%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO391^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:35 AM UTC 2026
% Result : Theorem 0.19s 0.32s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 23
% Syntax : Number of formulae : 219 ( 64 unt; 0 typ; 22 def)
% Number of atoms : 3584 ( 858 equ; 0 cnn)
% Maximal formula atoms : 113 ( 16 avg)
% Number of connectives : 4835 (1047 ~; 940 |; 222 &;2604 @)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 50 ( 9 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 28 con; 0-3 aty)
% Number of variables : 927 ( 0 sgn 927 !; 0 ?; 927 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cQ_7: $i > $i > $i > $o ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
cP_6: $i > $i > $o ).
thf(func_def_3,type,
cQ_6: $i > $i > $i > $o ).
thf(func_def_8,type,
cP_5: $i > $i > $o ).
thf(func_def_9,type,
cQ_5: $i > $i > $i > $o ).
thf(func_def_10,type,
cP_4: $i > $i > $o ).
thf(func_def_11,type,
cQ_4: $i > $i > $i > $o ).
thf(func_def_12,type,
cP_3: $i > $i > $o ).
thf(func_def_13,type,
cQ_3: $i > $i > $i > $o ).
thf(func_def_14,type,
cP_2: $i > $i > $o ).
thf(func_def_15,type,
cQ_2: $i > $i > $i > $o ).
thf(func_def_16,type,
cP_1: $i > $i > $o ).
thf(func_def_17,type,
cQ_1: $i > $i > $i > $o ).
thf(f1,conjecture,
~ ( ! [X0: $i] : ( cP_6 @ d @ X0 )
& ( cP_5 @ a @ a )
& ( cP_1 @ b @ b )
& ! [X0: $i,X1: $i,X2: $i] :
~ ( cQ_7 @ X0 @ X1 @ X2 )
& ( cP_6 @ c @ c )
& ! [X3: $i,X1: $i,X0: $i,X5: $i,X2: $i,X4: $i] :
( ~ ( cP_6 @ ( f @ X2 ) @ X5 )
| ~ ( cP_6 @ ( f @ X0 ) @ X3 )
| ~ ( cP_6 @ ( f @ X1 ) @ X4 )
| ~ ( cQ_6 @ X0 @ X1 @ X2 )
| ( cQ_7 @ X3 @ X4 @ X5 ) )
& ! [X0: $i,X1: $i] :
( ~ ( cP_4 @ X0 @ X1 )
| ( cP_4 @ ( f @ X0 ) @ X1 ) )
& ( cP_2 @ a @ a )
& ! [X0: $i,X1: $i] :
( ( cP_1 @ ( f @ X0 ) @ X1 )
| ~ ( cP_1 @ X0 @ X1 ) )
& ! [X4: $i,X0: $i,X2: $i,X1: $i,X3: $i,X5: $i] :
( ~ ( cQ_5 @ X0 @ X1 @ X2 )
| ( cQ_6 @ X3 @ X4 @ X5 )
| ~ ( cP_5 @ ( f @ X2 ) @ X5 )
| ~ ( cP_5 @ ( f @ X1 ) @ X4 )
| ~ ( cP_5 @ ( f @ X0 ) @ X3 ) )
& ( cP_2 @ b @ b )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ( cP_1 @ a @ a )
& ( cP_4 @ a @ a )
& ! [X4: $i,X3: $i,X2: $i,X0: $i,X1: $i,X5: $i] :
( ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ( cQ_3 @ X3 @ X4 @ X5 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 ) )
& ( cP_2 @ c @ c )
& ( cP_3 @ c @ c )
& ! [X0: $i] : ( cP_4 @ d @ X0 )
& ! [X0: $i,X1: $i] :
( ~ ( cP_2 @ X0 @ X1 )
| ( cP_2 @ ( f @ X0 ) @ X1 ) )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ( cP_1 @ c @ c )
& ! [X0: $i,X1: $i] :
( ( cP_5 @ ( f @ X0 ) @ X1 )
| ~ ( cP_5 @ X0 @ X1 ) )
& ! [X0: $i] : ( cP_3 @ d @ X0 )
& ( cQ_1 @ a @ b @ c )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X3: $i,X0: $i,X5: $i,X1: $i,X4: $i,X2: $i] :
( ~ ( cQ_3 @ X0 @ X1 @ X2 )
| ( cQ_4 @ X3 @ X4 @ X5 )
| ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ~ ( cP_3 @ ( f @ X0 ) @ X3 ) )
& ! [X0: $i] : ( cP_5 @ d @ X0 )
& ( cP_3 @ b @ b )
& ! [X5: $i,X0: $i,X3: $i,X1: $i,X4: $i,X2: $i] :
( ~ ( cP_4 @ ( f @ X0 ) @ X3 )
| ( cQ_5 @ X3 @ X4 @ X5 )
| ~ ( cQ_4 @ X0 @ X1 @ X2 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 ) )
& ( cP_6 @ a @ a )
& ( cP_3 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [X5: $i,X2: $i,X3: $i,X0: $i,X4: $i,X1: $i] :
( ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ( cQ_2 @ X3 @ X4 @ X5 ) )
& ! [X1: $i,X0: $i] :
( ~ ( cP_3 @ X0 @ X1 )
| ( cP_3 @ ( f @ X0 ) @ X1 ) )
& ! [X0: $i,X1: $i] :
( ( cP_6 @ ( f @ X0 ) @ X1 )
| ~ ( cP_6 @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM409_6) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X0: $i] : ( cP_6 @ d @ X0 )
& ( cP_5 @ a @ a )
& ( cP_1 @ b @ b )
& ! [X0: $i,X1: $i,X2: $i] :
~ ( cQ_7 @ X0 @ X1 @ X2 )
& ( cP_6 @ c @ c )
& ! [X3: $i,X1: $i,X0: $i,X5: $i,X2: $i,X4: $i] :
( ~ ( cP_6 @ ( f @ X2 ) @ X5 )
| ~ ( cP_6 @ ( f @ X0 ) @ X3 )
| ~ ( cP_6 @ ( f @ X1 ) @ X4 )
| ~ ( cQ_6 @ X0 @ X1 @ X2 )
| ( cQ_7 @ X3 @ X4 @ X5 ) )
& ! [X0: $i,X1: $i] :
( ~ ( cP_4 @ X0 @ X1 )
| ( cP_4 @ ( f @ X0 ) @ X1 ) )
& ( cP_2 @ a @ a )
& ! [X0: $i,X1: $i] :
( ( cP_1 @ ( f @ X0 ) @ X1 )
| ~ ( cP_1 @ X0 @ X1 ) )
& ! [X4: $i,X0: $i,X2: $i,X1: $i,X3: $i,X5: $i] :
( ~ ( cQ_5 @ X0 @ X1 @ X2 )
| ( cQ_6 @ X3 @ X4 @ X5 )
| ~ ( cP_5 @ ( f @ X2 ) @ X5 )
| ~ ( cP_5 @ ( f @ X1 ) @ X4 )
| ~ ( cP_5 @ ( f @ X0 ) @ X3 ) )
& ( cP_2 @ b @ b )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ( cP_1 @ a @ a )
& ( cP_4 @ a @ a )
& ! [X4: $i,X3: $i,X2: $i,X0: $i,X1: $i,X5: $i] :
( ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ( cQ_3 @ X3 @ X4 @ X5 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 ) )
& ( cP_2 @ c @ c )
& ( cP_3 @ c @ c )
& ! [X0: $i] : ( cP_4 @ d @ X0 )
& ! [X0: $i,X1: $i] :
( ~ ( cP_2 @ X0 @ X1 )
| ( cP_2 @ ( f @ X0 ) @ X1 ) )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ( cP_1 @ c @ c )
& ! [X0: $i,X1: $i] :
( ( cP_5 @ ( f @ X0 ) @ X1 )
| ~ ( cP_5 @ X0 @ X1 ) )
& ! [X0: $i] : ( cP_3 @ d @ X0 )
& ( cQ_1 @ a @ b @ c )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X3: $i,X0: $i,X5: $i,X1: $i,X4: $i,X2: $i] :
( ~ ( cQ_3 @ X0 @ X1 @ X2 )
| ( cQ_4 @ X3 @ X4 @ X5 )
| ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ~ ( cP_3 @ ( f @ X0 ) @ X3 ) )
& ! [X0: $i] : ( cP_5 @ d @ X0 )
& ( cP_3 @ b @ b )
& ! [X5: $i,X0: $i,X3: $i,X1: $i,X4: $i,X2: $i] :
( ~ ( cP_4 @ ( f @ X0 ) @ X3 )
| ( cQ_5 @ X3 @ X4 @ X5 )
| ~ ( cQ_4 @ X0 @ X1 @ X2 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 ) )
& ( cP_6 @ a @ a )
& ( cP_3 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [X5: $i,X2: $i,X3: $i,X0: $i,X4: $i,X1: $i] :
( ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ( cQ_2 @ X3 @ X4 @ X5 ) )
& ! [X1: $i,X0: $i] :
( ~ ( cP_3 @ X0 @ X1 )
| ( cP_3 @ ( f @ X0 ) @ X1 ) )
& ! [X0: $i,X1: $i] :
( ( cP_6 @ ( f @ X0 ) @ X1 )
| ~ ( cP_6 @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ~ ( ! [X0: $i] : ( cP_6 @ d @ X0 )
& ( cP_5 @ a @ a )
& ( cP_1 @ b @ b )
& ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_7 @ X1 @ X2 @ X3 )
& ( cP_6 @ c @ c )
& ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
( ~ ( cP_6 @ ( f @ X8 ) @ X7 )
| ~ ( cP_6 @ ( f @ X6 ) @ X4 )
| ~ ( cP_6 @ ( f @ X5 ) @ X9 )
| ~ ( cQ_6 @ X6 @ X5 @ X8 )
| ( cQ_7 @ X4 @ X9 @ X7 ) )
& ! [X10: $i,X11: $i] :
( ~ ( cP_4 @ X10 @ X11 )
| ( cP_4 @ ( f @ X10 ) @ X11 ) )
& ( cP_2 @ a @ a )
& ! [X12: $i,X13: $i] :
( ( cP_1 @ ( f @ X12 ) @ X13 )
| ~ ( cP_1 @ X12 @ X13 ) )
& ! [X14: $i,X15: $i,X16: $i,X17: $i,X18: $i,X19: $i] :
( ~ ( cQ_5 @ X15 @ X17 @ X16 )
| ( cQ_6 @ X18 @ X14 @ X19 )
| ~ ( cP_5 @ ( f @ X16 ) @ X19 )
| ~ ( cP_5 @ ( f @ X17 ) @ X14 )
| ~ ( cP_5 @ ( f @ X15 ) @ X18 ) )
& ( cP_2 @ b @ b )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ( cP_1 @ a @ a )
& ( cP_4 @ a @ a )
& ! [X20: $i,X21: $i,X22: $i,X23: $i,X24: $i,X25: $i] :
( ~ ( cP_2 @ ( f @ X22 ) @ X25 )
| ( cQ_3 @ X21 @ X20 @ X25 )
| ~ ( cP_2 @ ( f @ X24 ) @ X20 )
| ~ ( cQ_2 @ X23 @ X24 @ X22 )
| ~ ( cP_2 @ ( f @ X23 ) @ X21 ) )
& ( cP_2 @ c @ c )
& ( cP_3 @ c @ c )
& ! [X26: $i] : ( cP_4 @ d @ X26 )
& ! [X27: $i,X28: $i] :
( ~ ( cP_2 @ X27 @ X28 )
| ( cP_2 @ ( f @ X27 ) @ X28 ) )
& ! [X29: $i] : ( cP_2 @ d @ X29 )
