%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV126^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:21 AM UTC 2026
% Result : Theorem 1.66s 1.36s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 619 ( 216 equ; 0 cnn)
% Maximal formula atoms : 32 ( 13 avg)
% Number of connectives : 907 ( 100 ~; 103 |; 94 &; 567 @)
% ( 2 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 150 ( 150 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 211 ( 0 ^; 157 !; 54 ?; 211 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > a > $o ).
thf(func_def_5,type,
sK1: a ).
thf(func_def_6,type,
sK2: ( a > a > $o ) > $o ).
thf(func_def_7,type,
sK3: a ).
thf(func_def_8,type,
sK4: a > a > $o ).
thf(func_def_9,type,
sK5: a > a > $o ).
thf(func_def_10,type,
sK6: a > a > a > a > $o ).
thf(func_def_11,type,
sK7: a > a > a > a > $o ).
thf(func_def_12,type,
sK8: ( a > a > $o ) > a ).
thf(func_def_13,type,
sK9: ( a > a > $o ) > a ).
thf(func_def_16,type,
ph11:
!>[X0: $tType] : X0 ).
thf(f62,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f47,f54,f61]) ).
thf(f61,plain,
~ spl10_1,
inference(avatar_contradiction_clause,[status(thm)],[f60]) ).
thf(f60,plain,
( $false
| ~ spl10_1 ),
inference(subsumption_resolution,[status(thm)],[f59,f31]) ).
thf(f31,plain,
( ( sK5 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f29,f17]) ).
thf(f17,plain,
( ( sK5 @ sK3 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( sK2 @ sK5 )
= $true )
& ! [X6: a,X7: a] :
( ( ( ( sK6 @ X7 @ X6 @ X6 @ X7 )
!= $true )
& ( $true
= ( sK2 @ ( sK6 @ X7 @ X6 ) ) )
& ! [X9: a,X10: a] :
( ( $true
!= ( sK4 @ X10 @ X9 ) )
| ( $true
= ( sK6 @ X7 @ X6 @ X10 @ X9 ) ) )
& ( ( sK7 @ X7 @ X6 @ X6 @ X7 )
!= $true )
& ! [X12: a,X13: a] :
( ( ( sK0 @ X13 @ X12 )
!= $true )
| ( ( sK7 @ X7 @ X6 @ X13 @ X12 )
= $true ) )
& ( $true
= ( sK2 @ ( sK7 @ X7 @ X6 ) ) ) )
| ( ( sK5 @ X6 @ X7 )
= $true ) )
& ( ( sK5 @ sK3 @ sK1 )
!= $true )
& ! [X14: a > a > $o] :
( ( ( sK2 @ X14 )
!= $true )
| ( ( X14 @ sK3 @ sK1 )
= $true )
| ( ( ( ( sK4 @ ( sK9 @ X14 ) @ ( sK8 @ X14 ) )
= $true )
| ( ( sK0 @ ( sK9 @ X14 ) @ ( sK8 @ X14 ) )
= $true ) )
& ( ( X14 @ ( sK9 @ X14 ) @ ( sK8 @ X14 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9])],[f8,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > a > $o,X1: a,X2: ( a > a > $o ) > $o,X3: a,X4: a > a > $o] :
( ? [X5: a > a > $o] :
( ( ( X2 @ X5 )
= $true )
& ! [X6: a,X7: a] :
( ( ? [X8: a > a > $o] :
( ( ( X8 @ X6 @ X7 )
!= $true )
& ( ( X2 @ X8 )
= $true )
& ! [X9: a,X10: a] :
( ( $true
!= ( X4 @ X10 @ X9 ) )
| ( ( X8 @ X10 @ X9 )
= $true ) ) )
& ? [X11: a > a > $o] :
( ( ( X11 @ X6 @ X7 )
!= $true )
& ! [X12: a,X13: a] :
( ( $true
!= ( X0 @ X13 @ X12 ) )
| ( ( X11 @ X13 @ X12 )
= $true ) )
& ( ( X2 @ X11 )
= $true ) ) )
| ( ( X5 @ X6 @ X7 )
= $true ) )
& ( ( X5 @ X3 @ X1 )
!= $true ) )
& ! [X14: a > a > $o] :
( ( $true
!= ( X2 @ X14 ) )
| ( $true
= ( X14 @ X3 @ X1 ) )
| ? [X15: a,X16: a] :
( ( ( $true
= ( X4 @ X16 @ X15 ) )
| ( ( X0 @ X16 @ X15 )
= $true ) )
& ( $true
!= ( X14 @ X16 @ X15 ) ) ) ) )
=> ( ? [X5: a > a > $o] :
( ( ( sK2 @ X5 )
= $true )
& ! [X7: a,X6: a] :
( ( ? [X8: a > a > $o] :
( ( ( X8 @ X6 @ X7 )
!= $true )
& ( ( sK2 @ X8 )
= $true )
& ! [X10: a,X9: a] :
( ( $true
!= ( sK4 @ X10 @ X9 ) )
| ( ( X8 @ X10 @ X9 )
= $true ) ) )
& ? [X11: a > a > $o] :
( ( ( X11 @ X6 @ X7 )
!= $true )
& ! [X13: a,X12: a] :
( ( ( sK0 @ X13 @ X12 )
!= $true )
| ( ( X11 @ X13 @ X12 )
= $true ) )
& ( $true
= ( sK2 @ X11 ) ) ) )
| ( ( X5 @ X6 @ X7 )
= $true ) )
& ( $true
!= ( X5 @ sK3 @ sK1 ) ) )
& ! [X14: a > a > $o] :
( ( ( sK2 @ X14 )
!= $true )
| ( ( X14 @ sK3 @ sK1 )
= $true )
| ? [X16: a,X15: a] :
( ( ( ( sK4 @ X16 @ X15 )
= $true )
| ( ( sK0 @ X16 @ X15 )
= $true ) )
& ( $true
!= ( X14 @ X16 @ X15 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X5: a > a > $o] :
( ( ( sK2 @ X5 )
= $true )
& ! [X7: a,X6: a] :
( ( ? [X8: a > a > $o] :
( ( ( X8 @ X6 @ X7 )
!= $true )
& ( ( sK2 @ X8 )
= $true )
& ! [X10: a,X9: a] :
( ( $true
!= ( sK4 @ X10 @ X9 ) )
| ( ( X8 @ X10 @ X9 )
= $true ) ) )
& ? [X11: a > a > $o] :
( ( ( X11 @ X6 @ X7 )
!= $true )
& ! [X13: a,X12: a] :
( ( ( sK0 @ X13 @ X12 )
!= $true )
| ( ( X11 @ X13 @ X12 )
= $true ) )
& ( $true
= ( sK2 @ X11 ) ) ) )
| ( ( X5 @ X6 @ X7 )
= $true ) )
& ( $true
!= ( X5 @ sK3 @ sK1 ) ) )
=> ( ( ( sK2 @ sK5 )
= $true )
& ! [X7: a,X6: a] :
( ( ? [X8: a > a > $o] :
( ( ( X8 @ X6 @ X7 )
!= $true )
& ( ( sK2 @ X8 )
= $true )
& ! [X10: a,X9: a] :
( ( $true
!= ( sK4 @ X10 @ X9 ) )
| ( ( X8 @ X10 @ X9 )
= $true ) ) )
& ? [X11: a > a > $o] :
( ( ( X11 @ X6 @ X7 )
!= $true )
& ! [X13: a,X12: a] :
( ( ( sK0 @ X13 @ X12 )
!= $true )
| ( ( X11 @ X13 @ X12 )
= $true ) )
& ( $true
= ( sK2 @ X11 ) ) ) )
| ( ( sK5 @ X6 @ X7 )
= $true ) )
& ( ( sK5 @ sK3 @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X6: a,X7: a] :
( ? [X8: a > a > $o] :
( ( ( X8 @ X6 @ X7 )
!= $true )
& ( ( sK2 @ X8 )
= $true )
& ! [X10: a,X9: a] :
( ( $true
!= ( sK4 @ X10 @ X9 ) )
| ( ( X8 @ X10 @ X9 )
= $true ) ) )
