%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO331^5 : 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 : n018.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 09:53:58 AM UTC 2026
% Result : Theorem 1.58s 1.33s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 5 unt; 0 typ; 3 def)
% Number of atoms : 492 ( 126 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 829 ( 81 ~; 74 |; 64 &; 484 @)
% ( 3 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 96 ( 96 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 10 usr; 8 con; 0-2 aty)
% ( 26 !!; 26 ??; 0 @@+; 0 @@-)
% Number of variables : 181 ( 84 ^; 69 !; 28 ?; 181 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cK: ( a > $o ) > a > $o ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_13,type,
sK0: ( a > $o ) > a ).
thf(func_def_14,type,
sK1: ( a > $o ) > a ).
thf(func_def_15,type,
sK2: a ).
thf(func_def_16,type,
sK3: a > $o ).
thf(func_def_18,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f89,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f31,f43,f80,f88]) ).
thf(f88,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[status(thm)],[f87]) ).
thf(f87,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $true != $true )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f13,f26]) ).
thf(f26,plain,
( ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK2 )
= $true )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl4_1
<=> ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f13,plain,
( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: a > $o] :
( ( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ! [X2: a > $o] :
( ( $true
!= ( X2 @ ( sK0 @ X0 ) ) )
| ( ( $true
= ( X2 @ ( sK1 @ X2 ) ) )
& ( $true
!= ( cK @ X2 @ ( sK1 @ X2 ) ) ) ) ) )
| ! [X4: a] :
( ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X4 )
= $true )
| ( ( cK @ X0 @ X4 )
!= $true ) ) )
& ( $true
= ( sK3 @ sK2 ) )
& ! [X7: a] :
( ( $true
!= ( sK3 @ X7 ) )
| ( $true
= ( cK @ sK3 @ X7 ) ) )
& ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK2 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f11,f10,f9,f8]) ).
thf(f8,plain,
! [X0: a > $o] :
( ? [X1: a] :
( ( ( X0 @ X1 )
= $true )
& ! [X2: a > $o] :
( ( ( X2 @ X1 )
!= $true )
| ? [X3: a] :
( ( ( X2 @ X3 )
= $true )
& ( ( cK @ X2 @ X3 )
!= $true ) ) ) )
=> ( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ! [X2: a > $o] :
( ( $true
!= ( X2 @ ( sK0 @ X0 ) ) )
| ? [X3: a] :
( ( ( X2 @ X3 )
= $true )
& ( ( cK @ X2 @ X3 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X2: a > $o] :
( ? [X3: a] :
( ( ( X2 @ X3 )
= $true )
& ( ( cK @ X2 @ X3 )
!= $true ) )
=> ( ( $true
= ( X2 @ ( sK1 @ X2 ) ) )
& ( $true
!= ( cK @ X2 @ ( sK1 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X5: a] :
( ? [X6: a > $o] :
( ( ( X6 @ X5 )
= $true )
& ! [X7: a] :
( ( $true
!= ( X6 @ X7 ) )
| ( $true
= ( cK @ X6 @ X7 ) ) ) )
& ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X5 )
!= $true ) )
=> ( ? [X6: a > $o] :
( ( $true
= ( X6 @ sK2 ) )
& ! [X7: a] :
( ( $true
!= ( X6 @ X7 ) )
| ( $true
= ( cK @ X6 @ X7 ) ) ) )
& ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X6: a > $o] :
( ( $true
= ( X6 @ sK2 ) )
& ! [X7: a] :
( ( $true
!= ( X6 @ X7 ) )
| ( $true
= ( cK @ X6 @ X7 ) ) ) )
=> ( ( $true
= ( sK3 @ sK2 ) )
& ! [X7: a] :
( ( $true
!= ( sK3 @ X7 ) )
| ( $true
= ( cK @ sK3 @ X7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: a > $o] :
( ? [X1: a] :
( ( ( X0 @ X1 )
= $true )
& ! [X2: a > $o] :
( ( ( X2 @ X1 )
!= $true )
| ? [X3: a] :
( ( ( X2 @ X3 )
= $true )
& ( ( cK @ X2 @ X3 )
!= $true ) ) ) )
| ! [X4: a] :
( ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X4 )
= $true )
| ( ( cK @ X0 @ X4 )
!= $true ) ) )
& ? [X5: a] :
( ? [X6: a > $o] :
( ( ( X6 @ X5 )
= $true )
& ! [X7: a] :
( ( $true
!= ( X6 @ X7 ) )
| ( $true
= ( cK @ X6 @ X7 ) ) ) )
& ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X5 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: a > $o] :
( ! [X1: a] :
