%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU938^5 : 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 : n008.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 09:37:47 AM UTC 2026
% Result : Theorem 1.67s 1.39s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 360 ( 166 equ; 5 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 583 ( 78 ~; 64 |; 44 &; 357 @)
% ( 2 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 122 ( 122 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 213 ( 96 ^; 108 !; 9 ?; 213 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_2,type,
h: $i > $i ).
thf(func_def_8,type,
sK0: ( $i > $i ) > ( $i > $i ) > $i ).
thf(func_def_9,type,
sK1: ( $i > $i ) > ( $i > $i ) > ( $i > $i ) > $o ).
thf(func_def_10,type,
sK2: ( ( $i > $i ) > $o ) > ( $i > $i ) > $i > $i ).
thf(func_def_13,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f311,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f205,f284,f310]) ).
thf(f310,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[status(thm)],[f309]) ).
thf(f309,plain,
( $false
| ~ spl3_4 ),
inference(subsumption_resolution,[status(thm)],[f297,f14]) ).
thf(f14,plain,
( a
= ( h @ a ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i > $i,X1: $i > $i] :
( ( X0 = X1 )
| ( ( X0 @ ( sK0 @ X1 @ X0 ) )
!= ( X1 @ ( sK0 @ X1 @ X0 ) ) ) )
& ! [X3: $i > $i,X4: $i > $i] :
( ( ( $true
= ( sK1 @ X4 @ X3 @ X3 ) )
& ! [X6: $i > $i] :
( ( $true
!= ( sK1 @ X4 @ X3 @ X6 ) )
| ( $true
= ( sK1 @ X4 @ X3
@ ^ [Y0: $i] : ( X3 @ ( X6 @ Y0 ) ) ) ) )
& ( $true
!= ( sK1 @ X4 @ X3
@ ^ [Y0: $i] : ( X4 @ ( X3 @ Y0 ) ) ) ) )
| ! [X7: ( $i > $i ) > $o] :
( ( $true
= ( X7 @ X4 ) )
| ( ( $true
= ( X7 @ ( sK2 @ X7 @ X3 ) ) )
& ( $true
!= ( X7
@ ^ [Y0: $i] : ( X3 @ ( sK2 @ X7 @ X3 @ Y0 ) ) ) ) )
| ( $true
!= ( X7 @ X3 ) ) ) )
& ( a
= ( h @ a ) )
& ( a
!= ( h @ b ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9]) ).
thf(f9,plain,
! [X0: $i > $i,X1: $i > $i] :
( ? [X2: $i] :
( ( X0 @ X2 )
!= ( X1 @ X2 ) )
=> ( ( X0 @ ( sK0 @ X1 @ X0 ) )
!= ( X1 @ ( sK0 @ X1 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X3: $i > $i,X4: $i > $i] :
( ? [X5: ( $i > $i ) > $o] :
( ( ( X5 @ X3 )
= $true )
& ! [X6: $i > $i] :
( ( ( X5 @ X6 )
!= $true )
| ( $true
= ( X5
@ ^ [Y0: $i] : ( X3 @ ( X6 @ Y0 ) ) ) ) )
& ( $true
!= ( X5
@ ^ [Y0: $i] : ( X4 @ ( X3 @ Y0 ) ) ) ) )
=> ( ( $true
= ( sK1 @ X4 @ X3 @ X3 ) )
& ! [X6: $i > $i] :
( ( $true
!= ( sK1 @ X4 @ X3 @ X6 ) )
| ( $true
= ( sK1 @ X4 @ X3
@ ^ [Y0: $i] : ( X3 @ ( X6 @ Y0 ) ) ) ) )
& ( $true
!= ( sK1 @ X4 @ X3
@ ^ [Y0: $i] : ( X4 @ ( X3 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X3: $i > $i,X7: ( $i > $i ) > $o] :
( ? [X8: $i > $i] :
( ( $true
= ( X7 @ X8 ) )
& ( $true
!= ( X7
@ ^ [Y0: $i] : ( X3 @ ( X8 @ Y0 ) ) ) ) )
=> ( ( $true
= ( X7 @ ( sK2 @ X7 @ X3 ) ) )
& ( $true
!= ( X7
@ ^ [Y0: $i] : ( X3 @ ( sK2 @ X7 @ X3 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i > $i,X1: $i > $i] :
( ( X0 = X1 )
| ? [X2: $i] :
( ( X0 @ X2 )
!= ( X1 @ X2 ) ) )
& ! [X3: $i > $i,X4: $i > $i] :
( ? [X5: ( $i > $i ) > $o] :
( ( ( X5 @ X3 )
= $true )
& ! [X6: $i > $i] :
( ( ( X5 @ X6 )
!= $true )
| ( $true
= ( X5
@ ^ [Y0: $i] : ( X3 @ ( X6 @ Y0 ) ) ) ) )
& ( $true
!= ( X5
@ ^ [Y0: $i] : ( X4 @ ( X3 @ Y0 ) ) ) ) )
| ! [X7: ( $i > $i ) > $o] :
( ( $true
= ( X7 @ X4 ) )
| ? [X8: $i > $i] :
( ( $true
= ( X7 @ X8 ) )
& ( $true
!= ( X7
@ ^ [Y0: $i] : ( X3 @ ( X8 @ Y0 ) ) ) ) )
| ( $true
!= ( X7 @ X3 ) ) ) )
& ( a
= ( h @ a ) )
& ( a
!= ( h @ b ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X3: $i > $i,X4: $i > $i] :
( ! [X7: ( $i > $i ) > $o] :
( ( $true
= ( X7 @ X4 ) )
| ( $true
!= ( X7 @ X3 ) )
| ? [X8: $i > $i] :
( ( $true
= ( X7 @ X8 ) )
& ( $true
!= ( X7
@ ^ [Y0: $i] : ( X3 @ ( X8 @ Y0 ) ) ) ) ) )
| ? [X5: ( $i > $i ) > $o] :
( ( $true
!= ( X5
@ ^ [Y0: $i] : ( X4 @ ( X3 @ Y0 ) ) ) )
& ( ( X5 @ X3 )
= $true )
& ! [X6: $i > $i] :
( ( ( X5 @ X6 )
!= $true )
| ( $true
= ( X5
@ ^ [Y0: $i] : ( X3 @ ( X6 @ Y0 ) ) ) ) ) ) )
& ( a
= ( h @ a ) )
& ( a
!= ( h @ b ) )
& ! [X0: $i > $i,X1: $i > $i] :
( ( X0 = X1 )
| ? [X2: $i] :
( ( X0 @ X2 )
!= ( X1 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ( a
= ( h @ a ) )
& ( a
!= ( h @ b ) )
& ! [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
= ( X1 @ X2 ) )
=> ( X0 = X1 ) ) )
=> ~ ! [X3: $i > $i,X4: $i > $i] :
( ! [X5: ( $i > $i ) > $o] :
( ( ( ( X5 @ X3 )
= $true )
& ! [X6: $i > $i] :
( ( ( X5 @ X6 )
= $true )
=> ( $true
= ( X5
@ ^ [Y0: $i] : ( X3 @ ( X6 @ Y0 ) ) ) ) ) )
=> ( $true
= ( X5
@ ^ [Y0: $i] : ( X4 @ ( X3 @ Y0 ) ) ) ) )
=> ! [X7: ( $i > $i ) > $o] :
