%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV044^5 : 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 : n015.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 09:40:08 AM UTC 2026
% Result : Theorem 1.68s 1.49s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 3 unt; 0 typ; 4 def)
% Number of atoms : 734 ( 249 equ; 0 cnn)
% Maximal formula atoms : 22 ( 12 avg)
% Number of connectives : 1386 ( 169 ~; 142 |; 76 &; 946 @)
% ( 4 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 138 ( 138 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 242 ( 0 ^; 183 !; 59 ?; 242 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_7,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_5,type,
sP0: ( b > $o ) > ( b > a > a > $o ) > $o ).
thf(func_def_6,type,
sK1: ( b > $o ) > ( b > a > a > $o ) > b > a ).
thf(func_def_7,type,
sK2: ( b > $o ) > ( b > a > a > $o ) > b > a ).
thf(func_def_8,type,
sK3: ( b > $o ) > ( b > a > a > $o ) > b > a ).
thf(func_def_9,type,
sK4: ( b > $o ) > ( b > a > a > $o ) > b ).
thf(func_def_10,type,
sK5: b > a > a > $o ).
thf(func_def_11,type,
sK6: b > $o ).
thf(func_def_12,type,
sK7: b > a ).
thf(func_def_13,type,
sK8: b > a ).
thf(func_def_14,type,
sK9: b ).
thf(func_def_16,type,
ph11:
!>[X0: $tType] : X0 ).
thf(f97,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f37,f42,f46,f57,f96]) ).
thf(f96,plain,
~ spl10_1,
inference(avatar_contradiction_clause,[status(thm)],[f95]) ).
thf(f95,plain,
( $false
| ~ spl10_1 ),
inference(subsumption_resolution,[status(thm)],[f94,f32]) ).
thf(f32,plain,
( ( ( sP0 @ sK6 @ sK5 )
= $true )
| ~ spl10_1 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl10_1
<=> ( ( sP0 @ sK6 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition]) ).
thf(f94,plain,
( ( sP0 @ sK6 @ sK5 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $true != $true )
| ( ( sP0 @ sK6 @ sK5 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f92]) ).
thf(f92,plain,
( ( ( sP0 @ sK6 @ sK5 )
!= $true )
| ( ( sP0 @ sK6 @ sK5 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f85,f20]) ).
thf(f20,plain,
! [X0: b > a > a > $o,X1: b > $o] :
( ( $true
= ( X1 @ ( sK4 @ X1 @ X0 ) ) )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: b > a > a > $o,X1: b > $o] :
( ( ! [X5: b] :
( ( ( X0 @ X5 @ ( sK2 @ X1 @ X0 @ X5 ) @ ( sK3 @ X1 @ X0 @ X5 ) )
= $true )
| ( ( X1 @ X5 )
!= $true ) )
& ! [X6: b] :
( ( ( X1 @ X6 )
!= $true )
| ( ( X0 @ X6 @ ( sK1 @ X1 @ X0 @ X6 ) @ ( sK2 @ X1 @ X0 @ X6 ) )
= $true ) )
& ( ( X0 @ ( sK4 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 @ ( sK4 @ X1 @ X0 ) ) @ ( sK3 @ X1 @ X0 @ ( sK4 @ X1 @ X0 ) ) )
!= $true )
& ( $true
= ( X1 @ ( sK4 @ X1 @ X0 ) ) ) )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f11,f13,f12]) ).
thf(f12,plain,
! [X0: b > a > a > $o,X1: b > $o] :
( ? [X2: b > a,X3: b > a,X4: b > a] :
( ! [X5: b] :
( ( ( X0 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X5 ) )
= $true )
| ( ( X1 @ X5 )
!= $true ) )
& ! [X6: b] :
( ( ( X1 @ X6 )
!= $true )
| ( ( X0 @ X6 @ ( X2 @ X6 ) @ ( X3 @ X6 ) )
= $true ) )
& ? [X7: b] :
( ( $true
!= ( X0 @ X7 @ ( X2 @ X7 ) @ ( X4 @ X7 ) ) )
& ( $true
= ( X1 @ X7 ) ) ) )
=> ( ! [X5: b] :
( ( ( X0 @ X5 @ ( sK2 @ X1 @ X0 @ X5 ) @ ( sK3 @ X1 @ X0 @ X5 ) )
= $true )
| ( ( X1 @ X5 )
!= $true ) )
& ! [X6: b] :
( ( ( X1 @ X6 )
!= $true )
| ( ( X0 @ X6 @ ( sK1 @ X1 @ X0 @ X6 ) @ ( sK2 @ X1 @ X0 @ X6 ) )
= $true ) )
& ? [X7: b] :
( ( $true
!= ( X0 @ X7 @ ( sK1 @ X1 @ X0 @ X7 ) @ ( sK3 @ X1 @ X0 @ X7 ) ) )
& ( $true
= ( X1 @ X7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X0: b > a > a > $o,X1: b > $o] :
( ? [X7: b] :
( ( $true
!= ( X0 @ X7 @ ( sK1 @ X1 @ X0 @ X7 ) @ ( sK3 @ X1 @ X0 @ X7 ) ) )
& ( $true
= ( X1 @ X7 ) ) )
=> ( ( ( X0 @ ( sK4 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 @ ( sK4 @ X1 @ X0 ) ) @ ( sK3 @ X1 @ X0 @ ( sK4 @ X1 @ X0 ) ) )
!= $true )
& ( $true
= ( X1 @ ( sK4 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: b > a > a > $o,X1: b > $o] :
( ? [X2: b > a,X3: b > a,X4: b > a] :
( ! [X5: b] :
( ( ( X0 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X5 ) )
= $true )
| ( ( X1 @ X5 )
!= $true ) )
& ! [X6: b] :
( ( ( X1 @ X6 )
!= $true )
| ( ( X0 @ X6 @ ( X2 @ X6 ) @ ( X3 @ X6 ) )
= $true ) )
& ? [X7: b] :
( ( $true
!= ( X0 @ X7 @ ( X2 @ X7 ) @ ( X4 @ X7 ) ) )
& ( $true
= ( X1 @ X7 ) ) ) )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: b > a > a > $o,X1: b > $o] :
( ? [X13: b > a,X12: b > a,X14: b > a] :
( ! [X16: b] :
( ( ( X0 @ X16 @ ( X12 @ X16 ) @ ( X14 @ X16 ) )
= $true )
| ( ( X1 @ X16 )
!= $true ) )
& ! [X15: b] :
( ( $true
!= ( X1 @ X15 ) )
| ( ( X0 @ X15 @ ( X13 @ X15 ) @ ( X12 @ X15 ) )
= $true ) )
& ? [X17: b] :
( ( ( X0 @ X17 @ ( X13 @ X17 ) @ ( X14 @ X17 ) )
!= $true )
& ( ( X1 @ X17 )
= $true ) ) )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: b > a > a > $o,X1: b > $o] :
( ? [X13: b > a,X12: b > a,X14: b > a] :
( ! [X16: b] :
( ( ( X0 @ X16 @ ( X12 @ X16 ) @ ( X14 @ X16 ) )
= $true )
| ( ( X1 @ X16 )
!= $true ) )
& ! [X15: b] :
( ( $true
!= ( X1 @ X15 ) )
| ( ( X0 @ X15 @ ( X13 @ X15 ) @ ( X12 @ X15 ) )
= $true ) )
& ? [X17: b] :
( ( ( X0 @ X17 @ ( X13 @ X17 ) @ ( X14 @ X17 ) )
!= $true )
& ( ( X1 @ X17 )
= $true ) ) )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f85,plain,
! [X0: b > $o] :
( ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true )
| ( ( sP0 @ X0 @ sK5 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f82,f20]) ).
thf(f82,plain,
! [X0: b > $o] :
( ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true )
| ( $true
!= ( X0 @ ( sK4 @ X0 @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
! [X0: b > $o] :
( ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( $true != $true )
| ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true )
| ( $true
!= ( X0 @ ( sK4 @ X0 @ sK5 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f78]) ).
thf(f78,plain,
! [X0: b > $o] :
( ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true )
| ( $true
!= ( X0 @ ( sK4 @ X0 @ sK5 ) ) )
| ( $true != $true )
| ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( ( sP0 @ X0 @ sK5 )
!= $true ) ),
inference(superposition,[status(thm)],[f75,f23]) ).
thf(f23,plain,
! [X0: b > a > a > $o,X1: b > $o,X5: b] :
( ( ( X0 @ X5 @ ( sK2 @ X1 @ X0 @ X5 ) @ ( sK3 @ X1 @ X0 @ X5 ) )
= $true )
| ( ( sP0 @ X1 @ X0 )
!= $true )
| ( ( X1 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f75,plain,
! [X0: b > $o] :
( ( ( sK5 @ ( sK4 @ X0 @ sK5 ) @ ( sK2 @ X0 @ sK5 @ ( sK4 @ X0 @ sK5 ) ) @ ( sK3 @ X0 @ sK5 @ ( sK4 @ X0 @ sK5 ) ) )
!= $true )
| ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f74,f20]) ).
thf(f74,plain,
! [X0: b > $o] :
( ( $true
!= ( X0 @ ( sK4 @ X0 @ sK5 ) ) )
| ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true )
| ( ( sK5 @ ( sK4 @ X0 @ sK5 ) @ ( sK2 @ X0 @ sK5 @ ( sK4 @ X0 @ sK5 ) ) @ ( sK3 @ X0 @ sK5 @ ( sK4 @ X0 @ sK5 ) ) )
!= $true )
| ( ( sP0 @ X0 @ sK5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
! [X0: b > $o] :
( ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( $true
!= ( X0 @ ( sK4 @ X0 @ sK5 ) ) )
| ( ( sK5 @ ( sK4 @ X0 @ sK5 ) @ ( sK2 @ X0 @ sK5 @ ( sK4 @ X0 @ sK5 ) ) @ ( sK3 @ X0 @ sK5 @ ( sK4 @ X0 @ sK5 ) ) )
!= $true )
| ( $true != $true )
| ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f68]) ).
