%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUN023^1 : TPTP v9.2.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 09:27:12 AM UTC 2026
% Result : Theorem 1.56s 1.50s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 10 unt; 0 typ; 8 def)
% Number of atoms : 523 ( 201 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 701 ( 171 ~; 163 |; 16 &; 328 @)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 11 con; 0-3 aty)
% Number of variables : 209 ( 8 ^; 196 !; 5 ?; 209 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
ite: $o > $i > $i > $i ).
thf(func_def_8,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f798,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f33,f92,f159,f307,f435,f510,f539,f708,f797]) ).
thf(f797,plain,
~ spl0_28,
inference(avatar_contradiction_clause,[status(thm)],[f796]) ).
thf(f796,plain,
( $false
| ~ spl0_28 ),
inference(equality_resolution,[status(thm)],[f777]) ).
thf(f777,plain,
( ! [X0: $i] : ( zero != X0 )
| ~ spl0_28 ),
inference(beta_eta_normalization,[status(thm)],[f776]) ).
thf(f776,plain,
( ! [X0: $i] :
( ( ^ [Y0: $i] : zero
@ zero )
!= X0 )
| ~ spl0_28 ),
inference(equality_resolution,[status(thm)],[f745]) ).
thf(f745,plain,
( ! [X0: $i > $i,X1: $i] :
( ( zero
!= ( X0 @ ( s @ zero ) ) )
| ( ( X0 @ zero )
!= X1 ) )
| ~ spl0_28 ),
inference(equality_resolution,[status(thm)],[f306]) ).
thf(f306,plain,
( ! [X0: $i > $i,X1: $i,X5: $i] :
( ( zero != X1 )
| ( ( X0 @ zero )
!= X5 )
| ( ( X0 @ ( s @ zero ) )
!= X1 ) )
| ~ spl0_28 ),
inference(avatar_component_clause,[status(thm)],[f305]) ).
thf(f305,definition,
( spl0_28
<=> ! [X5: $i,X0: $i > $i,X1: $i] :
( ( ( X0 @ zero )
!= X5 )
| ( ( X0 @ ( s @ zero ) )
!= X1 )
| ( zero != X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition]) ).
thf(f708,plain,
~ spl0_27,
inference(avatar_contradiction_clause,[status(thm)],[f707]) ).
thf(f707,plain,
( $false
| ~ spl0_27 ),
inference(equality_resolution,[status(thm)],[f689]) ).
thf(f689,plain,
( ! [X1: $i] :
( ( s @ zero )
!= X1 )
| ~ spl0_27 ),
inference(beta_eta_normalization,[status(thm)],[f678]) ).
thf(f678,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( s
@ ( ^ [Y1: $i] : zero
@ Y0 ) )
@ ( s @ zero ) )
!= X1 )
| ~ spl0_27 ),
inference(equality_resolution,[status(thm)],[f673]) ).
thf(f673,plain,
( ! [X0: $i > $i,X1: $i] :
( ( ( s @ zero )
!= ( X0 @ zero ) )
| ( ( X0 @ ( s @ zero ) )
!= X1 ) )
| ~ spl0_27 ),
inference(equality_resolution,[status(thm)],[f303]) ).
thf(f303,plain,
( ! [X2: $i > $i,X3: $i,X4: $i] :
( ( ( s @ zero )
!= X4 )
| ( ( X2 @ zero )
!= X4 )
| ( ( X2 @ ( s @ zero ) )
!= X3 ) )
| ~ spl0_27 ),
inference(avatar_component_clause,[status(thm)],[f302]) ).
thf(f302,definition,
( spl0_27
<=> ! [X2: $i > $i,X4: $i,X3: $i] :
( ( ( X2 @ ( s @ zero ) )
!= X3 )
| ( ( X2 @ zero )
!= X4 )
| ( ( s @ zero )
!= X4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_27])],[avatar_definition]) ).
thf(f539,plain,
( spl0_4
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f167,f35,f38]) ).
thf(f38,definition,
( spl0_4
<=> ! [X4: $o] :
( ( $true = X4 )
| ( $false = X4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f35,definition,
( spl0_3
<=> ! [X5: $i > $o,X0: $i,X3: $i > $i,X2: $i,X1: $i > $i] :
( ( ( X1 @ zero )
!= X0 )
| ( ( s @ zero )
!= X2 )
| ( zero
!= ( ite @ ( X5 @ ( s @ zero ) ) @ ( X1 @ ( s @ zero ) ) @ ( X3 @ ( s @ zero ) ) ) )
| ( ( X3 @ zero )
!= X2 )
| ( $false
= ( X5 @ zero ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f167,plain,
! [X2: $i,X3: $i > $i,X0: $i,X1: $i > $i,X4: $o,X5: $i > $o] :
( ( $false
= ( X5 @ zero ) )
| ( $false = X4 )
| ( $true = X4 )
| ( ( X3 @ zero )
!= X2 )
| ( ( X1 @ zero )
!= X0 )
| ( ( s @ zero )
!= X2 )
| ( zero
!= ( ite @ ( X5 @ ( s @ zero ) ) @ ( X1 @ ( s @ zero ) ) @ ( X3 @ ( s @ zero ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f165]) ).
thf(f165,plain,
! [X2: $i,X3: $i > $i,X0: $i,X1: $i > $i,X4: $o,X5: $i > $o] :
( ( $true = X4 )
| ( zero
!= ( ite @ ( X5 @ ( s @ zero ) ) @ ( X1 @ ( s @ zero ) ) @ ( X3 @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= X2 )
| ( ( X5 @ zero )
!= X4 )
| ( ( X1 @ zero )
!= X0 )
| ( ( X3 @ zero )
!= X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f164]) ).
thf(f164,plain,
! [X2: $i,X3: $i > $i,X0: $i,X1: $i > $i,X4: $o,X5: $i > $o] :
( ( ( s @ zero )
!= X2 )
| ( $true = X4 )
| ( zero
!= ( ^ [Y0: $i] : ( ite @ ( X5 @ Y0 ) @ ( X1 @ Y0 ) @ ( X3 @ Y0 ) )
@ ( s @ zero ) ) )
| ( ( X1 @ zero )
!= X0 )
| ( ( X3 @ zero )
!= X2 )
| ( ( X5 @ zero )
!= X4 ) ),
inference(constrained_superposition,[status(thm)],[f11,f10]) ).
thf(f10,plain,
! [X6: $i,X4: $o,X5: $i] :
( ( ( ite @ X4 @ X6 @ X5 )
= X5 )
| ( $true = X4 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $o,X1: $i,X2: $i] :
( ( ( ite @ X0 @ X1 @ X2 )
= X1 )
| ( $true != X0 ) )
& ! [X3: $i > $i] :
( ( zero
!= ( X3 @ ( s @ zero ) ) )
| ( ( X3 @ zero )
!= ( s @ zero ) ) )
& ! [X4: $o,X5: $i,X6: $i] :
( ( ( ite @ X4 @ X6 @ X5 )
= X5 )
| ( $true = X4 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X4: $o,X5: $i,X3: $i] :
( ( ( ite @ X4 @ X5 @ X3 )
= X5 )
| ( $true != X4 ) )
& ! [X6: $i > $i] :
( ( zero
!= ( X6 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X6 @ zero ) ) )
& ! [X2: $o,X1: $i,X0: $i] :
( ( ( ite @ X2 @ X0 @ X1 )
= X1 )
| ( $true = X2 ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X6: $i > $i] :
( ( zero
!= ( X6 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X6 @ zero ) ) )
& ! [X2: $o,X1: $i,X0: $i] :
( ( ( ite @ X2 @ X0 @ X1 )
= X1 )
| ( $true = X2 ) )
& ! [X4: $o,X5: $i,X3: $i] :
( ( ( ite @ X4 @ X5 @ X3 )
= X5 )
| ( $true != X4 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: $i,X1: $i,X2: $o] :
( ( $true != X2 )
=> ( ( ite @ X2 @ X0 @ X1 )
= X1 ) )
& ! [X5: $i,X4: $o,X3: $i] :
( ( $true = X4 )
=> ( ( ite @ X4 @ X5 @ X3 )
= X5 ) ) )
=> ? [X6: $i > $i] :
( ( ( s @ zero )
= ( X6 @ zero ) )
& ( zero
= ( X6 @ ( s @ zero ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i,X1: $i,X2: $o] :
( ( $true != X2 )
=> ( ( ite @ X2 @ X0 @ X1 )
= X1 ) )
& ! [X5: $i,X4: $o,X3: $i] :
( ( $true = X4 )
=> ( ( ite @ X4 @ X5 @ X3 )
= X5 ) ) )
=> ? [X6: $i > $i] :
( ( ( s @ zero )
= ( X6 @ zero ) )
& ( zero
= ( X6 @ ( s @ zero ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i,X2: $o] :
( ~ X2
=> ( ( ite @ X2 @ X0 @ X1 )
= X1 ) )
& ! [X3: $i,X4: $o,X5: $i] :
( X4
=> ( ( ite @ X4 @ X5 @ X3 )
= X5 ) ) )
=> ? [X6: $i > $i] :
( ( zero
= ( X6 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X6 @ zero ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: $i,X2: $i,X0: $o] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X2: $i,X0: $o,X1: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) ) )
=> ? [X3: $i > $i] :
( ( zero
= ( X3 @ ( s @ zero ) ) )
& ( ( X3 @ zero )
= ( s @ zero ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: $i,X2: $i,X0: $o] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X2: $i,X0: $o,X1: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) ) )
=> ? [X3: $i > $i] :
( ( zero
= ( X3 @ ( s @ zero ) ) )
& ( ( X3 @ zero )
= ( s @ zero ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xws3VfhP2z/DTF2THF_16074.p',n8) ).
