%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO556^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n029.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 09:54:32 AM UTC 2026
% Result : Theorem 1.58s 1.43s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 127 ( 18 unt; 0 typ; 12 def)
% Number of atoms : 921 ( 322 equ; 3 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 1110 ( 234 ~; 246 |; 61 &; 486 @)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 29 usr; 20 con; 0-3 aty)
% ( 0 !!; 67 ??; 0 @@+; 0 @@-)
% Number of variables : 161 ( 90 ^; 63 !; 8 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
if: $o > $i > $i > $i ).
thf(func_def_15,type,
sK0: $i > $o ).
thf(func_def_17,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK3: $i > $i > $i ).
thf(func_def_22,type,
sK7: $i > ( $i > $o ) > $i ).
thf(func_def_23,type,
sK8: $i > $i ).
thf(func_def_27,type,
sK12: $i > $i ).
thf(func_def_29,type,
sK14: $i > $i ).
thf(func_def_33,type,
sK18: $i > $i ).
thf(func_def_37,type,
sK22: $i > $i ).
thf(func_def_41,type,
sK26: $i > $i ).
thf(func_def_43,type,
sK28: $i > $i ).
thf(f2011,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f222,f387,f397,f405,f537,f873,f875,f876,f879,f963,f990,f2003,f2010]) ).
thf(f2010,plain,
( ~ spl1_48
| ~ spl1_52 ),
inference(avatar_contradiction_clause,[status(thm)],[f2009]) ).
thf(f2009,plain,
( $false
| ~ spl1_48
| ~ spl1_52 ),
inference(trivial_inequality_removal,[status(thm)],[f2008]) ).
thf(f2008,plain,
( ( ( eps @ sK0 )
!= ( eps @ sK0 ) )
| ~ spl1_48
| ~ spl1_52 ),
inference(duplicate_literal_removal,[status(thm)],[f2007]) ).
thf(f2007,plain,
( ( ( eps @ sK0 )
!= ( eps @ sK0 ) )
| ( ( eps @ sK0 )
!= ( eps @ sK0 ) )
| ( ( eps @ sK0 )
!= ( eps @ sK0 ) )
| ~ spl1_48
| ~ spl1_52 ),
inference(superposition,[status(thm)],[f989,f1184]) ).
thf(f1184,plain,
( ( ( eps @ sK0 )
= ( sK22 @ ( eps @ sK0 ) ) )
| ~ spl1_52 ),
inference(avatar_component_clause,[status(thm)],[f1183]) ).
thf(f1183,definition,
( spl1_52
<=> ( ( eps @ sK0 )
= ( sK22 @ ( eps @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_52])],[avatar_definition]) ).
thf(f989,plain,
( ! [X0: $i] :
( ( ( eps @ sK0 )
!= ( sK22 @ X0 ) )
| ( ( sK22 @ X0 )
!= X0 )
| ( ( eps @ sK0 )
!= X0 ) )
| ~ spl1_48 ),
inference(avatar_component_clause,[status(thm)],[f988]) ).
thf(f988,definition,
( spl1_48
<=> ! [X0: $i] :
( ( ( sK22 @ X0 )
!= X0 )
| ( ( eps @ sK0 )
!= ( sK22 @ X0 ) )
| ( ( eps @ sK0 )
!= X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_48])],[avatar_definition]) ).
thf(f2003,plain,
( spl1_52
| ~ spl1_42 ),
inference(avatar_split_clause,[status(thm)],[f2002,f961,f1183]) ).
thf(f961,definition,
( spl1_42
<=> ! [X0: $i] :
( ( ( sK22 @ X0 )
= X0 )
| ( ( eps @ sK0 )
= ( sK22 @ X0 ) )
| ( ( eps @ sK0 )
!= X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_42])],[avatar_definition]) ).
thf(f2002,plain,
( ( ( eps @ sK0 )
= ( sK22 @ ( eps @ sK0 ) ) )
| ~ spl1_42 ),
inference(duplicate_literal_removal,[status(thm)],[f2001]) ).
thf(f2001,plain,
( ( ( eps @ sK0 )
= ( sK22 @ ( eps @ sK0 ) ) )
| ( ( eps @ sK0 )
= ( sK22 @ ( eps @ sK0 ) ) )
| ~ spl1_42 ),
inference(equality_resolution,[status(thm)],[f962]) ).
thf(f962,plain,
( ! [X0: $i] :
( ( ( eps @ sK0 )
!= X0 )
| ( ( sK22 @ X0 )
= X0 )
| ( ( eps @ sK0 )
= ( sK22 @ X0 ) ) )
| ~ spl1_42 ),
inference(avatar_component_clause,[status(thm)],[f961]) ).
thf(f990,plain,
( spl1_4
| spl1_48 ),
inference(avatar_split_clause,[status(thm)],[f939,f988,f205]) ).
thf(f205,definition,
( spl1_4
<=> ! [X1: $i] :
( ( sK0 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f939,plain,
! [X0: $i,X1: $i] :
( ( ( sK22 @ X0 )
!= X0 )
| ( ( sK0 @ X1 )
= $false )
| ( ( eps @ sK0 )
!= X0 )
| ( ( eps @ sK0 )
!= ( sK22 @ X0 ) ) ),
inference(pi_clausification,[status(thm)],[f938]) ).
thf(f938,plain,
! [X0: $i] :
( ( ( sK22 @ X0 )
!= X0 )
| ( ( eps @ sK0 )
!= ( sK22 @ X0 ) )
| ( ( ?? @ $i @ sK0 )
= $false )
| ( ( eps @ sK0 )
!= X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f937]) ).
thf(f937,plain,
! [X0: $i] :
( ( ( eps @ sK0 )
!= X0 )
| ( $false
= ( ( eps @ sK0 )
= ( sK22 @ X0 ) ) )
| ( ( ?? @ $i @ sK0 )
= $false )
| ( ( sK22 @ X0 )
!= X0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f936]) ).
thf(f936,plain,
! [X0: $i] :
( ( ( eps @ sK0 )
!= X0 )
| ( $false
= ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= ( sK22 @ X0 ) ) ) )
| ( ( sK22 @ X0 )
!= X0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f934]) ).
thf(f934,plain,
! [X0: $i] :
( ( ( eps @ sK0 )
!= X0 )
| ( ( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= ( sK22 @ X0 ) ) )
| ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK22 @ X0 ) )
& ~ ( ?? @ $i @ sK0 ) ) )
= $false )
| ( ( sK22 @ X0 )
!= X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f933]) ).
thf(f933,plain,
! [X0: $i] :
( ( $false
= ( X0
= ( sK22 @ X0 ) ) )
| ( ( eps @ sK0 )
!= X0 )
| ( ( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= ( sK22 @ X0 ) ) )
| ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK22 @ X0 ) )
& ~ ( ?? @ $i @ sK0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f931]) ).
thf(f931,plain,
! [X0: $i] :
( ( ( eps @ sK0 )
!= X0 )
| ( ( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= ( sK22 @ X0 ) ) )
| ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK22 @ X0 ) )
& ~ ( ?? @ $i @ sK0 ) ) )
!= ( X0
= ( sK22 @ X0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f930]) ).
thf(f930,plain,
! [X0: $i] :
( ( ( ^ [Y0: $i] :
( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= Y0 ) )
| ( ( ( eps
@ ^ [Y1: $i] : $false )
= Y0 )
& ~ ( ?? @ $i @ sK0 ) ) )
@ ( sK22 @ X0 ) )
!= ( X0
= ( sK22 @ X0 ) ) )
| ( ( eps @ sK0 )
!= X0 ) ),
inference(negative_extensionality,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: $i] :
( ( ( (=) @ X0 )
!= ( ^ [Y0: $i] :
( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= Y0 ) )
| ( ( ( eps
@ ^ [Y1: $i] : $false )
= Y0 )
& ~ ( ?? @ $i @ sK0 ) ) ) ) )
| ( ( eps @ sK0 )
!= X0 ) ),
inference(constrained_superposition,[status(thm)],[f20,f21]) ).
thf(f21,plain,
! [X0: $i] :
( ( eps @ ( (=) @ X0 ) )
= X0 ),
inference(leibniz_equality_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jUTSiai7C0/DTF2THF_27531.p',choiceax) ).
thf(f20,plain,
( ( eps @ sK0 )
!= ( eps
@ ^ [Y0: $i] :
( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= Y0 ) )
| ( ( ( eps
@ ^ [Y1: $i] : $false )
= Y0 )
& ~ ( ?? @ $i @ sK0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) )
@ ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
@ ( eps @ sK0 )
@ ( eps
@ ^ [Y0: $i] : $false ) )
!= ( eps @ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f18,f17]) ).
thf(f17,plain,
( if
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( if
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: $o,X1: $i,X2: $i] :
( eps
@ ^ [X3: $i] :
( ( ~ X0
& ( X2 = X3 ) )
| ( ( X1 = X3 )
& X0 ) ) ) )
= if ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X2: $o,X1: $i,X3: $i] :
( eps
@ ^ [X4: $i] :
( ( ~ X2
& ( X3 = X4 ) )
| ( ( X1 = X4 )
& X2 ) ) ) )
= if ),
file('/export/starexec/sandbox/tmp/tmp.jUTSiai7C0/DTF2THF_27531.p',ifd) ).
thf(f18,plain,
( ( eps @ sK0 )
!= ( if
@ ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
@ ( eps @ sK0 )
@ ( eps
@ ^ [Y0: $i] : $false ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( eps @ sK0 )
!= ( if
@ ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
@ ( eps @ sK0 )
@ ( eps
@ ^ [Y0: $i] : $false ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i > $o] :
( ( eps @ X0 )
!= ( if
@ ( ?? @ $i
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ ( eps @ X0 )
@ ( eps
@ ^ [Y0: $i] : $false ) ) )
=> ( ( eps @ sK0 )
!= ( if
@ ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
@ ( eps @ sK0 )
@ ( eps
@ ^ [Y0: $i] : $false ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: $i > $o] :
( ( eps @ X0 )
!= ( if
@ ( ?? @ $i
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ ( eps @ X0 )
@ ( eps
@ ^ [Y0: $i] : $false ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i > $o] :
( ( eps @ X0 )
= ( if
@ ( ?? @ $i
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ ( eps @ X0 )
@ ( eps
@ ^ [Y0: $i] : $false ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i > $o] :
( ( if
@ ? [X1: $i] : ( X0 @ X1 )
@ ( eps @ X0 )
@ ( eps
@ ^ [X2: $i] : $false ) )
= ( eps @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $i > $o] :
( ( if
@ ? [X1: $i] : ( X0 @ X1 )
@ ( eps @ X0 )
@ ( eps
@ ^ [X1: $i] : $false ) )
= ( eps @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $i > $o] :
( ( if
@ ? [X1: $i] : ( X0 @ X1 )
@ ( eps @ X0 )
@ ( eps
@ ^ [X1: $i] : $false ) )
= ( eps @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.jUTSiai7C0/DTF2THF_27531.p',conj) ).
thf(f963,plain,
( spl1_4
| spl1_42 ),
inference(avatar_split_clause,[status(thm)],[f959,f961,f205]) ).
thf(f959,plain,
! [X0: $i,X1: $i] :
( ( ( sK22 @ X0 )
= X0 )
| ( ( eps @ sK0 )
!= X0 )
| ( ( eps @ sK0 )
= ( sK22 @ X0 ) )
| ( ( sK0 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f958]) ).
thf(f958,plain,
! [X0: $i] :
( ( ( eps @ sK0 )
= ( sK22 @ X0 ) )
| ( ( eps @ sK0 )
!= X0 )
| ( ( sK22 @ X0 )
= X0 )
| ( ( ?? @ $i @ sK0 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f955]) ).
thf(f955,plain,
! [X0: $i] :
( ( ( eps @ sK0 )
!= X0 )
| ( ( ~ ( ?? @ $i @ sK0 ) )
= $true )
| ( ( eps @ sK0 )
= ( sK22 @ X0 ) )
| ( ( sK22 @ X0 )
= X0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f954]) ).
thf(f954,plain,
! [X0: $i] :
( ( ( eps @ sK0 )
= ( sK22 @ X0 ) )
| ( ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK22 @ X0 ) )
& ~ ( ?? @ $i @ sK0 ) )
= $true )
| ( ( sK22 @ X0 )
= X0 )
| ( ( eps @ sK0 )
!= X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f946]) ).
thf(f946,plain,
! [X0: $i] :
( ( ( ( eps @ sK0 )
= ( sK22 @ X0 ) )
= $true )
| ( ( sK22 @ X0 )
= X0 )
| ( ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK22 @ X0 ) )
& ~ ( ?? @ $i @ sK0 ) )
= $true )
| ( ( eps @ sK0 )
!= X0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f945]) ).
thf(f945,plain,
! [X0: $i] :
( ( ( eps @ sK0 )
!= X0 )
| ( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= ( sK22 @ X0 ) ) )
= $true )
| ( ( sK22 @ X0 )
= X0 )
| ( ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK22 @ X0 ) )
& ~ ( ?? @ $i @ sK0 ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f944]) ).
thf(f944,plain,
! [X0: $i] :
( ( ( X0
= ( sK22 @ X0 ) )
= $true )
| ( ( eps @ sK0 )
!= X0 )
| ( ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK22 @ X0 ) )
& ~ ( ?? @ $i @ sK0 ) )
= $true )
| ( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= ( sK22 @ X0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f932]) ).
