%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV127^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 09:40:21 AM UTC 2026
% Result : Theorem 1.84s 1.54s
% Output : Refutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 84 ( 4 unt; 0 typ; 7 def)
% Number of atoms : 1149 ( 393 equ; 0 cnn)
% Maximal formula atoms : 32 ( 13 avg)
% Number of connectives : 1642 ( 236 ~; 315 |; 74 &; 969 @)
% ( 7 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 268 ( 268 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 11 con; 0-2 aty)
% Number of variables : 242 ( 0 ^; 172 !; 70 ?; 242 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_5,type,
sK0: a > a > $o ).
thf(func_def_6,type,
sK1: a > a > $o ).
thf(func_def_7,type,
sK2: ( a > a > $o ) > $o ).
thf(func_def_8,type,
sK3: a ).
thf(func_def_9,type,
sK4: a ).
thf(func_def_10,type,
sK5: a > a > $o ).
thf(func_def_11,type,
sK6: ( a > a > $o ) > a ).
thf(func_def_12,type,
sK7: ( a > a > $o ) > a ).
thf(func_def_13,type,
sK8: ( a > a > $o ) > a ).
thf(func_def_14,type,
sK9: ( a > a > $o ) > a ).
thf(func_def_15,type,
sK10: ( a > a > $o ) > a ).
thf(func_def_16,type,
sK11: ( a > a > $o ) > a ).
thf(func_def_18,type,
ph13:
!>[X0: $tType] : X0 ).
thf(f105,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f33,f40,f51,f78,f81,f87,f90,f95,f104]) ).
thf(f104,plain,
( spl12_6
| spl12_2
| ~ spl12_7 ),
inference(avatar_split_clause,[status(thm)],[f103,f85,f30,f59]) ).
thf(f59,definition,
( spl12_6
<=> ( ( sK5 @ ( sK7 @ sK5 ) @ ( sK6 @ sK5 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_6])],[avatar_definition]) ).
thf(f30,definition,
( spl12_2
<=> ( $true
= ( sK0 @ ( sK11 @ sK5 ) @ ( sK10 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl12_2])],[avatar_definition]) ).
thf(f85,definition,
( spl12_7
<=> ! [X0: a > a > $o] :
( ( $true
= ( X0 @ ( sK7 @ sK5 ) @ ( sK6 @ sK5 ) ) )
| ( $true
= ( sK0 @ ( sK11 @ X0 ) @ ( sK10 @ X0 ) ) )
| ( $true
!= ( sK2 @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl12_7])],[avatar_definition]) ).
thf(f103,plain,
( ( $true
= ( sK0 @ ( sK11 @ sK5 ) @ ( sK10 @ sK5 ) ) )
| ( ( sK5 @ ( sK7 @ sK5 ) @ ( sK6 @ sK5 ) )
= $true )
| ~ spl12_7 ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
( ( ( sK5 @ ( sK7 @ sK5 ) @ ( sK6 @ sK5 ) )
= $true )
| ( $true != $true )
| ( $true
= ( sK0 @ ( sK11 @ sK5 ) @ ( sK10 @ sK5 ) ) )
| ~ spl12_7 ),
inference(superposition,[status(thm)],[f86,f20]) ).
thf(f20,plain,
( $true
= ( sK2 @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X6: a,X7: a] :
( ( ( $true
!= ( sK0 @ X7 @ X6 ) )
& ( $true
!= ( sK1 @ X7 @ X6 ) ) )
| ( ( sK5 @ X7 @ X6 )
= $true ) )
& ( $true
!= ( sK5 @ sK3 @ sK4 ) )
& ( $true
= ( sK2 @ sK5 ) )
& ! [X8: a > a > $o] :
( ( $true
!= ( sK2 @ X8 ) )
| ( $true
= ( X8 @ sK3 @ sK4 ) )
| ( ( $true
!= ( X8 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) ) )
& ( ! [X11: a > a > $o] :
( ( ( X11 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) )
= $true )
| ( ( $true
!= ( X11 @ ( sK8 @ X11 ) @ ( sK9 @ X11 ) ) )
& ( $true
= ( sK1 @ ( sK8 @ X11 ) @ ( sK9 @ X11 ) ) ) )
| ( $true
!= ( sK2 @ X11 ) ) )
| ! [X14: a > a > $o] :
( ( $true
!= ( sK2 @ X14 ) )
| ( ( $true
!= ( X14 @ ( sK11 @ X14 ) @ ( sK10 @ X14 ) ) )
& ( $true
= ( sK0 @ ( sK11 @ X14 ) @ ( sK10 @ X14 ) ) ) )
| ( $true
= ( X14 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f8,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > a > $o,X1: a > a > $o,X2: ( a > a > $o ) > $o,X3: a,X4: a] :
( ? [X5: a > a > $o] :
( ! [X6: a,X7: a] :
( ( ( $true
!= ( X0 @ X7 @ X6 ) )
& ( $true
!= ( X1 @ X7 @ X6 ) ) )
| ( ( X5 @ X7 @ X6 )
= $true ) )
& ( ( X5 @ X3 @ X4 )
!= $true )
& ( ( X2 @ X5 )
= $true ) )
& ! [X8: a > a > $o] :
( ( $true
!= ( X2 @ X8 ) )
| ( ( X8 @ X3 @ X4 )
= $true )
| ? [X9: a,X10: a] :
( ( $true
!= ( X8 @ X10 @ X9 ) )
& ( ! [X11: a > a > $o] :
( ( $true
= ( X11 @ X10 @ X9 ) )
| ? [X12: a,X13: a] :
( ( $true
!= ( X11 @ X12 @ X13 ) )
& ( ( X1 @ X12 @ X13 )
= $true ) )
| ( ( X2 @ X11 )
!= $true ) )
| ! [X14: a > a > $o] :
( ( $true
!= ( X2 @ X14 ) )
| ? [X15: a,X16: a] :
( ( $true
!= ( X14 @ X16 @ X15 ) )
& ( $true
= ( X0 @ X16 @ X15 ) ) )
| ( $true
= ( X14 @ X10 @ X9 ) ) ) ) ) ) )
=> ( ? [X5: a > a > $o] :
( ! [X7: a,X6: a] :
( ( ( $true
!= ( sK0 @ X7 @ X6 ) )
& ( $true
!= ( sK1 @ X7 @ X6 ) ) )
| ( ( X5 @ X7 @ X6 )
= $true ) )
& ( $true
!= ( X5 @ sK3 @ sK4 ) )
& ( $true
= ( sK2 @ X5 ) ) )
& ! [X8: a > a > $o] :
( ( $true
!= ( sK2 @ X8 ) )
| ( $true
= ( X8 @ sK3 @ sK4 ) )
| ? [X10: a,X9: a] :
( ( $true
!= ( X8 @ X10 @ X9 ) )
& ( ! [X11: a > a > $o] :
( ( $true
= ( X11 @ X10 @ X9 ) )
| ? [X13: a,X12: a] :
( ( $true
!= ( X11 @ X12 @ X13 ) )
& ( $true
= ( sK1 @ X12 @ X13 ) ) )
| ( $true
!= ( sK2 @ X11 ) ) )
| ! [X14: a > a > $o] :
( ( $true
!= ( sK2 @ X14 ) )
| ? [X16: a,X15: a] :
( ( $true
!= ( X14 @ X16 @ X15 ) )
& ( $true
= ( sK0 @ X16 @ X15 ) ) )
| ( $true
= ( X14 @ X10 @ X9 ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X5: a > a > $o] :
( ! [X7: a,X6: a] :
( ( ( $true
!= ( sK0 @ X7 @ X6 ) )
& ( $true
!= ( sK1 @ X7 @ X6 ) ) )
| ( ( X5 @ X7 @ X6 )
= $true ) )
& ( $true
!= ( X5 @ sK3 @ sK4 ) )
& ( $true
= ( sK2 @ X5 ) ) )
=> ( ! [X7: a,X6: a] :
( ( ( $true
!= ( sK0 @ X7 @ X6 ) )
& ( $true
!= ( sK1 @ X7 @ X6 ) ) )
| ( ( sK5 @ X7 @ X6 )
= $true ) )
& ( $true
!= ( sK5 @ sK3 @ sK4 ) )
& ( $true
= ( sK2 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X8: a > a > $o] :
( ? [X10: a,X9: a] :
( ( $true
!= ( X8 @ X10 @ X9 ) )
& ( ! [X11: a > a > $o] :
( ( $true
= ( X11 @ X10 @ X9 ) )
| ? [X13: a,X12: a] :
( ( $true
!= ( X11 @ X12 @ X13 ) )
& ( $true
= ( sK1 @ X12 @ X13 ) ) )
| ( $true
!= ( sK2 @ X11 ) ) )
| ! [X14: a > a > $o] :
( ( $true
!= ( sK2 @ X14 ) )
| ? [X16: a,X15: a] :
( ( $true
!= ( X14 @ X16 @ X15 ) )
& ( $true
= ( sK0 @ X16 @ X15 ) ) )
| ( $true
= ( X14 @ X10 @ X9 ) ) ) ) )
=> ( ( $true
!= ( X8 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) ) )
& ( ! [X11: a > a > $o] :
( ( ( X11 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) )
= $true )
| ? [X13: a,X12: a] :
( ( $true
!= ( X11 @ X12 @ X13 ) )
& ( $true
= ( sK1 @ X12 @ X13 ) ) )
| ( $true
!= ( sK2 @ X11 ) ) )
| ! [X14: a > a > $o] :
( ( $true
!= ( sK2 @ X14 ) )
| ? [X16: a,X15: a] :
( ( $true
!= ( X14 @ X16 @ X15 ) )
& ( $true
= ( sK0 @ X16 @ X15 ) ) )
| ( $true
= ( X14 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X11: a > a > $o] :
( ? [X13: a,X12: a] :
( ( $true
!= ( X11 @ X12 @ X13 ) )
& ( $true
= ( sK1 @ X12 @ X13 ) ) )
=> ( ( $true
!= ( X11 @ ( sK8 @ X11 ) @ ( sK9 @ X11 ) ) )
& ( $true
= ( sK1 @ ( sK8 @ X11 ) @ ( sK9 @ X11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X14: a > a > $o] :
( ? [X16: a,X15: a] :
( ( $true
!= ( X14 @ X16 @ X15 ) )
& ( $true
= ( sK0 @ X16 @ X15 ) ) )
=> ( ( $true
!= ( X14 @ ( sK11 @ X14 ) @ ( sK10 @ X14 ) ) )
& ( $true
= ( sK0 @ ( sK11 @ X14 ) @ ( sK10 @ X14 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > a > $o,X1: a > a > $o,X2: ( a > a > $o ) > $o,X3: a,X4: a] :
( ? [X5: a > a > $o] :
( ! [X6: a,X7: a] :
( ( ( $true
!= ( X0 @ X7 @ X6 ) )
& ( $true
!= ( X1 @ X7 @ X6 ) ) )
| ( ( X5 @ X7 @ X6 )
= $true ) )
& ( ( X5 @ X3 @ X4 )
!= $true )
& ( ( X2 @ X5 )
= $true ) )
& ! [X8: a > a > $o] :
( ( $true
!= ( X2 @ X8 ) )
| ( ( X8 @ X3 @ X4 )
= $true )
| ? [X9: a,X10: a] :
( ( $true
!= ( X8 @ X10 @ X9 ) )
& ( ! [X11: a > a > $o] :
( ( $true
= ( X11 @ X10 @ X9 ) )
| ? [X12: a,X13: a] :
( ( $true
!= ( X11 @ X12 @ X13 ) )
& ( ( X1 @ X12 @ X13 )
= $true ) )
| ( ( X2 @ X11 )
!= $true ) )
| ! [X14: a > a > $o] :
( ( $true
!= ( X2 @ X14 ) )
| ? [X15: a,X16: a] :
( ( $true
!= ( X14 @ X16 @ X15 ) )
