%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV120^5 : 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 09:40:20 AM UTC 2026
% Result : Theorem 1.51s 1.29s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 3 unt; 0 typ; 6 def)
% Number of atoms : 669 ( 223 equ; 0 cnn)
% Maximal formula atoms : 30 ( 9 avg)
% Number of connectives : 953 ( 141 ~; 139 |; 88 &; 547 @)
% ( 6 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 100 ( 100 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 11 con; 0-2 aty)
% Number of variables : 175 ( 0 ^; 117 !; 58 ?; 175 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_5,type,
sK0: a ).
thf(func_def_6,type,
sK1: a ).
thf(func_def_7,type,
sK2: ( a > a > $o ) > $o ).
thf(func_def_8,type,
sK3: a ).
thf(func_def_9,type,
sK4: ( a > a > $o ) > a ).
thf(func_def_10,type,
sK5: ( a > a > $o ) > a ).
thf(func_def_11,type,
sK6: ( a > a > $o ) > a ).
thf(func_def_12,type,
sK7: a > a > $o ).
thf(func_def_13,type,
sK8: ( a > a > $o ) > a ).
thf(func_def_14,type,
sK9: ( a > a > $o ) > a ).
thf(func_def_15,type,
sK10: ( a > a > $o ) > a ).
thf(func_def_17,type,
ph12:
!>[X0: $tType] : X0 ).
thf(f100,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f33,f48,f57,f66,f71,f86,f99]) ).
thf(f99,plain,
( spl11_2
| ~ spl11_1
| ~ spl11_6 ),
inference(avatar_split_clause,[status(thm)],[f98,f68,f26,f30]) ).
thf(f30,definition,
( spl11_2
<=> ( ( sK7 @ sK3 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_2])],[avatar_definition]) ).
thf(f26,definition,
( spl11_1
<=> ( ( sK7 @ ( sK10 @ sK7 ) @ ( sK8 @ sK7 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_1])],[avatar_definition]) ).
thf(f68,definition,
( spl11_6
<=> ( ( sK7 @ ( sK8 @ sK7 ) @ ( sK9 @ sK7 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_6])],[avatar_definition]) ).
thf(f98,plain,
( ( ( sK7 @ sK3 @ sK0 )
= $true )
| ~ spl11_1
| ~ spl11_6 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $true != $true )
| ( ( sK7 @ sK3 @ sK0 )
= $true )
| ~ spl11_1
| ~ spl11_6 ),
inference(forward_demodulation,[status(thm)],[f95,f19]) ).
thf(f19,plain,
( ( sK2 @ sK7 )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X4: a > a > $o] :
( ( ( X4 @ sK1 @ sK3 )
= $true )
| ( ( ( X4 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) )
= $true )
& ( ( X4 @ ( sK5 @ X4 ) @ ( sK6 @ X4 ) )
!= $true )
& ( ( X4 @ ( sK4 @ X4 ) @ ( sK6 @ X4 ) )
= $true ) )
| ( ( sK2 @ X4 )
!= $true ) )
& ( ( sK2 @ sK7 )
= $true )
& ! [X9: a,X10: a,X11: a] :
( ( ( sK7 @ X11 @ X10 )
!= $true )
| ( ( sK7 @ X11 @ X9 )
= $true )
| ( ( sK7 @ X10 @ X9 )
!= $true ) )
& ( ( sK7 @ sK1 @ sK0 )
!= $true )
& ! [X12: a > a > $o] :
( ( ( X12 @ sK3 @ sK0 )
= $true )
| ( ( ( X12 @ ( sK10 @ X12 ) @ ( sK9 @ X12 ) )
!= $true )
& ( ( X12 @ ( sK8 @ X12 ) @ ( sK9 @ X12 ) )
= $true )
& ( ( X12 @ ( sK10 @ X12 ) @ ( sK8 @ X12 ) )
= $true ) )
| ( ( sK2 @ X12 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10])],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a,X1: a,X2: ( a > a > $o ) > $o,X3: a] :
( ! [X4: a > a > $o] :
( ( ( X4 @ X1 @ X3 )
= $true )
| ? [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X5 )
= $true )
& ( ( X4 @ X6 @ X7 )
!= $true )
& ( ( X4 @ X5 @ X7 )
= $true ) )
| ( ( X2 @ X4 )
!= $true ) )
& ? [X8: a > a > $o] :
( ( ( X2 @ X8 )
= $true )
& ! [X9: a,X10: a,X11: a] :
( ( ( X8 @ X11 @ X10 )
!= $true )
| ( ( X8 @ X11 @ X9 )
= $true )
| ( ( X8 @ X10 @ X9 )
!= $true ) )
& ( ( X8 @ X1 @ X0 )
!= $true ) )
& ! [X12: a > a > $o] :
( ( ( X12 @ X3 @ X0 )
= $true )
| ? [X13: a,X14: a,X15: a] :
( ( ( X12 @ X15 @ X14 )
!= $true )
& ( ( X12 @ X13 @ X14 )
= $true )
& ( ( X12 @ X15 @ X13 )
= $true ) )
| ( ( X2 @ X12 )
!= $true ) ) )
=> ( ! [X4: a > a > $o] :
( ( ( X4 @ sK1 @ sK3 )
= $true )
| ? [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X5 )
= $true )
& ( ( X4 @ X6 @ X7 )
!= $true )
& ( ( X4 @ X5 @ X7 )
= $true ) )
| ( ( sK2 @ X4 )
!= $true ) )
& ? [X8: a > a > $o] :
( ( ( sK2 @ X8 )
= $true )
& ! [X9: a,X10: a,X11: a] :
( ( ( X8 @ X11 @ X10 )
!= $true )
| ( ( X8 @ X11 @ X9 )
= $true )
| ( ( X8 @ X10 @ X9 )
!= $true ) )
& ( ( X8 @ sK1 @ sK0 )
!= $true ) )
& ! [X12: a > a > $o] :
( ( ( X12 @ sK3 @ sK0 )
= $true )
| ? [X13: a,X14: a,X15: a] :
( ( ( X12 @ X15 @ X14 )
!= $true )
& ( ( X12 @ X13 @ X14 )
= $true )
& ( ( X12 @ X15 @ X13 )
= $true ) )
| ( ( sK2 @ X12 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X4: a > a > $o] :
( ? [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X5 )
= $true )
& ( ( X4 @ X6 @ X7 )
!= $true )
& ( ( X4 @ X5 @ X7 )
= $true ) )
=> ( ( ( X4 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) )
= $true )
& ( ( X4 @ ( sK5 @ X4 ) @ ( sK6 @ X4 ) )
!= $true )
& ( ( X4 @ ( sK4 @ X4 ) @ ( sK6 @ X4 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X8: a > a > $o] :
( ( ( sK2 @ X8 )
= $true )
& ! [X9: a,X10: a,X11: a] :
( ( ( X8 @ X11 @ X10 )
!= $true )
| ( ( X8 @ X11 @ X9 )
= $true )
| ( ( X8 @ X10 @ X9 )
!= $true ) )
& ( ( X8 @ sK1 @ sK0 )
!= $true ) )
=> ( ( ( sK2 @ sK7 )
= $true )
& ! [X11: a,X10: a,X9: a] :
( ( ( sK7 @ X11 @ X10 )
!= $true )
| ( ( sK7 @ X11 @ X9 )
= $true )
| ( ( sK7 @ X10 @ X9 )
!= $true ) )