& ( cP_1 @ c @ c )
& ! [X30: $i,X31: $i] :
( ( cP_5 @ ( f @ X30 ) @ X31 )
| ~ ( cP_5 @ X30 @ X31 ) )
& ! [X32: $i] : ( cP_3 @ d @ X32 )
& ( cQ_1 @ a @ b @ c )
& ! [X33: $i] : ( cP_1 @ d @ X33 )
& ! [X34: $i,X35: $i,X36: $i,X37: $i,X38: $i,X39: $i] :
( ~ ( cQ_3 @ X35 @ X37 @ X39 )
| ( cQ_4 @ X34 @ X38 @ X36 )
| ~ ( cP_3 @ ( f @ X39 ) @ X36 )
| ~ ( cP_3 @ ( f @ X37 ) @ X38 )
| ~ ( cP_3 @ ( f @ X35 ) @ X34 ) )
& ! [X40: $i] : ( cP_5 @ d @ X40 )
& ( cP_3 @ b @ b )
& ! [X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i] :
( ~ ( cP_4 @ ( f @ X42 ) @ X43 )
| ( cQ_5 @ X43 @ X45 @ X41 )
| ~ ( cQ_4 @ X42 @ X44 @ X46 )
| ~ ( cP_4 @ ( f @ X46 ) @ X41 )
| ~ ( cP_4 @ ( f @ X44 ) @ X45 ) )
& ( cP_6 @ a @ a )
& ( cP_3 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [X47: $i,X48: $i,X49: $i,X50: $i,X51: $i,X52: $i] :
( ~ ( cQ_1 @ X50 @ X52 @ X48 )
| ~ ( cP_1 @ ( f @ X52 ) @ X51 )
| ~ ( cP_1 @ ( f @ X50 ) @ X49 )
| ~ ( cP_1 @ ( f @ X48 ) @ X47 )
| ( cQ_2 @ X49 @ X51 @ X47 ) )
& ! [X53: $i,X54: $i] :
( ~ ( cP_3 @ X54 @ X53 )
| ( cP_3 @ ( f @ X54 ) @ X53 ) )
& ! [X55: $i,X56: $i] :
( ( cP_6 @ ( f @ X55 ) @ X56 )
| ~ ( cP_6 @ X55 @ X56 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i] :
( ( cP_6 @ d @ X0 )
= $true )
& ( ( cP_5 @ a @ a )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ! [X1: $i,X2: $i,X3: $i] :
( $true
!= ( cQ_7 @ X1 @ X2 @ X3 ) )
& ( ( cP_6 @ c @ c )
= $true )
& ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
( ( $true
!= ( cP_6 @ ( f @ X8 ) @ X7 ) )
| ( $true
!= ( cP_6 @ ( f @ X6 ) @ X4 ) )
| ( $true
!= ( cP_6 @ ( f @ X5 ) @ X9 ) )
| ( $true
!= ( cQ_6 @ X6 @ X5 @ X8 ) )
| ( $true
= ( cQ_7 @ X4 @ X9 @ X7 ) ) )
& ! [X10: $i,X11: $i] :
( ( $true
!= ( cP_4 @ X10 @ X11 ) )
| ( $true
= ( cP_4 @ ( f @ X10 ) @ X11 ) ) )
& ( ( cP_2 @ a @ a )
= $true )
& ! [X12: $i,X13: $i] :
( ( $true
= ( cP_1 @ ( f @ X12 ) @ X13 ) )
| ( $true
!= ( cP_1 @ X12 @ X13 ) ) )
& ! [X14: $i,X15: $i,X16: $i,X17: $i,X18: $i,X19: $i] :
( ( $true
!= ( cQ_5 @ X15 @ X17 @ X16 ) )
| ( $true
= ( cQ_6 @ X18 @ X14 @ X19 ) )
| ( $true
!= ( cP_5 @ ( f @ X16 ) @ X19 ) )
| ( $true
!= ( cP_5 @ ( f @ X17 ) @ X14 ) )
| ( $true
!= ( cP_5 @ ( f @ X15 ) @ X18 ) ) )
& ( ( cP_2 @ b @ b )
= $true )
& ( ( cP_5 @ b @ b )
= $true )
& ( ( cP_5 @ c @ c )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cP_4 @ a @ a )
= $true )
& ! [X20: $i,X21: $i,X22: $i,X23: $i,X24: $i,X25: $i] :
( ( $true
!= ( cP_2 @ ( f @ X22 ) @ X25 ) )
| ( $true
= ( cQ_3 @ X21 @ X20 @ X25 ) )
| ( ( cP_2 @ ( f @ X24 ) @ X20 )
!= $true )
| ( $true
!= ( cQ_2 @ X23 @ X24 @ X22 ) )
| ( ( cP_2 @ ( f @ X23 ) @ X21 )
!= $true ) )
& ( ( cP_2 @ c @ c )
= $true )
& ( ( cP_3 @ c @ c )
= $true )
& ! [X26: $i] :
( ( cP_4 @ d @ X26 )
= $true )
& ! [X27: $i,X28: $i] :
( ( $true
!= ( cP_2 @ X27 @ X28 ) )
| ( $true
= ( cP_2 @ ( f @ X27 ) @ X28 ) ) )
& ! [X29: $i] :
( $true
= ( cP_2 @ d @ X29 ) )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X30: $i,X31: $i] :
( ( $true
= ( cP_5 @ ( f @ X30 ) @ X31 ) )
| ( $true
!= ( cP_5 @ X30 @ X31 ) ) )
& ! [X32: $i] :
( $true
= ( cP_3 @ d @ X32 ) )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X33: $i] :
( $true
= ( cP_1 @ d @ X33 ) )
& ! [X34: $i,X35: $i,X36: $i,X37: $i,X38: $i,X39: $i] :
( ( ( cQ_3 @ X35 @ X37 @ X39 )
!= $true )
| ( $true
= ( cQ_4 @ X34 @ X38 @ X36 ) )
| ( $true
!= ( cP_3 @ ( f @ X39 ) @ X36 ) )
| ( $true
!= ( cP_3 @ ( f @ X37 ) @ X38 ) )
| ( ( cP_3 @ ( f @ X35 ) @ X34 )
!= $true ) )
& ! [X40: $i] :
( $true
= ( cP_5 @ d @ X40 ) )
& ( ( cP_3 @ b @ b )
= $true )
& ! [X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i] :
( ( $true
!= ( cP_4 @ ( f @ X42 ) @ X43 ) )
| ( $true
= ( cQ_5 @ X43 @ X45 @ X41 ) )
| ( ( cQ_4 @ X42 @ X44 @ X46 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X46 ) @ X41 ) )
| ( $true
!= ( cP_4 @ ( f @ X44 ) @ X45 ) ) )
& ( ( cP_6 @ a @ a )
= $true )
& ( ( cP_3 @ a @ a )
= $true )
& ( ( cP_6 @ b @ b )
= $true )
& ( ( cP_4 @ b @ b )
= $true )
& ( ( cP_4 @ c @ c )
= $true )
& ! [X47: $i,X48: $i,X49: $i,X50: $i,X51: $i,X52: $i] :
( ( $true
!= ( cQ_1 @ X50 @ X52 @ X48 ) )
| ( $true
!= ( cP_1 @ ( f @ X52 ) @ X51 ) )
| ( ( cP_1 @ ( f @ X50 ) @ X49 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X48 ) @ X47 ) )
| ( ( cQ_2 @ X49 @ X51 @ X47 )
= $true ) )
& ! [X53: $i,X54: $i] :
( ( ( cP_3 @ X54 @ X53 )
!= $true )
| ( $true
= ( cP_3 @ ( f @ X54 ) @ X53 ) ) )
& ! [X55: $i,X56: $i] :
( ( $true
= ( cP_6 @ ( f @ X55 ) @ X56 ) )
| ( $true
!= ( cP_6 @ X55 @ X56 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( cP_4 @ b @ b )
= $true )
& ( ( cP_3 @ b @ b )
= $true )
& ! [X30: $i,X31: $i] :
( ( $true
= ( cP_5 @ ( f @ X30 ) @ X31 ) )
| ( $true
!= ( cP_5 @ X30 @ X31 ) ) )
& ! [X10: $i,X11: $i] :
( ( $true
!= ( cP_4 @ X10 @ X11 ) )
| ( $true
= ( cP_4 @ ( f @ X10 ) @ X11 ) ) )
& ! [X32: $i] :
( $true
= ( cP_3 @ d @ X32 ) )
& ( ( cP_1 @ a @ a )
= $true )
& ! [X2: $i,X3: $i,X1: $i] :
( $true
!= ( cQ_7 @ X1 @ X2 @ X3 ) )
& ( ( cP_2 @ b @ b )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ! [X41: $i,X43: $i,X46: $i,X44: $i,X42: $i,X45: $i] :
( ( $true
!= ( cP_4 @ ( f @ X44 ) @ X45 ) )
| ( ( cQ_4 @ X42 @ X44 @ X46 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X42 ) @ X43 ) )
| ( $true
!= ( cP_4 @ ( f @ X46 ) @ X41 ) )
| ( $true
= ( cQ_5 @ X43 @ X45 @ X41 ) ) )
& ( ( cP_4 @ c @ c )
= $true )
& ( ( cP_2 @ a @ a )
= $true )
& ( ( cP_6 @ a @ a )
= $true )
& ! [X29: $i] :
( $true
= ( cP_2 @ d @ X29 ) )
& ! [X24: $i,X22: $i,X21: $i,X23: $i,X25: $i,X20: $i] :
( ( $true
!= ( cP_2 @ ( f @ X22 ) @ X25 ) )
| ( $true
= ( cQ_3 @ X21 @ X20 @ X25 ) )
| ( ( cP_2 @ ( f @ X24 ) @ X20 )
!= $true )
| ( ( cP_2 @ ( f @ X23 ) @ X21 )
!= $true )
| ( $true
!= ( cQ_2 @ X23 @ X24 @ X22 ) ) )
& ( ( cP_5 @ c @ c )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_6 @ b @ b )
= $true )
& ! [X28: $i,X27: $i] :
( ( $true
!= ( cP_2 @ X27 @ X28 ) )
| ( $true
= ( cP_2 @ ( f @ X27 ) @ X28 ) ) )
& ( ( cP_5 @ b @ b )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X54: $i,X53: $i] :
( ( $true
= ( cP_3 @ ( f @ X54 ) @ X53 ) )
| ( ( cP_3 @ X54 @ X53 )
!= $true ) )
& ( ( cP_3 @ c @ c )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X33: $i] :
( $true
= ( cP_1 @ d @ X33 ) )
& ! [X39: $i,X37: $i,X34: $i,X38: $i,X35: $i,X36: $i] :
( ( ( cP_3 @ ( f @ X35 ) @ X34 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X39 ) @ X36 ) )
| ( $true
= ( cQ_4 @ X34 @ X38 @ X36 ) )
| ( ( cQ_3 @ X35 @ X37 @ X39 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X37 ) @ X38 ) ) )
& ( ( cP_3 @ a @ a )
= $true )
& ! [X52: $i,X50: $i,X48: $i,X51: $i,X49: $i,X47: $i] :
( ( $true
!= ( cQ_1 @ X50 @ X52 @ X48 ) )
| ( ( cP_1 @ ( f @ X50 ) @ X49 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X48 ) @ X47 ) )
| ( $true
!= ( cP_1 @ ( f @ X52 ) @ X51 ) )
| ( ( cQ_2 @ X49 @ X51 @ X47 )
= $true ) )
& ! [X55: $i,X56: $i] :
( ( $true
= ( cP_6 @ ( f @ X55 ) @ X56 ) )
| ( $true
!= ( cP_6 @ X55 @ X56 ) ) )
& ! [X14: $i,X17: $i,X15: $i,X16: $i,X19: $i,X18: $i] :
( ( $true
!= ( cP_5 @ ( f @ X16 ) @ X19 ) )
| ( $true
!= ( cP_5 @ ( f @ X15 ) @ X18 ) )
| ( $true
!= ( cP_5 @ ( f @ X17 ) @ X14 ) )
