%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV136^5 : 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 : n017.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 09:40:22 AM UTC 2026
% Result : Theorem 1.65s 1.33s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 492 ( 154 equ; 0 cnn)
% Maximal formula atoms : 24 ( 10 avg)
% Number of connectives : 738 ( 91 ~; 83 |; 62 &; 468 @)
% ( 3 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 144 ( 0 ^; 108 !; 36 ?; 144 :)
% 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 > a > $o ) > a > a > $o ).
thf(func_def_6,type,
sK1: a > a > $o ).
thf(func_def_7,type,
sK2: a ).
thf(func_def_8,type,
sK3: a ).
thf(func_def_9,type,
sK4: ( a > $o ) > a ).
thf(func_def_10,type,
sK5: ( a > $o ) > a ).
thf(func_def_12,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f61,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f31,f40,f45,f60]) ).
thf(f60,plain,
( spl6_1
| ~ spl6_2
| ~ spl6_3 ),
inference(avatar_split_clause,[status(thm)],[f59,f37,f28,f24]) ).
thf(f24,definition,
( spl6_1
<=> ( $true
= ( sK0 @ sK1 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f28,definition,
( spl6_2
<=> ( $true
= ( sK0 @ sK1 @ sK2 @ ( sK4 @ ( sK0 @ sK1 @ sK2 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f37,definition,
( spl6_3
<=> ( $true
= ( sK1 @ ( sK4 @ ( sK0 @ sK1 @ sK2 ) ) @ ( sK5 @ ( sK0 @ sK1 @ sK2 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition]) ).
thf(f59,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 @ sK3 ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $true != $true )
| ( $true
= ( sK0 @ sK1 @ sK2 @ sK3 ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[status(thm)],[f56,f13]) ).
thf(f13,plain,
! [X12: a] :
( $true
= ( sK0 @ sK1 @ X12 @ X12 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X2: a,X3: a] :
( ( $true
= ( sK0 @ sK1 @ X2 @ X3 ) )
| ( $true
!= ( sK1 @ X2 @ X3 ) ) )
& ! [X4: a,X5: a,X6: a] :
( ( $true
!= ( sK0 @ sK1 @ X6 @ X5 ) )
| ( $true
!= ( sK0 @ sK1 @ X5 @ X4 ) )
| ( $true
= ( sK0 @ sK1 @ X6 @ X4 ) ) )
& ( $true
!= ( sK0 @ sK1 @ sK2 @ sK3 ) )
& ! [X9: a > $o] :
( ( ( X9 @ sK3 )
= $true )
| ( ( $true
= ( X9 @ ( sK4 @ X9 ) ) )
& ( $true
!= ( X9 @ ( sK5 @ X9 ) ) )
& ( $true
= ( sK1 @ ( sK4 @ X9 ) @ ( sK5 @ X9 ) ) ) )
| ( $true
!= ( X9 @ sK2 ) ) )
& ! [X12: a] :
( $true
= ( sK0 @ sK1 @ X12 @ X12 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: ( a > a > $o ) > a > a > $o,X1: a > a > $o] :
( ! [X2: a,X3: a] :
( ( $true
= ( X0 @ X1 @ X2 @ X3 ) )
| ( $true
!= ( X1 @ X2 @ X3 ) ) )
& ! [X4: a,X5: a,X6: a] :
( ( $true
!= ( X0 @ X1 @ X6 @ X5 ) )
| ( $true
!= ( X0 @ X1 @ X5 @ X4 ) )
| ( $true
= ( X0 @ X1 @ X6 @ X4 ) ) )
& ? [X7: a,X8: a] :
( ( $true
!= ( X0 @ X1 @ X7 @ X8 ) )
& ! [X9: a > $o] :
( ( $true
= ( X9 @ X8 ) )
| ? [X10: a,X11: a] :
( ( $true
= ( X9 @ X10 ) )
& ( $true
!= ( X9 @ X11 ) )
& ( $true
= ( X1 @ X10 @ X11 ) ) )
| ( $true
!= ( X9 @ X7 ) ) ) )
& ! [X12: a] :
( $true
= ( X0 @ X1 @ X12 @ X12 ) ) )
=> ( ! [X3: a,X2: a] :
( ( $true
= ( sK0 @ sK1 @ X2 @ X3 ) )
| ( $true
!= ( sK1 @ X2 @ X3 ) ) )
& ! [X6: a,X5: a,X4: a] :
( ( $true
!= ( sK0 @ sK1 @ X6 @ X5 ) )
| ( $true
!= ( sK0 @ sK1 @ X5 @ X4 ) )
| ( $true
= ( sK0 @ sK1 @ X6 @ X4 ) ) )
& ? [X8: a,X7: a] :
( ( $true
!= ( sK0 @ sK1 @ X7 @ X8 ) )
& ! [X9: a > $o] :
( ( $true
= ( X9 @ X8 ) )
| ? [X11: a,X10: a] :
( ( $true
= ( X9 @ X10 ) )
& ( $true
!= ( X9 @ X11 ) )
& ( $true
= ( sK1 @ X10 @ X11 ) ) )
| ( $true
!= ( X9 @ X7 ) ) ) )
& ! [X12: a] :
( $true
= ( sK0 @ sK1 @ X12 @ X12 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X8: a,X7: a] :
( ( $true
!= ( sK0 @ sK1 @ X7 @ X8 ) )
& ! [X9: a > $o] :
( ( $true
= ( X9 @ X8 ) )
| ? [X11: a,X10: a] :
( ( $true
= ( X9 @ X10 ) )
& ( $true
!= ( X9 @ X11 ) )
& ( $true
= ( sK1 @ X10 @ X11 ) ) )
| ( $true
!= ( X9 @ X7 ) ) ) )
=> ( ( $true
!= ( sK0 @ sK1 @ sK2 @ sK3 ) )
& ! [X9: a > $o] :
( ( ( X9 @ sK3 )
= $true )
| ? [X11: a,X10: a] :
( ( $true
= ( X9 @ X10 ) )
& ( $true
!= ( X9 @ X11 ) )
& ( $true
= ( sK1 @ X10 @ X11 ) ) )
| ( $true
!= ( X9 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X9: a > $o] :
( ? [X11: a,X10: a] :
( ( $true
= ( X9 @ X10 ) )
& ( $true
