%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO386^5 : 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 : n003.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 1.75s 1.48s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 78 ( 15 unt; 0 typ; 3 def)
% Number of atoms : 1291 ( 309 equ; 0 cnn)
% Maximal formula atoms : 59 ( 16 avg)
% Number of connectives : 1741 ( 333 ~; 271 |; 114 &;1020 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 369 ( 0 ^; 369 !; 0 ?; 369 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ_4: $i > $i > $i > $o ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
cP_3: $i > $i > $o ).
thf(func_def_3,type,
cQ_3: $i > $i > $i > $o ).
thf(func_def_8,type,
cP_2: $i > $i > $o ).
thf(func_def_9,type,
cQ_2: $i > $i > $i > $o ).
thf(func_def_10,type,
cP_1: $i > $i > $o ).
thf(func_def_11,type,
cQ_1: $i > $i > $i > $o ).
thf(f85,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f45,f58,f71,f84]) ).
thf(f84,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f83]) ).
thf(f83,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( $true != $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f81,f18]) ).
thf(f18,plain,
( ( cP_3 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cQ_1 @ a @ b @ c )
= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X0: $i] :
( ( cP_2 @ d @ X0 )
= $true )
& ! [X1: $i] :
( ( cP_1 @ d @ X1 )
= $true )
& ! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( ( cP_1 @ ( f @ X2 ) @ X7 )
!= $true )
| ( ( cP_1 @ ( f @ X5 ) @ X3 )
!= $true )
| ( ( cP_1 @ ( f @ X6 ) @ X4 )
!= $true )
| ( ( cQ_2 @ X4 @ X7 @ X3 )
= $true )
| ( ( cQ_1 @ X6 @ X2 @ X5 )
!= $true ) )
& ! [X8: $i,X9: $i] :
( ( $true
!= ( cP_3 @ X9 @ X8 ) )
| ( ( cP_3 @ ( f @ X9 ) @ X8 )
= $true ) )
& ! [X10: $i,X11: $i] :
( ( ( cP_2 @ X11 @ X10 )
!= $true )
| ( ( cP_2 @ ( f @ X11 ) @ X10 )
= $true ) )
& ( ( cP_1 @ c @ c )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ( ( cP_3 @ b @ b )
= $true )
& ! [X12: $i,X13: $i] :
( ( ( cP_1 @ ( f @ X13 ) @ X12 )
= $true )
| ( ( cP_1 @ X13 @ X12 )
!= $true ) )
& ( ( cP_1 @ b @ b )
= $true )
& ! [X14: $i,X15: $i,X16: $i] :
( ( cQ_4 @ X16 @ X15 @ X14 )
!= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cP_3 @ a @ a )
= $true )
& ! [X17: $i,X18: $i,X19: $i,X20: $i,X21: $i,X22: $i] :
( ( ( cP_2 @ ( f @ X20 ) @ X21 )
!= $true )
| ( ( cQ_3 @ X18 @ X17 @ X21 )
= $true )
| ( ( cP_2 @ ( f @ X19 ) @ X17 )
!= $true )
| ( ( cP_2 @ ( f @ X22 ) @ X18 )
!= $true )
| ( ( cQ_2 @ X22 @ X19 @ X20 )
!= $true ) )
& ( ( cP_2 @ a @ a )
= $true )
& ! [X23: $i] :
( ( cP_3 @ d @ X23 )
= $true )
& ( ( cP_3 @ c @ c )
= $true )
& ! [X24: $i,X25: $i,X26: $i,X27: $i,X28: $i,X29: $i] :
( ( ( cQ_3 @ X25 @ X26 @ X27 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X26 ) @ X28 ) )
| ( ( cQ_4 @ X24 @ X28 @ X29 )
= $true )
| ( ( cP_3 @ ( f @ X27 ) @ X29 )
!= $true )
| ( ( cP_3 @ ( f @ X25 ) @ X24 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( cQ_1 @ a @ b @ c )
= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X27: $i] :
( ( cP_2 @ d @ X27 )
= $true )
& ! [X6: $i] :
( $true
= ( cP_1 @ d @ X6 ) )
& ! [X20: $i,X22: $i,X25: $i,X21: $i,X24: $i,X23: $i] :
( ( ( cP_1 @ ( f @ X20 ) @ X23 )
!= $true )
| ( ( cP_1 @ ( f @ X21 ) @ X22 )
!= $true )
| ( ( cP_1 @ ( f @ X24 ) @ X25 )
!= $true )
| ( ( cQ_2 @ X25 @ X23 @ X22 )
= $true )
| ( ( cQ_1 @ X24 @ X20 @ X21 )
!= $true ) )
& ! [X9: $i,X10: $i] :
( ( ( cP_3 @ X10 @ X9 )
!= $true )
| ( ( cP_3 @ ( f @ X10 ) @ X9 )
= $true ) )
& ! [X28: $i,X29: $i] :
( ( ( cP_2 @ X29 @ X28 )
!= $true )
| ( ( cP_2 @ ( f @ X29 ) @ X28 )
= $true ) )
& ( ( cP_1 @ c @ c )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ( ( cP_3 @ b @ b )
= $true )
& ! [X8: $i,X7: $i] :
( ( ( cP_1 @ ( f @ X7 ) @ X8 )
= $true )
| ( $true
!= ( cP_1 @ X7 @ X8 ) ) )
& ( ( cP_1 @ b @ b )
= $true )
& ! [X12: $i,X11: $i,X13: $i] :
( ( cQ_4 @ X13 @ X11 @ X12 )
!= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cP_3 @ a @ a )
= $true )
& ! [X1: $i,X4: $i,X2: $i,X0: $i,X5: $i,X3: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X5 )
!= $true )
| ( ( cQ_3 @ X4 @ X1 @ X5 )
= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cQ_2 @ X3 @ X2 @ X0 )
!= $true ) )
& ( ( cP_2 @ a @ a )
= $true )
& ! [X26: $i] :
( ( cP_3 @ d @ X26 )
= $true )
& ( ( cP_3 @ c @ c )
= $true )
& ! [X16: $i,X15: $i,X17: $i,X19: $i,X18: $i,X14: $i] :
( ( $true
!= ( cQ_3 @ X15 @ X17 @ X19 ) )
| ( ( cP_3 @ ( f @ X17 ) @ X18 )
!= $true )
| ( ( cQ_4 @ X16 @ X18 @ X14 )
= $true )
| ( ( cP_3 @ ( f @ X19 ) @ X14 )
!= $true )
| ( ( cP_3 @ ( f @ X15 ) @ X16 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ( ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X5 )
!= $true )
| ( ( cQ_3 @ X4 @ X1 @ X5 )
= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cQ_2 @ X3 @ X2 @ X0 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X1 )
!= $true ) )
& ( ( cP_3 @ c @ c )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cP_2 @ c @ c )
= $true )
& ! [X6: $i] :
( $true
= ( cP_1 @ d @ X6 ) )
& ! [X7: $i,X8: $i] :
( ( $true
!= ( cP_1 @ X7 @ X8 ) )
| ( ( cP_1 @ ( f @ X7 ) @ X8 )
= $true ) )
& ! [X9: $i,X10: $i] :
( ( ( cP_3 @ X10 @ X9 )
!= $true )
| ( ( cP_3 @ ( f @ X10 ) @ X9 )
= $true ) )
& ! [X11: $i,X12: $i,X13: $i] :
( ( cQ_4 @ X13 @ X11 @ X12 )
!= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X14: $i,X15: $i,X16: $i,X17: $i,X18: $i,X19: $i] :
( ( ( cP_3 @ ( f @ X19 ) @ X14 )
!= $true )
| ( ( cQ_4 @ X16 @ X18 @ X14 )
= $true )
| ( ( cP_3 @ ( f @ X15 ) @ X16 )
!= $true )
| ( ( cP_3 @ ( f @ X17 ) @ X18 )
!= $true )
| ( $true
!= ( cQ_3 @ X15 @ X17 @ X19 ) ) )
& ( ( cP_3 @ b @ b )
= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ( ( cP_2 @ a @ a )
= $true )
& ! [X20: $i,X21: $i,X22: $i,X23: $i,X24: $i,X25: $i] :
( ( ( cQ_1 @ X24 @ X20 @ X21 )
!= $true )
| ( ( cP_1 @ ( f @ X21 ) @ X22 )
!= $true )
| ( ( cP_1 @ ( f @ X20 ) @ X23 )
!= $true )
| ( ( cP_1 @ ( f @ X24 ) @ X25 )
!= $true )
| ( ( cQ_2 @ X25 @ X23 @ X22 )
= $true ) )
& ( ( cP_1 @ b @ b )
= $true )
& ! [X26: $i] :
( ( cP_3 @ d @ X26 )
= $true )
& ! [X27: $i] :
( ( cP_2 @ d @ X27 )
= $true )
& ( ( cP_3 @ a @ a )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X28: $i,X29: $i] :
( ( ( cP_2 @ ( f @ X29 ) @ X28 )
= $true )
| ( ( cP_2 @ X29 @ X28 )
!= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( cP_2 @ ( f @ X0 ) @ X5 )
| ( cQ_3 @ X4 @ X1 @ X5 )
| ~ ( cP_2 @ ( f @ X3 ) @ X4 )
| ~ ( cQ_2 @ X3 @ X2 @ X0 )
| ~ ( cP_2 @ ( f @ X2 ) @ X1 ) )
& ( cP_3 @ c @ c )
& ( cP_1 @ a @ a )
& ( cP_2 @ c @ c )
& ! [X6: $i] : ( cP_1 @ d @ X6 )
& ! [X7: $i,X8: $i] :
( ~ ( cP_1 @ X7 @ X8 )
| ( cP_1 @ ( f @ X7 ) @ X8 ) )
& ! [X9: $i,X10: $i] :
( ~ ( cP_3 @ X10 @ X9 )
| ( cP_3 @ ( f @ X10 ) @ X9 ) )
& ! [X11: $i,X12: $i,X13: $i] :
~ ( cQ_4 @ X13 @ X11 @ X12 )
& ( cQ_1 @ a @ b @ c )
& ! [X14: $i,X15: $i,X16: $i,X17: $i,X18: $i,X19: $i] :
( ~ ( cP_3 @ ( f @ X19 ) @ X14 )
| ( cQ_4 @ X16 @ X18 @ X14 )
| ~ ( cP_3 @ ( f @ X15 ) @ X16 )
| ~ ( cP_3 @ ( f @ X17 ) @ X18 )
| ~ ( cQ_3 @ X15 @ X17 @ X19 ) )
& ( cP_3 @ b @ b )
& ( cP_2 @ b @ b )
& ( cP_2 @ a @ a )
& ! [X20: $i,X21: $i,X22: $i,X23: $i,X24: $i,X25: $i] :
( ~ ( cQ_1 @ X24 @ X20 @ X21 )
| ~ ( cP_1 @ ( f @ X21 ) @ X22 )
| ~ ( cP_1 @ ( f @ X20 ) @ X23 )
| ~ ( cP_1 @ ( f @ X24 ) @ X25 )
| ( cQ_2 @ X25 @ X23 @ X22 ) )
& ( cP_1 @ b @ b )
& ! [X26: $i] : ( cP_3 @ d @ X26 )
& ! [X27: $i] : ( cP_2 @ d @ X27 )
& ( cP_3 @ a @ a )
& ( cP_1 @ c @ c )
& ! [X28: $i,X29: $i] :
( ( cP_2 @ ( f @ X29 ) @ X28 )
| ~ ( cP_2 @ X29 @ X28 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X2: $i,X4: $i,X1: $i,X0: $i,X3: $i,X5: $i] :
( ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ( cQ_3 @ X3 @ X4 @ X5 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 ) )
