%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU901^5 : 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 : n009.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 09:37:42 AM UTC 2026
% Result : Theorem 1.60s 1.32s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 341 ( 159 equ; 0 cnn)
% Maximal formula atoms : 36 ( 11 avg)
% Number of connectives : 684 ( 75 ~; 63 |; 84 &; 418 @)
% ( 2 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 157 ( 0 ^; 119 !; 38 ?; 157 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_8,type,
a: $tType ).
thf(func_def_0,type,
g: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
a: $tType ).
thf(func_def_6,type,
sK0: b > $o ).
thf(func_def_7,type,
sK1: b > b ).
thf(func_def_8,type,
sK2: a > a ).
thf(func_def_9,type,
sK3: a > $o ).
thf(func_def_10,type,
sK4: g > b ).
thf(func_def_11,type,
sK5: g > g ).
thf(func_def_12,type,
sK6: b > a ).
thf(func_def_13,type,
sK7: g > $o ).
thf(func_def_14,type,
sK8: g ).
thf(f46,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f37,f41,f45]) ).
thf(f45,plain,
spl9_2,
inference(avatar_contradiction_clause,[status(thm)],[f44]) ).
thf(f44,plain,
( $false
| spl9_2 ),
inference(subsumption_resolution,[status(thm)],[f43,f14]) ).
thf(f14,plain,
( ( sK7 @ sK8 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X8: g] :
( ( ( sK7 @ X8 )
!= $true )
| ( ( sK7 @ ( sK5 @ X8 ) )
= $true ) )
& ! [X9: g] :
( ( ( sK4 @ ( sK5 @ X9 ) )
= ( sK1 @ ( sK4 @ X9 ) ) )
| ( ( sK7 @ X9 )
!= $true ) )
& ! [X10: g] :
( ( $true
= ( sK0 @ ( sK4 @ X10 ) ) )
| ( ( sK7 @ X10 )
!= $true ) )
& ! [X11: b] :
( ( ( sK0 @ X11 )
!= $true )
| ( $true
= ( sK0 @ ( sK1 @ X11 ) ) ) )
& ! [X12: a] :
( ( $true
= ( sK3 @ ( sK2 @ X12 ) ) )
| ( $true
!= ( sK3 @ X12 ) ) )
& ! [X13: b] :
( ( $true
!= ( sK0 @ X13 ) )
| ( ( sK0 @ ( sK1 @ X13 ) )
= $true ) )
& ! [X14: b] :
( ( $true
= ( sK3 @ ( sK6 @ X14 ) ) )
| ( ( sK0 @ X14 )
!= $true ) )
& ( ( sK7 @ sK8 )
= $true )
& ( ( sK2 @ ( sK6 @ ( sK4 @ sK8 ) ) )
!= ( sK6 @ ( sK4 @ ( sK5 @ sK8 ) ) ) )
& ! [X16: b] :
( ( ( sK2 @ ( sK6 @ X16 ) )
= ( sK6 @ ( sK1 @ X16 ) ) )
| ( ( sK0 @ X16 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: b > $o,X1: b > b,X2: a > a,X3: a > $o,X4: g > b,X5: g > g,X6: b > a,X7: g > $o] :
( ! [X8: g] :
( ( $true
!= ( X7 @ X8 ) )
| ( $true
= ( X7 @ ( X5 @ X8 ) ) ) )
& ! [X9: g] :
( ( ( X1 @ ( X4 @ X9 ) )
= ( X4 @ ( X5 @ X9 ) ) )
| ( ( X7 @ X9 )
!= $true ) )
& ! [X10: g] :
( ( ( X0 @ ( X4 @ X10 ) )
= $true )
| ( $true
!= ( X7 @ X10 ) ) )
& ! [X11: b] :
( ( $true
!= ( X0 @ X11 ) )
| ( $true
= ( X0 @ ( X1 @ X11 ) ) ) )
& ! [X12: a] :
( ( ( X3 @ ( X2 @ X12 ) )
= $true )
| ( ( X3 @ X12 )
!= $true ) )
& ! [X13: b] :
( ( $true
!= ( X0 @ X13 ) )
| ( ( X0 @ ( X1 @ X13 ) )
= $true ) )
& ! [X14: b] :
( ( $true
= ( X3 @ ( X6 @ X14 ) ) )
| ( $true
!= ( X0 @ X14 ) ) )
& ? [X15: g] :
( ( ( X7 @ X15 )
= $true )
& ( ( X6 @ ( X4 @ ( X5 @ X15 ) ) )
!= ( X2 @ ( X6 @ ( X4 @ X15 ) ) ) ) )
& ! [X16: b] :
( ( ( X6 @ ( X1 @ X16 ) )
= ( X2 @ ( X6 @ X16 ) ) )
| ( $true
!= ( X0 @ X16 ) ) ) )
=> ( ! [X8: g] :
( ( ( sK7 @ X8 )
!= $true )
| ( ( sK7 @ ( sK5 @ X8 ) )
= $true ) )
& ! [X9: g] :
( ( ( sK4 @ ( sK5 @ X9 ) )
= ( sK1 @ ( sK4 @ X9 ) ) )
| ( ( sK7 @ X9 )
!= $true ) )
& ! [X10: g] :
( ( $true
= ( sK0 @ ( sK4 @ X10 ) ) )
| ( ( sK7 @ X10 )
!= $true ) )
& ! [X11: b] :
( ( ( sK0 @ X11 )
!= $true )
| ( $true
= ( sK0 @ ( sK1 @ X11 ) ) ) )
& ! [X12: a] :
( ( $true
= ( sK3 @ ( sK2 @ X12 ) ) )
| ( $true
!= ( sK3 @ X12 ) ) )
& ! [X13: b] :
( ( $true
!= ( sK0 @ X13 ) )
| ( ( sK0 @ ( sK1 @ X13 ) )
= $true ) )
& ! [X14: b] :
( ( $true
= ( sK3 @ ( sK6 @ X14 ) ) )
| ( ( sK0 @ X14 )
!= $true ) )
& ? [X15: g] :
( ( $true
= ( sK7 @ X15 ) )
& ( ( sK6 @ ( sK4 @ ( sK5 @ X15 ) ) )
!= ( sK2 @ ( sK6 @ ( sK4 @ X15 ) ) ) ) )
& ! [X16: b] :
( ( ( sK2 @ ( sK6 @ X16 ) )
= ( sK6 @ ( sK1 @ X16 ) ) )
| ( ( sK0 @ X16 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X15: g] :
( ( $true
= ( sK7 @ X15 ) )
& ( ( sK6 @ ( sK4 @ ( sK5 @ X15 ) ) )
!= ( sK2 @ ( sK6 @ ( sK4 @ X15 ) ) ) ) )
=> ( ( ( sK7 @ sK8 )
= $true )
& ( ( sK2 @ ( sK6 @ ( sK4 @ sK8 ) ) )