!= ( X9 @ X11 ) )
& ( $true
= ( sK1 @ X10 @ X11 ) ) )
=> ( ( $true
= ( X9 @ ( sK4 @ X9 ) ) )
& ( $true
!= ( X9 @ ( sK5 @ X9 ) ) )
& ( $true
= ( sK1 @ ( sK4 @ X9 ) @ ( sK5 @ X9 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: ( a > a > $o ) > a > a > $o,X1: a > a > $o] :
( ! [X2: a,X3: a] :
( ( $true
= ( X0 @ X1 @ X2 @ X3 ) )
| ( $true
!= ( X1 @ X2 @ X3 ) ) )
& ! [X4: a,X5: a,X6: a] :
( ( $true
!= ( X0 @ X1 @ X6 @ X5 ) )
| ( $true
!= ( X0 @ X1 @ X5 @ X4 ) )
| ( $true
= ( X0 @ X1 @ X6 @ X4 ) ) )
& ? [X7: a,X8: a] :
( ( $true
!= ( X0 @ X1 @ X7 @ X8 ) )
& ! [X9: a > $o] :
( ( $true
= ( X9 @ X8 ) )
| ? [X10: a,X11: a] :
( ( $true
= ( X9 @ X10 ) )
& ( $true
!= ( X9 @ X11 ) )
& ( $true
= ( X1 @ X10 @ X11 ) ) )
| ( $true
!= ( X9 @ X7 ) ) ) )
& ! [X12: a] :
( $true
= ( X0 @ X1 @ X12 @ X12 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: ( a > a > $o ) > a > a > $o,X0: a > a > $o] :
( ! [X3: a,X4: a] :
( ( ( X1 @ X0 @ X3 @ X4 )
= $true )
| ( $true
!= ( X0 @ X3 @ X4 ) ) )
& ! [X5: a,X7: a,X6: a] :
( ( $true
!= ( X1 @ X0 @ X6 @ X7 ) )
| ( $true
!= ( X1 @ X0 @ X7 @ X5 ) )
| ( $true
= ( X1 @ X0 @ X6 @ X5 ) ) )
& ? [X9: a,X8: a] :
( ( ( X1 @ X0 @ X9 @ X8 )
!= $true )
& ! [X10: a > $o] :
( ( $true
= ( X10 @ X8 ) )
| ? [X12: a,X11: a] :
( ( $true
= ( X10 @ X12 ) )
& ( $true
!= ( X10 @ X11 ) )
& ( $true
= ( X0 @ X12 @ X11 ) ) )
| ( $true
!= ( X10 @ X9 ) ) ) )
& ! [X2: a] :
( ( X1 @ X0 @ X2 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > a > $o,X1: ( a > a > $o ) > a > a > $o] :
( ? [X9: a,X8: a] :
( ( ( X1 @ X0 @ X9 @ X8 )
!= $true )
& ! [X10: a > $o] :
( ( $true
= ( X10 @ X8 ) )
| ( $true
!= ( X10 @ X9 ) )
| ? [X11: a,X12: a] :
( ( $true
!= ( X10 @ X11 ) )
& ( $true
= ( X10 @ X12 ) )
& ( $true
= ( X0 @ X12 @ X11 ) ) ) ) )
& ! [X3: a,X4: a] :
( ( ( X1 @ X0 @ X3 @ X4 )
= $true )
| ( $true
!= ( X0 @ X3 @ X4 ) ) )
& ! [X2: a] :
( ( X1 @ X0 @ X2 @ X2 )
= $true )
& ! [X5: a,X6: a,X7: a] :
( ( $true
= ( X1 @ X0 @ X6 @ X5 ) )
| ( $true
!= ( X1 @ X0 @ X7 @ X5 ) )
| ( $true
!= ( X1 @ X0 @ X6 @ X7 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > a > $o,X1: ( a > a > $o ) > a > a > $o] :
( ( ! [X4: a,X3: a] :
( ( $true
= ( X0 @ X3 @ X4 ) )
=> ( ( X1 @ X0 @ X3 @ X4 )
= $true ) )
& ! [X2: a] :
( ( X1 @ X0 @ X2 @ X2 )
= $true )
& ! [X5: a,X6: a,X7: a] :
( ( ( $true
= ( X1 @ X0 @ X7 @ X5 ) )
& ( $true
= ( X1 @ X0 @ X6 @ X7 ) ) )
=> ( $true
= ( X1 @ X0 @ X6 @ X5 ) ) ) )
=> ! [X9: a,X8: a] :
( ! [X10: a > $o] :
( ! [X11: a,X12: a] :
( ( ( $true
= ( X10 @ X12 ) )
& ( $true
= ( X0 @ X12 @ X11 ) ) )
=> ( $true
= ( X10 @ X11 ) ) )
=> ( ( $true
= ( X10 @ X9 ) )
=> ( $true
= ( X10 @ X8 ) ) ) )
=> ( ( X1 @ X0 @ X9 @ X8 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: ( a > a > $o ) > a > a > $o] :
( ( ! [X2: a] : ( X1 @ X0 @ X2 @ X2 )
& ! [X3: a,X4: a] :
( ( X0 @ X3 @ X4 )
=> ( X1 @ X0 @ X3 @ X4 ) )
& ! [X5: a,X6: a,X7: a] :
( ( ( X1 @ X0 @ X7 @ X5 )
& ( X1 @ X0 @ X6 @ X7 ) )
=> ( X1 @ X0 @ X6 @ X5 ) ) )
=> ! [X8: a,X9: a] :
( ! [X10: a > $o] :
( ! [X11: a,X12: a] :
( ( ( X10 @ X12 )
& ( X0 @ X12 @ X11 ) )
=> ( X10 @ X11 ) )
=> ( ( X10 @ X9 )
=> ( X10 @ X8 ) ) )
=> ( X1 @ X0 @ X9 @ X8 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: ( a > a > $o ) > a > a > $o] :
( ( ! [X2: a] : ( X1 @ X0 @ X2 @ X2 )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X0 @ X2 @ X3 ) )
& ! [X4: a,X2: a,X3: a] :
( ( ( X1 @ X0 @ X3 @ X4 )
& ( X1 @ X0 @ X2 @ X3 ) )
=> ( X1 @ X0 @ X2 @ X4 ) ) )
=> ! [X3: a,X2: a] :
( ! [X5: a > $o] :
( ! [X4: a,X6: a] :
( ( ( X5 @ X6 )
& ( X0 @ X6 @ X4 ) )
=> ( X5 @ X4 ) )
=> ( ( X5 @ X2 )
=> ( X5 @ X3 ) ) )
=> ( X1 @ X0 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X1: ( a > a > $o ) > a > a > $o] :
( ( ! [X2: a] : ( X1 @ X0 @ X2 @ X2 )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X0 @ X2 @ X3 ) )
& ! [X4: a,X2: a,X3: a] :
( ( ( X1 @ X0 @ X3 @ X4 )
& ( X1 @ X0 @ X2 @ X3 ) )
=> ( X1 @ X0 @ X2 @ X4 ) ) )
=> ! [X3: a,X2: a] :
( ! [X5: a > $o] :
( ! [X4: a,X6: a] :
( ( ( X5 @ X6 )
& ( X0 @ X6 @ X4 ) )
=> ( X5 @ X4 ) )
=> ( ( X5 @ X2 )
=> ( X5 @ X3 ) ) )
=> ( X1 @ X0 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nGdl45nwNQ/DTF2THF_21974.p',cTHM203_pme) ).
