%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV186^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:30 AM UTC 2026
% Result : Theorem 0.32s 1.33s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 511 ( 190 equ; 0 cnn)
% Maximal formula atoms : 26 ( 11 avg)
% Number of connectives : 598 ( 110 ~; 97 |; 60 &; 284 @)
% ( 2 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 143 ( 143 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 172 ( 0 ^; 128 !; 44 ?; 172 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_4,type,
sK0: ( b > $o ) > ( b > $o ) > $o ).
thf(func_def_5,type,
sK1: ( b > $o ) > $o ).
thf(func_def_6,type,
sK2: b > $o ).
thf(func_def_7,type,
sK3: b > $o ).
thf(func_def_8,type,
sK4: b ).
thf(func_def_9,type,
sK5: b > $o ).
thf(func_def_10,type,
sK6: ( b > $o ) > ( b > $o ) > b ).
thf(func_def_13,type,
ph8:
!>[X0: $tType] : X0 ).
thf(f50,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f35,f39,f49]) ).
thf(f49,plain,
( spl7_2
| ~ spl7_1 ),
inference(avatar_split_clause,[status(thm)],[f48,f29,f33]) ).
thf(f33,definition,
( spl7_2
<=> ! [X0: b] :
( ( ( sK5 @ X0 )
= $true )
| ( ( sK3 @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition]) ).
thf(f29,definition,
( spl7_1
<=> ( ( sK2 @ ( sK6 @ sK2 @ sK5 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition]) ).
thf(f48,plain,
( ! [X0: b] :
( ( ( sK5 @ X0 )
= $true )
| ( ( sK3 @ X0 )
!= $true ) )
| ~ spl7_1 ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ! [X0: b] :
( ( $true != $true )
| ( ( sK5 @ X0 )
= $true )
| ( ( sK3 @ X0 )
!= $true ) )
| ~ spl7_1 ),
inference(superposition,[status(thm)],[f46,f17]) ).
thf(f17,plain,
( $true
= ( sK0 @ sK2 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( sK3 @ sK4 )
= $true )
& ( $true
= ( sK1 @ sK5 ) )
& ( ( sK5 @ sK4 )
!= $true )
& ! [X6: b] :
( ( $true
!= ( sK2 @ X6 ) )
| ! [X7: b > $o] :
( ( $true
= ( X7 @ X6 ) )
| ( ( sK1 @ X7 )
!= $true ) ) )
& ( $true
= ( sK0 @ sK2 @ sK3 ) )
& ! [X8: b > $o] :
( ( $true
!= ( sK1 @ X8 ) )
| ! [X9: b > $o,X10: b > $o] :
( ! [X11: b] :
( ( ( X8 @ X11 )
= $true )
| ( ( X10 @ X11 )
!= $true ) )
| ( $true
!= ( sK0 @ X9 @ X10 ) )
| ( ( $true
!= ( X8 @ ( sK6 @ X9 @ X8 ) ) )
& ( $true
= ( X9 @ ( sK6 @ X9 @ X8 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f8,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: ( b > $o ) > ( b > $o ) > $o,X1: ( b > $o ) > $o] :
( ? [X2: b > $o,X3: b > $o] :
( ? [X4: b] :
( ( ( X3 @ X4 )
= $true )
& ? [X5: b > $o] :
( ( $true
= ( X1 @ X5 ) )
& ( ( X5 @ X4 )
!= $true ) ) )
& ! [X6: b] :
( ( ( X2 @ X6 )
!= $true )
| ! [X7: b > $o] :
( ( $true
= ( X7 @ X6 ) )
| ( ( X1 @ X7 )
!= $true ) ) )
& ( $true
= ( X0 @ X2 @ X3 ) ) )
& ! [X8: b > $o] :
( ( $true
!= ( X1 @ X8 ) )
| ! [X9: b > $o,X10: b > $o] :
( ! [X11: b] :
( ( ( X8 @ X11 )
= $true )
| ( ( X10 @ X11 )
!= $true ) )
| ( $true
!= ( X0 @ X9 @ X10 ) )
| ? [X12: b] :
( ( $true
!= ( X8 @ X12 ) )
& ( $true
= ( X9 @ X12 ) ) ) ) ) )
=> ( ? [X3: b > $o,X2: b > $o] :
( ? [X4: b] :
( ( ( X3 @ X4 )
= $true )
& ? [X5: b > $o] :
( ( ( sK1 @ X5 )
= $true )
& ( ( X5 @ X4 )
!= $true ) ) )
& ! [X6: b] :
( ( ( X2 @ X6 )
!= $true )
| ! [X7: b > $o] :
( ( $true
= ( X7 @ X6 ) )
| ( ( sK1 @ X7 )
!= $true ) ) )
& ( $true
= ( sK0 @ X2 @ X3 ) ) )
& ! [X8: b > $o] :
( ( $true
!= ( sK1 @ X8 ) )
| ! [X10: b > $o,X9: b > $o] :
( ! [X11: b] :
( ( ( X8 @ X11 )
= $true )
| ( ( X10 @ X11 )
!= $true ) )
| ( $true
!= ( sK0 @ X9 @ X10 ) )
| ? [X12: b] :
( ( $true
!= ( X8 @ X12 ) )
& ( $true
= ( X9 @ X12 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: b > $o,X2: b > $o] :
( ? [X4: b] :
( ( ( X3 @ X4 )
= $true )
& ? [X5: b > $o] :
( ( ( sK1 @ X5 )
= $true )
& ( ( X5 @ X4 )
!= $true ) ) )
& ! [X6: b] :
( ( ( X2 @ X6 )
!= $true )
| ! [X7: b > $o] :
( ( $true
= ( X7 @ X6 ) )
| ( ( sK1 @ X7 )
!= $true ) ) )
& ( $true
= ( sK0 @ X2 @ X3 ) ) )
=> ( ? [X4: b] :
( ( $true
= ( sK3 @ X4 ) )
& ? [X5: b > $o] :
( ( ( sK1 @ X5 )
= $true )
& ( ( X5 @ X4 )
!= $true ) ) )
& ! [X6: b] :
( ( $true
!= ( sK2 @ X6 ) )
| ! [X7: b > $o] :
( ( $true
= ( X7 @ X6 ) )
| ( ( sK1 @ X7 )
!= $true ) ) )
& ( $true
= ( sK0 @ sK2 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X4: b] :
( ( $true
= ( sK3 @ X4 ) )
& ? [X5: b > $o] :
( ( ( sK1 @ X5 )
= $true )
& ( ( X5 @ X4 )
!= $true ) ) )
=> ( ( ( sK3 @ sK4 )
= $true )
& ? [X5: b > $o] :
( ( ( sK1 @ X5 )
= $true )
& ( ( X5 @ sK4 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X5: b > $o] :
( ( ( sK1 @ X5 )
= $true )
& ( ( X5 @ sK4 )
