375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.54/3.72 % (2375)Termination reason: Unknown
% 17.54/3.72 % (2375)Termination phase: Saturation
% 17.54/3.72
% 17.54/3.72 % (2375)Memory used [KB]: 2046
% 17.54/3.72 % (2375)Time elapsed: 0.864 s
% 17.54/3.72 % (2375)Instructions burned: 1913 (million)
% 17.54/3.72 % (2375)------------------------------
% 17.54/3.72 % (2375)------------------------------
% 17.54/3.74 % (2388)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_2178 for (2976ds/40Mi)
% 17.54/3.76 % (2388)Instruction limit reached!
% 17.54/3.76 % (2388)------------------------------
% 17.54/3.76 % (2388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.54/3.76 % (2388)Termination reason: Unknown
% 17.54/3.76 % (2388)Termination phase: Saturation
% 17.54/3.76
% 17.54/3.76 % (2388)Memory used [KB]: 5628
% 17.54/3.76 % (2388)Time elapsed: 0.020 s
% 17.54/3.76 % (2388)Instructions burned: 41 (million)
% 17.54/3.76 % (2388)------------------------------
% 17.54/3.76 % (2388)------------------------------
% 17.54/3.77 % (2383)Instruction limit reached!
% 17.54/3.77 % (2383)------------------------------
% 17.54/3.77 % (2383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.54/3.77 % (2383)Termination reason: Unknown
% 17.54/3.77 % (2383)Termination phase: Saturation
% 17.54/3.77
% 17.54/3.77 % (2383)Memory used [KB]: 6908
% 17.54/3.77 % (2383)Time elapsed: 0.445 s
% 17.54/3.77 % (2383)Instructions burned: 995 (million)
% 17.54/3.77 % (2383)------------------------------
% 17.54/3.77 % (2383)------------------------------
% 17.54/3.77 % (2389)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_2178 for (2975ds/294Mi)
% 17.54/3.79 % (2390)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_2178 for (2975ds/187Mi)
% 18.38/3.88 % (2390)Instruction limit reached!
% 18.38/3.88 % (2390)------------------------------
% 18.38/3.88 % (2390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.38/3.88 % (2390)Termination reason: Unknown
% 18.38/3.88 % (2390)Termination phase: Saturation
% 18.38/3.88
% 18.38/3.88 % (2390)Memory used [KB]: 6524
% 18.38/3.88 % (2390)Time elapsed: 0.092 s
% 18.38/3.88 % (2390)Instructions burned: 187 (million)
% 18.38/3.88 % (2390)------------------------------
% 18.38/3.88 % (2390)------------------------------
% 18.78/3.90 % (2391)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_2178 for (2974ds/371Mi)
% 18.78/3.91 % (2389)Instruction limit reached!
% 18.78/3.91 % (2389)------------------------------
% 18.78/3.91 % (2389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.78/3.91 % (2389)Termination reason: Unknown
% 18.78/3.91 % (2389)Termination phase: Saturation
% 18.78/3.91
% 18.78/3.91 % (2389)Memory used [KB]: 6140
% 18.78/3.91 % (2389)Time elapsed: 0.136 s
% 18.78/3.91 % (2389)Instructions burned: 295 (million)
% 18.78/3.91 % (2389)------------------------------
% 18.78/3.91 % (2389)------------------------------
% 18.78/3.92 % (2392)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_2178 for (2974ds/1827Mi)
% 18.78/3.94 % (2386)Instruction limit reached!
% 18.78/3.94 % (2386)------------------------------
% 18.78/3.94 % (2386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.78/3.94 % (2386)Termination reason: Unknown
% 18.78/3.94 % (2386)Termination phase: Saturation
% 18.78/3.94
% 18.78/3.94 % (2386)Memory used [KB]: 6780
% 18.78/3.94 % (2386)Time elapsed: 0.387 s
% 18.78/3.94 % (2386)Instructions burned: 833 (million)
% 18.78/3.94 % (2386)------------------------------
% 18.78/3.94 % (2386)------------------------------
% 18.78/3.96 % (2393)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_2178 for (2974ds/70Mi)
% 18.78/3.96 % (2387)Instruction limit reached!
% 18.78/3.96 % (2387)------------------------------
% 18.78/3.96 % (2387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.78/3.96 % (2387)Termination reason: Unknown
% 18.78/3.96 % (2387)Termination phase: Saturation
% 18.78/3.96
% 18.78/3.96 % (2387)Memory used [KB]: 11129
% 18.78/3.96 % (2387)Time elapsed: 0.304 s
% 18.78/3.96 % (2387)Instructions burned: 668 (million)
% 18.78/3.96 % (2387)------------------------------
% 18.78/3.96 % (2387)------------------------------
% 18.78/3.98 % (2394)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_2178 for (2973ds/316Mi)
% 18.78/3.99 % (2393)Instruction limit reached!
% 18.78/3.99 % (2393)------------------------------
% 18.78/3.99 % (2393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.78/3.99 % (2393)Termination reason: Unknown
% 18.78/3.99 % (2393)Termination phase: Saturation
% 18.78/3.99
% 18.78/3.99 % (2393)Memory used [KB]: 1279
% 18.78/3.99 % (2393)Time elapsed: 0.032 s
% 18.78/3.99 % (2393)Instructions burned: 70 (million)
% 18.78/3.99 % (2393)------------------------------
% 18.78/3.99 % (2393)------------------------------
% 18.78/4.01 % (2395)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_2178 for (2973ds/932Mi)
% 20.37/4.07 % (2391)Instruction limit reached!
% 20.37/4.07 % (2391)------------------------------
% 20.37/4.07 % (2391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.37/4.07 % (2391)Termination reason: Unknown
% 20.37/4.07 % (2391)Termination phase: Saturation
% 20.37/4.07
% 20.37/4.07 % (2391)Memory used [KB]: 6396
% 20.37/4.07 % (2391)Time elapsed: 0.176 s
% 20.37/4.07 % (2391)Instructions burned: 372 (million)
% 20.37/4.07 % (2391)------------------------------
% 20.37/4.07 % (2391)------------------------------
% 20.37/4.09 % (2396)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_2178 for (2972ds/4714Mi)
% 20.37/4.11 % (2394)Instruction limit reached!
% 20.37/4.11 % (2394)------------------------------
% 20.37/4.11 % (2394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.37/4.11 % (2394)Termination reason: Unknown
% 20.37/4.11 % (2394)Termination phase: Saturation
% 20.37/4.11
% 20.37/4.11 % (2394)Memory used [KB]: 6652
% 20.37/4.11 % (2394)Time elapsed: 0.139 s
% 20.37/4.11 % (2394)Instructions burned: 317 (million)
% 20.37/4.11 % (2394)------------------------------
% 20.37/4.11 % (2394)------------------------------
% 21.06/4.13 % (2397)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_2178 for (2972ds/8250Mi)
% 22.42/4.45 % (2395)Instruction limit reached!
% 22.42/4.45 % (2395)------------------------------
% 22.42/4.45 % (2395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.42/4.45 % (2395)Termination reason: Unknown
% 22.42/4.45 % (2395)Termination phase: Saturation
% 22.42/4.45
% 22.42/4.45 % (2395)Memory used [KB]: 8571
% 22.42/4.45 % (2395)Time elapsed: 0.445 s
% 22.42/4.45 % (2395)Instructions burned: 932 (million)
% 22.42/4.45 % (2395)------------------------------
% 22.42/4.45 % (2395)------------------------------
% 22.42/4.46 % (2398)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_2178 for (2969ds/770Mi)
% 22.87/4.52 % (2397)First to succeed.
% 22.87/4.54 % (2397)Refutation found. Thanks to Tanya!
% 22.87/4.54 % SZS status Theorem for DTF2THF_2178
% 22.87/4.54 % SZS output start Proof for DTF2THF_2178
% 22.87/4.54 thf(type_def_5, type, a: $tType).
% 22.87/4.54 thf(func_def_0, type, a: $tType).
% 22.87/4.54 thf(func_def_1, type, cR: a > a).
% 22.87/4.54 thf(func_def_2, type, cL: a > a).
% 22.87/4.54 thf(func_def_3, type, cPSI: (a > $o) > a > $o).
% 22.87/4.54 thf(func_def_4, type, cP: a > a > a).
% 22.87/4.54 thf(func_def_5, type, cZ: a).
% 22.87/4.54 thf(func_def_6, type, cPHI: (a > $o) > a > $o).
% 22.87/4.54 thf(func_def_21, type, sP0: a > (a > $o) > $o).
% 22.87/4.54 thf(func_def_22, type, sP1: a > (a > $o) > $o).
% 22.87/4.54 thf(func_def_23, type, sK2: a > (a > $o) > a).
% 22.87/4.54 thf(func_def_24, type, sK3: (a > $o) > a).
% 22.87/4.54 thf(func_def_25, type, sK4: (a > $o) > a > (a > $o) > a).
% 22.87/4.54 thf(func_def_26, type, sK5: a > (a > $o) > a).
% 22.87/4.54 thf(func_def_27, type, sK6: a > a > (a > $o) > a > $o).
% 22.87/4.54 thf(func_def_28, type, sK7: a > (a > $o) > a).
% 22.87/4.54 thf(func_def_29, type, sK8: (a > $o) > a).
% 22.87/4.54 thf(func_def_30, type, sK9: (a > $o) > a > (a > $o) > a).
% 22.87/4.54 thf(func_def_31, type, sK10: a > (a > $o) > a).
% 22.87/4.54 thf(func_def_32, type, sK11: a > a > (a > $o) > a > $o).
% 22.87/4.54 thf(func_def_33, type, sK12: (a > $o) > a).
% 22.87/4.54 thf(func_def_36, type, ph14: !>[X0: $tType]:(X0)).
% 22.87/4.54 thf(func_def_37, type, sK15: a).
% 22.87/4.54 thf(func_def_38, type, sK16: a).
% 22.87/4.54 thf(func_def_39, type, sK17: a).
% 22.87/4.54 thf(func_def_40, type, sK18: a).
% 22.87/4.54 thf(func_def_41, type, sK19: a).
% 22.87/4.54 thf(func_def_42, type, sK20: a).
% 22.87/4.54 thf(func_def_43, type, sK21: a).
% 22.87/4.54 thf(func_def_44, type, sK22: a).
% 22.87/4.54 thf(func_def_45, type, sK23: a).
% 22.87/4.54 thf(func_def_46, type, sK24: a).
% 22.87/4.54 thf(func_def_47, type, sK25: a).
% 22.87/4.54 thf(func_def_48, type, sK26: a).
% 22.87/4.54 thf(f2900,plain,(
% 22.87/4.54 $false),
% 22.87/4.54 inference(avatar_sat_refutation,[status(thm)],[f290,f295,f304,f309,f318,f323,f328,f333,f343,f347,f349,f1375,f1469,f1893,f2272,f2439,f2823,f2895])).
