%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO387^5 : 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 : n007.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 08:47:34 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 19
% Syntax : Number of formulae : 165 ( 48 unt; 0 typ; 18 def)
% Number of atoms : 2116 ( 480 equ; 0 cnn)
% Maximal formula atoms : 77 ( 12 avg)
% Number of connectives : 2751 ( 575 ~; 492 |; 150 &;1516 @)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 7 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 : 36 ( 33 usr; 24 con; 0-3 aty)
% Number of variables : 527 ( 0 sgn 527 !; 0 ?; 527 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cQ_5: $i > $i > $i > $o ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
cP_4: $i > $i > $o ).
thf(func_def_3,type,
cQ_4: $i > $i > $i > $o ).
thf(func_def_8,type,
cP_3: $i > $i > $o ).
thf(func_def_9,type,
cQ_3: $i > $i > $i > $o ).
thf(func_def_10,type,
cP_2: $i > $i > $o ).
thf(func_def_11,type,
cQ_2: $i > $i > $i > $o ).
thf(func_def_12,type,
cP_1: $i > $i > $o ).
thf(func_def_13,type,
cQ_1: $i > $i > $i > $o ).
thf(f1,conjecture,
~ ( ( cP_1 @ c @ c )
& ( cP_1 @ a @ a )
& ( cP_2 @ c @ c )
& ! [X2: $i,X0: $i,X1: $i] :
~ ( cQ_5 @ X0 @ X1 @ X2 )
& ( cP_4 @ b @ b )
& ! [X5: $i,X0: $i,X4: $i,X3: $i,X1: $i,X2: $i] :
( ~ ( cQ_3 @ X0 @ X1 @ X2 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ~ ( cP_3 @ ( f @ X0 ) @ X3 )
| ( cQ_4 @ X3 @ X4 @ X5 ) )
& ( cP_3 @ c @ c )
& ( cP_3 @ b @ b )
& ! [X1: $i,X0: $i] :
( ~ ( cP_3 @ X0 @ X1 )
| ( cP_3 @ ( f @ X0 ) @ X1 ) )
& ( cP_3 @ a @ a )
& ! [X0: $i,X2: $i,X5: $i,X4: $i,X1: $i,X3: $i] :
( ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 ) )
& ! [X1: $i,X0: $i] :
( ( cP_2 @ ( f @ X0 ) @ X1 )
| ~ ( cP_2 @ X0 @ X1 ) )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ! [X1: $i,X0: $i] :
( ( cP_1 @ ( f @ X0 ) @ X1 )
| ~ ( cP_1 @ X0 @ X1 ) )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ( cQ_1 @ a @ b @ c )
& ! [X0: $i] : ( cP_4 @ d @ X0 )
& ! [X1: $i,X0: $i] :
( ~ ( cP_4 @ X0 @ X1 )
| ( cP_4 @ ( f @ X0 ) @ X1 ) )
& ( cP_4 @ a @ a )
& ! [X0: $i] : ( cP_3 @ d @ X0 )
& ! [X1: $i,X3: $i,X2: $i,X4: $i,X5: $i,X0: $i] :
( ~ ( cP_4 @ ( f @ X0 ) @ X3 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 )
| ( cQ_5 @ X3 @ X4 @ X5 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ~ ( cQ_4 @ X0 @ X1 @ X2 ) )
& ( cP_1 @ b @ b )
& ! [X3: $i,X4: $i,X1: $i,X0: $i,X2: $i,X5: $i] :
( ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ( cQ_3 @ X3 @ X4 @ X5 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 ) )
& ( cP_4 @ c @ c )
& ( cP_2 @ b @ b )
& ( cP_2 @ a @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM409_4) ).
thf(f2,negated_conjecture,
~ ~ ( ( cP_1 @ c @ c )
& ( cP_1 @ a @ a )
& ( cP_2 @ c @ c )
& ! [X2: $i,X0: $i,X1: $i] :
~ ( cQ_5 @ X0 @ X1 @ X2 )
& ( cP_4 @ b @ b )
& ! [X5: $i,X0: $i,X4: $i,X3: $i,X1: $i,X2: $i] :
( ~ ( cQ_3 @ X0 @ X1 @ X2 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ~ ( cP_3 @ ( f @ X0 ) @ X3 )
| ( cQ_4 @ X3 @ X4 @ X5 ) )
& ( cP_3 @ c @ c )
& ( cP_3 @ b @ b )
& ! [X1: $i,X0: $i] :
( ~ ( cP_3 @ X0 @ X1 )
| ( cP_3 @ ( f @ X0 ) @ X1 ) )
& ( cP_3 @ a @ a )
& ! [X0: $i,X2: $i,X5: $i,X4: $i,X1: $i,X3: $i] :
( ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 ) )
& ! [X1: $i,X0: $i] :
( ( cP_2 @ ( f @ X0 ) @ X1 )
| ~ ( cP_2 @ X0 @ X1 ) )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ! [X1: $i,X0: $i] :
( ( cP_1 @ ( f @ X0 ) @ X1 )
| ~ ( cP_1 @ X0 @ X1 ) )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ( cQ_1 @ a @ b @ c )
& ! [X0: $i] : ( cP_4 @ d @ X0 )
& ! [X1: $i,X0: $i] :
( ~ ( cP_4 @ X0 @ X1 )
| ( cP_4 @ ( f @ X0 ) @ X1 ) )
& ( cP_4 @ a @ a )
& ! [X0: $i] : ( cP_3 @ d @ X0 )
& ! [X1: $i,X3: $i,X2: $i,X4: $i,X5: $i,X0: $i] :
( ~ ( cP_4 @ ( f @ X0 ) @ X3 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 )
| ( cQ_5 @ X3 @ X4 @ X5 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ~ ( cQ_4 @ X0 @ X1 @ X2 ) )