!= ( sK6 @ ( sK4 @ ( sK5 @ sK8 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: b > $o,X1: b > b,X2: a > a,X3: a > $o,X4: g > b,X5: g > g,X6: b > a,X7: g > $o] :
( ! [X8: g] :
( ( $true
!= ( X7 @ X8 ) )
| ( $true
= ( X7 @ ( X5 @ X8 ) ) ) )
& ! [X9: g] :
( ( ( X1 @ ( X4 @ X9 ) )
= ( X4 @ ( X5 @ X9 ) ) )
| ( ( X7 @ X9 )
!= $true ) )
& ! [X10: g] :
( ( ( X0 @ ( X4 @ X10 ) )
= $true )
| ( $true
!= ( X7 @ X10 ) ) )
& ! [X11: b] :
( ( $true
!= ( X0 @ X11 ) )
| ( $true
= ( X0 @ ( X1 @ X11 ) ) ) )
& ! [X12: a] :
( ( ( X3 @ ( X2 @ X12 ) )
= $true )
| ( ( X3 @ X12 )
!= $true ) )
& ! [X13: b] :
( ( $true
!= ( X0 @ X13 ) )
| ( ( X0 @ ( X1 @ X13 ) )
= $true ) )
& ! [X14: b] :
( ( $true
= ( X3 @ ( X6 @ X14 ) ) )
| ( $true
!= ( X0 @ X14 ) ) )
& ? [X15: g] :
( ( ( X7 @ X15 )
= $true )
& ( ( X6 @ ( X4 @ ( X5 @ X15 ) ) )
!= ( X2 @ ( X6 @ ( X4 @ X15 ) ) ) ) )
& ! [X16: b] :
( ( ( X6 @ ( X1 @ X16 ) )
= ( X2 @ ( X6 @ X16 ) ) )
| ( $true
!= ( X0 @ X16 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X3: b > $o,X0: b > b,X7: a > a,X6: a > $o,X2: g > b,X1: g > g,X5: b > a,X4: g > $o] :
( ! [X14: g] :
( ( ( X4 @ X14 )
!= $true )
| ( $true
= ( X4 @ ( X1 @ X14 ) ) ) )
& ! [X13: g] :
( ( ( X2 @ ( X1 @ X13 ) )
= ( X0 @ ( X2 @ X13 ) ) )
| ( ( X4 @ X13 )
!= $true ) )
& ! [X10: g] :
( ( $true
= ( X3 @ ( X2 @ X10 ) ) )
| ( $true
!= ( X4 @ X10 ) ) )
& ! [X15: b] :
( ( $true
!= ( X3 @ X15 ) )
| ( $true
= ( X3 @ ( X0 @ X15 ) ) ) )
& ! [X12: a] :
( ( ( X6 @ ( X7 @ X12 ) )
= $true )
| ( $true
!= ( X6 @ X12 ) ) )
& ! [X9: b] :
( ( $true
!= ( X3 @ X9 ) )
| ( ( X3 @ ( X0 @ X9 ) )
= $true ) )
& ! [X11: b] :
( ( ( X6 @ ( X5 @ X11 ) )
= $true )
| ( ( X3 @ X11 )
!= $true ) )
& ? [X16: g] :
( ( ( X4 @ X16 )
= $true )
& ( ( X7 @ ( X5 @ ( X2 @ X16 ) ) )
!= ( X5 @ ( X2 @ ( X1 @ X16 ) ) ) ) )
& ! [X8: b] :
( ( ( X7 @ ( X5 @ X8 ) )
= ( X5 @ ( X0 @ X8 ) ) )
| ( $true
!= ( X3 @ X8 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X4: g > $o,X0: b > b,X7: a > a,X3: b > $o,X6: a > $o,X2: g > b,X5: b > a,X1: g > g] :
( ? [X16: g] :
( ( ( X4 @ X16 )
= $true )
& ( ( X7 @ ( X5 @ ( X2 @ X16 ) ) )
!= ( X5 @ ( X2 @ ( X1 @ X16 ) ) ) ) )
& ! [X15: b] :
( ( $true
!= ( X3 @ X15 ) )
| ( $true
= ( X3 @ ( X0 @ X15 ) ) ) )
& ! [X13: g] :
( ( ( X2 @ ( X1 @ X13 ) )
= ( X0 @ ( X2 @ X13 ) ) )
| ( ( X4 @ X13 )
!= $true ) )
& ! [X8: b] :
( ( ( X7 @ ( X5 @ X8 ) )
= ( X5 @ ( X0 @ X8 ) ) )
| ( $true
!= ( X3 @ X8 ) ) )
& ! [X11: b] :
( ( ( X6 @ ( X5 @ X11 ) )
= $true )
| ( ( X3 @ X11 )
!= $true ) )
& ! [X12: a] :
( ( ( X6 @ ( X7 @ X12 ) )
= $true )
| ( $true
!= ( X6 @ X12 ) ) )
& ! [X9: b] :
( ( $true
!= ( X3 @ X9 ) )
| ( ( X3 @ ( X0 @ X9 ) )
= $true ) )
& ! [X14: g] :
( ( ( X4 @ X14 )
!= $true )
| ( $true
= ( X4 @ ( X1 @ X14 ) ) ) )
& ! [X10: g] :
( ( $true
= ( X3 @ ( X2 @ X10 ) ) )
| ( $true
!= ( X4 @ X10 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X4: g > $o,X0: b > b,X7: a > a,X3: b > $o,X6: a > $o,X2: g > b,X5: b > a,X1: g > g] :
( ( ! [X15: b] :
( ( $true
= ( X3 @ X15 ) )
=> ( $true
= ( X3 @ ( X0 @ X15 ) ) ) )
& ! [X13: g] :
( ( ( X4 @ X13 )
= $true )
=> ( ( X2 @ ( X1 @ X13 ) )
= ( X0 @ ( X2 @ X13 ) ) ) )
& ! [X8: b] :
( ( $true
= ( X3 @ X8 ) )
=> ( ( X7 @ ( X5 @ X8 ) )
= ( X5 @ ( X0 @ X8 ) ) ) )
& ! [X11: b] :
( ( ( X3 @ X11 )
= $true )
=> ( ( X6 @ ( X5 @ X11 ) )
= $true ) )
& ! [X12: a] :
( ( $true
= ( X6 @ X12 ) )
=> ( ( X6 @ ( X7 @ X12 ) )
= $true ) )
& ! [X9: b] :
( ( $true
= ( X3 @ X9 ) )
=> ( ( X3 @ ( X0 @ X9 ) )
= $true ) )
& ! [X14: g] :
( ( ( X4 @ X14 )
= $true )
=> ( $true
= ( X4 @ ( X1 @ X14 ) ) ) )
& ! [X10: g] :
( ( $true
= ( X4 @ X10 ) )
=> ( $true
= ( X3 @ ( X2 @ X10 ) ) ) ) )
=> ! [X16: g] :
( ( ( X4 @ X16 )
= $true )
=> ( ( X7 @ ( X5 @ ( X2 @ X16 ) ) )
= ( X5 @ ( X2 @ ( X1 @ X16 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: b > b,X1: g > g,X2: g > b,X3: b > $o,X4: g > $o,X5: b > a,X6: a > $o,X7: a > a] :
( ( ! [X8: b] :
( ( X3 @ X8 )
=> ( ( X7 @ ( X5 @ X8 ) )
= ( X5 @ ( X0 @ X8 ) ) ) )
& ! [X9: b] :
( ( X3 @ X9 )
=> ( X3 @ ( X0 @ X9 ) ) )
& ! [X10: g] :
( ( X4 @ X10 )
=> ( X3 @ ( X2 @ X10 ) ) )
& ! [X11: b] :