!= $true ) )
=> ( ( $true
= ( sK1 @ sK5 ) )
& ( ( sK5 @ sK4 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X8: b > $o,X9: b > $o] :
( ? [X12: b] :
( ( $true
!= ( X8 @ X12 ) )
& ( $true
= ( X9 @ X12 ) ) )
=> ( ( $true
!= ( X8 @ ( sK6 @ X9 @ X8 ) ) )
& ( $true
= ( X9 @ ( sK6 @ X9 @ X8 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: ( b > $o ) > ( b > $o ) > $o,X1: ( b > $o ) > $o] :
( ? [X2: b > $o,X3: b > $o] :
( ? [X4: b] :
( ( ( X3 @ X4 )
= $true )
& ? [X5: b > $o] :
( ( $true
= ( X1 @ X5 ) )
& ( ( X5 @ X4 )
!= $true ) ) )
& ! [X6: b] :
( ( ( X2 @ X6 )
!= $true )
| ! [X7: b > $o] :
( ( $true
= ( X7 @ X6 ) )
| ( ( X1 @ X7 )
!= $true ) ) )
& ( $true
= ( X0 @ X2 @ X3 ) ) )
& ! [X8: b > $o] :
( ( $true
!= ( X1 @ X8 ) )
| ! [X9: b > $o,X10: b > $o] :
( ! [X11: b] :
( ( ( X8 @ X11 )
= $true )
| ( ( X10 @ X11 )
!= $true ) )
| ( $true
!= ( X0 @ X9 @ X10 ) )
| ? [X12: b] :
( ( $true
!= ( X8 @ X12 ) )
& ( $true
= ( X9 @ X12 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: ( b > $o ) > ( b > $o ) > $o,X1: ( b > $o ) > $o] :
( ? [X8: b > $o,X7: b > $o] :
( ? [X11: b] :
( ( $true
= ( X7 @ X11 ) )
& ? [X12: b > $o] :
( ( ( X1 @ X12 )
= $true )
& ( ( X12 @ X11 )
!= $true ) ) )
& ! [X9: b] :
( ( ( X8 @ X9 )
!= $true )
| ! [X10: b > $o] :
( ( $true
= ( X10 @ X9 ) )
| ( $true
!= ( X1 @ X10 ) ) ) )
& ( ( X0 @ X8 @ X7 )
= $true ) )
& ! [X2: b > $o] :
( ( ( X1 @ X2 )
!= $true )
| ! [X3: b > $o,X4: b > $o] :
( ! [X6: b] :
( ( ( X2 @ X6 )
= $true )
| ( $true
!= ( X4 @ X6 ) ) )
| ( ( X0 @ X3 @ X4 )
!= $true )
| ? [X5: b] :
( ( ( X2 @ X5 )
!= $true )
& ( ( X3 @ X5 )
= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: ( b > $o ) > ( b > $o ) > $o,X1: ( b > $o ) > $o] :
( ? [X7: b > $o,X8: b > $o] :
( ? [X11: b] :
( ( $true
= ( X7 @ X11 ) )
& ? [X12: b > $o] :
( ( ( X1 @ X12 )
= $true )
& ( ( X12 @ X11 )
!= $true ) ) )
& ! [X9: b] :
( ( ( X8 @ X9 )
!= $true )
| ! [X10: b > $o] :
( ( $true
= ( X10 @ X9 ) )
| ( $true
!= ( X1 @ X10 ) ) ) )
& ( ( X0 @ X8 @ X7 )
= $true ) )
& ! [X2: b > $o] :
( ! [X4: b > $o,X3: b > $o] :
( ! [X6: b] :
( ( ( X2 @ X6 )
= $true )
| ( $true
!= ( X4 @ X6 ) ) )
| ? [X5: b] :
( ( ( X2 @ X5 )
!= $true )
& ( ( X3 @ X5 )
= $true ) )
| ( ( X0 @ X3 @ X4 )
!= $true ) )
| ( ( X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( b > $o ) > ( b > $o ) > $o,X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( ( X1 @ X2 )
= $true )
=> ! [X4: b > $o,X3: b > $o] :
( ( ! [X5: b] :
( ( ( X3 @ X5 )
= $true )
=> ( ( X2 @ X5 )
= $true ) )
& ( ( X0 @ X3 @ X4 )
= $true ) )
=> ! [X6: b] :
( ( $true
= ( X4 @ X6 ) )
=> ( ( X2 @ X6 )
= $true ) ) ) )
=> ! [X7: b > $o,X8: b > $o] :
( ( ! [X9: b] :
( ( ( X8 @ X9 )
= $true )
=> ! [X10: b > $o] :
( ( $true
= ( X1 @ X10 ) )
=> ( $true
= ( X10 @ X9 ) ) ) )
& ( ( X0 @ X8 @ X7 )
= $true ) )
=> ! [X11: b] :
( ( $true
= ( X7 @ X11 ) )
=> ! [X12: b > $o] :
( ( ( X1 @ X12 )
= $true )
=> ( ( X12 @ X11 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( b > $o ) > ( b > $o ) > $o,X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ! [X3: b > $o,X4: b > $o] :
( ( ! [X5: b] :
( ( X3 @ X5 )
=> ( X2 @ X5 ) )
& ( X0 @ X3 @ X4 ) )
=> ! [X6: b] :
( ( X4 @ X6 )
=> ( X2 @ X6 ) ) ) )
=> ! [X7: b > $o,X8: b > $o] :
( ( ! [X9: b] :
( ( X8 @ X9 )
=> ! [X10: b > $o] :
( ( X1 @ X10 )
=> ( X10 @ X9 ) ) )
& ( X0 @ X8 @ X7 ) )
=> ! [X11: b] :
( ( X7 @ X11 )
=> ! [X12: b > $o] :
( ( X1 @ X12 )
=> ( X12 @ X11 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( b > $o ) > ( b > $o ) > $o,X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ! [X3: b > $o,X4: b > $o] :
( ( ! [X5: b] :
( ( X3 @ X5 )
=> ( X2 @ X5 ) )
& ( X0 @ X3 @ X4 ) )
=> ! [X5: b] :
( ( X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ! [X4: b > $o,X3: b > $o] :
( ( ! [X2: b] :
( ( X3 @ X2 )
=> ! [X6: b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 ) ) )
& ( X0 @ X3 @ X4 ) )
=> ! [X2: b] :
( ( X4 @ X2 )
=> ! [X6: b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( b > $o ) > ( b > $o ) > $o,X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ! [X3: b > $o,X4: b > $o] :
( ( ! [X5: b] :
( ( X3 @ X5 )
=> ( X2 @ X5 ) )
& ( X0 @ X3 @ X4 ) )
=> ! [X5: b] :
( ( X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ! [X4: b > $o,X3: b > $o] :
( ( ! [X2: b] :
( ( X3 @ X2 )
=> ! [X6: b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 ) ) )
& ( X0 @ X3 @ X4 ) )
=> ! [X2: b] :
( ( X4 @ X2 )
=> ! [X6: b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jnvWById1Y/DTF2THF_5436.p',cTHM565_pme) ).
