%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO388^5 : 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 : n020.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 09:54:06 AM UTC 2026
% Result : Theorem 1.72s 1.38s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of formulae : 120 ( 21 unt; 0 typ; 6 def)
% Number of atoms : 2463 ( 621 equ; 0 cnn)
% Maximal formula atoms : 95 ( 20 avg)
% Number of connectives : 3373 ( 655 ~; 564 |; 186 &;1962 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 12 con; 0-3 aty)
% Number of variables : 708 ( 0 ^; 708 !; 0 ?; 708 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ_6: $i > $i > $i > $o ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
cP_5: $i > $i > $o ).
thf(func_def_3,type,
cQ_5: $i > $i > $i > $o ).
thf(func_def_8,type,
cP_4: $i > $i > $o ).
thf(func_def_9,type,
cQ_4: $i > $i > $i > $o ).
thf(func_def_10,type,
cP_3: $i > $i > $o ).
thf(func_def_11,type,
cQ_3: $i > $i > $i > $o ).
thf(func_def_12,type,
cP_2: $i > $i > $o ).
thf(func_def_13,type,
cQ_2: $i > $i > $i > $o ).
thf(func_def_14,type,
cP_1: $i > $i > $o ).
thf(func_def_15,type,
cQ_1: $i > $i > $i > $o ).
thf(f245,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f60,f143,f183,f188,f191,f241,f244]) ).
thf(f244,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[status(thm)],[f243]) ).
thf(f243,plain,
( $false
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f242]) ).
thf(f242,plain,
( ( $true != $true )
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f123,f39]) ).
thf(f39,plain,
( ( cP_5 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cP_5 @ b @ b )
= $true )
& ! [X0: $i,X1: $i,X2: $i] :
( ( cQ_6 @ X0 @ X2 @ X1 )
!= $true )
& ! [X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( $true
= ( cQ_3 @ X5 @ X8 @ X6 ) )
| ( ( cP_2 @ ( f @ X3 ) @ X6 )
!= $true )
| ( ( cQ_2 @ X7 @ X4 @ X3 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X7 ) @ X5 ) )
| ( ( cP_2 @ ( f @ X4 ) @ X8 )
!= $true ) )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ( ( cP_5 @ a @ a )
= $true )
& ! [X9: $i,X10: $i] :
( ( ( cP_3 @ ( f @ X10 ) @ X9 )
= $true )
| ( ( cP_3 @ X10 @ X9 )
!= $true ) )
& ! [X11: $i,X12: $i,X13: $i,X14: $i,X15: $i,X16: $i] :
( ( ( cP_4 @ ( f @ X12 ) @ X13 )
!= $true )
| ( $true
= ( cQ_5 @ X13 @ X15 @ X14 ) )
| ( $true
!= ( cP_4 @ ( f @ X16 ) @ X14 ) )
| ( $true
!= ( cP_4 @ ( f @ X11 ) @ X15 ) )
| ( ( cQ_4 @ X12 @ X11 @ X16 )
!= $true ) )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ( ( cP_2 @ a @ a )
= $true )
& ! [X17: $i] :
( $true
= ( cP_3 @ d @ X17 ) )
& ( ( cP_4 @ b @ b )
= $true )
& ! [X18: $i,X19: $i] :
( ( $true
= ( cP_2 @ ( f @ X19 ) @ X18 ) )
| ( ( cP_2 @ X19 @ X18 )
!= $true ) )
& ( ( cP_4 @ c @ c )
= $true )
& ! [X20: $i,X21: $i] :
( ( $true
= ( cP_1 @ ( f @ X21 ) @ X20 ) )
| ( $true
!= ( cP_1 @ X21 @ X20 ) ) )
& ( ( cP_5 @ c @ c )
= $true )
& ( ( cP_4 @ a @ a )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ! [X22: $i,X23: $i] :
( ( ( cP_5 @ X22 @ X23 )
!= $true )
| ( $true
= ( cP_5 @ ( f @ X22 ) @ X23 ) ) )
& ( ( cP_3 @ a @ a )
= $true )
& ! [X24: $i,X25: $i,X26: $i,X27: $i,X28: $i,X29: $i] :
( ( ( cQ_5 @ X27 @ X25 @ X24 )
!= $true )
| ( ( cP_5 @ ( f @ X27 ) @ X28 )
!= $true )
| ( $true
= ( cQ_6 @ X28 @ X26 @ X29 ) )
| ( ( cP_5 @ ( f @ X25 ) @ X26 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X24 ) @ X29 ) ) )
& ( ( cP_3 @ b @ b )
= $true )
& ! [X30: $i] :
( ( cP_1 @ d @ X30 )
= $true )
& ! [X31: $i,X32: $i,X33: $i,X34: $i,X35: $i,X36: $i] :
( ( ( cQ_2 @ X33 @ X32 @ X31 )
= $true )
| ( $true
!= ( cP_1 @ ( f @ X36 ) @ X31 ) )
| ( $true
!= ( cP_1 @ ( f @ X34 ) @ X32 ) )
| ( ( cQ_1 @ X35 @ X34 @ X36 )
!= $true )
| ( ( cP_1 @ ( f @ X35 ) @ X33 )
!= $true ) )
& ( ( cP_3 @ c @ c )
= $true )
& ! [X37: $i] :
( $true
= ( cP_2 @ d @ X37 ) )
& ! [X38: $i] :
( ( cP_5 @ d @ X38 )
= $true )
& ! [X39: $i,X40: $i] :
( ( $true
!= ( cP_4 @ X39 @ X40 ) )
| ( ( cP_4 @ ( f @ X39 ) @ X40 )
= $true ) )
& ! [X41: $i] :
( $true
= ( cP_4 @ d @ X41 ) )
& ! [X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i] :
( ( $true
!= ( cP_3 @ ( f @ X43 ) @ X45 ) )
| ( $true
!= ( cP_3 @ ( f @ X47 ) @ X42 ) )
| ( ( cQ_4 @ X45 @ X46 @ X42 )
= $true )
| ( ( cQ_3 @ X43 @ X44 @ X47 )
!= $true )
| ( ( cP_3 @ ( f @ X44 ) @ X46 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( cP_5 @ b @ b )
= $true )
& ! [X21: $i,X20: $i,X22: $i] :
( ( cQ_6 @ X21 @ X22 @ X20 )
!= $true )
& ! [X45: $i,X43: $i,X46: $i,X42: $i,X47: $i,X44: $i] :
( ( ( cQ_3 @ X46 @ X44 @ X42 )
= $true )
| ( $true
!= ( cP_2 @ ( f @ X45 ) @ X42 ) )
| ( $true
!= ( cQ_2 @ X47 @ X43 @ X45 ) )
| ( ( cP_2 @ ( f @ X47 ) @ X46 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X43 ) @ X44 ) ) )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ( ( cP_5 @ a @ a )
= $true )
& ! [X9: $i,X8: $i] :
( ( ( cP_3 @ ( f @ X8 ) @ X9 )
= $true )
| ( $true
!= ( cP_3 @ X8 @ X9 ) ) )
& ! [X23: $i,X27: $i,X28: $i,X26: $i,X25: $i,X24: $i] :
( ( $true
!= ( cP_4 @ ( f @ X27 ) @ X28 ) )
| ( ( cQ_5 @ X28 @ X25 @ X26 )
= $true )
| ( ( cP_4 @ ( f @ X24 ) @ X26 )
!= $true )
| ( ( cP_4 @ ( f @ X23 ) @ X25 )
!= $true )
| ( ( cQ_4 @ X27 @ X23 @ X24 )
!= $true ) )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ( ( cP_2 @ a @ a )
= $true )
& ! [X18: $i] :
( $true
= ( cP_3 @ d @ X18 ) )
& ( ( cP_4 @ b @ b )
= $true )
& ! [X30: $i,X29: $i] :
( ( ( cP_2 @ ( f @ X29 ) @ X30 )
= $true )
| ( $true
!= ( cP_2 @ X29 @ X30 ) ) )
& ( ( cP_4 @ c @ c )
= $true )
& ! [X38: $i,X37: $i] :
( ( $true
= ( cP_1 @ ( f @ X37 ) @ X38 ) )
| ( $true
!= ( cP_1 @ X37 @ X38 ) ) )
& ( ( cP_5 @ c @ c )
= $true )
& ( ( cP_4 @ a @ a )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ! [X17: $i,X16: $i] :
( ( ( cP_5 @ X17 @ X16 )
!= $true )
| ( $true
= ( cP_5 @ ( f @ X17 ) @ X16 ) ) )
& ( ( cP_3 @ a @ a )
= $true )
& ! [X4: $i,X0: $i,X5: $i,X3: $i,X2: $i,X1: $i] :
( ( ( cQ_5 @ X3 @ X0 @ X4 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X3 ) @ X2 ) )
| ( ( cQ_6 @ X2 @ X5 @ X1 )
= $true )
| ( ( cP_5 @ ( f @ X0 ) @ X5 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X4 ) @ X1 ) ) )
& ( ( cP_3 @ b @ b )
= $true )
& ! [X39: $i] :
( $true
= ( cP_1 @ d @ X39 ) )
& ! [X11: $i,X15: $i,X10: $i,X14: $i,X12: $i,X13: $i] :
( ( $true
= ( cQ_2 @ X10 @ X15 @ X11 ) )
| ( ( cP_1 @ ( f @ X13 ) @ X11 )
!= $true )
| ( ( cP_1 @ ( f @ X14 ) @ X15 )
!= $true )
| ( $true
!= ( cQ_1 @ X12 @ X14 @ X13 ) )
| ( $true
!= ( cP_1 @ ( f @ X12 ) @ X10 ) ) )
& ( ( cP_3 @ c @ c )
= $true )
& ! [X40: $i] :
( ( cP_2 @ d @ X40 )
= $true )
& ! [X41: $i] :
( ( cP_5 @ d @ X41 )
= $true )
& ! [X6: $i,X7: $i] :
( ( $true
!= ( cP_4 @ X6 @ X7 ) )
| ( ( cP_4 @ ( f @ X6 ) @ X7 )
= $true ) )
& ! [X19: $i] :
( ( cP_4 @ d @ X19 )
= $true )
& ! [X32: $i,X33: $i,X36: $i,X31: $i,X35: $i,X34: $i] :
( ( ( cP_3 @ ( f @ X33 ) @ X31 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X34 ) @ X32 ) )
| ( $true
= ( cQ_4 @ X31 @ X35 @ X32 ) )
| ( ( cQ_3 @ X33 @ X36 @ X34 )
!= $true )
| ( ( cP_3 @ ( f @ X36 ) @ X35 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ( ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( ( cQ_5 @ X3 @ X0 @ X4 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X3 ) @ X2 ) )
| ( ( cQ_6 @ X2 @ X5 @ X1 )
= $true )
| ( ( cP_5 @ ( f @ X0 ) @ X5 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X4 ) @ X1 ) ) )
& ! [X6: $i,X7: $i] :
( ( ( cP_4 @ ( f @ X6 ) @ X7 )
= $true )
| ( $true
!= ( cP_4 @ X6 @ X7 ) ) )
& ( ( cP_3 @ b @ b )
= $true )
& ! [X8: $i,X9: $i] :
( ( ( cP_3 @ ( f @ X8 ) @ X9 )
= $true )
| ( $true
!= ( cP_3 @ X8 @ X9 ) ) )
& ( ( cP_1 @ a @ a )
= $true )
& ! [X10: $i,X11: $i,X12: $i,X13: $i,X14: $i,X15: $i] :
( ( ( cP_1 @ ( f @ X14 ) @ X15 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X12 ) @ X10 ) )
| ( ( cP_1 @ ( f @ X13 ) @ X11 )
!= $true )
| ( $true
= ( cQ_2 @ X10 @ X15 @ X11 ) )
| ( $true
!= ( cQ_1 @ X12 @ X14 @ X13 ) ) )
& ! [X16: $i,X17: $i] :
( ( ( cP_5 @ X17 @ X16 )
!= $true )
| ( $true
= ( cP_5 @ ( f @ X17 ) @ X16 ) ) )
& ! [X18: $i] :
( $true
= ( cP_3 @ d @ X18 ) )
& ( ( cP_4 @ c @ c )
= $true )
& ! [X19: $i] :
( ( cP_4 @ d @ X19 )
= $true )
& ( ( cP_5 @ b @ b )
= $true )
& ! [X20: $i,X21: $i,X22: $i] :
( ( cQ_6 @ X21 @ X22 @ X20 )
!= $true )
& ! [X23: $i,X24: $i,X25: $i,X26: $i,X27: $i,X28: $i] :
( ( ( cQ_5 @ X28 @ X25 @ X26 )
= $true )
| ( ( cP_4 @ ( f @ X23 ) @ X25 )
!= $true )
| ( ( cQ_4 @ X27 @ X23 @ X24 )
!= $true )
| ( ( cP_4 @ ( f @ X24 ) @ X26 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X27 ) @ X28 ) ) )
& ! [X29: $i,X30: $i] :
( ( ( cP_2 @ ( f @ X29 ) @ X30 )
= $true )
| ( $true
!= ( cP_2 @ X29 @ X30 ) ) )
& ( ( cP_4 @ b @ b )
= $true )
& ( ( cP_5 @ c @ c )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_3 @ a @ a )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ( ( cP_3 @ c @ c )
= $true )
& ! [X31: $i,X32: $i,X33: $i,X34: $i,X35: $i,X36: $i] :
( ( ( cQ_3 @ X33 @ X36 @ X34 )
!= $true )
| ( ( cP_3 @ ( f @ X33 ) @ X31 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X34 ) @ X32 ) )
| ( $true
= ( cQ_4 @ X31 @ X35 @ X32 ) )
| ( ( cP_3 @ ( f @ X36 ) @ X35 )
!= $true ) )
& ( ( cP_2 @ a @ a )
= $true )
& ( ( cP_5 @ a @ a )
= $true )
& ! [X37: $i,X38: $i] :
( ( $true
!= ( cP_1 @ X37 @ X38 ) )
| ( $true
= ( cP_1 @ ( f @ X37 ) @ X38 ) ) )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X39: $i] :
( $true
= ( cP_1 @ d @ X39 ) )
& ! [X40: $i] :
( ( cP_2 @ d @ X40 )
= $true )
& ! [X41: $i] :
( ( cP_5 @ d @ X41 )
= $true )
& ! [X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i] :
( ( ( cP_2 @ ( f @ X47 ) @ X46 )
!= $true )
| ( $true
!= ( cQ_2 @ X47 @ X43 @ X45 ) )
| ( $true
!= ( cP_2 @ ( f @ X45 ) @ X42 ) )
| ( ( cQ_3 @ X46 @ X44 @ X42 )
= $true )
| ( $true
!= ( cP_2 @ ( f @ X43 ) @ X44 ) ) )
& ( ( cP_4 @ a @ a )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( cQ_5 @ X3 @ X0 @ X4 )
| ~ ( cP_5 @ ( f @ X3 ) @ X2 )
| ( cQ_6 @ X2 @ X5 @ X1 )
| ~ ( cP_5 @ ( f @ X0 ) @ X5 )
| ~ ( cP_5 @ ( f @ X4 ) @ X1 ) )
& ! [X6: $i,X7: $i] :
( ( cP_4 @ ( f @ X6 ) @ X7 )
| ~ ( cP_4 @ X6 @ X7 ) )
& ( cP_3 @ b @ b )
& ! [X8: $i,X9: $i] :
( ( cP_3 @ ( f @ X8 ) @ X9 )
| ~ ( cP_3 @ X8 @ X9 ) )
& ( cP_1 @ a @ a )
& ! [X10: $i,X11: $i,X12: $i,X13: $i,X14: $i,X15: $i] :
( ~ ( cP_1 @ ( f @ X14 ) @ X15 )
| ~ ( cP_1 @ ( f @ X12 ) @ X10 )
| ~ ( cP_1 @ ( f @ X13 ) @ X11 )
| ( cQ_2 @ X10 @ X15 @ X11 )
| ~ ( cQ_1 @ X12 @ X14 @ X13 ) )
& ! [X16: $i,X17: $i] :
( ~ ( cP_5 @ X17 @ X16 )
| ( cP_5 @ ( f @ X17 ) @ X16 ) )
& ! [X18: $i] : ( cP_3 @ d @ X18 )
& ( cP_4 @ c @ c )
& ! [X19: $i] : ( cP_4 @ d @ X19 )
& ( cP_5 @ b @ b )
& ! [X20: $i,X21: $i,X22: $i] :
~ ( cQ_6 @ X21 @ X22 @ X20 )
& ! [X23: $i,X24: $i,X25: $i,X26: $i,X27: $i,X28: $i] :
( ( cQ_5 @ X28 @ X25 @ X26 )
| ~ ( cP_4 @ ( f @ X23 ) @ X25 )
| ~ ( cQ_4 @ X27 @ X23 @ X24 )
| ~ ( cP_4 @ ( f @ X24 ) @ X26 )
| ~ ( cP_4 @ ( f @ X27 ) @ X28 ) )
& ! [X29: $i,X30: $i] :
( ( cP_2 @ ( f @ X29 ) @ X30 )
| ~ ( cP_2 @ X29 @ X30 ) )
& ( cP_4 @ b @ b )
& ( cP_5 @ c @ c )
& ( cP_2 @ c @ c )
& ( cP_1 @ b @ b )
& ( cP_3 @ a @ a )
& ( cP_1 @ c @ c )
& ( cP_3 @ c @ c )
& ! [X31: $i,X32: $i,X33: $i,X34: $i,X35: $i,X36: $i] :
( ~ ( cQ_3 @ X33 @ X36 @ X34 )
| ~ ( cP_3 @ ( f @ X33 ) @ X31 )
| ~ ( cP_3 @ ( f @ X34 ) @ X32 )
| ( cQ_4 @ X31 @ X35 @ X32 )
| ~ ( cP_3 @ ( f @ X36 ) @ X35 ) )
& ( cP_2 @ a @ a )
& ( cP_5 @ a @ a )
& ! [X37: $i,X38: $i] :
( ~ ( cP_1 @ X37 @ X38 )
| ( cP_1 @ ( f @ X37 ) @ X38 ) )
& ( cP_2 @ b @ b )
& ! [X39: $i] : ( cP_1 @ d @ X39 )
& ! [X40: $i] : ( cP_2 @ d @ X40 )
& ! [X41: $i] : ( cP_5 @ d @ X41 )
& ! [X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i] :
( ~ ( cP_2 @ ( f @ X47 ) @ X46 )
| ~ ( cQ_2 @ X47 @ X43 @ X45 )
| ~ ( cP_2 @ ( f @ X45 ) @ X42 )
| ( cQ_3 @ X46 @ X44 @ X42 )
| ~ ( cP_2 @ ( f @ X43 ) @ X44 ) )
& ( cP_4 @ a @ a )
& ( cQ_1 @ a @ b @ c ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X1: $i,X5: $i,X3: $i,X0: $i,X2: $i,X4: $i] :
( ~ ( cQ_5 @ X0 @ X1 @ X2 )
| ~ ( cP_5 @ ( f @ X0 ) @ X3 )
| ( cQ_6 @ X3 @ X4 @ X5 )
| ~ ( cP_5 @ ( f @ X1 ) @ X4 )
| ~ ( cP_5 @ ( f @ X2 ) @ X5 ) )
& ! [X0: $i,X1: $i] :
( ( cP_4 @ ( f @ X0 ) @ X1 )
| ~ ( cP_4 @ X0 @ X1 ) )
& ( cP_3 @ b @ b )
& ! [X0: $i,X1: $i] :
( ( cP_3 @ ( f @ X0 ) @ X1 )
| ~ ( cP_3 @ X0 @ X1 ) )
& ( cP_1 @ a @ a )
& ! [X3: $i,X5: $i,X0: $i,X2: $i,X1: $i,X4: $i] :
( ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 ) )
& ! [X1: $i,X0: $i] :
( ~ ( cP_5 @ X0 @ X1 )
| ( cP_5 @ ( f @ X0 ) @ X1 ) )
& ! [X0: $i] : ( cP_3 @ d @ X0 )
& ( cP_4 @ c @ c )
& ! [X0: $i] : ( cP_4 @ d @ X0 )
& ( cP_5 @ b @ b )
& ! [X2: $i,X0: $i,X1: $i] :
~ ( cQ_6 @ X0 @ X1 @ X2 )
& ! [X1: $i,X2: $i,X4: $i,X5: $i,X0: $i,X3: $i] :
