%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV137^5 : 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 : n027.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 09:40:22 AM UTC 2026
% Result : Theorem 0.25s 1.14s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 70 ( 5 unt; 0 typ; 8 def)
% Number of atoms : 617 ( 213 equ; 0 cnn)
% Maximal formula atoms : 30 ( 8 avg)
% Number of connectives : 733 ( 127 ~; 126 |; 76 &; 352 @)
% ( 8 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 13 con; 0-2 aty)
% Number of variables : 136 ( 0 ^; 90 !; 46 ?; 136 :)
% 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 ).
thf(func_def_6,type,
sK1: a > a > $o ).
thf(func_def_7,type,
sK2: a ).
thf(func_def_8,type,
sK3: a ).
thf(func_def_9,type,
sK4: ( a > $o ) > a ).
thf(func_def_10,type,
sK5: ( a > $o ) > a ).
thf(func_def_11,type,
sK6: ( a > $o ) > a ).
thf(func_def_12,type,
sK7: ( a > $o ) > a ).
thf(func_def_13,type,
sK8: a > $o ).
thf(func_def_15,type,
ph10:
!>[X0: $tType] : X0 ).
thf(f93,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f33,f40,f58,f61,f68,f79,f82,f87,f92]) ).
thf(f92,plain,
( spl9_4
| ~ spl9_1
| ~ spl9_7 ),
inference(avatar_split_clause,[status(thm)],[f91,f65,f26,f46]) ).
thf(f46,definition,
( spl9_4
<=> ( $true
= ( sK8 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl9_4])],[avatar_definition]) ).
thf(f26,definition,
( spl9_1
<=> ( $true
= ( sK8 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition]) ).
thf(f65,definition,
( spl9_7
<=> ( $true
= ( sK8 @ ( sK6 @ sK8 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_7])],[avatar_definition]) ).
thf(f91,plain,
( ( $true
= ( sK8 @ sK3 ) )
| ~ spl9_1
| ~ spl9_7 ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $true
= ( sK8 @ sK3 ) )
| ( $true != $true )
| ~ spl9_1
| ~ spl9_7 ),
inference(forward_demodulation,[status(thm)],[f89,f28]) ).
thf(f28,plain,
( ( $true
= ( sK8 @ sK2 ) )
| ~ spl9_1 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f89,plain,
( ( $true
= ( sK8 @ sK3 ) )
| ( $true
!= ( sK8 @ sK2 ) )
| ~ spl9_7 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $true != $true )
| ( $true
!= ( sK8 @ sK2 ) )
| ( $true
= ( sK8 @ sK3 ) )
| ~ spl9_7 ),
inference(superposition,[status(thm)],[f18,f67]) ).
thf(f67,plain,
( ( $true
= ( sK8 @ ( sK6 @ sK8 ) ) )
| ~ spl9_7 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f18,plain,
! [X7: a > $o] :
( ( $true
!= ( X7 @ ( sK6 @ X7 ) ) )
| ( ( X7 @ sK3 )
= $true )
| ( ( X7 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X4: a > $o] :
( ( $true
!= ( X4 @ sK0 ) )
| ( ( ( X4 @ ( sK5 @ X4 ) )
!= $true )
& ( ( sK1 @ ( sK4 @ X4 ) @ ( sK5 @ X4 ) )
= $true )
& ( ( X4 @ ( sK4 @ X4 ) )
= $true ) )
| ( $true
= ( X4 @ sK2 ) ) )
& ! [X7: a > $o] :
( ( ( ( sK1 @ ( sK7 @ X7 ) @ ( sK6 @ X7 ) )
= $true )
& ( $true
!= ( X7 @ ( sK6 @ X7 ) ) )
& ( ( X7 @ ( sK7 @ X7 ) )
= $true ) )
| ( ( X7 @ sK2 )
!= $true )
| ( ( X7 @ sK3 )
= $true ) )
& ! [X11: a,X12: a] :
( ( $true
!= ( sK1 @ X11 @ X12 ) )
| ( ( sK8 @ X11 )
!= $true )
| ( ( sK8 @ X12 )
= $true ) )
& ( $true
!= ( sK8 @ sK3 ) )
& ( ( sK8 @ sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a,X1: a > a > $o,X2: a,X3: a] :
( ! [X4: a > $o] :
( ( $true
!= ( X4 @ X0 ) )
| ? [X5: a,X6: a] :
( ( ( X4 @ X6 )
!= $true )
& ( $true
= ( X1 @ X5 @ X6 ) )
& ( ( X4 @ X5 )
= $true ) )
| ( ( X4 @ X2 )
= $true ) )
& ! [X7: a > $o] :
( ? [X8: a,X9: a] :
( ( $true
= ( X1 @ X9 @ X8 ) )
& ( $true
!= ( X7 @ X8 ) )
& ( ( X7 @ X9 )
= $true ) )
| ( $true
!= ( X7 @ X2 ) )
| ( $true
= ( X7 @ X3 ) ) )
& ? [X10: a > $o] :
( ! [X11: a,X12: a] :
( ( $true
!= ( X1 @ X11 @ X12 ) )
| ( ( X10 @ X11 )
!= $true )
| ( ( X10 @ X12 )
= $true ) )
& ( $true
!= ( X10 @ X3 ) )
& ( $true
= ( X10 @ X0 ) ) ) )
=> ( ! [X4: a > $o] :
( ( $true
!= ( X4 @ sK0 ) )
| ? [X6: a,X5: a] :
( ( ( X4 @ X6 )
!= $true )
& ( $true
= ( sK1 @ X5 @ X6 ) )
& ( ( X4 @ X5 )
= $true ) )
| ( $true
= ( X4 @ sK2 ) ) )
& ! [X7: a > $o] :
( ? [X9: a,X8: a] :
( ( ( sK1 @ X9 @ X8 )
= $true )
& ( $true
!= ( X7 @ X8 ) )
& ( ( X7 @ X9 )
= $true ) )
| ( ( X7 @ sK2 )
!= $true )
| ( ( X7 @ sK3 )
= $true ) )
& ? [X10: a > $o] :
( ! [X12: a,X11: a] :
( ( $true
!= ( sK1 @ X11 @ X12 ) )
| ( ( X10 @ X11 )
!= $true )
| ( ( X10 @ X12 )
= $true ) )
& ( $true
!= ( X10 @ sK3 ) )
& ( ( X10 @ sK0 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X4: a > $o] :
( ? [X6: a,X5: a] :
( ( ( X4 @ X6 )
!= $true )
& ( $true
= ( sK1 @ X5 @ X6 ) )
& ( ( X4 @ X5 )
= $true ) )
=> ( ( ( X4 @ ( sK5 @ X4 ) )
!= $true )
& ( ( sK1 @ ( sK4 @ X4 ) @ ( sK5 @ X4 ) )
= $true )
& ( ( X4 @ ( sK4 @ X4 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X7: a > $o] :
( ? [X9: a,X8: a] :
( ( ( sK1 @ X9 @ X8 )
= $true )
