%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO387^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:54:06 AM UTC 2026
% Result : Theorem 1.74s 1.35s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 98 ( 18 unt; 0 typ; 4 def)
% Number of atoms : 1844 ( 455 equ; 0 cnn)
% Maximal formula atoms : 77 ( 18 avg)
% Number of connectives : 2510 ( 483 ~; 407 |; 150 &;1466 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 10 con; 0-3 aty)
% Number of variables : 529 ( 0 ^; 529 !; 0 ?; 529 :)
% Comments :
%------------------------------------------------------------------------------
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(f162,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f53,f70,f118,f138,f161]) ).
thf(f161,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[status(thm)],[f160]) ).
thf(f160,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f159]) ).
thf(f159,plain,
( ( $true != $true )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f158,f20]) ).
thf(f20,plain,
( ( cP_4 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ! [X0: $i] :
( ( cP_4 @ d @ X0 )
= $true )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( $true
!= ( cP_2 @ ( f @ X4 ) @ X5 ) )
| ( ( cQ_2 @ X4 @ X3 @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X2 )
!= $true )
| ( ( cQ_3 @ X5 @ X2 @ X6 )
= $true )
| ( ( cP_2 @ ( f @ X1 ) @ X6 )
!= $true ) )
& ! [X7: $i,X8: $i] :
( ( $true
= ( cP_4 @ ( f @ X7 ) @ X8 ) )
| ( $true
!= ( cP_4 @ X7 @ X8 ) ) )
& ! [X9: $i,X10: $i,X11: $i,X12: $i,X13: $i,X14: $i] :
( ( ( cP_4 @ ( f @ X10 ) @ X12 )
!= $true )
| ( ( cQ_4 @ X11 @ X9 @ X10 )
!= $true )
| ( ( cP_4 @ ( f @ X11 ) @ X13 )
!= $true )
| ( $true
= ( cQ_5 @ X13 @ X14 @ X12 ) )
| ( ( cP_4 @ ( f @ X9 ) @ X14 )
!= $true ) )
& ( ( cP_3 @ b @ b )
= $true )
& ( ( cP_3 @ c @ c )
= $true )
& ( ( cP_4 @ a @ a )
= $true )
& ( ( cP_4 @ b @ b )
= $true )
& ! [X15: $i] :
( ( cP_3 @ d @ X15 )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ! [X16: $i,X17: $i,X18: $i,X19: $i,X20: $i,X21: $i] :
( ( ( cQ_2 @ X16 @ X19 @ X18 )
= $true )
| ( ( cP_1 @ ( f @ X21 ) @ X19 )
!= $true )
| ( ( cP_1 @ ( f @ X17 ) @ X18 )
!= $true )
| ( ( cP_1 @ ( f @ X20 ) @ X16 )
!= $true )
| ( ( cQ_1 @ X20 @ X21 @ X17 )
!= $true ) )
& ( ( cP_4 @ c @ c )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X22: $i,X23: $i] :
( ( ( cP_2 @ X23 @ X22 )
!= $true )
| ( ( cP_2 @ ( f @ X23 ) @ X22 )
= $true ) )
& ! [X24: $i] :
( ( cP_2 @ d @ X24 )
= $true )
& ! [X25: $i] :
( $true
= ( cP_1 @ d @ X25 ) )
& ! [X26: $i,X27: $i,X28: $i,X29: $i,X30: $i,X31: $i] :
( ( ( cP_3 @ ( f @ X27 ) @ X26 )
!= $true )
| ( ( cP_3 @ ( f @ X31 ) @ X29 )
!= $true )
| ( $true
!= ( cQ_3 @ X31 @ X28 @ X27 ) )
| ( ( cP_3 @ ( f @ X28 ) @ X30 )
!= $true )
| ( $true
= ( cQ_4 @ X29 @ X30 @ X26 ) ) )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X32: $i,X33: $i] :
( ( ( cP_1 @ X32 @ X33 )
!= $true )
| ( ( cP_1 @ ( f @ X32 ) @ X33 )
= $true ) )
& ! [X34: $i,X35: $i] :
( ( ( cP_3 @ X34 @ X35 )
!= $true )
| ( ( cP_3 @ ( f @ X34 ) @ X35 )
= $true ) )
& ! [X36: $i,X37: $i,X38: $i] :
( ( cQ_5 @ X37 @ X36 @ X38 )
!= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ( ( cP_2 @ a @ a )
= $true )
& ( ( cP_3 @ a @ a )
= $true ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ! [X38: $i] :
( ( cP_4 @ d @ X38 )
= $true )
& ! [X12: $i,X9: $i,X14: $i,X11: $i,X13: $i,X10: $i] :
( ( $true
!= ( cP_2 @ ( f @ X11 ) @ X13 ) )
| ( ( cQ_2 @ X11 @ X14 @ X12 )
!= $true )
| ( ( cP_2 @ ( f @ X14 ) @ X9 )
!= $true )
| ( ( cQ_3 @ X13 @ X9 @ X10 )
= $true )
| ( ( cP_2 @ ( f @ X12 ) @ X10 )
!= $true ) )
& ! [X30: $i,X31: $i] :
( ( ( cP_4 @ ( f @ X30 ) @ X31 )
= $true )
| ( ( cP_4 @ X30 @ X31 )
!= $true ) )
& ! [X3: $i,X4: $i,X1: $i,X5: $i,X2: $i,X6: $i] :
( ( $true
!= ( cP_4 @ ( f @ X4 ) @ X5 ) )
| ( $true
!= ( cQ_4 @ X1 @ X3 @ X4 ) )
| ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true )
| ( $true
= ( cQ_5 @ X2 @ X6 @ X5 ) )
| ( ( cP_4 @ ( f @ X3 ) @ X6 )
!= $true ) )
& ( ( cP_3 @ b @ b )
= $true )
& ( ( cP_3 @ c @ c )
= $true )
& ( ( cP_4 @ a @ a )
= $true )
& ( ( cP_4 @ b @ b )
= $true )
& ! [X7: $i] :
( ( cP_3 @ d @ X7 )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ! [X36: $i,X37: $i,X32: $i,X33: $i,X35: $i,X34: $i] :
( ( ( cQ_2 @ X36 @ X33 @ X32 )
= $true )
| ( ( cP_1 @ ( f @ X34 ) @ X33 )
!= $true )
| ( ( cP_1 @ ( f @ X37 ) @ X32 )
!= $true )
| ( ( cP_1 @ ( f @ X35 ) @ X36 )
!= $true )
| ( $true
!= ( cQ_1 @ X35 @ X34 @ X37 ) ) )
& ( ( cP_4 @ c @ c )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X20: $i,X21: $i] :
( ( ( cP_2 @ X21 @ X20 )
!= $true )
| ( $true
= ( cP_2 @ ( f @ X21 ) @ X20 ) ) )
& ! [X8: $i] :
( $true
= ( cP_2 @ d @ X8 ) )
& ! [X0: $i] :
( ( cP_1 @ d @ X0 )
= $true )
& ! [X23: $i,X22: $i,X24: $i,X25: $i,X26: $i,X27: $i] :
( ( ( cP_3 @ ( f @ X22 ) @ X23 )
!= $true )
| ( ( cP_3 @ ( f @ X27 ) @ X25 )
!= $true )
| ( $true
!= ( cQ_3 @ X27 @ X24 @ X22 ) )
| ( ( cP_3 @ ( f @ X24 ) @ X26 )
!= $true )
| ( ( cQ_4 @ X25 @ X26 @ X23 )
= $true ) )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X19: $i,X18: $i] :
( ( ( cP_1 @ X19 @ X18 )
!= $true )
| ( ( cP_1 @ ( f @ X19 ) @ X18 )
= $true ) )
& ! [X28: $i,X29: $i] :
( ( ( cP_3 @ X28 @ X29 )
!= $true )
| ( $true
= ( cP_3 @ ( f @ X28 ) @ X29 ) ) )
& ! [X16: $i,X17: $i,X15: $i] :
( ( cQ_5 @ X17 @ X16 @ X15 )
!= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ( ( cP_2 @ a @ a )
= $true )
& ( ( cP_3 @ a @ a )
= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ( ( ( cP_3 @ a @ a )
= $true )
& ! [X0: $i] :
( ( cP_1 @ d @ X0 )
= $true )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( $true
!= ( cQ_4 @ X1 @ X3 @ X4 ) )
| ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_4 @ ( f @ X3 ) @ X6 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X4 ) @ X5 ) )
| ( $true
= ( cQ_5 @ X2 @ X6 @ X5 ) ) )
& ! [X7: $i] :
( ( cP_3 @ d @ X7 )
= $true )
& ! [X8: $i] :
( $true
= ( cP_2 @ d @ X8 ) )
& ( ( cP_2 @ c @ c )
= $true )
& ! [X9: $i,X10: $i,X11: $i,X12: $i,X13: $i,X14: $i] :
( ( ( cP_2 @ ( f @ X12 ) @ X10 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X11 ) @ X13 ) )
| ( ( cQ_2 @ X11 @ X14 @ X12 )
!= $true )
| ( ( cP_2 @ ( f @ X14 ) @ X9 )
!= $true )
| ( ( cQ_3 @ X13 @ X9 @ X10 )
= $true ) )
& ! [X15: $i,X16: $i,X17: $i] :
( ( cQ_5 @ X17 @ X16 @ X15 )
!= $true )
& ( ( cP_3 @ b @ b )
= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ( ( cP_4 @ a @ a )
= $true )
& ( ( cP_4 @ c @ c )
= $true )
& ! [X18: $i,X19: $i] :
( ( ( cP_1 @ X19 @ X18 )
!= $true )
| ( ( cP_1 @ ( f @ X19 ) @ X18 )
= $true ) )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cP_3 @ c @ c )
= $true )
& ( ( cP_4 @ b @ b )
= $true )
& ( ( cP_2 @ a @ a )
= $true )
& ! [X20: $i,X21: $i] :
( ( $true
= ( cP_2 @ ( f @ X21 ) @ X20 ) )
| ( ( cP_2 @ X21 @ X20 )
!= $true ) )
& ! [X22: $i,X23: $i,X24: $i,X25: $i,X26: $i,X27: $i] :
( ( ( cP_3 @ ( f @ X27 ) @ X25 )
!= $true )
| ( $true
!= ( cQ_3 @ X27 @ X24 @ X22 ) )
| ( ( cP_3 @ ( f @ X24 ) @ X26 )
!= $true )
| ( ( cP_3 @ ( f @ X22 ) @ X23 )
!= $true )
| ( ( cQ_4 @ X25 @ X26 @ X23 )
= $true ) )
& ! [X28: $i,X29: $i] :
( ( $true
= ( cP_3 @ ( f @ X28 ) @ X29 ) )
| ( ( cP_3 @ X28 @ X29 )
!= $true ) )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X30: $i,X31: $i] :
( ( ( cP_4 @ X30 @ X31 )
!= $true )
| ( ( cP_4 @ ( f @ X30 ) @ X31 )
= $true ) )
& ! [X32: $i,X33: $i,X34: $i,X35: $i,X36: $i,X37: $i] :
( ( ( cP_1 @ ( f @ X34 ) @ X33 )
!= $true )
| ( ( cP_1 @ ( f @ X37 ) @ X32 )
!= $true )
| ( ( cQ_2 @ X36 @ X33 @ X32 )
= $true )
| ( ( cP_1 @ ( f @ X35 ) @ X36 )
!= $true )
| ( $true
!= ( cQ_1 @ X35 @ X34 @ X37 ) ) )
& ! [X38: $i] :
( ( cP_4 @ d @ X38 )
= $true )
& ( ( cP_1 @ b @ b )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ( ( cP_3 @ a @ a )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_4 @ X1 @ X3 @ X4 )
| ~ ( cP_4 @ ( f @ X1 ) @ X2 )
| ~ ( cP_4 @ ( f @ X3 ) @ X6 )
| ~ ( cP_4 @ ( f @ X4 ) @ X5 )
| ( cQ_5 @ X2 @ X6 @ X5 ) )
& ! [X7: $i] : ( cP_3 @ d @ X7 )
& ! [X8: $i] : ( cP_2 @ d @ X8 )
& ( cP_2 @ c @ c )
& ! [X9: $i,X10: $i,X11: $i,X12: $i,X13: $i,X14: $i] :
( ~ ( cP_2 @ ( f @ X12 ) @ X10 )
| ~ ( cP_2 @ ( f @ X11 ) @ X13 )
| ~ ( cQ_2 @ X11 @ X14 @ X12 )
| ~ ( cP_2 @ ( f @ X14 ) @ X9 )
| ( cQ_3 @ X13 @ X9 @ X10 ) )
& ! [X15: $i,X16: $i,X17: $i] :
~ ( cQ_5 @ X17 @ X16 @ X15 )
& ( cP_3 @ b @ b )
& ( cP_2 @ b @ b )
& ( cP_4 @ a @ a )
& ( cP_4 @ c @ c )
& ! [X18: $i,X19: $i] :
( ~ ( cP_1 @ X19 @ X18 )
| ( cP_1 @ ( f @ X19 ) @ X18 ) )
& ( cP_1 @ a @ a )
& ( cP_3 @ c @ c )
& ( cP_4 @ b @ b )
& ( cP_2 @ a @ a )
& ! [X20: $i,X21: $i] :
( ( cP_2 @ ( f @ X21 ) @ X20 )
| ~ ( cP_2 @ X21 @ X20 ) )
& ! [X22: $i,X23: $i,X24: $i,X25: $i,X26: $i,X27: $i] :
( ~ ( cP_3 @ ( f @ X27 ) @ X25 )
| ~ ( cQ_3 @ X27 @ X24 @ X22 )
| ~ ( cP_3 @ ( f @ X24 ) @ X26 )
| ~ ( cP_3 @ ( f @ X22 ) @ X23 )
| ( cQ_4 @ X25 @ X26 @ X23 ) )
& ! [X28: $i,X29: $i] :
( ( cP_3 @ ( f @ X28 ) @ X29 )
| ~ ( cP_3 @ X28 @ X29 ) )
& ( cQ_1 @ a @ b @ c )
& ( cP_1 @ c @ c )
& ! [X30: $i,X31: $i] :
( ~ ( cP_4 @ X30 @ X31 )
| ( cP_4 @ ( f @ X30 ) @ X31 ) )
& ! [X32: $i,X33: $i,X34: $i,X35: $i,X36: $i,X37: $i] :
( ~ ( cP_1 @ ( f @ X34 ) @ X33 )
| ~ ( cP_1 @ ( f @ X37 ) @ X32 )
| ( cQ_2 @ X36 @ X33 @ X32 )
| ~ ( cP_1 @ ( f @ X35 ) @ X36 )
| ~ ( cQ_1 @ X35 @ X34 @ X37 ) )
& ! [X38: $i] : ( cP_4 @ d @ X38 )
& ( cP_1 @ b @ b ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ( cP_3 @ a @ a )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X0: $i,X3: $i,X1: $i,X2: $i,X5: $i,X4: $i] :
( ~ ( cQ_4 @ X0 @ X1 @ X2 )
| ~ ( cP_4 @ ( f @ X0 ) @ X3 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ( cQ_5 @ X3 @ X4 @ X5 ) )
