%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO272^5 : 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 : n016.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 09:53:49 AM UTC 2026
% Result : Theorem 1.58s 1.36s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 544 ( 147 equ; 0 cnn)
% Maximal formula atoms : 16 ( 14 avg)
% Number of connectives : 812 ( 79 ~; 67 |; 63 &; 572 @)
% ( 8 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 213 ( 88 ^; 102 !; 23 ?; 213 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cHALF: $i > $i > $o ).
thf(func_def_1,type,
cDOUBLE: $i > $i > $o ).
thf(func_def_2,type,
cS: $i > $i ).
thf(func_def_9,type,
sK2: ( $i > $i > $o ) > $i ).
thf(func_def_10,type,
sK3: ( $i > $i > $o ) > $i ).
thf(func_def_11,type,
sK4: $i > $i > $i > $i > $o ).
thf(func_def_14,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f170,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f129,f156,f169]) ).
thf(f169,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[status(thm)],[f168]) ).
thf(f168,plain,
( $false
| ~ spl5_3 ),
inference(subsumption_resolution,[status(thm)],[f161,f21]) ).
thf(f21,plain,
( $true
= ( cDOUBLE @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( cHALF @ c0 @ c0 )
= $true )
& ( $true
!= ( cHALF @ sK1 @ sK0 ) )
& ( $true
= ( cDOUBLE @ sK0 @ sK1 ) )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( cHALF @ X2 @ X3 ) )
| ( ( cHALF @ ( cS @ ( cS @ X2 ) ) @ ( cS @ X3 ) )
= $true ) )
& ( ( cHALF @ ( cS @ c0 ) @ c0 )
= $true )
& ! [X4: $i,X5: $i] :
( ( ! [X6: $i > $i > $o] :
( ( ( X6 @ X4 @ X5 )
= $true )
| ( $true
!= ( X6 @ c0 @ c0 ) )
| ( ( $true
!= ( X6 @ ( cS @ ( sK2 @ X6 ) ) @ ( cS @ ( cS @ ( sK3 @ X6 ) ) ) ) )
& ( $true
= ( X6 @ ( sK2 @ X6 ) @ ( sK3 @ X6 ) ) ) ) )
| ( ( cDOUBLE @ X4 @ X5 )
!= $true ) )
& ( ( ( cDOUBLE @ X4 @ X5 )
= $true )
| ( ( ( sK4 @ X5 @ X4 @ X4 @ X5 )
!= $true )
& ( $true
= ( sK4 @ X5 @ X4 @ c0 @ c0 ) )
& ! [X10: $i,X11: $i] :
( ( ( sK4 @ X5 @ X4 @ ( cS @ X10 ) @ ( cS @ ( cS @ X11 ) ) )
= $true )
| ( $true
!= ( sK4 @ X5 @ X4 @ X10 @ X11 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i] :
( ( ( cHALF @ X1 @ X0 )
!= $true )
& ( ( cDOUBLE @ X0 @ X1 )
= $true ) )
=> ( ( $true
!= ( cHALF @ sK1 @ sK0 ) )
& ( $true
= ( cDOUBLE @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X6: $i > $i > $o] :
( ? [X7: $i,X8: $i] :
( ( $true
!= ( X6 @ ( cS @ X7 ) @ ( cS @ ( cS @ X8 ) ) ) )
& ( $true
= ( X6 @ X7 @ X8 ) ) )
=> ( ( $true
!= ( X6 @ ( cS @ ( sK2 @ X6 ) ) @ ( cS @ ( cS @ ( sK3 @ X6 ) ) ) ) )
& ( $true
= ( X6 @ ( sK2 @ X6 ) @ ( sK3 @ X6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X4: $i,X5: $i] :
( ? [X9: $i > $i > $o] :
( ( $true
!= ( X9 @ X4 @ X5 ) )
& ( ( X9 @ c0 @ c0 )
= $true )
& ! [X10: $i,X11: $i] :
( ( ( X9 @ ( cS @ X10 ) @ ( cS @ ( cS @ X11 ) ) )
= $true )
| ( $true
!= ( X9 @ X10 @ X11 ) ) ) )
=> ( ( ( sK4 @ X5 @ X4 @ X4 @ X5 )
!= $true )
& ( $true
= ( sK4 @ X5 @ X4 @ c0 @ c0 ) )
& ! [X11: $i,X10: $i] :
( ( ( sK4 @ X5 @ X4 @ ( cS @ X10 ) @ ( cS @ ( cS @ X11 ) ) )
= $true )
| ( $true
!= ( sK4 @ X5 @ X4 @ X10 @ X11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( ( cHALF @ c0 @ c0 )
= $true )
& ? [X0: $i,X1: $i] :
( ( ( cHALF @ X1 @ X0 )
!= $true )
& ( ( cDOUBLE @ X0 @ X1 )
= $true ) )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( cHALF @ X2 @ X3 ) )
| ( ( cHALF @ ( cS @ ( cS @ X2 ) ) @ ( cS @ X3 ) )
= $true ) )
& ( ( cHALF @ ( cS @ c0 ) @ c0 )
= $true )
& ! [X4: $i,X5: $i] :
( ( ! [X6: $i > $i > $o] :
( ( ( X6 @ X4 @ X5 )
= $true )
| ( $true
!= ( X6 @ c0 @ c0 ) )
| ? [X7: $i,X8: $i] :
( ( $true
!= ( X6 @ ( cS @ X7 ) @ ( cS @ ( cS @ X8 ) ) ) )
& ( $true
= ( X6 @ X7 @ X8 ) ) ) )
| ( ( cDOUBLE @ X4 @ X5 )
!= $true ) )
& ( ( ( cDOUBLE @ X4 @ X5 )
= $true )
| ? [X9: $i > $i > $o] :
( ( $true
!= ( X9 @ X4 @ X5 ) )
& ( ( X9 @ c0 @ c0 )
= $true )
& ! [X10: $i,X11: $i] :
( ( ( X9 @ ( cS @ X10 ) @ ( cS @ ( cS @ X11 ) ) )
= $true )
| ( $true
!= ( X9 @ X10 @ X11 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( cHALF @ c0 @ c0 )
= $true )
& ? [X7: $i,X8: $i] :
( ( $true
!= ( cHALF @ X8 @ X7 ) )
& ( ( cDOUBLE @ X7 @ X8 )
= $true ) )
& ! [X5: $i,X6: $i] :