& ( $true
= ( X0 @ X16 @ X15 ) ) )
| ( $true
= ( X14 @ X10 @ X9 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: a > a > $o,X0: a > a > $o,X4: ( a > a > $o ) > $o,X3: a,X2: a] :
( ? [X14: a > a > $o] :
( ! [X16: a,X15: a] :
( ( ( $true
!= ( X1 @ X15 @ X16 ) )
& ( $true
!= ( X0 @ X15 @ X16 ) ) )
| ( $true
= ( X14 @ X15 @ X16 ) ) )
& ( $true
!= ( X14 @ X3 @ X2 ) )
& ( $true
= ( X4 @ X14 ) ) )
& ! [X5: a > a > $o] :
( ( ( X4 @ X5 )
!= $true )
| ( $true
= ( X5 @ X3 @ X2 ) )
| ? [X7: a,X6: a] :
( ( ( X5 @ X6 @ X7 )
!= $true )
& ( ! [X11: a > a > $o] :
( ( ( X11 @ X6 @ X7 )
= $true )
| ? [X13: a,X12: a] :
( ( $true
!= ( X11 @ X13 @ X12 ) )
& ( $true
= ( X0 @ X13 @ X12 ) ) )
| ( $true
!= ( X4 @ X11 ) ) )
| ! [X8: a > a > $o] :
( ( $true
!= ( X4 @ X8 ) )
| ? [X10: a,X9: a] :
( ( ( X8 @ X9 @ X10 )
!= $true )
& ( ( X1 @ X9 @ X10 )
= $true ) )
| ( ( X8 @ X6 @ X7 )
= $true ) ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X3: a,X1: a > a > $o,X4: ( a > a > $o ) > $o,X0: a > a > $o,X2: a] :
( ? [X14: a > a > $o] :
( ( $true
!= ( X14 @ X3 @ X2 ) )
& ( $true
= ( X4 @ X14 ) )
& ! [X16: a,X15: a] :
( ( ( $true
!= ( X1 @ X15 @ X16 ) )
& ( $true
!= ( X0 @ X15 @ X16 ) ) )
| ( $true
= ( X14 @ X15 @ X16 ) ) ) )
& ! [X5: a > a > $o] :
( ( $true
= ( X5 @ X3 @ X2 ) )
| ? [X6: a,X7: a] :
( ( ( X5 @ X6 @ X7 )
!= $true )
& ( ! [X8: a > a > $o] :
( ( ( X8 @ X6 @ X7 )
= $true )
| ( $true
!= ( X4 @ X8 ) )
| ? [X10: a,X9: a] :
( ( ( X8 @ X9 @ X10 )
!= $true )
& ( ( X1 @ X9 @ X10 )
= $true ) ) )
| ! [X11: a > a > $o] :
( ( ( X11 @ X6 @ X7 )
= $true )
| ( $true
!= ( X4 @ X11 ) )
| ? [X13: a,X12: a] :
( ( $true
!= ( X11 @ X13 @ X12 ) )
& ( $true
= ( X0 @ X13 @ X12 ) ) ) ) ) )
| ( ( X4 @ X5 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X3: a,X1: a > a > $o,X4: ( a > a > $o ) > $o,X0: a > a > $o,X2: a] :
( ! [X5: a > a > $o] :
( ( ! [X6: a,X7: a] :
( ( ! [X8: a > a > $o] :
( ( ( $true
= ( X4 @ X8 ) )
& ! [X9: a,X10: a] :
( ( ( X1 @ X9 @ X10 )
= $true )
=> ( ( X8 @ X9 @ X10 )
= $true ) ) )
=> ( ( X8 @ X6 @ X7 )
= $true ) )
| ! [X11: a > a > $o] :
( ( ( $true
= ( X4 @ X11 ) )
& ! [X13: a,X12: a] :
( ( $true
= ( X0 @ X13 @ X12 ) )
=> ( $true
= ( X11 @ X13 @ X12 ) ) ) )
=> ( ( X11 @ X6 @ X7 )
= $true ) ) )
=> ( ( X5 @ X6 @ X7 )
= $true ) )
& ( ( X4 @ X5 )
= $true ) )
=> ( $true
= ( X5 @ X3 @ X2 ) ) )
=> ! [X14: a > a > $o] :
( ( ( $true
= ( X4 @ X14 ) )
& ! [X15: a,X16: a] :
( ( ( $true
= ( X0 @ X15 @ X16 ) )
| ( $true
= ( X1 @ X15 @ X16 ) ) )
=> ( $true
= ( X14 @ X15 @ X16 ) ) ) )
=> ( $true
= ( X14 @ X3 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a > a > $o,X2: a,X3: a,X4: ( a > a > $o ) > $o] :
( ! [X5: a > a > $o] :
( ( ( X4 @ X5 )
& ! [X6: a,X7: a] :
( ( ! [X8: a > a > $o] :
( ( ( X4 @ X8 )
& ! [X9: a,X10: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X6 @ X7 ) )
| ! [X11: a > a > $o] :
( ( ! [X12: a,X13: a] :
( ( X0 @ X13 @ X12 )
=> ( X11 @ X13 @ X12 ) )
& ( X4 @ X11 ) )
=> ( X11 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X2 ) )
=> ! [X14: a > a > $o] :
( ( ! [X15: a,X16: a] :
( ( ( X1 @ X15 @ X16 )
| ( X0 @ X15 @ X16 ) )
=> ( X14 @ X15 @ X16 ) )
& ( X4 @ X14 ) )
=> ( X14 @ X3 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > a > $o,X2: a > a > $o,X4: a,X3: a,X0: ( a > a > $o ) > $o] :
( ! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X6: a,X7: a] :
( ( ! [X8: a > a > $o] :
( ( ( X0 @ X8 )
& ! [X9: a,X10: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X6 @ X7 ) )
| ! [X8: a > a > $o] :
( ( ! [X10: a,X9: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ! [X5: a > a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X2 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
& ( X0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > a > $o,X2: a > a > $o,X4: a,X3: a,X0: ( a > a > $o ) > $o] :
( ! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X6: a,X7: a] :
( ( ! [X8: a > a > $o] :
( ( ( X0 @ X8 )
& ! [X9: a,X10: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X6 @ X7 ) )
| ! [X8: a > a > $o] :
( ( ! [X10: a,X9: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ! [X5: a > a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X2 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
& ( X0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qWSWpOFhzg/DTF2THF_15619.p',cTHM252A_pme) ).
thf(f86,plain,
( ! [X0: a > a > $o] :
( ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( sK0 @ ( sK11 @ X0 ) @ ( sK10 @ X0 ) ) )
| ( $true
= ( X0 @ ( sK7 @ sK5 ) @ ( sK6 @ sK5 ) ) ) )
| ~ spl12_7 ),
inference(avatar_component_clause,[status(thm)],[f85]) ).
thf(f95,plain,
( spl12_5
| ~ spl12_6 ),
inference(avatar_split_clause,[status(thm)],[f94,f59,f55]) ).
thf(f55,definition,
( spl12_5
<=> ( $true
= ( sK5 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl12_5])],[avatar_definition]) ).
thf(f94,plain,
( ( $true
= ( sK5 @ sK3 @ sK4 ) )
| ~ spl12_6 ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $true != $true )
| ( $true
= ( sK5 @ sK3 @ sK4 ) )
| ~ spl12_6 ),
inference(forward_demodulation,[status(thm)],[f92,f20]) ).
thf(f92,plain,
( ( $true
!= ( sK2 @ sK5 ) )
| ( $true
= ( sK5 @ sK3 @ sK4 ) )
| ~ spl12_6 ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
( ( $true
= ( sK5 @ sK3 @ sK4 ) )
| ( $true != $true )
| ( $true
!= ( sK2 @ sK5 ) )
| ~ spl12_6 ),
inference(superposition,[status(thm)],[f19,f61]) ).
thf(f61,plain,
( ( ( sK5 @ ( sK7 @ sK5 ) @ ( sK6 @ sK5 ) )
= $true )
| ~ spl12_6 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f19,plain,
! [X8: a > a > $o] :
( ( $true
!= ( X8 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) ) )
| ( $true
= ( X8 @ sK3 @ sK4 ) )
| ( $true
!= ( sK2 @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f90,plain,
( spl12_5
| spl12_6
| ~ spl12_3 ),
inference(avatar_split_clause,[status(thm)],[f89,f45,f59,f55]) ).
thf(f45,definition,
( spl12_3
<=> ! [X0: a > a > $o] :
( ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true
= ( X0 @ sK3 @ sK4 ) )
| ( $true
!= ( sK2 @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl12_3])],[avatar_definition]) ).
thf(f89,plain,
( ( $true
= ( sK5 @ sK3 @ sK4 ) )
| ( ( sK5 @ ( sK7 @ sK5 ) @ ( sK6 @ sK5 ) )
= $true )
| ~ spl12_3 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $true
= ( sK5 @ sK3 @ sK4 ) )
| ( $true != $true )
| ( ( sK5 @ ( sK7 @ sK5 ) @ ( sK6 @ sK5 ) )
= $true )
| ~ spl12_3 ),
inference(superposition,[status(thm)],[f46,f20]) ).
thf(f46,plain,
( ! [X0: a > a > $o] :
( ( $true
!= ( sK2 @ X0 ) )
| ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true
= ( X0 @ sK3 @ sK4 ) ) )
| ~ spl12_3 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f87,plain,
( spl12_6
| spl12_7
| spl12_5
| ~ spl12_4 ),
inference(avatar_split_clause,[status(thm)],[f83,f48,f55,f85,f59]) ).
thf(f48,definition,
( spl12_4
<=> ( $true
= ( sK1 @ ( sK8 @ sK5 ) @ ( sK9 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl12_4])],[avatar_definition]) ).
thf(f83,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK5 @ sK3 @ sK4 ) )
| ( $true
= ( X0 @ ( sK7 @ sK5 ) @ ( sK6 @ sK5 ) ) )
| ( $true
!= ( sK2 @ X0 ) )
| ( ( sK5 @ ( sK7 @ sK5 ) @ ( sK6 @ sK5 ) )
= $true )
| ( $true
= ( sK0 @ ( sK11 @ X0 ) @ ( sK10 @ X0 ) ) ) )
| ~ spl12_4 ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( X0 @ ( sK7 @ sK5 ) @ ( sK6 @ sK5 ) ) )
| ( $true != $true )
| ( ( sK5 @ ( sK7 @ sK5 ) @ ( sK6 @ sK5 ) )
= $true )
| ( $true
= ( sK0 @ ( sK11 @ X0 ) @ ( sK10 @ X0 ) ) )
| ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( sK5 @ sK3 @ sK4 ) ) )
| ~ spl12_4 ),
inference(superposition,[status(thm)],[f72,f20]) ).
