%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUN025^1 : 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 : n025.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 09:27:13 AM UTC 2026
% Result : Theorem 1.59s 1.61s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 100 ( 35 unt; 0 typ; 9 def)
% Number of atoms : 863 ( 326 equ; 0 cnn)
% Maximal formula atoms : 15 ( 8 avg)
% Number of connectives : 1329 ( 223 ~; 206 |; 34 &; 767 @)
% ( 9 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 13 usr; 14 con; 0-3 aty)
% ( 51 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 294 ( 75 ^; 216 !; 3 ?; 294 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
ite: $o > $i > $i > $i ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f544,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f91,f149,f184,f298,f357,f455,f477,f525,f541,f543]) ).
thf(f543,plain,
~ spl0_35,
inference(avatar_contradiction_clause,[status(thm)],[f542]) ).
thf(f542,plain,
( $false
| ~ spl0_35 ),
inference(equality_resolution,[status(thm)],[f499]) ).
thf(f499,plain,
( ! [X3: $i] :
( ( s @ zero )
!= X3 )
| ~ spl0_35 ),
inference(avatar_component_clause,[status(thm)],[f498]) ).
thf(f498,definition,
( spl0_35
<=> ! [X3: $i] :
( ( s @ zero )
!= X3 ) ),
introduced(definition,[new_symbols(naming,[spl0_35])],[avatar_definition]) ).
thf(f541,plain,
~ spl0_31,
inference(avatar_contradiction_clause,[status(thm)],[f540]) ).
thf(f540,plain,
( $false
| ~ spl0_31 ),
inference(equality_resolution,[status(thm)],[f454]) ).
thf(f454,plain,
( ! [X0: $i] : ( zero != X0 )
| ~ spl0_31 ),
inference(avatar_component_clause,[status(thm)],[f453]) ).
thf(f453,definition,
( spl0_31
<=> ! [X0: $i] : ( zero != X0 ) ),
introduced(definition,[new_symbols(naming,[spl0_31])],[avatar_definition]) ).
thf(f525,plain,
( spl0_35
| spl0_35
| ~ spl0_20 ),
inference(avatar_split_clause,[status(thm)],[f524,f296,f498,f498]) ).
thf(f296,definition,
( spl0_20
<=> ! [X3: $i,X7: $i,X9: $i,X2: $i > $i] :
( ( ( s @ zero )
!= X7 )
| ( ( s @ zero )
!= X3 )
| ( ( X2 @ zero )
!= X3 )
| ( ( X2 @ ( s @ zero ) )
!= X9 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X7 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition]) ).
thf(f524,plain,
( ! [X0: $i,X1: $i] :
( ( ( s @ zero )
!= X1 )
| ( ( s @ zero )
!= X0 ) )
| ~ spl0_20 ),
inference(duplicate_literal_removal,[status(thm)],[f523]) ).
thf(f523,plain,
( ! [X0: $i,X1: $i] :
( ( ( s @ zero )
!= X1 )
| ( ( s @ zero )
!= X0 )
| ( ( s @ zero )
!= X0 ) )
| ~ spl0_20 ),
inference(beta_eta_normalization,[status(thm)],[f520]) ).
thf(f520,plain,
( ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( s
@ ( ^ [Y1: $i] : zero
@ Y0 ) )
@ ( s @ zero ) )
!= X1 )
| ( ( ^ [Y0: $i] :
( s
@ ( ^ [Y1: $i] : zero
@ Y0 ) )
@ zero )
!= X0 )
| ( ( s @ zero )
!= X0 ) )
| ~ spl0_20 ),
inference(equality_resolution,[status(thm)],[f517]) ).
thf(f517,plain,
( ! [X2: $i,X0: $i,X1: $i > $i] :
( ( ( s @ zero )
!= ( X1 @ ( s @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= X0 )
| ( ( X1 @ zero )
!= X0 )
| ( ( X1 @ ( s @ zero ) )
!= X2 ) )
| ~ spl0_20 ),
inference(equality_resolution,[status(thm)],[f297]) ).
thf(f297,plain,
( ! [X2: $i > $i,X3: $i,X9: $i,X7: $i] :
( ( ( s @ zero )
!= X7 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( ( X2 @ ( s @ zero ) )
!= X9 )
| ( ( s @ zero )
!= X3 )
| ( ( X2 @ zero )
!= X3 ) )
| ~ spl0_20 ),
inference(avatar_component_clause,[status(thm)],[f296]) ).
thf(f477,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f476,f54,f51]) ).
thf(f51,definition,
( spl0_1
<=> ! [X0: $o] : ( $true = X0 ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f54,definition,
( spl0_2
<=> ! [X3: $i > $i,X4: $i,X5: $i > $i,X2: $i,X1: $i > $o] :
( ( ( s @ zero )
!= X2 )
| ( zero
!= ( ite @ ( X1 @ ( s @ zero ) ) @ ( X5 @ ( s @ zero ) ) @ ( X3 @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= ( ite @ ( X1 @ zero ) @ ( X5 @ zero ) @ ( X3 @ zero ) ) )
| ( ( X3 @ ( s @ ( s @ zero ) ) )
!= X2 )
| ( ( X1 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( X5 @ ( s @ ( s @ zero ) ) )
!= X4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f476,plain,
! [X2: $i > $i,X3: $i,X0: $i > $i,X1: $i,X4: $i > $o,X5: $o] :
( ( ( s @ zero )
!= X3 )
| ( ( s @ zero )
!= ( ite @ ( X4 @ zero ) @ ( X0 @ zero ) @ ( X2 @ zero ) ) )
| ( $true = X5 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X1 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X3 )
| ( zero
!= ( ite @ ( X4 @ ( s @ zero ) ) @ ( X0 @ ( s @ zero ) ) @ ( X2 @ ( s @ zero ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f474]) ).
thf(f474,plain,
! [X2: $i > $i,X3: $i,X0: $i > $i,X1: $i,X4: $i > $o,X5: $o] :
( ( $true = X5 )
| ( ( s @ zero )
!= ( ite @ ( X4 @ zero ) @ ( X0 @ zero ) @ ( X2 @ zero ) ) )
| ( zero
!= ( ite @ ( X4 @ ( s @ zero ) ) @ ( X0 @ ( s @ zero ) ) @ ( X2 @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= X3 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
= $true )
| ( $true = X5 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X3 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f466]) ).
thf(f466,plain,
! [X2: $i > $i,X3: $i,X0: $i > $i,X1: $i,X4: $i > $o,X5: $o] :
( ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X1 )
| ( $true = X5 )
| ( ( s @ zero )
!= ( ite @ ( X4 @ zero ) @ ( X0 @ zero ) @ ( X2 @ zero ) ) )
| ( ( s @ zero )
!= X3 )
| ( zero
!= ( ite @ ( X4 @ ( s @ zero ) ) @ ( X0 @ ( s @ zero ) ) @ ( X2 @ ( s @ zero ) ) ) )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X5 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X3 ) ),
inference(beta_eta_normalization,[status(thm)],[f463]) ).
thf(f463,plain,
! [X2: $i > $i,X3: $i,X0: $i > $i,X1: $i,X4: $i > $o,X5: $o] :
( ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X1 )
| ( zero
!= ( ^ [Y0: $i] : ( ite @ ( X4 @ Y0 ) @ ( X0 @ Y0 ) @ ( X2 @ Y0 ) )
@ ( s @ zero ) ) )
| ( $true = X5 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X5 )
| ( ( s @ zero )
!= ( ^ [Y0: $i] : ( ite @ ( X4 @ Y0 ) @ ( X0 @ Y0 ) @ ( X2 @ Y0 ) )
@ zero ) )
| ( ( s @ zero )
!= X3 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X3 ) ),
inference(constrained_superposition,[status(thm)],[f41,f20]) ).
thf(f20,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ( ite @ X3 @ X1 @ X2 )
= X2 )
| ( $true = X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $true = X3 )
| ( $true
= ( ( ite @ X3 @ X1 @ X2 )
= X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ( ~ X3 ) = $false )
| ( $true
= ( ( ite @ X3 @ X1 @ X2 )
= X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ~ X3
=> ( ( ite @ X3 @ X1 @ X2 )
= X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: $i,X3: $o,X1: $i] :
( $true
= ( ^ [Y0: $o] :
( ~ Y0
=> ( ( ite @ Y0 @ X1 @ X2 )
= X2 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ~ Y0
=> ( ( ite @ Y0 @ X1 @ X2 )
= X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ~ Y1
=> ( ( ite @ Y1 @ X1 @ Y0 )
= Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ~ Y1
=> ( ( ite @ Y1 @ X1 @ Y0 )
= Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ~ Y2
=> ( ( ite @ Y2 @ Y0 @ Y1 )
= Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ~ Y2
=> ( ( ite @ Y2 @ Y0 @ Y1 )
= Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( s @ Y0 )
!= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( Y2
=> ( ( ite @ Y2 @ Y1 @ Y0 )
= Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ~ Y2
=> ( ( ite @ Y2 @ Y0 @ Y1 )
= Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( s @ Y0 )
!= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( Y2
=> ( ( ite @ Y2 @ Y1 @ Y0 )
= Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ~ Y2
=> ( ( ite @ Y2 @ Y0 @ Y1 )
= Y1 ) ) ) ) ) )
=> ( ?? @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( zero
= ( Y0 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( Y0 @ ( s @ ( s @ zero ) ) ) )
& ( ( s @ zero )
= ( Y0 @ zero ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( s @ Y0 )
!= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( Y2
=> ( ( ite @ Y2 @ Y1 @ Y0 )
= Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ~ Y2
=> ( ( ite @ Y2 @ Y0 @ Y1 )
= Y1 ) ) ) ) ) )
=> ( ?? @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( zero
= ( Y0 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( Y0 @ ( s @ ( s @ zero ) ) ) )
& ( ( s @ zero )
= ( Y0 @ zero ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( s @ Y0 )
!= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( Y2
=> ( ( ite @ Y2 @ Y1 @ Y0 )
= Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ~ Y2
=> ( ( ite @ Y2 @ Y0 @ Y1 )
= Y1 ) ) ) ) ) )
=> ( ?? @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( zero
= ( Y0 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( Y0 @ ( s @ ( s @ zero ) ) ) )
& ( ( s @ zero )
= ( Y0 @ zero ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $o,X1: $i,X2: $i] :
( ~ X0
=> ( ( ite @ X0 @ X2 @ X1 )
= X1 ) )
& ! [X3: $o,X4: $i,X5: $i] :
( X3
=> ( ( ite @ X3 @ X4 @ X5 )
= X4 ) )
& ! [X6: $i] :
( ( s @ X6 )
!= X6 ) )
=> ? [X7: $i > $i] :
( ( ( s @ zero )
= ( X7 @ zero ) )
& ( ( s @ zero )
= ( X7 @ ( s @ ( s @ zero ) ) ) )
& ( zero
= ( X7 @ ( s @ zero ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $o,X2: $i,X1: $i] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X0: $o,X1: $i,X2: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= X3 ) )
=> ? [X4: $i > $i] :
( ( ( X4 @ zero )
= ( s @ zero ) )
& ( ( s @ zero )
= ( X4 @ ( s @ ( s @ zero ) ) ) )
& ( zero
= ( X4 @ ( s @ zero ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $o,X2: $i,X1: $i] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X0: $o,X1: $i,X2: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= X3 ) )
=> ? [X4: $i > $i] :
( ( ( X4 @ zero )
= ( s @ zero ) )
& ( ( s @ zero )
= ( X4 @ ( s @ ( s @ zero ) ) ) )
& ( zero
= ( X4 @ ( s @ zero ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.bLy8R3mVbL/DTF2THF_14135.p',n9) ).
thf(f41,plain,
! [X1: $i > $i] :
( ( ( s @ zero )
!= ( X1 @ ( s @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= ( X1 @ zero ) )
| ( zero
!= ( X1 @ ( s @ zero ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i > $i] :
( ( zero
!= ( X1 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X1 @ zero ) )
| ( ( ( s @ zero )
= ( X1 @ ( s @ ( s @ zero ) ) ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i > $i] :
( ( zero
!= ( X1 @ ( s @ zero ) ) )
| ( ( ( s @ zero )
= ( X1 @ zero ) )
= $false )
| ( ( ( s @ zero )
= ( X1 @ ( s @ ( s @ zero ) ) ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i > $i] :
( ( ( zero
= ( X1 @ ( s @ zero ) ) )
= $false )
| ( ( ( s @ zero )
= ( X1 @ zero ) )
= $false )
| ( ( ( s @ zero )
= ( X1 @ ( s @ ( s @ zero ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i > $i] :
( ( $false
= ( ( zero
= ( X1 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X1 @ ( s @ ( s @ zero ) ) ) ) ) )
| ( ( ( s @ zero )
= ( X1 @ zero ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i > $i] :
( ( ( zero
= ( X1 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X1 @ ( s @ ( s @ zero ) ) ) )
& ( ( s @ zero )
= ( X1 @ zero ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i > $i] :
( ( ^ [Y0: $i > $i] :
( ( zero
= ( Y0 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( Y0 @ ( s @ ( s @ zero ) ) ) )
& ( ( s @ zero )
= ( Y0 @ zero ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ?? @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( zero
= ( Y0 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( Y0 @ ( s @ ( s @ zero ) ) ) )
& ( ( s @ zero )
= ( Y0 @ zero ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f455,plain,
( spl0_31
| spl0_31
| ~ spl0_19 ),
inference(avatar_split_clause,[status(thm)],[f443,f293,f453,f453]) ).