& ( $true
!= ( X7 @ X8 ) )
& ( ( X7 @ X9 )
= $true ) )
=> ( ( ( sK1 @ ( sK7 @ X7 ) @ ( sK6 @ X7 ) )
= $true )
& ( $true
!= ( X7 @ ( sK6 @ X7 ) ) )
& ( ( X7 @ ( sK7 @ X7 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X10: a > $o] :
( ! [X12: a,X11: a] :
( ( $true
!= ( sK1 @ X11 @ X12 ) )
| ( ( X10 @ X11 )
!= $true )
| ( ( X10 @ X12 )
= $true ) )
& ( $true
!= ( X10 @ sK3 ) )
& ( ( X10 @ sK0 )
= $true ) )
=> ( ! [X12: a,X11: a] :
( ( $true
!= ( sK1 @ X11 @ X12 ) )
| ( ( sK8 @ X11 )
!= $true )
| ( ( sK8 @ X12 )
= $true ) )
& ( $true
!= ( sK8 @ sK3 ) )
& ( ( sK8 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a,X1: a > a > $o,X2: a,X3: a] :
( ! [X4: a > $o] :
( ( $true
!= ( X4 @ X0 ) )
| ? [X5: a,X6: a] :
( ( ( X4 @ X6 )
!= $true )
& ( $true
= ( X1 @ X5 @ X6 ) )
& ( ( X4 @ X5 )
= $true ) )
| ( ( X4 @ X2 )
= $true ) )
& ! [X7: a > $o] :
( ? [X8: a,X9: a] :
( ( $true
= ( X1 @ X9 @ X8 ) )
& ( $true
!= ( X7 @ X8 ) )
& ( ( X7 @ X9 )
= $true ) )
| ( $true
!= ( X7 @ X2 ) )
| ( $true
= ( X7 @ X3 ) ) )
& ? [X10: a > $o] :
( ! [X11: a,X12: a] :
( ( $true
!= ( X1 @ X11 @ X12 ) )
| ( ( X10 @ X11 )
!= $true )
| ( ( X10 @ X12 )
= $true ) )
& ( $true
!= ( X10 @ X3 ) )
& ( $true
= ( X10 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X2: a,X3: a > a > $o,X1: a,X0: a] :
( ! [X4: a > $o] :
( ( ( X4 @ X2 )
!= $true )
| ? [X6: a,X5: a] :
( ( ( X4 @ X5 )
!= $true )
& ( $true
= ( X3 @ X6 @ X5 ) )
& ( ( X4 @ X6 )
= $true ) )
| ( ( X4 @ X1 )
= $true ) )
& ! [X7: a > $o] :
( ? [X9: a,X8: a] :
( ( ( X3 @ X8 @ X9 )
= $true )
& ( ( X7 @ X9 )
!= $true )
& ( $true
= ( X7 @ X8 ) ) )
| ( ( X7 @ X1 )
!= $true )
| ( ( X7 @ X0 )
= $true ) )
& ? [X10: a > $o] :
( ! [X12: a,X11: a] :
( ( ( X3 @ X12 @ X11 )
!= $true )
| ( ( X10 @ X12 )
!= $true )
| ( ( X10 @ X11 )
= $true ) )
& ( $true
!= ( X10 @ X0 ) )
& ( ( X10 @ X2 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: a,X3: a > a > $o,X0: a,X2: a] :
( ? [X10: a > $o] :
( ( $true
!= ( X10 @ X0 ) )
& ( ( X10 @ X2 )
= $true )
& ! [X11: a,X12: a] :
( ( ( X10 @ X11 )
= $true )
| ( ( X10 @ X12 )
!= $true )
| ( ( X3 @ X12 @ X11 )
!= $true ) ) )
& ! [X7: a > $o] :
( ( ( X7 @ X0 )
= $true )
| ( ( X7 @ X1 )
!= $true )
| ? [X9: a,X8: a] :
( ( ( X7 @ X9 )
!= $true )
& ( $true
= ( X7 @ X8 ) )
& ( ( X3 @ X8 @ X9 )
= $true ) ) )
& ! [X4: a > $o] :
( ( ( X4 @ X1 )
= $true )
| ( ( X4 @ X2 )
!= $true )
| ? [X5: a,X6: a] :
( ( ( X4 @ X5 )
!= $true )
& ( ( X4 @ X6 )
= $true )
& ( $true
= ( X3 @ X6 @ X5 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: a,X3: a > a > $o,X0: a,X2: a] :
( ( ! [X7: a > $o] :
( ! [X9: a,X8: a] :
( ( ( $true
= ( X7 @ X8 ) )
& ( ( X3 @ X8 @ X9 )
= $true ) )
=> ( ( X7 @ X9 )
= $true ) )
=> ( ( ( X7 @ X1 )
= $true )
=> ( ( X7 @ X0 )
= $true ) ) )
& ! [X4: a > $o] :
( ! [X5: a,X6: a] :
( ( ( ( X4 @ X6 )
= $true )
& ( $true
= ( X3 @ X6 @ X5 ) ) )
=> ( ( X4 @ X5 )
= $true ) )
=> ( ( ( X4 @ X2 )
= $true )
=> ( ( X4 @ X1 )
= $true ) ) ) )
=> ! [X10: a > $o] :
( ! [X11: a,X12: a] :
( ( ( ( X10 @ X12 )
= $true )
& ( ( X3 @ X12 @ X11 )
= $true ) )
=> ( ( X10 @ X11 )
= $true ) )
=> ( ( ( X10 @ X2 )
= $true )
=> ( $true
= ( X10 @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a,X2: a,X3: a > a > $o] :
( ( ! [X4: a > $o] :
( ! [X5: a,X6: a] :
( ( ( X3 @ X6 @ X5 )
& ( X4 @ X6 ) )
=> ( X4 @ X5 ) )
=> ( ( X4 @ X2 )
=> ( X4 @ X1 ) ) )
& ! [X7: a > $o] :
( ! [X8: a,X9: a] :
( ( ( X3 @ X8 @ X9 )
& ( X7 @ X8 ) )
=> ( X7 @ X9 ) )
=> ( ( X7 @ X1 )
=> ( X7 @ X0 ) ) ) )
=> ! [X10: a > $o] :
( ! [X11: a,X12: a] :
( ( ( X3 @ X12 @ X11 )
& ( X10 @ X12 ) )
=> ( X10 @ X11 ) )
=> ( ( X10 @ X2 )
=> ( X10 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: a,X2: a,X1: a,X0: a > a > $o] :
( ( ! [X4: a > $o] :
( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
& ( X4 @ X5 ) )
=> ( X4 @ X6 ) )
=> ( ( X4 @ X1 )
=> ( X4 @ X2 ) ) )
& ! [X4: a > $o] :
( ! [X5: a,X6: a] :
( ( ( X0 @ X5 @ X6 )
& ( X4 @ X5 ) )
=> ( X4 @ X6 ) )
=> ( ( X4 @ X2 )
=> ( X4 @ X3 ) ) ) )
=> ! [X4: a > $o] :
( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
& ( X4 @ X5 ) )
=> ( X4 @ X6 ) )
=> ( ( X4 @ X1 )
=> ( X4 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X3: a,X2: a,X1: a,X0: a > a > $o] :
( ( ! [X4: a > $o] :
( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
& ( X4 @ X5 ) )
=> ( X4 @ X6 ) )
=> ( ( X4 @ X1 )
=> ( X4 @ X2 ) ) )
& ! [X4: a > $o] :
( ! [X5: a,X6: a] :
( ( ( X0 @ X5 @ X6 )
& ( X4 @ X5 ) )
=> ( X4 @ X6 ) )
=> ( ( X4 @ X2 )
=> ( X4 @ X3 ) ) ) )
=> ! [X4: a > $o] :
( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
& ( X4 @ X5 ) )
=> ( X4 @ X6 ) )
=> ( ( X4 @ X1 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rkKDCpOLdu/DTF2THF_19378.p',cTHM204_pme) ).