thf(f11,plain,
! [X3: $i > $i] :
( ( ( X3 @ zero )
!= ( s @ zero ) )
| ( zero
!= ( X3 @ ( s @ zero ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f510,plain,
( spl0_27
| spl0_21
| spl0_12
| spl0_28
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f501,f38,f31,f305,f125,f257,f302]) ).
thf(f257,definition,
( spl0_21
<=> ! [X1: $i > $o] :
( ( ( X1 @ zero )
= $true )
| ( $false
= ( X1 @ ( s @ zero ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition]) ).
thf(f125,definition,
( spl0_12
<=> ! [X4: $o] : ( $false = X4 ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f31,definition,
( spl0_2
<=> ! [X2: $i,X3: $i > $i,X0: $i,X5: $i > $o,X1: $i > $i] :
( ( $true
= ( X5 @ zero ) )
| ( zero
!= ( ite @ ( X5 @ ( s @ zero ) ) @ ( X1 @ ( s @ zero ) ) @ ( X3 @ ( s @ zero ) ) ) )
| ( ( X1 @ zero )
!= X0 )
| ( ( s @ zero )
!= X2 )
| ( ( X3 @ zero )
!= X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f501,plain,
( ! [X2: $i,X3: $i > $i,X0: $i,X1: $i > $i,X6: $i,X7: $i,X4: $o,X5: $i > $o] :
( ( ( X1 @ zero )
!= X6 )
| ( ( X3 @ ( s @ zero ) )
!= X2 )
| ( $true
= ( X5 @ zero ) )
| ( $false = X4 )
| ( zero != X2 )
| ( ( s @ zero )
!= X6 )
| ( ( X3 @ zero )
!= X7 )
| ( $false
= ( X5 @ ( s @ zero ) ) )
| ( ( X1 @ ( s @ zero ) )
!= X0 ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(duplicate_literal_removal,[status(thm)],[f500]) ).
thf(f500,plain,
( ! [X2: $i,X3: $i > $i,X0: $i,X1: $i > $i,X6: $i,X7: $i,X4: $o,X5: $i > $o] :
( ( ( X3 @ ( s @ zero ) )
!= X2 )
| ( ( X3 @ zero )
!= X7 )
| ( $false
= ( X5 @ ( s @ zero ) ) )
| ( $false = X4 )
| ( ( X1 @ zero )
!= X6 )
| ( $true
= ( X5 @ zero ) )
| ( ( X1 @ ( s @ zero ) )
!= X0 )
| ( zero != X2 )
| ( $false = X4 )
| ( ( s @ zero )
!= X6 ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f448]) ).
thf(f448,plain,
( ! [X2: $i,X3: $i > $i,X0: $i,X1: $i > $i,X6: $i,X7: $i,X4: $o,X5: $i > $o] :
( ( ( X1 @ ( s @ zero ) )
!= X0 )
| ( ( X1 @ zero )
!= X6 )
| ( zero != X2 )
| ( ( X5 @ ( s @ zero ) )
!= X4 )
| ( $false = X4 )
| ( ( X3 @ ( s @ zero ) )
!= X2 )
| ( ( X3 @ zero )
!= X7 )
| ( ( s @ zero )
!= X6 )
| ( $true
= ( X5 @ zero ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(constrained_superposition,[status(thm)],[f32,f310]) ).
thf(f310,plain,
( ! [X2: $i,X0: $o,X1: $i] :
( ( ( ite @ X0 @ X1 @ X2 )
= X1 )
| ( $false = X0 ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f13,f39]) ).
thf(f39,plain,
( ! [X4: $o] :
( ( $true = X4 )
| ( $false = X4 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f13,plain,
! [X2: $i,X1: $i] :
( ( ite @ $true @ X1 @ X2 )
= X1 ),
inference(equality_resolution,[status(thm)],[f12]) ).
thf(f12,plain,
! [X2: $i,X0: $o,X1: $i] :
( ( ( ite @ X0 @ X1 @ X2 )
= X1 )
| ( $true != X0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f32,plain,
( ! [X2: $i,X3: $i > $i,X0: $i,X1: $i > $i,X5: $i > $o] :
( ( zero
!= ( ite @ ( X5 @ ( s @ zero ) ) @ ( X1 @ ( s @ zero ) ) @ ( X3 @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= X2 )
| ( $true
= ( X5 @ zero ) )
| ( ( X3 @ zero )
!= X2 )
| ( ( X1 @ zero )
!= X0 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f435,plain,
~ spl0_21,
inference(avatar_contradiction_clause,[status(thm)],[f434]) ).
thf(f434,plain,
( $false
| ~ spl0_21 ),
inference(subsumption_resolution,[status(thm)],[f392,f18]) ).
thf(f18,plain,
( zero
!= ( s @ zero ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( zero
!= ( ^ [Y0: $i] :
( s
@ ( ^ [Y1: $i] : zero
@ Y0 ) )
@ ( s @ zero ) ) ),
inference(equality_resolution,[status(thm)],[f11]) ).
thf(f392,plain,
( ( zero
= ( s @ zero ) )
| ~ spl0_21 ),
inference(leibniz_equality_elimination,[status(thm)],[f258]) ).
thf(f258,plain,
( ! [X1: $i > $o] :
( ( $false
= ( X1 @ ( s @ zero ) ) )
| ( ( X1 @ zero )
= $true ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[status(thm)],[f257]) ).
thf(f307,plain,
( spl0_27
| spl0_28
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f271,f35,f305,f302]) ).
thf(f271,plain,
( ! [X2: $i > $i,X3: $i,X0: $i > $i,X1: $i,X4: $i,X5: $i] :
( ( ( X2 @ ( s @ zero ) )
!= X3 )
| ( ( X0 @ zero )
!= X5 )
| ( ( s @ zero )
!= X4 )
| ( zero != X1 )
| ( ( X2 @ zero )
!= X4 )
| ( ( X0 @ ( s @ zero ) )
!= X1 ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f270]) ).
thf(f270,plain,
( ! [X2: $i > $i,X3: $i,X0: $i > $i,X1: $i,X4: $i,X5: $i] :
( ( ( X0 @ zero )
!= X5 )
| ( zero != X1 )
| ( ( s @ zero )
!= X4 )
| ( ( X2 @ ( s @ zero ) )
!= X3 )
| ( ( X2 @ zero )
!= X4 )
| ( $true = $false )
| ( ( X0 @ ( s @ zero ) )
!= X1 ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f268]) ).
thf(f268,plain,
( ! [X2: $i > $i,X3: $i,X0: $i > $i,X1: $i,X4: $i,X5: $i] :
( ( ( X0 @ zero )
!= X5 )
| ( ( X2 @ zero )
!= X4 )
| ( ( X2 @ ( s @ zero ) )
!= X3 )
| ( ( s @ zero )
!= X4 )
| ( ( X0 @ ( s @ zero ) )
!= X1 )
| ( zero != X1 )
| ( ( ^ [Y0: $i] : $true
@ zero )
= $false ) )
| ~ spl0_3 ),
inference(constrained_superposition,[status(thm)],[f36,f13]) ).
thf(f36,plain,
( ! [X2: $i,X3: $i > $i,X0: $i,X1: $i > $i,X5: $i > $o] :
( ( zero
!= ( ite @ ( X5 @ ( s @ zero ) ) @ ( X1 @ ( s @ zero ) ) @ ( X3 @ ( s @ zero ) ) ) )
| ( $false
= ( X5 @ zero ) )
| ( ( X3 @ zero )
!= X2 )
| ( ( s @ zero )
!= X2 )
| ( ( X1 @ zero )
!= X0 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f159,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[status(thm)],[f158]) ).
thf(f158,plain,
( $false
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
( ( $false != $false )
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f3,f126]) ).
thf(f126,plain,
( ! [X4: $o] : ( $false = X4 )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f125]) ).
thf(f3,plain,
$true != $false,
introduced(definition,[],[fool_axiom]) ).
thf(f92,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f91]) ).
thf(f91,plain,
( $false
| ~ spl0_1 ),
inference(equality_resolution,[status(thm)],[f88]) ).
thf(f88,plain,
( ! [X0: $o] : ( $false != X0 )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f3,f29]) ).
thf(f29,plain,
( ! [X4: $o] : ( $true = X4 )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl0_1
<=> ! [X4: $o] : ( $true = X4 ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f33,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f26,f31,f28]) ).