( ( ( $true
= ( X7 @ X3 ) )
& ! [X8: $i > $i] :
( ( $true
= ( X7 @ X8 ) )
=> ( $true
= ( X7
@ ^ [Y0: $i] : ( X3 @ ( X8 @ Y0 ) ) ) ) ) )
=> ( $true
= ( X7 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( a
= ( h @ a ) )
& ( a
!= ( h @ b ) )
& ! [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
= ( X1 @ X2 ) )
=> ( X0 = X1 ) ) )
=> ~ ! [X3: $i > $i,X4: $i > $i] :
( ! [X5: ( $i > $i ) > $o] :
( ( ( ( X5 @ X3 )
= $true )
& ! [X6: $i > $i] :
( ( ( X5 @ X6 )
= $true )
=> ( $true
= ( X5
@ ^ [Y0: $i] : ( X3 @ ( X6 @ Y0 ) ) ) ) ) )
=> ( $true
= ( X5
@ ^ [Y0: $i] : ( X4 @ ( X3 @ Y0 ) ) ) ) )
=> ! [X9: ( $i > $i ) > $o] :
( ( ( $true
= ( X9 @ X3 ) )
& ! [X10: $i > $i] :
( ( $true
= ( X9 @ X10 ) )
=> ( $true
= ( X9
@ ^ [Y0: $i] : ( X3 @ ( X10 @ Y0 ) ) ) ) ) )
=> ( $true
= ( X9 @ X4 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( a
!= ( h @ b ) )
& ( a
= ( h @ a ) )
& ! [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
= ( X1 @ X2 ) )
=> ( X0 = X1 ) ) )
=> ~ ! [X3: $i > $i,X4: $i > $i] :
( ! [X5: ( $i > $i ) > $o] :
( ( ( X5 @ X3 )
& ! [X6: $i > $i] :
( ( X5 @ X6 )
=> ( X5
@ ^ [X7: $i] : ( X3 @ ( X6 @ X7 ) ) ) ) )
=> ( X5
@ ^ [X8: $i] : ( X4 @ ( X3 @ X8 ) ) ) )
=> ! [X9: ( $i > $i ) > $o] :
( ( ( X9 @ X3 )
& ! [X10: $i > $i] :
( ( X9 @ X10 )
=> ( X9
@ ^ [X11: $i] : ( X3 @ ( X10 @ X11 ) ) ) ) )
=> ( X9 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( a
!= ( h @ b ) )
& ( a
= ( h @ a ) )
& ! [X1: $i > $i,X0: $i > $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
= ( X1 @ X2 ) )
=> ( X0 = X1 ) ) )
=> ~ ! [X3: $i > $i,X4: $i > $i] :
( ! [X5: ( $i > $i ) > $o] :
( ( ( X5 @ X3 )
& ! [X6: $i > $i] :
( ( X5 @ X6 )
=> ( X5
@ ^ [X2: $i] : ( X3 @ ( X6 @ X2 ) ) ) ) )
=> ( X5
@ ^ [X2: $i] : ( X4 @ ( X3 @ X2 ) ) ) )
=> ! [X5: ( $i > $i ) > $o] :
( ( ( X5 @ X3 )
& ! [X7: $i > $i] :
( ( X5 @ X7 )
=> ( X5
@ ^ [X2: $i] : ( X3 @ ( X7 @ X2 ) ) ) ) )
=> ( X5 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( a
!= ( h @ b ) )
& ( a
= ( h @ a ) )
& ! [X1: $i > $i,X0: $i > $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
= ( X1 @ X2 ) )
=> ( X0 = X1 ) ) )
=> ~ ! [X3: $i > $i,X4: $i > $i] :
( ! [X5: ( $i > $i ) > $o] :
( ( ( X5 @ X3 )
& ! [X6: $i > $i] :
( ( X5 @ X6 )
=> ( X5
@ ^ [X2: $i] : ( X3 @ ( X6 @ X2 ) ) ) ) )
=> ( X5
@ ^ [X2: $i] : ( X4 @ ( X3 @ X2 ) ) ) )
=> ! [X5: ( $i > $i ) > $o] :
( ( ( X5 @ X3 )
& ! [X7: $i > $i] :
( ( X5 @ X7 )
=> ( X5
@ ^ [X2: $i] : ( X3 @ ( X7 @ X2 ) ) ) ) )
=> ( X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o7soIda66i/DTF2THF_27518.p',cTHM196_pme) ).
thf(f297,plain,
( ( a
!= ( h @ a ) )
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f13,f195]) ).
thf(f195,plain,
( ! [X0: $i] : ( a = X0 )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f194]) ).
thf(f194,definition,
( spl3_4
<=> ! [X0: $i] : ( a = X0 ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f13,plain,
( a
!= ( h @ b ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f284,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[status(thm)],[f283]) ).
thf(f283,plain,
( $false
| ~ spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f272,f14]) ).
thf(f272,plain,
( ( a
!= ( h @ a ) )
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f13,f245]) ).
thf(f245,plain,
( ! [X1: $i] :
( ( h @ a )
= X1 )
| ~ spl3_3 ),
inference(beta_eta_normalization,[status(thm)],[f232]) ).
thf(f232,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : Y0
@ X1 )
= ( ^ [Y0: $i] : ( h @ a )
@ X1 ) )
| ~ spl3_3 ),
inference(argument_congruence,[status(thm)],[f192]) ).
thf(f192,plain,
( ( ( ^ [Y0: $i] : ( h @ a ) )
= ( ^ [Y0: $i] : Y0 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f190]) ).
thf(f190,definition,
( spl3_3
<=> ( ( ^ [Y0: $i] : ( h @ a ) )
= ( ^ [Y0: $i] : Y0 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f205,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f173,f194,f190]) ).
thf(f173,plain,
! [X0: $i] :
( ( ( ^ [Y0: $i] : ( h @ a ) )
= ( ^ [Y0: $i] : Y0 ) )
| ( a = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f172]) ).
thf(f172,plain,
! [X0: $i] :
( ( ( ^ [Y0: $i] : ( h @ a ) )
!= ( ^ [Y0: $i] : ( h @ a ) ) )
| ( a = X0 )
| ( ( ^ [Y0: $i] : ( h @ a ) )
= ( ^ [Y0: $i] : Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f171]) ).
thf(f171,plain,
! [X0: $i] :
( ( ( ^ [Y0: $i] : ( h @ a ) )
= ( ^ [Y0: $i] : Y0 ) )
| ( a
= ( ^ [Y0: $i] : Y0
@ X0 ) )
| ( ( ^ [Y0: $i] : ( h @ a ) )
!= ( ^ [Y0: $i] :
( ^ [Y1: $i] : ( h @ a )
@ ( sK2
@ ( (=)
@ ^ [Y1: $i] : ( h @ a ) )
@ ^ [Y1: $i] : ( h @ a )
@ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f170]) ).