=> ( ( ( sK6 @ X7 @ X6 @ X6 @ X7 )
!= $true )
& ( $true
= ( sK2 @ ( sK6 @ X7 @ X6 ) ) )
& ! [X10: a,X9: a] :
( ( $true
!= ( sK4 @ X10 @ X9 ) )
| ( $true
= ( sK6 @ X7 @ X6 @ X10 @ X9 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X6: a,X7: a] :
( ? [X11: a > a > $o] :
( ( ( X11 @ X6 @ X7 )
!= $true )
& ! [X13: a,X12: a] :
( ( ( sK0 @ X13 @ X12 )
!= $true )
| ( ( X11 @ X13 @ X12 )
= $true ) )
& ( $true
= ( sK2 @ X11 ) ) )
=> ( ( ( sK7 @ X7 @ X6 @ X6 @ X7 )
!= $true )
& ! [X13: a,X12: a] :
( ( ( sK0 @ X13 @ X12 )
!= $true )
| ( ( sK7 @ X7 @ X6 @ X13 @ X12 )
= $true ) )
& ( $true
= ( sK2 @ ( sK7 @ X7 @ X6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X14: a > a > $o] :
( ? [X16: a,X15: a] :
( ( ( ( sK4 @ X16 @ X15 )
= $true )
| ( ( sK0 @ X16 @ X15 )
= $true ) )
& ( $true
!= ( X14 @ X16 @ X15 ) ) )
=> ( ( ( ( sK4 @ ( sK9 @ X14 ) @ ( sK8 @ X14 ) )
= $true )
| ( ( sK0 @ ( sK9 @ X14 ) @ ( sK8 @ X14 ) )
= $true ) )
& ( ( X14 @ ( sK9 @ X14 ) @ ( sK8 @ X14 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > a > $o,X1: a,X2: ( a > a > $o ) > $o,X3: a,X4: a > a > $o] :
( ? [X5: a > a > $o] :
( ( ( X2 @ X5 )
= $true )
& ! [X6: a,X7: a] :
( ( ? [X8: a > a > $o] :
( ( ( X8 @ X6 @ X7 )
!= $true )
& ( ( X2 @ X8 )
= $true )
& ! [X9: a,X10: a] :
( ( $true
!= ( X4 @ X10 @ X9 ) )
| ( ( X8 @ X10 @ X9 )
= $true ) ) )
& ? [X11: a > a > $o] :
( ( ( X11 @ X6 @ X7 )
!= $true )
& ! [X12: a,X13: a] :
( ( $true
!= ( X0 @ X13 @ X12 ) )
| ( ( X11 @ X13 @ X12 )
= $true ) )
& ( ( X2 @ X11 )
= $true ) ) )
| ( ( X5 @ X6 @ X7 )
= $true ) )
& ( ( X5 @ X3 @ X1 )
!= $true ) )
& ! [X14: a > a > $o] :
( ( $true
!= ( X2 @ X14 ) )
| ( $true
= ( X14 @ X3 @ X1 ) )
| ? [X15: a,X16: a] :
( ( ( $true
= ( X4 @ X16 @ X15 ) )
| ( ( X0 @ X16 @ X15 )
= $true ) )
& ( $true
!= ( X14 @ X16 @ X15 ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X2: a > a > $o,X0: a,X3: ( a > a > $o ) > $o,X4: a,X1: a > a > $o] :
( ? [X8: a > a > $o] :
( ( $true
= ( X3 @ X8 ) )
& ! [X9: a,X10: a] :
( ( ? [X14: a > a > $o] :
( ( ( X14 @ X9 @ X10 )
!= $true )
& ( $true
= ( X3 @ X14 ) )
& ! [X16: a,X15: a] :
( ( $true
!= ( X1 @ X15 @ X16 ) )
| ( $true
= ( X14 @ X15 @ X16 ) ) ) )
& ? [X11: a > a > $o] :
( ( ( X11 @ X9 @ X10 )
!= $true )
& ! [X13: a,X12: a] :
( ( ( X2 @ X12 @ X13 )
!= $true )
| ( $true
= ( X11 @ X12 @ X13 ) ) )
& ( ( X3 @ X11 )
= $true ) ) )
| ( ( X8 @ X9 @ X10 )
= $true ) )
& ( ( X8 @ X4 @ X0 )
!= $true ) )
& ! [X5: a > a > $o] :
( ( ( X3 @ X5 )
!= $true )
| ( ( X5 @ X4 @ X0 )
= $true )
| ? [X6: a,X7: a] :
( ( ( ( X1 @ X7 @ X6 )
= $true )
| ( ( X2 @ X7 @ X6 )
= $true ) )
& ( ( X5 @ X7 @ X6 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: a > a > $o,X0: a,X2: a > a > $o,X4: a,X3: ( a > a > $o ) > $o] :
( ? [X8: a > a > $o] :
( ( ( X8 @ X4 @ X0 )
!= $true )
& ( $true
= ( X3 @ X8 ) )
& ! [X9: a,X10: a] :
( ( ( X8 @ X9 @ X10 )
= $true )
| ( ? [X11: a > a > $o] :
( ( ( X11 @ X9 @ X10 )
!= $true )
& ( ( X3 @ X11 )
= $true )
& ! [X13: a,X12: a] :
( ( ( X2 @ X12 @ X13 )
!= $true )
| ( $true
= ( X11 @ X12 @ X13 ) ) ) )
& ? [X14: a > a > $o] :
( ( ( X14 @ X9 @ X10 )
!= $true )
& ! [X16: a,X15: a] :
( ( $true
!= ( X1 @ X15 @ X16 ) )
| ( $true
= ( X14 @ X15 @ X16 ) ) )
& ( $true
= ( X3 @ X14 ) ) ) ) ) )
& ! [X5: a > a > $o] :
( ( ( X5 @ X4 @ X0 )
= $true )
| ( ( X3 @ X5 )
!= $true )
| ? [X6: a,X7: a] :
( ( ( ( X1 @ X7 @ X6 )
= $true )
| ( ( X2 @ X7 @ X6 )
= $true ) )
& ( ( X5 @ X7 @ X6 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: a > a > $o,X0: a,X2: a > a > $o,X4: a,X3: ( a > a > $o ) > $o] :
( ! [X5: a > a > $o] :
( ( ( ( X3 @ X5 )
= $true )
& ! [X6: a,X7: a] :
( ( ( ( X1 @ X7 @ X6 )
= $true )
| ( ( X2 @ X7 @ X6 )
= $true ) )
=> ( ( X5 @ X7 @ X6 )
= $true ) ) )
=> ( ( X5 @ X4 @ X0 )
= $true ) )
=> ! [X8: a > a > $o] :
( ( ( $true
= ( X3 @ X8 ) )
& ! [X9: a,X10: a] :
( ( ! [X11: a > a > $o] :
( ( ( ( X3 @ X11 )
= $true )
& ! [X13: a,X12: a] :
( ( ( X2 @ X12 @ X13 )
= $true )
=> ( $true
= ( X11 @ X12 @ X13 ) ) ) )
=> ( ( X11 @ X9 @ X10 )
= $true ) )
| ! [X14: a > a > $o] :
( ( ! [X16: a,X15: a] :
( ( $true
= ( X1 @ X15 @ X16 ) )
=> ( $true
= ( X14 @ X15 @ X16 ) ) )
& ( $true
= ( X3 @ X14 ) ) )
=> ( ( X14 @ X9 @ X10 )
= $true ) ) )
=> ( ( X8 @ X9 @ X10 )
= $true ) ) )
=> ( ( X8 @ X4 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > a > $o,X2: a > a > $o,X3: ( a > a > $o ) > $o,X4: a] :
( ! [X5: a > a > $o] :
( ( ( X3 @ X5 )
& ! [X6: a,X7: a] :
( ( ( X2 @ X7 @ X6 )
| ( X1 @ X7 @ X6 ) )
=> ( X5 @ X7 @ X6 ) ) )
=> ( X5 @ X4 @ X0 ) )
=> ! [X8: a > a > $o] :
( ( ( X3 @ X8 )
& ! [X9: a,X10: a] :
( ( ! [X11: a > a > $o] :
( ( ! [X12: a,X13: a] :
( ( X2 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
& ( X3 @ X11 ) )
=> ( X11 @ X9 @ X10 ) )
| ! [X14: a > a > $o] :
( ( ! [X15: a,X16: a] :
( ( X1 @ X15 @ X16 )
=> ( X14 @ X15 @ X16 ) )
& ( X3 @ X14 ) )
=> ( X14 @ X9 @ X10 ) ) )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X4 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X4: a,X1: a > a > $o,X2: a > a > $o,X0: ( a > a > $o ) > $o,X3: a] :
( ! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X7: a,X6: a] :
( ( ( X2 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X6: a,X7: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) )
| ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X4: a,X1: a > a > $o,X2: a > a > $o,X0: ( a > a > $o ) > $o,X3: a] :
( ! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X7: a,X6: a] :
( ( ( X2 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X6: a,X7: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) )
| ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.c5Yfx2KjUO/DTF2THF_23422.p',cTHM252B_pme) ).
thf(f29,plain,
( ( ( sK5 @ sK3 @ sK1 )
= $true )
| ( ( sK5 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( sK5 @ sK3 @ sK1 )
= $true )
| ( $true != $true )
| ( ( sK5 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f15,f24]) ).
thf(f24,plain,
( ( sK2 @ sK5 )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f15,plain,
! [X14: a > a > $o] :
( ( ( sK2 @ X14 )
!= $true )
| ( ( X14 @ sK3 @ sK1 )
= $true )
| ( ( X14 @ ( sK9 @ X14 ) @ ( sK8 @ X14 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f59,plain,
( ( ( sK5 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) )
= $true )
| ~ spl10_1 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $true != $true )
| ( ( sK5 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) )
= $true )
| ~ spl10_1 ),
inference(duplicate_literal_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( sK5 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) )
= $true )
| ( $true != $true )
| ( ( sK5 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) )
= $true )
| ~ spl10_1 ),
inference(superposition,[status(thm)],[f23,f56]) ).
thf(f56,plain,
( ! [X0: a,X1: a] :
( ( $true
= ( sK6 @ X0 @ X1 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) )
| ( ( sK5 @ X1 @ X0 )
= $true ) )
| ~ spl10_1 ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( ( sK5 @ X1 @ X0 )
= $true )
| ( $true
= ( sK6 @ X0 @ X1 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) ) )
| ~ spl10_1 ),
inference(superposition,[status(thm)],[f21,f42]) ).
thf(f42,plain,
( ( $true
= ( sK4 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) )
| ~ spl10_1 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl10_1
<=> ( $true
= ( sK4 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition]) ).
thf(f21,plain,
! [X10: a,X6: a,X9: a,X7: a] :
( ( $true
!= ( sK4 @ X10 @ X9 ) )
| ( $true
= ( sK6 @ X7 @ X6 @ X10 @ X9 ) )
| ( ( sK5 @ X6 @ X7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f23,plain,
! [X6: a,X7: a] :
( ( ( sK6 @ X7 @ X6 @ X6 @ X7 )
!= $true )
| ( ( sK5 @ X6 @ X7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f54,plain,
~ spl10_2,
inference(avatar_contradiction_clause,[status(thm)],[f53]) ).
thf(f53,plain,
( $false
| ~ spl10_2 ),
inference(subsumption_resolution,[status(thm)],[f52,f31]) ).
thf(f52,plain,
( ( ( sK5 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) )
= $true )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true != $true )
| ( ( sK5 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) )
= $true )
| ~ spl10_2 ),
inference(duplicate_literal_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( sK5 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) )
= $true )
| ( ( sK5 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) )
= $true )
| ( $true != $true )
| ~ spl10_2 ),
inference(superposition,[status(thm)],[f20,f49]) ).
thf(f49,plain,
( ! [X0: a,X1: a] :
( ( $true
= ( sK7 @ X0 @ X1 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) )
| ( ( sK5 @ X1 @ X0 )
= $true ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true
= ( sK7 @ X0 @ X1 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) )
| ( ( sK5 @ X1 @ X0 )
= $true ) )
| ~ spl10_2 ),
inference(superposition,[status(thm)],[f19,f46]) ).
thf(f46,plain,
( ( $true
= ( sK0 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl10_2
<=> ( $true
= ( sK0 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition]) ).
thf(f19,plain,
! [X6: a,X7: a,X12: a,X13: a] :
( ( ( sK0 @ X13 @ X12 )
!= $true )
| ( ( sK7 @ X7 @ X6 @ X13 @ X12 )
= $true )
| ( ( sK5 @ X6 @ X7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f20,plain,
! [X6: a,X7: a] :
( ( ( sK7 @ X7 @ X6 @ X6 @ X7 )
!= $true )
| ( ( sK5 @ X6 @ X7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f47,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[status(thm)],[f38,f44,f40]) ).
thf(f38,plain,
( ( $true
= ( sK4 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) )
| ( $true
= ( sK0 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f35,f17]) ).
thf(f35,plain,
( ( $true
= ( sK4 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) )
| ( ( sK5 @ sK3 @ sK1 )
= $true )
| ( $true
= ( sK0 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( sK5 @ sK3 @ sK1 )
= $true )
| ( $true
= ( sK4 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) )
| ( $true
= ( sK0 @ ( sK9 @ sK5 ) @ ( sK8 @ sK5 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f16,f24]) ).