& ! [X0: $i] : ( cP_3 @ d @ X0 )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ( cP_2 @ c @ c )
& ! [X4: $i,X5: $i,X0: $i,X2: $i,X3: $i,X1: $i] :
( ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ( cQ_3 @ X3 @ X4 @ X5 ) )
& ! [X2: $i,X1: $i,X0: $i] :
~ ( cQ_5 @ X0 @ X1 @ X2 )
& ( cP_3 @ b @ b )
& ( cP_2 @ b @ b )
& ( cP_4 @ a @ a )
& ( cP_4 @ c @ c )
& ! [X1: $i,X0: $i] :
( ~ ( cP_1 @ X0 @ X1 )
| ( cP_1 @ ( f @ X0 ) @ X1 ) )
& ( cP_1 @ a @ a )
& ( cP_3 @ c @ c )
& ( cP_4 @ b @ b )
& ( cP_2 @ a @ a )
& ! [X1: $i,X0: $i] :
( ( cP_2 @ ( f @ X0 ) @ X1 )
| ~ ( cP_2 @ X0 @ X1 ) )
& ! [X2: $i,X5: $i,X1: $i,X3: $i,X4: $i,X0: $i] :
( ~ ( cP_3 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_3 @ X0 @ X1 @ X2 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ( cQ_4 @ X3 @ X4 @ X5 ) )
& ! [X0: $i,X1: $i] :
( ( cP_3 @ ( f @ X0 ) @ X1 )
| ~ ( cP_3 @ X0 @ X1 ) )
& ( cQ_1 @ a @ b @ c )
& ( cP_1 @ c @ c )
& ! [X0: $i,X1: $i] :
( ~ ( cP_4 @ X0 @ X1 )
| ( cP_4 @ ( f @ X0 ) @ X1 ) )
& ! [X5: $i,X4: $i,X1: $i,X0: $i,X3: $i,X2: $i] :
( ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 ) )
& ! [X0: $i] : ( cP_4 @ d @ X0 )
& ( cP_1 @ b @ b ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ( ( cP_3 @ a @ a )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X0: $i,X3: $i,X1: $i,X2: $i,X5: $i,X4: $i] :
( ~ ( cQ_4 @ X0 @ X1 @ X2 )
| ~ ( cP_4 @ ( f @ X0 ) @ X3 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ( cQ_5 @ X3 @ X4 @ X5 ) )
& ! [X0: $i] : ( cP_3 @ d @ X0 )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ( cP_2 @ c @ c )
& ! [X4: $i,X5: $i,X0: $i,X2: $i,X3: $i,X1: $i] :
( ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ( cQ_3 @ X3 @ X4 @ X5 ) )
& ! [X2: $i,X1: $i,X0: $i] :
~ ( cQ_5 @ X0 @ X1 @ X2 )
& ( cP_3 @ b @ b )
& ( cP_2 @ b @ b )
& ( cP_4 @ a @ a )
& ( cP_4 @ c @ c )
& ! [X1: $i,X0: $i] :
( ~ ( cP_1 @ X0 @ X1 )
| ( cP_1 @ ( f @ X0 ) @ X1 ) )
& ( cP_1 @ a @ a )
& ( cP_3 @ c @ c )
& ( cP_4 @ b @ b )
& ( cP_2 @ a @ a )
& ! [X1: $i,X0: $i] :
( ( cP_2 @ ( f @ X0 ) @ X1 )
| ~ ( cP_2 @ X0 @ X1 ) )
& ! [X2: $i,X5: $i,X1: $i,X3: $i,X4: $i,X0: $i] :
( ~ ( cP_3 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_3 @ X0 @ X1 @ X2 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ( cQ_4 @ X3 @ X4 @ X5 ) )
& ! [X0: $i,X1: $i] :
( ( cP_3 @ ( f @ X0 ) @ X1 )
| ~ ( cP_3 @ X0 @ X1 ) )
& ( cQ_1 @ a @ b @ c )
& ( cP_1 @ c @ c )
& ! [X0: $i,X1: $i] :
( ~ ( cP_4 @ X0 @ X1 )
| ( cP_4 @ ( f @ X0 ) @ X1 ) )
& ! [X5: $i,X4: $i,X1: $i,X0: $i,X3: $i,X2: $i] :
( ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 ) )
& ! [X0: $i] : ( cP_4 @ d @ X0 )
& ( cP_1 @ b @ b ) ),
file('/export/starexec/sandbox/tmp/tmp.CQMZgDnGfI/DTF2THF_25094.p',cTHM409_4) ).
thf(f158,plain,
( ! [X0: $i] :
( ( cP_4 @ c @ X0 )
!= $true )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f157]) ).
thf(f157,plain,
( ! [X0: $i] :
( ( ( cP_4 @ c @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f99,f26]) ).
thf(f26,plain,
( ( cP_3 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f99,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_3 @ c @ X0 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f98]) ).
thf(f98,definition,
( spl0_6
<=> ! [X0: $i,X1: $i] :
( ( ( cP_3 @ c @ X0 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f138,plain,
( spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f137,f45,f98]) ).
thf(f45,definition,
( spl0_1
<=> ! [X3: $i,X0: $i,X9: $i,X1: $i] :
( ( ( cP_4 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X9 )
!= $true )
| ( ( cP_3 @ ( f @ X9 ) @ X0 )
!= $true )
| ( ( cP_1 @ ( f @ c ) @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f137,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_3 @ c @ X0 )
!= $true ) )
| ~ spl0_1 ),
inference(subsumption_resolution,[status(thm)],[f136,f19]) ).
thf(f19,plain,
( ( cP_1 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f136,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_3 @ c @ X0 )
!= $true )
| ( ( cP_1 @ c @ c )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( cP_3 @ c @ X0 )
!= $true )
| ( ( cP_1 @ c @ c )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f126,f32]) ).
thf(f32,plain,
( ( cP_2 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f126,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( ( cP_1 @ c @ X2 )
!= $true )
| ( ( cP_3 @ X3 @ X0 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ X3 @ X0 )
!= $true )
| ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( ( cP_1 @ c @ X2 )
!= $true )
| ( $true != $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f124,f29]) ).
thf(f29,plain,
! [X8: $i,X7: $i] :
( ( $true
= ( cP_4 @ ( f @ X7 ) @ X8 ) )
| ( $true
!= ( cP_4 @ X7 @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f124,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_4 @ ( f @ X1 ) @ X3 )
!= $true )
| ( ( cP_1 @ c @ X2 )
!= $true )
| ( ( cP_2 @ X2 @ X0 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f123]) ).
thf(f123,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( cP_1 @ c @ X2 )
!= $true )
| ( ( cP_2 @ X2 @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X3 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f122,f12]) ).
thf(f12,plain,
! [X34: $i,X35: $i] :
( ( ( cP_3 @ ( f @ X34 ) @ X35 )
= $true )
| ( ( cP_3 @ X34 @ X35 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f122,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X0 ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true != $true )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f120,f18]) ).
thf(f18,plain,
! [X22: $i,X23: $i] :
( ( ( cP_2 @ ( f @ X23 ) @ X22 )
= $true )
| ( ( cP_2 @ X23 @ X22 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f120,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( ( cP_3 @ ( f @ X3 ) @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_3 @ ( f @ X3 ) @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( $true != $true )
| ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f46,f13]) ).
thf(f13,plain,
! [X32: $i,X33: $i] :
( ( ( cP_1 @ ( f @ X32 ) @ X33 )
= $true )
| ( ( cP_1 @ X32 @ X33 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f46,plain,
( ! [X3: $i,X0: $i,X1: $i,X9: $i] :
( ( ( cP_1 @ ( f @ c ) @ X3 )
!= $true )
| ( ( cP_4 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_3 @ ( f @ X9 ) @ X0 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X9 )
!= $true ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f118,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f117]) ).
thf(f117,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
( ( $true != $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f115,f25]) ).
thf(f25,plain,
( ( cP_4 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f115,plain,
( ! [X0: $i] :
( ( cP_4 @ a @ X0 )
!= $true )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f114]) ).
thf(f114,plain,
( ! [X0: $i] :
( ( ( cP_4 @ a @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f113,f8]) ).
thf(f8,plain,
( ( cP_3 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f113,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_3 @ a @ X0 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f85,f22]) ).
thf(f22,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f85,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_3 @ a @ X0 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ a @ a )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_3 @ a @ X0 )
!= $true )
| ( ( cP_1 @ a @ a )
!= $true )
| ( $true != $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f78,f9]) ).
thf(f9,plain,
( ( cP_2 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f78,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_2 @ X2 @ X3 ) )
| ( ( cP_3 @ X3 @ X0 )
!= $true )
| ( ( cP_1 @ a @ X2 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_1 @ a @ X2 )
!= $true )
| ( $true != $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_3 @ X3 @ X0 )
!= $true )
| ( $true
!= ( cP_2 @ X2 @ X3 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f76,f29]) ).
thf(f76,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_4 @ ( f @ X1 ) @ X3 )
!= $true )
| ( ( cP_1 @ a @ X2 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ X2 @ X0 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_4 @ ( f @ X1 ) @ X3 )
!= $true )
| ( ( cP_1 @ a @ X2 )
!= $true )
| ( $true != $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ X2 @ X0 )
!= $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f74,f12]) ).
thf(f74,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X0 ) ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X0 ) )
| ( ( cP_4 @ ( f @ X2 ) @ X3 )
!= $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f72,f18]) ).
thf(f72,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X0 ) )
| ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_3 @ ( f @ X3 ) @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( $true != $true )
| ( ( cP_3 @ ( f @ X3 ) @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X0 ) )
| ( ( cP_4 @ ( f @ X1 ) @ X2 )
!= $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f52,f13]) ).
thf(f52,plain,
( ! [X2: $i,X6: $i,X4: $i,X5: $i] :
( ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true )
| ( ( cP_4 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X4 )
!= $true ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl0_3
<=> ! [X5: $i,X4: $i,X6: $i,X2: $i] :
( ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_4 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X4 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f70,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f69]) ).
thf(f69,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f67,f24]) ).