% 22.87/4.54 thf(f2895,plain,(
% 22.87/4.54 ~spl13_11 | ~spl13_15 | ~spl13_16 | ~spl13_20),
% 22.87/4.54 inference(avatar_contradiction_clause,[status(thm)],[f2894])).
% 22.87/4.54 thf(f2894,plain,(
% 22.87/4.54 $false | (~spl13_11 | ~spl13_15 | ~spl13_16 | ~spl13_20)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f2879])).
% 22.87/4.54 thf(f2879,plain,(
% 22.87/4.54 ($true = $false) | (~spl13_11 | ~spl13_15 | ~spl13_16 | ~spl13_20)),
% 22.87/4.54 inference(backward_demodulation,[status(thm)],[f2674,f2630])).
% 22.87/4.54 thf(f2630,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $false) | (~spl13_11 | ~spl13_15 | ~spl13_20)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f2624])).
% 22.87/4.54 thf(f2624,plain,(
% 22.87/4.54 (sK15 != sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $false) | (~spl13_11 | ~spl13_15 | ~spl13_20)),
% 22.87/4.54 inference(superposition,[status(thm)],[f341,f2616])).
% 22.87/4.54 thf(f2616,plain,(
% 22.87/4.54 (sK15 = (cP @ sK22 @ sK18)) | (~spl13_11 | ~spl13_15)),
% 22.87/4.54 inference(backward_demodulation,[status(thm)],[f317,f2614])).
% 22.87/4.54 thf(f2614,plain,(
% 22.87/4.54 (sK23 = sK18) | (~spl13_11 | ~spl13_15)),
% 22.87/4.54 inference(forward_demodulation,[status(thm)],[f2610,f2467])).
% 22.87/4.54 thf(f2467,plain,(
% 22.87/4.54 ((cR @ sK15) = sK18) | ~spl13_11),
% 22.87/4.54 inference(superposition,[status(thm)],[f56,f299])).
% 22.87/4.54 thf(f299,plain,(
% 22.87/4.54 (sK15 = (cP @ sK19 @ sK18)) | ~spl13_11),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f297])).
% 22.87/4.54 thf(f297,definition,(
% 22.87/4.54 spl13_11 <=> (sK15 = (cP @ sK19 @ sK18))),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_11])],[avatar_definition])).
% 22.87/4.54 thf(f56,plain,(
% 22.87/4.54 ( ! [X6 : a,X5 : a] : (((cR @ (cP @ X6 @ X5)) = X5)) )),
% 22.87/4.54 inference(cnf_transformation,[status(thm)],[f31])).
% 22.87/4.54 thf(f31,plain,(
% 22.87/4.54 ! [X0 : a > $o] : (((X0 @ cZ) = $true) | ! [X1 : a] : (((X0 @ X1) != $true) | (((X0 @ (cL @ (sK12 @ X0))) != $true) & ($true = (X0 @ (sK12 @ X0)))))) & ! [X3 : a,X4 : a > $o] : ((((sP1 @ X3 @ X4) = $true) | ($true != (cPSI @ X4 @ X3))) & (($true = (cPSI @ X4 @ X3)) | ((sP1 @ X3 @ X4) != $true))) & ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2) & ((cP @ Y1 @ Y2) = Y0))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y1))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y1 @ Y2) = Y0) & ((cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y1)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y2) | (cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2))))))) | (cZ = Y0)))) & (cZ = (cR @ cZ)) & ! [X5 : a,X6 : a] : ((cR @ (cP @ X6 @ X5)) = X5) & ! [X7 : a] : ((((cP @ (cL @ X7) @ (cR @ X7)) = X7) | (cZ = X7)) & ((cZ != X7) | ((cP @ (cL @ X7) @ (cR @ X7)) != X7))) & ! [X8 : a,X9 : a] : ((cL @ (cP @ X9 @ X8)) = X9) & ! [X10 : a,X11 : a > $o] : ((($true = (cPHI @ X11 @ X10)) | ($true != (sP0 @ X10 @ X11))) & (($true = (sP0 @ X10 @ X11)) | ($true != (cPHI @ X11 @ X10)))) & (cZ = (cL @ cZ))),
% 22.87/4.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f29,f30])).
% 22.87/4.54 thf(f30,plain,(
% 22.87/4.54 ! [X0 : a > $o] : (? [X2 : a] : (($true != (X0 @ (cL @ X2))) & ((X0 @ X2) = $true)) => (((X0 @ (cL @ (sK12 @ X0))) != $true) & ($true = (X0 @ (sK12 @ X0)))))),
% 22.87/4.54 introduced(definition,[],[choice_axiom])).
% 22.87/4.54 thf(f29,plain,(
% 22.87/4.54 ! [X0 : a > $o] : (((X0 @ cZ) = $true) | ! [X1 : a] : (((X0 @ X1) != $true) | ? [X2 : a] : (($true != (X0 @ (cL @ X2))) & ((X0 @ X2) = $true)))) & ! [X3 : a,X4 : a > $o] : ((((sP1 @ X3 @ X4) = $true) | ($true != (cPSI @ X4 @ X3))) & (($true = (cPSI @ X4 @ X3)) | ((sP1 @ X3 @ X4) != $true))) & ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2) & ((cP @ Y1 @ Y2) = Y0))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y1))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y1 @ Y2) = Y0) & ((cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y1)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y2) | (cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2))))))) | (cZ = Y0)))) & (cZ = (cR @ cZ)) & ! [X5 : a,X6 : a] : ((cR @ (cP @ X6 @ X5)) = X5) & ! [X7 : a] : ((((cP @ (cL @ X7) @ (cR @ X7)) = X7) | (cZ = X7)) & ((cZ != X7) | ((cP @ (cL @ X7) @ (cR @ X7)) != X7))) & ! [X8 : a,X9 : a] : ((cL @ (cP @ X9 @ X8)) = X9) & ! [X10 : a,X11 : a > $o] : ((($true = (cPHI @ X11 @ X10)) | ($true != (sP0 @ X10 @ X11))) & (($true = (sP0 @ X10 @ X11)) | ($true != (cPHI @ X11 @ X10)))) & (cZ = (cL @ cZ))),
% 22.87/4.54 inference(rectify,[status(thm)],[f28])).
% 22.87/4.54 thf(f28,plain,(
% 22.87/4.54 ! [X19 : a > $o] : (($true = (X19 @ cZ)) | ! [X20 : a] : (($true != (X19 @ X20)) | ? [X21 : a] : (((X19 @ (cL @ X21)) != $true) & ($true = (X19 @ X21))))) & ! [X2 : a,X3 : a > $o] : ((((sP1 @ X2 @ X3) = $true) | ($true != (cPSI @ X3 @ X2))) & (($true = (cPSI @ X3 @ X2)) | ((sP1 @ X2 @ X3) != $true))) & ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2) & ((cP @ Y1 @ Y2) = Y0))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y1))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y1 @ Y2) = Y0) & ((cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y1)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y2) | (cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2))))))) | (cZ = Y0)))) & (cZ = (cR @ cZ)) & ! [X16 : a,X17 : a] : ((cR @ (cP @ X17 @ X16)) = X16) & ! [X18 : a] : ((((cP @ (cL @ X18) @ (cR @ X18)) = X18) | (cZ = X18)) & ((cZ != X18) | ((cP @ (cL @ X18) @ (cR @ X18)) != X18))) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1) & ! [X9 : a,X10 : a > $o] : ((($true = (cPHI @ X10 @ X9)) | ((sP0 @ X9 @ X10) != $true)) & (((sP0 @ X9 @ X10) = $true) | ($true != (cPHI @ X10 @ X9)))) & (cZ = (cL @ cZ))),
% 22.87/4.54 inference(nnf_transformation,[status(thm)],[f11])).
% 22.87/4.54 thf(f11,plain,(
% 22.87/4.54 ! [X19 : a > $o] : (($true = (X19 @ cZ)) | ! [X20 : a] : (($true != (X19 @ X20)) | ? [X21 : a] : (((X19 @ (cL @ X21)) != $true) & ($true = (X19 @ X21))))) & ! [X2 : a,X3 : a > $o] : (((sP1 @ X2 @ X3) = $true) <=> ($true = (cPSI @ X3 @ X2))) & ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2) & ((cP @ Y1 @ Y2) = Y0))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y1))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y1 @ Y2) = Y0) & ((cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y1)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y2) | (cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2))))))) | (cZ = Y0)))) & (cZ = (cR @ cZ)) & ! [X16 : a,X17 : a] : ((cR @ (cP @ X17 @ X16)) = X16) & ! [X18 : a] : (((cP @ (cL @ X18) @ (cR @ X18)) = X18) <=> (cZ != X18)) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1) & ! [X9 : a,X10 : a > $o] : (($true = (cPHI @ X10 @ X9)) <=> ((sP0 @ X9 @ X10) = $true)) & (cZ = (cL @ cZ))),
% 22.87/4.54 inference(definition_folding,[status(thm)],[f8,f10,f9])).
% 22.87/4.54 thf(f9,plain,(
% 22.87/4.54 ! [X10 : a > $o,X9 : a] : (((sP0 @ X9 @ X10) = $true) <=> ? [X11 : a] : (! [X12 : a] : (($true = (X10 @ X12)) | ? [X13 : a > $o] : (! [X14 : a] : (((X13 @ (cL @ X14)) = $true) | ((X13 @ X14) != $true)) & ((X13 @ X11) = $true) & ! [X15 : a] : (((cR @ X15) != X12) | ((X13 @ X15) != $true)))) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X11) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X9) = $true)))),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 22.87/4.54 thf(f10,plain,(
% 22.87/4.54 ! [X3 : a > $o,X2 : a] : (((sP1 @ X2 @ X3) = $true) <=> ? [X4 : a] : (! [X5 : a] : (((X3 @ X5) = $true) | ? [X6 : a > $o] : (! [X7 : a] : (($true != (X6 @ X7)) | ((X6 @ (cL @ X7)) = $true)) & ($true = (X6 @ X4)) & ! [X8 : a] : (((cR @ X8) != X5) | ((X6 @ X8) != $true)))) & ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2))))),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 22.87/4.54 thf(f8,plain,(
% 22.87/4.54 ! [X19 : a > $o] : (($true = (X19 @ cZ)) | ! [X20 : a] : (($true != (X19 @ X20)) | ? [X21 : a] : (((X19 @ (cL @ X21)) != $true) & ($true = (X19 @ X21))))) & ! [X2 : a,X3 : a > $o] : (? [X4 : a] : (! [X5 : a] : (((X3 @ X5) = $true) | ? [X6 : a > $o] : (! [X7 : a] : (($true != (X6 @ X7)) | ((X6 @ (cL @ X7)) = $true)) & ($true = (X6 @ X4)) & ! [X8 : a] : (((cR @ X8) != X5) | ((X6 @ X8) != $true)))) & ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2))) <=> ($true = (cPSI @ X3 @ X2))) & ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2) & ((cP @ Y1 @ Y2) = Y0))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y1))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y1 @ Y2) = Y0) & ((cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y1)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y2) | (cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2))))))) | (cZ = Y0)))) & (cZ = (cR @ cZ)) & ! [X16 : a,X17 : a] : ((cR @ (cP @ X17 @ X16)) = X16) & ! [X18 : a] : (((cP @ (cL @ X18) @ (cR @ X18)) = X18) <=> (cZ != X18)) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1) & ! [X9 : a,X10 : a > $o] : (($true = (cPHI @ X10 @ X9)) <=> ? [X11 : a] : (! [X12 : a] : (($true = (X10 @ X12)) | ? [X13 : a > $o] : (! [X14 : a] : (((X13 @ (cL @ X14)) = $true) | ((X13 @ X14) != $true)) & ((X13 @ X11) = $true) & ! [X15 : a] : (((cR @ X15) != X12) | ((X13 @ X15) != $true)))) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X11) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X9) = $true))) & (cZ = (cL @ cZ))),
% 22.87/4.54 inference(flattening,[status(thm)],[f7])).