& ( ( sK7 @ sK1 @ sK0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X12: a > a > $o] :
( ? [X13: a,X14: a,X15: a] :
( ( ( X12 @ X15 @ X14 )
!= $true )
& ( ( X12 @ X13 @ X14 )
= $true )
& ( ( X12 @ X15 @ X13 )
= $true ) )
=> ( ( ( X12 @ ( sK10 @ X12 ) @ ( sK9 @ X12 ) )
!= $true )
& ( ( X12 @ ( sK8 @ X12 ) @ ( sK9 @ X12 ) )
= $true )
& ( ( X12 @ ( sK10 @ X12 ) @ ( sK8 @ X12 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a,X1: a,X2: ( a > a > $o ) > $o,X3: a] :
( ! [X4: a > a > $o] :
( ( ( X4 @ X1 @ X3 )
= $true )
| ? [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X5 )
= $true )
& ( ( X4 @ X6 @ X7 )
!= $true )
& ( ( X4 @ X5 @ X7 )
= $true ) )
| ( ( X2 @ X4 )
!= $true ) )
& ? [X8: a > a > $o] :
( ( ( X2 @ X8 )
= $true )
& ! [X9: a,X10: a,X11: a] :
( ( ( X8 @ X11 @ X10 )
!= $true )
| ( ( X8 @ X11 @ X9 )
= $true )
| ( ( X8 @ X10 @ X9 )
!= $true ) )
& ( ( X8 @ X1 @ X0 )
!= $true ) )
& ! [X12: a > a > $o] :
( ( ( X12 @ X3 @ X0 )
= $true )
| ? [X13: a,X14: a,X15: a] :
( ( ( X12 @ X15 @ X14 )
!= $true )
& ( ( X12 @ X13 @ X14 )
= $true )
& ( ( X12 @ X15 @ X13 )
= $true ) )
| ( ( X2 @ X12 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a,X3: a,X2: ( a > a > $o ) > $o,X1: a] :
( ! [X4: a > a > $o] :
( ( ( X4 @ X3 @ X1 )
= $true )
| ? [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X5 )
= $true )
& ( ( X4 @ X6 @ X7 )
!= $true )
& ( ( X4 @ X5 @ X7 )
= $true ) )
| ( ( X2 @ X4 )
!= $true ) )
& ? [X12: a > a > $o] :
( ( ( X2 @ X12 )
= $true )
& ! [X15: a,X14: a,X13: a] :
( ( ( X12 @ X13 @ X14 )
!= $true )
| ( ( X12 @ X13 @ X15 )
= $true )
| ( ( X12 @ X14 @ X15 )
!= $true ) )
& ( ( X12 @ X3 @ X0 )
!= $true ) )
& ! [X8: a > a > $o] :
( ( ( X8 @ X1 @ X0 )
= $true )
| ? [X9: a,X10: a,X11: a] :
( ( ( X8 @ X11 @ X10 )
!= $true )
& ( ( X8 @ X9 @ X10 )
= $true )
& ( ( X8 @ X11 @ X9 )
= $true ) )
| ( ( X2 @ X8 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: a,X2: ( a > a > $o ) > $o,X0: a,X3: a] :
( ? [X12: a > a > $o] :
( ( ( X12 @ X3 @ X0 )
!= $true )
& ( ( X2 @ X12 )
= $true )
& ! [X13: a,X15: a,X14: a] :
( ( ( X12 @ X13 @ X15 )
= $true )
| ( ( X12 @ X13 @ X14 )
!= $true )
| ( ( X12 @ X14 @ X15 )
!= $true ) ) )
& ! [X8: a > a > $o] :
( ( ( X8 @ X1 @ X0 )
= $true )
| ( ( X2 @ X8 )
!= $true )
| ? [X10: a,X11: a,X9: a] :
( ( ( X8 @ X11 @ X10 )
!= $true )
& ( ( X8 @ X11 @ X9 )
= $true )
& ( ( X8 @ X9 @ X10 )
= $true ) ) )
& ! [X4: a > a > $o] :
( ( ( X4 @ X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
!= $true )
| ? [X5: a,X7: a,X6: a] :
( ( ( X4 @ X6 @ X7 )
!= $true )
& ( ( X4 @ X6 @ X5 )
= $true )
& ( ( X4 @ X5 @ X7 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: a,X2: ( a > a > $o ) > $o,X0: a,X3: a] :
( ( ! [X8: a > a > $o] :
( ( ( ( X2 @ X8 )
= $true )
& ! [X10: a,X11: a,X9: a] :
( ( ( ( X8 @ X11 @ X9 )
= $true )
& ( ( X8 @ X9 @ X10 )
= $true ) )
=> ( ( X8 @ X11 @ X10 )
= $true ) ) )
=> ( ( X8 @ X1 @ X0 )
= $true ) )
& ! [X4: a > a > $o] :
( ( ( ( X2 @ X4 )
= $true )
& ! [X5: a,X7: a,X6: a] :
( ( ( ( X4 @ X6 @ X5 )
= $true )
& ( ( X4 @ X5 @ X7 )
= $true ) )
=> ( ( X4 @ X6 @ X7 )
= $true ) ) )
=> ( ( X4 @ X3 @ X1 )
= $true ) ) )
=> ! [X12: a > a > $o] :
( ( ( ( X2 @ X12 )
= $true )
& ! [X13: a,X15: a,X14: a] :
( ( ( ( X12 @ X13 @ X14 )
= $true )
& ( ( X12 @ X14 @ X15 )
= $true ) )
=> ( ( X12 @ X13 @ X15 )
= $true ) ) )
=> ( ( X12 @ X3 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a,X2: ( a > a > $o ) > $o,X3: a] :
( ( ! [X4: a > a > $o] :
( ( ( X2 @ X4 )
& ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X5 )
& ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
=> ( X4 @ X3 @ X1 ) )
& ! [X8: a > a > $o] :
( ( ( X2 @ X8 )
& ! [X9: a,X10: a,X11: a] :
( ( ( X8 @ X11 @ X9 )
& ( X8 @ X9 @ X10 ) )
=> ( X8 @ X11 @ X10 ) ) )
=> ( X8 @ X1 @ X0 ) ) )
=> ! [X12: a > a > $o] :
( ( ( X2 @ X12 )
& ! [X13: a,X14: a,X15: a] :
( ( ( X12 @ X13 @ X14 )
& ( X12 @ X14 @ X15 ) )
=> ( X12 @ X13 @ X15 ) ) )
=> ( X12 @ X3 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: a,X2: a,X0: ( a > a > $o ) > $o,X1: a] :
( ( ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X6: a,X5: a,X7: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
& ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X6: a,X7: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X3: a,X2: a,X0: ( a > a > $o ) > $o,X1: a] :
( ( ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X6: a,X5: a,X7: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
& ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X6: a,X7: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iv9W0fRYgu/DTF2THF_2965.p',cTHM70_pme) ).
thf(f95,plain,
( ( ( sK2 @ sK7 )
!= $true )
| ( ( sK7 @ sK3 @ sK0 )
= $true )
| ~ spl11_1
| ~ spl11_6 ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ( $true != $true )
| ( ( sK7 @ sK3 @ sK0 )
= $true )
| ( ( sK2 @ sK7 )
!= $true )
| ~ spl11_1
| ~ spl11_6 ),
inference(superposition,[status(thm)],[f16,f91]) ).
thf(f91,plain,
( ( ( sK7 @ ( sK10 @ sK7 ) @ ( sK9 @ sK7 ) )
= $true )
| ~ spl11_1
| ~ spl11_6 ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ( sK7 @ ( sK10 @ sK7 ) @ ( sK9 @ sK7 ) )
= $true )
| ( $true != $true )
| ~ spl11_1
| ~ spl11_6 ),
inference(superposition,[status(thm)],[f75,f70]) ).