( ( cQ_5 @ X3 @ X4 @ X5 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 )
| ~ ( cQ_4 @ X0 @ X1 @ X2 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ~ ( cP_4 @ ( f @ X0 ) @ X3 ) )
& ! [X0: $i,X1: $i] :
( ( cP_2 @ ( f @ X0 ) @ X1 )
| ~ ( cP_2 @ X0 @ X1 ) )
& ( cP_4 @ b @ b )
& ( cP_5 @ c @ c )
& ( cP_2 @ c @ c )
& ( cP_1 @ b @ b )
& ( cP_3 @ a @ a )
& ( cP_1 @ c @ c )
& ( cP_3 @ c @ c )
& ! [X3: $i,X5: $i,X0: $i,X2: $i,X4: $i,X1: $i] :
( ~ ( cQ_3 @ X0 @ X1 @ X2 )
| ~ ( cP_3 @ ( f @ X0 ) @ X3 )
| ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ( cQ_4 @ X3 @ X4 @ X5 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 ) )
& ( cP_2 @ a @ a )
& ( cP_5 @ a @ a )
& ! [X0: $i,X1: $i] :
( ~ ( cP_1 @ X0 @ X1 )
| ( cP_1 @ ( f @ X0 ) @ X1 ) )
& ( cP_2 @ b @ b )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ! [X0: $i] : ( cP_5 @ d @ X0 )
& ! [X5: $i,X1: $i,X4: $i,X2: $i,X3: $i,X0: $i] :
( ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ( cQ_3 @ X3 @ X4 @ X5 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 ) )
& ( cP_4 @ a @ a )
& ( cQ_1 @ a @ b @ c ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ( ! [X1: $i,X5: $i,X3: $i,X0: $i,X2: $i,X4: $i] :
( ~ ( cQ_5 @ X0 @ X1 @ X2 )
| ~ ( cP_5 @ ( f @ X0 ) @ X3 )
| ( cQ_6 @ X3 @ X4 @ X5 )
| ~ ( cP_5 @ ( f @ X1 ) @ X4 )
| ~ ( cP_5 @ ( f @ X2 ) @ X5 ) )
& ! [X0: $i,X1: $i] :
( ( cP_4 @ ( f @ X0 ) @ X1 )
| ~ ( cP_4 @ X0 @ X1 ) )
& ( cP_3 @ b @ b )
& ! [X0: $i,X1: $i] :
( ( cP_3 @ ( f @ X0 ) @ X1 )
| ~ ( cP_3 @ X0 @ X1 ) )
& ( cP_1 @ a @ a )
& ! [X3: $i,X5: $i,X0: $i,X2: $i,X1: $i,X4: $i] :
( ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 ) )
& ! [X1: $i,X0: $i] :
( ~ ( cP_5 @ X0 @ X1 )
| ( cP_5 @ ( f @ X0 ) @ X1 ) )
& ! [X0: $i] : ( cP_3 @ d @ X0 )
& ( cP_4 @ c @ c )
& ! [X0: $i] : ( cP_4 @ d @ X0 )
& ( cP_5 @ b @ b )
& ! [X2: $i,X0: $i,X1: $i] :
~ ( cQ_6 @ X0 @ X1 @ X2 )
& ! [X1: $i,X2: $i,X4: $i,X5: $i,X0: $i,X3: $i] :
( ( cQ_5 @ X3 @ X4 @ X5 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 )
| ~ ( cQ_4 @ X0 @ X1 @ X2 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ~ ( cP_4 @ ( f @ X0 ) @ X3 ) )
& ! [X0: $i,X1: $i] :
( ( cP_2 @ ( f @ X0 ) @ X1 )
| ~ ( cP_2 @ X0 @ X1 ) )
& ( cP_4 @ b @ b )
& ( cP_5 @ c @ c )
& ( cP_2 @ c @ c )
& ( cP_1 @ b @ b )
& ( cP_3 @ a @ a )
& ( cP_1 @ c @ c )
& ( cP_3 @ c @ c )
& ! [X3: $i,X5: $i,X0: $i,X2: $i,X4: $i,X1: $i] :
( ~ ( cQ_3 @ X0 @ X1 @ X2 )
| ~ ( cP_3 @ ( f @ X0 ) @ X3 )
| ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ( cQ_4 @ X3 @ X4 @ X5 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 ) )
& ( cP_2 @ a @ a )
& ( cP_5 @ a @ a )
& ! [X0: $i,X1: $i] :
( ~ ( cP_1 @ X0 @ X1 )
| ( cP_1 @ ( f @ X0 ) @ X1 ) )
& ( cP_2 @ b @ b )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ! [X0: $i] : ( cP_5 @ d @ X0 )
& ! [X5: $i,X1: $i,X4: $i,X2: $i,X3: $i,X0: $i] :
( ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ( cQ_3 @ X3 @ X4 @ X5 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 ) )
& ( cP_4 @ a @ a )
& ( cQ_1 @ a @ b @ c ) ),
file('/export/starexec/sandbox2/tmp/tmp.4KjW3duxkU/DTF2THF_13451.p',cTHM409_5) ).
thf(f123,plain,
( ! [X0: $i] :
( $true
!= ( cP_5 @ b @ X0 ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f122]) ).
thf(f122,definition,
( spl0_11
<=> ! [X0: $i] :
( $true
!= ( cP_5 @ b @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f241,plain,
( spl0_11
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f240,f52,f122]) ).
thf(f52,definition,
( spl0_1
<=> ! [X11: $i,X0: $i,X6: $i,X2: $i,X1: $i] :
( ( $true
!= ( cP_1 @ ( f @ b ) @ X2 ) )
| ( ( cP_2 @ ( f @ X2 ) @ X6 )
!= $true )
| ( ( cP_4 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X1 ) @ X11 ) )
| ( $true
!= ( cP_3 @ ( f @ X6 ) @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f240,plain,
( ! [X0: $i] :
( $true
!= ( cP_5 @ b @ X0 ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f239]) ).
thf(f239,plain,
( ! [X0: $i] :
( ( $true
!= ( cP_5 @ b @ X0 ) )
| ( $true != $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f222,f26]) ).
thf(f26,plain,
( ( cP_4 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f222,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_4 @ b @ X0 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(subsumption_resolution,[status(thm)],[f211,f30]) ).
thf(f30,plain,
( ( cP_2 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f211,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_4 @ b @ X0 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ b @ b )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f206]) ).
thf(f206,plain,
( ! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP_2 @ b @ b )
!= $true )
| ( ( cP_4 @ b @ X0 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f203,f16]) ).
thf(f16,plain,
( ( cP_3 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f203,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ X2 @ X3 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ X3 @ X0 ) )
| ( ( cP_2 @ b @ X2 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f202]) ).
thf(f202,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ X2 @ X3 ) )
| ( $true != $true )
| ( ( cP_2 @ b @ X2 )
!= $true )
| ( $true
!= ( cP_4 @ X3 @ X0 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f201,f36]) ).
thf(f36,plain,
( ( cP_1 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f201,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_1 @ b @ X2 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ X3 @ X4 ) )
| ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( ( cP_4 @ X4 @ X0 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f200]) ).
thf(f200,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_1 @ b @ X2 ) )
| ( $true
!= ( cP_3 @ X3 @ X4 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( $true != $true )
| ( ( cP_4 @ X4 @ X0 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f199,f19]) ).
thf(f19,plain,
! [X22: $i,X23: $i] :
( ( $true
= ( cP_5 @ ( f @ X22 ) @ X23 ) )
| ( ( cP_5 @ X22 @ X23 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f199,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_5 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( $true
!= ( cP_3 @ X1 @ X4 ) )
| ( $true
!= ( cP_4 @ X4 @ X2 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f198]) ).
thf(f198,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ X1 @ X4 ) )
| ( $true != $true )
| ( $true
!= ( cP_4 @ X4 @ X2 ) )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X2 ) @ X3 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f197,f25]) ).
thf(f25,plain,
! [X18: $i,X19: $i] :
( ( $true
= ( cP_2 @ ( f @ X19 ) @ X18 ) )
| ( ( cP_2 @ X19 @ X18 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f197,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_2 @ ( f @ X2 ) @ X0 )
!= $true )
| ( $true
!= ( cP_1 @ b @ X2 ) )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ X1 @ X3 ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f196]) ).
thf(f196,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_1 @ b @ X2 ) )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( $true
!= ( cP_4 @ X1 @ X3 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ ( f @ X2 ) @ X0 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f195,f33]) ).
thf(f33,plain,
! [X10: $i,X9: $i] :
( ( ( cP_3 @ ( f @ X10 ) @ X9 )
= $true )
| ( ( cP_3 @ X10 @ X9 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f195,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_3 @ ( f @ X3 ) @ X0 ) )
| ( $true
!= ( cP_1 @ b @ X2 ) )
| ( ( cP_5 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f194]) ).
thf(f194,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_3 @ ( f @ X3 ) @ X0 ) )
| ( $true
!= ( cP_1 @ b @ X2 ) )
| ( $true != $true )
| ( ( cP_5 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f193,f10]) ).
thf(f10,plain,
! [X40: $i,X39: $i] :
( ( ( cP_4 @ ( f @ X39 ) @ X40 )
= $true )
| ( $true
!= ( cP_4 @ X39 @ X40 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f193,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_4 @ ( f @ X3 ) @ X1 ) )
| ( ( cP_2 @ ( f @ X0 ) @ X4 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( ( cP_3 @ ( f @ X4 ) @ X3 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X1 ) @ X2 ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f192]) ).
thf(f192,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_1 @ b @ X0 )
!= $true )
| ( ( cP_3 @ ( f @ X4 ) @ X3 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ ( f @ X0 ) @ X4 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X1 ) @ X2 ) )
| ( $true
!= ( cP_4 @ ( f @ X3 ) @ X1 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f53,f23]) ).
thf(f23,plain,
! [X21: $i,X20: $i] :
( ( $true
= ( cP_1 @ ( f @ X21 ) @ X20 ) )
| ( $true
!= ( cP_1 @ X21 @ X20 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f53,plain,
( ! [X2: $i,X0: $i,X11: $i,X1: $i,X6: $i] :
( ( $true
!= ( cP_1 @ ( f @ b ) @ X2 ) )
| ( $true
!= ( cP_5 @ ( f @ X1 ) @ X11 ) )
| ( ( cP_4 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X6 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X6 ) @ X0 ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f191,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[status(thm)],[f190]) ).
thf(f190,plain,
( $false
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f189]) ).
thf(f189,plain,
( ( $true != $true )
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f131,f34]) ).
thf(f34,plain,
( ( cP_5 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f131,plain,
( ! [X0: $i] :
( $true
!= ( cP_5 @ a @ X0 ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f130]) ).
thf(f130,definition,
( spl0_13
<=> ! [X0: $i] :
( $true
!= ( cP_5 @ a @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f188,plain,
( spl0_13
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f187,f90,f130]) ).
thf(f90,definition,
( spl0_6
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ a @ X2 ) )
| ( $true
!= ( cP_4 @ X2 @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f187,plain,
( ! [X0: $i] :
( $true
!= ( cP_5 @ a @ X0 ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f186]) ).
thf(f186,plain,
( ! [X0: $i] :
( ( $true
!= ( cP_5 @ a @ X0 ) )
| ( $true != $true ) )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f185,f21]) ).
thf(f21,plain,
( ( cP_4 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f185,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_4 @ a @ X0 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f184]) ).
thf(f184,plain,
( ! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ a @ X0 )
!= $true ) )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f91,f18]) ).
thf(f18,plain,
( ( cP_3 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f91,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ a @ X2 ) )
| ( $true
!= ( cP_4 @ X2 @ X0 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f183,plain,
( spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f182,f58,f90]) ).
thf(f58,definition,
( spl0_3
<=> ! [X13: $i,X14: $i,X12: $i,X3: $i,X7: $i] :
( ( $true
!= ( cP_1 @ ( f @ a ) @ X3 ) )
| ( ( cP_2 @ ( f @ X3 ) @ X7 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X12 ) @ X13 ) )
| ( $true
!= ( cP_3 @ ( f @ X7 ) @ X14 ) )
| ( $true
!= ( cP_4 @ ( f @ X14 ) @ X12 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f182,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_5 @ X1 @ X2 )
!= $true )
| ( ( cP_3 @ a @ X0 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f159,f20]) ).
thf(f20,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f159,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ a @ a )
!= $true )
| ( ( cP_5 @ X1 @ X2 )
!= $true )
| ( ( cP_3 @ a @ X0 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f157]) ).
thf(f157,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ a @ X0 )
!= $true )
| ( ( cP_5 @ X1 @ X2 )
!= $true )
| ( ( cP_1 @ a @ a )
!= $true )
| ( $true != $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f153,f28]) ).
thf(f28,plain,
( ( cP_2 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f153,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( $true
!= ( cP_3 @ X3 @ X4 ) )
| ( ( cP_1 @ a @ X2 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ X4 @ X0 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f152]) ).
thf(f152,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_3 @ X3 @ X4 ) )
| ( $true != $true )
| ( ( cP_4 @ X4 @ X0 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ a @ X2 )
!= $true )
| ( $true
!= ( cP_2 @ X2 @ X3 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f151,f19]) ).