thf(f24,plain,
( ( cP_4 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f67,plain,
( ! [X0: $i] :
( ( cP_4 @ b @ X0 )
!= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cP_4 @ b @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f65,f27]) ).
thf(f27,plain,
( ( cP_3 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f65,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_3 @ b @ X0 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_3 @ b @ X0 )
!= $true )
| ( $true != $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f63,f14]) ).
thf(f14,plain,
( ( cP_2 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f63,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ b @ X2 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_3 @ X2 @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ b @ X2 )
!= $true )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( ( cP_3 @ X2 @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f61,f33]) ).
thf(f33,plain,
( ( cP_1 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f61,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_1 @ b @ X2 ) )
| ( $true
!= ( cP_4 @ X1 @ X3 ) )
| ( ( cP_2 @ X2 @ X0 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ X2 @ X0 )
!= $true )
| ( $true
!= ( cP_1 @ b @ X2 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_4 @ X1 @ X3 ) )
| ( $true != $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f59,f12]) ).
thf(f59,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_4 @ X2 @ X3 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_4 @ X2 @ X3 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f57,f18]) ).
thf(f57,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( $true
!= ( cP_4 @ X1 @ X2 ) )
| ( ( cP_3 @ ( f @ X3 ) @ X1 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_1 @ b @ X0 )
!= $true )
| ( ( cP_3 @ ( f @ X3 ) @ X1 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( $true
!= ( cP_4 @ X1 @ X2 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f55,f13]) ).
thf(f55,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_1 @ ( f @ b ) @ X2 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_3 @ ( f @ X3 ) @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_1 @ ( f @ b ) @ X2 ) )
| ( ( cP_3 @ ( f @ X3 ) @ X0 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X3 ) )
| ( ( cP_4 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f49,f29]) ).
thf(f49,plain,
( ! [X10: $i,X11: $i,X8: $i,X7: $i] :
( ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) )
| ( ( cP_1 @ ( f @ b ) @ X10 )
!= $true )
| ( ( cP_2 @ ( f @ X10 ) @ X11 )
!= $true )
| ( ( cP_3 @ ( f @ X11 ) @ X7 )
!= $true ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl0_2
<=> ! [X11: $i,X10: $i,X8: $i,X7: $i] :
( ( ( cP_2 @ ( f @ X10 ) @ X11 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) )
| ( ( cP_1 @ ( f @ b ) @ X10 )
!= $true )
| ( ( cP_3 @ ( f @ X11 ) @ X7 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f53,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f43,f51,f48,f45]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cP_4 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_2 @ ( f @ X10 ) @ X11 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X9 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true )
| ( ( cP_1 @ ( f @ c ) @ X3 )
!= $true )
| ( ( cP_4 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_3 @ ( f @ X11 ) @ X7 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X4 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X10 )
!= $true )
| ( ( cP_3 @ ( f @ X9 ) @ X0 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,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 @ X10 ) @ X11 )
!= $true )
| ( ( cP_3 @ ( f @ X9 ) @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_1 @ ( f @ c ) @ X3 )
!= $true )
| ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ ( f @ X3 ) @ X9 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) )
| ( ( cP_3 @ ( f @ X11 ) @ X7 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X10 )
!= $true )
| ( ( cP_4 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X4 )
!= $true ) ),
inference(superposition,[status(thm)],[f41,f10]) ).
thf(f10,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f41,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 @ X12 @ X13 @ X14 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) )
| ( ( cP_1 @ ( f @ X12 ) @ X0 )
!= $true )
| ( ( cP_1 @ ( f @ X14 ) @ X2 )
!= $true )
| ( ( cP_3 @ ( f @ X3 ) @ X5 )
!= $true )
| ( ( cP_4 @ ( f @ X5 ) @ X9 )
!= $true )
| ( ( cP_4 @ ( f @ X10 ) @ X11 )
!= $true )
| ( ( cP_3 @ ( f @ X6 ) @ X7 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X6 ) )
| ( ( cP_2 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_3 @ ( f @ X4 ) @ X10 )
!= $true )
| ( ( cP_1 @ ( f @ X13 ) @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X14: $i,X4: $i,X5: $i,X12: $i,X13: $i] :
( ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) )
| ( ( cP_3 @ ( f @ X6 ) @ X7 )
!= $true )
| ( ( cQ_1 @ X12 @ X13 @ X14 )
!= $true )
| ( ( cP_2 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_1 @ ( f @ X13 ) @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X5 ) @ X9 )
!= $true )
| ( $true != $true )
| ( ( cP_3 @ ( f @ X3 ) @ X5 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X6 ) )
| ( ( cP_1 @ ( f @ X14 ) @ X2 )
!= $true )
| ( ( cP_3 @ ( f @ X4 ) @ X10 )
!= $true )
| ( ( cP_1 @ ( f @ X12 ) @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X10 ) @ X11 )
!= $true ) ),
inference(superposition,[status(thm)],[f39,f21]) ).
thf(f21,plain,
! [X21: $i,X18: $i,X19: $i,X16: $i,X17: $i,X20: $i] :
( ( ( cQ_2 @ X16 @ X19 @ X18 )
= $true )
| ( ( cQ_1 @ X20 @ X21 @ X17 )
!= $true )
| ( ( cP_1 @ ( f @ X17 ) @ X18 )
!= $true )
| ( ( cP_1 @ ( f @ X20 ) @ X16 )
!= $true )
| ( ( cP_1 @ ( f @ X21 ) @ X19 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f39,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 @ X10 @ X9 @ X11 ) )
| ( ( cP_2 @ ( f @ X10 ) @ X0 )
!= $true )
| ( ( cP_2 @ ( f @ X9 ) @ X1 )
!= $true )
| ( ( cP_3 @ ( f @ X0 ) @ X3 )
!= $true )
| ( ( cP_2 @ ( f @ X11 ) @ X2 )
!= $true )
| ( ( cP_4 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_3 @ ( f @ X2 ) @ X5 )
!= $true )
| ( ( cP_4 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X7 )
!= $true )
| ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,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 @ X11 ) @ X2 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_4 @ ( f @ X7 ) @ X8 ) )
| ( ( cP_4 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X7 )
!= $true )
| ( ( cP_2 @ ( f @ X9 ) @ X1 )
!= $true )
| ( $true
!= ( cQ_2 @ X10 @ X9 @ X11 ) )
| ( ( cP_3 @ ( f @ X2 ) @ X5 )
!= $true )
| ( ( cP_3 @ ( f @ X0 ) @ X3 )
!= $true )
| ( ( cP_2 @ ( f @ X10 ) @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X5 ) @ X6 )
!= $true ) ),
inference(superposition,[status(thm)],[f37,f30]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( cQ_3 @ X5 @ X2 @ X6 )
= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X2 )
!= $true )
| ( ( cQ_2 @ X4 @ X3 @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X1 ) @ X6 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X4 ) @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( cQ_3 @ X6 @ X7 @ X8 ) )
| ( ( cP_4 @ ( f @ X0 ) @ X3 )
!= $true )
| ( ( cP_3 @ ( f @ X6 ) @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X2 ) @ X5 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_3 @ ( f @ X7 ) @ X1 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X8 ) @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( cQ_3 @ X6 @ X7 @ X8 ) )
| ( $true != $true )
| ( ( cP_4 @ ( f @ X0 ) @ X3 )
!= $true )
| ( ( cP_3 @ ( f @ X6 ) @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X1 ) @ X4 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X8 ) @ X2 ) )
| ( ( cP_4 @ ( f @ X2 ) @ X5 )
!= $true )
| ( ( cP_3 @ ( f @ X7 ) @ X1 )
!= $true ) ),
inference(superposition,[status(thm)],[f35,f15]) ).
thf(f15,plain,
! [X31: $i,X28: $i,X29: $i,X26: $i,X27: $i,X30: $i] :
( ( $true
= ( cQ_4 @ X29 @ X30 @ X26 ) )
| ( $true
!= ( cQ_3 @ X31 @ X28 @ X27 ) )
| ( ( cP_3 @ ( f @ X27 ) @ X26 )
!= $true )
| ( ( cP_3 @ ( f @ X31 ) @ X29 )
!= $true )
| ( ( cP_3 @ ( f @ X28 ) @ X30 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cQ_4 @ X5 @ X3 @ X4 ) )
| ( ( cP_4 @ ( f @ X5 ) @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X3 ) @ X1 )
!= $true )
| ( ( cP_4 @ ( f @ X4 ) @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cQ_4 @ X5 @ X3 @ X4 ) )
| ( ( cP_4 @ ( f @ X4 ) @ X2 )
!= $true )
| ( $true != $true )
| ( ( cP_4 @ ( f @ X5 ) @ X0 )
!= $true )
| ( ( cP_4 @ ( f @ X3 ) @ X1 )
!= $true ) ),
inference(superposition,[status(thm)],[f11,f28]) ).
thf(f28,plain,
! [X10: $i,X11: $i,X9: $i,X14: $i,X12: $i,X13: $i] :
( ( $true
= ( cQ_5 @ X13 @ X14 @ X12 ) )
| ( ( cP_4 @ ( f @ X9 ) @ X14 )
!= $true )
| ( ( cP_4 @ ( f @ X10 ) @ X12 )
!= $true )
| ( ( cQ_4 @ X11 @ X9 @ X10 )
!= $true )
| ( ( cP_4 @ ( f @ X11 ) @ X13 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f11,plain,
! [X38: $i,X36: $i,X37: $i] :
( ( cQ_5 @ X37 @ X36 @ X38 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO387^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 14:30:35 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.43 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : SYO387^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.44 % Domain : Syntactic
% 0.18/0.44 % Problem : TPS problem THM409-4
% 0.18/0.44 % Version : Especial.
% 0.18/0.44 % English :
% 0.18/0.44
% 0.18/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.44 % Source : [Bro09]
% 0.18/0.44 % Names : tps_0578 [Bro09]
% 0.18/0.44 % : THM409-4 [TPS]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.33 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.20 v5.4.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.67 v4.0.0
% 0.18/0.44 % Syntax : Number of formulae : 15 ( 0 unt; 14 typ; 0 def)
% 0.18/0.44 % Number of atoms : 46 ( 0 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 46 ( 46 avg)
% 0.18/0.44 % Number of connectives : 185 ( 22 ~; 20 |; 25 &; 118 @)
% 0.18/0.44 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 41 ( 41 avg)
% 0.18/0.44 % Number of types : 2 ( 0 usr)
% 0.18/0.44 % Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 14 ( 14 usr; 4 con; 0-3 aty)
% 0.18/0.44 % Number of variables : 39 ( 0 ^; 39 !; 0 ?; 39 :)
% 0.18/0.44 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.44
% 0.18/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 thf(cQ_5,type,
% 0.18/0.44 cQ_5: $i > $i > $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(f,type,
% 0.18/0.44 f: $i > $i ).
% 0.18/0.44
% 0.18/0.44 thf(cP_4,type,
% 0.18/0.44 cP_4: $i > $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(cQ_4,type,
% 0.18/0.44 cQ_4: $i > $i > $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(d,type,
% 0.18/0.44 d: $i ).
% 0.18/0.44
% 0.18/0.44 thf(c,type,
% 0.18/0.44 c: $i ).
% 0.18/0.44
% 0.18/0.44 thf(b,type,
% 0.18/0.44 b: $i ).
% 0.18/0.44
% 0.18/0.44 thf(a,type,
% 0.18/0.44 a: $i ).