thf(f68,plain,
! [X0: b > $o] :
( ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( ( sK5 @ ( sK4 @ X0 @ sK5 ) @ ( sK2 @ X0 @ sK5 @ ( sK4 @ X0 @ sK5 ) ) @ ( sK3 @ X0 @ sK5 @ ( sK4 @ X0 @ sK5 ) ) )
!= $true )
| ( $true
!= ( X0 @ ( sK4 @ X0 @ sK5 ) ) )
| ( $true != $true )
| ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true )
| ( ( sP0 @ X0 @ sK5 )
!= $true ) ),
inference(superposition,[status(thm)],[f59,f22]) ).
thf(f22,plain,
! [X0: b > a > a > $o,X1: b > $o,X6: b] :
( ( ( X0 @ X6 @ ( sK1 @ X1 @ X0 @ X6 ) @ ( sK2 @ X1 @ X0 @ X6 ) )
= $true )
| ( ( X1 @ X6 )
!= $true )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f59,plain,
! [X0: b > $o,X1: a] :
( ( $true
!= ( sK5 @ ( sK4 @ X0 @ sK5 ) @ ( sK1 @ X0 @ sK5 @ ( sK4 @ X0 @ sK5 ) ) @ X1 ) )
| ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true )
| ( ( sK5 @ ( sK4 @ X0 @ sK5 ) @ X1 @ ( sK3 @ X0 @ sK5 @ ( sK4 @ X0 @ sK5 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: b > $o,X1: a] :
( ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true )
| ( $true != $true )
| ( ( sK5 @ ( sK4 @ X0 @ sK5 ) @ X1 @ ( sK3 @ X0 @ sK5 @ ( sK4 @ X0 @ sK5 ) ) )
!= $true )
| ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( $true
!= ( sK5 @ ( sK4 @ X0 @ sK5 ) @ ( sK1 @ X0 @ sK5 @ ( sK4 @ X0 @ sK5 ) ) @ X1 ) ) ),
inference(superposition,[status(thm)],[f21,f25]) ).
thf(f25,plain,
! [X8: a,X6: b,X9: a,X7: a] :
( ( $true
= ( sK5 @ X6 @ X9 @ X7 ) )
| ( ( sK6 @ X6 )
!= $true )
| ( ( sK5 @ X6 @ X8 @ X7 )
!= $true )
| ( ( sK5 @ X6 @ X9 @ X8 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ( ( sK5 @ sK9 @ ( sK8 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true )
& ( ( sK6 @ sK9 )
= $true )
& ! [X5: b] :
( ( ( sK6 @ X5 )
!= $true )
| ( ( sK5 @ X5 @ ( sK7 @ X5 ) @ ( sK8 @ X5 ) )
= $true ) ) )
| ( ( sP0 @ sK6 @ sK5 )
= $true ) )
& ! [X6: b] :
( ( ! [X7: a,X8: a,X9: a] :
( ( ( sK5 @ X6 @ X8 @ X7 )
!= $true )
| ( ( sK5 @ X6 @ X9 @ X8 )
!= $true )
| ( $true
= ( sK5 @ X6 @ X9 @ X7 ) ) )
& ! [X10: a,X11: a] :
( ( $true
!= ( sK5 @ X6 @ X11 @ X10 ) )
| ( ( sK5 @ X6 @ X10 @ X11 )
= $true ) ) )
| ( ( sK6 @ X6 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f15,f18,f17,f16]) ).
thf(f16,plain,
( ? [X0: b > a > a > $o,X1: b > $o] :
( ( ? [X2: b > a,X3: b > a] :
( ? [X4: b] :
( ( ( X0 @ X4 @ ( X3 @ X4 ) @ ( X2 @ X4 ) )
!= $true )
& ( ( X1 @ X4 )
= $true ) )
& ! [X5: b] :
( ( ( X1 @ X5 )
!= $true )
| ( $true
= ( X0 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X5 ) ) ) ) )
| ( ( sP0 @ X1 @ X0 )
= $true ) )
& ! [X6: b] :
( ( ! [X7: a,X8: a,X9: a] :
( ( $true
!= ( X0 @ X6 @ X8 @ X7 ) )
| ( ( X0 @ X6 @ X9 @ X8 )
!= $true )
| ( ( X0 @ X6 @ X9 @ X7 )
= $true ) )
& ! [X10: a,X11: a] :
( ( ( X0 @ X6 @ X11 @ X10 )
!= $true )
| ( ( X0 @ X6 @ X10 @ X11 )
= $true ) ) )
| ( ( X1 @ X6 )
!= $true ) ) )
=> ( ( ? [X3: b > a,X2: b > a] :
( ? [X4: b] :
( ( $true
!= ( sK5 @ X4 @ ( X3 @ X4 ) @ ( X2 @ X4 ) ) )
& ( ( sK6 @ X4 )
= $true ) )
& ! [X5: b] :
( ( ( sK6 @ X5 )
!= $true )
| ( ( sK5 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X5 ) )
= $true ) ) )
| ( ( sP0 @ sK6 @ sK5 )
= $true ) )
& ! [X6: b] :
( ( ! [X9: a,X8: a,X7: a] :
( ( ( sK5 @ X6 @ X8 @ X7 )
!= $true )
| ( ( sK5 @ X6 @ X9 @ X8 )
!= $true )
| ( $true
= ( sK5 @ X6 @ X9 @ X7 ) ) )
& ! [X11: a,X10: a] :
( ( $true
!= ( sK5 @ X6 @ X11 @ X10 ) )
| ( ( sK5 @ X6 @ X10 @ X11 )
= $true ) ) )
| ( ( sK6 @ X6 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X3: b > a,X2: b > a] :
( ? [X4: b] :
( ( $true
!= ( sK5 @ X4 @ ( X3 @ X4 ) @ ( X2 @ X4 ) ) )
& ( ( sK6 @ X4 )
= $true ) )
& ! [X5: b] :
( ( ( sK6 @ X5 )
!= $true )
| ( ( sK5 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X5 ) )
= $true ) ) )
=> ( ? [X4: b] :
( ( $true
!= ( sK5 @ X4 @ ( sK8 @ X4 ) @ ( sK7 @ X4 ) ) )
& ( ( sK6 @ X4 )
= $true ) )
& ! [X5: b] :
( ( ( sK6 @ X5 )
!= $true )
| ( ( sK5 @ X5 @ ( sK7 @ X5 ) @ ( sK8 @ X5 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X4: b] :
( ( $true
!= ( sK5 @ X4 @ ( sK8 @ X4 ) @ ( sK7 @ X4 ) ) )
& ( ( sK6 @ X4 )
= $true ) )
=> ( ( ( sK5 @ sK9 @ ( sK8 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true )
& ( ( sK6 @ sK9 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
? [X0: b > a > a > $o,X1: b > $o] :
( ( ? [X2: b > a,X3: b > a] :
( ? [X4: b] :
( ( ( X0 @ X4 @ ( X3 @ X4 ) @ ( X2 @ X4 ) )
!= $true )
& ( ( X1 @ X4 )
= $true ) )
& ! [X5: b] :
( ( ( X1 @ X5 )
!= $true )
| ( $true
= ( X0 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X5 ) ) ) ) )
| ( ( sP0 @ X1 @ X0 )
= $true ) )
& ! [X6: b] :
( ( ! [X7: a,X8: a,X9: a] :
( ( $true
!= ( X0 @ X6 @ X8 @ X7 ) )
| ( ( X0 @ X6 @ X9 @ X8 )
!= $true )
| ( ( X0 @ X6 @ X9 @ X7 )
= $true ) )
& ! [X10: a,X11: a] :
( ( ( X0 @ X6 @ X11 @ X10 )
!= $true )
| ( ( X0 @ X6 @ X10 @ X11 )
= $true ) ) )
| ( ( X1 @ X6 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
? [X0: b > a > a > $o,X1: b > $o] :
( ( ? [X8: b > a,X9: b > a] :
( ? [X11: b] :
( ( ( X0 @ X11 @ ( X9 @ X11 ) @ ( X8 @ X11 ) )
!= $true )
& ( ( X1 @ X11 )
= $true ) )
& ! [X10: b] :
( ( $true
!= ( X1 @ X10 ) )
| ( ( X0 @ X10 @ ( X8 @ X10 ) @ ( X9 @ X10 ) )
= $true ) ) )
| ( ( sP0 @ X1 @ X0 )
= $true ) )
& ! [X2: b] :
( ( ! [X4: a,X3: a,X5: a] :
( ( ( X0 @ X2 @ X3 @ X4 )
!= $true )
| ( ( X0 @ X2 @ X5 @ X3 )
!= $true )
| ( $true
= ( X0 @ X2 @ X5 @ X4 ) ) )
& ! [X7: a,X6: a] :
( ( ( X0 @ X2 @ X6 @ X7 )
!= $true )
| ( $true
= ( X0 @ X2 @ X7 @ X6 ) ) ) )
| ( $true
!= ( X1 @ X2 ) ) ) ),
inference(definition_folding,[status(thm)],[f7,f8]) ).