thf(f170,plain,
! [X0: $i] :
( ( ( ^ [Y0: $i] : ( h @ a ) )
!= ( ^ [Y0: $i] :
( ^ [Y1: $i] : ( h @ a )
@ ( sK2
@ ( (=)
@ ^ [Y1: $i] : ( h @ a ) )
@ ^ [Y1: $i] : ( h @ a )
@ Y0 ) ) ) )
| ( $true != $true )
| ( ( ^ [Y0: $i] : ( h @ a ) )
= ( ^ [Y0: $i] : Y0 ) )
| ( a
= ( ^ [Y0: $i] : Y0
@ X0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f165]) ).
thf(f165,plain,
! [X0: $i] :
( ( $true != $true )
| ( a
= ( ^ [Y0: $i] : Y0
@ X0 ) )
| ( ( ^ [Y0: $i] : ( h @ a ) )
= ( ^ [Y0: $i] : Y0 ) )
| ( ( ^ [Y0: $i] : ( h @ a ) )
= ( ^ [Y0: $i] : Y0 ) )
| ( ( ^ [Y0: $i] : ( h @ a ) )
!= ( ^ [Y0: $i] :
( ^ [Y1: $i] : ( h @ a )
@ ( sK2
@ ( (=)
@ ^ [Y1: $i] : ( h @ a ) )
@ ^ [Y1: $i] : ( h @ a )
@ Y0 ) ) ) ) ),
inference(superposition,[status(thm)],[f121,f160]) ).
thf(f160,plain,
! [X0: $i > $i,X1: $i] :
( ( $true
= ( sK1 @ X0
@ ^ [Y0: $i] : ( h @ a )
@ ^ [Y0: $i] : ( h @ a ) ) )
| ( ( ^ [Y0: $i] : ( h @ a ) )
= X0 )
| ( a
= ( X0 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f151]) ).
thf(f151,plain,
! [X0: $i > $i,X1: $i] :
( ( $true
= ( sK1 @ X0
@ ^ [Y0: $i] :
( h
@ ( ^ [Y1: $i] : a
@ Y0 ) )
@ ^ [Y0: $i] :
( h
@ ( ^ [Y1: $i] : a
@ Y0 ) ) ) )
| ( a
= ( X0 @ X1 ) )
| ( ( ^ [Y0: $i] :
( h
@ ( ^ [Y1: $i] : a
@ Y0 ) ) )
= X0 ) ),
inference(superposition,[status(thm)],[f14,f138]) ).
thf(f138,plain,
! [X2: $i,X0: $i > $i,X1: $i > $i] :
( ( ( X1 @ X2 )
= ( X0
@ ( sK2
@ ^ [Y0: $i > $i] : ( X1 != Y0 )
@ X0
@ X2 ) ) )
| ( $true
= ( sK1 @ X1 @ X0 @ X0 ) )
| ( X0 = X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f128]) ).
thf(f128,plain,
! [X2: $i,X0: $i > $i,X1: $i > $i] :
( ( ( X1 @ X2 )
= ( ^ [Y0: $i] :
( X0
@ ( sK2
@ ^ [Y1: $i > $i] : ( X1 != Y1 )
@ X0
@ Y0 ) )
@ X2 ) )
| ( $true
= ( sK1 @ X1 @ X0 @ X0 ) )
| ( X0 = X1 ) ),
inference(argument_congruence,[status(thm)],[f90]) ).
thf(f90,plain,
! [X0: $i > $i,X1: $i > $i] :
( ( ( ^ [Y0: $i] :
( X0
@ ( sK2
@ ^ [Y1: $i > $i] : ( X1 != Y1 )
@ X0
@ Y0 ) ) )
= X1 )
| ( X0 = X1 )
| ( $true
= ( sK1 @ X1 @ X0 @ X0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
! [X0: $i > $i,X1: $i > $i] :
( ( ( ^ [Y0: $i] :
( X0
@ ( sK2
@ ^ [Y1: $i > $i] : ( X1 != Y1 )
@ X0
@ Y0 ) ) )
= X1 )
| ( $true
= ( sK1 @ X1 @ X0 @ X0 ) )
| ( $true
= ( X1 = X0 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
! [X0: $i > $i,X1: $i > $i] :
( ( $true
= ( sK1 @ X1 @ X0 @ X0 ) )
| ( ( ^ [Y0: $i] :
( X0
@ ( sK2
@ ^ [Y1: $i > $i] : ( X1 != Y1 )
@ X0
@ Y0 ) ) )
= X1 )
| ( $true
!= ( X1 != X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X0: $i > $i,X1: $i > $i] :
( ( $true
!= ( ^ [Y0: $i > $i] : ( X1 != Y0 )
@ X0 ) )
| ( $true
= ( sK1 @ X1 @ X0 @ X0 ) )
| ( ( ^ [Y0: $i] :
( X0
@ ( sK2
@ ^ [Y1: $i > $i] : ( X1 != Y1 )
@ X0
@ Y0 ) ) )
= X1 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X3: $i > $i,X7: ( $i > $i ) > $o,X4: $i > $i] :
( ( $true
!= ( X7
@ ^ [Y0: $i] : ( X3 @ ( sK2 @ X7 @ X3 @ Y0 ) ) ) )
| ( $true
= ( X7 @ X4 ) )
| ( $true
!= ( X7 @ X3 ) )
| ( $true
= ( sK1 @ X4 @ X3 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f121,plain,
! [X0: $i > $i,X1: $i > $i] :
( ( $true
!= ( sK1 @ X1 @ X0
@ ^ [Y0: $i] : ( X1 @ ( X0 @ Y0 ) ) ) )
| ( X0 = X1 )
| ( ( ^ [Y0: $i] : ( X0 @ ( sK2 @ ( (=) @ X0 ) @ X0 @ Y0 ) ) )
!= X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
! [X0: $i > $i,X1: $i > $i] :
( ( X0 = X1 )
| ( $true
!= ( X0
= ( ^ [Y0: $i] : ( X0 @ ( sK2 @ ( (=) @ X0 ) @ X0 @ Y0 ) ) ) ) )
| ( $true
!= ( sK1 @ X1 @ X0
@ ^ [Y0: $i] : ( X1 @ ( X0 @ Y0 ) ) ) ) ),
inference(leibniz_equality_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X3: $i > $i,X7: ( $i > $i ) > $o,X4: $i > $i] :
( ( $true
!= ( sK1 @ X4 @ X3
@ ^ [Y0: $i] : ( X4 @ ( X3 @ Y0 ) ) ) )
| ( $true
= ( X7 @ X4 ) )
| ( $true
!= ( X7 @ X3 ) )
| ( $true
!= ( X7
@ ^ [Y0: $i] : ( X3 @ ( sK2 @ X7 @ X3 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU938^5 : 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
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:36:39 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : SEU938^5 : TPTP v9.2.1. Released v4.0.0.
% 0.26/0.46 % Domain : Set Theory (Functions)
% 0.26/0.46 % Problem : TPS problem THM196
% 0.26/0.46 % Version : Especial.