thf(f87,plain,
( spl9_5
| spl9_4
| ~ spl9_1 ),
inference(avatar_split_clause,[status(thm)],[f86,f26,f46,f50]) ).
thf(f50,definition,
( spl9_5
<=> ( ( sK8 @ ( sK7 @ sK8 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_5])],[avatar_definition]) ).
thf(f86,plain,
( ( ( sK8 @ ( sK7 @ sK8 ) )
= $true )
| ( $true
= ( sK8 @ sK3 ) )
| ~ spl9_1 ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
( ( $true
= ( sK8 @ sK3 ) )
| ( ( sK8 @ ( sK7 @ sK8 ) )
= $true )
| ( $true != $true )
| ~ spl9_1 ),
inference(superposition,[status(thm)],[f17,f28]) ).
thf(f17,plain,
! [X7: a > $o] :
( ( ( X7 @ sK2 )
!= $true )
| ( ( X7 @ ( sK7 @ X7 ) )
= $true )
| ( ( X7 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f82,plain,
spl9_8,
inference(avatar_contradiction_clause,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
| spl9_8 ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $true != $true )
| spl9_8 ),
inference(superposition,[status(thm)],[f78,f14]) ).
thf(f14,plain,
( ( sK8 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f78,plain,
( ( ( sK8 @ sK0 )
!= $true )
| spl9_8 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f76,definition,
( spl9_8
<=> ( ( sK8 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_8])],[avatar_definition]) ).
thf(f79,plain,
( spl9_1
| ~ spl9_8
| ~ spl9_2
| ~ spl9_3 ),
inference(avatar_split_clause,[status(thm)],[f74,f37,f30,f76,f26]) ).
thf(f30,definition,
( spl9_2
<=> ( ( sK8 @ ( sK4 @ sK8 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition]) ).
thf(f37,definition,
( spl9_3
<=> ( ( sK1 @ ( sK4 @ sK8 ) @ ( sK5 @ sK8 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition]) ).
thf(f74,plain,
( ( $true
= ( sK8 @ sK2 ) )
| ( ( sK8 @ sK0 )
!= $true )
| ~ spl9_2
| ~ spl9_3 ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $true != $true )
| ( ( sK8 @ sK0 )
!= $true )
| ( $true
= ( sK8 @ sK2 ) )
| ~ spl9_2
| ~ spl9_3 ),
inference(superposition,[status(thm)],[f22,f72]) ).
thf(f72,plain,
( ( ( sK8 @ ( sK5 @ sK8 ) )
= $true )
| ~ spl9_2
| ~ spl9_3 ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( sK8 @ ( sK5 @ sK8 ) )
= $true )
| ( $true != $true )
| ~ spl9_2
| ~ spl9_3 ),
inference(forward_demodulation,[status(thm)],[f70,f32]) ).
thf(f32,plain,
( ( ( sK8 @ ( sK4 @ sK8 ) )
= $true )
| ~ spl9_2 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f70,plain,
( ( ( sK8 @ ( sK4 @ sK8 ) )
!= $true )
| ( ( sK8 @ ( sK5 @ sK8 ) )
= $true )
| ~ spl9_3 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( ( sK8 @ ( sK5 @ sK8 ) )
= $true )
| ( $true != $true )
| ( ( sK8 @ ( sK4 @ sK8 ) )
!= $true )
| ~ spl9_3 ),
inference(superposition,[status(thm)],[f16,f39]) ).
thf(f39,plain,
( ( ( sK1 @ ( sK4 @ sK8 ) @ ( sK5 @ sK8 ) )
= $true )
| ~ spl9_3 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f16,plain,
! [X11: a,X12: a] :
( ( $true
!= ( sK1 @ X11 @ X12 ) )
| ( ( sK8 @ X11 )
!= $true )
| ( ( sK8 @ X12 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f22,plain,
! [X4: a > $o] :
( ( ( X4 @ ( sK5 @ X4 ) )
!= $true )
| ( $true
= ( X4 @ sK2 ) )
| ( $true
!= ( X4 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f68,plain,
( ~ spl9_5
| spl9_7
| ~ spl9_6 ),
inference(avatar_split_clause,[status(thm)],[f63,f55,f65,f50]) ).
thf(f55,definition,
( spl9_6
<=> ( $true
= ( sK1 @ ( sK7 @ sK8 ) @ ( sK6 @ sK8 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_6])],[avatar_definition]) ).
thf(f63,plain,
( ( $true
= ( sK8 @ ( sK6 @ sK8 ) ) )
| ( ( sK8 @ ( sK7 @ sK8 ) )
!= $true )
| ~ spl9_6 ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true != $true )
| ( $true
= ( sK8 @ ( sK6 @ sK8 ) ) )
| ( ( sK8 @ ( sK7 @ sK8 ) )
!= $true )
| ~ spl9_6 ),
inference(superposition,[status(thm)],[f16,f57]) ).
thf(f57,plain,
( ( $true
= ( sK1 @ ( sK7 @ sK8 ) @ ( sK6 @ sK8 ) ) )
| ~ spl9_6 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f61,plain,
~ spl9_4,
inference(avatar_contradiction_clause,[status(thm)],[f60]) ).
thf(f60,plain,
( $false
| ~ spl9_4 ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true != $true )
| ~ spl9_4 ),
inference(superposition,[status(thm)],[f15,f48]) ).
thf(f48,plain,
( ( $true
= ( sK8 @ sK3 ) )
| ~ spl9_4 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f15,plain,
( $true
!= ( sK8 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f58,plain,
( spl9_6
| spl9_4
| ~ spl9_1 ),
inference(avatar_split_clause,[status(thm)],[f43,f26,f46,f55]) ).
thf(f43,plain,
( ( $true
= ( sK8 @ sK3 ) )
| ( $true
= ( sK1 @ ( sK7 @ sK8 ) @ ( sK6 @ sK8 ) ) )
| ~ spl9_1 ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ( $true
= ( sK8 @ sK3 ) )
| ( $true != $true )
| ( $true
= ( sK1 @ ( sK7 @ sK8 ) @ ( sK6 @ sK8 ) ) )
| ~ spl9_1 ),
inference(superposition,[status(thm)],[f19,f28]) ).
thf(f19,plain,
! [X7: a > $o] :
( ( ( X7 @ sK2 )
!= $true )
| ( ( sK1 @ ( sK7 @ X7 ) @ ( sK6 @ X7 ) )
= $true )
| ( ( X7 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f40,plain,
( spl9_3
| spl9_1 ),
inference(avatar_split_clause,[status(thm)],[f35,f26,f37]) ).
thf(f35,plain,
( ( $true
= ( sK8 @ sK2 ) )
| ( ( sK1 @ ( sK4 @ sK8 ) @ ( sK5 @ sK8 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true
= ( sK8 @ sK2 ) )
| ( ( sK1 @ ( sK4 @ sK8 ) @ ( sK5 @ sK8 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f21,f14]) ).
