%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV124^5 : 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 : n011.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 09:40:20 AM UTC 2026
% Result : Theorem 1.81s 1.50s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 7 unt; 0 typ; 3 def)
% Number of atoms : 648 ( 203 equ; 0 cnn)
% Maximal formula atoms : 22 ( 10 avg)
% Number of connectives : 1092 ( 107 ~; 123 |; 78 &; 671 @)
% ( 3 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 254 ( 254 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 8 con; 0-5 aty)
% ( 46 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 289 ( 77 ^; 158 !; 54 ?; 289 :)
% 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_12,type,
sK0: ( a > a > $o ) > $o ).
thf(func_def_13,type,
sK1: ( a > a > $o ) > $o ).
thf(func_def_14,type,
sK2: a ).
thf(func_def_15,type,
sK3: a ).
thf(func_def_16,type,
sK4: a > a > $o ).
thf(func_def_17,type,
sK5: ( a > a > $o ) > a ).
thf(func_def_18,type,
sK6: ( a > a > $o ) > a ).
thf(func_def_19,type,
sK7: ( a > a > $o ) > a > a > $o ).
thf(func_def_21,type,
sK9: ( a > a > $o ) > a > a > a > a > $o ).
thf(func_def_22,type,
ph10:
!>[X0: $tType] : X0 ).
thf(f82,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f43,f54,f57,f81]) ).
thf(f81,plain,
( spl8_1
| ~ spl8_2
| ~ spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f80,f51,f40,f36]) ).
thf(f36,definition,
( spl8_1
<=> ( $true
= ( sK4 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f40,definition,
( spl8_2
<=> ( $true
= ( sK1 @ ( sK7 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f51,definition,
( spl8_3
<=> ( $true
= ( sK7 @ sK4 @ ( sK5 @ sK4 ) @ ( sK6 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition]) ).
thf(f80,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl8_2
| ~ spl8_3 ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( $true != $true )
| ~ spl8_2
| ~ spl8_3 ),
inference(forward_demodulation,[status(thm)],[f78,f19]) ).
thf(f19,plain,
( $true
= ( sK0 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true
= ( sK0 @ sK4 ) )
& ! [X5: a,X6: a] :
( ! [X7: a > a > $o] :
( ! [X8: a > a > $o] :
( ( $true
!= ( sK1 @ X8 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X7 ) )
| ( ( X7 @ X5 @ X6 )
!= $true ) )
| ( ( sK4 @ X5 @ X6 )
= $true ) )
& ( $true
!= ( sK4 @ sK2 @ sK3 ) )
& ! [X9: a > a > $o] :
( ( $true
!= ( sK0 @ X9 ) )
| ( $true
= ( X9 @ sK2 @ sK3 ) )
| ( ( $true
= ( sK7 @ X9 @ ( sK5 @ X9 ) @ ( sK6 @ X9 ) ) )
& ( $true
= ( sK1 @ ( sK7 @ X9 ) ) )
& ( ( X9 @ ( sK5 @ X9 ) @ ( sK6 @ X9 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o,X2: a,X3: a] :
( ? [X4: a > a > $o] :
( ( ( X0 @ X4 )
= $true )
& ! [X5: a,X6: a] :
( ! [X7: a > a > $o] :
( ! [X8: a > a > $o] :
( ( ( X1 @ X8 )
!= $true )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X7 ) )
| ( ( X7 @ X5 @ X6 )
!= $true ) )
| ( ( X4 @ X5 @ X6 )
= $true ) )
& ( ( X4 @ X2 @ X3 )
!= $true ) )
& ! [X9: a > a > $o] :
( ( $true
!= ( X0 @ X9 ) )
| ( $true
= ( X9 @ X2 @ X3 ) )
| ? [X10: a,X11: a] :
( ? [X12: a > a > $o] :
( ( ( X12 @ X10 @ X11 )
= $true )
& ( $true
= ( X1 @ X12 ) ) )
& ( $true
!= ( X9 @ X10 @ X11 ) ) ) ) )
=> ( ? [X4: a > a > $o] :
( ( $true
= ( sK0 @ X4 ) )
& ! [X6: a,X5: a] :
( ! [X7: a > a > $o] :
( ! [X8: a > a > $o] :
( ( $true
!= ( sK1 @ X8 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X7 ) )
| ( ( X7 @ X5 @ X6 )
!= $true ) )
| ( ( X4 @ X5 @ X6 )
= $true ) )
& ( $true
!= ( X4 @ sK2 @ sK3 ) ) )
& ! [X9: a > a > $o] :
( ( $true
!= ( sK0 @ X9 ) )
| ( $true
= ( X9 @ sK2 @ sK3 ) )
| ? [X11: a,X10: a] :
( ? [X12: a > a > $o] :
( ( ( X12 @ X10 @ X11 )
= $true )
& ( $true
= ( sK1 @ X12 ) ) )
& ( $true
!= ( X9 @ X10 @ X11 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X4: a > a > $o] :
( ( $true
= ( sK0 @ X4 ) )
& ! [X6: a,X5: a] :
( ! [X7: a > a > $o] :
( ! [X8: a > a > $o] :
( ( $true
!= ( sK1 @ X8 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X7 ) )
| ( ( X7 @ X5 @ X6 )
!= $true ) )
| ( ( X4 @ X5 @ X6 )
= $true ) )
& ( $true
!= ( X4 @ sK2 @ sK3 ) ) )
=> ( ( $true
= ( sK0 @ sK4 ) )
& ! [X6: a,X5: a] :
( ! [X7: a > a > $o] :
( ! [X8: a > a > $o] :
( ( $true
!= ( sK1 @ X8 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X7 ) )
| ( ( X7 @ X5 @ X6 )
!= $true ) )
| ( ( sK4 @ X5 @ X6 )
= $true ) )
& ( $true
!= ( sK4 @ sK2 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X9: a > a > $o] :
( ? [X11: a,X10: a] :
( ? [X12: a > a > $o] :
( ( ( X12 @ X10 @ X11 )
= $true )
& ( $true
= ( sK1 @ X12 ) ) )
& ( $true
!= ( X9 @ X10 @ X11 ) ) )
=> ( ? [X12: a > a > $o] :
( ( $true
= ( X12 @ ( sK5 @ X9 ) @ ( sK6 @ X9 ) ) )
& ( $true
= ( sK1 @ X12 ) ) )
& ( ( X9 @ ( sK5 @ X9 ) @ ( sK6 @ X9 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X9: a > a > $o] :
( ? [X12: a > a > $o] :
( ( $true
= ( X12 @ ( sK5 @ X9 ) @ ( sK6 @ X9 ) ) )
& ( $true
= ( sK1 @ X12 ) ) )
=> ( ( $true
= ( sK7 @ X9 @ ( sK5 @ X9 ) @ ( sK6 @ X9 ) ) )
& ( $true
= ( sK1 @ ( sK7 @ X9 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o,X2: a,X3: a] :
( ? [X4: a > a > $o] :
( ( ( X0 @ X4 )
= $true )
& ! [X5: a,X6: a] :
( ! [X7: a > a > $o] :
( ! [X8: a > a > $o] :
( ( ( X1 @ X8 )
!= $true )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X7 ) )