thf(f46,plain,
( ! [X0: b > $o,X1: b] :
( ( $true
!= ( sK0 @ sK2 @ X0 ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( X0 @ X1 )
!= $true ) )
| ~ spl7_1 ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ! [X0: b > $o,X1: b] :
( ( $true != $true )
| ( ( X0 @ X1 )
!= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
!= ( sK0 @ sK2 @ X0 ) ) )
| ~ spl7_1 ),
inference(superposition,[status(thm)],[f44,f41]) ).
thf(f41,plain,
( ( $true
= ( sK5 @ ( sK6 @ sK2 @ sK5 ) ) )
| ~ spl7_1 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true
= ( sK5 @ ( sK6 @ sK2 @ sK5 ) ) )
| ( $true != $true )
| ~ spl7_1 ),
inference(superposition,[status(thm)],[f23,f31]) ).
thf(f31,plain,
( ( ( sK2 @ ( sK6 @ sK2 @ sK5 ) )
= $true )
| ~ spl7_1 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f23,plain,
! [X0: b] :
( ( $true
!= ( sK2 @ X0 ) )
| ( ( sK5 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: b] :
( ( $true
!= ( sK2 @ X0 ) )
| ( $true != $true )
| ( ( sK5 @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f18,f20]) ).
thf(f20,plain,
( $true
= ( sK1 @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f18,plain,
! [X6: b,X7: b > $o] :
( ( ( sK1 @ X7 )
!= $true )
| ( $true
!= ( sK2 @ X6 ) )
| ( $true
= ( X7 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f44,plain,
! [X2: b,X0: b > $o,X1: b > $o] :
( ( $true
!= ( sK5 @ ( sK6 @ X0 @ sK5 ) ) )
| ( $true
!= ( sK0 @ X0 @ X1 ) )
| ( $true
!= ( X1 @ X2 ) )
| ( $true
= ( sK5 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: b,X0: b > $o,X1: b > $o] :
( ( $true
!= ( sK5 @ ( sK6 @ X0 @ sK5 ) ) )
| ( $true
!= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $true
!= ( X1 @ X2 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f16,f20]) ).
thf(f16,plain,
! [X10: b > $o,X11: b,X8: b > $o,X9: b > $o] :
( ( $true
!= ( sK1 @ X8 ) )
| ( $true
!= ( X8 @ ( sK6 @ X9 @ X8 ) ) )
| ( $true
!= ( sK0 @ X9 @ X10 ) )
| ( ( X10 @ X11 )
!= $true )
| ( ( X8 @ X11 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f39,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[status(thm)],[f38]) ).
thf(f38,plain,
( $false
| ~ spl7_2 ),
inference(subsumption_resolution,[status(thm)],[f37,f19]) ).
thf(f19,plain,
( ( sK5 @ sK4 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f37,plain,
( ( ( sK5 @ sK4 )
= $true )
| ~ spl7_2 ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true != $true )
| ( ( sK5 @ sK4 )
= $true )
| ~ spl7_2 ),
inference(superposition,[status(thm)],[f34,f21]) ).
thf(f21,plain,
( ( sK3 @ sK4 )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f34,plain,
( ! [X0: b] :
( ( ( sK3 @ X0 )
!= $true )
| ( ( sK5 @ X0 )
= $true ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f35,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[status(thm)],[f27,f33,f29]) ).
thf(f27,plain,
! [X0: b] :
( ( ( sK2 @ ( sK6 @ sK2 @ sK5 ) )
= $true )
| ( ( sK5 @ X0 )
= $true )
| ( ( sK3 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: b] :
( ( ( sK3 @ X0 )
!= $true )
| ( $true != $true )
| ( ( sK5 @ X0 )
= $true )
| ( ( sK2 @ ( sK6 @ sK2 @ sK5 ) )
= $true ) ),
inference(superposition,[status(thm)],[f25,f17]) ).
thf(f25,plain,
! [X2: b > $o,X0: b > $o,X1: b] :
( ( ( sK0 @ X2 @ X0 )
!= $true )
| ( ( X0 @ X1 )
!= $true )
| ( ( X2 @ ( sK6 @ X2 @ sK5 ) )
= $true )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: b > $o,X0: b > $o,X1: b] :
( ( ( X0 @ X1 )
!= $true )
| ( ( sK0 @ X2 @ X0 )
!= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( X2 @ ( sK6 @ X2 @ sK5 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f15,f20]) ).
thf(f15,plain,
! [X10: b > $o,X11: b,X8: b > $o,X9: b > $o] :
( ( $true
!= ( sK1 @ X8 ) )
| ( ( X10 @ X11 )
!= $true )
| ( $true
= ( X9 @ ( sK6 @ X9 @ X8 ) ) )
| ( $true
!= ( sK0 @ X9 @ X10 ) )
| ( ( X8 @ X11 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV186^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n013.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:41:23 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEV186^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Set Theory (Sets of sets)
% 0.28/0.46 % Problem : TPS problem THM565
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0482 [Bro09]
% 0.28/0.46 % : THM565 [TPS]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.28/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.28/0.46 % Number of connectives : 27 ( 0 ~; 0 |; 2 &; 15 @)
% 0.28/0.46 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 13 ( 13 avg)
% 0.28/0.46 % Number of types : 2 ( 1 usr)
% 0.28/0.46 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.28/0.46 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 % : Polymorphic definitions expanded.