% 22.87/4.54 thf(f7,plain,(
% 22.87/4.54 ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2) & ((cP @ Y1 @ Y2) = Y0))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y1))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y1 @ Y2) = Y0) & ((cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y1)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y2) | (cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2))))))) | (cZ = Y0)))) & (! [X2 : a,X3 : a > $o] : (? [X4 : a] : (($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2)) & ! [X5 : a] : (((X3 @ X5) = $true) | ? [X6 : a > $o] : (! [X8 : a] : (((cR @ X8) != X5) | ((X6 @ X8) != $true)) & (! [X7 : a] : (($true != (X6 @ X7)) | ((X6 @ (cL @ X7)) = $true)) & ($true = (X6 @ X4)))))) <=> ($true = (cPSI @ X3 @ X2))) & ! [X18 : a] : (((cP @ (cL @ X18) @ (cR @ X18)) = X18) <=> (cZ != X18)) & ! [X9 : a,X10 : a > $o] : (? [X11 : a] : (! [X12 : a] : (($true = (X10 @ X12)) | ? [X13 : a > $o] : (! [X15 : a] : (((cR @ X15) != X12) | ((X13 @ X15) != $true)) & (! [X14 : a] : (((X13 @ (cL @ X14)) = $true) | ((X13 @ X14) != $true)) & ((X13 @ X11) = $true)))) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X11) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X9) = $true)) <=> ($true = (cPHI @ X10 @ X9))) & (cZ = (cL @ cZ)) & ! [X16 : a,X17 : a] : ((cR @ (cP @ X17 @ X16)) = X16) & ! [X19 : a > $o] : (($true = (X19 @ cZ)) | ! [X20 : a] : (($true != (X19 @ X20)) | ? [X21 : a] : (((X19 @ (cL @ X21)) != $true) & ($true = (X19 @ X21))))) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1) & (cZ = (cR @ cZ)))),
% 22.87/4.54 inference(ennf_transformation,[status(thm)],[f6])).
% 22.87/4.54 thf(f6,plain,(
% 22.87/4.54 ~((! [X2 : a,X3 : a > $o] : (? [X4 : a] : (($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2)) & ! [X5 : a] : (! [X6 : a > $o] : ((! [X7 : a] : (($true = (X6 @ X7)) => ((X6 @ (cL @ X7)) = $true)) & ($true = (X6 @ X4))) => ? [X8 : a] : (((X6 @ X8) = $true) & ((cR @ X8) = X5))) => ((X3 @ X5) = $true))) <=> ($true = (cPSI @ X3 @ X2))) & ! [X18 : a] : (((cP @ (cL @ X18) @ (cR @ X18)) = X18) <=> (cZ != X18)) & ! [X9 : a,X10 : a > $o] : (? [X11 : a] : (! [X12 : a] : (! [X13 : a > $o] : ((! [X14 : a] : (((X13 @ X14) = $true) => ((X13 @ (cL @ X14)) = $true)) & ((X13 @ X11) = $true)) => ? [X15 : a] : (((X13 @ X15) = $true) & ((cR @ X15) = X12))) => ($true = (X10 @ X12))) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X11) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X9) = $true)) <=> ($true = (cPHI @ X10 @ X9))) & (cZ = (cL @ cZ)) & ! [X16 : a,X17 : a] : ((cR @ (cP @ X17 @ X16)) = X16) & ! [X19 : a > $o] : (? [X20 : a] : (! [X21 : a] : (($true = (X19 @ X21)) => ((X19 @ (cL @ X21)) = $true)) & ($true = (X19 @ X20))) => ($true = (X19 @ cZ))) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1) & (cZ = (cR @ cZ))) => ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2) & ((cP @ Y1 @ Y2) = Y0))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y1))))))) | (cZ = Y0))) = (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y1 @ Y2) = Y0) & ((cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y1)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y2) | (cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2))))))) | (cZ = Y0)))))),
% 22.87/4.54 inference(rectify,[status(thm)],[f5])).
% 22.87/4.54 thf(f5,plain,(
% 22.87/4.54 ~((! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1) & ! [X2 : a,X3 : a > $o] : (? [X4 : a] : (($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2)) & ! [X9 : a] : (! [X10 : a > $o] : ((! [X11 : a] : (((X10 @ X11) = $true) => ((X10 @ (cL @ X11)) = $true)) & ($true = (X10 @ X4))) => ? [X12 : a] : (($true = (X10 @ X12)) & ((cR @ X12) = X9))) => ((X3 @ X9) = $true))) <=> ($true = (cPSI @ X3 @ X2))) & (cZ = (cR @ cZ)) & (cZ = (cL @ cZ)) & ! [X13 : a,X14 : a > $o] : (? [X15 : a] : (! [X16 : a] : (! [X17 : a > $o] : ((! [X18 : a] : (((X17 @ X18) = $true) => ($true = (X17 @ (cL @ X18)))) & ($true = (X17 @ X15))) => ? [X19 : a] : (((X17 @ X19) = $true) & ((cR @ X19) = X16))) => ((X14 @ X16) = $true)) & ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X15) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X13))) <=> ($true = (cPHI @ X14 @ X13))) & ! [X24 : a,X25 : a] : ((cR @ (cP @ X25 @ X24)) = X24) & ! [X26 : a] : (((cP @ (cL @ X26) @ (cR @ X26)) = X26) <=> (cZ != X26)) & ! [X27 : a > $o] : (? [X28 : a] : (((X27 @ X28) = $true) & ! [X29 : a] : (((X27 @ X29) = $true) => ((X27 @ (cL @ X29)) = $true))) => ((X27 @ cZ) = $true))) => ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2) & ((cP @ Y1 @ Y2) = Y0))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y1))))))) | (cZ = Y0))) = (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y1 @ Y2) = Y0) & ((cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y1)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y2) | (cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2))))))) | (cZ = Y0)))))),
% 22.87/4.54 inference(fool_elimination,[status(thm)],[f4])).
% 22.87/4.54 thf(f4,plain,(
% 22.87/4.54 ~((! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1) & ! [X2 : a,X3 : a > $o] : (? [X4 : a] : ((cPSI @ (^[X5 : a] : (! [X6 : a > $o] : (((X6 @ X4) & ! [X7 : a] : ((X6 @ X7) => (X6 @ (cL @ X7)))) => ? [X8 : a] : ((X6 @ X8) & ((cR @ X8) = X5))))) @ X2) & ! [X9 : a] : (! [X10 : a > $o] : ((! [X11 : a] : ((X10 @ X11) => (X10 @ (cL @ X11))) & (X10 @ X4)) => ? [X12 : a] : ((X10 @ X12) & ((cR @ X12) = X9))) => (X3 @ X9))) <=> (cPSI @ X3 @ X2)) & (cZ = (cR @ cZ)) & (cZ = (cL @ cZ)) & ! [X13 : a,X14 : a > $o] : (? [X15 : a] : (! [X16 : a] : (! [X17 : a > $o] : ((! [X18 : a] : ((X17 @ X18) => (X17 @ (cL @ X18))) & (X17 @ X15)) => ? [X19 : a] : ((X17 @ X19) & ((cR @ X19) = X16))) => (X14 @ X16)) & (cPHI @ (^[X20 : a] : (! [X21 : a > $o] : ((! [X22 : a] : ((X21 @ X22) => (X21 @ (cL @ X22))) & (X21 @ X15)) => ? [X23 : a] : ((X21 @ X23) & ((cR @ X23) = X20))))) @ X13)) <=> (cPHI @ X14 @ X13)) & ! [X24 : a,X25 : a] : ((cR @ (cP @ X25 @ X24)) = X24) & ! [X26 : a] : (((cP @ (cL @ X26) @ (cR @ X26)) = X26) <=> (cZ != X26)) & ! [X27 : a > $o] : (? [X28 : a] : ((X27 @ X28) & ! [X29 : a] : ((X27 @ X29) => (X27 @ (cL @ X29)))) => (X27 @ cZ))) => ((^[X30 : a] : ((cZ = X30) | ? [X31 : a,X32 : a] : (((cPHI @ (^[X33 : a] : (! [X34 : a > $o] : ((! [X35 : a] : ((X34 @ X35) => (X34 @ (cL @ X35))) & (X34 @ X32)) => ? [X36 : a] : (((cR @ X36) = X33) & (X34 @ X36))))) @ X31) | (cPSI @ (^[X37 : a] : (! [X38 : a > $o] : (((X38 @ X32) & ! [X39 : a] : ((X38 @ X39) => (X38 @ (cL @ X39)))) => ? [X40 : a] : ((X38 @ X40) & ((cR @ X40) = X37))))) @ X31)) & ((cP @ X32 @ X31) = X30)))) = (^[X41 : a] : ((cZ = X41) | ? [X42 : a,X43 : a] : ((cPSI @ (^[X44 : a] : (! [X45 : a > $o] : (((X45 @ X42) & ! [X46 : a] : ((X45 @ X46) => (X45 @ (cL @ X46)))) => ? [X47 : a] : ((X45 @ X47) & ((cR @ X47) = X44))))) @ X43) & ((cP @ X42 @ X43) = X41)) | ? [X48 : a,X49 : a] : (((cP @ X49 @ X48) = X41) & (cPHI @ (^[X50 : a] : (! [X51 : a > $o] : ((! [X52 : a] : ((X51 @ X52) => (X51 @ (cL @ X52))) & (X51 @ X49)) => ? [X53 : a] : (((cR @ X53) = X50) & (X51 @ X53))))) @ X48)) | (cZ = X41)))))),
% 22.87/4.54 inference(rectify,[status(thm)],[f2])).