& ( cP_1 @ b @ b )
& ! [X3: $i,X4: $i,X1: $i,X0: $i,X2: $i,X5: $i] :
( ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ( cQ_3 @ X3 @ X4 @ X5 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 ) )
& ( cP_4 @ c @ c )
& ( cP_2 @ b @ b )
& ( cP_2 @ a @ a ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ~ ( ( cP_1 @ c @ c )
& ( cP_1 @ a @ a )
& ( cP_2 @ c @ c )
& ! [X0: $i,X1: $i,X2: $i] :
~ ( cQ_5 @ X1 @ X2 @ X0 )
& ( cP_4 @ b @ b )
& ! [X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ~ ( cQ_3 @ X4 @ X7 @ X8 )
| ~ ( cP_3 @ ( f @ X7 ) @ X5 )
| ~ ( cP_3 @ ( f @ X8 ) @ X3 )
| ~ ( cP_3 @ ( f @ X4 ) @ X6 )
| ( cQ_4 @ X6 @ X5 @ X3 ) )
& ( cP_3 @ c @ c )
& ( cP_3 @ b @ b )
& ! [X9: $i,X10: $i] :
( ~ ( cP_3 @ X10 @ X9 )
| ( cP_3 @ ( f @ X10 ) @ X9 ) )
& ( cP_3 @ a @ a )
& ! [X11: $i,X12: $i,X13: $i,X14: $i,X15: $i,X16: $i] :
( ~ ( cP_1 @ ( f @ X11 ) @ X16 )
| ~ ( cP_1 @ ( f @ X15 ) @ X14 )
| ~ ( cQ_1 @ X11 @ X15 @ X12 )
| ( cQ_2 @ X16 @ X14 @ X13 )
| ~ ( cP_1 @ ( f @ X12 ) @ X13 ) )
& ! [X17: $i,X18: $i] :
( ( cP_2 @ ( f @ X18 ) @ X17 )
| ~ ( cP_2 @ X18 @ X17 ) )
& ! [X19: $i] : ( cP_2 @ d @ X19 )
& ! [X20: $i,X21: $i] :
( ( cP_1 @ ( f @ X21 ) @ X20 )
| ~ ( cP_1 @ X21 @ X20 ) )
& ! [X22: $i] : ( cP_1 @ d @ X22 )
& ( cQ_1 @ a @ b @ c )
& ! [X23: $i] : ( cP_4 @ d @ X23 )
& ! [X24: $i,X25: $i] :
( ~ ( cP_4 @ X25 @ X24 )
| ( cP_4 @ ( f @ X25 ) @ X24 ) )
& ( cP_4 @ a @ a )
& ! [X26: $i] : ( cP_3 @ d @ X26 )
& ! [X27: $i,X28: $i,X29: $i,X30: $i,X31: $i,X32: $i] :
( ~ ( cP_4 @ ( f @ X32 ) @ X28 )
| ~ ( cP_4 @ ( f @ X27 ) @ X30 )
| ( cQ_5 @ X28 @ X30 @ X31 )
| ~ ( cP_4 @ ( f @ X29 ) @ X31 )
| ~ ( cQ_4 @ X32 @ X27 @ X29 ) )
& ( cP_1 @ b @ b )
& ! [X33: $i,X34: $i,X35: $i,X36: $i,X37: $i,X38: $i] :
( ~ ( cP_2 @ ( f @ X35 ) @ X34 )
| ~ ( cP_2 @ ( f @ X36 ) @ X33 )
| ( cQ_3 @ X33 @ X34 @ X38 )
| ~ ( cQ_2 @ X36 @ X35 @ X37 )
| ~ ( cP_2 @ ( f @ X37 ) @ X38 ) )
& ( cP_4 @ c @ c )
& ( cP_2 @ b @ b )
& ( cP_2 @ a @ a ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ~ ( ( ( cP_1 @ c @ c )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ! [X0: $i,X1: $i,X2: $i] :
( $true
!= ( cQ_5 @ X1 @ X2 @ X0 ) )
& ( ( cP_4 @ b @ b )
= $true )
& ! [X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( $true
!= ( cQ_3 @ X4 @ X7 @ X8 ) )
| ( ( cP_3 @ ( f @ X7 ) @ X5 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X8 ) @ X3 ) )
| ( ( cP_3 @ ( f @ X4 ) @ X6 )
!= $true )
| ( $true
= ( cQ_4 @ X6 @ X5 @ X3 ) ) )
& ( ( cP_3 @ c @ c )
= $true )
& ( ( cP_3 @ b @ b )
= $true )
& ! [X9: $i,X10: $i] :
( ( $true
!= ( cP_3 @ X10 @ X9 ) )
| ( $true
= ( cP_3 @ ( f @ X10 ) @ X9 ) ) )
& ( ( cP_3 @ a @ a )
= $true )
& ! [X11: $i,X12: $i,X13: $i,X14: $i,X15: $i,X16: $i] :
( ( $true
!= ( cP_1 @ ( f @ X11 ) @ X16 ) )
| ( ( cP_1 @ ( f @ X15 ) @ X14 )
!= $true )
| ( $true
!= ( cQ_1 @ X11 @ X15 @ X12 ) )
| ( $true
= ( cQ_2 @ X16 @ X14 @ X13 ) )
| ( $true
!= ( cP_1 @ ( f @ X12 ) @ X13 ) ) )
& ! [X17: $i,X18: $i] :
( ( $true
= ( cP_2 @ ( f @ X18 ) @ X17 ) )
| ( $true
!= ( cP_2 @ X18 @ X17 ) ) )
& ! [X19: $i] :
( ( cP_2 @ d @ X19 )
= $true )
& ! [X20: $i,X21: $i] :
( ( $true
= ( cP_1 @ ( f @ X21 ) @ X20 ) )
| ( $true
!= ( cP_1 @ X21 @ X20 ) ) )
& ! [X22: $i] :
( $true
= ( cP_1 @ d @ X22 ) )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X23: $i] :
( ( cP_4 @ d @ X23 )
= $true )
& ! [X24: $i,X25: $i] :
( ( $true
!= ( cP_4 @ X25 @ X24 ) )
| ( ( cP_4 @ ( f @ X25 ) @ X24 )
= $true ) )
& ( ( cP_4 @ a @ a )
= $true )
& ! [X26: $i] :
( $true
= ( cP_3 @ d @ X26 ) )
& ! [X27: $i,X28: $i,X29: $i,X30: $i,X31: $i,X32: $i] :
( ( $true
!= ( cP_4 @ ( f @ X32 ) @ X28 ) )
| ( $true
!= ( cP_4 @ ( f @ X27 ) @ X30 ) )
| ( $true
= ( cQ_5 @ X28 @ X30 @ X31 ) )
| ( $true
!= ( cP_4 @ ( f @ X29 ) @ X31 ) )
| ( $true
!= ( cQ_4 @ X32 @ X27 @ X29 ) ) )
& ( ( cP_1 @ b @ b )
= $true )
& ! [X33: $i,X34: $i,X35: $i,X36: $i,X37: $i,X38: $i] :
( ( ( cP_2 @ ( f @ X35 ) @ X34 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X36 ) @ X33 ) )
| ( $true