thf(f56,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 @ sK3 ) )
| ( $true
!= ( sK0 @ sK1 @ sK2 @ sK2 ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $true
!= ( sK0 @ sK1 @ sK2 @ sK2 ) )
| ( $true
= ( sK0 @ sK1 @ sK2 @ sK3 ) )
| ( $true != $true )
| ~ spl6_2
| ~ spl6_3 ),
inference(superposition,[status(thm)],[f15,f52]) ).
thf(f52,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 @ ( sK5 @ ( sK0 @ sK1 @ sK2 ) ) ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 @ ( sK5 @ ( sK0 @ sK1 @ sK2 ) ) ) )
| ( $true != $true )
| ~ spl6_2
| ~ spl6_3 ),
inference(superposition,[status(thm)],[f33,f47]) ).
thf(f47,plain,
( ( $true
= ( sK0 @ sK1 @ ( sK4 @ ( sK0 @ sK1 @ sK2 ) ) @ ( sK5 @ ( sK0 @ sK1 @ sK2 ) ) ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $true
= ( sK0 @ sK1 @ ( sK4 @ ( sK0 @ sK1 @ sK2 ) ) @ ( sK5 @ ( sK0 @ sK1 @ sK2 ) ) ) )
| ( $true != $true )
| ~ spl6_3 ),
inference(superposition,[status(thm)],[f19,f39]) ).
thf(f39,plain,
( ( $true
= ( sK1 @ ( sK4 @ ( sK0 @ sK1 @ sK2 ) ) @ ( sK5 @ ( sK0 @ sK1 @ sK2 ) ) ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f19,plain,
! [X2: a,X3: a] :
( ( $true
!= ( sK1 @ X2 @ X3 ) )
| ( $true
= ( sK0 @ sK1 @ X2 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f33,plain,
( ! [X0: a] :
( ( $true
!= ( sK0 @ sK1 @ ( sK4 @ ( sK0 @ sK1 @ sK2 ) ) @ X0 ) )
| ( $true
= ( sK0 @ sK1 @ sK2 @ X0 ) ) )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ! [X0: a] :
( ( $true
= ( sK0 @ sK1 @ sK2 @ X0 ) )
| ( $true != $true )
| ( $true
!= ( sK0 @ sK1 @ ( sK4 @ ( sK0 @ sK1 @ sK2 ) ) @ X0 ) ) )
| ~ spl6_2 ),
inference(superposition,[status(thm)],[f18,f30]) ).
thf(f30,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 @ ( sK4 @ ( sK0 @ sK1 @ sK2 ) ) ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f18,plain,
! [X6: a,X4: a,X5: a] :
( ( $true
!= ( sK0 @ sK1 @ X6 @ X5 ) )
| ( $true
= ( sK0 @ sK1 @ X6 @ X4 ) )
| ( $true
!= ( sK0 @ sK1 @ X5 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f15,plain,
! [X9: a > $o] :
( ( $true
!= ( X9 @ ( sK5 @ X9 ) ) )
| ( ( X9 @ sK3 )
= $true )
| ( $true
!= ( X9 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f45,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[status(thm)],[f44]) ).
thf(f44,plain,
( $false
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ( $true != $true )
| ~ spl6_1 ),
inference(superposition,[status(thm)],[f17,f26]) ).
thf(f26,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 @ sK3 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f17,plain,
( $true
!= ( sK0 @ sK1 @ sK2 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f40,plain,
( spl6_3
| spl6_1 ),
inference(avatar_split_clause,[status(thm)],[f35,f24,f37]) ).
thf(f35,plain,
( ( $true
= ( sK1 @ ( sK4 @ ( sK0 @ sK1 @ sK2 ) ) @ ( sK5 @ ( sK0 @ sK1 @ sK2 ) ) ) )
| ( $true
= ( sK0 @ sK1 @ sK2 @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true
= ( sK1 @ ( sK4 @ ( sK0 @ sK1 @ sK2 ) ) @ ( sK5 @ ( sK0 @ sK1 @ sK2 ) ) ) )
| ( $true != $true )
| ( $true
= ( sK0 @ sK1 @ sK2 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f14,f13]) ).
thf(f14,plain,
! [X9: a > $o] :
( ( $true
!= ( X9 @ sK2 ) )
| ( $true
= ( sK1 @ ( sK4 @ X9 ) @ ( sK5 @ X9 ) ) )
| ( ( X9 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f31,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f22,f28,f24]) ).
thf(f22,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 @ ( sK4 @ ( sK0 @ sK1 @ sK2 ) ) ) )
| ( $true
= ( sK0 @ sK1 @ sK2 @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 @ ( sK4 @ ( sK0 @ sK1 @ sK2 ) ) ) )
| ( $true != $true )
| ( $true
= ( sK0 @ sK1 @ sK2 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f16,f13]) ).
thf(f16,plain,
! [X9: a > $o] :
( ( $true
!= ( X9 @ sK2 ) )
| ( ( X9 @ sK3 )
= $true )
| ( $true
= ( X9 @ ( sK4 @ X9 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV136^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n017.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 12:39:11 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEV136^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.46 % Domain : Set Theory (Relations)
% 0.20/0.46 % Problem : TPS problem THM203
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : B&B-P's defn of TRCL is the minimal transitive reflexive
% 0.20/0.46 % relation containing r.