% 22.87/4.54 thf(f2,negated_conjecture,(
% 22.87/4.54 ~((! [X1 : a,X0 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & ! [X5 : a,X3 : a > $o] : (? [X0 : a] : ((cPSI @ (^[X1 : a] : (! [X7 : a > $o] : (((X7 @ X0) & ! [X8 : a] : ((X7 @ X8) => (X7 @ (cL @ X8)))) => ? [X9 : a] : ((X7 @ X9) & ((cR @ X9) = X1))))) @ X5) & ! [X10 : a] : (! [X7 : a > $o] : ((! [X8 : a] : ((X7 @ X8) => (X7 @ (cL @ X8))) & (X7 @ X0)) => ? [X9 : a] : ((X7 @ X9) & ((cR @ X9) = X10))) => (X3 @ X10))) <=> (cPSI @ X3 @ X5)) & (cZ = (cR @ cZ)) & (cZ = (cL @ cZ)) & ! [X5 : a,X3 : a > $o] : (? [X0 : a] : (! [X6 : a] : (! [X7 : a > $o] : ((! [X8 : a] : ((X7 @ X8) => (X7 @ (cL @ X8))) & (X7 @ X0)) => ? [X9 : a] : ((X7 @ X9) & ((cR @ X9) = X6))) => (X3 @ X6)) & (cPHI @ (^[X1 : a] : (! [X7 : a > $o] : ((! [X8 : a] : ((X7 @ X8) => (X7 @ (cL @ X8))) & (X7 @ X0)) => ? [X9 : a] : ((X7 @ X9) & ((cR @ X9) = X1))))) @ X5)) <=> (cPHI @ X3 @ X5)) & ! [X1 : a,X0 : a] : ((cR @ (cP @ X0 @ X1)) = X1) & ! [X2 : a] : (((cP @ (cL @ X2) @ (cR @ X2)) = X2) <=> (cZ != X2)) & ! [X3 : a > $o] : (? [X2 : a] : ((X3 @ X2) & ! [X4 : a] : ((X3 @ X4) => (X3 @ (cL @ X4)))) => (X3 @ cZ))) => ((^[X4 : a] : ((cZ = X4) | ? [X1 : a,X0 : a] : (((cPHI @ (^[X11 : a] : (! [X3 : a > $o] : ((! [X5 : a] : ((X3 @ X5) => (X3 @ (cL @ X5))) & (X3 @ X0)) => ? [X9 : a] : (((cR @ X9) = X11) & (X3 @ X9))))) @ X1) | (cPSI @ (^[X11 : a] : (! [X3 : a > $o] : (((X3 @ X0) & ! [X5 : a] : ((X3 @ X5) => (X3 @ (cL @ X5)))) => ? [X9 : a] : ((X3 @ X9) & ((cR @ X9) = X11))))) @ X1)) & ((cP @ X0 @ X1) = X4)))) = (^[X5 : a] : ((cZ = X5) | ? [X0 : a,X1 : a] : ((cPSI @ (^[X11 : a] : (! [X3 : a > $o] : (((X3 @ X0) & ! [X8 : a] : ((X3 @ X8) => (X3 @ (cL @ X8)))) => ? [X9 : a] : ((X3 @ X9) & ((cR @ X9) = X11))))) @ X1) & ((cP @ X0 @ X1) = X5)) | ? [X1 : a,X0 : a] : (((cP @ X0 @ X1) = X5) & (cPHI @ (^[X11 : a] : (! [X3 : a > $o] : ((! [X8 : a] : ((X3 @ X8) => (X3 @ (cL @ X8))) & (X3 @ X0)) => ? [X9 : a] : (((cR @ X9) = X11) & (X3 @ X9))))) @ X1)) | (cZ = X5)))))),
% 22.87/4.54 inference(negated_conjecture,[status(cth)],[f1])).
% 22.87/4.54 thf(f1,conjecture,(
% 22.87/4.54 (! [X1 : a,X0 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & ! [X5 : a,X3 : a > $o] : (? [X0 : a] : ((cPSI @ (^[X1 : a] : (! [X7 : a > $o] : (((X7 @ X0) & ! [X8 : a] : ((X7 @ X8) => (X7 @ (cL @ X8)))) => ? [X9 : a] : ((X7 @ X9) & ((cR @ X9) = X1))))) @ X5) & ! [X10 : a] : (! [X7 : a > $o] : ((! [X8 : a] : ((X7 @ X8) => (X7 @ (cL @ X8))) & (X7 @ X0)) => ? [X9 : a] : ((X7 @ X9) & ((cR @ X9) = X10))) => (X3 @ X10))) <=> (cPSI @ X3 @ X5)) & (cZ = (cR @ cZ)) & (cZ = (cL @ cZ)) & ! [X5 : a,X3 : a > $o] : (? [X0 : a] : (! [X6 : a] : (! [X7 : a > $o] : ((! [X8 : a] : ((X7 @ X8) => (X7 @ (cL @ X8))) & (X7 @ X0)) => ? [X9 : a] : ((X7 @ X9) & ((cR @ X9) = X6))) => (X3 @ X6)) & (cPHI @ (^[X1 : a] : (! [X7 : a > $o] : ((! [X8 : a] : ((X7 @ X8) => (X7 @ (cL @ X8))) & (X7 @ X0)) => ? [X9 : a] : ((X7 @ X9) & ((cR @ X9) = X1))))) @ X5)) <=> (cPHI @ X3 @ X5)) & ! [X1 : a,X0 : a] : ((cR @ (cP @ X0 @ X1)) = X1) & ! [X2 : a] : (((cP @ (cL @ X2) @ (cR @ X2)) = X2) <=> (cZ != X2)) & ! [X3 : a > $o] : (? [X2 : a] : ((X3 @ X2) & ! [X4 : a] : ((X3 @ X4) => (X3 @ (cL @ X4)))) => (X3 @ cZ))) => ((^[X4 : a] : ((cZ = X4) | ? [X1 : a,X0 : a] : (((cPHI @ (^[X11 : a] : (! [X3 : a > $o] : ((! [X5 : a] : ((X3 @ X5) => (X3 @ (cL @ X5))) & (X3 @ X0)) => ? [X9 : a] : (((cR @ X9) = X11) & (X3 @ X9))))) @ X1) | (cPSI @ (^[X11 : a] : (! [X3 : a > $o] : (((X3 @ X0) & ! [X5 : a] : ((X3 @ X5) => (X3 @ (cL @ X5)))) => ? [X9 : a] : ((X3 @ X9) & ((cR @ X9) = X11))))) @ X1)) & ((cP @ X0 @ X1) = X4)))) = (^[X5 : a] : ((cZ = X5) | ? [X0 : a,X1 : a] : ((cPSI @ (^[X11 : a] : (! [X3 : a > $o] : (((X3 @ X0) & ! [X8 : a] : ((X3 @ X8) => (X3 @ (cL @ X8)))) => ? [X9 : a] : ((X3 @ X9) & ((cR @ X9) = X11))))) @ X1) & ((cP @ X0 @ X1) = X5)) | ? [X1 : a,X0 : a] : (((cP @ X0 @ X1) = X5) & (cPHI @ (^[X11 : a] : (! [X3 : a > $o] : ((! [X8 : a] : ((X3 @ X8) => (X3 @ (cL @ X8))) & (X3 @ X0)) => ? [X9 : a] : (((cR @ X9) = X11) & (X3 @ X9))))) @ X1)) | (cZ = X5))))),
% 22.87/4.54 file('/export/starexec/sandbox/tmp/tmp.uDBwpsOxhs/DTF2THF_2178.p',cPU_X2310B_pme)).
% 22.87/4.54 thf(f2610,plain,(
% 22.87/4.54 (sK23 = (cR @ sK15)) | ~spl13_15),
% 22.87/4.54 inference(superposition,[status(thm)],[f56,f317])).
% 22.87/4.54 thf(f317,plain,(
% 22.87/4.54 ((cP @ sK22 @ sK23) = sK15) | ~spl13_15),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f315])).
% 22.87/4.54 thf(f315,definition,(
% 22.87/4.54 spl13_15 <=> ((cP @ sK22 @ sK23) = sK15)),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_15])],[avatar_definition])).
% 22.87/4.54 thf(f341,plain,(
% 22.87/4.54 ( ! [X2 : a,X1 : a] : (((cP @ X1 @ X2) != sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2) = $false)) ) | ~spl13_20),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f340])).
% 22.87/4.54 thf(f340,definition,(
% 22.87/4.54 spl13_20 <=> ! [X2 : a,X1 : a] : (((cP @ X1 @ X2) != sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2) = $false))),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_20])],[avatar_definition])).
% 22.87/4.54 thf(f2674,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true) | (~spl13_11 | ~spl13_15 | ~spl13_16)),
% 22.87/4.54 inference(forward_demodulation,[status(thm)],[f322,f2614])).
% 22.87/4.54 thf(f322,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK23) = $true) | ~spl13_16),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f320])).
% 22.87/4.54 thf(f320,definition,(
% 22.87/4.54 spl13_16 <=> ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK23) = $true)),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_16])],[avatar_definition])).
% 22.87/4.54 thf(f2823,plain,(
% 22.87/4.54 ~spl13_9 | ~spl13_10 | ~spl13_11 | ~spl13_20),
% 22.87/4.54 inference(avatar_contradiction_clause,[status(thm)],[f2822])).
% 22.87/4.54 thf(f2822,plain,(
% 22.87/4.54 $false | (~spl13_9 | ~spl13_10 | ~spl13_11 | ~spl13_20)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f2807])).
% 22.87/4.54 thf(f2807,plain,(
% 22.87/4.54 ($true = $false) | (~spl13_9 | ~spl13_10 | ~spl13_11 | ~spl13_20)),
% 22.87/4.54 inference(backward_demodulation,[status(thm)],[f2673,f2623])).
% 22.87/4.54 thf(f2623,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $false) | (~spl13_9 | ~spl13_11 | ~spl13_20)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f2617])).
% 22.87/4.54 thf(f2617,plain,(
% 22.87/4.54 (sK15 != sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $false) | (~spl13_9 | ~spl13_11 | ~spl13_20)),
% 22.87/4.54 inference(superposition,[status(thm)],[f341,f2606])).
% 22.87/4.54 thf(f2606,plain,(
% 22.87/4.54 ((cP @ sK24 @ sK18) = sK15) | (~spl13_9 | ~spl13_11)),
% 22.87/4.54 inference(backward_demodulation,[status(thm)],[f289,f2602])).
