%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV031^5 : 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 : n006.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 09:40:06 AM UTC 2026
% Result : Theorem 1.56s 1.22s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 72 ( 3 unt; 0 typ; 6 def)
% Number of atoms : 830 ( 286 equ; 0 cnn)
% Maximal formula atoms : 28 ( 11 avg)
% Number of connectives : 1340 ( 181 ~; 165 |; 100 &; 834 @)
% ( 6 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 258 ( 258 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 10 con; 0-3 aty)
% Number of variables : 275 ( 0 ^; 202 !; 73 ?; 275 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_5,type,
sP0: ( a > $o ) > ( a > ( a > b ) > ( a > b ) > $o ) > $o ).
thf(func_def_6,type,
sK1: ( a > $o ) > ( a > ( a > b ) > ( a > b ) > $o ) > a > b ).
thf(func_def_7,type,
sK2: ( a > $o ) > ( a > ( a > b ) > ( a > b ) > $o ) > a > b ).
thf(func_def_8,type,
sK3: ( a > $o ) > ( a > ( a > b ) > ( a > b ) > $o ) > a > b ).
thf(func_def_9,type,
sK4: ( a > $o ) > ( a > ( a > b ) > ( a > b ) > $o ) > a ).
thf(func_def_10,type,
sK5: a > ( a > b ) > ( a > b ) > $o ).
thf(func_def_11,type,
sK6: a > $o ).
thf(func_def_12,type,
sK7: a > b ).
thf(func_def_13,type,
sK8: a > b ).
thf(func_def_14,type,
sK9: a ).
thf(func_def_15,type,
sK10: a > b ).
thf(func_def_16,type,
sK11: a ).
thf(func_def_18,type,
ph13:
!>[X0: $tType] : X0 ).
thf(f119,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f46,f55,f59,f60,f61,f62,f91,f104,f118]) ).
thf(f118,plain,
( spl12_2
| ~ spl12_5
| ~ spl12_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f117]) ).
thf(f117,plain,
( $false
| spl12_2
| ~ spl12_5
| ~ spl12_6 ),
inference(subsumption_resolution,[status(thm)],[f116,f54]) ).
thf(f54,plain,
( ( $true
= ( sK6 @ sK9 ) )
| ~ spl12_5 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl12_5
<=> ( $true
= ( sK6 @ sK9 ) ) ),
introduced(definition,[new_symbols(naming,[spl12_5])],[avatar_definition]) ).
thf(f116,plain,
( ( $true
!= ( sK6 @ sK9 ) )
| spl12_2
| ~ spl12_5
| ~ spl12_6 ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
( ( $true
!= ( sK6 @ sK9 ) )
| ( $true != $true )
| spl12_2
| ~ spl12_5
| ~ spl12_6 ),
inference(superposition,[status(thm)],[f97,f58]) ).
thf(f58,plain,
( ! [X12: a] :
( ( ( sK5 @ X12 @ sK8 @ sK7 )
= $true )
| ( ( sK6 @ X12 )
!= $true ) )
| ~ spl12_6 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f57,definition,
( spl12_6
<=> ! [X12: a] :
( ( ( sK5 @ X12 @ sK8 @ sK7 )
= $true )
| ( ( sK6 @ X12 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl12_6])],[avatar_definition]) ).
thf(f97,plain,
( ( ( sK5 @ sK9 @ sK8 @ sK7 )
!= $true )
| spl12_2
| ~ spl12_5 ),
inference(subsumption_resolution,[status(thm)],[f94,f54]) ).
thf(f94,plain,
( ( $true
!= ( sK6 @ sK9 ) )
| ( ( sK5 @ sK9 @ sK8 @ sK7 )
!= $true )
| spl12_2 ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ( ( sK5 @ sK9 @ sK8 @ sK7 )
!= $true )
| ( $true != $true )
| ( $true
!= ( sK6 @ sK9 ) )
| spl12_2 ),
inference(superposition,[status(thm)],[f41,f31]) ).
thf(f31,plain,
! [X2: a,X8: a > b,X7: a > b] :
( ( $true
= ( sK5 @ X2 @ X7 @ X8 ) )
| ( $true
!= ( sK5 @ X2 @ X8 @ X7 ) )
| ( ( sK6 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ! [X2: a] :
( ( ( sK6 @ X2 )
!= $true )
| ( ! [X3: a > b] :
( $true
= ( sK5 @ X2 @ X3 @ X3 ) )
& ! [X4: a > b,X5: a > b,X6: a > b] :
( ( ( sK5 @ X2 @ X5 @ X4 )
!= $true )
| ( ( sK5 @ X2 @ X4 @ X6 )
!= $true )
| ( $true
= ( sK5 @ X2 @ X5 @ X6 ) ) )
& ! [X7: a > b,X8: a > b] :
( ( $true
= ( sK5 @ X2 @ X7 @ X8 ) )
| ( $true
!= ( sK5 @ X2 @ X8 @ X7 ) ) ) ) )
& ( ( ( $true
!= ( sK5 @ sK9 @ sK7 @ sK8 ) )
& ( $true
= ( sK6 @ sK9 ) )
& ! [X12: a] :
( ( ( sK5 @ X12 @ sK8 @ sK7 )
= $true )
| ( ( sK6 @ X12 )
!= $true ) ) )
| ( ( ( sK5 @ sK11 @ sK10 @ sK10 )
!= $true )
& ( $true
= ( sK6 @ sK11 ) ) )
| ( ( sP0 @ sK6 @ sK5 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f15,f19,f18,f17,f16]) ).
thf(f16,plain,
( ? [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ! [X2: a] :
( ( $true
!= ( X1 @ X2 ) )
| ( ! [X3: a > b] :
( ( X0 @ X2 @ X3 @ X3 )
= $true )
& ! [X4: a > b,X5: a > b,X6: a > b] :
( ( $true
!= ( X0 @ X2 @ X5 @ X4 ) )
| ( ( X0 @ X2 @ X4 @ X6 )
!= $true )
| ( ( X0 @ X2 @ X5 @ X6 )
= $true ) )
& ! [X7: a > b,X8: a > b] :
( ( $true
= ( X0 @ X2 @ X7 @ X8 ) )
| ( ( X0 @ X2 @ X8 @ X7 )
!= $true ) ) ) )
& ( ? [X9: a > b,X10: a > b] :
( ? [X11: a] :
( ( ( X0 @ X11 @ X9 @ X10 )
!= $true )
& ( $true
= ( X1 @ X11 ) ) )
& ! [X12: a] :
( ( $true
= ( X0 @ X12 @ X10 @ X9 ) )
| ( $true
!= ( X1 @ X12 ) ) ) )
| ? [X13: a > b,X14: a] :
( ( ( X0 @ X14 @ X13 @ X13 )
!= $true )
& ( ( X1 @ X14 )
= $true ) )
| ( ( sP0 @ X1 @ X0 )
= $true ) ) )
=> ( ! [X2: a] :
( ( ( sK6 @ X2 )
!= $true )
| ( ! [X3: a > b] :
( $true
= ( sK5 @ X2 @ X3 @ X3 ) )
& ! [X6: a > b,X5: a > b,X4: a > b] :
( ( ( sK5 @ X2 @ X5 @ X4 )
!= $true )
| ( ( sK5 @ X2 @ X4 @ X6 )
!= $true )
| ( $true
= ( sK5 @ X2 @ X5 @ X6 ) ) )
& ! [X8: a > b,X7: a > b] :
( ( $true
= ( sK5 @ X2 @ X7 @ X8 ) )
| ( $true
!= ( sK5 @ X2 @ X8 @ X7 ) ) ) ) )
& ( ? [X10: a > b,X9: a > b] :
( ? [X11: a] :
( ( $true
!= ( sK5 @ X11 @ X9 @ X10 ) )
& ( ( sK6 @ X11 )
= $true ) )
& ! [X12: a] :
( ( ( sK5 @ X12 @ X10 @ X9 )
= $true )
| ( ( sK6 @ X12 )
!= $true ) ) )
| ? [X14: a,X13: a > b] :
( ( ( sK5 @ X14 @ X13 @ X13 )
!= $true )
& ( ( sK6 @ X14 )
= $true ) )
| ( ( sP0 @ sK6 @ sK5 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X10: a > b,X9: a > b] :
( ? [X11: a] :
( ( $true
!= ( sK5 @ X11 @ X9 @ X10 ) )
& ( ( sK6 @ X11 )
= $true ) )
& ! [X12: a] :
( ( ( sK5 @ X12 @ X10 @ X9 )
= $true )
| ( ( sK6 @ X12 )
!= $true ) ) )
=> ( ? [X11: a] :
( ( $true
!= ( sK5 @ X11 @ sK7 @ sK8 ) )
& ( ( sK6 @ X11 )
= $true ) )
& ! [X12: a] :
( ( ( sK5 @ X12 @ sK8 @ sK7 )
= $true )
| ( ( sK6 @ X12 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X11: a] :
( ( $true
!= ( sK5 @ X11 @ sK7 @ sK8 ) )
& ( ( sK6 @ X11 )
= $true ) )
=> ( ( $true
!= ( sK5 @ sK9 @ sK7 @ sK8 ) )
& ( $true
= ( sK6 @ sK9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X14: a,X13: a > b] :
( ( ( sK5 @ X14 @ X13 @ X13 )
!= $true )
& ( ( sK6 @ X14 )
= $true ) )
=> ( ( ( sK5 @ sK11 @ sK10 @ sK10 )
!= $true )
& ( $true
= ( sK6 @ sK11 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
? [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ! [X2: a] :
( ( $true
!= ( X1 @ X2 ) )
| ( ! [X3: a > b] :
( ( X0 @ X2 @ X3 @ X3 )
= $true )
& ! [X4: a > b,X5: a > b,X6: a > b] :
( ( $true
!= ( X0 @ X2 @ X5 @ X4 ) )
| ( ( X0 @ X2 @ X4 @ X6 )
!= $true )
| ( ( X0 @ X2 @ X5 @ X6 )
= $true ) )
& ! [X7: a > b,X8: a > b] :
( ( $true
= ( X0 @ X2 @ X7 @ X8 ) )
| ( ( X0 @ X2 @ X8 @ X7 )
!= $true ) ) ) )
& ( ? [X9: a > b,X10: a > b] :
( ? [X11: a] :
( ( ( X0 @ X11 @ X9 @ X10 )
!= $true )
& ( $true
= ( X1 @ X11 ) ) )
& ! [X12: a] :
( ( $true
= ( X0 @ X12 @ X10 @ X9 ) )
| ( $true
!= ( X1 @ X12 ) ) ) )
| ? [X13: a > b,X14: a] :
( ( ( X0 @ X14 @ X13 @ X13 )
!= $true )
& ( ( X1 @ X14 )
= $true ) )
| ( ( sP0 @ X1 @ X0 )
= $true ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
? [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ! [X2: a] :
( ( $true
!= ( X1 @ X2 ) )
| ( ! [X3: a > b] :
( ( X0 @ X2 @ X3 @ X3 )
= $true )
& ! [X6: a > b,X8: a > b,X7: a > b] :
( ( ( X0 @ X2 @ X8 @ X6 )
!= $true )
| ( $true
!= ( X0 @ X2 @ X6 @ X7 ) )
| ( ( X0 @ X2 @ X8 @ X7 )
= $true ) )
& ! [X4: a > b,X5: a > b] :
( ( $true
= ( X0 @ X2 @ X4 @ X5 ) )
| ( $true
!= ( X0 @ X2 @ X5 @ X4 ) ) ) ) )
& ( ? [X11: a > b,X12: a > b] :
( ? [X14: a] :
( ( ( X0 @ X14 @ X11 @ X12 )
!= $true )
& ( ( X1 @ X14 )
= $true ) )
& ! [X13: a] :
( ( $true
= ( X0 @ X13 @ X12 @ X11 ) )
| ( ( X1 @ X13 )
!= $true ) ) )
| ? [X10: a > b,X9: a] :
( ( $true
!= ( X0 @ X9 @ X10 @ X10 ) )
& ( $true
= ( X1 @ X9 ) ) )
| ( ( sP0 @ X1 @ X0 )
= $true ) ) ),
inference(definition_folding,[status(thm)],[f7,f8]) ).
