%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO391^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:54:07 AM UTC 2026
% Result : Theorem 0.32s 1.38s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 8
% Syntax : Number of formulae : 145 ( 25 unt; 0 typ; 7 def)
% Number of atoms : 3222 ( 837 equ; 0 cnn)
% Maximal formula atoms : 113 ( 22 avg)
% Number of connectives : 4444 ( 879 ~; 770 |; 222 &;2566 @)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 54 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 13 con; 0-3 aty)
% Number of variables : 939 ( 0 ^; 939 !; 0 ?; 939 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ_7: $i > $i > $i > $o ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
cP_6: $i > $i > $o ).
thf(func_def_3,type,
cQ_6: $i > $i > $i > $o ).
thf(func_def_8,type,
cP_5: $i > $i > $o ).
thf(func_def_9,type,
cQ_5: $i > $i > $i > $o ).
thf(func_def_10,type,
cP_4: $i > $i > $o ).
thf(func_def_11,type,
cQ_4: $i > $i > $i > $o ).
thf(func_def_12,type,
cP_3: $i > $i > $o ).
thf(func_def_13,type,
cQ_3: $i > $i > $i > $o ).
thf(func_def_14,type,
cP_2: $i > $i > $o ).
thf(func_def_15,type,
cQ_2: $i > $i > $i > $o ).
thf(func_def_16,type,
cP_1: $i > $i > $o ).
thf(func_def_17,type,
cQ_1: $i > $i > $i > $o ).
thf(f223,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f69,f125,f142,f159,f168,f185,f217,f222]) ).
thf(f222,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[status(thm)],[f221]) ).
thf(f221,plain,
( $false
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f220]) ).
thf(f220,plain,
( ( $true != $true )
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f184,f34]) ).
thf(f34,plain,
( ( cP_6 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cP_1 @ b @ b )
= $true )
& ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( ( cP_3 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true
= ( cQ_4 @ X2 @ X1 @ X5 ) )
| ( $true
!= ( cP_3 @ ( f @ X4 ) @ X5 ) )
| ( $true
!= ( cP_3 @ ( f @ X3 ) @ X2 ) )
| ( ( cQ_3 @ X3 @ X0 @ X4 )
!= $true ) )
& ! [X6: $i,X7: $i,X8: $i,X9: $i,X10: $i,X11: $i] :
( ( ( cQ_1 @ X8 @ X7 @ X11 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X8 ) @ X10 ) )
| ( ( cP_1 @ ( f @ X11 ) @ X9 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X7 ) @ X6 ) )
| ( ( cQ_2 @ X10 @ X6 @ X9 )
= $true ) )
& ( ( cP_4 @ c @ c )
= $true )
& ! [X12: $i] :
( ( cP_1 @ d @ X12 )
= $true )
& ( ( cP_5 @ a @ a )
= $true )
& ( ( cP_6 @ a @ a )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ! [X13: $i] :
( ( cP_4 @ d @ X13 )
= $true )
& ! [X14: $i,X15: $i,X16: $i,X17: $i,X18: $i,X19: $i] :
( ( $true
!= ( cP_6 @ ( f @ X19 ) @ X18 ) )
| ( $true
!= ( cP_6 @ ( f @ X15 ) @ X17 ) )
| ( $true
!= ( cP_6 @ ( f @ X16 ) @ X14 ) )
| ( ( cQ_7 @ X18 @ X14 @ X17 )
= $true )
| ( ( cQ_6 @ X19 @ X16 @ X15 )
!= $true ) )
& ! [X20: $i,X21: $i,X22: $i,X23: $i,X24: $i,X25: $i] :
( ( ( cQ_5 @ X25 @ X23 @ X22 )
= $true )
| ( ( cQ_4 @ X21 @ X20 @ X24 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X20 ) @ X23 ) )
| ( $true
!= ( cP_4 @ ( f @ X21 ) @ X25 ) )
| ( ( cP_4 @ ( f @ X24 ) @ X22 )
!= $true ) )
& ( ( cP_6 @ b @ b )
= $true )
& ! [X26: $i,X27: $i,X28: $i] :
( ( cQ_7 @ X27 @ X28 @ X26 )
!= $true )
& ! [X29: $i,X30: $i,X31: $i,X32: $i,X33: $i,X34: $i] :
( ( $true
!= ( cQ_5 @ X34 @ X29 @ X32 ) )
| ( $true
!= ( cP_5 @ ( f @ X29 ) @ X33 ) )
| ( ( cQ_6 @ X30 @ X33 @ X31 )
= $true )
| ( $true
!= ( cP_5 @ ( f @ X32 ) @ X31 ) )
| ( $true
!= ( cP_5 @ ( f @ X34 ) @ X30 ) ) )
& ( ( cP_3 @ c @ c )
= $true )
& ( ( cP_5 @ c @ c )
= $true )
& ! [X35: $i,X36: $i,X37: $i,X38: $i,X39: $i,X40: $i] :
( ( ( cP_2 @ ( f @ X39 ) @ X40 )
!= $true )
| ( ( cP_2 @ ( f @ X38 ) @ X35 )
!= $true )
| ( ( cQ_3 @ X40 @ X36 @ X35 )
= $true )
| ( $true
!= ( cQ_2 @ X39 @ X37 @ X38 ) )
| ( $true
!= ( cP_2 @ ( f @ X37 ) @ X36 ) ) )
& ( ( cP_5 @ b @ b )
= $true )
& ! [X41: $i] :
( $true
= ( cP_5 @ d @ X41 ) )
& ! [X42: $i,X43: $i] :
( ( ( cP_5 @ X42 @ X43 )
!= $true )
| ( ( cP_5 @ ( f @ X42 ) @ X43 )
= $true ) )
& ! [X44: $i] :
( ( cP_3 @ d @ X44 )
= $true )
& ( ( cP_4 @ b @ b )
= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ( ( cP_3 @ a @ a )
= $true )
& ! [X45: $i,X46: $i] :
( ( ( cP_4 @ ( f @ X45 ) @ X46 )
= $true )
| ( $true
!= ( cP_4 @ X45 @ X46 ) ) )
& ( ( cP_3 @ b @ b )
= $true )
& ! [X47: $i] :
( ( cP_6 @ d @ X47 )
= $true )
& ( ( cP_4 @ a @ a )
= $true )
& ( ( cP_6 @ c @ c )
= $true )
& ! [X48: $i,X49: $i] :
( ( ( cP_2 @ X49 @ X48 )
!= $true )
| ( ( cP_2 @ ( f @ X49 ) @ X48 )
= $true ) )
& ( ( cP_1 @ a @ a )
= $true )
& ! [X50: $i,X51: $i] :
( ( ( cP_3 @ ( f @ X51 ) @ X50 )
= $true )
| ( $true
!= ( cP_3 @ X51 @ X50 ) ) )
& ( ( cP_1 @ c @ c )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X52: $i,X53: $i] :
( ( ( cP_6 @ X53 @ X52 )
!= $true )
| ( ( cP_6 @ ( f @ X53 ) @ X52 )
= $true ) )
& ! [X54: $i,X55: $i] :
( ( $true
!= ( cP_1 @ X54 @ X55 ) )
| ( $true
= ( cP_1 @ ( f @ X54 ) @ X55 ) ) )
& ( ( cP_2 @ a @ a )
= $true )
& ! [X56: $i] :
( $true
= ( cP_2 @ d @ X56 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( cP_1 @ b @ b )
= $true )
& ! [X33: $i,X37: $i,X38: $i,X35: $i,X34: $i,X36: $i] :
( ( ( cP_3 @ ( f @ X33 ) @ X37 )
!= $true )
| ( ( cQ_4 @ X38 @ X37 @ X36 )
= $true )
| ( ( cP_3 @ ( f @ X34 ) @ X36 )
!= $true )
| ( ( cP_3 @ ( f @ X35 ) @ X38 )
!= $true )
| ( $true
!= ( cQ_3 @ X35 @ X33 @ X34 ) ) )
& ! [X10: $i,X13: $i,X14: $i,X11: $i,X12: $i,X9: $i] :
( ( ( cQ_1 @ X14 @ X13 @ X9 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X14 ) @ X12 ) )
| ( ( cP_1 @ ( f @ X9 ) @ X11 )
!= $true )
| ( ( cP_1 @ ( f @ X13 ) @ X10 )
!= $true )
| ( $true
= ( cQ_2 @ X12 @ X10 @ X11 ) ) )
& ( ( cP_4 @ c @ c )
= $true )
& ! [X56: $i] :
( ( cP_1 @ d @ X56 )
= $true )
& ( ( cP_5 @ a @ a )
= $true )
& ( ( cP_6 @ a @ a )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ! [X20: $i] :
( $true
= ( cP_4 @ d @ X20 ) )
& ! [X51: $i,X54: $i,X55: $i,X50: $i,X53: $i,X52: $i] :
( ( ( cP_6 @ ( f @ X52 ) @ X53 )
!= $true )
| ( ( cP_6 @ ( f @ X54 ) @ X50 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X55 ) @ X51 ) )
| ( ( cQ_7 @ X53 @ X51 @ X50 )
= $true )
| ( $true
!= ( cQ_6 @ X52 @ X55 @ X54 ) ) )
& ! [X24: $i,X25: $i,X22: $i,X23: $i,X26: $i,X27: $i] :
( ( ( cQ_5 @ X27 @ X23 @ X22 )
= $true )
| ( $true
!= ( cQ_4 @ X25 @ X24 @ X26 ) )
| ( $true
!= ( cP_4 @ ( f @ X24 ) @ X23 ) )
| ( $true
!= ( cP_4 @ ( f @ X25 ) @ X27 ) )
| ( ( cP_4 @ ( f @ X26 ) @ X22 )
!= $true ) )
& ( ( cP_6 @ b @ b )
= $true )
& ! [X28: $i,X29: $i,X30: $i] :
( $true
!= ( cQ_7 @ X29 @ X30 @ X28 ) )
& ! [X46: $i,X44: $i,X49: $i,X45: $i,X48: $i,X47: $i] :
( ( ( cQ_5 @ X47 @ X46 @ X45 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X46 ) @ X48 ) )
| ( ( cQ_6 @ X44 @ X48 @ X49 )
= $true )
| ( ( cP_5 @ ( f @ X45 ) @ X49 )
!= $true )
| ( ( cP_5 @ ( f @ X47 ) @ X44 )
!= $true ) )
& ( ( cP_3 @ c @ c )
= $true )
& ( ( cP_5 @ c @ c )
= $true )
& ! [X5: $i,X4: $i,X1: $i,X2: $i,X3: $i,X0: $i] :
( ( ( cP_2 @ ( f @ X3 ) @ X0 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X5 )
!= $true )
| ( $true
= ( cQ_3 @ X0 @ X4 @ X5 ) )
| ( ( cQ_2 @ X3 @ X1 @ X2 )
!= $true )
| ( ( cP_2 @ ( f @ X1 ) @ X4 )
!= $true ) )
& ( ( cP_5 @ b @ b )
= $true )
& ! [X19: $i] :
( ( cP_5 @ d @ X19 )
= $true )
& ! [X42: $i,X41: $i] :
( ( $true
!= ( cP_5 @ X42 @ X41 ) )
| ( $true
= ( cP_5 @ ( f @ X42 ) @ X41 ) ) )
& ! [X21: $i] :
( ( cP_3 @ d @ X21 )
= $true )
& ( ( cP_4 @ b @ b )
= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ( ( cP_3 @ a @ a )
= $true )
& ! [X40: $i,X39: $i] :
( ( $true
= ( cP_4 @ ( f @ X40 ) @ X39 ) )
| ( ( cP_4 @ X40 @ X39 )
!= $true ) )
& ( ( cP_3 @ b @ b )
= $true )
& ! [X43: $i] :
( $true
= ( cP_6 @ d @ X43 ) )
& ( ( cP_4 @ a @ a )
= $true )
& ( ( cP_6 @ c @ c )
= $true )
& ! [X32: $i,X31: $i] :
( ( ( cP_2 @ X31 @ X32 )
!= $true )
| ( ( cP_2 @ ( f @ X31 ) @ X32 )
= $true ) )
& ( ( cP_1 @ a @ a )
= $true )
& ! [X15: $i,X16: $i] :
( ( ( cP_3 @ ( f @ X16 ) @ X15 )
= $true )
| ( ( cP_3 @ X16 @ X15 )
!= $true ) )
& ( ( cP_1 @ c @ c )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X6: $i,X7: $i] :
( ( $true
!= ( cP_6 @ X7 @ X6 ) )
| ( $true
= ( cP_6 @ ( f @ X7 ) @ X6 ) ) )
& ! [X17: $i,X18: $i] :
( ( $true
!= ( cP_1 @ X17 @ X18 ) )
| ( $true
= ( cP_1 @ ( f @ X17 ) @ X18 ) ) )
& ( ( cP_2 @ a @ a )
= $true )
& ! [X8: $i] :
( $true
= ( cP_2 @ d @ X8 ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ( ( ( cP_2 @ c @ c )
= $true )
& ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( $true
= ( cQ_3 @ X0 @ X4 @ X5 ) )
| ( ( cP_2 @ ( f @ X2 ) @ X5 )
!= $true )
| ( ( cQ_2 @ X3 @ X1 @ X2 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X0 )
!= $true )
| ( ( cP_2 @ ( f @ X1 ) @ X4 )
!= $true ) )
& ! [X6: $i,X7: $i] :
( ( $true
!= ( cP_6 @ X7 @ X6 ) )
| ( $true
= ( cP_6 @ ( f @ X7 ) @ X6 ) ) )
& ! [X8: $i] :
( $true
= ( cP_2 @ d @ X8 ) )
& ( ( cP_4 @ b @ b )
= $true )
& ( ( cP_3 @ c @ c )
= $true )
& ! [X9: $i,X10: $i,X11: $i,X12: $i,X13: $i,X14: $i] :
( ( $true
!= ( cP_1 @ ( f @ X14 ) @ X12 ) )
| ( ( cP_1 @ ( f @ X13 ) @ X10 )
!= $true )
| ( ( cP_1 @ ( f @ X9 ) @ X11 )
!= $true )
| ( ( cQ_1 @ X14 @ X13 @ X9 )
!= $true )
| ( $true
= ( cQ_2 @ X12 @ X10 @ X11 ) ) )
& ! [X15: $i,X16: $i] :
( ( ( cP_3 @ X16 @ X15 )
!= $true )
| ( ( cP_3 @ ( f @ X16 ) @ X15 )
= $true ) )
& ( ( cP_6 @ b @ b )
= $true )
& ! [X17: $i,X18: $i] :
( ( $true
= ( cP_1 @ ( f @ X17 ) @ X18 ) )
| ( $true
!= ( cP_1 @ X17 @ X18 ) ) )
& ( ( cP_4 @ a @ a )
= $true )
& ! [X19: $i] :
( ( cP_5 @ d @ X19 )
= $true )
& ! [X20: $i] :
( $true
= ( cP_4 @ d @ X20 ) )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X21: $i] :
( ( cP_3 @ d @ X21 )
= $true )
& ( ( cP_4 @ c @ c )
= $true )
& ! [X22: $i,X23: $i,X24: $i,X25: $i,X26: $i,X27: $i] :
( ( ( cQ_5 @ X27 @ X23 @ X22 )
= $true )
| ( $true
!= ( cQ_4 @ X25 @ X24 @ X26 ) )
| ( $true
!= ( cP_4 @ ( f @ X24 ) @ X23 ) )
| ( ( cP_4 @ ( f @ X26 ) @ X22 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X25 ) @ X27 ) ) )
& ! [X28: $i,X29: $i,X30: $i] :
( $true
!= ( cQ_7 @ X29 @ X30 @ X28 ) )
& ( ( cP_3 @ a @ a )
= $true )
& ( ( cP_3 @ b @ b )
= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X31: $i,X32: $i] :
( ( ( cP_2 @ X31 @ X32 )
!= $true )
| ( ( cP_2 @ ( f @ X31 ) @ X32 )
= $true ) )
& ( ( cP_5 @ c @ c )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X33: $i,X34: $i,X35: $i,X36: $i,X37: $i,X38: $i] :
( ( ( cP_3 @ ( f @ X34 ) @ X36 )
!= $true )
| ( ( cP_3 @ ( f @ X33 ) @ X37 )
!= $true )
| ( ( cQ_4 @ X38 @ X37 @ X36 )
= $true )
| ( $true
!= ( cQ_3 @ X35 @ X33 @ X34 ) )
| ( ( cP_3 @ ( f @ X35 ) @ X38 )
!= $true ) )
& ( ( cP_2 @ a @ a )
= $true )
& ( ( cP_6 @ c @ c )
= $true )
& ! [X39: $i,X40: $i] :
( ( ( cP_4 @ X40 @ X39 )
!= $true )
| ( $true
= ( cP_4 @ ( f @ X40 ) @ X39 ) ) )
& ( ( cP_6 @ a @ a )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ! [X41: $i,X42: $i] :
( ( $true
!= ( cP_5 @ X42 @ X41 ) )
| ( $true
= ( cP_5 @ ( f @ X42 ) @ X41 ) ) )
& ( ( cP_5 @ a @ a )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_5 @ b @ b )
= $true )
& ! [X43: $i] :
( $true
= ( cP_6 @ d @ X43 ) )
& ! [X44: $i,X45: $i,X46: $i,X47: $i,X48: $i,X49: $i] :
( ( ( cQ_5 @ X47 @ X46 @ X45 )
!= $true )
| ( ( cQ_6 @ X44 @ X48 @ X49 )
= $true )
| ( ( cP_5 @ ( f @ X45 ) @ X49 )
!= $true )
| ( ( cP_5 @ ( f @ X47 ) @ X44 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X46 ) @ X48 ) ) )
& ! [X50: $i,X51: $i,X52: $i,X53: $i,X54: $i,X55: $i] :
( ( ( cP_6 @ ( f @ X52 ) @ X53 )
!= $true )
| ( ( cQ_7 @ X53 @ X51 @ X50 )
= $true )
| ( $true
!= ( cQ_6 @ X52 @ X55 @ X54 ) )
| ( $true
!= ( cP_6 @ ( f @ X55 ) @ X51 ) )
| ( ( cP_6 @ ( f @ X54 ) @ X50 )
!= $true ) )
& ! [X56: $i] :
( ( cP_1 @ d @ X56 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ( ( cP_2 @ c @ c )
& ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cQ_3 @ X0 @ X4 @ X5 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ~ ( cQ_2 @ X3 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X3 ) @ X0 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 ) )
& ! [X6: $i,X7: $i] :
( ~ ( cP_6 @ X7 @ X6 )
| ( cP_6 @ ( f @ X7 ) @ X6 ) )
& ! [X8: $i] : ( cP_2 @ d @ X8 )
& ( cP_4 @ b @ b )
& ( cP_3 @ c @ c )
& ! [X9: $i,X10: $i,X11: $i,X12: $i,X13: $i,X14: $i] :
( ~ ( cP_1 @ ( f @ X14 ) @ X12 )
| ~ ( cP_1 @ ( f @ X13 ) @ X10 )
| ~ ( cP_1 @ ( f @ X9 ) @ X11 )
| ~ ( cQ_1 @ X14 @ X13 @ X9 )
| ( cQ_2 @ X12 @ X10 @ X11 ) )
& ! [X15: $i,X16: $i] :
( ~ ( cP_3 @ X16 @ X15 )
| ( cP_3 @ ( f @ X16 ) @ X15 ) )
& ( cP_6 @ b @ b )
& ! [X17: $i,X18: $i] :
( ( cP_1 @ ( f @ X17 ) @ X18 )
| ~ ( cP_1 @ X17 @ X18 ) )
& ( cP_4 @ a @ a )
& ! [X19: $i] : ( cP_5 @ d @ X19 )
& ! [X20: $i] : ( cP_4 @ d @ X20 )
& ( cP_1 @ c @ c )
& ! [X21: $i] : ( cP_3 @ d @ X21 )
& ( cP_4 @ c @ c )
& ! [X22: $i,X23: $i,X24: $i,X25: $i,X26: $i,X27: $i] :
( ( cQ_5 @ X27 @ X23 @ X22 )
| ~ ( cQ_4 @ X25 @ X24 @ X26 )
| ~ ( cP_4 @ ( f @ X24 ) @ X23 )
| ~ ( cP_4 @ ( f @ X26 ) @ X22 )
| ~ ( cP_4 @ ( f @ X25 ) @ X27 ) )
& ! [X28: $i,X29: $i,X30: $i] :
~ ( cQ_7 @ X29 @ X30 @ X28 )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_2 @ b @ b )
& ! [X31: $i,X32: $i] :
( ~ ( cP_2 @ X31 @ X32 )
| ( cP_2 @ ( f @ X31 ) @ X32 ) )
& ( cP_5 @ c @ c )
& ( cQ_1 @ a @ b @ c )
& ! [X33: $i,X34: $i,X35: $i,X36: $i,X37: $i,X38: $i] :
( ~ ( cP_3 @ ( f @ X34 ) @ X36 )
| ~ ( cP_3 @ ( f @ X33 ) @ X37 )
| ( cQ_4 @ X38 @ X37 @ X36 )
| ~ ( cQ_3 @ X35 @ X33 @ X34 )
| ~ ( cP_3 @ ( f @ X35 ) @ X38 ) )
& ( cP_2 @ a @ a )
& ( cP_6 @ c @ c )
& ! [X39: $i,X40: $i] :
( ~ ( cP_4 @ X40 @ X39 )
| ( cP_4 @ ( f @ X40 ) @ X39 ) )
& ( cP_6 @ a @ a )
& ( cP_1 @ a @ a )
& ! [X41: $i,X42: $i] :
( ~ ( cP_5 @ X42 @ X41 )
| ( cP_5 @ ( f @ X42 ) @ X41 ) )
& ( cP_5 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_5 @ b @ b )
& ! [X43: $i] : ( cP_6 @ d @ X43 )
& ! [X44: $i,X45: $i,X46: $i,X47: $i,X48: $i,X49: $i] :
( ~ ( cQ_5 @ X47 @ X46 @ X45 )
| ( cQ_6 @ X44 @ X48 @ X49 )
| ~ ( cP_5 @ ( f @ X45 ) @ X49 )
| ~ ( cP_5 @ ( f @ X47 ) @ X44 )
| ~ ( cP_5 @ ( f @ X46 ) @ X48 ) )
& ! [X50: $i,X51: $i,X52: $i,X53: $i,X54: $i,X55: $i] :
( ~ ( cP_6 @ ( f @ X52 ) @ X53 )
| ( cQ_7 @ X53 @ X51 @ X50 )
| ~ ( cQ_6 @ X52 @ X55 @ X54 )
| ~ ( cP_6 @ ( f @ X55 ) @ X51 )
| ~ ( cP_6 @ ( f @ X54 ) @ X50 ) )
& ! [X56: $i] : ( cP_1 @ d @ X56 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ( cP_2 @ c @ c )
& ! [X3: $i,X1: $i,X2: $i,X0: $i,X4: $i,X5: $i] :
( ( cQ_3 @ X3 @ X4 @ X5 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 ) )
& ! [X1: $i,X0: $i] :
( ~ ( cP_6 @ X0 @ X1 )
| ( cP_6 @ ( f @ X0 ) @ X1 ) )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ( cP_4 @ b @ b )
& ( cP_3 @ c @ c )
& ! [X2: $i,X4: $i,X5: $i,X3: $i,X1: $i,X0: $i] :
( ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ( cQ_2 @ X3 @ X4 @ X5 ) )
& ! [X1: $i,X0: $i] :
( ~ ( cP_3 @ X0 @ X1 )
| ( cP_3 @ ( f @ X0 ) @ X1 ) )
& ( cP_6 @ b @ b )
& ! [X0: $i,X1: $i] :
( ( cP_1 @ ( f @ X0 ) @ X1 )
| ~ ( cP_1 @ X0 @ X1 ) )
& ( cP_4 @ a @ a )
& ! [X0: $i] : ( cP_5 @ d @ X0 )
& ! [X0: $i] : ( cP_4 @ d @ X0 )
& ( cP_1 @ c @ c )
& ! [X0: $i] : ( cP_3 @ d @ X0 )
& ( cP_4 @ c @ c )
& ! [X5: $i,X4: $i,X1: $i,X0: $i,X2: $i,X3: $i] :
( ( cQ_5 @ X3 @ X4 @ X5 )
| ~ ( cQ_4 @ X0 @ X1 @ X2 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ~ ( cP_4 @ ( f @ X0 ) @ X3 ) )
& ! [X2: $i,X0: $i,X1: $i] :
~ ( cQ_7 @ X0 @ X1 @ X2 )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_2 @ b @ b )
& ! [X0: $i,X1: $i] :
( ~ ( cP_2 @ X0 @ X1 )
| ( cP_2 @ ( f @ X0 ) @ X1 ) )
& ( cP_5 @ c @ c )
& ( cQ_1 @ a @ b @ c )
& ! [X1: $i,X2: $i,X0: $i,X5: $i,X4: $i,X3: $i] :
( ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ( cQ_4 @ X3 @ X4 @ X5 )
| ~ ( cQ_3 @ X0 @ X1 @ X2 )
| ~ ( cP_3 @ ( f @ X0 ) @ X3 ) )
& ( cP_2 @ a @ a )
& ( cP_6 @ c @ c )
& ! [X1: $i,X0: $i] :
( ~ ( cP_4 @ X0 @ X1 )
| ( cP_4 @ ( f @ X0 ) @ X1 ) )
& ( cP_6 @ a @ a )
& ( cP_1 @ a @ a )
& ! [X1: $i,X0: $i] :
( ~ ( cP_5 @ X0 @ X1 )
| ( cP_5 @ ( f @ X0 ) @ X1 ) )
& ( cP_5 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_5 @ b @ b )
& ! [X0: $i] : ( cP_6 @ d @ X0 )
& ! [X3: $i,X2: $i,X1: $i,X0: $i,X4: $i,X5: $i] :
( ~ ( cQ_5 @ X0 @ X1 @ X2 )
| ( cQ_6 @ X3 @ X4 @ X5 )
| ~ ( cP_5 @ ( f @ X2 ) @ X5 )
| ~ ( cP_5 @ ( f @ X0 ) @ X3 )
| ~ ( cP_5 @ ( f @ X1 ) @ X4 ) )
& ! [X5: $i,X4: $i,X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ ( cP_6 @ ( f @ X0 ) @ X3 )
| ( cQ_7 @ X3 @ X4 @ X5 )
| ~ ( cQ_6 @ X0 @ X1 @ X2 )
| ~ ( cP_6 @ ( f @ X1 ) @ X4 )