thf(f932,plain,
! [X0: $i] :
( ( ( eps @ sK0 )
!= X0 )
| ( ( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= ( sK22 @ X0 ) ) )
| ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK22 @ X0 ) )
& ~ ( ?? @ $i @ sK0 ) ) )
= $true )
| ( ( X0
= ( sK22 @ X0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f931]) ).
thf(f879,plain,
( ~ spl1_4
| ~ spl1_27 ),
inference(avatar_contradiction_clause,[status(thm)],[f878]) ).
thf(f878,plain,
( $false
| ~ spl1_4
| ~ spl1_27 ),
inference(trivial_inequality_removal,[status(thm)],[f877]) ).
thf(f877,plain,
( ( $false = $true )
| ~ spl1_4
| ~ spl1_27 ),
inference(forward_demodulation,[status(thm)],[f536,f206]) ).
thf(f206,plain,
( ! [X1: $i] :
( ( sK0 @ X1 )
= $false )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f205]) ).
thf(f536,plain,
( ( ( sK0 @ sK15 )
= $true )
| ~ spl1_27 ),
inference(avatar_component_clause,[status(thm)],[f534]) ).
thf(f534,definition,
( spl1_27
<=> ( ( sK0 @ sK15 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_27])],[avatar_definition]) ).
thf(f876,plain,
( spl1_28
| ~ spl1_6
| ~ spl1_26 ),
inference(avatar_split_clause,[status(thm)],[f829,f531,f213,f539]) ).
thf(f539,definition,
( spl1_28
<=> ! [X0: $i] :
( ( sK4
!= ( sK14 @ X0 ) )
| ( sK4 != X0 )
| ( ( sK14 @ X0 )
!= X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_28])],[avatar_definition]) ).
thf(f213,definition,
( spl1_6
<=> ( ( eps
@ ^ [Y0: $i] : $false )
= sK4 ) ),
introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition]) ).
thf(f531,definition,
( spl1_26
<=> ! [X0: $i] :
( ( ( eps
@ ^ [Y0: $i] : $false )
!= ( sK14 @ X0 ) )
| ( ( sK14 @ X0 )
!= X0 )
| ( sK4 != X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_26])],[avatar_definition]) ).
thf(f829,plain,
( ! [X0: $i] :
( ( sK4 != X0 )
| ( ( sK14 @ X0 )
!= X0 )
| ( sK4
!= ( sK14 @ X0 ) ) )
| ~ spl1_6
| ~ spl1_26 ),
inference(forward_demodulation,[status(thm)],[f532,f215]) ).
thf(f215,plain,
( ( ( eps
@ ^ [Y0: $i] : $false )
= sK4 )
| ~ spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f213]) ).
thf(f532,plain,
( ! [X0: $i] :
( ( ( sK14 @ X0 )
!= X0 )
| ( ( eps
@ ^ [Y0: $i] : $false )
!= ( sK14 @ X0 ) )
| ( sK4 != X0 ) )
| ~ spl1_26 ),
inference(avatar_component_clause,[status(thm)],[f531]) ).
thf(f875,plain,
( spl1_21
| ~ spl1_3
| ~ spl1_6 ),
inference(avatar_split_clause,[status(thm)],[f658,f213,f201,f511]) ).
thf(f511,definition,
( spl1_21
<=> ! [X0: $i] :
( ( sK4 != X0 )
| ( sK4
= ( sK14 @ X0 ) )
| ( ( sK14 @ X0 )
= X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_21])],[avatar_definition]) ).
thf(f201,definition,
( spl1_3
<=> ( sK4
= ( eps @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f658,plain,
( ! [X0: $i] :
( ( ( sK14 @ X0 )
= X0 )
| ( sK4
= ( sK14 @ X0 ) )
| ( sK4 != X0 ) )
| ~ spl1_3
| ~ spl1_6 ),
inference(duplicate_literal_removal,[status(thm)],[f654]) ).
thf(f654,plain,
( ! [X0: $i] :
( ( sK4 != X0 )
| ( ( sK14 @ X0 )
= X0 )
| ( sK4
= ( sK14 @ X0 ) )
| ( sK4
= ( sK14 @ X0 ) ) )
| ~ spl1_3
| ~ spl1_6 ),
inference(backward_demodulation,[status(thm)],[f500,f215]) ).
thf(f500,plain,
( ! [X0: $i] :
( ( ( sK14 @ X0 )
= X0 )
| ( sK4
= ( sK14 @ X0 ) )
| ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK14 @ X0 ) )
| ( sK4 != X0 ) )
| ~ spl1_3 ),
inference(equality_proxy_clausification,[status(thm)],[f497]) ).
thf(f497,plain,
( ! [X0: $i] :
( ( ( sK4
= ( sK14 @ X0 ) )
= $true )
| ( ( sK14 @ X0 )
= X0 )
| ( sK4 != X0 )
| ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK14 @ X0 ) ) )
| ~ spl1_3 ),
inference(binary_proxy_clausification,[status(thm)],[f496]) ).
thf(f496,plain,
( ! [X0: $i] :
( ( ( ( ?? @ $i @ sK0 )
& ( sK4
= ( sK14 @ X0 ) ) )
= $true )
| ( ( sK14 @ X0 )
= X0 )
| ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK14 @ X0 ) )
| ( sK4 != X0 ) )
| ~ spl1_3 ),
inference(equality_proxy_clausification,[status(thm)],[f495]) ).
thf(f495,plain,
( ! [X0: $i] :
( ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK14 @ X0 ) )
= $true )
| ( sK4 != X0 )
| ( ( ( ?? @ $i @ sK0 )
& ( sK4
= ( sK14 @ X0 ) ) )
= $true )
| ( ( sK14 @ X0 )
= X0 ) )
| ~ spl1_3 ),
inference(equality_proxy_clausification,[status(thm)],[f494]) ).
thf(f494,plain,
( ! [X0: $i] :
( ( ( X0
= ( sK14 @ X0 ) )
= $true )
| ( ( ( ?? @ $i @ sK0 )
& ( sK4
= ( sK14 @ X0 ) ) )
= $true )
| ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK14 @ X0 ) )
= $true )
| ( sK4 != X0 ) )
| ~ spl1_3 ),
inference(binary_proxy_clausification,[status(thm)],[f492]) ).
thf(f492,plain,
( ! [X0: $i] :
( ( ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK14 @ X0 ) )
& ~ ( ?? @ $i @ sK0 ) )
= $true )
| ( ( X0
= ( sK14 @ X0 ) )
= $true )
| ( ( ( ?? @ $i @ sK0 )
& ( sK4
= ( sK14 @ X0 ) ) )
= $true )
| ( sK4 != X0 ) )
| ~ spl1_3 ),
inference(binary_proxy_clausification,[status(thm)],[f479]) ).
thf(f479,plain,
( ! [X0: $i] :
( ( ( ( ( ?? @ $i @ sK0 )
& ( sK4
= ( sK14 @ X0 ) ) )
| ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK14 @ X0 ) )
& ~ ( ?? @ $i @ sK0 ) ) )
= $true )
| ( ( X0
= ( sK14 @ X0 ) )
= $true )
| ( sK4 != X0 ) )
| ~ spl1_3 ),
inference(binary_proxy_clausification,[status(thm)],[f478]) ).
thf(f478,plain,
( ! [X0: $i] :
( ( ( X0
= ( sK14 @ X0 ) )
!= ( ( ( ?? @ $i @ sK0 )
& ( sK4
= ( sK14 @ X0 ) ) )
| ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK14 @ X0 ) )
& ~ ( ?? @ $i @ sK0 ) ) ) )
| ( sK4 != X0 ) )
| ~ spl1_3 ),
inference(beta_eta_normalization,[status(thm)],[f477]) ).
thf(f477,plain,
( ! [X0: $i] :
( ( ( ^ [Y0: $i] :
( ( ( ?? @ $i @ sK0 )
& ( sK4 = Y0 ) )
| ( ( ( eps
@ ^ [Y1: $i] : $false )
= Y0 )
& ~ ( ?? @ $i @ sK0 ) ) )
@ ( sK14 @ X0 ) )
!= ( X0
= ( sK14 @ X0 ) ) )
| ( sK4 != X0 ) )
| ~ spl1_3 ),
inference(negative_extensionality,[status(thm)],[f448]) ).
thf(f448,plain,
( ! [X0: $i] :
( ( ( (=) @ X0 )
!= ( ^ [Y0: $i] :
( ( ( ?? @ $i @ sK0 )
& ( sK4 = Y0 ) )
| ( ( ( eps
@ ^ [Y1: $i] : $false )
= Y0 )
& ~ ( ?? @ $i @ sK0 ) ) ) ) )
| ( sK4 != X0 ) )
| ~ spl1_3 ),
inference(constrained_superposition,[status(thm)],[f406,f21]) ).
thf(f406,plain,
( ( sK4
!= ( eps
@ ^ [Y0: $i] :
( ( ( ?? @ $i @ sK0 )
& ( sK4 = Y0 ) )
| ( ( ( eps
@ ^ [Y1: $i] : $false )
= Y0 )
& ~ ( ?? @ $i @ sK0 ) ) ) ) )
| ~ spl1_3 ),
inference(backward_demodulation,[status(thm)],[f20,f203]) ).
thf(f203,plain,
( ( sK4
= ( eps @ sK0 ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f201]) ).
thf(f873,plain,
( ~ spl1_21
| ~ spl1_28 ),
inference(avatar_contradiction_clause,[status(thm)],[f872]) ).
thf(f872,plain,
( $false
| ~ spl1_21
| ~ spl1_28 ),
inference(trivial_inequality_removal,[status(thm)],[f871]) ).
thf(f871,plain,
( ( sK4 != sK4 )
| ~ spl1_21
| ~ spl1_28 ),
inference(duplicate_literal_removal,[status(thm)],[f870]) ).
thf(f870,plain,
( ( sK4 != sK4 )
| ( sK4 != sK4 )
| ( sK4 != sK4 )
| ~ spl1_21
| ~ spl1_28 ),
inference(superposition,[status(thm)],[f540,f832]) ).
thf(f832,plain,
( ( sK4
= ( sK14 @ sK4 ) )
| ~ spl1_21 ),
inference(duplicate_literal_removal,[status(thm)],[f831]) ).
thf(f831,plain,
( ( sK4
= ( sK14 @ sK4 ) )
| ( sK4
= ( sK14 @ sK4 ) )
| ~ spl1_21 ),
inference(equality_resolution,[status(thm)],[f512]) ).
thf(f512,plain,
( ! [X0: $i] :
( ( sK4 != X0 )
| ( sK4
= ( sK14 @ X0 ) )
| ( ( sK14 @ X0 )
= X0 ) )
| ~ spl1_21 ),
inference(avatar_component_clause,[status(thm)],[f511]) ).
thf(f540,plain,
( ! [X0: $i] :
( ( sK4
!= ( sK14 @ X0 ) )
| ( ( sK14 @ X0 )
!= X0 )
| ( sK4 != X0 ) )
| ~ spl1_28 ),
inference(avatar_component_clause,[status(thm)],[f539]) ).
thf(f537,plain,
( spl1_26
| spl1_27
| ~ spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f491,f201,f534,f531]) ).
thf(f491,plain,
( ! [X0: $i] :
( ( ( eps
@ ^ [Y0: $i] : $false )
!= ( sK14 @ X0 ) )
| ( sK4 != X0 )
| ( ( sK14 @ X0 )
!= X0 )
| ( ( sK0 @ sK15 )
= $true ) )
| ~ spl1_3 ),
inference(sigma_clausification,[status(thm)],[f490]) ).
thf(f490,plain,
( ! [X0: $i] :
( ( ( eps
@ ^ [Y0: $i] : $false )
!= ( sK14 @ X0 ) )
| ( sK4 != X0 )
| ( ( sK14 @ X0 )
!= X0 )
| ( ( ?? @ $i @ sK0 )
= $true ) )
| ~ spl1_3 ),
inference(not_proxy_clausification,[status(thm)],[f489]) ).
thf(f489,plain,
( ! [X0: $i] :
( ( sK4 != X0 )
| ( ( sK14 @ X0 )
!= X0 )
| ( ( ~ ( ?? @ $i @ sK0 ) )
= $false )
| ( ( eps
@ ^ [Y0: $i] : $false )
!= ( sK14 @ X0 ) ) )
| ~ spl1_3 ),
inference(equality_proxy_clausification,[status(thm)],[f488]) ).
thf(f488,plain,
( ! [X0: $i] :
( ( $false
= ( X0
= ( sK14 @ X0 ) ) )
| ( ( eps
@ ^ [Y0: $i] : $false )
!= ( sK14 @ X0 ) )
| ( sK4 != X0 )
| ( ( ~ ( ?? @ $i @ sK0 ) )
= $false ) )
| ~ spl1_3 ),
inference(equality_proxy_clausification,[status(thm)],[f487]) ).
thf(f487,plain,
( ! [X0: $i] :
( ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK14 @ X0 ) )
= $false )
| ( ( ~ ( ?? @ $i @ sK0 ) )
= $false )
| ( sK4 != X0 )
| ( $false
= ( X0
= ( sK14 @ X0 ) ) ) )
| ~ spl1_3 ),
inference(binary_proxy_clausification,[status(thm)],[f481]) ).