| ( $true
!= ( cQ_5 @ X15 @ X17 @ X16 ) )
| ( $true
= ( cQ_6 @ X18 @ X14 @ X19 ) ) )
& ( ( cP_6 @ c @ c )
= $true )
& ! [X40: $i] :
( $true
= ( cP_5 @ d @ X40 ) )
& ! [X26: $i] :
( ( cP_4 @ d @ X26 )
= $true )
& ! [X12: $i,X13: $i] :
( ( $true
= ( cP_1 @ ( f @ X12 ) @ X13 ) )
| ( $true
!= ( cP_1 @ X12 @ X13 ) ) )
& ! [X7: $i,X5: $i,X4: $i,X9: $i,X8: $i,X6: $i] :
( ( $true
= ( cQ_7 @ X4 @ X9 @ X7 ) )
| ( $true
!= ( cP_6 @ ( f @ X8 ) @ X7 ) )
| ( $true
!= ( cQ_6 @ X6 @ X5 @ X8 ) )
| ( $true
!= ( cP_6 @ ( f @ X6 ) @ X4 ) )
| ( $true
!= ( cP_6 @ ( f @ X5 ) @ X9 ) ) )
& ( ( cP_5 @ a @ a )
= $true )
& ! [X0: $i] :
( ( cP_6 @ d @ X0 )
= $true )
& ( ( cP_4 @ a @ a )
= $true ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ( cP_4 @ b @ b )
= $true )
& ( ( cP_3 @ b @ b )
= $true )
& ! [X0: $i,X1: $i] :
( ( ( cP_5 @ ( f @ X0 ) @ X1 )
= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( cP_4 @ X2 @ X3 ) )
| ( $true
= ( cP_4 @ ( f @ X2 ) @ X3 ) ) )
& ! [X4: $i] :
( $true
= ( cP_3 @ d @ X4 ) )
& ( ( cP_1 @ a @ a )
= $true )
& ! [X5: $i,X6: $i,X7: $i] :
( $true
!= ( cQ_7 @ X7 @ X5 @ X6 ) )
& ( ( cP_2 @ b @ b )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ! [X8: $i,X9: $i,X10: $i,X11: $i,X12: $i,X13: $i] :
( ( ( cP_4 @ ( f @ X11 ) @ X13 )
!= $true )
| ( $true
!= ( cQ_4 @ X12 @ X11 @ X10 ) )
| ( $true
!= ( cP_4 @ ( f @ X12 ) @ X9 ) )
| ( ( cP_4 @ ( f @ X10 ) @ X8 )
!= $true )
| ( ( cQ_5 @ X9 @ X13 @ X8 )
= $true ) )
& ( ( cP_4 @ c @ c )
= $true )
& ( ( cP_2 @ a @ a )
= $true )
& ( ( cP_6 @ a @ a )
= $true )
& ! [X14: $i] :
( $true
= ( cP_2 @ d @ X14 ) )
& ! [X15: $i,X16: $i,X17: $i,X18: $i,X19: $i,X20: $i] :
( ( $true
!= ( cP_2 @ ( f @ X16 ) @ X19 ) )
| ( $true
= ( cQ_3 @ X17 @ X20 @ X19 ) )
| ( ( cP_2 @ ( f @ X15 ) @ X20 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X18 ) @ X17 ) )
| ( $true
!= ( cQ_2 @ X18 @ X15 @ X16 ) ) )
& ( ( cP_5 @ c @ c )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_6 @ b @ b )
= $true )
& ! [X21: $i,X22: $i] :
( ( $true
!= ( cP_2 @ X22 @ X21 ) )
| ( $true
= ( cP_2 @ ( f @ X22 ) @ X21 ) ) )
& ( ( cP_5 @ b @ b )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X23: $i,X24: $i] :
( ( $true
= ( cP_3 @ ( f @ X23 ) @ X24 ) )
| ( $true
!= ( cP_3 @ X23 @ X24 ) ) )
& ( ( cP_3 @ c @ c )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X25: $i] :
( $true
= ( cP_1 @ d @ X25 ) )
& ! [X26: $i,X27: $i,X28: $i,X29: $i,X30: $i,X31: $i] :
( ( ( cP_3 @ ( f @ X30 ) @ X28 )
!= $true )
| ( ( cP_3 @ ( f @ X26 ) @ X31 )
!= $true )
| ( ( cQ_4 @ X28 @ X29 @ X31 )
= $true )
| ( $true
!= ( cQ_3 @ X30 @ X27 @ X26 ) )
| ( ( cP_3 @ ( f @ X27 ) @ X29 )
!= $true ) )
& ( ( cP_3 @ a @ a )
= $true )
& ! [X32: $i,X33: $i,X34: $i,X35: $i,X36: $i,X37: $i] :
( ( ( cQ_1 @ X33 @ X32 @ X34 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X33 ) @ X36 ) )
| ( $true
!= ( cP_1 @ ( f @ X34 ) @ X37 ) )
| ( $true
!= ( cP_1 @ ( f @ X32 ) @ X35 ) )
| ( $true
= ( cQ_2 @ X36 @ X35 @ X37 ) ) )
& ! [X38: $i,X39: $i] :
( ( ( cP_6 @ ( f @ X38 ) @ X39 )
= $true )
| ( ( cP_6 @ X38 @ X39 )
!= $true ) )
& ! [X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i] :
( ( $true
!= ( cP_5 @ ( f @ X43 ) @ X44 ) )
| ( ( cP_5 @ ( f @ X42 ) @ X45 )
!= $true )
| ( ( cP_5 @ ( f @ X41 ) @ X40 )
!= $true )
| ( ( cQ_5 @ X42 @ X41 @ X43 )
!= $true )
| ( $true
= ( cQ_6 @ X45 @ X40 @ X44 ) ) )
& ( ( cP_6 @ c @ c )
= $true )
& ! [X46: $i] :
( $true
= ( cP_5 @ d @ X46 ) )
& ! [X47: $i] :
( $true
= ( cP_4 @ d @ X47 ) )
& ! [X48: $i,X49: $i] :
( ( ( cP_1 @ ( f @ X48 ) @ X49 )
= $true )
| ( $true
!= ( cP_1 @ X48 @ X49 ) ) )
& ! [X50: $i,X51: $i,X52: $i,X53: $i,X54: $i,X55: $i] :
( ( $true
= ( cQ_7 @ X52 @ X53 @ X50 ) )
| ( $true
!= ( cP_6 @ ( f @ X54 ) @ X50 ) )
| ( $true
!= ( cQ_6 @ X55 @ X51 @ X54 ) )
| ( $true
!= ( cP_6 @ ( f @ X55 ) @ X52 ) )
| ( $true
!= ( cP_6 @ ( f @ X51 ) @ X53 ) ) )
& ( ( cP_5 @ a @ a )
= $true )
& ! [X56: $i] :
( $true
= ( cP_6 @ d @ X56 ) )
& ( ( cP_4 @ a @ a )
= $true ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( cP_4 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
( ( cP_5 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
! [X50: $i,X51: $i,X54: $i,X55: $i,X52: $i,X53: $i] :
( ( $true
!= ( cP_6 @ ( f @ X55 ) @ X52 ) )
| ( $true
!= ( cQ_6 @ X55 @ X51 @ X54 ) )
| ( $true
= ( cQ_7 @ X52 @ X53 @ X50 ) )
| ( $true
!= ( cP_6 @ ( f @ X54 ) @ X50 ) )
| ( $true
!= ( cP_6 @ ( f @ X51 ) @ X53 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
! [X48: $i,X49: $i] :
( ( ( cP_1 @ ( f @ X48 ) @ X49 )
= $true )
| ( $true
!= ( cP_1 @ X48 @ X49 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f14,plain,
( ( cP_6 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
! [X40: $i,X41: $i,X44: $i,X45: $i,X42: $i,X43: $i] :
( ( $true
= ( cQ_6 @ X45 @ X40 @ X44 ) )
| ( ( cP_5 @ ( f @ X42 ) @ X45 )
!= $true )
| ( ( cQ_5 @ X42 @ X41 @ X43 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X43 ) @ X44 ) )
| ( ( cP_5 @ ( f @ X41 ) @ X40 )
!= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f16,plain,
! [X38: $i,X39: $i] :
( ( ( cP_6 @ ( f @ X38 ) @ X39 )
= $true )
| ( ( cP_6 @ X38 @ X39 )
!= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f17,plain,
! [X36: $i,X37: $i,X34: $i,X35: $i,X32: $i,X33: $i] :
( ( $true
= ( cQ_2 @ X36 @ X35 @ X37 ) )
| ( ( cQ_1 @ X33 @ X32 @ X34 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X34 ) @ X37 ) )
| ( $true
!= ( cP_1 @ ( f @ X32 ) @ X35 ) )
| ( $true
!= ( cP_1 @ ( f @ X33 ) @ X36 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f18,plain,
( ( cP_3 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f19,plain,
! [X31: $i,X28: $i,X29: $i,X26: $i,X27: $i,X30: $i] :
( ( ( cQ_4 @ X28 @ X29 @ X31 )
= $true )
| ( ( cP_3 @ ( f @ X26 ) @ X31 )
!= $true )
| ( ( cP_3 @ ( f @ X30 ) @ X28 )
!= $true )
| ( $true
!= ( cQ_3 @ X30 @ X27 @ X26 ) )
| ( ( cP_3 @ ( f @ X27 ) @ X29 )
!= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f21,plain,
( ( cP_1 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f22,plain,
( ( cP_3 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f23,plain,
! [X24: $i,X23: $i] :
( ( $true
= ( cP_3 @ ( f @ X23 ) @ X24 ) )
| ( $true
!= ( cP_3 @ X23 @ X24 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f24,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f25,plain,
( ( cP_5 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f26,plain,
! [X21: $i,X22: $i] :
( ( $true
= ( cP_2 @ ( f @ X22 ) @ X21 ) )
| ( $true
!= ( cP_2 @ X22 @ X21 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f27,plain,
( ( cP_6 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f28,plain,
( ( cP_1 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f29,plain,
( ( cP_5 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f30,plain,
! [X18: $i,X19: $i,X16: $i,X17: $i,X15: $i,X20: $i] :
( ( $true
= ( cQ_3 @ X17 @ X20 @ X19 ) )
| ( $true
!= ( cP_2 @ ( f @ X18 ) @ X17 ) )
| ( ( cP_2 @ ( f @ X15 ) @ X20 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X16 ) @ X19 ) )
| ( $true
!= ( cQ_2 @ X18 @ X15 @ X16 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f32,plain,