( ( X3 @ X11 )
=> ( X6 @ ( X5 @ X11 ) ) )
& ! [X12: a] :
( ( X6 @ X12 )
=> ( X6 @ ( X7 @ X12 ) ) )
& ! [X13: g] :
( ( X4 @ X13 )
=> ( ( X2 @ ( X1 @ X13 ) )
= ( X0 @ ( X2 @ X13 ) ) ) )
& ! [X14: g] :
( ( X4 @ X14 )
=> ( X4 @ ( X1 @ X14 ) ) )
& ! [X15: b] :
( ( X3 @ X15 )
=> ( X3 @ ( X0 @ X15 ) ) ) )
=> ! [X16: g] :
( ( X4 @ X16 )
=> ( ( X7 @ ( X5 @ ( X2 @ X16 ) ) )
= ( X5 @ ( X2 @ ( X1 @ X16 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X5: b > b,X3: g > g,X0: g > b,X4: b > $o,X2: g > $o,X1: b > a,X6: a > $o,X7: a > a] :
( ( ! [X8: b] :
( ( X4 @ X8 )
=> ( ( X1 @ ( X5 @ X8 ) )
= ( X7 @ ( X1 @ X8 ) ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( X0 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) )
& ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X0 @ ( X3 @ X8 ) )
= ( X5 @ ( X0 @ X8 ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) ) )
=> ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X1 @ ( X0 @ ( X3 @ X8 ) ) )
= ( X7 @ ( X1 @ ( X0 @ X8 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X5: b > b,X3: g > g,X0: g > b,X4: b > $o,X2: g > $o,X1: b > a,X6: a > $o,X7: a > a] :
( ( ! [X8: b] :
( ( X4 @ X8 )
=> ( ( X1 @ ( X5 @ X8 ) )
= ( X7 @ ( X1 @ X8 ) ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( X0 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) )
& ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X0 @ ( X3 @ X8 ) )
= ( X5 @ ( X0 @ X8 ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) ) )
=> ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X1 @ ( X0 @ ( X3 @ X8 ) ) )
= ( X7 @ ( X1 @ ( X0 @ X8 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ajzynUZ6gR/DTF2THF_8327.p',cTHM131D_pme) ).
thf(f43,plain,
( ( ( sK7 @ sK8 )
!= $true )
| spl9_2 ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( sK6 @ ( sK4 @ ( sK5 @ sK8 ) ) )
!= ( sK6 @ ( sK4 @ ( sK5 @ sK8 ) ) ) )
| ( ( sK7 @ sK8 )
!= $true )
| spl9_2 ),
inference(superposition,[status(thm)],[f36,f20]) ).
thf(f20,plain,
! [X9: g] :
( ( ( sK4 @ ( sK5 @ X9 ) )
= ( sK1 @ ( sK4 @ X9 ) ) )
| ( ( sK7 @ X9 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f36,plain,
( ( ( sK6 @ ( sK1 @ ( sK4 @ sK8 ) ) )
!= ( sK6 @ ( sK4 @ ( sK5 @ sK8 ) ) ) )
| spl9_2 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl9_2
<=> ( ( sK6 @ ( sK1 @ ( sK4 @ sK8 ) ) )
= ( sK6 @ ( sK4 @ ( sK5 @ sK8 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition]) ).
thf(f41,plain,
spl9_1,
inference(avatar_contradiction_clause,[status(thm)],[f40]) ).
thf(f40,plain,
( $false
| spl9_1 ),
inference(subsumption_resolution,[status(thm)],[f39,f14]) ).
thf(f39,plain,
( ( ( sK7 @ sK8 )
!= $true )
| spl9_1 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( sK7 @ sK8 )
!= $true )
| ( $true != $true )
| spl9_1 ),
inference(superposition,[status(thm)],[f32,f19]) ).
thf(f19,plain,
! [X10: g] :
( ( $true
= ( sK0 @ ( sK4 @ X10 ) ) )
| ( ( sK7 @ X10 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f32,plain,
( ( $true
!= ( sK0 @ ( sK4 @ sK8 ) ) )
| spl9_1 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl9_1
<=> ( $true
= ( sK0 @ ( sK4 @ sK8 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition]) ).
thf(f37,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[status(thm)],[f28,f34,f30]) ).
thf(f28,plain,
( ( $true
!= ( sK0 @ ( sK4 @ sK8 ) ) )
| ( ( sK6 @ ( sK1 @ ( sK4 @ sK8 ) ) )
!= ( sK6 @ ( sK4 @ ( sK5 @ sK8 ) ) ) ) ),
inference(superposition,[status(thm)],[f13,f12]) ).
thf(f12,plain,
! [X16: b] :
( ( ( sK2 @ ( sK6 @ X16 ) )
= ( sK6 @ ( sK1 @ X16 ) ) )
| ( ( sK0 @ X16 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f13,plain,
( ( sK2 @ ( sK6 @ ( sK4 @ sK8 ) ) )
!= ( sK6 @ ( sK4 @ ( sK5 @ sK8 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU901^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.28 % Computer : n009.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Tue Feb 24 12:36:10 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : SEU901^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.38 % Domain : Set Theory
% 0.18/0.38 % Problem : TPS problem THM131D
% 0.18/0.38 % Version : Especial.