thf(f8,plain,
! [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ? [X17: a > b,X15: a > b,X16: a > b] :
( ! [X19: a] :
( ( ( X0 @ X19 @ X15 @ X16 )
= $true )
| ( $true
!= ( X1 @ X19 ) ) )
& ! [X18: a] :
( ( ( X0 @ X18 @ X16 @ X17 )
= $true )
| ( $true
!= ( X1 @ X18 ) ) )
& ? [X20: a] :
( ( ( X0 @ X20 @ X15 @ X17 )
!= $true )
& ( $true
= ( X1 @ X20 ) ) ) )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f7,plain,
? [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ! [X2: a] :
( ( $true
!= ( X1 @ X2 ) )
| ( ! [X3: a > b] :
( ( X0 @ X2 @ X3 @ X3 )
= $true )
& ! [X6: a > b,X8: a > b,X7: a > b] :
( ( ( X0 @ X2 @ X8 @ X6 )
!= $true )
| ( $true
!= ( X0 @ X2 @ X6 @ X7 ) )
| ( ( X0 @ X2 @ X8 @ X7 )
= $true ) )
& ! [X4: a > b,X5: a > b] :
( ( $true
= ( X0 @ X2 @ X4 @ X5 ) )
| ( $true
!= ( X0 @ X2 @ X5 @ X4 ) ) ) ) )
& ( ? [X11: a > b,X12: a > b] :
( ? [X14: a] :
( ( ( X0 @ X14 @ X11 @ X12 )
!= $true )
& ( ( X1 @ X14 )
= $true ) )
& ! [X13: a] :
( ( $true
= ( X0 @ X13 @ X12 @ X11 ) )
| ( ( X1 @ X13 )
!= $true ) ) )
| ? [X10: a > b,X9: a] :
( ( $true
!= ( X0 @ X9 @ X10 @ X10 ) )
& ( $true
= ( X1 @ X9 ) ) )
| ? [X17: a > b,X15: a > b,X16: a > b] :
( ! [X19: a] :
( ( ( X0 @ X19 @ X15 @ X16 )
= $true )
| ( $true
!= ( X1 @ X19 ) ) )
& ! [X18: a] :
( ( ( X0 @ X18 @ X16 @ X17 )
= $true )
| ( $true
!= ( X1 @ X18 ) ) )
& ? [X20: a] :
( ( ( X0 @ X20 @ X15 @ X17 )
!= $true )
& ( $true
= ( X1 @ X20 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ( ? [X10: a > b,X9: a] :
( ( $true
!= ( X0 @ X9 @ X10 @ X10 ) )
& ( $true
= ( X1 @ X9 ) ) )
| ? [X11: a > b,X12: a > b] :
( ? [X14: a] :
( ( ( X0 @ X14 @ X11 @ X12 )
!= $true )
& ( ( X1 @ X14 )
= $true ) )
& ! [X13: a] :
( ( $true
= ( X0 @ X13 @ X12 @ X11 ) )
| ( ( X1 @ X13 )
!= $true ) ) )
| ? [X16: a > b,X17: a > b,X15: a > b] :
( ? [X20: a] :
( ( ( X0 @ X20 @ X15 @ X17 )
!= $true )
& ( $true
= ( X1 @ X20 ) ) )
& ! [X19: a] :
( ( ( X0 @ X19 @ X15 @ X16 )
= $true )
| ( $true
!= ( X1 @ X19 ) ) )
& ! [X18: a] :
( ( ( X0 @ X18 @ X16 @ X17 )
= $true )
| ( $true
!= ( X1 @ X18 ) ) ) ) )
& ! [X2: a] :
( ( ! [X7: a > b,X6: a > b,X8: a > b] :
( ( ( X0 @ X2 @ X8 @ X7 )
= $true )
| ( $true
!= ( X0 @ X2 @ X6 @ X7 ) )
| ( ( X0 @ X2 @ X8 @ X6 )
!= $true ) )
& ! [X4: a > b,X5: a > b] :
( ( $true
= ( X0 @ X2 @ X4 @ X5 ) )
| ( $true
!= ( X0 @ X2 @ X5 @ X4 ) ) )
& ! [X3: a > b] :
( ( X0 @ X2 @ X3 @ X3 )
= $true ) )
| ( $true
!= ( X1 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ! [X2: a] :
( ( $true
= ( X1 @ X2 ) )
=> ( ! [X7: a > b,X6: a > b,X8: a > b] :
( ( ( $true
= ( X0 @ X2 @ X6 @ X7 ) )
& ( ( X0 @ X2 @ X8 @ X6 )
= $true ) )
=> ( ( X0 @ X2 @ X8 @ X7 )
= $true ) )
& ! [X4: a > b,X5: a > b] :
( ( $true
= ( X0 @ X2 @ X5 @ X4 ) )
=> ( $true
= ( X0 @ X2 @ X4 @ X5 ) ) )
& ! [X3: a > b] :
( ( X0 @ X2 @ X3 @ X3 )
= $true ) ) )
=> ( ! [X10: a > b,X9: a] :
( ( $true
= ( X1 @ X9 ) )
=> ( $true
= ( X0 @ X9 @ X10 @ X10 ) ) )
& ! [X11: a > b,X12: a > b] :
( ! [X13: a] :
( ( ( X1 @ X13 )
= $true )
=> ( $true
= ( X0 @ X13 @ X12 @ X11 ) ) )
=> ! [X14: a] :
( ( ( X1 @ X14 )
= $true )
=> ( ( X0 @ X14 @ X11 @ X12 )
= $true ) ) )
& ! [X16: a > b,X17: a > b,X15: a > b] :
( ( ! [X19: a] :
( ( $true
= ( X1 @ X19 ) )
=> ( ( X0 @ X19 @ X15 @ X16 )
= $true ) )
& ! [X18: a] :
( ( $true
= ( X1 @ X18 ) )
=> ( ( X0 @ X18 @ X16 @ X17 )
= $true ) ) )
=> ! [X20: a] :
( ( $true
= ( X1 @ X20 ) )
=> ( ( X0 @ X20 @ X15 @ X17 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( ! [X3: a > b] : ( X0 @ X2 @ X3 @ X3 )
& ! [X4: a > b,X5: a > b] :
( ( X0 @ X2 @ X5 @ X4 )
=> ( X0 @ X2 @ X4 @ X5 ) )
& ! [X6: a > b,X7: a > b,X8: a > b] :
( ( ( X0 @ X2 @ X8 @ X6 )
& ( X0 @ X2 @ X6 @ X7 ) )
=> ( X0 @ X2 @ X8 @ X7 ) ) ) )
=> ( ! [X9: a,X10: a > b] :
( ( X1 @ X9 )
=> ( X0 @ X9 @ X10 @ X10 ) )
& ! [X11: a > b,X12: a > b] :
( ! [X13: a] :
( ( X1 @ X13 )
=> ( X0 @ X13 @ X12 @ X11 ) )
=> ! [X14: a] :
( ( X1 @ X14 )
=> ( X0 @ X14 @ X11 @ X12 ) ) )
& ! [X15: a > b,X16: a > b,X17: a > b] :
( ( ! [X18: a] :
( ( X1 @ X18 )
=> ( X0 @ X18 @ X16 @ X17 ) )
& ! [X19: a] :
( ( X1 @ X19 )
=> ( X0 @ X19 @ X15 @ X16 ) ) )
=> ! [X20: a] :
( ( X1 @ X20 )
=> ( X0 @ X20 @ X15 @ X17 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > ( a > b ) > ( a > b ) > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( ! [X3: a > b] : ( X1 @ X2 @ X3 @ X3 )
& ! [X4: a > b,X3: a > b] :
( ( X1 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 @ X3 ) )
& ! [X4: a > b,X5: a > b,X3: a > b] :
( ( ( X1 @ X2 @ X3 @ X4 )
& ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X2 @ X3 @ X5 ) ) ) )
=> ( ! [X3: a,X2: a > b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ X2 @ X2 ) )
& ! [X4: a > b,X2: a > b] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ X2 @ X4 ) )
=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ X4 @ X2 ) ) )
& ! [X2: a > b,X4: a > b,X5: a > b] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ X4 @ X5 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ X2 @ X4 ) ) )
=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ X2 @ X5 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > ( a > b ) > ( a > b ) > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( ! [X3: a > b] : ( X1 @ X2 @ X3 @ X3 )
& ! [X4: a > b,X3: a > b] :
( ( X1 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 @ X3 ) )
& ! [X4: a > b,X5: a > b,X3: a > b] :
( ( ( X1 @ X2 @ X3 @ X4 )
& ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X2 @ X3 @ X5 ) ) ) )
=> ( ! [X3: a,X2: a > b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ X2 @ X2 ) )
& ! [X4: a > b,X2: a > b] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ X2 @ X4 ) )
=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ X4 @ X2 ) ) )
& ! [X2: a > b,X4: a > b,X5: a > b] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ X4 @ X5 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ X2 @ X4 ) ) )
=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ X2 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UmcC3yIcGA/DTF2THF_5061.p',cTHM512_pme) ).