= ( cQ_3 @ X33 @ X34 @ X38 ) )
| ( ( cQ_2 @ X36 @ X35 @ X37 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X37 ) @ X38 ) ) )
& ( ( cP_4 @ c @ c )
= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ( ( cP_2 @ a @ a )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( cP_2 @ a @ a )
= $true )
& ! [X19: $i] :
( ( cP_2 @ d @ X19 )
= $true )
& ( ( cP_4 @ b @ b )
= $true )
& ! [X10: $i,X9: $i] :
( ( $true
= ( cP_3 @ ( f @ X10 ) @ X9 ) )
| ( $true
!= ( cP_3 @ X10 @ X9 ) ) )
& ( ( cP_2 @ c @ c )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_4 @ a @ a )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ! [X20: $i,X21: $i] :
( ( $true
= ( cP_1 @ ( f @ X21 ) @ X20 ) )
| ( $true
!= ( cP_1 @ X21 @ X20 ) ) )
& ! [X24: $i,X25: $i] :
( ( ( cP_4 @ ( f @ X25 ) @ X24 )
= $true )
| ( $true
!= ( cP_4 @ X25 @ X24 ) ) )
& ( ( cP_3 @ b @ b )
= $true )
& ( ( cP_3 @ c @ c )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X17: $i,X18: $i] :
( ( $true
!= ( cP_2 @ X18 @ X17 ) )
| ( $true
= ( cP_2 @ ( f @ X18 ) @ X17 ) ) )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X5: $i,X8: $i,X3: $i,X4: $i,X7: $i,X6: $i] :
( ( $true
!= ( cQ_3 @ X4 @ X7 @ X8 ) )
| ( $true
!= ( cP_3 @ ( f @ X8 ) @ X3 ) )
| ( $true
= ( cQ_4 @ X6 @ X5 @ X3 ) )
| ( ( cP_3 @ ( f @ X4 ) @ X6 )
!= $true )
| ( ( cP_3 @ ( f @ X7 ) @ X5 )
!= $true ) )
& ! [X16: $i,X15: $i,X13: $i,X12: $i,X14: $i,X11: $i] :
( ( $true
!= ( cP_1 @ ( f @ X11 ) @ X16 ) )
| ( $true
!= ( cQ_1 @ X11 @ X15 @ X12 ) )
| ( ( cP_1 @ ( f @ X15 ) @ X14 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ X12 ) @ X13 ) )
| ( $true
= ( cQ_2 @ X16 @ X14 @ X13 ) ) )
& ! [X32: $i,X29: $i,X27: $i,X31: $i,X30: $i,X28: $i] :
( ( $true
!= ( cP_4 @ ( f @ X32 ) @ X28 ) )
| ( $true
!= ( cP_4 @ ( f @ X29 ) @ X31 ) )
| ( $true
!= ( cP_4 @ ( f @ X27 ) @ X30 ) )
| ( $true
= ( cQ_5 @ X28 @ X30 @ X31 ) )
| ( $true
!= ( cQ_4 @ X32 @ X27 @ X29 ) ) )
& ! [X36: $i,X35: $i,X37: $i,X33: $i,X34: $i,X38: $i] :
( ( $true
!= ( cP_2 @ ( f @ X37 ) @ X38 ) )
| ( ( cP_2 @ ( f @ X35 ) @ X34 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X36 ) @ X33 ) )
| ( ( cQ_2 @ X36 @ X35 @ X37 )
!= $true )
| ( $true
= ( cQ_3 @ X33 @ X34 @ X38 ) ) )
& ! [X23: $i] :
( ( cP_4 @ d @ X23 )
= $true )
& ( ( cP_4 @ c @ c )
= $true )
& ( ( cP_3 @ a @ a )
= $true )
& ! [X26: $i] :
( $true
= ( cP_3 @ d @ X26 ) )
& ! [X22: $i] :
( $true
= ( cP_1 @ d @ X22 ) )
& ! [X0: $i,X1: $i,X2: $i] :
( $true
!= ( cQ_5 @ X1 @ X2 @ X0 ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ( cP_2 @ a @ a )
= $true )
& ! [X0: $i] :
( ( cP_2 @ d @ X0 )
= $true )
& ( ( cP_4 @ b @ b )
= $true )
& ! [X1: $i,X2: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
= $true )
| ( $true
!= ( cP_3 @ X1 @ X2 ) ) )
& ( ( cP_2 @ c @ c )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_4 @ a @ a )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ! [X3: $i,X4: $i] :
( ( $true
= ( cP_1 @ ( f @ X4 ) @ X3 ) )
| ( $true
!= ( cP_1 @ X4 @ X3 ) ) )
& ! [X5: $i,X6: $i] :
( ( $true
= ( cP_4 @ ( f @ X6 ) @ X5 ) )
| ( $true
!= ( cP_4 @ X6 @ X5 ) ) )
& ( ( cP_3 @ b @ b )
= $true )
& ( ( cP_3 @ c @ c )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X7: $i,X8: $i] :
( ( $true
!= ( cP_2 @ X8 @ X7 ) )
| ( $true
= ( cP_2 @ ( f @ X8 ) @ X7 ) ) )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X9: $i,X10: $i,X11: $i,X12: $i,X13: $i,X14: $i] :
( ( ( cQ_3 @ X12 @ X13 @ X10 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X10 ) @ X11 ) )
| ( $true
= ( cQ_4 @ X14 @ X9 @ X11 ) )
| ( ( cP_3 @ ( f @ X12 ) @ X14 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X13 ) @ X9 ) ) )
& ! [X15: $i,X16: $i,X17: $i,X18: $i,X19: $i,X20: $i] :
( ( $true
!= ( cP_1 @ ( f @ X20 ) @ X15 ) )
| ( $true
!= ( cQ_1 @ X20 @ X16 @ X18 ) )
| ( $true
!= ( cP_1 @ ( f @ X16 ) @ X19 ) )
| ( $true
!= ( cP_1 @ ( f @ X18 ) @ X17 ) )
| ( ( cQ_2 @ X15 @ X19 @ X17 )
= $true ) )
& ! [X21: $i,X22: $i,X23: $i,X24: $i,X25: $i,X26: $i] :