% 0.18/0.44
% 0.18/0.44 thf(cP_3,type,
% 0.18/0.44 cP_3: $i > $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(cQ_3,type,
% 0.18/0.44 cQ_3: $i > $i > $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(cP_2,type,
% 0.18/0.44 cP_2: $i > $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(cQ_2,type,
% 0.18/0.44 cQ_2: $i > $i > $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(cP_1,type,
% 0.18/0.44 cP_1: $i > $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(cQ_1,type,
% 0.18/0.44 cQ_1: $i > $i > $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(cTHM409_4,conjecture,
% 0.18/0.44 ~ ( ( cQ_1 @ a @ b @ c )
% 0.18/0.44 & ( cP_1 @ a @ a )
% 0.18/0.44 & ( cP_1 @ b @ b )
% 0.18/0.44 & ( cP_1 @ c @ c )
% 0.18/0.44 & ! [Xx: $i] : ( cP_1 @ d @ Xx )
% 0.18/0.44 & ! [Xx: $i,Xy: $i] :
% 0.18/0.44 ( ~ ( cP_1 @ Xx @ Xy )
% 0.18/0.44 | ( cP_1 @ ( f @ Xx ) @ Xy ) )
% 0.18/0.44 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.18/0.44 ( ~ ( cQ_1 @ Xx @ Xy @ Xz )
% 0.18/0.44 | ~ ( cP_1 @ ( f @ Xx ) @ Xu )
% 0.18/0.44 | ~ ( cP_1 @ ( f @ Xy ) @ Xv )
% 0.18/0.44 | ~ ( cP_1 @ ( f @ Xz ) @ Xw )
% 0.18/0.44 | ( cQ_2 @ Xu @ Xv @ Xw ) )
% 0.18/0.44 & ( cP_2 @ a @ a )
% 0.18/0.44 & ( cP_2 @ b @ b )
% 0.18/0.44 & ( cP_2 @ c @ c )
% 0.18/0.44 & ! [Xx: $i] : ( cP_2 @ d @ Xx )
% 0.18/0.44 & ! [Xx: $i,Xy: $i] :
% 0.18/0.44 ( ~ ( cP_2 @ Xx @ Xy )
% 0.18/0.44 | ( cP_2 @ ( f @ Xx ) @ Xy ) )
% 0.18/0.44 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.18/0.44 ( ~ ( cQ_2 @ Xx @ Xy @ Xz )
% 0.18/0.44 | ~ ( cP_2 @ ( f @ Xx ) @ Xu )
% 0.18/0.44 | ~ ( cP_2 @ ( f @ Xy ) @ Xv )
% 0.18/0.44 | ~ ( cP_2 @ ( f @ Xz ) @ Xw )
% 0.18/0.44 | ( cQ_3 @ Xu @ Xv @ Xw ) )
% 0.18/0.44 & ( cP_3 @ a @ a )
% 0.18/0.44 & ( cP_3 @ b @ b )
% 0.18/0.44 & ( cP_3 @ c @ c )
% 0.18/0.44 & ! [Xx: $i] : ( cP_3 @ d @ Xx )
% 0.18/0.44 & ! [Xx: $i,Xy: $i] :
% 0.18/0.44 ( ~ ( cP_3 @ Xx @ Xy )
% 0.18/0.44 | ( cP_3 @ ( f @ Xx ) @ Xy ) )
% 0.18/0.44 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.18/0.44 ( ~ ( cQ_3 @ Xx @ Xy @ Xz )
% 0.18/0.44 | ~ ( cP_3 @ ( f @ Xx ) @ Xu )
% 0.18/0.44 | ~ ( cP_3 @ ( f @ Xy ) @ Xv )
% 0.18/0.44 | ~ ( cP_3 @ ( f @ Xz ) @ Xw )
% 0.18/0.44 | ( cQ_4 @ Xu @ Xv @ Xw ) )
% 0.18/0.44 & ( cP_4 @ a @ a )
% 0.18/0.44 & ( cP_4 @ b @ b )
% 0.18/0.44 & ( cP_4 @ c @ c )
% 0.18/0.44 & ! [Xx: $i] : ( cP_4 @ d @ Xx )
% 0.18/0.44 & ! [Xx: $i,Xy: $i] :
% 0.18/0.44 ( ~ ( cP_4 @ Xx @ Xy )
% 0.18/0.44 | ( cP_4 @ ( f @ Xx ) @ Xy ) )
% 0.18/0.44 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.18/0.44 ( ~ ( cQ_4 @ Xx @ Xy @ Xz )
% 0.18/0.44 | ~ ( cP_4 @ ( f @ Xx ) @ Xu )
% 0.18/0.44 | ~ ( cP_4 @ ( f @ Xy ) @ Xv )
% 0.18/0.44 | ~ ( cP_4 @ ( f @ Xz ) @ Xw )
% 0.18/0.44 | ( cQ_5 @ Xu @ Xv @ Xw ) )
% 0.18/0.44 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.44 ~ ( cQ_5 @ Xx @ Xy @ Xz ) ) ).
% 0.18/0.44
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 ------------------------
% 1.74/1.31 ---- Embedded in THF ---
% 1.74/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.74/1.31 %%% Generated on Tue Feb 24 14:30:36 EST 2026
% 1.74/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.74/1.31 %%% Logic specification used:
% 1.74/1.31 %%% thf(spec, logic, $$dhol).
% 1.74/1.31
% 1.74/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.CQMZgDnGfI/DTF2DTF25094.p
% See solution above
% 1.74/1.31 ------------------------
% 1.74/1.32 ---- Cleaned THF ---
% 1.74/1.32 thf(cQ_5,type,
% 1.74/1.32 cQ_5: $i > $i > $i > $o ).
% 1.74/1.32
% 1.74/1.32 thf(f,type,
% 1.74/1.32 f: $i > $i ).
% 1.74/1.32
% 1.74/1.32 thf(cP_4,type,
% 1.74/1.32 cP_4: $i > $i > $o ).
% 1.74/1.32
% 1.74/1.32 thf(cQ_4,type,
% 1.74/1.32 cQ_4: $i > $i > $i > $o ).
% 1.74/1.32
% 1.74/1.32 thf(d,type,
% 1.74/1.32 d: $i ).
% 1.74/1.32
% 1.74/1.32 thf(c,type,
% 1.74/1.32 c: $i ).
% 1.74/1.32
% 1.74/1.32 thf(b,type,
% 1.74/1.32 b: $i ).
% 1.74/1.32
% 1.74/1.32 thf(a,type,
% 1.74/1.32 a: $i ).
% 1.74/1.32
% 1.74/1.32 thf(cP_3,type,
% 1.74/1.32 cP_3: $i > $i > $o ).
% 1.74/1.32
% 1.74/1.32 thf(cQ_3,type,
% 1.74/1.32 cQ_3: $i > $i > $i > $o ).
% 1.74/1.32
% 1.74/1.32 thf(cP_2,type,
% 1.74/1.32 cP_2: $i > $i > $o ).
% 1.74/1.32
% 1.74/1.32 thf(cQ_2,type,
% 1.74/1.32 cQ_2: $i > $i > $i > $o ).
% 1.74/1.32
% 1.74/1.32 thf(cP_1,type,
% 1.74/1.32 cP_1: $i > $i > $o ).
% 1.74/1.32
% 1.74/1.32 thf(cQ_1,type,
% 1.74/1.32 cQ_1: $i > $i > $i > $o ).
% 1.74/1.32
% 1.74/1.32 thf(cTHM409_4,conjecture,
% 1.74/1.32 ~ ( ( cQ_1 @ a @ b @ c )
% 1.74/1.32 & ( cP_1 @ a @ a )
% 1.74/1.32 & ( cP_1 @ b @ b )
% 1.74/1.32 & ( cP_1 @ c @ c )
% 1.74/1.32 & ! [Xx: $i] : ( cP_1 @ d @ Xx )
% 1.74/1.32 & ! [Xx: $i,Xy: $i] :
% 1.74/1.32 ( ~ ( cP_1 @ Xx @ Xy )
% 1.74/1.32 | ( cP_1 @ ( f @ Xx ) @ Xy ) )
% 1.74/1.32 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.74/1.32 ( ~ ( cQ_1 @ Xx @ Xy @ Xz )
% 1.74/1.32 | ~ ( cP_1 @ ( f @ Xx ) @ Xu )
% 1.74/1.32 | ~ ( cP_1 @ ( f @ Xy ) @ Xv )
% 1.74/1.32 | ~ ( cP_1 @ ( f @ Xz ) @ Xw )
% 1.74/1.32 | ( cQ_2 @ Xu @ Xv @ Xw ) )
% 1.74/1.32 & ( cP_2 @ a @ a )
% 1.74/1.32 & ( cP_2 @ b @ b )
% 1.74/1.32 & ( cP_2 @ c @ c )
% 1.74/1.32 & ! [Xx: $i] : ( cP_2 @ d @ Xx )
% 1.74/1.32 & ! [Xx: $i,Xy: $i] :
% 1.74/1.32 ( ~ ( cP_2 @ Xx @ Xy )
% 1.74/1.32 | ( cP_2 @ ( f @ Xx ) @ Xy ) )
% 1.74/1.32 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.74/1.32 ( ~ ( cQ_2 @ Xx @ Xy @ Xz )
% 1.74/1.32 | ~ ( cP_2 @ ( f @ Xx ) @ Xu )
% 1.74/1.32 | ~ ( cP_2 @ ( f @ Xy ) @ Xv )
% 1.74/1.32 | ~ ( cP_2 @ ( f @ Xz ) @ Xw )
% 1.74/1.32 | ( cQ_3 @ Xu @ Xv @ Xw ) )
% 1.74/1.32 & ( cP_3 @ a @ a )
% 1.74/1.32 & ( cP_3 @ b @ b )
% 1.74/1.32 & ( cP_3 @ c @ c )
% 1.74/1.32 & ! [Xx: $i] : ( cP_3 @ d @ Xx )
% 1.74/1.32 & ! [Xx: $i,Xy: $i] :
% 1.74/1.32 ( ~ ( cP_3 @ Xx @ Xy )
% 1.74/1.32 | ( cP_3 @ ( f @ Xx ) @ Xy ) )
% 1.74/1.32 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.74/1.32 ( ~ ( cQ_3 @ Xx @ Xy @ Xz )
% 1.74/1.32 | ~ ( cP_3 @ ( f @ Xx ) @ Xu )
% 1.74/1.32 | ~ ( cP_3 @ ( f @ Xy ) @ Xv )
% 1.74/1.32 | ~ ( cP_3 @ ( f @ Xz ) @ Xw )
% 1.74/1.32 | ( cQ_4 @ Xu @ Xv @ Xw ) )
% 1.74/1.32 & ( cP_4 @ a @ a )
% 1.74/1.32 & ( cP_4 @ b @ b )
% 1.74/1.32 & ( cP_4 @ c @ c )
% 1.74/1.32 & ! [Xx: $i] : ( cP_4 @ d @ Xx )
% 1.74/1.32 & ! [Xx: $i,Xy: $i] :
% 1.74/1.32 ( ~ ( cP_4 @ Xx @ Xy )
% 1.74/1.32 | ( cP_4 @ ( f @ Xx ) @ Xy ) )
% 1.74/1.32 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.74/1.32 ( ~ ( cQ_4 @ Xx @ Xy @ Xz )
% 1.74/1.32 | ~ ( cP_4 @ ( f @ Xx ) @ Xu )
% 1.74/1.32 | ~ ( cP_4 @ ( f @ Xy ) @ Xv )
% 1.74/1.32 | ~ ( cP_4 @ ( f @ Xz ) @ Xw )
% 1.74/1.32 | ( cQ_5 @ Xu @ Xv @ Xw ) )
% 1.74/1.32 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.74/1.32 ~ ( cQ_5 @ Xx @ Xy @ Xz ) ) ).
% 1.74/1.32 ------------------------
% 1.74/1.33 % (25283)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25094 for (2999ds/183Mi)
% 1.74/1.33 % (25289)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25094 for (2999ds/18Mi)
% 1.74/1.33 % (25288)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_25094 for (2999ds/275Mi)
% 1.74/1.34 % (25289)Instruction limit reached!
% 1.74/1.34 % (25289)------------------------------
% 1.74/1.34 % (25289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.34 % (25289)Termination reason: Unknown
% 1.74/1.34 % (25289)Termination phase: Saturation
% 1.74/1.34
% 1.74/1.34 % (25289)Memory used [KB]: 5628
% 1.74/1.34 % (25289)Time elapsed: 0.007 s
% 1.74/1.34 % (25289)Instructions burned: 18 (million)
% 1.74/1.34 % (25289)------------------------------
% 1.74/1.34 % (25289)------------------------------
% 1.74/1.34 % (25284)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_25094 for (2999ds/4Mi)
% 1.74/1.34 % (25287)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_25094 for (2999ds/2Mi)
% 1.74/1.34 % (25285)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_25094 for (2999ds/27Mi)
% 1.74/1.34 % (25287)Instruction limit reached!
% 1.74/1.34 % (25287)------------------------------
% 1.74/1.34 % (25287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.34 % (25287)Termination reason: Unknown
% 1.74/1.34 % (25287)Termination phase: shuffling
% 1.74/1.34
% 1.74/1.34 % (25287)Memory used [KB]: 1023
% 1.74/1.34 % (25287)Time elapsed: 0.003 s
% 1.74/1.34 % (25287)Instructions burned: 2 (million)
% 1.74/1.34 % (25287)------------------------------
% 1.74/1.34 % (25287)------------------------------
% 1.74/1.34 % (25284)Instruction limit reached!
% 1.74/1.34 % (25284)------------------------------
% 1.74/1.34 % (25284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.34 % (25284)Termination reason: Unknown
% 1.74/1.34 % (25284)Termination phase: Saturation
% 1.74/1.34
% 1.74/1.34 % (25284)Memory used [KB]: 5500
% 1.74/1.34 % (25284)Time elapsed: 0.005 s
% 1.74/1.34 % (25284)Instructions burned: 5 (million)
% 1.74/1.34 % (25284)------------------------------
% 1.74/1.34 % (25284)------------------------------
% 1.74/1.34 % (25283)First to succeed.