thf(f41,plain,
( ( $true
!= ( sK5 @ sK9 @ sK7 @ sK8 ) )
| spl12_2 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl12_2
<=> ( $true
= ( sK5 @ sK9 @ sK7 @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl12_2])],[avatar_definition]) ).
thf(f104,plain,
( ~ spl12_1
| spl12_4 ),
inference(avatar_split_clause,[status(thm)],[f102,f48,f35]) ).
thf(f35,definition,
( spl12_1
<=> ( $true
= ( sK6 @ sK11 ) ) ),
introduced(definition,[new_symbols(naming,[spl12_1])],[avatar_definition]) ).
thf(f48,definition,
( spl12_4
<=> ( ( sK5 @ sK11 @ sK10 @ sK10 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_4])],[avatar_definition]) ).
thf(f102,plain,
( ( $true
!= ( sK6 @ sK11 ) )
| spl12_4 ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $true
!= ( sK6 @ sK11 ) )
| ( $true != $true )
| spl12_4 ),
inference(superposition,[status(thm)],[f50,f33]) ).
thf(f33,plain,
! [X2: a,X3: a > b] :
( ( $true
= ( sK5 @ X2 @ X3 @ X3 ) )
| ( ( sK6 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f50,plain,
( ( ( sK5 @ sK11 @ sK10 @ sK10 )
!= $true )
| spl12_4 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f91,plain,
~ spl12_3,
inference(avatar_contradiction_clause,[status(thm)],[f90]) ).
thf(f90,plain,
( $false
| ~ spl12_3 ),
inference(subsumption_resolution,[status(thm)],[f89,f45]) ).
thf(f45,plain,
( ( ( sP0 @ sK6 @ sK5 )
= $true )
| ~ spl12_3 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl12_3
<=> ( ( sP0 @ sK6 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_3])],[avatar_definition]) ).
thf(f89,plain,
( ( sP0 @ sK6 @ sK5 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( ( sP0 @ sK6 @ sK5 )
!= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( ( sP0 @ sK6 @ sK5 )
!= $true )
| ( ( sP0 @ sK6 @ sK5 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f86,f21]) ).
thf(f21,plain,
! [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ( $true
= ( X1 @ ( sK4 @ X1 @ X0 ) ) )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ( ! [X5: a] :
( ( $true
= ( X0 @ X5 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) )
| ( $true
!= ( X1 @ X5 ) ) )
& ! [X6: a] :
( ( ( X0 @ X6 @ ( sK3 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) )
= $true )
| ( $true
!= ( X1 @ X6 ) ) )
& ( $true
!= ( X0 @ ( sK4 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) ) )
& ( $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: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ? [X2: a > b,X3: a > b,X4: a > b] :
( ! [X5: a] :
( ( $true
= ( X0 @ X5 @ X3 @ X4 ) )
| ( $true
!= ( X1 @ X5 ) ) )
& ! [X6: a] :
( ( ( X0 @ X6 @ X4 @ X2 )
= $true )
| ( $true
!= ( X1 @ X6 ) ) )
& ? [X7: a] :
( ( ( X0 @ X7 @ X3 @ X2 )
!= $true )
& ( $true
= ( X1 @ X7 ) ) ) )
=> ( ! [X5: a] :
( ( $true
= ( X0 @ X5 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) )
| ( $true
!= ( X1 @ X5 ) ) )
& ! [X6: a] :
( ( ( X0 @ X6 @ ( sK3 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) )
= $true )
| ( $true
!= ( X1 @ X6 ) ) )
& ? [X7: a] :
( ( $true
!= ( X0 @ X7 @ ( sK2 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) ) )
& ( $true
= ( X1 @ X7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ? [X7: a] :
( ( $true
!= ( X0 @ X7 @ ( sK2 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) ) )
& ( $true
= ( X1 @ X7 ) ) )
=> ( ( $true
!= ( X0 @ ( sK4 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) ) )
& ( $true
= ( X1 @ ( sK4 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ? [X2: a > b,X3: a > b,X4: a > b] :
( ! [X5: a] :
( ( $true
= ( X0 @ X5 @ X3 @ X4 ) )
| ( $true
!= ( X1 @ X5 ) ) )
& ! [X6: a] :
( ( ( X0 @ X6 @ X4 @ X2 )
= $true )
| ( $true
!= ( X1 @ X6 ) ) )
& ? [X7: a] :
( ( ( X0 @ X7 @ X3 @ X2 )
!= $true )
& ( $true
= ( X1 @ X7 ) ) ) )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ? [X17: a > b,X15: a > b,X16: a > b] :
( ! [X19: a] :
( ( ( X0 @ X19 @ X15 @ X16 )
= $true )
| ( $true
!= ( X1 @ X19 ) ) )
& ! [X18: a] :
( ( ( X0 @ X18 @ X16 @ X17 )
= $true )
| ( $true
!= ( X1 @ X18 ) ) )
& ? [X20: a] :
( ( ( X0 @ X20 @ X15 @ X17 )
!= $true )
& ( $true
= ( X1 @ X20 ) ) ) )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f86,plain,
! [X0: a > $o] :
( ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true )
| ( ( sP0 @ X0 @ sK5 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f85,f21]) ).
thf(f85,plain,
! [X0: a > $o] :
( ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true )
| ( $true
!= ( X0 @ ( sK4 @ X0 @ sK5 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f78,f24]) ).
thf(f24,plain,
! [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o,X5: a] :
( ( $true
= ( X0 @ X5 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) )
| ( ( sP0 @ X1 @ X0 )
!= $true )
| ( $true
!= ( X1 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f78,plain,
! [X0: a > $o] :
( ( $true
!= ( sK5 @ ( sK4 @ X0 @ sK5 ) @ ( sK2 @ X0 @ sK5 ) @ ( sK3 @ X0 @ sK5 ) ) )
| ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true )
| ( $true
!= ( X0 @ ( sK4 @ X0 @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
! [X0: a > $o] :
( ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( X0 @ ( sK4 @ X0 @ sK5 ) ) )
| ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( $true
!= ( sK5 @ ( sK4 @ X0 @ sK5 ) @ ( sK2 @ X0 @ sK5 ) @ ( sK3 @ X0 @ sK5 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f76]) ).
thf(f76,plain,
! [X0: a > $o] :
( ( $true
!= ( sK5 @ ( sK4 @ X0 @ sK5 ) @ ( sK2 @ X0 @ sK5 ) @ ( sK3 @ X0 @ sK5 ) ) )
| ( $true
!= ( X0 @ ( sK4 @ X0 @ sK5 ) ) )
| ( $true != $true )
| ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f66,f23]) ).
thf(f23,plain,
! [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o,X6: a] :
( ( ( X0 @ X6 @ ( sK3 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) )
= $true )
| ( ( sP0 @ X1 @ X0 )
!= $true )
| ( $true
!= ( X1 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f66,plain,
! [X0: a > $o,X1: a > b] :
( ( $true
!= ( sK5 @ ( sK4 @ X0 @ sK5 ) @ X1 @ ( sK1 @ X0 @ sK5 ) ) )
| ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true )
| ( ( sK5 @ ( sK4 @ X0 @ sK5 ) @ ( sK2 @ X0 @ sK5 ) @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X0: a > $o,X1: a > b] :
( ( ( sK5 @ ( sK4 @ X0 @ sK5 ) @ ( sK2 @ X0 @ sK5 ) @ X1 )
!= $true )
| ( ( sP0 @ X0 @ sK5 )
!= $true )
| ( $true
!= ( sK5 @ ( sK4 @ X0 @ sK5 ) @ X1 @ ( sK1 @ X0 @ sK5 ) ) )
| ( $true != $true )
| ( ( sK6 @ ( sK4 @ X0 @ sK5 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f22,f32]) ).
thf(f32,plain,
! [X2: a,X6: a > b,X4: a > b,X5: a > b] :
( ( $true
= ( sK5 @ X2 @ X5 @ X6 ) )
| ( ( sK6 @ X2 )
!= $true )
| ( ( sK5 @ X2 @ X5 @ X4 )
!= $true )
| ( ( sK5 @ X2 @ X4 @ X6 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f22,plain,
! [X0: a > ( a > b ) > ( a > b ) > $o,X1: a > $o] :
( ( $true
!= ( X0 @ ( sK4 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) ) )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f62,plain,
( spl12_1
| spl12_3
| spl12_5 ),
inference(avatar_split_clause,[status(thm)],[f27,f52,f43,f35]) ).