thf(f151,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_5 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X0 ) )
| ( $true
!= ( cP_3 @ X1 @ X4 ) )
| ( $true
!= ( cP_4 @ X4 @ X2 ) ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true != $true )
| ( $true
!= ( cP_1 @ a @ X0 ) )
| ( $true
!= ( cP_4 @ X4 @ X2 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ X1 @ X4 ) )
| ( $true
!= ( cP_5 @ ( f @ X2 ) @ X3 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f149,f25]) ).
thf(f149,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_2 @ ( f @ X4 ) @ X0 ) )
| ( ( cP_1 @ a @ X4 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ X1 @ X2 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f148]) ).
thf(f148,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_4 @ X1 @ X2 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X4 ) @ X0 ) )
| ( $true
!= ( cP_5 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_1 @ a @ X4 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true != $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f147,f33]) ).
thf(f147,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_3 @ ( f @ X3 ) @ X0 ) )
| ( ( cP_5 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_1 @ a @ X2 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f146]) ).
thf(f146,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_1 @ a @ X2 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X3 ) @ X0 ) )
| ( ( cP_5 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true != $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f145,f10]) ).
thf(f145,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_4 @ ( f @ X4 ) @ X2 ) )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X2 ) @ X3 ) )
| ( $true
!= ( cP_1 @ a @ X0 ) )
| ( ( cP_3 @ ( f @ X1 ) @ X4 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X4 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X0 ) )
| ( $true
!= ( cP_4 @ ( f @ X4 ) @ X2 ) )
| ( $true != $true )
| ( $true
!= ( cP_5 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f59,f23]) ).
thf(f59,plain,
( ! [X3: $i,X7: $i,X14: $i,X12: $i,X13: $i] :
( ( $true
!= ( cP_1 @ ( f @ a ) @ X3 ) )
| ( ( cP_2 @ ( f @ X3 ) @ X7 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X12 ) @ X13 ) )
| ( $true
!= ( cP_4 @ ( f @ X14 ) @ X12 ) )
| ( $true
!= ( cP_3 @ ( f @ X7 ) @ X14 ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f143,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f142]) ).
thf(f142,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f141]) ).
thf(f141,plain,
( ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f116,f22]) ).
thf(f22,plain,
( ( cP_5 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f116,plain,
( ! [X0: $i] :
( $true
!= ( cP_5 @ c @ X0 ) )
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f115,f13]) ).
thf(f13,plain,
( ( cP_3 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f115,plain,
( ! [X0: $i] :
( ( ( cP_3 @ c @ c )
!= $true )
| ( $true
!= ( cP_5 @ c @ X0 ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ! [X0: $i] :
( ( $true
!= ( cP_5 @ c @ X0 ) )
| ( $true != $true )
| ( ( cP_3 @ c @ c )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f97,f24]) ).
thf(f24,plain,
( ( cP_4 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f97,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_4 @ X2 @ X0 ) )
| ( ( cP_3 @ c @ X2 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f78,f29]) ).
thf(f29,plain,
( ( cP_1 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f78,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_4 @ X2 @ X0 ) )
| ( ( cP_1 @ c @ c )
!= $true )
| ( ( cP_3 @ c @ X2 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP_1 @ c @ c )
!= $true )
| ( $true
!= ( cP_4 @ X2 @ X0 ) )
| ( ( cP_3 @ c @ X2 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f70,f35]) ).
thf(f35,plain,
( ( cP_2 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f70,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ X4 @ X0 )
!= $true )
| ( $true
!= ( cP_3 @ X3 @ X4 ) )
| ( ( cP_1 @ c @ X2 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_4 @ X4 @ X0 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( $true
!= ( cP_3 @ X3 @ X4 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ c @ X2 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f68,f19]) ).
thf(f68,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_5 @ ( f @ X1 ) @ X4 )
!= $true )
| ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( $true
!= ( cP_3 @ X3 @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ c @ X2 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( $true != $true )
| ( $true
!= ( cP_3 @ X3 @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ c @ X2 )
!= $true )
| ( ( cP_5 @ ( f @ X1 ) @ X4 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f66,f10]) ).
thf(f66,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_4 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ c @ X0 )
!= $true )
| ( ( cP_3 @ X1 @ X2 )
!= $true )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_3 @ X1 @ X2 )
!= $true )
| ( $true != $true )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_1 @ c @ X0 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X2 ) @ X3 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f64,f25]) ).
thf(f64,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_2 @ ( f @ X4 ) @ X0 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X1 ) @ X2 ) )
| ( $true
!= ( cP_1 @ c @ X4 ) )
| ( $true
!= ( cP_5 @ ( f @ X2 ) @ X3 ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_1 @ c @ X4 ) )
| ( $true != $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X2 ) @ X3 ) )
| ( $true
!= ( cP_2 @ ( f @ X4 ) @ X0 ) )
| ( $true
!= ( cP_4 @ ( f @ X1 ) @ X2 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f62,f33]) ).
thf(f62,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_3 @ ( f @ X1 ) @ X2 ) )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_1 @ c @ X0 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X2 ) @ X3 ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_1 @ c @ X0 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_3 @ ( f @ X1 ) @ X2 ) )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X2 ) @ X3 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f56,f23]) ).
thf(f56,plain,
( ! [X10: $i,X8: $i,X9: $i,X4: $i,X5: $i] :
( ( ( cP_1 @ ( f @ c ) @ X10 )
!= $true )
| ( ( cP_2 @ ( f @ X10 ) @ X9 )
!= $true )
| ( ( cP_4 @ ( f @ X8 ) @ X4 )
!= $true )
| ( ( cP_5 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_3 @ ( f @ X9 ) @ X8 )
!= $true ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl0_2
<=> ! [X4: $i,X9: $i,X10: $i,X5: $i,X8: $i] :
( ( ( cP_5 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_1 @ ( f @ c ) @ X10 )
!= $true )
| ( ( cP_2 @ ( f @ X10 ) @ X9 )
!= $true )
| ( ( cP_3 @ ( f @ X9 ) @ X8 )
!= $true )
| ( ( cP_4 @ ( f @ X8 ) @ X4 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f60,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f50,f58,f55,f52]) ).
thf(f50,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] :
( ( ( cP_5 @ ( f @ X4 ) @ X5 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ b ) @ X2 ) )
| ( $true
!= ( cP_1 @ ( f @ a ) @ X3 ) )
| ( ( cP_4 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X6 ) @ X0 ) )
| ( $true
!= ( cP_5 @ ( f @ X12 ) @ X13 ) )
| ( $true
!= ( cP_4 @ ( f @ X14 ) @ X12 ) )
| ( $true
!= ( cP_5 @ ( f @ X1 ) @ X11 ) )
| ( ( cP_3 @ ( f @ X9 ) @ X8 )
!= $true )
| ( ( cP_2 @ ( f @ X10 ) @ X9 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X7 ) @ X14 ) )
| ( ( cP_2 @ ( f @ X3 ) @ X7 )
!= $true )
| ( ( cP_4 @ ( f @ X8 ) @ X4 )
!= $true )
| ( ( cP_1 @ ( f @ c ) @ X10 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X6 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,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 != $true )
| ( ( cP_4 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ a ) @ X3 ) )
| ( ( cP_4 @ ( f @ X8 ) @ X4 )
!= $true )
| ( ( cP_5 @ ( f @ X4 ) @ X5 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X6 ) @ X0 ) )
| ( ( cP_2 @ ( f @ X2 ) @ X6 )
!= $true )
| ( ( cP_1 @ ( f @ c ) @ X10 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ b ) @ X2 ) )
| ( $true
!= ( cP_5 @ ( f @ X1 ) @ X11 ) )
| ( ( cP_2 @ ( f @ X10 ) @ X9 )
!= $true )
| ( ( cP_3 @ ( f @ X9 ) @ X8 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X12 ) @ X13 ) )
| ( $true
!= ( cP_4 @ ( f @ X14 ) @ X12 ) )
| ( $true
!= ( cP_3 @ ( f @ X7 ) @ X14 ) )
| ( ( cP_2 @ ( f @ X3 ) @ X7 )
!= $true ) ),
inference(superposition,[status(thm)],[f48,f31]) ).
thf(f31,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f48,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] :
( ( $true
!= ( cQ_1 @ X15 @ X16 @ X17 ) )
| ( $true
!= ( cP_4 @ ( f @ X13 ) @ X11 ) )
| ( $true
!= ( cP_1 @ ( f @ X16 ) @ X1 ) )
| ( $true
!= ( cP_1 @ ( f @ X15 ) @ X0 ) )
| ( ( cP_5 @ ( f @ X8 ) @ X9 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X14 ) @ X13 ) )
| ( $true
!= ( cP_2 @ ( f @ X0 ) @ X10 ) )
| ( ( cP_4 @ ( f @ X4 ) @ X8 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X3 ) @ X4 ) )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_5 @ ( f @ X11 ) @ X12 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X1 ) @ X14 ) )
| ( ( cP_5 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_3 @ ( f @ X10 ) @ X7 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X17 ) @ X2 ) )
| ( ( cP_4 @ ( f @ X7 ) @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X16: $i,X14: $i,X4: $i,X17: $i,X15: $i,X5: $i,X12: $i,X13: $i] :
( ( $true
!= ( cP_1 @ ( f @ X15 ) @ X0 ) )
| ( $true
!= ( cP_1 @ ( f @ X17 ) @ X2 ) )
| ( $true
!= ( cP_2 @ ( f @ X0 ) @ X10 ) )
| ( ( cP_5 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_4 @ ( f @ X7 ) @ X5 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X13 ) @ X11 ) )
| ( $true
!= ( cQ_1 @ X15 @ X16 @ X17 ) )
| ( ( cP_5 @ ( f @ X11 ) @ X12 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X14 ) @ X13 ) )
| ( ( cP_5 @ ( f @ X8 ) @ X9 )
!= $true )
| ( ( cP_4 @ ( f @ X4 ) @ X8 )
!= $true )
| ( $true != $true )
| ( ( cP_3 @ ( f @ X10 ) @ X7 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X16 ) @ X1 ) )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X3 ) @ X4 ) )
| ( $true
!= ( cP_2 @ ( f @ X1 ) @ X14 ) ) ),
inference(superposition,[status(thm)],[f46,f14]) ).
thf(f14,plain,
! [X31: $i,X36: $i,X34: $i,X35: $i,X32: $i,X33: $i] :
( ( ( cQ_2 @ X33 @ X32 @ X31 )
= $true )
| ( ( cP_1 @ ( f @ X35 ) @ X33 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X34 ) @ X32 ) )
| ( ( cQ_1 @ X35 @ X34 @ X36 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X36 ) @ X31 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f46,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_2 @ X13 @ X14 @ X12 ) )
| ( $true
!= ( cP_3 @ ( f @ X2 ) @ X9 ) )
| ( ( cP_5 @ ( f @ X10 ) @ X11 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X8 ) @ X10 ) )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X13 ) @ X0 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X9 ) @ X3 ) )
| ( ( cP_5 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_4 @ ( f @ X7 ) @ X5 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X12 ) @ X2 ) )
| ( ( cP_3 @ ( f @ X1 ) @ X7 )
!= $true )
| ( ( cP_2 @ ( f @ X14 ) @ X1 )
!= $true )
| ( ( cP_3 @ ( f @ X0 ) @ X8 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,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] :
( ( ( cP_2 @ ( f @ X14 ) @ X1 )
!= $true )
| ( ( cP_5 @ ( f @ X10 ) @ X11 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X2 ) @ X9 ) )
| ( $true
!= ( cP_4 @ ( f @ X8 ) @ X10 ) )
| ( $true != $true )
| ( $true
!= ( cP_2 @ ( f @ X12 ) @ X2 ) )
| ( ( cP_5 @ ( f @ X5 ) @ X6 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X9 ) @ X3 ) )
| ( ( cP_2 @ ( f @ X13 ) @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X7 ) @ X5 )
!= $true )
| ( $true
!= ( cQ_2 @ X13 @ X14 @ X12 ) )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X7 )
!= $true )
| ( ( cP_3 @ ( f @ X0 ) @ X8 )
!= $true ) ),
inference(superposition,[status(thm)],[f44,f37]) ).
thf(f37,plain,
! [X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( cQ_3 @ X5 @ X8 @ X6 ) )
| ( ( cP_2 @ ( f @ X3 ) @ X6 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X7 ) @ X5 ) )
| ( ( cP_2 @ ( f @ X4 ) @ X8 )
!= $true )
| ( ( cQ_2 @ X7 @ X4 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f44,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] :
( ( ( cQ_3 @ X10 @ X9 @ X11 )
!= $true )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_5 @ ( f @ X5 ) @ X8 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X5 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X10 ) @ X0 ) )
| ( ( cP_3 @ ( f @ X11 ) @ X2 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_4 @ ( f @ X0 ) @ X6 )
!= $true )
| ( ( cP_3 @ ( f @ X9 ) @ X1 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X6 ) @ X7 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,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 != $true )
| ( ( cQ_3 @ X10 @ X9 @ X11 )
!= $true )
| ( ( cP_5 @ ( f @ X5 ) @ X8 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X5 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_3 @ ( f @ X9 ) @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X0 ) @ X6 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X10 ) @ X0 ) )
| ( $true
!= ( cP_5 @ ( f @ X6 ) @ X7 ) )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_3 @ ( f @ X11 ) @ X2 )
!= $true ) ),
inference(superposition,[status(thm)],[f42,f8]) ).
thf(f8,plain,
! [X46: $i,X47: $i,X44: $i,X45: $i,X42: $i,X43: $i] :
( ( ( cQ_4 @ X45 @ X46 @ X42 )
= $true )
| ( ( cP_3 @ ( f @ X44 ) @ X46 )
!= $true )
| ( ( cQ_3 @ X43 @ X44 @ X47 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X47 ) @ X42 ) )
| ( $true
!= ( cP_3 @ ( f @ X43 ) @ X45 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cQ_4 @ X6 @ X7 @ X8 )
!= $true )
| ( ( cP_5 @ ( f @ X2 ) @ X4 )
!= $true )
| ( ( cP_4 @ ( f @ X8 ) @ X2 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X7 ) @ X1 ) )
| ( ( cP_5 @ ( f @ X0 ) @ X3 )
!= $true )
| ( ( cP_5 @ ( f @ X1 ) @ X5 )
!= $true )
| ( ( cP_4 @ ( f @ X6 ) @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cQ_4 @ X6 @ X7 @ X8 )
!= $true )
| ( ( cP_5 @ ( f @ X0 ) @ X3 )
!= $true )
| ( ( cP_5 @ ( f @ X2 ) @ X4 )
!= $true )
| ( ( cP_5 @ ( f @ X1 ) @ X5 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X7 ) @ X1 ) )
| ( $true != $true )
| ( ( cP_4 @ ( f @ X6 ) @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X8 ) @ X2 )
!= $true ) ),
inference(superposition,[status(thm)],[f40,f32]) ).
thf(f32,plain,
! [X11: $i,X16: $i,X14: $i,X15: $i,X12: $i,X13: $i] :
( ( $true
= ( cQ_5 @ X13 @ X15 @ X14 ) )
| ( ( cQ_4 @ X12 @ X11 @ X16 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X11 ) @ X15 ) )
| ( ( cP_4 @ ( f @ X12 ) @ X13 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X16 ) @ X14 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f40,plain,
! [X28: $i,X29: $i,X26: $i,X27: $i,X24: $i,X25: $i] :
( ( ( cQ_5 @ X27 @ X25 @ X24 )
!= $true )
| ( ( cP_5 @ ( f @ X27 ) @ X28 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X24 ) @ X29 ) )
| ( ( cP_5 @ ( f @ X25 ) @ X26 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f17,f38]) ).
thf(f38,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( cQ_6 @ X0 @ X2 @ X1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f17,plain,
! [X28: $i,X29: $i,X26: $i,X27: $i,X24: $i,X25: $i] :
( ( ( cQ_5 @ X27 @ X25 @ X24 )
!= $true )
| ( ( cP_5 @ ( f @ X25 ) @ X26 )
!= $true )
| ( ( cP_5 @ ( f @ X27 ) @ X28 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X24 ) @ X29 ) )
| ( $true
= ( cQ_6 @ X28 @ X26 @ X29 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO388^5 : 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 : n020.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 14:29:57 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
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SYO388^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.47 % Domain : Syntactic
% 0.28/0.47 % Problem : TPS problem THM409-5
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Bro09]
% 0.28/0.47 % Names : tps_0579 [Bro09]
% 0.28/0.47 % : THM409-5 [TPS]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % 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
% 0.28/0.47 % Syntax : Number of formulae : 17 ( 0 unt; 16 typ; 0 def)
% 0.28/0.47 % Number of atoms : 57 ( 0 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 57 ( 57 avg)
% 0.28/0.47 % Number of connectives : 229 ( 27 ~; 25 |; 31 &; 146 @)
% 0.28/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 47 ( 47 avg)
% 0.28/0.47 % Number of types : 2 ( 0 usr)
% 0.28/0.47 % Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 16 ( 16 usr; 4 con; 0-3 aty)
% 0.28/0.47 % Number of variables : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% 0.28/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(cQ_6,type,
% 0.28/0.47 cQ_6: $i > $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(f,type,
% 0.28/0.47 f: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(cP_5,type,
% 0.28/0.47 cP_5: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cQ_5,type,
% 0.28/0.47 cQ_5: $i > $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(d,type,
% 0.28/0.47 d: $i ).