( ( ( X0 @ X1 )
= $true )
=> ? [X2: a > $o] :
( ( ( X2 @ X1 )
= $true )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( cK @ X2 @ X3 )
= $true ) ) ) )
=> ! [X4: a] :
( ( ( cK @ X0 @ X4 )
= $true )
=> ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X4 )
= $true ) ) )
=> ! [X5: a] :
( ? [X6: a > $o] :
( ! [X7: a] :
( ( $true
= ( X6 @ X7 ) )
=> ( $true
= ( cK @ X6 @ X7 ) ) )
& ( ( X6 @ X5 )
= $true ) )
=> ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X5 )
= $true ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: a > $o] :
( ! [X1: a] :
( ( ( X0 @ X1 )
= $true )
=> ? [X2: a > $o] :
( ( ( X2 @ X1 )
= $true )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( cK @ X2 @ X3 )
= $true ) ) ) )
=> ! [X4: a] :
( ( ( cK @ X0 @ X4 )
= $true )
=> ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X4 )
= $true ) ) )
=> ! [X8: a] :
( ? [X9: a > $o] :
( ( $true
= ( X9 @ X8 ) )
& ! [X10: a] :
( ( $true
= ( X9 @ X10 ) )
=> ( ( cK @ X9 @ X10 )
= $true ) ) )
=> ( $true
= ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X8 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
=> ? [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
& ( X2 @ X1 ) ) )
=> ! [X4: a] :
( ( cK @ X0 @ X4 )
=> ( cK
@ ^ [X5: a] :
? [X6: a > $o] :
( ! [X7: a] :
( ( X6 @ X7 )
=> ( cK @ X6 @ X7 ) )
& ( X6 @ X5 ) )
@ X4 ) ) )
=> ! [X8: a] :
( ? [X9: a > $o] :
( ( X9 @ X8 )
& ! [X10: a] :
( ( X9 @ X10 )
=> ( cK @ X9 @ X10 ) ) )
=> ( cK
@ ^ [X11: a] :
? [X12: a > $o] :
( ! [X13: a] :
( ( X12 @ X13 )
=> ( cK @ X12 @ X13 ) )
& ( X12 @ X11 ) )
@ X8 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
=> ? [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
& ( X2 @ X1 ) ) )
=> ! [X1: a] :
( ( cK @ X0 @ X1 )
=> ( cK
@ ^ [X3: a] :
? [X2: a > $o] :
( ! [X4: a] :
( ( X2 @ X4 )
=> ( cK @ X2 @ X4 ) )
& ( X2 @ X3 ) )
@ X1 ) ) )
=> ! [X1: a] :
( ? [X2: a > $o] :
( ( X2 @ X1 )
& ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) ) )
=> ( cK
@ ^ [X3: a] :
? [X2: a > $o] :
( ! [X4: a] :
( ( X2 @ X4 )
=> ( cK @ X2 @ X4 ) )
& ( X2 @ X3 ) )
@ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
=> ? [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
& ( X2 @ X1 ) ) )
=> ! [X1: a] :
( ( cK @ X0 @ X1 )
=> ( cK
@ ^ [X3: a] :
? [X2: a > $o] :
( ! [X4: a] :
( ( X2 @ X4 )
=> ( cK @ X2 @ X4 ) )
& ( X2 @ X3 ) )
@ X1 ) ) )
=> ! [X1: a] :
( ? [X2: a > $o] :
( ( X2 @ X1 )
& ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) ) )
=> ( cK
@ ^ [X3: a] :
? [X2: a > $o] :
( ! [X4: a] :
( ( X2 @ X4 )
=> ( cK @ X2 @ X4 ) )
& ( X2 @ X3 ) )
@ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YpJxvrLOfE/DTF2THF_9174.p',cTHM116_2SS_pme) ).
thf(f80,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(avatar_split_clause,[status(thm)],[f79,f41,f28,f24]) ).
thf(f28,definition,
( spl4_2
<=> ( $true
= ( sK3 @ ( sK0 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f41,definition,
( spl4_3
<=> ! [X0: a > $o] :
( ( $true
= ( X0 @ ( sK1 @ X0 ) ) )
| ( ( X0 @ ( sK0 @ sK3 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f79,plain,
( ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK2 )
= $true )
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( $true != $true )
| ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK2 )
= $true )
| ~ spl4_2
| ~ spl4_3 ),
inference(forward_demodulation,[status(thm)],[f70,f30]) ).
thf(f30,plain,
( ( $true
= ( sK3 @ ( sK0 @ sK3 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f70,plain,
( ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK2 )
= $true )
| ( $true
!= ( sK3 @ ( sK0 @ sK3 ) ) )
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $true
!= ( sK3 @ ( sK0 @ sK3 ) ) )
| ( $true != $true )
| ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK2 )
= $true )
| ~ spl4_2
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f59,f20]) ).
thf(f20,plain,
( ( cK @ sK3 @ sK2 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( cK @ sK3 @ sK2 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f14,f15]) ).