& ( cP_3 @ c @ c )
& ( cP_1 @ a @ a )
& ( cP_2 @ c @ c )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X0: $i,X1: $i] :
( ~ ( cP_1 @ X0 @ X1 )
| ( cP_1 @ ( f @ X0 ) @ X1 ) )
& ! [X1: $i,X0: $i] :
( ~ ( cP_3 @ X0 @ X1 )
| ( cP_3 @ ( f @ X0 ) @ X1 ) )
& ! [X1: $i,X2: $i,X0: $i] :
~ ( cQ_4 @ X0 @ X1 @ X2 )
& ( cQ_1 @ a @ b @ c )
& ! [X5: $i,X0: $i,X3: $i,X1: $i,X4: $i,X2: $i] :
( ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ( cQ_4 @ X3 @ X4 @ X5 )
| ~ ( cP_3 @ ( f @ X0 ) @ X3 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ~ ( cQ_3 @ X0 @ X1 @ X2 ) )
& ( cP_3 @ b @ b )
& ( cP_2 @ b @ b )
& ( cP_2 @ a @ a )
& ! [X1: $i,X2: $i,X5: $i,X4: $i,X0: $i,X3: $i] :
( ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ( cQ_2 @ X3 @ X4 @ X5 ) )
& ( cP_1 @ b @ b )
& ! [X0: $i] : ( cP_3 @ d @ X0 )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ( cP_3 @ a @ a )
& ( cP_1 @ c @ c )
& ! [X1: $i,X0: $i] :
( ( cP_2 @ ( f @ X0 ) @ X1 )
| ~ ( cP_2 @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ( ! [X2: $i,X4: $i,X1: $i,X0: $i,X3: $i,X5: $i] :
( ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ( cQ_3 @ X3 @ X4 @ X5 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 ) )
& ( cP_3 @ c @ c )
& ( cP_1 @ a @ a )
& ( cP_2 @ c @ c )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X0: $i,X1: $i] :
( ~ ( cP_1 @ X0 @ X1 )
| ( cP_1 @ ( f @ X0 ) @ X1 ) )
& ! [X1: $i,X0: $i] :
( ~ ( cP_3 @ X0 @ X1 )
| ( cP_3 @ ( f @ X0 ) @ X1 ) )
& ! [X1: $i,X2: $i,X0: $i] :
~ ( cQ_4 @ X0 @ X1 @ X2 )
& ( cQ_1 @ a @ b @ c )
& ! [X5: $i,X0: $i,X3: $i,X1: $i,X4: $i,X2: $i] :
( ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ( cQ_4 @ X3 @ X4 @ X5 )
| ~ ( cP_3 @ ( f @ X0 ) @ X3 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ~ ( cQ_3 @ X0 @ X1 @ X2 ) )
& ( cP_3 @ b @ b )
& ( cP_2 @ b @ b )
& ( cP_2 @ a @ a )
& ! [X1: $i,X2: $i,X5: $i,X4: $i,X0: $i,X3: $i] :
( ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ( cQ_2 @ X3 @ X4 @ X5 ) )
& ( cP_1 @ b @ b )
& ! [X0: $i] : ( cP_3 @ d @ X0 )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ( cP_3 @ a @ a )
& ( cP_1 @ c @ c )
& ! [X1: $i,X0: $i] :
( ( cP_2 @ ( f @ X0 ) @ X1 )
| ~ ( cP_2 @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.h2mhctsoah/DTF2THF_15428.p',cTHM409_3) ).
thf(f81,plain,
( ! [X0: $i] :
( ( cP_3 @ b @ X0 )
!= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ! [X0: $i] :
( ( ( cP_3 @ b @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f79,f26]) ).
thf(f26,plain,
( ( cP_2 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f79,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_2 @ b @ X0 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ b @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f77,f16]) ).
thf(f16,plain,
( ( cP_1 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f77,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_1 @ b @ X2 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ X2 @ X0 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP_1 @ b @ X2 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ X2 @ X0 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f75,f22]) ).
thf(f22,plain,
! [X8: $i,X9: $i] :
( ( ( cP_3 @ ( f @ X9 ) @ X8 )
= $true )
| ( $true
!= ( cP_3 @ X9 @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f75,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( $true != $true )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f73,f21]) ).
thf(f21,plain,
! [X10: $i,X11: $i] :
( ( ( cP_2 @ ( f @ X11 ) @ X10 )
= $true )
| ( ( cP_2 @ X11 @ X10 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f73,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f38,f17]) ).
thf(f17,plain,
! [X12: $i,X13: $i] :
( ( ( cP_1 @ ( f @ X13 ) @ X12 )
= $true )
| ( ( cP_1 @ X13 @ X12 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f38,plain,
( ! [X0: $i,X1: $i,X6: $i] :
( ( ( cP_1 @ ( f @ b ) @ X0 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X6 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl0_1
<=> ! [X6: $i,X0: $i,X1: $i] :
( ( ( cP_1 @ ( f @ b ) @ X0 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X6 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f71,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f70]) ).
thf(f70,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true != $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f68,f13]) ).
thf(f13,plain,
( ( cP_3 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f68,plain,
( ! [X0: $i] :
( ( cP_3 @ a @ X0 )
!= $true )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ! [X0: $i] :
( ( ( cP_3 @ a @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f66,f11]) ).
thf(f11,plain,
( ( cP_2 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f66,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( cP_2 @ a @ X0 ) )
| ( ( cP_3 @ X0 @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_2 @ a @ X0 ) )
| ( $true != $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f64,f14]) ).
thf(f14,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f64,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_1 @ a @ X2 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ X2 @ X0 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP_2 @ X2 @ X0 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ a @ X2 )
!= $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f62,f22]) ).
thf(f62,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X0 ) ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X0 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f60,f21]) ).
thf(f60,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X0 ) )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_1 @ a @ X0 ) )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f44,f17]) ).
thf(f44,plain,
( ! [X2: $i,X3: $i,X8: $i] :
( ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true )
| ( ( cP_3 @ ( f @ X3 ) @ X8 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl0_3
<=> ! [X2: $i,X8: $i,X3: $i] :
( ( ( cP_3 @ ( f @ X3 ) @ X8 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f58,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f57]) ).
thf(f57,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f55,f9]) ).
thf(f9,plain,
( ( cP_3 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f55,plain,
( ! [X0: $i] :
( ( cP_3 @ c @ X0 )
!= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cP_3 @ c @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f53,f19]) ).
thf(f19,plain,
( ( cP_2 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f53,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP_2 @ c @ X0 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP_2 @ c @ X0 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f51,f20]) ).
thf(f20,plain,
( ( cP_1 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f51,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_1 @ c @ X2 )
!= $true )
| ( ( cP_2 @ X2 @ X0 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP_2 @ X2 @ X0 )
!= $true )
| ( ( cP_3 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ c @ X2 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f49,f22]) ).
thf(f49,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_1 @ c @ X0 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_1 @ c @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f47,f21]) ).
thf(f47,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_1 @ c @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( $true != $true )
| ( ( cP_3 @ ( f @ X1 ) @ X2 )
!= $true )
| ( ( cP_1 @ c @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f41,f17]) ).