% 0.28/0.47
% 0.28/0.47 thf(c,type,
% 0.28/0.47 c: $i ).
% 0.28/0.47
% 0.28/0.47 thf(b,type,
% 0.28/0.47 b: $i ).
% 0.28/0.47
% 0.28/0.47 thf(a,type,
% 0.28/0.47 a: $i ).
% 0.28/0.47
% 0.28/0.47 thf(cP_4,type,
% 0.28/0.47 cP_4: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cQ_4,type,
% 0.28/0.47 cQ_4: $i > $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cP_3,type,
% 0.28/0.47 cP_3: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cQ_3,type,
% 0.28/0.47 cQ_3: $i > $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cP_2,type,
% 0.28/0.47 cP_2: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cQ_2,type,
% 0.28/0.47 cQ_2: $i > $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cP_1,type,
% 0.28/0.47 cP_1: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cQ_1,type,
% 0.28/0.47 cQ_1: $i > $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cTHM409_5,conjecture,
% 0.28/0.47 ~ ( ( cQ_1 @ a @ b @ c )
% 0.28/0.47 & ( cP_1 @ a @ a )
% 0.28/0.47 & ( cP_1 @ b @ b )
% 0.28/0.47 & ( cP_1 @ c @ c )
% 0.28/0.47 & ! [Xx: $i] : ( cP_1 @ d @ Xx )
% 0.28/0.47 & ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ~ ( cP_1 @ Xx @ Xy )
% 0.28/0.47 | ( cP_1 @ ( f @ Xx ) @ Xy ) )
% 0.28/0.47 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.28/0.47 ( ~ ( cQ_1 @ Xx @ Xy @ Xz )
% 0.28/0.47 | ~ ( cP_1 @ ( f @ Xx ) @ Xu )
% 0.28/0.47 | ~ ( cP_1 @ ( f @ Xy ) @ Xv )
% 0.28/0.47 | ~ ( cP_1 @ ( f @ Xz ) @ Xw )
% 0.28/0.47 | ( cQ_2 @ Xu @ Xv @ Xw ) )
% 0.28/0.47 & ( cP_2 @ a @ a )
% 0.28/0.47 & ( cP_2 @ b @ b )
% 0.28/0.47 & ( cP_2 @ c @ c )
% 0.28/0.47 & ! [Xx: $i] : ( cP_2 @ d @ Xx )
% 0.28/0.47 & ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ~ ( cP_2 @ Xx @ Xy )
% 0.28/0.47 | ( cP_2 @ ( f @ Xx ) @ Xy ) )
% 0.28/0.47 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.28/0.47 ( ~ ( cQ_2 @ Xx @ Xy @ Xz )
% 0.28/0.47 | ~ ( cP_2 @ ( f @ Xx ) @ Xu )
% 0.28/0.47 | ~ ( cP_2 @ ( f @ Xy ) @ Xv )
% 0.28/0.47 | ~ ( cP_2 @ ( f @ Xz ) @ Xw )
% 0.28/0.47 | ( cQ_3 @ Xu @ Xv @ Xw ) )
% 0.28/0.47 & ( cP_3 @ a @ a )
% 0.28/0.47 & ( cP_3 @ b @ b )
% 0.28/0.47 & ( cP_3 @ c @ c )
% 0.28/0.47 & ! [Xx: $i] : ( cP_3 @ d @ Xx )
% 0.28/0.47 & ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ~ ( cP_3 @ Xx @ Xy )
% 0.28/0.47 | ( cP_3 @ ( f @ Xx ) @ Xy ) )
% 0.28/0.47 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.28/0.47 ( ~ ( cQ_3 @ Xx @ Xy @ Xz )
% 0.28/0.47 | ~ ( cP_3 @ ( f @ Xx ) @ Xu )
% 0.28/0.47 | ~ ( cP_3 @ ( f @ Xy ) @ Xv )
% 0.28/0.47 | ~ ( cP_3 @ ( f @ Xz ) @ Xw )
% 0.28/0.47 | ( cQ_4 @ Xu @ Xv @ Xw ) )
% 0.28/0.47 & ( cP_4 @ a @ a )
% 0.28/0.47 & ( cP_4 @ b @ b )
% 0.28/0.47 & ( cP_4 @ c @ c )
% 0.28/0.47 & ! [Xx: $i] : ( cP_4 @ d @ Xx )
% 0.28/0.47 & ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ~ ( cP_4 @ Xx @ Xy )
% 0.28/0.47 | ( cP_4 @ ( f @ Xx ) @ Xy ) )
% 0.28/0.47 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.28/0.47 ( ~ ( cQ_4 @ Xx @ Xy @ Xz )
% 0.28/0.47 | ~ ( cP_4 @ ( f @ Xx ) @ Xu )
% 0.28/0.47 | ~ ( cP_4 @ ( f @ Xy ) @ Xv )
% 0.28/0.47 | ~ ( cP_4 @ ( f @ Xz ) @ Xw )
% 0.28/0.47 | ( cQ_5 @ Xu @ Xv @ Xw ) )
% 0.28/0.47 & ( cP_5 @ a @ a )
% 0.28/0.47 & ( cP_5 @ b @ b )
% 0.28/0.47 & ( cP_5 @ c @ c )
% 0.28/0.47 & ! [Xx: $i] : ( cP_5 @ d @ Xx )
% 0.28/0.47 & ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ~ ( cP_5 @ Xx @ Xy )
% 0.28/0.47 | ( cP_5 @ ( f @ Xx ) @ Xy ) )
% 0.28/0.47 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.28/0.47 ( ~ ( cQ_5 @ Xx @ Xy @ Xz )
% 0.28/0.47 | ~ ( cP_5 @ ( f @ Xx ) @ Xu )
% 0.28/0.47 | ~ ( cP_5 @ ( f @ Xy ) @ Xv )
% 0.28/0.47 | ~ ( cP_5 @ ( f @ Xz ) @ Xw )
% 0.28/0.47 | ( cQ_6 @ Xu @ Xv @ Xw ) )
% 0.28/0.47 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ~ ( cQ_6 @ Xx @ Xy @ Xz ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.72/1.32 ---- Embedded in THF ---
% 1.72/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.72/1.33 %%% Generated on Tue Feb 24 14:29:58 EST 2026
% 1.72/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.72/1.33 %%% Logic specification used:
% 1.72/1.33 %%% thf(spec, logic, $$dhol).
% 1.72/1.33
% 1.72/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.4KjW3duxkU/DTF2DTF13451.p
% See solution above
% 1.72/1.33 ------------------------
% 1.72/1.34 ---- Cleaned THF ---
% 1.72/1.34 thf(cQ_6,type,
% 1.72/1.34 cQ_6: $i > $i > $i > $o ).
% 1.72/1.34
% 1.72/1.34 thf(f,type,
% 1.72/1.34 f: $i > $i ).
% 1.72/1.34
% 1.72/1.34 thf(cP_5,type,
% 1.72/1.34 cP_5: $i > $i > $o ).
% 1.72/1.34
% 1.72/1.34 thf(cQ_5,type,
% 1.72/1.34 cQ_5: $i > $i > $i > $o ).
% 1.72/1.34
% 1.72/1.34 thf(d,type,
% 1.72/1.34 d: $i ).
% 1.72/1.34
% 1.72/1.34 thf(c,type,
% 1.72/1.34 c: $i ).
% 1.72/1.34
% 1.72/1.34 thf(b,type,
% 1.72/1.34 b: $i ).
% 1.72/1.34
% 1.72/1.34 thf(a,type,
% 1.72/1.34 a: $i ).
% 1.72/1.34
% 1.72/1.34 thf(cP_4,type,
% 1.72/1.34 cP_4: $i > $i > $o ).
% 1.72/1.34
% 1.72/1.34 thf(cQ_4,type,
% 1.72/1.34 cQ_4: $i > $i > $i > $o ).
% 1.72/1.34
% 1.72/1.34 thf(cP_3,type,
% 1.72/1.34 cP_3: $i > $i > $o ).
% 1.72/1.34
% 1.72/1.34 thf(cQ_3,type,
% 1.72/1.34 cQ_3: $i > $i > $i > $o ).
% 1.72/1.34
% 1.72/1.34 thf(cP_2,type,
% 1.72/1.34 cP_2: $i > $i > $o ).
% 1.72/1.34
% 1.72/1.34 thf(cQ_2,type,
% 1.72/1.34 cQ_2: $i > $i > $i > $o ).
% 1.72/1.34
% 1.72/1.34 thf(cP_1,type,
% 1.72/1.34 cP_1: $i > $i > $o ).
% 1.72/1.34
% 1.72/1.34 thf(cQ_1,type,
% 1.72/1.34 cQ_1: $i > $i > $i > $o ).
% 1.72/1.34
% 1.72/1.34 thf(cTHM409_5,conjecture,
% 1.72/1.34 ~ ( ( cQ_1 @ a @ b @ c )
% 1.72/1.34 & ( cP_1 @ a @ a )
% 1.72/1.34 & ( cP_1 @ b @ b )
% 1.72/1.34 & ( cP_1 @ c @ c )
% 1.72/1.34 & ! [Xx: $i] : ( cP_1 @ d @ Xx )
% 1.72/1.34 & ! [Xx: $i,Xy: $i] :
% 1.72/1.34 ( ~ ( cP_1 @ Xx @ Xy )
% 1.72/1.34 | ( cP_1 @ ( f @ Xx ) @ Xy ) )
% 1.72/1.34 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.72/1.34 ( ~ ( cQ_1 @ Xx @ Xy @ Xz )
% 1.72/1.34 | ~ ( cP_1 @ ( f @ Xx ) @ Xu )
% 1.72/1.34 | ~ ( cP_1 @ ( f @ Xy ) @ Xv )
% 1.72/1.34 | ~ ( cP_1 @ ( f @ Xz ) @ Xw )
% 1.72/1.34 | ( cQ_2 @ Xu @ Xv @ Xw ) )
% 1.72/1.34 & ( cP_2 @ a @ a )
% 1.72/1.34 & ( cP_2 @ b @ b )
% 1.72/1.34 & ( cP_2 @ c @ c )
% 1.72/1.34 & ! [Xx: $i] : ( cP_2 @ d @ Xx )
% 1.72/1.34 & ! [Xx: $i,Xy: $i] :
% 1.72/1.34 ( ~ ( cP_2 @ Xx @ Xy )
% 1.72/1.34 | ( cP_2 @ ( f @ Xx ) @ Xy ) )
% 1.72/1.34 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.72/1.34 ( ~ ( cQ_2 @ Xx @ Xy @ Xz )
% 1.72/1.34 | ~ ( cP_2 @ ( f @ Xx ) @ Xu )
% 1.72/1.34 | ~ ( cP_2 @ ( f @ Xy ) @ Xv )
% 1.72/1.34 | ~ ( cP_2 @ ( f @ Xz ) @ Xw )
% 1.72/1.34 | ( cQ_3 @ Xu @ Xv @ Xw ) )
% 1.72/1.34 & ( cP_3 @ a @ a )
% 1.72/1.34 & ( cP_3 @ b @ b )
% 1.72/1.34 & ( cP_3 @ c @ c )
% 1.72/1.34 & ! [Xx: $i] : ( cP_3 @ d @ Xx )
% 1.72/1.34 & ! [Xx: $i,Xy: $i] :
% 1.72/1.34 ( ~ ( cP_3 @ Xx @ Xy )
% 1.72/1.34 | ( cP_3 @ ( f @ Xx ) @ Xy ) )
% 1.72/1.34 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.72/1.34 ( ~ ( cQ_3 @ Xx @ Xy @ Xz )
% 1.72/1.34 | ~ ( cP_3 @ ( f @ Xx ) @ Xu )
% 1.72/1.34 | ~ ( cP_3 @ ( f @ Xy ) @ Xv )
% 1.72/1.34 | ~ ( cP_3 @ ( f @ Xz ) @ Xw )
% 1.72/1.34 | ( cQ_4 @ Xu @ Xv @ Xw ) )
% 1.72/1.34 & ( cP_4 @ a @ a )
% 1.72/1.34 & ( cP_4 @ b @ b )
% 1.72/1.34 & ( cP_4 @ c @ c )
% 1.72/1.34 & ! [Xx: $i] : ( cP_4 @ d @ Xx )
% 1.72/1.34 & ! [Xx: $i,Xy: $i] :
% 1.72/1.34 ( ~ ( cP_4 @ Xx @ Xy )
% 1.72/1.34 | ( cP_4 @ ( f @ Xx ) @ Xy ) )
% 1.72/1.34 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.72/1.34 ( ~ ( cQ_4 @ Xx @ Xy @ Xz )
% 1.72/1.34 | ~ ( cP_4 @ ( f @ Xx ) @ Xu )
% 1.72/1.34 | ~ ( cP_4 @ ( f @ Xy ) @ Xv )
% 1.72/1.34 | ~ ( cP_4 @ ( f @ Xz ) @ Xw )
% 1.72/1.34 | ( cQ_5 @ Xu @ Xv @ Xw ) )
% 1.72/1.34 & ( cP_5 @ a @ a )
% 1.72/1.34 & ( cP_5 @ b @ b )
% 1.72/1.34 & ( cP_5 @ c @ c )
% 1.72/1.34 & ! [Xx: $i] : ( cP_5 @ d @ Xx )
% 1.72/1.34 & ! [Xx: $i,Xy: $i] :
% 1.72/1.34 ( ~ ( cP_5 @ Xx @ Xy )
% 1.72/1.34 | ( cP_5 @ ( f @ Xx ) @ Xy ) )
% 1.72/1.34 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.72/1.34 ( ~ ( cQ_5 @ Xx @ Xy @ Xz )
% 1.72/1.34 | ~ ( cP_5 @ ( f @ Xx ) @ Xu )
% 1.72/1.34 | ~ ( cP_5 @ ( f @ Xy ) @ Xv )
% 1.72/1.34 | ~ ( cP_5 @ ( f @ Xz ) @ Xw )
% 1.72/1.34 | ( cQ_6 @ Xu @ Xv @ Xw ) )
% 1.72/1.34 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.72/1.34 ~ ( cQ_6 @ Xx @ Xy @ Xz ) ) ).
% 1.72/1.34 ------------------------
% 1.72/1.35 % (13730)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_13451 for (2999ds/275Mi)
% 1.72/1.36 % (13728)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13451 for (2999ds/2Mi)
% 1.72/1.36 % (13728)Instruction limit reached!
% 1.72/1.36 % (13728)------------------------------
% 1.72/1.36 % (13728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.36 % (13728)Termination reason: Unknown
% 1.72/1.36 % (13728)Termination phase: shuffling
% 1.72/1.36
% 1.72/1.36 % (13728)Memory used [KB]: 1023
% 1.72/1.36 % (13728)Time elapsed: 0.002 s
% 1.72/1.36 % (13728)Instructions burned: 3 (million)
% 1.72/1.36 % (13728)------------------------------
% 1.72/1.36 % (13728)------------------------------
% 1.72/1.36 % (13726)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_13451 for (2999ds/4Mi)
% 1.72/1.36 % (13725)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13451 for (2999ds/183Mi)
% 1.72/1.36 % (13727)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_13451 for (2999ds/27Mi)
% 1.72/1.36 % (13729)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_13451 for (2999ds/2Mi)
% 1.72/1.36 % (13731)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13451 for (2999ds/18Mi)
% 1.72/1.36 % (13729)Instruction limit reached!
% 1.72/1.36 % (13729)------------------------------
% 1.72/1.36 % (13729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.36 % (13729)Termination reason: Unknown
% 1.72/1.36 % (13729)Termination phase: shuffling
% 1.72/1.36
% 1.72/1.36 % (13729)Memory used [KB]: 1023
% 1.72/1.36 % (13729)Time elapsed: 0.003 s
% 1.72/1.36 % (13729)Instructions burned: 2 (million)
% 1.72/1.36 % (13729)------------------------------
% 1.72/1.36 % (13729)------------------------------
% 1.72/1.36 % (13726)Instruction limit reached!