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : tps_0426 [Bro09]
% 0.20/0.46 % : THM203 [TPS]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % 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
% 0.20/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.20/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.20/0.46 % Number of connectives : 37 ( 0 ~; 0 |; 4 &; 26 @)
% 0.20/0.46 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 15 ( 15 avg)
% 0.20/0.46 % Number of types : 2 ( 1 usr)
% 0.20/0.46 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.20/0.46 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.20/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.46 % : Polymorphic definitions expanded.
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(a_type,type,
% 0.20/0.46 a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(cTHM203_pme,conjecture,
% 0.20/0.46 ! [Xr: a > a > $o,T: ( a > a > $o ) > a > a > $o] :
% 0.20/0.46 ( ( ! [Xx: a] : ( T @ Xr @ Xx @ Xx )
% 0.20/0.46 & ! [Xx: a,Xy: a,Xz: a] :
% 0.20/0.46 ( ( ( T @ Xr @ Xx @ Xy )
% 0.20/0.46 & ( T @ Xr @ Xy @ Xz ) )
% 0.20/0.46 => ( T @ Xr @ Xx @ Xz ) )
% 0.20/0.46 & ! [Xx: a,Xy: a] :
% 0.20/0.46 ( ( Xr @ Xx @ Xy )
% 0.20/0.46 => ( T @ Xr @ Xx @ Xy ) ) )
% 0.20/0.46 => ! [Xx: a,Xy: a] :
% 0.20/0.46 ( ! [Xx0: a > $o] :
% 0.20/0.46 ( ! [Xy0: a,Xz: a] :
% 0.20/0.46 ( ( ( Xr @ Xy0 @ Xz )
% 0.20/0.46 & ( Xx0 @ Xy0 ) )
% 0.20/0.46 => ( Xx0 @ Xz ) )
% 0.20/0.46 => ( ( Xx0 @ Xx )
% 0.20/0.46 => ( Xx0 @ Xy ) ) )
% 0.20/0.46 => ( T @ Xr @ Xx @ Xy ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.49/1.28 ---- Embedded in THF ---
% 1.49/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.29 %%% Generated on Tue Feb 24 12:39:11 EST 2026
% 1.49/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.29 %%% Logic specification used:
% 1.49/1.29 %%% thf(spec, logic, $$dhol).
% 1.49/1.29
% 1.49/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.nGdl45nwNQ/DTF2DTF21974.p
% See solution above
% 1.49/1.29 ------------------------
% 1.49/1.30 ---- Cleaned THF ---
% 1.65/1.30 thf(a_type,type,
% 1.65/1.30 a: $tType ).
% 1.65/1.30
% 1.65/1.30 thf(cTHM203_pme,conjecture,
% 1.65/1.30 ! [Xr: a > a > $o,T: ( a > a > $o ) > a > a > $o] :
% 1.65/1.30 ( ( ! [Xx: a] : ( T @ Xr @ Xx @ Xx )
% 1.65/1.30 & ! [Xx: a,Xy: a,Xz: a] :
% 1.65/1.30 ( ( ( T @ Xr @ Xx @ Xy )
% 1.65/1.30 & ( T @ Xr @ Xy @ Xz ) )
% 1.65/1.30 => ( T @ Xr @ Xx @ Xz ) )
% 1.65/1.30 & ! [Xx: a,Xy: a] :
% 1.65/1.30 ( ( Xr @ Xx @ Xy )
% 1.65/1.30 => ( T @ Xr @ Xx @ Xy ) ) )
% 1.65/1.30 => ! [Xx: a,Xy: a] :
% 1.65/1.30 ( ! [Xx0: a > $o] :
% 1.65/1.30 ( ! [Xy0: a,Xz: a] :
% 1.65/1.30 ( ( ( Xr @ Xy0 @ Xz )
% 1.65/1.30 & ( Xx0 @ Xy0 ) )
% 1.65/1.30 => ( Xx0 @ Xz ) )
% 1.65/1.30 => ( ( Xx0 @ Xx )
% 1.65/1.30 => ( Xx0 @ Xy ) ) )
% 1.65/1.30 => ( T @ Xr @ Xx @ Xy ) ) ) ).
% 1.65/1.30 ------------------------
% 1.65/1.32 % (22158)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/18Mi)
% 1.65/1.32 % (22155)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/2Mi)
% 1.65/1.32 % (22155)Instruction limit reached!
% 1.65/1.32 % (22155)------------------------------
% 1.65/1.32 % (22155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (22155)Termination reason: Unknown
% 1.65/1.32 % (22155)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (22155)Memory used [KB]: 1023
% 1.65/1.32 % (22155)Time elapsed: 0.003 s
% 1.65/1.32 % (22155)Instructions burned: 2 (million)
% 1.65/1.32 % (22155)------------------------------
% 1.65/1.32 % (22155)------------------------------
% 1.65/1.32 % (22156)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_21974 for (2999ds/2Mi)
% 1.65/1.32 % (22153)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_21974 for (2999ds/4Mi)
% 1.65/1.32 % (22154)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_21974 for (2999ds/27Mi)
% 1.65/1.32 % (22156)Instruction limit reached!