thf(f41,plain,
( ! [X7: $i,X4: $i,X5: $i] :
( ( ( cP_1 @ ( f @ c ) @ X7 )
!= $true )
| ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_2 @ ( f @ X7 ) @ X4 )
!= $true ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl0_2
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( ( cP_1 @ ( f @ c ) @ X7 )
!= $true )
| ( ( cP_2 @ ( f @ X7 ) @ X4 )
!= $true )
| ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f45,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f35,f43,f40,f37]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cP_1 @ ( f @ b ) @ X0 )
!= $true )
| ( ( cP_3 @ ( f @ X3 ) @ X8 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true )
| ( ( cP_1 @ ( f @ c ) @ X7 )
!= $true )
| ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X6 )
!= $true )
| ( ( cP_2 @ ( f @ X7 ) @ X4 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true )
| ( $true != $true )
| ( ( cP_1 @ ( f @ b ) @ X0 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X6 )
!= $true )
| ( ( cP_2 @ ( f @ X7 ) @ X4 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true )
| ( ( cP_1 @ ( f @ c ) @ X7 )
!= $true )
| ( ( cP_3 @ ( f @ X3 ) @ X8 )
!= $true )
| ( ( cP_3 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X1 )
!= $true ) ),
inference(superposition,[status(thm)],[f33,f27]) ).
thf(f27,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X10: $i,X0: $i,X11: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cQ_1 @ X9 @ X11 @ X10 )
!= $true )
| ( ( cP_2 @ ( f @ X1 ) @ X3 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X7 )
!= $true )
| ( ( cP_1 @ ( f @ X11 ) @ X1 )
!= $true )
| ( ( cP_3 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_3 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X5 )
!= $true )
| ( ( cP_3 @ ( f @ X7 ) @ X8 )
!= $true )
| ( ( cP_1 @ ( f @ X9 ) @ X0 )
!= $true )
| ( ( cP_1 @ ( f @ X10 ) @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,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_1 @ ( f @ X9 ) @ X0 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X5 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X7 )
!= $true )
| ( ( cP_3 @ ( f @ X7 ) @ X8 )
!= $true )
| ( ( cP_3 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_1 @ ( f @ X10 ) @ X2 )
!= $true )
| ( $true != $true )
| ( ( cP_1 @ ( f @ X11 ) @ X1 )
!= $true )
| ( ( cP_3 @ ( f @ X5 ) @ X6 )
!= $true )
| ( ( cP_2 @ ( f @ X1 ) @ X3 )
!= $true )
| ( ( cQ_1 @ X9 @ X11 @ X10 )
!= $true ) ),
inference(superposition,[status(thm)],[f31,f23]) ).
thf(f23,plain,
! [X2: $i,X3: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cQ_2 @ X4 @ X7 @ X3 )
= $true )
| ( ( cP_1 @ ( f @ X6 ) @ X4 )
!= $true )
| ( ( cP_1 @ ( f @ X5 ) @ X3 )
!= $true )
| ( ( cP_1 @ ( f @ X2 ) @ X7 )
!= $true )
| ( ( cQ_1 @ X6 @ X2 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cQ_2 @ X6 @ X7 @ X8 )
!= $true )
| ( ( cP_2 @ ( f @ X7 ) @ X1 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X5 )
!= $true )
| ( ( cP_3 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_3 @ ( f @ X0 ) @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X8 ) @ X2 )
!= $true )
| ( ( cP_2 @ ( f @ X6 ) @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( cP_3 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_2 @ ( f @ X8 ) @ X2 )
!= $true )
| ( ( cP_3 @ ( f @ X0 ) @ X4 )
!= $true )
| ( ( cP_3 @ ( f @ X1 ) @ X5 )
!= $true )
| ( ( cP_2 @ ( f @ X7 ) @ X1 )
!= $true )
| ( ( cQ_2 @ X6 @ X7 @ X8 )
!= $true )
| ( ( cP_2 @ ( f @ X6 ) @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f29,f12]) ).
thf(f12,plain,
! [X21: $i,X18: $i,X19: $i,X17: $i,X22: $i,X20: $i] :
( ( ( cQ_3 @ X18 @ X17 @ X21 )
= $true )
| ( ( cQ_2 @ X22 @ X19 @ X20 )
!= $true )
| ( ( cP_2 @ ( f @ X20 ) @ X21 )
!= $true )
| ( ( cP_2 @ ( f @ X19 ) @ X17 )
!= $true )
| ( ( cP_2 @ ( f @ X22 ) @ X18 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cQ_3 @ X3 @ X4 @ X5 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X5 ) @ X2 ) )
| ( ( cP_3 @ ( f @ X3 ) @ X0 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X4 ) @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_3 @ ( f @ X4 ) @ X1 ) )
| ( ( cQ_3 @ X3 @ X4 @ X5 )
!= $true )
| ( ( cP_3 @ ( f @ X3 ) @ X0 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_3 @ ( f @ X5 ) @ X2 ) ) ),
inference(superposition,[status(thm)],[f15,f8]) ).
thf(f8,plain,
! [X28: $i,X29: $i,X26: $i,X27: $i,X24: $i,X25: $i] :
( ( ( cQ_4 @ X24 @ X28 @ X29 )
= $true )
| ( ( cP_3 @ ( f @ X25 ) @ X24 )
!= $true )
| ( ( cQ_3 @ X25 @ X26 @ X27 )
!= $true )
| ( $true
!= ( cP_3 @ ( f @ X26 ) @ X28 ) )
| ( ( cP_3 @ ( f @ X27 ) @ X29 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f15,plain,
! [X16: $i,X14: $i,X15: $i] :
( ( cQ_4 @ X16 @ X15 @ X14 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO386^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n003.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:29:25 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : SYO386^5 : TPTP v9.2.1. Released v4.0.0.
% 0.21/0.47 % Domain : Syntactic
% 0.21/0.47 % Problem : TPS problem THM409-3
% 0.21/0.47 % Version : Especial.
% 0.21/0.47 % English :
% 0.21/0.47
% 0.21/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.47 % Source : [Bro09]
% 0.21/0.47 % Names : tps_0553 [Bro09]
% 0.21/0.47 % : THM409-3 [TPS]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.33 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.20 v5.4.0, 0.25 v5.2.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.21/0.47 % Syntax : Number of formulae : 13 ( 0 unt; 12 typ; 0 def)
% 0.21/0.47 % Number of atoms : 35 ( 0 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 35 ( 35 avg)
% 0.21/0.47 % Number of connectives : 141 ( 17 ~; 15 |; 19 &; 90 @)
% 0.21/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 35 ( 35 avg)
% 0.21/0.47 % Number of types : 2 ( 0 usr)
% 0.21/0.47 % Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 12 ( 12 usr; 4 con; 0-3 aty)
% 0.21/0.47 % Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% 0.21/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 thf(cQ_4,type,
% 0.21/0.47 cQ_4: $i > $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(f,type,
% 0.21/0.47 f: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(cP_3,type,
% 0.21/0.47 cP_3: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(cQ_3,type,
% 0.21/0.47 cQ_3: $i > $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(d,type,
% 0.21/0.47 d: $i ).
% 0.21/0.47
% 0.21/0.47 thf(c,type,
% 0.21/0.47 c: $i ).
% 0.21/0.47
% 0.21/0.47 thf(b,type,
% 0.21/0.47 b: $i ).
% 0.21/0.47
% 0.21/0.47 thf(a,type,
% 0.21/0.47 a: $i ).
% 0.21/0.47
% 0.21/0.47 thf(cP_2,type,
% 0.21/0.47 cP_2: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(cQ_2,type,
% 0.21/0.47 cQ_2: $i > $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(cP_1,type,
% 0.21/0.47 cP_1: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(cQ_1,type,
% 0.21/0.47 cQ_1: $i > $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(cTHM409_3,conjecture,
% 0.21/0.47 ~ ( ( cQ_1 @ a @ b @ c )
% 0.21/0.47 & ( cP_1 @ a @ a )
% 0.21/0.47 & ( cP_1 @ b @ b )
% 0.21/0.47 & ( cP_1 @ c @ c )
% 0.21/0.47 & ! [Xx: $i] : ( cP_1 @ d @ Xx )
% 0.21/0.47 & ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ~ ( cP_1 @ Xx @ Xy )
% 0.21/0.47 | ( cP_1 @ ( f @ Xx ) @ Xy ) )
% 0.21/0.47 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.21/0.47 ( ~ ( cQ_1 @ Xx @ Xy @ Xz )
% 0.21/0.47 | ~ ( cP_1 @ ( f @ Xx ) @ Xu )
% 0.21/0.47 | ~ ( cP_1 @ ( f @ Xy ) @ Xv )
% 0.21/0.47 | ~ ( cP_1 @ ( f @ Xz ) @ Xw )
% 0.21/0.47 | ( cQ_2 @ Xu @ Xv @ Xw ) )
% 0.21/0.47 & ( cP_2 @ a @ a )
% 0.21/0.47 & ( cP_2 @ b @ b )
% 0.21/0.47 & ( cP_2 @ c @ c )
% 0.21/0.47 & ! [Xx: $i] : ( cP_2 @ d @ Xx )
% 0.21/0.47 & ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ~ ( cP_2 @ Xx @ Xy )
% 0.21/0.47 | ( cP_2 @ ( f @ Xx ) @ Xy ) )
% 0.21/0.47 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.21/0.47 ( ~ ( cQ_2 @ Xx @ Xy @ Xz )
% 0.21/0.47 | ~ ( cP_2 @ ( f @ Xx ) @ Xu )
% 0.21/0.47 | ~ ( cP_2 @ ( f @ Xy ) @ Xv )
% 0.21/0.47 | ~ ( cP_2 @ ( f @ Xz ) @ Xw )
% 0.21/0.47 | ( cQ_3 @ Xu @ Xv @ Xw ) )
% 0.21/0.47 & ( cP_3 @ a @ a )
% 0.21/0.47 & ( cP_3 @ b @ b )
% 0.21/0.47 & ( cP_3 @ c @ c )
% 0.21/0.47 & ! [Xx: $i] : ( cP_3 @ d @ Xx )
% 0.21/0.47 & ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ~ ( cP_3 @ Xx @ Xy )
% 0.21/0.47 | ( cP_3 @ ( f @ Xx ) @ Xy ) )
% 0.21/0.47 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.21/0.47 ( ~ ( cQ_3 @ Xx @ Xy @ Xz )
% 0.21/0.47 | ~ ( cP_3 @ ( f @ Xx ) @ Xu )
% 0.21/0.47 | ~ ( cP_3 @ ( f @ Xy ) @ Xv )
% 0.21/0.47 | ~ ( cP_3 @ ( f @ Xz ) @ Xw )
% 0.21/0.47 | ( cQ_4 @ Xu @ Xv @ Xw ) )
% 0.21/0.47 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.21/0.47 ~ ( cQ_4 @ Xx @ Xy @ Xz ) ) ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 1.75/1.44 ---- Embedded in THF ---
% 1.75/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.75/1.44 %%% Generated on Tue Feb 24 14:29:26 EST 2026
% 1.75/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 1.75/1.44 %%% Logic specification used:
% 1.75/1.44 %%% thf(spec, logic, $$dhol).