| ~ ( cP_6 @ ( f @ X2 ) @ X5 ) )
& ! [X0: $i] : ( cP_1 @ d @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ( ( cP_2 @ c @ c )
& ! [X3: $i,X1: $i,X2: $i,X0: $i,X4: $i,X5: $i] :
( ( cQ_3 @ X3 @ X4 @ X5 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 ) )
& ! [X1: $i,X0: $i] :
( ~ ( cP_6 @ X0 @ X1 )
| ( cP_6 @ ( f @ X0 ) @ X1 ) )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ( cP_4 @ b @ b )
& ( cP_3 @ c @ c )
& ! [X2: $i,X4: $i,X5: $i,X3: $i,X1: $i,X0: $i] :
( ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ( cQ_2 @ X3 @ X4 @ X5 ) )
& ! [X1: $i,X0: $i] :
( ~ ( cP_3 @ X0 @ X1 )
| ( cP_3 @ ( f @ X0 ) @ X1 ) )
& ( cP_6 @ b @ b )
& ! [X0: $i,X1: $i] :
( ( cP_1 @ ( f @ X0 ) @ X1 )
| ~ ( cP_1 @ X0 @ X1 ) )
& ( cP_4 @ a @ a )
& ! [X0: $i] : ( cP_5 @ d @ X0 )
& ! [X0: $i] : ( cP_4 @ d @ X0 )
& ( cP_1 @ c @ c )
& ! [X0: $i] : ( cP_3 @ d @ X0 )
& ( cP_4 @ c @ c )
& ! [X5: $i,X4: $i,X1: $i,X0: $i,X2: $i,X3: $i] :
( ( cQ_5 @ X3 @ X4 @ X5 )
| ~ ( cQ_4 @ X0 @ X1 @ X2 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ~ ( cP_4 @ ( f @ X0 ) @ X3 ) )
& ! [X2: $i,X0: $i,X1: $i] :
~ ( cQ_7 @ X0 @ X1 @ X2 )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_2 @ b @ b )
& ! [X0: $i,X1: $i] :
( ~ ( cP_2 @ X0 @ X1 )
| ( cP_2 @ ( f @ X0 ) @ X1 ) )
& ( cP_5 @ c @ c )
& ( cQ_1 @ a @ b @ c )
& ! [X1: $i,X2: $i,X0: $i,X5: $i,X4: $i,X3: $i] :
( ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ( cQ_4 @ X3 @ X4 @ X5 )
| ~ ( cQ_3 @ X0 @ X1 @ X2 )
| ~ ( cP_3 @ ( f @ X0 ) @ X3 ) )
& ( cP_2 @ a @ a )
& ( cP_6 @ c @ c )
& ! [X1: $i,X0: $i] :
( ~ ( cP_4 @ X0 @ X1 )
| ( cP_4 @ ( f @ X0 ) @ X1 ) )
& ( cP_6 @ a @ a )
& ( cP_1 @ a @ a )
& ! [X1: $i,X0: $i] :
( ~ ( cP_5 @ X0 @ X1 )
| ( cP_5 @ ( f @ X0 ) @ X1 ) )
& ( cP_5 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_5 @ b @ b )
& ! [X0: $i] : ( cP_6 @ d @ X0 )
& ! [X3: $i,X2: $i,X1: $i,X0: $i,X4: $i,X5: $i] :
( ~ ( cQ_5 @ X0 @ X1 @ X2 )
| ( cQ_6 @ X3 @ X4 @ X5 )
| ~ ( cP_5 @ ( f @ X2 ) @ X5 )
| ~ ( cP_5 @ ( f @ X0 ) @ X3 )
| ~ ( cP_5 @ ( f @ X1 ) @ X4 ) )
& ! [X5: $i,X4: $i,X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ ( cP_6 @ ( f @ X0 ) @ X3 )
| ( cQ_7 @ X3 @ X4 @ X5 )
| ~ ( cQ_6 @ X0 @ X1 @ X2 )
| ~ ( cP_6 @ ( f @ X1 ) @ X4 )
| ~ ( cP_6 @ ( f @ X2 ) @ X5 ) )
& ! [X0: $i] : ( cP_1 @ d @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.c39OTm3iHl/DTF2THF_5935.p',cTHM409_6) ).
thf(f184,plain,
( ! [X1: $i] :
( ( cP_6 @ b @ X1 )
!= $true )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f183]) ).
thf(f183,definition,
( spl0_11
<=> ! [X1: $i] :
( ( cP_6 @ b @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f217,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[status(thm)],[f216]) ).
thf(f216,plain,
( $false
| ~ spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f213,f20]) ).
thf(f20,plain,
( ( cP_3 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f213,plain,
( ( ( cP_3 @ b @ b )
!= $true )
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f211]) ).
thf(f211,plain,
( ( $true != $true )
| ( ( cP_3 @ b @ b )
!= $true )
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f181,f24]) ).
thf(f24,plain,
( ( cP_4 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f181,plain,
( ! [X0: $i] :
( ( $true
!= ( cP_4 @ X0 @ b ) )
| ( ( cP_3 @ b @ X0 )
!= $true ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f180]) ).
thf(f180,definition,
( spl0_10
<=> ! [X0: $i] :
( ( ( cP_3 @ b @ X0 )
!= $true )
| ( $true
!= ( cP_4 @ X0 @ b ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f185,plain,
( spl0_10
| spl0_11
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f178,f93,f183,f180]) ).
thf(f93,definition,
( spl0_4
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_3 @ b @ X0 )
!= $true )
| ( $true
!= ( cP_5 @ X1 @ X2 ) )
| ( ( cP_6 @ X2 @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f178,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_3 @ b @ X0 )
!= $true )
| ( ( cP_6 @ b @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ X0 @ b ) ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f171]) ).
thf(f171,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_6 @ b @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ X0 @ b ) )
| ( ( cP_3 @ b @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f94,f28]) ).
thf(f28,plain,
( ( cP_5 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f94,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_5 @ X1 @ X2 ) )
| ( ( cP_3 @ b @ X0 )
!= $true )
| ( ( cP_6 @ X2 @ X3 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f93]) ).
thf(f168,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[status(thm)],[f167]) ).
thf(f167,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f166]) ).
thf(f166,plain,
( ( $true != $true )
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f165,f39]) ).
thf(f39,plain,
( ( cP_6 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f165,plain,
( ! [X0: $i] :
( ( cP_6 @ a @ X0 )
!= $true )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f164]) ).
thf(f164,plain,
( ! [X0: $i] :
( ( ( cP_6 @ a @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f163,f40]) ).
thf(f40,plain,
( ( cP_5 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f163,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_5 @ a @ X0 )
!= $true )
| ( ( cP_6 @ X0 @ X1 )
!= $true ) )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f162]) ).
thf(f162,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( ( cP_5 @ a @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f161,f18]) ).
thf(f18,plain,
( ( cP_4 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f161,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_4 @ a @ X0 ) )
| ( $true
!= ( cP_6 @ X1 @ X2 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f160]) ).
thf(f160,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_6 @ X1 @ X2 ) )
| ( $true
!= ( cP_4 @ a @ X0 ) )
| ( $true != $true ) )
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f106,f22]) ).
thf(f22,plain,
( ( cP_3 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f106,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ a @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_5 @ X1 @ X2 ) )
| ( ( cP_6 @ X2 @ X3 )
!= $true ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f105]) ).
thf(f105,definition,
( spl0_7
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ( ( cP_6 @ X2 @ X3 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_5 @ X1 @ X2 ) )
| ( $true
!= ( cP_3 @ a @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f159,plain,
( spl0_7
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f158,f61,f105]) ).
thf(f61,definition,
( spl0_1
<=> ! [X16: $i,X10: $i,X11: $i,X12: $i,X17: $i,X15: $i] :
( ( ( cP_2 @ ( f @ X12 ) @ X10 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X12 )
!= $true )
| ( ( cP_3 @ ( f @ X10 ) @ X11 )
!= $true )
| ( ( cP_4 @ ( f @ X11 ) @ X15 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X15 ) @ X16 ) )
| ( ( cP_6 @ ( f @ X16 ) @ X17 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f158,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_6 @ X2 @ X3 )
!= $true )
| ( $true
!= ( cP_5 @ X1 @ X2 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ a @ X0 ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f157]) ).
thf(f157,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_5 @ X1 @ X2 ) )
| ( $true != $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_6 @ X2 @ X3 )
!= $true )
| ( $true
!= ( cP_3 @ a @ X0 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f156,f9]) ).
thf(f9,plain,
( ( cP_2 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f156,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_2 @ a @ X2 ) )
| ( ( cP_3 @ X2 @ X4 )
!= $true )
| ( ( cP_4 @ X4 @ X0 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_6 @ X1 @ X3 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f155]) ).
thf(f155,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_3 @ X2 @ X4 )
!= $true )
| ( $true != $true )
| ( ( cP_4 @ X4 @ X0 )
!= $true )
| ( $true
!= ( cP_2 @ a @ X2 ) )
| ( ( cP_6 @ X1 @ X3 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f154,f15]) ).
thf(f15,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f154,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ a @ X2 ) )
| ( ( cP_5 @ X4 @ X0 )
!= $true )
| ( $true
!= ( cP_2 @ X2 @ X5 ) )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( ( cP_3 @ X5 @ X3 )
!= $true )
| ( $true
!= ( cP_4 @ X3 @ X4 ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f153]) ).
thf(f153,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_3 @ X5 @ X3 )
!= $true )
| ( ( cP_5 @ X4 @ X0 )
!= $true )
| ( $true
!= ( cP_4 @ X3 @ X4 ) )
| ( $true
!= ( cP_1 @ a @ X2 ) )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_2 @ X2 @ X5 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f152,f11]) ).
thf(f11,plain,
! [X52: $i,X53: $i] :
( ( ( cP_6 @ ( f @ X53 ) @ X52 )
= $true )
| ( ( cP_6 @ X53 @ X52 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f152,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X3 ) )
| ( ( cP_4 @ X1 @ X2 )
!= $true )
| ( $true
!= ( cP_2 @ X3 @ X0 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_5 @ X2 @ X4 ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f151]) ).
thf(f151,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ a @ X3 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_5 @ X2 @ X4 ) )
| ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_4 @ X1 @ X2 )
!= $true )
| ( $true
!= ( cP_2 @ X3 @ X0 ) )
| ( $true != $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f150,f14]) ).
thf(f14,plain,
! [X50: $i,X51: $i] :
( ( ( cP_3 @ ( f @ X51 ) @ X50 )
= $true )
| ( $true
!= ( cP_3 @ X51 @ X50 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f150,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_3 @ ( f @ X1 ) @ X2 ) )
| ( $true
!= ( cP_4 @ X2 @ X3 ) )
| ( $true
!= ( cP_1 @ a @ X0 ) )
| ( $true
!= ( cP_5 @ X3 @ X4 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f149]) ).
thf(f149,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_5 @ X3 @ X4 ) )
| ( $true
!= ( cP_4 @ X2 @ X3 ) )
| ( $true
!= ( cP_3 @ ( f @ X1 ) @ X2 ) )
| ( $true
!= ( cP_1 @ a @ X0 ) )
| ( $true != $true )
| ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f148,f16]) ).
thf(f16,plain,
! [X48: $i,X49: $i] :
( ( ( cP_2 @ ( f @ X49 ) @ X48 )
= $true )
| ( ( cP_2 @ X49 @ X48 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f148,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_2 @ ( f @ X3 ) @ X2 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_5 @ X1 @ X4 )
!= $true )
| ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_3 @ ( f @ X2 ) @ X0 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X3 ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f147]) ).
thf(f147,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X3 ) @ X2 ) )
| ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_5 @ X1 @ X4 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X3 ) )
| ( $true != $true )
| ( ( cP_3 @ ( f @ X2 ) @ X0 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f146,f21]) ).
thf(f21,plain,
! [X46: $i,X45: $i] :
( ( ( cP_4 @ ( f @ X45 ) @ X46 )
= $true )
| ( $true
!= ( cP_4 @ X45 @ X46 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f146,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_4 @ ( f @ X4 ) @ X5 ) )
| ( ( cP_3 @ ( f @ X3 ) @ X4 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X0 ) )
| ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( ( cP_5 @ X5 @ X1 )
!= $true )
| ( ( cP_6 @ ( f @ X1 ) @ X2 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f145]) ).
thf(f145,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_6 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_5 @ X5 @ X1 )
!= $true )
| ( ( cP_3 @ ( f @ X3 ) @ X4 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X4 ) @ X5 ) )
| ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X0 ) )
| ( $true != $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f144,f10]) ).
thf(f10,plain,
! [X54: $i,X55: $i] :
( ( $true
= ( cP_1 @ ( f @ X54 ) @ X55 ) )
| ( $true
!= ( cP_1 @ X54 @ X55 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f144,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ ( f @ a ) @ X5 ) )
| ( ( cP_6 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X5 ) @ X2 )
!= $true )
| ( ( cP_3 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X3 ) @ X0 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f143]) ).
thf(f143,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( cP_6 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_4 @ ( f @ X3 ) @ X0 )
!= $true )
| ( ( cP_3 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_2 @ ( f @ X5 ) @ X2 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ a ) @ X5 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f62,f26]) ).
thf(f26,plain,
! [X42: $i,X43: $i] :
( ( ( cP_5 @ ( f @ X42 ) @ X43 )
= $true )
| ( ( cP_5 @ X42 @ X43 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f62,plain,
( ! [X10: $i,X11: $i,X16: $i,X17: $i,X15: $i,X12: $i] :
( ( $true
!= ( cP_5 @ ( f @ X15 ) @ X16 ) )
| ( ( cP_3 @ ( f @ X10 ) @ X11 )
!= $true )
| ( ( cP_4 @ ( f @ X11 ) @ X15 )
!= $true )
| ( ( cP_6 @ ( f @ X16 ) @ X17 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X12 )
!= $true )
| ( ( cP_2 @ ( f @ X12 ) @ X10 )
!= $true ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f142,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f141,f67,f93]) ).
thf(f67,definition,
( spl0_3
<=> ! [X1: $i,X4: $i,X0: $i,X13: $i,X8: $i,X7: $i] :
( ( $true
!= ( cP_2 @ ( f @ X4 ) @ X0 ) )
| ( ( cP_5 @ ( f @ X7 ) @ X8 )
!= $true )
| ( ( cP_3 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X7 )
!= $true )
| ( ( cP_6 @ ( f @ X8 ) @ X13 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X4 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f141,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ b @ X3 ) )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( ( cP_5 @ X2 @ X0 )
!= $true )
| ( ( cP_4 @ X3 @ X2 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f140]) ).
thf(f140,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ b @ X3 ) )
| ( ( cP_4 @ X3 @ X2 )
!= $true )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( cP_5 @ X2 @ X0 )
!= $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f139,f23]) ).
thf(f23,plain,
( ( cP_2 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f139,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_2 @ b @ X2 ) )
| ( ( cP_6 @ X1 @ X4 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ X2 @ X3 ) )
| ( ( cP_4 @ X3 @ X0 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f138]) ).
thf(f138,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true != $true )
| ( ( cP_6 @ X1 @ X4 )
!= $true )
| ( $true
!= ( cP_3 @ X2 @ X3 ) )
| ( ( cP_4 @ X3 @ X0 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_2 @ b @ X2 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f137,f45]) ).
thf(f45,plain,
( ( cP_1 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f137,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ b @ X5 ) )
| ( $true
!= ( cP_5 @ X3 @ X0 ) )
| ( ( cP_3 @ X4 @ X2 )
!= $true )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_2 @ X5 @ X4 ) )
| ( $true
!= ( cP_4 @ X2 @ X3 ) ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f136]) ).
thf(f136,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_5 @ X3 @ X0 ) )
| ( $true
!= ( cP_1 @ b @ X5 ) )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_2 @ X5 @ X4 ) )
| ( ( cP_3 @ X4 @ X2 )
!= $true )
| ( $true
!= ( cP_4 @ X2 @ X3 ) )
| ( $true != $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f135,f11]) ).
thf(f135,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_6 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_3 @ X4 @ X0 )
!= $true )
| ( $true
!= ( cP_1 @ b @ X5 ) )
| ( $true
!= ( cP_5 @ X1 @ X2 ) )
| ( $true
!= ( cP_2 @ X5 @ X4 ) ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f134]) ).
thf(f134,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_3 @ X4 @ X0 )
!= $true )
| ( $true
!= ( cP_1 @ b @ X5 ) )
| ( $true
!= ( cP_5 @ X1 @ X2 ) )
| ( $true
!= ( cP_6 @ ( f @ X2 ) @ X3 ) )
| ( $true != $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_2 @ X5 @ X4 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f133,f21]) ).