% 1.72/1.36 % (13726)------------------------------
% 1.72/1.36 % (13726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.36 % (13726)Termination reason: Unknown
% 1.72/1.36 % (13726)Termination phase: Property scanning
% 1.72/1.36
% 1.72/1.36 % (13726)Memory used [KB]: 1023
% 1.72/1.36 % (13726)Time elapsed: 0.004 s
% 1.72/1.36 % (13726)Instructions burned: 4 (million)
% 1.72/1.36 % (13726)------------------------------
% 1.72/1.36 % (13726)------------------------------
% 1.72/1.37 % (13732)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13451 for (2999ds/3Mi)
% 1.72/1.37 % (13732)Instruction limit reached!
% 1.72/1.37 % (13732)------------------------------
% 1.72/1.37 % (13732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.37 % (13732)Termination reason: Unknown
% 1.72/1.37 % (13732)Termination phase: Preprocessing 3
% 1.72/1.37
% 1.72/1.37 % (13732)Memory used [KB]: 1023
% 1.72/1.37 % (13732)Time elapsed: 0.003 s
% 1.72/1.37 % (13732)Instructions burned: 4 (million)
% 1.72/1.37 % (13732)------------------------------
% 1.72/1.37 % (13732)------------------------------
% 1.72/1.37 % (13730)First to succeed.
% 1.72/1.37 % (13731)Instruction limit reached!
% 1.72/1.37 % (13731)------------------------------
% 1.72/1.37 % (13731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.37 % (13731)Termination reason: Unknown
% 1.72/1.37 % (13731)Termination phase: Saturation
% 1.72/1.37
% 1.72/1.37 % (13731)Memory used [KB]: 5628
% 1.72/1.37 % (13731)Time elapsed: 0.014 s
% 1.72/1.37 % (13731)Instructions burned: 19 (million)
% 1.72/1.37 % (13731)------------------------------
% 1.72/1.37 % (13731)------------------------------
% 1.72/1.38 % (13735)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_13451 for (2999ds/3Mi)
% 1.72/1.38 % (13730)Refutation found. Thanks to Tanya!
% 1.72/1.38 % SZS status Theorem for DTF2THF_13451
% 1.72/1.38 % SZS output start Proof for DTF2THF_13451
% 1.72/1.38 thf(func_def_0, type, cQ_6: $i > $i > $i > $o).
% 1.72/1.38 thf(func_def_1, type, f: $i > $i).
% 1.72/1.38 thf(func_def_2, type, cP_5: $i > $i > $o).
% 1.72/1.38 thf(func_def_3, type, cQ_5: $i > $i > $i > $o).
% 1.72/1.38 thf(func_def_8, type, cP_4: $i > $i > $o).
% 1.72/1.38 thf(func_def_9, type, cQ_4: $i > $i > $i > $o).
% 1.72/1.38 thf(func_def_10, type, cP_3: $i > $i > $o).
% 1.72/1.38 thf(func_def_11, type, cQ_3: $i > $i > $i > $o).
% 1.72/1.38 thf(func_def_12, type, cP_2: $i > $i > $o).
% 1.72/1.38 thf(func_def_13, type, cQ_2: $i > $i > $i > $o).
% 1.72/1.38 thf(func_def_14, type, cP_1: $i > $i > $o).
% 1.72/1.38 thf(func_def_15, type, cQ_1: $i > $i > $i > $o).
% 1.72/1.38 thf(f245,plain,(
% 1.72/1.38 $false),
% 1.72/1.38 inference(avatar_sat_refutation,[status(thm)],[f60,f143,f183,f188,f191,f241,f244])).
% 1.72/1.38 thf(f244,plain,(
% 1.72/1.38 ~spl0_11),
% 1.72/1.38 inference(avatar_contradiction_clause,[status(thm)],[f243])).
% 1.72/1.38 thf(f243,plain,(
% 1.72/1.38 $false | ~spl0_11),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f242])).
% 1.72/1.38 thf(f242,plain,(
% 1.72/1.38 ($true != $true) | ~spl0_11),
% 1.72/1.38 inference(superposition,[status(thm)],[f123,f39])).
% 1.72/1.38 thf(f39,plain,(
% 1.72/1.38 ((cP_5 @ b @ b) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f7,plain,(
% 1.72/1.38 ((cP_5 @ b @ b) = $true) & ! [X0 : $i,X1 : $i,X2 : $i] : ((cQ_6 @ X0 @ X2 @ X1) != $true) & ! [X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i] : (($true = (cQ_3 @ X5 @ X8 @ X6)) | ((cP_2 @ (f @ X3) @ X6) != $true) | ((cQ_2 @ X7 @ X4 @ X3) != $true) | ($true != (cP_2 @ (f @ X7) @ X5)) | ((cP_2 @ (f @ X4) @ X8) != $true)) & ((cP_1 @ b @ b) = $true) & ((cP_2 @ c @ c) = $true) & ((cP_5 @ a @ a) = $true) & ! [X9 : $i,X10 : $i] : (((cP_3 @ (f @ X10) @ X9) = $true) | ((cP_3 @ X10 @ X9) != $true)) & ! [X11 : $i,X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i] : (((cP_4 @ (f @ X12) @ X13) != $true) | ($true = (cQ_5 @ X13 @ X15 @ X14)) | ($true != (cP_4 @ (f @ X16) @ X14)) | ($true != (cP_4 @ (f @ X11) @ X15)) | ((cQ_4 @ X12 @ X11 @ X16) != $true)) & ((cQ_1 @ a @ b @ c) = $true) & ((cP_2 @ b @ b) = $true) & ((cP_1 @ c @ c) = $true) & ((cP_2 @ a @ a) = $true) & ! [X17 : $i] : ($true = (cP_3 @ d @ X17)) & ((cP_4 @ b @ b) = $true) & ! [X18 : $i,X19 : $i] : (($true = (cP_2 @ (f @ X19) @ X18)) | ((cP_2 @ X19 @ X18) != $true)) & ((cP_4 @ c @ c) = $true) & ! [X20 : $i,X21 : $i] : (($true = (cP_1 @ (f @ X21) @ X20)) | ($true != (cP_1 @ X21 @ X20))) & ((cP_5 @ c @ c) = $true) & ((cP_4 @ a @ a) = $true) & ((cP_1 @ a @ a) = $true) & ! [X22 : $i,X23 : $i] : (((cP_5 @ X22 @ X23) != $true) | ($true = (cP_5 @ (f @ X22) @ X23))) & ((cP_3 @ a @ a) = $true) & ! [X24 : $i,X25 : $i,X26 : $i,X27 : $i,X28 : $i,X29 : $i] : (((cQ_5 @ X27 @ X25 @ X24) != $true) | ((cP_5 @ (f @ X27) @ X28) != $true) | ($true = (cQ_6 @ X28 @ X26 @ X29)) | ((cP_5 @ (f @ X25) @ X26) != $true) | ($true != (cP_5 @ (f @ X24) @ X29))) & ((cP_3 @ b @ b) = $true) & ! [X30 : $i] : ((cP_1 @ d @ X30) = $true) & ! [X31 : $i,X32 : $i,X33 : $i,X34 : $i,X35 : $i,X36 : $i] : (((cQ_2 @ X33 @ X32 @ X31) = $true) | ($true != (cP_1 @ (f @ X36) @ X31)) | ($true != (cP_1 @ (f @ X34) @ X32)) | ((cQ_1 @ X35 @ X34 @ X36) != $true) | ((cP_1 @ (f @ X35) @ X33) != $true)) & ((cP_3 @ c @ c) = $true) & ! [X37 : $i] : ($true = (cP_2 @ d @ X37)) & ! [X38 : $i] : ((cP_5 @ d @ X38) = $true) & ! [X39 : $i,X40 : $i] : (($true != (cP_4 @ X39 @ X40)) | ((cP_4 @ (f @ X39) @ X40) = $true)) & ! [X41 : $i] : ($true = (cP_4 @ d @ X41)) & ! [X42 : $i,X43 : $i,X44 : $i,X45 : $i,X46 : $i,X47 : $i] : (($true != (cP_3 @ (f @ X43) @ X45)) | ($true != (cP_3 @ (f @ X47) @ X42)) | ((cQ_4 @ X45 @ X46 @ X42) = $true) | ((cQ_3 @ X43 @ X44 @ X47) != $true) | ((cP_3 @ (f @ X44) @ X46) != $true))),
% 1.72/1.38 inference(rectify,[status(thm)],[f6])).
% 1.72/1.38 thf(f6,plain,(
% 1.72/1.38 ((cP_5 @ b @ b) = $true) & ! [X21 : $i,X20 : $i,X22 : $i] : ((cQ_6 @ X21 @ X22 @ X20) != $true) & ! [X45 : $i,X43 : $i,X46 : $i,X42 : $i,X47 : $i,X44 : $i] : (((cQ_3 @ X46 @ X44 @ X42) = $true) | ($true != (cP_2 @ (f @ X45) @ X42)) | ($true != (cQ_2 @ X47 @ X43 @ X45)) | ((cP_2 @ (f @ X47) @ X46) != $true) | ($true != (cP_2 @ (f @ X43) @ X44))) & ((cP_1 @ b @ b) = $true) & ((cP_2 @ c @ c) = $true) & ((cP_5 @ a @ a) = $true) & ! [X9 : $i,X8 : $i] : (((cP_3 @ (f @ X8) @ X9) = $true) | ($true != (cP_3 @ X8 @ X9))) & ! [X23 : $i,X27 : $i,X28 : $i,X26 : $i,X25 : $i,X24 : $i] : (($true != (cP_4 @ (f @ X27) @ X28)) | ((cQ_5 @ X28 @ X25 @ X26) = $true) | ((cP_4 @ (f @ X24) @ X26) != $true) | ((cP_4 @ (f @ X23) @ X25) != $true) | ((cQ_4 @ X27 @ X23 @ X24) != $true)) & ((cQ_1 @ a @ b @ c) = $true) & ((cP_2 @ b @ b) = $true) & ((cP_1 @ c @ c) = $true) & ((cP_2 @ a @ a) = $true) & ! [X18 : $i] : ($true = (cP_3 @ d @ X18)) & ((cP_4 @ b @ b) = $true) & ! [X30 : $i,X29 : $i] : (((cP_2 @ (f @ X29) @ X30) = $true) | ($true != (cP_2 @ X29 @ X30))) & ((cP_4 @ c @ c) = $true) & ! [X38 : $i,X37 : $i] : (($true = (cP_1 @ (f @ X37) @ X38)) | ($true != (cP_1 @ X37 @ X38))) & ((cP_5 @ c @ c) = $true) & ((cP_4 @ a @ a) = $true) & ((cP_1 @ a @ a) = $true) & ! [X17 : $i,X16 : $i] : (((cP_5 @ X17 @ X16) != $true) | ($true = (cP_5 @ (f @ X17) @ X16))) & ((cP_3 @ a @ a) = $true) & ! [X4 : $i,X0 : $i,X5 : $i,X3 : $i,X2 : $i,X1 : $i] : (((cQ_5 @ X3 @ X0 @ X4) != $true) | ($true != (cP_5 @ (f @ X3) @ X2)) | ((cQ_6 @ X2 @ X5 @ X1) = $true) | ((cP_5 @ (f @ X0) @ X5) != $true) | ($true != (cP_5 @ (f @ X4) @ X1))) & ((cP_3 @ b @ b) = $true) & ! [X39 : $i] : ($true = (cP_1 @ d @ X39)) & ! [X11 : $i,X15 : $i,X10 : $i,X14 : $i,X12 : $i,X13 : $i] : (($true = (cQ_2 @ X10 @ X15 @ X11)) | ((cP_1 @ (f @ X13) @ X11) != $true) | ((cP_1 @ (f @ X14) @ X15) != $true) | ($true != (cQ_1 @ X12 @ X14 @ X13)) | ($true != (cP_1 @ (f @ X12) @ X10))) & ((cP_3 @ c @ c) = $true) & ! [X40 : $i] : ((cP_2 @ d @ X40) = $true) & ! [X41 : $i] : ((cP_5 @ d @ X41) = $true) & ! [X6 : $i,X7 : $i] : (($true != (cP_4 @ X6 @ X7)) | ((cP_4 @ (f @ X6) @ X7) = $true)) & ! [X19 : $i] : ((cP_4 @ d @ X19) = $true) & ! [X32 : $i,X33 : $i,X36 : $i,X31 : $i,X35 : $i,X34 : $i] : (((cP_3 @ (f @ X33) @ X31) != $true) | ($true != (cP_3 @ (f @ X34) @ X32)) | ($true = (cQ_4 @ X31 @ X35 @ X32)) | ((cQ_3 @ X33 @ X36 @ X34) != $true) | ((cP_3 @ (f @ X36) @ X35) != $true))),
% 1.72/1.38 inference(flattening,[status(thm)],[f5])).
% 1.72/1.38 thf(f5,plain,(
% 1.72/1.38 ~~(! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : (~((cQ_5 @ X3 @ X0 @ X4) = $true) | ~($true = (cP_5 @ (f @ X3) @ X2)) | ((cQ_6 @ X2 @ X5 @ X1) = $true) | ~((cP_5 @ (f @ X0) @ X5) = $true) | ~($true = (cP_5 @ (f @ X4) @ X1))) & ! [X6 : $i,X7 : $i] : (((cP_4 @ (f @ X6) @ X7) = $true) | ~($true = (cP_4 @ X6 @ X7))) & ((cP_3 @ b @ b) = $true) & ! [X8 : $i,X9 : $i] : (((cP_3 @ (f @ X8) @ X9) = $true) | ~($true = (cP_3 @ X8 @ X9))) & ((cP_1 @ a @ a) = $true) & ! [X10 : $i,X11 : $i,X12 : $i,X13 : $i,X14 : $i,X15 : $i] : (~((cP_1 @ (f @ X14) @ X15) = $true) | ~($true = (cP_1 @ (f @ X12) @ X10)) | ~((cP_1 @ (f @ X13) @ X11) = $true) | ($true = (cQ_2 @ X10 @ X15 @ X11)) | ~($true = (cQ_1 @ X12 @ X14 @ X13))) & ! [X16 : $i,X17 : $i] : (~((cP_5 @ X17 @ X16) = $true) | ($true = (cP_5 @ (f @ X17) @ X16))) & ! [X18 : $i] : ($true = (cP_3 @ d @ X18)) & ((cP_4 @ c @ c) = $true) & ! [X19 : $i] : ((cP_4 @ d @ X19) = $true) & ((cP_5 @ b @ b) = $true) & ! [X20 : $i,X21 : $i,X22 : $i] : ~((cQ_6 @ X21 @ X22 @ X20) = $true) & ! [X23 : $i,X24 : $i,X25 : $i,X26 : $i,X27 : $i,X28 : $i] : (((cQ_5 @ X28 @ X25 @ X26) = $true) | ~((cP_4 @ (f @ X23) @ X25) = $true) | ~((cQ_4 @ X27 @ X23 @ X24) = $true) | ~((cP_4 @ (f @ X24) @ X26) = $true) | ~($true = (cP_4 @ (f @ X27) @ X28))) & ! [X29 : $i,X30 : $i] : (((cP_2 @ (f @ X29) @ X30) = $true) | ~($true = (cP_2 @ X29 @ X30))) & ((cP_4 @ b @ b) = $true) & ((cP_5 @ c @ c) = $true) & ((cP_2 @ c @ c) = $true) & ((cP_1 @ b @ b) = $true) & ((cP_3 @ a @ a) = $true) & ((cP_1 @ c @ c) = $true) & ((cP_3 @ c @ c) = $true) & ! [X31 : $i,X32 : $i,X33 : $i,X34 : $i,X35 : $i,X36 : $i] : (~((cQ_3 @ X33 @ X36 @ X34) = $true) | ~((cP_3 @ (f @ X33) @ X31) = $true) | ~($true = (cP_3 @ (f @ X34) @ X32)) | ($true = (cQ_4 @ X31 @ X35 @ X32)) | ~((cP_3 @ (f @ X36) @ X35) = $true)) & ((cP_2 @ a @ a) = $true) & ((cP_5 @ a @ a) = $true) & ! [X37 : $i,X38 : $i] : (~($true = (cP_1 @ X37 @ X38)) | ($true = (cP_1 @ (f @ X37) @ X38))) & ((cP_2 @ b @ b) = $true) & ! [X39 : $i] : ($true = (cP_1 @ d @ X39)) & ! [X40 : $i] : ((cP_2 @ d @ X40) = $true) & ! [X41 : $i] : ((cP_5 @ d @ X41) = $true) & ! [X42 : $i,X43 : $i,X44 : $i,X45 : $i,X46 : $i,X47 : $i] : (~((cP_2 @ (f @ X47) @ X46) = $true) | ~($true = (cQ_2 @ X47 @ X43 @ X45)) | ~($true = (cP_2 @ (f @ X45) @ X42)) | ((cQ_3 @ X46 @ X44 @ X42) = $true) | ~($true = (cP_2 @ (f @ X43) @ X44))) & ((cP_4 @ a @ a) = $true) & ((cQ_1 @ a @ b @ c) = $true))),
% 1.72/1.38 inference(fool_elimination,[status(thm)],[f4])).