% 1.74/1.34 % (25286)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25094 for (2999ds/2Mi)
% 1.74/1.34 % (25286)Instruction limit reached!
% 1.74/1.34 % (25286)------------------------------
% 1.74/1.34 % (25286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.34 % (25286)Termination reason: Unknown
% 1.74/1.34 % (25286)Termination phase: Property scanning
% 1.74/1.34
% 1.74/1.34 % (25286)Memory used [KB]: 1023
% 1.74/1.34 % (25286)Time elapsed: 0.003 s
% 1.74/1.34 % (25286)Instructions burned: 2 (million)
% 1.74/1.34 % (25286)------------------------------
% 1.74/1.34 % (25286)------------------------------
% 1.74/1.34 % (25288)Also succeeded, but the first one will report.
% 1.74/1.35 % (25283)Refutation found. Thanks to Tanya!
% 1.74/1.35 % SZS status Theorem for DTF2THF_25094
% 1.74/1.35 % SZS output start Proof for DTF2THF_25094
% 1.74/1.35 thf(func_def_0, type, cQ_5: $i > $i > $i > $o).
% 1.74/1.35 thf(func_def_1, type, f: $i > $i).
% 1.74/1.35 thf(func_def_2, type, cP_4: $i > $i > $o).
% 1.74/1.35 thf(func_def_3, type, cQ_4: $i > $i > $i > $o).
% 1.74/1.35 thf(func_def_8, type, cP_3: $i > $i > $o).
% 1.74/1.35 thf(func_def_9, type, cQ_3: $i > $i > $i > $o).
% 1.74/1.35 thf(func_def_10, type, cP_2: $i > $i > $o).
% 1.74/1.35 thf(func_def_11, type, cQ_2: $i > $i > $i > $o).
% 1.74/1.35 thf(func_def_12, type, cP_1: $i > $i > $o).
% 1.74/1.35 thf(func_def_13, type, cQ_1: $i > $i > $i > $o).
% 1.74/1.35 thf(f162,plain,(
% 1.74/1.35 $false),
% 1.74/1.35 inference(avatar_sat_refutation,[status(thm)],[f53,f70,f118,f138,f161])).
% 1.74/1.35 thf(f161,plain,(
% 1.74/1.35 ~spl0_6),
% 1.74/1.35 inference(avatar_contradiction_clause,[status(thm)],[f160])).
% 1.74/1.35 thf(f160,plain,(
% 1.74/1.35 $false | ~spl0_6),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f159])).
% 1.74/1.35 thf(f159,plain,(
% 1.74/1.35 ($true != $true) | ~spl0_6),
% 1.74/1.35 inference(superposition,[status(thm)],[f158,f20])).
% 1.74/1.35 thf(f20,plain,(
% 1.74/1.35 ((cP_4 @ c @ c) = $true)),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f7,plain,(
% 1.74/1.35 ((cP_1 @ b @ b) = $true) & ((cP_2 @ c @ c) = $true) & ! [X0 : $i] : ((cP_4 @ d @ X0) = $true) & ! [X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i,X6 : $i] : (($true != (cP_2 @ (f @ X4) @ X5)) | ((cQ_2 @ X4 @ X3 @ X1) != $true) | ((cP_2 @ (f @ X3) @ X2) != $true) | ((cQ_3 @ X5 @ X2 @ X6) = $true) | ((cP_2 @ (f @ X1) @ X6) != $true)) & ! [X7 : $i,X8 : $i] : (($true = (cP_4 @ (f @ X7) @ X8)) | ($true != (cP_4 @ X7 @ X8))) & ! [X9 : $i,X10 : $i,X11 : $i,X12 : $i,X13 : $i,X14 : $i] : (((cP_4 @ (f @ X10) @ X12) != $true) | ((cQ_4 @ X11 @ X9 @ X10) != $true) | ((cP_4 @ (f @ X11) @ X13) != $true) | ($true = (cQ_5 @ X13 @ X14 @ X12)) | ((cP_4 @ (f @ X9) @ X14) != $true)) & ((cP_3 @ b @ b) = $true) & ((cP_3 @ c @ c) = $true) & ((cP_4 @ a @ a) = $true) & ((cP_4 @ b @ b) = $true) & ! [X15 : $i] : ((cP_3 @ d @ X15) = $true) & ((cP_1 @ a @ a) = $true) & ! [X16 : $i,X17 : $i,X18 : $i,X19 : $i,X20 : $i,X21 : $i] : (((cQ_2 @ X16 @ X19 @ X18) = $true) | ((cP_1 @ (f @ X21) @ X19) != $true) | ((cP_1 @ (f @ X17) @ X18) != $true) | ((cP_1 @ (f @ X20) @ X16) != $true) | ((cQ_1 @ X20 @ X21 @ X17) != $true)) & ((cP_4 @ c @ c) = $true) & ((cP_1 @ c @ c) = $true) & ! [X22 : $i,X23 : $i] : (((cP_2 @ X23 @ X22) != $true) | ((cP_2 @ (f @ X23) @ X22) = $true)) & ! [X24 : $i] : ((cP_2 @ d @ X24) = $true) & ! [X25 : $i] : ($true = (cP_1 @ d @ X25)) & ! [X26 : $i,X27 : $i,X28 : $i,X29 : $i,X30 : $i,X31 : $i] : (((cP_3 @ (f @ X27) @ X26) != $true) | ((cP_3 @ (f @ X31) @ X29) != $true) | ($true != (cQ_3 @ X31 @ X28 @ X27)) | ((cP_3 @ (f @ X28) @ X30) != $true) | ($true = (cQ_4 @ X29 @ X30 @ X26))) & ((cP_2 @ b @ b) = $true) & ! [X32 : $i,X33 : $i] : (((cP_1 @ X32 @ X33) != $true) | ((cP_1 @ (f @ X32) @ X33) = $true)) & ! [X34 : $i,X35 : $i] : (((cP_3 @ X34 @ X35) != $true) | ((cP_3 @ (f @ X34) @ X35) = $true)) & ! [X36 : $i,X37 : $i,X38 : $i] : ((cQ_5 @ X37 @ X36 @ X38) != $true) & ((cQ_1 @ a @ b @ c) = $true) & ((cP_2 @ a @ a) = $true) & ((cP_3 @ a @ a) = $true)),
% 1.74/1.35 inference(rectify,[status(thm)],[f6])).
% 1.74/1.35 thf(f6,plain,(
% 1.74/1.35 ((cP_1 @ b @ b) = $true) & ((cP_2 @ c @ c) = $true) & ! [X38 : $i] : ((cP_4 @ d @ X38) = $true) & ! [X12 : $i,X9 : $i,X14 : $i,X11 : $i,X13 : $i,X10 : $i] : (($true != (cP_2 @ (f @ X11) @ X13)) | ((cQ_2 @ X11 @ X14 @ X12) != $true) | ((cP_2 @ (f @ X14) @ X9) != $true) | ((cQ_3 @ X13 @ X9 @ X10) = $true) | ((cP_2 @ (f @ X12) @ X10) != $true)) & ! [X30 : $i,X31 : $i] : (((cP_4 @ (f @ X30) @ X31) = $true) | ((cP_4 @ X30 @ X31) != $true)) & ! [X3 : $i,X4 : $i,X1 : $i,X5 : $i,X2 : $i,X6 : $i] : (($true != (cP_4 @ (f @ X4) @ X5)) | ($true != (cQ_4 @ X1 @ X3 @ X4)) | ((cP_4 @ (f @ X1) @ X2) != $true) | ($true = (cQ_5 @ X2 @ X6 @ X5)) | ((cP_4 @ (f @ X3) @ X6) != $true)) & ((cP_3 @ b @ b) = $true) & ((cP_3 @ c @ c) = $true) & ((cP_4 @ a @ a) = $true) & ((cP_4 @ b @ b) = $true) & ! [X7 : $i] : ((cP_3 @ d @ X7) = $true) & ((cP_1 @ a @ a) = $true) & ! [X36 : $i,X37 : $i,X32 : $i,X33 : $i,X35 : $i,X34 : $i] : (((cQ_2 @ X36 @ X33 @ X32) = $true) | ((cP_1 @ (f @ X34) @ X33) != $true) | ((cP_1 @ (f @ X37) @ X32) != $true) | ((cP_1 @ (f @ X35) @ X36) != $true) | ($true != (cQ_1 @ X35 @ X34 @ X37))) & ((cP_4 @ c @ c) = $true) & ((cP_1 @ c @ c) = $true) & ! [X20 : $i,X21 : $i] : (((cP_2 @ X21 @ X20) != $true) | ($true = (cP_2 @ (f @ X21) @ X20))) & ! [X8 : $i] : ($true = (cP_2 @ d @ X8)) & ! [X0 : $i] : ((cP_1 @ d @ X0) = $true) & ! [X23 : $i,X22 : $i,X24 : $i,X25 : $i,X26 : $i,X27 : $i] : (((cP_3 @ (f @ X22) @ X23) != $true) | ((cP_3 @ (f @ X27) @ X25) != $true) | ($true != (cQ_3 @ X27 @ X24 @ X22)) | ((cP_3 @ (f @ X24) @ X26) != $true) | ((cQ_4 @ X25 @ X26 @ X23) = $true)) & ((cP_2 @ b @ b) = $true) & ! [X19 : $i,X18 : $i] : (((cP_1 @ X19 @ X18) != $true) | ((cP_1 @ (f @ X19) @ X18) = $true)) & ! [X28 : $i,X29 : $i] : (((cP_3 @ X28 @ X29) != $true) | ($true = (cP_3 @ (f @ X28) @ X29))) & ! [X16 : $i,X17 : $i,X15 : $i] : ((cQ_5 @ X17 @ X16 @ X15) != $true) & ((cQ_1 @ a @ b @ c) = $true) & ((cP_2 @ a @ a) = $true) & ((cP_3 @ a @ a) = $true)),
% 1.74/1.35 inference(flattening,[status(thm)],[f5])).