thf(f481,plain,
( ! [X0: $i] :
( ( $false
= ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK14 @ X0 ) )
& ~ ( ?? @ $i @ sK0 ) ) )
| ( sK4 != X0 )
| ( $false
= ( X0
= ( sK14 @ X0 ) ) ) )
| ~ spl1_3 ),
inference(binary_proxy_clausification,[status(thm)],[f480]) ).
thf(f480,plain,
( ! [X0: $i] :
( ( $false
= ( ( ( ?? @ $i @ sK0 )
& ( sK4
= ( sK14 @ X0 ) ) )
| ( ( ( eps
@ ^ [Y0: $i] : $false )
= ( sK14 @ X0 ) )
& ~ ( ?? @ $i @ sK0 ) ) ) )
| ( $false
= ( X0
= ( sK14 @ X0 ) ) )
| ( sK4 != X0 ) )
| ~ spl1_3 ),
inference(binary_proxy_clausification,[status(thm)],[f478]) ).
thf(f405,plain,
( ~ spl1_4
| ~ spl1_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f404]) ).
thf(f404,plain,
( $false
| ~ spl1_4
| ~ spl1_7 ),
inference(trivial_inequality_removal,[status(thm)],[f403]) ).
thf(f403,plain,
( ( $false = $true )
| ~ spl1_4
| ~ spl1_7 ),
inference(forward_demodulation,[status(thm)],[f220,f206]) ).
thf(f220,plain,
( ( ( sK0 @ sK6 )
= $true )
| ~ spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f218]) ).
thf(f218,definition,
( spl1_7
<=> ( ( sK0 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition]) ).
thf(f397,plain,
( ~ spl1_4
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f396]) ).
thf(f396,plain,
( $false
| ~ spl1_4
| ~ spl1_5 ),
inference(trivial_inequality_removal,[status(thm)],[f395]) ).
thf(f395,plain,
( ( $false = $true )
| ~ spl1_4
| ~ spl1_5 ),
inference(forward_demodulation,[status(thm)],[f210,f206]) ).
thf(f210,plain,
( ( ( sK0 @ sK4 )
= $true )
| ~ spl1_5 ),
inference(avatar_component_clause,[status(thm)],[f208]) ).
thf(f208,definition,
( spl1_5
<=> ( ( sK0 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition]) ).
thf(f387,plain,
( spl1_3
| ~ spl1_4
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f386]) ).
thf(f386,plain,
( $false
| spl1_3
| ~ spl1_4
| ~ spl1_6 ),
inference(subsumption_resolution,[status(thm)],[f385,f206]) ).
thf(f385,plain,
( ( ( sK0 @ sK13 )
!= $false )
| spl1_3
| ~ spl1_6 ),
inference(beta_eta_normalization,[status(thm)],[f384]) ).
thf(f384,plain,
( ( ( sK0 @ sK13 )
!= ( ^ [Y0: $i] : $false
@ sK13 ) )
| spl1_3
| ~ spl1_6 ),
inference(negative_extensionality,[status(thm)],[f374]) ).
thf(f374,plain,
( ( ( ^ [Y0: $i] : $false )
!= sK0 )
| spl1_3
| ~ spl1_6 ),
inference(trivial_inequality_removal,[status(thm)],[f369]) ).
thf(f369,plain,
( ( ( ^ [Y0: $i] : $false )
!= sK0 )
| ( sK4 != sK4 )
| spl1_3
| ~ spl1_6 ),
inference(constrained_superposition,[status(thm)],[f202,f215]) ).
thf(f202,plain,
( ( sK4
!= ( eps @ sK0 ) )
| spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f201]) ).
thf(f222,plain,
( spl1_7
| spl1_5
| spl1_6 ),
inference(avatar_split_clause,[status(thm)],[f190,f213,f208,f218]) ).
thf(f190,plain,
( ( ( sK0 @ sK6 )
= $true )
| ( ( sK0 @ sK4 )
= $true )
| ( ( eps
@ ^ [Y0: $i] : $false )
= sK4 ) ),
inference(equality_proxy_clausification,[status(thm)],[f189]) ).
thf(f189,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( ( sK0 @ sK6 )
= $true )
| ( ( ( eps
@ ^ [Y0: $i] : $false )
= sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f187]) ).
thf(f187,plain,
( ( ( ( ( eps
@ ^ [Y0: $i] : $false )
= sK4 )
& ~ ( ?? @ $i @ sK0 ) )
= $true )
| ( ( sK0 @ sK6 )
= $true )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f186]) ).
thf(f186,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( ( ?? @ $i @ sK0 )
= $true )
| ( ( ( ( eps
@ ^ [Y0: $i] : $false )
= sK4 )
& ~ ( ?? @ $i @ sK0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f184]) ).
thf(f184,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= sK4 ) )
= $true )
| ( ( ( ( eps
@ ^ [Y0: $i] : $false )
= sK4 )
& ~ ( ?? @ $i @ sK0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f173]) ).
thf(f173,plain,
( ( ( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= sK4 ) )
| ( ( ( eps
@ ^ [Y0: $i] : $false )
= sK4 )
& ~ ( ?? @ $i @ sK0 ) ) )
= $true )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f172]) ).
thf(f172,plain,
( ( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= sK4 ) )
| ( ( ( eps
@ ^ [Y0: $i] : $false )
= sK4 )
& ~ ( ?? @ $i @ sK0 ) ) )
!= ( sK0 @ sK4 ) ),
inference(beta_eta_normalization,[status(thm)],[f171]) ).
thf(f171,plain,
( ( ^ [Y0: $i] :
( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= Y0 ) )
| ( ( ( eps
@ ^ [Y1: $i] : $false )
= Y0 )
& ~ ( ?? @ $i @ sK0 ) ) )
@ sK4 )
!= ( sK0 @ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ^ [Y0: $i] :
( ( ( ?? @ $i @ sK0 )
& ( ( eps @ sK0 )
= Y0 ) )
| ( ( ( eps
@ ^ [Y1: $i] : $false )
= Y0 )
& ~ ( ?? @ $i @ sK0 ) ) ) )
!= sK0 ),
inference(equality_resolution,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO556^1 : TPTP v9.2.1. Released v5.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n029.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 14:33:59 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SYO556^1 : TPTP v9.2.1. Released v5.2.0.
% 0.29/0.46 % Domain : Syntactic
% 0.29/0.46 % Problem : Relationship between if-then-else and choice on $
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro11] Brown (2011), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro11]
% 0.29/0.46 % Names : CHOICE28 [Bro11]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v6.0.0, 0.71 v5.5.0, 0.67 v5.4.0, 0.80 v5.2.0
% 0.29/0.46 % Syntax : Number of formulae : 5 ( 2 unt; 2 typ; 1 def)
% 0.29/0.46 % Number of atoms : 5 ( 4 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.29/0.46 % Number of connectives : 16 ( 1 ~; 1 |; 2 &; 11 @)
% 0.29/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 5 ( 3 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 4 ( 2 usr; 1 con; 0-3 aty)
% 0.29/0.46 % Number of variables : 9 ( 5 ^; 2 !; 2 ?; 9 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : A choice operator eps on $i is assumed. if-then-else on $i is
% 0.29/0.46 % defined using eps. eps satisfies the following equation:
% 0.29/0.46 % eps P = if (P nonempty) (eps P) (eps emptypred)
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(eps,type,
% 0.29/0.46 eps: ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(choiceax,axiom,
% 0.29/0.46 ! [P: $i > $o] :
% 0.29/0.46 ( ? [X: $i] : ( P @ X )
% 0.29/0.46 => ( P @ ( eps @ P ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(if,type,
% 0.29/0.46 if: $o > $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(ifd,definition,
% 0.29/0.46 ( if
% 0.29/0.46 = ( ^ [B: $o,X: $i,Y: $i] :
% 0.29/0.46 ( eps
% 0.29/0.46 @ ^ [Z: $i] :
% 0.29/0.46 ( ( B
% 0.29/0.46 & ( Z = X ) )
% 0.29/0.46 | ( ~ B
% 0.29/0.46 & ( Z = Y ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(conj,conjecture,
% 0.29/0.46 ! [P: $i > $o] :
% 0.29/0.46 ( ( eps @ P )
% 0.29/0.46 = ( if
% 0.29/0.46 @ ? [X: $i] : ( P @ X )
% 0.29/0.46 @ ( eps @ P )
% 0.29/0.46 @ ( eps
% 0.29/0.46 @ ^ [X: $i] : $false ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.47/1.25 ---- Embedded in THF ---
% 1.47/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.25 %%% Generated on Tue Feb 24 14:34:00 EST 2026
% 1.47/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.25 %%% Logic specification used:
% 1.47/1.25 %%% thf(spec, logic, $$dhol).
% 1.47/1.25
% 1.47/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.jUTSiai7C0/DTF2DTF27531.p
% See solution above
% 1.47/1.25 ------------------------
% 1.47/1.26 ---- Cleaned THF ---
% 1.47/1.26 thf(eps,type,
% 1.47/1.26 eps: ( $i > $o ) > $i ).
% 1.47/1.26
% 1.47/1.26 thf(choiceax,axiom,
% 1.47/1.26 ! [P: $i > $o] :
% 1.47/1.26 ( ? [X: $i] : ( P @ X )
% 1.47/1.26 => ( P @ ( eps @ P ) ) ) ).
% 1.47/1.26
% 1.47/1.26 thf(if,type,
% 1.47/1.26 if: $o > $i > $i > $i ).
% 1.47/1.26
% 1.47/1.26 thf(ifd,definition,
% 1.47/1.26 ( if
% 1.47/1.26 = ( ^ [B: $o,X: $i,Y: $i] :
% 1.47/1.26 ( eps
% 1.47/1.26 @ ^ [Z: $i] :
% 1.47/1.26 ( ( B
% 1.47/1.26 & ( Z = X ) )
% 1.47/1.26 | ( ~ B
% 1.47/1.26 & ( Z = Y ) ) ) ) ) ) ).
% 1.47/1.26
% 1.47/1.26 thf(conj,conjecture,
% 1.47/1.26 ! [P: $i > $o] :
% 1.47/1.26 ( ( eps @ P )
% 1.47/1.26 = ( if
% 1.47/1.26 @ ? [X: $i] : ( P @ X )
% 1.47/1.26 @ ( eps @ P )
% 1.47/1.26 @ ( eps
% 1.47/1.26 @ ^ [X: $i] : $false ) ) ) ).
% 1.47/1.26 ------------------------
% 1.47/1.27 % (27813)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_27531 for (2999ds/4Mi)
% 1.47/1.27 % (27812)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/183Mi)
% 1.47/1.27 % (27813)Instruction limit reached!
% 1.47/1.27 % (27813)------------------------------
% 1.47/1.27 % (27813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.27 % (27813)Termination reason: Unknown
% 1.47/1.27 % (27813)Termination phase: Saturation
% 1.47/1.27
% 1.47/1.27 % (27813)Memory used [KB]: 5500
% 1.47/1.27 % (27813)Time elapsed: 0.004 s
% 1.47/1.27 % (27813)Instructions burned: 6 (million)
% 1.47/1.27 % (27813)------------------------------
% 1.47/1.27 % (27813)------------------------------
% 1.47/1.28 % (27814)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_27531 for (2999ds/27Mi)
% 1.47/1.28 % (27815)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/2Mi)
% 1.47/1.28 % (27816)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_27531 for (2999ds/2Mi)
% 1.47/1.28 % (27817)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_27531 for (2999ds/275Mi)
% 1.47/1.28 % (27818)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/18Mi)
% 1.47/1.28 % (27816)Instruction limit reached!
% 1.47/1.28 % (27816)------------------------------
% 1.47/1.28 % (27816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (27816)Termination reason: Unknown
% 1.47/1.28 % (27816)Termination phase: Preprocessing 3
% 1.47/1.28
% 1.47/1.28 % (27816)Memory used [KB]: 895
% 1.47/1.28 % (27816)Time elapsed: 0.003 s
% 1.47/1.28 % (27816)Instructions burned: 2 (million)
% 1.47/1.28 % (27816)------------------------------
% 1.47/1.28 % (27816)------------------------------
% 1.47/1.28 % (27817)Refutation not found, incomplete strategy
% 1.47/1.28 % (27817)------------------------------
% 1.47/1.28 % (27817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (27815)Instruction limit reached!
% 1.47/1.28 % (27815)------------------------------
% 1.47/1.28 % (27815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (27815)Termination reason: Unknown
% 1.47/1.28 % (27817)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.28
% 1.47/1.28
% 1.47/1.28 % (27815)Termination phase: Saturation
% 1.47/1.28
% 1.47/1.28 % (27817)Memory used [KB]: 5500
% 1.47/1.28 % (27815)Memory used [KB]: 5500
% 1.47/1.28 % (27817)Time elapsed: 0.003 s
% 1.47/1.28 % (27815)Time elapsed: 0.004 s
% 1.47/1.28 % (27817)Instructions burned: 2 (million)
% 1.47/1.28 % (27815)Instructions burned: 2 (million)
% 1.47/1.28 % (27817)------------------------------
% 1.47/1.28 % (27817)------------------------------
% 1.47/1.28 % (27815)------------------------------
% 1.47/1.28 % (27815)------------------------------
% 1.47/1.28 % (27819)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/3Mi)
% 1.47/1.28 % (27819)Instruction limit reached!