thf(f7,plain,
? [X0: b > a > a > $o,X1: b > $o] :
( ( ? [X8: b > a,X9: b > a] :
( ? [X11: b] :
( ( ( X0 @ X11 @ ( X9 @ X11 ) @ ( X8 @ X11 ) )
!= $true )
& ( ( X1 @ X11 )
= $true ) )
& ! [X10: b] :
( ( $true
!= ( X1 @ X10 ) )
| ( ( X0 @ X10 @ ( X8 @ X10 ) @ ( X9 @ X10 ) )
= $true ) ) )
| ? [X13: b > a,X12: b > a,X14: b > a] :
( ! [X16: b] :
( ( ( X0 @ X16 @ ( X12 @ X16 ) @ ( X14 @ X16 ) )
= $true )
| ( ( X1 @ X16 )
!= $true ) )
& ! [X15: b] :
( ( $true
!= ( X1 @ X15 ) )
| ( ( X0 @ X15 @ ( X13 @ X15 ) @ ( X12 @ X15 ) )
= $true ) )
& ? [X17: b] :
( ( ( X0 @ X17 @ ( X13 @ X17 ) @ ( X14 @ X17 ) )
!= $true )
& ( ( X1 @ X17 )
= $true ) ) ) )
& ! [X2: b] :
( ( ! [X4: a,X3: a,X5: a] :
( ( ( X0 @ X2 @ X3 @ X4 )
!= $true )
| ( ( X0 @ X2 @ X5 @ X3 )
!= $true )
| ( $true
= ( X0 @ X2 @ X5 @ X4 ) ) )
& ! [X7: a,X6: a] :
( ( ( X0 @ X2 @ X6 @ X7 )
!= $true )
| ( $true
= ( X0 @ X2 @ X7 @ X6 ) ) ) )
| ( $true
!= ( X1 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: b > $o,X0: b > a > a > $o] :
( ( ? [X13: b > a,X14: b > a,X12: b > a] :
( ? [X17: b] :
( ( ( X0 @ X17 @ ( X13 @ X17 ) @ ( X14 @ X17 ) )
!= $true )
& ( ( X1 @ X17 )
= $true ) )
& ! [X16: b] :
( ( ( X0 @ X16 @ ( X12 @ X16 ) @ ( X14 @ X16 ) )
= $true )
| ( ( X1 @ X16 )
!= $true ) )
& ! [X15: b] :
( ( $true
!= ( X1 @ X15 ) )
| ( ( X0 @ X15 @ ( X13 @ X15 ) @ ( X12 @ X15 ) )
= $true ) ) )
| ? [X8: b > a,X9: b > a] :
( ? [X11: b] :
( ( ( X0 @ X11 @ ( X9 @ X11 ) @ ( X8 @ X11 ) )
!= $true )
& ( ( X1 @ X11 )
= $true ) )
& ! [X10: b] :
( ( $true
!= ( X1 @ X10 ) )
| ( ( X0 @ X10 @ ( X8 @ X10 ) @ ( X9 @ X10 ) )
= $true ) ) ) )
& ! [X2: b] :
( ( ! [X7: a,X6: a] :
( ( ( X0 @ X2 @ X6 @ X7 )
!= $true )
| ( $true
= ( X0 @ X2 @ X7 @ X6 ) ) )
& ! [X4: a,X3: a,X5: a] :
( ( $true
= ( X0 @ X2 @ X5 @ X4 ) )
| ( ( X0 @ X2 @ X5 @ X3 )
!= $true )
| ( ( X0 @ X2 @ X3 @ X4 )
!= $true ) ) )
| ( $true
!= ( X1 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: b > $o,X0: b > a > a > $o] :
( ! [X2: b] :
( ( $true
= ( X1 @ X2 ) )
=> ( ! [X6: a,X7: a] :
( ( ( X0 @ X2 @ X6 @ X7 )
= $true )
=> ( $true
= ( X0 @ X2 @ X7 @ X6 ) ) )
& ! [X4: a,X3: a,X5: a] :
( ( ( ( X0 @ X2 @ X5 @ X3 )
= $true )
& ( ( X0 @ X2 @ X3 @ X4 )
= $true ) )
=> ( $true
= ( X0 @ X2 @ X5 @ X4 ) ) ) ) )
=> ( ! [X13: b > a,X14: b > a,X12: b > a] :
( ( ! [X16: b] :
( ( ( X1 @ X16 )
= $true )
=> ( ( X0 @ X16 @ ( X12 @ X16 ) @ ( X14 @ X16 ) )
= $true ) )
& ! [X15: b] :
( ( $true
= ( X1 @ X15 ) )
=> ( ( X0 @ X15 @ ( X13 @ X15 ) @ ( X12 @ X15 ) )
= $true ) ) )
=> ! [X17: b] :
( ( ( X1 @ X17 )
= $true )
=> ( ( X0 @ X17 @ ( X13 @ X17 ) @ ( X14 @ X17 ) )
= $true ) ) )
& ! [X8: b > a,X9: b > a] :
( ! [X10: b] :
( ( $true
= ( X1 @ X10 ) )
=> ( ( X0 @ X10 @ ( X8 @ X10 ) @ ( X9 @ X10 ) )
= $true ) )
=> ! [X11: b] :
( ( ( X1 @ X11 )
= $true )
=> ( ( X0 @ X11 @ ( X9 @ X11 ) @ ( X8 @ X11 ) )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: b > a > a > $o,X1: b > $o] :
( ! [X2: b] :
( ( X1 @ X2 )
=> ( ! [X3: a,X4: a,X5: a] :
( ( ( X0 @ X2 @ X5 @ X3 )
& ( X0 @ X2 @ X3 @ X4 ) )
=> ( X0 @ X2 @ X5 @ X4 ) )
& ! [X6: a,X7: a] :
( ( X0 @ X2 @ X6 @ X7 )
=> ( X0 @ X2 @ X7 @ X6 ) ) ) )
=> ( ! [X8: b > a,X9: b > a] :
( ! [X10: b] :
( ( X1 @ X10 )
=> ( X0 @ X10 @ ( X8 @ X10 ) @ ( X9 @ X10 ) ) )
=> ! [X11: b] :
( ( X1 @ X11 )
=> ( X0 @ X11 @ ( X9 @ X11 ) @ ( X8 @ X11 ) ) ) )
& ! [X12: b > a,X13: b > a,X14: b > a] :
( ( ! [X15: b] :
( ( X1 @ X15 )
=> ( X0 @ X15 @ ( X13 @ X15 ) @ ( X12 @ X15 ) ) )
& ! [X16: b] :
( ( X1 @ X16 )
=> ( X0 @ X16 @ ( X12 @ X16 ) @ ( X14 @ X16 ) ) ) )
=> ! [X17: b] :
( ( X1 @ X17 )
=> ( X0 @ X17 @ ( X13 @ X17 ) @ ( X14 @ X17 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: b > a > a > $o,X0: b > $o] :
( ! [X2: b] :
( ( X0 @ X2 )
=> ( ! [X4: a,X5: a,X3: a] :
( ( ( X1 @ X2 @ X3 @ X4 )
& ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X2 @ X3 @ X5 ) )
& ! [X3: a,X4: a] :
( ( X1 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 @ X3 ) ) ) )
=> ( ! [X2: b > a,X4: b > a] :
( ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X2 @ X3 ) @ ( X4 @ X3 ) ) )
=> ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X4 @ X3 ) @ ( X2 @ X3 ) ) ) )
& ! [X4: b > a,X2: b > a,X5: b > a] :
( ( ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X2 @ X3 ) @ ( X4 @ X3 ) ) )
& ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X4 @ X3 ) @ ( X5 @ X3 ) ) ) )
=> ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X2 @ X3 ) @ ( X5 @ X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: b > a > a > $o,X0: b > $o] :
( ! [X2: b] :
( ( X0 @ X2 )
=> ( ! [X4: a,X5: a,X3: a] :
( ( ( X1 @ X2 @ X3 @ X4 )
& ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X2 @ X3 @ X5 ) )
& ! [X3: a,X4: a] :
( ( X1 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 @ X3 ) ) ) )
=> ( ! [X2: b > a,X4: b > a] :
( ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X2 @ X3 ) @ ( X4 @ X3 ) ) )
=> ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X4 @ X3 ) @ ( X2 @ X3 ) ) ) )
& ! [X4: b > a,X2: b > a,X5: b > a] :
( ( ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X2 @ X3 ) @ ( X4 @ X3 ) ) )
& ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X4 @ X3 ) @ ( X5 @ X3 ) ) ) )
=> ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X2 @ X3 ) @ ( X5 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x9MeSh7OKb/DTF2THF_10099.p',cTHM506_pme) ).
thf(f21,plain,
! [X0: b > a > a > $o,X1: b > $o] :
( ( ( X0 @ ( sK4 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 @ ( sK4 @ X1 @ X0 ) ) @ ( sK3 @ X1 @ X0 @ ( sK4 @ X1 @ X0 ) ) )
!= $true )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f57,plain,
( spl10_2
| ~ spl10_3
| ~ spl10_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f56]) ).
thf(f56,plain,
( $false
| spl10_2
| ~ spl10_3
| ~ spl10_4 ),
inference(subsumption_resolution,[status(thm)],[f55,f41]) ).
thf(f41,plain,
( ( ( sK6 @ sK9 )
= $true )
| ~ spl10_3 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl10_3
<=> ( ( sK6 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl10_3])],[avatar_definition]) ).
thf(f55,plain,
( ( ( sK6 @ sK9 )
!= $true )
| spl10_2
| ~ spl10_3
| ~ spl10_4 ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $true != $true )
| ( ( sK6 @ sK9 )
!= $true )
| spl10_2
| ~ spl10_3
| ~ spl10_4 ),
inference(superposition,[status(thm)],[f51,f45]) ).
thf(f45,plain,
( ! [X5: b] :
( ( ( sK5 @ X5 @ ( sK7 @ X5 ) @ ( sK8 @ X5 ) )
= $true )
| ( ( sK6 @ X5 )
!= $true ) )
| ~ spl10_4 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl10_4
<=> ! [X5: b] :
( ( ( sK5 @ X5 @ ( sK7 @ X5 ) @ ( sK8 @ X5 ) )
= $true )
| ( ( sK6 @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl10_4])],[avatar_definition]) ).
thf(f51,plain,
( ( $true
!= ( sK5 @ sK9 @ ( sK7 @ sK9 ) @ ( sK8 @ sK9 ) ) )
| spl10_2
| ~ spl10_3 ),
inference(subsumption_resolution,[status(thm)],[f50,f41]) ).