( ( $true
!= ( cHALF @ X5 @ X6 ) )
| ( $true
= ( cHALF @ ( cS @ ( cS @ X5 ) ) @ ( cS @ X6 ) ) ) )
& ( ( cHALF @ ( cS @ c0 ) @ c0 )
= $true )
& ! [X0: $i,X1: $i] :
( ( ! [X2: $i > $i > $o] :
( ( ( X2 @ X0 @ X1 )
= $true )
| ( ( X2 @ c0 @ c0 )
!= $true )
| ? [X3: $i,X4: $i] :
( ( ( X2 @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) )
!= $true )
& ( ( X2 @ X3 @ X4 )
= $true ) ) )
| ( ( cDOUBLE @ X0 @ X1 )
!= $true ) )
& ( ( ( cDOUBLE @ X0 @ X1 )
= $true )
| ? [X2: $i > $i > $o] :
( ( ( X2 @ X0 @ X1 )
!= $true )
& ( ( X2 @ c0 @ c0 )
= $true )
& ! [X3: $i,X4: $i] :
( ( ( X2 @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) )
= $true )
| ( ( X2 @ X3 @ X4 )
!= $true ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cHALF @ c0 @ c0 )
= $true )
& ? [X7: $i,X8: $i] :
( ( $true
!= ( cHALF @ X8 @ X7 ) )
& ( ( cDOUBLE @ X7 @ X8 )
= $true ) )
& ! [X5: $i,X6: $i] :
( ( $true
!= ( cHALF @ X5 @ X6 ) )
| ( $true
= ( cHALF @ ( cS @ ( cS @ X5 ) ) @ ( cS @ X6 ) ) ) )
& ( ( cHALF @ ( cS @ c0 ) @ c0 )
= $true )
& ! [X0: $i,X1: $i] :
( ! [X2: $i > $i > $o] :
( ( ( X2 @ X0 @ X1 )
= $true )
| ( ( X2 @ c0 @ c0 )
!= $true )
| ? [X3: $i,X4: $i] :
( ( ( X2 @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) )
!= $true )
& ( ( X2 @ X3 @ X4 )
= $true ) ) )
<=> ( ( cDOUBLE @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X7: $i,X8: $i] :
( ( $true
!= ( cHALF @ X8 @ X7 ) )
& ( ( cDOUBLE @ X7 @ X8 )
= $true ) )
& ! [X5: $i,X6: $i] :
( ( $true
!= ( cHALF @ X5 @ X6 ) )
| ( $true
= ( cHALF @ ( cS @ ( cS @ X5 ) ) @ ( cS @ X6 ) ) ) )
& ( ( cHALF @ c0 @ c0 )
= $true )
& ( ( cHALF @ ( cS @ c0 ) @ c0 )
= $true )
& ! [X1: $i,X0: $i] :
( ( ( cDOUBLE @ X0 @ X1 )
= $true )
<=> ! [X2: $i > $i > $o] :
( ( ( X2 @ X0 @ X1 )
= $true )
| ? [X3: $i,X4: $i] :
( ( ( X2 @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) )
!= $true )
& ( ( X2 @ X3 @ X4 )
= $true ) )
| ( ( X2 @ c0 @ c0 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X6: $i,X5: $i] :
( ( $true
= ( cHALF @ X5 @ X6 ) )
=> ( $true
= ( cHALF @ ( cS @ ( cS @ X5 ) ) @ ( cS @ X6 ) ) ) )
& ( ( cHALF @ c0 @ c0 )
= $true )
& ( ( cHALF @ ( cS @ c0 ) @ c0 )
= $true )
& ! [X1: $i,X0: $i] :
( ( ( cDOUBLE @ X0 @ X1 )
= $true )
<=> ! [X2: $i > $i > $o] :
( ( ! [X4: $i,X3: $i] :
( ( ( X2 @ X3 @ X4 )
= $true )
=> ( ( X2 @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) )
= $true ) )
& ( ( X2 @ c0 @ c0 )
= $true ) )
=> ( ( X2 @ X0 @ X1 )
= $true ) ) ) )
=> ! [X7: $i,X8: $i] :
( ( ( cDOUBLE @ X7 @ X8 )
= $true )
=> ( $true
= ( cHALF @ X8 @ X7 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( cHALF @ c0 @ c0 )
& ! [X0: $i,X1: $i] :
( ! [X2: $i > $i > $o] :
( ( ( X2 @ c0 @ c0 )
& ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X2 @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) ) ) )
=> ( X2 @ X0 @ X1 ) )
<=> ( cDOUBLE @ X0 @ X1 ) )
& ! [X5: $i,X6: $i] :
( ( cHALF @ X5 @ X6 )
=> ( cHALF @ ( cS @ ( cS @ X5 ) ) @ ( cS @ X6 ) ) )
& ( cHALF @ ( cS @ c0 ) @ c0 ) )
=> ! [X7: $i,X8: $i] :
( ( cDOUBLE @ X7 @ X8 )
=> ( cHALF @ X8 @ X7 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( cHALF @ c0 @ c0 )
& ! [X0: $i,X1: $i] :
( ! [X2: $i > $i > $o] :
( ( ( X2 @ c0 @ c0 )
& ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X2 @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) ) ) )
=> ( X2 @ X0 @ X1 ) )
<=> ( cDOUBLE @ X0 @ X1 ) )
& ! [X3: $i,X4: $i] :
( ( cHALF @ X3 @ X4 )
=> ( cHALF @ ( cS @ ( cS @ X3 ) ) @ ( cS @ X4 ) ) )
& ( cHALF @ ( cS @ c0 ) @ c0 ) )
=> ! [X0: $i,X1: $i] :
( ( cDOUBLE @ X0 @ X1 )
=> ( cHALF @ X1 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( cHALF @ c0 @ c0 )
& ! [X0: $i,X1: $i] :
( ! [X2: $i > $i > $o] :
( ( ( X2 @ c0 @ c0 )
& ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X2 @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) ) ) )
=> ( X2 @ X0 @ X1 ) )
<=> ( cDOUBLE @ X0 @ X1 ) )
& ! [X3: $i,X4: $i] :
( ( cHALF @ X3 @ X4 )
=> ( cHALF @ ( cS @ ( cS @ X3 ) ) @ ( cS @ X4 ) ) )
& ( cHALF @ ( cS @ c0 ) @ c0 ) )
=> ! [X0: $i,X1: $i] :
( ( cDOUBLE @ X0 @ X1 )
=> ( cHALF @ X1 @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KOSDt143hE/DTF2THF_11287.p',cTHM301A) ).