thf(f21,plain,
! [X4: a > $o] :
( ( $true
!= ( X4 @ sK0 ) )
| ( $true
= ( X4 @ sK2 ) )
| ( ( sK1 @ ( sK4 @ X4 ) @ ( sK5 @ X4 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f33,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[status(thm)],[f24,f30,f26]) ).
thf(f24,plain,
( ( $true
= ( sK8 @ sK2 ) )
| ( ( sK8 @ ( sK4 @ sK8 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
= ( sK8 @ sK2 ) )
| ( $true != $true )
| ( ( sK8 @ ( sK4 @ sK8 ) )
= $true ) ),
inference(superposition,[status(thm)],[f20,f14]) ).
thf(f20,plain,
! [X4: a > $o] :
( ( $true
!= ( X4 @ sK0 ) )
| ( $true
= ( X4 @ sK2 ) )
| ( ( X4 @ ( sK4 @ X4 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV137^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:40:52 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.44 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SEV137^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.44 % Domain : Set Theory (Relations)
% 0.17/0.44 % Problem : TPS problem THM204
% 0.17/0.44 % Version : Especial.
% 0.17/0.44 % English :
% 0.17/0.44
% 0.17/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.44 % Source : [Bro09]
% 0.17/0.44 % Names : tps_0472 [Bro09]
% 0.17/0.44 % : THM204 [TPS]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.17/0.44 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.17/0.44 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 0 ( 0 avg)
% 0.17/0.44 % Number of connectives : 32 ( 0 ~; 0 |; 4 &; 18 @)
% 0.17/0.44 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 15 ( 15 avg)
% 0.17/0.44 % Number of types : 2 ( 1 usr)
% 0.17/0.44 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.17/0.44 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.17/0.44 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.44 % : Polymorphic definitions expanded.
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf(a_type,type,
% 0.17/0.44 a: $tType ).
% 0.17/0.44
% 0.17/0.44 thf(cTHM204_pme,conjecture,
% 0.17/0.44 ! [Xr: a > a > $o,Xx: a,Xy: a,Xz: a] :
% 0.17/0.44 ( ( ! [Xx0: a > $o] :
% 0.17/0.44 ( ! [Xy0: a,Xz0: a] :
% 0.17/0.44 ( ( ( Xr @ Xy0 @ Xz0 )
% 0.17/0.44 & ( Xx0 @ Xy0 ) )
% 0.17/0.44 => ( Xx0 @ Xz0 ) )
% 0.17/0.44 => ( ( Xx0 @ Xx )
% 0.17/0.44 => ( Xx0 @ Xy ) ) )
% 0.17/0.44 & ! [Xx0: a > $o] :
% 0.17/0.44 ( ! [Xy0: a,Xz0: a] :
% 0.17/0.44 ( ( ( Xr @ Xy0 @ Xz0 )
% 0.17/0.44 & ( Xx0 @ Xy0 ) )
% 0.17/0.44 => ( Xx0 @ Xz0 ) )
% 0.17/0.44 => ( ( Xx0 @ Xy )
% 0.17/0.44 => ( Xx0 @ Xz ) ) ) )
% 0.17/0.44 => ! [Xx0: a > $o] :
% 0.17/0.44 ( ! [Xy0: a,Xz0: a] :
% 0.17/0.44 ( ( ( Xr @ Xy0 @ Xz0 )
% 0.17/0.44 & ( Xx0 @ Xy0 ) )
% 0.17/0.44 => ( Xx0 @ Xz0 ) )
% 0.17/0.44 => ( ( Xx0 @ Xx )
% 0.17/0.44 => ( Xx0 @ Xz ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 0.25/1.11 ---- Embedded in THF ---
% 0.25/1.11 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.25/1.11 %%% Generated on Tue Feb 24 12:40:52 EST 2026
% 0.25/1.11 %%% using '$$dhol' embedding, version 1.3.0.
% 0.25/1.11 %%% Logic specification used:
% 0.25/1.11 %%% thf(spec, logic, $$dhol).
% 0.25/1.11
% 0.25/1.11 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.rkKDCpOLdu/DTF2DTF19378.p
% See solution above
% 0.25/1.11 ------------------------
% 0.25/1.12 ---- Cleaned THF ---
% 0.25/1.12 thf(a_type,type,
% 0.25/1.12 a: $tType ).
% 0.25/1.12
% 0.25/1.12 thf(cTHM204_pme,conjecture,
% 0.25/1.12 ! [Xr: a > a > $o,Xx: a,Xy: a,Xz: a] :
% 0.25/1.12 ( ( ! [Xx0: a > $o] :
% 0.25/1.12 ( ! [Xy0: a,Xz0: a] :
% 0.25/1.12 ( ( ( Xr @ Xy0 @ Xz0 )
% 0.25/1.12 & ( Xx0 @ Xy0 ) )
% 0.25/1.12 => ( Xx0 @ Xz0 ) )
% 0.25/1.12 => ( ( Xx0 @ Xx )
% 0.25/1.12 => ( Xx0 @ Xy ) ) )
% 0.25/1.12 & ! [Xx0: a > $o] :
% 0.25/1.12 ( ! [Xy0: a,Xz0: a] :
% 0.25/1.12 ( ( ( Xr @ Xy0 @ Xz0 )
% 0.25/1.12 & ( Xx0 @ Xy0 ) )
% 0.25/1.12 => ( Xx0 @ Xz0 ) )
% 0.25/1.12 => ( ( Xx0 @ Xy )
% 0.25/1.12 => ( Xx0 @ Xz ) ) ) )
% 0.25/1.12 => ! [Xx0: a > $o] :
% 0.25/1.12 ( ! [Xy0: a,Xz0: a] :
% 0.25/1.12 ( ( ( Xr @ Xy0 @ Xz0 )
% 0.25/1.12 & ( Xx0 @ Xy0 ) )
% 0.25/1.12 => ( Xx0 @ Xz0 ) )
% 0.25/1.12 => ( ( Xx0 @ Xx )
% 0.25/1.12 => ( Xx0 @ Xz ) ) ) ) ).
% 0.25/1.12 ------------------------
% 0.25/1.14 % (19621)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19378 for (2999ds/2Mi)
% 0.25/1.14 % (19618)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_19378 for (2999ds/4Mi)
% 0.25/1.14 % (19620)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_19378 for (2999ds/27Mi)
% 0.25/1.14 % (19621)Instruction limit reached!
% 0.25/1.14 % (19621)------------------------------
% 0.25/1.14 % (19621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.14 % (19621)Termination reason: Unknown
% 0.25/1.14 % (19621)Termination phase: Saturation
% 0.25/1.14
% 0.25/1.14 % (19621)Memory used [KB]: 1023
% 0.25/1.14 % (19621)Time elapsed: 0.002 s
% 0.25/1.14 % (19621)Instructions burned: 2 (million)
% 0.25/1.14 % (19621)------------------------------
% 0.25/1.14 % (19621)------------------------------
% 0.25/1.14 % (19618)Instruction limit reached!