| ( ( X7 @ X5 @ X6 )
!= $true ) )
| ( ( X4 @ X5 @ X6 )
= $true ) )
& ( ( X4 @ X2 @ X3 )
!= $true ) )
& ! [X9: a > a > $o] :
( ( $true
!= ( X0 @ X9 ) )
| ( $true
= ( X9 @ X2 @ X3 ) )
| ? [X10: a,X11: a] :
( ? [X12: a > a > $o] :
( ( ( X12 @ X10 @ X11 )
= $true )
& ( $true
= ( X1 @ X12 ) ) )
& ( $true
!= ( X9 @ X10 @ X11 ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o,X2: a,X3: a] :
( ? [X8: a > a > $o] :
( ( ( X0 @ X8 )
= $true )
& ! [X9: a,X10: a] :
( ! [X11: a > a > $o] :
( ! [X12: a > a > $o] :
( ( $true
!= ( X1 @ X12 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X12 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X11 ) )
| ( ( X11 @ X9 @ X10 )
!= $true ) )
| ( $true
= ( X8 @ X9 @ X10 ) ) )
& ( $true
!= ( X8 @ X2 @ X3 ) ) )
& ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
!= $true )
| ( ( X4 @ X2 @ X3 )
= $true )
| ? [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( ( X7 @ X5 @ X6 )
= $true )
& ( ( X1 @ X7 )
= $true ) )
& ( ( X4 @ X5 @ X6 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o,X2: a,X3: a] :
( ? [X8: a > a > $o] :
( ( $true
!= ( X8 @ X2 @ X3 ) )
& ( ( X0 @ X8 )
= $true )
& ! [X9: a,X10: a] :
( ! [X11: a > a > $o] :
( ! [X12: a > a > $o] :
( ( $true
!= ( X1 @ X12 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X12 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X11 ) )
| ( ( X11 @ X9 @ X10 )
!= $true ) )
| ( $true
= ( X8 @ X9 @ X10 ) ) ) )
& ! [X4: a > a > $o] :
( ( ( X4 @ X2 @ X3 )
= $true )
| ( ( X0 @ X4 )
!= $true )
| ? [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( ( X7 @ X5 @ X6 )
= $true )
& ( ( X1 @ X7 )
= $true ) )
& ( ( X4 @ X5 @ X6 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o,X2: a,X3: a] :
( ! [X4: a > a > $o] :
( ( ( ( X0 @ X4 )
= $true )
& ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( ( X7 @ X5 @ X6 )
= $true )
& ( ( X1 @ X7 )
= $true ) )
=> ( ( X4 @ X5 @ X6 )
= $true ) ) )
=> ( ( X4 @ X2 @ X3 )
= $true ) )
=> ! [X8: a > a > $o] :
( ( ( ( X0 @ X8 )
= $true )
& ! [X9: a,X10: a] :
( ? [X11: a > a > $o] :
( ? [X12: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X12 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X11 )
& ( $true
= ( X1 @ X12 ) ) )
& ( ( X11 @ X9 @ X10 )
= $true ) )
=> ( $true
= ( X8 @ X9 @ X10 ) ) ) )
=> ( $true
= ( X8 @ X2 @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o,X2: a,X3: a] :
( ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( X1 @ X7 )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ? [X11: a > a > $o] :
( ( X11 @ X9 @ X10 )
& ? [X12: a > a > $o] :
( ( ( ^ [X13: a,X14: a] :
! [X15: a > a > $o] :
( ( ! [X16: a,X17: a] :
( ( X12 @ X17 @ X16 )
=> ( X15 @ X17 @ X16 ) )
& ( X0 @ X15 ) )
=> ( X15 @ X13 @ X14 ) ) )
= X11 )
& ( X1 @ X12 ) ) )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X2 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o,X2: a,X3: a] :
( ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( X1 @ X7 )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( X7 @ X5 @ X6 )
& ? [X8: a > a > $o] :
( ( ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ! [X13: a,X12: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
& ( X0 @ X11 ) )
=> ( X11 @ X9 @ X10 ) ) )
= X7 )
& ( X1 @ X8 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o,X2: a,X3: a] :
( ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( X1 @ X7 )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( X7 @ X5 @ X6 )
& ? [X8: a > a > $o] :
( ( ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ! [X13: a,X12: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
& ( X0 @ X11 ) )
=> ( X11 @ X9 @ X10 ) ) )
= X7 )
& ( X1 @ X8 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4CBTS5Mdks/DTF2THF_22429.p',cTHM254_A_pme) ).
thf(f78,plain,
( ( $true
!= ( sK0 @ sK4 ) )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl8_2
| ~ spl8_3 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( $true != $true )
| ( $true
!= ( sK0 @ sK4 ) )
| ~ spl8_2
| ~ spl8_3 ),
inference(superposition,[status(thm)],[f14,f75]) ).
thf(f75,plain,
( ( $true
= ( sK4 @ ( sK5 @ sK4 ) @ ( sK6 @ sK4 ) ) )
| ~ spl8_2
| ~ spl8_3 ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $true
= ( sK4 @ ( sK5 @ sK4 ) @ ( sK6 @ sK4 ) ) )
| ( $true = $false )
| ~ spl8_2
| ~ spl8_3 ),
inference(superposition,[status(thm)],[f53,f68]) ).
thf(f68,plain,
( ! [X0: a,X1: a] :
( ( ( sK7 @ sK4 @ X0 @ X1 )
= $false )
| ( $true
= ( sK4 @ X0 @ X1 ) ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ! [X0: a,X1: a] :
( ( ( sK7 @ sK4 @ X0 @ X1 )
= $false )
| ( $true
= ( sK4 @ X0 @ X1 ) )
| ( $true = $false ) )
| ~ spl8_2 ),
inference(duplicate_literal_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ! [X0: a,X1: a] :
( ( $true = $false )
| ( $true
= ( sK4 @ X0 @ X1 ) )
| ( $true
= ( sK4 @ X0 @ X1 ) )
| ( ( sK7 @ sK4 @ X0 @ X1 )
= $false ) )
| ~ spl8_2 ),
inference(superposition,[status(thm)],[f59,f45]) ).
thf(f45,plain,
( ! [X0: a,X1: a] :
( ( ( sK9 @ ( sK7 @ sK4 ) @ X0 @ X1 @ X0 @ X1 )
= $false )
| ( $true
= ( sK4 @ X0 @ X1 ) ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true
= ( sK4 @ X0 @ X1 ) )
| ( ( sK9 @ ( sK7 @ sK4 ) @ X0 @ X1 @ X0 @ X1 )
= $false ) )
| ~ spl8_2 ),
inference(superposition,[status(thm)],[f24,f42]) ).