% 22.87/4.54 thf(f2602,plain,(
% 22.87/4.54 (sK26 = sK18) | (~spl13_9 | ~spl13_11)),
% 22.87/4.54 inference(backward_demodulation,[status(thm)],[f2454,f2467])).
% 22.87/4.54 thf(f2454,plain,(
% 22.87/4.54 ((cR @ sK15) = sK26) | ~spl13_9),
% 22.87/4.54 inference(superposition,[status(thm)],[f56,f289])).
% 22.87/4.54 thf(f289,plain,(
% 22.87/4.54 ((cP @ sK24 @ sK26) = sK15) | ~spl13_9),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f287])).
% 22.87/4.54 thf(f287,definition,(
% 22.87/4.54 spl13_9 <=> ((cP @ sK24 @ sK26) = sK15)),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_9])],[avatar_definition])).
% 22.87/4.54 thf(f2673,plain,(
% 22.87/4.54 ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18)) | (~spl13_9 | ~spl13_10 | ~spl13_11)),
% 22.87/4.54 inference(forward_demodulation,[status(thm)],[f294,f2602])).
% 22.87/4.54 thf(f294,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK26) = $true) | ~spl13_10),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f292])).
% 22.87/4.54 thf(f292,definition,(
% 22.87/4.54 spl13_10 <=> ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK26) = $true)),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_10])],[avatar_definition])).
% 22.87/4.54 thf(f2439,plain,(
% 22.87/4.54 ~spl13_12 | ~spl13_13 | ~spl13_14 | ~spl13_20),
% 22.87/4.54 inference(avatar_contradiction_clause,[status(thm)],[f2438])).
% 22.87/4.54 thf(f2438,plain,(
% 22.87/4.54 $false | (~spl13_12 | ~spl13_13 | ~spl13_14 | ~spl13_20)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f2428])).
% 22.87/4.54 thf(f2428,plain,(
% 22.87/4.54 ($true = $false) | (~spl13_12 | ~spl13_13 | ~spl13_14 | ~spl13_20)),
% 22.87/4.54 inference(backward_demodulation,[status(thm)],[f2382,f2425])).
% 22.87/4.54 thf(f2425,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $false) | (~spl13_12 | ~spl13_14 | ~spl13_20)),
% 22.87/4.54 inference(forward_demodulation,[status(thm)],[f1917,f2380])).
% 22.87/4.54 thf(f2380,plain,(
% 22.87/4.54 (sK17 = sK25) | (~spl13_12 | ~spl13_14)),
% 22.87/4.54 inference(forward_demodulation,[status(thm)],[f1915,f1924])).
% 22.87/4.54 thf(f1924,plain,(
% 22.87/4.54 (sK17 = (cR @ sK15)) | ~spl13_14),
% 22.87/4.54 inference(superposition,[status(thm)],[f56,f313])).
% 22.87/4.54 thf(f313,plain,(
% 22.87/4.54 ((cP @ sK16 @ sK17) = sK15) | ~spl13_14),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f311])).
% 22.87/4.54 thf(f311,definition,(
% 22.87/4.54 spl13_14 <=> ((cP @ sK16 @ sK17) = sK15)),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_14])],[avatar_definition])).
% 22.87/4.54 thf(f1915,plain,(
% 22.87/4.54 (sK25 = (cR @ sK15)) | ~spl13_12),
% 22.87/4.54 inference(superposition,[status(thm)],[f56,f303])).
% 22.87/4.54 thf(f303,plain,(
% 22.87/4.54 ((cP @ sK24 @ sK25) = sK15) | ~spl13_12),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f301])).
% 22.87/4.54 thf(f301,definition,(
% 22.87/4.54 spl13_12 <=> ((cP @ sK24 @ sK25) = sK15)),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_12])],[avatar_definition])).
% 22.87/4.54 thf(f1917,plain,(
% 22.87/4.54 ($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK25)) | (~spl13_12 | ~spl13_20)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f1912])).
% 22.87/4.54 thf(f1912,plain,(
% 22.87/4.54 (sK15 != sK15) | ($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK25)) | (~spl13_12 | ~spl13_20)),
% 22.87/4.54 inference(superposition,[status(thm)],[f341,f303])).
% 22.87/4.54 thf(f2382,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | (~spl13_12 | ~spl13_13 | ~spl13_14)),
% 22.87/4.54 inference(forward_demodulation,[status(thm)],[f308,f2380])).
% 22.87/4.54 thf(f308,plain,(
% 22.87/4.54 ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK25)) | ~spl13_13),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f306])).
% 22.87/4.54 thf(f306,definition,(
% 22.87/4.54 spl13_13 <=> ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK25))),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_13])],[avatar_definition])).
% 22.87/4.54 thf(f2272,plain,(
% 22.87/4.54 ~spl13_8 | ~spl13_14 | ~spl13_20),
% 22.87/4.54 inference(avatar_contradiction_clause,[status(thm)],[f2271])).
% 22.87/4.54 thf(f2271,plain,(
% 22.87/4.54 $false | (~spl13_8 | ~spl13_14 | ~spl13_20)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f2270])).
% 22.87/4.54 thf(f2270,plain,(
% 22.87/4.54 ($true = $false) | (~spl13_8 | ~spl13_14 | ~spl13_20)),
% 22.87/4.54 inference(forward_demodulation,[status(thm)],[f285,f1926])).
% 22.87/4.54 thf(f1926,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $false) | (~spl13_14 | ~spl13_20)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f1921])).
% 22.87/4.54 thf(f1921,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $false) | (sK15 != sK15) | (~spl13_14 | ~spl13_20)),
% 22.87/4.54 inference(superposition,[status(thm)],[f341,f313])).
% 22.87/4.54 thf(f285,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | ~spl13_8),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f283])).
% 22.87/4.54 thf(f283,definition,(
% 22.87/4.54 spl13_8 <=> ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true)),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_8])],[avatar_definition])).
% 22.87/4.54 thf(f1893,plain,(
% 22.87/4.54 ~spl13_17 | ~spl13_18 | ~spl13_20),
% 22.87/4.54 inference(avatar_contradiction_clause,[status(thm)],[f1892])).
% 22.87/4.54 thf(f1892,plain,(
% 22.87/4.54 $false | (~spl13_17 | ~spl13_18 | ~spl13_20)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f1883])).
% 22.87/4.54 thf(f1883,plain,(
% 22.87/4.54 ($true = $false) | (~spl13_17 | ~spl13_18 | ~spl13_20)),
% 22.87/4.54 inference(backward_demodulation,[status(thm)],[f332,f1677])).
% 22.87/4.54 thf(f1677,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK20) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK21) = $false) | (~spl13_17 | ~spl13_20)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f1672])).
% 22.87/4.54 thf(f1672,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK20) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK21) = $false) | (sK15 != sK15) | (~spl13_17 | ~spl13_20)),
% 22.87/4.54 inference(superposition,[status(thm)],[f341,f327])).
% 22.87/4.54 thf(f327,plain,(
% 22.87/4.54 ((cP @ sK20 @ sK21) = sK15) | ~spl13_17),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f325])).
% 22.87/4.54 thf(f325,definition,(
% 22.87/4.54 spl13_17 <=> ((cP @ sK20 @ sK21) = sK15)),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_17])],[avatar_definition])).
% 22.87/4.54 thf(f332,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK20) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK21) = $true) | ~spl13_18),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f330])).
% 22.87/4.54 thf(f330,definition,(
% 22.87/4.54 spl13_18 <=> ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK20) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK21) = $true)),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_18])],[avatar_definition])).
% 22.87/4.54 thf(f1469,plain,(
% 22.87/4.54 ~spl13_6 | ~spl13_11 | ~spl13_19),
% 22.87/4.54 inference(avatar_contradiction_clause,[status(thm)],[f1468])).
% 22.87/4.54 thf(f1468,plain,(
% 22.87/4.54 $false | (~spl13_6 | ~spl13_11 | ~spl13_19)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f1458])).
% 22.87/4.54 thf(f1458,plain,(
% 22.87/4.54 ($true = $false) | (~spl13_6 | ~spl13_11 | ~spl13_19)),
% 22.87/4.54 inference(backward_demodulation,[status(thm)],[f277,f1422])).
% 22.87/4.54 thf(f1422,plain,(
% 22.87/4.54 ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18) = $false) | (~spl13_11 | ~spl13_19)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f1417])).
% 22.87/4.54 thf(f1417,plain,(
% 22.87/4.54 (sK15 != sK15) | ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18) = $false) | (~spl13_11 | ~spl13_19)),
% 22.87/4.54 inference(superposition,[status(thm)],[f337,f299])).
% 22.87/4.54 thf(f337,plain,(
% 22.87/4.54 ( ! [X2 : a,X1 : a] : (((cP @ X2 @ X1) != sK15) | ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X1) = $false)) ) | ~spl13_19),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f336])).
% 22.87/4.54 thf(f336,definition,(
% 22.87/4.54 spl13_19 <=> ! [X2 : a,X1 : a] : (((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X1) = $false) | ((cP @ X2 @ X1) != sK15))),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_19])],[avatar_definition])).
% 22.87/4.54 thf(f277,plain,(
% 22.87/4.54 ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ~spl13_6),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f275])).
% 22.87/4.54 thf(f275,definition,(
% 22.87/4.54 spl13_6 <=> ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18))),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_6])],[avatar_definition])).
% 22.87/4.54 thf(f1375,plain,(
% 22.87/4.54 ~spl13_7 | ~spl13_14 | ~spl13_19),
% 22.87/4.54 inference(avatar_contradiction_clause,[status(thm)],[f1374])).
% 22.87/4.54 thf(f1374,plain,(
% 22.87/4.54 $false | (~spl13_7 | ~spl13_14 | ~spl13_19)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f1361])).
% 22.87/4.54 thf(f1361,plain,(
% 22.87/4.54 ($true = $false) | (~spl13_7 | ~spl13_14 | ~spl13_19)),
% 22.87/4.54 inference(backward_demodulation,[status(thm)],[f281,f1327])).
% 22.87/4.54 thf(f1327,plain,(
% 22.87/4.54 ($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | (~spl13_14 | ~spl13_19)),
% 22.87/4.54 inference(trivial_inequality_removal,[status(thm)],[f1326])).
% 22.87/4.54 thf(f1326,plain,(
% 22.87/4.54 ($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | (sK15 != sK15) | (~spl13_14 | ~spl13_19)),
% 22.87/4.54 inference(superposition,[status(thm)],[f337,f313])).
% 22.87/4.54 thf(f281,plain,(
% 22.87/4.54 ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | ~spl13_7),
% 22.87/4.54 inference(avatar_component_clause,[status(thm)],[f279])).
% 22.87/4.54 thf(f279,definition,(
% 22.87/4.54 spl13_7 <=> ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17))),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_7])],[avatar_definition])).