thf(f26,plain,
! [X2: $i,X3: $i > $i,X0: $i,X1: $i > $i,X4: $o,X5: $i > $o] :
( ( $true
= ( X5 @ zero ) )
| ( ( s @ zero )
!= X2 )
| ( ( X1 @ zero )
!= X0 )
| ( ( X3 @ zero )
!= X2 )
| ( zero
!= ( ite @ ( X5 @ ( s @ zero ) ) @ ( X1 @ ( s @ zero ) ) @ ( X3 @ ( s @ zero ) ) ) )
| ( $true = X4 ) ),
inference(duplicate_literal_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: $i,X3: $i > $i,X0: $i,X1: $i > $i,X4: $o,X5: $i > $o] :
( ( $true = X4 )
| ( zero
!= ( ite @ ( X5 @ ( s @ zero ) ) @ ( X1 @ ( s @ zero ) ) @ ( X3 @ ( s @ zero ) ) ) )
| ( $true
= ( X5 @ zero ) )
| ( $true = X4 )
| ( ( X3 @ zero )
!= X2 )
| ( ( X1 @ zero )
!= X0 )
| ( ( s @ zero )
!= X2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: $i,X3: $i > $i,X0: $i,X1: $i > $i,X4: $o,X5: $i > $o] :
( ( ( s @ zero )
!= X2 )
| ( $true = X4 )
| ( ( X5 @ zero )
!= X4 )
| ( zero
!= ( ite @ ( X5 @ ( s @ zero ) ) @ ( X1 @ ( s @ zero ) ) @ ( X3 @ ( s @ zero ) ) ) )
| ( ( X1 @ zero )
!= X0 )
| ( ( X3 @ zero )
!= X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: $i,X3: $i > $i,X0: $i,X1: $i > $i,X4: $o,X5: $i > $o] :
( ( ( X3 @ zero )
!= X2 )
| ( zero
!= ( ^ [Y0: $i] : ( ite @ ( X5 @ Y0 ) @ ( X1 @ Y0 ) @ ( X3 @ Y0 ) )
@ ( s @ zero ) ) )
| ( ( X5 @ zero )
!= X4 )
| ( ( s @ zero )
!= X2 )
| ( ( X1 @ zero )
!= X0 )
| ( $true = X4 ) ),
inference(constrained_superposition,[status(thm)],[f11,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUN023^1 : TPTP v9.2.1. Released v6.4.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n012.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 11:19:30 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : NUN023^1 : TPTP v9.2.1. Released v6.4.0.
% 0.16/0.39 % Domain : Number Theory
% 0.16/0.39 % Problem : Function h s.t. h(0) = 1, h(1) = 0, no witness
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : Using an axiomatiztion of if-then-else, find the if-then-else
% 0.16/0.39 % term that expresses the function H.
% 0.16/0.39
% 0.16/0.39 % Refs : [Rie16] Riener (2016), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [TPTP]
% 0.16/0.39 % Names : ntape6-0-without-witness.tptp [Rie16]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.44 v9.1.0, 0.62 v9.0.0, 0.60 v8.2.0, 0.69 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.44 v7.3.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.57 v6.4.0
% 0.16/0.39 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.16/0.39 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 4 ( 4 avg)
% 0.16/0.39 % Number of connectives : 16 ( 1 ~; 0 |; 2 &; 10 @)
% 0.16/0.39 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 8 ( 8 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 4 ( 3 usr; 1 con; 0-3 aty)
% 0.16/0.39 % Number of variables : 7 ( 0 ^; 6 !; 1 ?; 7 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments :
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(n5,type,
% 0.16/0.39 zero: $i ).
% 0.16/0.39
% 0.16/0.39 thf(n6,type,
% 0.16/0.39 s: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(n7,type,
% 0.16/0.39 ite: $o > $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(n8,conjecture,
% 0.16/0.39 ( ( ! [X: $o,U: $i,V: $i] :
% 0.16/0.39 ( X
% 0.16/0.39 => ( ( ite @ X @ U @ V )
% 0.16/0.39 = U ) )
% 0.16/0.39 & ! [X: $o,U: $i,V: $i] :
% 0.16/0.39 ( ~ X
% 0.16/0.39 => ( ( ite @ X @ U @ V )
% 0.16/0.39 = V ) ) )
% 0.16/0.39 => ? [H: $i > $i] :
% 0.16/0.39 ( ( ( H @ zero )
% 0.16/0.39 = ( s @ zero ) )
% 0.16/0.39 & ( ( H @ ( s @ zero ) )
% 0.16/0.39 = zero ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 0.22/1.30 ---- Embedded in THF ---
% 0.22/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.22/1.30 %%% Generated on Tue Feb 24 11:19:31 EST 2026
% 0.22/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.22/1.30 %%% Logic specification used:
% 0.22/1.30 %%% thf(spec, logic, $$dhol).
% 0.22/1.30
% 0.22/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.xws3VfhP2z/DTF2DTF16074.p
% See solution above
% 0.22/1.30 ------------------------
% 0.22/1.31 ---- Cleaned THF ---
% 0.22/1.31 thf(n5,type,
% 0.22/1.31 zero: $i ).
% 0.22/1.31
% 0.22/1.31 thf(n6,type,
% 0.22/1.31 s: $i > $i ).
% 0.22/1.31
% 0.22/1.31 thf(n7,type,
% 0.22/1.31 ite: $o > $i > $i > $i ).
% 0.22/1.31
% 0.22/1.31 thf(n8,conjecture,
% 0.22/1.31 ( ( ! [X: $o,U: $i,V: $i] :
% 0.22/1.31 ( X
% 0.22/1.31 => ( ( ite @ X @ U @ V )
% 0.22/1.31 = U ) )
% 0.22/1.31 & ! [X: $o,U: $i,V: $i] :
% 0.22/1.31 ( ~ X
% 0.22/1.31 => ( ( ite @ X @ U @ V )
% 0.22/1.31 = V ) ) )
% 0.22/1.31 => ? [H: $i > $i] :
% 0.22/1.31 ( ( ( H @ zero )
% 0.22/1.31 = ( s @ zero ) )
% 0.22/1.31 & ( ( H @ ( s @ zero ) )
% 0.22/1.31 = zero ) ) ) ).
% 0.22/1.31 ------------------------
% 0.22/1.33 % (16175)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16074 for (3000ds/2Mi)
% 0.22/1.33 % (16173)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_16074 for (3000ds/4Mi)
% 0.22/1.33 % (16172)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16074 for (3000ds/183Mi)
% 0.22/1.33 % (16174)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_16074 for (3000ds/27Mi)
% 0.22/1.33 % (16178)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16074 for (3000ds/18Mi)
% 0.22/1.33 % (16177)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_16074 for (3000ds/275Mi)
% 0.22/1.33 % (16176)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_16074 for (3000ds/2Mi)
% 0.22/1.33 % (16175)Instruction limit reached!
% 0.22/1.33 % (16175)------------------------------
% 0.22/1.33 % (16175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (16175)Termination reason: Unknown
% 0.22/1.33 % (16175)Termination phase: Saturation
% 0.22/1.33 % (16176)Instruction limit reached!
% 0.22/1.33 % (16176)------------------------------
% 0.22/1.33 % (16176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (16176)Termination reason: Unknown
% 0.22/1.33 % (16176)Termination phase: Saturation
% 0.22/1.33
% 0.22/1.33 % (16176)Memory used [KB]: 5500
% 0.22/1.33 % (16176)Time elapsed: 0.003 s
% 0.22/1.33 % (16176)Instructions burned: 2 (million)
% 0.22/1.33 % (16176)------------------------------
% 0.22/1.33 % (16176)------------------------------
% 0.22/1.33
% 0.22/1.33 % (16175)Memory used [KB]: 5500
% 0.22/1.33 % (16175)Time elapsed: 0.003 s
% 0.22/1.33 % (16175)Instructions burned: 2 (million)
% 0.22/1.33 % (16175)------------------------------
% 0.22/1.33 % (16175)------------------------------
% 0.22/1.33 % (16177)Refutation not found, incomplete strategy
% 0.22/1.33 % (16177)------------------------------
% 0.22/1.33 % (16177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (16177)Termination reason: Refutation not found, incomplete strategy
% 0.22/1.33
% 0.22/1.33
% 0.22/1.33 % (16177)Memory used [KB]: 5500
% 0.22/1.33 % (16177)Time elapsed: 0.003 s
% 0.22/1.33 % (16177)Instructions burned: 2 (million)
% 0.22/1.33 % (16177)------------------------------
% 0.22/1.33 % (16177)------------------------------
% 0.22/1.33 % (16174)Refutation not found, incomplete strategy
% 0.22/1.33 % (16174)------------------------------
% 0.22/1.33 % (16174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (16174)Termination reason: Refutation not found, incomplete strategy
% 0.22/1.33
% 0.22/1.33
% 0.22/1.33 % (16174)Memory used [KB]: 5500
% 0.22/1.33 % (16174)Time elapsed: 0.004 s
% 0.22/1.33 % (16174)Instructions burned: 3 (million)
% 0.22/1.33 % (16174)------------------------------
% 0.22/1.33 % (16174)------------------------------
% 0.22/1.33 % (16173)Instruction limit reached!
% 0.22/1.33 % (16173)------------------------------
% 0.22/1.33 % (16173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (16173)Termination reason: Unknown
% 0.22/1.33 % (16173)Termination phase: Saturation
% 0.22/1.33
% 0.22/1.33 % (16173)Memory used [KB]: 5500
% 0.22/1.33 % (16173)Time elapsed: 0.005 s
% 0.22/1.33 % (16173)Instructions burned: 5 (million)
% 0.22/1.33 % (16173)------------------------------
% 0.22/1.33 % (16173)------------------------------
% 0.22/1.34 % (16178)Instruction limit reached!
% 0.22/1.34 % (16178)------------------------------
% 0.22/1.34 % (16178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.34 % (16178)Termination reason: Unknown
% 0.22/1.34 % (16178)Termination phase: Saturation
% 0.22/1.34
% 0.22/1.34 % (16178)Memory used [KB]: 5500
% 0.22/1.34 % (16178)Time elapsed: 0.012 s
% 0.22/1.34 % (16178)Instructions burned: 19 (million)
% 0.22/1.34 % (16178)------------------------------
% 0.22/1.34 % (16178)------------------------------
% 0.22/1.34 % (16179)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/3Mi)
% 0.22/1.34 % (16180)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_16074 for (2999ds/37Mi)
% 0.22/1.34 % (16181)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_16074 for (2999ds/15Mi)
% 0.22/1.35 % (16182)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_16074 for (2999ds/3Mi)
% 0.22/1.35 % (16183)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_16074 for (2999ds/1041Mi)
% 0.22/1.35 % (16179)Instruction limit reached!