% 1.65/1.32 % (22156)------------------------------
% 1.65/1.32 % (22156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (22156)Termination reason: Unknown
% 1.65/1.32 % (22156)Termination phase: Property scanning
% 1.65/1.32
% 1.65/1.32 % (22156)Memory used [KB]: 1023
% 1.65/1.32 % (22156)Time elapsed: 0.003 s
% 1.65/1.32 % (22156)Instructions burned: 2 (million)
% 1.65/1.32 % (22156)------------------------------
% 1.65/1.32 % (22156)------------------------------
% 1.65/1.32 % (22157)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_21974 for (2999ds/275Mi)
% 1.65/1.32 % (22153)Instruction limit reached!
% 1.65/1.32 % (22153)------------------------------
% 1.65/1.32 % (22153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (22153)Termination reason: Unknown
% 1.65/1.32 % (22153)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (22153)Memory used [KB]: 5500
% 1.65/1.32 % (22153)Time elapsed: 0.004 s
% 1.65/1.32 % (22153)Instructions burned: 4 (million)
% 1.65/1.32 % (22153)------------------------------
% 1.65/1.32 % (22153)------------------------------
% 1.65/1.33 % (22154)First to succeed.
% 1.65/1.33 % (22158)Instruction limit reached!
% 1.65/1.33 % (22158)------------------------------
% 1.65/1.33 % (22158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.33 % (22158)Termination reason: Unknown
% 1.65/1.33 % (22158)Termination phase: Saturation
% 1.65/1.33
% 1.65/1.33 % (22158)Memory used [KB]: 5628
% 1.65/1.33 % (22158)Time elapsed: 0.011 s
% 1.65/1.33 % (22158)Instructions burned: 18 (million)
% 1.65/1.33 % (22158)------------------------------
% 1.65/1.33 % (22158)------------------------------
% 1.65/1.33 % (22154)Refutation found. Thanks to Tanya!
% 1.65/1.33 % SZS status Theorem for DTF2THF_21974
% 1.65/1.33 % SZS output start Proof for DTF2THF_21974
% 1.65/1.33 thf(type_def_5, type, a: $tType).
% 1.65/1.33 thf(func_def_0, type, a: $tType).
% 1.65/1.33 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.65/1.33 thf(func_def_5, type, sK0: (a > a > $o) > a > a > $o).
% 1.65/1.33 thf(func_def_6, type, sK1: a > a > $o).
% 1.65/1.33 thf(func_def_7, type, sK2: a).
% 1.65/1.33 thf(func_def_8, type, sK3: a).
% 1.65/1.33 thf(func_def_9, type, sK4: (a > $o) > a).
% 1.65/1.33 thf(func_def_10, type, sK5: (a > $o) > a).
% 1.65/1.33 thf(func_def_12, type, ph7: !>[X0: $tType]:(X0)).
% 1.65/1.33 thf(f61,plain,(
% 1.65/1.33 $false),
% 1.65/1.33 inference(avatar_sat_refutation,[status(thm)],[f31,f40,f45,f60])).
% 1.65/1.33 thf(f60,plain,(
% 1.65/1.33 spl6_1 | ~spl6_2 | ~spl6_3),
% 1.65/1.33 inference(avatar_split_clause,[status(thm)],[f59,f37,f28,f24])).
% 1.65/1.33 thf(f24,definition,(
% 1.65/1.33 spl6_1 <=> ($true = (sK0 @ sK1 @ sK2 @ sK3))),
% 1.65/1.33 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.65/1.33 thf(f28,definition,(
% 1.65/1.33 spl6_2 <=> ($true = (sK0 @ sK1 @ sK2 @ (sK4 @ (sK0 @ sK1 @ sK2))))),
% 1.65/1.33 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.65/1.33 thf(f37,definition,(
% 1.65/1.33 spl6_3 <=> ($true = (sK1 @ (sK4 @ (sK0 @ sK1 @ sK2)) @ (sK5 @ (sK0 @ sK1 @ sK2))))),
% 1.65/1.33 introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition])).
% 1.65/1.33 thf(f59,plain,(
% 1.65/1.33 ($true = (sK0 @ sK1 @ sK2 @ sK3)) | (~spl6_2 | ~spl6_3)),
% 1.65/1.33 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.65/1.33 thf(f58,plain,(
% 1.65/1.33 ($true != $true) | ($true = (sK0 @ sK1 @ sK2 @ sK3)) | (~spl6_2 | ~spl6_3)),
% 1.65/1.33 inference(forward_demodulation,[status(thm)],[f56,f13])).
% 1.65/1.33 thf(f13,plain,(
% 1.65/1.33 ( ! [X12 : a] : (($true = (sK0 @ sK1 @ X12 @ X12))) )),
% 1.65/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.33 thf(f12,plain,(
% 1.65/1.33 ! [X2 : a,X3 : a] : (($true = (sK0 @ sK1 @ X2 @ X3)) | ($true != (sK1 @ X2 @ X3))) & ! [X4 : a,X5 : a,X6 : a] : (($true != (sK0 @ sK1 @ X6 @ X5)) | ($true != (sK0 @ sK1 @ X5 @ X4)) | ($true = (sK0 @ sK1 @ X6 @ X4))) & (($true != (sK0 @ sK1 @ sK2 @ sK3)) & ! [X9 : a > $o] : (((X9 @ sK3) = $true) | (($true = (X9 @ (sK4 @ X9))) & ($true != (X9 @ (sK5 @ X9))) & ($true = (sK1 @ (sK4 @ X9) @ (sK5 @ X9)))) | ($true != (X9 @ sK2)))) & ! [X12 : a] : ($true = (sK0 @ sK1 @ X12 @ X12))),
% 1.65/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9])).