thf(f42,plain,
( ( $true
= ( sK1 @ ( sK7 @ sK4 ) ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f24,plain,
! [X8: a > a > $o,X6: a,X5: a] :
( ( $true
!= ( sK1 @ X8 ) )
| ( ( sK4 @ X5 @ X6 )
= $true )
| ( $false
= ( sK9 @ X8 @ X5 @ X6 @ X5 @ X6 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X8: a > a > $o,X6: a,X5: a] :
( ( $true
!= ( sK1 @ X8 ) )
| ( ( ( ( sK0 @ ( sK9 @ X8 @ X5 @ X6 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X8 @ Y0 @ Y1 )
=> ( sK9 @ X8 @ X5 @ X6 @ Y0 @ Y1 ) ) ) ) )
=> ( sK9 @ X8 @ X5 @ X6 @ X5 @ X6 ) )
= $false )
| ( ( sK4 @ X5 @ X6 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X8: a > a > $o,X6: a,X5: a] :
( ( ( sK4 @ X5 @ X6 )
= $true )
| ( $true
!= ( sK1 @ X8 ) )
| ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( X8 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X5 @ X6 ) )
@ ( sK9 @ X8 @ X5 @ X6 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X8: a > a > $o,X6: a,X5: a] :
( ( $true
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( X8 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X5 @ X6 ) ) ) )
| ( $true
!= ( sK1 @ X8 ) )
| ( ( sK4 @ X5 @ X6 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X8: a > a > $o,X6: a,X5: a] :
( ( $true
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X5
@ X6 ) )
| ( ( sK4 @ X5 @ X6 )
= $true )
| ( $true
!= ( sK1 @ X8 ) ) ),
inference(equality_resolution,[status(thm)],[f18]) ).
thf(f18,plain,
! [X8: a > a > $o,X6: a,X7: a > a > $o,X5: a] :
( ( $true
!= ( sK1 @ X8 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X8 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X7 )
| ( ( X7 @ X5 @ X6 )
!= $true )
| ( ( sK4 @ X5 @ X6 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f59,plain,
( ! [X2: a,X3: a,X0: a,X1: a] :
( ( $true
= ( sK9 @ ( sK7 @ sK4 ) @ X2 @ X3 @ X0 @ X1 ) )
| ( $true
= ( sK4 @ X2 @ X3 ) )
| ( ( sK7 @ sK4 @ X0 @ X1 )
= $false ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ! [X2: a,X3: a,X0: a,X1: a] :
( ( $true
= ( sK4 @ X2 @ X3 ) )
| ( ( sK7 @ sK4 @ X0 @ X1 )
= $false )
| ( $true
= ( sK9 @ ( sK7 @ sK4 ) @ X2 @ X3 @ X0 @ X1 ) )
| ( $true != $true ) )
| ~ spl8_2 ),
inference(superposition,[status(thm)],[f32,f42]) ).
thf(f32,plain,
! [X10: a,X8: a > a > $o,X6: a,X9: a,X5: a] :
( ( $true
!= ( sK1 @ X8 ) )
| ( ( X8 @ X9 @ X10 )
= $false )
| ( ( sK4 @ X5 @ X6 )
= $true )
| ( $true
= ( sK9 @ X8 @ X5 @ X6 @ X9 @ X10 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X10: a,X8: a > a > $o,X6: a,X9: a,X5: a] :
( ( $true
!= ( sK1 @ X8 ) )
| ( $true
= ( ( X8 @ X9 @ X10 )
=> ( sK9 @ X8 @ X5 @ X6 @ X9 @ X10 ) ) )
| ( ( sK4 @ X5 @ X6 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X10: a,X8: a > a > $o,X6: a,X9: a,X5: a] :
( ( ( sK4 @ X5 @ X6 )
= $true )
| ( $true
!= ( sK1 @ X8 ) )
| ( $true
= ( ^ [Y0: a] :
( ( X8 @ X9 @ Y0 )
=> ( sK9 @ X8 @ X5 @ X6 @ X9 @ Y0 ) )
@ X10 ) ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X8: a > a > $o,X6: a,X9: a,X5: a] :
( ( $true
!= ( sK1 @ X8 ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( X8 @ X9 @ Y0 )
=> ( sK9 @ X8 @ X5 @ X6 @ X9 @ Y0 ) ) ) )
| ( ( sK4 @ X5 @ X6 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X8: a > a > $o,X6: a,X9: a,X5: a] :
( ( $true
!= ( sK1 @ X8 ) )
| ( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X8 @ Y0 @ Y1 )
=> ( sK9 @ X8 @ X5 @ X6 @ Y0 @ Y1 ) ) )
@ X9 ) )
| ( ( sK4 @ X5 @ X6 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X8: a > a > $o,X6: a,X5: a] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X8 @ Y0 @ Y1 )
=> ( sK9 @ X8 @ X5 @ X6 @ Y0 @ Y1 ) ) ) ) )
| ( $true
!= ( sK1 @ X8 ) )
| ( ( sK4 @ X5 @ X6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X8: a > a > $o,X6: a,X5: a] :
( ( $true
= ( ( sK0 @ ( sK9 @ X8 @ X5 @ X6 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X8 @ Y0 @ Y1 )
=> ( sK9 @ X8 @ X5 @ X6 @ Y0 @ Y1 ) ) ) ) ) )
| ( $true
!= ( sK1 @ X8 ) )
| ( ( sK4 @ X5 @ X6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f53,plain,
( ( $true
= ( sK7 @ sK4 @ ( sK5 @ sK4 ) @ ( sK6 @ sK4 ) ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f14,plain,
! [X9: a > a > $o] :
( ( ( X9 @ ( sK5 @ X9 ) @ ( sK6 @ X9 ) )
!= $true )
| ( $true
= ( X9 @ sK2 @ sK3 ) )
| ( $true
!= ( sK0 @ X9 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f57,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[status(thm)],[f56]) ).
thf(f56,plain,
( $false
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $true != $true )
| ~ spl8_1 ),
inference(superposition,[status(thm)],[f17,f38]) ).
thf(f38,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f17,plain,
( $true
!= ( sK4 @ sK2 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f54,plain,
( spl8_1
| spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f49,f51,f36]) ).
thf(f49,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( $true
= ( sK7 @ sK4 @ ( sK5 @ sK4 ) @ ( sK6 @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( $true != $true )
| ( $true
= ( sK7 @ sK4 @ ( sK5 @ sK4 ) @ ( sK6 @ sK4 ) ) ) ),
inference(superposition,[status(thm)],[f16,f19]) ).
thf(f16,plain,
! [X9: a > a > $o] :
( ( $true
!= ( sK0 @ X9 ) )
| ( $true
= ( sK7 @ X9 @ ( sK5 @ X9 ) @ ( sK6 @ X9 ) ) )
| ( $true
= ( X9 @ sK2 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f43,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f34,f40,f36]) ).
thf(f34,plain,
( ( $true
= ( sK1 @ ( sK7 @ sK4 ) ) )
| ( $true
= ( sK4 @ sK2 @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $true
= ( sK1 @ ( sK7 @ sK4 ) ) )
| ( $true != $true )
| ( $true
= ( sK4 @ sK2 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f15,f19]) ).
thf(f15,plain,
! [X9: a > a > $o] :
( ( $true
!= ( sK0 @ X9 ) )
| ( $true
= ( sK1 @ ( sK7 @ X9 ) ) )
| ( $true
= ( X9 @ sK2 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV124^5 : 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 : n011.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 12:40:32 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 : SEV124^5 : TPTP v9.2.1. Released v4.0.0.