thf(f50,plain,
( ( ( sK6 @ sK9 )
!= $true )
| ( $true
!= ( sK5 @ sK9 @ ( sK7 @ sK9 ) @ ( sK8 @ sK9 ) ) )
| spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true != $true )
| ( ( sK6 @ sK9 )
!= $true )
| ( $true
!= ( sK5 @ sK9 @ ( sK7 @ sK9 ) @ ( sK8 @ sK9 ) ) )
| spl10_2 ),
inference(superposition,[status(thm)],[f36,f24]) ).
thf(f24,plain,
! [X10: a,X11: a,X6: b] :
( ( ( sK5 @ X6 @ X10 @ X11 )
= $true )
| ( $true
!= ( sK5 @ X6 @ X11 @ X10 ) )
| ( ( sK6 @ X6 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f36,plain,
( ( ( sK5 @ sK9 @ ( sK8 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true )
| spl10_2 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl10_2
<=> ( ( sK5 @ sK9 @ ( sK8 @ sK9 ) @ ( sK7 @ sK9 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition]) ).
thf(f46,plain,
( spl10_4
| spl10_1 ),
inference(avatar_split_clause,[status(thm)],[f26,f30,f44]) ).
thf(f26,plain,
! [X5: b] :
( ( ( sK5 @ X5 @ ( sK7 @ X5 ) @ ( sK8 @ X5 ) )
= $true )
| ( ( sK6 @ X5 )
!= $true )
| ( ( sP0 @ sK6 @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f42,plain,
( spl10_1
| spl10_3 ),
inference(avatar_split_clause,[status(thm)],[f27,f39,f30]) ).
thf(f27,plain,
( ( ( sP0 @ sK6 @ sK5 )
= $true )
| ( ( sK6 @ sK9 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f37,plain,
( spl10_1
| ~ spl10_2 ),
inference(avatar_split_clause,[status(thm)],[f28,f34,f30]) ).
thf(f28,plain,
( ( ( sP0 @ sK6 @ sK5 )
= $true )
| ( ( sK5 @ sK9 @ ( sK8 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV044^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.31 % Computer : n015.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue Feb 24 12:39:31 EST 2026
% 0.13/0.31 % CPUTime :
% 0.13/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.41 ---- Original DTF file ---
% 0.16/0.41 thf(spec,logic,$$dhol).
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 % File : SEV044^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.41 % Domain : Set Theory (Relations)
% 0.16/0.41 % Problem : TPS problem from PERS-THMS
% 0.16/0.41 % Version : Especial.
% 0.16/0.41 % English :
% 0.16/0.41
% 0.16/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.41 % Source : [Bro09]
% 0.16/0.41 % Names : tps_1114 [Bro09]
% 0.16/0.41
% 0.16/0.41 % Status : Theorem
% 0.16/0.41 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 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 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.16/0.41 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.16/0.41 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.16/0.41 % Maximal formula atoms : 0 ( 0 avg)
% 0.16/0.41 % Number of connectives : 61 ( 0 ~; 0 |; 4 &; 46 @)
% 0.16/0.41 % ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% 0.16/0.41 % Maximal formula depth : 15 ( 15 avg)
% 0.16/0.41 % Number of types : 3 ( 2 usr)
% 0.16/0.41 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.16/0.41 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.16/0.41 % Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% 0.16/0.41 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.41
% 0.16/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 thf(b_type,type,
% 0.16/0.41 b: $tType ).
% 0.16/0.41
% 0.16/0.41 thf(a_type,type,
% 0.16/0.41 a: $tType ).
% 0.16/0.41
% 0.16/0.41 thf(cTHM506_pme,conjecture,
% 0.16/0.41 ! [Xs: b > $o,Xp: b > a > a > $o] :
% 0.16/0.41 ( ! [Xx: b] :
% 0.16/0.41 ( ( Xs @ Xx )
% 0.16/0.41 => ( ! [Xx0: a,Xy: a] :
% 0.16/0.41 ( ( Xp @ Xx @ Xx0 @ Xy )
% 0.16/0.41 => ( Xp @ Xx @ Xy @ Xx0 ) )
% 0.16/0.41 & ! [Xx0: a,Xy: a,Xz: a] :
% 0.16/0.41 ( ( ( Xp @ Xx @ Xx0 @ Xy )
% 0.16/0.41 & ( Xp @ Xx @ Xy @ Xz ) )
% 0.16/0.41 => ( Xp @ Xx @ Xx0 @ Xz ) ) ) )
% 0.16/0.41 => ( ! [Xx: b > a,Xy: b > a] :
% 0.16/0.41 ( ! [Xx0: b] :
% 0.16/0.41 ( ( Xs @ Xx0 )
% 0.16/0.41 => ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xx0 ) ) )
% 0.16/0.41 => ! [Xx0: b] :
% 0.16/0.41 ( ( Xs @ Xx0 )
% 0.16/0.41 => ( Xp @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xx0 ) ) ) )
% 0.16/0.41 & ! [Xx: b > a,Xy: b > a,Xz: b > a] :
% 0.16/0.41 ( ( ! [Xx0: b] :
% 0.16/0.41 ( ( Xs @ Xx0 )
% 0.16/0.41 => ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xx0 ) ) )
% 0.16/0.41 & ! [Xx0: b] :
% 0.16/0.41 ( ( Xs @ Xx0 )
% 0.16/0.41 => ( Xp @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xx0 ) ) ) )
% 0.16/0.41 => ! [Xx0: b] :
% 0.16/0.41 ( ( Xs @ Xx0 )
% 0.16/0.41 => ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xx0 ) ) ) ) ) ) ).
% 0.16/0.41
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 ------------------------
% 1.68/1.44 ---- Embedded in THF ---
% 1.68/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.44 %%% Generated on Tue Feb 24 12:39:32 EST 2026
% 1.68/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.44 %%% Logic specification used:
% 1.68/1.44 %%% thf(spec, logic, $$dhol).
% 1.68/1.44
% 1.68/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.x9MeSh7OKb/DTF2DTF10099.p
% See solution above
% 1.68/1.44 ------------------------
% 1.68/1.45 ---- Cleaned THF ---
% 1.68/1.45 thf(b_type,type,
% 1.68/1.45 b: $tType ).
% 1.68/1.45
% 1.68/1.45 thf(a_type,type,
% 1.68/1.45 a: $tType ).
% 1.68/1.45
% 1.68/1.45 thf(cTHM506_pme,conjecture,
% 1.68/1.45 ! [Xs: b > $o,Xp: b > a > a > $o] :
% 1.68/1.45 ( ! [Xx: b] :
% 1.68/1.45 ( ( Xs @ Xx )
% 1.68/1.45 => ( ! [Xx0: a,Xy: a] :
% 1.68/1.45 ( ( Xp @ Xx @ Xx0 @ Xy )
% 1.68/1.45 => ( Xp @ Xx @ Xy @ Xx0 ) )
% 1.68/1.45 & ! [Xx0: a,Xy: a,Xz: a] :
% 1.68/1.45 ( ( ( Xp @ Xx @ Xx0 @ Xy )
% 1.68/1.45 & ( Xp @ Xx @ Xy @ Xz ) )
% 1.68/1.45 => ( Xp @ Xx @ Xx0 @ Xz ) ) ) )
% 1.68/1.45 => ( ! [Xx: b > a,Xy: b > a] :
% 1.68/1.45 ( ! [Xx0: b] :
% 1.68/1.45 ( ( Xs @ Xx0 )
% 1.68/1.45 => ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xx0 ) ) )
% 1.68/1.45 => ! [Xx0: b] :
% 1.68/1.45 ( ( Xs @ Xx0 )
% 1.68/1.45 => ( Xp @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xx0 ) ) ) )
% 1.68/1.45 & ! [Xx: b > a,Xy: b > a,Xz: b > a] :
% 1.68/1.45 ( ( ! [Xx0: b] :
% 1.68/1.45 ( ( Xs @ Xx0 )
% 1.68/1.45 => ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xx0 ) ) )
% 1.68/1.45 & ! [Xx0: b] :
% 1.68/1.45 ( ( Xs @ Xx0 )
% 1.68/1.45 => ( Xp @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xx0 ) ) ) )
% 1.68/1.45 => ! [Xx0: b] :
% 1.68/1.45 ( ( Xs @ Xx0 )
% 1.68/1.45 => ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xx0 ) ) ) ) ) ) ).
% 1.68/1.45 ------------------------
% 1.68/1.47 % (10198)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10099 for (2999ds/183Mi)
% 1.68/1.47 % (10201)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10099 for (2999ds/2Mi)
% 1.68/1.47 % (10203)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_10099 for (2999ds/275Mi)
% 1.68/1.47 % (10204)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10099 for (2999ds/18Mi)
% 1.68/1.47 % (10199)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_10099 for (2999ds/4Mi)
% 1.68/1.48 % (10201)Instruction limit reached!
% 1.68/1.48 % (10201)------------------------------
% 1.68/1.48 % (10201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.48 % (10201)Termination reason: Unknown
% 1.68/1.48 % (10201)Termination phase: Preprocessing 3
% 1.68/1.48
% 1.68/1.48 % (10201)Memory used [KB]: 1023
% 1.68/1.48 % (10201)Time elapsed: 0.003 s
% 1.68/1.48 % (10201)Instructions burned: 2 (million)
% 1.68/1.48 % (10201)------------------------------
% 1.68/1.48 % (10201)------------------------------
% 1.68/1.48 % (10202)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_10099 for (2999ds/2Mi)
% 1.68/1.48 % (10199)Instruction limit reached!
% 1.68/1.48 % (10199)------------------------------
% 1.68/1.48 % (10199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.48 % (10199)Termination reason: Unknown
% 1.68/1.48 % (10199)Termination phase: Saturation
% 1.68/1.48
% 1.68/1.48 % (10199)Memory used [KB]: 5500
% 1.68/1.48 % (10199)Time elapsed: 0.004 s
% 1.68/1.48 % (10199)Instructions burned: 4 (million)
% 1.68/1.48 % (10199)------------------------------
% 1.68/1.48 % (10199)------------------------------
% 1.68/1.48 % (10202)Instruction limit reached!