% 1.65/1.33 thf(f9,plain,(
% 1.65/1.33 ? [X0 : (a > a > $o) > a > a > $o,X1 : a > a > $o] : (! [X2 : a,X3 : a] : (($true = (X0 @ X1 @ X2 @ X3)) | ($true != (X1 @ X2 @ X3))) & ! [X4 : a,X5 : a,X6 : a] : (($true != (X0 @ X1 @ X6 @ X5)) | ($true != (X0 @ X1 @ X5 @ X4)) | ($true = (X0 @ X1 @ X6 @ X4))) & ? [X7 : a,X8 : a] : (($true != (X0 @ X1 @ X7 @ X8)) & ! [X9 : a > $o] : (($true = (X9 @ X8)) | ? [X10 : a,X11 : a] : (($true = (X9 @ X10)) & ($true != (X9 @ X11)) & ($true = (X1 @ X10 @ X11))) | ($true != (X9 @ X7)))) & ! [X12 : a] : ($true = (X0 @ X1 @ X12 @ X12))) => (! [X3 : a,X2 : a] : (($true = (sK0 @ sK1 @ X2 @ X3)) | ($true != (sK1 @ X2 @ X3))) & ! [X6 : a,X5 : a,X4 : a] : (($true != (sK0 @ sK1 @ X6 @ X5)) | ($true != (sK0 @ sK1 @ X5 @ X4)) | ($true = (sK0 @ sK1 @ X6 @ X4))) & ? [X8 : a,X7 : a] : (($true != (sK0 @ sK1 @ X7 @ X8)) & ! [X9 : a > $o] : (($true = (X9 @ X8)) | ? [X11 : a,X10 : a] : (($true = (X9 @ X10)) & ($true != (X9 @ X11)) & ($true = (sK1 @ X10 @ X11))) | ($true != (X9 @ X7)))) & ! [X12 : a] : ($true = (sK0 @ sK1 @ X12 @ X12)))),
% 1.65/1.33 introduced(definition,[],[choice_axiom])).
% 1.65/1.33 thf(f10,plain,(
% 1.65/1.33 ? [X8 : a,X7 : a] : (($true != (sK0 @ sK1 @ X7 @ X8)) & ! [X9 : a > $o] : (($true = (X9 @ X8)) | ? [X11 : a,X10 : a] : (($true = (X9 @ X10)) & ($true != (X9 @ X11)) & ($true = (sK1 @ X10 @ X11))) | ($true != (X9 @ X7)))) => (($true != (sK0 @ sK1 @ sK2 @ sK3)) & ! [X9 : a > $o] : (((X9 @ sK3) = $true) | ? [X11 : a,X10 : a] : (($true = (X9 @ X10)) & ($true != (X9 @ X11)) & ($true = (sK1 @ X10 @ X11))) | ($true != (X9 @ sK2))))),
% 1.65/1.33 introduced(definition,[],[choice_axiom])).
% 1.65/1.33 thf(f11,plain,(
% 1.65/1.33 ! [X9 : a > $o] : (? [X11 : a,X10 : a] : (($true = (X9 @ X10)) & ($true != (X9 @ X11)) & ($true = (sK1 @ X10 @ X11))) => (($true = (X9 @ (sK4 @ X9))) & ($true != (X9 @ (sK5 @ X9))) & ($true = (sK1 @ (sK4 @ X9) @ (sK5 @ X9)))))),
% 1.65/1.33 introduced(definition,[],[choice_axiom])).
% 1.65/1.33 thf(f8,plain,(
% 1.65/1.33 ? [X0 : (a > a > $o) > a > a > $o,X1 : a > a > $o] : (! [X2 : a,X3 : a] : (($true = (X0 @ X1 @ X2 @ X3)) | ($true != (X1 @ X2 @ X3))) & ! [X4 : a,X5 : a,X6 : a] : (($true != (X0 @ X1 @ X6 @ X5)) | ($true != (X0 @ X1 @ X5 @ X4)) | ($true = (X0 @ X1 @ X6 @ X4))) & ? [X7 : a,X8 : a] : (($true != (X0 @ X1 @ X7 @ X8)) & ! [X9 : a > $o] : (($true = (X9 @ X8)) | ? [X10 : a,X11 : a] : (($true = (X9 @ X10)) & ($true != (X9 @ X11)) & ($true = (X1 @ X10 @ X11))) | ($true != (X9 @ X7)))) & ! [X12 : a] : ($true = (X0 @ X1 @ X12 @ X12)))),
% 1.65/1.33 inference(rectify,[status(thm)],[f7])).
% 1.65/1.33 thf(f7,plain,(
% 1.65/1.33 ? [X1 : (a > a > $o) > a > a > $o,X0 : a > a > $o] : (! [X3 : a,X4 : a] : (((X1 @ X0 @ X3 @ X4) = $true) | ($true != (X0 @ X3 @ X4))) & ! [X5 : a,X7 : a,X6 : a] : (($true != (X1 @ X0 @ X6 @ X7)) | ($true != (X1 @ X0 @ X7 @ X5)) | ($true = (X1 @ X0 @ X6 @ X5))) & ? [X9 : a,X8 : a] : (((X1 @ X0 @ X9 @ X8) != $true) & ! [X10 : a > $o] : (($true = (X10 @ X8)) | ? [X12 : a,X11 : a] : (($true = (X10 @ X12)) & ($true != (X10 @ X11)) & ($true = (X0 @ X12 @ X11))) | ($true != (X10 @ X9)))) & ! [X2 : a] : ((X1 @ X0 @ X2 @ X2) = $true))),
% 1.65/1.33 inference(flattening,[status(thm)],[f6])).
% 1.65/1.33 thf(f6,plain,(
% 1.65/1.33 ? [X0 : a > a > $o,X1 : (a > a > $o) > a > a > $o] : (? [X9 : a,X8 : a] : (((X1 @ X0 @ X9 @ X8) != $true) & ! [X10 : a > $o] : ((($true = (X10 @ X8)) | ($true != (X10 @ X9))) | ? [X11 : a,X12 : a] : (($true != (X10 @ X11)) & (($true = (X10 @ X12)) & ($true = (X0 @ X12 @ X11)))))) & (! [X3 : a,X4 : a] : (((X1 @ X0 @ X3 @ X4) = $true) | ($true != (X0 @ X3 @ X4))) & ! [X2 : a] : ((X1 @ X0 @ X2 @ X2) = $true) & ! [X5 : a,X6 : a,X7 : a] : (($true = (X1 @ X0 @ X6 @ X5)) | (($true != (X1 @ X0 @ X7 @ X5)) | ($true != (X1 @ X0 @ X6 @ X7))))))),
% 1.65/1.33 inference(ennf_transformation,[status(thm)],[f5])).