thf(f15,plain,
( $true
= ( sK3 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f14,plain,
! [X7: a] :
( ( $true
!= ( sK3 @ X7 ) )
| ( $true
= ( cK @ sK3 @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f59,plain,
( ! [X0: a > $o,X1: a] :
( ( ( cK @ X0 @ X1 )
!= $true )
| ( $true
= ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X1 ) )
| ( ( sK3 @ ( sK0 @ X0 ) )
!= $true ) )
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ! [X0: a > $o,X1: a] :
( ( $true != $true )
| ( $true
= ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X1 ) )
| ( ( sK3 @ ( sK0 @ X0 ) )
!= $true )
| ( ( cK @ X0 @ X1 )
!= $true ) )
| ~ spl4_2
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f16,f54]) ).
thf(f54,plain,
( ( ( cK @ sK3 @ ( sK1 @ sK3 ) )
= $true )
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( cK @ sK3 @ ( sK1 @ sK3 ) )
= $true )
| ( $true != $true )
| ~ spl4_2
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f14,f52]) ).
thf(f52,plain,
( ( $true
= ( sK3 @ ( sK1 @ sK3 ) ) )
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $true != $true )
| ( $true
= ( sK3 @ ( sK1 @ sK3 ) ) )
| ~ spl4_2
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f42,f30]) ).
thf(f42,plain,
( ! [X0: a > $o] :
( ( ( X0 @ ( sK0 @ sK3 ) )
!= $true )
| ( $true
= ( X0 @ ( sK1 @ X0 ) ) ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f16,plain,
! [X2: a > $o,X0: a > $o,X4: a] :
( ( $true
!= ( cK @ X2 @ ( sK1 @ X2 ) ) )
| ( ( cK @ X0 @ X4 )
!= $true )
| ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X4 )
= $true )
| ( $true
!= ( X2 @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f43,plain,
( spl4_3
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f39,f24,f41]) ).
thf(f39,plain,
! [X0: a > $o] :
( ( $true
= ( X0 @ ( sK1 @ X0 ) ) )
| ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK2 )
= $true )
| ( ( X0 @ ( sK0 @ sK3 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( $true
= ( X0 @ ( sK1 @ X0 ) ) )
| ( ( X0 @ ( sK0 @ sK3 ) )
!= $true )
| ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK2 )
= $true ) ),
inference(superposition,[status(thm)],[f17,f20]) ).
thf(f17,plain,
! [X2: a > $o,X0: a > $o,X4: a] :
( ( ( cK @ X0 @ X4 )
!= $true )
| ( $true
!= ( X2 @ ( sK0 @ X0 ) ) )
| ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X4 )
= $true )
| ( $true
= ( X2 @ ( sK1 @ X2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f31,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f22,f28,f24]) ).
thf(f22,plain,
( ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK2 )
= $true )
| ( $true
= ( sK3 @ ( sK0 @ sK3 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true != $true )
| ( $true
= ( sK3 @ ( sK0 @ sK3 ) ) )
| ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK2 )
= $true ) ),
inference(superposition,[status(thm)],[f18,f20]) ).
thf(f18,plain,
! [X0: a > $o,X4: a] :
( ( ( cK @ X0 @ X4 )
!= $true )
| ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
| ( ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO331^5 : 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
% 0.11/0.29 % Computer : n018.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 14:28:01 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 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 : SYO331^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.39 % Domain : Syntactic
% 0.18/0.39 % Problem : TPS problem from BASIC-HO-THMS
% 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_1045 [Bro09]
% 0.18/0.39
% 0.18/0.39 % Status : Theorem
% 0.18/0.39 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.1.0, 0.33 v6.0.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.25 v4.1.0, 0.33 v4.0.0
% 0.18/0.39 % Syntax : Number of formulae : 3 ( 0 unt; 2 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 : 36 ( 0 ~; 0 |; 4 &; 23 @)
% 0.18/0.39 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.18/0.39 % Maximal formula depth : 15 ( 15 avg)
% 0.18/0.39 % Number of types : 2 ( 1 usr)
% 0.18/0.39 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.18/0.39 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.18/0.39 % Number of variables : 14 ( 2 ^; 8 !; 4 ?; 14 :)
% 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(a_type,type,
% 0.18/0.39 a: $tType ).
% 0.18/0.39
% 0.18/0.39 thf(cK,type,
% 0.18/0.39 cK: ( a > $o ) > a > $o ).