thf(f27,plain,
( ( $true
= ( sK6 @ sK9 ) )
| ( $true
= ( sK6 @ sK11 ) )
| ( ( sP0 @ sK6 @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f61,plain,
( spl12_3
| ~ spl12_2
| ~ spl12_4 ),
inference(avatar_split_clause,[status(thm)],[f30,f48,f39,f43]) ).
thf(f30,plain,
( ( ( sP0 @ sK6 @ sK5 )
= $true )
| ( $true
!= ( sK5 @ sK9 @ sK7 @ sK8 ) )
| ( ( sK5 @ sK11 @ sK10 @ sK10 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f60,plain,
( spl12_6
| spl12_1
| spl12_3 ),
inference(avatar_split_clause,[status(thm)],[f25,f43,f35,f57]) ).
thf(f25,plain,
! [X12: a] :
( ( $true
= ( sK6 @ sK11 ) )
| ( ( sK6 @ X12 )
!= $true )
| ( ( sP0 @ sK6 @ sK5 )
= $true )
| ( ( sK5 @ X12 @ sK8 @ sK7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f59,plain,
( ~ spl12_4
| spl12_3
| spl12_6 ),
inference(avatar_split_clause,[status(thm)],[f26,f57,f43,f48]) ).
thf(f26,plain,
! [X12: a] :
( ( ( sK5 @ X12 @ sK8 @ sK7 )
= $true )
| ( ( sK5 @ sK11 @ sK10 @ sK10 )
!= $true )
| ( ( sK6 @ X12 )
!= $true )
| ( ( sP0 @ sK6 @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f55,plain,
( ~ spl12_4
| spl12_3
| spl12_5 ),
inference(avatar_split_clause,[status(thm)],[f28,f52,f43,f48]) ).
thf(f28,plain,
( ( ( sK5 @ sK11 @ sK10 @ sK10 )
!= $true )
| ( ( sP0 @ sK6 @ sK5 )
= $true )
| ( $true
= ( sK6 @ sK9 ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f46,plain,
( spl12_1
| ~ spl12_2
| spl12_3 ),
inference(avatar_split_clause,[status(thm)],[f29,f43,f39,f35]) ).
thf(f29,plain,
( ( $true
= ( sK6 @ sK11 ) )
| ( ( sP0 @ sK6 @ sK5 )
= $true )
| ( $true
!= ( sK5 @ sK9 @ sK7 @ sK8 ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV031^5 : 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
% 0.15/0.33 % Computer : n006.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:39:00 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : SEV031^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.45 % Domain : Set Theory (Relations)
% 0.31/0.45 % Problem : TPS problem from EQUIVALENCE-RELATIONS-THMS
% 0.31/0.45 % Version : Especial.
% 0.31/0.45 % English :
% 0.31/0.45
% 0.31/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.45 % Source : [Bro09]
% 0.31/0.45 % Names : tps_1127 [Bro09]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.5.0, 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
% 0.31/0.45 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.31/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.31/0.45 % Number of connectives : 61 ( 0 ~; 0 |; 6 &; 43 @)
% 0.31/0.45 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.31/0.45 % Maximal formula depth : 16 ( 16 avg)
% 0.31/0.45 % Number of types : 3 ( 2 usr)
% 0.31/0.45 % Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% 0.31/0.45 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.31/0.45 % Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% 0.31/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.45
% 0.31/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 thf(a_type,type,
% 0.31/0.45 a: $tType ).
% 0.31/0.45
% 0.31/0.45 thf(b_type,type,
% 0.31/0.45 b: $tType ).
% 0.31/0.45
% 0.31/0.45 thf(cTHM512_pme,conjecture,
% 0.31/0.45 ! [Xp: a > $o,Xe: a > ( a > b ) > ( a > b ) > $o] :
% 0.31/0.45 ( ! [Xx: a] :
% 0.31/0.45 ( ( Xp @ Xx )
% 0.31/0.45 => ( ! [Xx0: a > b] : ( Xe @ Xx @ Xx0 @ Xx0 )
% 0.31/0.45 & ! [Xx0: a > b,Xy: a > b] :
% 0.31/0.45 ( ( Xe @ Xx @ Xx0 @ Xy )
% 0.31/0.45 => ( Xe @ Xx @ Xy @ Xx0 ) )
% 0.31/0.45 & ! [Xx0: a > b,Xy: a > b,Xz: a > b] :
% 0.31/0.45 ( ( ( Xe @ Xx @ Xx0 @ Xy )
% 0.31/0.45 & ( Xe @ Xx @ Xy @ Xz ) )
% 0.31/0.45 => ( Xe @ Xx @ Xx0 @ Xz ) ) ) )
% 0.31/0.45 => ( ! [Xx: a > b,Xx0: a] :
% 0.31/0.45 ( ( Xp @ Xx0 )
% 0.31/0.45 => ( Xe @ Xx0 @ Xx @ Xx ) )
% 0.31/0.45 & ! [Xx: a > b,Xy: a > b] :
% 0.31/0.45 ( ! [Xx0: a] :
% 0.31/0.45 ( ( Xp @ Xx0 )
% 0.31/0.45 => ( Xe @ Xx0 @ Xx @ Xy ) )
% 0.31/0.45 => ! [Xx0: a] :
% 0.31/0.45 ( ( Xp @ Xx0 )
% 0.31/0.45 => ( Xe @ Xx0 @ Xy @ Xx ) ) )
% 0.31/0.45 & ! [Xx: a > b,Xy: a > b,Xz: a > b] :
% 0.31/0.45 ( ( ! [Xx0: a] :
% 0.31/0.45 ( ( Xp @ Xx0 )
% 0.31/0.45 => ( Xe @ Xx0 @ Xx @ Xy ) )
% 0.31/0.45 & ! [Xx0: a] :
% 0.31/0.45 ( ( Xp @ Xx0 )
% 0.31/0.45 => ( Xe @ Xx0 @ Xy @ Xz ) ) )
% 0.31/0.45 => ! [Xx0: a] :
% 0.31/0.45 ( ( Xp @ Xx0 )
% 0.31/0.45 => ( Xe @ Xx0 @ Xx @ Xz ) ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 ------------------------
% 1.39/1.19 ---- Embedded in THF ---
% 1.39/1.19 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.19 %%% Generated on Tue Feb 24 12:39:01 EST 2026
% 1.39/1.19 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.19 %%% Logic specification used:
% 1.39/1.19 %%% thf(spec, logic, $$dhol).
% 1.39/1.19
% 1.39/1.19 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.UmcC3yIcGA/DTF2DTF5061.p
% See solution above
% 1.39/1.19 ------------------------
% 1.56/1.20 ---- Cleaned THF ---
% 1.56/1.20 thf(a_type,type,
% 1.56/1.20 a: $tType ).
% 1.56/1.20
% 1.56/1.20 thf(b_type,type,
% 1.56/1.20 b: $tType ).
% 1.56/1.20
% 1.56/1.20 thf(cTHM512_pme,conjecture,
% 1.56/1.20 ! [Xp: a > $o,Xe: a > ( a > b ) > ( a > b ) > $o] :
% 1.56/1.20 ( ! [Xx: a] :
% 1.56/1.20 ( ( Xp @ Xx )
% 1.56/1.20 => ( ! [Xx0: a > b] : ( Xe @ Xx @ Xx0 @ Xx0 )
% 1.56/1.20 & ! [Xx0: a > b,Xy: a > b] :
% 1.56/1.20 ( ( Xe @ Xx @ Xx0 @ Xy )
% 1.56/1.20 => ( Xe @ Xx @ Xy @ Xx0 ) )
% 1.56/1.20 & ! [Xx0: a > b,Xy: a > b,Xz: a > b] :
% 1.56/1.20 ( ( ( Xe @ Xx @ Xx0 @ Xy )
% 1.56/1.20 & ( Xe @ Xx @ Xy @ Xz ) )
% 1.56/1.20 => ( Xe @ Xx @ Xx0 @ Xz ) ) ) )
% 1.56/1.20 => ( ! [Xx: a > b,Xx0: a] :
% 1.56/1.20 ( ( Xp @ Xx0 )
% 1.56/1.20 => ( Xe @ Xx0 @ Xx @ Xx ) )
% 1.56/1.20 & ! [Xx: a > b,Xy: a > b] :
% 1.56/1.20 ( ! [Xx0: a] :
% 1.56/1.20 ( ( Xp @ Xx0 )
% 1.56/1.20 => ( Xe @ Xx0 @ Xx @ Xy ) )
% 1.56/1.20 => ! [Xx0: a] :
% 1.56/1.20 ( ( Xp @ Xx0 )
% 1.56/1.20 => ( Xe @ Xx0 @ Xy @ Xx ) ) )
% 1.56/1.20 & ! [Xx: a > b,Xy: a > b,Xz: a > b] :
% 1.56/1.20 ( ( ! [Xx0: a] :
% 1.56/1.20 ( ( Xp @ Xx0 )
% 1.56/1.20 => ( Xe @ Xx0 @ Xx @ Xy ) )
% 1.56/1.20 & ! [Xx0: a] :
% 1.56/1.20 ( ( Xp @ Xx0 )
% 1.56/1.20 => ( Xe @ Xx0 @ Xy @ Xz ) ) )
% 1.56/1.20 => ! [Xx0: a] :
% 1.56/1.20 ( ( Xp @ Xx0 )
% 1.56/1.20 => ( Xe @ Xx0 @ Xx @ Xz ) ) ) ) ) ).
% 1.56/1.20 ------------------------
% 1.56/1.21 % (5345)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_5061 for (2999ds/275Mi)
% 1.56/1.21 % (5342)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_5061 for (2999ds/27Mi)
% 1.56/1.22 % (5345)First to succeed.
% 1.56/1.22 % (5340)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5061 for (2999ds/183Mi)
% 1.56/1.22 % (5341)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_5061 for (2999ds/4Mi)
% 1.56/1.22 % (5343)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5061 for (2999ds/2Mi)
% 1.56/1.22 % (5344)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_5061 for (2999ds/2Mi)
% 1.56/1.22 % (5346)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5061 for (2999ds/18Mi)
% 1.56/1.22 % (5343)Instruction limit reached!