thf(f70,plain,
( ( ( sK7 @ ( sK8 @ sK7 ) @ ( sK9 @ sK7 ) )
= $true )
| ~ spl11_6 ),
inference(avatar_component_clause,[status(thm)],[f68]) ).
thf(f75,plain,
( ! [X0: a] :
( ( ( sK7 @ ( sK8 @ sK7 ) @ X0 )
!= $true )
| ( ( sK7 @ ( sK10 @ sK7 ) @ X0 )
= $true ) )
| ~ spl11_1 ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ! [X0: a] :
( ( ( sK7 @ ( sK8 @ sK7 ) @ X0 )
!= $true )
| ( $true != $true )
| ( ( sK7 @ ( sK10 @ sK7 ) @ X0 )
= $true ) )
| ~ spl11_1 ),
inference(superposition,[status(thm)],[f18,f28]) ).
thf(f28,plain,
( ( ( sK7 @ ( sK10 @ sK7 ) @ ( sK8 @ sK7 ) )
= $true )
| ~ spl11_1 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f18,plain,
! [X10: a,X11: a,X9: a] :
( ( ( sK7 @ X11 @ X10 )
!= $true )
| ( ( sK7 @ X10 @ X9 )
!= $true )
| ( ( sK7 @ X11 @ X9 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f16,plain,
! [X12: a > a > $o] :
( ( ( X12 @ ( sK10 @ X12 ) @ ( sK9 @ X12 ) )
!= $true )
| ( ( X12 @ sK3 @ sK0 )
= $true )
| ( ( sK2 @ X12 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f86,plain,
( spl11_3
| ~ spl11_4
| ~ spl11_5 ),
inference(avatar_split_clause,[status(thm)],[f85,f63,f45,f41]) ).
thf(f41,definition,
( spl11_3
<=> ( ( sK7 @ sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_3])],[avatar_definition]) ).
thf(f45,definition,
( spl11_4
<=> ( ( sK7 @ ( sK4 @ sK7 ) @ ( sK6 @ sK7 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_4])],[avatar_definition]) ).
thf(f63,definition,
( spl11_5
<=> ( ( sK7 @ ( sK5 @ sK7 ) @ ( sK4 @ sK7 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_5])],[avatar_definition]) ).
thf(f85,plain,
( ( ( sK7 @ sK1 @ sK3 )
= $true )
| ~ spl11_4
| ~ spl11_5 ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
( ( $true != $true )
| ( ( sK7 @ sK1 @ sK3 )
= $true )
| ~ spl11_4
| ~ spl11_5 ),
inference(forward_demodulation,[status(thm)],[f82,f19]) ).
thf(f82,plain,
( ( ( sK2 @ sK7 )
!= $true )
| ( ( sK7 @ sK1 @ sK3 )
= $true )
| ~ spl11_4
| ~ spl11_5 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( ( sK2 @ sK7 )
!= $true )
| ( ( sK7 @ sK1 @ sK3 )
= $true )
| ( $true != $true )
| ~ spl11_4
| ~ spl11_5 ),
inference(superposition,[status(thm)],[f21,f79]) ).
thf(f79,plain,
( ( $true
= ( sK7 @ ( sK5 @ sK7 ) @ ( sK6 @ sK7 ) ) )
| ~ spl11_4
| ~ spl11_5 ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( $true
= ( sK7 @ ( sK5 @ sK7 ) @ ( sK6 @ sK7 ) ) )
| ( $true != $true )
| ~ spl11_4
| ~ spl11_5 ),
inference(superposition,[status(thm)],[f77,f47]) ).
thf(f47,plain,
( ( ( sK7 @ ( sK4 @ sK7 ) @ ( sK6 @ sK7 ) )
= $true )
| ~ spl11_4 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f77,plain,
( ! [X0: a] :
( ( $true
!= ( sK7 @ ( sK4 @ sK7 ) @ X0 ) )
| ( ( sK7 @ ( sK5 @ sK7 ) @ X0 )
= $true ) )
| ~ spl11_5 ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true
!= ( sK7 @ ( sK4 @ sK7 ) @ X0 ) )
| ( ( sK7 @ ( sK5 @ sK7 ) @ X0 )
= $true ) )
| ~ spl11_5 ),
inference(superposition,[status(thm)],[f18,f65]) ).
thf(f65,plain,
( ( ( sK7 @ ( sK5 @ sK7 ) @ ( sK4 @ sK7 ) )
= $true )
| ~ spl11_5 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f21,plain,
! [X4: a > a > $o] :
( ( ( X4 @ ( sK5 @ X4 ) @ ( sK6 @ X4 ) )
!= $true )
| ( ( sK2 @ X4 )
!= $true )
| ( ( X4 @ sK1 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f71,plain,
( spl11_6
| spl11_2 ),
inference(avatar_split_clause,[status(thm)],[f37,f30,f68]) ).
thf(f37,plain,
( ( ( sK7 @ ( sK8 @ sK7 ) @ ( sK9 @ sK7 ) )
= $true )
| ( ( sK7 @ sK3 @ sK0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( sK7 @ ( sK8 @ sK7 ) @ ( sK9 @ sK7 ) )
= $true )
| ( $true != $true )
| ( ( sK7 @ sK3 @ sK0 )
= $true ) ),
inference(superposition,[status(thm)],[f15,f19]) ).
thf(f15,plain,
! [X12: a > a > $o] :
( ( ( sK2 @ X12 )
!= $true )
| ( ( X12 @ sK3 @ sK0 )
= $true )
| ( ( X12 @ ( sK8 @ X12 ) @ ( sK9 @ X12 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f66,plain,
( spl11_3
| spl11_5 ),
inference(avatar_split_clause,[status(thm)],[f61,f63,f41]) ).
thf(f61,plain,
( ( ( sK7 @ sK1 @ sK3 )
= $true )
| ( ( sK7 @ ( sK5 @ sK7 ) @ ( sK4 @ sK7 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( sK7 @ sK1 @ sK3 )
= $true )
| ( ( sK7 @ ( sK5 @ sK7 ) @ ( sK4 @ sK7 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f22,f19]) ).
thf(f22,plain,
! [X4: a > a > $o] :
( ( ( sK2 @ X4 )
!= $true )
| ( ( X4 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) )
= $true )
| ( ( X4 @ sK1 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f57,plain,
( ~ spl11_2
| ~ spl11_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f56]) ).
thf(f56,plain,
( $false
| ~ spl11_2
| ~ spl11_3 ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true != $true )
| ~ spl11_2
| ~ spl11_3 ),
inference(superposition,[status(thm)],[f17,f52]) ).
thf(f52,plain,
( ( ( sK7 @ sK1 @ sK0 )
= $true )
| ~ spl11_2
| ~ spl11_3 ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true != $true )
| ( ( sK7 @ sK1 @ sK0 )
= $true )
| ~ spl11_2
| ~ spl11_3 ),
inference(superposition,[status(thm)],[f50,f32]) ).
thf(f32,plain,
( ( ( sK7 @ sK3 @ sK0 )
= $true )
| ~ spl11_2 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f50,plain,
( ! [X0: a] :
( ( ( sK7 @ sK3 @ X0 )
!= $true )
| ( ( sK7 @ sK1 @ X0 )
= $true ) )
| ~ spl11_3 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ! [X0: a] :
( ( ( sK7 @ sK3 @ X0 )
!= $true )
| ( $true != $true )
| ( ( sK7 @ sK1 @ X0 )
= $true ) )
| ~ spl11_3 ),
inference(superposition,[status(thm)],[f18,f43]) ).
thf(f43,plain,
( ( ( sK7 @ sK1 @ sK3 )
= $true )
| ~ spl11_3 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f17,plain,
( ( sK7 @ sK1 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f48,plain,
( spl11_3
| spl11_4 ),
inference(avatar_split_clause,[status(thm)],[f39,f45,f41]) ).