% 0.18/0.39
% 0.18/0.39 thf(cTHM116_2SS_pme,conjecture,
% 0.18/0.39 ( ! [X: a > $o] :
% 0.18/0.39 ( ! [Xx: a] :
% 0.18/0.39 ( ( X @ Xx )
% 0.18/0.39 => ? [S: a > $o] :
% 0.18/0.39 ( ! [Xx0: a] :
% 0.18/0.39 ( ( S @ Xx0 )
% 0.18/0.39 => ( cK @ S @ Xx0 ) )
% 0.18/0.39 & ( S @ Xx ) ) )
% 0.18/0.39 => ! [Xx: a] :
% 0.18/0.39 ( ( cK @ X @ Xx )
% 0.18/0.39 => ( cK
% 0.18/0.39 @ ^ [Xx0: a] :
% 0.18/0.39 ? [S: a > $o] :
% 0.18/0.39 ( ! [Xx1: a] :
% 0.18/0.39 ( ( S @ Xx1 )
% 0.18/0.39 => ( cK @ S @ Xx1 ) )
% 0.18/0.39 & ( S @ Xx0 ) )
% 0.18/0.39 @ Xx ) ) )
% 0.18/0.39 => ! [Xx: a] :
% 0.18/0.39 ( ? [S: a > $o] :
% 0.18/0.39 ( ! [Xx0: a] :
% 0.18/0.39 ( ( S @ Xx0 )
% 0.18/0.39 => ( cK @ S @ Xx0 ) )
% 0.18/0.39 & ( S @ Xx ) )
% 0.18/0.39 => ( cK
% 0.18/0.39 @ ^ [Xx0: a] :
% 0.18/0.39 ? [S: a > $o] :
% 0.18/0.39 ( ! [Xx1: a] :
% 0.18/0.39 ( ( S @ Xx1 )
% 0.18/0.39 => ( cK @ S @ Xx1 ) )
% 0.18/0.39 & ( S @ Xx0 ) )
% 0.18/0.39 @ Xx ) ) ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 1.38/1.29 ---- Embedded in THF ---
% 1.38/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.38/1.29 %%% Generated on Tue Feb 24 14:28:01 EST 2026
% 1.38/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.38/1.29 %%% Logic specification used:
% 1.38/1.29 %%% thf(spec, logic, $$dhol).
% 1.38/1.29
% 1.38/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YpJxvrLOfE/DTF2DTF9174.p
% See solution above
% 1.38/1.29 ------------------------
% 1.58/1.30 ---- Cleaned THF ---
% 1.58/1.30 thf(a_type,type,
% 1.58/1.30 a: $tType ).
% 1.58/1.30
% 1.58/1.30 thf(cK,type,
% 1.58/1.30 cK: ( a > $o ) > a > $o ).
% 1.58/1.30
% 1.58/1.30 thf(cTHM116_2SS_pme,conjecture,
% 1.58/1.30 ( ! [X: a > $o] :
% 1.58/1.30 ( ! [Xx: a] :
% 1.58/1.30 ( ( X @ Xx )
% 1.58/1.30 => ? [S: a > $o] :
% 1.58/1.30 ( ! [Xx0: a] :
% 1.58/1.30 ( ( S @ Xx0 )
% 1.58/1.30 => ( cK @ S @ Xx0 ) )
% 1.58/1.30 & ( S @ Xx ) ) )
% 1.58/1.30 => ! [Xx: a] :
% 1.58/1.30 ( ( cK @ X @ Xx )
% 1.58/1.30 => ( cK
% 1.58/1.30 @ ^ [Xx0: a] :
% 1.58/1.30 ? [S: a > $o] :
% 1.58/1.30 ( ! [Xx1: a] :
% 1.58/1.30 ( ( S @ Xx1 )
% 1.58/1.30 => ( cK @ S @ Xx1 ) )
% 1.58/1.30 & ( S @ Xx0 ) )
% 1.58/1.30 @ Xx ) ) )
% 1.58/1.30 => ! [Xx: a] :
% 1.58/1.30 ( ? [S: a > $o] :
% 1.58/1.30 ( ! [Xx0: a] :
% 1.58/1.30 ( ( S @ Xx0 )
% 1.58/1.30 => ( cK @ S @ Xx0 ) )
% 1.58/1.30 & ( S @ Xx ) )
% 1.58/1.30 => ( cK
% 1.58/1.30 @ ^ [Xx0: a] :
% 1.58/1.30 ? [S: a > $o] :
% 1.58/1.30 ( ! [Xx1: a] :
% 1.58/1.30 ( ( S @ Xx1 )
% 1.58/1.30 => ( cK @ S @ Xx1 ) )
% 1.58/1.30 & ( S @ Xx0 ) )
% 1.58/1.30 @ Xx ) ) ) ).
% 1.58/1.30 ------------------------
% 1.58/1.32 % (9277)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_9174 for (2999ds/275Mi)
% 1.58/1.32 % (9272)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9174 for (2999ds/183Mi)
% 1.58/1.32 % (9276)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_9174 for (2999ds/2Mi)
% 1.58/1.32 % (9273)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_9174 for (2999ds/4Mi)
% 1.58/1.32 % (9274)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_9174 for (2999ds/27Mi)
% 1.58/1.32 % (9275)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9174 for (2999ds/2Mi)
% 1.58/1.32 % (9278)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9174 for (2999ds/18Mi)
% 1.58/1.32 % (9275)Instruction limit reached!