% 0.25/1.14 % (19618)------------------------------
% 0.25/1.14 % (19618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.14 % (19618)Termination reason: Unknown
% 0.25/1.14 % (19618)Termination phase: Saturation
% 0.25/1.14
% 0.25/1.14 % (19618)Memory used [KB]: 5500
% 0.25/1.14 % (19618)Time elapsed: 0.003 s
% 0.25/1.14 % (19618)Instructions burned: 4 (million)
% 0.25/1.14 % (19618)------------------------------
% 0.25/1.14 % (19618)------------------------------
% 0.25/1.14 % (19620)First to succeed.
% 0.25/1.14 % (19620)Refutation found. Thanks to Tanya!
% 0.25/1.14 % SZS status Theorem for DTF2THF_19378
% 0.25/1.14 % SZS output start Proof for DTF2THF_19378
% 0.25/1.14 thf(type_def_5, type, a: $tType).
% 0.25/1.14 thf(func_def_0, type, a: $tType).
% 0.25/1.14 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.25/1.14 thf(func_def_5, type, sK0: a).
% 0.25/1.14 thf(func_def_6, type, sK1: a > a > $o).
% 0.25/1.14 thf(func_def_7, type, sK2: a).
% 0.25/1.14 thf(func_def_8, type, sK3: a).
% 0.25/1.14 thf(func_def_9, type, sK4: (a > $o) > a).
% 0.25/1.14 thf(func_def_10, type, sK5: (a > $o) > a).
% 0.25/1.14 thf(func_def_11, type, sK6: (a > $o) > a).
% 0.25/1.14 thf(func_def_12, type, sK7: (a > $o) > a).
% 0.25/1.14 thf(func_def_13, type, sK8: a > $o).
% 0.25/1.14 thf(func_def_15, type, ph10: !>[X0: $tType]:(X0)).
% 0.25/1.14 thf(f93,plain,(
% 0.25/1.14 $false),
% 0.25/1.14 inference(avatar_sat_refutation,[status(thm)],[f33,f40,f58,f61,f68,f79,f82,f87,f92])).
% 0.25/1.14 thf(f92,plain,(
% 0.25/1.14 spl9_4 | ~spl9_1 | ~spl9_7),
% 0.25/1.14 inference(avatar_split_clause,[status(thm)],[f91,f65,f26,f46])).
% 0.25/1.14 thf(f46,definition,(
% 0.25/1.14 spl9_4 <=> ($true = (sK8 @ sK3))),
% 0.25/1.14 introduced(definition,[new_symbols(naming,[spl9_4])],[avatar_definition])).
% 0.25/1.14 thf(f26,definition,(
% 0.25/1.14 spl9_1 <=> ($true = (sK8 @ sK2))),
% 0.25/1.14 introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition])).
% 0.25/1.14 thf(f65,definition,(
% 0.25/1.14 spl9_7 <=> ($true = (sK8 @ (sK6 @ sK8)))),
% 0.25/1.14 introduced(definition,[new_symbols(naming,[spl9_7])],[avatar_definition])).
% 0.25/1.14 thf(f91,plain,(
% 0.25/1.14 ($true = (sK8 @ sK3)) | (~spl9_1 | ~spl9_7)),
% 0.25/1.14 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 0.25/1.14 thf(f90,plain,(
% 0.25/1.14 ($true = (sK8 @ sK3)) | ($true != $true) | (~spl9_1 | ~spl9_7)),
% 0.25/1.14 inference(forward_demodulation,[status(thm)],[f89,f28])).
% 0.25/1.14 thf(f28,plain,(
% 0.25/1.14 ($true = (sK8 @ sK2)) | ~spl9_1),
% 0.25/1.14 inference(avatar_component_clause,[status(thm)],[f26])).
% 0.25/1.14 thf(f89,plain,(
% 0.25/1.14 ($true = (sK8 @ sK3)) | ($true != (sK8 @ sK2)) | ~spl9_7),
% 0.25/1.14 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 0.25/1.14 thf(f88,plain,(
% 0.25/1.14 ($true != $true) | ($true != (sK8 @ sK2)) | ($true = (sK8 @ sK3)) | ~spl9_7),
% 0.25/1.14 inference(superposition,[status(thm)],[f18,f67])).
% 0.25/1.14 thf(f67,plain,(
% 0.25/1.14 ($true = (sK8 @ (sK6 @ sK8))) | ~spl9_7),
% 0.25/1.14 inference(avatar_component_clause,[status(thm)],[f65])).
% 0.25/1.14 thf(f18,plain,(
% 0.25/1.14 ( ! [X7 : a > $o] : (($true != (X7 @ (sK6 @ X7))) | ((X7 @ sK3) = $true) | ((X7 @ sK2) != $true)) )),
% 0.25/1.14 inference(cnf_transformation,[status(thm)],[f13])).
% 0.25/1.14 thf(f13,plain,(
% 0.25/1.14 ! [X4 : a > $o] : (($true != (X4 @ sK0)) | (((X4 @ (sK5 @ X4)) != $true) & ((sK1 @ (sK4 @ X4) @ (sK5 @ X4)) = $true) & ((X4 @ (sK4 @ X4)) = $true)) | ($true = (X4 @ sK2))) & ! [X7 : a > $o] : ((((sK1 @ (sK7 @ X7) @ (sK6 @ X7)) = $true) & ($true != (X7 @ (sK6 @ X7))) & ((X7 @ (sK7 @ X7)) = $true)) | ((X7 @ sK2) != $true) | ((X7 @ sK3) = $true)) & (! [X11 : a,X12 : a] : (($true != (sK1 @ X11 @ X12)) | ((sK8 @ X11) != $true) | ((sK8 @ X12) = $true)) & ($true != (sK8 @ sK3)) & ((sK8 @ sK0) = $true))),
% 0.25/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f8,f12,f11,f10,f9])).
% 0.25/1.14 thf(f9,plain,(
% 0.25/1.14 ? [X0 : a,X1 : a > a > $o,X2 : a,X3 : a] : (! [X4 : a > $o] : (($true != (X4 @ X0)) | ? [X5 : a,X6 : a] : (((X4 @ X6) != $true) & ($true = (X1 @ X5 @ X6)) & ((X4 @ X5) = $true)) | ((X4 @ X2) = $true)) & ! [X7 : a > $o] : (? [X8 : a,X9 : a] : (($true = (X1 @ X9 @ X8)) & ($true != (X7 @ X8)) & ((X7 @ X9) = $true)) | ($true != (X7 @ X2)) | ($true = (X7 @ X3))) & ? [X10 : a > $o] : (! [X11 : a,X12 : a] : (($true != (X1 @ X11 @ X12)) | ((X10 @ X11) != $true) | ((X10 @ X12) = $true)) & ($true != (X10 @ X3)) & ($true = (X10 @ X0)))) => (! [X4 : a > $o] : (($true != (X4 @ sK0)) | ? [X6 : a,X5 : a] : (((X4 @ X6) != $true) & ($true = (sK1 @ X5 @ X6)) & ((X4 @ X5) = $true)) | ($true = (X4 @ sK2))) & ! [X7 : a > $o] : (? [X9 : a,X8 : a] : (((sK1 @ X9 @ X8) = $true) & ($true != (X7 @ X8)) & ((X7 @ X9) = $true)) | ((X7 @ sK2) != $true) | ((X7 @ sK3) = $true)) & ? [X10 : a > $o] : (! [X12 : a,X11 : a] : (($true != (sK1 @ X11 @ X12)) | ((X10 @ X11) != $true) | ((X10 @ X12) = $true)) & ($true != (X10 @ sK3)) & ((X10 @ sK0) = $true)))),
% 0.25/1.14 introduced(definition,[],[choice_axiom])).