% 1.47/1.28 % (27819)------------------------------
% 1.47/1.28 % (27819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (27819)Termination reason: Unknown
% 1.47/1.28 % (27819)Termination phase: Saturation
% 1.47/1.28
% 1.47/1.28 % (27819)Memory used [KB]: 5500
% 1.47/1.28 % (27819)Time elapsed: 0.002 s
% 1.47/1.28 % (27819)Instructions burned: 3 (million)
% 1.47/1.28 % (27819)------------------------------
% 1.47/1.28 % (27819)------------------------------
% 1.47/1.29 % (27814)Refutation not found, incomplete strategy
% 1.47/1.29 % (27814)------------------------------
% 1.47/1.29 % (27814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (27814)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.29
% 1.47/1.29
% 1.47/1.29 % (27814)Memory used [KB]: 5500
% 1.47/1.29 % (27814)Time elapsed: 0.011 s
% 1.47/1.29 % (27814)Instructions burned: 15 (million)
% 1.47/1.29 % (27814)------------------------------
% 1.47/1.29 % (27814)------------------------------
% 1.47/1.29 % (27818)Instruction limit reached!
% 1.47/1.29 % (27818)------------------------------
% 1.47/1.29 % (27818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (27818)Termination reason: Unknown
% 1.47/1.29 % (27818)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (27818)Memory used [KB]: 5628
% 1.47/1.29 % (27818)Time elapsed: 0.014 s
% 1.47/1.29 % (27818)Instructions burned: 18 (million)
% 1.47/1.29 % (27818)------------------------------
% 1.47/1.29 % (27818)------------------------------
% 1.47/1.29 % (27823)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/1041Mi)
% 1.58/1.30 % (27820)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_27531 for (2999ds/37Mi)
% 1.58/1.30 % (27821)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/15Mi)
% 1.58/1.30 % (27822)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_27531 for (2999ds/3Mi)
% 1.58/1.30 % (27823)Refutation not found, incomplete strategy
% 1.58/1.30 % (27823)------------------------------
% 1.58/1.30 % (27823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.30 % (27823)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.30
% 1.58/1.30
% 1.58/1.30 % (27823)Memory used [KB]: 5628
% 1.58/1.30 % (27823)Time elapsed: 0.007 s
% 1.58/1.30 % (27823)Instructions burned: 18 (million)
% 1.58/1.30 % (27823)------------------------------
% 1.58/1.30 % (27823)------------------------------
% 1.58/1.30 % (27821)Refutation not found, incomplete strategy
% 1.58/1.30 % (27821)------------------------------
% 1.58/1.30 % (27821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.30 % (27821)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.30
% 1.58/1.30
% 1.58/1.30 % (27821)Memory used [KB]: 5500
% 1.58/1.30 % (27821)Time elapsed: 0.003 s
% 1.58/1.30 % (27821)Instructions burned: 2 (million)
% 1.58/1.30 % (27821)------------------------------
% 1.58/1.30 % (27821)------------------------------
% 1.58/1.30 % (27822)Refutation not found, incomplete strategy
% 1.58/1.30 % (27822)------------------------------
% 1.58/1.30 % (27822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.30 % (27822)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.30
% 1.58/1.30
% 1.58/1.30 % (27822)Memory used [KB]: 5500
% 1.58/1.30 % (27822)Time elapsed: 0.004 s
% 1.58/1.30 % (27822)Instructions burned: 2 (million)
% 1.58/1.30 % (27822)------------------------------
% 1.58/1.30 % (27822)------------------------------
% 1.58/1.31 % (27824)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/7Mi)
% 1.58/1.31 % (27825)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/16Mi)
% 1.58/1.31 % (27824)Instruction limit reached!
% 1.58/1.31 % (27824)------------------------------
% 1.58/1.31 % (27824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (27824)Termination reason: Unknown
% 1.58/1.31 % (27824)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (27824)Memory used [KB]: 1023
% 1.58/1.31 % (27824)Time elapsed: 0.005 s
% 1.58/1.31 % (27824)Instructions burned: 9 (million)
% 1.58/1.31 % (27824)------------------------------
% 1.58/1.31 % (27824)------------------------------
% 1.58/1.31 % (27826)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/3Mi)
% 1.58/1.31 % (27826)Instruction limit reached!
% 1.58/1.31 % (27826)------------------------------
% 1.58/1.31 % (27826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (27826)Termination reason: Unknown
% 1.58/1.31 % (27826)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (27826)Memory used [KB]: 5500
% 1.58/1.31 % (27826)Time elapsed: 0.002 s
% 1.58/1.31 % (27826)Instructions burned: 3 (million)
% 1.58/1.31 % (27826)------------------------------
% 1.58/1.31 % (27826)------------------------------
% 1.58/1.32 % (27827)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/3Mi)
% 1.58/1.32 % (27820)Instruction limit reached!
% 1.58/1.32 % (27820)------------------------------
% 1.58/1.32 % (27820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (27820)Termination reason: Unknown
% 1.58/1.32 % (27820)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (27820)Memory used [KB]: 5756
% 1.58/1.32 % (27820)Time elapsed: 0.023 s
% 1.58/1.32 % (27820)Instructions burned: 37 (million)
% 1.58/1.32 % (27820)------------------------------
% 1.58/1.32 % (27820)------------------------------
% 1.58/1.32 % (27828)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/7Mi)
% 1.58/1.32 % (27829)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/3Mi)
% 1.58/1.32 % (27825)Instruction limit reached!
% 1.58/1.32 % (27825)------------------------------
% 1.58/1.32 % (27825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (27825)Termination reason: Unknown
% 1.58/1.32 % (27825)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (27825)Memory used [KB]: 5756
% 1.58/1.32 % (27825)Time elapsed: 0.013 s
% 1.58/1.32 % (27825)Instructions burned: 16 (million)
% 1.58/1.32 % (27825)------------------------------
% 1.58/1.32 % (27825)------------------------------
% 1.58/1.32 % (27830)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/4Mi)
% 1.58/1.32 % (27827)Instruction limit reached!
% 1.58/1.32 % (27827)------------------------------
% 1.58/1.32 % (27827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (27827)Termination reason: Unknown
% 1.58/1.32 % (27827)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (27827)Memory used [KB]: 1023
% 1.58/1.32 % (27827)Time elapsed: 0.004 s
% 1.58/1.32 % (27827)Instructions burned: 4 (million)
% 1.58/1.32 % (27827)------------------------------
% 1.58/1.32 % (27827)------------------------------
% 1.58/1.32 % (27829)Instruction limit reached!
% 1.58/1.32 % (27829)------------------------------
% 1.58/1.32 % (27829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (27829)Termination reason: Unknown
% 1.58/1.32 % (27829)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (27829)Memory used [KB]: 5500
% 1.58/1.32 % (27829)Time elapsed: 0.003 s
% 1.58/1.32 % (27829)Instructions burned: 5 (million)
% 1.58/1.32 % (27829)------------------------------
% 1.58/1.32 % (27829)------------------------------
% 1.58/1.32 % (27830)Instruction limit reached!
% 1.58/1.32 % (27830)------------------------------
% 1.58/1.32 % (27830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (27830)Termination reason: Unknown
% 1.58/1.32 % (27830)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (27830)Memory used [KB]: 5500
% 1.58/1.32 % (27830)Time elapsed: 0.003 s
% 1.58/1.32 % (27830)Instructions burned: 6 (million)
% 1.58/1.32 % (27830)------------------------------
% 1.58/1.32 % (27830)------------------------------
% 1.58/1.32 % (27828)Instruction limit reached!
% 1.58/1.32 % (27828)------------------------------
% 1.58/1.32 % (27828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (27828)Termination reason: Unknown
% 1.58/1.32 % (27828)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (27828)Memory used [KB]: 5500
% 1.58/1.32 % (27828)Time elapsed: 0.007 s
% 1.58/1.32 % (27828)Instructions burned: 8 (million)
% 1.58/1.32 % (27828)------------------------------
% 1.58/1.32 % (27828)------------------------------
% 1.58/1.33 % (27834)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/902Mi)
% 1.58/1.33 % (27835)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/21Mi)
% 1.58/1.33 % (27834)Refutation not found, incomplete strategy
% 1.58/1.33 % (27834)------------------------------
% 1.58/1.33 % (27834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (27834)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.33
% 1.58/1.33
% 1.58/1.33 % (27834)Memory used [KB]: 5500
% 1.58/1.33 % (27834)Time elapsed: 0.002 s
% 1.58/1.33 % (27834)Instructions burned: 1 (million)
% 1.58/1.33 % (27834)------------------------------
% 1.58/1.33 % (27834)------------------------------
% 1.58/1.33 % (27812)Instruction limit reached!
% 1.58/1.33 % (27812)------------------------------
% 1.58/1.33 % (27812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (27812)Termination reason: Unknown
% 1.58/1.33 % (27812)Termination phase: Saturation
% 1.58/1.33
% 1.58/1.33 % (27812)Memory used [KB]: 6396
% 1.58/1.33 % (27812)Time elapsed: 0.065 s
% 1.58/1.33 % (27812)Instructions burned: 184 (million)
% 1.58/1.33 % (27812)------------------------------
% 1.58/1.33 % (27812)------------------------------
% 1.58/1.34 % (27831)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/18Mi)
% 1.58/1.34 % (27832)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/710Mi)
% 1.58/1.34 % (27833)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/6Mi)
% 1.58/1.34 % (27835)Instruction limit reached!
% 1.58/1.34 % (27835)------------------------------
% 1.58/1.34 % (27835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (27835)Termination reason: Unknown
% 1.58/1.34 % (27835)Termination phase: Saturation
% 1.58/1.34
% 1.58/1.34 % (27835)Memory used [KB]: 5628
% 1.58/1.34 % (27835)Time elapsed: 0.009 s
% 1.58/1.34 % (27835)Instructions burned: 22 (million)
% 1.58/1.34 % (27835)------------------------------
% 1.58/1.34 % (27835)------------------------------
% 1.58/1.34 % (27836)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/5Mi)
% 1.58/1.34 % (27833)Instruction limit reached!
% 1.58/1.34 % (27833)------------------------------
% 1.58/1.34 % (27833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (27833)Termination reason: Unknown
% 1.58/1.34 % (27833)Termination phase: Saturation
% 1.58/1.34
% 1.58/1.34 % (27833)Memory used [KB]: 5500
% 1.58/1.34 % (27833)Time elapsed: 0.006 s
% 1.58/1.34 % (27833)Instructions burned: 7 (million)
% 1.58/1.34 % (27833)------------------------------
% 1.58/1.34 % (27833)------------------------------
% 1.58/1.34 % (27831)Refutation not found, incomplete strategy
% 1.58/1.34 % (27831)------------------------------
% 1.58/1.34 % (27831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (27831)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.34
% 1.58/1.34
% 1.58/1.34 % (27831)Memory used [KB]: 5500
% 1.58/1.34 % (27831)Time elapsed: 0.007 s
% 1.58/1.34 % (27831)Instructions burned: 7 (million)
% 1.58/1.34 % (27831)------------------------------
% 1.58/1.34 % (27831)------------------------------
% 1.58/1.34 % (27837)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/6Mi)
% 1.58/1.34 % (27837)Refutation not found, incomplete strategy
% 1.58/1.34 % (27837)------------------------------
% 1.58/1.34 % (27837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (27837)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.34
% 1.58/1.34
% 1.58/1.34 % (27837)Memory used [KB]: 5500
% 1.58/1.34 % (27837)Time elapsed: 0.002 s
% 1.58/1.34 % (27837)Instructions burned: 2 (million)
% 1.58/1.34 % (27837)------------------------------
% 1.58/1.34 % (27837)------------------------------
% 1.58/1.34 % (27836)Instruction limit reached!
% 1.58/1.34 % (27836)------------------------------
% 1.58/1.34 % (27836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (27836)Termination reason: Unknown
% 1.58/1.34 % (27836)Termination phase: Saturation
% 1.58/1.34
% 1.58/1.34 % (27836)Memory used [KB]: 5500
% 1.58/1.34 % (27836)Time elapsed: 0.005 s
% 1.58/1.34 % (27836)Instructions burned: 5 (million)
% 1.58/1.34 % (27836)------------------------------
% 1.58/1.34 % (27836)------------------------------
% 1.58/1.34 % (27838)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/377Mi)
% 1.58/1.35 % (27839)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/779Mi)
% 1.58/1.35 % (27839)Refutation not found, incomplete strategy
% 1.58/1.35 % (27839)------------------------------
% 1.58/1.35 % (27839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.35 % (27839)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.35
% 1.58/1.35
% 1.58/1.35 % (27839)Memory used [KB]: 5500
% 1.58/1.35 % (27839)Time elapsed: 0.002 s
% 1.58/1.35 % (27839)Instructions burned: 4 (million)
% 1.58/1.35 % (27839)------------------------------
% 1.58/1.35 % (27839)------------------------------
% 1.58/1.35 % (27842)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/17Mi)
% 1.58/1.36 % (27840)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/19Mi)
% 1.58/1.36 % (27840)Refutation not found, incomplete strategy
% 1.58/1.36 % (27840)------------------------------
% 1.58/1.36 % (27840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.36 % (27840)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.36
% 1.58/1.36
% 1.58/1.36 % (27840)Memory used [KB]: 5500
% 1.58/1.36 % (27840)Time elapsed: 0.002 s
% 1.58/1.36 % (27840)Instructions burned: 1 (million)
% 1.58/1.36 % (27840)------------------------------
% 1.58/1.36 % (27840)------------------------------
% 1.58/1.36 % (27844)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/30Mi)
% 1.58/1.36 % (27841)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/879Mi)
% 1.58/1.36 % (27842)Instruction limit reached!