thf(f133,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_4 @ ( f @ X2 ) @ X0 )
!= $true )
| ( ( cP_6 @ ( f @ X1 ) @ X5 )
!= $true )
| ( ( cP_3 @ X4 @ X2 )
!= $true )
| ( ( cP_2 @ X3 @ X4 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ b @ X3 ) ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_4 @ ( f @ X2 ) @ X0 )
!= $true )
| ( $true
!= ( cP_1 @ b @ X3 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_3 @ X4 @ X2 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ X3 @ X4 )
!= $true )
| ( ( cP_6 @ ( f @ X1 ) @ X5 )
!= $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f131,f26]) ).
thf(f131,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_5 @ ( f @ X5 ) @ X2 ) )
| ( ( cP_4 @ ( f @ X1 ) @ X5 )
!= $true )
| ( $true
!= ( cP_1 @ b @ X4 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X2 ) @ X3 ) )
| ( $true
!= ( cP_2 @ X4 @ X0 ) ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f130]) ).
thf(f130,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( $true
!= ( cP_1 @ b @ X4 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X5 ) @ X2 ) )
| ( $true
!= ( cP_6 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_4 @ ( f @ X1 ) @ X5 )
!= $true )
| ( $true
!= ( cP_2 @ X4 @ X0 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f129,f14]) ).
thf(f129,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_3 @ ( f @ X5 ) @ X4 ) )
| ( $true
!= ( cP_6 @ ( f @ X2 ) @ X3 ) )
| ( $true
!= ( cP_2 @ X0 @ X5 ) )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X1 ) @ X2 ) )
| ( ( cP_4 @ ( f @ X4 ) @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_4 @ ( f @ X4 ) @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X5 ) @ X4 ) )
| ( $true
!= ( cP_5 @ ( f @ X1 ) @ X2 ) )
| ( $true
!= ( cP_2 @ X0 @ X5 ) )
| ( $true != $true )
| ( $true
!= ( cP_6 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_1 @ b @ X0 )
!= $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f127,f10]) ).
thf(f127,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ ( f @ b ) @ X0 ) )
| ( ( cP_5 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X5 ) )
| ( $true
!= ( cP_4 @ ( f @ X4 ) @ X2 ) )
| ( ( cP_3 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_6 @ ( f @ X3 ) @ X5 ) )
| ( $true != $true )
| ( ( cP_3 @ ( f @ X1 ) @ X4 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X4 ) @ X2 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_5 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ b ) @ X0 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f68,f16]) ).
thf(f68,plain,
( ! [X0: $i,X1: $i,X8: $i,X7: $i,X4: $i,X13: $i] :
( ( $true
!= ( cP_2 @ ( f @ X4 ) @ X0 ) )
| ( ( cP_1 @ ( f @ b ) @ X4 )
!= $true )
| ( ( cP_6 @ ( f @ X8 ) @ X13 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X7 )
!= $true )
| ( ( cP_3 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_5 @ ( f @ X7 ) @ X8 )
!= $true ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f125,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f124]) ).
thf(f124,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f122,f17]) ).
thf(f17,plain,
( ( cP_6 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f122,plain,
( ! [X0: $i] :
( $true
!= ( cP_6 @ c @ X0 ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ! [X0: $i] :
( ( $true
!= ( cP_6 @ c @ X0 ) )
| ( $true != $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f120,f30]) ).
thf(f30,plain,
( ( cP_5 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f120,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_5 @ c @ X0 )
!= $true )
| ( ( cP_6 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_5 @ c @ X0 )
!= $true )
| ( $true != $true )
| ( ( cP_6 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f118,f42]) ).
thf(f42,plain,
( ( cP_4 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f118,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_4 @ c @ X2 )
!= $true )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( ( cP_5 @ X2 @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_4 @ c @ X2 )
!= $true )
| ( $true != $true )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( ( cP_5 @ X2 @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f116,f31]) ).
thf(f31,plain,
( ( cP_3 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f116,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ c @ X0 ) )
| ( ( cP_6 @ X2 @ X3 )
!= $true )
| ( $true
!= ( cP_5 @ X1 @ X2 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f87,f13]) ).
thf(f13,plain,
( ( cP_1 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f87,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_5 @ X1 @ X2 ) )
| ( ( cP_1 @ c @ c )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ c @ X0 ) )
| ( ( cP_6 @ X2 @ X3 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ c @ X0 ) )
| ( ( cP_6 @ X2 @ X3 )
!= $true )
| ( $true
!= ( cP_5 @ X1 @ X2 ) )
| ( ( cP_1 @ c @ c )
!= $true )
| ( $true != $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f81,f38]) ).
thf(f38,plain,
( ( cP_2 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f81,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_2 @ X5 @ X3 ) )
| ( ( cP_1 @ c @ X5 )
!= $true )
| ( ( cP_4 @ X2 @ X0 )
!= $true )
| ( ( cP_6 @ X1 @ X4 )
!= $true )
| ( ( cP_3 @ X3 @ X2 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_2 @ X5 @ X3 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ c @ X5 )
!= $true )
| ( $true != $true )
| ( ( cP_6 @ X1 @ X4 )
!= $true )
| ( ( cP_4 @ X2 @ X0 )
!= $true )
| ( ( cP_3 @ X3 @ X2 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f79,f26]) ).
thf(f79,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_5 @ ( f @ X1 ) @ X2 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_3 @ X5 @ X0 )
!= $true )
| ( $true
!= ( cP_6 @ X2 @ X4 ) )
| ( ( cP_1 @ c @ X3 )
!= $true )
| ( $true
!= ( cP_2 @ X3 @ X5 ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_1 @ c @ X3 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_2 @ X3 @ X5 ) )
| ( ( cP_3 @ X5 @ X0 )
!= $true )
| ( $true
!= ( cP_6 @ X2 @ X4 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X1 ) @ X2 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f77,f21]) ).
thf(f77,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_4 @ ( f @ X4 ) @ X5 ) )
| ( ( cP_5 @ ( f @ X5 ) @ X0 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X2 ) )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ X2 @ X3 )
!= $true )
| ( ( cP_3 @ X3 @ X4 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ c @ X2 ) )
| ( ( cP_2 @ X2 @ X3 )
!= $true )
| ( $true != $true )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( ( cP_5 @ ( f @ X5 ) @ X0 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X4 ) @ X5 ) )
| ( ( cP_3 @ X3 @ X4 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f75,f11]) ).
thf(f75,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_6 @ ( f @ X2 ) @ X3 ) )
| ( $true
!= ( cP_2 @ X5 @ X0 ) )
| ( ( cP_4 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_5 @ ( f @ X4 ) @ X2 )
!= $true )
| ( ( cP_1 @ c @ X5 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_4 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_5 @ ( f @ X4 ) @ X2 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_6 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ c @ X5 )
!= $true )
| ( $true
!= ( cP_2 @ X5 @ X0 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f73,f14]) ).
thf(f73,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_3 @ ( f @ X1 ) @ X2 ) )
| ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_1 @ c @ X0 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( cP_1 @ c @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X1 ) @ X2 ) )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f71,f10]) ).
thf(f71,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ ( f @ c ) @ X0 ) )
| ( $true
!= ( cP_3 @ ( f @ X1 ) @ X2 ) )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ c ) @ X0 ) )
| ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true )
| ( $true != $true )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X1 ) @ X2 ) )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f65,f16]) ).
thf(f65,plain,
( ! [X2: $i,X3: $i,X6: $i,X9: $i,X14: $i,X5: $i] :
( ( $true
!= ( cP_2 @ ( f @ X14 ) @ X5 ) )
| ( ( cP_3 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_4 @ ( f @ X6 ) @ X2 )
!= $true )
| ( ( cP_1 @ ( f @ c ) @ X14 )
!= $true )
| ( ( cP_5 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X9 ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl0_2
<=> ! [X5: $i,X2: $i,X9: $i,X14: $i,X6: $i,X3: $i] :
( ( ( cP_3 @ ( f @ X5 ) @ X6 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X9 ) )
| ( ( cP_1 @ ( f @ c ) @ X14 )
!= $true )
| ( ( cP_4 @ ( f @ X6 ) @ X2 )
!= $true )
| ( ( cP_5 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X14 ) @ X5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f69,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f59,f67,f64,f61]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X16: $i,X14: $i,X4: $i,X7: $i,X17: $i,X15: $i,X5: $i,X12: $i,X13: $i] :
( ( ( cP_2 @ ( f @ X12 ) @ X10 )
!= $true )
| ( ( cP_3 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_4 @ ( f @ X11 ) @ X15 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X14 ) @ X5 ) )
| ( ( cP_6 @ ( f @ X16 ) @ X17 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X15 ) @ X16 ) )
| ( $true
!= ( cP_2 @ ( f @ X4 ) @ X0 ) )
| ( ( cP_5 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_4 @ ( f @ X6 ) @ X2 )
!= $true )
| ( ( cP_3 @ ( f @ X10 ) @ X11 )
!= $true )
| ( ( cP_1 @ ( f @ c ) @ X14 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X9 ) )
| ( ( cP_1 @ ( f @ b ) @ X4 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X12 )
!= $true )
| ( ( cP_6 @ ( f @ X8 ) @ X13 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X7 )
!= $true )
| ( ( cP_3 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_5 @ ( f @ X7 ) @ X8 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X16: $i,X14: $i,X7: $i,X4: $i,X17: $i,X15: $i,X5: $i,X12: $i,X13: $i] :
( ( ( cP_6 @ ( f @ X8 ) @ X13 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X14 ) @ X5 ) )
| ( ( cP_5 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_6 @ ( f @ X16 ) @ X17 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_5 @ ( f @ X15 ) @ X16 ) )
| ( ( cP_4 @ ( f @ X11 ) @ X15 )
!= $true )
| ( ( cP_5 @ ( f @ X7 ) @ X8 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X9 ) )
| ( ( cP_2 @ ( f @ X12 ) @ X10 )
!= $true )
| ( ( cP_3 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_3 @ ( f @ X10 ) @ X11 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X7 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X4 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X4 ) @ X0 ) )
| ( ( cP_3 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_1 @ ( f @ c ) @ X14 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X12 )
!= $true )
| ( ( cP_4 @ ( f @ X6 ) @ X2 )
!= $true ) ),
inference(superposition,[status(thm)],[f57,f12]) ).
thf(f12,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X18: $i,X1: $i,X19: $i,X6: $i,X16: $i,X7: $i,X8: $i,X9: $i,X14: $i,X4: $i,X17: $i,X15: $i,X5: $i,X12: $i,X13: $i,X20: $i] :
( ( ( cQ_1 @ X18 @ X19 @ X20 )
!= $true )
| ( ( cP_3 @ ( f @ X15 ) @ X16 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X11 ) @ X6 ) )
| ( $true
!= ( cP_1 @ ( f @ X19 ) @ X1 ) )
| ( ( cP_3 @ ( f @ X12 ) @ X10 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X17 ) @ X13 ) )
| ( $true
!= ( cP_4 @ ( f @ X10 ) @ X11 ) )
| ( ( cP_6 @ ( f @ X6 ) @ X7 )
!= $true )
| ( ( cP_3 @ ( f @ X8 ) @ X9 )
!= $true )
| ( ( cP_1 @ ( f @ X18 ) @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X16 ) @ X17 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X13 ) @ X14 ) )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X12 ) )
| ( ( cP_2 @ ( f @ X0 ) @ X8 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X9 ) @ X3 ) )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_2 @ ( f @ X1 ) @ X15 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X20 ) @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X18: $i,X1: $i,X19: $i,X8: $i,X16: $i,X9: $i,X4: $i,X6: $i,X14: $i,X7: $i,X17: $i,X15: $i,X5: $i,X12: $i,X13: $i,X20: $i] :
( ( ( cP_1 @ ( f @ X18 ) @ X0 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X19 ) @ X1 ) )
| ( $true
!= ( cP_1 @ ( f @ X20 ) @ X2 ) )
| ( $true != $true )
| ( $true
!= ( cP_4 @ ( f @ X10 ) @ X11 ) )
| ( ( cP_3 @ ( f @ X15 ) @ X16 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X12 ) )
| ( ( cQ_1 @ X18 @ X19 @ X20 )
!= $true )
| ( ( cP_3 @ ( f @ X8 ) @ X9 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X8 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X9 ) @ X3 ) )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X1 ) @ X15 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X11 ) @ X6 ) )
| ( ( cP_3 @ ( f @ X12 ) @ X10 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X13 ) @ X14 ) )
| ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_6 @ ( f @ X6 ) @ X7 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X17 ) @ X13 ) )
| ( ( cP_4 @ ( f @ X16 ) @ X17 )
!= $true ) ),
inference(superposition,[status(thm)],[f55,f43]) ).
thf(f43,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( ( cQ_2 @ X10 @ X6 @ X9 )
= $true )
| ( $true
!= ( cP_1 @ ( f @ X8 ) @ X10 ) )
| ( ( cQ_1 @ X8 @ X7 @ X11 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X7 ) @ X6 ) )
| ( ( cP_1 @ ( f @ X11 ) @ X9 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X16: $i,X14: $i,X7: $i,X4: $i,X17: $i,X15: $i,X5: $i,X12: $i,X13: $i] :
( ( ( cQ_2 @ X17 @ X15 @ X16 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X14 ) @ X7 ) )
| ( ( cP_6 @ ( f @ X7 ) @ X8 )
!= $true )
| ( ( cP_6 @ ( f @ X11 ) @ X12 )
!= $true )
| ( ( cP_3 @ ( f @ X0 ) @ X6 )
!= $true )
| ( ( cP_4 @ ( f @ X10 ) @ X13 )
!= $true )
| ( ( cP_3 @ ( f @ X2 ) @ X10 )
!= $true )
| ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X3 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X3 ) @ X9 ) )
| ( $true
!= ( cP_2 @ ( f @ X17 ) @ X0 ) )
| ( ( cP_2 @ ( f @ X15 ) @ X1 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X13 ) @ X11 ) )
| ( $true
!= ( cP_4 @ ( f @ X6 ) @ X14 ) )
| ( $true
!= ( cP_5 @ ( f @ X9 ) @ X4 ) )
| ( $true
!= ( cP_2 @ ( f @ X16 ) @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X16: $i,X14: $i,X7: $i,X4: $i,X17: $i,X15: $i,X5: $i,X12: $i,X13: $i] :
( ( ( cP_2 @ ( f @ X15 ) @ X1 )
!= $true )
| ( ( cP_3 @ ( f @ X0 ) @ X6 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X16 ) @ X2 ) )
| ( ( cP_6 @ ( f @ X11 ) @ X12 )
!= $true )
| ( ( cP_3 @ ( f @ X2 ) @ X10 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X17 ) @ X0 ) )
| ( $true
!= ( cP_5 @ ( f @ X14 ) @ X7 ) )
| ( $true != $true )
| ( ( cP_6 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_4 @ ( f @ X10 ) @ X13 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X3 ) @ X9 ) )
| ( $true
!= ( cP_5 @ ( f @ X13 ) @ X11 ) )
| ( ( cQ_2 @ X17 @ X15 @ X16 )
!= $true )
| ( ( cP_6 @ ( f @ X7 ) @ X8 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X6 ) @ X14 ) )
| ( ( cP_3 @ ( f @ X1 ) @ X3 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X9 ) @ X4 ) ) ),
inference(superposition,[status(thm)],[f53,f29]) ).
thf(f29,plain,
! [X40: $i,X38: $i,X39: $i,X36: $i,X37: $i,X35: $i] :
( ( ( cQ_3 @ X40 @ X36 @ X35 )
= $true )
| ( $true
!= ( cP_2 @ ( f @ X37 ) @ X36 ) )
| ( ( cP_2 @ ( f @ X38 ) @ X35 )
!= $true )
| ( $true
!= ( cQ_2 @ X39 @ X37 @ X38 ) )
| ( ( cP_2 @ ( f @ X39 ) @ X40 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X14: $i,X4: $i,X5: $i,X12: $i,X13: $i] :
( ( $true
!= ( cQ_3 @ X13 @ X14 @ X12 ) )
| ( $true
!= ( cP_3 @ ( f @ X14 ) @ X1 ) )
| ( ( cP_6 @ ( f @ X8 ) @ X9 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X13 ) @ X0 ) )
| ( ( cP_6 @ ( f @ X6 ) @ X11 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X7 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X12 ) @ X2 ) )
| ( $true
!= ( cP_6 @ ( f @ X4 ) @ X10 ) )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_5 @ ( f @ X7 ) @ X8 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X5 ) @ X6 ) )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X0 ) @ X5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X14: $i,X4: $i,X5: $i,X12: $i,X13: $i] :
( ( $true
!= ( cP_3 @ ( f @ X12 ) @ X2 ) )
| ( $true
!= ( cP_3 @ ( f @ X13 ) @ X0 ) )
| ( ( cP_6 @ ( f @ X6 ) @ X11 )
!= $true )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_6 @ ( f @ X8 ) @ X9 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X14 ) @ X1 ) )
| ( $true
!= ( cP_4 @ ( f @ X0 ) @ X5 ) )
| ( ( cP_4 @ ( f @ X1 ) @ X7 )
!= $true )
| ( $true != $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cQ_3 @ X13 @ X14 @ X12 ) )
| ( $true
!= ( cP_6 @ ( f @ X4 ) @ X10 ) )
| ( $true
!= ( cP_5 @ ( f @ X5 ) @ X6 ) )
| ( ( cP_5 @ ( f @ X7 ) @ X8 )
!= $true ) ),
inference(superposition,[status(thm)],[f51,f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( cQ_4 @ X2 @ X1 @ X5 ) )
| ( $true
!= ( cP_3 @ ( f @ X4 ) @ X5 ) )
| ( ( cQ_3 @ X3 @ X0 @ X4 )
!= $true )
| ( ( cP_3 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X3 ) @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( cQ_4 @ X9 @ X10 @ X11 ) )
| ( $true
!= ( cP_4 @ ( f @ X11 ) @ X2 ) )
| ( $true
!= ( cP_5 @ ( f @ X2 ) @ X4 ) )
| ( ( cP_5 @ ( f @ X0 ) @ X3 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X10 ) @ X1 ) )
| ( ( cP_5 @ ( f @ X1 ) @ X6 )
!= $true )
| ( ( cP_6 @ ( f @ X6 ) @ X7 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X4 ) @ X8 ) )
| ( $true
!= ( cP_4 @ ( f @ X9 ) @ X0 ) )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_4 @ ( f @ X11 ) @ X2 ) )
| ( ( cP_6 @ ( f @ X6 ) @ X7 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X4 ) @ X8 ) )
| ( $true
!= ( cP_4 @ ( f @ X9 ) @ X0 ) )
| ( $true != $true )
| ( $true
!= ( cP_4 @ ( f @ X10 ) @ X1 ) )
| ( ( cP_5 @ ( f @ X1 ) @ X6 )
!= $true )
| ( $true
!= ( cQ_4 @ X9 @ X10 @ X11 ) )
| ( ( cP_5 @ ( f @ X0 ) @ X3 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X5 ) )
| ( $true
!= ( cP_5 @ ( f @ X2 ) @ X4 ) ) ),
inference(superposition,[status(thm)],[f49,f35]) ).
thf(f35,plain,
! [X21: $i,X24: $i,X22: $i,X25: $i,X23: $i,X20: $i] :
( ( ( cQ_5 @ X25 @ X23 @ X22 )
= $true )
| ( ( cQ_4 @ X21 @ X20 @ X24 )
!= $true )
| ( ( cP_4 @ ( f @ X24 ) @ X22 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X20 ) @ X23 ) )
| ( $true
!= ( cP_4 @ ( f @ X21 ) @ X25 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cQ_5 @ X8 @ X7 @ X6 )
!= $true )
| ( ( cP_5 @ ( f @ X8 ) @ X0 )
!= $true )
| ( ( cP_5 @ ( f @ X6 ) @ X2 )
!= $true )
| ( ( cP_6 @ ( f @ X0 ) @ X3 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X7 ) @ X1 ) )
| ( ( cP_6 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_6 @ ( f @ X2 ) @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cP_5 @ ( f @ X6 ) @ X2 )
!= $true )
| ( $true != $true )
| ( ( cP_6 @ ( f @ X0 ) @ X3 )
!= $true )
| ( ( cP_5 @ ( f @ X8 ) @ X0 )
!= $true )
| ( ( cP_6 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cQ_5 @ X8 @ X7 @ X6 )
!= $true )
| ( ( cP_6 @ ( f @ X2 ) @ X5 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X7 ) @ X1 ) ) ),
inference(superposition,[status(thm)],[f47,f32]) ).
thf(f32,plain,
! [X31: $i,X29: $i,X34: $i,X32: $i,X30: $i,X33: $i] :
( ( ( cQ_6 @ X30 @ X33 @ X31 )
= $true )
| ( $true
!= ( cP_5 @ ( f @ X32 ) @ X31 ) )
| ( $true
!= ( cP_5 @ ( f @ X29 ) @ X33 ) )
| ( $true
!= ( cP_5 @ ( f @ X34 ) @ X30 ) )
| ( $true
!= ( cQ_5 @ X34 @ X29 @ X32 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cQ_6 @ X4 @ X3 @ X5 ) )
| ( ( cP_6 @ ( f @ X4 ) @ X0 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X1 ) )
| ( ( cP_6 @ ( f @ X5 ) @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_6 @ ( f @ X5 ) @ X2 )
!= $true )
| ( $true
!= ( cQ_6 @ X4 @ X3 @ X5 ) )
| ( ( cP_6 @ ( f @ X4 ) @ X0 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f33,f36]) ).
thf(f36,plain,
! [X18: $i,X19: $i,X16: $i,X14: $i,X17: $i,X15: $i] :
( ( ( cQ_7 @ X18 @ X14 @ X17 )
= $true )
| ( $true
!= ( cP_6 @ ( f @ X16 ) @ X14 ) )
| ( ( cQ_6 @ X19 @ X16 @ X15 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X19 ) @ X18 ) )
| ( $true
!= ( cP_6 @ ( f @ X15 ) @ X17 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f33,plain,
! [X28: $i,X26: $i,X27: $i] :
( ( cQ_7 @ X27 @ X28 @ X26 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO391^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n015.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:30:01 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SYO391^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Syntactic
% 0.28/0.46 % Problem : TPS problem from MISC
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_1245 [Bro09]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.33 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.20 v5.4.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.67 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 19 ( 0 unt; 18 typ; 0 def)
% 0.28/0.46 % Number of atoms : 68 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 68 ( 68 avg)
% 0.28/0.46 % Number of connectives : 273 ( 32 ~; 30 |; 37 &; 174 @)
% 0.28/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 53 ( 53 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 18 ( 18 usr; 4 con; 0-3 aty)
% 0.28/0.46 % Number of variables : 57 ( 0 ^; 57 !; 0 ?; 57 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(cQ_7,type,
% 0.28/0.46 cQ_7: $i > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(f,type,
% 0.28/0.46 f: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(cP_6,type,
% 0.28/0.46 cP_6: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cQ_6,type,
% 0.28/0.46 cQ_6: $i > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(d,type,
% 0.28/0.46 d: $i ).