thf(f161,plain,
( ( $true
!= ( cDOUBLE @ sK0 @ sK1 ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[status(thm)],[f159]) ).
thf(f159,plain,
( ( $true
!= ( cDOUBLE @ sK0 @ sK1 ) )
| ( $true != $true )
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f22,f124]) ).
thf(f124,plain,
( ! [X0: $i,X1: $i] :
( ( ( cHALF @ X1 @ X0 )
= $true )
| ( ( cDOUBLE @ X0 @ X1 )
!= $true ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f123]) ).
thf(f123,definition,
( spl5_3
<=> ! [X0: $i,X1: $i] :
( ( ( cDOUBLE @ X0 @ X1 )
!= $true )
| ( ( cHALF @ X1 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f22,plain,
( $true
!= ( cHALF @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f156,plain,
( spl5_3
| spl5_4 ),
inference(avatar_split_clause,[status(thm)],[f155,f126,f123]) ).
thf(f126,definition,
( spl5_4
<=> ( $true
= ( cHALF
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( cHALF @ Y1 @ Y0 ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( cHALF @ Y1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f155,plain,
( ! [X0: $i,X1: $i] :
( ( ( cDOUBLE @ X0 @ X1 )
!= $true )
| ( ( cHALF @ X1 @ X0 )
= $true ) )
| spl5_4 ),
inference(subsumption_resolution,[status(thm)],[f154,f23]) ).
thf(f23,plain,
( ( cHALF @ c0 @ c0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f154,plain,
( ! [X0: $i,X1: $i] :
( ( ( cDOUBLE @ X0 @ X1 )
!= $true )
| ( ( cHALF @ X1 @ X0 )
= $true )
| ( ( cHALF @ c0 @ c0 )
!= $true ) )
| spl5_4 ),
inference(beta_eta_normalization,[status(thm)],[f153]) ).
thf(f153,plain,
( ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i,Y1: $i] :
( cHALF
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ X0
@ X1 )
= $true )
| ( $true
!= ( ^ [Y0: $i,Y1: $i] :
( cHALF
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ c0
@ c0 ) )
| ( ( cDOUBLE @ X0 @ X1 )
!= $true ) )
| spl5_4 ),
inference(trivial_inequality_removal,[status(thm)],[f152]) ).
thf(f152,plain,
( ! [X0: $i,X1: $i] :
( ( ( cDOUBLE @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( ^ [Y0: $i,Y1: $i] :
( cHALF
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ X0
@ X1 )
= $true )
| ( $true
!= ( ^ [Y0: $i,Y1: $i] :
( cHALF
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ c0
@ c0 ) ) )
| spl5_4 ),
inference(superposition,[status(thm)],[f128,f17]) ).
thf(f17,plain,
! [X6: $i > $i > $o,X4: $i,X5: $i] :
( ( $true
= ( X6 @ ( sK2 @ X6 ) @ ( sK3 @ X6 ) ) )
| ( ( cDOUBLE @ X4 @ X5 )
!= $true )
| ( $true
!= ( X6 @ c0 @ c0 ) )
| ( ( X6 @ X4 @ X5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f128,plain,
( ( $true
!= ( cHALF
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( cHALF @ Y1 @ Y0 ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( cHALF @ Y1 @ Y0 ) ) ) )
| spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f126]) ).
thf(f129,plain,
( spl5_3
| ~ spl5_4 ),
inference(avatar_split_clause,[status(thm)],[f121,f126,f123]) ).
thf(f121,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cHALF
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( cHALF @ Y1 @ Y0 ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( cHALF @ Y1 @ Y0 ) ) ) )
| ( ( cDOUBLE @ X0 @ X1 )
!= $true )
| ( ( cHALF @ X1 @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f107,f23]) ).
thf(f107,plain,
! [X0: $i,X1: $i] :
( ( ( cHALF @ X1 @ X0 )
= $true )
| ( ( cHALF @ c0 @ c0 )
!= $true )
| ( ( cDOUBLE @ X0 @ X1 )
!= $true )
| ( $true
!= ( cHALF
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( cHALF @ Y1 @ Y0 ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( cHALF @ Y1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f106]) ).
thf(f106,plain,
! [X0: $i,X1: $i] :
( ( ( cDOUBLE @ X0 @ X1 )
!= $true )
| ( ( cHALF
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( cHALF
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( cHALF
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) ) )
!= $true )
| ( ( ^ [Y0: $i,Y1: $i] :
( cHALF
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ X0
@ X1 )
= $true )
| ( $true
!= ( ^ [Y0: $i,Y1: $i] :
( cHALF
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ c0
@ c0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( ^ [Y0: $i,Y1: $i] :
( cHALF
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ X0
@ X1 )
= $true )
| ( $true
!= ( ^ [Y0: $i,Y1: $i] :
( cHALF
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ c0
@ c0 ) )
| ( ( cHALF
@ ( sK3
@ ^ [Y0: $i,Y1: $i] :
( cHALF
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] :
( cHALF
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) ) )
!= $true )
| ( ( cDOUBLE @ X0 @ X1 )
!= $true ) ),
inference(superposition,[status(thm)],[f18,f20]) ).
thf(f20,plain,
! [X2: $i,X3: $i] :
( ( ( cHALF @ ( cS @ ( cS @ X2 ) ) @ ( cS @ X3 ) )
= $true )
| ( $true
!= ( cHALF @ X2 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f18,plain,
! [X6: $i > $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( X6 @ ( cS @ ( sK2 @ X6 ) ) @ ( cS @ ( cS @ ( sK3 @ X6 ) ) ) ) )
| ( ( cDOUBLE @ X4 @ X5 )
!= $true )
| ( ( X6 @ X4 @ X5 )
= $true )
| ( $true
!= ( X6 @ c0 @ c0 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO272^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.30 % Computer : n016.cluster.edu
% 0.13/0.30 % Model : x86_64 x86_64
% 0.13/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30 % Memory : 8042.1875MB
% 0.13/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30 % CPULimit : 300
% 0.13/0.30 % WCLimit : 300
% 0.13/0.30 % DateTime : Tue Feb 24 14:27:51 EST 2026
% 0.13/0.30 % CPUTime :
% 0.13/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.39 ---- Original DTF file ---
% 0.18/0.39 thf(spec,logic,$$dhol).