% 0.25/1.14 thf(f10,plain,(
% 0.25/1.14 ! [X4 : a > $o] : (? [X6 : a,X5 : a] : (((X4 @ X6) != $true) & ($true = (sK1 @ X5 @ X6)) & ((X4 @ X5) = $true)) => (((X4 @ (sK5 @ X4)) != $true) & ((sK1 @ (sK4 @ X4) @ (sK5 @ X4)) = $true) & ((X4 @ (sK4 @ X4)) = $true)))),
% 0.25/1.14 introduced(definition,[],[choice_axiom])).
% 0.25/1.14 thf(f11,plain,(
% 0.25/1.14 ! [X7 : a > $o] : (? [X9 : a,X8 : a] : (((sK1 @ X9 @ X8) = $true) & ($true != (X7 @ X8)) & ((X7 @ X9) = $true)) => (((sK1 @ (sK7 @ X7) @ (sK6 @ X7)) = $true) & ($true != (X7 @ (sK6 @ X7))) & ((X7 @ (sK7 @ X7)) = $true)))),
% 0.25/1.14 introduced(definition,[],[choice_axiom])).
% 0.25/1.14 thf(f12,plain,(
% 0.25/1.14 ? [X10 : a > $o] : (! [X12 : a,X11 : a] : (($true != (sK1 @ X11 @ X12)) | ((X10 @ X11) != $true) | ((X10 @ X12) = $true)) & ($true != (X10 @ sK3)) & ((X10 @ sK0) = $true)) => (! [X12 : a,X11 : a] : (($true != (sK1 @ X11 @ X12)) | ((sK8 @ X11) != $true) | ((sK8 @ X12) = $true)) & ($true != (sK8 @ sK3)) & ((sK8 @ sK0) = $true))),
% 0.25/1.14 introduced(definition,[],[choice_axiom])).
% 0.25/1.14 thf(f8,plain,(
% 0.25/1.14 ? [X0 : a,X1 : a > a > $o,X2 : a,X3 : a] : (! [X4 : a > $o] : (($true != (X4 @ X0)) | ? [X5 : a,X6 : a] : (((X4 @ X6) != $true) & ($true = (X1 @ X5 @ X6)) & ((X4 @ X5) = $true)) | ((X4 @ X2) = $true)) & ! [X7 : a > $o] : (? [X8 : a,X9 : a] : (($true = (X1 @ X9 @ X8)) & ($true != (X7 @ X8)) & ((X7 @ X9) = $true)) | ($true != (X7 @ X2)) | ($true = (X7 @ X3))) & ? [X10 : a > $o] : (! [X11 : a,X12 : a] : (($true != (X1 @ X11 @ X12)) | ((X10 @ X11) != $true) | ((X10 @ X12) = $true)) & ($true != (X10 @ X3)) & ($true = (X10 @ X0))))),
% 0.25/1.14 inference(rectify,[status(thm)],[f7])).
% 0.25/1.14 thf(f7,plain,(
% 0.25/1.14 ? [X2 : a,X3 : a > a > $o,X1 : a,X0 : a] : (! [X4 : a > $o] : (((X4 @ X2) != $true) | ? [X6 : a,X5 : a] : (((X4 @ X5) != $true) & ($true = (X3 @ X6 @ X5)) & ((X4 @ X6) = $true)) | ((X4 @ X1) = $true)) & ! [X7 : a > $o] : (? [X9 : a,X8 : a] : (((X3 @ X8 @ X9) = $true) & ((X7 @ X9) != $true) & ($true = (X7 @ X8))) | ((X7 @ X1) != $true) | ((X7 @ X0) = $true)) & ? [X10 : a > $o] : (! [X12 : a,X11 : a] : (((X3 @ X12 @ X11) != $true) | ((X10 @ X12) != $true) | ((X10 @ X11) = $true)) & ($true != (X10 @ X0)) & ((X10 @ X2) = $true)))),
% 0.25/1.14 inference(flattening,[status(thm)],[f6])).
% 0.25/1.14 thf(f6,plain,(
% 0.25/1.14 ? [X1 : a,X3 : a > a > $o,X0 : a,X2 : a] : (? [X10 : a > $o] : ((($true != (X10 @ X0)) & ((X10 @ X2) = $true)) & ! [X11 : a,X12 : a] : (((X10 @ X11) = $true) | (((X10 @ X12) != $true) | ((X3 @ X12 @ X11) != $true)))) & (! [X7 : a > $o] : ((((X7 @ X0) = $true) | ((X7 @ X1) != $true)) | ? [X9 : a,X8 : a] : (((X7 @ X9) != $true) & (($true = (X7 @ X8)) & ((X3 @ X8 @ X9) = $true)))) & ! [X4 : a > $o] : ((((X4 @ X1) = $true) | ((X4 @ X2) != $true)) | ? [X5 : a,X6 : a] : (((X4 @ X5) != $true) & (((X4 @ X6) = $true) & ($true = (X3 @ X6 @ X5)))))))),
% 0.25/1.14 inference(ennf_transformation,[status(thm)],[f5])).
% 0.25/1.14 thf(f5,plain,(
% 0.25/1.14 ~! [X1 : a,X3 : a > a > $o,X0 : a,X2 : a] : ((! [X7 : a > $o] : (! [X9 : a,X8 : a] : ((($true = (X7 @ X8)) & ((X3 @ X8 @ X9) = $true)) => ((X7 @ X9) = $true)) => (((X7 @ X1) = $true) => ((X7 @ X0) = $true))) & ! [X4 : a > $o] : (! [X5 : a,X6 : a] : ((((X4 @ X6) = $true) & ($true = (X3 @ X6 @ X5))) => ((X4 @ X5) = $true)) => (((X4 @ X2) = $true) => ((X4 @ X1) = $true)))) => ! [X10 : a > $o] : (! [X11 : a,X12 : a] : ((((X10 @ X12) = $true) & ((X3 @ X12 @ X11) = $true)) => ((X10 @ X11) = $true)) => (((X10 @ X2) = $true) => ($true = (X10 @ X0)))))),
% 0.25/1.14 inference(fool_elimination,[status(thm)],[f4])).
% 0.25/1.14 thf(f4,plain,(
% 0.25/1.14 ~! [X0 : a,X1 : a,X2 : a,X3 : a > a > $o] : ((! [X4 : a > $o] : (! [X5 : a,X6 : a] : (((X3 @ X6 @ X5) & (X4 @ X6)) => (X4 @ X5)) => ((X4 @ X2) => (X4 @ X1))) & ! [X7 : a > $o] : (! [X8 : a,X9 : a] : (((X3 @ X8 @ X9) & (X7 @ X8)) => (X7 @ X9)) => ((X7 @ X1) => (X7 @ X0)))) => ! [X10 : a > $o] : (! [X11 : a,X12 : a] : (((X3 @ X12 @ X11) & (X10 @ X12)) => (X10 @ X11)) => ((X10 @ X2) => (X10 @ X0))))),
% 0.25/1.14 inference(rectify,[status(thm)],[f2])).