( ( ( cP_4 @ ( f @ X21 ) @ X26 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X22 ) @ X24 ) )
| ( $true
!= ( cP_4 @ ( f @ X23 ) @ X25 ) )
| ( $true
= ( cQ_5 @ X26 @ X25 @ X24 ) )
| ( ( cQ_4 @ X21 @ X23 @ X22 )
!= $true ) )
& ! [X27: $i,X28: $i,X29: $i,X30: $i,X31: $i,X32: $i] :
( ( ( cP_2 @ ( f @ X29 ) @ X32 )
!= $true )
| ( ( cP_2 @ ( f @ X28 ) @ X31 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X27 ) @ X30 ) )
| ( ( cQ_2 @ X27 @ X28 @ X29 )
!= $true )
| ( ( cQ_3 @ X30 @ X31 @ X32 )
= $true ) )
& ! [X33: $i] :
( $true
= ( cP_4 @ d @ X33 ) )
& ( ( cP_4 @ c @ c )
= $true )
& ( ( cP_3 @ a @ a )
= $true )
& ! [X34: $i] :
( $true
= ( cP_3 @ d @ X34 ) )
& ! [X35: $i] :
( $true
= ( cP_1 @ d @ X35 ) )
& ! [X36: $i,X37: $i,X38: $i] :
( ( cQ_5 @ X37 @ X38 @ X36 )
!= $true ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
! [X38: $i,X36: $i,X37: $i] :
( ( cQ_5 @ X37 @ X38 @ X36 )
!= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
( ( cP_3 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
( ( cP_4 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f13,plain,
! [X31: $i,X28: $i,X29: $i,X27: $i,X32: $i,X30: $i] :
( ( ( cQ_3 @ X30 @ X31 @ X32 )
= $true )
| ( ( cQ_2 @ X27 @ X28 @ X29 )
!= $true )
| ( ( cP_2 @ ( f @ X28 ) @ X31 )
!= $true )
| ( ( cP_2 @ ( f @ X29 ) @ X32 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X27 ) @ X30 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f14,plain,
! [X21: $i,X26: $i,X24: $i,X22: $i,X25: $i,X23: $i] :
( ( $true
!= ( cP_4 @ ( f @ X22 ) @ X24 ) )
| ( ( cQ_4 @ X21 @ X23 @ X22 )
!= $true )
| ( ( cP_4 @ ( f @ X21 ) @ X26 )
!= $true )
| ( $true
= ( cQ_5 @ X26 @ X25 @ X24 ) )
| ( $true
!= ( cP_4 @ ( f @ X23 ) @ X25 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
! [X18: $i,X19: $i,X16: $i,X17: $i,X15: $i,X20: $i] :
( ( ( cQ_2 @ X15 @ X19 @ X17 )
= $true )
| ( $true
!= ( cP_1 @ ( f @ X18 ) @ X17 ) )
| ( $true
!= ( cQ_1 @ X20 @ X16 @ X18 ) )
| ( $true
!= ( cP_1 @ ( f @ X20 ) @ X15 ) )
| ( $true
!= ( cP_1 @ ( f @ X16 ) @ X19 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f16,plain,
! [X10: $i,X11: $i,X9: $i,X14: $i,X12: $i,X13: $i] :
( ( $true
= ( cQ_4 @ X14 @ X9 @ X11 ) )
| ( $true
!= ( cP_3 @ ( f @ X10 ) @ X11 ) )
| ( ( cQ_3 @ X12 @ X13 @ X10 )
!= $true )
| ( ( cP_3 @ ( f @ X12 ) @ X14 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X13 ) @ X9 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f17,plain,
( ( cP_1 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f18,plain,
! [X8: $i,X7: $i] :
( ( $true
= ( cP_2 @ ( f @ X8 ) @ X7 ) )
| ( $true
!= ( cP_2 @ X8 @ X7 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f19,plain,
( ( cP_2 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f20,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f21,plain,
( ( cP_3 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f22,plain,
( ( cP_3 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f23,plain,
! [X6: $i,X5: $i] :
( ( $true
= ( cP_4 @ ( f @ X6 ) @ X5 ) )
| ( $true
!= ( cP_4 @ X6 @ X5 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f24,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( cP_1 @ ( f @ X4 ) @ X3 ) )
| ( $true
!= ( cP_1 @ X4 @ X3 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f25,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f26,plain,
( ( cP_4 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f27,plain,
( ( cP_1 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f28,plain,
( ( cP_2 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
= $true )
| ( $true
!= ( cP_3 @ X1 @ X2 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f30,plain,
( ( cP_4 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f32,plain,
( ( cP_2 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f35,definition,
( spl0_1
<=> ( ( cP_3 @ b @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f37,plain,
( ( ( cP_3 @ b @ b )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f38,plain,
spl0_1,
inference(avatar_split_clause,[],[f22,f35]) ).