% 1.58/1.36 % (27842)------------------------------
% 1.58/1.36 % (27842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.36 % (27842)Termination reason: Unknown
% 1.58/1.36 % (27842)Termination phase: Saturation
% 1.58/1.36
% 1.58/1.36 % (27842)Memory used [KB]: 5628
% 1.58/1.36 % (27842)Time elapsed: 0.009 s
% 1.58/1.36 % (27842)Instructions burned: 19 (million)
% 1.58/1.36 % (27842)------------------------------
% 1.58/1.36 % (27842)------------------------------
% 1.58/1.36 % (27843)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/3Mi)
% 1.58/1.36 % (27841)Refutation not found, incomplete strategy
% 1.58/1.36 % (27841)------------------------------
% 1.58/1.36 % (27841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.36 % (27841)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.36
% 1.58/1.36
% 1.58/1.36 % (27841)Memory used [KB]: 5500
% 1.58/1.36 % (27841)Time elapsed: 0.005 s
% 1.58/1.36 % (27841)Instructions burned: 5 (million)
% 1.58/1.36 % (27841)------------------------------
% 1.58/1.36 % (27841)------------------------------
% 1.58/1.36 % (27843)Instruction limit reached!
% 1.58/1.36 % (27843)------------------------------
% 1.58/1.36 % (27843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.36 % (27843)Termination reason: Unknown
% 1.58/1.36 % (27843)Termination phase: Saturation
% 1.58/1.36
% 1.58/1.36 % (27843)Memory used [KB]: 1023
% 1.58/1.36 % (27843)Time elapsed: 0.004 s
% 1.58/1.36 % (27843)Instructions burned: 3 (million)
% 1.58/1.36 % (27843)------------------------------
% 1.58/1.36 % (27843)------------------------------
% 1.58/1.36 % (27844)Refutation not found, incomplete strategy
% 1.58/1.36 % (27844)------------------------------
% 1.58/1.36 % (27844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.36 % (27844)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.36
% 1.58/1.36
% 1.58/1.36 % (27844)Memory used [KB]: 5500
% 1.58/1.36 % (27844)Time elapsed: 0.005 s
% 1.58/1.36 % (27844)Instructions burned: 12 (million)
% 1.58/1.36 % (27844)------------------------------
% 1.58/1.36 % (27844)------------------------------
% 1.58/1.37 % (27845)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/127Mi)
% 1.58/1.37 % (27846)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/100Mi)
% 1.58/1.37 % (27846)Refutation not found, incomplete strategy
% 1.58/1.37 % (27846)------------------------------
% 1.58/1.37 % (27846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.37 % (27846)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.37
% 1.58/1.37
% 1.58/1.37 % (27846)Memory used [KB]: 5500
% 1.58/1.37 % (27846)Time elapsed: 0.002 s
% 1.58/1.37 % (27846)Instructions burned: 1 (million)
% 1.58/1.37 % (27846)------------------------------
% 1.58/1.37 % (27846)------------------------------
% 1.58/1.37 % (27849)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/86Mi)
% 1.58/1.37 % (27849)Refutation not found, incomplete strategy
% 1.58/1.37 % (27849)------------------------------
% 1.58/1.37 % (27849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.37 % (27849)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.37
% 1.58/1.37
% 1.58/1.37 % (27849)Memory used [KB]: 5500
% 1.58/1.37 % (27849)Time elapsed: 0.003 s
% 1.58/1.37 % (27849)Instructions burned: 5 (million)
% 1.58/1.37 % (27849)------------------------------
% 1.58/1.37 % (27849)------------------------------
% 1.58/1.38 % (27847)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/3Mi)
% 1.58/1.38 % (27848)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/20Mi)
% 1.58/1.38 % (27847)Instruction limit reached!
% 1.58/1.38 % (27847)------------------------------
% 1.58/1.38 % (27847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.38 % (27847)Termination reason: Unknown
% 1.58/1.38 % (27847)Termination phase: Saturation
% 1.58/1.38
% 1.58/1.38 % (27847)Memory used [KB]: 5500
% 1.58/1.38 % (27847)Time elapsed: 0.003 s
% 1.58/1.38 % (27847)Instructions burned: 4 (million)
% 1.58/1.38 % (27847)------------------------------
% 1.58/1.38 % (27847)------------------------------
% 1.58/1.38 % (27850)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/107Mi)
% 1.58/1.38 % (27848)Refutation not found, incomplete strategy
% 1.58/1.38 % (27848)------------------------------
% 1.58/1.38 % (27848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.38 % (27848)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.38
% 1.58/1.38
% 1.58/1.38 % (27848)Memory used [KB]: 5500
% 1.58/1.38 % (27848)Time elapsed: 0.005 s
% 1.58/1.38 % (27848)Instructions burned: 7 (million)
% 1.58/1.38 % (27848)------------------------------
% 1.58/1.38 % (27848)------------------------------
% 1.58/1.38 % (27850)Refutation not found, incomplete strategy
% 1.58/1.38 % (27850)------------------------------
% 1.58/1.38 % (27850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.38 % (27850)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.38
% 1.58/1.38
% 1.58/1.38 % (27850)Memory used [KB]: 5500
% 1.58/1.38 % (27850)Time elapsed: 0.002 s
% 1.58/1.38 % (27850)Instructions burned: 1 (million)
% 1.58/1.38 % (27850)------------------------------
% 1.58/1.38 % (27850)------------------------------
% 1.58/1.38 % (27851)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_27531 for (2999ds/39Mi)
% 1.58/1.39 % (27852)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_27531 for (2998ds/448Mi)
% 1.58/1.39 % (27852)Refutation not found, incomplete strategy
% 1.58/1.39 % (27852)------------------------------
% 1.58/1.39 % (27852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.39 % (27852)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.39
% 1.58/1.39
% 1.58/1.39 % (27852)Memory used [KB]: 5500
% 1.58/1.39 % (27852)Time elapsed: 0.002 s
% 1.58/1.39 % (27852)Instructions burned: 1 (million)
% 1.58/1.39 % (27852)------------------------------
% 1.58/1.39 % (27852)------------------------------
% 1.58/1.39 % (27853)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_27531 for (2998ds/46Mi)
% 1.58/1.39 % (27854)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_27531 for (2998ds/98Mi)
% 1.58/1.40 % (27854)Refutation not found, incomplete strategy
% 1.58/1.40 % (27854)------------------------------
% 1.58/1.40 % (27854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.40 % (27854)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.40
% 1.58/1.40
% 1.58/1.40 % (27854)Memory used [KB]: 1023
% 1.58/1.40 % (27854)Time elapsed: 0.003 s
% 1.58/1.40 % (27854)Instructions burned: 3 (million)
% 1.58/1.40 % (27854)------------------------------
% 1.58/1.40 % (27854)------------------------------
% 1.58/1.40 % (27851)Instruction limit reached!
% 1.58/1.40 % (27851)------------------------------
% 1.58/1.40 % (27851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.40 % (27851)Termination reason: Unknown
% 1.58/1.40 % (27851)Termination phase: Saturation
% 1.58/1.40
% 1.58/1.40 % (27851)Memory used [KB]: 5756
% 1.58/1.40 % (27851)Time elapsed: 0.034 s
% 1.58/1.40 % (27851)Instructions burned: 42 (million)
% 1.58/1.40 % (27851)------------------------------
% 1.58/1.40 % (27851)------------------------------
% 1.58/1.40 % (27855)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_27531 for (2998ds/507Mi)
% 1.58/1.40 % (27855)Refutation not found, incomplete strategy
% 1.58/1.40 % (27855)------------------------------
% 1.58/1.40 % (27855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.40 % (27855)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.40
% 1.58/1.40
% 1.58/1.40 % (27855)Memory used [KB]: 5500
% 1.58/1.40 % (27855)Time elapsed: 0.003 s
% 1.58/1.40 % (27855)Instructions burned: 4 (million)
% 1.58/1.40 % (27855)------------------------------
% 1.58/1.40 % (27855)------------------------------
% 1.58/1.41 % (27857)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_27531 for (2998ds/39Mi)
% 1.58/1.41 % (27856)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_27531 for (2998ds/149Mi)
% 1.58/1.41 % (27853)Instruction limit reached!
% 1.58/1.41 % (27853)------------------------------
% 1.58/1.41 % (27853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.41 % (27853)Termination reason: Unknown
% 1.58/1.41 % (27853)Termination phase: Saturation
% 1.58/1.41
% 1.58/1.41 % (27853)Memory used [KB]: 5756
% 1.58/1.41 % (27853)Time elapsed: 0.018 s
% 1.58/1.41 % (27853)Instructions burned: 47 (million)
% 1.58/1.41 % (27853)------------------------------
% 1.58/1.41 % (27853)------------------------------
% 1.58/1.41 % (27858)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_27531 for (2998ds/6Mi)
% 1.58/1.41 % (27858)Instruction limit reached!
% 1.58/1.41 % (27858)------------------------------
% 1.58/1.41 % (27858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.41 % (27858)Termination reason: Unknown
% 1.58/1.41 % (27858)Termination phase: Saturation
% 1.58/1.41
% 1.58/1.41 % (27858)Memory used [KB]: 10106
% 1.58/1.41 % (27858)Time elapsed: 0.005 s
% 1.58/1.41 % (27858)Instructions burned: 9 (million)
% 1.58/1.41 % (27858)------------------------------
% 1.58/1.41 % (27858)------------------------------
% 1.58/1.42 % (27845)Instruction limit reached!
% 1.58/1.42 % (27845)------------------------------
% 1.58/1.42 % (27845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.42 % (27845)Termination reason: Unknown
% 1.58/1.42 % (27845)Termination phase: Saturation
% 1.58/1.42
% 1.58/1.42 % (27845)Memory used [KB]: 6012
% 1.58/1.42 % (27845)Time elapsed: 0.048 s
% 1.58/1.42 % (27845)Instructions burned: 127 (million)
% 1.58/1.42 % (27845)------------------------------
% 1.58/1.42 % (27845)------------------------------
% 1.58/1.42 % (27857)Instruction limit reached!
% 1.58/1.42 % (27857)------------------------------
% 1.58/1.42 % (27857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.42 % (27857)Termination reason: Unknown
% 1.58/1.42 % (27857)Termination phase: Saturation
% 1.58/1.42
% 1.58/1.42 % (27857)Memory used [KB]: 5628
% 1.58/1.42 % (27857)Time elapsed: 0.014 s
% 1.58/1.42 % (27857)Instructions burned: 42 (million)
% 1.58/1.42 % (27857)------------------------------
% 1.58/1.42 % (27857)------------------------------
% 1.58/1.42 % (27859)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_27531 for (2998ds/1087Mi)
% 1.58/1.42 % (27859)Refutation not found, incomplete strategy
% 1.58/1.42 % (27859)------------------------------
% 1.58/1.42 % (27859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.42 % (27859)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.42
% 1.58/1.42
% 1.58/1.42 % (27859)Memory used [KB]: 5500
% 1.58/1.42 % (27859)Time elapsed: 0.003 s
% 1.58/1.42 % (27859)Instructions burned: 3 (million)
% 1.58/1.42 % (27859)------------------------------
% 1.58/1.42 % (27859)------------------------------
% 1.58/1.42 % (27860)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_27531 for (2998ds/47Mi)
% 1.58/1.43 % (27832)First to succeed.
% 1.58/1.43 % (27861)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_27531 for (2998ds/44Mi)
% 1.58/1.43 % (27862)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_27531 for (2998ds/432Mi)
% 1.58/1.43 % (27861)Refutation not found, incomplete strategy
% 1.58/1.43 % (27861)------------------------------
% 1.58/1.43 % (27861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.43 % (27861)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.43
% 1.58/1.43
% 1.58/1.43 % (27861)Memory used [KB]: 1023
% 1.58/1.43 % (27861)Time elapsed: 0.002 s
% 1.58/1.43 % (27861)Instructions burned: 1 (million)
% 1.58/1.43 % (27861)------------------------------
% 1.58/1.43 % (27861)------------------------------
% 1.58/1.43 % (27832)Refutation found. Thanks to Tanya!
% 1.58/1.43 % SZS status Theorem for DTF2THF_27531
% 1.58/1.43 % SZS output start Proof for DTF2THF_27531
% 1.58/1.43 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.58/1.43 thf(func_def_2, type, if: $o > $i > $i > $i).
% 1.58/1.43 thf(func_def_15, type, sK0: $i > $o).
% 1.58/1.43 thf(func_def_17, type, ph2: !>[X0: $tType]:(X0)).
% 1.58/1.43 thf(func_def_18, type, sK3: $i > $i > $i).
% 1.58/1.43 thf(func_def_22, type, sK7: $i > ($i > $o) > $i).
% 1.58/1.43 thf(func_def_23, type, sK8: $i > $i).
% 1.58/1.43 thf(func_def_27, type, sK12: $i > $i).
% 1.58/1.43 thf(func_def_29, type, sK14: $i > $i).
% 1.58/1.43 thf(func_def_33, type, sK18: $i > $i).
% 1.58/1.43 thf(func_def_37, type, sK22: $i > $i).
% 1.58/1.43 thf(func_def_41, type, sK26: $i > $i).
% 1.58/1.43 thf(func_def_43, type, sK28: $i > $i).
% 1.58/1.43 thf(f2011,plain,(
% 1.58/1.43 $false),
% 1.58/1.43 inference(avatar_sat_refutation,[status(thm)],[f222,f387,f397,f405,f537,f873,f875,f876,f879,f963,f990,f2003,f2010])).