% 0.25/1.14 thf(f2,negated_conjecture,(
% 0.25/1.14 ~! [X3 : a,X2 : a,X1 : a,X0 : a > a > $o] : ((! [X4 : a > $o] : (! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) & (X4 @ X5)) => (X4 @ X6)) => ((X4 @ X1) => (X4 @ X2))) & ! [X4 : a > $o] : (! [X5 : a,X6 : a] : (((X0 @ X5 @ X6) & (X4 @ X5)) => (X4 @ X6)) => ((X4 @ X2) => (X4 @ X3)))) => ! [X4 : a > $o] : (! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) & (X4 @ X5)) => (X4 @ X6)) => ((X4 @ X1) => (X4 @ X3))))),
% 0.25/1.14 inference(negated_conjecture,[status(cth)],[f1])).
% 0.25/1.14 thf(f1,conjecture,(
% 0.25/1.14 ! [X3 : a,X2 : a,X1 : a,X0 : a > a > $o] : ((! [X4 : a > $o] : (! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) & (X4 @ X5)) => (X4 @ X6)) => ((X4 @ X1) => (X4 @ X2))) & ! [X4 : a > $o] : (! [X5 : a,X6 : a] : (((X0 @ X5 @ X6) & (X4 @ X5)) => (X4 @ X6)) => ((X4 @ X2) => (X4 @ X3)))) => ! [X4 : a > $o] : (! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) & (X4 @ X5)) => (X4 @ X6)) => ((X4 @ X1) => (X4 @ X3))))),
% 0.25/1.14 file('/export/starexec/sandbox2/tmp/tmp.rkKDCpOLdu/DTF2THF_19378.p',cTHM204_pme)).
% 0.25/1.14 thf(f87,plain,(
% 0.25/1.14 spl9_5 | spl9_4 | ~spl9_1),
% 0.25/1.14 inference(avatar_split_clause,[status(thm)],[f86,f26,f46,f50])).
% 0.25/1.14 thf(f50,definition,(
% 0.25/1.14 spl9_5 <=> ((sK8 @ (sK7 @ sK8)) = $true)),
% 0.25/1.14 introduced(definition,[new_symbols(naming,[spl9_5])],[avatar_definition])).
% 0.25/1.14 thf(f86,plain,(
% 0.25/1.14 ((sK8 @ (sK7 @ sK8)) = $true) | ($true = (sK8 @ sK3)) | ~spl9_1),
% 0.25/1.14 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 0.25/1.14 thf(f84,plain,(
% 0.25/1.14 ($true = (sK8 @ sK3)) | ((sK8 @ (sK7 @ sK8)) = $true) | ($true != $true) | ~spl9_1),
% 0.25/1.14 inference(superposition,[status(thm)],[f17,f28])).
% 0.25/1.14 thf(f17,plain,(
% 0.25/1.14 ( ! [X7 : a > $o] : (((X7 @ sK2) != $true) | ((X7 @ (sK7 @ X7)) = $true) | ((X7 @ sK3) = $true)) )),
% 0.25/1.14 inference(cnf_transformation,[status(thm)],[f13])).
% 0.25/1.14 thf(f82,plain,(
% 0.25/1.14 spl9_8),
% 0.25/1.14 inference(avatar_contradiction_clause,[status(thm)],[f81])).
% 0.25/1.14 thf(f81,plain,(
% 0.25/1.14 $false | spl9_8),
% 0.25/1.14 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 0.25/1.14 thf(f80,plain,(
% 0.25/1.14 ($true != $true) | spl9_8),
% 0.25/1.14 inference(superposition,[status(thm)],[f78,f14])).
% 0.25/1.14 thf(f14,plain,(
% 0.25/1.14 ((sK8 @ sK0) = $true)),
% 0.25/1.14 inference(cnf_transformation,[status(thm)],[f13])).
% 0.25/1.14 thf(f78,plain,(
% 0.25/1.14 ((sK8 @ sK0) != $true) | spl9_8),
% 0.25/1.14 inference(avatar_component_clause,[status(thm)],[f76])).
% 0.25/1.14 thf(f76,definition,(
% 0.25/1.14 spl9_8 <=> ((sK8 @ sK0) = $true)),
% 0.25/1.14 introduced(definition,[new_symbols(naming,[spl9_8])],[avatar_definition])).
% 0.25/1.14 thf(f79,plain,(
% 0.25/1.14 spl9_1 | ~spl9_8 | ~spl9_2 | ~spl9_3),
% 0.25/1.14 inference(avatar_split_clause,[status(thm)],[f74,f37,f30,f76,f26])).
% 0.25/1.14 thf(f30,definition,(
% 0.25/1.14 spl9_2 <=> ((sK8 @ (sK4 @ sK8)) = $true)),
% 0.25/1.14 introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition])).
% 0.25/1.14 thf(f37,definition,(
% 0.25/1.14 spl9_3 <=> ((sK1 @ (sK4 @ sK8) @ (sK5 @ sK8)) = $true)),
% 0.25/1.14 introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition])).
% 0.25/1.14 thf(f74,plain,(
% 0.25/1.14 ($true = (sK8 @ sK2)) | ((sK8 @ sK0) != $true) | (~spl9_2 | ~spl9_3)),
% 0.25/1.14 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 0.25/1.14 thf(f73,plain,(
% 0.25/1.14 ($true != $true) | ((sK8 @ sK0) != $true) | ($true = (sK8 @ sK2)) | (~spl9_2 | ~spl9_3)),
% 0.25/1.14 inference(superposition,[status(thm)],[f22,f72])).
% 0.25/1.14 thf(f72,plain,(
% 0.25/1.14 ((sK8 @ (sK5 @ sK8)) = $true) | (~spl9_2 | ~spl9_3)),
% 0.25/1.14 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 0.25/1.14 thf(f71,plain,(
% 0.25/1.14 ((sK8 @ (sK5 @ sK8)) = $true) | ($true != $true) | (~spl9_2 | ~spl9_3)),
% 0.25/1.14 inference(forward_demodulation,[status(thm)],[f70,f32])).
% 0.25/1.14 thf(f32,plain,(
% 0.25/1.14 ((sK8 @ (sK4 @ sK8)) = $true) | ~spl9_2),
% 0.25/1.14 inference(avatar_component_clause,[status(thm)],[f30])).
% 0.25/1.14 thf(f70,plain,(
% 0.25/1.14 ((sK8 @ (sK4 @ sK8)) != $true) | ((sK8 @ (sK5 @ sK8)) = $true) | ~spl9_3),
% 0.25/1.14 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 0.25/1.14 thf(f69,plain,(
% 0.25/1.14 ((sK8 @ (sK5 @ sK8)) = $true) | ($true != $true) | ((sK8 @ (sK4 @ sK8)) != $true) | ~spl9_3),
% 0.25/1.14 inference(superposition,[status(thm)],[f16,f39])).
% 0.25/1.14 thf(f39,plain,(
% 0.25/1.14 ((sK1 @ (sK4 @ sK8) @ (sK5 @ sK8)) = $true) | ~spl9_3),
% 0.25/1.14 inference(avatar_component_clause,[status(thm)],[f37])).