thf(f72,plain,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
!= ( sK2 @ X1 ) )
| ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( sK5 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( $true
= ( sK0 @ ( sK11 @ X0 ) @ ( sK10 @ X0 ) ) )
| ( ( X0 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) )
= $true )
| ( $true
= ( X1 @ sK3 @ sK4 ) ) )
| ~ spl12_4 ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK3 @ sK4 ) )
| ( $true
!= ( sK2 @ X0 ) )
| ( $true != $true )
| ( ( X0 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) )
= $true )
| ( $true
!= ( sK2 @ X1 ) )
| ( $true
= ( sK5 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( $true
= ( sK0 @ ( sK11 @ X0 ) @ ( sK10 @ X0 ) ) ) )
| ~ spl12_4 ),
inference(forward_demodulation,[status(thm)],[f70,f20]) ).
thf(f70,plain,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( sK5 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( $true
!= ( sK2 @ X1 ) )
| ( $true
= ( X1 @ sK3 @ sK4 ) )
| ( ( X0 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) )
= $true )
| ( $true
= ( sK0 @ ( sK11 @ X0 ) @ ( sK10 @ X0 ) ) )
| ( $true
!= ( sK2 @ sK5 ) ) )
| ~ spl12_4 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( X1 @ sK3 @ sK4 ) )
| ( $true
= ( sK5 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( $true
= ( sK0 @ ( sK11 @ X0 ) @ ( sK10 @ X0 ) ) )
| ( $true
!= ( sK2 @ sK5 ) )
| ( ( X0 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) )
= $true )
| ( $true
!= ( sK2 @ X1 ) )
| ( $true != $true ) )
| ~ spl12_4 ),
inference(superposition,[status(thm)],[f17,f64]) ).
thf(f64,plain,
( ( $true
= ( sK5 @ ( sK8 @ sK5 ) @ ( sK9 @ sK5 ) ) )
| ~ spl12_4 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true
= ( sK5 @ ( sK8 @ sK5 ) @ ( sK9 @ sK5 ) ) )
| ( $true != $true )
| ~ spl12_4 ),
inference(superposition,[status(thm)],[f22,f50]) ).
thf(f50,plain,
( ( $true
= ( sK1 @ ( sK8 @ sK5 ) @ ( sK9 @ sK5 ) ) )
| ~ spl12_4 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f22,plain,
! [X6: a,X7: a] :
( ( $true
!= ( sK1 @ X7 @ X6 ) )
| ( ( sK5 @ X7 @ X6 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f17,plain,
! [X11: a > a > $o,X8: a > a > $o,X14: a > a > $o] :
( ( $true
!= ( X11 @ ( sK8 @ X11 ) @ ( sK9 @ X11 ) ) )
| ( $true
= ( X14 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) ) )
| ( $true
= ( X8 @ sK3 @ sK4 ) )
| ( ( X11 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) )
= $true )
| ( $true
!= ( sK2 @ X11 ) )
| ( $true
!= ( sK2 @ X8 ) )
| ( $true
= ( sK0 @ ( sK11 @ X14 ) @ ( sK10 @ X14 ) ) )
| ( $true
!= ( sK2 @ X14 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f81,plain,
~ spl12_5,
inference(avatar_contradiction_clause,[status(thm)],[f80]) ).
thf(f80,plain,
( $false
| ~ spl12_5 ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $true != $true )
| ~ spl12_5 ),
inference(superposition,[status(thm)],[f21,f57]) ).
thf(f57,plain,
( ( $true
= ( sK5 @ sK3 @ sK4 ) )
| ~ spl12_5 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f21,plain,
( $true
!= ( sK5 @ sK3 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f78,plain,
( spl12_3
| ~ spl12_2
| ~ spl12_4 ),
inference(avatar_split_clause,[status(thm)],[f77,f48,f30,f45]) ).
thf(f77,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( X0 @ sK3 @ sK4 ) )
| ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true
!= ( sK2 @ X0 ) ) )
| ~ spl12_2
| ~ spl12_4 ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ! [X0: a > a > $o] :
( ( $true
!= ( sK2 @ X0 ) )
| ( $true != $true )
| ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true
= ( X0 @ sK3 @ sK4 ) ) )
| ~ spl12_2
| ~ spl12_4 ),
inference(forward_demodulation,[status(thm)],[f75,f20]) ).
thf(f75,plain,
( ! [X0: a > a > $o] :
( ( $true
!= ( sK2 @ X0 ) )
| ( $true
!= ( sK2 @ sK5 ) )
| ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true
= ( X0 @ sK3 @ sK4 ) ) )
| ~ spl12_2
| ~ spl12_4 ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( X0 @ sK3 @ sK4 ) )
| ( $true
!= ( sK2 @ sK5 ) )
| ( $true
!= ( sK2 @ X0 ) )
| ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true != $true ) )
| ~ spl12_2
| ~ spl12_4 ),
inference(duplicate_literal_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ! [X0: a > a > $o] :
( ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true
= ( X0 @ sK3 @ sK4 ) )
| ( $true != $true )
| ( $true
!= ( sK2 @ sK5 ) )
| ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true
!= ( sK2 @ X0 ) ) )
| ~ spl12_2
| ~ spl12_4 ),
inference(superposition,[status(thm)],[f68,f64]) ).
thf(f68,plain,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
!= ( X0 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( X0 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) )
= $true )
| ( $true
!= ( sK2 @ X1 ) )
| ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( sK5 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( $true
= ( X1 @ sK3 @ sK4 ) ) )
| ~ spl12_2 ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK3 @ sK4 ) )
| ( $true
!= ( sK2 @ X0 ) )
| ( $true
!= ( sK2 @ X1 ) )
| ( $true
= ( sK5 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( X0 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) )
= $true )
| ( $true
!= ( X0 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( $true != $true ) )
| ~ spl12_2 ),
inference(forward_demodulation,[status(thm)],[f66,f20]) ).
thf(f66,plain,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
!= ( sK2 @ X0 ) )
| ( $true
!= ( X0 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( $true
= ( X1 @ sK3 @ sK4 ) )
| ( $true
= ( sK5 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( $true
!= ( sK2 @ sK5 ) )
| ( ( X0 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) )
= $true )
| ( $true
!= ( sK2 @ X1 ) ) )
| ~ spl12_2 ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK3 @ sK4 ) )
| ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( sK5 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( X0 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) )
= $true )
| ( $true != $true )
| ( $true
!= ( sK2 @ X1 ) )
| ( $true
!= ( X0 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( $true
!= ( sK2 @ sK5 ) ) )
| ~ spl12_2 ),
inference(superposition,[status(thm)],[f18,f35]) ).
thf(f35,plain,
( ( $true
= ( sK5 @ ( sK11 @ sK5 ) @ ( sK10 @ sK5 ) ) )
| ~ spl12_2 ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true != $true )
| ( $true
= ( sK5 @ ( sK11 @ sK5 ) @ ( sK10 @ sK5 ) ) )
| ~ spl12_2 ),
inference(superposition,[status(thm)],[f23,f32]) ).
thf(f32,plain,
( ( $true
= ( sK0 @ ( sK11 @ sK5 ) @ ( sK10 @ sK5 ) ) )
| ~ spl12_2 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f23,plain,
! [X6: a,X7: a] :
( ( $true
!= ( sK0 @ X7 @ X6 ) )
| ( ( sK5 @ X7 @ X6 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f18,plain,
! [X11: a > a > $o,X8: a > a > $o,X14: a > a > $o] :
( ( $true
!= ( X14 @ ( sK11 @ X14 ) @ ( sK10 @ X14 ) ) )
| ( $true
!= ( X11 @ ( sK8 @ X11 ) @ ( sK9 @ X11 ) ) )
| ( $true
!= ( sK2 @ X14 ) )
| ( $true
!= ( sK2 @ X8 ) )
| ( $true
= ( X14 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) ) )
| ( $true
!= ( sK2 @ X11 ) )
| ( ( X11 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) )
= $true )
| ( $true
= ( X8 @ sK3 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f51,plain,
( spl12_3
| spl12_4
| ~ spl12_1 ),
inference(avatar_split_clause,[status(thm)],[f43,f27,f48,f45]) ).
thf(f27,definition,
( spl12_1
<=> ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) ) )
| ( $true
= ( X0 @ sK3 @ sK4 ) )
| ( $true
= ( sK1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( $true
!= ( sK2 @ X0 ) )
| ( $true
!= ( sK2 @ X1 ) )
| ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl12_1])],[avatar_definition]) ).
thf(f43,plain,
( ! [X0: a > a > $o] :
( ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true
= ( sK1 @ ( sK8 @ sK5 ) @ ( sK9 @ sK5 ) ) )
| ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( X0 @ sK3 @ sK4 ) ) )
| ~ spl12_1 ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ! [X0: a > a > $o] :
( ( $true != $true )
| ( $true
= ( X0 @ sK3 @ sK4 ) )
| ( $true
!= ( sK2 @ X0 ) )
| ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true
= ( sK1 @ ( sK8 @ sK5 ) @ ( sK9 @ sK5 ) ) ) )
| ~ spl12_1 ),
inference(duplicate_literal_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X0: a > a > $o] :
( ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true != $true )
| ( $true
= ( sK1 @ ( sK8 @ sK5 ) @ ( sK9 @ sK5 ) ) )
| ( $true
= ( X0 @ sK3 @ sK4 ) )
| ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true
!= ( sK2 @ X0 ) ) )
| ~ spl12_1 ),
inference(superposition,[status(thm)],[f28,f20]) ).
thf(f28,plain,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
!= ( sK2 @ X1 ) )
| ( $true
= ( sK1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( $true
= ( X0 @ sK3 @ sK4 ) )
| ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( X1 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) ) ) )
| ~ spl12_1 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f40,plain,
( spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[status(thm)],[f39,f30,f27]) ).
thf(f39,plain,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
= ( sK1 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( $true
= ( X1 @ sK3 @ sK4 ) )
| ( ( X0 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) )
= $true )
| ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( sK5 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( $true
!= ( sK2 @ X1 ) ) )
| ~ spl12_2 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true != $true )
| ( $true
= ( sK5 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( X0 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) )
= $true )
| ( $true
!= ( sK2 @ X1 ) )
| ( $true
= ( sK1 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( $true
= ( X1 @ sK3 @ sK4 ) )
| ( $true
!= ( sK2 @ X0 ) ) )
| ~ spl12_2 ),
inference(forward_demodulation,[status(thm)],[f37,f20]) ).