% 22.87/4.54 thf(f349,plain,(
% 22.87/4.54 spl13_19 | spl13_19),
% 22.87/4.54 inference(avatar_split_clause,[status(thm)],[f159,f336,f336])).
% 22.87/4.54 thf(f159,plain,(
% 22.87/4.54 ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (((cP @ X1 @ X2) != sK15) | ((cP @ X4 @ X3) != sK15) | ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X3) = $false) | ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X1)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2) = $false)) )),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f158])).
% 22.87/4.54 thf(f158,plain,(
% 22.87/4.54 ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (($false = ((cP @ X4 @ X3) = sK15)) | ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X3) = $false) | ((cP @ X1 @ X2) != sK15) | ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X1)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2) = $false)) )),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f157])).
% 22.87/4.54 thf(f157,plain,(
% 22.87/4.54 ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X1)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2) = $false) | ((cP @ X1 @ X2) != sK15) | ((((cP @ X4 @ X3) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X3)) = $false)) )),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f156])).
% 22.87/4.54 thf(f156,plain,(
% 22.87/4.54 ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (((cP @ X1 @ X2) != sK15) | ($false = ((^[Y0 : a]: (((cP @ Y0 @ X3) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: (((cR @ Y3) = Y1) & (Y2 @ Y3)))))))) @ X3))) @ X4)) | ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X1)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2) = $false)) )),
% 22.87/4.54 inference(pi_clausification,[status(thm)],[f155])).
% 22.87/4.54 thf(f155,plain,(
% 22.87/4.54 ( ! [X2 : a,X3 : a,X1 : a] : (((cP @ X1 @ X2) != sK15) | ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X1)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2) = $false) | ($false = (?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ X3) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: (((cR @ Y3) = Y1) & (Y2 @ Y3)))))))) @ X3)))))) )),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f154])).
% 22.87/4.54 thf(f154,plain,(
% 22.87/4.54 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))) @ X3) = $false) | ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X1)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2) = $false) | ((cP @ X1 @ X2) != sK15)) )),
% 22.87/4.54 inference(pi_clausification,[status(thm)],[f143])).
% 22.87/4.54 thf(f143,plain,(
% 22.87/4.54 ( ! [X2 : a,X1 : a] : (((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X1)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2) = $false) | ($false = (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | ((cP @ X1 @ X2) != sK15)) )),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f142])).
% 22.87/4.54 thf(f142,plain,(
% 22.87/4.54 ( ! [X2 : a,X1 : a] : (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $false) | ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X1)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2) = $false) | ((cP @ X1 @ X2) != sK15)) )),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f141])).
% 22.87/4.54 thf(f141,plain,(
% 22.87/4.54 ( ! [X2 : a,X1 : a] : ((((cP @ X1 @ X2) = sK15) = $false) | ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X1)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2) = $false) | ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $false)) )),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 22.87/4.54 thf(f139,plain,(
% 22.87/4.54 ( ! [X2 : a,X1 : a] : (($false = ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X1)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2))) | ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $false) | (((cP @ X1 @ X2) = sK15) = $false)) )),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f138])).
% 22.87/4.54 thf(f138,plain,(
% 22.87/4.54 ( ! [X2 : a,X1 : a] : (($false = (((cP @ X1 @ X2) = sK15) & ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X1)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X2) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2)))) | ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $false)) )),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f137])).
% 22.87/4.54 thf(f137,plain,(
% 22.87/4.54 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((cP @ X1 @ Y0) = sK15) & ((cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ X1)) => (?? @ a @ (^[Y3 : a]: (((cR @ Y3) = Y1) & (Y2 @ Y3)))))))) @ Y0) | (cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ X1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0)))) @ X2) = $false) | ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $false)) )),
% 22.87/4.54 inference(pi_clausification,[status(thm)],[f136])).
% 22.87/4.54 thf(f136,plain,(
% 22.87/4.54 ( ! [X1 : a] : (((?? @ a @ (^[Y0 : a]: (((cP @ X1 @ Y0) = sK15) & ((cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ X1)) => (?? @ a @ (^[Y3 : a]: (((cR @ Y3) = Y1) & (Y2 @ Y3)))))))) @ Y0) | (cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ X1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0))))) = $false) | ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $false)) )),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f135])).
% 22.87/4.54 thf(f135,plain,(
% 22.87/4.54 ( ! [X1 : a] : (($false = ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y0 @ Y1) = sK15) & ((cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y0)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y1) | (cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1)))))) @ X1)) | ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $false)) )),
% 22.87/4.54 inference(pi_clausification,[status(thm)],[f134])).
% 22.87/4.54 thf(f134,plain,(
% 22.87/4.54 ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y0 @ Y1) = sK15) & ((cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y0)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y1) | (cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1))))))) = $false) | ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $false)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f132])).
% 22.87/4.54 thf(f132,plain,(
% 22.87/4.54 (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | (cZ = sK15)) = $false) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y0 @ Y1) = sK15) & ((cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y0)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y1) | (cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1))))))) = $false)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 22.87/4.54 thf(f130,plain,(
% 22.87/4.54 ($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y0 @ Y1) = sK15) & ((cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y0)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y1) | (cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1))))))) | (cZ = sK15))) | (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | (cZ = sK15)) = $false)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 22.87/4.54 thf(f128,plain,(
% 22.87/4.54 (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | (cZ = sK15)) != ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y0 @ Y1) = sK15) & ((cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y0)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y1) | (cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1))))))) | (cZ = sK15)))),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f127])).
% 22.87/4.54 thf(f127,plain,(
% 22.87/4.54 (((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2) & ((cP @ Y1 @ Y2) = Y0))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y1))))))) | (cZ = Y0))) @ sK15) != ((^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y1 @ Y2) = Y0) & ((cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y1)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y2) | (cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2))))))) | (cZ = Y0))) @ sK15))),
% 22.87/4.54 inference(negative_extensionality,[status(thm)],[f58])).
% 22.87/4.54 thf(f58,plain,(
% 22.87/4.54 ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2) & ((cP @ Y1 @ Y2) = Y0))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y1))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y1 @ Y2) = Y0) & ((cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y1)) => (?? @ a @ (^[Y5 : a]: (((cR @ Y5) = Y3) & (Y4 @ Y5)))))))) @ Y2) | (cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y1) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y2))))))) | (cZ = Y0))))),
% 22.87/4.54 inference(cnf_transformation,[status(thm)],[f31])).
% 22.87/4.54 thf(f347,plain,(
% 22.87/4.54 spl13_20 | spl13_20),
% 22.87/4.54 inference(avatar_split_clause,[status(thm)],[f171,f340,f340])).
% 22.87/4.54 thf(f171,plain,(
% 22.87/4.54 ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X3) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X4)) | ((cP @ X1 @ X2) != sK15) | ((cP @ X3 @ X4) != sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2) = $false)) )),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f170])).
% 22.87/4.54 thf(f170,plain,(
% 22.87/4.54 ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (((cP @ X1 @ X2) != sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2) = $false) | ($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X3) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X4)) | (((cP @ X3 @ X4) = sK15) = $false)) )),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f169])).
% 22.87/4.54 thf(f169,plain,(
% 22.87/4.54 ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2) = $false) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X3) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X4) & ((cP @ X3 @ X4) = sK15)) = $false) | ((cP @ X1 @ X2) != sK15)) )),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f168])).
% 22.87/4.54 thf(f168,plain,(
% 22.87/4.54 ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (((cP @ X1 @ X2) != sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2) = $false) | ($false = ((^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ X3) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ X3 @ Y0) = sK15))) @ X4))) )),
% 22.87/4.54 inference(pi_clausification,[status(thm)],[f167])).
% 22.87/4.54 thf(f167,plain,(
% 22.87/4.54 ( ! [X2 : a,X3 : a,X1 : a] : (((cP @ X1 @ X2) != sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2) = $false) | ($false = (?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ X3) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ X3 @ Y0) = sK15)))))) )),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f166])).
% 22.87/4.54 thf(f166,plain,(
% 22.87/4.54 ( ! [X2 : a,X3 : a,X1 : a] : (((cP @ X1 @ X2) != sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2) = $false) | (((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))) @ X3) = $false)) )),
% 22.87/4.54 inference(pi_clausification,[status(thm)],[f163])).
% 22.87/4.54 thf(f163,plain,(
% 22.87/4.54 ( ! [X2 : a,X1 : a] : (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2) = $false) | ((cP @ X1 @ X2) != sK15) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))) = $false)) )),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f162])).
% 22.87/4.54 thf(f162,plain,(
% 22.87/4.54 ( ! [X2 : a,X1 : a] : (($false = ((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))))) | ((cP @ X1 @ X2) != sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2) = $false)) )),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f160])).
% 22.87/4.54 thf(f160,plain,(
% 22.87/4.54 ( ! [X2 : a,X1 : a] : (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $false) | ((cP @ X1 @ X2) != sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2) = $false)) )),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f140])).
% 22.87/4.54 thf(f140,plain,(
% 22.87/4.54 ( ! [X2 : a,X1 : a] : (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X2) = $false) | (((cP @ X1 @ X2) = sK15) = $false) | ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $false)) )),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 22.87/4.54 thf(f343,plain,(
% 22.87/4.54 ~spl13_5),
% 22.87/4.54 inference(avatar_split_clause,[status(thm)],[f196,f271])).
% 22.87/4.54 thf(f271,definition,(
% 22.87/4.54 spl13_5 <=> (cZ = sK15)),
% 22.87/4.54 introduced(definition,[new_symbols(naming,[spl13_5])],[avatar_definition])).
% 22.87/4.54 thf(f196,plain,(
% 22.87/4.54 (cZ != sK15)),
% 22.87/4.54 inference(duplicate_literal_removal,[status(thm)],[f195])).
% 22.87/4.54 thf(f195,plain,(
% 22.87/4.54 (cZ != sK15) | (cZ != sK15)),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f194])).
% 22.87/4.54 thf(f194,plain,(
% 22.87/4.54 ((cZ = sK15) = $false) | (cZ != sK15)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f192])).
% 22.87/4.54 thf(f192,plain,(
% 22.87/4.54 (cZ != sK15) | ($false = ((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))))),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f190])).
% 22.87/4.54 thf(f190,plain,(
% 22.87/4.54 (cZ != sK15) | ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $false)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f188])).
% 22.87/4.54 thf(f188,plain,(
% 22.87/4.54 (cZ != sK15) | (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | (cZ = sK15)) = $false)),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f131])).
% 22.87/4.54 thf(f131,plain,(
% 22.87/4.54 ((cZ = sK15) = $false) | (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | (cZ = sK15)) = $false)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 22.87/4.54 thf(f333,plain,(
% 22.87/4.54 spl13_14 | spl13_18 | spl13_11 | spl13_5),
% 22.87/4.54 inference(avatar_split_clause,[status(thm)],[f239,f271,f297,f330,f311])).