thf(f16,plain,
! [X14: a > a > $o] :
( ( ( sK2 @ X14 )
!= $true )
| ( ( sK0 @ ( sK9 @ X14 ) @ ( sK8 @ X14 ) )
= $true )
| ( ( X14 @ sK3 @ sK1 )
= $true )
| ( ( sK4 @ ( sK9 @ X14 ) @ ( sK8 @ X14 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV126^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n009.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:40:40 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEV126^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Set Theory (Relations)
% 0.31/0.46 % Problem : TPS problem from SETS-OF-RELNS-THMS
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_1091 [Bro09]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.2.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.00 v4.1.0, 0.33 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.31/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.31/0.46 % Number of connectives : 43 ( 0 ~; 2 |; 4 &; 28 @)
% 0.31/0.46 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 22 ( 22 avg)
% 0.31/0.46 % Number of types : 2 ( 1 usr)
% 0.31/0.46 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.31/0.46 % Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% 0.31/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(a_type,type,
% 0.31/0.46 a: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(cTHM252B_pme,conjecture,
% 0.31/0.46 ! [P: ( a > a > $o ) > $o,R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.31/0.46 ( ! [Xp: a > a > $o] :
% 0.31/0.46 ( ( ! [Xx0: a,Xy0: a] :
% 0.31/0.46 ( ( ( R @ Xx0 @ Xy0 )
% 0.31/0.46 | ( S @ Xx0 @ Xy0 ) )
% 0.31/0.46 => ( Xp @ Xx0 @ Xy0 ) )
% 0.31/0.46 & ( P @ Xp ) )
% 0.31/0.46 => ( Xp @ Xx @ Xy ) )
% 0.31/0.46 => ! [Xp: a > a > $o] :
% 0.31/0.46 ( ( ! [Xx0: a,Xy0: a] :
% 0.31/0.46 ( ( ! [Xp0: a > a > $o] :
% 0.31/0.46 ( ( ! [Xx1: a,Xy1: a] :
% 0.31/0.46 ( ( R @ Xx1 @ Xy1 )
% 0.31/0.46 => ( Xp0 @ Xx1 @ Xy1 ) )
% 0.31/0.46 & ( P @ Xp0 ) )
% 0.31/0.46 => ( Xp0 @ Xx0 @ Xy0 ) )
% 0.31/0.46 | ! [Xp0: a > a > $o] :
% 0.31/0.46 ( ( ! [Xx1: a,Xy1: a] :
% 0.31/0.46 ( ( S @ Xx1 @ Xy1 )
% 0.31/0.46 => ( Xp0 @ Xx1 @ Xy1 ) )
% 0.31/0.46 & ( P @ Xp0 ) )
% 0.31/0.46 => ( Xp0 @ Xx0 @ Xy0 ) ) )
% 0.31/0.46 => ( Xp @ Xx0 @ Xy0 ) )
% 0.31/0.46 & ( P @ Xp ) )
% 0.31/0.46 => ( Xp @ Xx @ Xy ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.66/1.32 ---- Embedded in THF ---
% 1.66/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.32 %%% Generated on Tue Feb 24 12:40:41 EST 2026
% 1.66/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.32 %%% Logic specification used:
% 1.66/1.32 %%% thf(spec, logic, $$dhol).
% 1.66/1.32
% 1.66/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.c5Yfx2KjUO/DTF2DTF23422.p
% See solution above
% 1.66/1.32 ------------------------
% 1.66/1.33 ---- Cleaned THF ---
% 1.66/1.33 thf(a_type,type,
% 1.66/1.33 a: $tType ).
% 1.66/1.33
% 1.66/1.33 thf(cTHM252B_pme,conjecture,
% 1.66/1.33 ! [P: ( a > a > $o ) > $o,R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 1.66/1.33 ( ! [Xp: a > a > $o] :
% 1.66/1.33 ( ( ! [Xx0: a,Xy0: a] :
% 1.66/1.33 ( ( ( R @ Xx0 @ Xy0 )
% 1.66/1.33 | ( S @ Xx0 @ Xy0 ) )
% 1.66/1.33 => ( Xp @ Xx0 @ Xy0 ) )
% 1.66/1.33 & ( P @ Xp ) )
% 1.66/1.33 => ( Xp @ Xx @ Xy ) )
% 1.66/1.33 => ! [Xp: a > a > $o] :
% 1.66/1.33 ( ( ! [Xx0: a,Xy0: a] :
% 1.66/1.33 ( ( ! [Xp0: a > a > $o] :
% 1.66/1.33 ( ( ! [Xx1: a,Xy1: a] :
% 1.66/1.33 ( ( R @ Xx1 @ Xy1 )
% 1.66/1.33 => ( Xp0 @ Xx1 @ Xy1 ) )
% 1.66/1.33 & ( P @ Xp0 ) )
% 1.66/1.33 => ( Xp0 @ Xx0 @ Xy0 ) )
% 1.66/1.33 | ! [Xp0: a > a > $o] :
% 1.66/1.33 ( ( ! [Xx1: a,Xy1: a] :
% 1.66/1.33 ( ( S @ Xx1 @ Xy1 )
% 1.66/1.33 => ( Xp0 @ Xx1 @ Xy1 ) )
% 1.66/1.33 & ( P @ Xp0 ) )
% 1.66/1.33 => ( Xp0 @ Xx0 @ Xy0 ) ) )
% 1.66/1.33 => ( Xp @ Xx0 @ Xy0 ) )
% 1.66/1.33 & ( P @ Xp ) )
% 1.66/1.33 => ( Xp @ Xx @ Xy ) ) ) ).
% 1.66/1.33 ------------------------
% 1.66/1.34 % (23609)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23422 for (2999ds/183Mi)
% 1.66/1.35 % (23611)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_23422 for (2999ds/27Mi)
% 1.66/1.35 % (23610)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_23422 for (2999ds/4Mi)
% 1.66/1.35 % (23613)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_23422 for (2999ds/2Mi)
% 1.66/1.35 % (23612)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23422 for (2999ds/2Mi)
% 1.66/1.35 % (23614)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_23422 for (2999ds/275Mi)
% 1.66/1.35 % (23615)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23422 for (2999ds/18Mi)
% 1.66/1.35 % (23612)Instruction limit reached!
% 1.66/1.35 % (23612)------------------------------
% 1.66/1.35 % (23612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (23612)Termination reason: Unknown
% 1.66/1.35 % (23612)Termination phase: Preprocessing 3
% 1.66/1.35
% 1.66/1.35 % (23612)Memory used [KB]: 895
% 1.66/1.35 % (23612)Time elapsed: 0.003 s
% 1.66/1.35 % (23612)Instructions burned: 2 (million)
% 1.66/1.35 % (23612)------------------------------
% 1.66/1.35 % (23612)------------------------------
% 1.66/1.35 % (23613)Instruction limit reached!
% 1.66/1.35 % (23613)------------------------------
% 1.66/1.35 % (23613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (23613)Termination reason: Unknown
% 1.66/1.35 % (23613)Termination phase: Property scanning
% 1.66/1.35
% 1.66/1.35 % (23613)Memory used [KB]: 1023
% 1.66/1.35 % (23613)Time elapsed: 0.003 s
% 1.66/1.35 % (23613)Instructions burned: 2 (million)
% 1.66/1.35 % (23613)------------------------------
% 1.66/1.35 % (23613)------------------------------
% 1.66/1.35 % (23610)Instruction limit reached!
% 1.66/1.35 % (23610)------------------------------
% 1.66/1.35 % (23610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (23610)Termination reason: Unknown
% 1.66/1.35 % (23610)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (23610)Memory used [KB]: 5500
% 1.66/1.35 % (23610)Time elapsed: 0.005 s
% 1.66/1.35 % (23610)Instructions burned: 5 (million)
% 1.66/1.35 % (23610)------------------------------
% 1.66/1.35 % (23610)------------------------------
% 1.66/1.36 % (23615)First to succeed.