% 0.21/0.47 % Domain : Set Theory (Relations)
% 0.21/0.47 % Problem : TPS problem from SETS-OF-RELNS-THMS
% 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_1078 [Bro09]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.30 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.20 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 1.00 v4.0.0
% 0.21/0.47 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.21/0.47 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 1 ( 1 avg)
% 0.21/0.47 % Number of connectives : 36 ( 0 ~; 0 |; 6 &; 23 @)
% 0.21/0.47 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 17 ( 17 avg)
% 0.21/0.47 % Number of types : 2 ( 1 usr)
% 0.21/0.47 % Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.21/0.47 % Number of variables : 18 ( 2 ^; 13 !; 3 ?; 18 :)
% 0.21/0.47 % SPC : TH0_THM_EQU_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(a_type,type,
% 0.21/0.47 a: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(cTHM254_A_pme,conjecture,
% 0.21/0.47 ! [PROP: ( a > a > $o ) > $o,S: ( a > a > $o ) > $o,Xx: a,Xy: a] :
% 0.21/0.47 ( ! [Xp: a > a > $o] :
% 0.21/0.47 ( ( ! [Xx0: a,Xy0: a] :
% 0.21/0.47 ( ? [R: a > a > $o] :
% 0.21/0.47 ( ( S @ R )
% 0.21/0.47 & ( R @ Xx0 @ Xy0 ) )
% 0.21/0.47 => ( Xp @ Xx0 @ Xy0 ) )
% 0.21/0.47 & ( PROP @ Xp ) )
% 0.21/0.47 => ( Xp @ Xx @ Xy ) )
% 0.21/0.47 => ! [Xp: a > a > $o] :
% 0.21/0.47 ( ( ! [Xx0: a,Xy0: a] :
% 0.21/0.47 ( ? [R: a > a > $o] :
% 0.21/0.47 ( ? [Q: a > a > $o] :
% 0.21/0.47 ( ( S @ Q )
% 0.21/0.47 & ( R
% 0.21/0.47 = ( ^ [Xx1: a,Xy1: a] :
% 0.21/0.47 ! [Xp0: a > a > $o] :
% 0.21/0.47 ( ( ! [Xx2: a,Xy2: a] :
% 0.21/0.47 ( ( Q @ Xx2 @ Xy2 )
% 0.21/0.47 => ( Xp0 @ Xx2 @ Xy2 ) )
% 0.21/0.47 & ( PROP @ Xp0 ) )
% 0.21/0.47 => ( Xp0 @ Xx1 @ Xy1 ) ) ) ) )
% 0.21/0.47 & ( R @ Xx0 @ Xy0 ) )
% 0.21/0.47 => ( Xp @ Xx0 @ Xy0 ) )
% 0.21/0.47 & ( PROP @ Xp ) )
% 0.21/0.47 => ( Xp @ Xx @ Xy ) ) ) ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 1.66/1.46 ---- Embedded in THF ---
% 1.66/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.46 %%% Generated on Tue Feb 24 12:40:33 EST 2026
% 1.66/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.46 %%% Logic specification used:
% 1.66/1.46 %%% thf(spec, logic, $$dhol).
% 1.66/1.46
% 1.66/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4CBTS5Mdks/DTF2DTF22429.p
% See solution above
% 1.66/1.46 ------------------------
% 1.66/1.47 ---- Cleaned THF ---
% 1.66/1.47 thf(a_type,type,
% 1.66/1.47 a: $tType ).
% 1.66/1.47
% 1.66/1.47 thf(cTHM254_A_pme,conjecture,
% 1.66/1.47 ! [PROP: ( a > a > $o ) > $o,S: ( a > a > $o ) > $o,Xx: a,Xy: a] :
% 1.66/1.47 ( ! [Xp: a > a > $o] :
% 1.66/1.47 ( ( ! [Xx0: a,Xy0: a] :
% 1.66/1.47 ( ? [R: a > a > $o] :
% 1.66/1.47 ( ( S @ R )
% 1.66/1.47 & ( R @ Xx0 @ Xy0 ) )
% 1.66/1.47 => ( Xp @ Xx0 @ Xy0 ) )
% 1.66/1.47 & ( PROP @ Xp ) )
% 1.66/1.47 => ( Xp @ Xx @ Xy ) )
% 1.66/1.47 => ! [Xp: a > a > $o] :
% 1.66/1.47 ( ( ! [Xx0: a,Xy0: a] :
% 1.66/1.47 ( ? [R: a > a > $o] :
% 1.66/1.47 ( ? [Q: a > a > $o] :
% 1.66/1.47 ( ( S @ Q )
% 1.66/1.47 & ( R
% 1.66/1.47 = ( ^ [Xx1: a,Xy1: a] :
% 1.66/1.47 ! [Xp0: a > a > $o] :
% 1.66/1.47 ( ( ! [Xx2: a,Xy2: a] :
% 1.66/1.47 ( ( Q @ Xx2 @ Xy2 )
% 1.66/1.47 => ( Xp0 @ Xx2 @ Xy2 ) )
% 1.66/1.47 & ( PROP @ Xp0 ) )
% 1.66/1.47 => ( Xp0 @ Xx1 @ Xy1 ) ) ) ) )
% 1.66/1.47 & ( R @ Xx0 @ Xy0 ) )
% 1.66/1.47 => ( Xp @ Xx0 @ Xy0 ) )
% 1.66/1.47 & ( PROP @ Xp ) )
% 1.66/1.47 => ( Xp @ Xx @ Xy ) ) ) ).
% 1.66/1.47 ------------------------
% 1.66/1.49 % (22529)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22429 for (2999ds/2Mi)
% 1.66/1.49 % (22528)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_22429 for (2999ds/27Mi)
% 1.66/1.49 % (22527)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_22429 for (2999ds/4Mi)
% 1.66/1.49 % (22526)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22429 for (2999ds/183Mi)
% 1.66/1.49 % (22531)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_22429 for (2999ds/275Mi)
% 1.66/1.49 % (22530)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_22429 for (2999ds/2Mi)
% 1.66/1.49 % (22532)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22429 for (2999ds/18Mi)
% 1.66/1.49 % (22529)Instruction limit reached!
% 1.66/1.49 % (22529)------------------------------
% 1.66/1.49 % (22529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.49 % (22530)Instruction limit reached!
% 1.66/1.49 % (22530)------------------------------
% 1.66/1.49 % (22530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.49 % (22529)Termination reason: Unknown
% 1.66/1.49 % (22529)Termination phase: Property scanning
% 1.66/1.49
% 1.66/1.49 % (22529)Memory used [KB]: 1023
% 1.66/1.49 % (22529)Time elapsed: 0.003 s
% 1.66/1.49 % (22529)Instructions burned: 3 (million)
% 1.66/1.49 % (22529)------------------------------
% 1.66/1.49 % (22529)------------------------------
% 1.66/1.49 % (22530)Termination reason: Unknown
% 1.66/1.49 % (22530)Termination phase: Saturation
% 1.66/1.49
% 1.66/1.49 % (22530)Memory used [KB]: 1023
% 1.66/1.49 % (22530)Time elapsed: 0.003 s
% 1.66/1.49 % (22530)Instructions burned: 3 (million)
% 1.66/1.49 % (22530)------------------------------
% 1.66/1.49 % (22530)------------------------------
% 1.66/1.49 % (22527)Instruction limit reached!