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(b_type,type,
% 0.28/0.46 b: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(cTHM565_pme,conjecture,
% 0.28/0.46 ! [P: ( b > $o ) > ( b > $o ) > $o,S: ( b > $o ) > $o] :
% 0.28/0.46 ( ! [Xx: b > $o] :
% 0.28/0.46 ( ( S @ Xx )
% 0.28/0.46 => ! [X: b > $o,Y: b > $o] :
% 0.28/0.46 ( ( ! [Xx0: b] :
% 0.28/0.46 ( ( X @ Xx0 )
% 0.28/0.46 => ( Xx @ Xx0 ) )
% 0.28/0.46 & ( P @ X @ Y ) )
% 0.28/0.46 => ! [Xx0: b] :
% 0.28/0.46 ( ( Y @ Xx0 )
% 0.28/0.46 => ( Xx @ Xx0 ) ) ) )
% 0.28/0.46 => ! [X: b > $o,Y: b > $o] :
% 0.28/0.46 ( ( ! [Xx: b] :
% 0.28/0.46 ( ( X @ Xx )
% 0.28/0.46 => ! [S0: b > $o] :
% 0.28/0.46 ( ( S @ S0 )
% 0.28/0.46 => ( S0 @ Xx ) ) )
% 0.28/0.46 & ( P @ X @ Y ) )
% 0.28/0.46 => ! [Xx: b] :
% 0.28/0.46 ( ( Y @ Xx )
% 0.28/0.46 => ! [S0: b > $o] :
% 0.28/0.46 ( ( S @ S0 )
% 0.28/0.46 => ( S0 @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 0.32/1.30 ---- Embedded in THF ---
% 0.32/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.30 %%% Generated on Tue Feb 24 12:41:24 EST 2026
% 0.32/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.30 %%% Logic specification used:
% 0.32/1.30 %%% thf(spec, logic, $$dhol).
% 0.32/1.30
% 0.32/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.jnvWById1Y/DTF2DTF5436.p
% See solution above
% 0.32/1.30 ------------------------
% 0.32/1.31 ---- Cleaned THF ---
% 0.32/1.31 thf(b_type,type,
% 0.32/1.31 b: $tType ).
% 0.32/1.31
% 0.32/1.31 thf(cTHM565_pme,conjecture,
% 0.32/1.31 ! [P: ( b > $o ) > ( b > $o ) > $o,S: ( b > $o ) > $o] :
% 0.32/1.31 ( ! [Xx: b > $o] :
% 0.32/1.31 ( ( S @ Xx )
% 0.32/1.31 => ! [X: b > $o,Y: b > $o] :
% 0.32/1.31 ( ( ! [Xx0: b] :
% 0.32/1.31 ( ( X @ Xx0 )
% 0.32/1.31 => ( Xx @ Xx0 ) )
% 0.32/1.31 & ( P @ X @ Y ) )
% 0.32/1.31 => ! [Xx0: b] :
% 0.32/1.31 ( ( Y @ Xx0 )
% 0.32/1.31 => ( Xx @ Xx0 ) ) ) )
% 0.32/1.31 => ! [X: b > $o,Y: b > $o] :
% 0.32/1.31 ( ( ! [Xx: b] :
% 0.32/1.31 ( ( X @ Xx )
% 0.32/1.31 => ! [S0: b > $o] :
% 0.32/1.31 ( ( S @ S0 )
% 0.32/1.31 => ( S0 @ Xx ) ) )
% 0.32/1.31 & ( P @ X @ Y ) )
% 0.32/1.31 => ! [Xx: b] :
% 0.32/1.31 ( ( Y @ Xx )
% 0.32/1.31 => ! [S0: b > $o] :
% 0.32/1.31 ( ( S @ S0 )
% 0.32/1.31 => ( S0 @ Xx ) ) ) ) ) ).
% 0.32/1.31 ------------------------
% 0.32/1.33 % (5629)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_5436 for (3000ds/2Mi)
% 0.32/1.33 % (5626)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_5436 for (3000ds/4Mi)
% 0.32/1.33 % (5629)Instruction limit reached!
% 0.32/1.33 % (5629)------------------------------
% 0.32/1.33 % (5629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.33 % (5629)Termination reason: Unknown
% 0.32/1.33 % (5629)Termination phase: Saturation
% 0.32/1.33
% 0.32/1.33 % (5629)Memory used [KB]: 895
% 0.32/1.33 % (5629)Time elapsed: 0.002 s
% 0.32/1.33 % (5629)Instructions burned: 2 (million)
% 0.32/1.33 % (5629)------------------------------
% 0.32/1.33 % (5629)------------------------------
% 0.32/1.33 % (5631)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5436 for (3000ds/18Mi)
% 0.32/1.33 % (5626)Instruction limit reached!
% 0.32/1.33 % (5626)------------------------------
% 0.32/1.33 % (5626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.33 % (5626)Termination reason: Unknown
% 0.32/1.33 % (5626)Termination phase: Saturation
% 0.32/1.33
% 0.32/1.33 % (5626)Memory used [KB]: 5500
% 0.32/1.33 % (5626)Time elapsed: 0.003 s
% 0.32/1.33 % (5626)Instructions burned: 5 (million)
% 0.32/1.33 % (5626)------------------------------
% 0.32/1.33 % (5626)------------------------------
% 0.32/1.33 % (5628)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5436 for (3000ds/2Mi)
% 0.32/1.33 % (5631)First to succeed.