% 0.28/0.46
% 0.28/0.46 thf(c,type,
% 0.28/0.46 c: $i ).
% 0.28/0.46
% 0.28/0.46 thf(b,type,
% 0.28/0.46 b: $i ).
% 0.28/0.46
% 0.28/0.46 thf(a,type,
% 0.28/0.46 a: $i ).
% 0.28/0.46
% 0.28/0.46 thf(cP_5,type,
% 0.28/0.46 cP_5: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cQ_5,type,
% 0.28/0.46 cQ_5: $i > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cP_4,type,
% 0.28/0.46 cP_4: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cQ_4,type,
% 0.28/0.46 cQ_4: $i > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cP_3,type,
% 0.28/0.46 cP_3: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cQ_3,type,
% 0.28/0.46 cQ_3: $i > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cP_2,type,
% 0.28/0.46 cP_2: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cQ_2,type,
% 0.28/0.46 cQ_2: $i > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cP_1,type,
% 0.28/0.46 cP_1: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cQ_1,type,
% 0.28/0.46 cQ_1: $i > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cTHM409_6,conjecture,
% 0.28/0.46 ~ ( ( cQ_1 @ a @ b @ c )
% 0.28/0.46 & ( cP_1 @ a @ a )
% 0.28/0.46 & ( cP_1 @ b @ b )
% 0.28/0.46 & ( cP_1 @ c @ c )
% 0.28/0.46 & ! [Xx: $i] : ( cP_1 @ d @ Xx )
% 0.28/0.46 & ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ~ ( cP_1 @ Xx @ Xy )
% 0.28/0.46 | ( cP_1 @ ( f @ Xx ) @ Xy ) )
% 0.28/0.46 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.28/0.46 ( ~ ( cQ_1 @ Xx @ Xy @ Xz )
% 0.28/0.46 | ~ ( cP_1 @ ( f @ Xx ) @ Xu )
% 0.28/0.46 | ~ ( cP_1 @ ( f @ Xy ) @ Xv )
% 0.28/0.46 | ~ ( cP_1 @ ( f @ Xz ) @ Xw )
% 0.28/0.46 | ( cQ_2 @ Xu @ Xv @ Xw ) )
% 0.28/0.46 & ( cP_2 @ a @ a )
% 0.28/0.46 & ( cP_2 @ b @ b )
% 0.28/0.46 & ( cP_2 @ c @ c )
% 0.28/0.46 & ! [Xx: $i] : ( cP_2 @ d @ Xx )
% 0.28/0.46 & ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ~ ( cP_2 @ Xx @ Xy )
% 0.28/0.46 | ( cP_2 @ ( f @ Xx ) @ Xy ) )
% 0.28/0.46 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.28/0.46 ( ~ ( cQ_2 @ Xx @ Xy @ Xz )
% 0.28/0.46 | ~ ( cP_2 @ ( f @ Xx ) @ Xu )
% 0.28/0.46 | ~ ( cP_2 @ ( f @ Xy ) @ Xv )
% 0.28/0.46 | ~ ( cP_2 @ ( f @ Xz ) @ Xw )
% 0.28/0.46 | ( cQ_3 @ Xu @ Xv @ Xw ) )
% 0.28/0.46 & ( cP_3 @ a @ a )
% 0.28/0.46 & ( cP_3 @ b @ b )
% 0.28/0.46 & ( cP_3 @ c @ c )
% 0.28/0.46 & ! [Xx: $i] : ( cP_3 @ d @ Xx )
% 0.28/0.46 & ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ~ ( cP_3 @ Xx @ Xy )
% 0.28/0.46 | ( cP_3 @ ( f @ Xx ) @ Xy ) )
% 0.28/0.46 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.28/0.46 ( ~ ( cQ_3 @ Xx @ Xy @ Xz )
% 0.28/0.46 | ~ ( cP_3 @ ( f @ Xx ) @ Xu )
% 0.28/0.46 | ~ ( cP_3 @ ( f @ Xy ) @ Xv )
% 0.28/0.46 | ~ ( cP_3 @ ( f @ Xz ) @ Xw )
% 0.28/0.46 | ( cQ_4 @ Xu @ Xv @ Xw ) )
% 0.28/0.46 & ( cP_4 @ a @ a )
% 0.28/0.46 & ( cP_4 @ b @ b )
% 0.28/0.46 & ( cP_4 @ c @ c )
% 0.28/0.46 & ! [Xx: $i] : ( cP_4 @ d @ Xx )
% 0.28/0.46 & ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ~ ( cP_4 @ Xx @ Xy )
% 0.28/0.46 | ( cP_4 @ ( f @ Xx ) @ Xy ) )
% 0.28/0.46 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.28/0.46 ( ~ ( cQ_4 @ Xx @ Xy @ Xz )
% 0.28/0.46 | ~ ( cP_4 @ ( f @ Xx ) @ Xu )
% 0.28/0.46 | ~ ( cP_4 @ ( f @ Xy ) @ Xv )
% 0.28/0.46 | ~ ( cP_4 @ ( f @ Xz ) @ Xw )
% 0.28/0.46 | ( cQ_5 @ Xu @ Xv @ Xw ) )
% 0.28/0.46 & ( cP_5 @ a @ a )
% 0.28/0.46 & ( cP_5 @ b @ b )
% 0.28/0.46 & ( cP_5 @ c @ c )
% 0.28/0.46 & ! [Xx: $i] : ( cP_5 @ d @ Xx )
% 0.28/0.46 & ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ~ ( cP_5 @ Xx @ Xy )
% 0.28/0.46 | ( cP_5 @ ( f @ Xx ) @ Xy ) )
% 0.28/0.46 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.28/0.46 ( ~ ( cQ_5 @ Xx @ Xy @ Xz )
% 0.28/0.46 | ~ ( cP_5 @ ( f @ Xx ) @ Xu )
% 0.28/0.46 | ~ ( cP_5 @ ( f @ Xy ) @ Xv )
% 0.28/0.46 | ~ ( cP_5 @ ( f @ Xz ) @ Xw )
% 0.28/0.46 | ( cQ_6 @ Xu @ Xv @ Xw ) )
% 0.28/0.46 & ( cP_6 @ a @ a )
% 0.28/0.46 & ( cP_6 @ b @ b )
% 0.28/0.46 & ( cP_6 @ c @ c )
% 0.28/0.46 & ! [Xx: $i] : ( cP_6 @ d @ Xx )
% 0.28/0.46 & ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ~ ( cP_6 @ Xx @ Xy )
% 0.28/0.46 | ( cP_6 @ ( f @ Xx ) @ Xy ) )
% 0.28/0.46 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.28/0.46 ( ~ ( cQ_6 @ Xx @ Xy @ Xz )
% 0.28/0.46 | ~ ( cP_6 @ ( f @ Xx ) @ Xu )
% 0.28/0.46 | ~ ( cP_6 @ ( f @ Xy ) @ Xv )
% 0.28/0.46 | ~ ( cP_6 @ ( f @ Xz ) @ Xw )
% 0.28/0.46 | ( cQ_7 @ Xu @ Xv @ Xw ) )
% 0.28/0.46 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.46 ~ ( cQ_7 @ Xx @ Xy @ Xz ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 0.32/1.30 ---- Embedded in THF ---
% 0.32/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.30 %%% Generated on Tue Feb 24 14:30:02 EST 2026
% 0.32/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.30 %%% Logic specification used:
% 0.32/1.30 %%% thf(spec, logic, $$dhol).
% 0.32/1.30
% 0.32/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.c39OTm3iHl/DTF2DTF5935.p
% See solution above
% 0.32/1.30 ------------------------
% 0.32/1.31 ---- Cleaned THF ---
% 0.32/1.31 thf(cQ_7,type,
% 0.32/1.31 cQ_7: $i > $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(f,type,
% 0.32/1.31 f: $i > $i ).
% 0.32/1.31
% 0.32/1.31 thf(cP_6,type,
% 0.32/1.31 cP_6: $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(cQ_6,type,
% 0.32/1.31 cQ_6: $i > $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(d,type,
% 0.32/1.31 d: $i ).
% 0.32/1.31
% 0.32/1.31 thf(c,type,
% 0.32/1.31 c: $i ).
% 0.32/1.31
% 0.32/1.31 thf(b,type,
% 0.32/1.31 b: $i ).
% 0.32/1.31
% 0.32/1.31 thf(a,type,
% 0.32/1.31 a: $i ).
% 0.32/1.31
% 0.32/1.31 thf(cP_5,type,
% 0.32/1.31 cP_5: $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(cQ_5,type,
% 0.32/1.31 cQ_5: $i > $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(cP_4,type,
% 0.32/1.31 cP_4: $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(cQ_4,type,
% 0.32/1.31 cQ_4: $i > $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(cP_3,type,
% 0.32/1.31 cP_3: $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(cQ_3,type,
% 0.32/1.31 cQ_3: $i > $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(cP_2,type,
% 0.32/1.31 cP_2: $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(cQ_2,type,
% 0.32/1.31 cQ_2: $i > $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(cP_1,type,
% 0.32/1.31 cP_1: $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(cQ_1,type,
% 0.32/1.31 cQ_1: $i > $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(cTHM409_6,conjecture,
% 0.32/1.31 ~ ( ( cQ_1 @ a @ b @ c )
% 0.32/1.31 & ( cP_1 @ a @ a )
% 0.32/1.31 & ( cP_1 @ b @ b )
% 0.32/1.31 & ( cP_1 @ c @ c )
% 0.32/1.31 & ! [Xx: $i] : ( cP_1 @ d @ Xx )
% 0.32/1.31 & ! [Xx: $i,Xy: $i] :
% 0.32/1.31 ( ~ ( cP_1 @ Xx @ Xy )
% 0.32/1.31 | ( cP_1 @ ( f @ Xx ) @ Xy ) )
% 0.32/1.31 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.32/1.31 ( ~ ( cQ_1 @ Xx @ Xy @ Xz )
% 0.32/1.31 | ~ ( cP_1 @ ( f @ Xx ) @ Xu )
% 0.32/1.31 | ~ ( cP_1 @ ( f @ Xy ) @ Xv )
% 0.32/1.31 | ~ ( cP_1 @ ( f @ Xz ) @ Xw )
% 0.32/1.31 | ( cQ_2 @ Xu @ Xv @ Xw ) )
% 0.32/1.31 & ( cP_2 @ a @ a )
% 0.32/1.31 & ( cP_2 @ b @ b )
% 0.32/1.31 & ( cP_2 @ c @ c )
% 0.32/1.31 & ! [Xx: $i] : ( cP_2 @ d @ Xx )
% 0.32/1.31 & ! [Xx: $i,Xy: $i] :
% 0.32/1.31 ( ~ ( cP_2 @ Xx @ Xy )
% 0.32/1.31 | ( cP_2 @ ( f @ Xx ) @ Xy ) )
% 0.32/1.31 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.32/1.31 ( ~ ( cQ_2 @ Xx @ Xy @ Xz )
% 0.32/1.31 | ~ ( cP_2 @ ( f @ Xx ) @ Xu )
% 0.32/1.31 | ~ ( cP_2 @ ( f @ Xy ) @ Xv )
% 0.32/1.31 | ~ ( cP_2 @ ( f @ Xz ) @ Xw )
% 0.32/1.31 | ( cQ_3 @ Xu @ Xv @ Xw ) )
% 0.32/1.31 & ( cP_3 @ a @ a )
% 0.32/1.31 & ( cP_3 @ b @ b )
% 0.32/1.31 & ( cP_3 @ c @ c )
% 0.32/1.31 & ! [Xx: $i] : ( cP_3 @ d @ Xx )
% 0.32/1.31 & ! [Xx: $i,Xy: $i] :
% 0.32/1.31 ( ~ ( cP_3 @ Xx @ Xy )
% 0.32/1.31 | ( cP_3 @ ( f @ Xx ) @ Xy ) )
% 0.32/1.31 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.32/1.31 ( ~ ( cQ_3 @ Xx @ Xy @ Xz )
% 0.32/1.31 | ~ ( cP_3 @ ( f @ Xx ) @ Xu )
% 0.32/1.31 | ~ ( cP_3 @ ( f @ Xy ) @ Xv )
% 0.32/1.31 | ~ ( cP_3 @ ( f @ Xz ) @ Xw )
% 0.32/1.31 | ( cQ_4 @ Xu @ Xv @ Xw ) )
% 0.32/1.31 & ( cP_4 @ a @ a )
% 0.32/1.31 & ( cP_4 @ b @ b )
% 0.32/1.31 & ( cP_4 @ c @ c )
% 0.32/1.31 & ! [Xx: $i] : ( cP_4 @ d @ Xx )
% 0.32/1.31 & ! [Xx: $i,Xy: $i] :
% 0.32/1.31 ( ~ ( cP_4 @ Xx @ Xy )
% 0.32/1.31 | ( cP_4 @ ( f @ Xx ) @ Xy ) )
% 0.32/1.31 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.32/1.31 ( ~ ( cQ_4 @ Xx @ Xy @ Xz )
% 0.32/1.31 | ~ ( cP_4 @ ( f @ Xx ) @ Xu )
% 0.32/1.31 | ~ ( cP_4 @ ( f @ Xy ) @ Xv )
% 0.32/1.31 | ~ ( cP_4 @ ( f @ Xz ) @ Xw )
% 0.32/1.31 | ( cQ_5 @ Xu @ Xv @ Xw ) )
% 0.32/1.31 & ( cP_5 @ a @ a )
% 0.32/1.31 & ( cP_5 @ b @ b )
% 0.32/1.31 & ( cP_5 @ c @ c )
% 0.32/1.31 & ! [Xx: $i] : ( cP_5 @ d @ Xx )
% 0.32/1.31 & ! [Xx: $i,Xy: $i] :
% 0.32/1.31 ( ~ ( cP_5 @ Xx @ Xy )
% 0.32/1.31 | ( cP_5 @ ( f @ Xx ) @ Xy ) )
% 0.32/1.31 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.32/1.31 ( ~ ( cQ_5 @ Xx @ Xy @ Xz )
% 0.32/1.31 | ~ ( cP_5 @ ( f @ Xx ) @ Xu )
% 0.32/1.31 | ~ ( cP_5 @ ( f @ Xy ) @ Xv )
% 0.32/1.31 | ~ ( cP_5 @ ( f @ Xz ) @ Xw )
% 0.32/1.31 | ( cQ_6 @ Xu @ Xv @ Xw ) )
% 0.32/1.31 & ( cP_6 @ a @ a )
% 0.32/1.31 & ( cP_6 @ b @ b )
% 0.32/1.31 & ( cP_6 @ c @ c )
% 0.32/1.31 & ! [Xx: $i] : ( cP_6 @ d @ Xx )
% 0.32/1.31 & ! [Xx: $i,Xy: $i] :
% 0.32/1.31 ( ~ ( cP_6 @ Xx @ Xy )
% 0.32/1.31 | ( cP_6 @ ( f @ Xx ) @ Xy ) )
% 0.32/1.31 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.32/1.31 ( ~ ( cQ_6 @ Xx @ Xy @ Xz )
% 0.32/1.31 | ~ ( cP_6 @ ( f @ Xx ) @ Xu )
% 0.32/1.31 | ~ ( cP_6 @ ( f @ Xy ) @ Xv )
% 0.32/1.31 | ~ ( cP_6 @ ( f @ Xz ) @ Xw )
% 0.32/1.31 | ( cQ_7 @ Xu @ Xv @ Xw ) )
% 0.32/1.31 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.32/1.31 ~ ( cQ_7 @ Xx @ Xy @ Xz ) ) ).
% 0.32/1.31 ------------------------
% 0.32/1.33 % (6229)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5935 for (2999ds/18Mi)
% 0.32/1.33 % (6225)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5935 for (2999ds/2Mi)
% 0.32/1.33 % (6225)Instruction limit reached!
% 0.32/1.33 % (6225)------------------------------
% 0.32/1.33 % (6225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.33 % (6225)Termination reason: Unknown
% 0.32/1.33 % (6225)Termination phase: shuffling
% 0.32/1.33
% 0.32/1.33 % (6225)Memory used [KB]: 1023
% 0.32/1.33 % (6225)Time elapsed: 0.002 s
% 0.32/1.33 % (6225)Instructions burned: 3 (million)
% 0.32/1.33 % (6225)------------------------------
% 0.32/1.33 % (6225)------------------------------
% 0.32/1.33 % (6229)Instruction limit reached!
% 0.32/1.33 % (6229)------------------------------
% 0.32/1.33 % (6229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.33 % (6229)Termination reason: Unknown
% 0.32/1.33 % (6229)Termination phase: Saturation
% 0.32/1.33
% 0.32/1.33 % (6229)Memory used [KB]: 5628
% 0.32/1.33 % (6229)Time elapsed: 0.008 s
% 0.32/1.33 % (6229)Instructions burned: 19 (million)
% 0.32/1.33 % (6229)------------------------------
% 0.32/1.33 % (6229)------------------------------
% 0.32/1.33 % (6222)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5935 for (2999ds/183Mi)
% 0.32/1.34 % (6223)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_5935 for (2999ds/4Mi)
% 0.32/1.34 % (6224)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_5935 for (2999ds/27Mi)
% 0.32/1.34 % (6226)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_5935 for (2999ds/2Mi)
% 0.32/1.34 % (6228)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_5935 for (2999ds/275Mi)
% 0.32/1.34 % (6226)Instruction limit reached!
% 0.32/1.34 % (6226)------------------------------
% 0.32/1.34 % (6226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.34 % (6226)Termination reason: Unknown
% 0.32/1.34 % (6226)Termination phase: shuffling
% 0.32/1.34
% 0.32/1.34 % (6226)Memory used [KB]: 1023
% 0.32/1.34 % (6226)Time elapsed: 0.003 s
% 0.32/1.34 % (6226)Instructions burned: 2 (million)
% 0.32/1.34 % (6226)------------------------------
% 0.32/1.34 % (6226)------------------------------
% 0.32/1.34 % (6223)Instruction limit reached!
% 0.32/1.34 % (6223)------------------------------
% 0.32/1.34 % (6223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.34 % (6223)Termination reason: Unknown
% 0.32/1.34 % (6223)Termination phase: Property scanning
% 0.32/1.34
% 0.32/1.34 % (6223)Memory used [KB]: 1023
% 0.32/1.34 % (6223)Time elapsed: 0.004 s
% 0.32/1.34 % (6223)Instructions burned: 4 (million)
% 0.32/1.34 % (6223)------------------------------
% 0.32/1.34 % (6223)------------------------------
% 0.32/1.34 % (6230)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5935 for (2999ds/3Mi)
% 0.32/1.34 % (6230)Instruction limit reached!
% 0.32/1.34 % (6230)------------------------------
% 0.32/1.34 % (6230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.34 % (6230)Termination reason: Unknown
% 0.32/1.34 % (6230)Termination phase: Preprocessing 2
% 0.32/1.34
% 0.32/1.34 % (6230)Memory used [KB]: 1023
% 0.32/1.34 % (6230)Time elapsed: 0.003 s
% 0.32/1.34 % (6230)Instructions burned: 4 (million)
% 0.32/1.34 % (6230)------------------------------
% 0.32/1.34 % (6230)------------------------------
% 0.32/1.34 % (6231)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_5935 for (2999ds/37Mi)
% 0.32/1.35 % (6234)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_5935 for (2999ds/1041Mi)
% 0.32/1.35 % (6224)Instruction limit reached!
% 0.32/1.35 % (6224)------------------------------
% 0.32/1.35 % (6224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.35 % (6224)Termination reason: Unknown
% 0.32/1.35 % (6224)Termination phase: Saturation
% 0.32/1.35
% 0.32/1.35 % (6224)Memory used [KB]: 5756
% 0.32/1.35 % (6224)Time elapsed: 0.019 s
% 0.32/1.35 % (6224)Instructions burned: 27 (million)
% 0.32/1.35 % (6224)------------------------------
% 0.32/1.35 % (6224)------------------------------
% 0.32/1.35 % (6232)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_5935 for (2999ds/15Mi)
% 0.32/1.35 % (6231)Instruction limit reached!
% 0.32/1.35 % (6231)------------------------------
% 0.32/1.35 % (6231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.35 % (6231)Termination reason: Unknown
% 0.32/1.35 % (6231)Termination phase: Saturation
% 0.32/1.35
% 0.32/1.35 % (6231)Memory used [KB]: 5628
% 0.32/1.35 % (6231)Time elapsed: 0.011 s
% 0.32/1.35 % (6231)Instructions burned: 40 (million)
% 0.32/1.35 % (6231)------------------------------
% 0.32/1.35 % (6231)------------------------------
% 0.32/1.35 % (6233)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_5935 for (2999ds/3Mi)
% 0.32/1.36 % (6233)Instruction limit reached!