% 1.75/1.44
% 1.75/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.h2mhctsoah/DTF2DTF15428.p
% See solution above
% 1.75/1.44 ------------------------
% 1.75/1.45 ---- Cleaned THF ---
% 1.75/1.45 thf(cQ_4,type,
% 1.75/1.45 cQ_4: $i > $i > $i > $o ).
% 1.75/1.45
% 1.75/1.45 thf(f,type,
% 1.75/1.45 f: $i > $i ).
% 1.75/1.45
% 1.75/1.45 thf(cP_3,type,
% 1.75/1.45 cP_3: $i > $i > $o ).
% 1.75/1.45
% 1.75/1.45 thf(cQ_3,type,
% 1.75/1.45 cQ_3: $i > $i > $i > $o ).
% 1.75/1.45
% 1.75/1.45 thf(d,type,
% 1.75/1.45 d: $i ).
% 1.75/1.45
% 1.75/1.45 thf(c,type,
% 1.75/1.45 c: $i ).
% 1.75/1.45
% 1.75/1.45 thf(b,type,
% 1.75/1.45 b: $i ).
% 1.75/1.45
% 1.75/1.45 thf(a,type,
% 1.75/1.45 a: $i ).
% 1.75/1.45
% 1.75/1.45 thf(cP_2,type,
% 1.75/1.45 cP_2: $i > $i > $o ).
% 1.75/1.45
% 1.75/1.45 thf(cQ_2,type,
% 1.75/1.45 cQ_2: $i > $i > $i > $o ).
% 1.75/1.45
% 1.75/1.45 thf(cP_1,type,
% 1.75/1.45 cP_1: $i > $i > $o ).
% 1.75/1.45
% 1.75/1.45 thf(cQ_1,type,
% 1.75/1.45 cQ_1: $i > $i > $i > $o ).
% 1.75/1.45
% 1.75/1.45 thf(cTHM409_3,conjecture,
% 1.75/1.45 ~ ( ( cQ_1 @ a @ b @ c )
% 1.75/1.45 & ( cP_1 @ a @ a )
% 1.75/1.45 & ( cP_1 @ b @ b )
% 1.75/1.45 & ( cP_1 @ c @ c )
% 1.75/1.45 & ! [Xx: $i] : ( cP_1 @ d @ Xx )
% 1.75/1.45 & ! [Xx: $i,Xy: $i] :
% 1.75/1.45 ( ~ ( cP_1 @ Xx @ Xy )
% 1.75/1.45 | ( cP_1 @ ( f @ Xx ) @ Xy ) )
% 1.75/1.45 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.75/1.45 ( ~ ( cQ_1 @ Xx @ Xy @ Xz )
% 1.75/1.45 | ~ ( cP_1 @ ( f @ Xx ) @ Xu )
% 1.75/1.45 | ~ ( cP_1 @ ( f @ Xy ) @ Xv )
% 1.75/1.45 | ~ ( cP_1 @ ( f @ Xz ) @ Xw )
% 1.75/1.45 | ( cQ_2 @ Xu @ Xv @ Xw ) )
% 1.75/1.45 & ( cP_2 @ a @ a )
% 1.75/1.45 & ( cP_2 @ b @ b )
% 1.75/1.45 & ( cP_2 @ c @ c )
% 1.75/1.45 & ! [Xx: $i] : ( cP_2 @ d @ Xx )
% 1.75/1.45 & ! [Xx: $i,Xy: $i] :
% 1.75/1.45 ( ~ ( cP_2 @ Xx @ Xy )
% 1.75/1.45 | ( cP_2 @ ( f @ Xx ) @ Xy ) )
% 1.75/1.45 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.75/1.45 ( ~ ( cQ_2 @ Xx @ Xy @ Xz )
% 1.75/1.45 | ~ ( cP_2 @ ( f @ Xx ) @ Xu )
% 1.75/1.45 | ~ ( cP_2 @ ( f @ Xy ) @ Xv )
% 1.75/1.45 | ~ ( cP_2 @ ( f @ Xz ) @ Xw )
% 1.75/1.45 | ( cQ_3 @ Xu @ Xv @ Xw ) )
% 1.75/1.45 & ( cP_3 @ a @ a )
% 1.75/1.45 & ( cP_3 @ b @ b )
% 1.75/1.45 & ( cP_3 @ c @ c )
% 1.75/1.45 & ! [Xx: $i] : ( cP_3 @ d @ Xx )
% 1.75/1.45 & ! [Xx: $i,Xy: $i] :
% 1.75/1.45 ( ~ ( cP_3 @ Xx @ Xy )
% 1.75/1.45 | ( cP_3 @ ( f @ Xx ) @ Xy ) )
% 1.75/1.45 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.75/1.45 ( ~ ( cQ_3 @ Xx @ Xy @ Xz )
% 1.75/1.45 | ~ ( cP_3 @ ( f @ Xx ) @ Xu )
% 1.75/1.45 | ~ ( cP_3 @ ( f @ Xy ) @ Xv )
% 1.75/1.45 | ~ ( cP_3 @ ( f @ Xz ) @ Xw )
% 1.75/1.45 | ( cQ_4 @ Xu @ Xv @ Xw ) )
% 1.75/1.45 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.75/1.45 ~ ( cQ_4 @ Xx @ Xy @ Xz ) ) ).
% 1.75/1.45 ------------------------
% 1.75/1.47 % (15530)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_15428 for (2999ds/2Mi)
% 1.75/1.47 % (15526)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15428 for (2999ds/183Mi)
% 1.75/1.47 % (15528)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_15428 for (2999ds/27Mi)
% 1.75/1.47 % (15529)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15428 for (2999ds/2Mi)
% 1.75/1.47 % (15531)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_15428 for (2999ds/275Mi)
% 1.75/1.47 % (15527)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_15428 for (2999ds/4Mi)
% 1.75/1.47 % (15532)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15428 for (2999ds/18Mi)
% 1.75/1.47 % (15529)Instruction limit reached!
% 1.75/1.47 % (15529)------------------------------
% 1.75/1.47 % (15529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.47 % (15529)Termination reason: Unknown
% 1.75/1.47 % (15529)Termination phase: shuffling
% 1.75/1.47
% 1.75/1.47 % (15530)Instruction limit reached!
% 1.75/1.47 % (15530)------------------------------
% 1.75/1.47 % (15530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.47 % (15530)Termination reason: Unknown
% 1.75/1.47 % (15530)Termination phase: Property scanning
% 1.75/1.47
% 1.75/1.47 % (15530)Memory used [KB]: 1023
% 1.75/1.47 % (15530)Time elapsed: 0.003 s
% 1.75/1.47 % (15530)Instructions burned: 3 (million)
% 1.75/1.47 % (15530)------------------------------
% 1.75/1.47 % (15530)------------------------------
% 1.75/1.47 % (15529)Memory used [KB]: 1023
% 1.75/1.47 % (15529)Time elapsed: 0.003 s
% 1.75/1.47 % (15529)Instructions burned: 3 (million)
% 1.75/1.47 % (15529)------------------------------
% 1.75/1.47 % (15529)------------------------------
% 1.75/1.47 % (15527)Instruction limit reached!
% 1.75/1.47 % (15527)------------------------------
% 1.75/1.47 % (15527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.47 % (15527)Termination reason: Unknown
% 1.75/1.47 % (15527)Termination phase: Saturation
% 1.75/1.47
% 1.75/1.47 % (15527)Memory used [KB]: 5500
% 1.75/1.47 % (15527)Time elapsed: 0.004 s
% 1.75/1.47 % (15527)Instructions burned: 4 (million)
% 1.75/1.47 % (15527)------------------------------
% 1.75/1.47 % (15527)------------------------------
% 1.75/1.48 % (15532)Instruction limit reached!
% 1.75/1.48 % (15532)------------------------------
% 1.75/1.48 % (15532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.48 % (15532)Termination reason: Unknown
% 1.75/1.48 % (15532)Termination phase: Saturation
% 1.75/1.48
% 1.75/1.48 % (15532)Memory used [KB]: 5628
% 1.75/1.48 % (15532)Time elapsed: 0.012 s
% 1.75/1.48 % (15532)Instructions burned: 19 (million)
% 1.75/1.48 % (15532)------------------------------
% 1.75/1.48 % (15532)------------------------------
% 1.75/1.48 % (15526)First to succeed.
% 1.75/1.48 % (15531)Also succeeded, but the first one will report.
% 1.75/1.48 % (15528)Instruction limit reached!