% 1.65/1.33 thf(f5,plain,(
% 1.65/1.33 ~! [X0 : a > a > $o,X1 : (a > a > $o) > a > a > $o] : ((! [X4 : a,X3 : a] : (($true = (X0 @ X3 @ X4)) => ((X1 @ X0 @ X3 @ X4) = $true)) & ! [X2 : a] : ((X1 @ X0 @ X2 @ X2) = $true) & ! [X5 : a,X6 : a,X7 : a] : ((($true = (X1 @ X0 @ X7 @ X5)) & ($true = (X1 @ X0 @ X6 @ X7))) => ($true = (X1 @ X0 @ X6 @ X5)))) => ! [X9 : a,X8 : a] : (! [X10 : a > $o] : (! [X11 : a,X12 : a] : ((($true = (X10 @ X12)) & ($true = (X0 @ X12 @ X11))) => ($true = (X10 @ X11))) => (($true = (X10 @ X9)) => ($true = (X10 @ X8)))) => ((X1 @ X0 @ X9 @ X8) = $true)))),
% 1.65/1.33 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.33 thf(f4,plain,(
% 1.65/1.33 ~! [X0 : a > a > $o,X1 : (a > a > $o) > a > a > $o] : ((! [X2 : a] : (X1 @ X0 @ X2 @ X2) & ! [X3 : a,X4 : a] : ((X0 @ X3 @ X4) => (X1 @ X0 @ X3 @ X4)) & ! [X5 : a,X6 : a,X7 : a] : (((X1 @ X0 @ X7 @ X5) & (X1 @ X0 @ X6 @ X7)) => (X1 @ X0 @ X6 @ X5))) => ! [X8 : a,X9 : a] : (! [X10 : a > $o] : (! [X11 : a,X12 : a] : (((X10 @ X12) & (X0 @ X12 @ X11)) => (X10 @ X11)) => ((X10 @ X9) => (X10 @ X8))) => (X1 @ X0 @ X9 @ X8)))),
% 1.65/1.33 inference(rectify,[status(thm)],[f2])).
% 1.65/1.33 thf(f2,negated_conjecture,(
% 1.65/1.33 ~! [X0 : a > a > $o,X1 : (a > a > $o) > a > a > $o] : ((! [X2 : a] : (X1 @ X0 @ X2 @ X2) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X1 @ X0 @ X2 @ X3)) & ! [X4 : a,X2 : a,X3 : a] : (((X1 @ X0 @ X3 @ X4) & (X1 @ X0 @ X2 @ X3)) => (X1 @ X0 @ X2 @ X4))) => ! [X3 : a,X2 : a] : (! [X5 : a > $o] : (! [X4 : a,X6 : a] : (((X5 @ X6) & (X0 @ X6 @ X4)) => (X5 @ X4)) => ((X5 @ X2) => (X5 @ X3))) => (X1 @ X0 @ X2 @ X3)))),
% 1.65/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.33 thf(f1,conjecture,(
% 1.65/1.33 ! [X0 : a > a > $o,X1 : (a > a > $o) > a > a > $o] : ((! [X2 : a] : (X1 @ X0 @ X2 @ X2) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X1 @ X0 @ X2 @ X3)) & ! [X4 : a,X2 : a,X3 : a] : (((X1 @ X0 @ X3 @ X4) & (X1 @ X0 @ X2 @ X3)) => (X1 @ X0 @ X2 @ X4))) => ! [X3 : a,X2 : a] : (! [X5 : a > $o] : (! [X4 : a,X6 : a] : (((X5 @ X6) & (X0 @ X6 @ X4)) => (X5 @ X4)) => ((X5 @ X2) => (X5 @ X3))) => (X1 @ X0 @ X2 @ X3)))),
% 1.65/1.33 file('/export/starexec/sandbox2/tmp/tmp.nGdl45nwNQ/DTF2THF_21974.p',cTHM203_pme)).
% 1.65/1.33 thf(f56,plain,(
% 1.65/1.33 ($true = (sK0 @ sK1 @ sK2 @ sK3)) | ($true != (sK0 @ sK1 @ sK2 @ sK2)) | (~spl6_2 | ~spl6_3)),
% 1.65/1.33 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.65/1.33 thf(f55,plain,(
% 1.65/1.33 ($true != (sK0 @ sK1 @ sK2 @ sK2)) | ($true = (sK0 @ sK1 @ sK2 @ sK3)) | ($true != $true) | (~spl6_2 | ~spl6_3)),
% 1.65/1.33 inference(superposition,[status(thm)],[f15,f52])).
% 1.65/1.33 thf(f52,plain,(
% 1.65/1.33 ($true = (sK0 @ sK1 @ sK2 @ (sK5 @ (sK0 @ sK1 @ sK2)))) | (~spl6_2 | ~spl6_3)),
% 1.65/1.33 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.65/1.33 thf(f50,plain,(
% 1.65/1.33 ($true = (sK0 @ sK1 @ sK2 @ (sK5 @ (sK0 @ sK1 @ sK2)))) | ($true != $true) | (~spl6_2 | ~spl6_3)),
% 1.65/1.33 inference(superposition,[status(thm)],[f33,f47])).
% 1.65/1.33 thf(f47,plain,(
% 1.65/1.33 ($true = (sK0 @ sK1 @ (sK4 @ (sK0 @ sK1 @ sK2)) @ (sK5 @ (sK0 @ sK1 @ sK2)))) | ~spl6_3),
% 1.65/1.33 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.65/1.33 thf(f46,plain,(
% 1.65/1.33 ($true = (sK0 @ sK1 @ (sK4 @ (sK0 @ sK1 @ sK2)) @ (sK5 @ (sK0 @ sK1 @ sK2)))) | ($true != $true) | ~spl6_3),
% 1.65/1.33 inference(superposition,[status(thm)],[f19,f39])).