thf(f293,definition,
( spl0_19
<=> ! [X5: $i,X4: $i > $i,X6: $i,X8: $i] :
( ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X8 )
| ( ( X4 @ ( s @ zero ) )
!= X6 )
| ( ( X4 @ zero )
!= X5 )
| ( zero != X6 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition]) ).
thf(f443,plain,
( ! [X0: $i,X1: $i] :
( ( zero != X1 )
| ( zero != X0 ) )
| ~ spl0_19 ),
inference(beta_eta_normalization,[status(thm)],[f441]) ).
thf(f441,plain,
( ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : zero
@ zero )
!= X0 )
| ( ( ^ [Y0: $i] : zero
@ ( s @ ( s @ zero ) ) )
!= X1 ) )
| ~ spl0_19 ),
inference(equality_resolution,[status(thm)],[f438]) ).
thf(f438,plain,
( ! [X2: $i,X0: $i > $i,X1: $i] :
( ( zero
!= ( X0 @ ( s @ zero ) ) )
| ( ( X0 @ zero )
!= X1 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X2 ) )
| ~ spl0_19 ),
inference(equality_resolution,[status(thm)],[f294]) ).
thf(f294,plain,
( ! [X8: $i,X6: $i,X4: $i > $i,X5: $i] :
( ( zero != X6 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X8 )
| ( ( X4 @ ( s @ zero ) )
!= X6 )
| ( ( X4 @ zero )
!= X5 ) )
| ~ spl0_19 ),
inference(avatar_component_clause,[status(thm)],[f293]) ).
thf(f357,plain,
~ spl0_18,
inference(avatar_contradiction_clause,[status(thm)],[f356]) ).
thf(f356,plain,
( $false
| ~ spl0_18 ),
inference(subsumption_resolution,[status(thm)],[f355,f44]) ).
thf(f44,plain,
( zero
!= ( s @ zero ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( s @ zero )
!= ( s @ zero ) )
| ( zero
!= ( s @ zero ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( s @ zero )
!= ( ^ [Y0: $i] :
( s
@ ( ^ [Y1: $i] : zero
@ Y0 ) )
@ zero ) )
| ( zero
!= ( ^ [Y0: $i] :
( s
@ ( ^ [Y1: $i] : zero
@ Y0 ) )
@ ( s @ zero ) ) ) ),
inference(equality_resolution,[status(thm)],[f41]) ).
thf(f355,plain,
( ( zero
= ( s @ zero ) )
| ~ spl0_18 ),
inference(equality_proxy_clausification,[status(thm)],[f354]) ).
thf(f354,plain,
( ( $true
= ( ( s @ zero )
= zero ) )
| ~ spl0_18 ),
inference(subsumption_resolution,[status(thm)],[f334,f34]) ).
thf(f34,plain,
! [X1: $i] :
( ( s @ X1 )
!= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( $false
= ( ( s @ X1 )
= X1 ) ),
inference(not_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i] :
( $true
= ( ( s @ X1 )
!= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( s @ Y0 )
!= Y0 )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( s @ Y0 )
!= Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( s @ Y0 )
!= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( Y2
=> ( ( ite @ Y2 @ Y1 @ Y0 )
= Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f334,plain,
( ( ( s @ zero )
= ( s @ ( s @ zero ) ) )
| ( $true
= ( ( s @ zero )
= zero ) )
| ~ spl0_18 ),
inference(leibniz_equality_elimination,[status(thm)],[f291]) ).
thf(f291,plain,
( ! [X0: $i > $o] :
( ( $true
= ( X0 @ ( s @ ( s @ zero ) ) ) )
| ( ( X0 @ ( s @ zero ) )
= $false )
| ( $true
= ( X0 @ zero ) ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f290]) ).
thf(f290,definition,
( spl0_18
<=> ! [X0: $i > $o] :
( ( ( X0 @ ( s @ zero ) )
= $false )
| ( $true
= ( X0 @ zero ) )
| ( $true
= ( X0 @ ( s @ ( s @ zero ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition]) ).
thf(f298,plain,
( spl0_18
| spl0_1
| spl0_19
| spl0_20
| ~ spl0_12 ),
inference(avatar_split_clause,[status(thm)],[f288,f147,f296,f293,f51,f290]) ).
thf(f147,definition,
( spl0_12
<=> ! [X1: $i,X4: $i > $i,X0: $i > $i,X6: $i,X5: $i,X2: $i > $o,X7: $i] :
( ( ( s @ zero )
!= ( ite @ ( X2 @ zero ) @ ( X0 @ zero ) @ ( X4 @ zero ) ) )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( s @ zero )
!= X6 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 )
| ( ( X2 @ ( s @ zero ) )
= $false )
| ( zero != X1 )
| ( ( X4 @ ( s @ zero ) )
!= X5 )
| ( ( X0 @ ( s @ zero ) )
!= X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f288,plain,
( ! [X2: $i > $i,X3: $i,X0: $i > $o,X1: $o,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i > $i,X5: $i] :
( ( ( s @ zero )
!= X7 )
| ( ( X0 @ ( s @ zero ) )
= $false )
| ( $true
= ( X0 @ ( s @ ( s @ zero ) ) ) )
| ( ( X2 @ ( s @ zero ) )
!= X9 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X8 )
| ( zero != X6 )
| ( ( X2 @ zero )
!= X3 )
| ( ( X4 @ zero )
!= X5 )
| ( ( X4 @ ( s @ zero ) )
!= X6 )
| ( $true
= ( X0 @ zero ) )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( $true = X1 )
| ( ( s @ zero )
!= X3 ) )
| ~ spl0_12 ),
inference(duplicate_literal_removal,[status(thm)],[f286]) ).
thf(f286,plain,
( ! [X2: $i > $i,X3: $i,X0: $i > $o,X1: $o,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i > $i,X5: $i] :
( ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( ( X4 @ zero )
!= X5 )
| ( ( X2 @ ( s @ zero ) )
!= X9 )
| ( zero != X6 )
| ( $true
= ( X0 @ zero ) )
| ( $true = X1 )
| ( $true = X1 )
| ( $true
= ( X0 @ ( s @ ( s @ zero ) ) ) )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X8 )
| ( ( X2 @ zero )
!= X3 )
| ( ( s @ zero )
!= X3 )
| ( ( X4 @ ( s @ zero ) )
!= X6 )
| ( ( X0 @ ( s @ zero ) )
= $false )
| ( ( s @ zero )
!= X7 ) )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f263]) ).
thf(f263,plain,
( ! [X2: $i > $i,X3: $i,X0: $i > $o,X1: $o,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i > $i,X5: $i] :
( ( ( X0 @ ( s @ zero ) )
= $false )
| ( ( s @ zero )
!= X3 )
| ( zero != X6 )
| ( $true = X1 )
| ( $true
= ( X0 @ ( s @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= X7 )
| ( ( X0 @ zero )
!= X1 )
| ( ( X4 @ zero )
!= X5 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( ( X2 @ ( s @ zero ) )
!= X9 )
| ( ( X2 @ zero )
!= X3 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X8 )
| ( ( X4 @ ( s @ zero ) )
!= X6 ) )
| ~ spl0_12 ),
inference(constrained_superposition,[status(thm)],[f148,f20]) ).
thf(f148,plain,
( ! [X2: $i > $o,X0: $i > $i,X1: $i,X6: $i,X7: $i,X4: $i > $i,X5: $i] :
( ( ( s @ zero )
!= ( ite @ ( X2 @ zero ) @ ( X0 @ zero ) @ ( X4 @ zero ) ) )
| ( ( s @ zero )
!= X6 )
| ( ( X0 @ ( s @ zero ) )
!= X1 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( ( X2 @ ( s @ zero ) )
= $false )
| ( zero != X1 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( X4 @ ( s @ zero ) )
!= X5 ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f147]) ).
thf(f184,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f183]) ).
thf(f183,plain,
( $false
| ~ spl0_1 ),
inference(equality_resolution,[status(thm)],[f174]) ).
thf(f174,plain,
( ! [X0: $o] : ( $false != X0 )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f3,f52]) ).
thf(f52,plain,
( ! [X0: $o] : ( $true = X0 )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f3,plain,
$true != $false,
introduced(definition,[],[fool_axiom]) ).
thf(f149,plain,
( spl0_12
| spl0_6
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f145,f54,f77,f147]) ).
thf(f77,definition,
( spl0_6
<=> ! [X0: $o] : ( $false = X0 ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f145,plain,
( ! [X2: $i > $o,X3: $o,X0: $i > $i,X1: $i,X6: $i,X7: $i,X4: $i > $i,X5: $i] :
( ( ( s @ zero )
!= ( ite @ ( X2 @ zero ) @ ( X0 @ zero ) @ ( X4 @ zero ) ) )
| ( ( X0 @ ( s @ zero ) )
!= X1 )
| ( ( X4 @ ( s @ zero ) )
!= X5 )
| ( zero != X1 )
| ( $false = X3 )
| ( ( X2 @ ( s @ zero ) )
= $false )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( ( s @ zero )
!= X6 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
= $true ) )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ! [X2: $i > $o,X3: $o,X0: $i > $i,X1: $i,X6: $i,X7: $i,X4: $i > $i,X5: $i] :
( ( zero != X1 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( X0 @ ( s @ zero ) )
!= X1 )
| ( ( s @ zero )
!= X6 )
| ( $false = X3 )
| ( $false = X3 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( ( s @ zero )
!= ( ite @ ( X2 @ zero ) @ ( X0 @ zero ) @ ( X4 @ zero ) ) )
| ( ( X2 @ ( s @ zero ) )
= $false )
| ( ( X4 @ ( s @ zero ) )
!= X5 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
( ! [X2: $i > $o,X3: $o,X0: $i > $i,X1: $i,X6: $i,X7: $i,X4: $i > $i,X5: $i] :
( ( ( X2 @ ( s @ zero ) )
!= X3 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( $false = X3 )
| ( zero != X1 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( X0 @ ( s @ zero ) )
!= X1 )
| ( ( X4 @ ( s @ zero ) )
!= X5 )
| ( ( s @ zero )
!= ( ite @ ( X2 @ zero ) @ ( X0 @ zero ) @ ( X4 @ zero ) ) )
| ( ( s @ zero )
!= X6 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 ) )
| ~ spl0_2 ),
inference(constrained_superposition,[status(thm)],[f55,f30]) ).
thf(f30,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ( ite @ X3 @ X2 @ X1 )
= X2 )
| ( $false = X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $true
= ( ( ite @ X3 @ X2 @ X1 )
= X2 ) )
| ( $false = X3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X3: $o,X1: $i] :
( $true
= ( X3
=> ( ( ite @ X3 @ X2 @ X1 )
= X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X3: $o,X1: $i] :
( $true
= ( ^ [Y0: $o] :
( Y0
=> ( ( ite @ Y0 @ X2 @ X1 )
= X2 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( ( ite @ Y0 @ X2 @ X1 )
= X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( Y1
=> ( ( ite @ Y1 @ Y0 @ X1 )
= Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( Y1
=> ( ( ite @ Y1 @ Y0 @ X1 )
= Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( Y2
=> ( ( ite @ Y2 @ Y1 @ Y0 )
= Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( Y2
=> ( ( ite @ Y2 @ Y1 @ Y0 )
= Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f55,plain,
( ! [X2: $i,X3: $i > $i,X1: $i > $o,X4: $i,X5: $i > $i] :
( ( zero
!= ( ite @ ( X1 @ ( s @ zero ) ) @ ( X5 @ ( s @ zero ) ) @ ( X3 @ ( s @ zero ) ) ) )
| ( ( X3 @ ( s @ ( s @ zero ) ) )
!= X2 )
| ( ( s @ zero )
!= ( ite @ ( X1 @ zero ) @ ( X5 @ zero ) @ ( X3 @ zero ) ) )
| ( ( X1 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( X5 @ ( s @ ( s @ zero ) ) )
!= X4 )
| ( ( s @ zero )
!= X2 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f91,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[status(thm)],[f90]) ).
thf(f90,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
( ( $false != $false )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f3,f78]) ).
thf(f78,plain,
( ! [X0: $o] : ( $false = X0 )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN025^1 : TPTP v9.2.1. Released v6.4.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n025.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:19:42 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : NUN025^1 : TPTP v9.2.1. Released v6.4.0.
% 0.29/0.46 % Domain : Number Theory
% 0.29/0.46 % Problem : Function h s.t. h(0) = 1, h(1) = 0, h(2) = 1, no witness
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : Using an axiomatiztion of if-then-else, find the if-then-else
% 0.29/0.46 % term that expresses the function H.
% 0.29/0.46
% 0.29/0.46 % Refs : [Rie16] Riener (2016), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [TPTP]
% 0.29/0.46 % Names : ntape6-2-without-witness.tptp [Rie16]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.67 v9.1.0, 0.75 v9.0.0, 0.70 v8.2.0, 0.77 v8.1.0, 0.73 v7.5.0, 0.71 v7.4.0, 0.89 v7.3.0, 1.00 v6.4.0
% 0.29/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.29/0.46 % Number of atoms : 6 ( 6 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 6 ( 6 avg)
% 0.29/0.46 % Number of connectives : 24 ( 2 ~; 0 |; 4 &; 15 @)
% 0.29/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 4 ( 3 usr; 1 con; 0-3 aty)
% 0.29/0.46 % Number of variables : 8 ( 0 ^; 7 !; 1 ?; 8 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments :
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(n6,type,
% 0.29/0.46 zero: $i ).