% 1.72/1.38 thf(f4,plain,(
% 1.72/1.38 ~~(! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : (~(cQ_5 @ X3 @ X0 @ X4) | ~(cP_5 @ (f @ X3) @ X2) | (cQ_6 @ X2 @ X5 @ X1) | ~(cP_5 @ (f @ X0) @ X5) | ~(cP_5 @ (f @ X4) @ X1)) & ! [X6 : $i,X7 : $i] : ((cP_4 @ (f @ X6) @ X7) | ~(cP_4 @ X6 @ X7)) & (cP_3 @ b @ b) & ! [X8 : $i,X9 : $i] : ((cP_3 @ (f @ X8) @ X9) | ~(cP_3 @ X8 @ X9)) & (cP_1 @ a @ a) & ! [X10 : $i,X11 : $i,X12 : $i,X13 : $i,X14 : $i,X15 : $i] : (~(cP_1 @ (f @ X14) @ X15) | ~(cP_1 @ (f @ X12) @ X10) | ~(cP_1 @ (f @ X13) @ X11) | (cQ_2 @ X10 @ X15 @ X11) | ~(cQ_1 @ X12 @ X14 @ X13)) & ! [X16 : $i,X17 : $i] : (~(cP_5 @ X17 @ X16) | (cP_5 @ (f @ X17) @ X16)) & ! [X18 : $i] : (cP_3 @ d @ X18) & (cP_4 @ c @ c) & ! [X19 : $i] : (cP_4 @ d @ X19) & (cP_5 @ b @ b) & ! [X20 : $i,X21 : $i,X22 : $i] : ~(cQ_6 @ X21 @ X22 @ X20) & ! [X23 : $i,X24 : $i,X25 : $i,X26 : $i,X27 : $i,X28 : $i] : ((cQ_5 @ X28 @ X25 @ X26) | ~(cP_4 @ (f @ X23) @ X25) | ~(cQ_4 @ X27 @ X23 @ X24) | ~(cP_4 @ (f @ X24) @ X26) | ~(cP_4 @ (f @ X27) @ X28)) & ! [X29 : $i,X30 : $i] : ((cP_2 @ (f @ X29) @ X30) | ~(cP_2 @ X29 @ X30)) & (cP_4 @ b @ b) & (cP_5 @ c @ c) & (cP_2 @ c @ c) & (cP_1 @ b @ b) & (cP_3 @ a @ a) & (cP_1 @ c @ c) & (cP_3 @ c @ c) & ! [X31 : $i,X32 : $i,X33 : $i,X34 : $i,X35 : $i,X36 : $i] : (~(cQ_3 @ X33 @ X36 @ X34) | ~(cP_3 @ (f @ X33) @ X31) | ~(cP_3 @ (f @ X34) @ X32) | (cQ_4 @ X31 @ X35 @ X32) | ~(cP_3 @ (f @ X36) @ X35)) & (cP_2 @ a @ a) & (cP_5 @ a @ a) & ! [X37 : $i,X38 : $i] : (~(cP_1 @ X37 @ X38) | (cP_1 @ (f @ X37) @ X38)) & (cP_2 @ b @ b) & ! [X39 : $i] : (cP_1 @ d @ X39) & ! [X40 : $i] : (cP_2 @ d @ X40) & ! [X41 : $i] : (cP_5 @ d @ X41) & ! [X42 : $i,X43 : $i,X44 : $i,X45 : $i,X46 : $i,X47 : $i] : (~(cP_2 @ (f @ X47) @ X46) | ~(cQ_2 @ X47 @ X43 @ X45) | ~(cP_2 @ (f @ X45) @ X42) | (cQ_3 @ X46 @ X44 @ X42) | ~(cP_2 @ (f @ X43) @ X44)) & (cP_4 @ a @ a) & (cQ_1 @ a @ b @ c))),
% 1.72/1.38 inference(rectify,[status(thm)],[f2])).
% 1.72/1.38 thf(f2,negated_conjecture,(
% 1.72/1.38 ~~(! [X1 : $i,X5 : $i,X3 : $i,X0 : $i,X2 : $i,X4 : $i] : (~(cQ_5 @ X0 @ X1 @ X2) | ~(cP_5 @ (f @ X0) @ X3) | (cQ_6 @ X3 @ X4 @ X5) | ~(cP_5 @ (f @ X1) @ X4) | ~(cP_5 @ (f @ X2) @ X5)) & ! [X0 : $i,X1 : $i] : ((cP_4 @ (f @ X0) @ X1) | ~(cP_4 @ X0 @ X1)) & (cP_3 @ b @ b) & ! [X0 : $i,X1 : $i] : ((cP_3 @ (f @ X0) @ X1) | ~(cP_3 @ X0 @ X1)) & (cP_1 @ a @ a) & ! [X3 : $i,X5 : $i,X0 : $i,X2 : $i,X1 : $i,X4 : $i] : (~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X0) @ X3) | ~(cP_1 @ (f @ X2) @ X5) | (cQ_2 @ X3 @ X4 @ X5) | ~(cQ_1 @ X0 @ X1 @ X2)) & ! [X1 : $i,X0 : $i] : (~(cP_5 @ X0 @ X1) | (cP_5 @ (f @ X0) @ X1)) & ! [X0 : $i] : (cP_3 @ d @ X0) & (cP_4 @ c @ c) & ! [X0 : $i] : (cP_4 @ d @ X0) & (cP_5 @ b @ b) & ! [X2 : $i,X0 : $i,X1 : $i] : ~(cQ_6 @ X0 @ X1 @ X2) & ! [X1 : $i,X2 : $i,X4 : $i,X5 : $i,X0 : $i,X3 : $i] : ((cQ_5 @ X3 @ X4 @ X5) | ~(cP_4 @ (f @ X1) @ X4) | ~(cQ_4 @ X0 @ X1 @ X2) | ~(cP_4 @ (f @ X2) @ X5) | ~(cP_4 @ (f @ X0) @ X3)) & ! [X0 : $i,X1 : $i] : ((cP_2 @ (f @ X0) @ X1) | ~(cP_2 @ X0 @ X1)) & (cP_4 @ b @ b) & (cP_5 @ c @ c) & (cP_2 @ c @ c) & (cP_1 @ b @ b) & (cP_3 @ a @ a) & (cP_1 @ c @ c) & (cP_3 @ c @ c) & ! [X3 : $i,X5 : $i,X0 : $i,X2 : $i,X4 : $i,X1 : $i] : (~(cQ_3 @ X0 @ X1 @ X2) | ~(cP_3 @ (f @ X0) @ X3) | ~(cP_3 @ (f @ X2) @ X5) | (cQ_4 @ X3 @ X4 @ X5) | ~(cP_3 @ (f @ X1) @ X4)) & (cP_2 @ a @ a) & (cP_5 @ a @ a) & ! [X0 : $i,X1 : $i] : (~(cP_1 @ X0 @ X1) | (cP_1 @ (f @ X0) @ X1)) & (cP_2 @ b @ b) & ! [X0 : $i] : (cP_1 @ d @ X0) & ! [X0 : $i] : (cP_2 @ d @ X0) & ! [X0 : $i] : (cP_5 @ d @ X0) & ! [X5 : $i,X1 : $i,X4 : $i,X2 : $i,X3 : $i,X0 : $i] : (~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2) | ~(cP_2 @ (f @ X2) @ X5) | (cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X1) @ X4)) & (cP_4 @ a @ a) & (cQ_1 @ a @ b @ c))),
% 1.72/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 1.72/1.38 thf(f1,conjecture,(
% 1.72/1.38 ~(! [X1 : $i,X5 : $i,X3 : $i,X0 : $i,X2 : $i,X4 : $i] : (~(cQ_5 @ X0 @ X1 @ X2) | ~(cP_5 @ (f @ X0) @ X3) | (cQ_6 @ X3 @ X4 @ X5) | ~(cP_5 @ (f @ X1) @ X4) | ~(cP_5 @ (f @ X2) @ X5)) & ! [X0 : $i,X1 : $i] : ((cP_4 @ (f @ X0) @ X1) | ~(cP_4 @ X0 @ X1)) & (cP_3 @ b @ b) & ! [X0 : $i,X1 : $i] : ((cP_3 @ (f @ X0) @ X1) | ~(cP_3 @ X0 @ X1)) & (cP_1 @ a @ a) & ! [X3 : $i,X5 : $i,X0 : $i,X2 : $i,X1 : $i,X4 : $i] : (~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X0) @ X3) | ~(cP_1 @ (f @ X2) @ X5) | (cQ_2 @ X3 @ X4 @ X5) | ~(cQ_1 @ X0 @ X1 @ X2)) & ! [X1 : $i,X0 : $i] : (~(cP_5 @ X0 @ X1) | (cP_5 @ (f @ X0) @ X1)) & ! [X0 : $i] : (cP_3 @ d @ X0) & (cP_4 @ c @ c) & ! [X0 : $i] : (cP_4 @ d @ X0) & (cP_5 @ b @ b) & ! [X2 : $i,X0 : $i,X1 : $i] : ~(cQ_6 @ X0 @ X1 @ X2) & ! [X1 : $i,X2 : $i,X4 : $i,X5 : $i,X0 : $i,X3 : $i] : ((cQ_5 @ X3 @ X4 @ X5) | ~(cP_4 @ (f @ X1) @ X4) | ~(cQ_4 @ X0 @ X1 @ X2) | ~(cP_4 @ (f @ X2) @ X5) | ~(cP_4 @ (f @ X0) @ X3)) & ! [X0 : $i,X1 : $i] : ((cP_2 @ (f @ X0) @ X1) | ~(cP_2 @ X0 @ X1)) & (cP_4 @ b @ b) & (cP_5 @ c @ c) & (cP_2 @ c @ c) & (cP_1 @ b @ b) & (cP_3 @ a @ a) & (cP_1 @ c @ c) & (cP_3 @ c @ c) & ! [X3 : $i,X5 : $i,X0 : $i,X2 : $i,X4 : $i,X1 : $i] : (~(cQ_3 @ X0 @ X1 @ X2) | ~(cP_3 @ (f @ X0) @ X3) | ~(cP_3 @ (f @ X2) @ X5) | (cQ_4 @ X3 @ X4 @ X5) | ~(cP_3 @ (f @ X1) @ X4)) & (cP_2 @ a @ a) & (cP_5 @ a @ a) & ! [X0 : $i,X1 : $i] : (~(cP_1 @ X0 @ X1) | (cP_1 @ (f @ X0) @ X1)) & (cP_2 @ b @ b) & ! [X0 : $i] : (cP_1 @ d @ X0) & ! [X0 : $i] : (cP_2 @ d @ X0) & ! [X0 : $i] : (cP_5 @ d @ X0) & ! [X5 : $i,X1 : $i,X4 : $i,X2 : $i,X3 : $i,X0 : $i] : (~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2) | ~(cP_2 @ (f @ X2) @ X5) | (cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X1) @ X4)) & (cP_4 @ a @ a) & (cQ_1 @ a @ b @ c))),
% 1.72/1.38 file('/export/starexec/sandbox2/tmp/tmp.4KjW3duxkU/DTF2THF_13451.p',cTHM409_5)).
% 1.72/1.38 thf(f123,plain,(
% 1.72/1.38 ( ! [X0 : $i] : (($true != (cP_5 @ b @ X0))) ) | ~spl0_11),
% 1.72/1.38 inference(avatar_component_clause,[status(thm)],[f122])).
% 1.72/1.38 thf(f122,definition,(
% 1.72/1.38 spl0_11 <=> ! [X0 : $i] : ($true != (cP_5 @ b @ X0))),
% 1.72/1.38 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.72/1.38 thf(f241,plain,(
% 1.72/1.38 spl0_11 | ~spl0_1),
% 1.72/1.38 inference(avatar_split_clause,[status(thm)],[f240,f52,f122])).
% 1.72/1.38 thf(f52,definition,(
% 1.72/1.38 spl0_1 <=> ! [X11 : $i,X0 : $i,X6 : $i,X2 : $i,X1 : $i] : (($true != (cP_1 @ (f @ b) @ X2)) | ((cP_2 @ (f @ X2) @ X6) != $true) | ((cP_4 @ (f @ X0) @ X1) != $true) | ($true != (cP_5 @ (f @ X1) @ X11)) | ($true != (cP_3 @ (f @ X6) @ X0)))),
% 1.72/1.38 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.72/1.38 thf(f240,plain,(
% 1.72/1.38 ( ! [X0 : $i] : (($true != (cP_5 @ b @ X0))) ) | ~spl0_1),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f239])).
% 1.72/1.38 thf(f239,plain,(
% 1.72/1.38 ( ! [X0 : $i] : (($true != (cP_5 @ b @ X0)) | ($true != $true)) ) | ~spl0_1),
% 1.72/1.38 inference(superposition,[status(thm)],[f222,f26])).
% 1.72/1.38 thf(f26,plain,(
% 1.72/1.38 ((cP_4 @ b @ b) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f222,plain,(
% 1.72/1.38 ( ! [X0 : $i,X1 : $i] : (((cP_4 @ b @ X0) != $true) | ((cP_5 @ X0 @ X1) != $true)) ) | ~spl0_1),
% 1.72/1.38 inference(subsumption_resolution,[status(thm)],[f211,f30])).
% 1.72/1.38 thf(f30,plain,(
% 1.72/1.38 ((cP_2 @ b @ b) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f211,plain,(
% 1.72/1.38 ( ! [X0 : $i,X1 : $i] : (((cP_4 @ b @ X0) != $true) | ((cP_5 @ X0 @ X1) != $true) | ((cP_2 @ b @ b) != $true)) ) | ~spl0_1),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f206])).
% 1.72/1.38 thf(f206,plain,(
% 1.72/1.38 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((cP_2 @ b @ b) != $true) | ((cP_4 @ b @ X0) != $true) | ((cP_5 @ X0 @ X1) != $true)) ) | ~spl0_1),
% 1.72/1.38 inference(superposition,[status(thm)],[f203,f16])).
% 1.72/1.38 thf(f16,plain,(
% 1.72/1.38 ((cP_3 @ b @ b) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f203,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_3 @ X2 @ X3)) | ((cP_5 @ X0 @ X1) != $true) | ($true != (cP_4 @ X3 @ X0)) | ((cP_2 @ b @ X2) != $true)) ) | ~spl0_1),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f202])).
% 1.72/1.38 thf(f202,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_5 @ X0 @ X1) != $true) | ($true != (cP_3 @ X2 @ X3)) | ($true != $true) | ((cP_2 @ b @ X2) != $true) | ($true != (cP_4 @ X3 @ X0))) ) | ~spl0_1),
% 1.72/1.38 inference(superposition,[status(thm)],[f201,f36])).
% 1.72/1.38 thf(f36,plain,(
% 1.72/1.38 ((cP_1 @ b @ b) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f201,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_1 @ b @ X2)) | ((cP_5 @ X0 @ X1) != $true) | ($true != (cP_3 @ X3 @ X4)) | ($true != (cP_2 @ X2 @ X3)) | ((cP_4 @ X4 @ X0) != $true)) ) | ~spl0_1),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f200])).
% 1.72/1.38 thf(f200,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_1 @ b @ X2)) | ($true != (cP_3 @ X3 @ X4)) | ((cP_5 @ X0 @ X1) != $true) | ($true != (cP_2 @ X2 @ X3)) | ($true != $true) | ((cP_4 @ X4 @ X0) != $true)) ) | ~spl0_1),
% 1.72/1.38 inference(superposition,[status(thm)],[f199,f19])).
% 1.72/1.38 thf(f19,plain,(
% 1.72/1.38 ( ! [X22 : $i,X23 : $i] : (($true = (cP_5 @ (f @ X22) @ X23)) | ((cP_5 @ X22 @ X23) != $true)) )),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f199,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_5 @ (f @ X2) @ X3)) | ((cP_1 @ b @ X0) != $true) | ($true != (cP_3 @ X1 @ X4)) | ($true != (cP_4 @ X4 @ X2)) | ((cP_2 @ X0 @ X1) != $true)) ) | ~spl0_1),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f198])).
% 1.72/1.38 thf(f198,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((cP_2 @ X0 @ X1) != $true) | ($true != (cP_3 @ X1 @ X4)) | ($true != $true) | ($true != (cP_4 @ X4 @ X2)) | ((cP_1 @ b @ X0) != $true) | ($true != (cP_5 @ (f @ X2) @ X3))) ) | ~spl0_1),
% 1.72/1.38 inference(superposition,[status(thm)],[f197,f25])).