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 % File : SYO272^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.39 % Domain : Syntactic
% 0.18/0.39 % Problem : TPS problem THM301A
% 0.18/0.39 % Version : Especial.
% 0.18/0.39 % English :
% 0.18/0.39
% 0.18/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.39 % Source : [Bro09]
% 0.18/0.39 % Names : tps_0399 [Bro09]
% 0.18/0.39 % : THM301A [TPS]
% 0.18/0.39
% 0.18/0.39 % Status : Theorem
% 0.18/0.39 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.33 v7.5.0, 0.42 v7.4.0, 0.33 v7.3.0, 0.50 v7.1.0, 0.43 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.50 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.75 v4.1.0, 0.67 v4.0.0
% 0.18/0.39 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.18/0.39 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.18/0.39 % Maximal formula atoms : 7 ( 7 avg)
% 0.18/0.39 % Number of connectives : 39 ( 0 ~; 0 |; 4 &; 29 @)
% 0.18/0.39 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.18/0.39 % Maximal formula depth : 15 ( 15 avg)
% 0.18/0.39 % Number of types : 2 ( 0 usr)
% 0.18/0.39 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.18/0.39 % Number of symbols : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.18/0.39 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.18/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.39
% 0.18/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 thf(cHALF,type,
% 0.18/0.39 cHALF: $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(cDOUBLE,type,
% 0.18/0.39 cDOUBLE: $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(cS,type,
% 0.18/0.39 cS: $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(c0,type,
% 0.18/0.39 c0: $i ).
% 0.18/0.39
% 0.18/0.39 thf(cTHM301A,conjecture,
% 0.18/0.39 ( ( ! [Xu: $i,Xv: $i] :
% 0.18/0.39 ( ( cDOUBLE @ Xu @ Xv )
% 0.18/0.39 <=> ! [Q: $i > $i > $o] :
% 0.18/0.39 ( ( ( Q @ c0 @ c0 )
% 0.18/0.39 & ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Q @ Xx @ Xy )
% 0.18/0.39 => ( Q @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) ) )
% 0.18/0.39 => ( Q @ Xu @ Xv ) ) )
% 0.18/0.39 & ( cHALF @ c0 @ c0 )
% 0.18/0.39 & ( cHALF @ ( cS @ c0 ) @ c0 )
% 0.18/0.39 & ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( cHALF @ Xx @ Xy )
% 0.18/0.39 => ( cHALF @ ( cS @ ( cS @ Xx ) ) @ ( cS @ Xy ) ) ) )
% 0.18/0.39 => ! [Xu: $i,Xv: $i] :
% 0.18/0.39 ( ( cDOUBLE @ Xu @ Xv )
% 0.18/0.39 => ( cHALF @ Xv @ Xu ) ) ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 1.58/1.31 ---- Embedded in THF ---
% 1.58/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.58/1.31 %%% Generated on Tue Feb 24 14:27:52 EST 2026
% 1.58/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.58/1.31 %%% Logic specification used:
% 1.58/1.31 %%% thf(spec, logic, $$dhol).
% 1.58/1.31
% 1.58/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.KOSDt143hE/DTF2DTF11287.p
% See solution above
% 1.58/1.31 ------------------------
% 1.58/1.32 ---- Cleaned THF ---
% 1.58/1.32 thf(cHALF,type,
% 1.58/1.32 cHALF: $i > $i > $o ).
% 1.58/1.32
% 1.58/1.32 thf(cDOUBLE,type,
% 1.58/1.32 cDOUBLE: $i > $i > $o ).
% 1.58/1.32
% 1.58/1.32 thf(cS,type,
% 1.58/1.32 cS: $i > $i ).
% 1.58/1.32
% 1.58/1.32 thf(c0,type,
% 1.58/1.32 c0: $i ).
% 1.58/1.32
% 1.58/1.32 thf(cTHM301A,conjecture,
% 1.58/1.32 ( ( ! [Xu: $i,Xv: $i] :
% 1.58/1.32 ( ( cDOUBLE @ Xu @ Xv )
% 1.58/1.32 <=> ! [Q: $i > $i > $o] :
% 1.58/1.32 ( ( ( Q @ c0 @ c0 )
% 1.58/1.32 & ! [Xx: $i,Xy: $i] :
% 1.58/1.32 ( ( Q @ Xx @ Xy )
% 1.58/1.32 => ( Q @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) ) )
% 1.58/1.32 => ( Q @ Xu @ Xv ) ) )
% 1.58/1.32 & ( cHALF @ c0 @ c0 )
% 1.58/1.32 & ( cHALF @ ( cS @ c0 ) @ c0 )
% 1.58/1.32 & ! [Xx: $i,Xy: $i] :
% 1.58/1.32 ( ( cHALF @ Xx @ Xy )
% 1.58/1.32 => ( cHALF @ ( cS @ ( cS @ Xx ) ) @ ( cS @ Xy ) ) ) )
% 1.58/1.32 => ! [Xu: $i,Xv: $i] :
% 1.58/1.32 ( ( cDOUBLE @ Xu @ Xv )
% 1.58/1.32 => ( cHALF @ Xv @ Xu ) ) ) ).
% 1.58/1.32 ------------------------
% 1.58/1.34 % (11386)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_11287 for (2999ds/4Mi)
% 1.58/1.34 % (11390)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_11287 for (2999ds/275Mi)
% 1.58/1.34 % (11389)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_11287 for (2999ds/2Mi)
% 1.58/1.34 % (11388)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11287 for (2999ds/2Mi)
% 1.58/1.34 % (11391)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11287 for (2999ds/18Mi)
% 1.58/1.34 % (11387)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_11287 for (2999ds/27Mi)
% 1.58/1.34 % (11385)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11287 for (2999ds/183Mi)
% 1.58/1.34 % (11388)Instruction limit reached!