% 0.29/0.46
% 0.29/0.46 thf(n7,type,
% 0.29/0.46 s: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(n8,type,
% 0.29/0.46 ite: $o > $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(n9,conjecture,
% 0.29/0.46 ( ( ! [X100: $o,U: $i,V: $i] :
% 0.29/0.46 ( X100
% 0.29/0.46 => ( ( ite @ X100 @ U @ V )
% 0.29/0.46 = U ) )
% 0.29/0.46 & ! [X100: $o,U: $i,V: $i] :
% 0.29/0.46 ( ~ X100
% 0.29/0.46 => ( ( ite @ X100 @ U @ V )
% 0.29/0.46 = V ) )
% 0.29/0.46 & ! [X: $i] :
% 0.29/0.46 ( ( s @ X )
% 0.29/0.46 != X ) )
% 0.29/0.46 => ? [H: $i > $i] :
% 0.29/0.46 ( ( ( H @ zero )
% 0.29/0.46 = ( s @ zero ) )
% 0.29/0.46 & ( ( H @ ( s @ zero ) )
% 0.29/0.46 = zero )
% 0.29/0.46 & ( ( H @ ( s @ ( s @ zero ) ) )
% 0.29/0.46 = ( s @ zero ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.48/1.25 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 11:19:43 EST 2026
% 1.48/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.25 %%% Logic specification used:
% 1.48/1.25 %%% thf(spec, logic, $$dhol).
% 1.48/1.25
% 1.48/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.bLy8R3mVbL/DTF2DTF14135.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.26 ---- Cleaned THF ---
% 1.48/1.26 thf(n6,type,
% 1.48/1.26 zero: $i ).
% 1.48/1.26
% 1.48/1.26 thf(n7,type,
% 1.48/1.26 s: $i > $i ).
% 1.48/1.26
% 1.48/1.26 thf(n8,type,
% 1.48/1.26 ite: $o > $i > $i > $i ).
% 1.48/1.26
% 1.48/1.26 thf(n9,conjecture,
% 1.48/1.26 ( ( ! [X100: $o,U: $i,V: $i] :
% 1.48/1.26 ( X100
% 1.48/1.26 => ( ( ite @ X100 @ U @ V )
% 1.48/1.26 = U ) )
% 1.48/1.26 & ! [X100: $o,U: $i,V: $i] :
% 1.48/1.26 ( ~ X100
% 1.48/1.26 => ( ( ite @ X100 @ U @ V )
% 1.48/1.26 = V ) )
% 1.48/1.26 & ! [X: $i] :
% 1.48/1.26 ( ( s @ X )
% 1.48/1.26 != X ) )
% 1.48/1.26 => ? [H: $i > $i] :
% 1.48/1.26 ( ( ( H @ zero )
% 1.48/1.26 = ( s @ zero ) )
% 1.48/1.26 & ( ( H @ ( s @ zero ) )
% 1.48/1.26 = zero )
% 1.48/1.26 & ( ( H @ ( s @ ( s @ zero ) ) )
% 1.48/1.26 = ( s @ zero ) ) ) ) ).
% 1.48/1.26 ------------------------
% 1.48/1.28 % (14358)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/18Mi)
% 1.48/1.28 % (14353)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_14135 for (2999ds/4Mi)
% 1.48/1.28 % (14353)Instruction limit reached!
% 1.48/1.28 % (14353)------------------------------
% 1.48/1.28 % (14353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (14353)Termination reason: Unknown
% 1.48/1.28 % (14353)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (14353)Memory used [KB]: 5500
% 1.48/1.28 % (14353)Time elapsed: 0.003 s
% 1.48/1.28 % (14353)Instructions burned: 4 (million)
% 1.48/1.28 % (14353)------------------------------
% 1.48/1.28 % (14353)------------------------------
% 1.48/1.28 % (14358)Instruction limit reached!
% 1.48/1.28 % (14358)------------------------------
% 1.48/1.28 % (14358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (14358)Termination reason: Unknown
% 1.48/1.28 % (14358)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (14358)Memory used [KB]: 5628
% 1.48/1.28 % (14358)Time elapsed: 0.008 s
% 1.48/1.28 % (14358)Instructions burned: 19 (million)
% 1.48/1.28 % (14358)------------------------------
% 1.48/1.28 % (14358)------------------------------
% 1.48/1.28 % (14352)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/183Mi)
% 1.48/1.28 % (14354)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_14135 for (2999ds/27Mi)
% 1.48/1.28 % (14355)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/2Mi)
% 1.48/1.28 % (14356)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_14135 for (2999ds/2Mi)
% 1.48/1.28 % (14357)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_14135 for (2999ds/275Mi)
% 1.48/1.29 % (14355)Instruction limit reached!
% 1.48/1.29 % (14355)------------------------------
% 1.48/1.29 % (14355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (14355)Termination reason: Unknown
% 1.48/1.29 % (14355)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (14355)Memory used [KB]: 895
% 1.48/1.29 % (14355)Time elapsed: 0.003 s
% 1.48/1.29 % (14355)Instructions burned: 2 (million)
% 1.48/1.29 % (14355)------------------------------
% 1.48/1.29 % (14355)------------------------------
% 1.48/1.29 % (14356)Instruction limit reached!
% 1.48/1.29 % (14356)------------------------------
% 1.48/1.29 % (14356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (14356)Termination reason: Unknown
% 1.48/1.29 % (14356)Termination phase: Property scanning
% 1.48/1.29
% 1.48/1.29 % (14356)Memory used [KB]: 895
% 1.48/1.29 % (14356)Time elapsed: 0.003 s
% 1.48/1.29 % (14356)Instructions burned: 2 (million)
% 1.48/1.29 % (14356)------------------------------
% 1.48/1.29 % (14356)------------------------------
% 1.48/1.29 % (14354)Refutation not found, incomplete strategy
% 1.48/1.29 % (14354)------------------------------
% 1.48/1.29 % (14354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (14354)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.29
% 1.48/1.29
% 1.48/1.29 % (14354)Memory used [KB]: 5500
% 1.48/1.29 % (14354)Time elapsed: 0.005 s
% 1.48/1.29 % (14354)Instructions burned: 4 (million)
% 1.48/1.29 % (14354)------------------------------
% 1.48/1.29 % (14354)------------------------------
% 1.48/1.29 % (14357)Refutation not found, incomplete strategy
% 1.48/1.29 % (14357)------------------------------
% 1.48/1.29 % (14357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (14357)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.29
% 1.48/1.29
% 1.48/1.29 % (14357)Memory used [KB]: 5500
% 1.48/1.29 % (14357)Time elapsed: 0.005 s
% 1.48/1.29 % (14357)Instructions burned: 2 (million)
% 1.48/1.29 % (14357)------------------------------
% 1.48/1.29 % (14357)------------------------------
% 1.48/1.29 % (14359)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/3Mi)
% 1.48/1.29 % (14359)Instruction limit reached!
% 1.48/1.29 % (14359)------------------------------
% 1.48/1.29 % (14359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (14359)Termination reason: Unknown
% 1.48/1.29 % (14359)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (14359)Memory used [KB]: 5500
% 1.48/1.29 % (14359)Time elapsed: 0.003 s
% 1.48/1.29 % (14359)Instructions burned: 3 (million)
% 1.48/1.29 % (14359)------------------------------
% 1.48/1.29 % (14359)------------------------------
% 1.48/1.29 % (14360)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_14135 for (2999ds/37Mi)
% 1.59/1.30 % (14365)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/16Mi)
% 1.59/1.30 % (14361)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_14135 for (2999ds/15Mi)
% 1.59/1.30 % (14362)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_14135 for (2999ds/3Mi)
% 1.59/1.30 % (14360)Instruction limit reached!
% 1.59/1.30 % (14360)------------------------------
% 1.59/1.30 % (14360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (14360)Termination reason: Unknown
% 1.59/1.30 % (14360)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (14360)Memory used [KB]: 5628
% 1.59/1.30 % (14360)Time elapsed: 0.013 s
% 1.59/1.30 % (14360)Instructions burned: 38 (million)
% 1.59/1.30 % (14360)------------------------------
% 1.59/1.30 % (14360)------------------------------
% 1.59/1.30 % (14362)Instruction limit reached!
% 1.59/1.30 % (14362)------------------------------
% 1.59/1.30 % (14362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (14362)Termination reason: Unknown
% 1.59/1.30 % (14362)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (14362)Memory used [KB]: 5500
% 1.59/1.30 % (14362)Time elapsed: 0.004 s
% 1.59/1.30 % (14362)Instructions burned: 3 (million)
% 1.59/1.30 % (14362)------------------------------
% 1.59/1.30 % (14362)------------------------------
% 1.59/1.31 % (14361)Refutation not found, incomplete strategy
% 1.59/1.31 % (14361)------------------------------
% 1.59/1.31 % (14361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.31 % (14363)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_14135 for (2999ds/1041Mi)
% 1.59/1.31 % (14361)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.31
% 1.59/1.31
% 1.59/1.31 % (14361)Memory used [KB]: 5500
% 1.59/1.31 % (14361)Time elapsed: 0.004 s
% 1.59/1.31 % (14361)Instructions burned: 3 (million)
% 1.59/1.31 % (14361)------------------------------
% 1.59/1.31 % (14361)------------------------------
% 1.59/1.31 % (14364)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/7Mi)
% 1.59/1.31 % (14365)Instruction limit reached!
% 1.59/1.31 % (14365)------------------------------
% 1.59/1.31 % (14365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.31 % (14365)Termination reason: Unknown
% 1.59/1.31 % (14365)Termination phase: Saturation
% 1.59/1.31
% 1.59/1.31 % (14365)Memory used [KB]: 5628
% 1.59/1.31 % (14365)Time elapsed: 0.008 s
% 1.59/1.31 % (14365)Instructions burned: 17 (million)
% 1.59/1.31 % (14365)------------------------------
% 1.59/1.31 % (14365)------------------------------
% 1.59/1.31 % (14364)Instruction limit reached!
% 1.59/1.31 % (14364)------------------------------
% 1.59/1.31 % (14364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.31 % (14364)Termination reason: Unknown
% 1.59/1.31 % (14364)Termination phase: Saturation
% 1.59/1.31
% 1.59/1.31 % (14364)Memory used [KB]: 1023
% 1.59/1.31 % (14364)Time elapsed: 0.007 s
% 1.59/1.31 % (14364)Instructions burned: 8 (million)
% 1.59/1.31 % (14364)------------------------------
% 1.59/1.31 % (14364)------------------------------
% 1.59/1.32 % (14369)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/3Mi)
% 1.59/1.32 % (14369)Instruction limit reached!
% 1.59/1.32 % (14369)------------------------------
% 1.59/1.32 % (14369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (14369)Termination reason: Unknown
% 1.59/1.32 % (14369)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (14369)Memory used [KB]: 5500
% 1.59/1.32 % (14369)Time elapsed: 0.003 s
% 1.59/1.32 % (14369)Instructions burned: 4 (million)
% 1.59/1.32 % (14369)------------------------------
% 1.59/1.32 % (14369)------------------------------
% 1.59/1.32 % (14367)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_14135 for (2999ds/3Mi)
% 1.59/1.32 % (14366)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_14135 for (2999ds/3Mi)
% 1.59/1.32 % (14367)Instruction limit reached!
% 1.59/1.32 % (14367)------------------------------
% 1.59/1.32 % (14367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (14367)Termination reason: Unknown
% 1.59/1.32 % (14367)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (14367)Memory used [KB]: 5500
% 1.59/1.32 % (14367)Time elapsed: 0.004 s
% 1.59/1.32 % (14367)Instructions burned: 3 (million)
% 1.59/1.32 % (14367)------------------------------
% 1.59/1.32 % (14367)------------------------------
% 1.59/1.32 % (14368)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/7Mi)
% 1.59/1.32 % (14366)Instruction limit reached!
% 1.59/1.32 % (14366)------------------------------
% 1.59/1.32 % (14366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (14366)Termination reason: Unknown
% 1.59/1.32 % (14366)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (14366)Memory used [KB]: 5500
% 1.59/1.32 % (14366)Time elapsed: 0.004 s
% 1.59/1.32 % (14366)Instructions burned: 3 (million)
% 1.59/1.32 % (14366)------------------------------
% 1.59/1.32 % (14366)------------------------------
% 1.59/1.33 % (14368)Refutation not found, incomplete strategy
% 1.59/1.33 % (14368)------------------------------
% 1.59/1.33 % (14368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (14368)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.33
% 1.59/1.33
% 1.59/1.33 % (14368)Memory used [KB]: 5500
% 1.59/1.33 % (14368)Time elapsed: 0.003 s
% 1.59/1.33 % (14368)Instructions burned: 2 (million)
% 1.59/1.33 % (14368)------------------------------
% 1.59/1.33 % (14368)------------------------------
% 1.59/1.33 % (14370)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/4Mi)
% 1.59/1.33 % (14371)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/18Mi)
% 1.59/1.33 % (14371)Refutation not found, incomplete strategy
% 1.59/1.33 % (14371)------------------------------
% 1.59/1.33 % (14371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (14371)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.33
% 1.59/1.33
% 1.59/1.33 % (14371)Memory used [KB]: 5500
% 1.59/1.33 % (14371)Time elapsed: 0.003 s
% 1.59/1.33 % (14371)Instructions burned: 3 (million)
% 1.59/1.33 % (14371)------------------------------
% 1.59/1.33 % (14371)------------------------------
% 1.59/1.33 % (14370)Instruction limit reached!