% 1.56/1.22 % (5343)------------------------------
% 1.56/1.22 % (5343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.22 % (5343)Termination reason: Unknown
% 1.56/1.22 % (5343)Termination phase: Property scanning
% 1.56/1.22
% 1.56/1.22 % (5343)Memory used [KB]: 895
% 1.56/1.22 % (5343)Time elapsed: 0.003 s
% 1.56/1.22 % (5343)Instructions burned: 2 (million)
% 1.56/1.22 % (5343)------------------------------
% 1.56/1.22 % (5343)------------------------------
% 1.56/1.22 % (5344)Instruction limit reached!
% 1.56/1.22 % (5344)------------------------------
% 1.56/1.22 % (5344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.22 % (5344)Termination reason: Unknown
% 1.56/1.22 % (5344)Termination phase: shuffling
% 1.56/1.22
% 1.56/1.22 % (5344)Memory used [KB]: 895
% 1.56/1.22 % (5344)Time elapsed: 0.003 s
% 1.56/1.22 % (5344)Instructions burned: 2 (million)
% 1.56/1.22 % (5344)------------------------------
% 1.56/1.22 % (5344)------------------------------
% 1.56/1.22 % (5345)Refutation found. Thanks to Tanya!
% 1.56/1.22 % SZS status Theorem for DTF2THF_5061
% 1.56/1.22 % SZS output start Proof for DTF2THF_5061
% 1.56/1.22 thf(type_def_5, type, a: $tType).
% 1.56/1.22 thf(type_def_7, type, b: $tType).
% 1.56/1.22 thf(func_def_0, type, a: $tType).
% 1.56/1.22 thf(func_def_1, type, b: $tType).
% 1.56/1.22 thf(func_def_5, type, sP0: (a > $o) > (a > (a > b) > (a > b) > $o) > $o).
% 1.56/1.22 thf(func_def_6, type, sK1: (a > $o) > (a > (a > b) > (a > b) > $o) > a > b).
% 1.56/1.22 thf(func_def_7, type, sK2: (a > $o) > (a > (a > b) > (a > b) > $o) > a > b).
% 1.56/1.22 thf(func_def_8, type, sK3: (a > $o) > (a > (a > b) > (a > b) > $o) > a > b).
% 1.56/1.22 thf(func_def_9, type, sK4: (a > $o) > (a > (a > b) > (a > b) > $o) > a).
% 1.56/1.22 thf(func_def_10, type, sK5: a > (a > b) > (a > b) > $o).
% 1.56/1.22 thf(func_def_11, type, sK6: a > $o).
% 1.56/1.22 thf(func_def_12, type, sK7: a > b).
% 1.56/1.22 thf(func_def_13, type, sK8: a > b).
% 1.56/1.22 thf(func_def_14, type, sK9: a).
% 1.56/1.22 thf(func_def_15, type, sK10: a > b).
% 1.56/1.22 thf(func_def_16, type, sK11: a).
% 1.56/1.22 thf(func_def_18, type, ph13: !>[X0: $tType]:(X0)).
% 1.56/1.22 thf(f119,plain,(
% 1.56/1.22 $false),
% 1.56/1.22 inference(avatar_sat_refutation,[status(thm)],[f46,f55,f59,f60,f61,f62,f91,f104,f118])).
% 1.56/1.22 thf(f118,plain,(
% 1.56/1.22 spl12_2 | ~spl12_5 | ~spl12_6),
% 1.56/1.22 inference(avatar_contradiction_clause,[status(thm)],[f117])).
% 1.56/1.22 thf(f117,plain,(
% 1.56/1.22 $false | (spl12_2 | ~spl12_5 | ~spl12_6)),
% 1.56/1.22 inference(subsumption_resolution,[status(thm)],[f116,f54])).
% 1.56/1.22 thf(f54,plain,(
% 1.56/1.22 ($true = (sK6 @ sK9)) | ~spl12_5),
% 1.56/1.22 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.56/1.22 thf(f52,definition,(
% 1.56/1.22 spl12_5 <=> ($true = (sK6 @ sK9))),
% 1.56/1.22 introduced(definition,[new_symbols(naming,[spl12_5])],[avatar_definition])).
% 1.56/1.22 thf(f116,plain,(
% 1.56/1.22 ($true != (sK6 @ sK9)) | (spl12_2 | ~spl12_5 | ~spl12_6)),
% 1.56/1.22 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.56/1.22 thf(f115,plain,(
% 1.56/1.22 ($true != (sK6 @ sK9)) | ($true != $true) | (spl12_2 | ~spl12_5 | ~spl12_6)),
% 1.56/1.22 inference(superposition,[status(thm)],[f97,f58])).
% 1.56/1.22 thf(f58,plain,(
% 1.56/1.22 ( ! [X12 : a] : (((sK5 @ X12 @ sK8 @ sK7) = $true) | ((sK6 @ X12) != $true)) ) | ~spl12_6),
% 1.56/1.22 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.56/1.22 thf(f57,definition,(
% 1.56/1.22 spl12_6 <=> ! [X12 : a] : (((sK5 @ X12 @ sK8 @ sK7) = $true) | ((sK6 @ X12) != $true))),
% 1.56/1.22 introduced(definition,[new_symbols(naming,[spl12_6])],[avatar_definition])).
% 1.56/1.22 thf(f97,plain,(
% 1.56/1.22 ((sK5 @ sK9 @ sK8 @ sK7) != $true) | (spl12_2 | ~spl12_5)),
% 1.56/1.22 inference(subsumption_resolution,[status(thm)],[f94,f54])).
% 1.56/1.22 thf(f94,plain,(
% 1.56/1.22 ($true != (sK6 @ sK9)) | ((sK5 @ sK9 @ sK8 @ sK7) != $true) | spl12_2),
% 1.56/1.22 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.56/1.22 thf(f93,plain,(
% 1.56/1.22 ((sK5 @ sK9 @ sK8 @ sK7) != $true) | ($true != $true) | ($true != (sK6 @ sK9)) | spl12_2),
% 1.56/1.22 inference(superposition,[status(thm)],[f41,f31])).
% 1.56/1.22 thf(f31,plain,(
% 1.56/1.22 ( ! [X2 : a,X8 : a > b,X7 : a > b] : (($true = (sK5 @ X2 @ X7 @ X8)) | ($true != (sK5 @ X2 @ X8 @ X7)) | ((sK6 @ X2) != $true)) )),
% 1.56/1.22 inference(cnf_transformation,[status(thm)],[f20])).
% 1.56/1.22 thf(f20,plain,(
% 1.56/1.22 ! [X2 : a] : (((sK6 @ X2) != $true) | (! [X3 : a > b] : ($true = (sK5 @ X2 @ X3 @ X3)) & ! [X4 : a > b,X5 : a > b,X6 : a > b] : (((sK5 @ X2 @ X5 @ X4) != $true) | ((sK5 @ X2 @ X4 @ X6) != $true) | ($true = (sK5 @ X2 @ X5 @ X6))) & ! [X7 : a > b,X8 : a > b] : (($true = (sK5 @ X2 @ X7 @ X8)) | ($true != (sK5 @ X2 @ X8 @ X7))))) & (((($true != (sK5 @ sK9 @ sK7 @ sK8)) & ($true = (sK6 @ sK9))) & ! [X12 : a] : (((sK5 @ X12 @ sK8 @ sK7) = $true) | ((sK6 @ X12) != $true))) | (((sK5 @ sK11 @ sK10 @ sK10) != $true) & ($true = (sK6 @ sK11))) | ((sP0 @ sK6 @ sK5) = $true))),
% 1.56/1.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f15,f19,f18,f17,f16])).
% 1.56/1.22 thf(f16,plain,(
% 1.56/1.22 ? [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : (! [X2 : a] : (($true != (X1 @ X2)) | (! [X3 : a > b] : ((X0 @ X2 @ X3 @ X3) = $true) & ! [X4 : a > b,X5 : a > b,X6 : a > b] : (($true != (X0 @ X2 @ X5 @ X4)) | ((X0 @ X2 @ X4 @ X6) != $true) | ((X0 @ X2 @ X5 @ X6) = $true)) & ! [X7 : a > b,X8 : a > b] : (($true = (X0 @ X2 @ X7 @ X8)) | ((X0 @ X2 @ X8 @ X7) != $true)))) & (? [X9 : a > b,X10 : a > b] : (? [X11 : a] : (((X0 @ X11 @ X9 @ X10) != $true) & ($true = (X1 @ X11))) & ! [X12 : a] : (($true = (X0 @ X12 @ X10 @ X9)) | ($true != (X1 @ X12)))) | ? [X13 : a > b,X14 : a] : (((X0 @ X14 @ X13 @ X13) != $true) & ((X1 @ X14) = $true)) | ((sP0 @ X1 @ X0) = $true))) => (! [X2 : a] : (((sK6 @ X2) != $true) | (! [X3 : a > b] : ($true = (sK5 @ X2 @ X3 @ X3)) & ! [X6 : a > b,X5 : a > b,X4 : a > b] : (((sK5 @ X2 @ X5 @ X4) != $true) | ((sK5 @ X2 @ X4 @ X6) != $true) | ($true = (sK5 @ X2 @ X5 @ X6))) & ! [X8 : a > b,X7 : a > b] : (($true = (sK5 @ X2 @ X7 @ X8)) | ($true != (sK5 @ X2 @ X8 @ X7))))) & (? [X10 : a > b,X9 : a > b] : (? [X11 : a] : (($true != (sK5 @ X11 @ X9 @ X10)) & ((sK6 @ X11) = $true)) & ! [X12 : a] : (((sK5 @ X12 @ X10 @ X9) = $true) | ((sK6 @ X12) != $true))) | ? [X14 : a,X13 : a > b] : (((sK5 @ X14 @ X13 @ X13) != $true) & ((sK6 @ X14) = $true)) | ((sP0 @ sK6 @ sK5) = $true)))),
% 1.56/1.22 introduced(definition,[],[choice_axiom])).