thf(f37,plain,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
!= ( sK2 @ X0 ) )
| ( $true
!= ( sK2 @ X1 ) )
| ( $true
= ( X1 @ sK3 @ sK4 ) )
| ( $true
= ( sK5 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( X0 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) )
= $true )
| ( $true
!= ( sK2 @ sK5 ) )
| ( $true
= ( sK1 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) ) )
| ~ spl12_2 ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( sK1 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( $true
= ( sK5 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( $true
!= ( sK2 @ X1 ) )
| ( $true
!= ( sK2 @ sK5 ) )
| ( $true != $true )
| ( ( X0 @ ( sK7 @ X1 ) @ ( sK6 @ X1 ) )
= $true )
| ( $true
= ( X1 @ sK3 @ sK4 ) ) )
| ~ spl12_2 ),
inference(superposition,[status(thm)],[f16,f35]) ).
thf(f16,plain,
! [X11: a > a > $o,X8: a > a > $o,X14: a > a > $o] :
( ( $true
!= ( X14 @ ( sK11 @ X14 ) @ ( sK10 @ X14 ) ) )
| ( $true
= ( sK1 @ ( sK8 @ X11 ) @ ( sK9 @ X11 ) ) )
| ( ( X11 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) )
= $true )
| ( $true
= ( X8 @ sK3 @ sK4 ) )
| ( $true
!= ( sK2 @ X11 ) )
| ( $true
!= ( sK2 @ X14 ) )
| ( $true
!= ( sK2 @ X8 ) )
| ( $true
= ( X14 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f33,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[status(thm)],[f25,f30,f27]) ).
thf(f25,plain,
! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
= ( sK0 @ ( sK11 @ sK5 ) @ ( sK10 @ sK5 ) ) )
| ( $true
= ( X1 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) ) )
| ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true )
| ( $true
!= ( sK2 @ X1 ) )
| ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( sK1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( $true
= ( X0 @ sK3 @ sK4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) ) )
| ( $true
= ( sK0 @ ( sK11 @ sK5 ) @ ( sK10 @ sK5 ) ) )
| ( $true
!= ( sK2 @ X1 ) )
| ( $true != $true )
| ( $true
= ( sK1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( $true
= ( X0 @ sK3 @ sK4 ) )
| ( $true
!= ( sK2 @ X0 ) )
| ( ( sK5 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f15,f20]) ).
thf(f15,plain,
! [X11: a > a > $o,X8: a > a > $o,X14: a > a > $o] :
( ( $true
!= ( sK2 @ X14 ) )
| ( $true
= ( sK0 @ ( sK11 @ X14 ) @ ( sK10 @ X14 ) ) )
| ( $true
= ( X14 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) ) )
| ( ( X11 @ ( sK7 @ X8 ) @ ( sK6 @ X8 ) )
= $true )
| ( $true
= ( sK1 @ ( sK8 @ X11 ) @ ( sK9 @ X11 ) ) )
| ( $true
!= ( sK2 @ X11 ) )
| ( $true
= ( X8 @ sK3 @ sK4 ) )
| ( $true
!= ( sK2 @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV127^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.36 % Computer : n005.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Tue Feb 24 12:40:44 EST 2026
% 0.17/0.37 % CPUTime :
% 0.17/0.37 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.48 ---- Original DTF file ---
% 0.29/0.48 thf(spec,logic,$$dhol).
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 % File : SEV127^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.48 % Domain : Set Theory (Relations)
% 0.29/0.48 % Problem : TPS problem from SETS-OF-RELNS-THMS
% 0.29/0.48 % Version : Especial.
% 0.29/0.48 % English :
% 0.29/0.48
% 0.29/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.48 % Source : [Bro09]
% 0.29/0.48 % Names : tps_1092 [Bro09]
% 0.29/0.48
% 0.29/0.48 % Status : Theorem
% 0.29/0.48 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.1.0, 0.33 v4.0.0
% 0.29/0.48 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.29/0.48 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.29/0.48 % Maximal formula atoms : 0 ( 0 avg)
% 0.29/0.48 % Number of connectives : 43 ( 0 ~; 2 |; 4 &; 28 @)
% 0.29/0.48 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.29/0.48 % Maximal formula depth : 22 ( 22 avg)
% 0.29/0.48 % Number of types : 2 ( 1 usr)
% 0.29/0.48 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.29/0.48 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.29/0.48 % Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% 0.29/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.48
% 0.29/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 thf(a_type,type,
% 0.29/0.48 a: $tType ).
% 0.29/0.48
% 0.29/0.48 thf(cTHM252A_pme,conjecture,
% 0.29/0.48 ! [P: ( a > a > $o ) > $o,R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.29/0.48 ( ! [Xp: a > a > $o] :
% 0.29/0.48 ( ( ! [Xx0: a,Xy0: a] :
% 0.29/0.48 ( ( ! [Xp0: a > a > $o] :
% 0.29/0.48 ( ( ! [Xx1: a,Xy1: a] :
% 0.29/0.48 ( ( R @ Xx1 @ Xy1 )
% 0.29/0.48 => ( Xp0 @ Xx1 @ Xy1 ) )
% 0.29/0.48 & ( P @ Xp0 ) )
% 0.29/0.48 => ( Xp0 @ Xx0 @ Xy0 ) )
% 0.29/0.48 | ! [Xp0: a > a > $o] :
% 0.29/0.48 ( ( ! [Xx1: a,Xy1: a] :
% 0.29/0.48 ( ( S @ Xx1 @ Xy1 )
% 0.29/0.48 => ( Xp0 @ Xx1 @ Xy1 ) )
% 0.29/0.48 & ( P @ Xp0 ) )
% 0.29/0.48 => ( Xp0 @ Xx0 @ Xy0 ) ) )
% 0.29/0.48 => ( Xp @ Xx0 @ Xy0 ) )
% 0.29/0.48 & ( P @ Xp ) )
% 0.29/0.48 => ( Xp @ Xx @ Xy ) )
% 0.29/0.48 => ! [Xp: a > a > $o] :
% 0.29/0.48 ( ( ! [Xx0: a,Xy0: a] :
% 0.29/0.48 ( ( ( R @ Xx0 @ Xy0 )
% 0.29/0.48 | ( S @ Xx0 @ Xy0 ) )
% 0.29/0.48 => ( Xp @ Xx0 @ Xy0 ) )
% 0.29/0.48 & ( P @ Xp ) )
% 0.29/0.48 => ( Xp @ Xx @ Xy ) ) ) ).
% 0.29/0.48
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 ------------------------
% 1.64/1.49 ---- Embedded in THF ---
% 1.64/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.50 %%% Generated on Tue Feb 24 12:40:46 EST 2026
% 1.64/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.50 %%% Logic specification used:
% 1.64/1.50 %%% thf(spec, logic, $$dhol).
% 1.64/1.50
% 1.64/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.qWSWpOFhzg/DTF2DTF15619.p
% See solution above
% 1.64/1.50 ------------------------
% 1.84/1.51 ---- Cleaned THF ---
% 1.84/1.51 thf(a_type,type,
% 1.84/1.51 a: $tType ).
% 1.84/1.51
% 1.84/1.51 thf(cTHM252A_pme,conjecture,
% 1.84/1.51 ! [P: ( a > a > $o ) > $o,R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 1.84/1.51 ( ! [Xp: a > a > $o] :
% 1.84/1.51 ( ( ! [Xx0: a,Xy0: a] :
% 1.84/1.51 ( ( ! [Xp0: a > a > $o] :
% 1.84/1.51 ( ( ! [Xx1: a,Xy1: a] :
% 1.84/1.51 ( ( R @ Xx1 @ Xy1 )
% 1.84/1.51 => ( Xp0 @ Xx1 @ Xy1 ) )
% 1.84/1.51 & ( P @ Xp0 ) )
% 1.84/1.51 => ( Xp0 @ Xx0 @ Xy0 ) )
% 1.84/1.51 | ! [Xp0: a > a > $o] :
% 1.84/1.51 ( ( ! [Xx1: a,Xy1: a] :
% 1.84/1.51 ( ( S @ Xx1 @ Xy1 )
% 1.84/1.51 => ( Xp0 @ Xx1 @ Xy1 ) )
% 1.84/1.51 & ( P @ Xp0 ) )
% 1.84/1.51 => ( Xp0 @ Xx0 @ Xy0 ) ) )
% 1.84/1.51 => ( Xp @ Xx0 @ Xy0 ) )
% 1.84/1.51 & ( P @ Xp ) )
% 1.84/1.51 => ( Xp @ Xx @ Xy ) )
% 1.84/1.51 => ! [Xp: a > a > $o] :
% 1.84/1.51 ( ( ! [Xx0: a,Xy0: a] :
% 1.84/1.51 ( ( ( R @ Xx0 @ Xy0 )
% 1.84/1.51 | ( S @ Xx0 @ Xy0 ) )
% 1.84/1.51 => ( Xp @ Xx0 @ Xy0 ) )
% 1.84/1.51 & ( P @ Xp ) )
% 1.84/1.51 => ( Xp @ Xx @ Xy ) ) ) ).
% 1.84/1.51 ------------------------
% 1.84/1.53 % (15717)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_15619 for (2999ds/4Mi)
% 1.84/1.53 % (15720)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_15619 for (2999ds/2Mi)
% 1.84/1.53 % (15719)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15619 for (2999ds/2Mi)
% 1.84/1.53 % (15718)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_15619 for (2999ds/27Mi)
% 1.84/1.53 % (15721)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_15619 for (2999ds/275Mi)
% 1.84/1.53 % (15722)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15619 for (2999ds/18Mi)
% 1.84/1.53 % (15716)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15619 for (2999ds/183Mi)
% 1.84/1.53 % (15720)Instruction limit reached!
% 1.84/1.53 % (15720)------------------------------
% 1.84/1.53 % (15720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.53 % (15720)Termination reason: Unknown
% 1.84/1.53 % (15720)Termination phase: shuffling
% 1.84/1.53
% 1.84/1.53 % (15720)Memory used [KB]: 1023
% 1.84/1.53 % (15720)Time elapsed: 0.002 s
% 1.84/1.53 % (15720)Instructions burned: 2 (million)
% 1.84/1.53 % (15720)------------------------------
% 1.84/1.53 % (15720)------------------------------
% 1.84/1.53 % (15717)Instruction limit reached!
% 1.84/1.53 % (15717)------------------------------
% 1.84/1.53 % (15717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.53 % (15717)Termination reason: Unknown
% 1.84/1.53 % (15717)Termination phase: Saturation
% 1.84/1.53
% 1.84/1.53 % (15717)Memory used [KB]: 5500
% 1.84/1.53 % (15717)Time elapsed: 0.004 s
% 1.84/1.53 % (15719)Instruction limit reached!
% 1.84/1.53 % (15719)------------------------------
% 1.84/1.53 % (15719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.53 % (15719)Termination reason: Unknown
% 1.84/1.53 % (15719)Termination phase: Preprocessing 3
% 1.84/1.53
% 1.84/1.53 % (15719)Memory used [KB]: 1023
% 1.84/1.53 % (15719)Time elapsed: 0.003 s
% 1.84/1.53 % (15719)Instructions burned: 2 (million)
% 1.84/1.53 % (15719)------------------------------
% 1.84/1.53 % (15719)------------------------------
% 1.84/1.53 % (15717)Instructions burned: 5 (million)
% 1.84/1.53 % (15717)------------------------------
% 1.84/1.53 % (15717)------------------------------
% 1.84/1.54 % (15722)Instruction limit reached!