thf(f40,definition,
( spl0_2
<=> ( ( cP_3 @ a @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f42,plain,
( ( ( cP_3 @ a @ a )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
spl0_2,
inference(avatar_split_clause,[],[f10,f40]) ).
thf(f45,definition,
( spl0_3
<=> ( ( cP_3 @ c @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f47,plain,
( ( ( cP_3 @ c @ c )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f48,plain,
spl0_3,
inference(avatar_split_clause,[],[f21,f45]) ).
thf(f50,definition,
( spl0_4
<=> ( ( cP_1 @ c @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f52,plain,
( ( ( cP_1 @ c @ c )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f53,plain,
spl0_4,
inference(avatar_split_clause,[],[f17,f50]) ).
thf(f55,definition,
( spl0_5
<=> ( ( cP_2 @ c @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f57,plain,
( ( ( cP_2 @ c @ c )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f58,plain,
spl0_5,
inference(avatar_split_clause,[],[f28,f55]) ).
thf(f60,definition,
( spl0_6
<=> ( ( cP_2 @ b @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f62,plain,
( ( ( cP_2 @ b @ b )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f63,plain,
spl0_6,
inference(avatar_split_clause,[],[f19,f60]) ).
thf(f65,definition,
( spl0_7
<=> ( ( cP_4 @ b @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
thf(f67,plain,
( ( ( cP_4 @ b @ b )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f68,plain,
spl0_7,
inference(avatar_split_clause,[],[f30,f65]) ).
thf(f70,definition,
( spl0_8
<=> ( ( cP_4 @ a @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
thf(f72,plain,
( ( ( cP_4 @ a @ a )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f73,plain,
spl0_8,
inference(avatar_split_clause,[],[f26,f70]) ).
thf(f75,definition,
( spl0_9
<=> ( ( cP_1 @ b @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
thf(f77,plain,
( ( ( cP_1 @ b @ b )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f75]) ).
thf(f78,plain,
spl0_9,
inference(avatar_split_clause,[],[f27,f75]) ).
thf(f80,definition,
( spl0_10
<=> ( ( cP_2 @ a @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
thf(f82,plain,
( ( ( cP_2 @ a @ a )
= $true )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f80]) ).
thf(f83,plain,
spl0_10,
inference(avatar_split_clause,[],[f32,f80]) ).
thf(f85,definition,
( spl0_11
<=> ( ( cP_4 @ c @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
thf(f87,plain,
( ( ( cP_4 @ c @ c )
= $true )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f85]) ).
thf(f88,plain,
spl0_11,
inference(avatar_split_clause,[],[f11,f85]) ).
thf(f90,definition,
( spl0_12
<=> ( ( cQ_1 @ a @ b @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
thf(f92,plain,
( ( ( cQ_1 @ a @ b @ c )
= $true )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f90]) ).
thf(f93,plain,
spl0_12,
inference(avatar_split_clause,[],[f20,f90]) ).
thf(f95,definition,
( spl0_13
<=> ( ( cP_1 @ a @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
thf(f97,plain,
( ( ( cP_1 @ a @ a )
= $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f95]) ).
thf(f98,plain,
spl0_13,
inference(avatar_split_clause,[],[f25,f95]) ).
thf(f99,plain,
! [X21: $i,X26: $i,X24: $i,X22: $i,X25: $i,X23: $i] :
( ( ( cQ_4 @ X21 @ X23 @ X22 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X23 ) @ X25 ) )
| ( $true
!= ( cP_4 @ ( f @ X22 ) @ X24 ) )
| ( ( cP_4 @ ( f @ X21 ) @ X26 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f14,f7]) ).
thf(f100,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_3 @ ( f @ X7 ) @ X0 ) )
| ( ( cQ_3 @ X7 @ X8 @ X6 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X8 ) @ X1 ) )
| ( $true
!= ( cP_4 @ ( f @ X0 ) @ X5 ) )
| ( $true
!= ( cP_4 @ ( f @ X2 ) @ X4 ) )
| ( $true != $true )
| ( $true
!= ( cP_3 @ ( f @ X6 ) @ X2 ) )
| ( $true
!= ( cP_4 @ ( f @ X1 ) @ X3 ) ) ),
inference(superposition,[],[f99,f16]) ).
thf(f101,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cQ_3 @ X7 @ X8 @ X6 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X2 ) @ X4 ) )
| ( $true
!= ( cP_4 @ ( f @ X1 ) @ X3 ) )
| ( $true
!= ( cP_4 @ ( f @ X0 ) @ X5 ) )
| ( $true
!= ( cP_3 @ ( f @ X7 ) @ X0 ) )
| ( $true
!= ( cP_3 @ ( f @ X6 ) @ X2 ) )
| ( $true
!= ( cP_3 @ ( f @ X8 ) @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) )
| ( $true
!= ( cP_3 @ ( f @ X1 ) @ X5 ) )
| ( $true != $true )
| ( $true
!= ( cP_2 @ ( f @ X10 ) @ X1 ) )
| ( $true
!= ( cP_2 @ ( f @ X11 ) @ X2 ) )
| ( $true
!= ( cQ_2 @ X9 @ X10 @ X11 ) )
| ( $true
!= ( cP_4 @ ( f @ X5 ) @ X6 ) )
| ( $true
!= ( cP_3 @ ( f @ X0 ) @ X7 ) )
| ( ( cP_2 @ ( f @ X9 ) @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X3 ) @ X4 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X2 ) @ X3 ) ) ),
inference(superposition,[],[f101,f13]) ).