% 1.75/1.48 % (15528)------------------------------
% 1.75/1.48 % (15528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.48 % (15528)Termination reason: Unknown
% 1.75/1.48 % (15528)Termination phase: Saturation
% 1.75/1.48
% 1.75/1.48 % (15528)Memory used [KB]: 5628
% 1.75/1.48 % (15528)Time elapsed: 0.017 s
% 1.75/1.48 % (15528)Instructions burned: 27 (million)
% 1.75/1.48 % (15528)------------------------------
% 1.75/1.48 % (15528)------------------------------
% 1.75/1.48 % (15526)Refutation found. Thanks to Tanya!
% 1.75/1.48 % SZS status Theorem for DTF2THF_15428
% 1.75/1.48 % SZS output start Proof for DTF2THF_15428
% 1.75/1.48 thf(func_def_0, type, cQ_4: $i > $i > $i > $o).
% 1.75/1.48 thf(func_def_1, type, f: $i > $i).
% 1.75/1.48 thf(func_def_2, type, cP_3: $i > $i > $o).
% 1.75/1.48 thf(func_def_3, type, cQ_3: $i > $i > $i > $o).
% 1.75/1.48 thf(func_def_8, type, cP_2: $i > $i > $o).
% 1.75/1.48 thf(func_def_9, type, cQ_2: $i > $i > $i > $o).
% 1.75/1.48 thf(func_def_10, type, cP_1: $i > $i > $o).
% 1.75/1.48 thf(func_def_11, type, cQ_1: $i > $i > $i > $o).
% 1.75/1.48 thf(f85,plain,(
% 1.75/1.48 $false),
% 1.75/1.48 inference(avatar_sat_refutation,[status(thm)],[f45,f58,f71,f84])).
% 1.75/1.48 thf(f84,plain,(
% 1.75/1.48 ~spl0_1),
% 1.75/1.48 inference(avatar_contradiction_clause,[status(thm)],[f83])).
% 1.75/1.48 thf(f83,plain,(
% 1.75/1.48 $false | ~spl0_1),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.75/1.48 thf(f82,plain,(
% 1.75/1.48 ($true != $true) | ~spl0_1),
% 1.75/1.48 inference(superposition,[status(thm)],[f81,f18])).
% 1.75/1.48 thf(f18,plain,(
% 1.75/1.48 ((cP_3 @ b @ b) = $true)),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.48 thf(f7,plain,(
% 1.75/1.48 ((cQ_1 @ a @ b @ c) = $true) & ((cP_2 @ b @ b) = $true) & ! [X0 : $i] : ((cP_2 @ d @ X0) = $true) & ! [X1 : $i] : ((cP_1 @ d @ X1) = $true) & ! [X2 : $i,X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (((cP_1 @ (f @ X2) @ X7) != $true) | ((cP_1 @ (f @ X5) @ X3) != $true) | ((cP_1 @ (f @ X6) @ X4) != $true) | ((cQ_2 @ X4 @ X7 @ X3) = $true) | ((cQ_1 @ X6 @ X2 @ X5) != $true)) & ! [X8 : $i,X9 : $i] : (($true != (cP_3 @ X9 @ X8)) | ((cP_3 @ (f @ X9) @ X8) = $true)) & ! [X10 : $i,X11 : $i] : (((cP_2 @ X11 @ X10) != $true) | ((cP_2 @ (f @ X11) @ X10) = $true)) & ((cP_1 @ c @ c) = $true) & ((cP_2 @ c @ c) = $true) & ((cP_3 @ b @ b) = $true) & ! [X12 : $i,X13 : $i] : (((cP_1 @ (f @ X13) @ X12) = $true) | ((cP_1 @ X13 @ X12) != $true)) & ((cP_1 @ b @ b) = $true) & ! [X14 : $i,X15 : $i,X16 : $i] : ((cQ_4 @ X16 @ X15 @ X14) != $true) & ((cP_1 @ a @ a) = $true) & ((cP_3 @ a @ a) = $true) & ! [X17 : $i,X18 : $i,X19 : $i,X20 : $i,X21 : $i,X22 : $i] : (((cP_2 @ (f @ X20) @ X21) != $true) | ((cQ_3 @ X18 @ X17 @ X21) = $true) | ((cP_2 @ (f @ X19) @ X17) != $true) | ((cP_2 @ (f @ X22) @ X18) != $true) | ((cQ_2 @ X22 @ X19 @ X20) != $true)) & ((cP_2 @ a @ a) = $true) & ! [X23 : $i] : ((cP_3 @ d @ X23) = $true) & ((cP_3 @ c @ c) = $true) & ! [X24 : $i,X25 : $i,X26 : $i,X27 : $i,X28 : $i,X29 : $i] : (((cQ_3 @ X25 @ X26 @ X27) != $true) | ($true != (cP_3 @ (f @ X26) @ X28)) | ((cQ_4 @ X24 @ X28 @ X29) = $true) | ((cP_3 @ (f @ X27) @ X29) != $true) | ((cP_3 @ (f @ X25) @ X24) != $true))),
% 1.75/1.48 inference(rectify,[status(thm)],[f6])).
% 1.75/1.48 thf(f6,plain,(
% 1.75/1.48 ((cQ_1 @ a @ b @ c) = $true) & ((cP_2 @ b @ b) = $true) & ! [X27 : $i] : ((cP_2 @ d @ X27) = $true) & ! [X6 : $i] : ($true = (cP_1 @ d @ X6)) & ! [X20 : $i,X22 : $i,X25 : $i,X21 : $i,X24 : $i,X23 : $i] : (((cP_1 @ (f @ X20) @ X23) != $true) | ((cP_1 @ (f @ X21) @ X22) != $true) | ((cP_1 @ (f @ X24) @ X25) != $true) | ((cQ_2 @ X25 @ X23 @ X22) = $true) | ((cQ_1 @ X24 @ X20 @ X21) != $true)) & ! [X9 : $i,X10 : $i] : (((cP_3 @ X10 @ X9) != $true) | ((cP_3 @ (f @ X10) @ X9) = $true)) & ! [X28 : $i,X29 : $i] : (((cP_2 @ X29 @ X28) != $true) | ((cP_2 @ (f @ X29) @ X28) = $true)) & ((cP_1 @ c @ c) = $true) & ((cP_2 @ c @ c) = $true) & ((cP_3 @ b @ b) = $true) & ! [X8 : $i,X7 : $i] : (((cP_1 @ (f @ X7) @ X8) = $true) | ($true != (cP_1 @ X7 @ X8))) & ((cP_1 @ b @ b) = $true) & ! [X12 : $i,X11 : $i,X13 : $i] : ((cQ_4 @ X13 @ X11 @ X12) != $true) & ((cP_1 @ a @ a) = $true) & ((cP_3 @ a @ a) = $true) & ! [X1 : $i,X4 : $i,X2 : $i,X0 : $i,X5 : $i,X3 : $i] : (((cP_2 @ (f @ X0) @ X5) != $true) | ((cQ_3 @ X4 @ X1 @ X5) = $true) | ((cP_2 @ (f @ X2) @ X1) != $true) | ((cP_2 @ (f @ X3) @ X4) != $true) | ((cQ_2 @ X3 @ X2 @ X0) != $true)) & ((cP_2 @ a @ a) = $true) & ! [X26 : $i] : ((cP_3 @ d @ X26) = $true) & ((cP_3 @ c @ c) = $true) & ! [X16 : $i,X15 : $i,X17 : $i,X19 : $i,X18 : $i,X14 : $i] : (($true != (cQ_3 @ X15 @ X17 @ X19)) | ((cP_3 @ (f @ X17) @ X18) != $true) | ((cQ_4 @ X16 @ X18 @ X14) = $true) | ((cP_3 @ (f @ X19) @ X14) != $true) | ((cP_3 @ (f @ X15) @ X16) != $true))),
% 1.75/1.48 inference(flattening,[status(thm)],[f5])).
% 1.75/1.48 thf(f5,plain,(
% 1.75/1.48 ~~(! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : (~((cP_2 @ (f @ X0) @ X5) = $true) | ((cQ_3 @ X4 @ X1 @ X5) = $true) | ~((cP_2 @ (f @ X3) @ X4) = $true) | ~((cQ_2 @ X3 @ X2 @ X0) = $true) | ~((cP_2 @ (f @ X2) @ X1) = $true)) & ((cP_3 @ c @ c) = $true) & ((cP_1 @ a @ a) = $true) & ((cP_2 @ c @ c) = $true) & ! [X6 : $i] : ($true = (cP_1 @ d @ X6)) & ! [X7 : $i,X8 : $i] : (~($true = (cP_1 @ X7 @ X8)) | ((cP_1 @ (f @ X7) @ X8) = $true)) & ! [X9 : $i,X10 : $i] : (~((cP_3 @ X10 @ X9) = $true) | ((cP_3 @ (f @ X10) @ X9) = $true)) & ! [X11 : $i,X12 : $i,X13 : $i] : ~((cQ_4 @ X13 @ X11 @ X12) = $true) & ((cQ_1 @ a @ b @ c) = $true) & ! [X14 : $i,X15 : $i,X16 : $i,X17 : $i,X18 : $i,X19 : $i] : (~((cP_3 @ (f @ X19) @ X14) = $true) | ((cQ_4 @ X16 @ X18 @ X14) = $true) | ~((cP_3 @ (f @ X15) @ X16) = $true) | ~((cP_3 @ (f @ X17) @ X18) = $true) | ~($true = (cQ_3 @ X15 @ X17 @ X19))) & ((cP_3 @ b @ b) = $true) & ((cP_2 @ b @ b) = $true) & ((cP_2 @ a @ a) = $true) & ! [X20 : $i,X21 : $i,X22 : $i,X23 : $i,X24 : $i,X25 : $i] : (~((cQ_1 @ X24 @ X20 @ X21) = $true) | ~((cP_1 @ (f @ X21) @ X22) = $true) | ~((cP_1 @ (f @ X20) @ X23) = $true) | ~((cP_1 @ (f @ X24) @ X25) = $true) | ((cQ_2 @ X25 @ X23 @ X22) = $true)) & ((cP_1 @ b @ b) = $true) & ! [X26 : $i] : ((cP_3 @ d @ X26) = $true) & ! [X27 : $i] : ((cP_2 @ d @ X27) = $true) & ((cP_3 @ a @ a) = $true) & ((cP_1 @ c @ c) = $true) & ! [X28 : $i,X29 : $i] : (((cP_2 @ (f @ X29) @ X28) = $true) | ~((cP_2 @ X29 @ X28) = $true)))),
% 1.75/1.48 inference(fool_elimination,[status(thm)],[f4])).