thf(f39,plain,
( ( ( sK7 @ ( sK4 @ sK7 ) @ ( sK6 @ sK7 ) )
= $true )
| ( ( sK7 @ sK1 @ sK3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( sK7 @ sK1 @ sK3 )
= $true )
| ( $true != $true )
| ( ( sK7 @ ( sK4 @ sK7 ) @ ( sK6 @ sK7 ) )
= $true ) ),
inference(superposition,[status(thm)],[f20,f19]) ).
thf(f20,plain,
! [X4: a > a > $o] :
( ( ( sK2 @ X4 )
!= $true )
| ( ( X4 @ sK1 @ sK3 )
= $true )
| ( ( X4 @ ( sK4 @ X4 ) @ ( sK6 @ X4 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f33,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[status(thm)],[f24,f30,f26]) ).
thf(f24,plain,
( ( ( sK7 @ ( sK10 @ sK7 ) @ ( sK8 @ sK7 ) )
= $true )
| ( ( sK7 @ sK3 @ sK0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( sK7 @ ( sK10 @ sK7 ) @ ( sK8 @ sK7 ) )
= $true )
| ( $true != $true )
| ( ( sK7 @ sK3 @ sK0 )
= $true ) ),
inference(superposition,[status(thm)],[f14,f19]) ).
thf(f14,plain,
! [X12: a > a > $o] :
( ( ( sK2 @ X12 )
!= $true )
| ( ( X12 @ sK3 @ sK0 )
= $true )
| ( ( X12 @ ( sK10 @ X12 ) @ ( sK8 @ X12 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV120^5 : 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
% 0.17/0.34 % Computer : n013.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:40:38 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEV120^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Set Theory (Relations)
% 0.29/0.46 % Problem : TPS problem THM70
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : The intersection of any class of transitive relations is
% 0.29/0.46 % transitive.
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0440 [Bro09]
% 0.29/0.46 % : THM70 [TPS]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % 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, 0.10 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 v6.0.0, 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
% 0.29/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.29/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.29/0.46 % Number of connectives : 41 ( 0 ~; 0 |; 7 &; 27 @)
% 0.29/0.46 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 17 ( 17 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.29/0.46 % Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 % : Polymorphic definitions expanded.
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(a_type,type,
% 0.29/0.46 a: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(cTHM70_pme,conjecture,
% 0.29/0.46 ! [S: ( a > a > $o ) > $o,Xx: a,Xy: a,Xz: a] :
% 0.29/0.46 ( ( ! [Xp: a > a > $o] :
% 0.29/0.46 ( ( ! [Xx0: a,Xy0: a,Xz0: a] :
% 0.29/0.46 ( ( ( Xp @ Xx0 @ Xy0 )
% 0.29/0.46 & ( Xp @ Xy0 @ Xz0 ) )
% 0.29/0.46 => ( Xp @ Xx0 @ Xz0 ) )
% 0.29/0.46 & ( S @ Xp ) )
% 0.29/0.46 => ( Xp @ Xx @ Xy ) )
% 0.29/0.46 & ! [Xp: a > a > $o] :
% 0.29/0.46 ( ( ! [Xx0: a,Xy0: a,Xz0: a] :
% 0.29/0.46 ( ( ( Xp @ Xx0 @ Xy0 )
% 0.29/0.46 & ( Xp @ Xy0 @ Xz0 ) )
% 0.29/0.46 => ( Xp @ Xx0 @ Xz0 ) )
% 0.29/0.46 & ( S @ Xp ) )
% 0.29/0.46 => ( Xp @ Xy @ Xz ) ) )
% 0.29/0.46 => ! [Xp: a > a > $o] :
% 0.29/0.46 ( ( ! [Xx0: a,Xy0: a,Xz0: a] :
% 0.29/0.46 ( ( ( Xp @ Xx0 @ Xy0 )
% 0.29/0.46 & ( Xp @ Xy0 @ Xz0 ) )
% 0.29/0.46 => ( Xp @ Xx0 @ Xz0 ) )
% 0.29/0.46 & ( S @ Xp ) )
% 0.29/0.46 => ( Xp @ Xx @ Xz ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.51/1.25 ---- Embedded in THF ---
% 1.51/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.26 %%% Generated on Tue Feb 24 12:40:39 EST 2026
% 1.51/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.26 %%% Logic specification used:
% 1.51/1.26 %%% thf(spec, logic, $$dhol).
% 1.51/1.26
% 1.51/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.iv9W0fRYgu/DTF2DTF2965.p
% See solution above
% 1.51/1.26 ------------------------
% 1.51/1.27 ---- Cleaned THF ---
% 1.51/1.27 thf(a_type,type,
% 1.51/1.27 a: $tType ).
% 1.51/1.27
% 1.51/1.27 thf(cTHM70_pme,conjecture,
% 1.51/1.27 ! [S: ( a > a > $o ) > $o,Xx: a,Xy: a,Xz: a] :
% 1.51/1.27 ( ( ! [Xp: a > a > $o] :
% 1.51/1.27 ( ( ! [Xx0: a,Xy0: a,Xz0: a] :
% 1.51/1.27 ( ( ( Xp @ Xx0 @ Xy0 )
% 1.51/1.27 & ( Xp @ Xy0 @ Xz0 ) )
% 1.51/1.27 => ( Xp @ Xx0 @ Xz0 ) )
% 1.51/1.27 & ( S @ Xp ) )
% 1.51/1.27 => ( Xp @ Xx @ Xy ) )
% 1.51/1.27 & ! [Xp: a > a > $o] :
% 1.51/1.27 ( ( ! [Xx0: a,Xy0: a,Xz0: a] :
% 1.51/1.27 ( ( ( Xp @ Xx0 @ Xy0 )
% 1.51/1.27 & ( Xp @ Xy0 @ Xz0 ) )
% 1.51/1.27 => ( Xp @ Xx0 @ Xz0 ) )
% 1.51/1.27 & ( S @ Xp ) )
% 1.51/1.27 => ( Xp @ Xy @ Xz ) ) )
% 1.51/1.27 => ! [Xp: a > a > $o] :
% 1.51/1.27 ( ( ! [Xx0: a,Xy0: a,Xz0: a] :
% 1.51/1.27 ( ( ( Xp @ Xx0 @ Xy0 )
% 1.51/1.27 & ( Xp @ Xy0 @ Xz0 ) )
% 1.51/1.27 => ( Xp @ Xx0 @ Xz0 ) )
% 1.51/1.27 & ( S @ Xp ) )
% 1.51/1.27 => ( Xp @ Xx @ Xz ) ) ) ).
% 1.51/1.27 ------------------------
% 1.51/1.28 % (3239)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_2965 for (2999ds/2Mi)
% 1.51/1.28 % (3239)Instruction limit reached!
% 1.51/1.28 % (3239)------------------------------
% 1.51/1.28 % (3239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.28 % (3239)Termination reason: Unknown
% 1.51/1.28 % (3239)Termination phase: Property scanning
% 1.51/1.28
% 1.51/1.28 % (3237)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_2965 for (2999ds/27Mi)
% 1.51/1.28 % (3239)Memory used [KB]: 1023
% 1.51/1.28 % (3239)Time elapsed: 0.002 s
% 1.51/1.28 % (3239)Instructions burned: 3 (million)
% 1.51/1.28 % (3239)------------------------------
% 1.51/1.28 % (3239)------------------------------
% 1.51/1.29 % (3237)First to succeed.