% 1.58/1.32 % (9275)------------------------------
% 1.58/1.32 % (9275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (9275)Termination reason: Unknown
% 1.58/1.32 % (9275)Termination phase: Property scanning
% 1.58/1.32 % (9276)Instruction limit reached!
% 1.58/1.32 % (9276)------------------------------
% 1.58/1.32 % (9276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32
% 1.58/1.32 % (9275)Memory used [KB]: 1023
% 1.58/1.32 % (9275)Time elapsed: 0.003 s
% 1.58/1.32 % (9275)Instructions burned: 2 (million)
% 1.58/1.32 % (9275)------------------------------
% 1.58/1.32 % (9275)------------------------------
% 1.58/1.32 % (9276)Termination reason: Unknown
% 1.58/1.32 % (9276)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (9276)Memory used [KB]: 895
% 1.58/1.32 % (9276)Time elapsed: 0.003 s
% 1.58/1.32 % (9276)Instructions burned: 2 (million)
% 1.58/1.32 % (9276)------------------------------
% 1.58/1.32 % (9276)------------------------------
% 1.58/1.32 % (9273)Instruction limit reached!
% 1.58/1.32 % (9273)------------------------------
% 1.58/1.32 % (9273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (9273)Termination reason: Unknown
% 1.58/1.32 % (9273)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (9273)Memory used [KB]: 5500
% 1.58/1.32 % (9273)Time elapsed: 0.004 s
% 1.58/1.32 % (9273)Instructions burned: 4 (million)
% 1.58/1.32 % (9273)------------------------------
% 1.58/1.32 % (9273)------------------------------
% 1.58/1.33 % (9277)Refutation not found, incomplete strategy
% 1.58/1.33 % (9277)------------------------------
% 1.58/1.33 % (9277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (9277)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.33
% 1.58/1.33
% 1.58/1.33 % (9277)Memory used [KB]: 5500
% 1.58/1.33 % (9277)Time elapsed: 0.008 s
% 1.58/1.33 % (9277)Instructions burned: 12 (million)
% 1.58/1.33 % (9277)------------------------------
% 1.58/1.33 % (9277)------------------------------
% 1.58/1.33 % (9274)First to succeed.
% 1.58/1.33 % (9274)Refutation found. Thanks to Tanya!
% 1.58/1.33 % SZS status Theorem for DTF2THF_9174
% 1.58/1.33 % SZS output start Proof for DTF2THF_9174
% 1.58/1.33 thf(type_def_5, type, a: $tType).
% 1.58/1.33 thf(func_def_0, type, a: $tType).
% 1.58/1.33 thf(func_def_1, type, cK: (a > $o) > a > $o).
% 1.58/1.33 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.58/1.33 thf(func_def_13, type, sK0: (a > $o) > a).
% 1.58/1.33 thf(func_def_14, type, sK1: (a > $o) > a).
% 1.58/1.33 thf(func_def_15, type, sK2: a).
% 1.58/1.33 thf(func_def_16, type, sK3: a > $o).
% 1.58/1.33 thf(func_def_18, type, ph5: !>[X0: $tType]:(X0)).
% 1.58/1.33 thf(f89,plain,(
% 1.58/1.33 $false),
% 1.58/1.33 inference(avatar_sat_refutation,[status(thm)],[f31,f43,f80,f88])).
% 1.58/1.33 thf(f88,plain,(
% 1.58/1.33 ~spl4_1),
% 1.58/1.33 inference(avatar_contradiction_clause,[status(thm)],[f87])).
% 1.58/1.33 thf(f87,plain,(
% 1.58/1.33 $false | ~spl4_1),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.58/1.33 thf(f83,plain,(
% 1.58/1.33 ($true != $true) | ~spl4_1),
% 1.58/1.33 inference(superposition,[status(thm)],[f13,f26])).
% 1.58/1.33 thf(f26,plain,(
% 1.58/1.33 ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK2) = $true) | ~spl4_1),
% 1.58/1.33 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.58/1.33 thf(f24,definition,(
% 1.58/1.33 spl4_1 <=> ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK2) = $true)),
% 1.58/1.33 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.58/1.33 thf(f13,plain,(
% 1.58/1.33 ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK2) != $true)),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.58/1.33 thf(f12,plain,(
% 1.58/1.33 ! [X0 : a > $o] : ((($true = (X0 @ (sK0 @ X0))) & ! [X2 : a > $o] : (($true != (X2 @ (sK0 @ X0))) | (($true = (X2 @ (sK1 @ X2))) & ($true != (cK @ X2 @ (sK1 @ X2)))))) | ! [X4 : a] : (((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X4) = $true) | ((cK @ X0 @ X4) != $true))) & ((($true = (sK3 @ sK2)) & ! [X7 : a] : (($true != (sK3 @ X7)) | ($true = (cK @ sK3 @ X7)))) & ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK2) != $true))),
% 1.58/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f11,f10,f9,f8])).