% 0.22/1.35 % (16179)------------------------------
% 0.22/1.35 % (16179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.35 % (16179)Termination reason: Unknown
% 0.22/1.35 % (16179)Termination phase: Saturation
% 0.22/1.35 % (16181)Refutation not found, incomplete strategy
% 0.22/1.35 % (16181)------------------------------
% 0.22/1.35 % (16181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.35 % (16181)Termination reason: Refutation not found, incomplete strategy
% 0.22/1.35
% 0.22/1.35
% 0.22/1.35 % (16181)Memory used [KB]: 5500
% 0.22/1.35 % (16181)Time elapsed: 0.003 s
% 0.22/1.35 % (16181)Instructions burned: 2 (million)
% 0.22/1.35 % (16181)------------------------------
% 0.22/1.35 % (16181)------------------------------
% 0.22/1.35
% 0.22/1.35 % (16179)Memory used [KB]: 5500
% 0.22/1.35 % (16179)Time elapsed: 0.004 s
% 0.22/1.35 % (16179)Instructions burned: 4 (million)
% 0.22/1.35 % (16179)------------------------------
% 0.22/1.35 % (16179)------------------------------
% 0.22/1.35 % (16182)Instruction limit reached!
% 0.22/1.35 % (16182)------------------------------
% 0.22/1.35 % (16182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.35 % (16182)Termination reason: Unknown
% 0.22/1.35 % (16182)Termination phase: Saturation
% 0.22/1.35
% 0.22/1.35 % (16182)Memory used [KB]: 5500
% 0.22/1.35 % (16182)Time elapsed: 0.004 s
% 0.22/1.35 % (16182)Instructions burned: 4 (million)
% 0.22/1.35 % (16182)------------------------------
% 0.22/1.35 % (16182)------------------------------
% 0.22/1.35 % (16184)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/7Mi)
% 0.22/1.36 % (16184)Instruction limit reached!
% 0.22/1.36 % (16184)------------------------------
% 0.22/1.36 % (16184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.36 % (16184)Termination reason: Unknown
% 0.22/1.36 % (16184)Termination phase: Saturation
% 0.22/1.36
% 0.22/1.36 % (16184)Memory used [KB]: 1023
% 0.22/1.36 % (16184)Time elapsed: 0.005 s
% 0.22/1.36 % (16184)Instructions burned: 7 (million)
% 0.22/1.36 % (16184)------------------------------
% 0.22/1.36 % (16184)------------------------------
% 0.22/1.36 % (16186)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_16074 for (2999ds/3Mi)
% 0.22/1.36 % (16185)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/16Mi)
% 0.22/1.36 % (16180)Instruction limit reached!
% 0.22/1.36 % (16180)------------------------------
% 0.22/1.36 % (16180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.36 % (16180)Termination reason: Unknown
% 0.22/1.36 % (16180)Termination phase: Saturation
% 0.22/1.36
% 0.22/1.36 % (16180)Memory used [KB]: 5628
% 0.22/1.36 % (16180)Time elapsed: 0.021 s
% 0.22/1.36 % (16180)Instructions burned: 38 (million)
% 0.22/1.36 % (16180)------------------------------
% 0.22/1.36 % (16180)------------------------------
% 0.22/1.36 % (16187)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_16074 for (2999ds/3Mi)
% 0.22/1.36 % (16186)Instruction limit reached!
% 0.22/1.36 % (16186)------------------------------
% 0.22/1.36 % (16186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.36 % (16186)Termination reason: Unknown
% 0.22/1.36 % (16186)Termination phase: Saturation
% 0.22/1.36
% 0.22/1.36 % (16186)Memory used [KB]: 5500
% 0.22/1.36 % (16186)Time elapsed: 0.003 s
% 0.22/1.36 % (16186)Instructions burned: 3 (million)
% 0.22/1.36 % (16186)------------------------------
% 0.22/1.36 % (16186)------------------------------
% 0.22/1.37 % (16187)Instruction limit reached!
% 0.22/1.37 % (16187)------------------------------
% 0.22/1.37 % (16187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.37 % (16187)Termination reason: Unknown
% 0.22/1.37 % (16187)Termination phase: Saturation
% 0.22/1.37
% 0.22/1.37 % (16187)Memory used [KB]: 1023
% 0.22/1.37 % (16187)Time elapsed: 0.003 s
% 0.22/1.37 % (16187)Instructions burned: 3 (million)
% 0.22/1.37 % (16187)------------------------------
% 0.22/1.37 % (16187)------------------------------
% 0.22/1.37 % (16185)Instruction limit reached!
% 0.22/1.37 % (16185)------------------------------
% 0.22/1.37 % (16185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.37 % (16185)Termination reason: Unknown
% 0.22/1.37 % (16185)Termination phase: Saturation
% 0.22/1.37
% 0.22/1.37 % (16185)Memory used [KB]: 5628
% 0.22/1.37 % (16185)Time elapsed: 0.011 s
% 0.22/1.37 % (16185)Instructions burned: 17 (million)
% 0.22/1.37 % (16185)------------------------------
% 0.22/1.37 % (16185)------------------------------
% 0.22/1.37 % (16188)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/7Mi)
% 0.22/1.37 % (16188)Refutation not found, incomplete strategy
% 0.22/1.37 % (16188)------------------------------
% 0.22/1.37 % (16188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.37 % (16188)Termination reason: Refutation not found, incomplete strategy
% 0.22/1.37
% 0.22/1.37
% 0.22/1.37 % (16188)Memory used [KB]: 5500
% 0.22/1.37 % (16188)Time elapsed: 0.002 s
% 0.22/1.37 % (16188)Instructions burned: 1 (million)
% 0.22/1.37 % (16188)------------------------------
% 0.22/1.37 % (16188)------------------------------
% 0.22/1.38 % (16189)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/3Mi)
% 0.22/1.38 % (16190)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/4Mi)
% 0.22/1.38 % (16189)Instruction limit reached!
% 0.22/1.38 % (16189)------------------------------
% 0.22/1.38 % (16189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.38 % (16189)Termination reason: Unknown
% 0.22/1.38 % (16189)Termination phase: Saturation
% 0.22/1.38
% 0.22/1.38 % (16189)Memory used [KB]: 5500
% 0.22/1.38 % (16189)Time elapsed: 0.003 s
% 0.22/1.38 % (16189)Instructions burned: 3 (million)
% 0.22/1.38 % (16189)------------------------------
% 0.22/1.38 % (16189)------------------------------
% 0.22/1.38 % (16191)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/18Mi)
% 0.22/1.38 % (16190)Instruction limit reached!
% 0.22/1.38 % (16190)------------------------------
% 0.22/1.38 % (16190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.38 % (16190)Termination reason: Unknown
% 0.22/1.38 % (16190)Termination phase: Saturation
% 0.22/1.38
% 0.22/1.38 % (16190)Memory used [KB]: 5500
% 0.22/1.38 % (16190)Time elapsed: 0.004 s
% 0.22/1.38 % (16190)Instructions burned: 4 (million)
% 0.22/1.38 % (16190)------------------------------
% 0.22/1.38 % (16190)------------------------------
% 0.22/1.38 % (16191)Refutation not found, incomplete strategy
% 0.22/1.38 % (16191)------------------------------
% 0.22/1.38 % (16191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.38 % (16191)Termination reason: Refutation not found, incomplete strategy
% 0.22/1.38
% 0.22/1.38
% 0.22/1.38 % (16191)Memory used [KB]: 5500
% 0.22/1.38 % (16191)Time elapsed: 0.003 s
% 0.22/1.38 % (16191)Instructions burned: 3 (million)
% 0.22/1.38 % (16191)------------------------------
% 0.22/1.38 % (16191)------------------------------
% 0.22/1.39 % (16192)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/710Mi)
% 0.22/1.39 % (16193)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/6Mi)
% 0.22/1.39 % (16193)Instruction limit reached!
% 0.22/1.39 % (16193)------------------------------
% 0.22/1.39 % (16193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.39 % (16193)Termination reason: Unknown
% 0.22/1.39 % (16193)Termination phase: Saturation
% 0.22/1.39
% 0.22/1.39 % (16193)Memory used [KB]: 5500
% 0.22/1.39 % (16193)Time elapsed: 0.006 s
% 0.22/1.39 % (16193)Instructions burned: 7 (million)
% 0.22/1.39 % (16193)------------------------------
% 0.22/1.39 % (16193)------------------------------
% 1.56/1.40 % (16194)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_16074 for (2999ds/902Mi)
% 1.56/1.40 % (16195)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_16074 for (2999ds/21Mi)
% 1.56/1.40 % (16194)Refutation not found, incomplete strategy
% 1.56/1.40 % (16194)------------------------------
% 1.56/1.40 % (16194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.40 % (16194)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.40
% 1.56/1.40
% 1.56/1.40 % (16194)Memory used [KB]: 5500
% 1.56/1.40 % (16194)Time elapsed: 0.003 s
% 1.56/1.40 % (16194)Instructions burned: 2 (million)
% 1.56/1.40 % (16194)------------------------------
% 1.56/1.40 % (16194)------------------------------
% 1.56/1.40 % (16196)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/5Mi)
% 1.56/1.40 % (16196)Instruction limit reached!