% 1.84/1.54 % (15722)------------------------------
% 1.84/1.54 % (15722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.54 % (15722)Termination reason: Unknown
% 1.84/1.54 % (15722)Termination phase: Saturation
% 1.84/1.54
% 1.84/1.54 % (15722)Memory used [KB]: 5628
% 1.84/1.54 % (15722)Time elapsed: 0.012 s
% 1.84/1.54 % (15722)Instructions burned: 18 (million)
% 1.84/1.54 % (15722)------------------------------
% 1.84/1.54 % (15722)------------------------------
% 1.84/1.54 % (15718)First to succeed.
% 1.84/1.54 % (15723)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15619 for (2999ds/3Mi)
% 1.84/1.54 % (15718)Refutation found. Thanks to Tanya!
% 1.84/1.54 % SZS status Theorem for DTF2THF_15619
% 1.84/1.54 % SZS output start Proof for DTF2THF_15619
% 1.84/1.54 thf(type_def_5, type, a: $tType).
% 1.84/1.54 thf(func_def_0, type, a: $tType).
% 1.84/1.54 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.84/1.54 thf(func_def_5, type, sK0: a > a > $o).
% 1.84/1.54 thf(func_def_6, type, sK1: a > a > $o).
% 1.84/1.54 thf(func_def_7, type, sK2: (a > a > $o) > $o).
% 1.84/1.54 thf(func_def_8, type, sK3: a).
% 1.84/1.54 thf(func_def_9, type, sK4: a).
% 1.84/1.54 thf(func_def_10, type, sK5: a > a > $o).
% 1.84/1.54 thf(func_def_11, type, sK6: (a > a > $o) > a).
% 1.84/1.54 thf(func_def_12, type, sK7: (a > a > $o) > a).
% 1.84/1.54 thf(func_def_13, type, sK8: (a > a > $o) > a).
% 1.84/1.54 thf(func_def_14, type, sK9: (a > a > $o) > a).
% 1.84/1.54 thf(func_def_15, type, sK10: (a > a > $o) > a).
% 1.84/1.54 thf(func_def_16, type, sK11: (a > a > $o) > a).
% 1.84/1.54 thf(func_def_18, type, ph13: !>[X0: $tType]:(X0)).
% 1.84/1.54 thf(f105,plain,(
% 1.84/1.54 $false),
% 1.84/1.54 inference(avatar_sat_refutation,[status(thm)],[f33,f40,f51,f78,f81,f87,f90,f95,f104])).
% 1.84/1.54 thf(f104,plain,(
% 1.84/1.54 spl12_6 | spl12_2 | ~spl12_7),
% 1.84/1.54 inference(avatar_split_clause,[status(thm)],[f103,f85,f30,f59])).
% 1.84/1.54 thf(f59,definition,(
% 1.84/1.54 spl12_6 <=> ((sK5 @ (sK7 @ sK5) @ (sK6 @ sK5)) = $true)),
% 1.84/1.54 introduced(definition,[new_symbols(naming,[spl12_6])],[avatar_definition])).
% 1.84/1.54 thf(f30,definition,(
% 1.84/1.54 spl12_2 <=> ($true = (sK0 @ (sK11 @ sK5) @ (sK10 @ sK5)))),
% 1.84/1.54 introduced(definition,[new_symbols(naming,[spl12_2])],[avatar_definition])).
% 1.84/1.54 thf(f85,definition,(
% 1.84/1.54 spl12_7 <=> ! [X0 : a > a > $o] : (($true = (X0 @ (sK7 @ sK5) @ (sK6 @ sK5))) | ($true = (sK0 @ (sK11 @ X0) @ (sK10 @ X0))) | ($true != (sK2 @ X0)))),
% 1.84/1.54 introduced(definition,[new_symbols(naming,[spl12_7])],[avatar_definition])).
% 1.84/1.54 thf(f103,plain,(
% 1.84/1.54 ($true = (sK0 @ (sK11 @ sK5) @ (sK10 @ sK5))) | ((sK5 @ (sK7 @ sK5) @ (sK6 @ sK5)) = $true) | ~spl12_7),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.84/1.54 thf(f102,plain,(
% 1.84/1.54 ((sK5 @ (sK7 @ sK5) @ (sK6 @ sK5)) = $true) | ($true != $true) | ($true = (sK0 @ (sK11 @ sK5) @ (sK10 @ sK5))) | ~spl12_7),
% 1.84/1.54 inference(superposition,[status(thm)],[f86,f20])).
% 1.84/1.54 thf(f20,plain,(
% 1.84/1.54 ($true = (sK2 @ sK5))),
% 1.84/1.54 inference(cnf_transformation,[status(thm)],[f14])).
% 1.84/1.54 thf(f14,plain,(
% 1.84/1.54 (! [X6 : a,X7 : a] : ((($true != (sK0 @ X7 @ X6)) & ($true != (sK1 @ X7 @ X6))) | ((sK5 @ X7 @ X6) = $true)) & ($true != (sK5 @ sK3 @ sK4)) & ($true = (sK2 @ sK5))) & ! [X8 : a > a > $o] : (($true != (sK2 @ X8)) | ($true = (X8 @ sK3 @ sK4)) | (($true != (X8 @ (sK7 @ X8) @ (sK6 @ X8))) & (! [X11 : a > a > $o] : (((X11 @ (sK7 @ X8) @ (sK6 @ X8)) = $true) | (($true != (X11 @ (sK8 @ X11) @ (sK9 @ X11))) & ($true = (sK1 @ (sK8 @ X11) @ (sK9 @ X11)))) | ($true != (sK2 @ X11))) | ! [X14 : a > a > $o] : (($true != (sK2 @ X14)) | (($true != (X14 @ (sK11 @ X14) @ (sK10 @ X14))) & ($true = (sK0 @ (sK11 @ X14) @ (sK10 @ X14)))) | ($true = (X14 @ (sK7 @ X8) @ (sK6 @ X8)))))))),
% 1.84/1.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f8,f13,f12,f11,f10,f9])).
% 1.84/1.54 thf(f9,plain,(
% 1.84/1.54 ? [X0 : a > a > $o,X1 : a > a > $o,X2 : (a > a > $o) > $o,X3 : a,X4 : a] : (? [X5 : a > a > $o] : (! [X6 : a,X7 : a] : ((($true != (X0 @ X7 @ X6)) & ($true != (X1 @ X7 @ X6))) | ((X5 @ X7 @ X6) = $true)) & ((X5 @ X3 @ X4) != $true) & ((X2 @ X5) = $true)) & ! [X8 : a > a > $o] : (($true != (X2 @ X8)) | ((X8 @ X3 @ X4) = $true) | ? [X9 : a,X10 : a] : (($true != (X8 @ X10 @ X9)) & (! [X11 : a > a > $o] : (($true = (X11 @ X10 @ X9)) | ? [X12 : a,X13 : a] : (($true != (X11 @ X12 @ X13)) & ((X1 @ X12 @ X13) = $true)) | ((X2 @ X11) != $true)) | ! [X14 : a > a > $o] : (($true != (X2 @ X14)) | ? [X15 : a,X16 : a] : (($true != (X14 @ X16 @ X15)) & ($true = (X0 @ X16 @ X15))) | ($true = (X14 @ X10 @ X9))))))) => (? [X5 : a > a > $o] : (! [X7 : a,X6 : a] : ((($true != (sK0 @ X7 @ X6)) & ($true != (sK1 @ X7 @ X6))) | ((X5 @ X7 @ X6) = $true)) & ($true != (X5 @ sK3 @ sK4)) & ($true = (sK2 @ X5))) & ! [X8 : a > a > $o] : (($true != (sK2 @ X8)) | ($true = (X8 @ sK3 @ sK4)) | ? [X10 : a,X9 : a] : (($true != (X8 @ X10 @ X9)) & (! [X11 : a > a > $o] : (($true = (X11 @ X10 @ X9)) | ? [X13 : a,X12 : a] : (($true != (X11 @ X12 @ X13)) & ($true = (sK1 @ X12 @ X13))) | ($true != (sK2 @ X11))) | ! [X14 : a > a > $o] : (($true != (sK2 @ X14)) | ? [X16 : a,X15 : a] : (($true != (X14 @ X16 @ X15)) & ($true = (sK0 @ X16 @ X15))) | ($true = (X14 @ X10 @ X9)))))))),
% 1.84/1.54 introduced(definition,[],[choice_axiom])).
% 1.84/1.54 thf(f10,plain,(
% 1.84/1.54 ? [X5 : a > a > $o] : (! [X7 : a,X6 : a] : ((($true != (sK0 @ X7 @ X6)) & ($true != (sK1 @ X7 @ X6))) | ((X5 @ X7 @ X6) = $true)) & ($true != (X5 @ sK3 @ sK4)) & ($true = (sK2 @ X5))) => (! [X7 : a,X6 : a] : ((($true != (sK0 @ X7 @ X6)) & ($true != (sK1 @ X7 @ X6))) | ((sK5 @ X7 @ X6) = $true)) & ($true != (sK5 @ sK3 @ sK4)) & ($true = (sK2 @ sK5)))),
% 1.84/1.54 introduced(definition,[],[choice_axiom])).
% 1.84/1.54 thf(f11,plain,(
% 1.84/1.54 ! [X8 : a > a > $o] : (? [X10 : a,X9 : a] : (($true != (X8 @ X10 @ X9)) & (! [X11 : a > a > $o] : (($true = (X11 @ X10 @ X9)) | ? [X13 : a,X12 : a] : (($true != (X11 @ X12 @ X13)) & ($true = (sK1 @ X12 @ X13))) | ($true != (sK2 @ X11))) | ! [X14 : a > a > $o] : (($true != (sK2 @ X14)) | ? [X16 : a,X15 : a] : (($true != (X14 @ X16 @ X15)) & ($true = (sK0 @ X16 @ X15))) | ($true = (X14 @ X10 @ X9))))) => (($true != (X8 @ (sK7 @ X8) @ (sK6 @ X8))) & (! [X11 : a > a > $o] : (((X11 @ (sK7 @ X8) @ (sK6 @ X8)) = $true) | ? [X13 : a,X12 : a] : (($true != (X11 @ X12 @ X13)) & ($true = (sK1 @ X12 @ X13))) | ($true != (sK2 @ X11))) | ! [X14 : a > a > $o] : (($true != (sK2 @ X14)) | ? [X16 : a,X15 : a] : (($true != (X14 @ X16 @ X15)) & ($true = (sK0 @ X16 @ X15))) | ($true = (X14 @ (sK7 @ X8) @ (sK6 @ X8)))))))),
% 1.84/1.54 introduced(definition,[],[choice_axiom])).
% 1.84/1.54 thf(f12,plain,(
% 1.84/1.54 ! [X11 : a > a > $o] : (? [X13 : a,X12 : a] : (($true != (X11 @ X12 @ X13)) & ($true = (sK1 @ X12 @ X13))) => (($true != (X11 @ (sK8 @ X11) @ (sK9 @ X11))) & ($true = (sK1 @ (sK8 @ X11) @ (sK9 @ X11)))))),
% 1.84/1.54 introduced(definition,[],[choice_axiom])).