% 0.18/0.38 % English :
% 0.18/0.38
% 0.18/0.38 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.38 % Source : [Bro09]
% 0.18/0.38 % Names : tps_0479 [Bro09]
% 0.18/0.38 % : THM131D [TPS]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % Rating : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.18/0.38 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.18/0.38 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 3 ( 3 avg)
% 0.18/0.38 % Number of connectives : 52 ( 0 ~; 0 |; 7 &; 35 @)
% 0.18/0.38 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 21 ( 21 avg)
% 0.18/0.38 % Number of types : 4 ( 3 usr)
% 0.18/0.38 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.18/0.38 % Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% 0.18/0.38 % SPC : TH0_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.38 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.38 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.38 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.38 % : Polymorphic definitions expanded.
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf(g_type,type,
% 0.18/0.38 g: $tType ).
% 0.18/0.38
% 0.18/0.38 thf(b_type,type,
% 0.18/0.38 b: $tType ).
% 0.18/0.38
% 0.18/0.38 thf(a_type,type,
% 0.18/0.38 a: $tType ).
% 0.18/0.38
% 0.18/0.38 thf(cTHM131D_pme,conjecture,
% 0.18/0.38 ! [Xh1: g > b,Xh2: b > a,Xs1: g > $o,Xf1: g > g,Xs2: b > $o,Xf2: b > b,Xs3: a > $o,Xf3: a > a] :
% 0.18/0.38 ( ( ! [Xx: g] :
% 0.18/0.38 ( ( Xs1 @ Xx )
% 0.18/0.38 => ( Xs1 @ ( Xf1 @ Xx ) ) )
% 0.18/0.38 & ! [Xx: b] :
% 0.18/0.38 ( ( Xs2 @ Xx )
% 0.18/0.38 => ( Xs2 @ ( Xf2 @ Xx ) ) )
% 0.18/0.38 & ! [Xx: g] :
% 0.18/0.38 ( ( Xs1 @ Xx )
% 0.18/0.38 => ( Xs2 @ ( Xh1 @ Xx ) ) )
% 0.18/0.38 & ! [Xx: g] :
% 0.18/0.38 ( ( Xs1 @ Xx )
% 0.18/0.38 => ( ( Xh1 @ ( Xf1 @ Xx ) )
% 0.18/0.38 = ( Xf2 @ ( Xh1 @ Xx ) ) ) )
% 0.18/0.38 & ! [Xx: b] :
% 0.18/0.38 ( ( Xs2 @ Xx )
% 0.18/0.38 => ( Xs2 @ ( Xf2 @ Xx ) ) )
% 0.18/0.38 & ! [Xx: a] :
% 0.18/0.38 ( ( Xs3 @ Xx )
% 0.18/0.38 => ( Xs3 @ ( Xf3 @ Xx ) ) )
% 0.18/0.38 & ! [Xx: b] :
% 0.18/0.38 ( ( Xs2 @ Xx )
% 0.18/0.38 => ( Xs3 @ ( Xh2 @ Xx ) ) )
% 0.18/0.38 & ! [Xx: b] :
% 0.18/0.38 ( ( Xs2 @ Xx )
% 0.18/0.38 => ( ( Xh2 @ ( Xf2 @ Xx ) )
% 0.18/0.38 = ( Xf3 @ ( Xh2 @ Xx ) ) ) ) )
% 0.18/0.38 => ! [Xx: g] :
% 0.18/0.38 ( ( Xs1 @ Xx )
% 0.18/0.38 => ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx ) ) )
% 0.18/0.38 = ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 1.41/1.29 ---- Embedded in THF ---
% 1.41/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.41/1.29 %%% Generated on Tue Feb 24 12:36:11 EST 2026
% 1.41/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.41/1.29 %%% Logic specification used:
% 1.41/1.29 %%% thf(spec, logic, $$dhol).
% 1.41/1.29
% 1.41/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ajzynUZ6gR/DTF2DTF8327.p
% See solution above
% 1.41/1.29 ------------------------
% 1.41/1.30 ---- Cleaned THF ---
% 1.60/1.30 thf(g_type,type,
% 1.60/1.30 g: $tType ).
% 1.60/1.30
% 1.60/1.30 thf(b_type,type,
% 1.60/1.30 b: $tType ).
% 1.60/1.30
% 1.60/1.30 thf(a_type,type,
% 1.60/1.30 a: $tType ).