% 1.59/1.33 % (14370)------------------------------
% 1.59/1.33 % (14370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (14370)Termination reason: Unknown
% 1.59/1.33 % (14370)Termination phase: Saturation
% 1.59/1.33
% 1.59/1.33 % (14370)Memory used [KB]: 5500
% 1.59/1.33 % (14370)Time elapsed: 0.005 s
% 1.59/1.33 % (14370)Instructions burned: 4 (million)
% 1.59/1.33 % (14370)------------------------------
% 1.59/1.33 % (14370)------------------------------
% 1.59/1.34 % (14372)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/710Mi)
% 1.59/1.34 % (14375)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_14135 for (2999ds/21Mi)
% 1.59/1.34 % (14373)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/6Mi)
% 1.59/1.34 % (14374)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_14135 for (2999ds/902Mi)
% 1.59/1.35 % (14374)Refutation not found, incomplete strategy
% 1.59/1.35 % (14374)------------------------------
% 1.59/1.35 % (14374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (14374)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.35
% 1.59/1.35
% 1.59/1.35 % (14374)Memory used [KB]: 5500
% 1.59/1.35 % (14374)Time elapsed: 0.004 s
% 1.59/1.35 % (14374)Instructions burned: 3 (million)
% 1.59/1.35 % (14374)------------------------------
% 1.59/1.35 % (14374)------------------------------
% 1.59/1.35 % (14373)Instruction limit reached!
% 1.59/1.35 % (14373)------------------------------
% 1.59/1.35 % (14373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (14373)Termination reason: Unknown
% 1.59/1.35 % (14373)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (14373)Memory used [KB]: 5500
% 1.59/1.35 % (14373)Time elapsed: 0.006 s
% 1.59/1.35 % (14373)Instructions burned: 6 (million)
% 1.59/1.35 % (14373)------------------------------
% 1.59/1.35 % (14373)------------------------------
% 1.59/1.35 % (14375)Instruction limit reached!
% 1.59/1.35 % (14375)------------------------------
% 1.59/1.35 % (14375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (14375)Termination reason: Unknown
% 1.59/1.35 % (14375)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (14375)Memory used [KB]: 5628
% 1.59/1.35 % (14375)Time elapsed: 0.010 s
% 1.59/1.35 % (14375)Instructions burned: 21 (million)
% 1.59/1.35 % (14375)------------------------------
% 1.59/1.35 % (14375)------------------------------
% 1.59/1.35 % (14376)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/5Mi)
% 1.59/1.35 % (14376)Instruction limit reached!
% 1.59/1.35 % (14376)------------------------------
% 1.59/1.35 % (14376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (14376)Termination reason: Unknown
% 1.59/1.35 % (14376)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (14376)Memory used [KB]: 5500
% 1.59/1.35 % (14376)Time elapsed: 0.005 s
% 1.59/1.35 % (14376)Instructions burned: 5 (million)
% 1.59/1.35 % (14376)------------------------------
% 1.59/1.35 % (14376)------------------------------
% 1.59/1.36 % (14379)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_14135 for (2999ds/779Mi)
% 1.59/1.36 % (14378)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/377Mi)
% 1.59/1.36 % (14377)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_14135 for (2999ds/6Mi)
% 1.59/1.36 % (14378)Refutation not found, incomplete strategy
% 1.59/1.36 % (14378)------------------------------
% 1.59/1.36 % (14378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (14378)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.36
% 1.59/1.36
% 1.59/1.36 % (14378)Memory used [KB]: 5500
% 1.59/1.36 % (14378)Time elapsed: 0.003 s
% 1.59/1.36 % (14378)Instructions burned: 3 (million)
% 1.59/1.36 % (14378)------------------------------
% 1.59/1.36 % (14378)------------------------------
% 1.59/1.37 % (14377)Instruction limit reached!
% 1.59/1.37 % (14377)------------------------------
% 1.59/1.37 % (14377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.37 % (14377)Termination reason: Unknown
% 1.59/1.37 % (14377)Termination phase: Saturation
% 1.59/1.37
% 1.59/1.37 % (14377)Memory used [KB]: 5500
% 1.59/1.37 % (14377)Time elapsed: 0.005 s
% 1.59/1.37 % (14377)Instructions burned: 6 (million)
% 1.59/1.37 % (14377)------------------------------
% 1.59/1.37 % (14377)------------------------------
% 1.59/1.37 % (14352)Instruction limit reached!
% 1.59/1.37 % (14352)------------------------------
% 1.59/1.37 % (14352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.37 % (14352)Termination reason: Unknown
% 1.59/1.37 % (14352)Termination phase: Saturation
% 1.59/1.37
% 1.59/1.37 % (14352)Memory used [KB]: 6140
% 1.59/1.37 % (14352)Time elapsed: 0.085 s
% 1.59/1.37 % (14352)Instructions burned: 185 (million)
% 1.59/1.37 % (14352)------------------------------
% 1.59/1.37 % (14352)------------------------------
% 1.59/1.37 % (14380)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_14135 for (2999ds/19Mi)
% 1.59/1.37 % (14380)Refutation not found, incomplete strategy
% 1.59/1.37 % (14380)------------------------------
% 1.59/1.37 % (14380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.37 % (14380)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.37
% 1.59/1.37
% 1.59/1.37 % (14380)Memory used [KB]: 5500
% 1.59/1.37 % (14380)Time elapsed: 0.006 s
% 1.59/1.37 % (14380)Instructions burned: 7 (million)
% 1.59/1.37 % (14380)------------------------------
% 1.59/1.37 % (14380)------------------------------
% 1.59/1.37 % (14379)Refutation not found, incomplete strategy
% 1.59/1.37 % (14379)------------------------------
% 1.59/1.37 % (14379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.37 % (14379)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.37
% 1.59/1.37
% 1.59/1.37 % (14379)Memory used [KB]: 5628
% 1.59/1.37 % (14379)Time elapsed: 0.018 s
% 1.59/1.37 % (14379)Instructions burned: 48 (million)
% 1.59/1.37 % (14379)------------------------------
% 1.59/1.37 % (14379)------------------------------
% 1.59/1.38 % (14381)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/879Mi)
% 1.59/1.38 % (14383)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/3Mi)
% 1.59/1.38 % (14381)Refutation not found, incomplete strategy
% 1.59/1.38 % (14381)------------------------------
% 1.59/1.38 % (14381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.38 % (14381)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.38
% 1.59/1.38
% 1.59/1.38 % (14381)Memory used [KB]: 5500
% 1.59/1.38 % (14381)Time elapsed: 0.002 s
% 1.59/1.38 % (14381)Instructions burned: 2 (million)
% 1.59/1.38 % (14381)------------------------------
% 1.59/1.38 % (14381)------------------------------
% 1.59/1.38 % (14383)Instruction limit reached!
% 1.59/1.38 % (14383)------------------------------
% 1.59/1.38 % (14383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.38 % (14383)Termination reason: Unknown
% 1.59/1.38 % (14383)Termination phase: Saturation
% 1.59/1.38
% 1.59/1.38 % (14383)Memory used [KB]: 5500
% 1.59/1.38 % (14383)Time elapsed: 0.003 s
% 1.59/1.38 % (14383)Instructions burned: 4 (million)
% 1.59/1.38 % (14383)------------------------------
% 1.59/1.38 % (14383)------------------------------
% 1.59/1.38 % (14382)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/17Mi)
% 1.59/1.38 % (14385)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/127Mi)
% 1.59/1.39 % (14386)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/100Mi)
% 1.59/1.39 % (14387)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_14135 for (2999ds/3Mi)
% 1.59/1.39 % (14384)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_14135 for (2999ds/30Mi)
% 1.59/1.39 % (14387)Instruction limit reached!
% 1.59/1.39 % (14387)------------------------------
% 1.59/1.39 % (14387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.39 % (14387)Termination reason: Unknown
% 1.59/1.39 % (14387)Termination phase: Saturation
% 1.59/1.39
% 1.59/1.39 % (14387)Memory used [KB]: 5500
% 1.59/1.39 % (14387)Time elapsed: 0.003 s
% 1.59/1.39 % (14387)Instructions burned: 4 (million)
% 1.59/1.39 % (14387)------------------------------
% 1.59/1.39 % (14387)------------------------------
% 1.59/1.39 % (14386)Refutation not found, incomplete strategy
% 1.59/1.39 % (14386)------------------------------
% 1.59/1.39 % (14386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.39 % (14386)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.39
% 1.59/1.39
% 1.59/1.39 % (14386)Memory used [KB]: 5500
% 1.59/1.39 % (14386)Time elapsed: 0.003 s
% 1.59/1.39 % (14386)Instructions burned: 3 (million)
% 1.59/1.39 % (14386)------------------------------
% 1.59/1.39 % (14386)------------------------------
% 1.59/1.39 % (14382)Instruction limit reached!
% 1.59/1.39 % (14382)------------------------------
% 1.59/1.39 % (14382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.39 % (14382)Termination reason: Unknown
% 1.59/1.39 % (14382)Termination phase: Saturation
% 1.59/1.39
% 1.59/1.39 % (14382)Memory used [KB]: 5628
% 1.59/1.39 % (14382)Time elapsed: 0.013 s
% 1.59/1.39 % (14382)Instructions burned: 18 (million)
% 1.59/1.39 % (14382)------------------------------
% 1.59/1.39 % (14382)------------------------------
% 1.59/1.40 % (14388)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_14135 for (2998ds/20Mi)
% 1.59/1.40 % (14389)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_14135 for (2998ds/86Mi)
% 1.59/1.40 % (14388)Refutation not found, incomplete strategy
% 1.59/1.40 % (14388)------------------------------
% 1.59/1.40 % (14388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.40 % (14388)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.40
% 1.59/1.40
% 1.59/1.40 % (14388)Memory used [KB]: 5500
% 1.59/1.40 % (14388)Time elapsed: 0.002 s
% 1.59/1.40 % (14388)Instructions burned: 3 (million)
% 1.59/1.40 % (14388)------------------------------
% 1.59/1.40 % (14388)------------------------------
% 1.59/1.40 % (14384)Instruction limit reached!
% 1.59/1.40 % (14384)------------------------------
% 1.59/1.40 % (14384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.40 % (14384)Termination reason: Unknown
% 1.59/1.40 % (14384)Termination phase: Saturation
% 1.59/1.40
% 1.59/1.40 % (14384)Memory used [KB]: 5628
% 1.59/1.40 % (14384)Time elapsed: 0.014 s
% 1.59/1.40 % (14384)Instructions burned: 30 (million)
% 1.59/1.40 % (14384)------------------------------
% 1.59/1.40 % (14384)------------------------------
% 1.59/1.41 % (14392)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_14135 for (2998ds/448Mi)
% 1.59/1.41 % (14391)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_14135 for (2998ds/39Mi)
% 1.59/1.41 % (14390)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_14135 for (2998ds/107Mi)
% 1.59/1.41 % (14390)Refutation not found, incomplete strategy
% 1.59/1.41 % (14390)------------------------------
% 1.59/1.41 % (14390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.41 % (14390)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.41
% 1.59/1.41
% 1.59/1.41 % (14390)Memory used [KB]: 5500
% 1.59/1.41 % (14390)Time elapsed: 0.004 s
% 1.59/1.41 % (14390)Instructions burned: 3 (million)
% 1.59/1.41 % (14390)------------------------------
% 1.59/1.41 % (14390)------------------------------
% 1.59/1.42 % (14392)Refutation not found, incomplete strategy
% 1.59/1.42 % (14392)------------------------------
% 1.59/1.42 % (14392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.42 % (14392)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.42
% 1.59/1.42
% 1.59/1.42 % (14392)Memory used [KB]: 5628
% 1.59/1.42 % (14392)Time elapsed: 0.006 s
% 1.59/1.42 % (14392)Instructions burned: 14 (million)
% 1.59/1.42 % (14392)------------------------------
% 1.59/1.42 % (14392)------------------------------
% 1.59/1.42 % (14394)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_14135 for (2998ds/98Mi)
% 1.59/1.43 % (14391)Instruction limit reached!
% 1.59/1.43 % (14391)------------------------------
% 1.59/1.43 % (14391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.43 % (14391)Termination reason: Unknown
% 1.59/1.43 % (14391)Termination phase: Saturation
% 1.59/1.43
% 1.59/1.43 % (14391)Memory used [KB]: 5756
% 1.59/1.43 % (14391)Time elapsed: 0.038 s
% 1.59/1.43 % (14391)Instructions burned: 41 (million)
% 1.59/1.43 % (14391)------------------------------
% 1.59/1.43 % (14391)------------------------------
% 1.59/1.43 % (14393)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_14135 for (2998ds/46Mi)
% 1.59/1.43 % (14394)Refutation not found, incomplete strategy
% 1.59/1.43 % (14394)------------------------------
% 1.59/1.43 % (14394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.43 % (14394)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.43
% 1.59/1.43
% 1.59/1.43 % (14394)Memory used [KB]: 1023
% 1.59/1.43 % (14394)Time elapsed: 0.028 s
% 1.59/1.43 % (14394)Instructions burned: 9 (million)
% 1.59/1.43 % (14394)------------------------------
% 1.59/1.43 % (14394)------------------------------
% 1.59/1.43 % (14385)Instruction limit reached!
% 1.59/1.43 % (14385)------------------------------
% 1.59/1.43 % (14385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.43 % (14385)Termination reason: Unknown
% 1.59/1.43 % (14385)Termination phase: Saturation
% 1.59/1.43
% 1.59/1.43 % (14385)Memory used [KB]: 5884
% 1.59/1.43 % (14385)Time elapsed: 0.046 s
% 1.59/1.43 % (14385)Instructions burned: 128 (million)
% 1.59/1.43 % (14385)------------------------------
% 1.59/1.43 % (14385)------------------------------
% 1.59/1.43 % (14389)Instruction limit reached!