% 1.58/1.33 thf(f8,plain,(
% 1.58/1.33 ! [X0 : a > $o] : (? [X1 : a] : (((X0 @ X1) = $true) & ! [X2 : a > $o] : (((X2 @ X1) != $true) | ? [X3 : a] : (((X2 @ X3) = $true) & ((cK @ X2 @ X3) != $true)))) => (($true = (X0 @ (sK0 @ X0))) & ! [X2 : a > $o] : (($true != (X2 @ (sK0 @ X0))) | ? [X3 : a] : (((X2 @ X3) = $true) & ((cK @ X2 @ X3) != $true)))))),
% 1.58/1.33 introduced(definition,[],[choice_axiom])).
% 1.58/1.33 thf(f9,plain,(
% 1.58/1.33 ! [X2 : a > $o] : (? [X3 : a] : (((X2 @ X3) = $true) & ((cK @ X2 @ X3) != $true)) => (($true = (X2 @ (sK1 @ X2))) & ($true != (cK @ X2 @ (sK1 @ X2)))))),
% 1.58/1.33 introduced(definition,[],[choice_axiom])).
% 1.58/1.33 thf(f10,plain,(
% 1.58/1.33 ? [X5 : a] : (? [X6 : a > $o] : (((X6 @ X5) = $true) & ! [X7 : a] : (($true != (X6 @ X7)) | ($true = (cK @ X6 @ X7)))) & ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X5) != $true)) => (? [X6 : a > $o] : (($true = (X6 @ sK2)) & ! [X7 : a] : (($true != (X6 @ X7)) | ($true = (cK @ X6 @ X7)))) & ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK2) != $true))),
% 1.58/1.33 introduced(definition,[],[choice_axiom])).
% 1.58/1.33 thf(f11,plain,(
% 1.58/1.33 ? [X6 : a > $o] : (($true = (X6 @ sK2)) & ! [X7 : a] : (($true != (X6 @ X7)) | ($true = (cK @ X6 @ X7)))) => (($true = (sK3 @ sK2)) & ! [X7 : a] : (($true != (sK3 @ X7)) | ($true = (cK @ sK3 @ X7))))),
% 1.58/1.33 introduced(definition,[],[choice_axiom])).
% 1.58/1.33 thf(f7,plain,(
% 1.58/1.33 ! [X0 : a > $o] : (? [X1 : a] : (((X0 @ X1) = $true) & ! [X2 : a > $o] : (((X2 @ X1) != $true) | ? [X3 : a] : (((X2 @ X3) = $true) & ((cK @ X2 @ X3) != $true)))) | ! [X4 : a] : (((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X4) = $true) | ((cK @ X0 @ X4) != $true))) & ? [X5 : a] : (? [X6 : a > $o] : (((X6 @ X5) = $true) & ! [X7 : a] : (($true != (X6 @ X7)) | ($true = (cK @ X6 @ X7)))) & ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X5) != $true))),
% 1.58/1.33 inference(ennf_transformation,[status(thm)],[f6])).
% 1.58/1.33 thf(f6,plain,(
% 1.58/1.33 ~(! [X0 : a > $o] : (! [X1 : a] : (((X0 @ X1) = $true) => ? [X2 : a > $o] : (((X2 @ X1) = $true) & ! [X3 : a] : (((X2 @ X3) = $true) => ((cK @ X2 @ X3) = $true)))) => ! [X4 : a] : (((cK @ X0 @ X4) = $true) => ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X4) = $true))) => ! [X5 : a] : (? [X6 : a > $o] : (! [X7 : a] : (($true = (X6 @ X7)) => ($true = (cK @ X6 @ X7))) & ((X6 @ X5) = $true)) => ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X5) = $true)))),
% 1.58/1.33 inference(rectify,[status(thm)],[f5])).
% 1.58/1.33 thf(f5,plain,(
% 1.58/1.33 ~(! [X0 : a > $o] : (! [X1 : a] : (((X0 @ X1) = $true) => ? [X2 : a > $o] : (((X2 @ X1) = $true) & ! [X3 : a] : (((X2 @ X3) = $true) => ((cK @ X2 @ X3) = $true)))) => ! [X4 : a] : (((cK @ X0 @ X4) = $true) => ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X4) = $true))) => ! [X8 : a] : (? [X9 : a > $o] : (($true = (X9 @ X8)) & ! [X10 : a] : (($true = (X9 @ X10)) => ((cK @ X9 @ X10) = $true))) => ($true = (cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X8))))),
% 1.58/1.33 inference(fool_elimination,[status(thm)],[f4])).