( ( cP_6 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f33,plain,
( ( cP_2 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f34,plain,
( ( cP_4 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f35,plain,
! [X10: $i,X11: $i,X8: $i,X9: $i,X12: $i,X13: $i] :
( ( ( cQ_5 @ X9 @ X13 @ X8 )
= $true )
| ( $true
!= ( cQ_4 @ X12 @ X11 @ X10 ) )
| ( ( cP_4 @ ( f @ X10 ) @ X8 )
!= $true )
| ( ( cP_4 @ ( f @ X11 ) @ X13 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X12 ) @ X9 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f36,plain,
( ( cP_2 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f37,plain,
( ( cP_2 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f38,plain,
! [X6: $i,X7: $i,X5: $i] :
( $true
!= ( cQ_7 @ X7 @ X5 @ X6 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f39,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f41,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( cP_4 @ ( f @ X2 ) @ X3 ) )
| ( $true
!= ( cP_4 @ X2 @ X3 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f42,plain,
! [X0: $i,X1: $i] :
( ( ( cP_5 @ ( f @ X0 ) @ X1 )
= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f43,plain,
( ( cP_3 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f44,plain,
( ( cP_4 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f47,definition,
( spl0_1
<=> ( ( cP_5 @ c @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f49,plain,
( ( ( cP_5 @ c @ c )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f47]) ).
thf(f50,plain,
spl0_1,
inference(avatar_split_clause,[],[f29,f47]) ).
thf(f52,definition,
( spl0_2
<=> ( ( cP_2 @ a @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f54,plain,
( ( ( cP_2 @ a @ a )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f55,plain,
spl0_2,
inference(avatar_split_clause,[],[f33,f52]) ).
thf(f57,definition,
( spl0_3
<=> ( ( cP_5 @ b @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f59,plain,
( ( ( cP_5 @ b @ b )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f57]) ).
thf(f60,plain,
spl0_3,
inference(avatar_split_clause,[],[f25,f57]) ).
thf(f62,definition,
( spl0_4
<=> ( ( cP_3 @ c @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f64,plain,
( ( ( cP_3 @ c @ c )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f65,plain,
spl0_4,
inference(avatar_split_clause,[],[f22,f62]) ).
thf(f67,definition,
( spl0_5
<=> ( ( cP_6 @ b @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f69,plain,
( ( ( cP_6 @ b @ b )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f70,plain,
spl0_5,
inference(avatar_split_clause,[],[f27,f67]) ).
thf(f72,definition,
( spl0_6
<=> ( ( cP_2 @ b @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f74,plain,
( ( ( cP_2 @ b @ b )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f72]) ).
thf(f75,plain,
spl0_6,
inference(avatar_split_clause,[],[f37,f72]) ).
thf(f77,definition,
( spl0_7
<=> ( ( cP_3 @ b @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
thf(f79,plain,
( ( ( cP_3 @ b @ b )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f77]) ).
thf(f80,plain,
spl0_7,
inference(avatar_split_clause,[],[f43,f77]) ).
thf(f82,definition,
( spl0_8
<=> ( ( cP_1 @ a @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
thf(f84,plain,
( ( ( cP_1 @ a @ a )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f85,plain,
spl0_8,
inference(avatar_split_clause,[],[f39,f82]) ).
thf(f87,definition,
( spl0_9
<=> ( ( cP_6 @ c @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
thf(f89,plain,
( ( ( cP_6 @ c @ c )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f90,plain,
spl0_9,
inference(avatar_split_clause,[],[f14,f87]) ).
thf(f92,definition,
( spl0_10
<=> ( ( cP_1 @ b @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
thf(f94,plain,
( ( ( cP_1 @ b @ b )
= $true )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f95,plain,
spl0_10,
inference(avatar_split_clause,[],[f28,f92]) ).
thf(f97,definition,
( spl0_11
<=> ( ( cP_1 @ c @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
thf(f99,plain,
( ( ( cP_1 @ c @ c )
= $true )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f100,plain,
spl0_11,
inference(avatar_split_clause,[],[f21,f97]) ).
thf(f102,definition,
( spl0_12
<=> ( ( cP_3 @ a @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
thf(f104,plain,
( ( ( cP_3 @ a @ a )
= $true )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f102]) ).
thf(f105,plain,
spl0_12,
inference(avatar_split_clause,[],[f18,f102]) ).
thf(f107,definition,
( spl0_13
<=> ( ( cP_5 @ a @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
thf(f109,plain,
( ( ( cP_5 @ a @ a )
= $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f107]) ).
thf(f110,plain,
spl0_13,
inference(avatar_split_clause,[],[f9,f107]) ).
thf(f112,definition,
( spl0_14
<=> ( ( cP_2 @ c @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
thf(f114,plain,
( ( ( cP_2 @ c @ c )
= $true )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f112]) ).
thf(f115,plain,
spl0_14,
inference(avatar_split_clause,[],[f36,f112]) ).
thf(f117,definition,
( spl0_15
<=> ( ( cP_4 @ c @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
thf(f119,plain,
( ( ( cP_4 @ c @ c )
= $true )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f120,plain,
spl0_15,
inference(avatar_split_clause,[],[f34,f117]) ).
thf(f122,definition,
( spl0_16
<=> ( ( cQ_1 @ a @ b @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
thf(f124,plain,
( ( ( cQ_1 @ a @ b @ c )
= $true )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f122]) ).
thf(f125,plain,
spl0_16,
inference(avatar_split_clause,[],[f24,f122]) ).
thf(f127,definition,
( spl0_17
<=> ( ( cP_4 @ a @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
thf(f129,plain,
( ( ( cP_4 @ a @ a )
= $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f127]) ).
thf(f130,plain,
spl0_17,
inference(avatar_split_clause,[],[f7,f127]) ).
thf(f132,definition,
( spl0_18
<=> ( ( cP_6 @ a @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
thf(f134,plain,
( ( ( cP_6 @ a @ a )
= $true )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f135,plain,
spl0_18,
inference(avatar_split_clause,[],[f32,f132]) ).
thf(f137,definition,
( spl0_19
<=> ( ( cP_4 @ b @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
thf(f139,plain,
( ( ( cP_4 @ b @ b )
= $true )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f140,plain,
spl0_19,
inference(avatar_split_clause,[],[f44,f137]) ).
thf(f141,plain,
! [X50: $i,X51: $i,X54: $i,X55: $i,X52: $i,X53: $i] :
( ( $true
!= ( cQ_6 @ X55 @ X51 @ X54 ) )
| ( $true
!= ( cP_6 @ ( f @ X54 ) @ X50 ) )
| ( $true
!= ( cP_6 @ ( f @ X51 ) @ X53 ) )
| ( $true
!= ( cP_6 @ ( f @ X55 ) @ X52 ) ) ),
inference(forward_subsumption_resolution,[],[f10,f38]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_5 @ ( f @ X6 ) @ X0 ) )
| ( $true != $true )
| ( $true
!= ( cP_5 @ ( f @ X7 ) @ X1 ) )
| ( ( cQ_5 @ X6 @ X7 @ X8 )
!= $true )
| ( ( cP_5 @ ( f @ X8 ) @ X2 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X0 ) @ X5 ) )
| ( ( cP_6 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_6 @ ( f @ X2 ) @ X3 )
!= $true ) ),
inference(superposition,[],[f141,f15]) ).