% 1.59/1.43 % (14389)------------------------------
% 1.59/1.43 % (14389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.43 % (14389)Termination reason: Unknown
% 1.59/1.43 % (14389)Termination phase: Saturation
% 1.59/1.43
% 1.59/1.43 % (14389)Memory used [KB]: 5884
% 1.59/1.43 % (14389)Time elapsed: 0.053 s
% 1.59/1.43 % (14389)Instructions burned: 86 (million)
% 1.59/1.43 % (14389)------------------------------
% 1.59/1.43 % (14389)------------------------------
% 1.59/1.44 % (14395)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_14135 for (2998ds/507Mi)
% 1.59/1.44 % (14395)Refutation not found, incomplete strategy
% 1.59/1.44 % (14395)------------------------------
% 1.59/1.44 % (14395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.44 % (14395)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.44
% 1.59/1.44
% 1.59/1.44 % (14395)Memory used [KB]: 5500
% 1.59/1.44 % (14395)Time elapsed: 0.003 s
% 1.59/1.44 % (14395)Instructions burned: 4 (million)
% 1.59/1.44 % (14395)------------------------------
% 1.59/1.44 % (14395)------------------------------
% 1.59/1.44 % (14397)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_14135 for (2998ds/39Mi)
% 1.59/1.44 % (14396)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_14135 for (2998ds/149Mi)
% 1.59/1.44 % (14397)Refutation not found, incomplete strategy
% 1.59/1.44 % (14397)------------------------------
% 1.59/1.44 % (14397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.44 % (14397)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.44
% 1.59/1.44
% 1.59/1.44 % (14397)Memory used [KB]: 5500
% 1.59/1.44 % (14397)Time elapsed: 0.002 s
% 1.59/1.44 % (14397)Instructions burned: 3 (million)
% 1.59/1.44 % (14397)------------------------------
% 1.59/1.44 % (14397)------------------------------
% 1.59/1.44 % (14398)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_14135 for (2998ds/6Mi)
% 1.59/1.44 % (14398)Instruction limit reached!
% 1.59/1.44 % (14398)------------------------------
% 1.59/1.44 % (14398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.44 % (14398)Termination reason: Unknown
% 1.59/1.44 % (14398)Termination phase: Saturation
% 1.59/1.44
% 1.59/1.44 % (14398)Memory used [KB]: 9978
% 1.59/1.44 % (14398)Time elapsed: 0.005 s
% 1.59/1.44 % (14398)Instructions burned: 7 (million)
% 1.59/1.44 % (14398)------------------------------
% 1.59/1.44 % (14398)------------------------------
% 1.59/1.45 % (14393)Instruction limit reached!
% 1.59/1.45 % (14393)------------------------------
% 1.59/1.45 % (14393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.45 % (14393)Termination reason: Unknown
% 1.59/1.45 % (14393)Termination phase: Saturation
% 1.59/1.45
% 1.59/1.45 % (14393)Memory used [KB]: 5628
% 1.59/1.45 % (14393)Time elapsed: 0.041 s
% 1.59/1.45 % (14393)Instructions burned: 47 (million)
% 1.59/1.45 % (14393)------------------------------
% 1.59/1.45 % (14393)------------------------------
% 1.59/1.45 % (14399)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_14135 for (2998ds/1087Mi)
% 1.59/1.45 % (14399)Refutation not found, incomplete strategy
% 1.59/1.45 % (14399)------------------------------
% 1.59/1.45 % (14399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.45 % (14399)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.45
% 1.59/1.45
% 1.59/1.45 % (14399)Memory used [KB]: 5500
% 1.59/1.45 % (14399)Time elapsed: 0.003 s
% 1.59/1.45 % (14399)Instructions burned: 3 (million)
% 1.59/1.45 % (14399)------------------------------
% 1.59/1.45 % (14399)------------------------------
% 1.59/1.45 % (14400)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_14135 for (2998ds/47Mi)
% 1.59/1.45 % (14401)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_14135 for (2998ds/44Mi)
% 1.59/1.46 % (14402)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_14135 for (2998ds/432Mi)
% 1.59/1.46 % (14403)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_14135 for (2998ds/62Mi)
% 1.59/1.46 % (14400)Instruction limit reached!
% 1.59/1.46 % (14400)------------------------------
% 1.59/1.46 % (14400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.46 % (14400)Termination reason: Unknown
% 1.59/1.46 % (14400)Termination phase: Saturation
% 1.59/1.46
% 1.59/1.46 % (14400)Memory used [KB]: 5628
% 1.59/1.46 % (14400)Time elapsed: 0.016 s
% 1.59/1.46 % (14400)Instructions burned: 49 (million)
% 1.59/1.46 % (14400)------------------------------
% 1.59/1.46 % (14400)------------------------------
% 1.59/1.47 % (14401)Instruction limit reached!
% 1.59/1.47 % (14401)------------------------------
% 1.59/1.47 % (14401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.47 % (14401)Termination reason: Unknown
% 1.59/1.47 % (14401)Termination phase: Saturation
% 1.59/1.47
% 1.59/1.47 % (14401)Memory used [KB]: 1151
% 1.59/1.47 % (14401)Time elapsed: 0.017 s
% 1.59/1.47 % (14401)Instructions burned: 45 (million)
% 1.59/1.47 % (14401)------------------------------
% 1.59/1.47 % (14401)------------------------------
% 1.59/1.47 % (14404)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/31Mi)
% 1.59/1.48 % (14405)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/96Mi)
% 1.59/1.48 % (14403)Instruction limit reached!
% 1.59/1.48 % (14403)------------------------------
% 1.59/1.48 % (14403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.48 % (14403)Termination reason: Unknown
% 1.59/1.48 % (14403)Termination phase: Saturation
% 1.59/1.48
% 1.59/1.48 % (14403)Memory used [KB]: 5756
% 1.59/1.48 % (14403)Time elapsed: 0.023 s
% 1.59/1.48 % (14403)Instructions burned: 62 (million)
% 1.59/1.48 % (14403)------------------------------
% 1.59/1.48 % (14403)------------------------------
% 1.59/1.48 % (14404)Instruction limit reached!
% 1.59/1.48 % (14404)------------------------------
% 1.59/1.48 % (14404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.48 % (14404)Termination reason: Unknown
% 1.59/1.48 % (14404)Termination phase: Saturation
% 1.59/1.48
% 1.59/1.48 % (14404)Memory used [KB]: 5628
% 1.59/1.48 % (14404)Time elapsed: 0.012 s
% 1.59/1.48 % (14404)Instructions burned: 33 (million)
% 1.59/1.48 % (14404)------------------------------
% 1.59/1.48 % (14404)------------------------------
% 1.59/1.49 % (14396)Instruction limit reached!
% 1.59/1.49 % (14396)------------------------------
% 1.59/1.49 % (14396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.49 % (14396)Termination reason: Unknown
% 1.59/1.49 % (14396)Termination phase: Saturation
% 1.59/1.49
% 1.59/1.49 % (14396)Memory used [KB]: 5884
% 1.59/1.49 % (14396)Time elapsed: 0.053 s
% 1.59/1.49 % (14396)Instructions burned: 150 (million)
% 1.59/1.49 % (14396)------------------------------
% 1.59/1.49 % (14396)------------------------------
% 1.59/1.49 % (14406)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/453Mi)
% 1.59/1.49 % (14407)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/71Mi)
% 1.59/1.50 % (14408)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/83Mi)
% 1.59/1.50 % (14406)Refutation not found, incomplete strategy
% 1.59/1.50 % (14406)------------------------------
% 1.59/1.50 % (14406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.50 % (14406)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.50
% 1.59/1.50
% 1.59/1.50 % (14406)Memory used [KB]: 5628
% 1.59/1.50 % (14406)Time elapsed: 0.012 s
% 1.59/1.50 % (14406)Instructions burned: 29 (million)
% 1.59/1.50 % (14406)------------------------------
% 1.59/1.50 % (14406)------------------------------
% 1.59/1.51 % (14409)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/11Mi)
% 1.59/1.51 % (14405)Instruction limit reached!
% 1.59/1.51 % (14405)------------------------------
% 1.59/1.51 % (14405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.51 % (14405)Termination reason: Unknown
% 1.59/1.51 % (14405)Termination phase: Saturation
% 1.59/1.51
% 1.59/1.51 % (14405)Memory used [KB]: 5756
% 1.59/1.51 % (14405)Time elapsed: 0.036 s
% 1.59/1.51 % (14405)Instructions burned: 98 (million)
% 1.59/1.51 % (14405)------------------------------
% 1.59/1.51 % (14405)------------------------------
% 1.59/1.52 % (14409)Instruction limit reached!
% 1.59/1.52 % (14409)------------------------------
% 1.59/1.52 % (14409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.52 % (14409)Termination reason: Unknown
% 1.59/1.52 % (14409)Termination phase: Saturation
% 1.59/1.52
% 1.59/1.52 % (14409)Memory used [KB]: 5500
% 1.59/1.52 % (14409)Time elapsed: 0.006 s
% 1.59/1.52 % (14409)Instructions burned: 12 (million)
% 1.59/1.52 % (14409)------------------------------
% 1.59/1.52 % (14409)------------------------------
% 1.59/1.52 % (14407)Instruction limit reached!
% 1.59/1.52 % (14407)------------------------------
% 1.59/1.52 % (14407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.52 % (14407)Termination reason: Unknown
% 1.59/1.52 % (14407)Termination phase: Saturation
% 1.59/1.52
% 1.59/1.52 % (14407)Memory used [KB]: 5756
% 1.59/1.52 % (14407)Time elapsed: 0.024 s
% 1.59/1.52 % (14407)Instructions burned: 71 (million)
% 1.59/1.52 % (14407)------------------------------
% 1.59/1.52 % (14407)------------------------------
% 1.59/1.52 % (14410)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/41Mi)
% 1.59/1.53 % (14411)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/6Mi)
% 1.59/1.53 % (14412)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/150Mi)
% 1.59/1.53 % (14411)Instruction limit reached!
% 1.59/1.53 % (14411)------------------------------
% 1.59/1.53 % (14411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.53 % (14411)Termination reason: Unknown
% 1.59/1.53 % (14411)Termination phase: Saturation
% 1.59/1.53
% 1.59/1.53 % (14411)Memory used [KB]: 5500
% 1.59/1.53 % (14411)Time elapsed: 0.004 s
% 1.59/1.53 % (14411)Instructions burned: 6 (million)
% 1.59/1.53 % (14411)------------------------------
% 1.59/1.53 % (14411)------------------------------
% 1.59/1.53 % (14408)Instruction limit reached!
% 1.59/1.53 % (14408)------------------------------
% 1.59/1.53 % (14408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.53 % (14408)Termination reason: Unknown
% 1.59/1.53 % (14408)Termination phase: Saturation
% 1.59/1.53
% 1.59/1.53 % (14408)Memory used [KB]: 5756
% 1.59/1.53 % (14408)Time elapsed: 0.031 s
% 1.59/1.53 % (14408)Instructions burned: 85 (million)
% 1.59/1.53 % (14408)------------------------------
% 1.59/1.53 % (14408)------------------------------
% 1.59/1.54 % (14410)Instruction limit reached!
% 1.59/1.54 % (14410)------------------------------
% 1.59/1.54 % (14410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.54 % (14410)Termination reason: Unknown
% 1.59/1.54 % (14410)Termination phase: Saturation
% 1.59/1.54
% 1.59/1.54 % (14410)Memory used [KB]: 5628
% 1.59/1.54 % (14410)Time elapsed: 0.016 s
% 1.59/1.54 % (14410)Instructions burned: 43 (million)
% 1.59/1.54 % (14410)------------------------------
% 1.59/1.54 % (14410)------------------------------
% 1.59/1.54 % (14413)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/343Mi)
% 1.59/1.54 % (14414)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/109Mi)
% 1.59/1.54 % (14413)Refutation not found, incomplete strategy
% 1.59/1.54 % (14413)------------------------------
% 1.59/1.54 % (14413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.54 % (14413)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.54
% 1.59/1.54
% 1.59/1.54 % (14413)Memory used [KB]: 5500
% 1.59/1.54 % (14413)Time elapsed: 0.003 s
% 1.59/1.54 % (14413)Instructions burned: 3 (million)
% 1.59/1.54 % (14413)------------------------------
% 1.59/1.54 % (14413)------------------------------
% 1.59/1.55 % (14415)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/253Mi)
% 1.59/1.55 % (14415)Refutation not found, incomplete strategy
% 1.59/1.55 % (14415)------------------------------
% 1.59/1.55 % (14415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.55 % (14415)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.55
% 1.59/1.55
% 1.59/1.55 % (14415)Memory used [KB]: 5500
% 1.59/1.55 % (14415)Time elapsed: 0.003 s
% 1.59/1.55 % (14415)Instructions burned: 3 (million)
% 1.59/1.55 % (14415)------------------------------
% 1.59/1.55 % (14415)------------------------------
% 1.59/1.55 % (14416)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/140Mi)
% 1.59/1.55 % (14416)Refutation not found, incomplete strategy
% 1.59/1.55 % (14416)------------------------------
% 1.59/1.55 % (14416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.55 % (14416)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.55
% 1.59/1.55
% 1.59/1.55 % (14416)Memory used [KB]: 5500
% 1.59/1.55 % (14416)Time elapsed: 0.003 s
% 1.59/1.55 % (14416)Instructions burned: 3 (million)
% 1.59/1.55 % (14416)------------------------------
% 1.59/1.55 % (14416)------------------------------
% 1.59/1.56 % (14417)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/614Mi)
% 1.59/1.56 % (14417)Refutation not found, incomplete strategy
% 1.59/1.56 % (14417)------------------------------
% 1.59/1.56 % (14417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.56 % (14417)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.56
% 1.59/1.56
% 1.59/1.56 % (14417)Memory used [KB]: 5500
% 1.59/1.56 % (14417)Time elapsed: 0.003 s
% 1.59/1.56 % (14417)Instructions burned: 3 (million)
% 1.59/1.56 % (14417)------------------------------
% 1.59/1.56 % (14417)------------------------------
% 1.59/1.56 % (14418)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/202Mi)
% 1.59/1.57 % (14372)Instruction limit reached!