% 0.32/1.33 % (5628)Instruction limit reached!
% 0.32/1.33 % (5628)------------------------------
% 0.32/1.33 % (5628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.33 % (5628)Termination reason: Unknown
% 0.32/1.33 % (5628)Termination phase: Saturation
% 0.32/1.33
% 0.32/1.33 % (5628)Memory used [KB]: 5500
% 0.32/1.33 % (5628)Time elapsed: 0.004 s
% 0.32/1.33 % (5628)Instructions burned: 2 (million)
% 0.32/1.33 % (5628)------------------------------
% 0.32/1.33 % (5628)------------------------------
% 0.32/1.33 % (5625)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5436 for (3000ds/183Mi)
% 0.32/1.33 % (5627)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_5436 for (3000ds/27Mi)
% 0.32/1.33 % (5630)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_5436 for (3000ds/275Mi)
% 0.32/1.33 % (5631)Refutation found. Thanks to Tanya!
% 0.32/1.33 % SZS status Theorem for DTF2THF_5436
% 0.32/1.33 % SZS output start Proof for DTF2THF_5436
% 0.32/1.33 thf(type_def_5, type, b: $tType).
% 0.32/1.33 thf(func_def_0, type, b: $tType).
% 0.32/1.33 thf(func_def_4, type, sK0: (b > $o) > (b > $o) > $o).
% 0.32/1.33 thf(func_def_5, type, sK1: (b > $o) > $o).
% 0.32/1.33 thf(func_def_6, type, sK2: b > $o).
% 0.32/1.33 thf(func_def_7, type, sK3: b > $o).
% 0.32/1.33 thf(func_def_8, type, sK4: b).
% 0.32/1.33 thf(func_def_9, type, sK5: b > $o).
% 0.32/1.33 thf(func_def_10, type, sK6: (b > $o) > (b > $o) > b).
% 0.32/1.33 thf(func_def_13, type, ph8: !>[X0: $tType]:(X0)).
% 0.32/1.33 thf(f50,plain,(
% 0.32/1.33 $false),
% 0.32/1.33 inference(avatar_sat_refutation,[status(thm)],[f35,f39,f49])).
% 0.32/1.33 thf(f49,plain,(
% 0.32/1.33 spl7_2 | ~spl7_1),
% 0.32/1.33 inference(avatar_split_clause,[status(thm)],[f48,f29,f33])).
% 0.32/1.33 thf(f33,definition,(
% 0.32/1.33 spl7_2 <=> ! [X0 : b] : (((sK5 @ X0) = $true) | ((sK3 @ X0) != $true))),
% 0.32/1.33 introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition])).
% 0.32/1.33 thf(f29,definition,(
% 0.32/1.33 spl7_1 <=> ((sK2 @ (sK6 @ sK2 @ sK5)) = $true)),
% 0.32/1.33 introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition])).
% 0.32/1.34 thf(f48,plain,(
% 0.32/1.34 ( ! [X0 : b] : (((sK5 @ X0) = $true) | ((sK3 @ X0) != $true)) ) | ~spl7_1),
% 0.32/1.34 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 0.32/1.34 thf(f47,plain,(
% 0.32/1.34 ( ! [X0 : b] : (($true != $true) | ((sK5 @ X0) = $true) | ((sK3 @ X0) != $true)) ) | ~spl7_1),
% 0.32/1.34 inference(superposition,[status(thm)],[f46,f17])).
% 0.32/1.34 thf(f17,plain,(
% 0.32/1.34 ($true = (sK0 @ sK2 @ sK3))),
% 0.32/1.34 inference(cnf_transformation,[status(thm)],[f14])).
% 0.32/1.34 thf(f14,plain,(
% 0.32/1.34 ((((sK3 @ sK4) = $true) & (($true = (sK1 @ sK5)) & ((sK5 @ sK4) != $true))) & ! [X6 : b] : (($true != (sK2 @ X6)) | ! [X7 : b > $o] : (($true = (X7 @ X6)) | ((sK1 @ X7) != $true))) & ($true = (sK0 @ sK2 @ sK3))) & ! [X8 : b > $o] : (($true != (sK1 @ X8)) | ! [X9 : b > $o,X10 : b > $o] : (! [X11 : b] : (((X8 @ X11) = $true) | ((X10 @ X11) != $true)) | ($true != (sK0 @ X9 @ X10)) | (($true != (X8 @ (sK6 @ X9 @ X8))) & ($true = (X9 @ (sK6 @ X9 @ X8))))))),
% 0.32/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f8,f13,f12,f11,f10,f9])).
% 0.32/1.34 thf(f9,plain,(
% 0.32/1.34 ? [X0 : (b > $o) > (b > $o) > $o,X1 : (b > $o) > $o] : (? [X2 : b > $o,X3 : b > $o] : (? [X4 : b] : (((X3 @ X4) = $true) & ? [X5 : b > $o] : (($true = (X1 @ X5)) & ((X5 @ X4) != $true))) & ! [X6 : b] : (((X2 @ X6) != $true) | ! [X7 : b > $o] : (($true = (X7 @ X6)) | ((X1 @ X7) != $true))) & ($true = (X0 @ X2 @ X3))) & ! [X8 : b > $o] : (($true != (X1 @ X8)) | ! [X9 : b > $o,X10 : b > $o] : (! [X11 : b] : (((X8 @ X11) = $true) | ((X10 @ X11) != $true)) | ($true != (X0 @ X9 @ X10)) | ? [X12 : b] : (($true != (X8 @ X12)) & ($true = (X9 @ X12)))))) => (? [X3 : b > $o,X2 : b > $o] : (? [X4 : b] : (((X3 @ X4) = $true) & ? [X5 : b > $o] : (((sK1 @ X5) = $true) & ((X5 @ X4) != $true))) & ! [X6 : b] : (((X2 @ X6) != $true) | ! [X7 : b > $o] : (($true = (X7 @ X6)) | ((sK1 @ X7) != $true))) & ($true = (sK0 @ X2 @ X3))) & ! [X8 : b > $o] : (($true != (sK1 @ X8)) | ! [X10 : b > $o,X9 : b > $o] : (! [X11 : b] : (((X8 @ X11) = $true) | ((X10 @ X11) != $true)) | ($true != (sK0 @ X9 @ X10)) | ? [X12 : b] : (($true != (X8 @ X12)) & ($true = (X9 @ X12))))))),
% 0.32/1.34 introduced(definition,[],[choice_axiom])).