% 1.51/1.29 % (3235)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2965 for (2999ds/183Mi)
% 1.51/1.29 % (3236)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_2965 for (2999ds/4Mi)
% 1.51/1.29 % (3238)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2965 for (2999ds/2Mi)
% 1.51/1.29 % (3240)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_2965 for (2999ds/275Mi)
% 1.51/1.29 % (3241)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2965 for (2999ds/18Mi)
% 1.51/1.29 % (3238)Instruction limit reached!
% 1.51/1.29 % (3238)------------------------------
% 1.51/1.29 % (3238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (3238)Termination reason: Unknown
% 1.51/1.29 % (3238)Termination phase: Preprocessing 3
% 1.51/1.29
% 1.51/1.29 % (3238)Memory used [KB]: 895
% 1.51/1.29 % (3238)Time elapsed: 0.003 s
% 1.51/1.29 % (3238)Instructions burned: 2 (million)
% 1.51/1.29 % (3238)------------------------------
% 1.51/1.29 % (3238)------------------------------
% 1.51/1.29 % (3237)Refutation found. Thanks to Tanya!
% 1.51/1.29 % SZS status Theorem for DTF2THF_2965
% 1.51/1.29 % SZS output start Proof for DTF2THF_2965
% 1.51/1.29 thf(type_def_5, type, a: $tType).
% 1.51/1.29 thf(func_def_0, type, a: $tType).
% 1.51/1.29 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.51/1.29 thf(func_def_5, type, sK0: a).
% 1.51/1.29 thf(func_def_6, type, sK1: a).
% 1.51/1.29 thf(func_def_7, type, sK2: (a > a > $o) > $o).
% 1.51/1.29 thf(func_def_8, type, sK3: a).
% 1.51/1.29 thf(func_def_9, type, sK4: (a > a > $o) > a).
% 1.51/1.29 thf(func_def_10, type, sK5: (a > a > $o) > a).
% 1.51/1.29 thf(func_def_11, type, sK6: (a > a > $o) > a).
% 1.51/1.29 thf(func_def_12, type, sK7: a > a > $o).
% 1.51/1.29 thf(func_def_13, type, sK8: (a > a > $o) > a).
% 1.51/1.29 thf(func_def_14, type, sK9: (a > a > $o) > a).
% 1.51/1.29 thf(func_def_15, type, sK10: (a > a > $o) > a).
% 1.51/1.29 thf(func_def_17, type, ph12: !>[X0: $tType]:(X0)).
% 1.51/1.29 thf(f100,plain,(
% 1.51/1.29 $false),
% 1.51/1.29 inference(avatar_sat_refutation,[status(thm)],[f33,f48,f57,f66,f71,f86,f99])).
% 1.51/1.29 thf(f99,plain,(
% 1.51/1.29 spl11_2 | ~spl11_1 | ~spl11_6),
% 1.51/1.29 inference(avatar_split_clause,[status(thm)],[f98,f68,f26,f30])).
% 1.51/1.29 thf(f30,definition,(
% 1.51/1.29 spl11_2 <=> ((sK7 @ sK3 @ sK0) = $true)),
% 1.51/1.29 introduced(definition,[new_symbols(naming,[spl11_2])],[avatar_definition])).
% 1.51/1.29 thf(f26,definition,(
% 1.51/1.29 spl11_1 <=> ((sK7 @ (sK10 @ sK7) @ (sK8 @ sK7)) = $true)),
% 1.51/1.29 introduced(definition,[new_symbols(naming,[spl11_1])],[avatar_definition])).
% 1.51/1.29 thf(f68,definition,(
% 1.51/1.29 spl11_6 <=> ((sK7 @ (sK8 @ sK7) @ (sK9 @ sK7)) = $true)),
% 1.51/1.29 introduced(definition,[new_symbols(naming,[spl11_6])],[avatar_definition])).
% 1.51/1.29 thf(f98,plain,(
% 1.51/1.29 ((sK7 @ sK3 @ sK0) = $true) | (~spl11_1 | ~spl11_6)),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.51/1.29 thf(f97,plain,(
% 1.51/1.29 ($true != $true) | ((sK7 @ sK3 @ sK0) = $true) | (~spl11_1 | ~spl11_6)),
% 1.51/1.29 inference(forward_demodulation,[status(thm)],[f95,f19])).
% 1.51/1.29 thf(f19,plain,(
% 1.51/1.29 ((sK2 @ sK7) = $true)),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.29 thf(f13,plain,(
% 1.51/1.29 ! [X4 : a > a > $o] : (((X4 @ sK1 @ sK3) = $true) | (((X4 @ (sK5 @ X4) @ (sK4 @ X4)) = $true) & ((X4 @ (sK5 @ X4) @ (sK6 @ X4)) != $true) & ((X4 @ (sK4 @ X4) @ (sK6 @ X4)) = $true)) | ((sK2 @ X4) != $true)) & (((sK2 @ sK7) = $true) & ! [X9 : a,X10 : a,X11 : a] : (((sK7 @ X11 @ X10) != $true) | ((sK7 @ X11 @ X9) = $true) | ((sK7 @ X10 @ X9) != $true)) & ((sK7 @ sK1 @ sK0) != $true)) & ! [X12 : a > a > $o] : (((X12 @ sK3 @ sK0) = $true) | (((X12 @ (sK10 @ X12) @ (sK9 @ X12)) != $true) & ((X12 @ (sK8 @ X12) @ (sK9 @ X12)) = $true) & ((X12 @ (sK10 @ X12) @ (sK8 @ X12)) = $true)) | ((sK2 @ X12) != $true))),
% 1.51/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10])],[f8,f12,f11,f10,f9])).
% 1.51/1.29 thf(f9,plain,(
% 1.51/1.29 ? [X0 : a,X1 : a,X2 : (a > a > $o) > $o,X3 : a] : (! [X4 : a > a > $o] : (((X4 @ X1 @ X3) = $true) | ? [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X5) = $true) & ((X4 @ X6 @ X7) != $true) & ((X4 @ X5 @ X7) = $true)) | ((X2 @ X4) != $true)) & ? [X8 : a > a > $o] : (((X2 @ X8) = $true) & ! [X9 : a,X10 : a,X11 : a] : (((X8 @ X11 @ X10) != $true) | ((X8 @ X11 @ X9) = $true) | ((X8 @ X10 @ X9) != $true)) & ((X8 @ X1 @ X0) != $true)) & ! [X12 : a > a > $o] : (((X12 @ X3 @ X0) = $true) | ? [X13 : a,X14 : a,X15 : a] : (((X12 @ X15 @ X14) != $true) & ((X12 @ X13 @ X14) = $true) & ((X12 @ X15 @ X13) = $true)) | ((X2 @ X12) != $true))) => (! [X4 : a > a > $o] : (((X4 @ sK1 @ sK3) = $true) | ? [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X5) = $true) & ((X4 @ X6 @ X7) != $true) & ((X4 @ X5 @ X7) = $true)) | ((sK2 @ X4) != $true)) & ? [X8 : a > a > $o] : (((sK2 @ X8) = $true) & ! [X9 : a,X10 : a,X11 : a] : (((X8 @ X11 @ X10) != $true) | ((X8 @ X11 @ X9) = $true) | ((X8 @ X10 @ X9) != $true)) & ((X8 @ sK1 @ sK0) != $true)) & ! [X12 : a > a > $o] : (((X12 @ sK3 @ sK0) = $true) | ? [X13 : a,X14 : a,X15 : a] : (((X12 @ X15 @ X14) != $true) & ((X12 @ X13 @ X14) = $true) & ((X12 @ X15 @ X13) = $true)) | ((sK2 @ X12) != $true)))),
% 1.51/1.29 introduced(definition,[],[choice_axiom])).