% 1.60/1.30
% 1.60/1.30 thf(cTHM131D_pme,conjecture,
% 1.60/1.30 ! [Xh1: g > b,Xh2: b > a,Xs1: g > $o,Xf1: g > g,Xs2: b > $o,Xf2: b > b,Xs3: a > $o,Xf3: a > a] :
% 1.60/1.30 ( ( ! [Xx: g] :
% 1.60/1.30 ( ( Xs1 @ Xx )
% 1.60/1.30 => ( Xs1 @ ( Xf1 @ Xx ) ) )
% 1.60/1.30 & ! [Xx: b] :
% 1.60/1.30 ( ( Xs2 @ Xx )
% 1.60/1.30 => ( Xs2 @ ( Xf2 @ Xx ) ) )
% 1.60/1.30 & ! [Xx: g] :
% 1.60/1.30 ( ( Xs1 @ Xx )
% 1.60/1.30 => ( Xs2 @ ( Xh1 @ Xx ) ) )
% 1.60/1.30 & ! [Xx: g] :
% 1.60/1.30 ( ( Xs1 @ Xx )
% 1.60/1.30 => ( ( Xh1 @ ( Xf1 @ Xx ) )
% 1.60/1.30 = ( Xf2 @ ( Xh1 @ Xx ) ) ) )
% 1.60/1.30 & ! [Xx: b] :
% 1.60/1.30 ( ( Xs2 @ Xx )
% 1.60/1.30 => ( Xs2 @ ( Xf2 @ Xx ) ) )
% 1.60/1.30 & ! [Xx: a] :
% 1.60/1.30 ( ( Xs3 @ Xx )
% 1.60/1.30 => ( Xs3 @ ( Xf3 @ Xx ) ) )
% 1.60/1.30 & ! [Xx: b] :
% 1.60/1.30 ( ( Xs2 @ Xx )
% 1.60/1.30 => ( Xs3 @ ( Xh2 @ Xx ) ) )
% 1.60/1.30 & ! [Xx: b] :
% 1.60/1.30 ( ( Xs2 @ Xx )
% 1.60/1.30 => ( ( Xh2 @ ( Xf2 @ Xx ) )
% 1.60/1.30 = ( Xf3 @ ( Xh2 @ Xx ) ) ) ) )
% 1.60/1.30 => ! [Xx: g] :
% 1.60/1.30 ( ( Xs1 @ Xx )
% 1.60/1.30 => ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx ) ) )
% 1.60/1.30 = ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) ) ) ) ).
% 1.60/1.30 ------------------------
% 1.60/1.32 % (8432)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8327 for (2999ds/18Mi)
% 1.60/1.32 % (8431)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_8327 for (2999ds/275Mi)
% 1.60/1.32 % (8426)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8327 for (2999ds/183Mi)
% 1.60/1.32 % (8430)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_8327 for (2999ds/2Mi)
% 1.60/1.32 % (8428)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_8327 for (2999ds/27Mi)
% 1.60/1.32 % (8429)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8327 for (2999ds/2Mi)
% 1.60/1.32 % (8427)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_8327 for (2999ds/4Mi)
% 1.60/1.32 % (8429)Instruction limit reached!
% 1.60/1.32 % (8429)------------------------------
% 1.60/1.32 % (8429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (8429)Termination reason: Unknown
% 1.60/1.32 % (8430)Instruction limit reached!
% 1.60/1.32 % (8430)------------------------------
% 1.60/1.32 % (8430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (8429)Termination phase: Preprocessing 3
% 1.60/1.32
% 1.60/1.32 % (8429)Memory used [KB]: 1023
% 1.60/1.32 % (8429)Time elapsed: 0.003 s
% 1.60/1.32 % (8429)Instructions burned: 2 (million)
% 1.60/1.32 % (8429)------------------------------
% 1.60/1.32 % (8429)------------------------------
% 1.60/1.32 % (8430)Termination reason: Unknown
% 1.60/1.32 % (8430)Termination phase: Property scanning
% 1.60/1.32
% 1.60/1.32 % (8430)Memory used [KB]: 1023
% 1.60/1.32 % (8430)Time elapsed: 0.003 s
% 1.60/1.32 % (8430)Instructions burned: 3 (million)
% 1.60/1.32 % (8430)------------------------------
% 1.60/1.32 % (8430)------------------------------
% 1.60/1.32 % (8427)Instruction limit reached!
% 1.60/1.32 % (8427)------------------------------
% 1.60/1.32 % (8427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (8427)Termination reason: Unknown
% 1.60/1.32 % (8427)Termination phase: Saturation
% 1.60/1.32
% 1.60/1.32 % (8427)Memory used [KB]: 5500
% 1.60/1.32 % (8427)Time elapsed: 0.005 s
% 1.60/1.32 % (8427)Instructions burned: 5 (million)
% 1.60/1.32 % (8427)------------------------------
% 1.60/1.32 % (8427)------------------------------
% 1.60/1.32 % (8431)First to succeed.
% 1.60/1.32 % (8426)Also succeeded, but the first one will report.
% 1.60/1.32 % (8428)Also succeeded, but the first one will report.
% 1.60/1.32 % (8431)Refutation found. Thanks to Tanya!
% 1.60/1.32 % SZS status Theorem for DTF2THF_8327
% 1.60/1.32 % SZS output start Proof for DTF2THF_8327
% 1.60/1.32 thf(type_def_5, type, g: $tType).
% 1.60/1.32 thf(type_def_6, type, b: $tType).
% 1.60/1.32 thf(type_def_8, type, a: $tType).
% 1.60/1.32 thf(func_def_0, type, g: $tType).
% 1.60/1.32 thf(func_def_1, type, b: $tType).
% 1.60/1.32 thf(func_def_2, type, a: $tType).
% 1.60/1.32 thf(func_def_6, type, sK0: b > $o).
% 1.60/1.32 thf(func_def_7, type, sK1: b > b).
% 1.60/1.32 thf(func_def_8, type, sK2: a > a).
% 1.60/1.32 thf(func_def_9, type, sK3: a > $o).
% 1.60/1.32 thf(func_def_10, type, sK4: g > b).
% 1.60/1.32 thf(func_def_11, type, sK5: g > g).
% 1.60/1.32 thf(func_def_12, type, sK6: b > a).
% 1.60/1.32 thf(func_def_13, type, sK7: g > $o).
% 1.60/1.32 thf(func_def_14, type, sK8: g).
% 1.60/1.32 thf(f46,plain,(
% 1.60/1.32 $false),
% 1.60/1.32 inference(avatar_sat_refutation,[status(thm)],[f37,f41,f45])).
% 1.60/1.32 thf(f45,plain,(
% 1.60/1.32 spl9_2),
% 1.60/1.32 inference(avatar_contradiction_clause,[status(thm)],[f44])).
% 1.60/1.32 thf(f44,plain,(
% 1.60/1.32 $false | spl9_2),
% 1.60/1.32 inference(subsumption_resolution,[status(thm)],[f43,f14])).