% 1.72/1.38 thf(f25,plain,(
% 1.72/1.38 ( ! [X18 : $i,X19 : $i] : (($true = (cP_2 @ (f @ X19) @ X18)) | ((cP_2 @ X19 @ X18) != $true)) )),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f197,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((cP_2 @ (f @ X2) @ X0) != $true) | ($true != (cP_1 @ b @ X2)) | ((cP_5 @ (f @ X3) @ X4) != $true) | ((cP_3 @ X0 @ X1) != $true) | ($true != (cP_4 @ X1 @ X3))) ) | ~spl0_1),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f196])).
% 1.72/1.38 thf(f196,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_1 @ b @ X2)) | ((cP_5 @ (f @ X3) @ X4) != $true) | ($true != (cP_4 @ X1 @ X3)) | ((cP_3 @ X0 @ X1) != $true) | ($true != $true) | ((cP_2 @ (f @ X2) @ X0) != $true)) ) | ~spl0_1),
% 1.72/1.38 inference(superposition,[status(thm)],[f195,f33])).
% 1.72/1.38 thf(f33,plain,(
% 1.72/1.38 ( ! [X10 : $i,X9 : $i] : (((cP_3 @ (f @ X10) @ X9) = $true) | ((cP_3 @ X10 @ X9) != $true)) )),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f195,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_3 @ (f @ X3) @ X0)) | ($true != (cP_1 @ b @ X2)) | ((cP_5 @ (f @ X1) @ X4) != $true) | ((cP_2 @ (f @ X2) @ X3) != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_1),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f194])).
% 1.72/1.38 thf(f194,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_3 @ (f @ X3) @ X0)) | ($true != (cP_1 @ b @ X2)) | ($true != $true) | ((cP_5 @ (f @ X1) @ X4) != $true) | ((cP_4 @ X0 @ X1) != $true) | ((cP_2 @ (f @ X2) @ X3) != $true)) ) | ~spl0_1),
% 1.72/1.38 inference(superposition,[status(thm)],[f193,f10])).
% 1.72/1.38 thf(f10,plain,(
% 1.72/1.38 ( ! [X40 : $i,X39 : $i] : (((cP_4 @ (f @ X39) @ X40) = $true) | ($true != (cP_4 @ X39 @ X40))) )),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f193,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_4 @ (f @ X3) @ X1)) | ((cP_2 @ (f @ X0) @ X4) != $true) | ((cP_1 @ b @ X0) != $true) | ((cP_3 @ (f @ X4) @ X3) != $true) | ($true != (cP_5 @ (f @ X1) @ X2))) ) | ~spl0_1),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f192])).
% 1.72/1.38 thf(f192,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((cP_1 @ b @ X0) != $true) | ((cP_3 @ (f @ X4) @ X3) != $true) | ($true != $true) | ((cP_2 @ (f @ X0) @ X4) != $true) | ($true != (cP_5 @ (f @ X1) @ X2)) | ($true != (cP_4 @ (f @ X3) @ X1))) ) | ~spl0_1),
% 1.72/1.38 inference(superposition,[status(thm)],[f53,f23])).
% 1.72/1.38 thf(f23,plain,(
% 1.72/1.38 ( ! [X21 : $i,X20 : $i] : (($true = (cP_1 @ (f @ X21) @ X20)) | ($true != (cP_1 @ X21 @ X20))) )),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f53,plain,(
% 1.72/1.38 ( ! [X2 : $i,X0 : $i,X11 : $i,X1 : $i,X6 : $i] : (($true != (cP_1 @ (f @ b) @ X2)) | ($true != (cP_5 @ (f @ X1) @ X11)) | ((cP_4 @ (f @ X0) @ X1) != $true) | ((cP_2 @ (f @ X2) @ X6) != $true) | ($true != (cP_3 @ (f @ X6) @ X0))) ) | ~spl0_1),
% 1.72/1.38 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.72/1.38 thf(f191,plain,(
% 1.72/1.38 ~spl0_13),
% 1.72/1.38 inference(avatar_contradiction_clause,[status(thm)],[f190])).
% 1.72/1.38 thf(f190,plain,(
% 1.72/1.38 $false | ~spl0_13),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f189])).
% 1.72/1.38 thf(f189,plain,(
% 1.72/1.38 ($true != $true) | ~spl0_13),
% 1.72/1.38 inference(superposition,[status(thm)],[f131,f34])).
% 1.72/1.38 thf(f34,plain,(
% 1.72/1.38 ((cP_5 @ a @ a) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f131,plain,(
% 1.72/1.38 ( ! [X0 : $i] : (($true != (cP_5 @ a @ X0))) ) | ~spl0_13),
% 1.72/1.38 inference(avatar_component_clause,[status(thm)],[f130])).
% 1.72/1.38 thf(f130,definition,(
% 1.72/1.38 spl0_13 <=> ! [X0 : $i] : ($true != (cP_5 @ a @ X0))),
% 1.72/1.38 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.72/1.38 thf(f188,plain,(
% 1.72/1.38 spl0_13 | ~spl0_6),
% 1.72/1.38 inference(avatar_split_clause,[status(thm)],[f187,f90,f130])).
% 1.72/1.38 thf(f90,definition,(
% 1.72/1.38 spl0_6 <=> ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_5 @ X0 @ X1) != $true) | ($true != (cP_3 @ a @ X2)) | ($true != (cP_4 @ X2 @ X0)))),
% 1.72/1.38 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.72/1.38 thf(f187,plain,(
% 1.72/1.38 ( ! [X0 : $i] : (($true != (cP_5 @ a @ X0))) ) | ~spl0_6),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f186])).
% 1.72/1.38 thf(f186,plain,(
% 1.72/1.38 ( ! [X0 : $i] : (($true != (cP_5 @ a @ X0)) | ($true != $true)) ) | ~spl0_6),
% 1.72/1.38 inference(superposition,[status(thm)],[f185,f21])).
% 1.72/1.38 thf(f21,plain,(
% 1.72/1.38 ((cP_4 @ a @ a) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f185,plain,(
% 1.72/1.38 ( ! [X0 : $i,X1 : $i] : (((cP_4 @ a @ X0) != $true) | ((cP_5 @ X0 @ X1) != $true)) ) | ~spl0_6),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f184])).
% 1.72/1.38 thf(f184,plain,(
% 1.72/1.38 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((cP_5 @ X0 @ X1) != $true) | ((cP_4 @ a @ X0) != $true)) ) | ~spl0_6),
% 1.72/1.38 inference(superposition,[status(thm)],[f91,f18])).
% 1.72/1.38 thf(f18,plain,(
% 1.72/1.38 ((cP_3 @ a @ a) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f91,plain,(
% 1.72/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (cP_3 @ a @ X2)) | ($true != (cP_4 @ X2 @ X0)) | ((cP_5 @ X0 @ X1) != $true)) ) | ~spl0_6),
% 1.72/1.38 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.72/1.38 thf(f183,plain,(
% 1.72/1.38 spl0_6 | ~spl0_3),
% 1.72/1.38 inference(avatar_split_clause,[status(thm)],[f182,f58,f90])).
% 1.72/1.38 thf(f58,definition,(
% 1.72/1.38 spl0_3 <=> ! [X13 : $i,X14 : $i,X12 : $i,X3 : $i,X7 : $i] : (($true != (cP_1 @ (f @ a) @ X3)) | ((cP_2 @ (f @ X3) @ X7) != $true) | ($true != (cP_5 @ (f @ X12) @ X13)) | ($true != (cP_3 @ (f @ X7) @ X14)) | ($true != (cP_4 @ (f @ X14) @ X12)))),
% 1.72/1.38 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.72/1.38 thf(f182,plain,(
% 1.72/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_5 @ X1 @ X2) != $true) | ((cP_3 @ a @ X0) != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_3),
% 1.72/1.38 inference(subsumption_resolution,[status(thm)],[f159,f20])).
% 1.72/1.38 thf(f20,plain,(
% 1.72/1.38 ((cP_1 @ a @ a) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f159,plain,(
% 1.72/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_4 @ X0 @ X1) != $true) | ((cP_1 @ a @ a) != $true) | ((cP_5 @ X1 @ X2) != $true) | ((cP_3 @ a @ X0) != $true)) ) | ~spl0_3),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f157])).
% 1.72/1.38 thf(f157,plain,(
% 1.72/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_3 @ a @ X0) != $true) | ((cP_5 @ X1 @ X2) != $true) | ((cP_1 @ a @ a) != $true) | ($true != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_3),
% 1.72/1.38 inference(superposition,[status(thm)],[f153,f28])).
% 1.72/1.38 thf(f28,plain,(
% 1.72/1.38 ((cP_2 @ a @ a) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f153,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_2 @ X2 @ X3)) | ($true != (cP_3 @ X3 @ X4)) | ((cP_1 @ a @ X2) != $true) | ((cP_5 @ X0 @ X1) != $true) | ((cP_4 @ X4 @ X0) != $true)) ) | ~spl0_3),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f152])).
% 1.72/1.38 thf(f152,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_3 @ X3 @ X4)) | ($true != $true) | ((cP_4 @ X4 @ X0) != $true) | ((cP_5 @ X0 @ X1) != $true) | ((cP_1 @ a @ X2) != $true) | ($true != (cP_2 @ X2 @ X3))) ) | ~spl0_3),
% 1.72/1.38 inference(superposition,[status(thm)],[f151,f19])).
% 1.72/1.38 thf(f151,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_5 @ (f @ X2) @ X3)) | ((cP_2 @ X0 @ X1) != $true) | ($true != (cP_1 @ a @ X0)) | ($true != (cP_3 @ X1 @ X4)) | ($true != (cP_4 @ X4 @ X2))) ) | ~spl0_3),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.72/1.38 thf(f150,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != $true) | ($true != (cP_1 @ a @ X0)) | ($true != (cP_4 @ X4 @ X2)) | ((cP_2 @ X0 @ X1) != $true) | ($true != (cP_3 @ X1 @ X4)) | ($true != (cP_5 @ (f @ X2) @ X3))) ) | ~spl0_3),
% 1.72/1.38 inference(superposition,[status(thm)],[f149,f25])).
% 1.72/1.38 thf(f149,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_2 @ (f @ X4) @ X0)) | ((cP_1 @ a @ X4) != $true) | ($true != (cP_5 @ (f @ X2) @ X3)) | ((cP_3 @ X0 @ X1) != $true) | ((cP_4 @ X1 @ X2) != $true)) ) | ~spl0_3),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f148])).
% 1.72/1.38 thf(f148,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((cP_4 @ X1 @ X2) != $true) | ($true != (cP_2 @ (f @ X4) @ X0)) | ($true != (cP_5 @ (f @ X2) @ X3)) | ((cP_1 @ a @ X4) != $true) | ((cP_3 @ X0 @ X1) != $true) | ($true != $true)) ) | ~spl0_3),
% 1.72/1.38 inference(superposition,[status(thm)],[f147,f33])).
% 1.72/1.38 thf(f147,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_3 @ (f @ X3) @ X0)) | ((cP_5 @ (f @ X1) @ X4) != $true) | ((cP_2 @ (f @ X2) @ X3) != $true) | ((cP_1 @ a @ X2) != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_3),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f146])).
% 1.72/1.38 thf(f146,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((cP_1 @ a @ X2) != $true) | ((cP_4 @ X0 @ X1) != $true) | ($true != (cP_3 @ (f @ X3) @ X0)) | ((cP_5 @ (f @ X1) @ X4) != $true) | ((cP_2 @ (f @ X2) @ X3) != $true) | ($true != $true)) ) | ~spl0_3),
% 1.72/1.38 inference(superposition,[status(thm)],[f145,f10])).
% 1.72/1.38 thf(f145,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_4 @ (f @ X4) @ X2)) | ((cP_2 @ (f @ X0) @ X1) != $true) | ($true != (cP_5 @ (f @ X2) @ X3)) | ($true != (cP_1 @ a @ X0)) | ((cP_3 @ (f @ X1) @ X4) != $true)) ) | ~spl0_3),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.72/1.38 thf(f144,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((cP_3 @ (f @ X1) @ X4) != $true) | ($true != (cP_1 @ a @ X0)) | ($true != (cP_4 @ (f @ X4) @ X2)) | ($true != $true) | ($true != (cP_5 @ (f @ X2) @ X3)) | ((cP_2 @ (f @ X0) @ X1) != $true)) ) | ~spl0_3),
% 1.72/1.38 inference(superposition,[status(thm)],[f59,f23])).
% 1.72/1.38 thf(f59,plain,(
% 1.72/1.38 ( ! [X3 : $i,X7 : $i,X14 : $i,X12 : $i,X13 : $i] : (($true != (cP_1 @ (f @ a) @ X3)) | ((cP_2 @ (f @ X3) @ X7) != $true) | ($true != (cP_5 @ (f @ X12) @ X13)) | ($true != (cP_4 @ (f @ X14) @ X12)) | ($true != (cP_3 @ (f @ X7) @ X14))) ) | ~spl0_3),
% 1.72/1.38 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.72/1.38 thf(f143,plain,(
% 1.72/1.38 ~spl0_2),
% 1.72/1.38 inference(avatar_contradiction_clause,[status(thm)],[f142])).
% 1.72/1.38 thf(f142,plain,(
% 1.72/1.38 $false | ~spl0_2),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f141])).
% 1.72/1.38 thf(f141,plain,(
% 1.72/1.38 ($true != $true) | ~spl0_2),
% 1.72/1.38 inference(superposition,[status(thm)],[f116,f22])).
% 1.72/1.38 thf(f22,plain,(
% 1.72/1.38 ((cP_5 @ c @ c) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f116,plain,(
% 1.72/1.38 ( ! [X0 : $i] : (($true != (cP_5 @ c @ X0))) ) | ~spl0_2),
% 1.72/1.38 inference(subsumption_resolution,[status(thm)],[f115,f13])).
% 1.72/1.38 thf(f13,plain,(
% 1.72/1.38 ((cP_3 @ c @ c) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f115,plain,(
% 1.72/1.38 ( ! [X0 : $i] : (((cP_3 @ c @ c) != $true) | ($true != (cP_5 @ c @ X0))) ) | ~spl0_2),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.72/1.38 thf(f107,plain,(
% 1.72/1.38 ( ! [X0 : $i] : (($true != (cP_5 @ c @ X0)) | ($true != $true) | ((cP_3 @ c @ c) != $true)) ) | ~spl0_2),
% 1.72/1.38 inference(superposition,[status(thm)],[f97,f24])).
% 1.72/1.38 thf(f24,plain,(
% 1.72/1.38 ((cP_4 @ c @ c) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f97,plain,(
% 1.72/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (cP_4 @ X2 @ X0)) | ((cP_3 @ c @ X2) != $true) | ((cP_5 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 1.72/1.38 inference(subsumption_resolution,[status(thm)],[f78,f29])).
% 1.72/1.38 thf(f29,plain,(
% 1.72/1.38 ((cP_1 @ c @ c) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f78,plain,(
% 1.72/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (cP_4 @ X2 @ X0)) | ((cP_1 @ c @ c) != $true) | ((cP_3 @ c @ X2) != $true) | ((cP_5 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.72/1.38 thf(f72,plain,(
% 1.72/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((cP_1 @ c @ c) != $true) | ($true != (cP_4 @ X2 @ X0)) | ((cP_3 @ c @ X2) != $true) | ((cP_5 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 1.72/1.38 inference(superposition,[status(thm)],[f70,f35])).
% 1.72/1.38 thf(f35,plain,(
% 1.72/1.38 ((cP_2 @ c @ c) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f70,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_2 @ X2 @ X3)) | ((cP_5 @ X0 @ X1) != $true) | ((cP_4 @ X4 @ X0) != $true) | ($true != (cP_3 @ X3 @ X4)) | ((cP_1 @ c @ X2) != $true)) ) | ~spl0_2),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.72/1.38 thf(f69,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((cP_4 @ X4 @ X0) != $true) | ($true != $true) | ($true != (cP_2 @ X2 @ X3)) | ($true != (cP_3 @ X3 @ X4)) | ((cP_5 @ X0 @ X1) != $true) | ((cP_1 @ c @ X2) != $true)) ) | ~spl0_2),
% 1.72/1.38 inference(superposition,[status(thm)],[f68,f19])).
% 1.72/1.38 thf(f68,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((cP_5 @ (f @ X1) @ X4) != $true) | ($true != (cP_2 @ X2 @ X3)) | ($true != (cP_3 @ X3 @ X0)) | ((cP_4 @ X0 @ X1) != $true) | ((cP_1 @ c @ X2) != $true)) ) | ~spl0_2),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.72/1.38 thf(f67,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_2 @ X2 @ X3)) | ($true != $true) | ($true != (cP_3 @ X3 @ X0)) | ((cP_4 @ X0 @ X1) != $true) | ((cP_1 @ c @ X2) != $true) | ((cP_5 @ (f @ X1) @ X4) != $true)) ) | ~spl0_2),
% 1.72/1.38 inference(superposition,[status(thm)],[f66,f10])).