% 0.26/0.46 % English : It is not true that if [k COMPOSE j] is an iterate of j, provided
% 0.26/0.46 % we assume extensionality and the existence of the described
% 0.26/0.46 % function h (which can be proved if we have distinct elements a
% 0.26/0.46 % and b and descriptions).
% 0.26/0.46
% 0.26/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.26/0.46 % Source : [Bro09]
% 0.26/0.46 % Names : tps_0337 [Bro09]
% 0.26/0.46 % : THM196 [TPS]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.60 v8.2.0, 0.77 v8.1.0, 0.73 v7.5.0, 0.43 v7.4.0, 0.78 v7.3.0, 0.89 v7.2.0, 0.88 v7.1.0, 1.00 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.3.0, 1.00 v5.2.0, 0.80 v4.1.0, 0.67 v4.0.0
% 0.26/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.26/0.46 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.26/0.46 % Number of connectives : 31 ( 2 ~; 0 |; 4 &; 18 @)
% 0.26/0.46 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 15 ( 15 avg)
% 0.26/0.46 % Number of types : 2 ( 0 usr)
% 0.26/0.46 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.26/0.46 % Number of variables : 12 ( 3 ^; 9 !; 0 ?; 12 :)
% 0.26/0.46 % SPC : TH0_THM_EQU_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.26/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.26/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.26/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.26/0.46 % : Polymorphic definitions expanded.
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf(a,type,
% 0.26/0.46 a: $i ).
% 0.26/0.46
% 0.26/0.46 thf(b,type,
% 0.26/0.46 b: $i ).
% 0.26/0.46
% 0.26/0.46 thf(h,type,
% 0.26/0.46 h: $i > $i ).
% 0.26/0.46
% 0.26/0.46 thf(cTHM196_pme,conjecture,
% 0.26/0.46 ( ( ( ( h @ a )
% 0.26/0.46 = a )
% 0.26/0.46 & ( ( h @ b )
% 0.26/0.46 != a )
% 0.26/0.46 & ! [Xf: $i > $i,Xg: $i > $i] :
% 0.26/0.46 ( ! [Xx: $i] :
% 0.26/0.46 ( ( Xf @ Xx )
% 0.26/0.46 = ( Xg @ Xx ) )
% 0.26/0.46 => ( Xf = Xg ) ) )
% 0.26/0.46 => ~ ! [Xj: $i > $i,Xk: $i > $i] :
% 0.26/0.46 ( ! [Xp: ( $i > $i ) > $o] :
% 0.26/0.46 ( ( ( Xp @ Xj )
% 0.26/0.46 & ! [Xj_6: $i > $i] :
% 0.26/0.46 ( ( Xp @ Xj_6 )
% 0.26/0.46 => ( Xp
% 0.26/0.46 @ ^ [Xx: $i] : ( Xj @ ( Xj_6 @ Xx ) ) ) ) )
% 0.26/0.46 => ( Xp
% 0.26/0.46 @ ^ [Xx: $i] : ( Xk @ ( Xj @ Xx ) ) ) )
% 0.26/0.46 => ! [Xp: ( $i > $i ) > $o] :
% 0.26/0.46 ( ( ( Xp @ Xj )
% 0.26/0.46 & ! [Xj_7: $i > $i] :
% 0.26/0.46 ( ( Xp @ Xj_7 )
% 0.26/0.46 => ( Xp
% 0.26/0.46 @ ^ [Xx: $i] : ( Xj @ ( Xj_7 @ Xx ) ) ) ) )
% 0.26/0.46 => ( Xp @ Xk ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 1.67/1.32 ---- Embedded in THF ---
% 1.67/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.32 %%% Generated on Tue Feb 24 12:36:40 EST 2026
% 1.67/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.32 %%% Logic specification used:
% 1.67/1.32 %%% thf(spec, logic, $$dhol).
% 1.67/1.32
% 1.67/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.o7soIda66i/DTF2DTF27518.p
% See solution above
% 1.67/1.32 ------------------------
% 1.67/1.33 ---- Cleaned THF ---
% 1.67/1.33 thf(a,type,
% 1.67/1.33 a: $i ).
% 1.67/1.33
% 1.67/1.33 thf(b,type,
% 1.67/1.33 b: $i ).
% 1.67/1.33
% 1.67/1.33 thf(h,type,
% 1.67/1.33 h: $i > $i ).
% 1.67/1.33
% 1.67/1.33 thf(cTHM196_pme,conjecture,
% 1.67/1.33 ( ( ( ( h @ a )
% 1.67/1.33 = a )
% 1.67/1.33 & ( ( h @ b )
% 1.67/1.33 != a )
% 1.67/1.33 & ! [Xf: $i > $i,Xg: $i > $i] :
% 1.67/1.33 ( ! [Xx: $i] :
% 1.67/1.33 ( ( Xf @ Xx )
% 1.67/1.33 = ( Xg @ Xx ) )
% 1.67/1.33 => ( Xf = Xg ) ) )
% 1.67/1.33 => ~ ! [Xj: $i > $i,Xk: $i > $i] :
% 1.67/1.33 ( ! [Xp: ( $i > $i ) > $o] :
% 1.67/1.33 ( ( ( Xp @ Xj )
% 1.67/1.33 & ! [Xj_6: $i > $i] :
% 1.67/1.33 ( ( Xp @ Xj_6 )
% 1.67/1.33 => ( Xp
% 1.67/1.33 @ ^ [Xx: $i] : ( Xj @ ( Xj_6 @ Xx ) ) ) ) )
% 1.67/1.33 => ( Xp
% 1.67/1.33 @ ^ [Xx: $i] : ( Xk @ ( Xj @ Xx ) ) ) )
% 1.67/1.33 => ! [Xp: ( $i > $i ) > $o] :
% 1.67/1.33 ( ( ( Xp @ Xj )
% 1.67/1.33 & ! [Xj_7: $i > $i] :
% 1.67/1.33 ( ( Xp @ Xj_7 )
% 1.67/1.33 => ( Xp
% 1.67/1.33 @ ^ [Xx: $i] : ( Xj @ ( Xj_7 @ Xx ) ) ) ) )
% 1.67/1.33 => ( Xp @ Xk ) ) ) ) ).
% 1.67/1.33 ------------------------
% 1.67/1.35 % (27722)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27518 for (3000ds/183Mi)
% 1.67/1.35 % (27723)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_27518 for (3000ds/4Mi)
% 1.67/1.35 % (27726)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_27518 for (3000ds/2Mi)
% 1.67/1.35 % (27726)Instruction limit reached!
% 1.67/1.35 % (27726)------------------------------
% 1.67/1.35 % (27726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (27726)Termination reason: Unknown
% 1.67/1.35 % (27726)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (27726)Memory used [KB]: 5500
% 1.67/1.35 % (27726)Time elapsed: 0.003 s
% 1.67/1.35 % (27727)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_27518 for (3000ds/275Mi)
% 1.67/1.35 % (27726)Instructions burned: 3 (million)
% 1.67/1.35 % (27726)------------------------------
% 1.67/1.35 % (27726)------------------------------
% 1.67/1.35 % (27723)Instruction limit reached!