thf(f103,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( cQ_2 @ X9 @ X10 @ X11 ) )
| ( $true
!= ( cP_2 @ ( f @ X10 ) @ X1 ) )
| ( ( cP_4 @ ( f @ X3 ) @ X4 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) )
| ( $true
!= ( cP_3 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_2 @ ( f @ X9 ) @ X0 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X1 ) @ X5 ) )
| ( $true
!= ( cP_4 @ ( f @ X5 ) @ X6 ) )
| ( $true
!= ( cP_2 @ ( f @ X11 ) @ X2 ) )
| ( $true
!= ( cP_3 @ ( f @ X0 ) @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f102]) ).
thf(f104,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 @ X0 ) @ X9 )
!= $true )
| ( $true != $true )
| ( ( cP_1 @ ( f @ X12 ) @ X2 )
!= $true )
| ( ( cP_3 @ ( f @ X3 ) @ X10 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X1 ) @ X3 ) )
| ( ( cP_1 @ ( f @ X14 ) @ X1 )
!= $true )
| ( ( cQ_1 @ X13 @ X14 @ X12 )
!= $true )
| ( ( cP_1 @ ( f @ X13 ) @ X0 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X9 ) @ X6 ) )
| ( ( cP_4 @ ( f @ X6 ) @ X7 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X10 ) @ X11 ) )
| ( $true
!= ( cP_3 @ ( f @ X8 ) @ X4 ) )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X8 ) )
| ( $true
!= ( cP_4 @ ( f @ X4 ) @ X5 ) ) ),
inference(superposition,[],[f103,f15]) ).
thf(f105,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] :
( ( ( cQ_1 @ X13 @ X14 @ X12 )
!= $true )
| ( ( cP_4 @ ( f @ X6 ) @ X7 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X4 ) @ X5 ) )
| ( $true
!= ( cP_3 @ ( f @ X9 ) @ X6 ) )
| ( ( cP_2 @ ( f @ X0 ) @ X9 )
!= $true )
| ( ( cP_1 @ ( f @ X13 ) @ X0 )
!= $true )
| ( ( cP_1 @ ( f @ X14 ) @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X10 ) @ X11 ) )
| ( $true
!= ( cP_2 @ ( f @ X1 ) @ X3 ) )
| ( $true
!= ( cP_3 @ ( f @ X8 ) @ X4 ) )
| ( ( cP_1 @ ( f @ X12 ) @ X2 )
!= $true )
| ( ( cP_3 @ ( f @ X3 ) @ X10 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f106,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_2 @ ( f @ X6 ) @ X9 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X9 ) @ X7 ) )
| ( $true
!= ( cP_1 @ ( f @ b ) @ X6 ) )
| ( $true
!= ( cP_3 @ ( f @ X4 ) @ X0 ) )
| ( $true
!= ( cP_2 @ ( f @ X5 ) @ X4 ) )
| ( ( cP_2 @ ( f @ X11 ) @ X10 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_3 @ ( f @ X10 ) @ X2 ) )
| ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) )
| ( ( cP_4 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X5 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ c ) @ X11 ) ) )
| ~ spl0_12 ),
inference(superposition,[],[f105,f92]) ).
thf(f107,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_2 @ ( f @ X6 ) @ X9 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X5 ) @ X4 ) )
| ( $true
!= ( cP_1 @ ( f @ c ) @ X11 ) )
| ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) )
| ( ( cP_1 @ ( f @ a ) @ X5 )
!= $true )
| ( ( cP_4 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ b ) @ X6 ) )
| ( $true
!= ( cP_3 @ ( f @ X4 ) @ X0 ) )
| ( $true
!= ( cP_3 @ ( f @ X10 ) @ X2 ) )
| ( $true
!= ( cP_3 @ ( f @ X9 ) @ X7 ) )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_2 @ ( f @ X11 ) @ X10 )
!= $true ) )
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f109,definition,
( spl0_14
<=> ! [X10: $i,X11: $i,X3: $i,X2: $i] :
( ( $true
!= ( cP_1 @ ( f @ c ) @ X11 ) )
| ( ( cP_2 @ ( f @ X11 ) @ X10 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X10 ) @ X2 ) )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
thf(f110,plain,
( ! [X2: $i,X3: $i,X10: $i,X11: $i] :
( ( $true
!= ( cP_1 @ ( f @ c ) @ X11 ) )
| ( ( cP_2 @ ( f @ X11 ) @ X10 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X10 ) @ X2 ) )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f109]) ).
thf(f112,definition,
( spl0_15
<=> ! [X9: $i,X7: $i,X6: $i,X8: $i] :
( ( ( cP_2 @ ( f @ X6 ) @ X9 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X9 ) @ X7 ) )
| ( $true
!= ( cP_1 @ ( f @ b ) @ X6 ) )
| ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
thf(f113,plain,
( ! [X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( cP_1 @ ( f @ b ) @ X6 ) )
| ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) )
| ( ( cP_2 @ ( f @ X6 ) @ X9 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X9 ) @ X7 ) ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f112]) ).
thf(f115,definition,
( spl0_16
<=> ! [X4: $i,X0: $i,X5: $i,X1: $i] :
( ( $true
!= ( cP_2 @ ( f @ X5 ) @ X4 ) )
| ( $true
!= ( cP_3 @ ( f @ X4 ) @ X0 ) )
| ( ( cP_4 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
thf(f116,plain,
( ! [X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_2 @ ( f @ X5 ) @ X4 ) )
| ( ( cP_1 @ ( f @ a ) @ X5 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X4 ) @ X0 ) )
| ( ( cP_4 @ ( f @ X0 ) @ X1 )
!= $true ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f115]) ).