% 1.84/1.54 thf(f13,plain,(
% 1.84/1.54 ! [X14 : a > a > $o] : (? [X16 : a,X15 : a] : (($true != (X14 @ X16 @ X15)) & ($true = (sK0 @ X16 @ X15))) => (($true != (X14 @ (sK11 @ X14) @ (sK10 @ X14))) & ($true = (sK0 @ (sK11 @ X14) @ (sK10 @ X14)))))),
% 1.84/1.54 introduced(definition,[],[choice_axiom])).
% 1.84/1.54 thf(f8,plain,(
% 1.84/1.54 ? [X0 : a > a > $o,X1 : a > a > $o,X2 : (a > a > $o) > $o,X3 : a,X4 : a] : (? [X5 : a > a > $o] : (! [X6 : a,X7 : a] : ((($true != (X0 @ X7 @ X6)) & ($true != (X1 @ X7 @ X6))) | ((X5 @ X7 @ X6) = $true)) & ((X5 @ X3 @ X4) != $true) & ((X2 @ X5) = $true)) & ! [X8 : a > a > $o] : (($true != (X2 @ X8)) | ((X8 @ X3 @ X4) = $true) | ? [X9 : a,X10 : a] : (($true != (X8 @ X10 @ X9)) & (! [X11 : a > a > $o] : (($true = (X11 @ X10 @ X9)) | ? [X12 : a,X13 : a] : (($true != (X11 @ X12 @ X13)) & ((X1 @ X12 @ X13) = $true)) | ((X2 @ X11) != $true)) | ! [X14 : a > a > $o] : (($true != (X2 @ X14)) | ? [X15 : a,X16 : a] : (($true != (X14 @ X16 @ X15)) & ($true = (X0 @ X16 @ X15))) | ($true = (X14 @ X10 @ X9)))))))),
% 1.84/1.54 inference(rectify,[status(thm)],[f7])).
% 1.84/1.54 thf(f7,plain,(
% 1.84/1.54 ? [X1 : a > a > $o,X0 : a > a > $o,X4 : (a > a > $o) > $o,X3 : a,X2 : a] : (? [X14 : a > a > $o] : (! [X16 : a,X15 : a] : ((($true != (X1 @ X15 @ X16)) & ($true != (X0 @ X15 @ X16))) | ($true = (X14 @ X15 @ X16))) & ($true != (X14 @ X3 @ X2)) & ($true = (X4 @ X14))) & ! [X5 : a > a > $o] : (((X4 @ X5) != $true) | ($true = (X5 @ X3 @ X2)) | ? [X7 : a,X6 : a] : (((X5 @ X6 @ X7) != $true) & (! [X11 : a > a > $o] : (((X11 @ X6 @ X7) = $true) | ? [X13 : a,X12 : a] : (($true != (X11 @ X13 @ X12)) & ($true = (X0 @ X13 @ X12))) | ($true != (X4 @ X11))) | ! [X8 : a > a > $o] : (($true != (X4 @ X8)) | ? [X10 : a,X9 : a] : (((X8 @ X9 @ X10) != $true) & ((X1 @ X9 @ X10) = $true)) | ((X8 @ X6 @ X7) = $true))))))),
% 1.84/1.54 inference(flattening,[status(thm)],[f6])).
% 1.84/1.54 thf(f6,plain,(
% 1.84/1.54 ? [X3 : a,X1 : a > a > $o,X4 : (a > a > $o) > $o,X0 : a > a > $o,X2 : a] : (? [X14 : a > a > $o] : (($true != (X14 @ X3 @ X2)) & (($true = (X4 @ X14)) & ! [X16 : a,X15 : a] : ((($true != (X1 @ X15 @ X16)) & ($true != (X0 @ X15 @ X16))) | ($true = (X14 @ X15 @ X16))))) & ! [X5 : a > a > $o] : (($true = (X5 @ X3 @ X2)) | (? [X6 : a,X7 : a] : (((X5 @ X6 @ X7) != $true) & (! [X8 : a > a > $o] : (((X8 @ X6 @ X7) = $true) | (($true != (X4 @ X8)) | ? [X10 : a,X9 : a] : (((X8 @ X9 @ X10) != $true) & ((X1 @ X9 @ X10) = $true)))) | ! [X11 : a > a > $o] : (((X11 @ X6 @ X7) = $true) | (($true != (X4 @ X11)) | ? [X13 : a,X12 : a] : (($true != (X11 @ X13 @ X12)) & ($true = (X0 @ X13 @ X12))))))) | ((X4 @ X5) != $true))))),
% 1.84/1.54 inference(ennf_transformation,[status(thm)],[f5])).
% 1.84/1.54 thf(f5,plain,(
% 1.84/1.54 ~! [X3 : a,X1 : a > a > $o,X4 : (a > a > $o) > $o,X0 : a > a > $o,X2 : a] : (! [X5 : a > a > $o] : ((! [X6 : a,X7 : a] : ((! [X8 : a > a > $o] : ((($true = (X4 @ X8)) & ! [X9 : a,X10 : a] : (((X1 @ X9 @ X10) = $true) => ((X8 @ X9 @ X10) = $true))) => ((X8 @ X6 @ X7) = $true)) | ! [X11 : a > a > $o] : ((($true = (X4 @ X11)) & ! [X13 : a,X12 : a] : (($true = (X0 @ X13 @ X12)) => ($true = (X11 @ X13 @ X12)))) => ((X11 @ X6 @ X7) = $true))) => ((X5 @ X6 @ X7) = $true)) & ((X4 @ X5) = $true)) => ($true = (X5 @ X3 @ X2))) => ! [X14 : a > a > $o] : ((($true = (X4 @ X14)) & ! [X15 : a,X16 : a] : ((($true = (X0 @ X15 @ X16)) | ($true = (X1 @ X15 @ X16))) => ($true = (X14 @ X15 @ X16)))) => ($true = (X14 @ X3 @ X2))))),
% 1.84/1.54 inference(fool_elimination,[status(thm)],[f4])).
% 1.84/1.54 thf(f4,plain,(
% 1.84/1.54 ~! [X0 : a > a > $o,X1 : a > a > $o,X2 : a,X3 : a,X4 : (a > a > $o) > $o] : (! [X5 : a > a > $o] : (((X4 @ X5) & ! [X6 : a,X7 : a] : ((! [X8 : a > a > $o] : (((X4 @ X8) & ! [X9 : a,X10 : a] : ((X1 @ X9 @ X10) => (X8 @ X9 @ X10))) => (X8 @ X6 @ X7)) | ! [X11 : a > a > $o] : ((! [X12 : a,X13 : a] : ((X0 @ X13 @ X12) => (X11 @ X13 @ X12)) & (X4 @ X11)) => (X11 @ X6 @ X7))) => (X5 @ X6 @ X7))) => (X5 @ X3 @ X2)) => ! [X14 : a > a > $o] : ((! [X15 : a,X16 : a] : (((X1 @ X15 @ X16) | (X0 @ X15 @ X16)) => (X14 @ X15 @ X16)) & (X4 @ X14)) => (X14 @ X3 @ X2)))),
% 1.84/1.54 inference(rectify,[status(thm)],[f2])).
% 1.84/1.54 thf(f2,negated_conjecture,(
% 1.84/1.54 ~! [X1 : a > a > $o,X2 : a > a > $o,X4 : a,X3 : a,X0 : (a > a > $o) > $o] : (! [X5 : a > a > $o] : (((X0 @ X5) & ! [X6 : a,X7 : a] : ((! [X8 : a > a > $o] : (((X0 @ X8) & ! [X9 : a,X10 : a] : ((X2 @ X9 @ X10) => (X8 @ X9 @ X10))) => (X8 @ X6 @ X7)) | ! [X8 : a > a > $o] : ((! [X10 : a,X9 : a] : ((X1 @ X9 @ X10) => (X8 @ X9 @ X10)) & (X0 @ X8)) => (X8 @ X6 @ X7))) => (X5 @ X6 @ X7))) => (X5 @ X3 @ X4)) => ! [X5 : a > a > $o] : ((! [X6 : a,X7 : a] : (((X2 @ X6 @ X7) | (X1 @ X6 @ X7)) => (X5 @ X6 @ X7)) & (X0 @ X5)) => (X5 @ X3 @ X4)))),
% 1.84/1.54 inference(negated_conjecture,[status(cth)],[f1])).
% 1.84/1.54 thf(f1,conjecture,(
% 1.84/1.54 ! [X1 : a > a > $o,X2 : a > a > $o,X4 : a,X3 : a,X0 : (a > a > $o) > $o] : (! [X5 : a > a > $o] : (((X0 @ X5) & ! [X6 : a,X7 : a] : ((! [X8 : a > a > $o] : (((X0 @ X8) & ! [X9 : a,X10 : a] : ((X2 @ X9 @ X10) => (X8 @ X9 @ X10))) => (X8 @ X6 @ X7)) | ! [X8 : a > a > $o] : ((! [X10 : a,X9 : a] : ((X1 @ X9 @ X10) => (X8 @ X9 @ X10)) & (X0 @ X8)) => (X8 @ X6 @ X7))) => (X5 @ X6 @ X7))) => (X5 @ X3 @ X4)) => ! [X5 : a > a > $o] : ((! [X6 : a,X7 : a] : (((X2 @ X6 @ X7) | (X1 @ X6 @ X7)) => (X5 @ X6 @ X7)) & (X0 @ X5)) => (X5 @ X3 @ X4)))),
% 1.84/1.54 file('/export/starexec/sandbox2/tmp/tmp.qWSWpOFhzg/DTF2THF_15619.p',cTHM252A_pme)).
% 1.84/1.54 thf(f86,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o] : (($true != (sK2 @ X0)) | ($true = (sK0 @ (sK11 @ X0) @ (sK10 @ X0))) | ($true = (X0 @ (sK7 @ sK5) @ (sK6 @ sK5)))) ) | ~spl12_7),
% 1.84/1.54 inference(avatar_component_clause,[status(thm)],[f85])).
% 1.84/1.54 thf(f95,plain,(
% 1.84/1.54 spl12_5 | ~spl12_6),
% 1.84/1.54 inference(avatar_split_clause,[status(thm)],[f94,f59,f55])).
% 1.84/1.54 thf(f55,definition,(
% 1.84/1.54 spl12_5 <=> ($true = (sK5 @ sK3 @ sK4))),
% 1.84/1.54 introduced(definition,[new_symbols(naming,[spl12_5])],[avatar_definition])).
% 1.84/1.54 thf(f94,plain,(
% 1.84/1.54 ($true = (sK5 @ sK3 @ sK4)) | ~spl12_6),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.84/1.54 thf(f93,plain,(
% 1.84/1.54 ($true != $true) | ($true = (sK5 @ sK3 @ sK4)) | ~spl12_6),
% 1.84/1.54 inference(forward_demodulation,[status(thm)],[f92,f20])).