% 1.67/1.35 % (27723)------------------------------
% 1.67/1.35 % (27723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (27723)Termination reason: Unknown
% 1.67/1.35 % (27723)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (27723)Memory used [KB]: 5500
% 1.67/1.35 % (27723)Time elapsed: 0.004 s
% 1.67/1.35 % (27723)Instructions burned: 5 (million)
% 1.67/1.35 % (27723)------------------------------
% 1.67/1.35 % (27723)------------------------------
% 1.67/1.37 % (27725)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27518 for (3000ds/2Mi)
% 1.67/1.37 % (27728)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27518 for (3000ds/18Mi)
% 1.67/1.37 % (27724)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_27518 for (3000ds/27Mi)
% 1.67/1.37 % (27725)Instruction limit reached!
% 1.67/1.37 % (27725)------------------------------
% 1.67/1.37 % (27725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (27725)Termination reason: Unknown
% 1.67/1.37 % (27725)Termination phase: Property scanning
% 1.67/1.37
% 1.67/1.37 % (27725)Memory used [KB]: 1023
% 1.67/1.37 % (27725)Time elapsed: 0.004 s
% 1.67/1.37 % (27725)Instructions burned: 2 (million)
% 1.67/1.37 % (27725)------------------------------
% 1.67/1.37 % (27725)------------------------------
% 1.67/1.37 % (27735)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_27518 for (2999ds/37Mi)
% 1.67/1.38 % (27728)Instruction limit reached!
% 1.67/1.38 % (27728)------------------------------
% 1.67/1.38 % (27728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.38 % (27728)Termination reason: Unknown
% 1.67/1.38 % (27728)Termination phase: Saturation
% 1.67/1.38
% 1.67/1.38 % (27728)Memory used [KB]: 5628
% 1.67/1.38 % (27728)Time elapsed: 0.020 s
% 1.67/1.38 % (27728)Instructions burned: 18 (million)
% 1.67/1.38 % (27728)------------------------------
% 1.67/1.38 % (27728)------------------------------
% 1.67/1.38 % (27734)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27518 for (2999ds/3Mi)
% 1.67/1.39 % (27735)Instruction limit reached!
% 1.67/1.39 % (27735)------------------------------
% 1.67/1.39 % (27735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (27735)Termination reason: Unknown
% 1.67/1.39 % (27735)Termination phase: Saturation
% 1.67/1.39
% 1.67/1.39 % (27735)Memory used [KB]: 5628
% 1.67/1.39 % (27735)Time elapsed: 0.015 s
% 1.67/1.39 % (27735)Instructions burned: 39 (million)
% 1.67/1.39 % (27735)------------------------------
% 1.67/1.39 % (27735)------------------------------
% 1.67/1.39 % (27734)Instruction limit reached!
% 1.67/1.39 % (27734)------------------------------
% 1.67/1.39 % (27734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (27734)Termination reason: Unknown
% 1.67/1.39 % (27734)Termination phase: Saturation
% 1.67/1.39
% 1.67/1.39 % (27734)Memory used [KB]: 5500
% 1.67/1.39 % (27734)Time elapsed: 0.005 s
% 1.67/1.39 % (27734)Instructions burned: 3 (million)
% 1.67/1.39 % (27734)------------------------------
% 1.67/1.39 % (27734)------------------------------
% 1.67/1.39 % (27724)Instruction limit reached!
% 1.67/1.39 % (27724)------------------------------
% 1.67/1.39 % (27724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (27724)Termination reason: Unknown
% 1.67/1.39 % (27724)Termination phase: Saturation
% 1.67/1.39
% 1.67/1.39 % (27724)Memory used [KB]: 5500
% 1.67/1.39 % (27724)Time elapsed: 0.027 s
% 1.67/1.39 % (27724)Instructions burned: 27 (million)
% 1.67/1.39 % (27724)------------------------------
% 1.67/1.39 % (27724)------------------------------
% 1.67/1.39 % (27722)First to succeed.
% 1.67/1.39 % (27743)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27518 for (2999ds/3Mi)
% 1.67/1.39 % (27722)Refutation found. Thanks to Tanya!
% 1.67/1.39 % SZS status Theorem for DTF2THF_27518
% 1.67/1.39 % SZS output start Proof for DTF2THF_27518
% 1.67/1.39 thf(func_def_2, type, h: $i > $i).
% 1.67/1.39 thf(func_def_8, type, sK0: ($i > $i) > ($i > $i) > $i).
% 1.67/1.39 thf(func_def_9, type, sK1: ($i > $i) > ($i > $i) > ($i > $i) > $o).
% 1.67/1.39 thf(func_def_10, type, sK2: (($i > $i) > $o) > ($i > $i) > $i > $i).
% 1.67/1.39 thf(func_def_13, type, ph4: !>[X0: $tType]:(X0)).
% 1.67/1.39 thf(f311,plain,(
% 1.67/1.39 $false),
% 1.67/1.39 inference(avatar_sat_refutation,[status(thm)],[f205,f284,f310])).
% 1.67/1.39 thf(f310,plain,(
% 1.67/1.39 ~spl3_4),
% 1.67/1.39 inference(avatar_contradiction_clause,[status(thm)],[f309])).
% 1.67/1.39 thf(f309,plain,(
% 1.67/1.39 $false | ~spl3_4),
% 1.67/1.39 inference(subsumption_resolution,[status(thm)],[f297,f14])).
% 1.67/1.39 thf(f14,plain,(
% 1.67/1.39 (a = (h @ a))),
% 1.67/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.39 thf(f12,plain,(
% 1.67/1.39 ! [X0 : $i > $i,X1 : $i > $i] : ((X0 = X1) | ((X0 @ (sK0 @ X1 @ X0)) != (X1 @ (sK0 @ X1 @ X0)))) & ! [X3 : $i > $i,X4 : $i > $i] : ((($true = (sK1 @ X4 @ X3 @ X3)) & ! [X6 : $i > $i] : (($true != (sK1 @ X4 @ X3 @ X6)) | ($true = (sK1 @ X4 @ X3 @ (^[Y0 : $i]: (X3 @ (X6 @ Y0)))))) & ($true != (sK1 @ X4 @ X3 @ (^[Y0 : $i]: (X4 @ (X3 @ Y0)))))) | ! [X7 : ($i > $i) > $o] : (($true = (X7 @ X4)) | (($true = (X7 @ (sK2 @ X7 @ X3))) & ($true != (X7 @ (^[Y0 : $i]: (X3 @ (sK2 @ X7 @ X3 @ Y0)))))) | ($true != (X7 @ X3)))) & (a = (h @ a)) & (a != (h @ b))),
% 1.67/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9])).
% 1.67/1.39 thf(f9,plain,(
% 1.67/1.39 ! [X0 : $i > $i,X1 : $i > $i] : (? [X2 : $i] : ((X0 @ X2) != (X1 @ X2)) => ((X0 @ (sK0 @ X1 @ X0)) != (X1 @ (sK0 @ X1 @ X0))))),
% 1.67/1.39 introduced(definition,[],[choice_axiom])).