thf(f143,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cQ_5 @ X6 @ X7 @ X8 )
!= $true )
| ( ( cP_6 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_5 @ ( f @ X8 ) @ X2 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X6 ) @ X0 ) )
| ( $true
!= ( cP_6 @ ( f @ X0 ) @ X5 ) )
| ( $true
!= ( cP_5 @ ( f @ X7 ) @ X1 ) )
| ( ( cP_6 @ ( f @ X2 ) @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f142]) ).
thf(f144,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] :
( ( ( cP_4 @ ( f @ X11 ) @ X2 )
!= $true )
| ( ( cP_5 @ ( f @ X1 ) @ X3 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X6 ) @ X7 ) )
| ( $true
!= ( cP_5 @ ( f @ X0 ) @ X6 ) )
| ( ( cQ_4 @ X9 @ X10 @ X11 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X4 ) )
| ( ( cP_5 @ ( f @ X2 ) @ X5 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X5 ) @ X8 ) )
| ( $true
!= ( cP_4 @ ( f @ X9 ) @ X0 ) )
| ( $true != $true )
| ( $true
!= ( cP_4 @ ( f @ X10 ) @ X1 ) ) ),
inference(superposition,[],[f143,f35]) ).
thf(f145,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_4 @ X9 @ X10 @ X11 )
!= $true )
| ( ( cP_5 @ ( f @ X1 ) @ X3 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X9 ) @ X0 ) )
| ( ( cP_4 @ ( f @ X11 ) @ X2 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X10 ) @ X1 ) )
| ( $true
!= ( cP_5 @ ( f @ X0 ) @ X6 ) )
| ( ( cP_5 @ ( f @ X2 ) @ X5 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X4 ) )
| ( $true
!= ( cP_6 @ ( f @ X5 ) @ X8 ) )
| ( $true
!= ( cP_6 @ ( f @ X6 ) @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f144]) ).
thf(f146,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_3 @ ( f @ X12 ) @ X2 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X6 ) @ X8 ) )
| ( $true
!= ( cP_6 @ ( f @ X8 ) @ X10 ) )
| ( $true != $true )
| ( $true
!= ( cP_3 @ ( f @ X14 ) @ X1 ) )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X1 ) @ X3 ) )
| ( $true
!= ( cP_4 @ ( f @ X0 ) @ X5 ) )
| ( $true
!= ( cP_3 @ ( f @ X13 ) @ X0 ) )
| ( $true
!= ( cQ_3 @ X13 @ X14 @ X12 ) )
| ( ( cP_6 @ ( f @ X4 ) @ X9 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X7 ) @ X11 ) )
| ( $true
!= ( cP_5 @ ( f @ X5 ) @ X7 ) )
| ( $true
!= ( cP_4 @ ( f @ X2 ) @ X6 ) ) ),
inference(superposition,[],[f145,f19]) ).
thf(f147,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X14: $i,X4: $i,X5: $i,X12: $i,X13: $i] :
( ( $true
!= ( cQ_3 @ X13 @ X14 @ X12 ) )
| ( $true
!= ( cP_6 @ ( f @ X8 ) @ X10 ) )
| ( $true
!= ( cP_4 @ ( f @ X0 ) @ X5 ) )
| ( $true
!= ( cP_5 @ ( f @ X5 ) @ X7 ) )
| ( $true
!= ( cP_4 @ ( f @ X2 ) @ X6 ) )
| ( ( cP_3 @ ( f @ X12 ) @ X2 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X14 ) @ X1 ) )
| ( $true
!= ( cP_3 @ ( f @ X13 ) @ X0 ) )
| ( $true
!= ( cP_6 @ ( f @ X7 ) @ X11 ) )
| ( $true
!= ( cP_5 @ ( f @ X6 ) @ X8 ) )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_6 @ ( f @ X4 ) @ X9 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X1 ) @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f146]) ).
thf(f148,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,X16: $i,X17: $i,X15: $i,X5: $i,X12: $i,X13: $i] :
( ( $true
!= ( cP_2 @ ( f @ X15 ) @ X0 ) )
| ( $true
!= ( cP_5 @ ( f @ X9 ) @ X3 ) )
| ( $true
!= ( cP_3 @ ( f @ X1 ) @ X10 ) )
| ( $true
!= ( cP_2 @ ( f @ X17 ) @ X2 ) )
| ( $true != $true )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X4 ) )
| ( $true
!= ( cP_4 @ ( f @ X8 ) @ X9 ) )
| ( $true
!= ( cP_6 @ ( f @ X7 ) @ X11 ) )
| ( ( cP_6 @ ( f @ X13 ) @ X14 )
!= $true )
| ( ( cP_4 @ ( f @ X5 ) @ X6 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X6 ) @ X7 ) )
| ( $true
!= ( cP_5 @ ( f @ X12 ) @ X13 ) )
| ( $true
!= ( cP_2 @ ( f @ X16 ) @ X1 ) )
| ( $true
!= ( cQ_2 @ X15 @ X16 @ X17 ) )
| ( $true
!= ( cP_4 @ ( f @ X10 ) @ X12 ) )
| ( ( cP_3 @ ( f @ X0 ) @ X5 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X2 ) @ X8 ) ) ),
inference(superposition,[],[f147,f30]) ).
thf(f149,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X16: $i,X7: $i,X4: $i,X14: $i,X17: $i,X15: $i,X5: $i,X12: $i,X13: $i] :
( ( $true
!= ( cQ_2 @ X15 @ X16 @ X17 ) )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X4 ) )
| ( $true
!= ( cP_5 @ ( f @ X12 ) @ X13 ) )
| ( $true
!= ( cP_5 @ ( f @ X9 ) @ X3 ) )
| ( $true
!= ( cP_6 @ ( f @ X7 ) @ X11 ) )
| ( $true
!= ( cP_2 @ ( f @ X15 ) @ X0 ) )
| ( $true
!= ( cP_5 @ ( f @ X6 ) @ X7 ) )
| ( ( cP_3 @ ( f @ X0 ) @ X5 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X10 ) @ X12 ) )
| ( ( cP_4 @ ( f @ X5 ) @ X6 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X8 ) @ X9 ) )
| ( ( cP_6 @ ( f @ X13 ) @ X14 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X17 ) @ X2 ) )
| ( $true
!= ( cP_2 @ ( f @ X16 ) @ X1 ) )
| ( $true
!= ( cP_3 @ ( f @ X2 ) @ X8 ) )
| ( $true
!= ( cP_3 @ ( f @ X1 ) @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X18: $i,X8: $i,X19: $i,X6: $i,X7: $i,X14: $i,X4: $i,X16: $i,X1: $i,X9: $i,X17: $i,X15: $i,X5: $i,X12: $i,X13: $i,X20: $i] :
( ( $true
!= ( cQ_1 @ X18 @ X19 @ X20 ) )
| ( $true
!= ( cP_1 @ ( f @ X18 ) @ X0 ) )
| ( ( cP_5 @ ( f @ X5 ) @ X6 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X10 ) @ X12 ) )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X4 ) )
| ( $true
!= ( cP_4 @ ( f @ X12 ) @ X11 ) )
| ( $true
!= ( cP_5 @ ( f @ X11 ) @ X8 ) )
| ( $true
!= ( cP_3 @ ( f @ X17 ) @ X13 ) )
| ( ( cP_4 @ ( f @ X14 ) @ X7 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X0 ) @ X10 ) )
| ( ( cP_6 @ ( f @ X6 ) @ X15 )
!= $true )
| ( ( cP_3 @ ( f @ X16 ) @ X14 )
!= $true )
| ( ( cP_5 @ ( f @ X7 ) @ X3 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X19 ) @ X1 ) )
| ( $true
!= ( cP_1 @ ( f @ X20 ) @ X2 ) )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X16 ) )
| ( $true != $true )
| ( $true
!= ( cP_2 @ ( f @ X1 ) @ X17 ) )
| ( ( cP_4 @ ( f @ X13 ) @ X5 )
!= $true )
| ( ( cP_6 @ ( f @ X8 ) @ X9 )
!= $true ) ),
inference(superposition,[],[f149,f17]) ).
thf(f151,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X18: $i,X1: $i,X19: $i,X6: $i,X8: $i,X7: $i,X4: $i,X16: $i,X14: $i,X9: $i,X17: $i,X15: $i,X5: $i,X12: $i,X13: $i,X20: $i] :
( ( $true
!= ( cQ_1 @ X18 @ X19 @ X20 ) )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X4 ) )
| ( $true
!= ( cP_2 @ ( f @ X1 ) @ X17 ) )
| ( $true
!= ( cP_3 @ ( f @ X10 ) @ X12 ) )
| ( $true
!= ( cP_2 @ ( f @ X0 ) @ X10 ) )
| ( ( cP_5 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_4 @ ( f @ X13 ) @ X5 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X11 ) @ X8 ) )
| ( ( cP_5 @ ( f @ X7 ) @ X3 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X12 ) @ X11 ) )
| ( $true
!= ( cP_1 @ ( f @ X18 ) @ X0 ) )
| ( ( cP_3 @ ( f @ X16 ) @ X14 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X20 ) @ X2 ) )
| ( ( cP_6 @ ( f @ X6 ) @ X15 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X17 ) @ X13 ) )
| ( ( cP_6 @ ( f @ X8 ) @ X9 )
!= $true )
| ( ( cP_4 @ ( f @ X14 ) @ X7 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X19 ) @ X1 ) )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f150]) ).
thf(f152,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 != $true )
| ( ( cP_6 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X8 ) @ X16 ) )
| ( $true
!= ( cP_1 @ ( f @ a ) @ X6 ) )
| ( ( cP_2 @ ( f @ X15 ) @ X13 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X5 ) @ X10 ) )
| ( $true
!= ( cP_3 @ ( f @ X13 ) @ X14 ) )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X2 )
!= $true )
| ( ( cP_4 @ ( f @ X14 ) @ X12 )
!= $true )
| ( ( cP_6 @ ( f @ X11 ) @ X17 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X3 ) @ X9 ) )
| ( $true
!= ( cP_5 @ ( f @ X12 ) @ X0 ) )
| ( $true
!= ( cP_2 @ ( f @ X6 ) @ X4 ) )
| ( ( cP_5 @ ( f @ X10 ) @ X11 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ c ) @ X15 ) )
| ( $true
!= ( cP_5 @ ( f @ X7 ) @ X8 ) )
| ( $true
!= ( cP_4 @ ( f @ X9 ) @ X7 ) ) )
| ~ spl0_16 ),
inference(superposition,[],[f151,f124]) ).