% 0.32/1.36 % (6233)------------------------------
% 0.32/1.36 % (6233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.36 % (6233)Termination reason: Unknown
% 0.32/1.36 % (6233)Termination phase: Preprocessing 1
% 0.32/1.36
% 0.32/1.36 % (6233)Memory used [KB]: 1023
% 0.32/1.36 % (6233)Time elapsed: 0.004 s
% 0.32/1.36 % (6233)Instructions burned: 4 (million)
% 0.32/1.36 % (6233)------------------------------
% 0.32/1.36 % (6233)------------------------------
% 0.32/1.36 % (6232)Instruction limit reached!
% 0.32/1.36 % (6232)------------------------------
% 0.32/1.36 % (6232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.36 % (6232)Termination reason: Unknown
% 0.32/1.36 % (6232)Termination phase: Saturation
% 0.32/1.36
% 0.32/1.36 % (6232)Memory used [KB]: 5756
% 0.32/1.36 % (6232)Time elapsed: 0.011 s
% 0.32/1.36 % (6232)Instructions burned: 15 (million)
% 0.32/1.36 % (6232)------------------------------
% 0.32/1.36 % (6232)------------------------------
% 0.32/1.36 % (6236)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5935 for (2999ds/16Mi)
% 0.32/1.37 % (6236)Instruction limit reached!
% 0.32/1.37 % (6236)------------------------------
% 0.32/1.37 % (6236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.37 % (6236)Termination reason: Unknown
% 0.32/1.37 % (6236)Termination phase: Saturation
% 0.32/1.37
% 0.32/1.37 % (6236)Memory used [KB]: 5756
% 0.32/1.37 % (6236)Time elapsed: 0.006 s
% 0.32/1.37 % (6236)Instructions burned: 18 (million)
% 0.32/1.37 % (6236)------------------------------
% 0.32/1.37 % (6236)------------------------------
% 0.32/1.37 % (6235)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5935 for (2999ds/7Mi)
% 0.32/1.37 % (6235)Instruction limit reached!
% 0.32/1.37 % (6235)------------------------------
% 0.32/1.37 % (6235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.37 % (6235)Termination reason: Unknown
% 0.32/1.37 % (6235)Termination phase: Saturation
% 0.32/1.37
% 0.32/1.37 % (6235)Memory used [KB]: 1151
% 0.32/1.37 % (6235)Time elapsed: 0.006 s
% 0.32/1.37 % (6235)Instructions burned: 7 (million)
% 0.32/1.37 % (6235)------------------------------
% 0.32/1.37 % (6235)------------------------------
% 0.32/1.37 % (6237)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_5935 for (2999ds/3Mi)
% 0.32/1.37 % (6222)First to succeed.
% 0.32/1.38 % (6237)Instruction limit reached!
% 0.32/1.38 % (6237)------------------------------
% 0.32/1.38 % (6237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.38 % (6237)Termination reason: Unknown
% 0.32/1.38 % (6237)Termination phase: SInE selection
% 0.32/1.38
% 0.32/1.38 % (6237)Memory used [KB]: 1023
% 0.32/1.38 % (6237)Time elapsed: 0.004 s
% 0.32/1.38 % (6237)Instructions burned: 4 (million)
% 0.32/1.38 % (6237)------------------------------
% 0.32/1.38 % (6237)------------------------------
% 0.32/1.38 % (6239)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5935 for (2999ds/7Mi)
% 0.32/1.38 % (6239)Instruction limit reached!
% 0.32/1.38 % (6239)------------------------------
% 0.32/1.38 % (6239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.38 % (6239)Termination reason: Unknown
% 0.32/1.38 % (6239)Termination phase: Saturation
% 0.32/1.38
% 0.32/1.38 % (6239)Memory used [KB]: 5628
% 0.32/1.38 % (6239)Time elapsed: 0.003 s
% 0.32/1.38 % (6239)Instructions burned: 7 (million)
% 0.32/1.38 % (6239)------------------------------
% 0.32/1.38 % (6239)------------------------------
% 0.32/1.38 % (6222)Refutation found. Thanks to Tanya!
% 0.32/1.38 % SZS status Theorem for DTF2THF_5935
% 0.32/1.38 % SZS output start Proof for DTF2THF_5935
% 0.32/1.38 thf(func_def_0, type, cQ_7: $i > $i > $i > $o).
% 0.32/1.38 thf(func_def_1, type, f: $i > $i).
% 0.32/1.38 thf(func_def_2, type, cP_6: $i > $i > $o).
% 0.32/1.38 thf(func_def_3, type, cQ_6: $i > $i > $i > $o).
% 0.32/1.38 thf(func_def_8, type, cP_5: $i > $i > $o).
% 0.32/1.38 thf(func_def_9, type, cQ_5: $i > $i > $i > $o).
% 0.32/1.38 thf(func_def_10, type, cP_4: $i > $i > $o).
% 0.32/1.38 thf(func_def_11, type, cQ_4: $i > $i > $i > $o).
% 0.32/1.38 thf(func_def_12, type, cP_3: $i > $i > $o).
% 0.32/1.38 thf(func_def_13, type, cQ_3: $i > $i > $i > $o).
% 0.32/1.38 thf(func_def_14, type, cP_2: $i > $i > $o).
% 0.32/1.38 thf(func_def_15, type, cQ_2: $i > $i > $i > $o).
% 0.32/1.38 thf(func_def_16, type, cP_1: $i > $i > $o).
% 0.32/1.38 thf(func_def_17, type, cQ_1: $i > $i > $i > $o).
% 0.32/1.38 thf(f223,plain,(
% 0.32/1.38 $false),
% 0.32/1.38 inference(avatar_sat_refutation,[status(thm)],[f69,f125,f142,f159,f168,f185,f217,f222])).
% 0.32/1.38 thf(f222,plain,(
% 0.32/1.38 ~spl0_11),
% 0.32/1.38 inference(avatar_contradiction_clause,[status(thm)],[f221])).
% 0.32/1.38 thf(f221,plain,(
% 0.32/1.38 $false | ~spl0_11),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f220])).
% 0.32/1.38 thf(f220,plain,(
% 0.32/1.38 ($true != $true) | ~spl0_11),
% 0.32/1.38 inference(superposition,[status(thm)],[f184,f34])).
% 0.32/1.38 thf(f34,plain,(
% 0.32/1.38 ((cP_6 @ b @ b) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f7,plain,(
% 0.32/1.38 ((cP_1 @ b @ b) = $true) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : (((cP_3 @ (f @ X0) @ X1) != $true) | ($true = (cQ_4 @ X2 @ X1 @ X5)) | ($true != (cP_3 @ (f @ X4) @ X5)) | ($true != (cP_3 @ (f @ X3) @ X2)) | ((cQ_3 @ X3 @ X0 @ X4) != $true)) & ! [X6 : $i,X7 : $i,X8 : $i,X9 : $i,X10 : $i,X11 : $i] : (((cQ_1 @ X8 @ X7 @ X11) != $true) | ($true != (cP_1 @ (f @ X8) @ X10)) | ((cP_1 @ (f @ X11) @ X9) != $true) | ($true != (cP_1 @ (f @ X7) @ X6)) | ((cQ_2 @ X10 @ X6 @ X9) = $true)) & ((cP_4 @ c @ c) = $true) & ! [X12 : $i] : ((cP_1 @ d @ X12) = $true) & ((cP_5 @ a @ a) = $true) & ((cP_6 @ a @ a) = $true) & ((cP_2 @ c @ c) = $true) & ! [X13 : $i] : ((cP_4 @ d @ X13) = $true) & ! [X14 : $i,X15 : $i,X16 : $i,X17 : $i,X18 : $i,X19 : $i] : (($true != (cP_6 @ (f @ X19) @ X18)) | ($true != (cP_6 @ (f @ X15) @ X17)) | ($true != (cP_6 @ (f @ X16) @ X14)) | ((cQ_7 @ X18 @ X14 @ X17) = $true) | ((cQ_6 @ X19 @ X16 @ X15) != $true)) & ! [X20 : $i,X21 : $i,X22 : $i,X23 : $i,X24 : $i,X25 : $i] : (((cQ_5 @ X25 @ X23 @ X22) = $true) | ((cQ_4 @ X21 @ X20 @ X24) != $true) | ($true != (cP_4 @ (f @ X20) @ X23)) | ($true != (cP_4 @ (f @ X21) @ X25)) | ((cP_4 @ (f @ X24) @ X22) != $true)) & ((cP_6 @ b @ b) = $true) & ! [X26 : $i,X27 : $i,X28 : $i] : ((cQ_7 @ X27 @ X28 @ X26) != $true) & ! [X29 : $i,X30 : $i,X31 : $i,X32 : $i,X33 : $i,X34 : $i] : (($true != (cQ_5 @ X34 @ X29 @ X32)) | ($true != (cP_5 @ (f @ X29) @ X33)) | ((cQ_6 @ X30 @ X33 @ X31) = $true) | ($true != (cP_5 @ (f @ X32) @ X31)) | ($true != (cP_5 @ (f @ X34) @ X30))) & ((cP_3 @ c @ c) = $true) & ((cP_5 @ c @ c) = $true) & ! [X35 : $i,X36 : $i,X37 : $i,X38 : $i,X39 : $i,X40 : $i] : (((cP_2 @ (f @ X39) @ X40) != $true) | ((cP_2 @ (f @ X38) @ X35) != $true) | ((cQ_3 @ X40 @ X36 @ X35) = $true) | ($true != (cQ_2 @ X39 @ X37 @ X38)) | ($true != (cP_2 @ (f @ X37) @ X36))) & ((cP_5 @ b @ b) = $true) & ! [X41 : $i] : ($true = (cP_5 @ d @ X41)) & ! [X42 : $i,X43 : $i] : (((cP_5 @ X42 @ X43) != $true) | ((cP_5 @ (f @ X42) @ X43) = $true)) & ! [X44 : $i] : ((cP_3 @ d @ X44) = $true) & ((cP_4 @ b @ b) = $true) & ((cP_2 @ b @ b) = $true) & ((cP_3 @ a @ a) = $true) & ! [X45 : $i,X46 : $i] : (((cP_4 @ (f @ X45) @ X46) = $true) | ($true != (cP_4 @ X45 @ X46))) & ((cP_3 @ b @ b) = $true) & ! [X47 : $i] : ((cP_6 @ d @ X47) = $true) & ((cP_4 @ a @ a) = $true) & ((cP_6 @ c @ c) = $true) & ! [X48 : $i,X49 : $i] : (((cP_2 @ X49 @ X48) != $true) | ((cP_2 @ (f @ X49) @ X48) = $true)) & ((cP_1 @ a @ a) = $true) & ! [X50 : $i,X51 : $i] : (((cP_3 @ (f @ X51) @ X50) = $true) | ($true != (cP_3 @ X51 @ X50))) & ((cP_1 @ c @ c) = $true) & ((cQ_1 @ a @ b @ c) = $true) & ! [X52 : $i,X53 : $i] : (((cP_6 @ X53 @ X52) != $true) | ((cP_6 @ (f @ X53) @ X52) = $true)) & ! [X54 : $i,X55 : $i] : (($true != (cP_1 @ X54 @ X55)) | ($true = (cP_1 @ (f @ X54) @ X55))) & ((cP_2 @ a @ a) = $true) & ! [X56 : $i] : ($true = (cP_2 @ d @ X56))),
% 0.32/1.38 inference(rectify,[status(thm)],[f6])).
% 0.32/1.38 thf(f6,plain,(
% 0.32/1.38 ((cP_1 @ b @ b) = $true) & ! [X33 : $i,X37 : $i,X38 : $i,X35 : $i,X34 : $i,X36 : $i] : (((cP_3 @ (f @ X33) @ X37) != $true) | ((cQ_4 @ X38 @ X37 @ X36) = $true) | ((cP_3 @ (f @ X34) @ X36) != $true) | ((cP_3 @ (f @ X35) @ X38) != $true) | ($true != (cQ_3 @ X35 @ X33 @ X34))) & ! [X10 : $i,X13 : $i,X14 : $i,X11 : $i,X12 : $i,X9 : $i] : (((cQ_1 @ X14 @ X13 @ X9) != $true) | ($true != (cP_1 @ (f @ X14) @ X12)) | ((cP_1 @ (f @ X9) @ X11) != $true) | ((cP_1 @ (f @ X13) @ X10) != $true) | ($true = (cQ_2 @ X12 @ X10 @ X11))) & ((cP_4 @ c @ c) = $true) & ! [X56 : $i] : ((cP_1 @ d @ X56) = $true) & ((cP_5 @ a @ a) = $true) & ((cP_6 @ a @ a) = $true) & ((cP_2 @ c @ c) = $true) & ! [X20 : $i] : ($true = (cP_4 @ d @ X20)) & ! [X51 : $i,X54 : $i,X55 : $i,X50 : $i,X53 : $i,X52 : $i] : (((cP_6 @ (f @ X52) @ X53) != $true) | ((cP_6 @ (f @ X54) @ X50) != $true) | ($true != (cP_6 @ (f @ X55) @ X51)) | ((cQ_7 @ X53 @ X51 @ X50) = $true) | ($true != (cQ_6 @ X52 @ X55 @ X54))) & ! [X24 : $i,X25 : $i,X22 : $i,X23 : $i,X26 : $i,X27 : $i] : (((cQ_5 @ X27 @ X23 @ X22) = $true) | ($true != (cQ_4 @ X25 @ X24 @ X26)) | ($true != (cP_4 @ (f @ X24) @ X23)) | ($true != (cP_4 @ (f @ X25) @ X27)) | ((cP_4 @ (f @ X26) @ X22) != $true)) & ((cP_6 @ b @ b) = $true) & ! [X28 : $i,X29 : $i,X30 : $i] : ($true != (cQ_7 @ X29 @ X30 @ X28)) & ! [X46 : $i,X44 : $i,X49 : $i,X45 : $i,X48 : $i,X47 : $i] : (((cQ_5 @ X47 @ X46 @ X45) != $true) | ($true != (cP_5 @ (f @ X46) @ X48)) | ((cQ_6 @ X44 @ X48 @ X49) = $true) | ((cP_5 @ (f @ X45) @ X49) != $true) | ((cP_5 @ (f @ X47) @ X44) != $true)) & ((cP_3 @ c @ c) = $true) & ((cP_5 @ c @ c) = $true) & ! [X5 : $i,X4 : $i,X1 : $i,X2 : $i,X3 : $i,X0 : $i] : (((cP_2 @ (f @ X3) @ X0) != $true) | ((cP_2 @ (f @ X2) @ X5) != $true) | ($true = (cQ_3 @ X0 @ X4 @ X5)) | ((cQ_2 @ X3 @ X1 @ X2) != $true) | ((cP_2 @ (f @ X1) @ X4) != $true)) & ((cP_5 @ b @ b) = $true) & ! [X19 : $i] : ((cP_5 @ d @ X19) = $true) & ! [X42 : $i,X41 : $i] : (($true != (cP_5 @ X42 @ X41)) | ($true = (cP_5 @ (f @ X42) @ X41))) & ! [X21 : $i] : ((cP_3 @ d @ X21) = $true) & ((cP_4 @ b @ b) = $true) & ((cP_2 @ b @ b) = $true) & ((cP_3 @ a @ a) = $true) & ! [X40 : $i,X39 : $i] : (($true = (cP_4 @ (f @ X40) @ X39)) | ((cP_4 @ X40 @ X39) != $true)) & ((cP_3 @ b @ b) = $true) & ! [X43 : $i] : ($true = (cP_6 @ d @ X43)) & ((cP_4 @ a @ a) = $true) & ((cP_6 @ c @ c) = $true) & ! [X32 : $i,X31 : $i] : (((cP_2 @ X31 @ X32) != $true) | ((cP_2 @ (f @ X31) @ X32) = $true)) & ((cP_1 @ a @ a) = $true) & ! [X15 : $i,X16 : $i] : (((cP_3 @ (f @ X16) @ X15) = $true) | ((cP_3 @ X16 @ X15) != $true)) & ((cP_1 @ c @ c) = $true) & ((cQ_1 @ a @ b @ c) = $true) & ! [X6 : $i,X7 : $i] : (($true != (cP_6 @ X7 @ X6)) | ($true = (cP_6 @ (f @ X7) @ X6))) & ! [X17 : $i,X18 : $i] : (($true != (cP_1 @ X17 @ X18)) | ($true = (cP_1 @ (f @ X17) @ X18))) & ((cP_2 @ a @ a) = $true) & ! [X8 : $i] : ($true = (cP_2 @ d @ X8))),
% 0.32/1.38 inference(flattening,[status(thm)],[f5])).
% 0.32/1.38 thf(f5,plain,(
% 0.32/1.38 ~~(((cP_2 @ c @ c) = $true) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : (($true = (cQ_3 @ X0 @ X4 @ X5)) | ~((cP_2 @ (f @ X2) @ X5) = $true) | ~((cQ_2 @ X3 @ X1 @ X2) = $true) | ~((cP_2 @ (f @ X3) @ X0) = $true) | ~((cP_2 @ (f @ X1) @ X4) = $true)) & ! [X6 : $i,X7 : $i] : (~($true = (cP_6 @ X7 @ X6)) | ($true = (cP_6 @ (f @ X7) @ X6))) & ! [X8 : $i] : ($true = (cP_2 @ d @ X8)) & ((cP_4 @ b @ b) = $true) & ((cP_3 @ c @ c) = $true) & ! [X9 : $i,X10 : $i,X11 : $i,X12 : $i,X13 : $i,X14 : $i] : (~($true = (cP_1 @ (f @ X14) @ X12)) | ~((cP_1 @ (f @ X13) @ X10) = $true) | ~((cP_1 @ (f @ X9) @ X11) = $true) | ~((cQ_1 @ X14 @ X13 @ X9) = $true) | ($true = (cQ_2 @ X12 @ X10 @ X11))) & ! [X15 : $i,X16 : $i] : (~((cP_3 @ X16 @ X15) = $true) | ((cP_3 @ (f @ X16) @ X15) = $true)) & ((cP_6 @ b @ b) = $true) & ! [X17 : $i,X18 : $i] : (($true = (cP_1 @ (f @ X17) @ X18)) | ~($true = (cP_1 @ X17 @ X18))) & ((cP_4 @ a @ a) = $true) & ! [X19 : $i] : ((cP_5 @ d @ X19) = $true) & ! [X20 : $i] : ($true = (cP_4 @ d @ X20)) & ((cP_1 @ c @ c) = $true) & ! [X21 : $i] : ((cP_3 @ d @ X21) = $true) & ((cP_4 @ c @ c) = $true) & ! [X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i,X27 : $i] : (((cQ_5 @ X27 @ X23 @ X22) = $true) | ~($true = (cQ_4 @ X25 @ X24 @ X26)) | ~($true = (cP_4 @ (f @ X24) @ X23)) | ~((cP_4 @ (f @ X26) @ X22) = $true) | ~($true = (cP_4 @ (f @ X25) @ X27))) & ! [X28 : $i,X29 : $i,X30 : $i] : ~($true = (cQ_7 @ X29 @ X30 @ X28)) & ((cP_3 @ a @ a) = $true) & ((cP_3 @ b @ b) = $true) & ((cP_2 @ b @ b) = $true) & ! [X31 : $i,X32 : $i] : (~((cP_2 @ X31 @ X32) = $true) | ((cP_2 @ (f @ X31) @ X32) = $true)) & ((cP_5 @ c @ c) = $true) & ((cQ_1 @ a @ b @ c) = $true) & ! [X33 : $i,X34 : $i,X35 : $i,X36 : $i,X37 : $i,X38 : $i] : (~((cP_3 @ (f @ X34) @ X36) = $true) | ~((cP_3 @ (f @ X33) @ X37) = $true) | ((cQ_4 @ X38 @ X37 @ X36) = $true) | ~($true = (cQ_3 @ X35 @ X33 @ X34)) | ~((cP_3 @ (f @ X35) @ X38) = $true)) & ((cP_2 @ a @ a) = $true) & ((cP_6 @ c @ c) = $true) & ! [X39 : $i,X40 : $i] : (~((cP_4 @ X40 @ X39) = $true) | ($true = (cP_4 @ (f @ X40) @ X39))) & ((cP_6 @ a @ a) = $true) & ((cP_1 @ a @ a) = $true) & ! [X41 : $i,X42 : $i] : (~($true = (cP_5 @ X42 @ X41)) | ($true = (cP_5 @ (f @ X42) @ X41))) & ((cP_5 @ a @ a) = $true) & ((cP_1 @ b @ b) = $true) & ((cP_5 @ b @ b) = $true) & ! [X43 : $i] : ($true = (cP_6 @ d @ X43)) & ! [X44 : $i,X45 : $i,X46 : $i,X47 : $i,X48 : $i,X49 : $i] : (~((cQ_5 @ X47 @ X46 @ X45) = $true) | ((cQ_6 @ X44 @ X48 @ X49) = $true) | ~((cP_5 @ (f @ X45) @ X49) = $true) | ~((cP_5 @ (f @ X47) @ X44) = $true) | ~($true = (cP_5 @ (f @ X46) @ X48))) & ! [X50 : $i,X51 : $i,X52 : $i,X53 : $i,X54 : $i,X55 : $i] : (~((cP_6 @ (f @ X52) @ X53) = $true) | ((cQ_7 @ X53 @ X51 @ X50) = $true) | ~($true = (cQ_6 @ X52 @ X55 @ X54)) | ~($true = (cP_6 @ (f @ X55) @ X51)) | ~((cP_6 @ (f @ X54) @ X50) = $true)) & ! [X56 : $i] : ((cP_1 @ d @ X56) = $true))),
% 0.32/1.38 inference(fool_elimination,[status(thm)],[f4])).