% 1.74/1.35 thf(f5,plain,(
% 1.74/1.35 ~~(((cP_3 @ a @ a) = $true) & ! [X0 : $i] : ((cP_1 @ d @ X0) = $true) & ! [X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i,X6 : $i] : (~($true = (cQ_4 @ X1 @ X3 @ X4)) | ~((cP_4 @ (f @ X1) @ X2) = $true) | ~((cP_4 @ (f @ X3) @ X6) = $true) | ~($true = (cP_4 @ (f @ X4) @ X5)) | ($true = (cQ_5 @ X2 @ X6 @ X5))) & ! [X7 : $i] : ((cP_3 @ d @ X7) = $true) & ! [X8 : $i] : ($true = (cP_2 @ d @ X8)) & ((cP_2 @ c @ c) = $true) & ! [X9 : $i,X10 : $i,X11 : $i,X12 : $i,X13 : $i,X14 : $i] : (~((cP_2 @ (f @ X12) @ X10) = $true) | ~($true = (cP_2 @ (f @ X11) @ X13)) | ~((cQ_2 @ X11 @ X14 @ X12) = $true) | ~((cP_2 @ (f @ X14) @ X9) = $true) | ((cQ_3 @ X13 @ X9 @ X10) = $true)) & ! [X15 : $i,X16 : $i,X17 : $i] : ~((cQ_5 @ X17 @ X16 @ X15) = $true) & ((cP_3 @ b @ b) = $true) & ((cP_2 @ b @ b) = $true) & ((cP_4 @ a @ a) = $true) & ((cP_4 @ c @ c) = $true) & ! [X18 : $i,X19 : $i] : (~((cP_1 @ X19 @ X18) = $true) | ((cP_1 @ (f @ X19) @ X18) = $true)) & ((cP_1 @ a @ a) = $true) & ((cP_3 @ c @ c) = $true) & ((cP_4 @ b @ b) = $true) & ((cP_2 @ a @ a) = $true) & ! [X20 : $i,X21 : $i] : (($true = (cP_2 @ (f @ X21) @ X20)) | ~((cP_2 @ X21 @ X20) = $true)) & ! [X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i,X27 : $i] : (~((cP_3 @ (f @ X27) @ X25) = $true) | ~($true = (cQ_3 @ X27 @ X24 @ X22)) | ~((cP_3 @ (f @ X24) @ X26) = $true) | ~((cP_3 @ (f @ X22) @ X23) = $true) | ((cQ_4 @ X25 @ X26 @ X23) = $true)) & ! [X28 : $i,X29 : $i] : (($true = (cP_3 @ (f @ X28) @ X29)) | ~((cP_3 @ X28 @ X29) = $true)) & ((cQ_1 @ a @ b @ c) = $true) & ((cP_1 @ c @ c) = $true) & ! [X30 : $i,X31 : $i] : (~((cP_4 @ X30 @ X31) = $true) | ((cP_4 @ (f @ X30) @ X31) = $true)) & ! [X32 : $i,X33 : $i,X34 : $i,X35 : $i,X36 : $i,X37 : $i] : (~((cP_1 @ (f @ X34) @ X33) = $true) | ~((cP_1 @ (f @ X37) @ X32) = $true) | ((cQ_2 @ X36 @ X33 @ X32) = $true) | ~((cP_1 @ (f @ X35) @ X36) = $true) | ~($true = (cQ_1 @ X35 @ X34 @ X37))) & ! [X38 : $i] : ((cP_4 @ d @ X38) = $true) & ((cP_1 @ b @ b) = $true))),
% 1.74/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.74/1.35 thf(f4,plain,(
% 1.74/1.35 ~~((cP_3 @ a @ a) & ! [X0 : $i] : (cP_1 @ d @ X0) & ! [X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i,X6 : $i] : (~(cQ_4 @ X1 @ X3 @ X4) | ~(cP_4 @ (f @ X1) @ X2) | ~(cP_4 @ (f @ X3) @ X6) | ~(cP_4 @ (f @ X4) @ X5) | (cQ_5 @ X2 @ X6 @ X5)) & ! [X7 : $i] : (cP_3 @ d @ X7) & ! [X8 : $i] : (cP_2 @ d @ X8) & (cP_2 @ c @ c) & ! [X9 : $i,X10 : $i,X11 : $i,X12 : $i,X13 : $i,X14 : $i] : (~(cP_2 @ (f @ X12) @ X10) | ~(cP_2 @ (f @ X11) @ X13) | ~(cQ_2 @ X11 @ X14 @ X12) | ~(cP_2 @ (f @ X14) @ X9) | (cQ_3 @ X13 @ X9 @ X10)) & ! [X15 : $i,X16 : $i,X17 : $i] : ~(cQ_5 @ X17 @ X16 @ X15) & (cP_3 @ b @ b) & (cP_2 @ b @ b) & (cP_4 @ a @ a) & (cP_4 @ c @ c) & ! [X18 : $i,X19 : $i] : (~(cP_1 @ X19 @ X18) | (cP_1 @ (f @ X19) @ X18)) & (cP_1 @ a @ a) & (cP_3 @ c @ c) & (cP_4 @ b @ b) & (cP_2 @ a @ a) & ! [X20 : $i,X21 : $i] : ((cP_2 @ (f @ X21) @ X20) | ~(cP_2 @ X21 @ X20)) & ! [X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i,X27 : $i] : (~(cP_3 @ (f @ X27) @ X25) | ~(cQ_3 @ X27 @ X24 @ X22) | ~(cP_3 @ (f @ X24) @ X26) | ~(cP_3 @ (f @ X22) @ X23) | (cQ_4 @ X25 @ X26 @ X23)) & ! [X28 : $i,X29 : $i] : ((cP_3 @ (f @ X28) @ X29) | ~(cP_3 @ X28 @ X29)) & (cQ_1 @ a @ b @ c) & (cP_1 @ c @ c) & ! [X30 : $i,X31 : $i] : (~(cP_4 @ X30 @ X31) | (cP_4 @ (f @ X30) @ X31)) & ! [X32 : $i,X33 : $i,X34 : $i,X35 : $i,X36 : $i,X37 : $i] : (~(cP_1 @ (f @ X34) @ X33) | ~(cP_1 @ (f @ X37) @ X32) | (cQ_2 @ X36 @ X33 @ X32) | ~(cP_1 @ (f @ X35) @ X36) | ~(cQ_1 @ X35 @ X34 @ X37)) & ! [X38 : $i] : (cP_4 @ d @ X38) & (cP_1 @ b @ b))),
% 1.74/1.35 inference(rectify,[status(thm)],[f2])).
% 1.74/1.35 thf(f2,negated_conjecture,(
% 1.74/1.35 ~~((cP_3 @ a @ a) & ! [X0 : $i] : (cP_1 @ d @ X0) & ! [X0 : $i,X3 : $i,X1 : $i,X2 : $i,X5 : $i,X4 : $i] : (~(cQ_4 @ X0 @ X1 @ X2) | ~(cP_4 @ (f @ X0) @ X3) | ~(cP_4 @ (f @ X1) @ X4) | ~(cP_4 @ (f @ X2) @ X5) | (cQ_5 @ X3 @ X4 @ X5)) & ! [X0 : $i] : (cP_3 @ d @ X0) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_2 @ c @ c) & ! [X4 : $i,X5 : $i,X0 : $i,X2 : $i,X3 : $i,X1 : $i] : (~(cP_2 @ (f @ X2) @ X5) | ~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2) | ~(cP_2 @ (f @ X1) @ X4) | (cQ_3 @ X3 @ X4 @ X5)) & ! [X2 : $i,X1 : $i,X0 : $i] : ~(cQ_5 @ X0 @ X1 @ X2) & (cP_3 @ b @ b) & (cP_2 @ b @ b) & (cP_4 @ a @ a) & (cP_4 @ c @ c) & ! [X1 : $i,X0 : $i] : (~(cP_1 @ X0 @ X1) | (cP_1 @ (f @ X0) @ X1)) & (cP_1 @ a @ a) & (cP_3 @ c @ c) & (cP_4 @ b @ b) & (cP_2 @ a @ a) & ! [X1 : $i,X0 : $i] : ((cP_2 @ (f @ X0) @ X1) | ~(cP_2 @ X0 @ X1)) & ! [X2 : $i,X5 : $i,X1 : $i,X3 : $i,X4 : $i,X0 : $i] : (~(cP_3 @ (f @ X0) @ X3) | ~(cQ_3 @ X0 @ X1 @ X2) | ~(cP_3 @ (f @ X1) @ X4) | ~(cP_3 @ (f @ X2) @ X5) | (cQ_4 @ X3 @ X4 @ X5)) & ! [X0 : $i,X1 : $i] : ((cP_3 @ (f @ X0) @ X1) | ~(cP_3 @ X0 @ X1)) & (cQ_1 @ a @ b @ c) & (cP_1 @ c @ c) & ! [X0 : $i,X1 : $i] : (~(cP_4 @ X0 @ X1) | (cP_4 @ (f @ X0) @ X1)) & ! [X5 : $i,X4 : $i,X1 : $i,X0 : $i,X3 : $i,X2 : $i] : (~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X2) @ X5) | (cQ_2 @ X3 @ X4 @ X5) | ~(cP_1 @ (f @ X0) @ X3) | ~(cQ_1 @ X0 @ X1 @ X2)) & ! [X0 : $i] : (cP_4 @ d @ X0) & (cP_1 @ b @ b))),
% 1.74/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 1.74/1.35 thf(f1,conjecture,(
% 1.74/1.35 ~((cP_3 @ a @ a) & ! [X0 : $i] : (cP_1 @ d @ X0) & ! [X0 : $i,X3 : $i,X1 : $i,X2 : $i,X5 : $i,X4 : $i] : (~(cQ_4 @ X0 @ X1 @ X2) | ~(cP_4 @ (f @ X0) @ X3) | ~(cP_4 @ (f @ X1) @ X4) | ~(cP_4 @ (f @ X2) @ X5) | (cQ_5 @ X3 @ X4 @ X5)) & ! [X0 : $i] : (cP_3 @ d @ X0) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_2 @ c @ c) & ! [X4 : $i,X5 : $i,X0 : $i,X2 : $i,X3 : $i,X1 : $i] : (~(cP_2 @ (f @ X2) @ X5) | ~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2) | ~(cP_2 @ (f @ X1) @ X4) | (cQ_3 @ X3 @ X4 @ X5)) & ! [X2 : $i,X1 : $i,X0 : $i] : ~(cQ_5 @ X0 @ X1 @ X2) & (cP_3 @ b @ b) & (cP_2 @ b @ b) & (cP_4 @ a @ a) & (cP_4 @ c @ c) & ! [X1 : $i,X0 : $i] : (~(cP_1 @ X0 @ X1) | (cP_1 @ (f @ X0) @ X1)) & (cP_1 @ a @ a) & (cP_3 @ c @ c) & (cP_4 @ b @ b) & (cP_2 @ a @ a) & ! [X1 : $i,X0 : $i] : ((cP_2 @ (f @ X0) @ X1) | ~(cP_2 @ X0 @ X1)) & ! [X2 : $i,X5 : $i,X1 : $i,X3 : $i,X4 : $i,X0 : $i] : (~(cP_3 @ (f @ X0) @ X3) | ~(cQ_3 @ X0 @ X1 @ X2) | ~(cP_3 @ (f @ X1) @ X4) | ~(cP_3 @ (f @ X2) @ X5) | (cQ_4 @ X3 @ X4 @ X5)) & ! [X0 : $i,X1 : $i] : ((cP_3 @ (f @ X0) @ X1) | ~(cP_3 @ X0 @ X1)) & (cQ_1 @ a @ b @ c) & (cP_1 @ c @ c) & ! [X0 : $i,X1 : $i] : (~(cP_4 @ X0 @ X1) | (cP_4 @ (f @ X0) @ X1)) & ! [X5 : $i,X4 : $i,X1 : $i,X0 : $i,X3 : $i,X2 : $i] : (~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X2) @ X5) | (cQ_2 @ X3 @ X4 @ X5) | ~(cP_1 @ (f @ X0) @ X3) | ~(cQ_1 @ X0 @ X1 @ X2)) & ! [X0 : $i] : (cP_4 @ d @ X0) & (cP_1 @ b @ b))),
% 1.74/1.35 file('/export/starexec/sandbox/tmp/tmp.CQMZgDnGfI/DTF2THF_25094.p',cTHM409_4)).
% 1.74/1.35 thf(f158,plain,(
% 1.74/1.35 ( ! [X0 : $i] : (((cP_4 @ c @ X0) != $true)) ) | ~spl0_6),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f157])).
% 1.74/1.35 thf(f157,plain,(
% 1.74/1.35 ( ! [X0 : $i] : (((cP_4 @ c @ X0) != $true) | ($true != $true)) ) | ~spl0_6),
% 1.74/1.35 inference(superposition,[status(thm)],[f99,f26])).
% 1.74/1.35 thf(f26,plain,(
% 1.74/1.35 ((cP_3 @ c @ c) = $true)),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f99,plain,(
% 1.74/1.35 ( ! [X0 : $i,X1 : $i] : (((cP_3 @ c @ X0) != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_6),
% 1.74/1.35 inference(avatar_component_clause,[status(thm)],[f98])).
% 1.74/1.35 thf(f98,definition,(
% 1.74/1.35 spl0_6 <=> ! [X0 : $i,X1 : $i] : (((cP_3 @ c @ X0) != $true) | ((cP_4 @ X0 @ X1) != $true))),
% 1.74/1.35 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.74/1.35 thf(f138,plain,(
% 1.74/1.35 spl0_6 | ~spl0_1),
% 1.74/1.35 inference(avatar_split_clause,[status(thm)],[f137,f45,f98])).
% 1.74/1.35 thf(f45,definition,(
% 1.74/1.35 spl0_1 <=> ! [X3 : $i,X0 : $i,X9 : $i,X1 : $i] : (((cP_4 @ (f @ X0) @ X1) != $true) | ((cP_2 @ (f @ X3) @ X9) != $true) | ((cP_3 @ (f @ X9) @ X0) != $true) | ((cP_1 @ (f @ c) @ X3) != $true))),
% 1.74/1.35 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.74/1.35 thf(f137,plain,(
% 1.74/1.35 ( ! [X0 : $i,X1 : $i] : (((cP_4 @ X0 @ X1) != $true) | ((cP_3 @ c @ X0) != $true)) ) | ~spl0_1),
% 1.74/1.35 inference(subsumption_resolution,[status(thm)],[f136,f19])).
% 1.74/1.35 thf(f19,plain,(
% 1.74/1.35 ((cP_1 @ c @ c) = $true)),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f136,plain,(
% 1.74/1.35 ( ! [X0 : $i,X1 : $i] : (((cP_3 @ c @ X0) != $true) | ((cP_1 @ c @ c) != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_1),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 1.74/1.35 thf(f128,plain,(
% 1.74/1.35 ( ! [X0 : $i,X1 : $i] : (((cP_4 @ X0 @ X1) != $true) | ($true != $true) | ((cP_3 @ c @ X0) != $true) | ((cP_1 @ c @ c) != $true)) ) | ~spl0_1),
% 1.74/1.35 inference(superposition,[status(thm)],[f126,f32])).