thf(f153,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,X16: $i,X17: $i,X15: $i,X5: $i,X12: $i,X13: $i] :
( ( $true
!= ( cP_2 @ ( f @ X6 ) @ X4 ) )
| ( ( cP_6 @ ( f @ X11 ) @ X17 )
!= $true )
| ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_2 @ ( f @ X15 ) @ X13 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X7 ) @ X8 ) )
| ( $true
!= ( cP_3 @ ( f @ X13 ) @ X14 ) )
| ( $true
!= ( cP_4 @ ( f @ X5 ) @ X10 ) )
| ( ( cP_5 @ ( f @ X10 ) @ X11 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ c ) @ X15 ) )
| ( $true
!= ( cP_5 @ ( f @ X12 ) @ X0 ) )
| ( $true
!= ( cP_3 @ ( f @ X3 ) @ X9 ) )
| ( ( cP_4 @ ( f @ X14 ) @ X12 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ a ) @ X6 ) )
| ( $true
!= ( cP_4 @ ( f @ X9 ) @ X7 ) )
| ( ( cP_1 @ ( f @ b ) @ X2 )
!= $true )
| ( ( cP_6 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X8 ) @ X16 ) ) )
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f152]) ).
thf(f155,definition,
( spl0_20
<=> ! [X15: $i,X13: $i,X0: $i,X14: $i,X12: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X15 ) @ X13 )
!= $true )
| ( ( cP_6 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X14 ) @ X12 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X12 ) @ X0 ) )
| ( $true
!= ( cP_1 @ ( f @ c ) @ X15 ) )
| ( $true
!= ( cP_3 @ ( f @ X13 ) @ X14 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
thf(f156,plain,
( ! [X0: $i,X1: $i,X14: $i,X15: $i,X12: $i,X13: $i] :
( ( $true
!= ( cP_1 @ ( f @ c ) @ X15 ) )
| ( ( cP_2 @ ( f @ X15 ) @ X13 )
!= $true )
| ( ( cP_6 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X13 ) @ X14 ) )
| ( ( cP_4 @ ( f @ X14 ) @ X12 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X12 ) @ X0 ) ) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f155]) ).
thf(f158,definition,
( spl0_21
<=> ! [X5: $i,X17: $i,X4: $i,X11: $i,X6: $i,X10: $i] :
( ( $true
!= ( cP_2 @ ( f @ X6 ) @ X4 ) )
| ( $true
!= ( cP_1 @ ( f @ a ) @ X6 ) )
| ( ( cP_5 @ ( f @ X10 ) @ X11 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X5 ) @ X10 ) )
| ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_6 @ ( f @ X11 ) @ X17 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
thf(f159,plain,
( ! [X10: $i,X11: $i,X6: $i,X4: $i,X17: $i,X5: $i] :
( ( $true
!= ( cP_1 @ ( f @ a ) @ X6 ) )
| ( ( cP_6 @ ( f @ X11 ) @ X17 )
!= $true )
| ( ( cP_5 @ ( f @ X10 ) @ X11 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X6 ) @ X4 ) )
| ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X5 ) @ X10 ) ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f158]) ).
thf(f161,definition,
( spl0_22
<=> ! [X3: $i,X9: $i,X7: $i,X8: $i,X16: $i,X2: $i] :
( ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X8 ) @ X16 ) )
| ( ( cP_1 @ ( f @ b ) @ X2 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X9 ) @ X7 ) )
| ( $true
!= ( cP_3 @ ( f @ X3 ) @ X9 ) )
| ( $true
!= ( cP_5 @ ( f @ X7 ) @ X8 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
thf(f162,plain,
( ! [X2: $i,X3: $i,X8: $i,X9: $i,X16: $i,X7: $i] :
( ( $true
!= ( cP_3 @ ( f @ X3 ) @ X9 ) )
| ( $true
!= ( cP_6 @ ( f @ X8 ) @ X16 ) )
| ( $true
!= ( cP_4 @ ( f @ X9 ) @ X7 ) )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X2 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X7 ) @ X8 ) ) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f161]) ).
thf(f163,plain,
( spl0_20
| spl0_21
| spl0_22
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f153,f122,f161,f158,f155]) ).
thf(f164,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_5 @ ( f @ X3 ) @ X1 ) )
| ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_6 @ ( f @ X1 ) @ X2 ) )
| ( ( cP_1 @ a @ X0 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X5 ) @ X3 ) )
| ( $true
!= ( cP_2 @ ( f @ X0 ) @ X4 ) ) )
| ~ spl0_21 ),
inference(superposition,[],[f159,f11]) ).
thf(f165,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_2 @ ( f @ X0 ) @ X4 ) )
| ( $true
!= ( cP_5 @ ( f @ X3 ) @ X1 ) )
| ( ( cP_1 @ a @ X0 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X5 ) @ X3 ) )
| ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X1 ) @ X2 ) ) )
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f164]) ).
thf(f166,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_6 @ ( f @ X3 ) @ X5 ) )
| ( ( cP_5 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true != $true )
| ( ( cP_4 @ ( f @ X4 ) @ X2 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ a @ X0 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X4 )
!= $true ) )
| ~ spl0_21 ),
inference(superposition,[],[f165,f26]) ).
thf(f167,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_6 @ ( f @ X3 ) @ X5 ) )
| ( ( cP_5 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X4 ) @ X2 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_1 @ a @ X0 )
!= $true ) )
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f166]) ).
thf(f168,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( $true != $true )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ a @ X3 )
!= $true )
| ( ( cP_4 @ ( f @ X5 ) @ X2 )
!= $true )
| ( ( cP_5 @ ( f @ X2 ) @ X0 )
!= $true )
| ( $true
!= ( cP_2 @ X3 @ X4 ) ) )
| ~ spl0_21 ),
inference(superposition,[],[f167,f16]) ).
thf(f169,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( $true
!= ( cP_2 @ X3 @ X4 ) )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( ( cP_5 @ ( f @ X2 ) @ X0 )
!= $true )
| ( ( cP_1 @ a @ X3 )
!= $true )
| ( ( cP_4 @ ( f @ X5 ) @ X2 )
!= $true ) )
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f168]) ).
thf(f170,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_2 @ X2 @ X0 ) )
| ( $true
!= ( cP_1 @ a @ X2 ) )
| ( $true
!= ( cP_5 @ ( f @ X5 ) @ X3 ) )
| ( $true != $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X1 ) @ X5 ) )
| ( $true
!= ( cP_6 @ X3 @ X4 ) ) )
| ~ spl0_21 ),
inference(superposition,[],[f169,f23]) ).
thf(f171,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_4 @ ( f @ X1 ) @ X5 ) )
| ( $true
!= ( cP_1 @ a @ X2 ) )
| ( $true
!= ( cP_2 @ X2 @ X0 ) )
| ( $true
!= ( cP_5 @ ( f @ X5 ) @ X3 ) )
| ( $true
!= ( cP_6 @ X3 @ X4 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true ) )
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f170]) ).
thf(f172,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ a @ X2 ) )
| ( $true != $true )
| ( ( cP_5 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_2 @ X2 @ X3 )
!= $true )
| ( ( cP_3 @ X3 @ X0 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_6 @ X4 @ X5 )
!= $true ) )
| ~ spl0_21 ),
inference(superposition,[],[f171,f41]) ).
thf(f173,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_5 @ ( f @ X1 ) @ X4 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X2 ) )
| ( ( cP_2 @ X2 @ X3 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_3 @ X3 @ X0 )
!= $true )
| ( ( cP_6 @ X4 @ X5 )
!= $true ) )
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f174,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_2 @ X2 @ X3 )
!= $true )
| ( ( cP_6 @ X1 @ X5 )
!= $true )
| ( $true
!= ( cP_3 @ X3 @ X4 ) )
| ( $true
!= ( cP_1 @ a @ X2 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ X4 @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_21 ),
inference(superposition,[],[f173,f42]) ).
thf(f175,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ a @ X2 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ X2 @ X3 )
!= $true )
| ( ( cP_4 @ X4 @ X0 )
!= $true )
| ( $true
!= ( cP_3 @ X3 @ X4 ) )
| ( ( cP_6 @ X1 @ X5 )
!= $true ) )
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f176,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_6 @ X1 @ X4 ) )
| ( ( cP_4 @ X3 @ X0 )
!= $true )
| ( $true
!= ( cP_3 @ X2 @ X3 ) )
| ( $true
!= ( cP_2 @ a @ X2 ) )
| ( $true != $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_8
| ~ spl0_21 ),
inference(superposition,[],[f175,f84]) ).
thf(f177,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_2 @ a @ X2 ) )
| ( ( cP_4 @ X3 @ X0 )
!= $true )
| ( $true
!= ( cP_3 @ X2 @ X3 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_6 @ X1 @ X4 ) ) )
| ~ spl0_8
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f178,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_5 @ X1 @ X2 )
!= $true )
| ( $true
!= ( cP_6 @ X2 @ X3 ) )
| ( $true
!= ( cP_3 @ a @ X0 ) )
| ( $true != $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_21 ),
inference(superposition,[],[f177,f54]) ).
thf(f179,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ a @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_6 @ X2 @ X3 ) )
| ( ( cP_5 @ X1 @ X2 )
!= $true ) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f178]) ).
thf(f180,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP_6 @ X1 @ X2 )
!= $true )
| ( $true
!= ( cP_4 @ a @ X0 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_21 ),
inference(superposition,[],[f179,f104]) ).
thf(f181,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_4 @ a @ X0 ) )
| ( ( cP_6 @ X1 @ X2 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f180]) ).
thf(f182,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( ( cP_5 @ a @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17
| ~ spl0_21 ),
inference(superposition,[],[f181,f129]) ).
thf(f183,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_5 @ a @ X0 )
!= $true )
| ( ( cP_6 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f182]) ).
thf(f184,plain,
( ! [X0: $i] :
( ( ( cP_6 @ a @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_21 ),
inference(superposition,[],[f183,f109]) ).
thf(f185,plain,
( ! [X0: $i] :
( ( cP_6 @ a @ X0 )
!= $true )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f184]) ).
thf(f186,plain,
( ( $true != $true )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(superposition,[],[f185,f134]) ).
thf(f187,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f186]) ).
thf(f188,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f187]) ).
thf(f189,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_5 @ ( f @ X4 ) @ X2 ) )
| ( ( cP_2 @ ( f @ X5 ) @ X0 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X4 )
!= $true )
| ( $true != $true )
| ( ( cP_6 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ b ) @ X5 ) ) )
| ~ spl0_22 ),
inference(superposition,[],[f162,f23]) ).