% 1.60/1.32 thf(f14,plain,(
% 1.60/1.32 ((sK7 @ sK8) = $true)),
% 1.60/1.32 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.32 thf(f11,plain,(
% 1.60/1.32 ! [X8 : g] : (((sK7 @ X8) != $true) | ((sK7 @ (sK5 @ X8)) = $true)) & ! [X9 : g] : (((sK4 @ (sK5 @ X9)) = (sK1 @ (sK4 @ X9))) | ((sK7 @ X9) != $true)) & ! [X10 : g] : (($true = (sK0 @ (sK4 @ X10))) | ((sK7 @ X10) != $true)) & ! [X11 : b] : (((sK0 @ X11) != $true) | ($true = (sK0 @ (sK1 @ X11)))) & ! [X12 : a] : (($true = (sK3 @ (sK2 @ X12))) | ($true != (sK3 @ X12))) & ! [X13 : b] : (($true != (sK0 @ X13)) | ((sK0 @ (sK1 @ X13)) = $true)) & ! [X14 : b] : (($true = (sK3 @ (sK6 @ X14))) | ((sK0 @ X14) != $true)) & (((sK7 @ sK8) = $true) & ((sK2 @ (sK6 @ (sK4 @ sK8))) != (sK6 @ (sK4 @ (sK5 @ sK8))))) & ! [X16 : b] : (((sK2 @ (sK6 @ X16)) = (sK6 @ (sK1 @ X16))) | ((sK0 @ X16) != $true))),
% 1.60/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f8,f10,f9])).
% 1.60/1.32 thf(f9,plain,(
% 1.60/1.32 ? [X0 : b > $o,X1 : b > b,X2 : a > a,X3 : a > $o,X4 : g > b,X5 : g > g,X6 : b > a,X7 : g > $o] : (! [X8 : g] : (($true != (X7 @ X8)) | ($true = (X7 @ (X5 @ X8)))) & ! [X9 : g] : (((X1 @ (X4 @ X9)) = (X4 @ (X5 @ X9))) | ((X7 @ X9) != $true)) & ! [X10 : g] : (((X0 @ (X4 @ X10)) = $true) | ($true != (X7 @ X10))) & ! [X11 : b] : (($true != (X0 @ X11)) | ($true = (X0 @ (X1 @ X11)))) & ! [X12 : a] : (((X3 @ (X2 @ X12)) = $true) | ((X3 @ X12) != $true)) & ! [X13 : b] : (($true != (X0 @ X13)) | ((X0 @ (X1 @ X13)) = $true)) & ! [X14 : b] : (($true = (X3 @ (X6 @ X14))) | ($true != (X0 @ X14))) & ? [X15 : g] : (((X7 @ X15) = $true) & ((X6 @ (X4 @ (X5 @ X15))) != (X2 @ (X6 @ (X4 @ X15))))) & ! [X16 : b] : (((X6 @ (X1 @ X16)) = (X2 @ (X6 @ X16))) | ($true != (X0 @ X16)))) => (! [X8 : g] : (((sK7 @ X8) != $true) | ((sK7 @ (sK5 @ X8)) = $true)) & ! [X9 : g] : (((sK4 @ (sK5 @ X9)) = (sK1 @ (sK4 @ X9))) | ((sK7 @ X9) != $true)) & ! [X10 : g] : (($true = (sK0 @ (sK4 @ X10))) | ((sK7 @ X10) != $true)) & ! [X11 : b] : (((sK0 @ X11) != $true) | ($true = (sK0 @ (sK1 @ X11)))) & ! [X12 : a] : (($true = (sK3 @ (sK2 @ X12))) | ($true != (sK3 @ X12))) & ! [X13 : b] : (($true != (sK0 @ X13)) | ((sK0 @ (sK1 @ X13)) = $true)) & ! [X14 : b] : (($true = (sK3 @ (sK6 @ X14))) | ((sK0 @ X14) != $true)) & ? [X15 : g] : (($true = (sK7 @ X15)) & ((sK6 @ (sK4 @ (sK5 @ X15))) != (sK2 @ (sK6 @ (sK4 @ X15))))) & ! [X16 : b] : (((sK2 @ (sK6 @ X16)) = (sK6 @ (sK1 @ X16))) | ((sK0 @ X16) != $true)))),
% 1.60/1.32 introduced(definition,[],[choice_axiom])).
% 1.60/1.32 thf(f10,plain,(
% 1.60/1.32 ? [X15 : g] : (($true = (sK7 @ X15)) & ((sK6 @ (sK4 @ (sK5 @ X15))) != (sK2 @ (sK6 @ (sK4 @ X15))))) => (((sK7 @ sK8) = $true) & ((sK2 @ (sK6 @ (sK4 @ sK8))) != (sK6 @ (sK4 @ (sK5 @ sK8)))))),
% 1.60/1.32 introduced(definition,[],[choice_axiom])).
% 1.60/1.32 thf(f8,plain,(
% 1.60/1.32 ? [X0 : b > $o,X1 : b > b,X2 : a > a,X3 : a > $o,X4 : g > b,X5 : g > g,X6 : b > a,X7 : g > $o] : (! [X8 : g] : (($true != (X7 @ X8)) | ($true = (X7 @ (X5 @ X8)))) & ! [X9 : g] : (((X1 @ (X4 @ X9)) = (X4 @ (X5 @ X9))) | ((X7 @ X9) != $true)) & ! [X10 : g] : (((X0 @ (X4 @ X10)) = $true) | ($true != (X7 @ X10))) & ! [X11 : b] : (($true != (X0 @ X11)) | ($true = (X0 @ (X1 @ X11)))) & ! [X12 : a] : (((X3 @ (X2 @ X12)) = $true) | ((X3 @ X12) != $true)) & ! [X13 : b] : (($true != (X0 @ X13)) | ((X0 @ (X1 @ X13)) = $true)) & ! [X14 : b] : (($true = (X3 @ (X6 @ X14))) | ($true != (X0 @ X14))) & ? [X15 : g] : (((X7 @ X15) = $true) & ((X6 @ (X4 @ (X5 @ X15))) != (X2 @ (X6 @ (X4 @ X15))))) & ! [X16 : b] : (((X6 @ (X1 @ X16)) = (X2 @ (X6 @ X16))) | ($true != (X0 @ X16))))),
% 1.60/1.32 inference(rectify,[status(thm)],[f7])).