% 1.56/1.22 thf(f17,plain,(
% 1.56/1.22 ? [X10 : a > b,X9 : a > b] : (? [X11 : a] : (($true != (sK5 @ X11 @ X9 @ X10)) & ((sK6 @ X11) = $true)) & ! [X12 : a] : (((sK5 @ X12 @ X10 @ X9) = $true) | ((sK6 @ X12) != $true))) => (? [X11 : a] : (($true != (sK5 @ X11 @ sK7 @ sK8)) & ((sK6 @ X11) = $true)) & ! [X12 : a] : (((sK5 @ X12 @ sK8 @ sK7) = $true) | ((sK6 @ X12) != $true)))),
% 1.56/1.22 introduced(definition,[],[choice_axiom])).
% 1.56/1.22 thf(f18,plain,(
% 1.56/1.22 ? [X11 : a] : (($true != (sK5 @ X11 @ sK7 @ sK8)) & ((sK6 @ X11) = $true)) => (($true != (sK5 @ sK9 @ sK7 @ sK8)) & ($true = (sK6 @ sK9)))),
% 1.56/1.22 introduced(definition,[],[choice_axiom])).
% 1.56/1.22 thf(f19,plain,(
% 1.56/1.22 ? [X14 : a,X13 : a > b] : (((sK5 @ X14 @ X13 @ X13) != $true) & ((sK6 @ X14) = $true)) => (((sK5 @ sK11 @ sK10 @ sK10) != $true) & ($true = (sK6 @ sK11)))),
% 1.56/1.22 introduced(definition,[],[choice_axiom])).
% 1.56/1.22 thf(f15,plain,(
% 1.56/1.22 ? [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : (! [X2 : a] : (($true != (X1 @ X2)) | (! [X3 : a > b] : ((X0 @ X2 @ X3 @ X3) = $true) & ! [X4 : a > b,X5 : a > b,X6 : a > b] : (($true != (X0 @ X2 @ X5 @ X4)) | ((X0 @ X2 @ X4 @ X6) != $true) | ((X0 @ X2 @ X5 @ X6) = $true)) & ! [X7 : a > b,X8 : a > b] : (($true = (X0 @ X2 @ X7 @ X8)) | ((X0 @ X2 @ X8 @ X7) != $true)))) & (? [X9 : a > b,X10 : a > b] : (? [X11 : a] : (((X0 @ X11 @ X9 @ X10) != $true) & ($true = (X1 @ X11))) & ! [X12 : a] : (($true = (X0 @ X12 @ X10 @ X9)) | ($true != (X1 @ X12)))) | ? [X13 : a > b,X14 : a] : (((X0 @ X14 @ X13 @ X13) != $true) & ((X1 @ X14) = $true)) | ((sP0 @ X1 @ X0) = $true)))),
% 1.56/1.22 inference(rectify,[status(thm)],[f9])).
% 1.56/1.22 thf(f9,plain,(
% 1.56/1.22 ? [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : (! [X2 : a] : (($true != (X1 @ X2)) | (! [X3 : a > b] : ((X0 @ X2 @ X3 @ X3) = $true) & ! [X6 : a > b,X8 : a > b,X7 : a > b] : (((X0 @ X2 @ X8 @ X6) != $true) | ($true != (X0 @ X2 @ X6 @ X7)) | ((X0 @ X2 @ X8 @ X7) = $true)) & ! [X4 : a > b,X5 : a > b] : (($true = (X0 @ X2 @ X4 @ X5)) | ($true != (X0 @ X2 @ X5 @ X4))))) & (? [X11 : a > b,X12 : a > b] : (? [X14 : a] : (((X0 @ X14 @ X11 @ X12) != $true) & ((X1 @ X14) = $true)) & ! [X13 : a] : (($true = (X0 @ X13 @ X12 @ X11)) | ((X1 @ X13) != $true))) | ? [X10 : a > b,X9 : a] : (($true != (X0 @ X9 @ X10 @ X10)) & ($true = (X1 @ X9))) | ((sP0 @ X1 @ X0) = $true)))),
% 1.56/1.22 inference(definition_folding,[status(thm)],[f7,f8])).
% 1.56/1.22 thf(f8,plain,(
% 1.56/1.22 ! [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : (? [X17 : a > b,X15 : a > b,X16 : a > b] : (! [X19 : a] : (((X0 @ X19 @ X15 @ X16) = $true) | ($true != (X1 @ X19))) & ! [X18 : a] : (((X0 @ X18 @ X16 @ X17) = $true) | ($true != (X1 @ X18))) & ? [X20 : a] : (((X0 @ X20 @ X15 @ X17) != $true) & ($true = (X1 @ X20)))) | ~((sP0 @ X1 @ X0) = $true))),
% 1.56/1.22 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.56/1.22 thf(f7,plain,(
% 1.56/1.22 ? [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : (! [X2 : a] : (($true != (X1 @ X2)) | (! [X3 : a > b] : ((X0 @ X2 @ X3 @ X3) = $true) & ! [X6 : a > b,X8 : a > b,X7 : a > b] : (((X0 @ X2 @ X8 @ X6) != $true) | ($true != (X0 @ X2 @ X6 @ X7)) | ((X0 @ X2 @ X8 @ X7) = $true)) & ! [X4 : a > b,X5 : a > b] : (($true = (X0 @ X2 @ X4 @ X5)) | ($true != (X0 @ X2 @ X5 @ X4))))) & (? [X11 : a > b,X12 : a > b] : (? [X14 : a] : (((X0 @ X14 @ X11 @ X12) != $true) & ((X1 @ X14) = $true)) & ! [X13 : a] : (($true = (X0 @ X13 @ X12 @ X11)) | ((X1 @ X13) != $true))) | ? [X10 : a > b,X9 : a] : (($true != (X0 @ X9 @ X10 @ X10)) & ($true = (X1 @ X9))) | ? [X17 : a > b,X15 : a > b,X16 : a > b] : (! [X19 : a] : (((X0 @ X19 @ X15 @ X16) = $true) | ($true != (X1 @ X19))) & ! [X18 : a] : (((X0 @ X18 @ X16 @ X17) = $true) | ($true != (X1 @ X18))) & ? [X20 : a] : (((X0 @ X20 @ X15 @ X17) != $true) & ($true = (X1 @ X20))))))),
% 1.56/1.22 inference(flattening,[status(thm)],[f6])).
% 1.56/1.22 thf(f6,plain,(
% 1.56/1.22 ? [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : ((? [X10 : a > b,X9 : a] : (($true != (X0 @ X9 @ X10 @ X10)) & ($true = (X1 @ X9))) | ? [X11 : a > b,X12 : a > b] : (? [X14 : a] : (((X0 @ X14 @ X11 @ X12) != $true) & ((X1 @ X14) = $true)) & ! [X13 : a] : (($true = (X0 @ X13 @ X12 @ X11)) | ((X1 @ X13) != $true))) | ? [X16 : a > b,X17 : a > b,X15 : a > b] : (? [X20 : a] : (((X0 @ X20 @ X15 @ X17) != $true) & ($true = (X1 @ X20))) & (! [X19 : a] : (((X0 @ X19 @ X15 @ X16) = $true) | ($true != (X1 @ X19))) & ! [X18 : a] : (((X0 @ X18 @ X16 @ X17) = $true) | ($true != (X1 @ X18)))))) & ! [X2 : a] : ((! [X7 : a > b,X6 : a > b,X8 : a > b] : (((X0 @ X2 @ X8 @ X7) = $true) | (($true != (X0 @ X2 @ X6 @ X7)) | ((X0 @ X2 @ X8 @ X6) != $true))) & ! [X4 : a > b,X5 : a > b] : (($true = (X0 @ X2 @ X4 @ X5)) | ($true != (X0 @ X2 @ X5 @ X4))) & ! [X3 : a > b] : ((X0 @ X2 @ X3 @ X3) = $true)) | ($true != (X1 @ X2))))),
% 1.56/1.22 inference(ennf_transformation,[status(thm)],[f5])).
% 1.56/1.22 thf(f5,plain,(
% 1.56/1.22 ~! [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : (! [X2 : a] : (($true = (X1 @ X2)) => (! [X7 : a > b,X6 : a > b,X8 : a > b] : ((($true = (X0 @ X2 @ X6 @ X7)) & ((X0 @ X2 @ X8 @ X6) = $true)) => ((X0 @ X2 @ X8 @ X7) = $true)) & ! [X4 : a > b,X5 : a > b] : (($true = (X0 @ X2 @ X5 @ X4)) => ($true = (X0 @ X2 @ X4 @ X5))) & ! [X3 : a > b] : ((X0 @ X2 @ X3 @ X3) = $true))) => (! [X10 : a > b,X9 : a] : (($true = (X1 @ X9)) => ($true = (X0 @ X9 @ X10 @ X10))) & ! [X11 : a > b,X12 : a > b] : (! [X13 : a] : (((X1 @ X13) = $true) => ($true = (X0 @ X13 @ X12 @ X11))) => ! [X14 : a] : (((X1 @ X14) = $true) => ((X0 @ X14 @ X11 @ X12) = $true))) & ! [X16 : a > b,X17 : a > b,X15 : a > b] : ((! [X19 : a] : (($true = (X1 @ X19)) => ((X0 @ X19 @ X15 @ X16) = $true)) & ! [X18 : a] : (($true = (X1 @ X18)) => ((X0 @ X18 @ X16 @ X17) = $true))) => ! [X20 : a] : (($true = (X1 @ X20)) => ((X0 @ X20 @ X15 @ X17) = $true)))))),
% 1.56/1.22 inference(fool_elimination,[status(thm)],[f4])).