thf(f190,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ ( f @ b ) @ X5 ) )
| ( ( cP_6 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X4 ) @ X2 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X5 ) @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X4 )
!= $true ) )
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f189]) ).
thf(f191,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( $true
!= ( cP_5 @ ( f @ X3 ) @ X1 ) )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X0 ) @ X4 ) )
| ( $true
!= ( cP_3 @ X4 @ X5 ) )
| ( $true
!= ( cP_4 @ ( f @ X5 ) @ X3 ) )
| ( $true
!= ( cP_6 @ ( f @ X1 ) @ X2 ) ) )
| ~ spl0_22 ),
inference(superposition,[],[f190,f11]) ).
thf(f192,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_2 @ ( f @ X0 ) @ X4 ) )
| ( $true
!= ( cP_5 @ ( f @ X3 ) @ X1 ) )
| ( $true
!= ( cP_6 @ ( f @ X1 ) @ X2 ) )
| ( $true
!= ( cP_4 @ ( f @ X5 ) @ X3 ) )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( $true
!= ( cP_3 @ X4 @ X5 ) ) )
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f191]) ).
thf(f193,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_5 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X4 ) )
| ( $true
!= ( cP_3 @ X1 @ X5 ) )
| ( ( cP_4 @ ( f @ X5 ) @ X2 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true ) )
| ~ spl0_22 ),
inference(superposition,[],[f192,f26]) ).
thf(f194,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_6 @ ( f @ X3 ) @ X4 ) )
| ( $true
!= ( cP_3 @ X1 @ X5 ) )
| ( ( cP_4 @ ( f @ X5 ) @ X2 )
!= $true )
| ( ( cP_5 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f193]) ).
thf(f195,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X3 ) @ X4 ) )
| ( $true != $true )
| ( ( cP_2 @ X5 @ X2 )
!= $true )
| ( $true
!= ( cP_1 @ b @ X5 ) )
| ( $true
!= ( cP_5 @ ( f @ X4 ) @ X0 ) )
| ( $true
!= ( cP_3 @ X2 @ X3 ) ) )
| ~ spl0_22 ),
inference(superposition,[],[f194,f16]) ).
thf(f196,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_4 @ ( f @ X3 ) @ X4 ) )
| ( $true
!= ( cP_3 @ X2 @ X3 ) )
| ( $true
!= ( cP_5 @ ( f @ X4 ) @ X0 ) )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ b @ X5 ) )
| ( ( cP_2 @ X5 @ X2 )
!= $true ) )
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f195]) ).
thf(f197,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( cP_5 @ ( f @ X1 ) @ X3 )
!= $true )
| ( $true
!= ( cP_3 @ X2 @ X0 ) )
| ( ( cP_2 @ X5 @ X2 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ b @ X5 ) )
| ( $true
!= ( cP_6 @ X3 @ X4 ) ) )
| ~ spl0_22 ),
inference(superposition,[],[f196,f41]) ).
thf(f198,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_5 @ ( f @ X1 ) @ X3 )
!= $true )
| ( ( cP_2 @ X5 @ X2 )
!= $true )
| ( $true
!= ( cP_3 @ X2 @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ b @ X5 ) )
| ( $true
!= ( cP_6 @ X3 @ X4 ) ) )
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f197]) ).
thf(f199,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_4 @ X4 @ X0 )
!= $true )
| ( ( cP_6 @ X1 @ X5 )
!= $true )
| ( ( cP_2 @ X2 @ X3 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_3 @ X3 @ X4 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ b @ X2 ) ) )
| ~ spl0_22 ),
inference(superposition,[],[f198,f42]) ).
thf(f200,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ b @ X2 ) )
| ( ( cP_4 @ X4 @ X0 )
!= $true )
| ( ( cP_2 @ X2 @ X3 )
!= $true )
| ( ( cP_6 @ X1 @ X5 )
!= $true )
| ( $true
!= ( cP_3 @ X3 @ X4 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f199]) ).
thf(f201,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_5 @ X1 @ X3 )
!= $true )
| ( $true
!= ( cP_2 @ b @ X2 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_6 @ X3 @ X4 ) )
| ( $true != $true )
| ( $true
!= ( cP_3 @ X2 @ X0 ) ) )
| ~ spl0_10
| ~ spl0_22 ),
inference(superposition,[],[f200,f94]) ).
thf(f202,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_2 @ b @ X2 ) )
| ( $true
!= ( cP_3 @ X2 @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_6 @ X3 @ X4 ) )
| ( ( cP_5 @ X1 @ X3 )
!= $true ) )
| ~ spl0_10
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f201]) ).
thf(f203,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( cP_3 @ b @ X0 ) )
| ( ( cP_5 @ X1 @ X2 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_6 @ X2 @ X3 ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_22 ),
inference(superposition,[],[f202,f74]) ).
thf(f204,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ b @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_5 @ X1 @ X2 )
!= $true )
| ( $true
!= ( cP_6 @ X2 @ X3 ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f203]) ).
thf(f205,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( cP_4 @ b @ X0 ) )
| ( ( cP_6 @ X1 @ X2 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_22 ),
inference(superposition,[],[f204,f79]) ).
thf(f206,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_4 @ b @ X0 ) )
| ( ( cP_6 @ X1 @ X2 )
!= $true )
| ( ( cP_5 @ X0 @ X1 )
!= $true ) )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f205]) ).
thf(f207,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_5 @ b @ X0 ) ) )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_19
| ~ spl0_22 ),
inference(superposition,[],[f206,f139]) ).
thf(f208,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( cP_5 @ b @ X0 ) )
| ( ( cP_6 @ X0 @ X1 )
!= $true ) )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_19
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f207]) ).
thf(f209,plain,
( ! [X0: $i] :
( ( $true
!= ( cP_6 @ b @ X0 ) )
| ( $true != $true ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_19
| ~ spl0_22 ),
inference(superposition,[],[f208,f59]) ).
thf(f210,plain,
( ! [X0: $i] :
( $true
!= ( cP_6 @ b @ X0 ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_19
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f209]) ).
thf(f211,plain,
( ( $true != $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_19
| ~ spl0_22 ),
inference(superposition,[],[f210,f69]) ).
thf(f212,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_19
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f211]) ).
thf(f213,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_19
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f212]) ).
thf(f214,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_6 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_5 @ ( f @ X5 ) @ X2 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X4 ) @ X5 )
!= $true ) )
| ~ spl0_20 ),
inference(superposition,[],[f156,f11]) ).
thf(f215,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_6 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_5 @ ( f @ X5 ) @ X2 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_3 @ ( f @ X1 ) @ X4 )
!= $true ) )
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f214]) ).
thf(f216,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_6 @ ( f @ X4 ) @ X5 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X2 ) @ X3 ) )
| ( $true != $true )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X0 ) ) )
| ~ spl0_20 ),
inference(superposition,[],[f215,f26]) ).
thf(f217,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_4 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_5 @ ( f @ X3 ) @ X4 )
!= $true )
| ( $true
!= ( cP_6 @ ( f @ X4 ) @ X5 ) )
| ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f216]) ).
thf(f218,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_6 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true != $true )
| ( ( cP_3 @ ( f @ X5 ) @ X0 )
!= $true )
| ( ( cP_2 @ X4 @ X5 )
!= $true )
| ( $true
!= ( cP_5 @ ( f @ X1 ) @ X2 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X4 ) ) )
| ~ spl0_20 ),
inference(superposition,[],[f217,f41]) ).
thf(f219,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_5 @ ( f @ X1 ) @ X2 ) )
| ( ( cP_3 @ ( f @ X5 ) @ X0 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X4 ) )
| ( ( cP_6 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ X4 @ X5 )
!= $true ) )
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f218]) ).
thf(f220,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ X3 @ X0 )
!= $true )
| ( $true
!= ( cP_2 @ X4 @ X2 ) )
| ( $true
!= ( cP_6 @ ( f @ X1 ) @ X5 ) )
| ( $true
!= ( cP_1 @ c @ X4 ) )
| ( $true != $true )
| ( $true
!= ( cP_3 @ ( f @ X2 ) @ X3 ) ) )
| ~ spl0_20 ),
inference(superposition,[],[f219,f42]) ).
thf(f221,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_3 @ ( f @ X2 ) @ X3 ) )
| ( $true
!= ( cP_2 @ X4 @ X2 ) )
| ( $true
!= ( cP_1 @ c @ X4 ) )
| ( $true
!= ( cP_6 @ ( f @ X1 ) @ X5 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ X3 @ X0 )
!= $true ) )
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f220]) ).
thf(f222,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_4 @ X1 @ X5 ) )
| ( $true
!= ( cP_5 @ X5 @ X3 ) )
| ( $true
!= ( cP_6 @ ( f @ X3 ) @ X4 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_2 @ X2 @ X0 ) )
| ( $true != $true )
| ( $true
!= ( cP_1 @ c @ X2 ) ) )
| ~ spl0_20 ),
inference(superposition,[],[f221,f23]) ).
thf(f223,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_6 @ ( f @ X3 ) @ X4 ) )
| ( $true
!= ( cP_5 @ X5 @ X3 ) )
| ( $true
!= ( cP_1 @ c @ X2 ) )
| ( $true
!= ( cP_4 @ X1 @ X5 ) )
| ( $true
!= ( cP_2 @ X2 @ X0 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true ) )
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f222]) ).
thf(f224,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_2 @ X3 @ X5 ) )
| ( $true
!= ( cP_4 @ X4 @ X2 ) )
| ( $true
!= ( cP_1 @ c @ X3 ) )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_5 @ X2 @ X0 ) )
| ( $true
!= ( cP_3 @ X5 @ X4 ) )
| ( $true != $true ) )
| ~ spl0_20 ),
inference(superposition,[],[f223,f16]) ).
thf(f225,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ c @ X3 ) )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ X5 @ X4 ) )
| ( $true
!= ( cP_2 @ X3 @ X5 ) )
| ( $true
!= ( cP_4 @ X4 @ X2 ) )
| ( $true
!= ( cP_5 @ X2 @ X0 ) ) )
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f224]) ).
thf(f226,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_3 @ X2 @ X3 ) )
| ( $true != $true )
| ( ( cP_6 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_5 @ X4 @ X0 ) )
| ( $true
!= ( cP_4 @ X3 @ X4 ) )
| ( $true
!= ( cP_2 @ c @ X2 ) ) )
| ~ spl0_11
| ~ spl0_20 ),
inference(superposition,[],[f225,f99]) ).