% 1.60/1.32 thf(f7,plain,(
% 1.60/1.32 ? [X3 : b > $o,X0 : b > b,X7 : a > a,X6 : a > $o,X2 : g > b,X1 : g > g,X5 : b > a,X4 : g > $o] : (! [X14 : g] : (((X4 @ X14) != $true) | ($true = (X4 @ (X1 @ X14)))) & ! [X13 : g] : (((X2 @ (X1 @ X13)) = (X0 @ (X2 @ X13))) | ((X4 @ X13) != $true)) & ! [X10 : g] : (($true = (X3 @ (X2 @ X10))) | ($true != (X4 @ X10))) & ! [X15 : b] : (($true != (X3 @ X15)) | ($true = (X3 @ (X0 @ X15)))) & ! [X12 : a] : (((X6 @ (X7 @ X12)) = $true) | ($true != (X6 @ X12))) & ! [X9 : b] : (($true != (X3 @ X9)) | ((X3 @ (X0 @ X9)) = $true)) & ! [X11 : b] : (((X6 @ (X5 @ X11)) = $true) | ((X3 @ X11) != $true)) & ? [X16 : g] : (((X4 @ X16) = $true) & ((X7 @ (X5 @ (X2 @ X16))) != (X5 @ (X2 @ (X1 @ X16))))) & ! [X8 : b] : (((X7 @ (X5 @ X8)) = (X5 @ (X0 @ X8))) | ($true != (X3 @ X8))))),
% 1.60/1.32 inference(flattening,[status(thm)],[f6])).
% 1.60/1.32 thf(f6,plain,(
% 1.60/1.32 ? [X4 : g > $o,X0 : b > b,X7 : a > a,X3 : b > $o,X6 : a > $o,X2 : g > b,X5 : b > a,X1 : g > g] : (? [X16 : g] : (((X4 @ X16) = $true) & ((X7 @ (X5 @ (X2 @ X16))) != (X5 @ (X2 @ (X1 @ X16))))) & (! [X15 : b] : (($true != (X3 @ X15)) | ($true = (X3 @ (X0 @ X15)))) & ! [X13 : g] : (((X2 @ (X1 @ X13)) = (X0 @ (X2 @ X13))) | ((X4 @ X13) != $true)) & ! [X8 : b] : (((X7 @ (X5 @ X8)) = (X5 @ (X0 @ X8))) | ($true != (X3 @ X8))) & ! [X11 : b] : (((X6 @ (X5 @ X11)) = $true) | ((X3 @ X11) != $true)) & ! [X12 : a] : (((X6 @ (X7 @ X12)) = $true) | ($true != (X6 @ X12))) & ! [X9 : b] : (($true != (X3 @ X9)) | ((X3 @ (X0 @ X9)) = $true)) & ! [X14 : g] : (((X4 @ X14) != $true) | ($true = (X4 @ (X1 @ X14)))) & ! [X10 : g] : (($true = (X3 @ (X2 @ X10))) | ($true != (X4 @ X10)))))),
% 1.60/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.60/1.32 thf(f5,plain,(
% 1.60/1.32 ~! [X4 : g > $o,X0 : b > b,X7 : a > a,X3 : b > $o,X6 : a > $o,X2 : g > b,X5 : b > a,X1 : g > g] : ((! [X15 : b] : (($true = (X3 @ X15)) => ($true = (X3 @ (X0 @ X15)))) & ! [X13 : g] : (((X4 @ X13) = $true) => ((X2 @ (X1 @ X13)) = (X0 @ (X2 @ X13)))) & ! [X8 : b] : (($true = (X3 @ X8)) => ((X7 @ (X5 @ X8)) = (X5 @ (X0 @ X8)))) & ! [X11 : b] : (((X3 @ X11) = $true) => ((X6 @ (X5 @ X11)) = $true)) & ! [X12 : a] : (($true = (X6 @ X12)) => ((X6 @ (X7 @ X12)) = $true)) & ! [X9 : b] : (($true = (X3 @ X9)) => ((X3 @ (X0 @ X9)) = $true)) & ! [X14 : g] : (((X4 @ X14) = $true) => ($true = (X4 @ (X1 @ X14)))) & ! [X10 : g] : (($true = (X4 @ X10)) => ($true = (X3 @ (X2 @ X10))))) => ! [X16 : g] : (((X4 @ X16) = $true) => ((X7 @ (X5 @ (X2 @ X16))) = (X5 @ (X2 @ (X1 @ X16))))))),
% 1.60/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.60/1.32 thf(f4,plain,(
% 1.60/1.32 ~! [X0 : b > b,X1 : g > g,X2 : g > b,X3 : b > $o,X4 : g > $o,X5 : b > a,X6 : a > $o,X7 : a > a] : ((! [X8 : b] : ((X3 @ X8) => ((X7 @ (X5 @ X8)) = (X5 @ (X0 @ X8)))) & ! [X9 : b] : ((X3 @ X9) => (X3 @ (X0 @ X9))) & ! [X10 : g] : ((X4 @ X10) => (X3 @ (X2 @ X10))) & ! [X11 : b] : ((X3 @ X11) => (X6 @ (X5 @ X11))) & ! [X12 : a] : ((X6 @ X12) => (X6 @ (X7 @ X12))) & ! [X13 : g] : ((X4 @ X13) => ((X2 @ (X1 @ X13)) = (X0 @ (X2 @ X13)))) & ! [X14 : g] : ((X4 @ X14) => (X4 @ (X1 @ X14))) & ! [X15 : b] : ((X3 @ X15) => (X3 @ (X0 @ X15)))) => ! [X16 : g] : ((X4 @ X16) => ((X7 @ (X5 @ (X2 @ X16))) = (X5 @ (X2 @ (X1 @ X16))))))),
% 1.60/1.32 inference(rectify,[status(thm)],[f2])).