% 1.59/1.57 % (14372)------------------------------
% 1.59/1.57 % (14372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.57 % (14372)Termination reason: Unknown
% 1.59/1.57 % (14372)Termination phase: Saturation
% 1.59/1.57
% 1.59/1.57 % (14372)Memory used [KB]: 6652
% 1.59/1.57 % (14372)Time elapsed: 0.236 s
% 1.59/1.57 % (14372)Instructions burned: 710 (million)
% 1.59/1.57 % (14372)------------------------------
% 1.59/1.57 % (14372)------------------------------
% 1.59/1.57 % (14419)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/339Mi)
% 1.59/1.57 % (14414)Instruction limit reached!
% 1.59/1.57 % (14414)------------------------------
% 1.59/1.57 % (14414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.57 % (14414)Termination reason: Unknown
% 1.59/1.57 % (14414)Termination phase: Saturation
% 1.59/1.57
% 1.59/1.57 % (14414)Memory used [KB]: 5884
% 1.59/1.57 % (14414)Time elapsed: 0.036 s
% 1.59/1.57 % (14414)Instructions burned: 109 (million)
% 1.59/1.57 % (14414)------------------------------
% 1.59/1.57 % (14414)------------------------------
% 1.59/1.57 % (14412)Instruction limit reached!
% 1.59/1.57 % (14412)------------------------------
% 1.59/1.57 % (14412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.57 % (14412)Termination reason: Unknown
% 1.59/1.57 % (14412)Termination phase: Saturation
% 1.59/1.57
% 1.59/1.57 % (14412)Memory used [KB]: 5884
% 1.59/1.57 % (14412)Time elapsed: 0.049 s
% 1.59/1.57 % (14412)Instructions burned: 152 (million)
% 1.59/1.57 % (14412)------------------------------
% 1.59/1.57 % (14412)------------------------------
% 1.59/1.57 % (14419)Refutation not found, incomplete strategy
% 1.59/1.57 % (14419)------------------------------
% 1.59/1.57 % (14419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.57 % (14419)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.57
% 1.59/1.57
% 1.59/1.57 % (14419)Memory used [KB]: 5500
% 1.59/1.57 % (14419)Time elapsed: 0.003 s
% 1.59/1.57 % (14419)Instructions burned: 5 (million)
% 1.59/1.57 % (14419)------------------------------
% 1.59/1.57 % (14419)------------------------------
% 1.59/1.58 % (14420)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=283:si=on:rtra=on_0 on DTF2THF_14135 for (2997ds/283Mi)
% 1.59/1.58 % (14421)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_14135 for (2996ds/134Mi)
% 1.59/1.58 % (14422)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_14135 for (2996ds/298Mi)
% 1.59/1.59 % (14423)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_14135 for (2996ds/192Mi)
% 1.59/1.60 % (14402)Instruction limit reached!
% 1.59/1.60 % (14402)------------------------------
% 1.59/1.60 % (14402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.60 % (14402)Termination reason: Unknown
% 1.59/1.60 % (14402)Termination phase: Saturation
% 1.59/1.60
% 1.59/1.60 % (14402)Memory used [KB]: 2686
% 1.59/1.60 % (14402)Time elapsed: 0.143 s
% 1.59/1.60 % (14402)Instructions burned: 432 (million)
% 1.59/1.60 % (14402)------------------------------
% 1.59/1.60 % (14402)------------------------------
% 1.59/1.61 % (14424)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_14135 for (2996ds/258Mi)
% 1.59/1.61 % (14422)First to succeed.
% 1.59/1.61 % (14422)Refutation found. Thanks to Tanya!
% 1.59/1.61 % SZS status Theorem for DTF2THF_14135
% 1.59/1.61 % SZS output start Proof for DTF2THF_14135
% 1.59/1.61 thf(func_def_1, type, s: $i > $i).
% 1.59/1.61 thf(func_def_2, type, ite: $o > $i > $i > $i).
% 1.59/1.61 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 1.59/1.61 thf(f544,plain,(
% 1.59/1.61 $false),
% 1.59/1.61 inference(avatar_sat_refutation,[status(thm)],[f91,f149,f184,f298,f357,f455,f477,f525,f541,f543])).
% 1.59/1.61 thf(f543,plain,(
% 1.59/1.61 ~spl0_35),
% 1.59/1.61 inference(avatar_contradiction_clause,[status(thm)],[f542])).
% 1.59/1.61 thf(f542,plain,(
% 1.59/1.61 $false | ~spl0_35),
% 1.59/1.61 inference(equality_resolution,[status(thm)],[f499])).
% 1.59/1.61 thf(f499,plain,(
% 1.59/1.61 ( ! [X3 : $i] : (((s @ zero) != X3)) ) | ~spl0_35),
% 1.59/1.61 inference(avatar_component_clause,[status(thm)],[f498])).
% 1.59/1.61 thf(f498,definition,(
% 1.59/1.61 spl0_35 <=> ! [X3 : $i] : ((s @ zero) != X3)),
% 1.59/1.61 introduced(definition,[new_symbols(naming,[spl0_35])],[avatar_definition])).
% 1.59/1.61 thf(f541,plain,(
% 1.59/1.61 ~spl0_31),
% 1.59/1.61 inference(avatar_contradiction_clause,[status(thm)],[f540])).
% 1.59/1.61 thf(f540,plain,(
% 1.59/1.61 $false | ~spl0_31),
% 1.59/1.61 inference(equality_resolution,[status(thm)],[f454])).
% 1.59/1.61 thf(f454,plain,(
% 1.59/1.61 ( ! [X0 : $i] : ((zero != X0)) ) | ~spl0_31),
% 1.59/1.61 inference(avatar_component_clause,[status(thm)],[f453])).
% 1.59/1.61 thf(f453,definition,(
% 1.59/1.61 spl0_31 <=> ! [X0 : $i] : (zero != X0)),
% 1.59/1.61 introduced(definition,[new_symbols(naming,[spl0_31])],[avatar_definition])).
% 1.59/1.61 thf(f525,plain,(
% 1.59/1.61 spl0_35 | spl0_35 | ~spl0_20),
% 1.59/1.61 inference(avatar_split_clause,[status(thm)],[f524,f296,f498,f498])).
% 1.59/1.61 thf(f296,definition,(
% 1.59/1.61 spl0_20 <=> ! [X3 : $i,X7 : $i,X9 : $i,X2 : $i > $i] : (((s @ zero) != X7) | ((s @ zero) != X3) | ((X2 @ zero) != X3) | ((X2 @ (s @ zero)) != X9) | ((X2 @ (s @ (s @ zero))) != X7))),
% 1.59/1.61 introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition])).
% 1.59/1.61 thf(f524,plain,(
% 1.59/1.61 ( ! [X0 : $i,X1 : $i] : (((s @ zero) != X1) | ((s @ zero) != X0)) ) | ~spl0_20),
% 1.59/1.61 inference(duplicate_literal_removal,[status(thm)],[f523])).
% 1.59/1.61 thf(f523,plain,(
% 1.59/1.61 ( ! [X0 : $i,X1 : $i] : (((s @ zero) != X1) | ((s @ zero) != X0) | ((s @ zero) != X0)) ) | ~spl0_20),
% 1.59/1.61 inference(beta_eta_normalization,[status(thm)],[f520])).
% 1.59/1.61 thf(f520,plain,(
% 1.59/1.61 ( ! [X0 : $i,X1 : $i] : ((((^[Y0 : $i]: (s @ ((^[Y1 : $i]: (zero)) @ Y0))) @ (s @ zero)) != X1) | (((^[Y0 : $i]: (s @ ((^[Y1 : $i]: (zero)) @ Y0))) @ zero) != X0) | ((s @ zero) != X0)) ) | ~spl0_20),
% 1.59/1.61 inference(equality_resolution,[status(thm)],[f517])).
% 1.59/1.61 thf(f517,plain,(
% 1.59/1.61 ( ! [X2 : $i,X0 : $i,X1 : $i > $i] : (((s @ zero) != (X1 @ (s @ (s @ zero)))) | ((s @ zero) != X0) | ((X1 @ zero) != X0) | ((X1 @ (s @ zero)) != X2)) ) | ~spl0_20),
% 1.59/1.61 inference(equality_resolution,[status(thm)],[f297])).
% 1.59/1.61 thf(f297,plain,(
% 1.59/1.61 ( ! [X2 : $i > $i,X3 : $i,X9 : $i,X7 : $i] : (((s @ zero) != X7) | ((X2 @ (s @ (s @ zero))) != X7) | ((X2 @ (s @ zero)) != X9) | ((s @ zero) != X3) | ((X2 @ zero) != X3)) ) | ~spl0_20),
% 1.59/1.61 inference(avatar_component_clause,[status(thm)],[f296])).
% 1.59/1.61 thf(f477,plain,(
% 1.59/1.61 spl0_1 | spl0_2),
% 1.59/1.61 inference(avatar_split_clause,[status(thm)],[f476,f54,f51])).
% 1.59/1.61 thf(f51,definition,(
% 1.59/1.61 spl0_1 <=> ! [X0 : $o] : ($true = X0)),
% 1.59/1.61 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.59/1.61 thf(f54,definition,(
% 1.59/1.61 spl0_2 <=> ! [X3 : $i > $i,X4 : $i,X5 : $i > $i,X2 : $i,X1 : $i > $o] : (((s @ zero) != X2) | (zero != (ite @ (X1 @ (s @ zero)) @ (X5 @ (s @ zero)) @ (X3 @ (s @ zero)))) | ((s @ zero) != (ite @ (X1 @ zero) @ (X5 @ zero) @ (X3 @ zero))) | ((X3 @ (s @ (s @ zero))) != X2) | ((X1 @ (s @ (s @ zero))) = $true) | ((X5 @ (s @ (s @ zero))) != X4))),
% 1.59/1.61 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.59/1.61 thf(f476,plain,(
% 1.59/1.61 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $i,X1 : $i,X4 : $i > $o,X5 : $o] : (((s @ zero) != X3) | ((s @ zero) != (ite @ (X4 @ zero) @ (X0 @ zero) @ (X2 @ zero))) | ($true = X5) | ((X0 @ (s @ (s @ zero))) != X1) | ((X4 @ (s @ (s @ zero))) = $true) | ((X2 @ (s @ (s @ zero))) != X3) | (zero != (ite @ (X4 @ (s @ zero)) @ (X0 @ (s @ zero)) @ (X2 @ (s @ zero))))) )),
% 1.59/1.61 inference(duplicate_literal_removal,[status(thm)],[f474])).
% 1.59/1.61 thf(f474,plain,(
% 1.59/1.61 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $i,X1 : $i,X4 : $i > $o,X5 : $o] : (($true = X5) | ((s @ zero) != (ite @ (X4 @ zero) @ (X0 @ zero) @ (X2 @ zero))) | (zero != (ite @ (X4 @ (s @ zero)) @ (X0 @ (s @ zero)) @ (X2 @ (s @ zero)))) | ((s @ zero) != X3) | ((X4 @ (s @ (s @ zero))) = $true) | ($true = X5) | ((X2 @ (s @ (s @ zero))) != X3) | ((X0 @ (s @ (s @ zero))) != X1)) )),
% 1.59/1.61 inference(binary_proxy_clausification,[status(thm)],[f466])).
% 1.59/1.61 thf(f466,plain,(
% 1.59/1.61 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $i,X1 : $i,X4 : $i > $o,X5 : $o] : (((X0 @ (s @ (s @ zero))) != X1) | ($true = X5) | ((s @ zero) != (ite @ (X4 @ zero) @ (X0 @ zero) @ (X2 @ zero))) | ((s @ zero) != X3) | (zero != (ite @ (X4 @ (s @ zero)) @ (X0 @ (s @ zero)) @ (X2 @ (s @ zero)))) | ((X4 @ (s @ (s @ zero))) != X5) | ((X2 @ (s @ (s @ zero))) != X3)) )),
% 1.59/1.61 inference(beta_eta_normalization,[status(thm)],[f463])).
% 1.59/1.61 thf(f463,plain,(
% 1.59/1.61 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $i,X1 : $i,X4 : $i > $o,X5 : $o] : (((X0 @ (s @ (s @ zero))) != X1) | (zero != ((^[Y0 : $i]: (ite @ (X4 @ Y0) @ (X0 @ Y0) @ (X2 @ Y0))) @ (s @ zero))) | ($true = X5) | ((X4 @ (s @ (s @ zero))) != X5) | ((s @ zero) != ((^[Y0 : $i]: (ite @ (X4 @ Y0) @ (X0 @ Y0) @ (X2 @ Y0))) @ zero)) | ((s @ zero) != X3) | ((X2 @ (s @ (s @ zero))) != X3)) )),
% 1.59/1.61 inference(constrained_superposition,[status(thm)],[f41,f20])).