% 1.68/1.48 % (10202)------------------------------
% 1.68/1.48 % (10202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.48 % (10202)Termination reason: Unknown
% 1.68/1.48 % (10202)Termination phase: shuffling
% 1.68/1.48
% 1.68/1.48 % (10202)Memory used [KB]: 895
% 1.68/1.48 % (10202)Time elapsed: 0.002 s
% 1.68/1.48 % (10202)Instructions burned: 2 (million)
% 1.68/1.48 % (10202)------------------------------
% 1.68/1.48 % (10202)------------------------------
% 1.68/1.48 % (10200)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_10099 for (2999ds/27Mi)
% 1.68/1.48 % (10204)Instruction limit reached!
% 1.68/1.48 % (10204)------------------------------
% 1.68/1.48 % (10204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.48 % (10204)Termination reason: Unknown
% 1.68/1.48 % (10204)Termination phase: Saturation
% 1.68/1.48
% 1.68/1.48 % (10204)Memory used [KB]: 5628
% 1.68/1.48 % (10204)Time elapsed: 0.011 s
% 1.68/1.48 % (10204)Instructions burned: 18 (million)
% 1.68/1.48 % (10204)------------------------------
% 1.68/1.48 % (10204)------------------------------
% 1.68/1.48 % (10203)First to succeed.
% 1.68/1.49 % (10203)Refutation found. Thanks to Tanya!
% 1.68/1.49 % SZS status Theorem for DTF2THF_10099
% 1.68/1.49 % SZS output start Proof for DTF2THF_10099
% 1.68/1.49 thf(type_def_5, type, b: $tType).
% 1.68/1.49 thf(type_def_7, type, a: $tType).
% 1.68/1.49 thf(func_def_0, type, b: $tType).
% 1.68/1.49 thf(func_def_1, type, a: $tType).
% 1.68/1.49 thf(func_def_5, type, sP0: (b > $o) > (b > a > a > $o) > $o).
% 1.68/1.49 thf(func_def_6, type, sK1: (b > $o) > (b > a > a > $o) > b > a).
% 1.68/1.49 thf(func_def_7, type, sK2: (b > $o) > (b > a > a > $o) > b > a).
% 1.68/1.49 thf(func_def_8, type, sK3: (b > $o) > (b > a > a > $o) > b > a).
% 1.68/1.49 thf(func_def_9, type, sK4: (b > $o) > (b > a > a > $o) > b).
% 1.68/1.49 thf(func_def_10, type, sK5: b > a > a > $o).
% 1.68/1.49 thf(func_def_11, type, sK6: b > $o).
% 1.68/1.49 thf(func_def_12, type, sK7: b > a).
% 1.68/1.49 thf(func_def_13, type, sK8: b > a).
% 1.68/1.49 thf(func_def_14, type, sK9: b).
% 1.68/1.49 thf(func_def_16, type, ph11: !>[X0: $tType]:(X0)).
% 1.68/1.49 thf(f97,plain,(
% 1.68/1.49 $false),
% 1.68/1.49 inference(avatar_sat_refutation,[status(thm)],[f37,f42,f46,f57,f96])).
% 1.68/1.49 thf(f96,plain,(
% 1.68/1.49 ~spl10_1),
% 1.68/1.49 inference(avatar_contradiction_clause,[status(thm)],[f95])).
% 1.68/1.49 thf(f95,plain,(
% 1.68/1.49 $false | ~spl10_1),
% 1.68/1.49 inference(subsumption_resolution,[status(thm)],[f94,f32])).
% 1.68/1.49 thf(f32,plain,(
% 1.68/1.49 ((sP0 @ sK6 @ sK5) = $true) | ~spl10_1),
% 1.68/1.49 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.68/1.49 thf(f30,definition,(
% 1.68/1.49 spl10_1 <=> ((sP0 @ sK6 @ sK5) = $true)),
% 1.68/1.49 introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition])).
% 1.68/1.49 thf(f94,plain,(
% 1.68/1.49 ((sP0 @ sK6 @ sK5) != $true)),
% 1.68/1.49 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.68/1.49 thf(f93,plain,(
% 1.68/1.49 ($true != $true) | ((sP0 @ sK6 @ sK5) != $true)),
% 1.68/1.49 inference(duplicate_literal_removal,[status(thm)],[f92])).
% 1.68/1.49 thf(f92,plain,(
% 1.68/1.49 ((sP0 @ sK6 @ sK5) != $true) | ((sP0 @ sK6 @ sK5) != $true) | ($true != $true)),
% 1.68/1.49 inference(superposition,[status(thm)],[f85,f20])).
% 1.68/1.49 thf(f20,plain,(
% 1.68/1.49 ( ! [X0 : b > a > a > $o,X1 : b > $o] : (($true = (X1 @ (sK4 @ X1 @ X0))) | ((sP0 @ X1 @ X0) != $true)) )),
% 1.68/1.49 inference(cnf_transformation,[status(thm)],[f14])).
% 1.68/1.49 thf(f14,plain,(
% 1.68/1.49 ! [X0 : b > a > a > $o,X1 : b > $o] : ((! [X5 : b] : (((X0 @ X5 @ (sK2 @ X1 @ X0 @ X5) @ (sK3 @ X1 @ X0 @ X5)) = $true) | ((X1 @ X5) != $true)) & ! [X6 : b] : (((X1 @ X6) != $true) | ((X0 @ X6 @ (sK1 @ X1 @ X0 @ X6) @ (sK2 @ X1 @ X0 @ X6)) = $true)) & (((X0 @ (sK4 @ X1 @ X0) @ (sK1 @ X1 @ X0 @ (sK4 @ X1 @ X0)) @ (sK3 @ X1 @ X0 @ (sK4 @ X1 @ X0))) != $true) & ($true = (X1 @ (sK4 @ X1 @ X0))))) | ((sP0 @ X1 @ X0) != $true))),
% 1.68/1.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f11,f13,f12])).
% 1.68/1.49 thf(f12,plain,(
% 1.68/1.49 ! [X0 : b > a > a > $o,X1 : b > $o] : (? [X2 : b > a,X3 : b > a,X4 : b > a] : (! [X5 : b] : (((X0 @ X5 @ (X3 @ X5) @ (X4 @ X5)) = $true) | ((X1 @ X5) != $true)) & ! [X6 : b] : (((X1 @ X6) != $true) | ((X0 @ X6 @ (X2 @ X6) @ (X3 @ X6)) = $true)) & ? [X7 : b] : (($true != (X0 @ X7 @ (X2 @ X7) @ (X4 @ X7))) & ($true = (X1 @ X7)))) => (! [X5 : b] : (((X0 @ X5 @ (sK2 @ X1 @ X0 @ X5) @ (sK3 @ X1 @ X0 @ X5)) = $true) | ((X1 @ X5) != $true)) & ! [X6 : b] : (((X1 @ X6) != $true) | ((X0 @ X6 @ (sK1 @ X1 @ X0 @ X6) @ (sK2 @ X1 @ X0 @ X6)) = $true)) & ? [X7 : b] : (($true != (X0 @ X7 @ (sK1 @ X1 @ X0 @ X7) @ (sK3 @ X1 @ X0 @ X7))) & ($true = (X1 @ X7)))))),
% 1.68/1.49 introduced(definition,[],[choice_axiom])).
% 1.68/1.49 thf(f13,plain,(
% 1.68/1.49 ! [X0 : b > a > a > $o,X1 : b > $o] : (? [X7 : b] : (($true != (X0 @ X7 @ (sK1 @ X1 @ X0 @ X7) @ (sK3 @ X1 @ X0 @ X7))) & ($true = (X1 @ X7))) => (((X0 @ (sK4 @ X1 @ X0) @ (sK1 @ X1 @ X0 @ (sK4 @ X1 @ X0)) @ (sK3 @ X1 @ X0 @ (sK4 @ X1 @ X0))) != $true) & ($true = (X1 @ (sK4 @ X1 @ X0)))))),
% 1.68/1.49 introduced(definition,[],[choice_axiom])).
% 1.68/1.49 thf(f11,plain,(
% 1.68/1.49 ! [X0 : b > a > a > $o,X1 : b > $o] : (? [X2 : b > a,X3 : b > a,X4 : b > a] : (! [X5 : b] : (((X0 @ X5 @ (X3 @ X5) @ (X4 @ X5)) = $true) | ((X1 @ X5) != $true)) & ! [X6 : b] : (((X1 @ X6) != $true) | ((X0 @ X6 @ (X2 @ X6) @ (X3 @ X6)) = $true)) & ? [X7 : b] : (($true != (X0 @ X7 @ (X2 @ X7) @ (X4 @ X7))) & ($true = (X1 @ X7)))) | ((sP0 @ X1 @ X0) != $true))),
% 1.68/1.49 inference(rectify,[status(thm)],[f10])).
% 1.68/1.49 thf(f10,plain,(
% 1.68/1.49 ! [X0 : b > a > a > $o,X1 : b > $o] : (? [X13 : b > a,X12 : b > a,X14 : b > a] : (! [X16 : b] : (((X0 @ X16 @ (X12 @ X16) @ (X14 @ X16)) = $true) | ((X1 @ X16) != $true)) & ! [X15 : b] : (($true != (X1 @ X15)) | ((X0 @ X15 @ (X13 @ X15) @ (X12 @ X15)) = $true)) & ? [X17 : b] : (((X0 @ X17 @ (X13 @ X17) @ (X14 @ X17)) != $true) & ((X1 @ X17) = $true))) | ((sP0 @ X1 @ X0) != $true))),
% 1.68/1.49 inference(nnf_transformation,[status(thm)],[f8])).