% 1.56/1.40 % (16196)------------------------------
% 1.56/1.40 % (16196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.40 % (16196)Termination reason: Unknown
% 1.56/1.40 % (16196)Termination phase: Saturation
% 1.56/1.40
% 1.56/1.40 % (16196)Memory used [KB]: 5500
% 1.56/1.40 % (16196)Time elapsed: 0.004 s
% 1.56/1.40 % (16196)Instructions burned: 5 (million)
% 1.56/1.40 % (16196)------------------------------
% 1.56/1.40 % (16196)------------------------------
% 1.56/1.41 % (16197)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_16074 for (2999ds/6Mi)
% 1.56/1.41 % (16195)Instruction limit reached!
% 1.56/1.41 % (16195)------------------------------
% 1.56/1.41 % (16195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.41 % (16195)Termination reason: Unknown
% 1.56/1.41 % (16195)Termination phase: Saturation
% 1.56/1.41
% 1.56/1.41 % (16195)Memory used [KB]: 5628
% 1.56/1.41 % (16195)Time elapsed: 0.014 s
% 1.56/1.41 % (16195)Instructions burned: 22 (million)
% 1.56/1.41 % (16195)------------------------------
% 1.56/1.41 % (16195)------------------------------
% 1.56/1.41 % (16197)Instruction limit reached!
% 1.56/1.41 % (16197)------------------------------
% 1.56/1.41 % (16197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.41 % (16197)Termination reason: Unknown
% 1.56/1.41 % (16197)Termination phase: Saturation
% 1.56/1.41
% 1.56/1.41 % (16197)Memory used [KB]: 5500
% 1.56/1.41 % (16197)Time elapsed: 0.005 s
% 1.56/1.41 % (16197)Instructions burned: 8 (million)
% 1.56/1.41 % (16197)------------------------------
% 1.56/1.41 % (16197)------------------------------
% 1.56/1.42 % (16198)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/377Mi)
% 1.56/1.42 % (16198)Refutation not found, incomplete strategy
% 1.56/1.42 % (16198)------------------------------
% 1.56/1.42 % (16198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.42 % (16198)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.42
% 1.56/1.42
% 1.56/1.42 % (16198)Memory used [KB]: 5500
% 1.56/1.42 % (16198)Time elapsed: 0.003 s
% 1.56/1.42 % (16198)Instructions burned: 3 (million)
% 1.56/1.42 % (16198)------------------------------
% 1.56/1.42 % (16198)------------------------------
% 1.56/1.42 % (16199)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_16074 for (2999ds/779Mi)
% 1.56/1.42 % (16172)Instruction limit reached!
% 1.56/1.42 % (16172)------------------------------
% 1.56/1.42 % (16172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.42 % (16172)Termination reason: Unknown
% 1.56/1.42 % (16172)Termination phase: Saturation
% 1.56/1.42
% 1.56/1.42 % (16172)Memory used [KB]: 6140
% 1.56/1.42 % (16172)Time elapsed: 0.094 s
% 1.56/1.42 % (16172)Instructions burned: 184 (million)
% 1.56/1.42 % (16172)------------------------------
% 1.56/1.42 % (16172)------------------------------
% 1.56/1.43 % (16199)Refutation not found, incomplete strategy
% 1.56/1.43 % (16199)------------------------------
% 1.56/1.43 % (16199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.43 % (16199)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.43
% 1.56/1.43
% 1.56/1.43 % (16199)Memory used [KB]: 5500
% 1.56/1.43 % (16199)Time elapsed: 0.009 s
% 1.56/1.43 % (16199)Instructions burned: 14 (million)
% 1.56/1.43 % (16199)------------------------------
% 1.56/1.43 % (16199)------------------------------
% 1.56/1.43 % (16200)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_16074 for (2999ds/19Mi)
% 1.56/1.43 % (16201)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/879Mi)
% 1.56/1.43 % (16200)Refutation not found, incomplete strategy
% 1.56/1.43 % (16200)------------------------------
% 1.56/1.43 % (16200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.43 % (16200)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.43
% 1.56/1.43
% 1.56/1.43 % (16200)Memory used [KB]: 5500
% 1.56/1.43 % (16200)Time elapsed: 0.004 s
% 1.56/1.43 % (16200)Instructions burned: 5 (million)
% 1.56/1.43 % (16200)------------------------------
% 1.56/1.43 % (16200)------------------------------
% 1.56/1.43 % (16201)Refutation not found, incomplete strategy
% 1.56/1.43 % (16201)------------------------------
% 1.56/1.43 % (16201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.43 % (16201)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.43
% 1.56/1.43
% 1.56/1.43 % (16201)Memory used [KB]: 5500
% 1.56/1.43 % (16201)Time elapsed: 0.003 s
% 1.56/1.43 % (16201)Instructions burned: 3 (million)
% 1.56/1.43 % (16201)------------------------------
% 1.56/1.43 % (16201)------------------------------
% 1.56/1.43 % (16202)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/17Mi)
% 1.56/1.43 % (16203)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/3Mi)
% 1.56/1.44 % (16203)Instruction limit reached!
% 1.56/1.44 % (16203)------------------------------
% 1.56/1.44 % (16203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.44 % (16203)Termination reason: Unknown
% 1.56/1.44 % (16203)Termination phase: Saturation
% 1.56/1.44
% 1.56/1.44 % (16203)Memory used [KB]: 1023
% 1.56/1.44 % (16203)Time elapsed: 0.003 s
% 1.56/1.44 % (16203)Instructions burned: 3 (million)
% 1.56/1.44 % (16203)------------------------------
% 1.56/1.44 % (16203)------------------------------
% 1.56/1.44 % (16204)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_16074 for (2999ds/30Mi)
% 1.56/1.44 % (16202)Instruction limit reached!
% 1.56/1.44 % (16202)------------------------------
% 1.56/1.44 % (16202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.44 % (16202)Termination reason: Unknown
% 1.56/1.44 % (16202)Termination phase: Saturation
% 1.56/1.44
% 1.56/1.44 % (16202)Memory used [KB]: 5628
% 1.56/1.44 % (16202)Time elapsed: 0.012 s
% 1.56/1.44 % (16202)Instructions burned: 18 (million)
% 1.56/1.44 % (16202)------------------------------
% 1.56/1.44 % (16202)------------------------------
% 1.56/1.45 % (16205)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_16074 for (2998ds/127Mi)
% 1.56/1.45 % (16206)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_16074 for (2998ds/100Mi)
% 1.56/1.45 % (16206)Refutation not found, incomplete strategy
% 1.56/1.45 % (16206)------------------------------
% 1.56/1.45 % (16206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.45 % (16206)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.45
% 1.56/1.45
% 1.56/1.45 % (16206)Memory used [KB]: 5500
% 1.56/1.45 % (16206)Time elapsed: 0.004 s
% 1.56/1.45 % (16206)Instructions burned: 3 (million)
% 1.56/1.45 % (16206)------------------------------
% 1.56/1.45 % (16206)------------------------------
% 1.56/1.45 % (16207)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_16074 for (2998ds/3Mi)
% 1.56/1.45 % (16207)Instruction limit reached!
% 1.56/1.45 % (16207)------------------------------
% 1.56/1.45 % (16207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.45 % (16207)Termination reason: Unknown
% 1.56/1.45 % (16207)Termination phase: Saturation
% 1.56/1.45
% 1.56/1.45 % (16207)Memory used [KB]: 5500
% 1.56/1.45 % (16207)Time elapsed: 0.003 s
% 1.56/1.45 % (16207)Instructions burned: 3 (million)
% 1.56/1.45 % (16207)------------------------------
% 1.56/1.45 % (16207)------------------------------
% 1.56/1.46 % (16204)Instruction limit reached!
% 1.56/1.46 % (16204)------------------------------
% 1.56/1.46 % (16204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.46 % (16204)Termination reason: Unknown
% 1.56/1.46 % (16204)Termination phase: Saturation
% 1.56/1.46
% 1.56/1.46 % (16204)Memory used [KB]: 5628
% 1.56/1.46 % (16204)Time elapsed: 0.039 s
% 1.56/1.46 % (16204)Instructions burned: 31 (million)
% 1.56/1.46 % (16208)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_16074 for (2998ds/20Mi)
% 1.56/1.46 % (16204)------------------------------
% 1.56/1.46 % (16204)------------------------------
% 1.56/1.46 % (16208)Refutation not found, incomplete strategy
% 1.56/1.46 % (16208)------------------------------
% 1.56/1.46 % (16208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.46 % (16208)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.46
% 1.56/1.46
% 1.56/1.46 % (16208)Memory used [KB]: 5500
% 1.56/1.46 % (16208)Time elapsed: 0.003 s
% 1.56/1.46 % (16208)Instructions burned: 2 (million)
% 1.56/1.46 % (16208)------------------------------
% 1.56/1.46 % (16208)------------------------------
% 1.56/1.47 % (16209)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_16074 for (2998ds/86Mi)
% 1.56/1.47 % (16210)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_16074 for (2998ds/107Mi)
% 1.56/1.47 % (16210)Refutation not found, incomplete strategy
% 1.56/1.47 % (16210)------------------------------
% 1.56/1.47 % (16210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.47 % (16210)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.47
% 1.56/1.47
% 1.56/1.47 % (16210)Memory used [KB]: 5500
% 1.56/1.47 % (16210)Time elapsed: 0.003 s
% 1.56/1.47 % (16210)Instructions burned: 2 (million)
% 1.56/1.47 % (16210)------------------------------
% 1.56/1.47 % (16210)------------------------------
% 1.56/1.48 % (16211)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_16074 for (2998ds/39Mi)
% 1.56/1.48 % (16212)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_16074 for (2998ds/448Mi)
% 1.56/1.49 % (16212)Refutation not found, incomplete strategy
% 1.56/1.49 % (16212)------------------------------
% 1.56/1.49 % (16212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.49 % (16212)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.49
% 1.56/1.49
% 1.56/1.49 % (16212)Memory used [KB]: 5628
% 1.56/1.49 % (16212)Time elapsed: 0.009 s
% 1.56/1.49 % (16212)Instructions burned: 14 (million)
% 1.56/1.49 % (16212)------------------------------
% 1.56/1.49 % (16212)------------------------------
% 1.56/1.49 % (16213)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_16074 for (2998ds/46Mi)
% 1.56/1.49 % (16211)Instruction limit reached!