% 22.87/4.54 thf(f239,plain,(
% 22.87/4.54 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK20) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK21) = $true) | (cZ = sK15) | (sK15 = (cP @ sK19 @ sK18)) | ((cP @ sK16 @ sK17) = sK15)),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f238])).
% 22.87/4.54 thf(f238,plain,(
% 22.87/4.54 ($true = ((cP @ sK16 @ sK17) = sK15)) | (cZ = sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK20) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK21) = $true) | (sK15 = (cP @ sK19 @ sK18))),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f236])).
% 22.87/4.54 thf(f236,plain,(
% 22.87/4.54 (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK20) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK21) & ((cP @ sK20 @ sK21) = sK15)) = $true) | ($true = ((cP @ sK16 @ sK17) = sK15)) | (sK15 = (cP @ sK19 @ sK18)) | (cZ = sK15)),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f235])).
% 22.87/4.54 thf(f235,plain,(
% 22.87/4.54 (((cP @ sK19 @ sK18) = sK15) = $true) | (cZ = sK15) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK20) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK21) & ((cP @ sK20 @ sK21) = sK15)) = $true) | ($true = ((cP @ sK16 @ sK17) = sK15))),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f234])).
% 22.87/4.54 thf(f234,plain,(
% 22.87/4.54 (cZ = sK15) | (((cP @ sK19 @ sK18) = sK15) = $true) | ($true = ((cP @ sK16 @ sK17) = sK15)) | ($true = ((^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK20) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ sK20 @ Y0) = sK15))) @ sK21))),
% 22.87/4.54 inference(sigma_clausification,[status(thm)],[f233])).
% 22.87/4.54 thf(f233,plain,(
% 22.87/4.54 ((?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK20) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ sK20 @ Y0) = sK15)))) = $true) | (cZ = sK15) | ($true = ((cP @ sK16 @ sK17) = sK15)) | (((cP @ sK19 @ sK18) = sK15) = $true)),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f232])).
% 22.87/4.54 thf(f232,plain,(
% 22.87/4.54 (((cP @ sK19 @ sK18) = sK15) = $true) | ($true = ((cP @ sK16 @ sK17) = sK15)) | ($true = ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))) @ sK20)) | (cZ = sK15)),
% 22.87/4.54 inference(sigma_clausification,[status(thm)],[f231])).
% 22.87/4.54 thf(f231,plain,(
% 22.87/4.54 ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))) = $true) | (cZ = sK15) | (((cP @ sK19 @ sK18) = sK15) = $true) | ($true = ((cP @ sK16 @ sK17) = sK15))),
% 22.87/4.54 inference(duplicate_literal_removal,[status(thm)],[f230])).
% 22.87/4.54 thf(f230,plain,(
% 22.87/4.54 ($true = ((cP @ sK16 @ sK17) = sK15)) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))) = $true) | (cZ = sK15) | (cZ = sK15) | (((cP @ sK19 @ sK18) = sK15) = $true)),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f229])).
% 22.87/4.54 thf(f229,plain,(
% 22.87/4.54 ((cZ = sK15) = $true) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))) = $true) | (((cP @ sK19 @ sK18) = sK15) = $true) | ($true = ((cP @ sK16 @ sK17) = sK15)) | (cZ = sK15)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f227])).
% 22.87/4.54 thf(f227,plain,(
% 22.87/4.54 ($true = (((cP @ sK19 @ sK18) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18))) | ((cZ = sK15) = $true) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))) = $true) | (cZ = sK15) | ($true = ((cP @ sK16 @ sK17) = sK15))),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f225])).
% 22.87/4.54 thf(f225,plain,(
% 22.87/4.54 ($true = (((cP @ sK16 @ sK17) = sK15) & ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17)))) | ($true = (((cP @ sK19 @ sK18) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18))) | ((cZ = sK15) = $true) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))) = $true) | (cZ = sK15)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f224])).
% 22.87/4.54 thf(f224,plain,(
% 22.87/4.54 (cZ = sK15) | ($true = ((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))))) | ($true = (((cP @ sK19 @ sK18) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18))) | ($true = (((cP @ sK16 @ sK17) = sK15) & ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17))))),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f223])).
% 22.87/4.54 thf(f223,plain,(
% 22.87/4.54 ($true = ((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))))) | (cZ = sK15) | (((^[Y0 : a]: (((cP @ Y0 @ sK18) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: (((cR @ Y3) = Y1) & (Y2 @ Y3)))))))) @ sK18))) @ sK19) = $true) | ($true = (((cP @ sK16 @ sK17) = sK15) & ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17))))),
% 22.87/4.54 inference(sigma_clausification,[status(thm)],[f222])).
% 22.87/4.54 thf(f222,plain,(
% 22.87/4.54 ($true = (?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ sK18) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: (((cR @ Y3) = Y1) & (Y2 @ Y3)))))))) @ sK18))))) | ($true = ((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))))) | (cZ = sK15) | ($true = (((cP @ sK16 @ sK17) = sK15) & ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17))))),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f221])).
% 22.87/4.54 thf(f221,plain,(
% 22.87/4.54 ($true = (((cP @ sK16 @ sK17) = sK15) & ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17)))) | ($true = ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))) @ sK18)) | ($true = ((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))))) | (cZ = sK15)),
% 22.87/4.54 inference(sigma_clausification,[status(thm)],[f220])).
% 22.87/4.54 thf(f220,plain,(
% 22.87/4.54 ($true = (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | ($true = ((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))))) | (cZ = sK15) | ($true = (((cP @ sK16 @ sK17) = sK15) & ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17))))),
% 22.87/4.54 inference(duplicate_literal_removal,[status(thm)],[f219])).
% 22.87/4.54 thf(f219,plain,(
% 22.87/4.54 ($true = (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | ($true = ((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))))) | (cZ = sK15) | (cZ = sK15) | ($true = (((cP @ sK16 @ sK17) = sK15) & ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17))))),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f218])).
% 22.87/4.54 thf(f218,plain,(
% 22.87/4.54 (cZ = sK15) | ((cZ = sK15) = $true) | ($true = (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | ($true = (((cP @ sK16 @ sK17) = sK15) & ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17)))) | ($true = ((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))))),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f217])).
% 22.87/4.54 thf(f217,plain,(
% 22.87/4.54 (cZ = sK15) | ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $true) | ($true = (((cP @ sK16 @ sK17) = sK15) & ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17)))) | ((cZ = sK15) = $true)),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f216])).
% 22.87/4.54 thf(f216,plain,(
% 22.87/4.54 ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $true) | ((cZ = sK15) = $true) | (cZ = sK15) | (((^[Y0 : a]: (((cP @ sK16 @ Y0) = sK15) & ((cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ sK16)) => (?? @ a @ (^[Y3 : a]: (((cR @ Y3) = Y1) & (Y2 @ Y3)))))))) @ Y0) | (cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK16) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0)))) @ sK17) = $true)),
% 22.87/4.54 inference(sigma_clausification,[status(thm)],[f215])).
% 22.87/4.54 thf(f215,plain,(
% 22.87/4.54 ($true = (?? @ a @ (^[Y0 : a]: (((cP @ sK16 @ Y0) = sK15) & ((cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ sK16)) => (?? @ a @ (^[Y3 : a]: (((cR @ Y3) = Y1) & (Y2 @ Y3)))))))) @ Y0) | (cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK16) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0)))))) | (cZ = sK15) | ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) = $true) | ((cZ = sK15) = $true)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f214])).
% 22.87/4.54 thf(f214,plain,(
% 22.87/4.54 (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | (cZ = sK15)) = $true) | ($true = (?? @ a @ (^[Y0 : a]: (((cP @ sK16 @ Y0) = sK15) & ((cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ sK16)) => (?? @ a @ (^[Y3 : a]: (((cR @ Y3) = Y1) & (Y2 @ Y3)))))))) @ Y0) | (cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK16) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0)))))) | (cZ = sK15)),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f213])).
% 22.87/4.54 thf(f213,plain,(
% 22.87/4.54 ((cZ = sK15) = $true) | ($true = (?? @ a @ (^[Y0 : a]: (((cP @ sK16 @ Y0) = sK15) & ((cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ sK16)) => (?? @ a @ (^[Y3 : a]: (((cR @ Y3) = Y1) & (Y2 @ Y3)))))))) @ Y0) | (cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK16) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0)))))) | (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | (cZ = sK15)) = $true)),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f212])).
% 22.87/4.54 thf(f212,plain,(
% 22.87/4.54 (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | (cZ = sK15)) = $true) | ($true = ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y0 @ Y1) = sK15) & ((cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y0)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y1) | (cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1)))))) @ sK16)) | ((cZ = sK15) = $true)),
% 22.87/4.54 inference(sigma_clausification,[status(thm)],[f211])).
% 22.87/4.54 thf(f211,plain,(
% 22.87/4.54 ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y0 @ Y1) = sK15) & ((cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y0)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y1) | (cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1))))))) = $true) | (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | (cZ = sK15)) = $true) | ((cZ = sK15) = $true)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f129])).
% 22.87/4.54 thf(f129,plain,(
% 22.87/4.54 ($true = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y0 @ Y1) = sK15) & ((cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y0)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y1) | (cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1))))))) | (cZ = sK15))) | (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: (((cR @ Y4) = Y2) & (Y3 @ Y4)))))))) @ Y0))))))) | (cZ = sK15)) = $true)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 22.87/4.54 thf(f328,plain,(
% 22.87/4.54 spl13_11 | spl13_5 | spl13_17 | spl13_14),
% 22.87/4.54 inference(avatar_split_clause,[status(thm)],[f241,f311,f325,f271,f297])).
% 22.87/4.54 thf(f241,plain,(
% 22.87/4.54 (sK15 = (cP @ sK19 @ sK18)) | ((cP @ sK20 @ sK21) = sK15) | (cZ = sK15) | ((cP @ sK16 @ sK17) = sK15)),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f240])).
% 22.87/4.54 thf(f240,plain,(
% 22.87/4.54 ((cP @ sK20 @ sK21) = sK15) | (cZ = sK15) | ($true = ((cP @ sK16 @ sK17) = sK15)) | (sK15 = (cP @ sK19 @ sK18))),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f237])).
% 22.87/4.54 thf(f237,plain,(
% 22.87/4.54 (sK15 = (cP @ sK19 @ sK18)) | (cZ = sK15) | ($true = ((cP @ sK20 @ sK21) = sK15)) | ($true = ((cP @ sK16 @ sK17) = sK15))),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f236])).