% 1.75/1.48 thf(f4,plain,(
% 1.75/1.48 ~~(! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : (~(cP_2 @ (f @ X0) @ X5) | (cQ_3 @ X4 @ X1 @ X5) | ~(cP_2 @ (f @ X3) @ X4) | ~(cQ_2 @ X3 @ X2 @ X0) | ~(cP_2 @ (f @ X2) @ X1)) & (cP_3 @ c @ c) & (cP_1 @ a @ a) & (cP_2 @ c @ c) & ! [X6 : $i] : (cP_1 @ d @ X6) & ! [X7 : $i,X8 : $i] : (~(cP_1 @ X7 @ X8) | (cP_1 @ (f @ X7) @ X8)) & ! [X9 : $i,X10 : $i] : (~(cP_3 @ X10 @ X9) | (cP_3 @ (f @ X10) @ X9)) & ! [X11 : $i,X12 : $i,X13 : $i] : ~(cQ_4 @ X13 @ X11 @ X12) & (cQ_1 @ a @ b @ c) & ! [X14 : $i,X15 : $i,X16 : $i,X17 : $i,X18 : $i,X19 : $i] : (~(cP_3 @ (f @ X19) @ X14) | (cQ_4 @ X16 @ X18 @ X14) | ~(cP_3 @ (f @ X15) @ X16) | ~(cP_3 @ (f @ X17) @ X18) | ~(cQ_3 @ X15 @ X17 @ X19)) & (cP_3 @ b @ b) & (cP_2 @ b @ b) & (cP_2 @ a @ a) & ! [X20 : $i,X21 : $i,X22 : $i,X23 : $i,X24 : $i,X25 : $i] : (~(cQ_1 @ X24 @ X20 @ X21) | ~(cP_1 @ (f @ X21) @ X22) | ~(cP_1 @ (f @ X20) @ X23) | ~(cP_1 @ (f @ X24) @ X25) | (cQ_2 @ X25 @ X23 @ X22)) & (cP_1 @ b @ b) & ! [X26 : $i] : (cP_3 @ d @ X26) & ! [X27 : $i] : (cP_2 @ d @ X27) & (cP_3 @ a @ a) & (cP_1 @ c @ c) & ! [X28 : $i,X29 : $i] : ((cP_2 @ (f @ X29) @ X28) | ~(cP_2 @ X29 @ X28)))),
% 1.75/1.48 inference(rectify,[status(thm)],[f2])).
% 1.75/1.48 thf(f2,negated_conjecture,(
% 1.75/1.48 ~~(! [X2 : $i,X4 : $i,X1 : $i,X0 : $i,X3 : $i,X5 : $i] : (~(cP_2 @ (f @ X2) @ X5) | (cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2) | ~(cP_2 @ (f @ X1) @ X4)) & (cP_3 @ c @ c) & (cP_1 @ a @ a) & (cP_2 @ c @ c) & ! [X0 : $i] : (cP_1 @ d @ X0) & ! [X0 : $i,X1 : $i] : (~(cP_1 @ X0 @ X1) | (cP_1 @ (f @ X0) @ X1)) & ! [X1 : $i,X0 : $i] : (~(cP_3 @ X0 @ X1) | (cP_3 @ (f @ X0) @ X1)) & ! [X1 : $i,X2 : $i,X0 : $i] : ~(cQ_4 @ X0 @ X1 @ X2) & (cQ_1 @ a @ b @ c) & ! [X5 : $i,X0 : $i,X3 : $i,X1 : $i,X4 : $i,X2 : $i] : (~(cP_3 @ (f @ X2) @ X5) | (cQ_4 @ X3 @ X4 @ X5) | ~(cP_3 @ (f @ X0) @ X3) | ~(cP_3 @ (f @ X1) @ X4) | ~(cQ_3 @ X0 @ X1 @ X2)) & (cP_3 @ b @ b) & (cP_2 @ b @ b) & (cP_2 @ a @ a) & ! [X1 : $i,X2 : $i,X5 : $i,X4 : $i,X0 : $i,X3 : $i] : (~(cQ_1 @ X0 @ X1 @ X2) | ~(cP_1 @ (f @ X2) @ X5) | ~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X0) @ X3) | (cQ_2 @ X3 @ X4 @ X5)) & (cP_1 @ b @ b) & ! [X0 : $i] : (cP_3 @ d @ X0) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_3 @ a @ a) & (cP_1 @ c @ c) & ! [X1 : $i,X0 : $i] : ((cP_2 @ (f @ X0) @ X1) | ~(cP_2 @ X0 @ X1)))),
% 1.75/1.48 inference(negated_conjecture,[status(cth)],[f1])).
% 1.75/1.48 thf(f1,conjecture,(
% 1.75/1.48 ~(! [X2 : $i,X4 : $i,X1 : $i,X0 : $i,X3 : $i,X5 : $i] : (~(cP_2 @ (f @ X2) @ X5) | (cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2) | ~(cP_2 @ (f @ X1) @ X4)) & (cP_3 @ c @ c) & (cP_1 @ a @ a) & (cP_2 @ c @ c) & ! [X0 : $i] : (cP_1 @ d @ X0) & ! [X0 : $i,X1 : $i] : (~(cP_1 @ X0 @ X1) | (cP_1 @ (f @ X0) @ X1)) & ! [X1 : $i,X0 : $i] : (~(cP_3 @ X0 @ X1) | (cP_3 @ (f @ X0) @ X1)) & ! [X1 : $i,X2 : $i,X0 : $i] : ~(cQ_4 @ X0 @ X1 @ X2) & (cQ_1 @ a @ b @ c) & ! [X5 : $i,X0 : $i,X3 : $i,X1 : $i,X4 : $i,X2 : $i] : (~(cP_3 @ (f @ X2) @ X5) | (cQ_4 @ X3 @ X4 @ X5) | ~(cP_3 @ (f @ X0) @ X3) | ~(cP_3 @ (f @ X1) @ X4) | ~(cQ_3 @ X0 @ X1 @ X2)) & (cP_3 @ b @ b) & (cP_2 @ b @ b) & (cP_2 @ a @ a) & ! [X1 : $i,X2 : $i,X5 : $i,X4 : $i,X0 : $i,X3 : $i] : (~(cQ_1 @ X0 @ X1 @ X2) | ~(cP_1 @ (f @ X2) @ X5) | ~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X0) @ X3) | (cQ_2 @ X3 @ X4 @ X5)) & (cP_1 @ b @ b) & ! [X0 : $i] : (cP_3 @ d @ X0) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_3 @ a @ a) & (cP_1 @ c @ c) & ! [X1 : $i,X0 : $i] : ((cP_2 @ (f @ X0) @ X1) | ~(cP_2 @ X0 @ X1)))),
% 1.75/1.48 file('/export/starexec/sandbox/tmp/tmp.h2mhctsoah/DTF2THF_15428.p',cTHM409_3)).
% 1.75/1.48 thf(f81,plain,(
% 1.75/1.48 ( ! [X0 : $i] : (((cP_3 @ b @ X0) != $true)) ) | ~spl0_1),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.75/1.48 thf(f80,plain,(
% 1.75/1.48 ( ! [X0 : $i] : (((cP_3 @ b @ X0) != $true) | ($true != $true)) ) | ~spl0_1),
% 1.75/1.48 inference(superposition,[status(thm)],[f79,f26])).
% 1.75/1.48 thf(f26,plain,(
% 1.75/1.48 ((cP_2 @ b @ b) = $true)),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.48 thf(f79,plain,(
% 1.75/1.48 ( ! [X0 : $i,X1 : $i] : (((cP_2 @ b @ X0) != $true) | ((cP_3 @ X0 @ X1) != $true)) ) | ~spl0_1),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.75/1.48 thf(f78,plain,(
% 1.75/1.48 ( ! [X0 : $i,X1 : $i] : (((cP_3 @ X0 @ X1) != $true) | ((cP_2 @ b @ X0) != $true) | ($true != $true)) ) | ~spl0_1),
% 1.75/1.48 inference(superposition,[status(thm)],[f77,f16])).
% 1.75/1.48 thf(f16,plain,(
% 1.75/1.48 ((cP_1 @ b @ b) = $true)),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.48 thf(f77,plain,(
% 1.75/1.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_1 @ b @ X2) != $true) | ((cP_3 @ X0 @ X1) != $true) | ((cP_2 @ X2 @ X0) != $true)) ) | ~spl0_1),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.75/1.48 thf(f76,plain,(
% 1.75/1.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((cP_1 @ b @ X2) != $true) | ((cP_3 @ X0 @ X1) != $true) | ((cP_2 @ X2 @ X0) != $true)) ) | ~spl0_1),
% 1.75/1.48 inference(superposition,[status(thm)],[f75,f22])).