% 0.32/1.34 thf(f10,plain,(
% 0.32/1.34 ? [X3 : b > $o,X2 : b > $o] : (? [X4 : b] : (((X3 @ X4) = $true) & ? [X5 : b > $o] : (((sK1 @ X5) = $true) & ((X5 @ X4) != $true))) & ! [X6 : b] : (((X2 @ X6) != $true) | ! [X7 : b > $o] : (($true = (X7 @ X6)) | ((sK1 @ X7) != $true))) & ($true = (sK0 @ X2 @ X3))) => (? [X4 : b] : (($true = (sK3 @ X4)) & ? [X5 : b > $o] : (((sK1 @ X5) = $true) & ((X5 @ X4) != $true))) & ! [X6 : b] : (($true != (sK2 @ X6)) | ! [X7 : b > $o] : (($true = (X7 @ X6)) | ((sK1 @ X7) != $true))) & ($true = (sK0 @ sK2 @ sK3)))),
% 0.32/1.34 introduced(definition,[],[choice_axiom])).
% 0.32/1.34 thf(f11,plain,(
% 0.32/1.34 ? [X4 : b] : (($true = (sK3 @ X4)) & ? [X5 : b > $o] : (((sK1 @ X5) = $true) & ((X5 @ X4) != $true))) => (((sK3 @ sK4) = $true) & ? [X5 : b > $o] : (((sK1 @ X5) = $true) & ((X5 @ sK4) != $true)))),
% 0.32/1.34 introduced(definition,[],[choice_axiom])).
% 0.32/1.34 thf(f12,plain,(
% 0.32/1.34 ? [X5 : b > $o] : (((sK1 @ X5) = $true) & ((X5 @ sK4) != $true)) => (($true = (sK1 @ sK5)) & ((sK5 @ sK4) != $true))),
% 0.32/1.34 introduced(definition,[],[choice_axiom])).
% 0.32/1.34 thf(f13,plain,(
% 0.32/1.34 ! [X8 : b > $o,X9 : b > $o] : (? [X12 : b] : (($true != (X8 @ X12)) & ($true = (X9 @ X12))) => (($true != (X8 @ (sK6 @ X9 @ X8))) & ($true = (X9 @ (sK6 @ X9 @ X8)))))),
% 0.32/1.34 introduced(definition,[],[choice_axiom])).
% 0.32/1.34 thf(f8,plain,(
% 0.32/1.34 ? [X0 : (b > $o) > (b > $o) > $o,X1 : (b > $o) > $o] : (? [X2 : b > $o,X3 : b > $o] : (? [X4 : b] : (((X3 @ X4) = $true) & ? [X5 : b > $o] : (($true = (X1 @ X5)) & ((X5 @ X4) != $true))) & ! [X6 : b] : (((X2 @ X6) != $true) | ! [X7 : b > $o] : (($true = (X7 @ X6)) | ((X1 @ X7) != $true))) & ($true = (X0 @ X2 @ X3))) & ! [X8 : b > $o] : (($true != (X1 @ X8)) | ! [X9 : b > $o,X10 : b > $o] : (! [X11 : b] : (((X8 @ X11) = $true) | ((X10 @ X11) != $true)) | ($true != (X0 @ X9 @ X10)) | ? [X12 : b] : (($true != (X8 @ X12)) & ($true = (X9 @ X12))))))),
% 0.32/1.34 inference(rectify,[status(thm)],[f7])).
% 0.32/1.34 thf(f7,plain,(
% 0.32/1.34 ? [X0 : (b > $o) > (b > $o) > $o,X1 : (b > $o) > $o] : (? [X8 : b > $o,X7 : b > $o] : (? [X11 : b] : (($true = (X7 @ X11)) & ? [X12 : b > $o] : (((X1 @ X12) = $true) & ((X12 @ X11) != $true))) & ! [X9 : b] : (((X8 @ X9) != $true) | ! [X10 : b > $o] : (($true = (X10 @ X9)) | ($true != (X1 @ X10)))) & ((X0 @ X8 @ X7) = $true)) & ! [X2 : b > $o] : (((X1 @ X2) != $true) | ! [X3 : b > $o,X4 : b > $o] : (! [X6 : b] : (((X2 @ X6) = $true) | ($true != (X4 @ X6))) | ((X0 @ X3 @ X4) != $true) | ? [X5 : b] : (((X2 @ X5) != $true) & ((X3 @ X5) = $true)))))),
% 0.32/1.34 inference(flattening,[status(thm)],[f6])).
% 0.32/1.34 thf(f6,plain,(
% 0.32/1.34 ? [X0 : (b > $o) > (b > $o) > $o,X1 : (b > $o) > $o] : (? [X7 : b > $o,X8 : b > $o] : (? [X11 : b] : (($true = (X7 @ X11)) & ? [X12 : b > $o] : (((X1 @ X12) = $true) & ((X12 @ X11) != $true))) & (! [X9 : b] : (((X8 @ X9) != $true) | ! [X10 : b > $o] : (($true = (X10 @ X9)) | ($true != (X1 @ X10)))) & ((X0 @ X8 @ X7) = $true))) & ! [X2 : b > $o] : (! [X4 : b > $o,X3 : b > $o] : (! [X6 : b] : (((X2 @ X6) = $true) | ($true != (X4 @ X6))) | (? [X5 : b] : (((X2 @ X5) != $true) & ((X3 @ X5) = $true)) | ((X0 @ X3 @ X4) != $true))) | ((X1 @ X2) != $true)))),
% 0.32/1.34 inference(ennf_transformation,[status(thm)],[f5])).