% 1.66/1.49 % (22527)------------------------------
% 1.66/1.49 % (22527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.49 % (22527)Termination reason: Unknown
% 1.66/1.49 % (22527)Termination phase: Saturation
% 1.66/1.49
% 1.66/1.49 % (22527)Memory used [KB]: 5500
% 1.66/1.49 % (22527)Time elapsed: 0.004 s
% 1.66/1.49 % (22527)Instructions burned: 4 (million)
% 1.66/1.49 % (22527)------------------------------
% 1.66/1.49 % (22527)------------------------------
% 1.81/1.50 % (22528)First to succeed.
% 1.81/1.50 % (22532)Also succeeded, but the first one will report.
% 1.81/1.50 % (22528)Refutation found. Thanks to Tanya!
% 1.81/1.50 % SZS status Theorem for DTF2THF_22429
% 1.81/1.50 % SZS output start Proof for DTF2THF_22429
% 1.81/1.50 thf(type_def_5, type, a: $tType).
% 1.81/1.50 thf(func_def_0, type, a: $tType).
% 1.81/1.50 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.81/1.50 thf(func_def_12, type, sK0: (a > a > $o) > $o).
% 1.81/1.50 thf(func_def_13, type, sK1: (a > a > $o) > $o).
% 1.81/1.50 thf(func_def_14, type, sK2: a).
% 1.81/1.50 thf(func_def_15, type, sK3: a).
% 1.81/1.50 thf(func_def_16, type, sK4: a > a > $o).
% 1.81/1.50 thf(func_def_17, type, sK5: (a > a > $o) > a).
% 1.81/1.50 thf(func_def_18, type, sK6: (a > a > $o) > a).
% 1.81/1.50 thf(func_def_19, type, sK7: (a > a > $o) > a > a > $o).
% 1.81/1.50 thf(func_def_21, type, sK9: (a > a > $o) > a > a > a > a > $o).
% 1.81/1.50 thf(func_def_22, type, ph10: !>[X0: $tType]:(X0)).
% 1.81/1.50 thf(f82,plain,(
% 1.81/1.50 $false),
% 1.81/1.50 inference(avatar_sat_refutation,[status(thm)],[f43,f54,f57,f81])).
% 1.81/1.50 thf(f81,plain,(
% 1.81/1.50 spl8_1 | ~spl8_2 | ~spl8_3),
% 1.81/1.50 inference(avatar_split_clause,[status(thm)],[f80,f51,f40,f36])).
% 1.81/1.50 thf(f36,definition,(
% 1.81/1.50 spl8_1 <=> ($true = (sK4 @ sK2 @ sK3))),
% 1.81/1.50 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 1.81/1.50 thf(f40,definition,(
% 1.81/1.50 spl8_2 <=> ($true = (sK1 @ (sK7 @ sK4)))),
% 1.81/1.50 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 1.81/1.50 thf(f51,definition,(
% 1.81/1.50 spl8_3 <=> ($true = (sK7 @ sK4 @ (sK5 @ sK4) @ (sK6 @ sK4)))),
% 1.81/1.50 introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition])).
% 1.81/1.50 thf(f80,plain,(
% 1.81/1.50 ($true = (sK4 @ sK2 @ sK3)) | (~spl8_2 | ~spl8_3)),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.81/1.50 thf(f79,plain,(
% 1.81/1.50 ($true = (sK4 @ sK2 @ sK3)) | ($true != $true) | (~spl8_2 | ~spl8_3)),
% 1.81/1.50 inference(forward_demodulation,[status(thm)],[f78,f19])).
% 1.81/1.50 thf(f19,plain,(
% 1.81/1.50 ($true = (sK0 @ sK4))),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.50 thf(f13,plain,(
% 1.81/1.50 (($true = (sK0 @ sK4)) & ! [X5 : a,X6 : a] : (! [X7 : a > a > $o] : (! [X8 : a > a > $o] : (($true != (sK1 @ X8)) | ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != X7)) | ((X7 @ X5 @ X6) != $true)) | ((sK4 @ X5 @ X6) = $true)) & ($true != (sK4 @ sK2 @ sK3))) & ! [X9 : a > a > $o] : (($true != (sK0 @ X9)) | ($true = (X9 @ sK2 @ sK3)) | ((($true = (sK7 @ X9 @ (sK5 @ X9) @ (sK6 @ X9))) & ($true = (sK1 @ (sK7 @ X9)))) & ((X9 @ (sK5 @ X9) @ (sK6 @ X9)) != $true)))),
% 1.81/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f8,f12,f11,f10,f9])).
% 1.81/1.50 thf(f9,plain,(
% 1.81/1.50 ? [X0 : (a > a > $o) > $o,X1 : (a > a > $o) > $o,X2 : a,X3 : a] : (? [X4 : a > a > $o] : (((X0 @ X4) = $true) & ! [X5 : a,X6 : a] : (! [X7 : a > a > $o] : (! [X8 : a > a > $o] : (((X1 @ X8) != $true) | ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != X7)) | ((X7 @ X5 @ X6) != $true)) | ((X4 @ X5 @ X6) = $true)) & ((X4 @ X2 @ X3) != $true)) & ! [X9 : a > a > $o] : (($true != (X0 @ X9)) | ($true = (X9 @ X2 @ X3)) | ? [X10 : a,X11 : a] : (? [X12 : a > a > $o] : (((X12 @ X10 @ X11) = $true) & ($true = (X1 @ X12))) & ($true != (X9 @ X10 @ X11))))) => (? [X4 : a > a > $o] : (($true = (sK0 @ X4)) & ! [X6 : a,X5 : a] : (! [X7 : a > a > $o] : (! [X8 : a > a > $o] : (($true != (sK1 @ X8)) | ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != X7)) | ((X7 @ X5 @ X6) != $true)) | ((X4 @ X5 @ X6) = $true)) & ($true != (X4 @ sK2 @ sK3))) & ! [X9 : a > a > $o] : (($true != (sK0 @ X9)) | ($true = (X9 @ sK2 @ sK3)) | ? [X11 : a,X10 : a] : (? [X12 : a > a > $o] : (((X12 @ X10 @ X11) = $true) & ($true = (sK1 @ X12))) & ($true != (X9 @ X10 @ X11)))))),
% 1.81/1.50 introduced(definition,[],[choice_axiom])).
% 1.81/1.50 thf(f10,plain,(
% 1.81/1.50 ? [X4 : a > a > $o] : (($true = (sK0 @ X4)) & ! [X6 : a,X5 : a] : (! [X7 : a > a > $o] : (! [X8 : a > a > $o] : (($true != (sK1 @ X8)) | ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != X7)) | ((X7 @ X5 @ X6) != $true)) | ((X4 @ X5 @ X6) = $true)) & ($true != (X4 @ sK2 @ sK3))) => (($true = (sK0 @ sK4)) & ! [X6 : a,X5 : a] : (! [X7 : a > a > $o] : (! [X8 : a > a > $o] : (($true != (sK1 @ X8)) | ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != X7)) | ((X7 @ X5 @ X6) != $true)) | ((sK4 @ X5 @ X6) = $true)) & ($true != (sK4 @ sK2 @ sK3)))),
% 1.81/1.50 introduced(definition,[],[choice_axiom])).