% 1.58/1.33 thf(f4,plain,(
% 1.58/1.33 ~(! [X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) => ? [X2 : a > $o] : (! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3)) & (X2 @ X1))) => ! [X4 : a] : ((cK @ X0 @ X4) => (cK @ (^[X5 : a] : (? [X6 : a > $o] : (! [X7 : a] : ((X6 @ X7) => (cK @ X6 @ X7)) & (X6 @ X5)))) @ X4))) => ! [X8 : a] : (? [X9 : a > $o] : ((X9 @ X8) & ! [X10 : a] : ((X9 @ X10) => (cK @ X9 @ X10))) => (cK @ (^[X11 : a] : (? [X12 : a > $o] : (! [X13 : a] : ((X12 @ X13) => (cK @ X12 @ X13)) & (X12 @ X11)))) @ X8)))),
% 1.58/1.33 inference(rectify,[status(thm)],[f2])).
% 1.58/1.33 thf(f2,negated_conjecture,(
% 1.58/1.33 ~(! [X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) => ? [X2 : a > $o] : (! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3)) & (X2 @ X1))) => ! [X1 : a] : ((cK @ X0 @ X1) => (cK @ (^[X3 : a] : (? [X2 : a > $o] : (! [X4 : a] : ((X2 @ X4) => (cK @ X2 @ X4)) & (X2 @ X3)))) @ X1))) => ! [X1 : a] : (? [X2 : a > $o] : ((X2 @ X1) & ! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3))) => (cK @ (^[X3 : a] : (? [X2 : a > $o] : (! [X4 : a] : ((X2 @ X4) => (cK @ X2 @ X4)) & (X2 @ X3)))) @ X1)))),
% 1.58/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 1.58/1.33 thf(f1,conjecture,(
% 1.58/1.33 ! [X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) => ? [X2 : a > $o] : (! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3)) & (X2 @ X1))) => ! [X1 : a] : ((cK @ X0 @ X1) => (cK @ (^[X3 : a] : (? [X2 : a > $o] : (! [X4 : a] : ((X2 @ X4) => (cK @ X2 @ X4)) & (X2 @ X3)))) @ X1))) => ! [X1 : a] : (? [X2 : a > $o] : ((X2 @ X1) & ! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3))) => (cK @ (^[X3 : a] : (? [X2 : a > $o] : (! [X4 : a] : ((X2 @ X4) => (cK @ X2 @ X4)) & (X2 @ X3)))) @ X1))),
% 1.58/1.33 file('/export/starexec/sandbox2/tmp/tmp.YpJxvrLOfE/DTF2THF_9174.p',cTHM116_2SS_pme)).
% 1.58/1.33 thf(f80,plain,(
% 1.58/1.33 spl4_1 | ~spl4_2 | ~spl4_3),
% 1.58/1.33 inference(avatar_split_clause,[status(thm)],[f79,f41,f28,f24])).
% 1.58/1.33 thf(f28,definition,(
% 1.58/1.33 spl4_2 <=> ($true = (sK3 @ (sK0 @ sK3)))),
% 1.58/1.33 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.58/1.33 thf(f41,definition,(
% 1.58/1.33 spl4_3 <=> ! [X0 : a > $o] : (($true = (X0 @ (sK1 @ X0))) | ((X0 @ (sK0 @ sK3)) != $true))),
% 1.58/1.33 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.58/1.33 thf(f79,plain,(
% 1.58/1.33 ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK2) = $true) | (~spl4_2 | ~spl4_3)),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.58/1.33 thf(f78,plain,(
% 1.58/1.33 ($true != $true) | ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK2) = $true) | (~spl4_2 | ~spl4_3)),
% 1.58/1.33 inference(forward_demodulation,[status(thm)],[f70,f30])).
% 1.58/1.33 thf(f30,plain,(
% 1.58/1.33 ($true = (sK3 @ (sK0 @ sK3))) | ~spl4_2),
% 1.58/1.33 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.58/1.33 thf(f70,plain,(
% 1.58/1.33 ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK2) = $true) | ($true != (sK3 @ (sK0 @ sK3))) | (~spl4_2 | ~spl4_3)),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.58/1.33 thf(f65,plain,(
% 1.58/1.33 ($true != (sK3 @ (sK0 @ sK3))) | ($true != $true) | ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK2) = $true) | (~spl4_2 | ~spl4_3)),
% 1.58/1.33 inference(superposition,[status(thm)],[f59,f20])).
% 1.58/1.33 thf(f20,plain,(
% 1.58/1.33 ((cK @ sK3 @ sK2) = $true)),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.58/1.33 thf(f19,plain,(
% 1.58/1.33 ((cK @ sK3 @ sK2) = $true) | ($true != $true)),
% 1.58/1.33 inference(superposition,[status(thm)],[f14,f15])).