thf(f117,plain,
( spl0_14
| spl0_15
| spl0_16
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f107,f90,f115,f112,f109]) ).
thf(f118,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X3 ) @ X1 ) )
| ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true )
| ( $true != $true ) )
| ~ spl0_15 ),
inference(superposition,[],[f113,f24]) ).
thf(f119,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ ( f @ X3 ) @ X1 ) )
| ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true ) )
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f120,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_1 @ b @ X3 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X3 ) @ X0 ) )
| ( $true != $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true ) )
| ~ spl0_15 ),
inference(superposition,[],[f119,f29]) ).
thf(f121,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_2 @ ( f @ X3 ) @ X0 ) )
| ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ b @ X3 )
!= $true ) )
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f120]) ).
thf(f122,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ X1 @ X2 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( $true != $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true ) )
| ~ spl0_15 ),
inference(superposition,[],[f121,f18]) ).
thf(f123,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( $true
!= ( cP_3 @ X1 @ X2 ) ) )
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f122]) ).
thf(f124,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ b @ X2 )
!= $true )
| ( ( cP_3 @ X3 @ X0 )
!= $true )
| ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( $true != $true ) )
| ~ spl0_15 ),
inference(superposition,[],[f123,f23]) ).
thf(f125,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_3 @ X3 @ X0 )
!= $true )
| ( ( cP_1 @ b @ X2 )
!= $true ) )
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f124]) ).
thf(f128,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ b @ b )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_3 @ b @ X0 ) ) )
| ~ spl0_6
| ~ spl0_15 ),
inference(superposition,[],[f125,f62]) ).
thf(f131,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_1 @ b @ b )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ b @ X0 ) ) )
| ~ spl0_6
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f128]) ).
thf(f136,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ b @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f131,f77]) ).
thf(f138,definition,
( spl0_17
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ c @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
thf(f139,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ c @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f138]) ).
thf(f158,definition,
( spl0_22
<=> ! [X0: $i,X1: $i] :
( ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ a @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
thf(f159,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ a @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f158]) ).
thf(f161,plain,
( ! [X0: $i] :
( ( $true
!= ( cP_4 @ b @ X0 ) )
| ( $true != $true ) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15 ),
inference(superposition,[],[f136,f37]) ).
thf(f162,plain,
( ! [X0: $i] :
( $true
!= ( cP_4 @ b @ X0 ) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f161]) ).
thf(f163,plain,
( ( $true != $true )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_15 ),
inference(superposition,[],[f162,f67]) ).
thf(f164,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f163]) ).
thf(f165,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f164]) ).
thf(f166,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X0 )
!= $true ) )
| ~ spl0_16 ),
inference(superposition,[],[f116,f18]) ).
thf(f167,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_1 @ ( f @ a ) @ X0 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true ) )
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f166]) ).
thf(f168,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_1 @ a @ X0 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_16 ),
inference(superposition,[],[f167,f24]) ).
thf(f169,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ a @ X0 )
!= $true ) )
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f168]) ).
thf(f170,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_2 @ X3 @ X0 ) )
| ( $true != $true )
| ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X3 ) ) )
| ~ spl0_16 ),
inference(superposition,[],[f169,f29]) ).
thf(f171,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true )
| ( $true
!= ( cP_2 @ X3 @ X0 ) )
| ( $true
!= ( cP_1 @ a @ X3 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true ) )
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f170]) ).
thf(f172,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( $true
!= ( cP_1 @ a @ X2 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( cP_3 @ X3 @ X0 )
!= $true ) )
| ~ spl0_16 ),
inference(superposition,[],[f171,f23]) ).
thf(f173,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_1 @ a @ X2 ) )
| ( ( cP_3 @ X3 @ X0 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_2 @ X2 @ X3 ) ) )
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f174,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_2 @ a @ X0 ) )
| ( $true != $true )
| ( $true
!= ( cP_4 @ X1 @ X2 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true ) )
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f173,f97]) ).
thf(f175,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_2 @ a @ X0 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ X1 @ X2 ) ) )
| ~ spl0_13
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f176,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_3 @ a @ X0 ) ) )
| ~ spl0_10
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f175,f82]) ).
thf(f177,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( cP_3 @ a @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_10
| ~ spl0_13
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f178,plain,
( spl0_22
| ~ spl0_10
| ~ spl0_13
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f177,f115,f95,f80,f158]) ).
thf(f179,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cP_4 @ a @ X0 )
!= $true ) )
| ~ spl0_2
| ~ spl0_22 ),
inference(superposition,[],[f159,f42]) ).
thf(f180,plain,
( ! [X0: $i] :
( ( cP_4 @ a @ X0 )
!= $true )
| ~ spl0_2
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f179]) ).
thf(f181,plain,
( ( $true != $true )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_22 ),
inference(superposition,[],[f180,f72]) ).
thf(f182,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f181]) ).
thf(f183,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f182]) ).
thf(f184,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true != $true ) )
| ~ spl0_14 ),
inference(superposition,[],[f110,f24]) ).
thf(f185,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true ) )
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f184]) ).
thf(f186,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_14 ),
inference(superposition,[],[f185,f18]) ).
thf(f187,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f186]) ).
thf(f188,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true )
| ( $true
!= ( cP_2 @ X3 @ X0 ) )
| ( $true
!= ( cP_1 @ c @ X3 ) ) )
| ~ spl0_14 ),
inference(superposition,[],[f187,f29]) ).
thf(f189,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X3 ) )
| ( $true
!= ( cP_2 @ X3 @ X0 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true ) )
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f188]) ).
thf(f190,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ X3 @ X0 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( ( cP_1 @ c @ X2 )
!= $true ) )
| ~ spl0_14 ),
inference(superposition,[],[f189,f23]) ).
thf(f191,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ c @ X2 )
!= $true )
| ( ( cP_3 @ X3 @ X0 )
!= $true ) )
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f190]) ).