% 1.81/1.50 thf(f11,plain,(
% 1.81/1.50 ! [X9 : a > a > $o] : (? [X11 : a,X10 : a] : (? [X12 : a > a > $o] : (((X12 @ X10 @ X11) = $true) & ($true = (sK1 @ X12))) & ($true != (X9 @ X10 @ X11))) => (? [X12 : a > a > $o] : (($true = (X12 @ (sK5 @ X9) @ (sK6 @ X9))) & ($true = (sK1 @ X12))) & ((X9 @ (sK5 @ X9) @ (sK6 @ X9)) != $true)))),
% 1.81/1.50 introduced(definition,[],[choice_axiom])).
% 1.81/1.50 thf(f12,plain,(
% 1.81/1.50 ! [X9 : a > a > $o] : (? [X12 : a > a > $o] : (($true = (X12 @ (sK5 @ X9) @ (sK6 @ X9))) & ($true = (sK1 @ X12))) => (($true = (sK7 @ X9 @ (sK5 @ X9) @ (sK6 @ X9))) & ($true = (sK1 @ (sK7 @ X9)))))),
% 1.81/1.50 introduced(definition,[],[choice_axiom])).
% 1.81/1.50 thf(f8,plain,(
% 1.81/1.50 ? [X0 : (a > a > $o) > $o,X1 : (a > a > $o) > $o,X2 : a,X3 : a] : (? [X4 : a > a > $o] : (((X0 @ X4) = $true) & ! [X5 : a,X6 : a] : (! [X7 : a > a > $o] : (! [X8 : a > a > $o] : (((X1 @ X8) != $true) | ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != X7)) | ((X7 @ X5 @ X6) != $true)) | ((X4 @ X5 @ X6) = $true)) & ((X4 @ X2 @ X3) != $true)) & ! [X9 : a > a > $o] : (($true != (X0 @ X9)) | ($true = (X9 @ X2 @ X3)) | ? [X10 : a,X11 : a] : (? [X12 : a > a > $o] : (((X12 @ X10 @ X11) = $true) & ($true = (X1 @ X12))) & ($true != (X9 @ X10 @ X11)))))),
% 1.81/1.50 inference(rectify,[status(thm)],[f7])).
% 1.81/1.50 thf(f7,plain,(
% 1.81/1.50 ? [X0 : (a > a > $o) > $o,X1 : (a > a > $o) > $o,X2 : a,X3 : a] : (? [X8 : a > a > $o] : (((X0 @ X8) = $true) & ! [X9 : a,X10 : a] : (! [X11 : a > a > $o] : (! [X12 : a > a > $o] : (($true != (X1 @ X12)) | ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != X11)) | ((X11 @ X9 @ X10) != $true)) | ($true = (X8 @ X9 @ X10))) & ($true != (X8 @ X2 @ X3))) & ! [X4 : a > a > $o] : (((X0 @ X4) != $true) | ((X4 @ X2 @ X3) = $true) | ? [X5 : a,X6 : a] : (? [X7 : a > a > $o] : (((X7 @ X5 @ X6) = $true) & ((X1 @ X7) = $true)) & ((X4 @ X5 @ X6) != $true))))),
% 1.81/1.50 inference(flattening,[status(thm)],[f6])).
% 1.81/1.50 thf(f6,plain,(
% 1.81/1.50 ? [X0 : (a > a > $o) > $o,X1 : (a > a > $o) > $o,X2 : a,X3 : a] : (? [X8 : a > a > $o] : (($true != (X8 @ X2 @ X3)) & (((X0 @ X8) = $true) & ! [X9 : a,X10 : a] : (! [X11 : a > a > $o] : (! [X12 : a > a > $o] : (($true != (X1 @ X12)) | ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != X11)) | ((X11 @ X9 @ X10) != $true)) | ($true = (X8 @ X9 @ X10))))) & ! [X4 : a > a > $o] : (((X4 @ X2 @ X3) = $true) | (((X0 @ X4) != $true) | ? [X5 : a,X6 : a] : (? [X7 : a > a > $o] : (((X7 @ X5 @ X6) = $true) & ((X1 @ X7) = $true)) & ((X4 @ X5 @ X6) != $true)))))),
% 1.81/1.50 inference(ennf_transformation,[status(thm)],[f5])).
% 1.81/1.50 thf(f5,plain,(
% 1.81/1.50 ~! [X0 : (a > a > $o) > $o,X1 : (a > a > $o) > $o,X2 : a,X3 : a] : (! [X4 : a > a > $o] : ((((X0 @ X4) = $true) & ! [X5 : a,X6 : a] : (? [X7 : a > a > $o] : (((X7 @ X5 @ X6) = $true) & ((X1 @ X7) = $true)) => ((X4 @ X5 @ X6) = $true))) => ((X4 @ X2 @ X3) = $true)) => ! [X8 : a > a > $o] : ((((X0 @ X8) = $true) & ! [X9 : a,X10 : a] : (? [X11 : a > a > $o] : (? [X12 : a > a > $o] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((X0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) = X11) & ($true = (X1 @ X12))) & ((X11 @ X9 @ X10) = $true)) => ($true = (X8 @ X9 @ X10)))) => ($true = (X8 @ X2 @ X3))))),
% 1.81/1.50 inference(fool_elimination,[status(thm)],[f4])).
% 1.81/1.50 thf(f4,plain,(
% 1.81/1.50 ~! [X0 : (a > a > $o) > $o,X1 : (a > a > $o) > $o,X2 : a,X3 : a] : (! [X4 : a > a > $o] : (((X0 @ X4) & ! [X5 : a,X6 : a] : (? [X7 : a > a > $o] : ((X1 @ X7) & (X7 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) => ! [X8 : a > a > $o] : ((! [X9 : a,X10 : a] : (? [X11 : a > a > $o] : ((X11 @ X9 @ X10) & ? [X12 : a > a > $o] : (((^[X13 : a, X14 : a] : (! [X15 : a > a > $o] : ((! [X16 : a,X17 : a] : ((X12 @ X17 @ X16) => (X15 @ X17 @ X16)) & (X0 @ X15)) => (X15 @ X13 @ X14)))) = X11) & (X1 @ X12))) => (X8 @ X9 @ X10)) & (X0 @ X8)) => (X8 @ X2 @ X3)))),
% 1.81/1.50 inference(rectify,[status(thm)],[f2])).
% 1.81/1.50 thf(f2,negated_conjecture,(
% 1.81/1.50 ~! [X0 : (a > a > $o) > $o,X1 : (a > a > $o) > $o,X2 : a,X3 : a] : (! [X4 : a > a > $o] : (((X0 @ X4) & ! [X5 : a,X6 : a] : (? [X7 : a > a > $o] : ((X1 @ X7) & (X7 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) => ! [X4 : a > a > $o] : ((! [X5 : a,X6 : a] : (? [X7 : a > a > $o] : ((X7 @ X5 @ X6) & ? [X8 : a > a > $o] : (((^[X9 : a, X10 : a] : (! [X11 : a > a > $o] : ((! [X13 : a,X12 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13)) & (X0 @ X11)) => (X11 @ X9 @ X10)))) = X7) & (X1 @ X8))) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))),
% 1.81/1.50 inference(negated_conjecture,[status(cth)],[f1])).