% 1.68/1.49 thf(f8,plain,(
% 1.68/1.49 ! [X0 : b > a > a > $o,X1 : b > $o] : (? [X13 : b > a,X12 : b > a,X14 : b > a] : (! [X16 : b] : (((X0 @ X16 @ (X12 @ X16) @ (X14 @ X16)) = $true) | ((X1 @ X16) != $true)) & ! [X15 : b] : (($true != (X1 @ X15)) | ((X0 @ X15 @ (X13 @ X15) @ (X12 @ X15)) = $true)) & ? [X17 : b] : (((X0 @ X17 @ (X13 @ X17) @ (X14 @ X17)) != $true) & ((X1 @ X17) = $true))) | ~((sP0 @ X1 @ X0) = $true))),
% 1.68/1.49 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.68/1.49 thf(f85,plain,(
% 1.68/1.49 ( ! [X0 : b > $o] : (((sK6 @ (sK4 @ X0 @ sK5)) != $true) | ((sP0 @ X0 @ sK5) != $true)) )),
% 1.68/1.49 inference(subsumption_resolution,[status(thm)],[f82,f20])).
% 1.68/1.49 thf(f82,plain,(
% 1.68/1.49 ( ! [X0 : b > $o] : (((sP0 @ X0 @ sK5) != $true) | ((sK6 @ (sK4 @ X0 @ sK5)) != $true) | ($true != (X0 @ (sK4 @ X0 @ sK5)))) )),
% 1.68/1.49 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.68/1.49 thf(f81,plain,(
% 1.68/1.49 ( ! [X0 : b > $o] : (((sP0 @ X0 @ sK5) != $true) | ($true != $true) | ((sK6 @ (sK4 @ X0 @ sK5)) != $true) | ($true != (X0 @ (sK4 @ X0 @ sK5)))) )),
% 1.68/1.49 inference(duplicate_literal_removal,[status(thm)],[f78])).
% 1.68/1.49 thf(f78,plain,(
% 1.68/1.49 ( ! [X0 : b > $o] : (((sK6 @ (sK4 @ X0 @ sK5)) != $true) | ($true != (X0 @ (sK4 @ X0 @ sK5))) | ($true != $true) | ((sP0 @ X0 @ sK5) != $true) | ((sP0 @ X0 @ sK5) != $true)) )),
% 1.68/1.49 inference(superposition,[status(thm)],[f75,f23])).
% 1.68/1.49 thf(f23,plain,(
% 1.68/1.49 ( ! [X0 : b > a > a > $o,X1 : b > $o,X5 : b] : (((X0 @ X5 @ (sK2 @ X1 @ X0 @ X5) @ (sK3 @ X1 @ X0 @ X5)) = $true) | ((sP0 @ X1 @ X0) != $true) | ((X1 @ X5) != $true)) )),
% 1.68/1.49 inference(cnf_transformation,[status(thm)],[f14])).
% 1.68/1.49 thf(f75,plain,(
% 1.68/1.49 ( ! [X0 : b > $o] : (((sK5 @ (sK4 @ X0 @ sK5) @ (sK2 @ X0 @ sK5 @ (sK4 @ X0 @ sK5)) @ (sK3 @ X0 @ sK5 @ (sK4 @ X0 @ sK5))) != $true) | ((sP0 @ X0 @ sK5) != $true) | ((sK6 @ (sK4 @ X0 @ sK5)) != $true)) )),
% 1.68/1.49 inference(subsumption_resolution,[status(thm)],[f74,f20])).
% 1.68/1.49 thf(f74,plain,(
% 1.68/1.49 ( ! [X0 : b > $o] : (($true != (X0 @ (sK4 @ X0 @ sK5))) | ((sK6 @ (sK4 @ X0 @ sK5)) != $true) | ((sK5 @ (sK4 @ X0 @ sK5) @ (sK2 @ X0 @ sK5 @ (sK4 @ X0 @ sK5)) @ (sK3 @ X0 @ sK5 @ (sK4 @ X0 @ sK5))) != $true) | ((sP0 @ X0 @ sK5) != $true)) )),
% 1.68/1.49 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.68/1.49 thf(f73,plain,(
% 1.68/1.49 ( ! [X0 : b > $o] : (((sP0 @ X0 @ sK5) != $true) | ($true != (X0 @ (sK4 @ X0 @ sK5))) | ((sK5 @ (sK4 @ X0 @ sK5) @ (sK2 @ X0 @ sK5 @ (sK4 @ X0 @ sK5)) @ (sK3 @ X0 @ sK5 @ (sK4 @ X0 @ sK5))) != $true) | ($true != $true) | ((sK6 @ (sK4 @ X0 @ sK5)) != $true)) )),
% 1.68/1.49 inference(duplicate_literal_removal,[status(thm)],[f68])).
% 1.68/1.49 thf(f68,plain,(
% 1.68/1.49 ( ! [X0 : b > $o] : (((sP0 @ X0 @ sK5) != $true) | ((sK5 @ (sK4 @ X0 @ sK5) @ (sK2 @ X0 @ sK5 @ (sK4 @ X0 @ sK5)) @ (sK3 @ X0 @ sK5 @ (sK4 @ X0 @ sK5))) != $true) | ($true != (X0 @ (sK4 @ X0 @ sK5))) | ($true != $true) | ((sK6 @ (sK4 @ X0 @ sK5)) != $true) | ((sP0 @ X0 @ sK5) != $true)) )),
% 1.68/1.49 inference(superposition,[status(thm)],[f59,f22])).
% 1.68/1.49 thf(f22,plain,(
% 1.68/1.49 ( ! [X0 : b > a > a > $o,X1 : b > $o,X6 : b] : (((X0 @ X6 @ (sK1 @ X1 @ X0 @ X6) @ (sK2 @ X1 @ X0 @ X6)) = $true) | ((X1 @ X6) != $true) | ((sP0 @ X1 @ X0) != $true)) )),
% 1.68/1.49 inference(cnf_transformation,[status(thm)],[f14])).
% 1.68/1.49 thf(f59,plain,(
% 1.68/1.49 ( ! [X0 : b > $o,X1 : a] : (($true != (sK5 @ (sK4 @ X0 @ sK5) @ (sK1 @ X0 @ sK5 @ (sK4 @ X0 @ sK5)) @ X1)) | ((sP0 @ X0 @ sK5) != $true) | ((sK6 @ (sK4 @ X0 @ sK5)) != $true) | ((sK5 @ (sK4 @ X0 @ sK5) @ X1 @ (sK3 @ X0 @ sK5 @ (sK4 @ X0 @ sK5))) != $true)) )),
% 1.68/1.49 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.68/1.49 thf(f58,plain,(
% 1.68/1.49 ( ! [X0 : b > $o,X1 : a] : (((sK6 @ (sK4 @ X0 @ sK5)) != $true) | ($true != $true) | ((sK5 @ (sK4 @ X0 @ sK5) @ X1 @ (sK3 @ X0 @ sK5 @ (sK4 @ X0 @ sK5))) != $true) | ((sP0 @ X0 @ sK5) != $true) | ($true != (sK5 @ (sK4 @ X0 @ sK5) @ (sK1 @ X0 @ sK5 @ (sK4 @ X0 @ sK5)) @ X1))) )),
% 1.68/1.49 inference(superposition,[status(thm)],[f21,f25])).
% 1.68/1.49 thf(f25,plain,(
% 1.68/1.49 ( ! [X8 : a,X6 : b,X9 : a,X7 : a] : (($true = (sK5 @ X6 @ X9 @ X7)) | ((sK6 @ X6) != $true) | ((sK5 @ X6 @ X8 @ X7) != $true) | ((sK5 @ X6 @ X9 @ X8) != $true)) )),
% 1.68/1.49 inference(cnf_transformation,[status(thm)],[f19])).
% 1.68/1.49 thf(f19,plain,(
% 1.68/1.49 (((((sK5 @ sK9 @ (sK8 @ sK9) @ (sK7 @ sK9)) != $true) & ((sK6 @ sK9) = $true)) & ! [X5 : b] : (((sK6 @ X5) != $true) | ((sK5 @ X5 @ (sK7 @ X5) @ (sK8 @ X5)) = $true))) | ((sP0 @ sK6 @ sK5) = $true)) & ! [X6 : b] : ((! [X7 : a,X8 : a,X9 : a] : (((sK5 @ X6 @ X8 @ X7) != $true) | ((sK5 @ X6 @ X9 @ X8) != $true) | ($true = (sK5 @ X6 @ X9 @ X7))) & ! [X10 : a,X11 : a] : (($true != (sK5 @ X6 @ X11 @ X10)) | ((sK5 @ X6 @ X10 @ X11) = $true))) | ((sK6 @ X6) != $true))),
% 1.68/1.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f15,f18,f17,f16])).
% 1.68/1.49 thf(f16,plain,(
% 1.68/1.49 ? [X0 : b > a > a > $o,X1 : b > $o] : ((? [X2 : b > a,X3 : b > a] : (? [X4 : b] : (((X0 @ X4 @ (X3 @ X4) @ (X2 @ X4)) != $true) & ((X1 @ X4) = $true)) & ! [X5 : b] : (((X1 @ X5) != $true) | ($true = (X0 @ X5 @ (X2 @ X5) @ (X3 @ X5))))) | ((sP0 @ X1 @ X0) = $true)) & ! [X6 : b] : ((! [X7 : a,X8 : a,X9 : a] : (($true != (X0 @ X6 @ X8 @ X7)) | ((X0 @ X6 @ X9 @ X8) != $true) | ((X0 @ X6 @ X9 @ X7) = $true)) & ! [X10 : a,X11 : a] : (((X0 @ X6 @ X11 @ X10) != $true) | ((X0 @ X6 @ X10 @ X11) = $true))) | ((X1 @ X6) != $true))) => ((? [X3 : b > a,X2 : b > a] : (? [X4 : b] : (($true != (sK5 @ X4 @ (X3 @ X4) @ (X2 @ X4))) & ((sK6 @ X4) = $true)) & ! [X5 : b] : (((sK6 @ X5) != $true) | ((sK5 @ X5 @ (X2 @ X5) @ (X3 @ X5)) = $true))) | ((sP0 @ sK6 @ sK5) = $true)) & ! [X6 : b] : ((! [X9 : a,X8 : a,X7 : a] : (((sK5 @ X6 @ X8 @ X7) != $true) | ((sK5 @ X6 @ X9 @ X8) != $true) | ($true = (sK5 @ X6 @ X9 @ X7))) & ! [X11 : a,X10 : a] : (($true != (sK5 @ X6 @ X11 @ X10)) | ((sK5 @ X6 @ X10 @ X11) = $true))) | ((sK6 @ X6) != $true)))),
% 1.68/1.49 introduced(definition,[],[choice_axiom])).