% 1.59/1.61 thf(f20,plain,(
% 1.59/1.61 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((ite @ X3 @ X1 @ X2) = X2) | ($true = X3)) )),
% 1.59/1.61 inference(equality_proxy_clausification,[status(thm)],[f19])).
% 1.59/1.61 thf(f19,plain,(
% 1.59/1.61 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = X3) | ($true = ((ite @ X3 @ X1 @ X2) = X2))) )),
% 1.59/1.61 inference(not_proxy_clausification,[status(thm)],[f18])).
% 1.59/1.61 thf(f18,plain,(
% 1.59/1.61 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((~ X3) = $false) | ($true = ((ite @ X3 @ X1 @ X2) = X2))) )),
% 1.59/1.61 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.59/1.61 thf(f17,plain,(
% 1.59/1.61 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((~ X3) => ((ite @ X3 @ X1 @ X2) = X2)) = $true)) )),
% 1.59/1.61 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.59/1.61 thf(f16,plain,(
% 1.59/1.61 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = ((^[Y0 : $o]: ((~ Y0) => ((ite @ Y0 @ X1 @ X2) = X2))) @ X3))) )),
% 1.59/1.61 inference(pi_clausification,[status(thm)],[f15])).
% 1.59/1.61 thf(f15,plain,(
% 1.59/1.61 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $o @ (^[Y0 : $o]: ((~ Y0) => ((ite @ Y0 @ X1 @ X2) = X2)))))) )),
% 1.59/1.61 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.59/1.61 thf(f14,plain,(
% 1.59/1.61 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((~ Y1) => ((ite @ Y1 @ X1 @ Y0) = Y0))))) @ X2))) )),
% 1.59/1.61 inference(pi_clausification,[status(thm)],[f13])).
% 1.59/1.61 thf(f13,plain,(
% 1.59/1.61 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((~ Y1) => ((ite @ Y1 @ X1 @ Y0) = Y0)))))))) )),
% 1.59/1.61 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.59/1.61 thf(f12,plain,(
% 1.59/1.61 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y0 @ Y1) = Y1))))))) @ X1))) )),
% 1.59/1.61 inference(pi_clausification,[status(thm)],[f10])).
% 1.59/1.61 thf(f10,plain,(
% 1.59/1.61 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y0 @ Y1) = Y1)))))))))),
% 1.59/1.61 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.59/1.61 thf(f9,plain,(
% 1.59/1.61 ($true = (((!! @ $i @ (^[Y0 : $i]: (~ ((s @ Y0) = Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1))))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y0 @ Y1) = Y1))))))))))),
% 1.59/1.61 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.59/1.61 thf(f7,plain,(
% 1.59/1.61 (((((!! @ $i @ (^[Y0 : $i]: (~ ((s @ Y0) = Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1))))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y0 @ Y1) = Y1))))))))) => (?? @ ($i > $i) @ (^[Y0 : $i > $i]: (((zero = (Y0 @ (s @ zero))) & ((s @ zero) = (Y0 @ (s @ (s @ zero))))) & ((s @ zero) = (Y0 @ zero)))))) = $false)),
% 1.59/1.61 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.59/1.61 thf(f6,plain,(
% 1.59/1.61 ((~ ((((!! @ $i @ (^[Y0 : $i]: (~ ((s @ Y0) = Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1))))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y0 @ Y1) = Y1))))))))) => (?? @ ($i > $i) @ (^[Y0 : $i > $i]: (((zero = (Y0 @ (s @ zero))) & ((s @ zero) = (Y0 @ (s @ (s @ zero))))) & ((s @ zero) = (Y0 @ zero))))))) = $true)),
% 1.59/1.61 inference(cnf_transformation,[status(thm)],[f5])).
% 1.59/1.61 thf(f5,plain,(
% 1.59/1.61 ((~ ((((!! @ $i @ (^[Y0 : $i]: (~ ((s @ Y0) = Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1))))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y0 @ Y1) = Y1))))))))) => (?? @ ($i > $i) @ (^[Y0 : $i > $i]: (((zero = (Y0 @ (s @ zero))) & ((s @ zero) = (Y0 @ (s @ (s @ zero))))) & ((s @ zero) = (Y0 @ zero))))))) = $true)),
% 1.59/1.61 inference(fool_elimination,[status(thm)],[f4])).
% 1.59/1.61 thf(f4,plain,(
% 1.59/1.61 ~((! [X0 : $o,X1 : $i,X2 : $i] : (~X0 => ((ite @ X0 @ X2 @ X1) = X1)) & ! [X3 : $o,X4 : $i,X5 : $i] : (X3 => ((ite @ X3 @ X4 @ X5) = X4)) & ! [X6 : $i] : ((s @ X6) != X6)) => ? [X7 : $i > $i] : (((s @ zero) = (X7 @ zero)) & ((s @ zero) = (X7 @ (s @ (s @ zero)))) & (zero = (X7 @ (s @ zero)))))),
% 1.59/1.61 inference(rectify,[status(thm)],[f2])).
% 1.59/1.61 thf(f2,negated_conjecture,(
% 1.59/1.61 ~((! [X0 : $o,X2 : $i,X1 : $i] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X0 : $o,X1 : $i,X2 : $i] : (X0 => ((ite @ X0 @ X1 @ X2) = X1)) & ! [X3 : $i] : ((s @ X3) != X3)) => ? [X4 : $i > $i] : (((X4 @ zero) = (s @ zero)) & ((s @ zero) = (X4 @ (s @ (s @ zero)))) & (zero = (X4 @ (s @ zero)))))),
% 1.59/1.61 inference(negated_conjecture,[status(cth)],[f1])).
% 1.59/1.61 thf(f1,conjecture,(
% 1.59/1.61 (! [X0 : $o,X2 : $i,X1 : $i] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X0 : $o,X1 : $i,X2 : $i] : (X0 => ((ite @ X0 @ X1 @ X2) = X1)) & ! [X3 : $i] : ((s @ X3) != X3)) => ? [X4 : $i > $i] : (((X4 @ zero) = (s @ zero)) & ((s @ zero) = (X4 @ (s @ (s @ zero)))) & (zero = (X4 @ (s @ zero))))),
% 1.59/1.61 file('/export/starexec/sandbox2/tmp/tmp.bLy8R3mVbL/DTF2THF_14135.p',n9)).
% 1.59/1.61 thf(f41,plain,(
% 1.59/1.61 ( ! [X1 : $i > $i] : (((s @ zero) != (X1 @ (s @ (s @ zero)))) | ((s @ zero) != (X1 @ zero)) | (zero != (X1 @ (s @ zero)))) )),
% 1.59/1.61 inference(equality_proxy_clausification,[status(thm)],[f40])).
% 1.59/1.61 thf(f40,plain,(
% 1.59/1.61 ( ! [X1 : $i > $i] : ((zero != (X1 @ (s @ zero))) | ((s @ zero) != (X1 @ zero)) | (((s @ zero) = (X1 @ (s @ (s @ zero)))) = $false)) )),
% 1.59/1.61 inference(equality_proxy_clausification,[status(thm)],[f39])).
% 1.59/1.61 thf(f39,plain,(
% 1.59/1.61 ( ! [X1 : $i > $i] : ((zero != (X1 @ (s @ zero))) | (((s @ zero) = (X1 @ zero)) = $false) | (((s @ zero) = (X1 @ (s @ (s @ zero)))) = $false)) )),
% 1.59/1.61 inference(equality_proxy_clausification,[status(thm)],[f38])).
% 1.59/1.61 thf(f38,plain,(
% 1.59/1.61 ( ! [X1 : $i > $i] : (((zero = (X1 @ (s @ zero))) = $false) | (((s @ zero) = (X1 @ zero)) = $false) | (((s @ zero) = (X1 @ (s @ (s @ zero)))) = $false)) )),
% 1.59/1.61 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.59/1.61 thf(f37,plain,(
% 1.59/1.61 ( ! [X1 : $i > $i] : (($false = ((zero = (X1 @ (s @ zero))) & ((s @ zero) = (X1 @ (s @ (s @ zero)))))) | (((s @ zero) = (X1 @ zero)) = $false)) )),
% 1.59/1.61 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.59/1.61 thf(f36,plain,(
% 1.59/1.61 ( ! [X1 : $i > $i] : (((((zero = (X1 @ (s @ zero))) & ((s @ zero) = (X1 @ (s @ (s @ zero))))) & ((s @ zero) = (X1 @ zero))) = $false)) )),
% 1.59/1.61 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.59/1.61 thf(f35,plain,(
% 1.59/1.61 ( ! [X1 : $i > $i] : ((((^[Y0 : $i > $i]: (((zero = (Y0 @ (s @ zero))) & ((s @ zero) = (Y0 @ (s @ (s @ zero))))) & ((s @ zero) = (Y0 @ zero)))) @ X1) = $false)) )),
% 1.59/1.61 inference(pi_clausification,[status(thm)],[f8])).
% 1.59/1.61 thf(f8,plain,(
% 1.59/1.61 ((?? @ ($i > $i) @ (^[Y0 : $i > $i]: (((zero = (Y0 @ (s @ zero))) & ((s @ zero) = (Y0 @ (s @ (s @ zero))))) & ((s @ zero) = (Y0 @ zero))))) = $false)),
% 1.59/1.61 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.59/1.61 thf(f455,plain,(
% 1.59/1.61 spl0_31 | spl0_31 | ~spl0_19),
% 1.59/1.61 inference(avatar_split_clause,[status(thm)],[f443,f293,f453,f453])).
% 1.59/1.61 thf(f293,definition,(
% 1.59/1.61 spl0_19 <=> ! [X5 : $i,X4 : $i > $i,X6 : $i,X8 : $i] : (((X4 @ (s @ (s @ zero))) != X8) | ((X4 @ (s @ zero)) != X6) | ((X4 @ zero) != X5) | (zero != X6))),
% 1.59/1.61 introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition])).
% 1.59/1.61 thf(f443,plain,(
% 1.59/1.61 ( ! [X0 : $i,X1 : $i] : ((zero != X1) | (zero != X0)) ) | ~spl0_19),
% 1.59/1.61 inference(beta_eta_normalization,[status(thm)],[f441])).
% 1.59/1.61 thf(f441,plain,(
% 1.59/1.61 ( ! [X0 : $i,X1 : $i] : ((((^[Y0 : $i]: (zero)) @ zero) != X0) | (((^[Y0 : $i]: (zero)) @ (s @ (s @ zero))) != X1)) ) | ~spl0_19),
% 1.59/1.61 inference(equality_resolution,[status(thm)],[f438])).
% 1.59/1.61 thf(f438,plain,(
% 1.59/1.61 ( ! [X2 : $i,X0 : $i > $i,X1 : $i] : ((zero != (X0 @ (s @ zero))) | ((X0 @ zero) != X1) | ((X0 @ (s @ (s @ zero))) != X2)) ) | ~spl0_19),
% 1.59/1.61 inference(equality_resolution,[status(thm)],[f294])).
% 1.59/1.61 thf(f294,plain,(
% 1.59/1.61 ( ! [X8 : $i,X6 : $i,X4 : $i > $i,X5 : $i] : ((zero != X6) | ((X4 @ (s @ (s @ zero))) != X8) | ((X4 @ (s @ zero)) != X6) | ((X4 @ zero) != X5)) ) | ~spl0_19),
% 1.59/1.61 inference(avatar_component_clause,[status(thm)],[f293])).
% 1.59/1.61 thf(f357,plain,(
% 1.59/1.61 ~spl0_18),
% 1.59/1.61 inference(avatar_contradiction_clause,[status(thm)],[f356])).
% 1.59/1.61 thf(f356,plain,(
% 1.59/1.61 $false | ~spl0_18),
% 1.59/1.61 inference(subsumption_resolution,[status(thm)],[f355,f44])).
% 1.59/1.61 thf(f44,plain,(
% 1.59/1.61 (zero != (s @ zero))),
% 1.59/1.61 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.59/1.61 thf(f43,plain,(
% 1.59/1.61 ((s @ zero) != (s @ zero)) | (zero != (s @ zero))),
% 1.59/1.61 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.59/1.61 thf(f42,plain,(
% 1.59/1.61 ((s @ zero) != ((^[Y0 : $i]: (s @ ((^[Y1 : $i]: (zero)) @ Y0))) @ zero)) | (zero != ((^[Y0 : $i]: (s @ ((^[Y1 : $i]: (zero)) @ Y0))) @ (s @ zero)))),
% 1.59/1.61 inference(equality_resolution,[status(thm)],[f41])).
% 1.59/1.61 thf(f355,plain,(
% 1.59/1.61 (zero = (s @ zero)) | ~spl0_18),
% 1.59/1.61 inference(equality_proxy_clausification,[status(thm)],[f354])).
% 1.59/1.61 thf(f354,plain,(
% 1.59/1.61 ($true = ((s @ zero) = zero)) | ~spl0_18),
% 1.59/1.61 inference(subsumption_resolution,[status(thm)],[f334,f34])).
% 1.59/1.61 thf(f34,plain,(
% 1.59/1.61 ( ! [X1 : $i] : (((s @ X1) != X1)) )),
% 1.59/1.61 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.59/1.61 thf(f33,plain,(
% 1.59/1.61 ( ! [X1 : $i] : (($false = ((s @ X1) = X1))) )),
% 1.59/1.61 inference(not_proxy_clausification,[status(thm)],[f32])).
% 1.59/1.61 thf(f32,plain,(
% 1.59/1.61 ( ! [X1 : $i] : (($true = (~ ((s @ X1) = X1)))) )),
% 1.59/1.61 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.59/1.61 thf(f31,plain,(
% 1.59/1.61 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (~ ((s @ Y0) = Y0))) @ X1))) )),
% 1.59/1.61 inference(pi_clausification,[status(thm)],[f22])).