% 1.81/1.50 thf(f1,conjecture,(
% 1.81/1.50 ! [X0 : (a > a > $o) > $o,X1 : (a > a > $o) > $o,X2 : a,X3 : a] : (! [X4 : a > a > $o] : (((X0 @ X4) & ! [X5 : a,X6 : a] : (? [X7 : a > a > $o] : ((X1 @ X7) & (X7 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) => ! [X4 : a > a > $o] : ((! [X5 : a,X6 : a] : (? [X7 : a > a > $o] : ((X7 @ X5 @ X6) & ? [X8 : a > a > $o] : (((^[X9 : a, X10 : a] : (! [X11 : a > a > $o] : ((! [X13 : a,X12 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13)) & (X0 @ X11)) => (X11 @ X9 @ X10)))) = X7) & (X1 @ X8))) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))),
% 1.81/1.50 file('/export/starexec/sandbox/tmp/tmp.4CBTS5Mdks/DTF2THF_22429.p',cTHM254_A_pme)).
% 1.81/1.50 thf(f78,plain,(
% 1.81/1.50 ($true != (sK0 @ sK4)) | ($true = (sK4 @ sK2 @ sK3)) | (~spl8_2 | ~spl8_3)),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.81/1.50 thf(f77,plain,(
% 1.81/1.50 ($true = (sK4 @ sK2 @ sK3)) | ($true != $true) | ($true != (sK0 @ sK4)) | (~spl8_2 | ~spl8_3)),
% 1.81/1.50 inference(superposition,[status(thm)],[f14,f75])).
% 1.81/1.50 thf(f75,plain,(
% 1.81/1.50 ($true = (sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))) | (~spl8_2 | ~spl8_3)),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.81/1.50 thf(f73,plain,(
% 1.81/1.50 ($true = (sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))) | ($true = $false) | (~spl8_2 | ~spl8_3)),
% 1.81/1.50 inference(superposition,[status(thm)],[f53,f68])).
% 1.81/1.50 thf(f68,plain,(
% 1.81/1.50 ( ! [X0 : a,X1 : a] : (((sK7 @ sK4 @ X0 @ X1) = $false) | ($true = (sK4 @ X0 @ X1))) ) | ~spl8_2),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.81/1.50 thf(f67,plain,(
% 1.81/1.50 ( ! [X0 : a,X1 : a] : (((sK7 @ sK4 @ X0 @ X1) = $false) | ($true = (sK4 @ X0 @ X1)) | ($true = $false)) ) | ~spl8_2),
% 1.81/1.50 inference(duplicate_literal_removal,[status(thm)],[f64])).
% 1.81/1.50 thf(f64,plain,(
% 1.81/1.50 ( ! [X0 : a,X1 : a] : (($true = $false) | ($true = (sK4 @ X0 @ X1)) | ($true = (sK4 @ X0 @ X1)) | ((sK7 @ sK4 @ X0 @ X1) = $false)) ) | ~spl8_2),
% 1.81/1.50 inference(superposition,[status(thm)],[f59,f45])).
% 1.81/1.50 thf(f45,plain,(
% 1.81/1.50 ( ! [X0 : a,X1 : a] : (((sK9 @ (sK7 @ sK4) @ X0 @ X1 @ X0 @ X1) = $false) | ($true = (sK4 @ X0 @ X1))) ) | ~spl8_2),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.81/1.50 thf(f44,plain,(
% 1.81/1.50 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = (sK4 @ X0 @ X1)) | ((sK9 @ (sK7 @ sK4) @ X0 @ X1 @ X0 @ X1) = $false)) ) | ~spl8_2),
% 1.81/1.50 inference(superposition,[status(thm)],[f24,f42])).
% 1.81/1.50 thf(f42,plain,(
% 1.81/1.50 ($true = (sK1 @ (sK7 @ sK4))) | ~spl8_2),
% 1.81/1.50 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.81/1.50 thf(f24,plain,(
% 1.81/1.50 ( ! [X8 : a > a > $o,X6 : a,X5 : a] : (($true != (sK1 @ X8)) | ((sK4 @ X5 @ X6) = $true) | ($false = (sK9 @ X8 @ X5 @ X6 @ X5 @ X6))) )),
% 1.81/1.50 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.81/1.50 thf(f23,plain,(
% 1.81/1.50 ( ! [X8 : a > a > $o,X6 : a,X5 : a] : (($true != (sK1 @ X8)) | ((((sK0 @ (sK9 @ X8 @ X5 @ X6)) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X8 @ Y0 @ Y1) => (sK9 @ X8 @ X5 @ X6 @ Y0 @ Y1))))))) => (sK9 @ X8 @ X5 @ X6 @ X5 @ X6)) = $false) | ((sK4 @ X5 @ X6) = $true)) )),
% 1.81/1.50 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.81/1.50 thf(f22,plain,(
% 1.81/1.50 ( ! [X8 : a > a > $o,X6 : a,X5 : a] : (((sK4 @ X5 @ X6) = $true) | ($true != (sK1 @ X8)) | ($false = ((^[Y0 : a > a > $o]: (((sK0 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((X8 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ X5 @ X6))) @ (sK9 @ X8 @ X5 @ X6)))) )),
% 1.81/1.50 inference(sigma_clausification,[status(thm)],[f21])).
% 1.81/1.50 thf(f21,plain,(
% 1.81/1.50 ( ! [X8 : a > a > $o,X6 : a,X5 : a] : (($true != (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK0 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((X8 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ X5 @ X6))))) | ($true != (sK1 @ X8)) | ((sK4 @ X5 @ X6) = $true)) )),
% 1.81/1.50 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.81/1.50 thf(f20,plain,(
% 1.81/1.50 ( ! [X8 : a > a > $o,X6 : a,X5 : a] : (($true != ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) @ X5 @ X6)) | ((sK4 @ X5 @ X6) = $true) | ($true != (sK1 @ X8))) )),
% 1.81/1.50 inference(equality_resolution,[status(thm)],[f18])).
% 1.81/1.50 thf(f18,plain,(
% 1.81/1.50 ( ! [X8 : a > a > $o,X6 : a,X7 : a > a > $o,X5 : a] : (($true != (sK1 @ X8)) | ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK0 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != X7) | ((X7 @ X5 @ X6) != $true) | ((sK4 @ X5 @ X6) = $true)) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.50 thf(f59,plain,(
% 1.81/1.50 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : (($true = (sK9 @ (sK7 @ sK4) @ X2 @ X3 @ X0 @ X1)) | ($true = (sK4 @ X2 @ X3)) | ((sK7 @ sK4 @ X0 @ X1) = $false)) ) | ~spl8_2),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.81/1.50 thf(f58,plain,(
% 1.81/1.50 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : (($true = (sK4 @ X2 @ X3)) | ((sK7 @ sK4 @ X0 @ X1) = $false) | ($true = (sK9 @ (sK7 @ sK4) @ X2 @ X3 @ X0 @ X1)) | ($true != $true)) ) | ~spl8_2),
% 1.81/1.50 inference(superposition,[status(thm)],[f32,f42])).