% 1.68/1.49 thf(f17,plain,(
% 1.68/1.49 ? [X3 : b > a,X2 : b > a] : (? [X4 : b] : (($true != (sK5 @ X4 @ (X3 @ X4) @ (X2 @ X4))) & ((sK6 @ X4) = $true)) & ! [X5 : b] : (((sK6 @ X5) != $true) | ((sK5 @ X5 @ (X2 @ X5) @ (X3 @ X5)) = $true))) => (? [X4 : b] : (($true != (sK5 @ X4 @ (sK8 @ X4) @ (sK7 @ X4))) & ((sK6 @ X4) = $true)) & ! [X5 : b] : (((sK6 @ X5) != $true) | ((sK5 @ X5 @ (sK7 @ X5) @ (sK8 @ X5)) = $true)))),
% 1.68/1.49 introduced(definition,[],[choice_axiom])).
% 1.68/1.49 thf(f18,plain,(
% 1.68/1.49 ? [X4 : b] : (($true != (sK5 @ X4 @ (sK8 @ X4) @ (sK7 @ X4))) & ((sK6 @ X4) = $true)) => (((sK5 @ sK9 @ (sK8 @ sK9) @ (sK7 @ sK9)) != $true) & ((sK6 @ sK9) = $true))),
% 1.68/1.49 introduced(definition,[],[choice_axiom])).
% 1.68/1.49 thf(f15,plain,(
% 1.68/1.49 ? [X0 : b > a > a > $o,X1 : b > $o] : ((? [X2 : b > a,X3 : b > a] : (? [X4 : b] : (((X0 @ X4 @ (X3 @ X4) @ (X2 @ X4)) != $true) & ((X1 @ X4) = $true)) & ! [X5 : b] : (((X1 @ X5) != $true) | ($true = (X0 @ X5 @ (X2 @ X5) @ (X3 @ X5))))) | ((sP0 @ X1 @ X0) = $true)) & ! [X6 : b] : ((! [X7 : a,X8 : a,X9 : a] : (($true != (X0 @ X6 @ X8 @ X7)) | ((X0 @ X6 @ X9 @ X8) != $true) | ((X0 @ X6 @ X9 @ X7) = $true)) & ! [X10 : a,X11 : a] : (((X0 @ X6 @ X11 @ X10) != $true) | ((X0 @ X6 @ X10 @ X11) = $true))) | ((X1 @ X6) != $true)))),
% 1.68/1.49 inference(rectify,[status(thm)],[f9])).
% 1.68/1.49 thf(f9,plain,(
% 1.68/1.49 ? [X0 : b > a > a > $o,X1 : b > $o] : ((? [X8 : b > a,X9 : b > a] : (? [X11 : b] : (((X0 @ X11 @ (X9 @ X11) @ (X8 @ X11)) != $true) & ((X1 @ X11) = $true)) & ! [X10 : b] : (($true != (X1 @ X10)) | ((X0 @ X10 @ (X8 @ X10) @ (X9 @ X10)) = $true))) | ((sP0 @ X1 @ X0) = $true)) & ! [X2 : b] : ((! [X4 : a,X3 : a,X5 : a] : (((X0 @ X2 @ X3 @ X4) != $true) | ((X0 @ X2 @ X5 @ X3) != $true) | ($true = (X0 @ X2 @ X5 @ X4))) & ! [X7 : a,X6 : a] : (((X0 @ X2 @ X6 @ X7) != $true) | ($true = (X0 @ X2 @ X7 @ X6)))) | ($true != (X1 @ X2))))),
% 1.68/1.49 inference(definition_folding,[status(thm)],[f7,f8])).
% 1.68/1.49 thf(f7,plain,(
% 1.68/1.49 ? [X0 : b > a > a > $o,X1 : b > $o] : ((? [X8 : b > a,X9 : b > a] : (? [X11 : b] : (((X0 @ X11 @ (X9 @ X11) @ (X8 @ X11)) != $true) & ((X1 @ X11) = $true)) & ! [X10 : b] : (($true != (X1 @ X10)) | ((X0 @ X10 @ (X8 @ X10) @ (X9 @ X10)) = $true))) | ? [X13 : b > a,X12 : b > a,X14 : b > a] : (! [X16 : b] : (((X0 @ X16 @ (X12 @ X16) @ (X14 @ X16)) = $true) | ((X1 @ X16) != $true)) & ! [X15 : b] : (($true != (X1 @ X15)) | ((X0 @ X15 @ (X13 @ X15) @ (X12 @ X15)) = $true)) & ? [X17 : b] : (((X0 @ X17 @ (X13 @ X17) @ (X14 @ X17)) != $true) & ((X1 @ X17) = $true)))) & ! [X2 : b] : ((! [X4 : a,X3 : a,X5 : a] : (((X0 @ X2 @ X3 @ X4) != $true) | ((X0 @ X2 @ X5 @ X3) != $true) | ($true = (X0 @ X2 @ X5 @ X4))) & ! [X7 : a,X6 : a] : (((X0 @ X2 @ X6 @ X7) != $true) | ($true = (X0 @ X2 @ X7 @ X6)))) | ($true != (X1 @ X2))))),
% 1.68/1.49 inference(flattening,[status(thm)],[f6])).
% 1.68/1.49 thf(f6,plain,(
% 1.68/1.49 ? [X1 : b > $o,X0 : b > a > a > $o] : ((? [X13 : b > a,X14 : b > a,X12 : b > a] : (? [X17 : b] : (((X0 @ X17 @ (X13 @ X17) @ (X14 @ X17)) != $true) & ((X1 @ X17) = $true)) & (! [X16 : b] : (((X0 @ X16 @ (X12 @ X16) @ (X14 @ X16)) = $true) | ((X1 @ X16) != $true)) & ! [X15 : b] : (($true != (X1 @ X15)) | ((X0 @ X15 @ (X13 @ X15) @ (X12 @ X15)) = $true)))) | ? [X8 : b > a,X9 : b > a] : (? [X11 : b] : (((X0 @ X11 @ (X9 @ X11) @ (X8 @ X11)) != $true) & ((X1 @ X11) = $true)) & ! [X10 : b] : (($true != (X1 @ X10)) | ((X0 @ X10 @ (X8 @ X10) @ (X9 @ X10)) = $true)))) & ! [X2 : b] : ((! [X7 : a,X6 : a] : (((X0 @ X2 @ X6 @ X7) != $true) | ($true = (X0 @ X2 @ X7 @ X6))) & ! [X4 : a,X3 : a,X5 : a] : (($true = (X0 @ X2 @ X5 @ X4)) | (((X0 @ X2 @ X5 @ X3) != $true) | ((X0 @ X2 @ X3 @ X4) != $true)))) | ($true != (X1 @ X2))))),
% 1.68/1.49 inference(ennf_transformation,[status(thm)],[f5])).
% 1.68/1.49 thf(f5,plain,(
% 1.68/1.49 ~! [X1 : b > $o,X0 : b > a > a > $o] : (! [X2 : b] : (($true = (X1 @ X2)) => (! [X6 : a,X7 : a] : (((X0 @ X2 @ X6 @ X7) = $true) => ($true = (X0 @ X2 @ X7 @ X6))) & ! [X4 : a,X3 : a,X5 : a] : ((((X0 @ X2 @ X5 @ X3) = $true) & ((X0 @ X2 @ X3 @ X4) = $true)) => ($true = (X0 @ X2 @ X5 @ X4))))) => (! [X13 : b > a,X14 : b > a,X12 : b > a] : ((! [X16 : b] : (((X1 @ X16) = $true) => ((X0 @ X16 @ (X12 @ X16) @ (X14 @ X16)) = $true)) & ! [X15 : b] : (($true = (X1 @ X15)) => ((X0 @ X15 @ (X13 @ X15) @ (X12 @ X15)) = $true))) => ! [X17 : b] : (((X1 @ X17) = $true) => ((X0 @ X17 @ (X13 @ X17) @ (X14 @ X17)) = $true))) & ! [X8 : b > a,X9 : b > a] : (! [X10 : b] : (($true = (X1 @ X10)) => ((X0 @ X10 @ (X8 @ X10) @ (X9 @ X10)) = $true)) => ! [X11 : b] : (((X1 @ X11) = $true) => ((X0 @ X11 @ (X9 @ X11) @ (X8 @ X11)) = $true)))))),
% 1.68/1.49 inference(fool_elimination,[status(thm)],[f4])).
% 1.68/1.49 thf(f4,plain,(
% 1.68/1.49 ~! [X0 : b > a > a > $o,X1 : b > $o] : (! [X2 : b] : ((X1 @ X2) => (! [X3 : a,X4 : a,X5 : a] : (((X0 @ X2 @ X5 @ X3) & (X0 @ X2 @ X3 @ X4)) => (X0 @ X2 @ X5 @ X4)) & ! [X6 : a,X7 : a] : ((X0 @ X2 @ X6 @ X7) => (X0 @ X2 @ X7 @ X6)))) => (! [X8 : b > a,X9 : b > a] : (! [X10 : b] : ((X1 @ X10) => (X0 @ X10 @ (X8 @ X10) @ (X9 @ X10))) => ! [X11 : b] : ((X1 @ X11) => (X0 @ X11 @ (X9 @ X11) @ (X8 @ X11)))) & ! [X12 : b > a,X13 : b > a,X14 : b > a] : ((! [X15 : b] : ((X1 @ X15) => (X0 @ X15 @ (X13 @ X15) @ (X12 @ X15))) & ! [X16 : b] : ((X1 @ X16) => (X0 @ X16 @ (X12 @ X16) @ (X14 @ X16)))) => ! [X17 : b] : ((X1 @ X17) => (X0 @ X17 @ (X13 @ X17) @ (X14 @ X17))))))),
% 1.68/1.49 inference(rectify,[status(thm)],[f2])).