% 1.51/1.29 thf(f10,plain,(
% 1.51/1.29 ! [X4 : a > a > $o] : (? [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X5) = $true) & ((X4 @ X6 @ X7) != $true) & ((X4 @ X5 @ X7) = $true)) => (((X4 @ (sK5 @ X4) @ (sK4 @ X4)) = $true) & ((X4 @ (sK5 @ X4) @ (sK6 @ X4)) != $true) & ((X4 @ (sK4 @ X4) @ (sK6 @ X4)) = $true)))),
% 1.51/1.29 introduced(definition,[],[choice_axiom])).
% 1.51/1.29 thf(f11,plain,(
% 1.51/1.29 ? [X8 : a > a > $o] : (((sK2 @ X8) = $true) & ! [X9 : a,X10 : a,X11 : a] : (((X8 @ X11 @ X10) != $true) | ((X8 @ X11 @ X9) = $true) | ((X8 @ X10 @ X9) != $true)) & ((X8 @ sK1 @ sK0) != $true)) => (((sK2 @ sK7) = $true) & ! [X11 : a,X10 : a,X9 : a] : (((sK7 @ X11 @ X10) != $true) | ((sK7 @ X11 @ X9) = $true) | ((sK7 @ X10 @ X9) != $true)) & ((sK7 @ sK1 @ sK0) != $true))),
% 1.51/1.29 introduced(definition,[],[choice_axiom])).
% 1.51/1.29 thf(f12,plain,(
% 1.51/1.29 ! [X12 : a > a > $o] : (? [X13 : a,X14 : a,X15 : a] : (((X12 @ X15 @ X14) != $true) & ((X12 @ X13 @ X14) = $true) & ((X12 @ X15 @ X13) = $true)) => (((X12 @ (sK10 @ X12) @ (sK9 @ X12)) != $true) & ((X12 @ (sK8 @ X12) @ (sK9 @ X12)) = $true) & ((X12 @ (sK10 @ X12) @ (sK8 @ X12)) = $true)))),
% 1.51/1.29 introduced(definition,[],[choice_axiom])).
% 1.51/1.29 thf(f8,plain,(
% 1.51/1.29 ? [X0 : a,X1 : a,X2 : (a > a > $o) > $o,X3 : a] : (! [X4 : a > a > $o] : (((X4 @ X1 @ X3) = $true) | ? [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X5) = $true) & ((X4 @ X6 @ X7) != $true) & ((X4 @ X5 @ X7) = $true)) | ((X2 @ X4) != $true)) & ? [X8 : a > a > $o] : (((X2 @ X8) = $true) & ! [X9 : a,X10 : a,X11 : a] : (((X8 @ X11 @ X10) != $true) | ((X8 @ X11 @ X9) = $true) | ((X8 @ X10 @ X9) != $true)) & ((X8 @ X1 @ X0) != $true)) & ! [X12 : a > a > $o] : (((X12 @ X3 @ X0) = $true) | ? [X13 : a,X14 : a,X15 : a] : (((X12 @ X15 @ X14) != $true) & ((X12 @ X13 @ X14) = $true) & ((X12 @ X15 @ X13) = $true)) | ((X2 @ X12) != $true)))),
% 1.51/1.29 inference(rectify,[status(thm)],[f7])).
% 1.51/1.29 thf(f7,plain,(
% 1.51/1.29 ? [X0 : a,X3 : a,X2 : (a > a > $o) > $o,X1 : a] : (! [X4 : a > a > $o] : (((X4 @ X3 @ X1) = $true) | ? [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X5) = $true) & ((X4 @ X6 @ X7) != $true) & ((X4 @ X5 @ X7) = $true)) | ((X2 @ X4) != $true)) & ? [X12 : a > a > $o] : (((X2 @ X12) = $true) & ! [X15 : a,X14 : a,X13 : a] : (((X12 @ X13 @ X14) != $true) | ((X12 @ X13 @ X15) = $true) | ((X12 @ X14 @ X15) != $true)) & ((X12 @ X3 @ X0) != $true)) & ! [X8 : a > a > $o] : (((X8 @ X1 @ X0) = $true) | ? [X9 : a,X10 : a,X11 : a] : (((X8 @ X11 @ X10) != $true) & ((X8 @ X9 @ X10) = $true) & ((X8 @ X11 @ X9) = $true)) | ((X2 @ X8) != $true)))),
% 1.51/1.29 inference(flattening,[status(thm)],[f6])).
% 1.51/1.29 thf(f6,plain,(
% 1.51/1.29 ? [X1 : a,X2 : (a > a > $o) > $o,X0 : a,X3 : a] : (? [X12 : a > a > $o] : (((X12 @ X3 @ X0) != $true) & (((X2 @ X12) = $true) & ! [X13 : a,X15 : a,X14 : a] : (((X12 @ X13 @ X15) = $true) | (((X12 @ X13 @ X14) != $true) | ((X12 @ X14 @ X15) != $true))))) & (! [X8 : a > a > $o] : (((X8 @ X1 @ X0) = $true) | (((X2 @ X8) != $true) | ? [X10 : a,X11 : a,X9 : a] : (((X8 @ X11 @ X10) != $true) & (((X8 @ X11 @ X9) = $true) & ((X8 @ X9 @ X10) = $true))))) & ! [X4 : a > a > $o] : (((X4 @ X3 @ X1) = $true) | (((X2 @ X4) != $true) | ? [X5 : a,X7 : a,X6 : a] : (((X4 @ X6 @ X7) != $true) & (((X4 @ X6 @ X5) = $true) & ((X4 @ X5 @ X7) = $true)))))))),
% 1.51/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.29 thf(f5,plain,(
% 1.51/1.29 ~! [X1 : a,X2 : (a > a > $o) > $o,X0 : a,X3 : a] : ((! [X8 : a > a > $o] : ((((X2 @ X8) = $true) & ! [X10 : a,X11 : a,X9 : a] : ((((X8 @ X11 @ X9) = $true) & ((X8 @ X9 @ X10) = $true)) => ((X8 @ X11 @ X10) = $true))) => ((X8 @ X1 @ X0) = $true)) & ! [X4 : a > a > $o] : ((((X2 @ X4) = $true) & ! [X5 : a,X7 : a,X6 : a] : ((((X4 @ X6 @ X5) = $true) & ((X4 @ X5 @ X7) = $true)) => ((X4 @ X6 @ X7) = $true))) => ((X4 @ X3 @ X1) = $true))) => ! [X12 : a > a > $o] : ((((X2 @ X12) = $true) & ! [X13 : a,X15 : a,X14 : a] : ((((X12 @ X13 @ X14) = $true) & ((X12 @ X14 @ X15) = $true)) => ((X12 @ X13 @ X15) = $true))) => ((X12 @ X3 @ X0) = $true)))),
% 1.51/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.29 thf(f4,plain,(
% 1.51/1.29 ~! [X0 : a,X1 : a,X2 : (a > a > $o) > $o,X3 : a] : ((! [X4 : a > a > $o] : (((X2 @ X4) & ! [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X5) & (X4 @ X5 @ X7)) => (X4 @ X6 @ X7))) => (X4 @ X3 @ X1)) & ! [X8 : a > a > $o] : (((X2 @ X8) & ! [X9 : a,X10 : a,X11 : a] : (((X8 @ X11 @ X9) & (X8 @ X9 @ X10)) => (X8 @ X11 @ X10))) => (X8 @ X1 @ X0))) => ! [X12 : a > a > $o] : (((X2 @ X12) & ! [X13 : a,X14 : a,X15 : a] : (((X12 @ X13 @ X14) & (X12 @ X14 @ X15)) => (X12 @ X13 @ X15))) => (X12 @ X3 @ X0)))),
% 1.51/1.29 inference(rectify,[status(thm)],[f2])).