thf(f193,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_1 @ c @ c )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_3 @ c @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_5
| ~ spl0_14 ),
inference(superposition,[],[f191,f57]) ).
thf(f200,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_1 @ c @ c )
!= $true )
| ( $true
!= ( cP_3 @ c @ X0 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_5
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f193]) ).
thf(f215,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ c @ X0 ) ) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f200,f52]) ).
thf(f221,plain,
( spl0_17
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f215,f109,f55,f50,f138]) ).
thf(f222,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cP_4 @ c @ X0 ) ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f139,f47]) ).
thf(f223,plain,
( ! [X0: $i] :
( $true
!= ( cP_4 @ c @ X0 ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f222]) ).
thf(f224,plain,
( ( $true != $true )
| ~ spl0_3
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f223,f87]) ).
thf(f225,plain,
( $false
| ~ spl0_3
| ~ spl0_11
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f224]) ).
thf(f226,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f225]) ).
cnf(s1,plain,
spl0_1,
inference(sat_conversion,[],[f38]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f48]) ).
cnf(s4,plain,
spl0_4,
inference(sat_conversion,[],[f53]) ).
cnf(s5,plain,
spl0_5,
inference(sat_conversion,[],[f58]) ).
cnf(s6,plain,
spl0_6,
inference(sat_conversion,[],[f63]) ).
cnf(s7,plain,
spl0_7,
inference(sat_conversion,[],[f68]) ).
cnf(s8,plain,
spl0_8,
inference(sat_conversion,[],[f73]) ).
cnf(s9,plain,
spl0_9,
inference(sat_conversion,[],[f78]) ).
cnf(s10,plain,
spl0_10,
inference(sat_conversion,[],[f83]) ).
cnf(s11,plain,
spl0_11,
inference(sat_conversion,[],[f88]) ).
cnf(s12,plain,
spl0_12,
inference(sat_conversion,[],[f93]) ).
cnf(s13,plain,
spl0_13,
inference(sat_conversion,[],[f98]) ).
cnf(s14,plain,
( ~ spl0_12
| spl0_14
| spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f117]) ).
cnf(s18,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_15 ),
inference(sat_conversion,[],[f165]) ).
cnf(s19,plain,
( ~ spl0_10
| ~ spl0_13
| ~ spl0_16
| spl0_22 ),
inference(sat_conversion,[],[f178]) ).
cnf(s20,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_22 ),
inference(sat_conversion,[],[f183]) ).
cnf(s24,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f221]) ).
cnf(s25,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_17 ),
inference(sat_conversion,[],[f226]) ).
cnf(s26,plain,
~ spl0_17,
inference(rat,[],[s25,s11,s3]) ).
cnf(s27,plain,
~ spl0_14,
inference(rat,[],[s24,s4,s5,s26]) ).
cnf(s28,plain,
~ spl0_22,
inference(rat,[],[s20,s8,s2]) ).
cnf(s29,plain,
~ spl0_16,
inference(rat,[],[s19,s10,s13,s28]) ).
cnf(s30,plain,
spl0_15,
inference(rat,[],[s14,s27,s12,s29]) ).
cnf(s33,plain,
~ spl0_1,
inference(rat,[],[s18,s6,s9,s7,s30]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s1,s33]) ).
thf(f227,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO387^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n007.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 16:48:11 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.21/0.31 % (3630315)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (3630326)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (3630326)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
% 0.21/0.31 % (3630326)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=1773134365:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (3630320)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4225756585:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (3630322)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2285353046:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (3630321)lrs+10_16_si=on:nwc=1.5:random_seed=1640720852:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (3630323)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=1081735380: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)
% 0.21/0.31 % (3630324)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=197812901:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (3630325)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1321911692:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (3630322)Instruction limit reached!
% 0.21/0.31 % (3630322)------------------------------
% 0.21/0.31 % (3630322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3630322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3630322)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3630322)Termination reason: Instruction limit
% 0.21/0.31 % (3630322)Termination phase: Saturation
% 0.21/0.31 % (3630322)Time elapsed: 0.002 s
% 0.21/0.31 % (3630322)Peak memory usage: 11 MB
% 0.21/0.31 % (3630322)Instructions burned: 3 (million)
% 0.21/0.31 % (3630321)Instruction limit reached!
% 0.21/0.31 % (3630321)------------------------------
% 0.21/0.31 % (3630321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3630321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3630321)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3630321)Termination reason: Instruction limit
% 0.21/0.31 % (3630321)Termination phase: Saturation
% 0.21/0.31 % (3630321)Time elapsed: 0.009 s
% 0.21/0.31 % (3630321)Peak memory usage: 12 MB
% 0.21/0.31 % (3630321)Instructions burned: 19 (million)
% 0.21/0.31 % (3630324)Instruction limit reached!
% 0.21/0.31 % (3630324)------------------------------
% 0.21/0.31 % (3630324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3630324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3630324)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3630324)Termination reason: Instruction limit
% 0.21/0.31 % (3630324)Termination phase: Saturation
% 0.21/0.31 % (3630324)Time elapsed: 0.013 s
% 0.21/0.31 % (3630324)Peak memory usage: 11 MB
% 0.21/0.31 % (3630324)Instructions burned: 24 (million)
% 0.21/0.31 % (3630323) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3630315-3630323"...
% 0.21/0.31 % (3630323)...printing done.
% 0.21/0.31 % (3630334)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1548854890:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.31 % (3630323)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (3630323)------------------------------
% 0.21/0.31 % (3630323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3630323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3630323)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3630323)Termination reason: Refutation
% 0.21/0.31 % (3630323)Time elapsed: 0.018 s
% 0.21/0.31 % (3630323)Peak memory usage: 13 MB
% 0.21/0.31 % (3630323)Instructions burned: 34 (million)
% 0.21/0.31 % (3630315)Success in time 0.065 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------