% 1.68/1.49 thf(f2,negated_conjecture,(
% 1.68/1.49 ~! [X1 : b > a > a > $o,X0 : b > $o] : (! [X2 : b] : ((X0 @ X2) => (! [X4 : a,X5 : a,X3 : a] : (((X1 @ X2 @ X3 @ X4) & (X1 @ X2 @ X4 @ X5)) => (X1 @ X2 @ X3 @ X5)) & ! [X3 : a,X4 : a] : ((X1 @ X2 @ X3 @ X4) => (X1 @ X2 @ X4 @ X3)))) => (! [X2 : b > a,X4 : b > a] : (! [X3 : b] : ((X0 @ X3) => (X1 @ X3 @ (X2 @ X3) @ (X4 @ X3))) => ! [X3 : b] : ((X0 @ X3) => (X1 @ X3 @ (X4 @ X3) @ (X2 @ X3)))) & ! [X4 : b > a,X2 : b > a,X5 : b > a] : ((! [X3 : b] : ((X0 @ X3) => (X1 @ X3 @ (X2 @ X3) @ (X4 @ X3))) & ! [X3 : b] : ((X0 @ X3) => (X1 @ X3 @ (X4 @ X3) @ (X5 @ X3)))) => ! [X3 : b] : ((X0 @ X3) => (X1 @ X3 @ (X2 @ X3) @ (X5 @ X3))))))),
% 1.68/1.49 inference(negated_conjecture,[status(cth)],[f1])).
% 1.68/1.49 thf(f1,conjecture,(
% 1.68/1.49 ! [X1 : b > a > a > $o,X0 : b > $o] : (! [X2 : b] : ((X0 @ X2) => (! [X4 : a,X5 : a,X3 : a] : (((X1 @ X2 @ X3 @ X4) & (X1 @ X2 @ X4 @ X5)) => (X1 @ X2 @ X3 @ X5)) & ! [X3 : a,X4 : a] : ((X1 @ X2 @ X3 @ X4) => (X1 @ X2 @ X4 @ X3)))) => (! [X2 : b > a,X4 : b > a] : (! [X3 : b] : ((X0 @ X3) => (X1 @ X3 @ (X2 @ X3) @ (X4 @ X3))) => ! [X3 : b] : ((X0 @ X3) => (X1 @ X3 @ (X4 @ X3) @ (X2 @ X3)))) & ! [X4 : b > a,X2 : b > a,X5 : b > a] : ((! [X3 : b] : ((X0 @ X3) => (X1 @ X3 @ (X2 @ X3) @ (X4 @ X3))) & ! [X3 : b] : ((X0 @ X3) => (X1 @ X3 @ (X4 @ X3) @ (X5 @ X3)))) => ! [X3 : b] : ((X0 @ X3) => (X1 @ X3 @ (X2 @ X3) @ (X5 @ X3))))))),
% 1.68/1.49 file('/export/starexec/sandbox/tmp/tmp.x9MeSh7OKb/DTF2THF_10099.p',cTHM506_pme)).
% 1.68/1.49 thf(f21,plain,(
% 1.68/1.49 ( ! [X0 : b > a > a > $o,X1 : b > $o] : (((X0 @ (sK4 @ X1 @ X0) @ (sK1 @ X1 @ X0 @ (sK4 @ X1 @ X0)) @ (sK3 @ X1 @ X0 @ (sK4 @ X1 @ X0))) != $true) | ((sP0 @ X1 @ X0) != $true)) )),
% 1.68/1.49 inference(cnf_transformation,[status(thm)],[f14])).
% 1.68/1.49 thf(f57,plain,(
% 1.68/1.49 spl10_2 | ~spl10_3 | ~spl10_4),
% 1.68/1.49 inference(avatar_contradiction_clause,[status(thm)],[f56])).
% 1.68/1.49 thf(f56,plain,(
% 1.68/1.49 $false | (spl10_2 | ~spl10_3 | ~spl10_4)),
% 1.68/1.49 inference(subsumption_resolution,[status(thm)],[f55,f41])).
% 1.68/1.49 thf(f41,plain,(
% 1.68/1.49 ((sK6 @ sK9) = $true) | ~spl10_3),
% 1.68/1.49 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.68/1.49 thf(f39,definition,(
% 1.68/1.49 spl10_3 <=> ((sK6 @ sK9) = $true)),
% 1.68/1.49 introduced(definition,[new_symbols(naming,[spl10_3])],[avatar_definition])).
% 1.68/1.49 thf(f55,plain,(
% 1.68/1.49 ((sK6 @ sK9) != $true) | (spl10_2 | ~spl10_3 | ~spl10_4)),
% 1.68/1.49 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.68/1.49 thf(f52,plain,(
% 1.68/1.49 ($true != $true) | ((sK6 @ sK9) != $true) | (spl10_2 | ~spl10_3 | ~spl10_4)),
% 1.68/1.49 inference(superposition,[status(thm)],[f51,f45])).
% 1.68/1.49 thf(f45,plain,(
% 1.68/1.49 ( ! [X5 : b] : (((sK5 @ X5 @ (sK7 @ X5) @ (sK8 @ X5)) = $true) | ((sK6 @ X5) != $true)) ) | ~spl10_4),
% 1.68/1.49 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.68/1.49 thf(f44,definition,(
% 1.68/1.49 spl10_4 <=> ! [X5 : b] : (((sK5 @ X5 @ (sK7 @ X5) @ (sK8 @ X5)) = $true) | ((sK6 @ X5) != $true))),
% 1.68/1.49 introduced(definition,[new_symbols(naming,[spl10_4])],[avatar_definition])).
% 1.68/1.49 thf(f51,plain,(
% 1.68/1.49 ($true != (sK5 @ sK9 @ (sK7 @ sK9) @ (sK8 @ sK9))) | (spl10_2 | ~spl10_3)),
% 1.68/1.49 inference(subsumption_resolution,[status(thm)],[f50,f41])).
% 1.68/1.49 thf(f50,plain,(
% 1.68/1.49 ((sK6 @ sK9) != $true) | ($true != (sK5 @ sK9 @ (sK7 @ sK9) @ (sK8 @ sK9))) | spl10_2),
% 1.68/1.49 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.68/1.49 thf(f47,plain,(
% 1.68/1.49 ($true != $true) | ((sK6 @ sK9) != $true) | ($true != (sK5 @ sK9 @ (sK7 @ sK9) @ (sK8 @ sK9))) | spl10_2),
% 1.68/1.49 inference(superposition,[status(thm)],[f36,f24])).
% 1.68/1.49 thf(f24,plain,(
% 1.68/1.49 ( ! [X10 : a,X11 : a,X6 : b] : (((sK5 @ X6 @ X10 @ X11) = $true) | ($true != (sK5 @ X6 @ X11 @ X10)) | ((sK6 @ X6) != $true)) )),
% 1.68/1.49 inference(cnf_transformation,[status(thm)],[f19])).
% 1.68/1.49 thf(f36,plain,(
% 1.68/1.49 ((sK5 @ sK9 @ (sK8 @ sK9) @ (sK7 @ sK9)) != $true) | spl10_2),
% 1.68/1.49 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.68/1.49 thf(f34,definition,(
% 1.68/1.49 spl10_2 <=> ((sK5 @ sK9 @ (sK8 @ sK9) @ (sK7 @ sK9)) = $true)),
% 1.68/1.49 introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition])).
% 1.68/1.49 thf(f46,plain,(
% 1.68/1.49 spl10_4 | spl10_1),
% 1.68/1.49 inference(avatar_split_clause,[status(thm)],[f26,f30,f44])).
% 1.68/1.49 thf(f26,plain,(
% 1.68/1.49 ( ! [X5 : b] : (((sK5 @ X5 @ (sK7 @ X5) @ (sK8 @ X5)) = $true) | ((sK6 @ X5) != $true) | ((sP0 @ sK6 @ sK5) = $true)) )),
% 1.68/1.49 inference(cnf_transformation,[status(thm)],[f19])).
% 1.68/1.49 thf(f42,plain,(
% 1.68/1.49 spl10_1 | spl10_3),
% 1.68/1.49 inference(avatar_split_clause,[status(thm)],[f27,f39,f30])).
% 1.68/1.49 thf(f27,plain,(
% 1.68/1.49 ((sP0 @ sK6 @ sK5) = $true) | ((sK6 @ sK9) = $true)),
% 1.68/1.49 inference(cnf_transformation,[status(thm)],[f19])).
% 1.68/1.49 thf(f37,plain,(
% 1.68/1.49 spl10_1 | ~spl10_2),
% 1.68/1.49 inference(avatar_split_clause,[status(thm)],[f28,f34,f30])).
% 1.68/1.49 thf(f28,plain,(
% 1.68/1.49 ((sP0 @ sK6 @ sK5) = $true) | ((sK5 @ sK9 @ (sK8 @ sK9) @ (sK7 @ sK9)) != $true)),
% 1.68/1.49 inference(cnf_transformation,[status(thm)],[f19])).
% 1.68/1.49 % SZS output end Proof for DTF2THF_10099
% 1.68/1.49 % (10203)------------------------------
% 1.68/1.49 % (10203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.49 % (10203)Termination reason: Refutation
% 1.68/1.49
% 1.68/1.49 % (10203)Memory used [KB]: 5628
% 1.68/1.49 % (10203)Time elapsed: 0.015 s
% 1.68/1.49 % (10203)Instructions burned: 21 (million)
% 1.68/1.49 % (10203)------------------------------
% 1.68/1.49 % (10203)------------------------------
% 1.68/1.49 % (10197)Success in time 0.03 s
%------------------------------------------------------------------------------