% 1.58/1.34 % (11388)------------------------------
% 1.58/1.34 % (11388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (11388)Termination reason: Unknown
% 1.58/1.34 % (11388)Termination phase: Preprocessing 3
% 1.58/1.34
% 1.58/1.34 % (11388)Memory used [KB]: 895
% 1.58/1.34 % (11389)Instruction limit reached!
% 1.58/1.34 % (11389)------------------------------
% 1.58/1.34 % (11389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (11389)Termination reason: Unknown
% 1.58/1.34 % (11389)Termination phase: Property scanning
% 1.58/1.34
% 1.58/1.34 % (11389)Memory used [KB]: 895
% 1.58/1.34 % (11389)Time elapsed: 0.003 s
% 1.58/1.34 % (11389)Instructions burned: 2 (million)
% 1.58/1.34 % (11389)------------------------------
% 1.58/1.34 % (11389)------------------------------
% 1.58/1.34 % (11388)Time elapsed: 0.003 s
% 1.58/1.34 % (11388)Instructions burned: 2 (million)
% 1.58/1.34 % (11388)------------------------------
% 1.58/1.34 % (11388)------------------------------
% 1.58/1.34 % (11386)Instruction limit reached!
% 1.58/1.34 % (11386)------------------------------
% 1.58/1.34 % (11386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (11386)Termination reason: Unknown
% 1.58/1.34 % (11386)Termination phase: Saturation
% 1.58/1.34
% 1.58/1.34 % (11386)Memory used [KB]: 5500
% 1.58/1.34 % (11386)Time elapsed: 0.005 s
% 1.58/1.34 % (11386)Instructions burned: 5 (million)
% 1.58/1.34 % (11386)------------------------------
% 1.58/1.34 % (11386)------------------------------
% 1.58/1.35 % (11391)Instruction limit reached!
% 1.58/1.35 % (11391)------------------------------
% 1.58/1.35 % (11391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.35 % (11391)Termination reason: Unknown
% 1.58/1.35 % (11391)Termination phase: Saturation
% 1.58/1.35
% 1.58/1.35 % (11391)Memory used [KB]: 5628
% 1.58/1.35 % (11391)Time elapsed: 0.012 s
% 1.58/1.35 % (11391)Instructions burned: 19 (million)
% 1.58/1.35 % (11391)------------------------------
% 1.58/1.35 % (11391)------------------------------
% 1.58/1.35 % (11387)Instruction limit reached!
% 1.58/1.35 % (11387)------------------------------
% 1.58/1.35 % (11387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.35 % (11387)Termination reason: Unknown
% 1.58/1.35 % (11387)Termination phase: Saturation
% 1.58/1.35
% 1.58/1.35 % (11387)Memory used [KB]: 5628
% 1.58/1.35 % (11387)Time elapsed: 0.017 s
% 1.58/1.35 % (11387)Instructions burned: 28 (million)
% 1.58/1.35 % (11387)------------------------------
% 1.58/1.35 % (11387)------------------------------
% 1.58/1.36 % (11393)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_11287 for (2999ds/37Mi)
% 1.58/1.36 % (11394)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_11287 for (2999ds/15Mi)
% 1.58/1.36 % (11392)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11287 for (2999ds/3Mi)
% 1.58/1.36 % (11385)First to succeed.
% 1.58/1.36 % (11392)Instruction limit reached!
% 1.58/1.36 % (11392)------------------------------
% 1.58/1.36 % (11392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.36 % (11392)Termination reason: Unknown
% 1.58/1.36 % (11392)Termination phase: Saturation
% 1.58/1.36
% 1.58/1.36 % (11392)Memory used [KB]: 5500
% 1.58/1.36 % (11392)Time elapsed: 0.004 s
% 1.58/1.36 % (11392)Instructions burned: 4 (million)
% 1.58/1.36 % (11392)------------------------------
% 1.58/1.36 % (11392)------------------------------
% 1.58/1.36 % (11385)Refutation found. Thanks to Tanya!
% 1.58/1.36 % SZS status Theorem for DTF2THF_11287
% 1.58/1.36 % SZS output start Proof for DTF2THF_11287
% 1.58/1.36 thf(func_def_0, type, cHALF: $i > $i > $o).
% 1.58/1.36 thf(func_def_1, type, cDOUBLE: $i > $i > $o).
% 1.58/1.36 thf(func_def_2, type, cS: $i > $i).
% 1.58/1.36 thf(func_def_9, type, sK2: ($i > $i > $o) > $i).
% 1.58/1.36 thf(func_def_10, type, sK3: ($i > $i > $o) > $i).
% 1.58/1.36 thf(func_def_11, type, sK4: $i > $i > $i > $i > $o).
% 1.58/1.36 thf(func_def_14, type, ph6: !>[X0: $tType]:(X0)).
% 1.58/1.36 thf(f170,plain,(
% 1.58/1.36 $false),
% 1.58/1.36 inference(avatar_sat_refutation,[status(thm)],[f129,f156,f169])).
% 1.58/1.36 thf(f169,plain,(
% 1.58/1.36 ~spl5_3),
% 1.58/1.36 inference(avatar_contradiction_clause,[status(thm)],[f168])).
% 1.58/1.36 thf(f168,plain,(
% 1.58/1.36 $false | ~spl5_3),
% 1.58/1.36 inference(subsumption_resolution,[status(thm)],[f161,f21])).
% 1.58/1.36 thf(f21,plain,(
% 1.58/1.36 ($true = (cDOUBLE @ sK0 @ sK1))),
% 1.58/1.36 inference(cnf_transformation,[status(thm)],[f13])).
% 1.58/1.36 thf(f13,plain,(
% 1.58/1.36 ((cHALF @ c0 @ c0) = $true) & (($true != (cHALF @ sK1 @ sK0)) & ($true = (cDOUBLE @ sK0 @ sK1))) & ! [X2 : $i,X3 : $i] : (($true != (cHALF @ X2 @ X3)) | ((cHALF @ (cS @ (cS @ X2)) @ (cS @ X3)) = $true)) & ((cHALF @ (cS @ c0) @ c0) = $true) & ! [X4 : $i,X5 : $i] : ((! [X6 : $i > $i > $o] : (((X6 @ X4 @ X5) = $true) | ($true != (X6 @ c0 @ c0)) | (($true != (X6 @ (cS @ (sK2 @ X6)) @ (cS @ (cS @ (sK3 @ X6))))) & ($true = (X6 @ (sK2 @ X6) @ (sK3 @ X6))))) | ((cDOUBLE @ X4 @ X5) != $true)) & (((cDOUBLE @ X4 @ X5) = $true) | (((sK4 @ X5 @ X4 @ X4 @ X5) != $true) & ($true = (sK4 @ X5 @ X4 @ c0 @ c0)) & ! [X10 : $i,X11 : $i] : (((sK4 @ X5 @ X4 @ (cS @ X10) @ (cS @ (cS @ X11))) = $true) | ($true != (sK4 @ X5 @ X4 @ X10 @ X11))))))),
% 1.58/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f12,f11,f10])).