% 1.51/1.29 thf(f2,negated_conjecture,(
% 1.51/1.29 ~! [X3 : a,X2 : a,X0 : (a > a > $o) > $o,X1 : a] : ((! [X4 : a > a > $o] : (((X0 @ X4) & ! [X6 : a,X5 : a,X7 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7))) => (X4 @ X1 @ X2)) & ! [X4 : a > a > $o] : (((X0 @ X4) & ! [X6 : a,X7 : a,X5 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7))) => (X4 @ X2 @ X3))) => ! [X4 : a > a > $o] : (((X0 @ X4) & ! [X5 : a,X6 : a,X7 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7))) => (X4 @ X1 @ X3)))),
% 1.51/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.29 thf(f1,conjecture,(
% 1.51/1.29 ! [X3 : a,X2 : a,X0 : (a > a > $o) > $o,X1 : a] : ((! [X4 : a > a > $o] : (((X0 @ X4) & ! [X6 : a,X5 : a,X7 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7))) => (X4 @ X1 @ X2)) & ! [X4 : a > a > $o] : (((X0 @ X4) & ! [X6 : a,X7 : a,X5 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7))) => (X4 @ X2 @ X3))) => ! [X4 : a > a > $o] : (((X0 @ X4) & ! [X5 : a,X6 : a,X7 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7))) => (X4 @ X1 @ X3)))),
% 1.51/1.29 file('/export/starexec/sandbox/tmp/tmp.iv9W0fRYgu/DTF2THF_2965.p',cTHM70_pme)).
% 1.51/1.29 thf(f95,plain,(
% 1.51/1.29 ((sK2 @ sK7) != $true) | ((sK7 @ sK3 @ sK0) = $true) | (~spl11_1 | ~spl11_6)),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.51/1.29 thf(f94,plain,(
% 1.51/1.29 ($true != $true) | ((sK7 @ sK3 @ sK0) = $true) | ((sK2 @ sK7) != $true) | (~spl11_1 | ~spl11_6)),
% 1.51/1.29 inference(superposition,[status(thm)],[f16,f91])).
% 1.51/1.29 thf(f91,plain,(
% 1.51/1.29 ((sK7 @ (sK10 @ sK7) @ (sK9 @ sK7)) = $true) | (~spl11_1 | ~spl11_6)),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.51/1.29 thf(f89,plain,(
% 1.51/1.29 ((sK7 @ (sK10 @ sK7) @ (sK9 @ sK7)) = $true) | ($true != $true) | (~spl11_1 | ~spl11_6)),
% 1.51/1.29 inference(superposition,[status(thm)],[f75,f70])).
% 1.51/1.29 thf(f70,plain,(
% 1.51/1.29 ((sK7 @ (sK8 @ sK7) @ (sK9 @ sK7)) = $true) | ~spl11_6),
% 1.51/1.29 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.51/1.29 thf(f75,plain,(
% 1.51/1.29 ( ! [X0 : a] : (((sK7 @ (sK8 @ sK7) @ X0) != $true) | ((sK7 @ (sK10 @ sK7) @ X0) = $true)) ) | ~spl11_1),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.51/1.29 thf(f74,plain,(
% 1.51/1.29 ( ! [X0 : a] : (((sK7 @ (sK8 @ sK7) @ X0) != $true) | ($true != $true) | ((sK7 @ (sK10 @ sK7) @ X0) = $true)) ) | ~spl11_1),
% 1.51/1.29 inference(superposition,[status(thm)],[f18,f28])).
% 1.51/1.29 thf(f28,plain,(
% 1.51/1.29 ((sK7 @ (sK10 @ sK7) @ (sK8 @ sK7)) = $true) | ~spl11_1),
% 1.51/1.29 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.51/1.29 thf(f18,plain,(
% 1.51/1.29 ( ! [X10 : a,X11 : a,X9 : a] : (((sK7 @ X11 @ X10) != $true) | ((sK7 @ X10 @ X9) != $true) | ((sK7 @ X11 @ X9) = $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.29 thf(f16,plain,(
% 1.51/1.29 ( ! [X12 : a > a > $o] : (((X12 @ (sK10 @ X12) @ (sK9 @ X12)) != $true) | ((X12 @ sK3 @ sK0) = $true) | ((sK2 @ X12) != $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.29 thf(f86,plain,(
% 1.51/1.29 spl11_3 | ~spl11_4 | ~spl11_5),
% 1.51/1.29 inference(avatar_split_clause,[status(thm)],[f85,f63,f45,f41])).
% 1.51/1.29 thf(f41,definition,(
% 1.51/1.29 spl11_3 <=> ((sK7 @ sK1 @ sK3) = $true)),
% 1.51/1.29 introduced(definition,[new_symbols(naming,[spl11_3])],[avatar_definition])).
% 1.51/1.29 thf(f45,definition,(
% 1.51/1.29 spl11_4 <=> ((sK7 @ (sK4 @ sK7) @ (sK6 @ sK7)) = $true)),
% 1.51/1.29 introduced(definition,[new_symbols(naming,[spl11_4])],[avatar_definition])).
% 1.51/1.29 thf(f63,definition,(
% 1.51/1.29 spl11_5 <=> ((sK7 @ (sK5 @ sK7) @ (sK4 @ sK7)) = $true)),
% 1.51/1.29 introduced(definition,[new_symbols(naming,[spl11_5])],[avatar_definition])).
% 1.51/1.29 thf(f85,plain,(
% 1.51/1.29 ((sK7 @ sK1 @ sK3) = $true) | (~spl11_4 | ~spl11_5)),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.51/1.29 thf(f84,plain,(
% 1.51/1.29 ($true != $true) | ((sK7 @ sK1 @ sK3) = $true) | (~spl11_4 | ~spl11_5)),
% 1.51/1.29 inference(forward_demodulation,[status(thm)],[f82,f19])).
% 1.51/1.29 thf(f82,plain,(
% 1.51/1.29 ((sK2 @ sK7) != $true) | ((sK7 @ sK1 @ sK3) = $true) | (~spl11_4 | ~spl11_5)),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.51/1.29 thf(f81,plain,(
% 1.51/1.29 ((sK2 @ sK7) != $true) | ((sK7 @ sK1 @ sK3) = $true) | ($true != $true) | (~spl11_4 | ~spl11_5)),
% 1.51/1.29 inference(superposition,[status(thm)],[f21,f79])).
% 1.51/1.29 thf(f79,plain,(
% 1.51/1.29 ($true = (sK7 @ (sK5 @ sK7) @ (sK6 @ sK7))) | (~spl11_4 | ~spl11_5)),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.51/1.29 thf(f78,plain,(
% 1.51/1.29 ($true = (sK7 @ (sK5 @ sK7) @ (sK6 @ sK7))) | ($true != $true) | (~spl11_4 | ~spl11_5)),
% 1.51/1.29 inference(superposition,[status(thm)],[f77,f47])).
% 1.51/1.29 thf(f47,plain,(
% 1.51/1.29 ((sK7 @ (sK4 @ sK7) @ (sK6 @ sK7)) = $true) | ~spl11_4),
% 1.51/1.29 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.51/1.29 thf(f77,plain,(
% 1.51/1.29 ( ! [X0 : a] : (($true != (sK7 @ (sK4 @ sK7) @ X0)) | ((sK7 @ (sK5 @ sK7) @ X0) = $true)) ) | ~spl11_5),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.51/1.29 thf(f76,plain,(
% 1.51/1.29 ( ! [X0 : a] : (($true != $true) | ($true != (sK7 @ (sK4 @ sK7) @ X0)) | ((sK7 @ (sK5 @ sK7) @ X0) = $true)) ) | ~spl11_5),
% 1.51/1.29 inference(superposition,[status(thm)],[f18,f65])).