% 1.74/1.35 thf(f32,plain,(
% 1.74/1.35 ((cP_2 @ c @ c) = $true)),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f126,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_2 @ X2 @ X3)) | ((cP_1 @ c @ X2) != $true) | ((cP_3 @ X3 @ X0) != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_1),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.74/1.35 thf(f125,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_3 @ X3 @ X0) != $true) | ($true != (cP_2 @ X2 @ X3)) | ((cP_1 @ c @ X2) != $true) | ($true != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_1),
% 1.74/1.35 inference(superposition,[status(thm)],[f124,f29])).
% 1.74/1.35 thf(f29,plain,(
% 1.74/1.35 ( ! [X8 : $i,X7 : $i] : (($true = (cP_4 @ (f @ X7) @ X8)) | ($true != (cP_4 @ X7 @ X8))) )),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f124,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_4 @ (f @ X1) @ X3) != $true) | ((cP_1 @ c @ X2) != $true) | ((cP_2 @ X2 @ X0) != $true) | ((cP_3 @ X0 @ X1) != $true)) ) | ~spl0_1),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f123])).
% 1.74/1.35 thf(f123,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_3 @ X0 @ X1) != $true) | ($true != $true) | ((cP_1 @ c @ X2) != $true) | ((cP_2 @ X2 @ X0) != $true) | ((cP_4 @ (f @ X1) @ X3) != $true)) ) | ~spl0_1),
% 1.74/1.35 inference(superposition,[status(thm)],[f122,f12])).
% 1.74/1.35 thf(f12,plain,(
% 1.74/1.35 ( ! [X34 : $i,X35 : $i] : (((cP_3 @ (f @ X34) @ X35) = $true) | ((cP_3 @ X34 @ X35) != $true)) )),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f122,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_3 @ (f @ X1) @ X2) != $true) | ((cP_2 @ X0 @ X1) != $true) | ((cP_4 @ (f @ X2) @ X3) != $true) | ($true != (cP_1 @ c @ X0))) ) | ~spl0_1),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.74/1.35 thf(f121,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_4 @ (f @ X2) @ X3) != $true) | ($true != $true) | ((cP_3 @ (f @ X1) @ X2) != $true) | ($true != (cP_1 @ c @ X0)) | ((cP_2 @ X0 @ X1) != $true)) ) | ~spl0_1),
% 1.74/1.35 inference(superposition,[status(thm)],[f120,f18])).
% 1.74/1.35 thf(f18,plain,(
% 1.74/1.35 ( ! [X22 : $i,X23 : $i] : (((cP_2 @ (f @ X23) @ X22) = $true) | ((cP_2 @ X23 @ X22) != $true)) )),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f120,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_2 @ (f @ X0) @ X3) != $true) | ((cP_3 @ (f @ X3) @ X1) != $true) | ($true != (cP_1 @ c @ X0)) | ((cP_4 @ (f @ X1) @ X2) != $true)) ) | ~spl0_1),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.74/1.35 thf(f119,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_1 @ c @ X0)) | ((cP_3 @ (f @ X3) @ X1) != $true) | ((cP_2 @ (f @ X0) @ X3) != $true) | ($true != $true) | ((cP_4 @ (f @ X1) @ X2) != $true)) ) | ~spl0_1),
% 1.74/1.35 inference(superposition,[status(thm)],[f46,f13])).
% 1.74/1.35 thf(f13,plain,(
% 1.74/1.35 ( ! [X32 : $i,X33 : $i] : (((cP_1 @ (f @ X32) @ X33) = $true) | ((cP_1 @ X32 @ X33) != $true)) )),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f46,plain,(
% 1.74/1.35 ( ! [X3 : $i,X0 : $i,X1 : $i,X9 : $i] : (((cP_1 @ (f @ c) @ X3) != $true) | ((cP_4 @ (f @ X0) @ X1) != $true) | ((cP_3 @ (f @ X9) @ X0) != $true) | ((cP_2 @ (f @ X3) @ X9) != $true)) ) | ~spl0_1),
% 1.74/1.35 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.74/1.35 thf(f118,plain,(
% 1.74/1.35 ~spl0_3),
% 1.74/1.35 inference(avatar_contradiction_clause,[status(thm)],[f117])).
% 1.74/1.35 thf(f117,plain,(
% 1.74/1.35 $false | ~spl0_3),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.74/1.35 thf(f116,plain,(
% 1.74/1.35 ($true != $true) | ~spl0_3),
% 1.74/1.35 inference(superposition,[status(thm)],[f115,f25])).
% 1.74/1.35 thf(f25,plain,(
% 1.74/1.35 ((cP_4 @ a @ a) = $true)),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f115,plain,(
% 1.74/1.35 ( ! [X0 : $i] : (((cP_4 @ a @ X0) != $true)) ) | ~spl0_3),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f114])).
% 1.74/1.35 thf(f114,plain,(
% 1.74/1.35 ( ! [X0 : $i] : (((cP_4 @ a @ X0) != $true) | ($true != $true)) ) | ~spl0_3),
% 1.74/1.35 inference(superposition,[status(thm)],[f113,f8])).
% 1.74/1.35 thf(f8,plain,(
% 1.74/1.35 ((cP_3 @ a @ a) = $true)),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f113,plain,(
% 1.74/1.35 ( ! [X0 : $i,X1 : $i] : (((cP_3 @ a @ X0) != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_3),
% 1.74/1.35 inference(subsumption_resolution,[status(thm)],[f85,f22])).
% 1.74/1.35 thf(f22,plain,(
% 1.74/1.35 ((cP_1 @ a @ a) = $true)),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f85,plain,(
% 1.74/1.35 ( ! [X0 : $i,X1 : $i] : (((cP_3 @ a @ X0) != $true) | ((cP_4 @ X0 @ X1) != $true) | ((cP_1 @ a @ a) != $true)) ) | ~spl0_3),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.74/1.35 thf(f82,plain,(
% 1.74/1.35 ( ! [X0 : $i,X1 : $i] : (((cP_3 @ a @ X0) != $true) | ((cP_1 @ a @ a) != $true) | ($true != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_3),
% 1.74/1.35 inference(superposition,[status(thm)],[f78,f9])).
% 1.74/1.35 thf(f9,plain,(
% 1.74/1.35 ((cP_2 @ a @ a) = $true)),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f78,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_2 @ X2 @ X3)) | ((cP_3 @ X3 @ X0) != $true) | ((cP_1 @ a @ X2) != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_3),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.74/1.35 thf(f77,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_1 @ a @ X2) != $true) | ($true != $true) | ((cP_4 @ X0 @ X1) != $true) | ((cP_3 @ X3 @ X0) != $true) | ($true != (cP_2 @ X2 @ X3))) ) | ~spl0_3),
% 1.74/1.35 inference(superposition,[status(thm)],[f76,f29])).
% 1.74/1.35 thf(f76,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_4 @ (f @ X1) @ X3) != $true) | ((cP_1 @ a @ X2) != $true) | ((cP_3 @ X0 @ X1) != $true) | ((cP_2 @ X2 @ X0) != $true)) ) | ~spl0_3),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.74/1.35 thf(f75,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_4 @ (f @ X1) @ X3) != $true) | ((cP_1 @ a @ X2) != $true) | ($true != $true) | ((cP_3 @ X0 @ X1) != $true) | ((cP_2 @ X2 @ X0) != $true)) ) | ~spl0_3),
% 1.74/1.35 inference(superposition,[status(thm)],[f74,f12])).
% 1.74/1.35 thf(f74,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_3 @ (f @ X1) @ X2) != $true) | ((cP_2 @ X0 @ X1) != $true) | ((cP_4 @ (f @ X2) @ X3) != $true) | ($true != (cP_1 @ a @ X0))) ) | ~spl0_3),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.74/1.35 thf(f73,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_2 @ X0 @ X1) != $true) | ($true != $true) | ((cP_3 @ (f @ X1) @ X2) != $true) | ($true != (cP_1 @ a @ X0)) | ((cP_4 @ (f @ X2) @ X3) != $true)) ) | ~spl0_3),
% 1.74/1.35 inference(superposition,[status(thm)],[f72,f18])).
% 1.74/1.35 thf(f72,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_2 @ (f @ X0) @ X3) != $true) | ($true != (cP_1 @ a @ X0)) | ((cP_4 @ (f @ X1) @ X2) != $true) | ((cP_3 @ (f @ X3) @ X1) != $true)) ) | ~spl0_3),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.74/1.35 thf(f71,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_2 @ (f @ X0) @ X3) != $true) | ($true != $true) | ((cP_3 @ (f @ X3) @ X1) != $true) | ($true != (cP_1 @ a @ X0)) | ((cP_4 @ (f @ X1) @ X2) != $true)) ) | ~spl0_3),
% 1.74/1.35 inference(superposition,[status(thm)],[f52,f13])).
% 1.74/1.35 thf(f52,plain,(
% 1.74/1.35 ( ! [X2 : $i,X6 : $i,X4 : $i,X5 : $i] : (((cP_1 @ (f @ a) @ X2) != $true) | ((cP_4 @ (f @ X5) @ X6) != $true) | ((cP_3 @ (f @ X4) @ X5) != $true) | ((cP_2 @ (f @ X2) @ X4) != $true)) ) | ~spl0_3),
% 1.74/1.35 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.74/1.35 thf(f51,definition,(
% 1.74/1.35 spl0_3 <=> ! [X5 : $i,X4 : $i,X6 : $i,X2 : $i] : (((cP_3 @ (f @ X4) @ X5) != $true) | ((cP_4 @ (f @ X5) @ X6) != $true) | ((cP_1 @ (f @ a) @ X2) != $true) | ((cP_2 @ (f @ X2) @ X4) != $true))),
% 1.74/1.35 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.74/1.35 thf(f70,plain,(
% 1.74/1.35 ~spl0_2),
% 1.74/1.35 inference(avatar_contradiction_clause,[status(thm)],[f69])).
% 1.74/1.35 thf(f69,plain,(
% 1.74/1.35 $false | ~spl0_2),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.74/1.35 thf(f68,plain,(
% 1.74/1.35 ($true != $true) | ~spl0_2),
% 1.74/1.35 inference(superposition,[status(thm)],[f67,f24])).
% 1.74/1.35 thf(f24,plain,(
% 1.74/1.35 ((cP_4 @ b @ b) = $true)),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f67,plain,(
% 1.74/1.35 ( ! [X0 : $i] : (((cP_4 @ b @ X0) != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.74/1.35 thf(f66,plain,(
% 1.74/1.35 ( ! [X0 : $i] : (($true != $true) | ((cP_4 @ b @ X0) != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(superposition,[status(thm)],[f65,f27])).
% 1.74/1.35 thf(f27,plain,(
% 1.74/1.35 ((cP_3 @ b @ b) = $true)),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f65,plain,(
% 1.74/1.35 ( ! [X0 : $i,X1 : $i] : (((cP_3 @ b @ X0) != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.74/1.35 thf(f64,plain,(
% 1.74/1.35 ( ! [X0 : $i,X1 : $i] : (((cP_3 @ b @ X0) != $true) | ($true != $true) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(superposition,[status(thm)],[f63,f14])).
% 1.74/1.35 thf(f14,plain,(
% 1.74/1.35 ((cP_2 @ b @ b) = $true)),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f63,plain,(
% 1.74/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_2 @ b @ X2) != $true) | ((cP_4 @ X0 @ X1) != $true) | ((cP_3 @ X2 @ X0) != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.74/1.35 thf(f62,plain,(
% 1.74/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_2 @ b @ X2) != $true) | ((cP_4 @ X0 @ X1) != $true) | ((cP_3 @ X2 @ X0) != $true) | ($true != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(superposition,[status(thm)],[f61,f33])).
% 1.74/1.35 thf(f33,plain,(
% 1.74/1.35 ((cP_1 @ b @ b) = $true)),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f61,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_1 @ b @ X2)) | ($true != (cP_4 @ X1 @ X3)) | ((cP_2 @ X2 @ X0) != $true) | ((cP_3 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.74/1.35 thf(f60,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_2 @ X2 @ X0) != $true) | ($true != (cP_1 @ b @ X2)) | ((cP_3 @ X0 @ X1) != $true) | ($true != (cP_4 @ X1 @ X3)) | ($true != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(superposition,[status(thm)],[f59,f12])).