% 0.32/1.34 thf(f5,plain,(
% 0.32/1.34 ~! [X0 : (b > $o) > (b > $o) > $o,X1 : (b > $o) > $o] : (! [X2 : b > $o] : (((X1 @ X2) = $true) => ! [X4 : b > $o,X3 : b > $o] : ((! [X5 : b] : (((X3 @ X5) = $true) => ((X2 @ X5) = $true)) & ((X0 @ X3 @ X4) = $true)) => ! [X6 : b] : (($true = (X4 @ X6)) => ((X2 @ X6) = $true)))) => ! [X7 : b > $o,X8 : b > $o] : ((! [X9 : b] : (((X8 @ X9) = $true) => ! [X10 : b > $o] : (($true = (X1 @ X10)) => ($true = (X10 @ X9)))) & ((X0 @ X8 @ X7) = $true)) => ! [X11 : b] : (($true = (X7 @ X11)) => ! [X12 : b > $o] : (((X1 @ X12) = $true) => ((X12 @ X11) = $true)))))),
% 0.32/1.34 inference(fool_elimination,[status(thm)],[f4])).
% 0.32/1.34 thf(f4,plain,(
% 0.32/1.34 ~! [X0 : (b > $o) > (b > $o) > $o,X1 : (b > $o) > $o] : (! [X2 : b > $o] : ((X1 @ X2) => ! [X3 : b > $o,X4 : b > $o] : ((! [X5 : b] : ((X3 @ X5) => (X2 @ X5)) & (X0 @ X3 @ X4)) => ! [X6 : b] : ((X4 @ X6) => (X2 @ X6)))) => ! [X7 : b > $o,X8 : b > $o] : ((! [X9 : b] : ((X8 @ X9) => ! [X10 : b > $o] : ((X1 @ X10) => (X10 @ X9))) & (X0 @ X8 @ X7)) => ! [X11 : b] : ((X7 @ X11) => ! [X12 : b > $o] : ((X1 @ X12) => (X12 @ X11)))))),
% 0.32/1.34 inference(rectify,[status(thm)],[f2])).
% 0.32/1.34 thf(f2,negated_conjecture,(
% 0.32/1.34 ~! [X0 : (b > $o) > (b > $o) > $o,X1 : (b > $o) > $o] : (! [X2 : b > $o] : ((X1 @ X2) => ! [X3 : b > $o,X4 : b > $o] : ((! [X5 : b] : ((X3 @ X5) => (X2 @ X5)) & (X0 @ X3 @ X4)) => ! [X5 : b] : ((X4 @ X5) => (X2 @ X5)))) => ! [X4 : b > $o,X3 : b > $o] : ((! [X2 : b] : ((X3 @ X2) => ! [X6 : b > $o] : ((X1 @ X6) => (X6 @ X2))) & (X0 @ X3 @ X4)) => ! [X2 : b] : ((X4 @ X2) => ! [X6 : b > $o] : ((X1 @ X6) => (X6 @ X2)))))),
% 0.32/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 0.32/1.34 thf(f1,conjecture,(
% 0.32/1.34 ! [X0 : (b > $o) > (b > $o) > $o,X1 : (b > $o) > $o] : (! [X2 : b > $o] : ((X1 @ X2) => ! [X3 : b > $o,X4 : b > $o] : ((! [X5 : b] : ((X3 @ X5) => (X2 @ X5)) & (X0 @ X3 @ X4)) => ! [X5 : b] : ((X4 @ X5) => (X2 @ X5)))) => ! [X4 : b > $o,X3 : b > $o] : ((! [X2 : b] : ((X3 @ X2) => ! [X6 : b > $o] : ((X1 @ X6) => (X6 @ X2))) & (X0 @ X3 @ X4)) => ! [X2 : b] : ((X4 @ X2) => ! [X6 : b > $o] : ((X1 @ X6) => (X6 @ X2)))))),
% 0.32/1.34 file('/export/starexec/sandbox/tmp/tmp.jnvWById1Y/DTF2THF_5436.p',cTHM565_pme)).
% 0.32/1.34 thf(f46,plain,(
% 0.32/1.34 ( ! [X0 : b > $o,X1 : b] : (($true != (sK0 @ sK2 @ X0)) | ($true = (sK5 @ X1)) | ((X0 @ X1) != $true)) ) | ~spl7_1),
% 0.32/1.34 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 0.32/1.34 thf(f45,plain,(
% 0.32/1.34 ( ! [X0 : b > $o,X1 : b] : (($true != $true) | ((X0 @ X1) != $true) | ($true = (sK5 @ X1)) | ($true != (sK0 @ sK2 @ X0))) ) | ~spl7_1),
% 0.32/1.34 inference(superposition,[status(thm)],[f44,f41])).
% 0.32/1.34 thf(f41,plain,(
% 0.32/1.34 ($true = (sK5 @ (sK6 @ sK2 @ sK5))) | ~spl7_1),
% 0.32/1.34 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 0.32/1.34 thf(f40,plain,(
% 0.32/1.34 ($true = (sK5 @ (sK6 @ sK2 @ sK5))) | ($true != $true) | ~spl7_1),
% 0.32/1.34 inference(superposition,[status(thm)],[f23,f31])).
% 0.32/1.34 thf(f31,plain,(
% 0.32/1.34 ((sK2 @ (sK6 @ sK2 @ sK5)) = $true) | ~spl7_1),
% 0.32/1.34 inference(avatar_component_clause,[status(thm)],[f29])).
% 0.32/1.34 thf(f23,plain,(
% 0.32/1.34 ( ! [X0 : b] : (($true != (sK2 @ X0)) | ((sK5 @ X0) = $true)) )),
% 0.32/1.34 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 0.32/1.34 thf(f22,plain,(
% 0.32/1.34 ( ! [X0 : b] : (($true != (sK2 @ X0)) | ($true != $true) | ((sK5 @ X0) = $true)) )),
% 0.32/1.34 inference(superposition,[status(thm)],[f18,f20])).
% 0.32/1.34 thf(f20,plain,(
% 0.32/1.34 ($true = (sK1 @ sK5))),
% 0.32/1.34 inference(cnf_transformation,[status(thm)],[f14])).