thf(f227,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( cP_2 @ c @ X2 ) )
| ( $true
!= ( cP_4 @ X3 @ X4 ) )
| ( $true
!= ( cP_5 @ X4 @ X0 ) )
| ( $true
!= ( cP_3 @ X2 @ X3 ) )
| ( ( cP_6 @ X0 @ X1 )
!= $true ) )
| ~ spl0_11
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f226]) ).
thf(f228,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_6 @ X2 @ X3 ) )
| ( $true != $true )
| ( ( cP_5 @ X1 @ X2 )
!= $true )
| ( $true
!= ( cP_3 @ c @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_11
| ~ spl0_14
| ~ spl0_20 ),
inference(superposition,[],[f227,f114]) ).
thf(f229,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ c @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_5 @ X1 @ X2 )
!= $true )
| ( $true
!= ( cP_6 @ X2 @ X3 ) ) )
| ~ spl0_11
| ~ spl0_14
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f228]) ).
thf(f230,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ c @ X0 ) )
| ( ( cP_6 @ X1 @ X2 )
!= $true )
| ( $true != $true ) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_14
| ~ spl0_20 ),
inference(superposition,[],[f229,f64]) ).
thf(f231,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_4 @ c @ X0 ) )
| ( ( cP_5 @ X0 @ X1 )
!= $true )
| ( ( cP_6 @ X1 @ X2 )
!= $true ) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_14
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f230]) ).
thf(f232,plain,
( ! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( cP_5 @ c @ X0 ) )
| ( ( cP_6 @ X0 @ X1 )
!= $true ) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f231,f119]) ).
thf(f233,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( cP_5 @ c @ X0 ) )
| ( ( cP_6 @ X0 @ X1 )
!= $true ) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f232]) ).
thf(f234,plain,
( ! [X0: $i] :
( ( $true
!= ( cP_6 @ c @ X0 ) )
| ( $true != $true ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f233,f49]) ).
thf(f235,plain,
( ! [X0: $i] :
( $true
!= ( cP_6 @ c @ X0 ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f234]) ).
thf(f236,plain,
( ( $true != $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f235,f89]) ).
thf(f237,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f236]) ).
thf(f238,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f237]) ).
cnf(s1,plain,
spl0_1,
inference(sat_conversion,[],[f50]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f55]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f60]) ).
cnf(s4,plain,
spl0_4,
inference(sat_conversion,[],[f65]) ).
cnf(s5,plain,
spl0_5,
inference(sat_conversion,[],[f70]) ).
cnf(s6,plain,
spl0_6,
inference(sat_conversion,[],[f75]) ).
cnf(s7,plain,
spl0_7,
inference(sat_conversion,[],[f80]) ).
cnf(s8,plain,
spl0_8,
inference(sat_conversion,[],[f85]) ).
cnf(s9,plain,
spl0_9,
inference(sat_conversion,[],[f90]) ).
cnf(s10,plain,
spl0_10,
inference(sat_conversion,[],[f95]) ).
cnf(s11,plain,
spl0_11,
inference(sat_conversion,[],[f100]) ).
cnf(s12,plain,
spl0_12,
inference(sat_conversion,[],[f105]) ).
cnf(s13,plain,
spl0_13,
inference(sat_conversion,[],[f110]) ).
cnf(s14,plain,
spl0_14,
inference(sat_conversion,[],[f115]) ).
cnf(s15,plain,
spl0_15,
inference(sat_conversion,[],[f120]) ).
cnf(s16,plain,
spl0_16,
inference(sat_conversion,[],[f125]) ).
cnf(s17,plain,
spl0_17,
inference(sat_conversion,[],[f130]) ).
cnf(s18,plain,
spl0_18,
inference(sat_conversion,[],[f135]) ).
cnf(s19,plain,
spl0_19,
inference(sat_conversion,[],[f140]) ).
cnf(s20,plain,
( ~ spl0_16
| spl0_20
| spl0_21
| spl0_22 ),
inference(sat_conversion,[],[f163]) ).
cnf(s21,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(sat_conversion,[],[f188]) ).
cnf(s22,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_19
| ~ spl0_22 ),
inference(sat_conversion,[],[f213]) ).
cnf(s23,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(sat_conversion,[],[f238]) ).
cnf(s24,plain,
~ spl0_22,
inference(rat,[],[s22,s5,s19,s10,s7,s6,s3]) ).
cnf(s25,plain,
~ spl0_21,
inference(rat,[],[s21,s8,s18,s17,s13,s12,s2]) ).
cnf(s26,plain,
spl0_20,
inference(rat,[],[s20,s24,s16,s25]) ).
cnf(s27,plain,
~ spl0_1,
inference(rat,[],[s23,s4,s15,s14,s11,s9,s26]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s1,s27]) ).
thf(f239,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO391^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:56:06 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.32 % (1503778)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.32 % (1503785)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3209641284:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.32 % (1503785)Instruction limit reached!
% 0.19/0.32 % (1503785)------------------------------
% 0.19/0.32 % (1503785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1503785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1503785)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1503785)Termination reason: Instruction limit
% 0.19/0.32 % (1503785)Termination phase: Saturation
% 0.19/0.32 % (1503785)Time elapsed: 0.002 s
% 0.19/0.32 % (1503785)Peak memory usage: 11 MB
% 0.19/0.32 % (1503785)Instructions burned: 6 (million)
% 0.19/0.32 % (1503784)lrs+10_16_si=on:nwc=1.5:random_seed=1241446947:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.32 % (1503783)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=692251276:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.32 % (1503791)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2736367871:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.32 % (1503791)Instruction limit reached!
% 0.19/0.32 % (1503791)------------------------------
% 0.19/0.32 % (1503791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1503791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1503791)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1503791)Termination reason: Instruction limit
% 0.19/0.32 % (1503791)Termination phase: Property scanning
% 0.19/0.32 % (1503791)Time elapsed: 0.001 s
% 0.19/0.32 % (1503791)Peak memory usage: 10 MB
% 0.19/0.32 % (1503791)Instructions burned: 4 (million)
% 0.19/0.32 % (1503784)Instruction limit reached!
% 0.19/0.32 % (1503784)------------------------------
% 0.19/0.32 % (1503784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1503784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1503784)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1503784)Termination reason: Instruction limit
% 0.19/0.32 % (1503784)Termination phase: Saturation
% 0.19/0.32 % (1503784)Time elapsed: 0.010 s
% 0.19/0.32 % (1503784)Peak memory usage: 12 MB
% 0.19/0.32 % (1503784)Instructions burned: 20 (million)
% 0.19/0.32 % (1503786)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4234622243:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.32 % (1503796)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.19/0.32 % (1503796)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1899136134:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.19/0.32 % (1503796)Instruction limit reached!
% 0.19/0.32 % (1503796)------------------------------
% 0.19/0.32 % (1503796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1503796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1503796)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1503796)Termination reason: Instruction limit
% 0.19/0.32 % (1503796)Termination phase: Saturation
% 0.19/0.32 % (1503796)Time elapsed: 0.002 s
% 0.19/0.32 % (1503796)Peak memory usage: 11 MB
% 0.19/0.32 % (1503796)Instructions burned: 8 (million)
% 0.19/0.32 % (1503789)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.32 % (1503789)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.19/0.32 % (1503795)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1106585485:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.19/0.32 % (1503787)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1588235960:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.32 % (1503788)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3663082368:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.32 % (1503789)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2892022924:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.32 % (1503795)Instruction limit reached!
% 0.19/0.32 % (1503795)------------------------------
% 0.19/0.32 % (1503795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1503795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1503795)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1503795)Termination reason: Instruction limit
% 0.19/0.32 % (1503795)Termination phase: Saturation
% 0.19/0.32 % (1503795)Time elapsed: 0.003 s
% 0.19/0.32 % (1503795)Peak memory usage: 11 MB
% 0.19/0.32 % (1503795)Instructions burned: 6 (million)
% 0.19/0.32 % (1503799)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2441831335:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.19/0.32 % (1503786) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1503778-1503786"...
% 0.19/0.32 % (1503799)Instruction limit reached!
% 0.19/0.32 % (1503799)------------------------------
% 0.19/0.32 % (1503799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1503799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1503799)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1503799)Termination reason: Instruction limit
% 0.19/0.32 % (1503799)Termination phase: Saturation
% 0.19/0.32 % (1503799)Time elapsed: 0.003 s
% 0.19/0.32 % (1503799)Peak memory usage: 12 MB
% 0.19/0.32 % (1503799)Instructions burned: 12 (million)
% 0.19/0.32 % (1503787)Instruction limit reached!
% 0.19/0.32 % (1503787)------------------------------
% 0.19/0.32 % (1503787)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1503787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1503787)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1503787)Termination reason: Instruction limit
% 0.19/0.32 % (1503787)Termination phase: Saturation
% 0.19/0.32 % (1503787)Time elapsed: 0.013 s
% 0.19/0.32 % (1503787)Peak memory usage: 12 MB
% 0.19/0.32 % (1503787)Instructions burned: 25 (million)
% 0.19/0.32 % (1503783)Instruction limit reached!
% 0.19/0.32 % (1503783)------------------------------
% 0.19/0.32 % (1503783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1503783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1503783)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1503783)Termination reason: Instruction limit
% 0.19/0.32 % (1503783)Termination phase: Saturation
% 0.19/0.32 % (1503783)Time elapsed: 0.045 s
% 0.19/0.32 % (1503783)Peak memory usage: 12 MB
% 0.19/0.32 % (1503783)Instructions burned: 88 (million)
% 0.19/0.32 % (1503806)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=4027537745:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.19/0.32 % (1503804)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.19/0.32 % (1503804)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.19/0.32 % (1503786)...printing done.
% 0.19/0.32 % (1503786)Refutation found. Thanks to Tanya!
% 0.19/0.32 % SZS status Theorem for theBenchmark
% 0.19/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.32 % (1503786)------------------------------
% 0.19/0.32 % (1503786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1503786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1503786)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1503786)Termination reason: Refutation
% 0.19/0.32 % (1503786)Time elapsed: 0.033 s
% 0.19/0.32 % (1503786)Peak memory usage: 13 MB
% 0.19/0.32 % (1503786)Instructions burned: 56 (million)
% 0.19/0.32 % (1503778)Success in time 0.087 s
% 0.19/0.32 % Vampire exiting
%------------------------------------------------------------------------------