% 1.56/1.22 thf(f4,plain,(
% 1.56/1.22 ~! [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : (! [X2 : a] : ((X1 @ X2) => (! [X3 : a > b] : (X0 @ X2 @ X3 @ X3) & ! [X4 : a > b,X5 : a > b] : ((X0 @ X2 @ X5 @ X4) => (X0 @ X2 @ X4 @ X5)) & ! [X6 : a > b,X7 : a > b,X8 : a > b] : (((X0 @ X2 @ X8 @ X6) & (X0 @ X2 @ X6 @ X7)) => (X0 @ X2 @ X8 @ X7)))) => (! [X9 : a,X10 : a > b] : ((X1 @ X9) => (X0 @ X9 @ X10 @ X10)) & ! [X11 : a > b,X12 : a > b] : (! [X13 : a] : ((X1 @ X13) => (X0 @ X13 @ X12 @ X11)) => ! [X14 : a] : ((X1 @ X14) => (X0 @ X14 @ X11 @ X12))) & ! [X15 : a > b,X16 : a > b,X17 : a > b] : ((! [X18 : a] : ((X1 @ X18) => (X0 @ X18 @ X16 @ X17)) & ! [X19 : a] : ((X1 @ X19) => (X0 @ X19 @ X15 @ X16))) => ! [X20 : a] : ((X1 @ X20) => (X0 @ X20 @ X15 @ X17)))))),
% 1.56/1.22 inference(rectify,[status(thm)],[f2])).
% 1.56/1.22 thf(f2,negated_conjecture,(
% 1.56/1.22 ~! [X1 : a > (a > b) > (a > b) > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (! [X3 : a > b] : (X1 @ X2 @ X3 @ X3) & ! [X4 : a > b,X3 : a > b] : ((X1 @ X2 @ X3 @ X4) => (X1 @ X2 @ X4 @ X3)) & ! [X4 : a > b,X5 : a > b,X3 : a > b] : (((X1 @ X2 @ X3 @ X4) & (X1 @ X2 @ X4 @ X5)) => (X1 @ X2 @ X3 @ X5)))) => (! [X3 : a,X2 : a > b] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X2)) & ! [X4 : a > b,X2 : a > b] : (! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X4)) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X4 @ X2))) & ! [X2 : a > b,X4 : a > b,X5 : a > b] : ((! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X4 @ X5)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X4))) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X5)))))),
% 1.56/1.22 inference(negated_conjecture,[status(cth)],[f1])).
% 1.56/1.22 thf(f1,conjecture,(
% 1.56/1.22 ! [X1 : a > (a > b) > (a > b) > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (! [X3 : a > b] : (X1 @ X2 @ X3 @ X3) & ! [X4 : a > b,X3 : a > b] : ((X1 @ X2 @ X3 @ X4) => (X1 @ X2 @ X4 @ X3)) & ! [X4 : a > b,X5 : a > b,X3 : a > b] : (((X1 @ X2 @ X3 @ X4) & (X1 @ X2 @ X4 @ X5)) => (X1 @ X2 @ X3 @ X5)))) => (! [X3 : a,X2 : a > b] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X2)) & ! [X4 : a > b,X2 : a > b] : (! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X4)) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X4 @ X2))) & ! [X2 : a > b,X4 : a > b,X5 : a > b] : ((! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X4 @ X5)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X4))) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X5)))))),
% 1.56/1.22 file('/export/starexec/sandbox/tmp/tmp.UmcC3yIcGA/DTF2THF_5061.p',cTHM512_pme)).
% 1.56/1.22 thf(f41,plain,(
% 1.56/1.22 ($true != (sK5 @ sK9 @ sK7 @ sK8)) | spl12_2),
% 1.56/1.22 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.56/1.22 thf(f39,definition,(
% 1.56/1.22 spl12_2 <=> ($true = (sK5 @ sK9 @ sK7 @ sK8))),
% 1.56/1.22 introduced(definition,[new_symbols(naming,[spl12_2])],[avatar_definition])).
% 1.56/1.22 thf(f104,plain,(
% 1.56/1.22 ~spl12_1 | spl12_4),
% 1.56/1.22 inference(avatar_split_clause,[status(thm)],[f102,f48,f35])).
% 1.56/1.22 thf(f35,definition,(
% 1.56/1.22 spl12_1 <=> ($true = (sK6 @ sK11))),
% 1.56/1.22 introduced(definition,[new_symbols(naming,[spl12_1])],[avatar_definition])).
% 1.56/1.22 thf(f48,definition,(
% 1.56/1.22 spl12_4 <=> ((sK5 @ sK11 @ sK10 @ sK10) = $true)),
% 1.56/1.22 introduced(definition,[new_symbols(naming,[spl12_4])],[avatar_definition])).
% 1.56/1.22 thf(f102,plain,(
% 1.56/1.22 ($true != (sK6 @ sK11)) | spl12_4),
% 1.56/1.22 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.56/1.22 thf(f98,plain,(
% 1.56/1.22 ($true != (sK6 @ sK11)) | ($true != $true) | spl12_4),
% 1.56/1.22 inference(superposition,[status(thm)],[f50,f33])).
% 1.56/1.22 thf(f33,plain,(
% 1.56/1.22 ( ! [X2 : a,X3 : a > b] : (($true = (sK5 @ X2 @ X3 @ X3)) | ((sK6 @ X2) != $true)) )),
% 1.56/1.22 inference(cnf_transformation,[status(thm)],[f20])).
% 1.56/1.22 thf(f50,plain,(
% 1.56/1.22 ((sK5 @ sK11 @ sK10 @ sK10) != $true) | spl12_4),
% 1.56/1.22 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.56/1.22 thf(f91,plain,(
% 1.56/1.22 ~spl12_3),
% 1.56/1.22 inference(avatar_contradiction_clause,[status(thm)],[f90])).
% 1.56/1.22 thf(f90,plain,(
% 1.56/1.22 $false | ~spl12_3),
% 1.56/1.22 inference(subsumption_resolution,[status(thm)],[f89,f45])).
% 1.56/1.22 thf(f45,plain,(
% 1.56/1.22 ((sP0 @ sK6 @ sK5) = $true) | ~spl12_3),
% 1.56/1.22 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.56/1.22 thf(f43,definition,(
% 1.56/1.22 spl12_3 <=> ((sP0 @ sK6 @ sK5) = $true)),
% 1.56/1.22 introduced(definition,[new_symbols(naming,[spl12_3])],[avatar_definition])).
% 1.56/1.22 thf(f89,plain,(
% 1.56/1.22 ((sP0 @ sK6 @ sK5) != $true)),
% 1.56/1.22 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.56/1.22 thf(f88,plain,(
% 1.56/1.22 ((sP0 @ sK6 @ sK5) != $true) | ($true != $true)),
% 1.56/1.22 inference(duplicate_literal_removal,[status(thm)],[f87])).
% 1.56/1.22 thf(f87,plain,(
% 1.56/1.22 ((sP0 @ sK6 @ sK5) != $true) | ((sP0 @ sK6 @ sK5) != $true) | ($true != $true)),
% 1.56/1.22 inference(superposition,[status(thm)],[f86,f21])).
% 1.56/1.22 thf(f21,plain,(
% 1.56/1.22 ( ! [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : (($true = (X1 @ (sK4 @ X1 @ X0))) | ((sP0 @ X1 @ X0) != $true)) )),
% 1.56/1.22 inference(cnf_transformation,[status(thm)],[f14])).
% 1.56/1.22 thf(f14,plain,(
% 1.56/1.22 ! [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : ((! [X5 : a] : (($true = (X0 @ X5 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) | ($true != (X1 @ X5))) & ! [X6 : a] : (((X0 @ X6 @ (sK3 @ X1 @ X0) @ (sK1 @ X1 @ X0)) = $true) | ($true != (X1 @ X6))) & (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0))) & ($true = (X1 @ (sK4 @ X1 @ X0))))) | ((sP0 @ X1 @ X0) != $true))),
% 1.56/1.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f11,f13,f12])).
% 1.56/1.22 thf(f12,plain,(
% 1.56/1.22 ! [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : (? [X2 : a > b,X3 : a > b,X4 : a > b] : (! [X5 : a] : (($true = (X0 @ X5 @ X3 @ X4)) | ($true != (X1 @ X5))) & ! [X6 : a] : (((X0 @ X6 @ X4 @ X2) = $true) | ($true != (X1 @ X6))) & ? [X7 : a] : (((X0 @ X7 @ X3 @ X2) != $true) & ($true = (X1 @ X7)))) => (! [X5 : a] : (($true = (X0 @ X5 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) | ($true != (X1 @ X5))) & ! [X6 : a] : (((X0 @ X6 @ (sK3 @ X1 @ X0) @ (sK1 @ X1 @ X0)) = $true) | ($true != (X1 @ X6))) & ? [X7 : a] : (($true != (X0 @ X7 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0))) & ($true = (X1 @ X7)))))),
% 1.56/1.22 introduced(definition,[],[choice_axiom])).
% 1.56/1.22 thf(f13,plain,(
% 1.56/1.22 ! [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : (? [X7 : a] : (($true != (X0 @ X7 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0))) & ($true = (X1 @ X7))) => (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0))) & ($true = (X1 @ (sK4 @ X1 @ X0)))))),
% 1.56/1.22 introduced(definition,[],[choice_axiom])).
% 1.56/1.22 thf(f11,plain,(
% 1.56/1.22 ! [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : (? [X2 : a > b,X3 : a > b,X4 : a > b] : (! [X5 : a] : (($true = (X0 @ X5 @ X3 @ X4)) | ($true != (X1 @ X5))) & ! [X6 : a] : (((X0 @ X6 @ X4 @ X2) = $true) | ($true != (X1 @ X6))) & ? [X7 : a] : (((X0 @ X7 @ X3 @ X2) != $true) & ($true = (X1 @ X7)))) | ((sP0 @ X1 @ X0) != $true))),
% 1.56/1.22 inference(rectify,[status(thm)],[f10])).