% 1.66/1.36 % (23611)Also succeeded, but the first one will report.
% 1.66/1.36 % (23614)Also succeeded, but the first one will report.
% 1.66/1.36 % (23615)Refutation found. Thanks to Tanya!
% 1.66/1.36 % SZS status Theorem for DTF2THF_23422
% 1.66/1.36 % SZS output start Proof for DTF2THF_23422
% 1.66/1.36 thf(type_def_5, type, a: $tType).
% 1.66/1.36 thf(func_def_0, type, a: $tType).
% 1.66/1.36 thf(func_def_4, type, sK0: a > a > $o).
% 1.66/1.36 thf(func_def_5, type, sK1: a).
% 1.66/1.36 thf(func_def_6, type, sK2: (a > a > $o) > $o).
% 1.66/1.36 thf(func_def_7, type, sK3: a).
% 1.66/1.36 thf(func_def_8, type, sK4: a > a > $o).
% 1.66/1.36 thf(func_def_9, type, sK5: a > a > $o).
% 1.66/1.36 thf(func_def_10, type, sK6: a > a > a > a > $o).
% 1.66/1.36 thf(func_def_11, type, sK7: a > a > a > a > $o).
% 1.66/1.36 thf(func_def_12, type, sK8: (a > a > $o) > a).
% 1.66/1.36 thf(func_def_13, type, sK9: (a > a > $o) > a).
% 1.66/1.36 thf(func_def_16, type, ph11: !>[X0: $tType]:(X0)).
% 1.66/1.36 thf(f62,plain,(
% 1.66/1.36 $false),
% 1.66/1.36 inference(avatar_sat_refutation,[status(thm)],[f47,f54,f61])).
% 1.66/1.36 thf(f61,plain,(
% 1.66/1.36 ~spl10_1),
% 1.66/1.36 inference(avatar_contradiction_clause,[status(thm)],[f60])).
% 1.66/1.36 thf(f60,plain,(
% 1.66/1.36 $false | ~spl10_1),
% 1.66/1.36 inference(subsumption_resolution,[status(thm)],[f59,f31])).
% 1.66/1.36 thf(f31,plain,(
% 1.66/1.36 ((sK5 @ (sK9 @ sK5) @ (sK8 @ sK5)) != $true)),
% 1.66/1.36 inference(subsumption_resolution,[status(thm)],[f29,f17])).
% 1.66/1.36 thf(f17,plain,(
% 1.66/1.36 ((sK5 @ sK3 @ sK1) != $true)),
% 1.66/1.36 inference(cnf_transformation,[status(thm)],[f14])).
% 1.66/1.36 thf(f14,plain,(
% 1.66/1.36 (((sK2 @ sK5) = $true) & ! [X6 : a,X7 : a] : (((((sK6 @ X7 @ X6 @ X6 @ X7) != $true) & ($true = (sK2 @ (sK6 @ X7 @ X6))) & ! [X9 : a,X10 : a] : (($true != (sK4 @ X10 @ X9)) | ($true = (sK6 @ X7 @ X6 @ X10 @ X9)))) & (((sK7 @ X7 @ X6 @ X6 @ X7) != $true) & ! [X12 : a,X13 : a] : (((sK0 @ X13 @ X12) != $true) | ((sK7 @ X7 @ X6 @ X13 @ X12) = $true)) & ($true = (sK2 @ (sK7 @ X7 @ X6))))) | ((sK5 @ X6 @ X7) = $true)) & ((sK5 @ sK3 @ sK1) != $true)) & ! [X14 : a > a > $o] : (((sK2 @ X14) != $true) | ((X14 @ sK3 @ sK1) = $true) | ((((sK4 @ (sK9 @ X14) @ (sK8 @ X14)) = $true) | ((sK0 @ (sK9 @ X14) @ (sK8 @ X14)) = $true)) & ((X14 @ (sK9 @ X14) @ (sK8 @ X14)) != $true)))),
% 1.66/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9])],[f8,f13,f12,f11,f10,f9])).
% 1.66/1.36 thf(f9,plain,(
% 1.66/1.36 ? [X0 : a > a > $o,X1 : a,X2 : (a > a > $o) > $o,X3 : a,X4 : a > a > $o] : (? [X5 : a > a > $o] : (((X2 @ X5) = $true) & ! [X6 : a,X7 : a] : ((? [X8 : a > a > $o] : (((X8 @ X6 @ X7) != $true) & ((X2 @ X8) = $true) & ! [X9 : a,X10 : a] : (($true != (X4 @ X10 @ X9)) | ((X8 @ X10 @ X9) = $true))) & ? [X11 : a > a > $o] : (((X11 @ X6 @ X7) != $true) & ! [X12 : a,X13 : a] : (($true != (X0 @ X13 @ X12)) | ((X11 @ X13 @ X12) = $true)) & ((X2 @ X11) = $true))) | ((X5 @ X6 @ X7) = $true)) & ((X5 @ X3 @ X1) != $true)) & ! [X14 : a > a > $o] : (($true != (X2 @ X14)) | ($true = (X14 @ X3 @ X1)) | ? [X15 : a,X16 : a] : ((($true = (X4 @ X16 @ X15)) | ((X0 @ X16 @ X15) = $true)) & ($true != (X14 @ X16 @ X15))))) => (? [X5 : a > a > $o] : (((sK2 @ X5) = $true) & ! [X7 : a,X6 : a] : ((? [X8 : a > a > $o] : (((X8 @ X6 @ X7) != $true) & ((sK2 @ X8) = $true) & ! [X10 : a,X9 : a] : (($true != (sK4 @ X10 @ X9)) | ((X8 @ X10 @ X9) = $true))) & ? [X11 : a > a > $o] : (((X11 @ X6 @ X7) != $true) & ! [X13 : a,X12 : a] : (((sK0 @ X13 @ X12) != $true) | ((X11 @ X13 @ X12) = $true)) & ($true = (sK2 @ X11)))) | ((X5 @ X6 @ X7) = $true)) & ($true != (X5 @ sK3 @ sK1))) & ! [X14 : a > a > $o] : (((sK2 @ X14) != $true) | ((X14 @ sK3 @ sK1) = $true) | ? [X16 : a,X15 : a] : ((((sK4 @ X16 @ X15) = $true) | ((sK0 @ X16 @ X15) = $true)) & ($true != (X14 @ X16 @ X15)))))),
% 1.66/1.36 introduced(definition,[],[choice_axiom])).