% 1.72/1.38 thf(f66,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_4 @ (f @ X2) @ X3)) | ((cP_2 @ X0 @ X1) != $true) | ((cP_1 @ c @ X0) != $true) | ((cP_3 @ X1 @ X2) != $true) | ((cP_5 @ (f @ X3) @ X4) != $true)) ) | ~spl0_2),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.72/1.38 thf(f65,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((cP_3 @ X1 @ X2) != $true) | ($true != $true) | ((cP_5 @ (f @ X3) @ X4) != $true) | ((cP_1 @ c @ X0) != $true) | ((cP_2 @ X0 @ X1) != $true) | ($true != (cP_4 @ (f @ X2) @ X3))) ) | ~spl0_2),
% 1.72/1.38 inference(superposition,[status(thm)],[f64,f25])).
% 1.72/1.38 thf(f64,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_2 @ (f @ X4) @ X0)) | ((cP_3 @ X0 @ X1) != $true) | ($true != (cP_4 @ (f @ X1) @ X2)) | ($true != (cP_1 @ c @ X4)) | ($true != (cP_5 @ (f @ X2) @ X3))) ) | ~spl0_2),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.72/1.38 thf(f63,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_1 @ c @ X4)) | ($true != $true) | ((cP_3 @ X0 @ X1) != $true) | ($true != (cP_5 @ (f @ X2) @ X3)) | ($true != (cP_2 @ (f @ X4) @ X0)) | ($true != (cP_4 @ (f @ X1) @ X2))) ) | ~spl0_2),
% 1.72/1.38 inference(superposition,[status(thm)],[f62,f33])).
% 1.72/1.38 thf(f62,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (cP_3 @ (f @ X1) @ X2)) | ((cP_5 @ (f @ X3) @ X4) != $true) | ((cP_1 @ c @ X0) != $true) | ((cP_2 @ (f @ X0) @ X1) != $true) | ($true != (cP_4 @ (f @ X2) @ X3))) ) | ~spl0_2),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.72/1.38 thf(f61,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((cP_1 @ c @ X0) != $true) | ($true != $true) | ($true != (cP_3 @ (f @ X1) @ X2)) | ((cP_2 @ (f @ X0) @ X1) != $true) | ((cP_5 @ (f @ X3) @ X4) != $true) | ($true != (cP_4 @ (f @ X2) @ X3))) ) | ~spl0_2),
% 1.72/1.38 inference(superposition,[status(thm)],[f56,f23])).
% 1.72/1.38 thf(f56,plain,(
% 1.72/1.38 ( ! [X10 : $i,X8 : $i,X9 : $i,X4 : $i,X5 : $i] : (((cP_1 @ (f @ c) @ X10) != $true) | ((cP_2 @ (f @ X10) @ X9) != $true) | ((cP_4 @ (f @ X8) @ X4) != $true) | ((cP_5 @ (f @ X4) @ X5) != $true) | ((cP_3 @ (f @ X9) @ X8) != $true)) ) | ~spl0_2),
% 1.72/1.38 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.72/1.38 thf(f55,definition,(
% 1.72/1.38 spl0_2 <=> ! [X4 : $i,X9 : $i,X10 : $i,X5 : $i,X8 : $i] : (((cP_5 @ (f @ X4) @ X5) != $true) | ((cP_1 @ (f @ c) @ X10) != $true) | ((cP_2 @ (f @ X10) @ X9) != $true) | ((cP_3 @ (f @ X9) @ X8) != $true) | ((cP_4 @ (f @ X8) @ X4) != $true))),
% 1.72/1.38 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.72/1.38 thf(f60,plain,(
% 1.72/1.38 spl0_1 | spl0_2 | spl0_3),
% 1.72/1.38 inference(avatar_split_clause,[status(thm)],[f50,f58,f55,f52])).
% 1.72/1.38 thf(f50,plain,(
% 1.72/1.38 ( ! [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] : (((cP_5 @ (f @ X4) @ X5) != $true) | ($true != (cP_1 @ (f @ b) @ X2)) | ($true != (cP_1 @ (f @ a) @ X3)) | ((cP_4 @ (f @ X0) @ X1) != $true) | ($true != (cP_3 @ (f @ X6) @ X0)) | ($true != (cP_5 @ (f @ X12) @ X13)) | ($true != (cP_4 @ (f @ X14) @ X12)) | ($true != (cP_5 @ (f @ X1) @ X11)) | ((cP_3 @ (f @ X9) @ X8) != $true) | ((cP_2 @ (f @ X10) @ X9) != $true) | ($true != (cP_3 @ (f @ X7) @ X14)) | ((cP_2 @ (f @ X3) @ X7) != $true) | ((cP_4 @ (f @ X8) @ X4) != $true) | ((cP_1 @ (f @ c) @ X10) != $true) | ((cP_2 @ (f @ X2) @ X6) != $true)) )),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.72/1.38 thf(f49,plain,(
% 1.72/1.38 ( ! [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 != $true) | ((cP_4 @ (f @ X0) @ X1) != $true) | ($true != (cP_1 @ (f @ a) @ X3)) | ((cP_4 @ (f @ X8) @ X4) != $true) | ((cP_5 @ (f @ X4) @ X5) != $true) | ($true != (cP_3 @ (f @ X6) @ X0)) | ((cP_2 @ (f @ X2) @ X6) != $true) | ((cP_1 @ (f @ c) @ X10) != $true) | ($true != (cP_1 @ (f @ b) @ X2)) | ($true != (cP_5 @ (f @ X1) @ X11)) | ((cP_2 @ (f @ X10) @ X9) != $true) | ((cP_3 @ (f @ X9) @ X8) != $true) | ($true != (cP_5 @ (f @ X12) @ X13)) | ($true != (cP_4 @ (f @ X14) @ X12)) | ($true != (cP_3 @ (f @ X7) @ X14)) | ((cP_2 @ (f @ X3) @ X7) != $true)) )),
% 1.72/1.38 inference(superposition,[status(thm)],[f48,f31])).
% 1.72/1.38 thf(f31,plain,(
% 1.72/1.38 ((cQ_1 @ a @ b @ c) = $true)),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f48,plain,(
% 1.72/1.38 ( ! [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 : $i] : (($true != (cQ_1 @ X15 @ X16 @ X17)) | ($true != (cP_4 @ (f @ X13) @ X11)) | ($true != (cP_1 @ (f @ X16) @ X1)) | ($true != (cP_1 @ (f @ X15) @ X0)) | ((cP_5 @ (f @ X8) @ X9) != $true) | ($true != (cP_3 @ (f @ X14) @ X13)) | ($true != (cP_2 @ (f @ X0) @ X10)) | ((cP_4 @ (f @ X4) @ X8) != $true) | ($true != (cP_3 @ (f @ X3) @ X4)) | ((cP_2 @ (f @ X2) @ X3) != $true) | ((cP_5 @ (f @ X11) @ X12) != $true) | ($true != (cP_2 @ (f @ X1) @ X14)) | ((cP_5 @ (f @ X5) @ X6) != $true) | ((cP_3 @ (f @ X10) @ X7) != $true) | ($true != (cP_1 @ (f @ X17) @ X2)) | ((cP_4 @ (f @ X7) @ X5) != $true)) )),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.72/1.38 thf(f47,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X16 : $i,X14 : $i,X4 : $i,X17 : $i,X15 : $i,X5 : $i,X12 : $i,X13 : $i] : (($true != (cP_1 @ (f @ X15) @ X0)) | ($true != (cP_1 @ (f @ X17) @ X2)) | ($true != (cP_2 @ (f @ X0) @ X10)) | ((cP_5 @ (f @ X5) @ X6) != $true) | ((cP_4 @ (f @ X7) @ X5) != $true) | ($true != (cP_4 @ (f @ X13) @ X11)) | ($true != (cQ_1 @ X15 @ X16 @ X17)) | ((cP_5 @ (f @ X11) @ X12) != $true) | ($true != (cP_3 @ (f @ X14) @ X13)) | ((cP_5 @ (f @ X8) @ X9) != $true) | ((cP_4 @ (f @ X4) @ X8) != $true) | ($true != $true) | ((cP_3 @ (f @ X10) @ X7) != $true) | ($true != (cP_1 @ (f @ X16) @ X1)) | ((cP_2 @ (f @ X2) @ X3) != $true) | ($true != (cP_3 @ (f @ X3) @ X4)) | ($true != (cP_2 @ (f @ X1) @ X14))) )),
% 1.72/1.38 inference(superposition,[status(thm)],[f46,f14])).
% 1.72/1.38 thf(f14,plain,(
% 1.72/1.38 ( ! [X31 : $i,X36 : $i,X34 : $i,X35 : $i,X32 : $i,X33 : $i] : (((cQ_2 @ X33 @ X32 @ X31) = $true) | ((cP_1 @ (f @ X35) @ X33) != $true) | ($true != (cP_1 @ (f @ X34) @ X32)) | ((cQ_1 @ X35 @ X34 @ X36) != $true) | ($true != (cP_1 @ (f @ X36) @ X31))) )),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f46,plain,(
% 1.72/1.38 ( ! [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_2 @ X13 @ X14 @ X12)) | ($true != (cP_3 @ (f @ X2) @ X9)) | ((cP_5 @ (f @ X10) @ X11) != $true) | ($true != (cP_4 @ (f @ X8) @ X10)) | ((cP_5 @ (f @ X3) @ X4) != $true) | ((cP_2 @ (f @ X13) @ X0) != $true) | ($true != (cP_4 @ (f @ X9) @ X3)) | ((cP_5 @ (f @ X5) @ X6) != $true) | ((cP_4 @ (f @ X7) @ X5) != $true) | ($true != (cP_2 @ (f @ X12) @ X2)) | ((cP_3 @ (f @ X1) @ X7) != $true) | ((cP_2 @ (f @ X14) @ X1) != $true) | ((cP_3 @ (f @ X0) @ X8) != $true)) )),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.72/1.38 thf(f45,plain,(
% 1.72/1.38 ( ! [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] : (((cP_2 @ (f @ X14) @ X1) != $true) | ((cP_5 @ (f @ X10) @ X11) != $true) | ($true != (cP_3 @ (f @ X2) @ X9)) | ($true != (cP_4 @ (f @ X8) @ X10)) | ($true != $true) | ($true != (cP_2 @ (f @ X12) @ X2)) | ((cP_5 @ (f @ X5) @ X6) != $true) | ($true != (cP_4 @ (f @ X9) @ X3)) | ((cP_2 @ (f @ X13) @ X0) != $true) | ((cP_4 @ (f @ X7) @ X5) != $true) | ($true != (cQ_2 @ X13 @ X14 @ X12)) | ((cP_5 @ (f @ X3) @ X4) != $true) | ((cP_3 @ (f @ X1) @ X7) != $true) | ((cP_3 @ (f @ X0) @ X8) != $true)) )),
% 1.72/1.38 inference(superposition,[status(thm)],[f44,f37])).
% 1.72/1.38 thf(f37,plain,(
% 1.72/1.38 ( ! [X3 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (cQ_3 @ X5 @ X8 @ X6)) | ((cP_2 @ (f @ X3) @ X6) != $true) | ($true != (cP_2 @ (f @ X7) @ X5)) | ((cP_2 @ (f @ X4) @ X8) != $true) | ((cQ_2 @ X7 @ X4 @ X3) != $true)) )),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f44,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((cQ_3 @ X10 @ X9 @ X11) != $true) | ((cP_5 @ (f @ X3) @ X4) != $true) | ((cP_5 @ (f @ X5) @ X8) != $true) | ((cP_4 @ (f @ X1) @ X5) != $true) | ($true != (cP_3 @ (f @ X10) @ X0)) | ((cP_3 @ (f @ X11) @ X2) != $true) | ($true != (cP_4 @ (f @ X2) @ X3)) | ((cP_4 @ (f @ X0) @ X6) != $true) | ((cP_3 @ (f @ X9) @ X1) != $true) | ($true != (cP_5 @ (f @ X6) @ X7))) )),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.72/1.38 thf(f43,plain,(
% 1.72/1.38 ( ! [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 != $true) | ((cQ_3 @ X10 @ X9 @ X11) != $true) | ((cP_5 @ (f @ X5) @ X8) != $true) | ((cP_4 @ (f @ X1) @ X5) != $true) | ($true != (cP_4 @ (f @ X2) @ X3)) | ((cP_3 @ (f @ X9) @ X1) != $true) | ((cP_4 @ (f @ X0) @ X6) != $true) | ($true != (cP_3 @ (f @ X10) @ X0)) | ($true != (cP_5 @ (f @ X6) @ X7)) | ((cP_5 @ (f @ X3) @ X4) != $true) | ((cP_3 @ (f @ X11) @ X2) != $true)) )),
% 1.72/1.38 inference(superposition,[status(thm)],[f42,f8])).
% 1.72/1.38 thf(f8,plain,(
% 1.72/1.38 ( ! [X46 : $i,X47 : $i,X44 : $i,X45 : $i,X42 : $i,X43 : $i] : (((cQ_4 @ X45 @ X46 @ X42) = $true) | ((cP_3 @ (f @ X44) @ X46) != $true) | ((cQ_3 @ X43 @ X44 @ X47) != $true) | ($true != (cP_3 @ (f @ X47) @ X42)) | ($true != (cP_3 @ (f @ X43) @ X45))) )),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f42,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((cQ_4 @ X6 @ X7 @ X8) != $true) | ((cP_5 @ (f @ X2) @ X4) != $true) | ((cP_4 @ (f @ X8) @ X2) != $true) | ($true != (cP_4 @ (f @ X7) @ X1)) | ((cP_5 @ (f @ X0) @ X3) != $true) | ((cP_5 @ (f @ X1) @ X5) != $true) | ((cP_4 @ (f @ X6) @ X0) != $true)) )),
% 1.72/1.38 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.72/1.38 thf(f41,plain,(
% 1.72/1.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((cQ_4 @ X6 @ X7 @ X8) != $true) | ((cP_5 @ (f @ X0) @ X3) != $true) | ((cP_5 @ (f @ X2) @ X4) != $true) | ((cP_5 @ (f @ X1) @ X5) != $true) | ($true != (cP_4 @ (f @ X7) @ X1)) | ($true != $true) | ((cP_4 @ (f @ X6) @ X0) != $true) | ((cP_4 @ (f @ X8) @ X2) != $true)) )),
% 1.72/1.38 inference(superposition,[status(thm)],[f40,f32])).
% 1.72/1.38 thf(f32,plain,(
% 1.72/1.38 ( ! [X11 : $i,X16 : $i,X14 : $i,X15 : $i,X12 : $i,X13 : $i] : (($true = (cQ_5 @ X13 @ X15 @ X14)) | ((cQ_4 @ X12 @ X11 @ X16) != $true) | ($true != (cP_4 @ (f @ X11) @ X15)) | ((cP_4 @ (f @ X12) @ X13) != $true) | ($true != (cP_4 @ (f @ X16) @ X14))) )),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f40,plain,(
% 1.72/1.38 ( ! [X28 : $i,X29 : $i,X26 : $i,X27 : $i,X24 : $i,X25 : $i] : (((cQ_5 @ X27 @ X25 @ X24) != $true) | ((cP_5 @ (f @ X27) @ X28) != $true) | ($true != (cP_5 @ (f @ X24) @ X29)) | ((cP_5 @ (f @ X25) @ X26) != $true)) )),
% 1.72/1.38 inference(subsumption_resolution,[status(thm)],[f17,f38])).
% 1.72/1.38 thf(f38,plain,(
% 1.72/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cQ_6 @ X0 @ X2 @ X1) != $true)) )),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 thf(f17,plain,(
% 1.72/1.38 ( ! [X28 : $i,X29 : $i,X26 : $i,X27 : $i,X24 : $i,X25 : $i] : (((cQ_5 @ X27 @ X25 @ X24) != $true) | ((cP_5 @ (f @ X25) @ X26) != $true) | ((cP_5 @ (f @ X27) @ X28) != $true) | ($true != (cP_5 @ (f @ X24) @ X29)) | ($true = (cQ_6 @ X28 @ X26 @ X29))) )),
% 1.72/1.38 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.38 % SZS output end Proof for DTF2THF_13451
% 1.72/1.38 % (13730)------------------------------
% 1.72/1.38 % (13730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.38 % (13730)Termination reason: Refutation
% 1.72/1.38
% 1.72/1.38 % (13730)Memory used [KB]: 5884
% 1.72/1.38 % (13730)Time elapsed: 0.023 s
% 1.72/1.38 % (13730)Instructions burned: 57 (million)
% 1.72/1.38 % (13730)------------------------------
% 1.72/1.38 % (13730)------------------------------
% 1.72/1.38 % (13724)Success in time 0.031 s
%------------------------------------------------------------------------------