% 1.56/1.49 % (16211)------------------------------
% 1.56/1.49 % (16211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.49 % (16211)Termination reason: Unknown
% 1.56/1.49 % (16211)Termination phase: Saturation
% 1.56/1.49
% 1.56/1.50 % (16211)Memory used [KB]: 5756
% 1.56/1.50 % (16211)Time elapsed: 0.021 s
% 1.56/1.50 % (16211)Instructions burned: 39 (million)
% 1.56/1.50 % (16211)------------------------------
% 1.56/1.50 % (16211)------------------------------
% 1.56/1.50 % (16192)First to succeed.
% 1.56/1.50 % (16214)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_16074 for (2998ds/98Mi)
% 1.56/1.50 % (16192)Refutation found. Thanks to Tanya!
% 1.56/1.50 % SZS status Theorem for DTF2THF_16074
% 1.56/1.50 % SZS output start Proof for DTF2THF_16074
% 1.56/1.50 thf(func_def_1, type, s: $i > $i).
% 1.56/1.50 thf(func_def_2, type, ite: $o > $i > $i > $i).
% 1.56/1.50 thf(func_def_8, type, ph1: !>[X0: $tType]:(X0)).
% 1.56/1.50 thf(f798,plain,(
% 1.56/1.50 $false),
% 1.56/1.50 inference(avatar_sat_refutation,[status(thm)],[f33,f92,f159,f307,f435,f510,f539,f708,f797])).
% 1.56/1.50 thf(f797,plain,(
% 1.56/1.50 ~spl0_28),
% 1.56/1.50 inference(avatar_contradiction_clause,[status(thm)],[f796])).
% 1.56/1.50 thf(f796,plain,(
% 1.56/1.50 $false | ~spl0_28),
% 1.56/1.50 inference(equality_resolution,[status(thm)],[f777])).
% 1.56/1.50 thf(f777,plain,(
% 1.56/1.50 ( ! [X0 : $i] : ((zero != X0)) ) | ~spl0_28),
% 1.56/1.50 inference(beta_eta_normalization,[status(thm)],[f776])).
% 1.56/1.50 thf(f776,plain,(
% 1.56/1.50 ( ! [X0 : $i] : ((((^[Y0 : $i]: (zero)) @ zero) != X0)) ) | ~spl0_28),
% 1.56/1.50 inference(equality_resolution,[status(thm)],[f745])).
% 1.56/1.50 thf(f745,plain,(
% 1.56/1.50 ( ! [X0 : $i > $i,X1 : $i] : ((zero != (X0 @ (s @ zero))) | ((X0 @ zero) != X1)) ) | ~spl0_28),
% 1.56/1.50 inference(equality_resolution,[status(thm)],[f306])).
% 1.56/1.50 thf(f306,plain,(
% 1.56/1.50 ( ! [X0 : $i > $i,X1 : $i,X5 : $i] : ((zero != X1) | ((X0 @ zero) != X5) | ((X0 @ (s @ zero)) != X1)) ) | ~spl0_28),
% 1.56/1.50 inference(avatar_component_clause,[status(thm)],[f305])).
% 1.56/1.50 thf(f305,definition,(
% 1.56/1.50 spl0_28 <=> ! [X5 : $i,X0 : $i > $i,X1 : $i] : (((X0 @ zero) != X5) | ((X0 @ (s @ zero)) != X1) | (zero != X1))),
% 1.56/1.50 introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition])).
% 1.56/1.50 thf(f708,plain,(
% 1.56/1.50 ~spl0_27),
% 1.56/1.50 inference(avatar_contradiction_clause,[status(thm)],[f707])).
% 1.56/1.50 thf(f707,plain,(
% 1.56/1.50 $false | ~spl0_27),
% 1.56/1.50 inference(equality_resolution,[status(thm)],[f689])).
% 1.56/1.50 thf(f689,plain,(
% 1.56/1.50 ( ! [X1 : $i] : (((s @ zero) != X1)) ) | ~spl0_27),
% 1.56/1.50 inference(beta_eta_normalization,[status(thm)],[f678])).
% 1.56/1.50 thf(f678,plain,(
% 1.56/1.50 ( ! [X1 : $i] : ((((^[Y0 : $i]: (s @ ((^[Y1 : $i]: (zero)) @ Y0))) @ (s @ zero)) != X1)) ) | ~spl0_27),
% 1.56/1.50 inference(equality_resolution,[status(thm)],[f673])).
% 1.56/1.50 thf(f673,plain,(
% 1.56/1.50 ( ! [X0 : $i > $i,X1 : $i] : (((s @ zero) != (X0 @ zero)) | ((X0 @ (s @ zero)) != X1)) ) | ~spl0_27),
% 1.56/1.50 inference(equality_resolution,[status(thm)],[f303])).
% 1.56/1.50 thf(f303,plain,(
% 1.56/1.50 ( ! [X2 : $i > $i,X3 : $i,X4 : $i] : (((s @ zero) != X4) | ((X2 @ zero) != X4) | ((X2 @ (s @ zero)) != X3)) ) | ~spl0_27),
% 1.56/1.50 inference(avatar_component_clause,[status(thm)],[f302])).
% 1.56/1.50 thf(f302,definition,(
% 1.56/1.50 spl0_27 <=> ! [X2 : $i > $i,X4 : $i,X3 : $i] : (((X2 @ (s @ zero)) != X3) | ((X2 @ zero) != X4) | ((s @ zero) != X4))),
% 1.56/1.50 introduced(definition,[new_symbols(naming,[spl0_27])],[avatar_definition])).
% 1.56/1.50 thf(f539,plain,(
% 1.56/1.50 spl0_4 | spl0_3),
% 1.56/1.50 inference(avatar_split_clause,[status(thm)],[f167,f35,f38])).
% 1.56/1.50 thf(f38,definition,(
% 1.56/1.50 spl0_4 <=> ! [X4 : $o] : (($true = X4) | ($false = X4))),
% 1.56/1.50 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.56/1.50 thf(f35,definition,(
% 1.56/1.50 spl0_3 <=> ! [X5 : $i > $o,X0 : $i,X3 : $i > $i,X2 : $i,X1 : $i > $i] : (((X1 @ zero) != X0) | ((s @ zero) != X2) | (zero != (ite @ (X5 @ (s @ zero)) @ (X1 @ (s @ zero)) @ (X3 @ (s @ zero)))) | ((X3 @ zero) != X2) | ($false = (X5 @ zero)))),
% 1.56/1.50 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.56/1.50 thf(f167,plain,(
% 1.56/1.50 ( ! [X2 : $i,X3 : $i > $i,X0 : $i,X1 : $i > $i,X4 : $o,X5 : $i > $o] : (($false = (X5 @ zero)) | ($false = X4) | ($true = X4) | ((X3 @ zero) != X2) | ((X1 @ zero) != X0) | ((s @ zero) != X2) | (zero != (ite @ (X5 @ (s @ zero)) @ (X1 @ (s @ zero)) @ (X3 @ (s @ zero))))) )),
% 1.56/1.50 inference(binary_proxy_clausification,[status(thm)],[f165])).
% 1.56/1.50 thf(f165,plain,(
% 1.56/1.50 ( ! [X2 : $i,X3 : $i > $i,X0 : $i,X1 : $i > $i,X4 : $o,X5 : $i > $o] : (($true = X4) | (zero != (ite @ (X5 @ (s @ zero)) @ (X1 @ (s @ zero)) @ (X3 @ (s @ zero)))) | ((s @ zero) != X2) | ((X5 @ zero) != X4) | ((X1 @ zero) != X0) | ((X3 @ zero) != X2)) )),
% 1.56/1.50 inference(beta_eta_normalization,[status(thm)],[f164])).
% 1.56/1.50 thf(f164,plain,(
% 1.56/1.50 ( ! [X2 : $i,X3 : $i > $i,X0 : $i,X1 : $i > $i,X4 : $o,X5 : $i > $o] : (((s @ zero) != X2) | ($true = X4) | (zero != ((^[Y0 : $i]: (ite @ (X5 @ Y0) @ (X1 @ Y0) @ (X3 @ Y0))) @ (s @ zero))) | ((X1 @ zero) != X0) | ((X3 @ zero) != X2) | ((X5 @ zero) != X4)) )),
% 1.56/1.50 inference(constrained_superposition,[status(thm)],[f11,f10])).