% 1.60/1.32 thf(f2,negated_conjecture,(
% 1.60/1.32 ~! [X5 : b > b,X3 : g > g,X0 : g > b,X4 : b > $o,X2 : g > $o,X1 : b > a,X6 : a > $o,X7 : a > a] : ((! [X8 : b] : ((X4 @ X8) => ((X1 @ (X5 @ X8)) = (X7 @ (X1 @ X8)))) & ! [X8 : b] : ((X4 @ X8) => (X4 @ (X5 @ X8))) & ! [X8 : g] : ((X2 @ X8) => (X4 @ (X0 @ X8))) & ! [X8 : b] : ((X4 @ X8) => (X6 @ (X1 @ X8))) & ! [X8 : a] : ((X6 @ X8) => (X6 @ (X7 @ X8))) & ! [X8 : g] : ((X2 @ X8) => ((X0 @ (X3 @ X8)) = (X5 @ (X0 @ X8)))) & ! [X8 : g] : ((X2 @ X8) => (X2 @ (X3 @ X8))) & ! [X8 : b] : ((X4 @ X8) => (X4 @ (X5 @ X8)))) => ! [X8 : g] : ((X2 @ X8) => ((X1 @ (X0 @ (X3 @ X8))) = (X7 @ (X1 @ (X0 @ X8))))))),
% 1.60/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.60/1.32 thf(f1,conjecture,(
% 1.60/1.32 ! [X5 : b > b,X3 : g > g,X0 : g > b,X4 : b > $o,X2 : g > $o,X1 : b > a,X6 : a > $o,X7 : a > a] : ((! [X8 : b] : ((X4 @ X8) => ((X1 @ (X5 @ X8)) = (X7 @ (X1 @ X8)))) & ! [X8 : b] : ((X4 @ X8) => (X4 @ (X5 @ X8))) & ! [X8 : g] : ((X2 @ X8) => (X4 @ (X0 @ X8))) & ! [X8 : b] : ((X4 @ X8) => (X6 @ (X1 @ X8))) & ! [X8 : a] : ((X6 @ X8) => (X6 @ (X7 @ X8))) & ! [X8 : g] : ((X2 @ X8) => ((X0 @ (X3 @ X8)) = (X5 @ (X0 @ X8)))) & ! [X8 : g] : ((X2 @ X8) => (X2 @ (X3 @ X8))) & ! [X8 : b] : ((X4 @ X8) => (X4 @ (X5 @ X8)))) => ! [X8 : g] : ((X2 @ X8) => ((X1 @ (X0 @ (X3 @ X8))) = (X7 @ (X1 @ (X0 @ X8))))))),
% 1.60/1.32 file('/export/starexec/sandbox2/tmp/tmp.ajzynUZ6gR/DTF2THF_8327.p',cTHM131D_pme)).
% 1.60/1.32 thf(f43,plain,(
% 1.60/1.32 ((sK7 @ sK8) != $true) | spl9_2),
% 1.60/1.32 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.60/1.32 thf(f42,plain,(
% 1.60/1.32 ((sK6 @ (sK4 @ (sK5 @ sK8))) != (sK6 @ (sK4 @ (sK5 @ sK8)))) | ((sK7 @ sK8) != $true) | spl9_2),
% 1.60/1.32 inference(superposition,[status(thm)],[f36,f20])).
% 1.60/1.32 thf(f20,plain,(
% 1.60/1.32 ( ! [X9 : g] : (((sK4 @ (sK5 @ X9)) = (sK1 @ (sK4 @ X9))) | ((sK7 @ X9) != $true)) )),
% 1.60/1.32 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.32 thf(f36,plain,(
% 1.60/1.32 ((sK6 @ (sK1 @ (sK4 @ sK8))) != (sK6 @ (sK4 @ (sK5 @ sK8)))) | spl9_2),
% 1.60/1.32 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.60/1.32 thf(f34,definition,(
% 1.60/1.32 spl9_2 <=> ((sK6 @ (sK1 @ (sK4 @ sK8))) = (sK6 @ (sK4 @ (sK5 @ sK8))))),
% 1.60/1.32 introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition])).
% 1.60/1.32 thf(f41,plain,(
% 1.60/1.32 spl9_1),
% 1.60/1.32 inference(avatar_contradiction_clause,[status(thm)],[f40])).
% 1.60/1.32 thf(f40,plain,(
% 1.60/1.32 $false | spl9_1),
% 1.60/1.32 inference(subsumption_resolution,[status(thm)],[f39,f14])).
% 1.60/1.32 thf(f39,plain,(
% 1.60/1.32 ((sK7 @ sK8) != $true) | spl9_1),
% 1.60/1.32 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.60/1.32 thf(f38,plain,(
% 1.60/1.32 ((sK7 @ sK8) != $true) | ($true != $true) | spl9_1),
% 1.60/1.32 inference(superposition,[status(thm)],[f32,f19])).
% 1.60/1.32 thf(f19,plain,(
% 1.60/1.32 ( ! [X10 : g] : (($true = (sK0 @ (sK4 @ X10))) | ((sK7 @ X10) != $true)) )),
% 1.60/1.32 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.32 thf(f32,plain,(
% 1.60/1.32 ($true != (sK0 @ (sK4 @ sK8))) | spl9_1),
% 1.60/1.32 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.60/1.32 thf(f30,definition,(
% 1.60/1.32 spl9_1 <=> ($true = (sK0 @ (sK4 @ sK8)))),
% 1.60/1.32 introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition])).
% 1.60/1.32 thf(f37,plain,(
% 1.60/1.32 ~spl9_1 | ~spl9_2),
% 1.60/1.32 inference(avatar_split_clause,[status(thm)],[f28,f34,f30])).
% 1.60/1.32 thf(f28,plain,(
% 1.60/1.32 ($true != (sK0 @ (sK4 @ sK8))) | ((sK6 @ (sK1 @ (sK4 @ sK8))) != (sK6 @ (sK4 @ (sK5 @ sK8))))),
% 1.60/1.32 inference(superposition,[status(thm)],[f13,f12])).
% 1.60/1.32 thf(f12,plain,(
% 1.60/1.32 ( ! [X16 : b] : (((sK2 @ (sK6 @ X16)) = (sK6 @ (sK1 @ X16))) | ((sK0 @ X16) != $true)) )),
% 1.60/1.32 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.32 thf(f13,plain,(
% 1.60/1.32 ((sK2 @ (sK6 @ (sK4 @ sK8))) != (sK6 @ (sK4 @ (sK5 @ sK8))))),
% 1.60/1.32 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.32 % SZS output end Proof for DTF2THF_8327
% 1.60/1.32 % (8431)------------------------------
% 1.60/1.32 % (8431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (8431)Termination reason: Refutation
% 1.60/1.32
% 1.60/1.32 % (8431)Memory used [KB]: 5628
% 1.60/1.32 % (8431)Time elapsed: 0.008 s
% 1.60/1.32 % (8431)Instructions burned: 7 (million)
% 1.60/1.32 % (8431)------------------------------
% 1.60/1.32 % (8431)------------------------------
% 1.60/1.32 % (8425)Success in time 0.019 s
%------------------------------------------------------------------------------