% 1.58/1.43 thf(f2010,plain,(
% 1.58/1.43 ~spl1_48 | ~spl1_52),
% 1.58/1.43 inference(avatar_contradiction_clause,[status(thm)],[f2009])).
% 1.58/1.43 thf(f2009,plain,(
% 1.58/1.43 $false | (~spl1_48 | ~spl1_52)),
% 1.58/1.43 inference(trivial_inequality_removal,[status(thm)],[f2008])).
% 1.58/1.43 thf(f2008,plain,(
% 1.58/1.43 ((eps @ sK0) != (eps @ sK0)) | (~spl1_48 | ~spl1_52)),
% 1.58/1.43 inference(duplicate_literal_removal,[status(thm)],[f2007])).
% 1.58/1.43 thf(f2007,plain,(
% 1.58/1.43 ((eps @ sK0) != (eps @ sK0)) | ((eps @ sK0) != (eps @ sK0)) | ((eps @ sK0) != (eps @ sK0)) | (~spl1_48 | ~spl1_52)),
% 1.58/1.43 inference(superposition,[status(thm)],[f989,f1184])).
% 1.58/1.43 thf(f1184,plain,(
% 1.58/1.43 ((eps @ sK0) = (sK22 @ (eps @ sK0))) | ~spl1_52),
% 1.58/1.43 inference(avatar_component_clause,[status(thm)],[f1183])).
% 1.58/1.43 thf(f1183,definition,(
% 1.58/1.43 spl1_52 <=> ((eps @ sK0) = (sK22 @ (eps @ sK0)))),
% 1.58/1.43 introduced(definition,[new_symbols(naming,[spl1_52])],[avatar_definition])).
% 1.58/1.43 thf(f989,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ sK0) != (sK22 @ X0)) | ((sK22 @ X0) != X0) | ((eps @ sK0) != X0)) ) | ~spl1_48),
% 1.58/1.43 inference(avatar_component_clause,[status(thm)],[f988])).
% 1.58/1.43 thf(f988,definition,(
% 1.58/1.43 spl1_48 <=> ! [X0 : $i] : (((sK22 @ X0) != X0) | ((eps @ sK0) != (sK22 @ X0)) | ((eps @ sK0) != X0))),
% 1.58/1.43 introduced(definition,[new_symbols(naming,[spl1_48])],[avatar_definition])).
% 1.58/1.43 thf(f2003,plain,(
% 1.58/1.43 spl1_52 | ~spl1_42),
% 1.58/1.43 inference(avatar_split_clause,[status(thm)],[f2002,f961,f1183])).
% 1.58/1.43 thf(f961,definition,(
% 1.58/1.43 spl1_42 <=> ! [X0 : $i] : (((sK22 @ X0) = X0) | ((eps @ sK0) = (sK22 @ X0)) | ((eps @ sK0) != X0))),
% 1.58/1.43 introduced(definition,[new_symbols(naming,[spl1_42])],[avatar_definition])).
% 1.58/1.43 thf(f2002,plain,(
% 1.58/1.43 ((eps @ sK0) = (sK22 @ (eps @ sK0))) | ~spl1_42),
% 1.58/1.43 inference(duplicate_literal_removal,[status(thm)],[f2001])).
% 1.58/1.43 thf(f2001,plain,(
% 1.58/1.43 ((eps @ sK0) = (sK22 @ (eps @ sK0))) | ((eps @ sK0) = (sK22 @ (eps @ sK0))) | ~spl1_42),
% 1.58/1.43 inference(equality_resolution,[status(thm)],[f962])).
% 1.58/1.43 thf(f962,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ sK0) != X0) | ((sK22 @ X0) = X0) | ((eps @ sK0) = (sK22 @ X0))) ) | ~spl1_42),
% 1.58/1.43 inference(avatar_component_clause,[status(thm)],[f961])).
% 1.58/1.43 thf(f990,plain,(
% 1.58/1.43 spl1_4 | spl1_48),
% 1.58/1.43 inference(avatar_split_clause,[status(thm)],[f939,f988,f205])).
% 1.58/1.43 thf(f205,definition,(
% 1.58/1.43 spl1_4 <=> ! [X1 : $i] : ((sK0 @ X1) = $false)),
% 1.58/1.43 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.58/1.43 thf(f939,plain,(
% 1.58/1.43 ( ! [X0 : $i,X1 : $i] : (((sK22 @ X0) != X0) | ((sK0 @ X1) = $false) | ((eps @ sK0) != X0) | ((eps @ sK0) != (sK22 @ X0))) )),
% 1.58/1.43 inference(pi_clausification,[status(thm)],[f938])).
% 1.58/1.43 thf(f938,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((sK22 @ X0) != X0) | ((eps @ sK0) != (sK22 @ X0)) | ((?? @ $i @ sK0) = $false) | ((eps @ sK0) != X0)) )),
% 1.58/1.43 inference(equality_proxy_clausification,[status(thm)],[f937])).
% 1.58/1.43 thf(f937,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ sK0) != X0) | ($false = ((eps @ sK0) = (sK22 @ X0))) | ((?? @ $i @ sK0) = $false) | ((sK22 @ X0) != X0)) )),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f936])).
% 1.58/1.43 thf(f936,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ sK0) != X0) | ($false = ((?? @ $i @ sK0) & ((eps @ sK0) = (sK22 @ X0)))) | ((sK22 @ X0) != X0)) )),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f934])).
% 1.58/1.43 thf(f934,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ sK0) != X0) | ((((?? @ $i @ sK0) & ((eps @ sK0) = (sK22 @ X0))) | (((eps @ (^[Y0 : $i]: ($false))) = (sK22 @ X0)) & (~ (?? @ $i @ sK0)))) = $false) | ((sK22 @ X0) != X0)) )),
% 1.58/1.43 inference(equality_proxy_clausification,[status(thm)],[f933])).
% 1.58/1.43 thf(f933,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (($false = (X0 = (sK22 @ X0))) | ((eps @ sK0) != X0) | ((((?? @ $i @ sK0) & ((eps @ sK0) = (sK22 @ X0))) | (((eps @ (^[Y0 : $i]: ($false))) = (sK22 @ X0)) & (~ (?? @ $i @ sK0)))) = $false)) )),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f931])).
% 1.58/1.43 thf(f931,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ sK0) != X0) | ((((?? @ $i @ sK0) & ((eps @ sK0) = (sK22 @ X0))) | (((eps @ (^[Y0 : $i]: ($false))) = (sK22 @ X0)) & (~ (?? @ $i @ sK0)))) != (X0 = (sK22 @ X0)))) )),
% 1.58/1.43 inference(beta_eta_normalization,[status(thm)],[f930])).
% 1.58/1.43 thf(f930,plain,(
% 1.58/1.43 ( ! [X0 : $i] : ((((^[Y0 : $i]: (((?? @ $i @ sK0) & ((eps @ sK0) = Y0)) | (((eps @ (^[Y1 : $i]: ($false))) = Y0) & (~ (?? @ $i @ sK0))))) @ (sK22 @ X0)) != (X0 = (sK22 @ X0))) | ((eps @ sK0) != X0)) )),
% 1.58/1.43 inference(negative_extensionality,[status(thm)],[f33])).
% 1.58/1.43 thf(f33,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((= @ X0) != (^[Y0 : $i]: (((?? @ $i @ sK0) & ((eps @ sK0) = Y0)) | (((eps @ (^[Y1 : $i]: ($false))) = Y0) & (~ (?? @ $i @ sK0)))))) | ((eps @ sK0) != X0)) )),
% 1.58/1.43 inference(constrained_superposition,[status(thm)],[f20,f21])).
% 1.58/1.43 thf(f21,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ (= @ X0)) = X0)) )),
% 1.58/1.43 inference(leibniz_equality_elimination,[status(thm)],[f16])).
% 1.58/1.43 thf(f16,plain,(
% 1.58/1.43 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ X1) != $true) | ((X0 @ (eps @ X0)) = $true)) )),
% 1.58/1.43 inference(cnf_transformation,[status(thm)],[f12])).
% 1.58/1.43 thf(f12,plain,(
% 1.58/1.43 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) != $true) | ((X0 @ (eps @ X0)) = $true))),
% 1.58/1.43 inference(ennf_transformation,[status(thm)],[f9])).
% 1.58/1.43 thf(f9,plain,(
% 1.58/1.43 ! [X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) = $true) => ((X0 @ (eps @ X0)) = $true))),
% 1.58/1.43 inference(fool_elimination,[status(thm)],[f8])).
% 1.58/1.43 thf(f8,plain,(
% 1.58/1.43 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 1.58/1.43 inference(rectify,[status(thm)],[f1])).
% 1.58/1.43 thf(f1,axiom,(
% 1.58/1.43 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 1.58/1.43 file('/export/starexec/sandbox/tmp/tmp.jUTSiai7C0/DTF2THF_27531.p',choiceax)).
% 1.58/1.43 thf(f20,plain,(
% 1.58/1.43 ((eps @ sK0) != (eps @ (^[Y0 : $i]: (((?? @ $i @ sK0) & ((eps @ sK0) = Y0)) | (((eps @ (^[Y1 : $i]: ($false))) = Y0) & (~ (?? @ $i @ sK0)))))))),
% 1.58/1.43 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.58/1.43 thf(f19,plain,(
% 1.58/1.43 (((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((Y2 = Y3) & (~ Y0)))))))))) @ (?? @ $i @ (^[Y0 : $i]: (sK0 @ Y0))) @ (eps @ sK0) @ (eps @ (^[Y0 : $i]: ($false)))) != (eps @ sK0))),
% 1.58/1.43 inference(definition_unfolding,[status(thm)],[f18,f17])).
% 1.58/1.43 thf(f17,plain,(
% 1.58/1.43 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((Y2 = Y3) & (~ Y0)))))))))))),
% 1.58/1.43 inference(cnf_transformation,[status(thm)],[f11])).
% 1.58/1.43 thf(f11,plain,(
% 1.58/1.43 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((Y2 = Y3) & (~ Y0)))))))))))),
% 1.58/1.43 inference(fool_elimination,[status(thm)],[f10])).
% 1.58/1.43 thf(f10,plain,(
% 1.58/1.43 ((^[X0 : $o, X1 : $i, X2 : $i] : (eps @ (^[X3 : $i] : ((~X0 & (X2 = X3)) | ((X1 = X3) & X0))))) = if)),
% 1.58/1.43 inference(rectify,[status(thm)],[f2])).
% 1.58/1.43 thf(f2,axiom,(
% 1.58/1.43 ((^[X2 : $o, X1 : $i, X3 : $i] : (eps @ (^[X4 : $i] : ((~X2 & (X3 = X4)) | ((X1 = X4) & X2))))) = if)),
% 1.58/1.43 file('/export/starexec/sandbox/tmp/tmp.jUTSiai7C0/DTF2THF_27531.p',ifd)).
% 1.58/1.43 thf(f18,plain,(
% 1.58/1.43 ((eps @ sK0) != (if @ (?? @ $i @ (^[Y0 : $i]: (sK0 @ Y0))) @ (eps @ sK0) @ (eps @ (^[Y0 : $i]: ($false)))))),
% 1.58/1.43 inference(cnf_transformation,[status(thm)],[f15])).
% 1.58/1.43 thf(f15,plain,(
% 1.58/1.43 ((eps @ sK0) != (if @ (?? @ $i @ (^[Y0 : $i]: (sK0 @ Y0))) @ (eps @ sK0) @ (eps @ (^[Y0 : $i]: ($false)))))),
% 1.58/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14])).
% 1.58/1.43 thf(f14,plain,(
% 1.58/1.43 ? [X0 : $i > $o] : ((eps @ X0) != (if @ (?? @ $i @ (^[Y0 : $i]: (X0 @ Y0))) @ (eps @ X0) @ (eps @ (^[Y0 : $i]: ($false))))) => ((eps @ sK0) != (if @ (?? @ $i @ (^[Y0 : $i]: (sK0 @ Y0))) @ (eps @ sK0) @ (eps @ (^[Y0 : $i]: ($false)))))),
% 1.58/1.43 introduced(definition,[],[choice_axiom])).
% 1.58/1.43 thf(f13,plain,(
% 1.58/1.43 ? [X0 : $i > $o] : ((eps @ X0) != (if @ (?? @ $i @ (^[Y0 : $i]: (X0 @ Y0))) @ (eps @ X0) @ (eps @ (^[Y0 : $i]: ($false)))))),
% 1.58/1.43 inference(ennf_transformation,[status(thm)],[f7])).
% 1.58/1.43 thf(f7,plain,(
% 1.58/1.43 ~! [X0 : $i > $o] : ((eps @ X0) = (if @ (?? @ $i @ (^[Y0 : $i]: (X0 @ Y0))) @ (eps @ X0) @ (eps @ (^[Y0 : $i]: ($false)))))),
% 1.58/1.43 inference(fool_elimination,[status(thm)],[f6])).
% 1.58/1.43 thf(f6,plain,(
% 1.58/1.43 ~! [X0 : $i > $o] : ((if @ ? [X1 : $i] : (X0 @ X1) @ (eps @ X0) @ (eps @ (^[X2 : $i] : ($false)))) = (eps @ X0))),
% 1.58/1.43 inference(rectify,[status(thm)],[f4])).