% 1.56/1.22 thf(f10,plain,(
% 1.56/1.22 ! [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : (? [X17 : a > b,X15 : a > b,X16 : a > b] : (! [X19 : a] : (((X0 @ X19 @ X15 @ X16) = $true) | ($true != (X1 @ X19))) & ! [X18 : a] : (((X0 @ X18 @ X16 @ X17) = $true) | ($true != (X1 @ X18))) & ? [X20 : a] : (((X0 @ X20 @ X15 @ X17) != $true) & ($true = (X1 @ X20)))) | ((sP0 @ X1 @ X0) != $true))),
% 1.56/1.22 inference(nnf_transformation,[status(thm)],[f8])).
% 1.56/1.22 thf(f86,plain,(
% 1.56/1.22 ( ! [X0 : a > $o] : (((sK6 @ (sK4 @ X0 @ sK5)) != $true) | ((sP0 @ X0 @ sK5) != $true)) )),
% 1.56/1.22 inference(subsumption_resolution,[status(thm)],[f85,f21])).
% 1.56/1.22 thf(f85,plain,(
% 1.56/1.22 ( ! [X0 : a > $o] : (((sP0 @ X0 @ sK5) != $true) | ((sK6 @ (sK4 @ X0 @ sK5)) != $true) | ($true != (X0 @ (sK4 @ X0 @ sK5)))) )),
% 1.56/1.22 inference(subsumption_resolution,[status(thm)],[f78,f24])).
% 1.56/1.22 thf(f24,plain,(
% 1.56/1.22 ( ! [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o,X5 : a] : (($true = (X0 @ X5 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) | ((sP0 @ X1 @ X0) != $true) | ($true != (X1 @ X5))) )),
% 1.56/1.22 inference(cnf_transformation,[status(thm)],[f14])).
% 1.56/1.22 thf(f78,plain,(
% 1.56/1.22 ( ! [X0 : a > $o] : (($true != (sK5 @ (sK4 @ X0 @ sK5) @ (sK2 @ X0 @ sK5) @ (sK3 @ X0 @ sK5))) | ((sP0 @ X0 @ sK5) != $true) | ((sK6 @ (sK4 @ X0 @ sK5)) != $true) | ($true != (X0 @ (sK4 @ X0 @ sK5)))) )),
% 1.56/1.22 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.56/1.22 thf(f77,plain,(
% 1.56/1.22 ( ! [X0 : a > $o] : (((sK6 @ (sK4 @ X0 @ sK5)) != $true) | ($true != $true) | ($true != (X0 @ (sK4 @ X0 @ sK5))) | ((sP0 @ X0 @ sK5) != $true) | ($true != (sK5 @ (sK4 @ X0 @ sK5) @ (sK2 @ X0 @ sK5) @ (sK3 @ X0 @ sK5)))) )),
% 1.56/1.22 inference(duplicate_literal_removal,[status(thm)],[f76])).
% 1.56/1.22 thf(f76,plain,(
% 1.56/1.22 ( ! [X0 : a > $o] : (($true != (sK5 @ (sK4 @ X0 @ sK5) @ (sK2 @ X0 @ sK5) @ (sK3 @ X0 @ sK5))) | ($true != (X0 @ (sK4 @ X0 @ sK5))) | ($true != $true) | ((sP0 @ X0 @ sK5) != $true) | ((sP0 @ X0 @ sK5) != $true) | ((sK6 @ (sK4 @ X0 @ sK5)) != $true)) )),
% 1.56/1.22 inference(superposition,[status(thm)],[f66,f23])).
% 1.56/1.22 thf(f23,plain,(
% 1.56/1.22 ( ! [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o,X6 : a] : (((X0 @ X6 @ (sK3 @ X1 @ X0) @ (sK1 @ X1 @ X0)) = $true) | ((sP0 @ X1 @ X0) != $true) | ($true != (X1 @ X6))) )),
% 1.56/1.22 inference(cnf_transformation,[status(thm)],[f14])).
% 1.56/1.22 thf(f66,plain,(
% 1.56/1.22 ( ! [X0 : a > $o,X1 : a > b] : (($true != (sK5 @ (sK4 @ X0 @ sK5) @ X1 @ (sK1 @ X0 @ sK5))) | ((sP0 @ X0 @ sK5) != $true) | ((sK6 @ (sK4 @ X0 @ sK5)) != $true) | ((sK5 @ (sK4 @ X0 @ sK5) @ (sK2 @ X0 @ sK5) @ X1) != $true)) )),
% 1.56/1.22 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.56/1.22 thf(f65,plain,(
% 1.56/1.22 ( ! [X0 : a > $o,X1 : a > b] : (((sK5 @ (sK4 @ X0 @ sK5) @ (sK2 @ X0 @ sK5) @ X1) != $true) | ((sP0 @ X0 @ sK5) != $true) | ($true != (sK5 @ (sK4 @ X0 @ sK5) @ X1 @ (sK1 @ X0 @ sK5))) | ($true != $true) | ((sK6 @ (sK4 @ X0 @ sK5)) != $true)) )),
% 1.56/1.22 inference(superposition,[status(thm)],[f22,f32])).
% 1.56/1.22 thf(f32,plain,(
% 1.56/1.22 ( ! [X2 : a,X6 : a > b,X4 : a > b,X5 : a > b] : (($true = (sK5 @ X2 @ X5 @ X6)) | ((sK6 @ X2) != $true) | ((sK5 @ X2 @ X5 @ X4) != $true) | ((sK5 @ X2 @ X4 @ X6) != $true)) )),
% 1.56/1.22 inference(cnf_transformation,[status(thm)],[f20])).
% 1.56/1.22 thf(f22,plain,(
% 1.56/1.22 ( ! [X0 : a > (a > b) > (a > b) > $o,X1 : a > $o] : (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0))) | ((sP0 @ X1 @ X0) != $true)) )),
% 1.56/1.22 inference(cnf_transformation,[status(thm)],[f14])).
% 1.56/1.22 thf(f62,plain,(
% 1.56/1.22 spl12_1 | spl12_3 | spl12_5),
% 1.56/1.22 inference(avatar_split_clause,[status(thm)],[f27,f52,f43,f35])).
% 1.56/1.22 thf(f27,plain,(
% 1.56/1.22 ($true = (sK6 @ sK9)) | ($true = (sK6 @ sK11)) | ((sP0 @ sK6 @ sK5) = $true)),
% 1.56/1.22 inference(cnf_transformation,[status(thm)],[f20])).
% 1.56/1.22 thf(f61,plain,(
% 1.56/1.22 spl12_3 | ~spl12_2 | ~spl12_4),
% 1.56/1.22 inference(avatar_split_clause,[status(thm)],[f30,f48,f39,f43])).
% 1.56/1.22 thf(f30,plain,(
% 1.56/1.22 ((sP0 @ sK6 @ sK5) = $true) | ($true != (sK5 @ sK9 @ sK7 @ sK8)) | ((sK5 @ sK11 @ sK10 @ sK10) != $true)),
% 1.56/1.22 inference(cnf_transformation,[status(thm)],[f20])).
% 1.56/1.22 thf(f60,plain,(
% 1.56/1.22 spl12_6 | spl12_1 | spl12_3),
% 1.56/1.22 inference(avatar_split_clause,[status(thm)],[f25,f43,f35,f57])).
% 1.56/1.22 thf(f25,plain,(
% 1.56/1.22 ( ! [X12 : a] : (($true = (sK6 @ sK11)) | ((sK6 @ X12) != $true) | ((sP0 @ sK6 @ sK5) = $true) | ((sK5 @ X12 @ sK8 @ sK7) = $true)) )),
% 1.56/1.22 inference(cnf_transformation,[status(thm)],[f20])).
% 1.56/1.22 thf(f59,plain,(
% 1.56/1.22 ~spl12_4 | spl12_3 | spl12_6),
% 1.56/1.22 inference(avatar_split_clause,[status(thm)],[f26,f57,f43,f48])).
% 1.56/1.22 thf(f26,plain,(
% 1.56/1.22 ( ! [X12 : a] : (((sK5 @ X12 @ sK8 @ sK7) = $true) | ((sK5 @ sK11 @ sK10 @ sK10) != $true) | ((sK6 @ X12) != $true) | ((sP0 @ sK6 @ sK5) = $true)) )),
% 1.56/1.22 inference(cnf_transformation,[status(thm)],[f20])).
% 1.56/1.22 thf(f55,plain,(
% 1.56/1.22 ~spl12_4 | spl12_3 | spl12_5),
% 1.56/1.22 inference(avatar_split_clause,[status(thm)],[f28,f52,f43,f48])).
% 1.56/1.22 thf(f28,plain,(
% 1.56/1.22 ((sK5 @ sK11 @ sK10 @ sK10) != $true) | ((sP0 @ sK6 @ sK5) = $true) | ($true = (sK6 @ sK9))),
% 1.56/1.22 inference(cnf_transformation,[status(thm)],[f20])).
% 1.56/1.22 thf(f46,plain,(
% 1.56/1.22 spl12_1 | ~spl12_2 | spl12_3),
% 1.56/1.22 inference(avatar_split_clause,[status(thm)],[f29,f43,f39,f35])).
% 1.56/1.22 thf(f29,plain,(
% 1.56/1.22 ($true = (sK6 @ sK11)) | ((sP0 @ sK6 @ sK5) = $true) | ($true != (sK5 @ sK9 @ sK7 @ sK8))),
% 1.56/1.22 inference(cnf_transformation,[status(thm)],[f20])).
% 1.56/1.22 % SZS output end Proof for DTF2THF_5061
% 1.56/1.22 % (5345)------------------------------
% 1.56/1.22 % (5345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.22 % (5345)Termination reason: Refutation
% 1.56/1.22
% 1.56/1.22 % (5345)Memory used [KB]: 5628
% 1.56/1.22 % (5345)Time elapsed: 0.010 s
% 1.56/1.22 % (5345)Instructions burned: 20 (million)
% 1.56/1.22 % (5345)------------------------------
% 1.56/1.22 % (5345)------------------------------
% 1.56/1.22 % (5339)Success in time 0.019 s
%------------------------------------------------------------------------------