% 1.67/1.39 thf(f10,plain,(
% 1.67/1.39 ! [X3 : $i > $i,X4 : $i > $i] : (? [X5 : ($i > $i) > $o] : (((X5 @ X3) = $true) & ! [X6 : $i > $i] : (((X5 @ X6) != $true) | ($true = (X5 @ (^[Y0 : $i]: (X3 @ (X6 @ Y0)))))) & ($true != (X5 @ (^[Y0 : $i]: (X4 @ (X3 @ Y0)))))) => (($true = (sK1 @ X4 @ X3 @ X3)) & ! [X6 : $i > $i] : (($true != (sK1 @ X4 @ X3 @ X6)) | ($true = (sK1 @ X4 @ X3 @ (^[Y0 : $i]: (X3 @ (X6 @ Y0)))))) & ($true != (sK1 @ X4 @ X3 @ (^[Y0 : $i]: (X4 @ (X3 @ Y0)))))))),
% 1.67/1.39 introduced(definition,[],[choice_axiom])).
% 1.67/1.39 thf(f11,plain,(
% 1.67/1.39 ! [X3 : $i > $i,X7 : ($i > $i) > $o] : (? [X8 : $i > $i] : (($true = (X7 @ X8)) & ($true != (X7 @ (^[Y0 : $i]: (X3 @ (X8 @ Y0)))))) => (($true = (X7 @ (sK2 @ X7 @ X3))) & ($true != (X7 @ (^[Y0 : $i]: (X3 @ (sK2 @ X7 @ X3 @ Y0)))))))),
% 1.67/1.39 introduced(definition,[],[choice_axiom])).
% 1.67/1.39 thf(f8,plain,(
% 1.67/1.39 ! [X0 : $i > $i,X1 : $i > $i] : ((X0 = X1) | ? [X2 : $i] : ((X0 @ X2) != (X1 @ X2))) & ! [X3 : $i > $i,X4 : $i > $i] : (? [X5 : ($i > $i) > $o] : (((X5 @ X3) = $true) & ! [X6 : $i > $i] : (((X5 @ X6) != $true) | ($true = (X5 @ (^[Y0 : $i]: (X3 @ (X6 @ Y0)))))) & ($true != (X5 @ (^[Y0 : $i]: (X4 @ (X3 @ Y0)))))) | ! [X7 : ($i > $i) > $o] : (($true = (X7 @ X4)) | ? [X8 : $i > $i] : (($true = (X7 @ X8)) & ($true != (X7 @ (^[Y0 : $i]: (X3 @ (X8 @ Y0)))))) | ($true != (X7 @ X3)))) & (a = (h @ a)) & (a != (h @ b))),
% 1.67/1.39 inference(flattening,[status(thm)],[f7])).
% 1.67/1.39 thf(f7,plain,(
% 1.67/1.39 ! [X3 : $i > $i,X4 : $i > $i] : (! [X7 : ($i > $i) > $o] : (($true = (X7 @ X4)) | (($true != (X7 @ X3)) | ? [X8 : $i > $i] : (($true = (X7 @ X8)) & ($true != (X7 @ (^[Y0 : $i]: (X3 @ (X8 @ Y0)))))))) | ? [X5 : ($i > $i) > $o] : (($true != (X5 @ (^[Y0 : $i]: (X4 @ (X3 @ Y0))))) & (((X5 @ X3) = $true) & ! [X6 : $i > $i] : (((X5 @ X6) != $true) | ($true = (X5 @ (^[Y0 : $i]: (X3 @ (X6 @ Y0))))))))) & ((a = (h @ a)) & (a != (h @ b)) & ! [X0 : $i > $i,X1 : $i > $i] : ((X0 = X1) | ? [X2 : $i] : ((X0 @ X2) != (X1 @ X2))))),
% 1.67/1.39 inference(ennf_transformation,[status(thm)],[f6])).
% 1.67/1.39 thf(f6,plain,(
% 1.67/1.39 ~(((a = (h @ a)) & (a != (h @ b)) & ! [X0 : $i > $i,X1 : $i > $i] : (! [X2 : $i] : ((X0 @ X2) = (X1 @ X2)) => (X0 = X1))) => ~! [X3 : $i > $i,X4 : $i > $i] : (! [X5 : ($i > $i) > $o] : ((((X5 @ X3) = $true) & ! [X6 : $i > $i] : (((X5 @ X6) = $true) => ($true = (X5 @ (^[Y0 : $i]: (X3 @ (X6 @ Y0))))))) => ($true = (X5 @ (^[Y0 : $i]: (X4 @ (X3 @ Y0)))))) => ! [X7 : ($i > $i) > $o] : ((($true = (X7 @ X3)) & ! [X8 : $i > $i] : (($true = (X7 @ X8)) => ($true = (X7 @ (^[Y0 : $i]: (X3 @ (X8 @ Y0))))))) => ($true = (X7 @ X4)))))),
% 1.67/1.39 inference(rectify,[status(thm)],[f5])).
% 1.67/1.39 thf(f5,plain,(
% 1.67/1.39 ~(((a = (h @ a)) & (a != (h @ b)) & ! [X0 : $i > $i,X1 : $i > $i] : (! [X2 : $i] : ((X0 @ X2) = (X1 @ X2)) => (X0 = X1))) => ~! [X3 : $i > $i,X4 : $i > $i] : (! [X5 : ($i > $i) > $o] : ((((X5 @ X3) = $true) & ! [X6 : $i > $i] : (((X5 @ X6) = $true) => ($true = (X5 @ (^[Y0 : $i]: (X3 @ (X6 @ Y0))))))) => ($true = (X5 @ (^[Y0 : $i]: (X4 @ (X3 @ Y0)))))) => ! [X9 : ($i > $i) > $o] : ((($true = (X9 @ X3)) & ! [X10 : $i > $i] : (($true = (X9 @ X10)) => ($true = (X9 @ (^[Y0 : $i]: (X3 @ (X10 @ Y0))))))) => ($true = (X9 @ X4)))))),
% 1.67/1.39 inference(fool_elimination,[status(thm)],[f4])).
% 1.67/1.39 thf(f4,plain,(
% 1.67/1.39 ~(((a != (h @ b)) & (a = (h @ a)) & ! [X0 : $i > $i,X1 : $i > $i] : (! [X2 : $i] : ((X0 @ X2) = (X1 @ X2)) => (X0 = X1))) => ~! [X3 : $i > $i,X4 : $i > $i] : (! [X5 : ($i > $i) > $o] : (((X5 @ X3) & ! [X6 : $i > $i] : ((X5 @ X6) => (X5 @ (^[X7 : $i] : (X3 @ (X6 @ X7)))))) => (X5 @ (^[X8 : $i] : (X4 @ (X3 @ X8))))) => ! [X9 : ($i > $i) > $o] : (((X9 @ X3) & ! [X10 : $i > $i] : ((X9 @ X10) => (X9 @ (^[X11 : $i] : (X3 @ (X10 @ X11)))))) => (X9 @ X4))))),
% 1.67/1.39 inference(rectify,[status(thm)],[f2])).