% 1.56/1.50 thf(f10,plain,(
% 1.56/1.50 ( ! [X6 : $i,X4 : $o,X5 : $i] : (((ite @ X4 @ X6 @ X5) = X5) | ($true = X4)) )),
% 1.56/1.50 inference(cnf_transformation,[status(thm)],[f9])).
% 1.56/1.50 thf(f9,plain,(
% 1.56/1.50 ! [X0 : $o,X1 : $i,X2 : $i] : (((ite @ X0 @ X1 @ X2) = X1) | ($true != X0)) & ! [X3 : $i > $i] : ((zero != (X3 @ (s @ zero))) | ((X3 @ zero) != (s @ zero))) & ! [X4 : $o,X5 : $i,X6 : $i] : (((ite @ X4 @ X6 @ X5) = X5) | ($true = X4))),
% 1.56/1.50 inference(rectify,[status(thm)],[f8])).
% 1.56/1.50 thf(f8,plain,(
% 1.56/1.50 ! [X4 : $o,X5 : $i,X3 : $i] : (((ite @ X4 @ X5 @ X3) = X5) | ($true != X4)) & ! [X6 : $i > $i] : ((zero != (X6 @ (s @ zero))) | ((s @ zero) != (X6 @ zero))) & ! [X2 : $o,X1 : $i,X0 : $i] : (((ite @ X2 @ X0 @ X1) = X1) | ($true = X2))),
% 1.56/1.50 inference(flattening,[status(thm)],[f7])).
% 1.56/1.50 thf(f7,plain,(
% 1.56/1.50 ! [X6 : $i > $i] : ((zero != (X6 @ (s @ zero))) | ((s @ zero) != (X6 @ zero))) & (! [X2 : $o,X1 : $i,X0 : $i] : (((ite @ X2 @ X0 @ X1) = X1) | ($true = X2)) & ! [X4 : $o,X5 : $i,X3 : $i] : (((ite @ X4 @ X5 @ X3) = X5) | ($true != X4)))),
% 1.56/1.50 inference(ennf_transformation,[status(thm)],[f6])).
% 1.56/1.50 thf(f6,plain,(
% 1.56/1.50 ~((! [X0 : $i,X1 : $i,X2 : $o] : (($true != X2) => ((ite @ X2 @ X0 @ X1) = X1)) & ! [X5 : $i,X4 : $o,X3 : $i] : (($true = X4) => ((ite @ X4 @ X5 @ X3) = X5))) => ? [X6 : $i > $i] : (((s @ zero) = (X6 @ zero)) & (zero = (X6 @ (s @ zero)))))),
% 1.56/1.50 inference(flattening,[status(thm)],[f5])).
% 1.56/1.50 thf(f5,plain,(
% 1.56/1.50 ~((! [X0 : $i,X1 : $i,X2 : $o] : (~($true = X2) => ((ite @ X2 @ X0 @ X1) = X1)) & ! [X5 : $i,X4 : $o,X3 : $i] : (($true = X4) => ((ite @ X4 @ X5 @ X3) = X5))) => ? [X6 : $i > $i] : (((s @ zero) = (X6 @ zero)) & (zero = (X6 @ (s @ zero)))))),
% 1.56/1.50 inference(fool_elimination,[status(thm)],[f4])).
% 1.56/1.50 thf(f4,plain,(
% 1.56/1.50 ~((! [X0 : $i,X1 : $i,X2 : $o] : (~X2 => ((ite @ X2 @ X0 @ X1) = X1)) & ! [X3 : $i,X4 : $o,X5 : $i] : (X4 => ((ite @ X4 @ X5 @ X3) = X5))) => ? [X6 : $i > $i] : ((zero = (X6 @ (s @ zero))) & ((s @ zero) = (X6 @ zero))))),
% 1.56/1.50 inference(rectify,[status(thm)],[f2])).
% 1.56/1.50 thf(f2,negated_conjecture,(
% 1.56/1.50 ~((! [X1 : $i,X2 : $i,X0 : $o] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X2 : $i,X0 : $o,X1 : $i] : (X0 => ((ite @ X0 @ X1 @ X2) = X1))) => ? [X3 : $i > $i] : ((zero = (X3 @ (s @ zero))) & ((X3 @ zero) = (s @ zero))))),
% 1.56/1.50 inference(negated_conjecture,[status(cth)],[f1])).
% 1.56/1.50 thf(f1,conjecture,(
% 1.56/1.50 (! [X1 : $i,X2 : $i,X0 : $o] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X2 : $i,X0 : $o,X1 : $i] : (X0 => ((ite @ X0 @ X1 @ X2) = X1))) => ? [X3 : $i > $i] : ((zero = (X3 @ (s @ zero))) & ((X3 @ zero) = (s @ zero)))),
% 1.56/1.50 file('/export/starexec/sandbox2/tmp/tmp.xws3VfhP2z/DTF2THF_16074.p',n8)).
% 1.56/1.50 thf(f11,plain,(
% 1.56/1.50 ( ! [X3 : $i > $i] : (((X3 @ zero) != (s @ zero)) | (zero != (X3 @ (s @ zero)))) )),
% 1.56/1.50 inference(cnf_transformation,[status(thm)],[f9])).
% 1.56/1.50 thf(f510,plain,(
% 1.56/1.50 spl0_27 | spl0_21 | spl0_12 | spl0_28 | ~spl0_2 | ~spl0_4),
% 1.56/1.50 inference(avatar_split_clause,[status(thm)],[f501,f38,f31,f305,f125,f257,f302])).
% 1.56/1.50 thf(f257,definition,(
% 1.56/1.50 spl0_21 <=> ! [X1 : $i > $o] : (((X1 @ zero) = $true) | ($false = (X1 @ (s @ zero))))),
% 1.56/1.50 introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition])).
% 1.56/1.50 thf(f125,definition,(
% 1.56/1.50 spl0_12 <=> ! [X4 : $o] : ($false = X4)),
% 1.56/1.50 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.56/1.50 thf(f31,definition,(
% 1.56/1.50 spl0_2 <=> ! [X2 : $i,X3 : $i > $i,X0 : $i,X5 : $i > $o,X1 : $i > $i] : (($true = (X5 @ zero)) | (zero != (ite @ (X5 @ (s @ zero)) @ (X1 @ (s @ zero)) @ (X3 @ (s @ zero)))) | ((X1 @ zero) != X0) | ((s @ zero) != X2) | ((X3 @ zero) != X2))),
% 1.56/1.50 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.56/1.50 thf(f501,plain,(
% 1.56/1.50 ( ! [X2 : $i,X3 : $i > $i,X0 : $i,X1 : $i > $i,X6 : $i,X7 : $i,X4 : $o,X5 : $i > $o] : (((X1 @ zero) != X6) | ((X3 @ (s @ zero)) != X2) | ($true = (X5 @ zero)) | ($false = X4) | (zero != X2) | ((s @ zero) != X6) | ((X3 @ zero) != X7) | ($false = (X5 @ (s @ zero))) | ((X1 @ (s @ zero)) != X0)) ) | (~spl0_2 | ~spl0_4)),
% 1.56/1.50 inference(duplicate_literal_removal,[status(thm)],[f500])).
% 1.56/1.50 thf(f500,plain,(
% 1.56/1.50 ( ! [X2 : $i,X3 : $i > $i,X0 : $i,X1 : $i > $i,X6 : $i,X7 : $i,X4 : $o,X5 : $i > $o] : (((X3 @ (s @ zero)) != X2) | ((X3 @ zero) != X7) | ($false = (X5 @ (s @ zero))) | ($false = X4) | ((X1 @ zero) != X6) | ($true = (X5 @ zero)) | ((X1 @ (s @ zero)) != X0) | (zero != X2) | ($false = X4) | ((s @ zero) != X6)) ) | (~spl0_2 | ~spl0_4)),
% 1.56/1.50 inference(binary_proxy_clausification,[status(thm)],[f448])).
% 1.56/1.50 thf(f448,plain,(
% 1.56/1.50 ( ! [X2 : $i,X3 : $i > $i,X0 : $i,X1 : $i > $i,X6 : $i,X7 : $i,X4 : $o,X5 : $i > $o] : (((X1 @ (s @ zero)) != X0) | ((X1 @ zero) != X6) | (zero != X2) | ((X5 @ (s @ zero)) != X4) | ($false = X4) | ((X3 @ (s @ zero)) != X2) | ((X3 @ zero) != X7) | ((s @ zero) != X6) | ($true = (X5 @ zero))) ) | (~spl0_2 | ~spl0_4)),
% 1.56/1.50 inference(constrained_superposition,[status(thm)],[f32,f310])).
% 1.56/1.50 thf(f310,plain,(
% 1.56/1.50 ( ! [X2 : $i,X0 : $o,X1 : $i] : (((ite @ X0 @ X1 @ X2) = X1) | ($false = X0)) ) | ~spl0_4),
% 1.56/1.50 inference(superposition,[status(thm)],[f13,f39])).
% 1.56/1.50 thf(f39,plain,(
% 1.56/1.50 ( ! [X4 : $o] : (($true = X4) | ($false = X4)) ) | ~spl0_4),
% 1.56/1.50 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.56/1.50 thf(f13,plain,(
% 1.56/1.50 ( ! [X2 : $i,X1 : $i] : (((ite @ $true @ X1 @ X2) = X1)) )),
% 1.56/1.50 inference(equality_resolution,[status(thm)],[f12])).
% 1.56/1.50 thf(f12,plain,(
% 1.56/1.50 ( ! [X2 : $i,X0 : $o,X1 : $i] : (((ite @ X0 @ X1 @ X2) = X1) | ($true != X0)) )),
% 1.56/1.50 inference(cnf_transformation,[status(thm)],[f9])).