% 1.59/1.61 thf(f22,plain,(
% 1.59/1.61 ($true = (!! @ $i @ (^[Y0 : $i]: (~ ((s @ Y0) = Y0)))))),
% 1.59/1.61 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.59/1.61 thf(f11,plain,(
% 1.59/1.61 ($true = ((!! @ $i @ (^[Y0 : $i]: (~ ((s @ Y0) = Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1))))))))))),
% 1.59/1.61 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.59/1.61 thf(f334,plain,(
% 1.59/1.61 ((s @ zero) = (s @ (s @ zero))) | ($true = ((s @ zero) = zero)) | ~spl0_18),
% 1.59/1.61 inference(leibniz_equality_elimination,[status(thm)],[f291])).
% 1.59/1.61 thf(f291,plain,(
% 1.59/1.61 ( ! [X0 : $i > $o] : (($true = (X0 @ (s @ (s @ zero)))) | ((X0 @ (s @ zero)) = $false) | ($true = (X0 @ zero))) ) | ~spl0_18),
% 1.59/1.61 inference(avatar_component_clause,[status(thm)],[f290])).
% 1.59/1.61 thf(f290,definition,(
% 1.59/1.61 spl0_18 <=> ! [X0 : $i > $o] : (((X0 @ (s @ zero)) = $false) | ($true = (X0 @ zero)) | ($true = (X0 @ (s @ (s @ zero)))))),
% 1.59/1.61 introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition])).
% 1.59/1.61 thf(f298,plain,(
% 1.59/1.61 spl0_18 | spl0_1 | spl0_19 | spl0_20 | ~spl0_12),
% 1.59/1.61 inference(avatar_split_clause,[status(thm)],[f288,f147,f296,f293,f51,f290])).
% 1.59/1.61 thf(f147,definition,(
% 1.59/1.61 spl0_12 <=> ! [X1 : $i,X4 : $i > $i,X0 : $i > $i,X6 : $i,X5 : $i,X2 : $i > $o,X7 : $i] : (((s @ zero) != (ite @ (X2 @ zero) @ (X0 @ zero) @ (X4 @ zero))) | ((X2 @ (s @ (s @ zero))) = $true) | ((s @ zero) != X6) | ((X0 @ (s @ (s @ zero))) != X7) | ((X4 @ (s @ (s @ zero))) != X6) | ((X2 @ (s @ zero)) = $false) | (zero != X1) | ((X4 @ (s @ zero)) != X5) | ((X0 @ (s @ zero)) != X1))),
% 1.59/1.61 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.59/1.61 thf(f288,plain,(
% 1.59/1.61 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $o,X1 : $o,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i > $i,X5 : $i] : (((s @ zero) != X7) | ((X0 @ (s @ zero)) = $false) | ($true = (X0 @ (s @ (s @ zero)))) | ((X2 @ (s @ zero)) != X9) | ((X4 @ (s @ (s @ zero))) != X8) | (zero != X6) | ((X2 @ zero) != X3) | ((X4 @ zero) != X5) | ((X4 @ (s @ zero)) != X6) | ($true = (X0 @ zero)) | ((X2 @ (s @ (s @ zero))) != X7) | ($true = X1) | ((s @ zero) != X3)) ) | ~spl0_12),
% 1.59/1.61 inference(duplicate_literal_removal,[status(thm)],[f286])).
% 1.59/1.61 thf(f286,plain,(
% 1.59/1.61 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $o,X1 : $o,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i > $i,X5 : $i] : (((X2 @ (s @ (s @ zero))) != X7) | ((X4 @ zero) != X5) | ((X2 @ (s @ zero)) != X9) | (zero != X6) | ($true = (X0 @ zero)) | ($true = X1) | ($true = X1) | ($true = (X0 @ (s @ (s @ zero)))) | ((X4 @ (s @ (s @ zero))) != X8) | ((X2 @ zero) != X3) | ((s @ zero) != X3) | ((X4 @ (s @ zero)) != X6) | ((X0 @ (s @ zero)) = $false) | ((s @ zero) != X7)) ) | ~spl0_12),
% 1.59/1.61 inference(binary_proxy_clausification,[status(thm)],[f263])).
% 1.59/1.61 thf(f263,plain,(
% 1.59/1.61 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $o,X1 : $o,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i > $i,X5 : $i] : (((X0 @ (s @ zero)) = $false) | ((s @ zero) != X3) | (zero != X6) | ($true = X1) | ($true = (X0 @ (s @ (s @ zero)))) | ((s @ zero) != X7) | ((X0 @ zero) != X1) | ((X4 @ zero) != X5) | ((X2 @ (s @ (s @ zero))) != X7) | ((X2 @ (s @ zero)) != X9) | ((X2 @ zero) != X3) | ((X4 @ (s @ (s @ zero))) != X8) | ((X4 @ (s @ zero)) != X6)) ) | ~spl0_12),
% 1.59/1.61 inference(constrained_superposition,[status(thm)],[f148,f20])).
% 1.59/1.61 thf(f148,plain,(
% 1.59/1.61 ( ! [X2 : $i > $o,X0 : $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i > $i,X5 : $i] : (((s @ zero) != (ite @ (X2 @ zero) @ (X0 @ zero) @ (X4 @ zero))) | ((s @ zero) != X6) | ((X0 @ (s @ zero)) != X1) | ((X4 @ (s @ (s @ zero))) != X6) | ((X0 @ (s @ (s @ zero))) != X7) | ((X2 @ (s @ zero)) = $false) | (zero != X1) | ((X2 @ (s @ (s @ zero))) = $true) | ((X4 @ (s @ zero)) != X5)) ) | ~spl0_12),
% 1.59/1.61 inference(avatar_component_clause,[status(thm)],[f147])).
% 1.59/1.61 thf(f184,plain,(
% 1.59/1.61 ~spl0_1),
% 1.59/1.61 inference(avatar_contradiction_clause,[status(thm)],[f183])).
% 1.59/1.61 thf(f183,plain,(
% 1.59/1.61 $false | ~spl0_1),
% 1.59/1.61 inference(equality_resolution,[status(thm)],[f174])).
% 1.59/1.61 thf(f174,plain,(
% 1.59/1.61 ( ! [X0 : $o] : (($false != X0)) ) | ~spl0_1),
% 1.59/1.61 inference(superposition,[status(thm)],[f3,f52])).
% 1.59/1.61 thf(f52,plain,(
% 1.59/1.61 ( ! [X0 : $o] : (($true = X0)) ) | ~spl0_1),
% 1.59/1.61 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.59/1.61 thf(f3,plain,(
% 1.59/1.61 ($true != $false)),
% 1.59/1.61 introduced(definition,[],[fool_axiom])).
% 1.59/1.61 thf(f149,plain,(
% 1.59/1.61 spl0_12 | spl0_6 | ~spl0_2),
% 1.59/1.61 inference(avatar_split_clause,[status(thm)],[f145,f54,f77,f147])).
% 1.59/1.61 thf(f77,definition,(
% 1.59/1.61 spl0_6 <=> ! [X0 : $o] : ($false = X0)),
% 1.59/1.61 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.59/1.61 thf(f145,plain,(
% 1.59/1.61 ( ! [X2 : $i > $o,X3 : $o,X0 : $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i > $i,X5 : $i] : (((s @ zero) != (ite @ (X2 @ zero) @ (X0 @ zero) @ (X4 @ zero))) | ((X0 @ (s @ zero)) != X1) | ((X4 @ (s @ zero)) != X5) | (zero != X1) | ($false = X3) | ((X2 @ (s @ zero)) = $false) | ((X4 @ (s @ (s @ zero))) != X6) | ((X0 @ (s @ (s @ zero))) != X7) | ((s @ zero) != X6) | ((X2 @ (s @ (s @ zero))) = $true)) ) | ~spl0_2),
% 1.59/1.61 inference(duplicate_literal_removal,[status(thm)],[f144])).
% 1.59/1.61 thf(f144,plain,(
% 1.59/1.61 ( ! [X2 : $i > $o,X3 : $o,X0 : $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i > $i,X5 : $i] : ((zero != X1) | ((X2 @ (s @ (s @ zero))) = $true) | ((X0 @ (s @ zero)) != X1) | ((s @ zero) != X6) | ($false = X3) | ($false = X3) | ((X0 @ (s @ (s @ zero))) != X7) | ((s @ zero) != (ite @ (X2 @ zero) @ (X0 @ zero) @ (X4 @ zero))) | ((X2 @ (s @ zero)) = $false) | ((X4 @ (s @ zero)) != X5) | ((X4 @ (s @ (s @ zero))) != X6)) ) | ~spl0_2),
% 1.59/1.61 inference(binary_proxy_clausification,[status(thm)],[f116])).
% 1.59/1.61 thf(f116,plain,(
% 1.59/1.61 ( ! [X2 : $i > $o,X3 : $o,X0 : $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i > $i,X5 : $i] : (((X2 @ (s @ zero)) != X3) | ((X0 @ (s @ (s @ zero))) != X7) | ($false = X3) | (zero != X1) | ((X2 @ (s @ (s @ zero))) = $true) | ((X0 @ (s @ zero)) != X1) | ((X4 @ (s @ zero)) != X5) | ((s @ zero) != (ite @ (X2 @ zero) @ (X0 @ zero) @ (X4 @ zero))) | ((s @ zero) != X6) | ((X4 @ (s @ (s @ zero))) != X6)) ) | ~spl0_2),
% 1.59/1.61 inference(constrained_superposition,[status(thm)],[f55,f30])).
% 1.59/1.61 thf(f30,plain,(
% 1.59/1.61 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((ite @ X3 @ X2 @ X1) = X2) | ($false = X3)) )),
% 1.59/1.61 inference(equality_proxy_clausification,[status(thm)],[f29])).
% 1.59/1.61 thf(f29,plain,(
% 1.59/1.61 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = ((ite @ X3 @ X2 @ X1) = X2)) | ($false = X3)) )),
% 1.59/1.61 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.59/1.61 thf(f28,plain,(
% 1.59/1.61 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = (X3 => ((ite @ X3 @ X2 @ X1) = X2)))) )),
% 1.59/1.61 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.59/1.61 thf(f27,plain,(
% 1.59/1.61 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = ((^[Y0 : $o]: (Y0 => ((ite @ Y0 @ X2 @ X1) = X2))) @ X3))) )),
% 1.59/1.61 inference(pi_clausification,[status(thm)],[f26])).
% 1.59/1.61 thf(f26,plain,(
% 1.59/1.61 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $o @ (^[Y0 : $o]: (Y0 => ((ite @ Y0 @ X2 @ X1) = X2)))))) )),
% 1.59/1.61 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.59/1.61 thf(f25,plain,(
% 1.59/1.61 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (Y1 => ((ite @ Y1 @ Y0 @ X1) = Y0))))) @ X2))) )),
% 1.59/1.61 inference(pi_clausification,[status(thm)],[f24])).
% 1.59/1.61 thf(f24,plain,(
% 1.59/1.61 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (Y1 => ((ite @ Y1 @ Y0 @ X1) = Y0)))))) = $true)) )),
% 1.59/1.61 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.59/1.61 thf(f23,plain,(
% 1.59/1.61 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1))))))) @ X1))) )),
% 1.59/1.61 inference(pi_clausification,[status(thm)],[f21])).
% 1.59/1.61 thf(f21,plain,(
% 1.59/1.61 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1)))))))))),
% 1.59/1.61 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.59/1.61 thf(f55,plain,(
% 1.59/1.61 ( ! [X2 : $i,X3 : $i > $i,X1 : $i > $o,X4 : $i,X5 : $i > $i] : ((zero != (ite @ (X1 @ (s @ zero)) @ (X5 @ (s @ zero)) @ (X3 @ (s @ zero)))) | ((X3 @ (s @ (s @ zero))) != X2) | ((s @ zero) != (ite @ (X1 @ zero) @ (X5 @ zero) @ (X3 @ zero))) | ((X1 @ (s @ (s @ zero))) = $true) | ((X5 @ (s @ (s @ zero))) != X4) | ((s @ zero) != X2)) ) | ~spl0_2),
% 1.59/1.61 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.59/1.61 thf(f91,plain,(
% 1.59/1.61 ~spl0_6),
% 1.59/1.61 inference(avatar_contradiction_clause,[status(thm)],[f90])).
% 1.59/1.61 thf(f90,plain,(
% 1.59/1.61 $false | ~spl0_6),
% 1.59/1.61 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.59/1.61 thf(f89,plain,(
% 1.59/1.61 ($false != $false) | ~spl0_6),
% 1.59/1.61 inference(superposition,[status(thm)],[f3,f78])).
% 1.59/1.61 thf(f78,plain,(
% 1.59/1.61 ( ! [X0 : $o] : (($false = X0)) ) | ~spl0_6),
% 1.59/1.61 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.59/1.61 % SZS output end Proof for DTF2THF_14135
% 1.59/1.61 % (14422)------------------------------
% 1.59/1.61 % (14422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.61 % (14422)Termination reason: Refutation
% 1.59/1.61
% 1.59/1.61 % (14422)Memory used [KB]: 5884
% 1.59/1.61 % (14422)Time elapsed: 0.031 s
% 1.59/1.61 % (14422)Instructions burned: 87 (million)
% 1.59/1.61 % (14422)------------------------------
% 1.59/1.61 % (14422)------------------------------
% 1.59/1.61 % (14351)Success in time 0.339 s
%------------------------------------------------------------------------------