% 1.67/1.39 thf(f2,negated_conjecture,(
% 1.67/1.39 ~(((a != (h @ b)) & (a = (h @ a)) & ! [X1 : $i > $i,X0 : $i > $i] : (! [X2 : $i] : ((X0 @ X2) = (X1 @ X2)) => (X0 = X1))) => ~! [X3 : $i > $i,X4 : $i > $i] : (! [X5 : ($i > $i) > $o] : (((X5 @ X3) & ! [X6 : $i > $i] : ((X5 @ X6) => (X5 @ (^[X2 : $i] : (X3 @ (X6 @ X2)))))) => (X5 @ (^[X2 : $i] : (X4 @ (X3 @ X2))))) => ! [X5 : ($i > $i) > $o] : (((X5 @ X3) & ! [X7 : $i > $i] : ((X5 @ X7) => (X5 @ (^[X2 : $i] : (X3 @ (X7 @ X2)))))) => (X5 @ X4))))),
% 1.67/1.39 inference(negated_conjecture,[status(cth)],[f1])).
% 1.67/1.39 thf(f1,conjecture,(
% 1.67/1.39 ((a != (h @ b)) & (a = (h @ a)) & ! [X1 : $i > $i,X0 : $i > $i] : (! [X2 : $i] : ((X0 @ X2) = (X1 @ X2)) => (X0 = X1))) => ~! [X3 : $i > $i,X4 : $i > $i] : (! [X5 : ($i > $i) > $o] : (((X5 @ X3) & ! [X6 : $i > $i] : ((X5 @ X6) => (X5 @ (^[X2 : $i] : (X3 @ (X6 @ X2)))))) => (X5 @ (^[X2 : $i] : (X4 @ (X3 @ X2))))) => ! [X5 : ($i > $i) > $o] : (((X5 @ X3) & ! [X7 : $i > $i] : ((X5 @ X7) => (X5 @ (^[X2 : $i] : (X3 @ (X7 @ X2)))))) => (X5 @ X4)))),
% 1.67/1.39 file('/export/starexec/sandbox/tmp/tmp.o7soIda66i/DTF2THF_27518.p',cTHM196_pme)).
% 1.67/1.39 thf(f297,plain,(
% 1.67/1.39 (a != (h @ a)) | ~spl3_4),
% 1.67/1.39 inference(superposition,[status(thm)],[f13,f195])).
% 1.67/1.39 thf(f195,plain,(
% 1.67/1.39 ( ! [X0 : $i] : ((a = X0)) ) | ~spl3_4),
% 1.67/1.39 inference(avatar_component_clause,[status(thm)],[f194])).
% 1.67/1.39 thf(f194,definition,(
% 1.67/1.39 spl3_4 <=> ! [X0 : $i] : (a = X0)),
% 1.67/1.39 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.67/1.39 thf(f13,plain,(
% 1.67/1.39 (a != (h @ b))),
% 1.67/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.39 thf(f284,plain,(
% 1.67/1.39 ~spl3_3),
% 1.67/1.39 inference(avatar_contradiction_clause,[status(thm)],[f283])).
% 1.67/1.39 thf(f283,plain,(
% 1.67/1.39 $false | ~spl3_3),
% 1.67/1.39 inference(subsumption_resolution,[status(thm)],[f272,f14])).
% 1.67/1.39 thf(f272,plain,(
% 1.67/1.39 (a != (h @ a)) | ~spl3_3),
% 1.67/1.39 inference(superposition,[status(thm)],[f13,f245])).
% 1.67/1.39 thf(f245,plain,(
% 1.67/1.39 ( ! [X1 : $i] : (((h @ a) = X1)) ) | ~spl3_3),
% 1.67/1.39 inference(beta_eta_normalization,[status(thm)],[f232])).
% 1.67/1.39 thf(f232,plain,(
% 1.67/1.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (Y0)) @ X1) = ((^[Y0 : $i]: (h @ a)) @ X1))) ) | ~spl3_3),
% 1.67/1.39 inference(argument_congruence,[status(thm)],[f192])).
% 1.67/1.39 thf(f192,plain,(
% 1.67/1.39 ((^[Y0 : $i]: (h @ a)) = (^[Y0 : $i]: (Y0))) | ~spl3_3),
% 1.67/1.39 inference(avatar_component_clause,[status(thm)],[f190])).
% 1.67/1.39 thf(f190,definition,(
% 1.67/1.39 spl3_3 <=> ((^[Y0 : $i]: (h @ a)) = (^[Y0 : $i]: (Y0)))),
% 1.67/1.39 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.67/1.39 thf(f205,plain,(
% 1.67/1.39 spl3_3 | spl3_4),
% 1.67/1.39 inference(avatar_split_clause,[status(thm)],[f173,f194,f190])).
% 1.67/1.39 thf(f173,plain,(
% 1.67/1.39 ( ! [X0 : $i] : (((^[Y0 : $i]: (h @ a)) = (^[Y0 : $i]: (Y0))) | (a = X0)) )),
% 1.67/1.39 inference(trivial_inequality_removal,[status(thm)],[f172])).
% 1.67/1.39 thf(f172,plain,(
% 1.67/1.39 ( ! [X0 : $i] : (((^[Y0 : $i]: (h @ a)) != (^[Y0 : $i]: (h @ a))) | (a = X0) | ((^[Y0 : $i]: (h @ a)) = (^[Y0 : $i]: (Y0)))) )),
% 1.67/1.39 inference(beta_eta_normalization,[status(thm)],[f171])).
% 1.67/1.39 thf(f171,plain,(
% 1.67/1.39 ( ! [X0 : $i] : (((^[Y0 : $i]: (h @ a)) = (^[Y0 : $i]: (Y0))) | (a = ((^[Y0 : $i]: (Y0)) @ X0)) | ((^[Y0 : $i]: (h @ a)) != (^[Y0 : $i]: ((^[Y1 : $i]: (h @ a)) @ (sK2 @ (= @ (^[Y1 : $i]: (h @ a))) @ (^[Y1 : $i]: (h @ a)) @ Y0))))) )),
% 1.67/1.39 inference(trivial_inequality_removal,[status(thm)],[f170])).
% 1.67/1.39 thf(f170,plain,(
% 1.67/1.39 ( ! [X0 : $i] : (((^[Y0 : $i]: (h @ a)) != (^[Y0 : $i]: ((^[Y1 : $i]: (h @ a)) @ (sK2 @ (= @ (^[Y1 : $i]: (h @ a))) @ (^[Y1 : $i]: (h @ a)) @ Y0)))) | ($true != $true) | ((^[Y0 : $i]: (h @ a)) = (^[Y0 : $i]: (Y0))) | (a = ((^[Y0 : $i]: (Y0)) @ X0))) )),
% 1.67/1.39 inference(duplicate_literal_removal,[status(thm)],[f165])).
% 1.67/1.39 thf(f165,plain,(
% 1.67/1.39 ( ! [X0 : $i] : (($true != $true) | (a = ((^[Y0 : $i]: (Y0)) @ X0)) | ((^[Y0 : $i]: (h @ a)) = (^[Y0 : $i]: (Y0))) | ((^[Y0 : $i]: (h @ a)) = (^[Y0 : $i]: (Y0))) | ((^[Y0 : $i]: (h @ a)) != (^[Y0 : $i]: ((^[Y1 : $i]: (h @ a)) @ (sK2 @ (= @ (^[Y1 : $i]: (h @ a))) @ (^[Y1 : $i]: (h @ a)) @ Y0))))) )),
% 1.67/1.39 inference(superposition,[status(thm)],[f121,f160])).