% 1.56/1.50 thf(f32,plain,(
% 1.56/1.50 ( ! [X2 : $i,X3 : $i > $i,X0 : $i,X1 : $i > $i,X5 : $i > $o] : ((zero != (ite @ (X5 @ (s @ zero)) @ (X1 @ (s @ zero)) @ (X3 @ (s @ zero)))) | ((s @ zero) != X2) | ($true = (X5 @ zero)) | ((X3 @ zero) != X2) | ((X1 @ zero) != X0)) ) | ~spl0_2),
% 1.56/1.50 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.56/1.50 thf(f435,plain,(
% 1.56/1.50 ~spl0_21),
% 1.56/1.50 inference(avatar_contradiction_clause,[status(thm)],[f434])).
% 1.56/1.50 thf(f434,plain,(
% 1.56/1.50 $false | ~spl0_21),
% 1.56/1.50 inference(subsumption_resolution,[status(thm)],[f392,f18])).
% 1.56/1.50 thf(f18,plain,(
% 1.56/1.50 (zero != (s @ zero))),
% 1.56/1.50 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.56/1.50 thf(f16,plain,(
% 1.56/1.50 (zero != ((^[Y0 : $i]: (s @ ((^[Y1 : $i]: (zero)) @ Y0))) @ (s @ zero)))),
% 1.56/1.51 inference(equality_resolution,[status(thm)],[f11])).
% 1.56/1.51 thf(f392,plain,(
% 1.56/1.51 (zero = (s @ zero)) | ~spl0_21),
% 1.56/1.51 inference(leibniz_equality_elimination,[status(thm)],[f258])).
% 1.56/1.51 thf(f258,plain,(
% 1.56/1.51 ( ! [X1 : $i > $o] : (($false = (X1 @ (s @ zero))) | ((X1 @ zero) = $true)) ) | ~spl0_21),
% 1.56/1.51 inference(avatar_component_clause,[status(thm)],[f257])).
% 1.56/1.51 thf(f307,plain,(
% 1.56/1.51 spl0_27 | spl0_28 | ~spl0_3),
% 1.56/1.51 inference(avatar_split_clause,[status(thm)],[f271,f35,f305,f302])).
% 1.56/1.51 thf(f271,plain,(
% 1.56/1.51 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $i,X1 : $i,X4 : $i,X5 : $i] : (((X2 @ (s @ zero)) != X3) | ((X0 @ zero) != X5) | ((s @ zero) != X4) | (zero != X1) | ((X2 @ zero) != X4) | ((X0 @ (s @ zero)) != X1)) ) | ~spl0_3),
% 1.56/1.51 inference(trivial_inequality_removal,[status(thm)],[f270])).
% 1.56/1.51 thf(f270,plain,(
% 1.56/1.51 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $i,X1 : $i,X4 : $i,X5 : $i] : (((X0 @ zero) != X5) | (zero != X1) | ((s @ zero) != X4) | ((X2 @ (s @ zero)) != X3) | ((X2 @ zero) != X4) | ($true = $false) | ((X0 @ (s @ zero)) != X1)) ) | ~spl0_3),
% 1.56/1.51 inference(beta_eta_normalization,[status(thm)],[f268])).
% 1.56/1.51 thf(f268,plain,(
% 1.56/1.51 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $i,X1 : $i,X4 : $i,X5 : $i] : (((X0 @ zero) != X5) | ((X2 @ zero) != X4) | ((X2 @ (s @ zero)) != X3) | ((s @ zero) != X4) | ((X0 @ (s @ zero)) != X1) | (zero != X1) | (((^[Y0 : $i]: ($true)) @ zero) = $false)) ) | ~spl0_3),
% 1.56/1.51 inference(constrained_superposition,[status(thm)],[f36,f13])).
% 1.56/1.51 thf(f36,plain,(
% 1.56/1.51 ( ! [X2 : $i,X3 : $i > $i,X0 : $i,X1 : $i > $i,X5 : $i > $o] : ((zero != (ite @ (X5 @ (s @ zero)) @ (X1 @ (s @ zero)) @ (X3 @ (s @ zero)))) | ($false = (X5 @ zero)) | ((X3 @ zero) != X2) | ((s @ zero) != X2) | ((X1 @ zero) != X0)) ) | ~spl0_3),
% 1.56/1.51 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.56/1.51 thf(f159,plain,(
% 1.56/1.51 ~spl0_12),
% 1.56/1.51 inference(avatar_contradiction_clause,[status(thm)],[f158])).
% 1.56/1.51 thf(f158,plain,(
% 1.56/1.51 $false | ~spl0_12),
% 1.56/1.51 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 1.56/1.51 thf(f154,plain,(
% 1.56/1.51 ($false != $false) | ~spl0_12),
% 1.56/1.51 inference(superposition,[status(thm)],[f3,f126])).
% 1.56/1.51 thf(f126,plain,(
% 1.56/1.51 ( ! [X4 : $o] : (($false = X4)) ) | ~spl0_12),
% 1.56/1.51 inference(avatar_component_clause,[status(thm)],[f125])).
% 1.56/1.51 thf(f3,plain,(
% 1.56/1.51 ($true != $false)),
% 1.56/1.51 introduced(definition,[],[fool_axiom])).
% 1.56/1.51 thf(f92,plain,(
% 1.56/1.51 ~spl0_1),
% 1.56/1.51 inference(avatar_contradiction_clause,[status(thm)],[f91])).
% 1.56/1.51 thf(f91,plain,(
% 1.56/1.51 $false | ~spl0_1),
% 1.56/1.51 inference(equality_resolution,[status(thm)],[f88])).
% 1.56/1.51 thf(f88,plain,(
% 1.56/1.51 ( ! [X0 : $o] : (($false != X0)) ) | ~spl0_1),
% 1.56/1.51 inference(superposition,[status(thm)],[f3,f29])).
% 1.56/1.51 thf(f29,plain,(
% 1.56/1.51 ( ! [X4 : $o] : (($true = X4)) ) | ~spl0_1),
% 1.56/1.51 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.56/1.51 thf(f28,definition,(
% 1.56/1.51 spl0_1 <=> ! [X4 : $o] : ($true = X4)),
% 1.56/1.51 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.56/1.51 thf(f33,plain,(
% 1.56/1.51 spl0_1 | spl0_2),
% 1.56/1.51 inference(avatar_split_clause,[status(thm)],[f26,f31,f28])).
% 1.56/1.51 thf(f26,plain,(
% 1.56/1.51 ( ! [X2 : $i,X3 : $i > $i,X0 : $i,X1 : $i > $i,X4 : $o,X5 : $i > $o] : (($true = (X5 @ zero)) | ((s @ zero) != X2) | ((X1 @ zero) != X0) | ((X3 @ zero) != X2) | (zero != (ite @ (X5 @ (s @ zero)) @ (X1 @ (s @ zero)) @ (X3 @ (s @ zero)))) | ($true = X4)) )),
% 1.56/1.51 inference(duplicate_literal_removal,[status(thm)],[f24])).
% 1.56/1.51 thf(f24,plain,(
% 1.56/1.51 ( ! [X2 : $i,X3 : $i > $i,X0 : $i,X1 : $i > $i,X4 : $o,X5 : $i > $o] : (($true = X4) | (zero != (ite @ (X5 @ (s @ zero)) @ (X1 @ (s @ zero)) @ (X3 @ (s @ zero)))) | ($true = (X5 @ zero)) | ($true = X4) | ((X3 @ zero) != X2) | ((X1 @ zero) != X0) | ((s @ zero) != X2)) )),
% 1.56/1.51 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.56/1.51 thf(f23,plain,(
% 1.56/1.51 ( ! [X2 : $i,X3 : $i > $i,X0 : $i,X1 : $i > $i,X4 : $o,X5 : $i > $o] : (((s @ zero) != X2) | ($true = X4) | ((X5 @ zero) != X4) | (zero != (ite @ (X5 @ (s @ zero)) @ (X1 @ (s @ zero)) @ (X3 @ (s @ zero)))) | ((X1 @ zero) != X0) | ((X3 @ zero) != X2)) )),
% 1.56/1.51 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.56/1.51 thf(f22,plain,(
% 1.56/1.51 ( ! [X2 : $i,X3 : $i > $i,X0 : $i,X1 : $i > $i,X4 : $o,X5 : $i > $o] : (((X3 @ zero) != X2) | (zero != ((^[Y0 : $i]: (ite @ (X5 @ Y0) @ (X1 @ Y0) @ (X3 @ Y0))) @ (s @ zero))) | ((X5 @ zero) != X4) | ((s @ zero) != X2) | ((X1 @ zero) != X0) | ($true = X4)) )),
% 1.56/1.51 inference(constrained_superposition,[status(thm)],[f11,f10])).
% 1.56/1.51 % SZS output end Proof for DTF2THF_16074
% 1.56/1.51 % (16192)------------------------------
% 1.56/1.51 % (16192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.51 % (16192)Termination reason: Refutation
% 1.56/1.51
% 1.56/1.51 % (16192)Memory used [KB]: 6012
% 1.56/1.51 % (16192)Time elapsed: 0.116 s
% 1.56/1.51 % (16192)Instructions burned: 220 (million)
% 1.56/1.51 % (16192)------------------------------
% 1.56/1.51 % (16192)------------------------------
% 1.56/1.51 % (16171)Success in time 0.193 s
%------------------------------------------------------------------------------