% 0.25/1.14 thf(f16,plain,(
% 0.25/1.14 ( ! [X11 : a,X12 : a] : (($true != (sK1 @ X11 @ X12)) | ((sK8 @ X11) != $true) | ((sK8 @ X12) = $true)) )),
% 0.25/1.14 inference(cnf_transformation,[status(thm)],[f13])).
% 0.25/1.14 thf(f22,plain,(
% 0.25/1.14 ( ! [X4 : a > $o] : (((X4 @ (sK5 @ X4)) != $true) | ($true = (X4 @ sK2)) | ($true != (X4 @ sK0))) )),
% 0.25/1.14 inference(cnf_transformation,[status(thm)],[f13])).
% 0.25/1.14 thf(f68,plain,(
% 0.25/1.14 ~spl9_5 | spl9_7 | ~spl9_6),
% 0.25/1.14 inference(avatar_split_clause,[status(thm)],[f63,f55,f65,f50])).
% 0.25/1.14 thf(f55,definition,(
% 0.25/1.14 spl9_6 <=> ($true = (sK1 @ (sK7 @ sK8) @ (sK6 @ sK8)))),
% 0.25/1.14 introduced(definition,[new_symbols(naming,[spl9_6])],[avatar_definition])).
% 0.25/1.14 thf(f63,plain,(
% 0.25/1.14 ($true = (sK8 @ (sK6 @ sK8))) | ((sK8 @ (sK7 @ sK8)) != $true) | ~spl9_6),
% 0.25/1.14 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 0.25/1.14 thf(f62,plain,(
% 0.25/1.14 ($true != $true) | ($true = (sK8 @ (sK6 @ sK8))) | ((sK8 @ (sK7 @ sK8)) != $true) | ~spl9_6),
% 0.25/1.14 inference(superposition,[status(thm)],[f16,f57])).
% 0.25/1.14 thf(f57,plain,(
% 0.25/1.14 ($true = (sK1 @ (sK7 @ sK8) @ (sK6 @ sK8))) | ~spl9_6),
% 0.25/1.14 inference(avatar_component_clause,[status(thm)],[f55])).
% 0.25/1.14 thf(f61,plain,(
% 0.25/1.14 ~spl9_4),
% 0.25/1.14 inference(avatar_contradiction_clause,[status(thm)],[f60])).
% 0.25/1.14 thf(f60,plain,(
% 0.25/1.14 $false | ~spl9_4),
% 0.25/1.14 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 0.25/1.14 thf(f59,plain,(
% 0.25/1.14 ($true != $true) | ~spl9_4),
% 0.25/1.14 inference(superposition,[status(thm)],[f15,f48])).
% 0.25/1.14 thf(f48,plain,(
% 0.25/1.14 ($true = (sK8 @ sK3)) | ~spl9_4),
% 0.25/1.14 inference(avatar_component_clause,[status(thm)],[f46])).
% 0.25/1.14 thf(f15,plain,(
% 0.25/1.14 ($true != (sK8 @ sK3))),
% 0.25/1.14 inference(cnf_transformation,[status(thm)],[f13])).
% 0.25/1.14 thf(f58,plain,(
% 0.25/1.14 spl9_6 | spl9_4 | ~spl9_1),
% 0.25/1.14 inference(avatar_split_clause,[status(thm)],[f43,f26,f46,f55])).
% 0.25/1.14 thf(f43,plain,(
% 0.25/1.14 ($true = (sK8 @ sK3)) | ($true = (sK1 @ (sK7 @ sK8) @ (sK6 @ sK8))) | ~spl9_1),
% 0.25/1.14 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 0.25/1.14 thf(f41,plain,(
% 0.25/1.14 ($true = (sK8 @ sK3)) | ($true != $true) | ($true = (sK1 @ (sK7 @ sK8) @ (sK6 @ sK8))) | ~spl9_1),
% 0.25/1.14 inference(superposition,[status(thm)],[f19,f28])).
% 0.25/1.14 thf(f19,plain,(
% 0.25/1.14 ( ! [X7 : a > $o] : (((X7 @ sK2) != $true) | ((sK1 @ (sK7 @ X7) @ (sK6 @ X7)) = $true) | ((X7 @ sK3) = $true)) )),
% 0.25/1.14 inference(cnf_transformation,[status(thm)],[f13])).
% 0.25/1.14 thf(f40,plain,(
% 0.25/1.14 spl9_3 | spl9_1),
% 0.25/1.14 inference(avatar_split_clause,[status(thm)],[f35,f26,f37])).
% 0.25/1.14 thf(f35,plain,(
% 0.25/1.14 ($true = (sK8 @ sK2)) | ((sK1 @ (sK4 @ sK8) @ (sK5 @ sK8)) = $true)),
% 0.25/1.14 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 0.25/1.14 thf(f34,plain,(
% 0.25/1.14 ($true = (sK8 @ sK2)) | ((sK1 @ (sK4 @ sK8) @ (sK5 @ sK8)) = $true) | ($true != $true)),
% 0.25/1.14 inference(superposition,[status(thm)],[f21,f14])).
% 0.25/1.14 thf(f21,plain,(
% 0.25/1.14 ( ! [X4 : a > $o] : (($true != (X4 @ sK0)) | ($true = (X4 @ sK2)) | ((sK1 @ (sK4 @ X4) @ (sK5 @ X4)) = $true)) )),
% 0.25/1.14 inference(cnf_transformation,[status(thm)],[f13])).
% 0.25/1.14 thf(f33,plain,(
% 0.25/1.14 spl9_1 | spl9_2),
% 0.25/1.14 inference(avatar_split_clause,[status(thm)],[f24,f30,f26])).
% 0.25/1.14 thf(f24,plain,(
% 0.25/1.14 ($true = (sK8 @ sK2)) | ((sK8 @ (sK4 @ sK8)) = $true)),
% 0.25/1.14 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 0.25/1.14 thf(f23,plain,(
% 0.25/1.14 ($true = (sK8 @ sK2)) | ($true != $true) | ((sK8 @ (sK4 @ sK8)) = $true)),
% 0.25/1.14 inference(superposition,[status(thm)],[f20,f14])).
% 0.25/1.14 thf(f20,plain,(
% 0.25/1.14 ( ! [X4 : a > $o] : (($true != (X4 @ sK0)) | ($true = (X4 @ sK2)) | ((X4 @ (sK4 @ X4)) = $true)) )),
% 0.25/1.14 inference(cnf_transformation,[status(thm)],[f13])).
% 0.25/1.14 % SZS output end Proof for DTF2THF_19378
% 0.25/1.14 % (19620)------------------------------
% 0.25/1.14 % (19620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.14 % (19620)Termination reason: Refutation
% 0.25/1.14
% 0.25/1.14 % (19620)Memory used [KB]: 5628
% 0.25/1.14 % (19620)Time elapsed: 0.006 s
% 0.25/1.14 % (19620)Instructions burned: 9 (million)
% 0.25/1.14 % (19620)------------------------------
% 0.25/1.14 % (19620)------------------------------
% 0.25/1.14 % (19614)Success in time 0.015 s
%------------------------------------------------------------------------------