% 1.58/1.33 thf(f15,plain,(
% 1.58/1.33 ($true = (sK3 @ sK2))),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.58/1.33 thf(f14,plain,(
% 1.58/1.33 ( ! [X7 : a] : (($true != (sK3 @ X7)) | ($true = (cK @ sK3 @ X7))) )),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.58/1.33 thf(f59,plain,(
% 1.58/1.33 ( ! [X0 : a > $o,X1 : a] : (((cK @ X0 @ X1) != $true) | ($true = (cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X1)) | ((sK3 @ (sK0 @ X0)) != $true)) ) | (~spl4_2 | ~spl4_3)),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.58/1.33 thf(f55,plain,(
% 1.58/1.33 ( ! [X0 : a > $o,X1 : a] : (($true != $true) | ($true = (cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X1)) | ((sK3 @ (sK0 @ X0)) != $true) | ((cK @ X0 @ X1) != $true)) ) | (~spl4_2 | ~spl4_3)),
% 1.58/1.33 inference(superposition,[status(thm)],[f16,f54])).
% 1.58/1.33 thf(f54,plain,(
% 1.58/1.33 ((cK @ sK3 @ (sK1 @ sK3)) = $true) | (~spl4_2 | ~spl4_3)),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.58/1.33 thf(f53,plain,(
% 1.58/1.33 ((cK @ sK3 @ (sK1 @ sK3)) = $true) | ($true != $true) | (~spl4_2 | ~spl4_3)),
% 1.58/1.33 inference(superposition,[status(thm)],[f14,f52])).
% 1.58/1.33 thf(f52,plain,(
% 1.58/1.33 ($true = (sK3 @ (sK1 @ sK3))) | (~spl4_2 | ~spl4_3)),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.58/1.33 thf(f49,plain,(
% 1.58/1.33 ($true != $true) | ($true = (sK3 @ (sK1 @ sK3))) | (~spl4_2 | ~spl4_3)),
% 1.58/1.33 inference(superposition,[status(thm)],[f42,f30])).
% 1.58/1.33 thf(f42,plain,(
% 1.58/1.33 ( ! [X0 : a > $o] : (((X0 @ (sK0 @ sK3)) != $true) | ($true = (X0 @ (sK1 @ X0)))) ) | ~spl4_3),
% 1.58/1.33 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.58/1.33 thf(f16,plain,(
% 1.58/1.33 ( ! [X2 : a > $o,X0 : a > $o,X4 : a] : (($true != (cK @ X2 @ (sK1 @ X2))) | ((cK @ X0 @ X4) != $true) | ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X4) = $true) | ($true != (X2 @ (sK0 @ X0)))) )),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.58/1.33 thf(f43,plain,(
% 1.58/1.33 spl4_3 | spl4_1),
% 1.58/1.33 inference(avatar_split_clause,[status(thm)],[f39,f24,f41])).
% 1.58/1.33 thf(f39,plain,(
% 1.58/1.33 ( ! [X0 : a > $o] : (($true = (X0 @ (sK1 @ X0))) | ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK2) = $true) | ((X0 @ (sK0 @ sK3)) != $true)) )),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.58/1.33 thf(f36,plain,(
% 1.58/1.33 ( ! [X0 : a > $o] : (($true != $true) | ($true = (X0 @ (sK1 @ X0))) | ((X0 @ (sK0 @ sK3)) != $true) | ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK2) = $true)) )),
% 1.58/1.33 inference(superposition,[status(thm)],[f17,f20])).
% 1.58/1.33 thf(f17,plain,(
% 1.58/1.33 ( ! [X2 : a > $o,X0 : a > $o,X4 : a] : (((cK @ X0 @ X4) != $true) | ($true != (X2 @ (sK0 @ X0))) | ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X4) = $true) | ($true = (X2 @ (sK1 @ X2)))) )),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.58/1.33 thf(f31,plain,(
% 1.58/1.33 spl4_1 | spl4_2),
% 1.58/1.33 inference(avatar_split_clause,[status(thm)],[f22,f28,f24])).
% 1.58/1.33 thf(f22,plain,(
% 1.58/1.33 ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK2) = $true) | ($true = (sK3 @ (sK0 @ sK3)))),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.58/1.33 thf(f21,plain,(
% 1.58/1.33 ($true != $true) | ($true = (sK3 @ (sK0 @ sK3))) | ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK2) = $true)),
% 1.58/1.33 inference(superposition,[status(thm)],[f18,f20])).
% 1.58/1.33 thf(f18,plain,(
% 1.58/1.33 ( ! [X0 : a > $o,X4 : a] : (((cK @ X0 @ X4) != $true) | ($true = (X0 @ (sK0 @ X0))) | ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X4) = $true)) )),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.58/1.33 % SZS output end Proof for DTF2THF_9174
% 1.58/1.33 % (9274)------------------------------
% 1.58/1.33 % (9274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (9274)Termination reason: Refutation
% 1.58/1.33
% 1.58/1.33 % (9274)Memory used [KB]: 5628
% 1.58/1.33 % (9274)Time elapsed: 0.011 s
% 1.58/1.33 % (9274)Instructions burned: 12 (million)
% 1.58/1.33 % (9274)------------------------------
% 1.58/1.33 % (9274)------------------------------
% 1.58/1.33 % (9271)Success in time 0.025 s
%------------------------------------------------------------------------------