% 1.67/1.39 thf(f160,plain,(
% 1.67/1.39 ( ! [X0 : $i > $i,X1 : $i] : (($true = (sK1 @ X0 @ (^[Y0 : $i]: (h @ a)) @ (^[Y0 : $i]: (h @ a)))) | ((^[Y0 : $i]: (h @ a)) = X0) | (a = (X0 @ X1))) )),
% 1.67/1.39 inference(beta_eta_normalization,[status(thm)],[f151])).
% 1.67/1.39 thf(f151,plain,(
% 1.67/1.39 ( ! [X0 : $i > $i,X1 : $i] : (($true = (sK1 @ X0 @ (^[Y0 : $i]: (h @ ((^[Y1 : $i]: (a)) @ Y0))) @ (^[Y0 : $i]: (h @ ((^[Y1 : $i]: (a)) @ Y0))))) | (a = (X0 @ X1)) | ((^[Y0 : $i]: (h @ ((^[Y1 : $i]: (a)) @ Y0))) = X0)) )),
% 1.67/1.39 inference(superposition,[status(thm)],[f14,f138])).
% 1.67/1.39 thf(f138,plain,(
% 1.67/1.39 ( ! [X2 : $i,X0 : $i > $i,X1 : $i > $i] : (((X1 @ X2) = (X0 @ (sK2 @ (^[Y0 : $i > $i]: (~ (X1 = Y0))) @ X0 @ X2))) | ($true = (sK1 @ X1 @ X0 @ X0)) | (X0 = X1)) )),
% 1.67/1.39 inference(beta_eta_normalization,[status(thm)],[f128])).
% 1.67/1.39 thf(f128,plain,(
% 1.67/1.39 ( ! [X2 : $i,X0 : $i > $i,X1 : $i > $i] : (((X1 @ X2) = ((^[Y0 : $i]: (X0 @ (sK2 @ (^[Y1 : $i > $i]: (~ (X1 = Y1))) @ X0 @ Y0))) @ X2)) | ($true = (sK1 @ X1 @ X0 @ X0)) | (X0 = X1)) )),
% 1.67/1.39 inference(argument_congruence,[status(thm)],[f90])).
% 1.67/1.39 thf(f90,plain,(
% 1.67/1.39 ( ! [X0 : $i > $i,X1 : $i > $i] : (((^[Y0 : $i]: (X0 @ (sK2 @ (^[Y1 : $i > $i]: (~ (X1 = Y1))) @ X0 @ Y0))) = X1) | (X0 = X1) | ($true = (sK1 @ X1 @ X0 @ X0))) )),
% 1.67/1.39 inference(equality_proxy_clausification,[status(thm)],[f89])).
% 1.67/1.39 thf(f89,plain,(
% 1.67/1.39 ( ! [X0 : $i > $i,X1 : $i > $i] : (((^[Y0 : $i]: (X0 @ (sK2 @ (^[Y1 : $i > $i]: (~ (X1 = Y1))) @ X0 @ Y0))) = X1) | ($true = (sK1 @ X1 @ X0 @ X0)) | ($true = (X1 = X0))) )),
% 1.67/1.39 inference(not_proxy_clausification,[status(thm)],[f88])).
% 1.67/1.39 thf(f88,plain,(
% 1.67/1.39 ( ! [X0 : $i > $i,X1 : $i > $i] : (($true = (sK1 @ X1 @ X0 @ X0)) | ((^[Y0 : $i]: (X0 @ (sK2 @ (^[Y1 : $i > $i]: (~ (X1 = Y1))) @ X0 @ Y0))) = X1) | ($true != (~ (X1 = X0)))) )),
% 1.67/1.39 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.67/1.39 thf(f75,plain,(
% 1.67/1.39 ( ! [X0 : $i > $i,X1 : $i > $i] : (($true != ((^[Y0 : $i > $i]: (~ (X1 = Y0))) @ X0)) | ($true = (sK1 @ X1 @ X0 @ X0)) | ((^[Y0 : $i]: (X0 @ (sK2 @ (^[Y1 : $i > $i]: (~ (X1 = Y1))) @ X0 @ Y0))) = X1)) )),
% 1.67/1.39 inference(leibniz_equality_elimination,[status(thm)],[f19])).
% 1.67/1.39 thf(f19,plain,(
% 1.67/1.39 ( ! [X3 : $i > $i,X7 : ($i > $i) > $o,X4 : $i > $i] : (($true != (X7 @ (^[Y0 : $i]: (X3 @ (sK2 @ X7 @ X3 @ Y0))))) | ($true = (X7 @ X4)) | ($true != (X7 @ X3)) | ($true = (sK1 @ X4 @ X3 @ X3))) )),
% 1.67/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.39 thf(f121,plain,(
% 1.67/1.39 ( ! [X0 : $i > $i,X1 : $i > $i] : (($true != (sK1 @ X1 @ X0 @ (^[Y0 : $i]: (X1 @ (X0 @ Y0))))) | (X0 = X1) | ((^[Y0 : $i]: (X0 @ (sK2 @ (= @ X0) @ X0 @ Y0))) != X0)) )),
% 1.67/1.39 inference(equality_proxy_clausification,[status(thm)],[f111])).
% 1.67/1.39 thf(f111,plain,(
% 1.67/1.39 ( ! [X0 : $i > $i,X1 : $i > $i] : ((X0 = X1) | ($true != (X0 = (^[Y0 : $i]: (X0 @ (sK2 @ (= @ X0) @ X0 @ Y0))))) | ($true != (sK1 @ X1 @ X0 @ (^[Y0 : $i]: (X1 @ (X0 @ Y0)))))) )),
% 1.67/1.39 inference(leibniz_equality_elimination,[status(thm)],[f15])).
% 1.67/1.39 thf(f15,plain,(
% 1.67/1.39 ( ! [X3 : $i > $i,X7 : ($i > $i) > $o,X4 : $i > $i] : (($true != (sK1 @ X4 @ X3 @ (^[Y0 : $i]: (X4 @ (X3 @ Y0))))) | ($true = (X7 @ X4)) | ($true != (X7 @ X3)) | ($true != (X7 @ (^[Y0 : $i]: (X3 @ (sK2 @ X7 @ X3 @ Y0)))))) )),
% 1.67/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.39 % SZS output end Proof for DTF2THF_27518
% 1.67/1.39 % (27722)------------------------------
% 1.67/1.39 % (27722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (27722)Termination reason: Refutation
% 1.67/1.39
% 1.67/1.39 % (27722)Memory used [KB]: 6140
% 1.67/1.39 % (27722)Time elapsed: 0.048 s
% 1.67/1.39 % (27722)Instructions burned: 116 (million)
% 1.67/1.39 % (27722)------------------------------
% 1.67/1.39 % (27722)------------------------------
% 1.67/1.39 % (27721)Success in time 0.054 s
%------------------------------------------------------------------------------