% 1.58/1.43 thf(f4,negated_conjecture,(
% 1.58/1.43 ~! [X0 : $i > $o] : ((if @ ? [X1 : $i] : (X0 @ X1) @ (eps @ X0) @ (eps @ (^[X1 : $i] : ($false)))) = (eps @ X0))),
% 1.58/1.43 inference(negated_conjecture,[status(cth)],[f3])).
% 1.58/1.43 thf(f3,conjecture,(
% 1.58/1.43 ! [X0 : $i > $o] : ((if @ ? [X1 : $i] : (X0 @ X1) @ (eps @ X0) @ (eps @ (^[X1 : $i] : ($false)))) = (eps @ X0))),
% 1.58/1.43 file('/export/starexec/sandbox/tmp/tmp.jUTSiai7C0/DTF2THF_27531.p',conj)).
% 1.58/1.43 thf(f963,plain,(
% 1.58/1.43 spl1_4 | spl1_42),
% 1.58/1.43 inference(avatar_split_clause,[status(thm)],[f959,f961,f205])).
% 1.58/1.43 thf(f959,plain,(
% 1.58/1.43 ( ! [X0 : $i,X1 : $i] : (((sK22 @ X0) = X0) | ((eps @ sK0) != X0) | ((eps @ sK0) = (sK22 @ X0)) | ((sK0 @ X1) = $false)) )),
% 1.58/1.43 inference(pi_clausification,[status(thm)],[f958])).
% 1.58/1.43 thf(f958,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ sK0) = (sK22 @ X0)) | ((eps @ sK0) != X0) | ((sK22 @ X0) = X0) | ((?? @ $i @ sK0) = $false)) )),
% 1.58/1.43 inference(not_proxy_clausification,[status(thm)],[f955])).
% 1.58/1.43 thf(f955,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ sK0) != X0) | ((~ (?? @ $i @ sK0)) = $true) | ((eps @ sK0) = (sK22 @ X0)) | ((sK22 @ X0) = X0)) )),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f954])).
% 1.58/1.43 thf(f954,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ sK0) = (sK22 @ X0)) | ((((eps @ (^[Y0 : $i]: ($false))) = (sK22 @ X0)) & (~ (?? @ $i @ sK0))) = $true) | ((sK22 @ X0) = X0) | ((eps @ sK0) != X0)) )),
% 1.58/1.43 inference(equality_proxy_clausification,[status(thm)],[f946])).
% 1.58/1.43 thf(f946,plain,(
% 1.58/1.43 ( ! [X0 : $i] : ((((eps @ sK0) = (sK22 @ X0)) = $true) | ((sK22 @ X0) = X0) | ((((eps @ (^[Y0 : $i]: ($false))) = (sK22 @ X0)) & (~ (?? @ $i @ sK0))) = $true) | ((eps @ sK0) != X0)) )),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f945])).
% 1.58/1.43 thf(f945,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ sK0) != X0) | (((?? @ $i @ sK0) & ((eps @ sK0) = (sK22 @ X0))) = $true) | ((sK22 @ X0) = X0) | ((((eps @ (^[Y0 : $i]: ($false))) = (sK22 @ X0)) & (~ (?? @ $i @ sK0))) = $true)) )),
% 1.58/1.43 inference(equality_proxy_clausification,[status(thm)],[f944])).
% 1.58/1.43 thf(f944,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((X0 = (sK22 @ X0)) = $true) | ((eps @ sK0) != X0) | ((((eps @ (^[Y0 : $i]: ($false))) = (sK22 @ X0)) & (~ (?? @ $i @ sK0))) = $true) | (((?? @ $i @ sK0) & ((eps @ sK0) = (sK22 @ X0))) = $true)) )),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f932])).
% 1.58/1.43 thf(f932,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ sK0) != X0) | ((((?? @ $i @ sK0) & ((eps @ sK0) = (sK22 @ X0))) | (((eps @ (^[Y0 : $i]: ($false))) = (sK22 @ X0)) & (~ (?? @ $i @ sK0)))) = $true) | ((X0 = (sK22 @ X0)) = $true)) )),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f931])).
% 1.58/1.43 thf(f879,plain,(
% 1.58/1.43 ~spl1_4 | ~spl1_27),
% 1.58/1.43 inference(avatar_contradiction_clause,[status(thm)],[f878])).
% 1.58/1.43 thf(f878,plain,(
% 1.58/1.43 $false | (~spl1_4 | ~spl1_27)),
% 1.58/1.43 inference(trivial_inequality_removal,[status(thm)],[f877])).
% 1.58/1.43 thf(f877,plain,(
% 1.58/1.43 ($false = $true) | (~spl1_4 | ~spl1_27)),
% 1.58/1.43 inference(forward_demodulation,[status(thm)],[f536,f206])).
% 1.58/1.43 thf(f206,plain,(
% 1.58/1.43 ( ! [X1 : $i] : (((sK0 @ X1) = $false)) ) | ~spl1_4),
% 1.58/1.43 inference(avatar_component_clause,[status(thm)],[f205])).
% 1.58/1.43 thf(f536,plain,(
% 1.58/1.43 ((sK0 @ sK15) = $true) | ~spl1_27),
% 1.58/1.43 inference(avatar_component_clause,[status(thm)],[f534])).
% 1.58/1.43 thf(f534,definition,(
% 1.58/1.43 spl1_27 <=> ((sK0 @ sK15) = $true)),
% 1.58/1.43 introduced(definition,[new_symbols(naming,[spl1_27])],[avatar_definition])).
% 1.58/1.43 thf(f876,plain,(
% 1.58/1.43 spl1_28 | ~spl1_6 | ~spl1_26),
% 1.58/1.43 inference(avatar_split_clause,[status(thm)],[f829,f531,f213,f539])).
% 1.58/1.43 thf(f539,definition,(
% 1.58/1.43 spl1_28 <=> ! [X0 : $i] : ((sK4 != (sK14 @ X0)) | (sK4 != X0) | ((sK14 @ X0) != X0))),
% 1.58/1.43 introduced(definition,[new_symbols(naming,[spl1_28])],[avatar_definition])).
% 1.58/1.43 thf(f213,definition,(
% 1.58/1.43 spl1_6 <=> ((eps @ (^[Y0 : $i]: ($false))) = sK4)),
% 1.58/1.43 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 1.58/1.43 thf(f531,definition,(
% 1.58/1.43 spl1_26 <=> ! [X0 : $i] : (((eps @ (^[Y0 : $i]: ($false))) != (sK14 @ X0)) | ((sK14 @ X0) != X0) | (sK4 != X0))),
% 1.58/1.43 introduced(definition,[new_symbols(naming,[spl1_26])],[avatar_definition])).
% 1.58/1.43 thf(f829,plain,(
% 1.58/1.43 ( ! [X0 : $i] : ((sK4 != X0) | ((sK14 @ X0) != X0) | (sK4 != (sK14 @ X0))) ) | (~spl1_6 | ~spl1_26)),
% 1.58/1.43 inference(forward_demodulation,[status(thm)],[f532,f215])).
% 1.58/1.43 thf(f215,plain,(
% 1.58/1.43 ((eps @ (^[Y0 : $i]: ($false))) = sK4) | ~spl1_6),
% 1.58/1.43 inference(avatar_component_clause,[status(thm)],[f213])).
% 1.58/1.43 thf(f532,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((sK14 @ X0) != X0) | ((eps @ (^[Y0 : $i]: ($false))) != (sK14 @ X0)) | (sK4 != X0)) ) | ~spl1_26),
% 1.58/1.43 inference(avatar_component_clause,[status(thm)],[f531])).
% 1.58/1.43 thf(f875,plain,(
% 1.58/1.43 spl1_21 | ~spl1_3 | ~spl1_6),
% 1.58/1.43 inference(avatar_split_clause,[status(thm)],[f658,f213,f201,f511])).
% 1.58/1.43 thf(f511,definition,(
% 1.58/1.43 spl1_21 <=> ! [X0 : $i] : ((sK4 != X0) | (sK4 = (sK14 @ X0)) | ((sK14 @ X0) = X0))),
% 1.58/1.43 introduced(definition,[new_symbols(naming,[spl1_21])],[avatar_definition])).
% 1.58/1.43 thf(f201,definition,(
% 1.58/1.43 spl1_3 <=> (sK4 = (eps @ sK0))),
% 1.58/1.43 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.58/1.43 thf(f658,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((sK14 @ X0) = X0) | (sK4 = (sK14 @ X0)) | (sK4 != X0)) ) | (~spl1_3 | ~spl1_6)),
% 1.58/1.43 inference(duplicate_literal_removal,[status(thm)],[f654])).
% 1.58/1.43 thf(f654,plain,(
% 1.58/1.43 ( ! [X0 : $i] : ((sK4 != X0) | ((sK14 @ X0) = X0) | (sK4 = (sK14 @ X0)) | (sK4 = (sK14 @ X0))) ) | (~spl1_3 | ~spl1_6)),
% 1.58/1.43 inference(backward_demodulation,[status(thm)],[f500,f215])).
% 1.58/1.43 thf(f500,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((sK14 @ X0) = X0) | (sK4 = (sK14 @ X0)) | ((eps @ (^[Y0 : $i]: ($false))) = (sK14 @ X0)) | (sK4 != X0)) ) | ~spl1_3),
% 1.58/1.43 inference(equality_proxy_clausification,[status(thm)],[f497])).
% 1.58/1.43 thf(f497,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((sK4 = (sK14 @ X0)) = $true) | ((sK14 @ X0) = X0) | (sK4 != X0) | ((eps @ (^[Y0 : $i]: ($false))) = (sK14 @ X0))) ) | ~spl1_3),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f496])).
% 1.58/1.43 thf(f496,plain,(
% 1.58/1.43 ( ! [X0 : $i] : ((((?? @ $i @ sK0) & (sK4 = (sK14 @ X0))) = $true) | ((sK14 @ X0) = X0) | ((eps @ (^[Y0 : $i]: ($false))) = (sK14 @ X0)) | (sK4 != X0)) ) | ~spl1_3),
% 1.58/1.43 inference(equality_proxy_clausification,[status(thm)],[f495])).
% 1.58/1.43 thf(f495,plain,(
% 1.58/1.43 ( ! [X0 : $i] : ((((eps @ (^[Y0 : $i]: ($false))) = (sK14 @ X0)) = $true) | (sK4 != X0) | (((?? @ $i @ sK0) & (sK4 = (sK14 @ X0))) = $true) | ((sK14 @ X0) = X0)) ) | ~spl1_3),
% 1.58/1.43 inference(equality_proxy_clausification,[status(thm)],[f494])).
% 1.58/1.43 thf(f494,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((X0 = (sK14 @ X0)) = $true) | (((?? @ $i @ sK0) & (sK4 = (sK14 @ X0))) = $true) | (((eps @ (^[Y0 : $i]: ($false))) = (sK14 @ X0)) = $true) | (sK4 != X0)) ) | ~spl1_3),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f492])).
% 1.58/1.43 thf(f492,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((((eps @ (^[Y0 : $i]: ($false))) = (sK14 @ X0)) & (~ (?? @ $i @ sK0))) = $true) | ((X0 = (sK14 @ X0)) = $true) | (((?? @ $i @ sK0) & (sK4 = (sK14 @ X0))) = $true) | (sK4 != X0)) ) | ~spl1_3),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f479])).
% 1.58/1.43 thf(f479,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((((?? @ $i @ sK0) & (sK4 = (sK14 @ X0))) | (((eps @ (^[Y0 : $i]: ($false))) = (sK14 @ X0)) & (~ (?? @ $i @ sK0)))) = $true) | ((X0 = (sK14 @ X0)) = $true) | (sK4 != X0)) ) | ~spl1_3),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f478])).
% 1.58/1.43 thf(f478,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((X0 = (sK14 @ X0)) != (((?? @ $i @ sK0) & (sK4 = (sK14 @ X0))) | (((eps @ (^[Y0 : $i]: ($false))) = (sK14 @ X0)) & (~ (?? @ $i @ sK0))))) | (sK4 != X0)) ) | ~spl1_3),
% 1.58/1.43 inference(beta_eta_normalization,[status(thm)],[f477])).
% 1.58/1.43 thf(f477,plain,(
% 1.58/1.43 ( ! [X0 : $i] : ((((^[Y0 : $i]: (((?? @ $i @ sK0) & (sK4 = Y0)) | (((eps @ (^[Y1 : $i]: ($false))) = Y0) & (~ (?? @ $i @ sK0))))) @ (sK14 @ X0)) != (X0 = (sK14 @ X0))) | (sK4 != X0)) ) | ~spl1_3),
% 1.58/1.43 inference(negative_extensionality,[status(thm)],[f448])).
% 1.58/1.43 thf(f448,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((= @ X0) != (^[Y0 : $i]: (((?? @ $i @ sK0) & (sK4 = Y0)) | (((eps @ (^[Y1 : $i]: ($false))) = Y0) & (~ (?? @ $i @ sK0)))))) | (sK4 != X0)) ) | ~spl1_3),
% 1.58/1.43 inference(constrained_superposition,[status(thm)],[f406,f21])).
% 1.58/1.43 thf(f406,plain,(
% 1.58/1.43 (sK4 != (eps @ (^[Y0 : $i]: (((?? @ $i @ sK0) & (sK4 = Y0)) | (((eps @ (^[Y1 : $i]: ($false))) = Y0) & (~ (?? @ $i @ sK0))))))) | ~spl1_3),
% 1.58/1.43 inference(backward_demodulation,[status(thm)],[f20,f203])).