% 1.81/1.50 thf(f32,plain,(
% 1.81/1.50 ( ! [X10 : a,X8 : a > a > $o,X6 : a,X9 : a,X5 : a] : (($true != (sK1 @ X8)) | ((X8 @ X9 @ X10) = $false) | ((sK4 @ X5 @ X6) = $true) | ($true = (sK9 @ X8 @ X5 @ X6 @ X9 @ X10))) )),
% 1.81/1.50 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.81/1.50 thf(f31,plain,(
% 1.81/1.50 ( ! [X10 : a,X8 : a > a > $o,X6 : a,X9 : a,X5 : a] : (($true != (sK1 @ X8)) | ($true = ((X8 @ X9 @ X10) => (sK9 @ X8 @ X5 @ X6 @ X9 @ X10))) | ((sK4 @ X5 @ X6) = $true)) )),
% 1.81/1.50 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.81/1.50 thf(f30,plain,(
% 1.81/1.50 ( ! [X10 : a,X8 : a > a > $o,X6 : a,X9 : a,X5 : a] : (((sK4 @ X5 @ X6) = $true) | ($true != (sK1 @ X8)) | ($true = ((^[Y0 : a]: ((X8 @ X9 @ Y0) => (sK9 @ X8 @ X5 @ X6 @ X9 @ Y0))) @ X10))) )),
% 1.81/1.50 inference(pi_clausification,[status(thm)],[f29])).
% 1.81/1.50 thf(f29,plain,(
% 1.81/1.50 ( ! [X8 : a > a > $o,X6 : a,X9 : a,X5 : a] : (($true != (sK1 @ X8)) | ($true = (!! @ a @ (^[Y0 : a]: ((X8 @ X9 @ Y0) => (sK9 @ X8 @ X5 @ X6 @ X9 @ Y0))))) | ((sK4 @ X5 @ X6) = $true)) )),
% 1.81/1.50 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.81/1.50 thf(f28,plain,(
% 1.81/1.50 ( ! [X8 : a > a > $o,X6 : a,X9 : a,X5 : a] : (($true != (sK1 @ X8)) | ($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X8 @ Y0 @ Y1) => (sK9 @ X8 @ X5 @ X6 @ Y0 @ Y1))))) @ X9)) | ((sK4 @ X5 @ X6) = $true)) )),
% 1.81/1.50 inference(pi_clausification,[status(thm)],[f26])).
% 1.81/1.50 thf(f26,plain,(
% 1.81/1.50 ( ! [X8 : a > a > $o,X6 : a,X5 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X8 @ Y0 @ Y1) => (sK9 @ X8 @ X5 @ X6 @ Y0 @ Y1))))))) | ($true != (sK1 @ X8)) | ((sK4 @ X5 @ X6) = $true)) )),
% 1.81/1.50 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.81/1.50 thf(f25,plain,(
% 1.81/1.50 ( ! [X8 : a > a > $o,X6 : a,X5 : a] : (($true = ((sK0 @ (sK9 @ X8 @ X5 @ X6)) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X8 @ Y0 @ Y1) => (sK9 @ X8 @ X5 @ X6 @ Y0 @ Y1)))))))) | ($true != (sK1 @ X8)) | ((sK4 @ X5 @ X6) = $true)) )),
% 1.81/1.50 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.81/1.50 thf(f53,plain,(
% 1.81/1.50 ($true = (sK7 @ sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))) | ~spl8_3),
% 1.81/1.50 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.81/1.50 thf(f14,plain,(
% 1.81/1.50 ( ! [X9 : a > a > $o] : (((X9 @ (sK5 @ X9) @ (sK6 @ X9)) != $true) | ($true = (X9 @ sK2 @ sK3)) | ($true != (sK0 @ X9))) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.50 thf(f57,plain,(
% 1.81/1.50 ~spl8_1),
% 1.81/1.50 inference(avatar_contradiction_clause,[status(thm)],[f56])).
% 1.81/1.50 thf(f56,plain,(
% 1.81/1.50 $false | ~spl8_1),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.81/1.50 thf(f55,plain,(
% 1.81/1.50 ($true != $true) | ~spl8_1),
% 1.81/1.50 inference(superposition,[status(thm)],[f17,f38])).
% 1.81/1.50 thf(f38,plain,(
% 1.81/1.50 ($true = (sK4 @ sK2 @ sK3)) | ~spl8_1),
% 1.81/1.50 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.81/1.50 thf(f17,plain,(
% 1.81/1.50 ($true != (sK4 @ sK2 @ sK3))),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.50 thf(f54,plain,(
% 1.81/1.50 spl8_1 | spl8_3),
% 1.81/1.50 inference(avatar_split_clause,[status(thm)],[f49,f51,f36])).
% 1.81/1.50 thf(f49,plain,(
% 1.81/1.50 ($true = (sK4 @ sK2 @ sK3)) | ($true = (sK7 @ sK4 @ (sK5 @ sK4) @ (sK6 @ sK4)))),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.81/1.50 thf(f48,plain,(
% 1.81/1.50 ($true = (sK4 @ sK2 @ sK3)) | ($true != $true) | ($true = (sK7 @ sK4 @ (sK5 @ sK4) @ (sK6 @ sK4)))),
% 1.81/1.50 inference(superposition,[status(thm)],[f16,f19])).
% 1.81/1.50 thf(f16,plain,(
% 1.81/1.50 ( ! [X9 : a > a > $o] : (($true != (sK0 @ X9)) | ($true = (sK7 @ X9 @ (sK5 @ X9) @ (sK6 @ X9))) | ($true = (X9 @ sK2 @ sK3))) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.50 thf(f43,plain,(
% 1.81/1.50 spl8_1 | spl8_2),
% 1.81/1.50 inference(avatar_split_clause,[status(thm)],[f34,f40,f36])).
% 1.81/1.50 thf(f34,plain,(
% 1.81/1.50 ($true = (sK1 @ (sK7 @ sK4))) | ($true = (sK4 @ sK2 @ sK3))),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.81/1.50 thf(f33,plain,(
% 1.81/1.50 ($true = (sK1 @ (sK7 @ sK4))) | ($true != $true) | ($true = (sK4 @ sK2 @ sK3))),
% 1.81/1.50 inference(superposition,[status(thm)],[f15,f19])).
% 1.81/1.50 thf(f15,plain,(
% 1.81/1.50 ( ! [X9 : a > a > $o] : (($true != (sK0 @ X9)) | ($true = (sK1 @ (sK7 @ X9))) | ($true = (X9 @ sK2 @ sK3))) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.50 % SZS output end Proof for DTF2THF_22429
% 1.81/1.50 % (22528)------------------------------
% 1.81/1.50 % (22528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.50 % (22528)Termination reason: Refutation
% 1.81/1.50
% 1.81/1.50 % (22528)Memory used [KB]: 5628
% 1.81/1.50 % (22528)Time elapsed: 0.012 s
% 1.81/1.50 % (22528)Instructions burned: 13 (million)
% 1.81/1.50 % (22528)------------------------------
% 1.81/1.50 % (22528)------------------------------
% 1.81/1.50 % (22525)Success in time 0.025 s
%------------------------------------------------------------------------------