% 1.74/1.35 thf(f59,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_3 @ (f @ X1) @ X2) != $true) | ((cP_2 @ X0 @ X1) != $true) | ((cP_4 @ X2 @ X3) != $true) | ((cP_1 @ b @ X0) != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.74/1.35 thf(f58,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_2 @ X0 @ X1) != $true) | ($true != $true) | ((cP_3 @ (f @ X1) @ X2) != $true) | ((cP_4 @ X2 @ X3) != $true) | ((cP_1 @ b @ X0) != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(superposition,[status(thm)],[f57,f18])).
% 1.74/1.35 thf(f57,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_2 @ (f @ X0) @ X3) != $true) | ($true != (cP_4 @ X1 @ X2)) | ((cP_3 @ (f @ X3) @ X1) != $true) | ((cP_1 @ b @ X0) != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.74/1.35 thf(f56,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP_1 @ b @ X0) != $true) | ((cP_3 @ (f @ X3) @ X1) != $true) | ($true != $true) | ((cP_2 @ (f @ X0) @ X3) != $true) | ($true != (cP_4 @ X1 @ X2))) ) | ~spl0_2),
% 1.74/1.35 inference(superposition,[status(thm)],[f55,f13])).
% 1.74/1.35 thf(f55,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_1 @ (f @ b) @ X2)) | ((cP_4 @ X0 @ X1) != $true) | ($true != (cP_2 @ (f @ X2) @ X3)) | ((cP_3 @ (f @ X3) @ X0) != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.74/1.35 thf(f54,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP_1 @ (f @ b) @ X2)) | ((cP_3 @ (f @ X3) @ X0) != $true) | ($true != $true) | ($true != (cP_2 @ (f @ X2) @ X3)) | ((cP_4 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(superposition,[status(thm)],[f49,f29])).
% 1.74/1.35 thf(f49,plain,(
% 1.74/1.35 ( ! [X10 : $i,X11 : $i,X8 : $i,X7 : $i] : (($true != (cP_4 @ (f @ X7) @ X8)) | ((cP_1 @ (f @ b) @ X10) != $true) | ((cP_2 @ (f @ X10) @ X11) != $true) | ((cP_3 @ (f @ X11) @ X7) != $true)) ) | ~spl0_2),
% 1.74/1.35 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.74/1.35 thf(f48,definition,(
% 1.74/1.35 spl0_2 <=> ! [X11 : $i,X10 : $i,X8 : $i,X7 : $i] : (((cP_2 @ (f @ X10) @ X11) != $true) | ($true != (cP_4 @ (f @ X7) @ X8)) | ((cP_1 @ (f @ b) @ X10) != $true) | ((cP_3 @ (f @ X11) @ X7) != $true))),
% 1.74/1.35 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.74/1.35 thf(f53,plain,(
% 1.74/1.35 spl0_1 | spl0_2 | spl0_3),
% 1.74/1.35 inference(avatar_split_clause,[status(thm)],[f43,f51,f48,f45])).
% 1.74/1.35 thf(f43,plain,(
% 1.74/1.35 ( ! [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 @ X0) @ X1) != $true) | ((cP_3 @ (f @ X4) @ X5) != $true) | ((cP_2 @ (f @ X10) @ X11) != $true) | ((cP_2 @ (f @ X3) @ X9) != $true) | ((cP_1 @ (f @ a) @ X2) != $true) | ((cP_1 @ (f @ c) @ X3) != $true) | ((cP_4 @ (f @ X5) @ X6) != $true) | ((cP_3 @ (f @ X11) @ X7) != $true) | ((cP_2 @ (f @ X2) @ X4) != $true) | ((cP_1 @ (f @ b) @ X10) != $true) | ((cP_3 @ (f @ X9) @ X0) != $true) | ($true != (cP_4 @ (f @ X7) @ X8))) )),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.74/1.35 thf(f42,plain,(
% 1.74/1.35 ( ! [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 @ X10) @ X11) != $true) | ((cP_3 @ (f @ X9) @ X0) != $true) | ((cP_4 @ (f @ X5) @ X6) != $true) | ((cP_1 @ (f @ c) @ X3) != $true) | ((cP_3 @ (f @ X4) @ X5) != $true) | ($true != $true) | ((cP_2 @ (f @ X3) @ X9) != $true) | ((cP_1 @ (f @ a) @ X2) != $true) | ($true != (cP_4 @ (f @ X7) @ X8)) | ((cP_3 @ (f @ X11) @ X7) != $true) | ((cP_1 @ (f @ b) @ X10) != $true) | ((cP_4 @ (f @ X0) @ X1) != $true) | ((cP_2 @ (f @ X2) @ X4) != $true)) )),
% 1.74/1.35 inference(superposition,[status(thm)],[f41,f10])).
% 1.74/1.35 thf(f10,plain,(
% 1.74/1.35 ((cQ_1 @ a @ b @ c) = $true)),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f41,plain,(
% 1.74/1.35 ( ! [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 @ X12 @ X13 @ X14) != $true) | ($true != (cP_4 @ (f @ X7) @ X8)) | ((cP_1 @ (f @ X12) @ X0) != $true) | ((cP_1 @ (f @ X14) @ X2) != $true) | ((cP_3 @ (f @ X3) @ X5) != $true) | ((cP_4 @ (f @ X5) @ X9) != $true) | ((cP_4 @ (f @ X10) @ X11) != $true) | ((cP_3 @ (f @ X6) @ X7) != $true) | ((cP_2 @ (f @ X0) @ X3) != $true) | ($true != (cP_2 @ (f @ X2) @ X6)) | ((cP_2 @ (f @ X1) @ X4) != $true) | ((cP_3 @ (f @ X4) @ X10) != $true) | ((cP_1 @ (f @ X13) @ X1) != $true)) )),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.74/1.35 thf(f40,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X14 : $i,X4 : $i,X5 : $i,X12 : $i,X13 : $i] : (($true != (cP_4 @ (f @ X7) @ X8)) | ((cP_3 @ (f @ X6) @ X7) != $true) | ((cQ_1 @ X12 @ X13 @ X14) != $true) | ((cP_2 @ (f @ X1) @ X4) != $true) | ((cP_1 @ (f @ X13) @ X1) != $true) | ((cP_4 @ (f @ X5) @ X9) != $true) | ($true != $true) | ((cP_3 @ (f @ X3) @ X5) != $true) | ((cP_2 @ (f @ X0) @ X3) != $true) | ($true != (cP_2 @ (f @ X2) @ X6)) | ((cP_1 @ (f @ X14) @ X2) != $true) | ((cP_3 @ (f @ X4) @ X10) != $true) | ((cP_1 @ (f @ X12) @ X0) != $true) | ((cP_4 @ (f @ X10) @ X11) != $true)) )),
% 1.74/1.35 inference(superposition,[status(thm)],[f39,f21])).
% 1.74/1.35 thf(f21,plain,(
% 1.74/1.35 ( ! [X21 : $i,X18 : $i,X19 : $i,X16 : $i,X17 : $i,X20 : $i] : (((cQ_2 @ X16 @ X19 @ X18) = $true) | ((cQ_1 @ X20 @ X21 @ X17) != $true) | ((cP_1 @ (f @ X17) @ X18) != $true) | ((cP_1 @ (f @ X20) @ X16) != $true) | ((cP_1 @ (f @ X21) @ X19) != $true)) )),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f39,plain,(
% 1.74/1.35 ( ! [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 @ X10 @ X9 @ X11)) | ((cP_2 @ (f @ X10) @ X0) != $true) | ((cP_2 @ (f @ X9) @ X1) != $true) | ((cP_3 @ (f @ X0) @ X3) != $true) | ((cP_2 @ (f @ X11) @ X2) != $true) | ((cP_4 @ (f @ X5) @ X6) != $true) | ((cP_3 @ (f @ X2) @ X5) != $true) | ((cP_4 @ (f @ X3) @ X4) != $true) | ((cP_3 @ (f @ X1) @ X7) != $true) | ($true != (cP_4 @ (f @ X7) @ X8))) )),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.74/1.35 thf(f38,plain,(
% 1.74/1.35 ( ! [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 @ X11) @ X2) != $true) | ($true != $true) | ($true != (cP_4 @ (f @ X7) @ X8)) | ((cP_4 @ (f @ X3) @ X4) != $true) | ((cP_3 @ (f @ X1) @ X7) != $true) | ((cP_2 @ (f @ X9) @ X1) != $true) | ($true != (cQ_2 @ X10 @ X9 @ X11)) | ((cP_3 @ (f @ X2) @ X5) != $true) | ((cP_3 @ (f @ X0) @ X3) != $true) | ((cP_2 @ (f @ X10) @ X0) != $true) | ((cP_4 @ (f @ X5) @ X6) != $true)) )),
% 1.74/1.35 inference(superposition,[status(thm)],[f37,f30])).
% 1.74/1.35 thf(f30,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((cQ_3 @ X5 @ X2 @ X6) = $true) | ((cP_2 @ (f @ X3) @ X2) != $true) | ((cQ_2 @ X4 @ X3 @ X1) != $true) | ((cP_2 @ (f @ X1) @ X6) != $true) | ($true != (cP_2 @ (f @ X4) @ X5))) )),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f37,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != (cQ_3 @ X6 @ X7 @ X8)) | ((cP_4 @ (f @ X0) @ X3) != $true) | ((cP_3 @ (f @ X6) @ X0) != $true) | ((cP_4 @ (f @ X2) @ X5) != $true) | ((cP_4 @ (f @ X1) @ X4) != $true) | ((cP_3 @ (f @ X7) @ X1) != $true) | ($true != (cP_3 @ (f @ X8) @ X2))) )),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.74/1.35 thf(f36,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != (cQ_3 @ X6 @ X7 @ X8)) | ($true != $true) | ((cP_4 @ (f @ X0) @ X3) != $true) | ((cP_3 @ (f @ X6) @ X0) != $true) | ((cP_4 @ (f @ X1) @ X4) != $true) | ($true != (cP_3 @ (f @ X8) @ X2)) | ((cP_4 @ (f @ X2) @ X5) != $true) | ((cP_3 @ (f @ X7) @ X1) != $true)) )),
% 1.74/1.35 inference(superposition,[status(thm)],[f35,f15])).
% 1.74/1.35 thf(f15,plain,(
% 1.74/1.35 ( ! [X31 : $i,X28 : $i,X29 : $i,X26 : $i,X27 : $i,X30 : $i] : (($true = (cQ_4 @ X29 @ X30 @ X26)) | ($true != (cQ_3 @ X31 @ X28 @ X27)) | ((cP_3 @ (f @ X27) @ X26) != $true) | ((cP_3 @ (f @ X31) @ X29) != $true) | ((cP_3 @ (f @ X28) @ X30) != $true)) )),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f35,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cQ_4 @ X5 @ X3 @ X4)) | ((cP_4 @ (f @ X5) @ X0) != $true) | ((cP_4 @ (f @ X3) @ X1) != $true) | ((cP_4 @ (f @ X4) @ X2) != $true)) )),
% 1.74/1.35 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.74/1.35 thf(f34,plain,(
% 1.74/1.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cQ_4 @ X5 @ X3 @ X4)) | ((cP_4 @ (f @ X4) @ X2) != $true) | ($true != $true) | ((cP_4 @ (f @ X5) @ X0) != $true) | ((cP_4 @ (f @ X3) @ X1) != $true)) )),
% 1.74/1.35 inference(superposition,[status(thm)],[f11,f28])).
% 1.74/1.35 thf(f28,plain,(
% 1.74/1.35 ( ! [X10 : $i,X11 : $i,X9 : $i,X14 : $i,X12 : $i,X13 : $i] : (($true = (cQ_5 @ X13 @ X14 @ X12)) | ((cP_4 @ (f @ X9) @ X14) != $true) | ((cP_4 @ (f @ X10) @ X12) != $true) | ((cQ_4 @ X11 @ X9 @ X10) != $true) | ((cP_4 @ (f @ X11) @ X13) != $true)) )),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 thf(f11,plain,(
% 1.74/1.35 ( ! [X38 : $i,X36 : $i,X37 : $i] : (((cQ_5 @ X37 @ X36 @ X38) != $true)) )),
% 1.74/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.74/1.35 % SZS output end Proof for DTF2THF_25094
% 1.74/1.35 % (25283)------------------------------
% 1.74/1.35 % (25283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.35 % (25283)Termination reason: Refutation
% 1.74/1.35
% 1.74/1.35 % (25283)Memory used [KB]: 5756
% 1.74/1.35 % (25283)Time elapsed: 0.015 s
% 1.74/1.35 % (25283)Instructions burned: 31 (million)
% 1.74/1.35 % (25283)------------------------------
% 1.74/1.35 % (25283)------------------------------
% 1.74/1.35 % (25282)Success in time 0.022 s
%------------------------------------------------------------------------------