% 1.51/1.29 thf(f65,plain,(
% 1.51/1.29 ((sK7 @ (sK5 @ sK7) @ (sK4 @ sK7)) = $true) | ~spl11_5),
% 1.51/1.29 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.51/1.29 thf(f21,plain,(
% 1.51/1.29 ( ! [X4 : a > a > $o] : (((X4 @ (sK5 @ X4) @ (sK6 @ X4)) != $true) | ((sK2 @ X4) != $true) | ((X4 @ sK1 @ sK3) = $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.29 thf(f71,plain,(
% 1.51/1.29 spl11_6 | spl11_2),
% 1.51/1.29 inference(avatar_split_clause,[status(thm)],[f37,f30,f68])).
% 1.51/1.29 thf(f37,plain,(
% 1.51/1.29 ((sK7 @ (sK8 @ sK7) @ (sK9 @ sK7)) = $true) | ((sK7 @ sK3 @ sK0) = $true)),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.51/1.29 thf(f36,plain,(
% 1.51/1.29 ((sK7 @ (sK8 @ sK7) @ (sK9 @ sK7)) = $true) | ($true != $true) | ((sK7 @ sK3 @ sK0) = $true)),
% 1.51/1.29 inference(superposition,[status(thm)],[f15,f19])).
% 1.51/1.29 thf(f15,plain,(
% 1.51/1.29 ( ! [X12 : a > a > $o] : (((sK2 @ X12) != $true) | ((X12 @ sK3 @ sK0) = $true) | ((X12 @ (sK8 @ X12) @ (sK9 @ X12)) = $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.29 thf(f66,plain,(
% 1.51/1.29 spl11_3 | spl11_5),
% 1.51/1.29 inference(avatar_split_clause,[status(thm)],[f61,f63,f41])).
% 1.51/1.29 thf(f61,plain,(
% 1.51/1.29 ((sK7 @ sK1 @ sK3) = $true) | ((sK7 @ (sK5 @ sK7) @ (sK4 @ sK7)) = $true)),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.51/1.29 thf(f60,plain,(
% 1.51/1.29 ((sK7 @ sK1 @ sK3) = $true) | ((sK7 @ (sK5 @ sK7) @ (sK4 @ sK7)) = $true) | ($true != $true)),
% 1.51/1.29 inference(superposition,[status(thm)],[f22,f19])).
% 1.51/1.29 thf(f22,plain,(
% 1.51/1.29 ( ! [X4 : a > a > $o] : (((sK2 @ X4) != $true) | ((X4 @ (sK5 @ X4) @ (sK4 @ X4)) = $true) | ((X4 @ sK1 @ sK3) = $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.29 thf(f57,plain,(
% 1.51/1.29 ~spl11_2 | ~spl11_3),
% 1.51/1.29 inference(avatar_contradiction_clause,[status(thm)],[f56])).
% 1.51/1.29 thf(f56,plain,(
% 1.51/1.29 $false | (~spl11_2 | ~spl11_3)),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.51/1.29 thf(f53,plain,(
% 1.51/1.29 ($true != $true) | (~spl11_2 | ~spl11_3)),
% 1.51/1.29 inference(superposition,[status(thm)],[f17,f52])).
% 1.51/1.29 thf(f52,plain,(
% 1.51/1.29 ((sK7 @ sK1 @ sK0) = $true) | (~spl11_2 | ~spl11_3)),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.51/1.29 thf(f51,plain,(
% 1.51/1.29 ($true != $true) | ((sK7 @ sK1 @ sK0) = $true) | (~spl11_2 | ~spl11_3)),
% 1.51/1.29 inference(superposition,[status(thm)],[f50,f32])).
% 1.51/1.29 thf(f32,plain,(
% 1.51/1.29 ((sK7 @ sK3 @ sK0) = $true) | ~spl11_2),
% 1.51/1.29 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.51/1.29 thf(f50,plain,(
% 1.51/1.29 ( ! [X0 : a] : (((sK7 @ sK3 @ X0) != $true) | ((sK7 @ sK1 @ X0) = $true)) ) | ~spl11_3),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.51/1.29 thf(f49,plain,(
% 1.51/1.29 ( ! [X0 : a] : (((sK7 @ sK3 @ X0) != $true) | ($true != $true) | ((sK7 @ sK1 @ X0) = $true)) ) | ~spl11_3),
% 1.51/1.29 inference(superposition,[status(thm)],[f18,f43])).
% 1.51/1.29 thf(f43,plain,(
% 1.51/1.29 ((sK7 @ sK1 @ sK3) = $true) | ~spl11_3),
% 1.51/1.29 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.51/1.29 thf(f17,plain,(
% 1.51/1.29 ((sK7 @ sK1 @ sK0) != $true)),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.29 thf(f48,plain,(
% 1.51/1.29 spl11_3 | spl11_4),
% 1.51/1.29 inference(avatar_split_clause,[status(thm)],[f39,f45,f41])).
% 1.51/1.29 thf(f39,plain,(
% 1.51/1.29 ((sK7 @ (sK4 @ sK7) @ (sK6 @ sK7)) = $true) | ((sK7 @ sK1 @ sK3) = $true)),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.51/1.29 thf(f38,plain,(
% 1.51/1.29 ((sK7 @ sK1 @ sK3) = $true) | ($true != $true) | ((sK7 @ (sK4 @ sK7) @ (sK6 @ sK7)) = $true)),
% 1.51/1.29 inference(superposition,[status(thm)],[f20,f19])).
% 1.51/1.29 thf(f20,plain,(
% 1.51/1.29 ( ! [X4 : a > a > $o] : (((sK2 @ X4) != $true) | ((X4 @ sK1 @ sK3) = $true) | ((X4 @ (sK4 @ X4) @ (sK6 @ X4)) = $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.29 thf(f33,plain,(
% 1.51/1.29 spl11_1 | spl11_2),
% 1.51/1.29 inference(avatar_split_clause,[status(thm)],[f24,f30,f26])).
% 1.51/1.29 thf(f24,plain,(
% 1.51/1.29 ((sK7 @ (sK10 @ sK7) @ (sK8 @ sK7)) = $true) | ((sK7 @ sK3 @ sK0) = $true)),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.51/1.29 thf(f23,plain,(
% 1.51/1.29 ((sK7 @ (sK10 @ sK7) @ (sK8 @ sK7)) = $true) | ($true != $true) | ((sK7 @ sK3 @ sK0) = $true)),
% 1.51/1.29 inference(superposition,[status(thm)],[f14,f19])).
% 1.51/1.29 thf(f14,plain,(
% 1.51/1.29 ( ! [X12 : a > a > $o] : (((sK2 @ X12) != $true) | ((X12 @ sK3 @ sK0) = $true) | ((X12 @ (sK10 @ X12) @ (sK8 @ X12)) = $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.29 % SZS output end Proof for DTF2THF_2965
% 1.51/1.29 % (3237)------------------------------
% 1.51/1.29 % (3237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (3237)Termination reason: Refutation
% 1.51/1.29
% 1.51/1.29 % (3237)Memory used [KB]: 5628
% 1.51/1.29 % (3237)Time elapsed: 0.009 s
% 1.51/1.29 % (3237)Instructions burned: 14 (million)
% 1.51/1.29 % (3237)------------------------------
% 1.51/1.29 % (3237)------------------------------
% 1.51/1.29 % (3234)Success in time 0.018 s
%------------------------------------------------------------------------------