% 1.84/1.54 thf(f92,plain,(
% 1.84/1.54 ($true != (sK2 @ sK5)) | ($true = (sK5 @ sK3 @ sK4)) | ~spl12_6),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.84/1.54 thf(f91,plain,(
% 1.84/1.54 ($true = (sK5 @ sK3 @ sK4)) | ($true != $true) | ($true != (sK2 @ sK5)) | ~spl12_6),
% 1.84/1.54 inference(superposition,[status(thm)],[f19,f61])).
% 1.84/1.54 thf(f61,plain,(
% 1.84/1.54 ((sK5 @ (sK7 @ sK5) @ (sK6 @ sK5)) = $true) | ~spl12_6),
% 1.84/1.54 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.84/1.54 thf(f19,plain,(
% 1.84/1.54 ( ! [X8 : a > a > $o] : (($true != (X8 @ (sK7 @ X8) @ (sK6 @ X8))) | ($true = (X8 @ sK3 @ sK4)) | ($true != (sK2 @ X8))) )),
% 1.84/1.54 inference(cnf_transformation,[status(thm)],[f14])).
% 1.84/1.54 thf(f90,plain,(
% 1.84/1.54 spl12_5 | spl12_6 | ~spl12_3),
% 1.84/1.54 inference(avatar_split_clause,[status(thm)],[f89,f45,f59,f55])).
% 1.84/1.54 thf(f45,definition,(
% 1.84/1.54 spl12_3 <=> ! [X0 : a > a > $o] : (((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true = (X0 @ sK3 @ sK4)) | ($true != (sK2 @ X0)))),
% 1.84/1.54 introduced(definition,[new_symbols(naming,[spl12_3])],[avatar_definition])).
% 1.84/1.54 thf(f89,plain,(
% 1.84/1.54 ($true = (sK5 @ sK3 @ sK4)) | ((sK5 @ (sK7 @ sK5) @ (sK6 @ sK5)) = $true) | ~spl12_3),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.84/1.54 thf(f88,plain,(
% 1.84/1.54 ($true = (sK5 @ sK3 @ sK4)) | ($true != $true) | ((sK5 @ (sK7 @ sK5) @ (sK6 @ sK5)) = $true) | ~spl12_3),
% 1.84/1.54 inference(superposition,[status(thm)],[f46,f20])).
% 1.84/1.54 thf(f46,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o] : (($true != (sK2 @ X0)) | ((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true = (X0 @ sK3 @ sK4))) ) | ~spl12_3),
% 1.84/1.54 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.84/1.54 thf(f87,plain,(
% 1.84/1.54 spl12_6 | spl12_7 | spl12_5 | ~spl12_4),
% 1.84/1.54 inference(avatar_split_clause,[status(thm)],[f83,f48,f55,f85,f59])).
% 1.84/1.54 thf(f48,definition,(
% 1.84/1.54 spl12_4 <=> ($true = (sK1 @ (sK8 @ sK5) @ (sK9 @ sK5)))),
% 1.84/1.54 introduced(definition,[new_symbols(naming,[spl12_4])],[avatar_definition])).
% 1.84/1.54 thf(f83,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o] : (($true = (sK5 @ sK3 @ sK4)) | ($true = (X0 @ (sK7 @ sK5) @ (sK6 @ sK5))) | ($true != (sK2 @ X0)) | ((sK5 @ (sK7 @ sK5) @ (sK6 @ sK5)) = $true) | ($true = (sK0 @ (sK11 @ X0) @ (sK10 @ X0)))) ) | ~spl12_4),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.84/1.54 thf(f82,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o] : (($true = (X0 @ (sK7 @ sK5) @ (sK6 @ sK5))) | ($true != $true) | ((sK5 @ (sK7 @ sK5) @ (sK6 @ sK5)) = $true) | ($true = (sK0 @ (sK11 @ X0) @ (sK10 @ X0))) | ($true != (sK2 @ X0)) | ($true = (sK5 @ sK3 @ sK4))) ) | ~spl12_4),
% 1.84/1.54 inference(superposition,[status(thm)],[f72,f20])).
% 1.84/1.54 thf(f72,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true != (sK2 @ X1)) | ($true != (sK2 @ X0)) | ($true = (sK5 @ (sK7 @ X1) @ (sK6 @ X1))) | ($true = (sK0 @ (sK11 @ X0) @ (sK10 @ X0))) | ((X0 @ (sK7 @ X1) @ (sK6 @ X1)) = $true) | ($true = (X1 @ sK3 @ sK4))) ) | ~spl12_4),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.84/1.54 thf(f71,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true = (X1 @ sK3 @ sK4)) | ($true != (sK2 @ X0)) | ($true != $true) | ((X0 @ (sK7 @ X1) @ (sK6 @ X1)) = $true) | ($true != (sK2 @ X1)) | ($true = (sK5 @ (sK7 @ X1) @ (sK6 @ X1))) | ($true = (sK0 @ (sK11 @ X0) @ (sK10 @ X0)))) ) | ~spl12_4),
% 1.84/1.54 inference(forward_demodulation,[status(thm)],[f70,f20])).
% 1.84/1.54 thf(f70,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true != (sK2 @ X0)) | ($true = (sK5 @ (sK7 @ X1) @ (sK6 @ X1))) | ($true != (sK2 @ X1)) | ($true = (X1 @ sK3 @ sK4)) | ((X0 @ (sK7 @ X1) @ (sK6 @ X1)) = $true) | ($true = (sK0 @ (sK11 @ X0) @ (sK10 @ X0))) | ($true != (sK2 @ sK5))) ) | ~spl12_4),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.84/1.54 thf(f69,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true != (sK2 @ X0)) | ($true = (X1 @ sK3 @ sK4)) | ($true = (sK5 @ (sK7 @ X1) @ (sK6 @ X1))) | ($true = (sK0 @ (sK11 @ X0) @ (sK10 @ X0))) | ($true != (sK2 @ sK5)) | ((X0 @ (sK7 @ X1) @ (sK6 @ X1)) = $true) | ($true != (sK2 @ X1)) | ($true != $true)) ) | ~spl12_4),
% 1.84/1.54 inference(superposition,[status(thm)],[f17,f64])).
% 1.84/1.54 thf(f64,plain,(
% 1.84/1.54 ($true = (sK5 @ (sK8 @ sK5) @ (sK9 @ sK5))) | ~spl12_4),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.84/1.54 thf(f63,plain,(
% 1.84/1.54 ($true = (sK5 @ (sK8 @ sK5) @ (sK9 @ sK5))) | ($true != $true) | ~spl12_4),
% 1.84/1.54 inference(superposition,[status(thm)],[f22,f50])).
% 1.84/1.54 thf(f50,plain,(
% 1.84/1.54 ($true = (sK1 @ (sK8 @ sK5) @ (sK9 @ sK5))) | ~spl12_4),
% 1.84/1.54 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.84/1.54 thf(f22,plain,(
% 1.84/1.54 ( ! [X6 : a,X7 : a] : (($true != (sK1 @ X7 @ X6)) | ((sK5 @ X7 @ X6) = $true)) )),
% 1.84/1.54 inference(cnf_transformation,[status(thm)],[f14])).
% 1.84/1.54 thf(f17,plain,(
% 1.84/1.54 ( ! [X11 : a > a > $o,X8 : a > a > $o,X14 : a > a > $o] : (($true != (X11 @ (sK8 @ X11) @ (sK9 @ X11))) | ($true = (X14 @ (sK7 @ X8) @ (sK6 @ X8))) | ($true = (X8 @ sK3 @ sK4)) | ((X11 @ (sK7 @ X8) @ (sK6 @ X8)) = $true) | ($true != (sK2 @ X11)) | ($true != (sK2 @ X8)) | ($true = (sK0 @ (sK11 @ X14) @ (sK10 @ X14))) | ($true != (sK2 @ X14))) )),
% 1.84/1.54 inference(cnf_transformation,[status(thm)],[f14])).
% 1.84/1.54 thf(f81,plain,(
% 1.84/1.54 ~spl12_5),
% 1.84/1.54 inference(avatar_contradiction_clause,[status(thm)],[f80])).
% 1.84/1.54 thf(f80,plain,(
% 1.84/1.54 $false | ~spl12_5),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.84/1.54 thf(f79,plain,(
% 1.84/1.54 ($true != $true) | ~spl12_5),
% 1.84/1.54 inference(superposition,[status(thm)],[f21,f57])).
% 1.84/1.54 thf(f57,plain,(
% 1.84/1.54 ($true = (sK5 @ sK3 @ sK4)) | ~spl12_5),
% 1.84/1.54 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.84/1.54 thf(f21,plain,(
% 1.84/1.54 ($true != (sK5 @ sK3 @ sK4))),
% 1.84/1.54 inference(cnf_transformation,[status(thm)],[f14])).
% 1.84/1.54 thf(f78,plain,(
% 1.84/1.54 spl12_3 | ~spl12_2 | ~spl12_4),
% 1.84/1.54 inference(avatar_split_clause,[status(thm)],[f77,f48,f30,f45])).
% 1.84/1.54 thf(f77,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o] : (($true = (X0 @ sK3 @ sK4)) | ((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true != (sK2 @ X0))) ) | (~spl12_2 | ~spl12_4)),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.84/1.54 thf(f76,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o] : (($true != (sK2 @ X0)) | ($true != $true) | ((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true = (X0 @ sK3 @ sK4))) ) | (~spl12_2 | ~spl12_4)),
% 1.84/1.54 inference(forward_demodulation,[status(thm)],[f75,f20])).
% 1.84/1.54 thf(f75,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o] : (($true != (sK2 @ X0)) | ($true != (sK2 @ sK5)) | ((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true = (X0 @ sK3 @ sK4))) ) | (~spl12_2 | ~spl12_4)),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.84/1.54 thf(f74,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o] : (($true = (X0 @ sK3 @ sK4)) | ($true != (sK2 @ sK5)) | ($true != (sK2 @ X0)) | ((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true != $true)) ) | (~spl12_2 | ~spl12_4)),
% 1.84/1.54 inference(duplicate_literal_removal,[status(thm)],[f73])).
% 1.84/1.54 thf(f73,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o] : (((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true = (X0 @ sK3 @ sK4)) | ($true != $true) | ($true != (sK2 @ sK5)) | ((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true != (sK2 @ X0))) ) | (~spl12_2 | ~spl12_4)),
% 1.84/1.54 inference(superposition,[status(thm)],[f68,f64])).
% 1.84/1.54 thf(f68,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true != (X0 @ (sK8 @ X0) @ (sK9 @ X0))) | ((X0 @ (sK7 @ X1) @ (sK6 @ X1)) = $true) | ($true != (sK2 @ X1)) | ($true != (sK2 @ X0)) | ($true = (sK5 @ (sK7 @ X1) @ (sK6 @ X1))) | ($true = (X1 @ sK3 @ sK4))) ) | ~spl12_2),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.84/1.54 thf(f67,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true = (X1 @ sK3 @ sK4)) | ($true != (sK2 @ X0)) | ($true != (sK2 @ X1)) | ($true = (sK5 @ (sK7 @ X1) @ (sK6 @ X1))) | ((X0 @ (sK7 @ X1) @ (sK6 @ X1)) = $true) | ($true != (X0 @ (sK8 @ X0) @ (sK9 @ X0))) | ($true != $true)) ) | ~spl12_2),
% 1.84/1.54 inference(forward_demodulation,[status(thm)],[f66,f20])).