% 0.32/1.38 thf(f4,plain,(
% 0.32/1.38 ~~((cP_2 @ c @ c) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_3 @ X0 @ X4 @ X5) | ~(cP_2 @ (f @ X2) @ X5) | ~(cQ_2 @ X3 @ X1 @ X2) | ~(cP_2 @ (f @ X3) @ X0) | ~(cP_2 @ (f @ X1) @ X4)) & ! [X6 : $i,X7 : $i] : (~(cP_6 @ X7 @ X6) | (cP_6 @ (f @ X7) @ X6)) & ! [X8 : $i] : (cP_2 @ d @ X8) & (cP_4 @ b @ b) & (cP_3 @ c @ c) & ! [X9 : $i,X10 : $i,X11 : $i,X12 : $i,X13 : $i,X14 : $i] : (~(cP_1 @ (f @ X14) @ X12) | ~(cP_1 @ (f @ X13) @ X10) | ~(cP_1 @ (f @ X9) @ X11) | ~(cQ_1 @ X14 @ X13 @ X9) | (cQ_2 @ X12 @ X10 @ X11)) & ! [X15 : $i,X16 : $i] : (~(cP_3 @ X16 @ X15) | (cP_3 @ (f @ X16) @ X15)) & (cP_6 @ b @ b) & ! [X17 : $i,X18 : $i] : ((cP_1 @ (f @ X17) @ X18) | ~(cP_1 @ X17 @ X18)) & (cP_4 @ a @ a) & ! [X19 : $i] : (cP_5 @ d @ X19) & ! [X20 : $i] : (cP_4 @ d @ X20) & (cP_1 @ c @ c) & ! [X21 : $i] : (cP_3 @ d @ X21) & (cP_4 @ c @ c) & ! [X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i,X27 : $i] : ((cQ_5 @ X27 @ X23 @ X22) | ~(cQ_4 @ X25 @ X24 @ X26) | ~(cP_4 @ (f @ X24) @ X23) | ~(cP_4 @ (f @ X26) @ X22) | ~(cP_4 @ (f @ X25) @ X27)) & ! [X28 : $i,X29 : $i,X30 : $i] : ~(cQ_7 @ X29 @ X30 @ X28) & (cP_3 @ a @ a) & (cP_3 @ b @ b) & (cP_2 @ b @ b) & ! [X31 : $i,X32 : $i] : (~(cP_2 @ X31 @ X32) | (cP_2 @ (f @ X31) @ X32)) & (cP_5 @ c @ c) & (cQ_1 @ a @ b @ c) & ! [X33 : $i,X34 : $i,X35 : $i,X36 : $i,X37 : $i,X38 : $i] : (~(cP_3 @ (f @ X34) @ X36) | ~(cP_3 @ (f @ X33) @ X37) | (cQ_4 @ X38 @ X37 @ X36) | ~(cQ_3 @ X35 @ X33 @ X34) | ~(cP_3 @ (f @ X35) @ X38)) & (cP_2 @ a @ a) & (cP_6 @ c @ c) & ! [X39 : $i,X40 : $i] : (~(cP_4 @ X40 @ X39) | (cP_4 @ (f @ X40) @ X39)) & (cP_6 @ a @ a) & (cP_1 @ a @ a) & ! [X41 : $i,X42 : $i] : (~(cP_5 @ X42 @ X41) | (cP_5 @ (f @ X42) @ X41)) & (cP_5 @ a @ a) & (cP_1 @ b @ b) & (cP_5 @ b @ b) & ! [X43 : $i] : (cP_6 @ d @ X43) & ! [X44 : $i,X45 : $i,X46 : $i,X47 : $i,X48 : $i,X49 : $i] : (~(cQ_5 @ X47 @ X46 @ X45) | (cQ_6 @ X44 @ X48 @ X49) | ~(cP_5 @ (f @ X45) @ X49) | ~(cP_5 @ (f @ X47) @ X44) | ~(cP_5 @ (f @ X46) @ X48)) & ! [X50 : $i,X51 : $i,X52 : $i,X53 : $i,X54 : $i,X55 : $i] : (~(cP_6 @ (f @ X52) @ X53) | (cQ_7 @ X53 @ X51 @ X50) | ~(cQ_6 @ X52 @ X55 @ X54) | ~(cP_6 @ (f @ X55) @ X51) | ~(cP_6 @ (f @ X54) @ X50)) & ! [X56 : $i] : (cP_1 @ d @ X56))),
% 0.32/1.38 inference(rectify,[status(thm)],[f2])).
% 0.32/1.38 thf(f2,negated_conjecture,(
% 0.32/1.38 ~~((cP_2 @ c @ c) & ! [X3 : $i,X1 : $i,X2 : $i,X0 : $i,X4 : $i,X5 : $i] : ((cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X2) @ X5) | ~(cQ_2 @ X0 @ X1 @ X2) | ~(cP_2 @ (f @ X0) @ X3) | ~(cP_2 @ (f @ X1) @ X4)) & ! [X1 : $i,X0 : $i] : (~(cP_6 @ X0 @ X1) | (cP_6 @ (f @ X0) @ X1)) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_4 @ b @ b) & (cP_3 @ c @ c) & ! [X2 : $i,X4 : $i,X5 : $i,X3 : $i,X1 : $i,X0 : $i] : (~(cP_1 @ (f @ X0) @ X3) | ~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X2) @ X5) | ~(cQ_1 @ X0 @ X1 @ X2) | (cQ_2 @ X3 @ X4 @ X5)) & ! [X1 : $i,X0 : $i] : (~(cP_3 @ X0 @ X1) | (cP_3 @ (f @ X0) @ X1)) & (cP_6 @ b @ b) & ! [X0 : $i,X1 : $i] : ((cP_1 @ (f @ X0) @ X1) | ~(cP_1 @ X0 @ X1)) & (cP_4 @ a @ a) & ! [X0 : $i] : (cP_5 @ d @ X0) & ! [X0 : $i] : (cP_4 @ d @ X0) & (cP_1 @ c @ c) & ! [X0 : $i] : (cP_3 @ d @ X0) & (cP_4 @ c @ c) & ! [X5 : $i,X4 : $i,X1 : $i,X0 : $i,X2 : $i,X3 : $i] : ((cQ_5 @ X3 @ X4 @ X5) | ~(cQ_4 @ X0 @ X1 @ X2) | ~(cP_4 @ (f @ X1) @ X4) | ~(cP_4 @ (f @ X2) @ X5) | ~(cP_4 @ (f @ X0) @ X3)) & ! [X2 : $i,X0 : $i,X1 : $i] : ~(cQ_7 @ X0 @ X1 @ X2) & (cP_3 @ a @ a) & (cP_3 @ b @ b) & (cP_2 @ b @ b) & ! [X0 : $i,X1 : $i] : (~(cP_2 @ X0 @ X1) | (cP_2 @ (f @ X0) @ X1)) & (cP_5 @ c @ c) & (cQ_1 @ a @ b @ c) & ! [X1 : $i,X2 : $i,X0 : $i,X5 : $i,X4 : $i,X3 : $i] : (~(cP_3 @ (f @ X2) @ X5) | ~(cP_3 @ (f @ X1) @ X4) | (cQ_4 @ X3 @ X4 @ X5) | ~(cQ_3 @ X0 @ X1 @ X2) | ~(cP_3 @ (f @ X0) @ X3)) & (cP_2 @ a @ a) & (cP_6 @ c @ c) & ! [X1 : $i,X0 : $i] : (~(cP_4 @ X0 @ X1) | (cP_4 @ (f @ X0) @ X1)) & (cP_6 @ a @ a) & (cP_1 @ a @ a) & ! [X1 : $i,X0 : $i] : (~(cP_5 @ X0 @ X1) | (cP_5 @ (f @ X0) @ X1)) & (cP_5 @ a @ a) & (cP_1 @ b @ b) & (cP_5 @ b @ b) & ! [X0 : $i] : (cP_6 @ d @ X0) & ! [X3 : $i,X2 : $i,X1 : $i,X0 : $i,X4 : $i,X5 : $i] : (~(cQ_5 @ X0 @ X1 @ X2) | (cQ_6 @ X3 @ X4 @ X5) | ~(cP_5 @ (f @ X2) @ X5) | ~(cP_5 @ (f @ X0) @ X3) | ~(cP_5 @ (f @ X1) @ X4)) & ! [X5 : $i,X4 : $i,X0 : $i,X3 : $i,X2 : $i,X1 : $i] : (~(cP_6 @ (f @ X0) @ X3) | (cQ_7 @ X3 @ X4 @ X5) | ~(cQ_6 @ X0 @ X1 @ X2) | ~(cP_6 @ (f @ X1) @ X4) | ~(cP_6 @ (f @ X2) @ X5)) & ! [X0 : $i] : (cP_1 @ d @ X0))),
% 0.32/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.32/1.38 thf(f1,conjecture,(
% 0.32/1.38 ~((cP_2 @ c @ c) & ! [X3 : $i,X1 : $i,X2 : $i,X0 : $i,X4 : $i,X5 : $i] : ((cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X2) @ X5) | ~(cQ_2 @ X0 @ X1 @ X2) | ~(cP_2 @ (f @ X0) @ X3) | ~(cP_2 @ (f @ X1) @ X4)) & ! [X1 : $i,X0 : $i] : (~(cP_6 @ X0 @ X1) | (cP_6 @ (f @ X0) @ X1)) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_4 @ b @ b) & (cP_3 @ c @ c) & ! [X2 : $i,X4 : $i,X5 : $i,X3 : $i,X1 : $i,X0 : $i] : (~(cP_1 @ (f @ X0) @ X3) | ~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X2) @ X5) | ~(cQ_1 @ X0 @ X1 @ X2) | (cQ_2 @ X3 @ X4 @ X5)) & ! [X1 : $i,X0 : $i] : (~(cP_3 @ X0 @ X1) | (cP_3 @ (f @ X0) @ X1)) & (cP_6 @ b @ b) & ! [X0 : $i,X1 : $i] : ((cP_1 @ (f @ X0) @ X1) | ~(cP_1 @ X0 @ X1)) & (cP_4 @ a @ a) & ! [X0 : $i] : (cP_5 @ d @ X0) & ! [X0 : $i] : (cP_4 @ d @ X0) & (cP_1 @ c @ c) & ! [X0 : $i] : (cP_3 @ d @ X0) & (cP_4 @ c @ c) & ! [X5 : $i,X4 : $i,X1 : $i,X0 : $i,X2 : $i,X3 : $i] : ((cQ_5 @ X3 @ X4 @ X5) | ~(cQ_4 @ X0 @ X1 @ X2) | ~(cP_4 @ (f @ X1) @ X4) | ~(cP_4 @ (f @ X2) @ X5) | ~(cP_4 @ (f @ X0) @ X3)) & ! [X2 : $i,X0 : $i,X1 : $i] : ~(cQ_7 @ X0 @ X1 @ X2) & (cP_3 @ a @ a) & (cP_3 @ b @ b) & (cP_2 @ b @ b) & ! [X0 : $i,X1 : $i] : (~(cP_2 @ X0 @ X1) | (cP_2 @ (f @ X0) @ X1)) & (cP_5 @ c @ c) & (cQ_1 @ a @ b @ c) & ! [X1 : $i,X2 : $i,X0 : $i,X5 : $i,X4 : $i,X3 : $i] : (~(cP_3 @ (f @ X2) @ X5) | ~(cP_3 @ (f @ X1) @ X4) | (cQ_4 @ X3 @ X4 @ X5) | ~(cQ_3 @ X0 @ X1 @ X2) | ~(cP_3 @ (f @ X0) @ X3)) & (cP_2 @ a @ a) & (cP_6 @ c @ c) & ! [X1 : $i,X0 : $i] : (~(cP_4 @ X0 @ X1) | (cP_4 @ (f @ X0) @ X1)) & (cP_6 @ a @ a) & (cP_1 @ a @ a) & ! [X1 : $i,X0 : $i] : (~(cP_5 @ X0 @ X1) | (cP_5 @ (f @ X0) @ X1)) & (cP_5 @ a @ a) & (cP_1 @ b @ b) & (cP_5 @ b @ b) & ! [X0 : $i] : (cP_6 @ d @ X0) & ! [X3 : $i,X2 : $i,X1 : $i,X0 : $i,X4 : $i,X5 : $i] : (~(cQ_5 @ X0 @ X1 @ X2) | (cQ_6 @ X3 @ X4 @ X5) | ~(cP_5 @ (f @ X2) @ X5) | ~(cP_5 @ (f @ X0) @ X3) | ~(cP_5 @ (f @ X1) @ X4)) & ! [X5 : $i,X4 : $i,X0 : $i,X3 : $i,X2 : $i,X1 : $i] : (~(cP_6 @ (f @ X0) @ X3) | (cQ_7 @ X3 @ X4 @ X5) | ~(cQ_6 @ X0 @ X1 @ X2) | ~(cP_6 @ (f @ X1) @ X4) | ~(cP_6 @ (f @ X2) @ X5)) & ! [X0 : $i] : (cP_1 @ d @ X0))),
% 0.32/1.38 file('/export/starexec/sandbox2/tmp/tmp.c39OTm3iHl/DTF2THF_5935.p',cTHM409_6)).
% 0.32/1.38 thf(f184,plain,(
% 0.32/1.38 ( ! [X1 : $i] : (((cP_6 @ b @ X1) != $true)) ) | ~spl0_11),
% 0.32/1.38 inference(avatar_component_clause,[status(thm)],[f183])).
% 0.32/1.38 thf(f183,definition,(
% 0.32/1.38 spl0_11 <=> ! [X1 : $i] : ((cP_6 @ b @ X1) != $true)),
% 0.32/1.38 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 0.32/1.38 thf(f217,plain,(
% 0.32/1.38 ~spl0_10),
% 0.32/1.38 inference(avatar_contradiction_clause,[status(thm)],[f216])).
% 0.32/1.38 thf(f216,plain,(
% 0.32/1.38 $false | ~spl0_10),
% 0.32/1.38 inference(subsumption_resolution,[status(thm)],[f213,f20])).
% 0.32/1.38 thf(f20,plain,(
% 0.32/1.38 ((cP_3 @ b @ b) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f213,plain,(
% 0.32/1.38 ((cP_3 @ b @ b) != $true) | ~spl0_10),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f211])).
% 0.32/1.38 thf(f211,plain,(
% 0.32/1.38 ($true != $true) | ((cP_3 @ b @ b) != $true) | ~spl0_10),
% 0.32/1.38 inference(superposition,[status(thm)],[f181,f24])).
% 0.32/1.38 thf(f24,plain,(
% 0.32/1.38 ((cP_4 @ b @ b) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f181,plain,(
% 0.32/1.38 ( ! [X0 : $i] : (($true != (cP_4 @ X0 @ b)) | ((cP_3 @ b @ X0) != $true)) ) | ~spl0_10),
% 0.32/1.38 inference(avatar_component_clause,[status(thm)],[f180])).
% 0.32/1.38 thf(f180,definition,(
% 0.32/1.38 spl0_10 <=> ! [X0 : $i] : (((cP_3 @ b @ X0) != $true) | ($true != (cP_4 @ X0 @ b)))),
% 0.32/1.38 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 0.32/1.38 thf(f185,plain,(
% 0.32/1.38 spl0_10 | spl0_11 | ~spl0_4),
% 0.32/1.38 inference(avatar_split_clause,[status(thm)],[f178,f93,f183,f180])).
% 0.32/1.38 thf(f93,definition,(
% 0.32/1.38 spl0_4 <=> ! [X0 : $i,X3 : $i,X2 : $i,X1 : $i] : (((cP_4 @ X0 @ X1) != $true) | ((cP_3 @ b @ X0) != $true) | ($true != (cP_5 @ X1 @ X2)) | ((cP_6 @ X2 @ X3) != $true))),
% 0.32/1.38 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 0.32/1.38 thf(f178,plain,(
% 0.32/1.38 ( ! [X0 : $i,X1 : $i] : (((cP_3 @ b @ X0) != $true) | ((cP_6 @ b @ X1) != $true) | ($true != (cP_4 @ X0 @ b))) ) | ~spl0_4),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f171])).
% 0.32/1.38 thf(f171,plain,(
% 0.32/1.38 ( ! [X0 : $i,X1 : $i] : (((cP_6 @ b @ X1) != $true) | ($true != (cP_4 @ X0 @ b)) | ((cP_3 @ b @ X0) != $true) | ($true != $true)) ) | ~spl0_4),
% 0.32/1.38 inference(superposition,[status(thm)],[f94,f28])).
% 0.32/1.38 thf(f28,plain,(
% 0.32/1.38 ((cP_5 @ b @ b) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f94,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_5 @ X1 @ X2)) | ((cP_3 @ b @ X0) != $true) | ((cP_6 @ X2 @ X3) != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_4),
% 0.32/1.38 inference(avatar_component_clause,[status(thm)],[f93])).
% 0.32/1.38 thf(f168,plain,(
% 0.32/1.38 ~spl0_7),
% 0.32/1.38 inference(avatar_contradiction_clause,[status(thm)],[f167])).
% 0.32/1.38 thf(f167,plain,(
% 0.32/1.38 $false | ~spl0_7),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f166])).
% 0.32/1.38 thf(f166,plain,(
% 0.32/1.38 ($true != $true) | ~spl0_7),
% 0.32/1.38 inference(superposition,[status(thm)],[f165,f39])).
% 0.32/1.38 thf(f39,plain,(
% 0.32/1.38 ((cP_6 @ a @ a) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f165,plain,(
% 0.32/1.38 ( ! [X0 : $i] : (((cP_6 @ a @ X0) != $true)) ) | ~spl0_7),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f164])).
% 0.32/1.38 thf(f164,plain,(
% 0.32/1.38 ( ! [X0 : $i] : (((cP_6 @ a @ X0) != $true) | ($true != $true)) ) | ~spl0_7),
% 0.32/1.38 inference(superposition,[status(thm)],[f163,f40])).
% 0.32/1.38 thf(f40,plain,(
% 0.32/1.38 ((cP_5 @ a @ a) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f163,plain,(
% 0.32/1.38 ( ! [X0 : $i,X1 : $i] : (((cP_5 @ a @ X0) != $true) | ((cP_6 @ X0 @ X1) != $true)) ) | ~spl0_7),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f162])).
% 0.32/1.38 thf(f162,plain,(
% 0.32/1.38 ( ! [X0 : $i,X1 : $i] : (((cP_6 @ X0 @ X1) != $true) | ((cP_5 @ a @ X0) != $true) | ($true != $true)) ) | ~spl0_7),
% 0.32/1.38 inference(superposition,[status(thm)],[f161,f18])).
% 0.32/1.38 thf(f18,plain,(
% 0.32/1.38 ((cP_4 @ a @ a) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f161,plain,(
% 0.32/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (cP_4 @ a @ X0)) | ($true != (cP_6 @ X1 @ X2)) | ((cP_5 @ X0 @ X1) != $true)) ) | ~spl0_7),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f160])).
% 0.32/1.38 thf(f160,plain,(
% 0.32/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_5 @ X0 @ X1) != $true) | ($true != (cP_6 @ X1 @ X2)) | ($true != (cP_4 @ a @ X0)) | ($true != $true)) ) | ~spl0_7),
% 0.32/1.38 inference(superposition,[status(thm)],[f106,f22])).
% 0.32/1.38 thf(f22,plain,(
% 0.32/1.38 ((cP_3 @ a @ a) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f106,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_3 @ a @ X0)) | ((cP_4 @ X0 @ X1) != $true) | ($true != (cP_5 @ X1 @ X2)) | ((cP_6 @ X2 @ X3) != $true)) ) | ~spl0_7),
% 0.32/1.38 inference(avatar_component_clause,[status(thm)],[f105])).
% 0.32/1.38 thf(f105,definition,(
% 0.32/1.38 spl0_7 <=> ! [X0 : $i,X3 : $i,X2 : $i,X1 : $i] : (((cP_6 @ X2 @ X3) != $true) | ((cP_4 @ X0 @ X1) != $true) | ($true != (cP_5 @ X1 @ X2)) | ($true != (cP_3 @ a @ X0)))),
% 0.32/1.38 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 0.32/1.38 thf(f159,plain,(
% 0.32/1.38 spl0_7 | ~spl0_1),
% 0.32/1.38 inference(avatar_split_clause,[status(thm)],[f158,f61,f105])).
% 0.32/1.38 thf(f61,definition,(
% 0.32/1.38 spl0_1 <=> ! [X16 : $i,X10 : $i,X11 : $i,X12 : $i,X17 : $i,X15 : $i] : (((cP_2 @ (f @ X12) @ X10) != $true) | ((cP_1 @ (f @ a) @ X12) != $true) | ((cP_3 @ (f @ X10) @ X11) != $true) | ((cP_4 @ (f @ X11) @ X15) != $true) | ($true != (cP_5 @ (f @ X15) @ X16)) | ((cP_6 @ (f @ X16) @ X17) != $true))),
% 0.32/1.38 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 0.32/1.38 thf(f158,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_6 @ X2 @ X3) != $true) | ($true != (cP_5 @ X1 @ X2)) | ((cP_4 @ X0 @ X1) != $true) | ($true != (cP_3 @ a @ X0))) ) | ~spl0_1),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f157])).
% 0.32/1.38 thf(f157,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_5 @ X1 @ X2)) | ($true != $true) | ((cP_4 @ X0 @ X1) != $true) | ((cP_6 @ X2 @ X3) != $true) | ($true != (cP_3 @ a @ X0))) ) | ~spl0_1),
% 0.32/1.38 inference(superposition,[status(thm)],[f156,f9])).