% 0.32/1.34 thf(f18,plain,(
% 0.32/1.34 ( ! [X6 : b,X7 : b > $o] : (((sK1 @ X7) != $true) | ($true != (sK2 @ X6)) | ($true = (X7 @ X6))) )),
% 0.32/1.34 inference(cnf_transformation,[status(thm)],[f14])).
% 0.32/1.34 thf(f44,plain,(
% 0.32/1.34 ( ! [X2 : b,X0 : b > $o,X1 : b > $o] : (($true != (sK5 @ (sK6 @ X0 @ sK5))) | ($true != (sK0 @ X0 @ X1)) | ($true != (X1 @ X2)) | ($true = (sK5 @ X2))) )),
% 0.32/1.34 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 0.32/1.34 thf(f43,plain,(
% 0.32/1.34 ( ! [X2 : b,X0 : b > $o,X1 : b > $o] : (($true != (sK5 @ (sK6 @ X0 @ sK5))) | ($true != (sK0 @ X0 @ X1)) | ($true = (sK5 @ X2)) | ($true != (X1 @ X2)) | ($true != $true)) )),
% 0.32/1.34 inference(superposition,[status(thm)],[f16,f20])).
% 0.32/1.34 thf(f16,plain,(
% 0.32/1.34 ( ! [X10 : b > $o,X11 : b,X8 : b > $o,X9 : b > $o] : (($true != (sK1 @ X8)) | ($true != (X8 @ (sK6 @ X9 @ X8))) | ($true != (sK0 @ X9 @ X10)) | ((X10 @ X11) != $true) | ((X8 @ X11) = $true)) )),
% 0.32/1.34 inference(cnf_transformation,[status(thm)],[f14])).
% 0.32/1.34 thf(f39,plain,(
% 0.32/1.34 ~spl7_2),
% 0.32/1.34 inference(avatar_contradiction_clause,[status(thm)],[f38])).
% 0.32/1.34 thf(f38,plain,(
% 0.32/1.34 $false | ~spl7_2),
% 0.32/1.34 inference(subsumption_resolution,[status(thm)],[f37,f19])).
% 0.32/1.34 thf(f19,plain,(
% 0.32/1.34 ((sK5 @ sK4) != $true)),
% 0.32/1.34 inference(cnf_transformation,[status(thm)],[f14])).
% 0.32/1.34 thf(f37,plain,(
% 0.32/1.34 ((sK5 @ sK4) = $true) | ~spl7_2),
% 0.32/1.34 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 0.32/1.34 thf(f36,plain,(
% 0.32/1.34 ($true != $true) | ((sK5 @ sK4) = $true) | ~spl7_2),
% 0.32/1.34 inference(superposition,[status(thm)],[f34,f21])).
% 0.32/1.34 thf(f21,plain,(
% 0.32/1.34 ((sK3 @ sK4) = $true)),
% 0.32/1.34 inference(cnf_transformation,[status(thm)],[f14])).
% 0.32/1.34 thf(f34,plain,(
% 0.32/1.34 ( ! [X0 : b] : (((sK3 @ X0) != $true) | ((sK5 @ X0) = $true)) ) | ~spl7_2),
% 0.32/1.34 inference(avatar_component_clause,[status(thm)],[f33])).
% 0.32/1.34 thf(f35,plain,(
% 0.32/1.34 spl7_1 | spl7_2),
% 0.32/1.34 inference(avatar_split_clause,[status(thm)],[f27,f33,f29])).
% 0.32/1.34 thf(f27,plain,(
% 0.32/1.34 ( ! [X0 : b] : (((sK2 @ (sK6 @ sK2 @ sK5)) = $true) | ((sK5 @ X0) = $true) | ((sK3 @ X0) != $true)) )),
% 0.32/1.34 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 0.32/1.34 thf(f26,plain,(
% 0.32/1.34 ( ! [X0 : b] : (((sK3 @ X0) != $true) | ($true != $true) | ((sK5 @ X0) = $true) | ((sK2 @ (sK6 @ sK2 @ sK5)) = $true)) )),
% 0.32/1.34 inference(superposition,[status(thm)],[f25,f17])).
% 0.32/1.34 thf(f25,plain,(
% 0.32/1.34 ( ! [X2 : b > $o,X0 : b > $o,X1 : b] : (((sK0 @ X2 @ X0) != $true) | ((X0 @ X1) != $true) | ((X2 @ (sK6 @ X2 @ sK5)) = $true) | ($true = (sK5 @ X1))) )),
% 0.32/1.34 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 0.32/1.34 thf(f24,plain,(
% 0.32/1.34 ( ! [X2 : b > $o,X0 : b > $o,X1 : b] : (((X0 @ X1) != $true) | ((sK0 @ X2 @ X0) != $true) | ($true = (sK5 @ X1)) | ((X2 @ (sK6 @ X2 @ sK5)) = $true) | ($true != $true)) )),
% 0.32/1.34 inference(superposition,[status(thm)],[f15,f20])).
% 0.32/1.34 thf(f15,plain,(
% 0.32/1.34 ( ! [X10 : b > $o,X11 : b,X8 : b > $o,X9 : b > $o] : (($true != (sK1 @ X8)) | ((X10 @ X11) != $true) | ($true = (X9 @ (sK6 @ X9 @ X8))) | ($true != (sK0 @ X9 @ X10)) | ((X8 @ X11) = $true)) )),
% 0.32/1.34 inference(cnf_transformation,[status(thm)],[f14])).
% 0.32/1.34 % SZS output end Proof for DTF2THF_5436
% 0.32/1.34 % (5631)------------------------------
% 0.32/1.34 % (5631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.34 % (5631)Termination reason: Refutation
% 0.32/1.34
% 0.32/1.34 % (5631)Memory used [KB]: 5628
% 0.32/1.34 % (5631)Time elapsed: 0.008 s
% 0.32/1.34 % (5631)Instructions burned: 8 (million)
% 0.32/1.34 % (5631)------------------------------
% 0.32/1.34 % (5631)------------------------------
% 0.32/1.34 % (5624)Success in time 0.009 s
%------------------------------------------------------------------------------