% 1.66/1.36 thf(f10,plain,(
% 1.66/1.36 ? [X5 : a > a > $o] : (((sK2 @ X5) = $true) & ! [X7 : a,X6 : a] : ((? [X8 : a > a > $o] : (((X8 @ X6 @ X7) != $true) & ((sK2 @ X8) = $true) & ! [X10 : a,X9 : a] : (($true != (sK4 @ X10 @ X9)) | ((X8 @ X10 @ X9) = $true))) & ? [X11 : a > a > $o] : (((X11 @ X6 @ X7) != $true) & ! [X13 : a,X12 : a] : (((sK0 @ X13 @ X12) != $true) | ((X11 @ X13 @ X12) = $true)) & ($true = (sK2 @ X11)))) | ((X5 @ X6 @ X7) = $true)) & ($true != (X5 @ sK3 @ sK1))) => (((sK2 @ sK5) = $true) & ! [X7 : a,X6 : a] : ((? [X8 : a > a > $o] : (((X8 @ X6 @ X7) != $true) & ((sK2 @ X8) = $true) & ! [X10 : a,X9 : a] : (($true != (sK4 @ X10 @ X9)) | ((X8 @ X10 @ X9) = $true))) & ? [X11 : a > a > $o] : (((X11 @ X6 @ X7) != $true) & ! [X13 : a,X12 : a] : (((sK0 @ X13 @ X12) != $true) | ((X11 @ X13 @ X12) = $true)) & ($true = (sK2 @ X11)))) | ((sK5 @ X6 @ X7) = $true)) & ((sK5 @ sK3 @ sK1) != $true))),
% 1.66/1.36 introduced(definition,[],[choice_axiom])).
% 1.66/1.36 thf(f11,plain,(
% 1.66/1.36 ! [X6 : a,X7 : a] : (? [X8 : a > a > $o] : (((X8 @ X6 @ X7) != $true) & ((sK2 @ X8) = $true) & ! [X10 : a,X9 : a] : (($true != (sK4 @ X10 @ X9)) | ((X8 @ X10 @ X9) = $true))) => (((sK6 @ X7 @ X6 @ X6 @ X7) != $true) & ($true = (sK2 @ (sK6 @ X7 @ X6))) & ! [X10 : a,X9 : a] : (($true != (sK4 @ X10 @ X9)) | ($true = (sK6 @ X7 @ X6 @ X10 @ X9)))))),
% 1.66/1.36 introduced(definition,[],[choice_axiom])).
% 1.66/1.36 thf(f12,plain,(
% 1.66/1.36 ! [X6 : a,X7 : a] : (? [X11 : a > a > $o] : (((X11 @ X6 @ X7) != $true) & ! [X13 : a,X12 : a] : (((sK0 @ X13 @ X12) != $true) | ((X11 @ X13 @ X12) = $true)) & ($true = (sK2 @ X11))) => (((sK7 @ X7 @ X6 @ X6 @ X7) != $true) & ! [X13 : a,X12 : a] : (((sK0 @ X13 @ X12) != $true) | ((sK7 @ X7 @ X6 @ X13 @ X12) = $true)) & ($true = (sK2 @ (sK7 @ X7 @ X6)))))),
% 1.66/1.36 introduced(definition,[],[choice_axiom])).
% 1.66/1.36 thf(f13,plain,(
% 1.66/1.36 ! [X14 : a > a > $o] : (? [X16 : a,X15 : a] : ((((sK4 @ X16 @ X15) = $true) | ((sK0 @ X16 @ X15) = $true)) & ($true != (X14 @ X16 @ X15))) => ((((sK4 @ (sK9 @ X14) @ (sK8 @ X14)) = $true) | ((sK0 @ (sK9 @ X14) @ (sK8 @ X14)) = $true)) & ((X14 @ (sK9 @ X14) @ (sK8 @ X14)) != $true)))),
% 1.66/1.36 introduced(definition,[],[choice_axiom])).
% 1.66/1.36 thf(f8,plain,(
% 1.66/1.36 ? [X0 : a > a > $o,X1 : a,X2 : (a > a > $o) > $o,X3 : a,X4 : a > a > $o] : (? [X5 : a > a > $o] : (((X2 @ X5) = $true) & ! [X6 : a,X7 : a] : ((? [X8 : a > a > $o] : (((X8 @ X6 @ X7) != $true) & ((X2 @ X8) = $true) & ! [X9 : a,X10 : a] : (($true != (X4 @ X10 @ X9)) | ((X8 @ X10 @ X9) = $true))) & ? [X11 : a > a > $o] : (((X11 @ X6 @ X7) != $true) & ! [X12 : a,X13 : a] : (($true != (X0 @ X13 @ X12)) | ((X11 @ X13 @ X12) = $true)) & ((X2 @ X11) = $true))) | ((X5 @ X6 @ X7) = $true)) & ((X5 @ X3 @ X1) != $true)) & ! [X14 : a > a > $o] : (($true != (X2 @ X14)) | ($true = (X14 @ X3 @ X1)) | ? [X15 : a,X16 : a] : ((($true = (X4 @ X16 @ X15)) | ((X0 @ X16 @ X15) = $true)) & ($true != (X14 @ X16 @ X15)))))),
% 1.66/1.36 inference(rectify,[status(thm)],[f7])).
% 1.66/1.36 thf(f7,plain,(
% 1.66/1.36 ? [X2 : a > a > $o,X0 : a,X3 : (a > a > $o) > $o,X4 : a,X1 : a > a > $o] : (? [X8 : a > a > $o] : (($true = (X3 @ X8)) & ! [X9 : a,X10 : a] : ((? [X14 : a > a > $o] : (((X14 @ X9 @ X10) != $true) & ($true = (X3 @ X14)) & ! [X16 : a,X15 : a] : (($true != (X1 @ X15 @ X16)) | ($true = (X14 @ X15 @ X16)))) & ? [X11 : a > a > $o] : (((X11 @ X9 @ X10) != $true) & ! [X13 : a,X12 : a] : (((X2 @ X12 @ X13) != $true) | ($true = (X11 @ X12 @ X13))) & ((X3 @ X11) = $true))) | ((X8 @ X9 @ X10) = $true)) & ((X8 @ X4 @ X0) != $true)) & ! [X5 : a > a > $o] : (((X3 @ X5) != $true) | ((X5 @ X4 @ X0) = $true) | ? [X6 : a,X7 : a] : ((((X1 @ X7 @ X6) = $true) | ((X2 @ X7 @ X6) = $true)) & ((X5 @ X7 @ X6) != $true))))),
% 1.66/1.36 inference(flattening,[status(thm)],[f6])).
% 1.66/1.36 thf(f6,plain,(
% 1.66/1.36 ? [X1 : a > a > $o,X0 : a,X2 : a > a > $o,X4 : a,X3 : (a > a > $o) > $o] : (? [X8 : a > a > $o] : (((X8 @ X4 @ X0) != $true) & (($true = (X3 @ X8)) & ! [X9 : a,X10 : a] : (((X8 @ X9 @ X10) = $true) | (? [X11 : a > a > $o] : (((X11 @ X9 @ X10) != $true) & (((X3 @ X11) = $true) & ! [X13 : a,X12 : a] : (((X2 @ X12 @ X13) != $true) | ($true = (X11 @ X12 @ X13))))) & ? [X14 : a > a > $o] : (((X14 @ X9 @ X10) != $true) & (! [X16 : a,X15 : a] : (($true != (X1 @ X15 @ X16)) | ($true = (X14 @ X15 @ X16))) & ($true = (X3 @ X14)))))))) & ! [X5 : a > a > $o] : (((X5 @ X4 @ X0) = $true) | (((X3 @ X5) != $true) | ? [X6 : a,X7 : a] : ((((X1 @ X7 @ X6) = $true) | ((X2 @ X7 @ X6) = $true)) & ((X5 @ X7 @ X6) != $true)))))),
% 1.66/1.36 inference(ennf_transformation,[status(thm)],[f5])).