% 1.58/1.36 thf(f10,plain,(
% 1.58/1.36 ? [X0 : $i,X1 : $i] : (((cHALF @ X1 @ X0) != $true) & ((cDOUBLE @ X0 @ X1) = $true)) => (($true != (cHALF @ sK1 @ sK0)) & ($true = (cDOUBLE @ sK0 @ sK1)))),
% 1.58/1.36 introduced(definition,[],[choice_axiom])).
% 1.58/1.36 thf(f11,plain,(
% 1.58/1.36 ! [X6 : $i > $i > $o] : (? [X7 : $i,X8 : $i] : (($true != (X6 @ (cS @ X7) @ (cS @ (cS @ X8)))) & ($true = (X6 @ X7 @ X8))) => (($true != (X6 @ (cS @ (sK2 @ X6)) @ (cS @ (cS @ (sK3 @ X6))))) & ($true = (X6 @ (sK2 @ X6) @ (sK3 @ X6)))))),
% 1.58/1.36 introduced(definition,[],[choice_axiom])).
% 1.58/1.36 thf(f12,plain,(
% 1.58/1.36 ! [X4 : $i,X5 : $i] : (? [X9 : $i > $i > $o] : (($true != (X9 @ X4 @ X5)) & ((X9 @ c0 @ c0) = $true) & ! [X10 : $i,X11 : $i] : (((X9 @ (cS @ X10) @ (cS @ (cS @ X11))) = $true) | ($true != (X9 @ X10 @ X11)))) => (((sK4 @ X5 @ X4 @ X4 @ X5) != $true) & ($true = (sK4 @ X5 @ X4 @ c0 @ c0)) & ! [X11 : $i,X10 : $i] : (((sK4 @ X5 @ X4 @ (cS @ X10) @ (cS @ (cS @ X11))) = $true) | ($true != (sK4 @ X5 @ X4 @ X10 @ X11)))))),
% 1.58/1.36 introduced(definition,[],[choice_axiom])).
% 1.58/1.36 thf(f9,plain,(
% 1.58/1.36 ((cHALF @ c0 @ c0) = $true) & ? [X0 : $i,X1 : $i] : (((cHALF @ X1 @ X0) != $true) & ((cDOUBLE @ X0 @ X1) = $true)) & ! [X2 : $i,X3 : $i] : (($true != (cHALF @ X2 @ X3)) | ((cHALF @ (cS @ (cS @ X2)) @ (cS @ X3)) = $true)) & ((cHALF @ (cS @ c0) @ c0) = $true) & ! [X4 : $i,X5 : $i] : ((! [X6 : $i > $i > $o] : (((X6 @ X4 @ X5) = $true) | ($true != (X6 @ c0 @ c0)) | ? [X7 : $i,X8 : $i] : (($true != (X6 @ (cS @ X7) @ (cS @ (cS @ X8)))) & ($true = (X6 @ X7 @ X8)))) | ((cDOUBLE @ X4 @ X5) != $true)) & (((cDOUBLE @ X4 @ X5) = $true) | ? [X9 : $i > $i > $o] : (($true != (X9 @ X4 @ X5)) & ((X9 @ c0 @ c0) = $true) & ! [X10 : $i,X11 : $i] : (((X9 @ (cS @ X10) @ (cS @ (cS @ X11))) = $true) | ($true != (X9 @ X10 @ X11))))))),
% 1.58/1.36 inference(rectify,[status(thm)],[f8])).
% 1.58/1.36 thf(f8,plain,(
% 1.58/1.36 ((cHALF @ c0 @ c0) = $true) & ? [X7 : $i,X8 : $i] : (($true != (cHALF @ X8 @ X7)) & ((cDOUBLE @ X7 @ X8) = $true)) & ! [X5 : $i,X6 : $i] : (($true != (cHALF @ X5 @ X6)) | ($true = (cHALF @ (cS @ (cS @ X5)) @ (cS @ X6)))) & ((cHALF @ (cS @ c0) @ c0) = $true) & ! [X0 : $i,X1 : $i] : ((! [X2 : $i > $i > $o] : (((X2 @ X0 @ X1) = $true) | ((X2 @ c0 @ c0) != $true) | ? [X3 : $i,X4 : $i] : (((X2 @ (cS @ X3) @ (cS @ (cS @ X4))) != $true) & ((X2 @ X3 @ X4) = $true))) | ((cDOUBLE @ X0 @ X1) != $true)) & (((cDOUBLE @ X0 @ X1) = $true) | ? [X2 : $i > $i > $o] : (((X2 @ X0 @ X1) != $true) & ((X2 @ c0 @ c0) = $true) & ! [X3 : $i,X4 : $i] : (((X2 @ (cS @ X3) @ (cS @ (cS @ X4))) = $true) | ((X2 @ X3 @ X4) != $true)))))),
% 1.58/1.36 inference(nnf_transformation,[status(thm)],[f7])).
% 1.58/1.36 thf(f7,plain,(
% 1.58/1.36 ((cHALF @ c0 @ c0) = $true) & ? [X7 : $i,X8 : $i] : (($true != (cHALF @ X8 @ X7)) & ((cDOUBLE @ X7 @ X8) = $true)) & ! [X5 : $i,X6 : $i] : (($true != (cHALF @ X5 @ X6)) | ($true = (cHALF @ (cS @ (cS @ X5)) @ (cS @ X6)))) & ((cHALF @ (cS @ c0) @ c0) = $true) & ! [X0 : $i,X1 : $i] : (! [X2 : $i > $i > $o] : (((X2 @ X0 @ X1) = $true) | ((X2 @ c0 @ c0) != $true) | ? [X3 : $i,X4 : $i] : (((X2 @ (cS @ X3) @ (cS @ (cS @ X4))) != $true) & ((X2 @ X3 @ X4) = $true))) <=> ((cDOUBLE @ X0 @ X1) = $true))),
% 1.58/1.36 inference(flattening,[status(thm)],[f6])).