% 22.87/4.54 thf(f323,plain,(
% 22.87/4.54 spl13_16 | spl13_14 | spl13_5 | spl13_6),
% 22.87/4.54 inference(avatar_split_clause,[status(thm)],[f250,f275,f271,f311,f320])).
% 22.87/4.54 thf(f250,plain,(
% 22.87/4.54 ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ((cP @ sK16 @ sK17) = sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK23) = $true) | (cZ = sK15)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f248])).
% 22.87/4.54 thf(f248,plain,(
% 22.87/4.54 ($true = ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK23) & ((cP @ sK22 @ sK23) = sK15))) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ((cP @ sK16 @ sK17) = sK15) | (cZ = sK15)),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f247])).
% 22.87/4.54 thf(f247,plain,(
% 22.87/4.54 ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ((cP @ sK16 @ sK17) = sK15) | (cZ = sK15) | (((^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK22) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ sK22 @ Y0) = sK15))) @ sK23) = $true)),
% 22.87/4.54 inference(sigma_clausification,[status(thm)],[f246])).
% 22.87/4.54 thf(f246,plain,(
% 22.87/4.54 (cZ = sK15) | ((?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK22) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ sK22 @ Y0) = sK15)))) = $true) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ((cP @ sK16 @ sK17) = sK15)),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f245])).
% 22.87/4.54 thf(f245,plain,(
% 22.87/4.54 (cZ = sK15) | ($true = ((cP @ sK16 @ sK17) = sK15)) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ((?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK22) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ sK22 @ Y0) = sK15)))) = $true)),
% 22.87/4.54 inference(duplicate_literal_removal,[status(thm)],[f244])).
% 22.87/4.54 thf(f244,plain,(
% 22.87/4.54 ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | (cZ = sK15) | (cZ = sK15) | ((?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK22) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ sK22 @ Y0) = sK15)))) = $true) | ($true = ((cP @ sK16 @ sK17) = sK15))),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f243])).
% 22.87/4.54 thf(f243,plain,(
% 22.87/4.54 ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ((cZ = sK15) = $true) | ($true = ((cP @ sK16 @ sK17) = sK15)) | ((?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK22) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ sK22 @ Y0) = sK15)))) = $true) | (cZ = sK15)),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f242])).
% 22.87/4.54 thf(f242,plain,(
% 22.87/4.54 (cZ = sK15) | ($true = ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))) @ sK22)) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ((cZ = sK15) = $true) | ($true = ((cP @ sK16 @ sK17) = sK15))),
% 22.87/4.54 inference(sigma_clausification,[status(thm)],[f228])).
% 22.87/4.54 thf(f228,plain,(
% 22.87/4.54 ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))) = $true) | ($true = ((cP @ sK16 @ sK17) = sK15)) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ((cZ = sK15) = $true) | (cZ = sK15)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f227])).
% 22.87/4.54 thf(f318,plain,(
% 22.87/4.54 spl13_5 | spl13_14 | spl13_15 | spl13_6),
% 22.87/4.54 inference(avatar_split_clause,[status(thm)],[f251,f275,f315,f311,f271])).
% 22.87/4.54 thf(f251,plain,(
% 22.87/4.54 ((cP @ sK16 @ sK17) = sK15) | (cZ = sK15) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ((cP @ sK22 @ sK23) = sK15)),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f249])).
% 22.87/4.54 thf(f249,plain,(
% 22.87/4.54 ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ((cP @ sK16 @ sK17) = sK15) | (cZ = sK15) | (((cP @ sK22 @ sK23) = sK15) = $true)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f248])).
% 22.87/4.54 thf(f309,plain,(
% 22.87/4.54 spl13_7 | spl13_8 | spl13_5 | spl13_11 | spl13_13),
% 22.87/4.54 inference(avatar_split_clause,[status(thm)],[f263,f306,f297,f271,f283,f279])).
% 22.87/4.54 thf(f263,plain,(
% 22.87/4.54 (sK15 = (cP @ sK19 @ sK18)) | ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK25)) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | (cZ = sK15)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f261])).
% 22.87/4.54 thf(f261,plain,(
% 22.87/4.54 ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | (sK15 = (cP @ sK19 @ sK18)) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | (cZ = sK15) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK25) & ((cP @ sK24 @ sK25) = sK15)) = $true)),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f260])).
% 22.87/4.54 thf(f260,plain,(
% 22.87/4.54 ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | (cZ = sK15) | (sK15 = (cP @ sK19 @ sK18)) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | (((^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK24) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ sK24 @ Y0) = sK15))) @ sK25) = $true)),
% 22.87/4.54 inference(sigma_clausification,[status(thm)],[f259])).
% 22.87/4.54 thf(f259,plain,(
% 22.87/4.54 (sK15 = (cP @ sK19 @ sK18)) | ((?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK24) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ sK24 @ Y0) = sK15)))) = $true) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | (cZ = sK15)),
% 22.87/4.54 inference(equality_proxy_clausification,[status(thm)],[f258])).
% 22.87/4.54 thf(f258,plain,(
% 22.87/4.54 (((cP @ sK19 @ sK18) = sK15) = $true) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | (cZ = sK15) | ((?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK24) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ sK24 @ Y0) = sK15)))) = $true)),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f256])).
% 22.87/4.54 thf(f256,plain,(
% 22.87/4.54 (cZ = sK15) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | ($true = (((cP @ sK19 @ sK18) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18))) | ((?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK24) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ sK24 @ Y0) = sK15)))) = $true) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true)),
% 22.87/4.54 inference(beta_eta_normalization,[status(thm)],[f255])).
% 22.87/4.54 thf(f255,plain,(
% 22.87/4.54 (cZ = sK15) | ($true = (((cP @ sK19 @ sK18) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18))) | (((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15))))) @ sK24) = $true) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17))),
% 22.87/4.54 inference(sigma_clausification,[status(thm)],[f254])).
% 22.87/4.54 thf(f254,plain,(
% 22.87/4.54 (cZ = sK15) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))) = $true) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | ($true = (((cP @ sK19 @ sK18) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)))),
% 22.87/4.54 inference(binary_proxy_clausification,[status(thm)],[f253])).
% 22.87/4.54 thf(f253,plain,(
% 22.87/4.54 (cZ = sK15) | ($true = ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17))) | ($true = (((cP @ sK19 @ sK18) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18))) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))) = $true)),
% 22.87/4.54 inference(duplicate_literal_removal,[status(thm)],[f252])).
% 22.87/4.54 thf(f252,plain,(
% 22.87/4.54 (cZ = sK15) | ($true = ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17))) | ($true = (((cP @ sK19 @ sK18) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18))) | (cZ = sK15) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))) = $true)),
% 22.87/4.55 inference(equality_proxy_clausification,[status(thm)],[f226])).
% 22.87/4.55 thf(f226,plain,(
% 22.87/4.55 ((cZ = sK15) = $true) | (cZ = sK15) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y0) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y1) & ((cP @ Y0 @ Y1) = sK15)))))) = $true) | ($true = (((cP @ sK19 @ sK18) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18))) | ($true = ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17) | (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17)))),
% 22.87/4.55 inference(binary_proxy_clausification,[status(thm)],[f225])).
% 22.87/4.55 thf(f304,plain,(
% 22.87/4.55 spl13_7 | spl13_5 | spl13_11 | spl13_8 | spl13_12),
% 22.87/4.55 inference(avatar_split_clause,[status(thm)],[f264,f301,f283,f297,f271,f279])).
% 22.87/4.55 thf(f264,plain,(
% 22.87/4.55 ((cP @ sK24 @ sK25) = sK15) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | (sK15 = (cP @ sK19 @ sK18)) | (cZ = sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true)),
% 22.87/4.55 inference(equality_proxy_clausification,[status(thm)],[f262])).
% 22.87/4.55 thf(f262,plain,(
% 22.87/4.55 (((cP @ sK24 @ sK25) = sK15) = $true) | (cZ = sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | (sK15 = (cP @ sK19 @ sK18))),
% 22.87/4.55 inference(binary_proxy_clausification,[status(thm)],[f261])).
% 22.87/4.55 thf(f295,plain,(
% 22.87/4.55 spl13_10 | spl13_7 | spl13_6 | spl13_8 | spl13_5),
% 22.87/4.55 inference(avatar_split_clause,[status(thm)],[f268,f271,f283,f275,f279,f292])).
% 22.87/4.55 thf(f268,plain,(
% 22.87/4.55 ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK26) = $true) | (cZ = sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17))),
% 22.87/4.55 inference(binary_proxy_clausification,[status(thm)],[f266])).
% 22.87/4.55 thf(f266,plain,(
% 22.87/4.55 ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | (cZ = sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | ($true = ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK24) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK26) & ((cP @ sK24 @ sK26) = sK15)))),
% 22.87/4.55 inference(beta_eta_normalization,[status(thm)],[f265])).
% 22.87/4.55 thf(f265,plain,(
% 22.87/4.55 ($true = ((^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK24) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ sK24 @ Y0) = sK15))) @ sK26)) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | (cZ = sK15)),
% 22.87/4.55 inference(sigma_clausification,[status(thm)],[f257])).
% 22.87/4.55 thf(f257,plain,(
% 22.87/4.55 ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | (cZ = sK15) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ((?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ sK24) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ Y0) & ((cP @ sK24 @ Y0) = sK15)))) = $true)),
% 22.87/4.55 inference(binary_proxy_clausification,[status(thm)],[f256])).
% 22.87/4.55 thf(f290,plain,(
% 22.87/4.55 spl13_5 | spl13_6 | spl13_7 | spl13_8 | spl13_9),
% 22.87/4.55 inference(avatar_split_clause,[status(thm)],[f269,f287,f283,f279,f275,f271])).
% 22.87/4.55 thf(f269,plain,(
% 22.87/4.55 (cZ = sK15) | ((cP @ sK24 @ sK26) = sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17))),
% 22.87/4.55 inference(equality_proxy_clausification,[status(thm)],[f267])).
% 22.87/4.55 thf(f267,plain,(
% 22.87/4.55 ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK19)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK18)) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK16)) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ sK17)) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK17) = $true) | ($true = ((cP @ sK24 @ sK26) = sK15)) | (cZ = sK15)),
% 22.87/4.55 inference(binary_proxy_clausification,[status(thm)],[f266])).
% 22.87/4.55 % SZS output end Proof for DTF2THF_2178
% 22.87/4.55 % (2397)------------------------------
% 22.87/4.55 % (2397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.87/4.55 % (2397)Termination reason: Refutation
% 22.87/4.55
% 22.87/4.55 % (2397)Memory used [KB]: 6908
% 22.87/4.55 % (2397)Time elapsed: 0.414 s
% 22.87/4.55 % (2397)Instructions burned: 841 (million)
% 22.87/4.55 % (2397)------------------------------
% 22.87/4.55 % (2397)------------------------------
% 22.87/4.55 % (2275)Success in time 3.193 s
%------------------------------------------------------------------------------