% 1.65/1.33 thf(f39,plain,(
% 1.65/1.33 ($true = (sK1 @ (sK4 @ (sK0 @ sK1 @ sK2)) @ (sK5 @ (sK0 @ sK1 @ sK2)))) | ~spl6_3),
% 1.65/1.33 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.65/1.33 thf(f19,plain,(
% 1.65/1.33 ( ! [X2 : a,X3 : a] : (($true != (sK1 @ X2 @ X3)) | ($true = (sK0 @ sK1 @ X2 @ X3))) )),
% 1.65/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.33 thf(f33,plain,(
% 1.65/1.33 ( ! [X0 : a] : (($true != (sK0 @ sK1 @ (sK4 @ (sK0 @ sK1 @ sK2)) @ X0)) | ($true = (sK0 @ sK1 @ sK2 @ X0))) ) | ~spl6_2),
% 1.65/1.33 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.65/1.33 thf(f32,plain,(
% 1.65/1.33 ( ! [X0 : a] : (($true = (sK0 @ sK1 @ sK2 @ X0)) | ($true != $true) | ($true != (sK0 @ sK1 @ (sK4 @ (sK0 @ sK1 @ sK2)) @ X0))) ) | ~spl6_2),
% 1.65/1.33 inference(superposition,[status(thm)],[f18,f30])).
% 1.65/1.33 thf(f30,plain,(
% 1.65/1.33 ($true = (sK0 @ sK1 @ sK2 @ (sK4 @ (sK0 @ sK1 @ sK2)))) | ~spl6_2),
% 1.65/1.33 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.65/1.33 thf(f18,plain,(
% 1.65/1.33 ( ! [X6 : a,X4 : a,X5 : a] : (($true != (sK0 @ sK1 @ X6 @ X5)) | ($true = (sK0 @ sK1 @ X6 @ X4)) | ($true != (sK0 @ sK1 @ X5 @ X4))) )),
% 1.65/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.33 thf(f15,plain,(
% 1.65/1.33 ( ! [X9 : a > $o] : (($true != (X9 @ (sK5 @ X9))) | ((X9 @ sK3) = $true) | ($true != (X9 @ sK2))) )),
% 1.65/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.33 thf(f45,plain,(
% 1.65/1.33 ~spl6_1),
% 1.65/1.33 inference(avatar_contradiction_clause,[status(thm)],[f44])).
% 1.65/1.33 thf(f44,plain,(
% 1.65/1.33 $false | ~spl6_1),
% 1.65/1.33 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.65/1.33 thf(f41,plain,(
% 1.65/1.33 ($true != $true) | ~spl6_1),
% 1.65/1.33 inference(superposition,[status(thm)],[f17,f26])).
% 1.65/1.33 thf(f26,plain,(
% 1.65/1.33 ($true = (sK0 @ sK1 @ sK2 @ sK3)) | ~spl6_1),
% 1.65/1.33 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.65/1.33 thf(f17,plain,(
% 1.65/1.33 ($true != (sK0 @ sK1 @ sK2 @ sK3))),
% 1.65/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.33 thf(f40,plain,(
% 1.65/1.33 spl6_3 | spl6_1),
% 1.65/1.33 inference(avatar_split_clause,[status(thm)],[f35,f24,f37])).
% 1.65/1.33 thf(f35,plain,(
% 1.65/1.33 ($true = (sK1 @ (sK4 @ (sK0 @ sK1 @ sK2)) @ (sK5 @ (sK0 @ sK1 @ sK2)))) | ($true = (sK0 @ sK1 @ sK2 @ sK3))),
% 1.65/1.33 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.65/1.33 thf(f34,plain,(
% 1.65/1.33 ($true = (sK1 @ (sK4 @ (sK0 @ sK1 @ sK2)) @ (sK5 @ (sK0 @ sK1 @ sK2)))) | ($true != $true) | ($true = (sK0 @ sK1 @ sK2 @ sK3))),
% 1.65/1.33 inference(superposition,[status(thm)],[f14,f13])).
% 1.65/1.33 thf(f14,plain,(
% 1.65/1.33 ( ! [X9 : a > $o] : (($true != (X9 @ sK2)) | ($true = (sK1 @ (sK4 @ X9) @ (sK5 @ X9))) | ((X9 @ sK3) = $true)) )),
% 1.65/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.33 thf(f31,plain,(
% 1.65/1.33 spl6_1 | spl6_2),
% 1.65/1.33 inference(avatar_split_clause,[status(thm)],[f22,f28,f24])).
% 1.65/1.33 thf(f22,plain,(
% 1.65/1.33 ($true = (sK0 @ sK1 @ sK2 @ (sK4 @ (sK0 @ sK1 @ sK2)))) | ($true = (sK0 @ sK1 @ sK2 @ sK3))),
% 1.65/1.33 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.65/1.33 thf(f21,plain,(
% 1.65/1.33 ($true = (sK0 @ sK1 @ sK2 @ (sK4 @ (sK0 @ sK1 @ sK2)))) | ($true != $true) | ($true = (sK0 @ sK1 @ sK2 @ sK3))),
% 1.65/1.33 inference(superposition,[status(thm)],[f16,f13])).
% 1.65/1.33 thf(f16,plain,(
% 1.65/1.33 ( ! [X9 : a > $o] : (($true != (X9 @ sK2)) | ((X9 @ sK3) = $true) | ($true = (X9 @ (sK4 @ X9)))) )),
% 1.65/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.33 % SZS output end Proof for DTF2THF_21974
% 1.65/1.33 % (22154)------------------------------
% 1.65/1.33 % (22154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.33 % (22154)Termination reason: Refutation
% 1.65/1.33
% 1.65/1.33 % (22154)Memory used [KB]: 5628
% 1.65/1.33 % (22154)Time elapsed: 0.010 s
% 1.65/1.33 % (22154)Instructions burned: 8 (million)
% 1.65/1.33 % (22154)------------------------------
% 1.65/1.33 % (22154)------------------------------
% 1.65/1.33 % (22150)Success in time 0.022 s
%------------------------------------------------------------------------------