% 1.75/1.48 thf(f22,plain,(
% 1.75/1.48 ( ! [X8 : $i,X9 : $i] : (((cP_3 @ (f @ X9) @ X8) = $true) | ($true != (cP_3 @ X9 @ X8))) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.48 thf(f75,plain,(
% 1.75/1.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_3 @ (f @ X1) @ X2) != $true) | ((cP_2 @ X0 @ X1) != $true) | ((cP_1 @ b @ X0) != $true)) ) | ~spl0_1),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.75/1.48 thf(f74,plain,(
% 1.75/1.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_2 @ X0 @ X1) != $true) | ((cP_1 @ b @ X0) != $true) | ($true != $true) | ((cP_3 @ (f @ X1) @ X2) != $true)) ) | ~spl0_1),
% 1.75/1.48 inference(superposition,[status(thm)],[f73,f21])).
% 1.75/1.48 thf(f21,plain,(
% 1.75/1.48 ( ! [X10 : $i,X11 : $i] : (((cP_2 @ (f @ X11) @ X10) = $true) | ((cP_2 @ X11 @ X10) != $true)) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.48 thf(f73,plain,(
% 1.75/1.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_2 @ (f @ X0) @ X1) != $true) | ((cP_1 @ b @ X0) != $true) | ((cP_3 @ (f @ X1) @ X2) != $true)) ) | ~spl0_1),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.75/1.48 thf(f72,plain,(
% 1.75/1.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_3 @ (f @ X1) @ X2) != $true) | ($true != $true) | ((cP_2 @ (f @ X0) @ X1) != $true) | ((cP_1 @ b @ X0) != $true)) ) | ~spl0_1),
% 1.75/1.48 inference(superposition,[status(thm)],[f38,f17])).
% 1.75/1.48 thf(f17,plain,(
% 1.75/1.48 ( ! [X12 : $i,X13 : $i] : (((cP_1 @ (f @ X13) @ X12) = $true) | ((cP_1 @ X13 @ X12) != $true)) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.48 thf(f38,plain,(
% 1.75/1.48 ( ! [X0 : $i,X1 : $i,X6 : $i] : (((cP_1 @ (f @ b) @ X0) != $true) | ((cP_3 @ (f @ X1) @ X6) != $true) | ((cP_2 @ (f @ X0) @ X1) != $true)) ) | ~spl0_1),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.75/1.48 thf(f37,definition,(
% 1.75/1.48 spl0_1 <=> ! [X6 : $i,X0 : $i,X1 : $i] : (((cP_1 @ (f @ b) @ X0) != $true) | ((cP_3 @ (f @ X1) @ X6) != $true) | ((cP_2 @ (f @ X0) @ X1) != $true))),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.75/1.48 thf(f71,plain,(
% 1.75/1.48 ~spl0_3),
% 1.75/1.48 inference(avatar_contradiction_clause,[status(thm)],[f70])).
% 1.75/1.48 thf(f70,plain,(
% 1.75/1.48 $false | ~spl0_3),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.75/1.48 thf(f69,plain,(
% 1.75/1.48 ($true != $true) | ~spl0_3),
% 1.75/1.48 inference(superposition,[status(thm)],[f68,f13])).
% 1.75/1.48 thf(f13,plain,(
% 1.75/1.48 ((cP_3 @ a @ a) = $true)),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.48 thf(f68,plain,(
% 1.75/1.48 ( ! [X0 : $i] : (((cP_3 @ a @ X0) != $true)) ) | ~spl0_3),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.75/1.48 thf(f67,plain,(
% 1.75/1.48 ( ! [X0 : $i] : (((cP_3 @ a @ X0) != $true) | ($true != $true)) ) | ~spl0_3),
% 1.75/1.48 inference(superposition,[status(thm)],[f66,f11])).
% 1.75/1.48 thf(f11,plain,(
% 1.75/1.48 ((cP_2 @ a @ a) = $true)),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.48 thf(f66,plain,(
% 1.75/1.48 ( ! [X0 : $i,X1 : $i] : (($true != (cP_2 @ a @ X0)) | ((cP_3 @ X0 @ X1) != $true)) ) | ~spl0_3),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.75/1.49 thf(f65,plain,(
% 1.75/1.49 ( ! [X0 : $i,X1 : $i] : (((cP_3 @ X0 @ X1) != $true) | ($true != (cP_2 @ a @ X0)) | ($true != $true)) ) | ~spl0_3),
% 1.75/1.49 inference(superposition,[status(thm)],[f64,f14])).
% 1.75/1.49 thf(f14,plain,(
% 1.75/1.49 ((cP_1 @ a @ a) = $true)),
% 1.75/1.49 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.49 thf(f64,plain,(
% 1.75/1.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_1 @ a @ X2) != $true) | ((cP_3 @ X0 @ X1) != $true) | ((cP_2 @ X2 @ X0) != $true)) ) | ~spl0_3),
% 1.75/1.49 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.75/1.49 thf(f63,plain,(
% 1.75/1.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((cP_2 @ X2 @ X0) != $true) | ((cP_3 @ X0 @ X1) != $true) | ((cP_1 @ a @ X2) != $true)) ) | ~spl0_3),
% 1.75/1.49 inference(superposition,[status(thm)],[f62,f22])).
% 1.75/1.49 thf(f62,plain,(
% 1.75/1.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_3 @ (f @ X1) @ X2) != $true) | ((cP_2 @ X0 @ X1) != $true) | ($true != (cP_1 @ a @ X0))) ) | ~spl0_3),
% 1.75/1.49 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.75/1.49 thf(f61,plain,(
% 1.75/1.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_3 @ (f @ X1) @ X2) != $true) | ($true != $true) | ((cP_2 @ X0 @ X1) != $true) | ($true != (cP_1 @ a @ X0))) ) | ~spl0_3),
% 1.75/1.49 inference(superposition,[status(thm)],[f60,f21])).
% 1.75/1.49 thf(f60,plain,(
% 1.75/1.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_2 @ (f @ X0) @ X1) != $true) | ($true != (cP_1 @ a @ X0)) | ((cP_3 @ (f @ X1) @ X2) != $true)) ) | ~spl0_3),
% 1.75/1.49 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.75/1.49 thf(f59,plain,(
% 1.75/1.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_3 @ (f @ X1) @ X2) != $true) | ($true != $true) | ($true != (cP_1 @ a @ X0)) | ((cP_2 @ (f @ X0) @ X1) != $true)) ) | ~spl0_3),
% 1.75/1.49 inference(superposition,[status(thm)],[f44,f17])).
% 1.75/1.49 thf(f44,plain,(
% 1.75/1.49 ( ! [X2 : $i,X3 : $i,X8 : $i] : (((cP_1 @ (f @ a) @ X2) != $true) | ((cP_3 @ (f @ X3) @ X8) != $true) | ((cP_2 @ (f @ X2) @ X3) != $true)) ) | ~spl0_3),
% 1.75/1.49 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.75/1.49 thf(f43,definition,(
% 1.75/1.49 spl0_3 <=> ! [X2 : $i,X8 : $i,X3 : $i] : (((cP_3 @ (f @ X3) @ X8) != $true) | ((cP_1 @ (f @ a) @ X2) != $true) | ((cP_2 @ (f @ X2) @ X3) != $true))),
% 1.75/1.49 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.75/1.49 thf(f58,plain,(
% 1.75/1.49 ~spl0_2),
% 1.75/1.49 inference(avatar_contradiction_clause,[status(thm)],[f57])).
% 1.75/1.49 thf(f57,plain,(
% 1.75/1.49 $false | ~spl0_2),
% 1.75/1.49 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.75/1.49 thf(f56,plain,(
% 1.75/1.49 ($true != $true) | ~spl0_2),
% 1.75/1.49 inference(superposition,[status(thm)],[f55,f9])).
% 1.75/1.49 thf(f9,plain,(
% 1.75/1.49 ((cP_3 @ c @ c) = $true)),
% 1.75/1.49 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.49 thf(f55,plain,(
% 1.75/1.49 ( ! [X0 : $i] : (((cP_3 @ c @ X0) != $true)) ) | ~spl0_2),
% 1.75/1.49 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.75/1.49 thf(f54,plain,(
% 1.75/1.49 ( ! [X0 : $i] : (($true != $true) | ((cP_3 @ c @ X0) != $true)) ) | ~spl0_2),
% 1.75/1.49 inference(superposition,[status(thm)],[f53,f19])).
% 1.75/1.49 thf(f19,plain,(
% 1.75/1.49 ((cP_2 @ c @ c) = $true)),
% 1.75/1.49 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.49 thf(f53,plain,(
% 1.75/1.49 ( ! [X0 : $i,X1 : $i] : (((cP_2 @ c @ X0) != $true) | ((cP_3 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 1.75/1.49 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.75/1.49 thf(f52,plain,(
% 1.75/1.49 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((cP_2 @ c @ X0) != $true) | ((cP_3 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 1.75/1.49 inference(superposition,[status(thm)],[f51,f20])).
% 1.75/1.49 thf(f20,plain,(
% 1.75/1.49 ((cP_1 @ c @ c) = $true)),
% 1.75/1.49 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.49 thf(f51,plain,(
% 1.75/1.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_1 @ c @ X2) != $true) | ((cP_2 @ X2 @ X0) != $true) | ((cP_3 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 1.75/1.49 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.75/1.49 thf(f50,plain,(
% 1.75/1.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((cP_2 @ X2 @ X0) != $true) | ((cP_3 @ X0 @ X1) != $true) | ((cP_1 @ c @ X2) != $true)) ) | ~spl0_2),
% 1.75/1.49 inference(superposition,[status(thm)],[f49,f22])).