% 1.66/1.36 thf(f5,plain,(
% 1.66/1.36 ~! [X1 : a > a > $o,X0 : a,X2 : a > a > $o,X4 : a,X3 : (a > a > $o) > $o] : (! [X5 : a > a > $o] : ((((X3 @ X5) = $true) & ! [X6 : a,X7 : a] : ((((X1 @ X7 @ X6) = $true) | ((X2 @ X7 @ X6) = $true)) => ((X5 @ X7 @ X6) = $true))) => ((X5 @ X4 @ X0) = $true)) => ! [X8 : a > a > $o] : ((($true = (X3 @ X8)) & ! [X9 : a,X10 : a] : ((! [X11 : a > a > $o] : ((((X3 @ X11) = $true) & ! [X13 : a,X12 : a] : (((X2 @ X12 @ X13) = $true) => ($true = (X11 @ X12 @ X13)))) => ((X11 @ X9 @ X10) = $true)) | ! [X14 : a > a > $o] : ((! [X16 : a,X15 : a] : (($true = (X1 @ X15 @ X16)) => ($true = (X14 @ X15 @ X16))) & ($true = (X3 @ X14))) => ((X14 @ X9 @ X10) = $true))) => ((X8 @ X9 @ X10) = $true))) => ((X8 @ X4 @ X0) = $true)))),
% 1.66/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.36 thf(f4,plain,(
% 1.66/1.36 ~! [X0 : a,X1 : a > a > $o,X2 : a > a > $o,X3 : (a > a > $o) > $o,X4 : a] : (! [X5 : a > a > $o] : (((X3 @ X5) & ! [X6 : a,X7 : a] : (((X2 @ X7 @ X6) | (X1 @ X7 @ X6)) => (X5 @ X7 @ X6))) => (X5 @ X4 @ X0)) => ! [X8 : a > a > $o] : (((X3 @ X8) & ! [X9 : a,X10 : a] : ((! [X11 : a > a > $o] : ((! [X12 : a,X13 : a] : ((X2 @ X12 @ X13) => (X11 @ X12 @ X13)) & (X3 @ X11)) => (X11 @ X9 @ X10)) | ! [X14 : a > a > $o] : ((! [X15 : a,X16 : a] : ((X1 @ X15 @ X16) => (X14 @ X15 @ X16)) & (X3 @ X14)) => (X14 @ X9 @ X10))) => (X8 @ X9 @ X10))) => (X8 @ X4 @ X0)))),
% 1.66/1.36 inference(rectify,[status(thm)],[f2])).
% 1.66/1.36 thf(f2,negated_conjecture,(
% 1.66/1.36 ~! [X4 : a,X1 : a > a > $o,X2 : a > a > $o,X0 : (a > a > $o) > $o,X3 : a] : (! [X5 : a > a > $o] : (((X0 @ X5) & ! [X7 : a,X6 : a] : (((X2 @ X6 @ X7) | (X1 @ X6 @ X7)) => (X5 @ X6 @ X7))) => (X5 @ X3 @ X4)) => ! [X5 : a > a > $o] : (((X0 @ X5) & ! [X6 : a,X7 : a] : ((! [X8 : a > a > $o] : ((! [X9 : a,X10 : a] : ((X2 @ X9 @ X10) => (X8 @ X9 @ X10)) & (X0 @ X8)) => (X8 @ X6 @ X7)) | ! [X8 : a > a > $o] : ((! [X9 : a,X10 : a] : ((X1 @ X9 @ X10) => (X8 @ X9 @ X10)) & (X0 @ X8)) => (X8 @ X6 @ X7))) => (X5 @ X6 @ X7))) => (X5 @ X3 @ X4)))),
% 1.66/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.36 thf(f1,conjecture,(
% 1.66/1.36 ! [X4 : a,X1 : a > a > $o,X2 : a > a > $o,X0 : (a > a > $o) > $o,X3 : a] : (! [X5 : a > a > $o] : (((X0 @ X5) & ! [X7 : a,X6 : a] : (((X2 @ X6 @ X7) | (X1 @ X6 @ X7)) => (X5 @ X6 @ X7))) => (X5 @ X3 @ X4)) => ! [X5 : a > a > $o] : (((X0 @ X5) & ! [X6 : a,X7 : a] : ((! [X8 : a > a > $o] : ((! [X9 : a,X10 : a] : ((X2 @ X9 @ X10) => (X8 @ X9 @ X10)) & (X0 @ X8)) => (X8 @ X6 @ X7)) | ! [X8 : a > a > $o] : ((! [X9 : a,X10 : a] : ((X1 @ X9 @ X10) => (X8 @ X9 @ X10)) & (X0 @ X8)) => (X8 @ X6 @ X7))) => (X5 @ X6 @ X7))) => (X5 @ X3 @ X4)))),
% 1.66/1.36 file('/export/starexec/sandbox2/tmp/tmp.c5Yfx2KjUO/DTF2THF_23422.p',cTHM252B_pme)).
% 1.66/1.36 thf(f29,plain,(
% 1.66/1.36 ((sK5 @ sK3 @ sK1) = $true) | ((sK5 @ (sK9 @ sK5) @ (sK8 @ sK5)) != $true)),
% 1.66/1.36 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.66/1.36 thf(f27,plain,(
% 1.66/1.36 ((sK5 @ sK3 @ sK1) = $true) | ($true != $true) | ((sK5 @ (sK9 @ sK5) @ (sK8 @ sK5)) != $true)),
% 1.66/1.36 inference(superposition,[status(thm)],[f15,f24])).
% 1.66/1.36 thf(f24,plain,(
% 1.66/1.36 ((sK2 @ sK5) = $true)),
% 1.66/1.36 inference(cnf_transformation,[status(thm)],[f14])).
% 1.66/1.36 thf(f15,plain,(
% 1.66/1.36 ( ! [X14 : a > a > $o] : (((sK2 @ X14) != $true) | ((X14 @ sK3 @ sK1) = $true) | ((X14 @ (sK9 @ X14) @ (sK8 @ X14)) != $true)) )),
% 1.66/1.36 inference(cnf_transformation,[status(thm)],[f14])).
% 1.66/1.36 thf(f59,plain,(
% 1.66/1.36 ((sK5 @ (sK9 @ sK5) @ (sK8 @ sK5)) = $true) | ~spl10_1),
% 1.66/1.36 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.66/1.36 thf(f58,plain,(
% 1.66/1.36 ($true != $true) | ((sK5 @ (sK9 @ sK5) @ (sK8 @ sK5)) = $true) | ~spl10_1),
% 1.66/1.36 inference(duplicate_literal_removal,[status(thm)],[f57])).
% 1.66/1.36 thf(f57,plain,(
% 1.66/1.36 ((sK5 @ (sK9 @ sK5) @ (sK8 @ sK5)) = $true) | ($true != $true) | ((sK5 @ (sK9 @ sK5) @ (sK8 @ sK5)) = $true) | ~spl10_1),
% 1.66/1.36 inference(superposition,[status(thm)],[f23,f56])).