% 1.58/1.36 thf(f6,plain,(
% 1.58/1.36 ? [X7 : $i,X8 : $i] : (($true != (cHALF @ X8 @ X7)) & ((cDOUBLE @ X7 @ X8) = $true)) & (! [X5 : $i,X6 : $i] : (($true != (cHALF @ X5 @ X6)) | ($true = (cHALF @ (cS @ (cS @ X5)) @ (cS @ X6)))) & ((cHALF @ c0 @ c0) = $true) & ((cHALF @ (cS @ c0) @ c0) = $true) & ! [X1 : $i,X0 : $i] : (((cDOUBLE @ X0 @ X1) = $true) <=> ! [X2 : $i > $i > $o] : (((X2 @ X0 @ X1) = $true) | (? [X3 : $i,X4 : $i] : (((X2 @ (cS @ X3) @ (cS @ (cS @ X4))) != $true) & ((X2 @ X3 @ X4) = $true)) | ((X2 @ c0 @ c0) != $true)))))),
% 1.58/1.36 inference(ennf_transformation,[status(thm)],[f5])).
% 1.58/1.36 thf(f5,plain,(
% 1.58/1.36 ~((! [X6 : $i,X5 : $i] : (($true = (cHALF @ X5 @ X6)) => ($true = (cHALF @ (cS @ (cS @ X5)) @ (cS @ X6)))) & ((cHALF @ c0 @ c0) = $true) & ((cHALF @ (cS @ c0) @ c0) = $true) & ! [X1 : $i,X0 : $i] : (((cDOUBLE @ X0 @ X1) = $true) <=> ! [X2 : $i > $i > $o] : ((! [X4 : $i,X3 : $i] : (((X2 @ X3 @ X4) = $true) => ((X2 @ (cS @ X3) @ (cS @ (cS @ X4))) = $true)) & ((X2 @ c0 @ c0) = $true)) => ((X2 @ X0 @ X1) = $true)))) => ! [X7 : $i,X8 : $i] : (((cDOUBLE @ X7 @ X8) = $true) => ($true = (cHALF @ X8 @ X7))))),
% 1.58/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 1.58/1.36 thf(f4,plain,(
% 1.58/1.36 ~(((cHALF @ c0 @ c0) & ! [X0 : $i,X1 : $i] : (! [X2 : $i > $i > $o] : (((X2 @ c0 @ c0) & ! [X3 : $i,X4 : $i] : ((X2 @ X3 @ X4) => (X2 @ (cS @ X3) @ (cS @ (cS @ X4))))) => (X2 @ X0 @ X1)) <=> (cDOUBLE @ X0 @ X1)) & ! [X5 : $i,X6 : $i] : ((cHALF @ X5 @ X6) => (cHALF @ (cS @ (cS @ X5)) @ (cS @ X6))) & (cHALF @ (cS @ c0) @ c0)) => ! [X7 : $i,X8 : $i] : ((cDOUBLE @ X7 @ X8) => (cHALF @ X8 @ X7)))),
% 1.58/1.36 inference(rectify,[status(thm)],[f2])).
% 1.58/1.36 thf(f2,negated_conjecture,(
% 1.58/1.36 ~(((cHALF @ c0 @ c0) & ! [X0 : $i,X1 : $i] : (! [X2 : $i > $i > $o] : (((X2 @ c0 @ c0) & ! [X3 : $i,X4 : $i] : ((X2 @ X3 @ X4) => (X2 @ (cS @ X3) @ (cS @ (cS @ X4))))) => (X2 @ X0 @ X1)) <=> (cDOUBLE @ X0 @ X1)) & ! [X3 : $i,X4 : $i] : ((cHALF @ X3 @ X4) => (cHALF @ (cS @ (cS @ X3)) @ (cS @ X4))) & (cHALF @ (cS @ c0) @ c0)) => ! [X0 : $i,X1 : $i] : ((cDOUBLE @ X0 @ X1) => (cHALF @ X1 @ X0)))),
% 1.58/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.58/1.36 thf(f1,conjecture,(
% 1.58/1.36 ((cHALF @ c0 @ c0) & ! [X0 : $i,X1 : $i] : (! [X2 : $i > $i > $o] : (((X2 @ c0 @ c0) & ! [X3 : $i,X4 : $i] : ((X2 @ X3 @ X4) => (X2 @ (cS @ X3) @ (cS @ (cS @ X4))))) => (X2 @ X0 @ X1)) <=> (cDOUBLE @ X0 @ X1)) & ! [X3 : $i,X4 : $i] : ((cHALF @ X3 @ X4) => (cHALF @ (cS @ (cS @ X3)) @ (cS @ X4))) & (cHALF @ (cS @ c0) @ c0)) => ! [X0 : $i,X1 : $i] : ((cDOUBLE @ X0 @ X1) => (cHALF @ X1 @ X0))),
% 1.58/1.36 file('/export/starexec/sandbox2/tmp/tmp.KOSDt143hE/DTF2THF_11287.p',cTHM301A)).
% 1.58/1.36 thf(f161,plain,(
% 1.58/1.36 ($true != (cDOUBLE @ sK0 @ sK1)) | ~spl5_3),
% 1.58/1.36 inference(trivial_inequality_removal,[status(thm)],[f159])).
% 1.58/1.36 thf(f159,plain,(
% 1.58/1.36 ($true != (cDOUBLE @ sK0 @ sK1)) | ($true != $true) | ~spl5_3),
% 1.58/1.36 inference(superposition,[status(thm)],[f22,f124])).
% 1.58/1.36 thf(f124,plain,(
% 1.58/1.36 ( ! [X0 : $i,X1 : $i] : (((cHALF @ X1 @ X0) = $true) | ((cDOUBLE @ X0 @ X1) != $true)) ) | ~spl5_3),
% 1.58/1.36 inference(avatar_component_clause,[status(thm)],[f123])).