% 1.84/1.54 thf(f66,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true != (sK2 @ X0)) | ($true != (X0 @ (sK8 @ X0) @ (sK9 @ X0))) | ($true = (X1 @ sK3 @ sK4)) | ($true = (sK5 @ (sK7 @ X1) @ (sK6 @ X1))) | ($true != (sK2 @ sK5)) | ((X0 @ (sK7 @ X1) @ (sK6 @ X1)) = $true) | ($true != (sK2 @ X1))) ) | ~spl12_2),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.84/1.54 thf(f65,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true = (X1 @ sK3 @ sK4)) | ($true != (sK2 @ X0)) | ($true = (sK5 @ (sK7 @ X1) @ (sK6 @ X1))) | ((X0 @ (sK7 @ X1) @ (sK6 @ X1)) = $true) | ($true != $true) | ($true != (sK2 @ X1)) | ($true != (X0 @ (sK8 @ X0) @ (sK9 @ X0))) | ($true != (sK2 @ sK5))) ) | ~spl12_2),
% 1.84/1.54 inference(superposition,[status(thm)],[f18,f35])).
% 1.84/1.54 thf(f35,plain,(
% 1.84/1.54 ($true = (sK5 @ (sK11 @ sK5) @ (sK10 @ sK5))) | ~spl12_2),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.84/1.54 thf(f34,plain,(
% 1.84/1.54 ($true != $true) | ($true = (sK5 @ (sK11 @ sK5) @ (sK10 @ sK5))) | ~spl12_2),
% 1.84/1.54 inference(superposition,[status(thm)],[f23,f32])).
% 1.84/1.54 thf(f32,plain,(
% 1.84/1.54 ($true = (sK0 @ (sK11 @ sK5) @ (sK10 @ sK5))) | ~spl12_2),
% 1.84/1.54 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.84/1.54 thf(f23,plain,(
% 1.84/1.54 ( ! [X6 : a,X7 : a] : (($true != (sK0 @ X7 @ X6)) | ((sK5 @ X7 @ X6) = $true)) )),
% 1.84/1.54 inference(cnf_transformation,[status(thm)],[f14])).
% 1.84/1.54 thf(f18,plain,(
% 1.84/1.54 ( ! [X11 : a > a > $o,X8 : a > a > $o,X14 : a > a > $o] : (($true != (X14 @ (sK11 @ X14) @ (sK10 @ X14))) | ($true != (X11 @ (sK8 @ X11) @ (sK9 @ X11))) | ($true != (sK2 @ X14)) | ($true != (sK2 @ X8)) | ($true = (X14 @ (sK7 @ X8) @ (sK6 @ X8))) | ($true != (sK2 @ X11)) | ((X11 @ (sK7 @ X8) @ (sK6 @ X8)) = $true) | ($true = (X8 @ sK3 @ sK4))) )),
% 1.84/1.54 inference(cnf_transformation,[status(thm)],[f14])).
% 1.84/1.54 thf(f51,plain,(
% 1.84/1.54 spl12_3 | spl12_4 | ~spl12_1),
% 1.84/1.54 inference(avatar_split_clause,[status(thm)],[f43,f27,f48,f45])).
% 1.84/1.54 thf(f27,definition,(
% 1.84/1.54 spl12_1 <=> ! [X0 : a > a > $o,X1 : a > a > $o] : (($true = (X1 @ (sK7 @ X0) @ (sK6 @ X0))) | ($true = (X0 @ sK3 @ sK4)) | ($true = (sK1 @ (sK8 @ X1) @ (sK9 @ X1))) | ($true != (sK2 @ X0)) | ($true != (sK2 @ X1)) | ((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true))),
% 1.84/1.54 introduced(definition,[new_symbols(naming,[spl12_1])],[avatar_definition])).
% 1.84/1.54 thf(f43,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o] : (((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true = (sK1 @ (sK8 @ sK5) @ (sK9 @ sK5))) | ($true != (sK2 @ X0)) | ($true = (X0 @ sK3 @ sK4))) ) | ~spl12_1),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.84/1.54 thf(f42,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o] : (($true != $true) | ($true = (X0 @ sK3 @ sK4)) | ($true != (sK2 @ X0)) | ((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true = (sK1 @ (sK8 @ sK5) @ (sK9 @ sK5)))) ) | ~spl12_1),
% 1.84/1.54 inference(duplicate_literal_removal,[status(thm)],[f41])).
% 1.84/1.54 thf(f41,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o] : (((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true != $true) | ($true = (sK1 @ (sK8 @ sK5) @ (sK9 @ sK5))) | ($true = (X0 @ sK3 @ sK4)) | ((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true != (sK2 @ X0))) ) | ~spl12_1),
% 1.84/1.54 inference(superposition,[status(thm)],[f28,f20])).
% 1.84/1.54 thf(f28,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true != (sK2 @ X1)) | ($true = (sK1 @ (sK8 @ X1) @ (sK9 @ X1))) | ($true = (X0 @ sK3 @ sK4)) | ((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true != (sK2 @ X0)) | ($true = (X1 @ (sK7 @ X0) @ (sK6 @ X0)))) ) | ~spl12_1),
% 1.84/1.54 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.84/1.54 thf(f40,plain,(
% 1.84/1.54 spl12_1 | ~spl12_2),
% 1.84/1.54 inference(avatar_split_clause,[status(thm)],[f39,f30,f27])).
% 1.84/1.54 thf(f39,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true = (sK1 @ (sK8 @ X0) @ (sK9 @ X0))) | ($true = (X1 @ sK3 @ sK4)) | ((X0 @ (sK7 @ X1) @ (sK6 @ X1)) = $true) | ($true != (sK2 @ X0)) | ($true = (sK5 @ (sK7 @ X1) @ (sK6 @ X1))) | ($true != (sK2 @ X1))) ) | ~spl12_2),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.84/1.54 thf(f38,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true != $true) | ($true = (sK5 @ (sK7 @ X1) @ (sK6 @ X1))) | ((X0 @ (sK7 @ X1) @ (sK6 @ X1)) = $true) | ($true != (sK2 @ X1)) | ($true = (sK1 @ (sK8 @ X0) @ (sK9 @ X0))) | ($true = (X1 @ sK3 @ sK4)) | ($true != (sK2 @ X0))) ) | ~spl12_2),
% 1.84/1.54 inference(forward_demodulation,[status(thm)],[f37,f20])).
% 1.84/1.54 thf(f37,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true != (sK2 @ X0)) | ($true != (sK2 @ X1)) | ($true = (X1 @ sK3 @ sK4)) | ($true = (sK5 @ (sK7 @ X1) @ (sK6 @ X1))) | ((X0 @ (sK7 @ X1) @ (sK6 @ X1)) = $true) | ($true != (sK2 @ sK5)) | ($true = (sK1 @ (sK8 @ X0) @ (sK9 @ X0)))) ) | ~spl12_2),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.84/1.54 thf(f36,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true != (sK2 @ X0)) | ($true = (sK1 @ (sK8 @ X0) @ (sK9 @ X0))) | ($true = (sK5 @ (sK7 @ X1) @ (sK6 @ X1))) | ($true != (sK2 @ X1)) | ($true != (sK2 @ sK5)) | ($true != $true) | ((X0 @ (sK7 @ X1) @ (sK6 @ X1)) = $true) | ($true = (X1 @ sK3 @ sK4))) ) | ~spl12_2),
% 1.84/1.54 inference(superposition,[status(thm)],[f16,f35])).
% 1.84/1.54 thf(f16,plain,(
% 1.84/1.54 ( ! [X11 : a > a > $o,X8 : a > a > $o,X14 : a > a > $o] : (($true != (X14 @ (sK11 @ X14) @ (sK10 @ X14))) | ($true = (sK1 @ (sK8 @ X11) @ (sK9 @ X11))) | ((X11 @ (sK7 @ X8) @ (sK6 @ X8)) = $true) | ($true = (X8 @ sK3 @ sK4)) | ($true != (sK2 @ X11)) | ($true != (sK2 @ X14)) | ($true != (sK2 @ X8)) | ($true = (X14 @ (sK7 @ X8) @ (sK6 @ X8)))) )),
% 1.84/1.54 inference(cnf_transformation,[status(thm)],[f14])).
% 1.84/1.54 thf(f33,plain,(
% 1.84/1.54 spl12_1 | spl12_2),
% 1.84/1.54 inference(avatar_split_clause,[status(thm)],[f25,f30,f27])).
% 1.84/1.54 thf(f25,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true = (sK0 @ (sK11 @ sK5) @ (sK10 @ sK5))) | ($true = (X1 @ (sK7 @ X0) @ (sK6 @ X0))) | ((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true) | ($true != (sK2 @ X1)) | ($true != (sK2 @ X0)) | ($true = (sK1 @ (sK8 @ X1) @ (sK9 @ X1))) | ($true = (X0 @ sK3 @ sK4))) )),
% 1.84/1.54 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.84/1.54 thf(f24,plain,(
% 1.84/1.54 ( ! [X0 : a > a > $o,X1 : a > a > $o] : (($true = (X1 @ (sK7 @ X0) @ (sK6 @ X0))) | ($true = (sK0 @ (sK11 @ sK5) @ (sK10 @ sK5))) | ($true != (sK2 @ X1)) | ($true != $true) | ($true = (sK1 @ (sK8 @ X1) @ (sK9 @ X1))) | ($true = (X0 @ sK3 @ sK4)) | ($true != (sK2 @ X0)) | ((sK5 @ (sK7 @ X0) @ (sK6 @ X0)) = $true)) )),
% 1.84/1.54 inference(superposition,[status(thm)],[f15,f20])).
% 1.84/1.54 thf(f15,plain,(
% 1.84/1.54 ( ! [X11 : a > a > $o,X8 : a > a > $o,X14 : a > a > $o] : (($true != (sK2 @ X14)) | ($true = (sK0 @ (sK11 @ X14) @ (sK10 @ X14))) | ($true = (X14 @ (sK7 @ X8) @ (sK6 @ X8))) | ((X11 @ (sK7 @ X8) @ (sK6 @ X8)) = $true) | ($true = (sK1 @ (sK8 @ X11) @ (sK9 @ X11))) | ($true != (sK2 @ X11)) | ($true = (X8 @ sK3 @ sK4)) | ($true != (sK2 @ X8))) )),
% 1.84/1.54 inference(cnf_transformation,[status(thm)],[f14])).
% 1.84/1.54 % SZS output end Proof for DTF2THF_15619
% 1.84/1.54 % (15718)------------------------------
% 1.84/1.54 % (15718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.54 % (15718)Termination reason: Refutation
% 1.84/1.54
% 1.84/1.54 % (15718)Memory used [KB]: 5628
% 1.84/1.54 % (15718)Time elapsed: 0.018 s
% 1.84/1.54 % (15718)Instructions burned: 23 (million)
% 1.84/1.54 % (15718)------------------------------
% 1.84/1.54 % (15718)------------------------------
% 1.84/1.54 % (15715)Success in time 0.033 s
%------------------------------------------------------------------------------