% 1.58/1.43 thf(f203,plain,(
% 1.58/1.43 (sK4 = (eps @ sK0)) | ~spl1_3),
% 1.58/1.43 inference(avatar_component_clause,[status(thm)],[f201])).
% 1.58/1.43 thf(f873,plain,(
% 1.58/1.43 ~spl1_21 | ~spl1_28),
% 1.58/1.43 inference(avatar_contradiction_clause,[status(thm)],[f872])).
% 1.58/1.43 thf(f872,plain,(
% 1.58/1.43 $false | (~spl1_21 | ~spl1_28)),
% 1.58/1.43 inference(trivial_inequality_removal,[status(thm)],[f871])).
% 1.58/1.43 thf(f871,plain,(
% 1.58/1.43 (sK4 != sK4) | (~spl1_21 | ~spl1_28)),
% 1.58/1.43 inference(duplicate_literal_removal,[status(thm)],[f870])).
% 1.58/1.43 thf(f870,plain,(
% 1.58/1.43 (sK4 != sK4) | (sK4 != sK4) | (sK4 != sK4) | (~spl1_21 | ~spl1_28)),
% 1.58/1.43 inference(superposition,[status(thm)],[f540,f832])).
% 1.58/1.43 thf(f832,plain,(
% 1.58/1.43 (sK4 = (sK14 @ sK4)) | ~spl1_21),
% 1.58/1.43 inference(duplicate_literal_removal,[status(thm)],[f831])).
% 1.58/1.43 thf(f831,plain,(
% 1.58/1.43 (sK4 = (sK14 @ sK4)) | (sK4 = (sK14 @ sK4)) | ~spl1_21),
% 1.58/1.43 inference(equality_resolution,[status(thm)],[f512])).
% 1.58/1.43 thf(f512,plain,(
% 1.58/1.43 ( ! [X0 : $i] : ((sK4 != X0) | (sK4 = (sK14 @ X0)) | ((sK14 @ X0) = X0)) ) | ~spl1_21),
% 1.58/1.43 inference(avatar_component_clause,[status(thm)],[f511])).
% 1.58/1.43 thf(f540,plain,(
% 1.58/1.43 ( ! [X0 : $i] : ((sK4 != (sK14 @ X0)) | ((sK14 @ X0) != X0) | (sK4 != X0)) ) | ~spl1_28),
% 1.58/1.43 inference(avatar_component_clause,[status(thm)],[f539])).
% 1.58/1.43 thf(f537,plain,(
% 1.58/1.43 spl1_26 | spl1_27 | ~spl1_3),
% 1.58/1.43 inference(avatar_split_clause,[status(thm)],[f491,f201,f534,f531])).
% 1.58/1.43 thf(f491,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ (^[Y0 : $i]: ($false))) != (sK14 @ X0)) | (sK4 != X0) | ((sK14 @ X0) != X0) | ((sK0 @ sK15) = $true)) ) | ~spl1_3),
% 1.58/1.43 inference(sigma_clausification,[status(thm)],[f490])).
% 1.58/1.43 thf(f490,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (((eps @ (^[Y0 : $i]: ($false))) != (sK14 @ X0)) | (sK4 != X0) | ((sK14 @ X0) != X0) | ((?? @ $i @ sK0) = $true)) ) | ~spl1_3),
% 1.58/1.43 inference(not_proxy_clausification,[status(thm)],[f489])).
% 1.58/1.43 thf(f489,plain,(
% 1.58/1.43 ( ! [X0 : $i] : ((sK4 != X0) | ((sK14 @ X0) != X0) | ((~ (?? @ $i @ sK0)) = $false) | ((eps @ (^[Y0 : $i]: ($false))) != (sK14 @ X0))) ) | ~spl1_3),
% 1.58/1.43 inference(equality_proxy_clausification,[status(thm)],[f488])).
% 1.58/1.43 thf(f488,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (($false = (X0 = (sK14 @ X0))) | ((eps @ (^[Y0 : $i]: ($false))) != (sK14 @ X0)) | (sK4 != X0) | ((~ (?? @ $i @ sK0)) = $false)) ) | ~spl1_3),
% 1.58/1.43 inference(equality_proxy_clausification,[status(thm)],[f487])).
% 1.58/1.43 thf(f487,plain,(
% 1.58/1.43 ( ! [X0 : $i] : ((((eps @ (^[Y0 : $i]: ($false))) = (sK14 @ X0)) = $false) | ((~ (?? @ $i @ sK0)) = $false) | (sK4 != X0) | ($false = (X0 = (sK14 @ X0)))) ) | ~spl1_3),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f481])).
% 1.58/1.43 thf(f481,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (($false = (((eps @ (^[Y0 : $i]: ($false))) = (sK14 @ X0)) & (~ (?? @ $i @ sK0)))) | (sK4 != X0) | ($false = (X0 = (sK14 @ X0)))) ) | ~spl1_3),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f480])).
% 1.58/1.43 thf(f480,plain,(
% 1.58/1.43 ( ! [X0 : $i] : (($false = (((?? @ $i @ sK0) & (sK4 = (sK14 @ X0))) | (((eps @ (^[Y0 : $i]: ($false))) = (sK14 @ X0)) & (~ (?? @ $i @ sK0))))) | ($false = (X0 = (sK14 @ X0))) | (sK4 != X0)) ) | ~spl1_3),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f478])).
% 1.58/1.43 thf(f405,plain,(
% 1.58/1.43 ~spl1_4 | ~spl1_7),
% 1.58/1.43 inference(avatar_contradiction_clause,[status(thm)],[f404])).
% 1.58/1.43 thf(f404,plain,(
% 1.58/1.43 $false | (~spl1_4 | ~spl1_7)),
% 1.58/1.43 inference(trivial_inequality_removal,[status(thm)],[f403])).
% 1.58/1.43 thf(f403,plain,(
% 1.58/1.43 ($false = $true) | (~spl1_4 | ~spl1_7)),
% 1.58/1.43 inference(forward_demodulation,[status(thm)],[f220,f206])).
% 1.58/1.43 thf(f220,plain,(
% 1.58/1.43 ((sK0 @ sK6) = $true) | ~spl1_7),
% 1.58/1.43 inference(avatar_component_clause,[status(thm)],[f218])).
% 1.58/1.43 thf(f218,definition,(
% 1.58/1.43 spl1_7 <=> ((sK0 @ sK6) = $true)),
% 1.58/1.43 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.58/1.43 thf(f397,plain,(
% 1.58/1.43 ~spl1_4 | ~spl1_5),
% 1.58/1.43 inference(avatar_contradiction_clause,[status(thm)],[f396])).
% 1.58/1.43 thf(f396,plain,(
% 1.58/1.43 $false | (~spl1_4 | ~spl1_5)),
% 1.58/1.43 inference(trivial_inequality_removal,[status(thm)],[f395])).
% 1.58/1.43 thf(f395,plain,(
% 1.58/1.43 ($false = $true) | (~spl1_4 | ~spl1_5)),
% 1.58/1.43 inference(forward_demodulation,[status(thm)],[f210,f206])).
% 1.58/1.43 thf(f210,plain,(
% 1.58/1.43 ((sK0 @ sK4) = $true) | ~spl1_5),
% 1.58/1.43 inference(avatar_component_clause,[status(thm)],[f208])).
% 1.58/1.43 thf(f208,definition,(
% 1.58/1.43 spl1_5 <=> ((sK0 @ sK4) = $true)),
% 1.58/1.43 introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition])).
% 1.58/1.43 thf(f387,plain,(
% 1.58/1.43 spl1_3 | ~spl1_4 | ~spl1_6),
% 1.58/1.43 inference(avatar_contradiction_clause,[status(thm)],[f386])).
% 1.58/1.43 thf(f386,plain,(
% 1.58/1.43 $false | (spl1_3 | ~spl1_4 | ~spl1_6)),
% 1.58/1.43 inference(subsumption_resolution,[status(thm)],[f385,f206])).
% 1.58/1.43 thf(f385,plain,(
% 1.58/1.43 ((sK0 @ sK13) != $false) | (spl1_3 | ~spl1_6)),
% 1.58/1.43 inference(beta_eta_normalization,[status(thm)],[f384])).
% 1.58/1.43 thf(f384,plain,(
% 1.58/1.43 ((sK0 @ sK13) != ((^[Y0 : $i]: ($false)) @ sK13)) | (spl1_3 | ~spl1_6)),
% 1.58/1.43 inference(negative_extensionality,[status(thm)],[f374])).
% 1.58/1.43 thf(f374,plain,(
% 1.58/1.43 ((^[Y0 : $i]: ($false)) != sK0) | (spl1_3 | ~spl1_6)),
% 1.58/1.43 inference(trivial_inequality_removal,[status(thm)],[f369])).
% 1.58/1.43 thf(f369,plain,(
% 1.58/1.43 ((^[Y0 : $i]: ($false)) != sK0) | (sK4 != sK4) | (spl1_3 | ~spl1_6)),
% 1.58/1.43 inference(constrained_superposition,[status(thm)],[f202,f215])).
% 1.58/1.43 thf(f202,plain,(
% 1.58/1.43 (sK4 != (eps @ sK0)) | spl1_3),
% 1.58/1.43 inference(avatar_component_clause,[status(thm)],[f201])).
% 1.58/1.43 thf(f222,plain,(
% 1.58/1.43 spl1_7 | spl1_5 | spl1_6),
% 1.58/1.43 inference(avatar_split_clause,[status(thm)],[f190,f213,f208,f218])).
% 1.58/1.43 thf(f190,plain,(
% 1.58/1.43 ((sK0 @ sK6) = $true) | ((sK0 @ sK4) = $true) | ((eps @ (^[Y0 : $i]: ($false))) = sK4)),
% 1.58/1.43 inference(equality_proxy_clausification,[status(thm)],[f189])).
% 1.58/1.43 thf(f189,plain,(
% 1.58/1.43 ((sK0 @ sK4) = $true) | ((sK0 @ sK6) = $true) | (((eps @ (^[Y0 : $i]: ($false))) = sK4) = $true)),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f187])).
% 1.58/1.43 thf(f187,plain,(
% 1.58/1.43 ((((eps @ (^[Y0 : $i]: ($false))) = sK4) & (~ (?? @ $i @ sK0))) = $true) | ((sK0 @ sK6) = $true) | ((sK0 @ sK4) = $true)),
% 1.58/1.43 inference(sigma_clausification,[status(thm)],[f186])).
% 1.58/1.43 thf(f186,plain,(
% 1.58/1.43 ((sK0 @ sK4) = $true) | ((?? @ $i @ sK0) = $true) | ((((eps @ (^[Y0 : $i]: ($false))) = sK4) & (~ (?? @ $i @ sK0))) = $true)),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f184])).
% 1.58/1.43 thf(f184,plain,(
% 1.58/1.43 ((sK0 @ sK4) = $true) | (((?? @ $i @ sK0) & ((eps @ sK0) = sK4)) = $true) | ((((eps @ (^[Y0 : $i]: ($false))) = sK4) & (~ (?? @ $i @ sK0))) = $true)),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f173])).
% 1.58/1.43 thf(f173,plain,(
% 1.58/1.43 ((((?? @ $i @ sK0) & ((eps @ sK0) = sK4)) | (((eps @ (^[Y0 : $i]: ($false))) = sK4) & (~ (?? @ $i @ sK0)))) = $true) | ((sK0 @ sK4) = $true)),
% 1.58/1.43 inference(binary_proxy_clausification,[status(thm)],[f172])).
% 1.58/1.43 thf(f172,plain,(
% 1.58/1.43 ((((?? @ $i @ sK0) & ((eps @ sK0) = sK4)) | (((eps @ (^[Y0 : $i]: ($false))) = sK4) & (~ (?? @ $i @ sK0)))) != (sK0 @ sK4))),
% 1.58/1.43 inference(beta_eta_normalization,[status(thm)],[f171])).
% 1.58/1.43 thf(f171,plain,(
% 1.58/1.43 (((^[Y0 : $i]: (((?? @ $i @ sK0) & ((eps @ sK0) = Y0)) | (((eps @ (^[Y1 : $i]: ($false))) = Y0) & (~ (?? @ $i @ sK0))))) @ sK4) != (sK0 @ sK4))),
% 1.58/1.43 inference(negative_extensionality,[status(thm)],[f34])).
% 1.58/1.43 thf(f34,plain,(
% 1.58/1.43 ((^[Y0 : $i]: (((?? @ $i @ sK0) & ((eps @ sK0) = Y0)) | (((eps @ (^[Y1 : $i]: ($false))) = Y0) & (~ (?? @ $i @ sK0))))) != sK0)),
% 1.58/1.43 inference(equality_resolution,[status(thm)],[f20])).
% 1.58/1.43 % SZS output end Proof for DTF2THF_27531
% 1.58/1.43 % (27832)------------------------------
% 1.58/1.43 % (27832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.43 % (27832)Termination reason: Refutation
% 1.58/1.43
% 1.58/1.43 % (27832)Memory used [KB]: 6268
% 1.58/1.43 % (27832)Time elapsed: 0.092 s
% 1.58/1.43 % (27832)Instructions burned: 199 (million)
% 1.58/1.43 % (27832)------------------------------
% 1.58/1.43 % (27832)------------------------------
% 1.58/1.43 % (27811)Success in time 0.163 s
%------------------------------------------------------------------------------