% 1.58/1.36 thf(f123,definition,(
% 1.58/1.36 spl5_3 <=> ! [X0 : $i,X1 : $i] : (((cDOUBLE @ X0 @ X1) != $true) | ((cHALF @ X1 @ X0) = $true))),
% 1.58/1.36 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.58/1.36 thf(f22,plain,(
% 1.58/1.36 ($true != (cHALF @ sK1 @ sK0))),
% 1.58/1.36 inference(cnf_transformation,[status(thm)],[f13])).
% 1.58/1.36 thf(f156,plain,(
% 1.58/1.36 spl5_3 | spl5_4),
% 1.58/1.36 inference(avatar_split_clause,[status(thm)],[f155,f126,f123])).
% 1.58/1.36 thf(f126,definition,(
% 1.58/1.36 spl5_4 <=> ($true = (cHALF @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))))),
% 1.58/1.36 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.58/1.36 thf(f155,plain,(
% 1.58/1.36 ( ! [X0 : $i,X1 : $i] : (((cDOUBLE @ X0 @ X1) != $true) | ((cHALF @ X1 @ X0) = $true)) ) | spl5_4),
% 1.58/1.36 inference(subsumption_resolution,[status(thm)],[f154,f23])).
% 1.58/1.36 thf(f23,plain,(
% 1.58/1.36 ((cHALF @ c0 @ c0) = $true)),
% 1.58/1.36 inference(cnf_transformation,[status(thm)],[f13])).
% 1.58/1.36 thf(f154,plain,(
% 1.58/1.36 ( ! [X0 : $i,X1 : $i] : (((cDOUBLE @ X0 @ X1) != $true) | ((cHALF @ X1 @ X0) = $true) | ((cHALF @ c0 @ c0) != $true)) ) | spl5_4),
% 1.58/1.36 inference(beta_eta_normalization,[status(thm)],[f153])).
% 1.58/1.36 thf(f153,plain,(
% 1.58/1.36 ( ! [X0 : $i,X1 : $i] : ((((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X0 @ X1) = $true) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c0 @ c0)) | ((cDOUBLE @ X0 @ X1) != $true)) ) | spl5_4),
% 1.58/1.36 inference(trivial_inequality_removal,[status(thm)],[f152])).
% 1.58/1.36 thf(f152,plain,(
% 1.58/1.36 ( ! [X0 : $i,X1 : $i] : (((cDOUBLE @ X0 @ X1) != $true) | ($true != $true) | (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X0 @ X1) = $true) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c0 @ c0))) ) | spl5_4),
% 1.58/1.36 inference(superposition,[status(thm)],[f128,f17])).
% 1.58/1.36 thf(f17,plain,(
% 1.58/1.36 ( ! [X6 : $i > $i > $o,X4 : $i,X5 : $i] : (($true = (X6 @ (sK2 @ X6) @ (sK3 @ X6))) | ((cDOUBLE @ X4 @ X5) != $true) | ($true != (X6 @ c0 @ c0)) | ((X6 @ X4 @ X5) = $true)) )),
% 1.58/1.36 inference(cnf_transformation,[status(thm)],[f13])).
% 1.58/1.36 thf(f128,plain,(
% 1.58/1.36 ($true != (cHALF @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))) | spl5_4),
% 1.58/1.36 inference(avatar_component_clause,[status(thm)],[f126])).
% 1.58/1.36 thf(f129,plain,(
% 1.58/1.36 spl5_3 | ~spl5_4),
% 1.58/1.36 inference(avatar_split_clause,[status(thm)],[f121,f126,f123])).
% 1.58/1.36 thf(f121,plain,(
% 1.58/1.36 ( ! [X0 : $i,X1 : $i] : (($true != (cHALF @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))) | ((cDOUBLE @ X0 @ X1) != $true) | ((cHALF @ X1 @ X0) = $true)) )),
% 1.58/1.36 inference(subsumption_resolution,[status(thm)],[f107,f23])).
% 1.58/1.36 thf(f107,plain,(
% 1.58/1.36 ( ! [X0 : $i,X1 : $i] : (((cHALF @ X1 @ X0) = $true) | ((cHALF @ c0 @ c0) != $true) | ((cDOUBLE @ X0 @ X1) != $true) | ($true != (cHALF @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))))) )),
% 1.58/1.36 inference(beta_eta_normalization,[status(thm)],[f106])).
% 1.58/1.36 thf(f106,plain,(
% 1.58/1.36 ( ! [X0 : $i,X1 : $i] : (((cDOUBLE @ X0 @ X1) != $true) | ((cHALF @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))) != $true) | (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X0 @ X1) = $true) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c0 @ c0))) )),
% 1.58/1.36 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.58/1.36 thf(f81,plain,(
% 1.58/1.36 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X0 @ X1) = $true) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c0 @ c0)) | ((cHALF @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))) != $true) | ((cDOUBLE @ X0 @ X1) != $true)) )),
% 1.58/1.36 inference(superposition,[status(thm)],[f18,f20])).
% 1.58/1.36 thf(f20,plain,(
% 1.58/1.36 ( ! [X2 : $i,X3 : $i] : (((cHALF @ (cS @ (cS @ X2)) @ (cS @ X3)) = $true) | ($true != (cHALF @ X2 @ X3))) )),
% 1.58/1.36 inference(cnf_transformation,[status(thm)],[f13])).
% 1.58/1.36 thf(f18,plain,(
% 1.58/1.36 ( ! [X6 : $i > $i > $o,X4 : $i,X5 : $i] : (($true != (X6 @ (cS @ (sK2 @ X6)) @ (cS @ (cS @ (sK3 @ X6))))) | ((cDOUBLE @ X4 @ X5) != $true) | ((X6 @ X4 @ X5) = $true) | ($true != (X6 @ c0 @ c0))) )),
% 1.58/1.36 inference(cnf_transformation,[status(thm)],[f13])).
% 1.58/1.36 % SZS output end Proof for DTF2THF_11287
% 1.58/1.36 % (11385)------------------------------
% 1.58/1.36 % (11385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.36 % (11385)Termination reason: Refutation
% 1.58/1.36
% 1.58/1.36 % (11385)Memory used [KB]: 5756
% 1.58/1.36 % (11385)Time elapsed: 0.023 s
% 1.58/1.36 % (11385)Instructions burned: 36 (million)
% 1.58/1.36 % (11385)------------------------------
% 1.58/1.36 % (11385)------------------------------
% 1.58/1.36 % (11384)Success in time 0.034 s
%------------------------------------------------------------------------------