% 1.66/1.36 thf(f56,plain,(
% 1.66/1.36 ( ! [X0 : a,X1 : a] : (($true = (sK6 @ X0 @ X1 @ (sK9 @ sK5) @ (sK8 @ sK5))) | ((sK5 @ X1 @ X0) = $true)) ) | ~spl10_1),
% 1.66/1.36 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.66/1.36 thf(f55,plain,(
% 1.66/1.36 ( ! [X0 : a,X1 : a] : (($true != $true) | ((sK5 @ X1 @ X0) = $true) | ($true = (sK6 @ X0 @ X1 @ (sK9 @ sK5) @ (sK8 @ sK5)))) ) | ~spl10_1),
% 1.66/1.36 inference(superposition,[status(thm)],[f21,f42])).
% 1.66/1.36 thf(f42,plain,(
% 1.66/1.36 ($true = (sK4 @ (sK9 @ sK5) @ (sK8 @ sK5))) | ~spl10_1),
% 1.66/1.36 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.66/1.36 thf(f40,definition,(
% 1.66/1.36 spl10_1 <=> ($true = (sK4 @ (sK9 @ sK5) @ (sK8 @ sK5)))),
% 1.66/1.36 introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition])).
% 1.66/1.36 thf(f21,plain,(
% 1.66/1.36 ( ! [X10 : a,X6 : a,X9 : a,X7 : a] : (($true != (sK4 @ X10 @ X9)) | ($true = (sK6 @ X7 @ X6 @ X10 @ X9)) | ((sK5 @ X6 @ X7) = $true)) )),
% 1.66/1.36 inference(cnf_transformation,[status(thm)],[f14])).
% 1.66/1.36 thf(f23,plain,(
% 1.66/1.36 ( ! [X6 : a,X7 : a] : (((sK6 @ X7 @ X6 @ X6 @ X7) != $true) | ((sK5 @ X6 @ X7) = $true)) )),
% 1.66/1.36 inference(cnf_transformation,[status(thm)],[f14])).
% 1.66/1.36 thf(f54,plain,(
% 1.66/1.36 ~spl10_2),
% 1.66/1.36 inference(avatar_contradiction_clause,[status(thm)],[f53])).
% 1.66/1.36 thf(f53,plain,(
% 1.66/1.36 $false | ~spl10_2),
% 1.66/1.36 inference(subsumption_resolution,[status(thm)],[f52,f31])).
% 1.66/1.36 thf(f52,plain,(
% 1.66/1.36 ((sK5 @ (sK9 @ sK5) @ (sK8 @ sK5)) = $true) | ~spl10_2),
% 1.66/1.36 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.66/1.36 thf(f51,plain,(
% 1.66/1.36 ($true != $true) | ((sK5 @ (sK9 @ sK5) @ (sK8 @ sK5)) = $true) | ~spl10_2),
% 1.66/1.36 inference(duplicate_literal_removal,[status(thm)],[f50])).
% 1.66/1.36 thf(f50,plain,(
% 1.66/1.36 ((sK5 @ (sK9 @ sK5) @ (sK8 @ sK5)) = $true) | ((sK5 @ (sK9 @ sK5) @ (sK8 @ sK5)) = $true) | ($true != $true) | ~spl10_2),
% 1.66/1.36 inference(superposition,[status(thm)],[f20,f49])).
% 1.66/1.36 thf(f49,plain,(
% 1.66/1.36 ( ! [X0 : a,X1 : a] : (($true = (sK7 @ X0 @ X1 @ (sK9 @ sK5) @ (sK8 @ sK5))) | ((sK5 @ X1 @ X0) = $true)) ) | ~spl10_2),
% 1.66/1.36 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.66/1.36 thf(f48,plain,(
% 1.66/1.36 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = (sK7 @ X0 @ X1 @ (sK9 @ sK5) @ (sK8 @ sK5))) | ((sK5 @ X1 @ X0) = $true)) ) | ~spl10_2),
% 1.66/1.36 inference(superposition,[status(thm)],[f19,f46])).
% 1.66/1.36 thf(f46,plain,(
% 1.66/1.36 ($true = (sK0 @ (sK9 @ sK5) @ (sK8 @ sK5))) | ~spl10_2),
% 1.66/1.36 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.66/1.36 thf(f44,definition,(
% 1.66/1.36 spl10_2 <=> ($true = (sK0 @ (sK9 @ sK5) @ (sK8 @ sK5)))),
% 1.66/1.36 introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition])).
% 1.66/1.36 thf(f19,plain,(
% 1.66/1.36 ( ! [X6 : a,X7 : a,X12 : a,X13 : a] : (((sK0 @ X13 @ X12) != $true) | ((sK7 @ X7 @ X6 @ X13 @ X12) = $true) | ((sK5 @ X6 @ X7) = $true)) )),
% 1.66/1.36 inference(cnf_transformation,[status(thm)],[f14])).
% 1.66/1.36 thf(f20,plain,(
% 1.66/1.36 ( ! [X6 : a,X7 : a] : (((sK7 @ X7 @ X6 @ X6 @ X7) != $true) | ((sK5 @ X6 @ X7) = $true)) )),
% 1.66/1.36 inference(cnf_transformation,[status(thm)],[f14])).
% 1.66/1.36 thf(f47,plain,(
% 1.66/1.36 spl10_1 | spl10_2),
% 1.66/1.36 inference(avatar_split_clause,[status(thm)],[f38,f44,f40])).
% 1.66/1.36 thf(f38,plain,(
% 1.66/1.36 ($true = (sK4 @ (sK9 @ sK5) @ (sK8 @ sK5))) | ($true = (sK0 @ (sK9 @ sK5) @ (sK8 @ sK5)))),
% 1.66/1.36 inference(subsumption_resolution,[status(thm)],[f35,f17])).
% 1.66/1.36 thf(f35,plain,(
% 1.66/1.36 ($true = (sK4 @ (sK9 @ sK5) @ (sK8 @ sK5))) | ((sK5 @ sK3 @ sK1) = $true) | ($true = (sK0 @ (sK9 @ sK5) @ (sK8 @ sK5)))),
% 1.66/1.36 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.66/1.36 thf(f34,plain,(
% 1.66/1.36 ((sK5 @ sK3 @ sK1) = $true) | ($true = (sK4 @ (sK9 @ sK5) @ (sK8 @ sK5))) | ($true = (sK0 @ (sK9 @ sK5) @ (sK8 @ sK5))) | ($true != $true)),
% 1.66/1.36 inference(superposition,[status(thm)],[f16,f24])).
% 1.66/1.36 thf(f16,plain,(
% 1.66/1.36 ( ! [X14 : a > a > $o] : (((sK2 @ X14) != $true) | ((sK0 @ (sK9 @ X14) @ (sK8 @ X14)) = $true) | ((X14 @ sK3 @ sK1) = $true) | ((sK4 @ (sK9 @ X14) @ (sK8 @ X14)) = $true)) )),
% 1.66/1.36 inference(cnf_transformation,[status(thm)],[f14])).
% 1.66/1.36 % SZS output end Proof for DTF2THF_23422
% 1.66/1.36 % (23615)------------------------------
% 1.66/1.36 % (23615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (23615)Termination reason: Refutation
% 1.66/1.36
% 1.66/1.36 % (23615)Memory used [KB]: 5628
% 1.66/1.36 % (23615)Time elapsed: 0.015 s
% 1.66/1.36 % (23615)Instructions burned: 14 (million)
% 1.66/1.36 % (23615)------------------------------
% 1.66/1.36 % (23615)------------------------------
% 1.66/1.36 % (23606)Success in time 0.031 s
%------------------------------------------------------------------------------