% 0.32/1.38 thf(f9,plain,(
% 0.32/1.38 ((cP_2 @ a @ a) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f156,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_2 @ a @ X2)) | ((cP_3 @ X2 @ X4) != $true) | ((cP_4 @ X4 @ X0) != $true) | ((cP_5 @ X0 @ X1) != $true) | ((cP_6 @ X1 @ X3) != $true)) ) | ~spl0_1),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f155])).
% 0.32/1.38 thf(f155,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((cP_5 @ X0 @ X1) != $true) | ((cP_3 @ X2 @ X4) != $true) | ($true != $true) | ((cP_4 @ X4 @ X0) != $true) | ($true != (cP_2 @ a @ X2)) | ((cP_6 @ X1 @ X3) != $true)) ) | ~spl0_1),
% 0.32/1.38 inference(superposition,[status(thm)],[f154,f15])).
% 0.32/1.38 thf(f15,plain,(
% 0.32/1.38 ((cP_1 @ a @ a) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f154,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_1 @ a @ X2)) | ((cP_5 @ X4 @ X0) != $true) | ($true != (cP_2 @ X2 @ X5)) | ((cP_6 @ X0 @ X1) != $true) | ((cP_3 @ X5 @ X3) != $true) | ($true != (cP_4 @ X3 @ X4))) ) | ~spl0_1),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f153])).
% 0.32/1.38 thf(f153,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_3 @ X5 @ X3) != $true) | ((cP_5 @ X4 @ X0) != $true) | ($true != (cP_4 @ X3 @ X4)) | ($true != (cP_1 @ a @ X2)) | ((cP_6 @ X0 @ X1) != $true) | ($true != $true) | ($true != (cP_2 @ X2 @ X5))) ) | ~spl0_1),
% 0.32/1.38 inference(superposition,[status(thm)],[f152,f11])).
% 0.32/1.38 thf(f11,plain,(
% 0.32/1.38 ( ! [X52 : $i,X53 : $i] : (((cP_6 @ (f @ X53) @ X52) = $true) | ((cP_6 @ X53 @ X52) != $true)) )),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f152,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_6 @ (f @ X4) @ X5) != $true) | ($true != (cP_1 @ a @ X3)) | ((cP_4 @ X1 @ X2) != $true) | ($true != (cP_2 @ X3 @ X0)) | ((cP_3 @ X0 @ X1) != $true) | ($true != (cP_5 @ X2 @ X4))) ) | ~spl0_1),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f151])).
% 0.32/1.38 thf(f151,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_1 @ a @ X3)) | ((cP_3 @ X0 @ X1) != $true) | ($true != (cP_5 @ X2 @ X4)) | ((cP_6 @ (f @ X4) @ X5) != $true) | ((cP_4 @ X1 @ X2) != $true) | ($true != (cP_2 @ X3 @ X0)) | ($true != $true)) ) | ~spl0_1),
% 0.32/1.38 inference(superposition,[status(thm)],[f150,f14])).
% 0.32/1.38 thf(f14,plain,(
% 0.32/1.38 ( ! [X50 : $i,X51 : $i] : (((cP_3 @ (f @ X51) @ X50) = $true) | ($true != (cP_3 @ X51 @ X50))) )),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f150,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_3 @ (f @ X1) @ X2)) | ($true != (cP_4 @ X2 @ X3)) | ($true != (cP_1 @ a @ X0)) | ($true != (cP_5 @ X3 @ X4)) | ((cP_2 @ X0 @ X1) != $true) | ((cP_6 @ (f @ X4) @ X5) != $true)) ) | ~spl0_1),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f149])).
% 0.32/1.38 thf(f149,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_5 @ X3 @ X4)) | ($true != (cP_4 @ X2 @ X3)) | ($true != (cP_3 @ (f @ X1) @ X2)) | ($true != (cP_1 @ a @ X0)) | ($true != $true) | ((cP_6 @ (f @ X4) @ X5) != $true) | ((cP_2 @ X0 @ X1) != $true)) ) | ~spl0_1),
% 0.32/1.38 inference(superposition,[status(thm)],[f148,f16])).
% 0.32/1.38 thf(f16,plain,(
% 0.32/1.38 ( ! [X48 : $i,X49 : $i] : (((cP_2 @ (f @ X49) @ X48) = $true) | ((cP_2 @ X49 @ X48) != $true)) )),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f148,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_2 @ (f @ X3) @ X2)) | ((cP_4 @ X0 @ X1) != $true) | ((cP_5 @ X1 @ X4) != $true) | ((cP_6 @ (f @ X4) @ X5) != $true) | ((cP_3 @ (f @ X2) @ X0) != $true) | ($true != (cP_1 @ a @ X3))) ) | ~spl0_1),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f147])).
% 0.32/1.38 thf(f147,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_4 @ X0 @ X1) != $true) | ($true != (cP_2 @ (f @ X3) @ X2)) | ((cP_6 @ (f @ X4) @ X5) != $true) | ((cP_5 @ X1 @ X4) != $true) | ($true != (cP_1 @ a @ X3)) | ($true != $true) | ((cP_3 @ (f @ X2) @ X0) != $true)) ) | ~spl0_1),
% 0.32/1.38 inference(superposition,[status(thm)],[f146,f21])).
% 0.32/1.38 thf(f21,plain,(
% 0.32/1.38 ( ! [X46 : $i,X45 : $i] : (((cP_4 @ (f @ X45) @ X46) = $true) | ($true != (cP_4 @ X45 @ X46))) )),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f146,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_4 @ (f @ X4) @ X5)) | ((cP_3 @ (f @ X3) @ X4) != $true) | ($true != (cP_1 @ a @ X0)) | ((cP_2 @ (f @ X0) @ X3) != $true) | ((cP_5 @ X5 @ X1) != $true) | ((cP_6 @ (f @ X1) @ X2) != $true)) ) | ~spl0_1),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f145])).
% 0.32/1.38 thf(f145,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_6 @ (f @ X1) @ X2) != $true) | ((cP_5 @ X5 @ X1) != $true) | ((cP_3 @ (f @ X3) @ X4) != $true) | ($true != (cP_4 @ (f @ X4) @ X5)) | ((cP_2 @ (f @ X0) @ X3) != $true) | ($true != (cP_1 @ a @ X0)) | ($true != $true)) ) | ~spl0_1),
% 0.32/1.38 inference(superposition,[status(thm)],[f144,f10])).
% 0.32/1.38 thf(f10,plain,(
% 0.32/1.38 ( ! [X54 : $i,X55 : $i] : (($true = (cP_1 @ (f @ X54) @ X55)) | ($true != (cP_1 @ X54 @ X55))) )),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f144,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_1 @ (f @ a) @ X5)) | ((cP_6 @ (f @ X1) @ X4) != $true) | ((cP_2 @ (f @ X5) @ X2) != $true) | ((cP_3 @ (f @ X2) @ X3) != $true) | ((cP_5 @ X0 @ X1) != $true) | ((cP_4 @ (f @ X3) @ X0) != $true)) ) | ~spl0_1),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f143])).
% 0.32/1.38 thf(f143,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((cP_6 @ (f @ X1) @ X4) != $true) | ((cP_4 @ (f @ X3) @ X0) != $true) | ((cP_3 @ (f @ X2) @ X3) != $true) | ((cP_2 @ (f @ X5) @ X2) != $true) | ((cP_5 @ X0 @ X1) != $true) | ($true != (cP_1 @ (f @ a) @ X5))) ) | ~spl0_1),
% 0.32/1.38 inference(superposition,[status(thm)],[f62,f26])).
% 0.32/1.38 thf(f26,plain,(
% 0.32/1.38 ( ! [X42 : $i,X43 : $i] : (((cP_5 @ (f @ X42) @ X43) = $true) | ((cP_5 @ X42 @ X43) != $true)) )),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f62,plain,(
% 0.32/1.38 ( ! [X10 : $i,X11 : $i,X16 : $i,X17 : $i,X15 : $i,X12 : $i] : (($true != (cP_5 @ (f @ X15) @ X16)) | ((cP_3 @ (f @ X10) @ X11) != $true) | ((cP_4 @ (f @ X11) @ X15) != $true) | ((cP_6 @ (f @ X16) @ X17) != $true) | ((cP_1 @ (f @ a) @ X12) != $true) | ((cP_2 @ (f @ X12) @ X10) != $true)) ) | ~spl0_1),
% 0.32/1.38 inference(avatar_component_clause,[status(thm)],[f61])).
% 0.32/1.38 thf(f142,plain,(
% 0.32/1.38 spl0_4 | ~spl0_3),
% 0.32/1.38 inference(avatar_split_clause,[status(thm)],[f141,f67,f93])).
% 0.32/1.38 thf(f67,definition,(
% 0.32/1.38 spl0_3 <=> ! [X1 : $i,X4 : $i,X0 : $i,X13 : $i,X8 : $i,X7 : $i] : (($true != (cP_2 @ (f @ X4) @ X0)) | ((cP_5 @ (f @ X7) @ X8) != $true) | ((cP_3 @ (f @ X0) @ X1) != $true) | ((cP_4 @ (f @ X1) @ X7) != $true) | ((cP_6 @ (f @ X8) @ X13) != $true) | ((cP_1 @ (f @ b) @ X4) != $true))),
% 0.32/1.38 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 0.32/1.38 thf(f141,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_3 @ b @ X3)) | ((cP_6 @ X0 @ X1) != $true) | ((cP_5 @ X2 @ X0) != $true) | ((cP_4 @ X3 @ X2) != $true)) ) | ~spl0_3),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f140])).
% 0.32/1.38 thf(f140,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_3 @ b @ X3)) | ((cP_4 @ X3 @ X2) != $true) | ((cP_6 @ X0 @ X1) != $true) | ($true != $true) | ((cP_5 @ X2 @ X0) != $true)) ) | ~spl0_3),
% 0.32/1.38 inference(superposition,[status(thm)],[f139,f23])).
% 0.32/1.38 thf(f23,plain,(
% 0.32/1.38 ((cP_2 @ b @ b) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f139,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_2 @ b @ X2)) | ((cP_6 @ X1 @ X4) != $true) | ((cP_5 @ X0 @ X1) != $true) | ($true != (cP_3 @ X2 @ X3)) | ((cP_4 @ X3 @ X0) != $true)) ) | ~spl0_3),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f138])).
% 0.32/1.38 thf(f138,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != $true) | ((cP_6 @ X1 @ X4) != $true) | ($true != (cP_3 @ X2 @ X3)) | ((cP_4 @ X3 @ X0) != $true) | ((cP_5 @ X0 @ X1) != $true) | ($true != (cP_2 @ b @ X2))) ) | ~spl0_3),
% 0.32/1.38 inference(superposition,[status(thm)],[f137,f45])).
% 0.32/1.38 thf(f45,plain,(
% 0.32/1.38 ((cP_1 @ b @ b) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f137,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_1 @ b @ X5)) | ($true != (cP_5 @ X3 @ X0)) | ((cP_3 @ X4 @ X2) != $true) | ((cP_6 @ X0 @ X1) != $true) | ($true != (cP_2 @ X5 @ X4)) | ($true != (cP_4 @ X2 @ X3))) ) | ~spl0_3),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f136])).
% 0.32/1.38 thf(f136,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_5 @ X3 @ X0)) | ($true != (cP_1 @ b @ X5)) | ((cP_6 @ X0 @ X1) != $true) | ($true != (cP_2 @ X5 @ X4)) | ((cP_3 @ X4 @ X2) != $true) | ($true != (cP_4 @ X2 @ X3)) | ($true != $true)) ) | ~spl0_3),
% 0.32/1.38 inference(superposition,[status(thm)],[f135,f11])).
% 0.32/1.38 thf(f135,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_6 @ (f @ X2) @ X3)) | ((cP_4 @ X0 @ X1) != $true) | ((cP_3 @ X4 @ X0) != $true) | ($true != (cP_1 @ b @ X5)) | ($true != (cP_5 @ X1 @ X2)) | ($true != (cP_2 @ X5 @ X4))) ) | ~spl0_3),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f134])).
% 0.32/1.38 thf(f134,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_3 @ X4 @ X0) != $true) | ($true != (cP_1 @ b @ X5)) | ($true != (cP_5 @ X1 @ X2)) | ($true != (cP_6 @ (f @ X2) @ X3)) | ($true != $true) | ((cP_4 @ X0 @ X1) != $true) | ($true != (cP_2 @ X5 @ X4))) ) | ~spl0_3),
% 0.32/1.38 inference(superposition,[status(thm)],[f133,f21])).
% 0.32/1.38 thf(f133,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_4 @ (f @ X2) @ X0) != $true) | ((cP_6 @ (f @ X1) @ X5) != $true) | ((cP_3 @ X4 @ X2) != $true) | ((cP_2 @ X3 @ X4) != $true) | ((cP_5 @ X0 @ X1) != $true) | ($true != (cP_1 @ b @ X3))) ) | ~spl0_3),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 0.32/1.38 thf(f132,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_4 @ (f @ X2) @ X0) != $true) | ($true != (cP_1 @ b @ X3)) | ((cP_5 @ X0 @ X1) != $true) | ((cP_3 @ X4 @ X2) != $true) | ($true != $true) | ((cP_2 @ X3 @ X4) != $true) | ((cP_6 @ (f @ X1) @ X5) != $true)) ) | ~spl0_3),
% 0.32/1.38 inference(superposition,[status(thm)],[f131,f26])).
% 0.32/1.38 thf(f131,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_5 @ (f @ X5) @ X2)) | ((cP_4 @ (f @ X1) @ X5) != $true) | ($true != (cP_1 @ b @ X4)) | ((cP_3 @ X0 @ X1) != $true) | ($true != (cP_6 @ (f @ X2) @ X3)) | ($true != (cP_2 @ X4 @ X0))) ) | ~spl0_3),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f130])).
% 0.32/1.38 thf(f130,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true != (cP_1 @ b @ X4)) | ((cP_3 @ X0 @ X1) != $true) | ($true != (cP_5 @ (f @ X5) @ X2)) | ($true != (cP_6 @ (f @ X2) @ X3)) | ((cP_4 @ (f @ X1) @ X5) != $true) | ($true != (cP_2 @ X4 @ X0))) ) | ~spl0_3),
% 0.32/1.38 inference(superposition,[status(thm)],[f129,f14])).
% 0.32/1.38 thf(f129,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_3 @ (f @ X5) @ X4)) | ($true != (cP_6 @ (f @ X2) @ X3)) | ($true != (cP_2 @ X0 @ X5)) | ((cP_1 @ b @ X0) != $true) | ($true != (cP_5 @ (f @ X1) @ X2)) | ((cP_4 @ (f @ X4) @ X1) != $true)) ) | ~spl0_3),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 0.32/1.38 thf(f128,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_4 @ (f @ X4) @ X1) != $true) | ($true != (cP_3 @ (f @ X5) @ X4)) | ($true != (cP_5 @ (f @ X1) @ X2)) | ($true != (cP_2 @ X0 @ X5)) | ($true != $true) | ($true != (cP_6 @ (f @ X2) @ X3)) | ((cP_1 @ b @ X0) != $true)) ) | ~spl0_3),
% 0.32/1.38 inference(superposition,[status(thm)],[f127,f10])).
% 0.32/1.38 thf(f127,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_1 @ (f @ b) @ X0)) | ((cP_5 @ (f @ X2) @ X3) != $true) | ($true != (cP_6 @ (f @ X3) @ X5)) | ($true != (cP_4 @ (f @ X4) @ X2)) | ((cP_3 @ (f @ X1) @ X4) != $true) | ((cP_2 @ X0 @ X1) != $true)) ) | ~spl0_3),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 0.32/1.38 thf(f126,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_6 @ (f @ X3) @ X5)) | ($true != $true) | ((cP_3 @ (f @ X1) @ X4) != $true) | ($true != (cP_4 @ (f @ X4) @ X2)) | ((cP_2 @ X0 @ X1) != $true) | ((cP_5 @ (f @ X2) @ X3) != $true) | ($true != (cP_1 @ (f @ b) @ X0))) ) | ~spl0_3),
% 0.32/1.38 inference(superposition,[status(thm)],[f68,f16])).
% 0.32/1.38 thf(f68,plain,(
% 0.32/1.38 ( ! [X0 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i,X13 : $i] : (($true != (cP_2 @ (f @ X4) @ X0)) | ((cP_1 @ (f @ b) @ X4) != $true) | ((cP_6 @ (f @ X8) @ X13) != $true) | ((cP_4 @ (f @ X1) @ X7) != $true) | ((cP_3 @ (f @ X0) @ X1) != $true) | ((cP_5 @ (f @ X7) @ X8) != $true)) ) | ~spl0_3),
% 0.32/1.38 inference(avatar_component_clause,[status(thm)],[f67])).
% 0.32/1.38 thf(f125,plain,(
% 0.32/1.38 ~spl0_2),
% 0.32/1.38 inference(avatar_contradiction_clause,[status(thm)],[f124])).
% 0.32/1.38 thf(f124,plain,(
% 0.32/1.38 $false | ~spl0_2),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f123])).
% 0.32/1.38 thf(f123,plain,(
% 0.32/1.38 ($true != $true) | ~spl0_2),
% 0.32/1.38 inference(superposition,[status(thm)],[f122,f17])).
% 0.32/1.38 thf(f17,plain,(
% 0.32/1.38 ((cP_6 @ c @ c) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f122,plain,(
% 0.32/1.38 ( ! [X0 : $i] : (($true != (cP_6 @ c @ X0))) ) | ~spl0_2),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 0.32/1.38 thf(f121,plain,(
% 0.32/1.38 ( ! [X0 : $i] : (($true != (cP_6 @ c @ X0)) | ($true != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(superposition,[status(thm)],[f120,f30])).
% 0.32/1.38 thf(f30,plain,(
% 0.32/1.38 ((cP_5 @ c @ c) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f120,plain,(
% 0.32/1.38 ( ! [X0 : $i,X1 : $i] : (((cP_5 @ c @ X0) != $true) | ((cP_6 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 0.32/1.38 thf(f119,plain,(
% 0.32/1.38 ( ! [X0 : $i,X1 : $i] : (((cP_5 @ c @ X0) != $true) | ($true != $true) | ((cP_6 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(superposition,[status(thm)],[f118,f42])).
% 0.32/1.38 thf(f42,plain,(
% 0.32/1.38 ((cP_4 @ c @ c) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f118,plain,(
% 0.32/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_4 @ c @ X2) != $true) | ((cP_6 @ X0 @ X1) != $true) | ((cP_5 @ X2 @ X0) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 0.32/1.38 thf(f117,plain,(
% 0.32/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_4 @ c @ X2) != $true) | ($true != $true) | ((cP_6 @ X0 @ X1) != $true) | ((cP_5 @ X2 @ X0) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(superposition,[status(thm)],[f116,f31])).
% 0.32/1.38 thf(f31,plain,(
% 0.32/1.38 ((cP_3 @ c @ c) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f116,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_3 @ c @ X0)) | ((cP_6 @ X2 @ X3) != $true) | ($true != (cP_5 @ X1 @ X2)) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(subsumption_resolution,[status(thm)],[f87,f13])).
% 0.32/1.38 thf(f13,plain,(
% 0.32/1.38 ((cP_1 @ c @ c) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f87,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_5 @ X1 @ X2)) | ((cP_1 @ c @ c) != $true) | ((cP_4 @ X0 @ X1) != $true) | ($true != (cP_3 @ c @ X0)) | ((cP_6 @ X2 @ X3) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 0.32/1.38 thf(f83,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_3 @ c @ X0)) | ((cP_6 @ X2 @ X3) != $true) | ($true != (cP_5 @ X1 @ X2)) | ((cP_1 @ c @ c) != $true) | ($true != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(superposition,[status(thm)],[f81,f38])).
% 0.32/1.38 thf(f38,plain,(
% 0.32/1.38 ((cP_2 @ c @ c) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f81,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_2 @ X5 @ X3)) | ((cP_1 @ c @ X5) != $true) | ((cP_4 @ X2 @ X0) != $true) | ((cP_6 @ X1 @ X4) != $true) | ((cP_3 @ X3 @ X2) != $true) | ((cP_5 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 0.32/1.38 thf(f80,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_2 @ X5 @ X3)) | ((cP_5 @ X0 @ X1) != $true) | ((cP_1 @ c @ X5) != $true) | ($true != $true) | ((cP_6 @ X1 @ X4) != $true) | ((cP_4 @ X2 @ X0) != $true) | ((cP_3 @ X3 @ X2) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(superposition,[status(thm)],[f79,f26])).
% 0.32/1.38 thf(f79,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_5 @ (f @ X1) @ X2)) | ((cP_4 @ X0 @ X1) != $true) | ((cP_3 @ X5 @ X0) != $true) | ($true != (cP_6 @ X2 @ X4)) | ((cP_1 @ c @ X3) != $true) | ($true != (cP_2 @ X3 @ X5))) ) | ~spl0_2),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 0.32/1.38 thf(f78,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_1 @ c @ X3) != $true) | ($true != $true) | ($true != (cP_2 @ X3 @ X5)) | ((cP_3 @ X5 @ X0) != $true) | ($true != (cP_6 @ X2 @ X4)) | ((cP_4 @ X0 @ X1) != $true) | ($true != (cP_5 @ (f @ X1) @ X2))) ) | ~spl0_2),
% 0.32/1.38 inference(superposition,[status(thm)],[f77,f21])).
% 0.32/1.38 thf(f77,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_4 @ (f @ X4) @ X5)) | ((cP_5 @ (f @ X5) @ X0) != $true) | ($true != (cP_1 @ c @ X2)) | ((cP_6 @ X0 @ X1) != $true) | ((cP_2 @ X2 @ X3) != $true) | ((cP_3 @ X3 @ X4) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 0.32/1.38 thf(f76,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_1 @ c @ X2)) | ((cP_2 @ X2 @ X3) != $true) | ($true != $true) | ((cP_6 @ X0 @ X1) != $true) | ((cP_5 @ (f @ X5) @ X0) != $true) | ($true != (cP_4 @ (f @ X4) @ X5)) | ((cP_3 @ X3 @ X4) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(superposition,[status(thm)],[f75,f11])).