% 1.75/1.49 thf(f49,plain,(
% 1.75/1.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_3 @ (f @ X1) @ X2) != $true) | ((cP_1 @ c @ X0) != $true) | ((cP_2 @ X0 @ X1) != $true)) ) | ~spl0_2),
% 1.75/1.49 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.75/1.49 thf(f48,plain,(
% 1.75/1.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_2 @ X0 @ X1) != $true) | ((cP_3 @ (f @ X1) @ X2) != $true) | ((cP_1 @ c @ X0) != $true) | ($true != $true)) ) | ~spl0_2),
% 1.75/1.49 inference(superposition,[status(thm)],[f47,f21])).
% 1.75/1.49 thf(f47,plain,(
% 1.75/1.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_2 @ (f @ X0) @ X1) != $true) | ((cP_3 @ (f @ X1) @ X2) != $true) | ((cP_1 @ c @ X0) != $true)) ) | ~spl0_2),
% 1.75/1.49 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.75/1.49 thf(f46,plain,(
% 1.75/1.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_2 @ (f @ X0) @ X1) != $true) | ($true != $true) | ((cP_3 @ (f @ X1) @ X2) != $true) | ((cP_1 @ c @ X0) != $true)) ) | ~spl0_2),
% 1.75/1.49 inference(superposition,[status(thm)],[f41,f17])).
% 1.75/1.49 thf(f41,plain,(
% 1.75/1.49 ( ! [X7 : $i,X4 : $i,X5 : $i] : (((cP_1 @ (f @ c) @ X7) != $true) | ((cP_3 @ (f @ X4) @ X5) != $true) | ((cP_2 @ (f @ X7) @ X4) != $true)) ) | ~spl0_2),
% 1.75/1.49 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.75/1.49 thf(f40,definition,(
% 1.75/1.49 spl0_2 <=> ! [X4 : $i,X5 : $i,X7 : $i] : (((cP_1 @ (f @ c) @ X7) != $true) | ((cP_2 @ (f @ X7) @ X4) != $true) | ((cP_3 @ (f @ X4) @ X5) != $true))),
% 1.75/1.49 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.75/1.49 thf(f45,plain,(
% 1.75/1.49 spl0_1 | spl0_2 | spl0_3),
% 1.75/1.49 inference(avatar_split_clause,[status(thm)],[f35,f43,f40,f37])).
% 1.75/1.49 thf(f35,plain,(
% 1.75/1.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((cP_1 @ (f @ b) @ X0) != $true) | ((cP_3 @ (f @ X3) @ X8) != $true) | ((cP_1 @ (f @ a) @ X2) != $true) | ((cP_1 @ (f @ c) @ X7) != $true) | ((cP_3 @ (f @ X4) @ X5) != $true) | ((cP_2 @ (f @ X2) @ X3) != $true) | ((cP_2 @ (f @ X0) @ X1) != $true) | ((cP_3 @ (f @ X1) @ X6) != $true) | ((cP_2 @ (f @ X7) @ X4) != $true)) )),
% 1.75/1.49 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.75/1.49 thf(f34,plain,(
% 1.75/1.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((cP_2 @ (f @ X2) @ X3) != $true) | ($true != $true) | ((cP_1 @ (f @ b) @ X0) != $true) | ((cP_3 @ (f @ X1) @ X6) != $true) | ((cP_2 @ (f @ X7) @ X4) != $true) | ((cP_1 @ (f @ a) @ X2) != $true) | ((cP_1 @ (f @ c) @ X7) != $true) | ((cP_3 @ (f @ X3) @ X8) != $true) | ((cP_3 @ (f @ X4) @ X5) != $true) | ((cP_2 @ (f @ X0) @ X1) != $true)) )),
% 1.75/1.49 inference(superposition,[status(thm)],[f33,f27])).
% 1.75/1.49 thf(f27,plain,(
% 1.75/1.49 ((cQ_1 @ a @ b @ c) = $true)),
% 1.75/1.49 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.49 thf(f33,plain,(
% 1.75/1.49 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((cQ_1 @ X9 @ X11 @ X10) != $true) | ((cP_2 @ (f @ X1) @ X3) != $true) | ((cP_2 @ (f @ X0) @ X7) != $true) | ((cP_1 @ (f @ X11) @ X1) != $true) | ((cP_3 @ (f @ X5) @ X6) != $true) | ((cP_3 @ (f @ X3) @ X4) != $true) | ((cP_2 @ (f @ X2) @ X5) != $true) | ((cP_3 @ (f @ X7) @ X8) != $true) | ((cP_1 @ (f @ X9) @ X0) != $true) | ((cP_1 @ (f @ X10) @ X2) != $true)) )),
% 1.75/1.49 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.75/1.49 thf(f32,plain,(
% 1.75/1.49 ( ! [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_1 @ (f @ X9) @ X0) != $true) | ((cP_2 @ (f @ X2) @ X5) != $true) | ((cP_2 @ (f @ X0) @ X7) != $true) | ((cP_3 @ (f @ X7) @ X8) != $true) | ((cP_3 @ (f @ X3) @ X4) != $true) | ((cP_1 @ (f @ X10) @ X2) != $true) | ($true != $true) | ((cP_1 @ (f @ X11) @ X1) != $true) | ((cP_3 @ (f @ X5) @ X6) != $true) | ((cP_2 @ (f @ X1) @ X3) != $true) | ((cQ_1 @ X9 @ X11 @ X10) != $true)) )),
% 1.75/1.49 inference(superposition,[status(thm)],[f31,f23])).
% 1.75/1.49 thf(f23,plain,(
% 1.75/1.49 ( ! [X2 : $i,X3 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((cQ_2 @ X4 @ X7 @ X3) = $true) | ((cP_1 @ (f @ X6) @ X4) != $true) | ((cP_1 @ (f @ X5) @ X3) != $true) | ((cP_1 @ (f @ X2) @ X7) != $true) | ((cQ_1 @ X6 @ X2 @ X5) != $true)) )),
% 1.75/1.49 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.49 thf(f31,plain,(
% 1.75/1.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((cQ_2 @ X6 @ X7 @ X8) != $true) | ((cP_2 @ (f @ X7) @ X1) != $true) | ((cP_3 @ (f @ X1) @ X5) != $true) | ((cP_3 @ (f @ X2) @ X3) != $true) | ((cP_3 @ (f @ X0) @ X4) != $true) | ((cP_2 @ (f @ X8) @ X2) != $true) | ((cP_2 @ (f @ X6) @ X0) != $true)) )),
% 1.75/1.49 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.75/1.49 thf(f30,plain,(
% 1.75/1.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((cP_3 @ (f @ X2) @ X3) != $true) | ((cP_2 @ (f @ X8) @ X2) != $true) | ((cP_3 @ (f @ X0) @ X4) != $true) | ((cP_3 @ (f @ X1) @ X5) != $true) | ((cP_2 @ (f @ X7) @ X1) != $true) | ((cQ_2 @ X6 @ X7 @ X8) != $true) | ((cP_2 @ (f @ X6) @ X0) != $true)) )),
% 1.75/1.49 inference(superposition,[status(thm)],[f29,f12])).
% 1.75/1.49 thf(f12,plain,(
% 1.75/1.49 ( ! [X21 : $i,X18 : $i,X19 : $i,X17 : $i,X22 : $i,X20 : $i] : (((cQ_3 @ X18 @ X17 @ X21) = $true) | ((cQ_2 @ X22 @ X19 @ X20) != $true) | ((cP_2 @ (f @ X20) @ X21) != $true) | ((cP_2 @ (f @ X19) @ X17) != $true) | ((cP_2 @ (f @ X22) @ X18) != $true)) )),
% 1.75/1.49 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.49 thf(f29,plain,(
% 1.75/1.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cQ_3 @ X3 @ X4 @ X5) != $true) | ($true != (cP_3 @ (f @ X5) @ X2)) | ((cP_3 @ (f @ X3) @ X0) != $true) | ($true != (cP_3 @ (f @ X4) @ X1))) )),
% 1.75/1.49 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.75/1.49 thf(f28,plain,(
% 1.75/1.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != (cP_3 @ (f @ X4) @ X1)) | ((cQ_3 @ X3 @ X4 @ X5) != $true) | ((cP_3 @ (f @ X3) @ X0) != $true) | ($true != $true) | ($true != (cP_3 @ (f @ X5) @ X2))) )),
% 1.75/1.49 inference(superposition,[status(thm)],[f15,f8])).
% 1.75/1.49 thf(f8,plain,(
% 1.75/1.49 ( ! [X28 : $i,X29 : $i,X26 : $i,X27 : $i,X24 : $i,X25 : $i] : (((cQ_4 @ X24 @ X28 @ X29) = $true) | ((cP_3 @ (f @ X25) @ X24) != $true) | ((cQ_3 @ X25 @ X26 @ X27) != $true) | ($true != (cP_3 @ (f @ X26) @ X28)) | ((cP_3 @ (f @ X27) @ X29) != $true)) )),
% 1.75/1.49 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.49 thf(f15,plain,(
% 1.75/1.49 ( ! [X16 : $i,X14 : $i,X15 : $i] : (((cQ_4 @ X16 @ X15 @ X14) != $true)) )),
% 1.75/1.49 inference(cnf_transformation,[status(thm)],[f7])).
% 1.75/1.49 % SZS output end Proof for DTF2THF_15428
% 1.75/1.49 % (15526)------------------------------
% 1.75/1.49 % (15526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.49 % (15526)Termination reason: Refutation
% 1.75/1.49
% 1.75/1.49 % (15526)Memory used [KB]: 5756
% 1.75/1.49 % (15526)Time elapsed: 0.016 s
% 1.75/1.49 % (15526)Instructions burned: 20 (million)
% 1.75/1.49 % (15526)------------------------------
% 1.75/1.49 % (15526)------------------------------
% 1.75/1.49 % (15525)Success in time 0.03 s
%------------------------------------------------------------------------------