% 0.32/1.38 thf(f75,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_6 @ (f @ X2) @ X3)) | ($true != (cP_2 @ X5 @ X0)) | ((cP_4 @ (f @ X1) @ X4) != $true) | ((cP_3 @ X0 @ X1) != $true) | ((cP_5 @ (f @ X4) @ X2) != $true) | ((cP_1 @ c @ X5) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 0.32/1.38 thf(f74,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_4 @ (f @ X1) @ X4) != $true) | ((cP_5 @ (f @ X4) @ X2) != $true) | ($true != $true) | ($true != (cP_6 @ (f @ X2) @ X3)) | ((cP_3 @ X0 @ X1) != $true) | ((cP_1 @ c @ X5) != $true) | ($true != (cP_2 @ X5 @ X0))) ) | ~spl0_2),
% 0.32/1.38 inference(superposition,[status(thm)],[f73,f14])).
% 0.32/1.38 thf(f73,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_3 @ (f @ X1) @ X2)) | ((cP_6 @ (f @ X4) @ X5) != $true) | ((cP_5 @ (f @ X3) @ X4) != $true) | ((cP_1 @ c @ X0) != $true) | ((cP_2 @ X0 @ X1) != $true) | ((cP_4 @ (f @ X2) @ X3) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 0.32/1.38 thf(f72,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((cP_1 @ c @ X0) != $true) | ((cP_4 @ (f @ X2) @ X3) != $true) | ((cP_6 @ (f @ X4) @ X5) != $true) | ((cP_2 @ X0 @ X1) != $true) | ($true != (cP_3 @ (f @ X1) @ X2)) | ((cP_5 @ (f @ X3) @ X4) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(superposition,[status(thm)],[f71,f10])).
% 0.32/1.38 thf(f71,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_1 @ (f @ c) @ X0)) | ($true != (cP_3 @ (f @ X1) @ X2)) | ((cP_4 @ (f @ X2) @ X3) != $true) | ((cP_2 @ X0 @ X1) != $true) | ((cP_6 @ (f @ X4) @ X5) != $true) | ((cP_5 @ (f @ X3) @ X4) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 0.32/1.38 thf(f70,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_2 @ X0 @ X1) != $true) | ($true != (cP_1 @ (f @ c) @ X0)) | ((cP_6 @ (f @ X4) @ X5) != $true) | ($true != $true) | ((cP_5 @ (f @ X3) @ X4) != $true) | ($true != (cP_3 @ (f @ X1) @ X2)) | ((cP_4 @ (f @ X2) @ X3) != $true)) ) | ~spl0_2),
% 0.32/1.38 inference(superposition,[status(thm)],[f65,f16])).
% 0.32/1.38 thf(f65,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X6 : $i,X9 : $i,X14 : $i,X5 : $i] : (($true != (cP_2 @ (f @ X14) @ X5)) | ((cP_3 @ (f @ X5) @ X6) != $true) | ((cP_4 @ (f @ X6) @ X2) != $true) | ((cP_1 @ (f @ c) @ X14) != $true) | ((cP_5 @ (f @ X2) @ X3) != $true) | ($true != (cP_6 @ (f @ X3) @ X9))) ) | ~spl0_2),
% 0.32/1.38 inference(avatar_component_clause,[status(thm)],[f64])).
% 0.32/1.38 thf(f64,definition,(
% 0.32/1.38 spl0_2 <=> ! [X5 : $i,X2 : $i,X9 : $i,X14 : $i,X6 : $i,X3 : $i] : (((cP_3 @ (f @ X5) @ X6) != $true) | ($true != (cP_6 @ (f @ X3) @ X9)) | ((cP_1 @ (f @ c) @ X14) != $true) | ((cP_4 @ (f @ X6) @ X2) != $true) | ((cP_5 @ (f @ X2) @ X3) != $true) | ($true != (cP_2 @ (f @ X14) @ X5)))),
% 0.32/1.38 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 0.32/1.38 thf(f69,plain,(
% 0.32/1.38 spl0_1 | spl0_2 | spl0_3),
% 0.32/1.38 inference(avatar_split_clause,[status(thm)],[f59,f67,f64,f61])).
% 0.32/1.38 thf(f59,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X16 : $i,X14 : $i,X4 : $i,X7 : $i,X17 : $i,X15 : $i,X5 : $i,X12 : $i,X13 : $i] : (((cP_2 @ (f @ X12) @ X10) != $true) | ((cP_3 @ (f @ X5) @ X6) != $true) | ((cP_4 @ (f @ X11) @ X15) != $true) | ($true != (cP_2 @ (f @ X14) @ X5)) | ((cP_6 @ (f @ X16) @ X17) != $true) | ($true != (cP_5 @ (f @ X15) @ X16)) | ($true != (cP_2 @ (f @ X4) @ X0)) | ((cP_5 @ (f @ X2) @ X3) != $true) | ((cP_4 @ (f @ X6) @ X2) != $true) | ((cP_3 @ (f @ X10) @ X11) != $true) | ((cP_1 @ (f @ c) @ X14) != $true) | ($true != (cP_6 @ (f @ X3) @ X9)) | ((cP_1 @ (f @ b) @ X4) != $true) | ((cP_1 @ (f @ a) @ X12) != $true) | ((cP_6 @ (f @ X8) @ X13) != $true) | ((cP_4 @ (f @ X1) @ X7) != $true) | ((cP_3 @ (f @ X0) @ X1) != $true) | ((cP_5 @ (f @ X7) @ X8) != $true)) )),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 0.32/1.38 thf(f58,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X16 : $i,X14 : $i,X7 : $i,X4 : $i,X17 : $i,X15 : $i,X5 : $i,X12 : $i,X13 : $i] : (((cP_6 @ (f @ X8) @ X13) != $true) | ($true != (cP_2 @ (f @ X14) @ X5)) | ((cP_5 @ (f @ X2) @ X3) != $true) | ((cP_6 @ (f @ X16) @ X17) != $true) | ($true != $true) | ($true != (cP_5 @ (f @ X15) @ X16)) | ((cP_4 @ (f @ X11) @ X15) != $true) | ((cP_5 @ (f @ X7) @ X8) != $true) | ($true != (cP_6 @ (f @ X3) @ X9)) | ((cP_2 @ (f @ X12) @ X10) != $true) | ((cP_3 @ (f @ X5) @ X6) != $true) | ((cP_3 @ (f @ X10) @ X11) != $true) | ((cP_4 @ (f @ X1) @ X7) != $true) | ((cP_1 @ (f @ b) @ X4) != $true) | ($true != (cP_2 @ (f @ X4) @ X0)) | ((cP_3 @ (f @ X0) @ X1) != $true) | ((cP_1 @ (f @ c) @ X14) != $true) | ((cP_1 @ (f @ a) @ X12) != $true) | ((cP_4 @ (f @ X6) @ X2) != $true)) )),
% 0.32/1.38 inference(superposition,[status(thm)],[f57,f12])).
% 0.32/1.38 thf(f12,plain,(
% 0.32/1.38 ((cQ_1 @ a @ b @ c) = $true)),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f57,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X18 : $i,X1 : $i,X19 : $i,X6 : $i,X16 : $i,X7 : $i,X8 : $i,X9 : $i,X14 : $i,X4 : $i,X17 : $i,X15 : $i,X5 : $i,X12 : $i,X13 : $i,X20 : $i] : (((cQ_1 @ X18 @ X19 @ X20) != $true) | ((cP_3 @ (f @ X15) @ X16) != $true) | ($true != (cP_5 @ (f @ X11) @ X6)) | ($true != (cP_1 @ (f @ X19) @ X1)) | ((cP_3 @ (f @ X12) @ X10) != $true) | ($true != (cP_5 @ (f @ X17) @ X13)) | ($true != (cP_4 @ (f @ X10) @ X11)) | ((cP_6 @ (f @ X6) @ X7) != $true) | ((cP_3 @ (f @ X8) @ X9) != $true) | ((cP_1 @ (f @ X18) @ X0) != $true) | ((cP_4 @ (f @ X16) @ X17) != $true) | ($true != (cP_6 @ (f @ X13) @ X14)) | ($true != (cP_2 @ (f @ X2) @ X12)) | ((cP_2 @ (f @ X0) @ X8) != $true) | ($true != (cP_4 @ (f @ X9) @ X3)) | ((cP_5 @ (f @ X3) @ X4) != $true) | ((cP_6 @ (f @ X4) @ X5) != $true) | ((cP_2 @ (f @ X1) @ X15) != $true) | ($true != (cP_1 @ (f @ X20) @ X2))) )),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 0.32/1.38 thf(f56,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X18 : $i,X1 : $i,X19 : $i,X8 : $i,X16 : $i,X9 : $i,X4 : $i,X6 : $i,X14 : $i,X7 : $i,X17 : $i,X15 : $i,X5 : $i,X12 : $i,X13 : $i,X20 : $i] : (((cP_1 @ (f @ X18) @ X0) != $true) | ($true != (cP_1 @ (f @ X19) @ X1)) | ($true != (cP_1 @ (f @ X20) @ X2)) | ($true != $true) | ($true != (cP_4 @ (f @ X10) @ X11)) | ((cP_3 @ (f @ X15) @ X16) != $true) | ($true != (cP_2 @ (f @ X2) @ X12)) | ((cQ_1 @ X18 @ X19 @ X20) != $true) | ((cP_3 @ (f @ X8) @ X9) != $true) | ((cP_2 @ (f @ X0) @ X8) != $true) | ($true != (cP_4 @ (f @ X9) @ X3)) | ((cP_5 @ (f @ X3) @ X4) != $true) | ((cP_2 @ (f @ X1) @ X15) != $true) | ($true != (cP_5 @ (f @ X11) @ X6)) | ((cP_3 @ (f @ X12) @ X10) != $true) | ($true != (cP_6 @ (f @ X13) @ X14)) | ((cP_6 @ (f @ X4) @ X5) != $true) | ((cP_6 @ (f @ X6) @ X7) != $true) | ($true != (cP_5 @ (f @ X17) @ X13)) | ((cP_4 @ (f @ X16) @ X17) != $true)) )),
% 0.32/1.38 inference(superposition,[status(thm)],[f55,f43])).
% 0.32/1.38 thf(f43,plain,(
% 0.32/1.38 ( ! [X10 : $i,X11 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (((cQ_2 @ X10 @ X6 @ X9) = $true) | ($true != (cP_1 @ (f @ X8) @ X10)) | ((cQ_1 @ X8 @ X7 @ X11) != $true) | ($true != (cP_1 @ (f @ X7) @ X6)) | ((cP_1 @ (f @ X11) @ X9) != $true)) )),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f55,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X16 : $i,X14 : $i,X7 : $i,X4 : $i,X17 : $i,X15 : $i,X5 : $i,X12 : $i,X13 : $i] : (((cQ_2 @ X17 @ X15 @ X16) != $true) | ($true != (cP_5 @ (f @ X14) @ X7)) | ((cP_6 @ (f @ X7) @ X8) != $true) | ((cP_6 @ (f @ X11) @ X12) != $true) | ((cP_3 @ (f @ X0) @ X6) != $true) | ((cP_4 @ (f @ X10) @ X13) != $true) | ((cP_3 @ (f @ X2) @ X10) != $true) | ((cP_6 @ (f @ X4) @ X5) != $true) | ((cP_3 @ (f @ X1) @ X3) != $true) | ($true != (cP_4 @ (f @ X3) @ X9)) | ($true != (cP_2 @ (f @ X17) @ X0)) | ((cP_2 @ (f @ X15) @ X1) != $true) | ($true != (cP_5 @ (f @ X13) @ X11)) | ($true != (cP_4 @ (f @ X6) @ X14)) | ($true != (cP_5 @ (f @ X9) @ X4)) | ($true != (cP_2 @ (f @ X16) @ X2))) )),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 0.32/1.38 thf(f54,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X16 : $i,X14 : $i,X7 : $i,X4 : $i,X17 : $i,X15 : $i,X5 : $i,X12 : $i,X13 : $i] : (((cP_2 @ (f @ X15) @ X1) != $true) | ((cP_3 @ (f @ X0) @ X6) != $true) | ($true != (cP_2 @ (f @ X16) @ X2)) | ((cP_6 @ (f @ X11) @ X12) != $true) | ((cP_3 @ (f @ X2) @ X10) != $true) | ($true != (cP_2 @ (f @ X17) @ X0)) | ($true != (cP_5 @ (f @ X14) @ X7)) | ($true != $true) | ((cP_6 @ (f @ X4) @ X5) != $true) | ((cP_4 @ (f @ X10) @ X13) != $true) | ($true != (cP_4 @ (f @ X3) @ X9)) | ($true != (cP_5 @ (f @ X13) @ X11)) | ((cQ_2 @ X17 @ X15 @ X16) != $true) | ((cP_6 @ (f @ X7) @ X8) != $true) | ($true != (cP_4 @ (f @ X6) @ X14)) | ((cP_3 @ (f @ X1) @ X3) != $true) | ($true != (cP_5 @ (f @ X9) @ X4))) )),
% 0.32/1.38 inference(superposition,[status(thm)],[f53,f29])).
% 0.32/1.38 thf(f29,plain,(
% 0.32/1.38 ( ! [X40 : $i,X38 : $i,X39 : $i,X36 : $i,X37 : $i,X35 : $i] : (((cQ_3 @ X40 @ X36 @ X35) = $true) | ($true != (cP_2 @ (f @ X37) @ X36)) | ((cP_2 @ (f @ X38) @ X35) != $true) | ($true != (cQ_2 @ X39 @ X37 @ X38)) | ((cP_2 @ (f @ X39) @ X40) != $true)) )),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f53,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X14 : $i,X4 : $i,X5 : $i,X12 : $i,X13 : $i] : (($true != (cQ_3 @ X13 @ X14 @ X12)) | ($true != (cP_3 @ (f @ X14) @ X1)) | ((cP_6 @ (f @ X8) @ X9) != $true) | ($true != (cP_3 @ (f @ X13) @ X0)) | ((cP_6 @ (f @ X6) @ X11) != $true) | ((cP_4 @ (f @ X1) @ X7) != $true) | ($true != (cP_3 @ (f @ X12) @ X2)) | ($true != (cP_6 @ (f @ X4) @ X10)) | ((cP_4 @ (f @ X2) @ X3) != $true) | ((cP_5 @ (f @ X7) @ X8) != $true) | ($true != (cP_5 @ (f @ X5) @ X6)) | ((cP_5 @ (f @ X3) @ X4) != $true) | ($true != (cP_4 @ (f @ X0) @ X5))) )),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 0.32/1.38 thf(f52,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X14 : $i,X4 : $i,X5 : $i,X12 : $i,X13 : $i] : (($true != (cP_3 @ (f @ X12) @ X2)) | ($true != (cP_3 @ (f @ X13) @ X0)) | ((cP_6 @ (f @ X6) @ X11) != $true) | ((cP_5 @ (f @ X3) @ X4) != $true) | ((cP_6 @ (f @ X8) @ X9) != $true) | ($true != (cP_3 @ (f @ X14) @ X1)) | ($true != (cP_4 @ (f @ X0) @ X5)) | ((cP_4 @ (f @ X1) @ X7) != $true) | ($true != $true) | ((cP_4 @ (f @ X2) @ X3) != $true) | ($true != (cQ_3 @ X13 @ X14 @ X12)) | ($true != (cP_6 @ (f @ X4) @ X10)) | ($true != (cP_5 @ (f @ X5) @ X6)) | ((cP_5 @ (f @ X7) @ X8) != $true)) )),
% 0.32/1.38 inference(superposition,[status(thm)],[f51,f44])).
% 0.32/1.38 thf(f44,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = (cQ_4 @ X2 @ X1 @ X5)) | ($true != (cP_3 @ (f @ X4) @ X5)) | ((cQ_3 @ X3 @ X0 @ X4) != $true) | ((cP_3 @ (f @ X0) @ X1) != $true) | ($true != (cP_3 @ (f @ X3) @ X2))) )),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f51,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != (cQ_4 @ X9 @ X10 @ X11)) | ($true != (cP_4 @ (f @ X11) @ X2)) | ($true != (cP_5 @ (f @ X2) @ X4)) | ((cP_5 @ (f @ X0) @ X3) != $true) | ($true != (cP_4 @ (f @ X10) @ X1)) | ((cP_5 @ (f @ X1) @ X6) != $true) | ((cP_6 @ (f @ X6) @ X7) != $true) | ($true != (cP_6 @ (f @ X4) @ X8)) | ($true != (cP_4 @ (f @ X9) @ X0)) | ($true != (cP_6 @ (f @ X3) @ X5))) )),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 0.32/1.38 thf(f50,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != (cP_4 @ (f @ X11) @ X2)) | ((cP_6 @ (f @ X6) @ X7) != $true) | ($true != (cP_6 @ (f @ X4) @ X8)) | ($true != (cP_4 @ (f @ X9) @ X0)) | ($true != $true) | ($true != (cP_4 @ (f @ X10) @ X1)) | ((cP_5 @ (f @ X1) @ X6) != $true) | ($true != (cQ_4 @ X9 @ X10 @ X11)) | ((cP_5 @ (f @ X0) @ X3) != $true) | ($true != (cP_6 @ (f @ X3) @ X5)) | ($true != (cP_5 @ (f @ X2) @ X4))) )),
% 0.32/1.38 inference(superposition,[status(thm)],[f49,f35])).
% 0.32/1.38 thf(f35,plain,(
% 0.32/1.38 ( ! [X21 : $i,X24 : $i,X22 : $i,X25 : $i,X23 : $i,X20 : $i] : (((cQ_5 @ X25 @ X23 @ X22) = $true) | ((cQ_4 @ X21 @ X20 @ X24) != $true) | ((cP_4 @ (f @ X24) @ X22) != $true) | ($true != (cP_4 @ (f @ X20) @ X23)) | ($true != (cP_4 @ (f @ X21) @ X25))) )),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f49,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((cQ_5 @ X8 @ X7 @ X6) != $true) | ((cP_5 @ (f @ X8) @ X0) != $true) | ((cP_5 @ (f @ X6) @ X2) != $true) | ((cP_6 @ (f @ X0) @ X3) != $true) | ($true != (cP_5 @ (f @ X7) @ X1)) | ((cP_6 @ (f @ X1) @ X4) != $true) | ((cP_6 @ (f @ X2) @ X5) != $true)) )),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 0.32/1.38 thf(f48,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((cP_5 @ (f @ X6) @ X2) != $true) | ($true != $true) | ((cP_6 @ (f @ X0) @ X3) != $true) | ((cP_5 @ (f @ X8) @ X0) != $true) | ((cP_6 @ (f @ X1) @ X4) != $true) | ((cQ_5 @ X8 @ X7 @ X6) != $true) | ((cP_6 @ (f @ X2) @ X5) != $true) | ($true != (cP_5 @ (f @ X7) @ X1))) )),
% 0.32/1.38 inference(superposition,[status(thm)],[f47,f32])).
% 0.32/1.38 thf(f32,plain,(
% 0.32/1.38 ( ! [X31 : $i,X29 : $i,X34 : $i,X32 : $i,X30 : $i,X33 : $i] : (((cQ_6 @ X30 @ X33 @ X31) = $true) | ($true != (cP_5 @ (f @ X32) @ X31)) | ($true != (cP_5 @ (f @ X29) @ X33)) | ($true != (cP_5 @ (f @ X34) @ X30)) | ($true != (cQ_5 @ X34 @ X29 @ X32))) )),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f47,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cQ_6 @ X4 @ X3 @ X5)) | ((cP_6 @ (f @ X4) @ X0) != $true) | ($true != (cP_6 @ (f @ X3) @ X1)) | ((cP_6 @ (f @ X5) @ X2) != $true)) )),
% 0.32/1.38 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 0.32/1.38 thf(f46,plain,(
% 0.32/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP_6 @ (f @ X5) @ X2) != $true) | ($true != (cQ_6 @ X4 @ X3 @ X5)) | ((cP_6 @ (f @ X4) @ X0) != $true) | ($true != (cP_6 @ (f @ X3) @ X1)) | ($true != $true)) )),
% 0.32/1.38 inference(superposition,[status(thm)],[f33,f36])).
% 0.32/1.38 thf(f36,plain,(
% 0.32/1.38 ( ! [X18 : $i,X19 : $i,X16 : $i,X14 : $i,X17 : $i,X15 : $i] : (((cQ_7 @ X18 @ X14 @ X17) = $true) | ($true != (cP_6 @ (f @ X16) @ X14)) | ((cQ_6 @ X19 @ X16 @ X15) != $true) | ($true != (cP_6 @ (f @ X19) @ X18)) | ($true != (cP_6 @ (f @ X15) @ X17))) )),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 thf(f33,plain,(
% 0.32/1.38 ( ! [X28 : $i,X26 : $i,X27 : $i] : (((cQ_7 @ X27 @ X28 @ X26) != $true)) )),
% 0.32/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.32/1.38 % SZS output end Proof for DTF2THF_5935
% 0.32/1.38 % (6222)------------------------------
% 0.32/1.38 % (6222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.38 % (6222)Termination reason: Refutation
% 0.32/1.38
% 0.32/1.38 % (6222)Memory used [KB]: 6012
% 0.32/1.38 % (6222)Time elapsed: 0.046 s
% 0.32/1.38 % (6222)Instructions burned: 66 (million)
% 0.32/1.38 % (6222)------------------------------
% 0.32/1.38 % (6222)------------------------------
% 0.32/1.38 % (6221)Success in time 0.057 s
%------------------------------------------------------------------------------