%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUN024^1 : 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 : n020.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 1.67s 1.60s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 115 ( 39 unt; 0 typ; 12 def)
% Number of atoms : 938 ( 346 equ; 0 cnn)
% Maximal formula atoms : 15 ( 8 avg)
% Number of connectives : 1394 ( 243 ~; 219 |; 44 &; 772 @)
% ( 12 <=>; 37 =>; 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 : 21 ( 16 usr; 17 con; 0-3 aty)
% ( 63 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 310 ( 84 ^; 223 !; 3 ?; 310 :)
% 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(f1600,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f224,f229,f571,f1117,f1279,f1343,f1361,f1457,f1546,f1548,f1561,f1585,f1598]) ).
thf(f1598,plain,
~ spl0_115,
inference(avatar_contradiction_clause,[status(thm)],[f1597]) ).
thf(f1597,plain,
( $false
| ~ spl0_115 ),
inference(trivial_inequality_removal,[status(thm)],[f1593]) ).
thf(f1593,plain,
( ( zero != zero )
| ~ spl0_115 ),
inference(superposition,[status(thm)],[f22,f1456]) ).
thf(f1456,plain,
( ( zero
= ( s @ zero ) )
| ~ spl0_115 ),
inference(avatar_component_clause,[status(thm)],[f1454]) ).
thf(f1454,definition,
( spl0_115
<=> ( zero
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(naming,[spl0_115])],[avatar_definition]) ).
thf(f22,plain,
! [X1: $i] :
( ( s @ X1 )
!= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i] :
( ( ( s @ X1 )
= X1 )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( ( ( s @ X1 )
!= X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( s @ Y0 )
!= Y0 )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( s @ Y0 )
!= Y0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( zero
!= ( s @ 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
@ ^ [Y0: $i] :
( ( s @ Y0 )
!= Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( zero
!= ( s @ 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
@ ^ [Y0: $i] :
( ( s @ Y0 )
!= Y0 ) ) )
=> ( ?? @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( ( s @ zero )
= ( Y0 @ zero ) )
& ( zero
= ( Y0 @ ( s @ ( s @ zero ) ) ) )
& ( zero
= ( Y0 @ ( s @ zero ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( zero
!= ( s @ 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
@ ^ [Y0: $i] :
( ( s @ Y0 )
!= Y0 ) ) )
=> ( ?? @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( ( s @ zero )
= ( Y0 @ zero ) )
& ( zero
= ( Y0 @ ( s @ ( s @ zero ) ) ) )
& ( zero
= ( Y0 @ ( s @ zero ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( zero
!= ( s @ 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
@ ^ [Y0: $i] :
( ( s @ Y0 )
!= Y0 ) ) )
=> ( ?? @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( ( s @ zero )
= ( Y0 @ zero ) )
& ( zero
= ( Y0 @ ( s @ ( s @ zero ) ) ) )
& ( zero
= ( Y0 @ ( s @ zero ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( s @ X0 )
!= X0 )
& ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X3 @ X2 )
= X2 ) )
& ! [X4: $o,X5: $i,X6: $i] :
( X4
=> ( ( ite @ X4 @ X5 @ X6 )
= X5 ) )
& ! [X7: $i] :
( zero
!= ( s @ X7 ) ) )
=> ? [X8: $i > $i] :
( ( zero
= ( X8 @ ( s @ zero ) ) )
& ( zero
= ( X8 @ ( s @ ( s @ zero ) ) ) )
& ( ( s @ zero )
= ( X8 @ zero ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: $i] :
( ( s @ X3 )
!= X3 )
& ! [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 )
!= zero ) )
=> ? [X4: $i > $i] :
( ( zero
= ( X4 @ ( s @ zero ) ) )
& ( zero
= ( X4 @ ( s @ ( s @ zero ) ) ) )
& ( ( X4 @ zero )
= ( s @ zero ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X3: $i] :
( ( s @ X3 )
!= X3 )
& ! [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 )
!= zero ) )
=> ? [X4: $i > $i] :
( ( zero
= ( X4 @ ( s @ zero ) ) )
& ( zero
= ( X4 @ ( s @ ( s @ zero ) ) ) )
& ( ( X4 @ zero )
= ( s @ zero ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7Cj4tebpTh/DTF2THF_3149.p',n9) ).
thf(f1585,plain,
( spl0_4
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f1584,f64,f67]) ).
thf(f67,definition,
( spl0_4
<=> ! [X0: $o] : ( $true = X0 ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f64,definition,
( spl0_3
<=> ! [X3: $i > $i,X4: $i,X5: $i > $i,X2: $i,X1: $i > $o] :
( ( zero != X2 )
| ( ( X5 @ ( s @ ( s @ zero ) ) )
!= X4 )
| ( ( s @ zero )
!= ( ite @ ( X1 @ zero ) @ ( X5 @ zero ) @ ( X3 @ zero ) ) )
| ( zero
!= ( ite @ ( X1 @ ( s @ zero ) ) @ ( X5 @ ( s @ zero ) ) @ ( X3 @ ( s @ zero ) ) ) )
| ( ( X1 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( X3 @ ( s @ ( s @ zero ) ) )
!= X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f1584,plain,
! [X2: $i > $o,X3: $o,X0: $i > $i,X1: $i,X4: $i > $i,X5: $i] :
( ( zero != X5 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X1 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X5 )
| ( $true = X3 )
| ( zero
!= ( ite @ ( X2 @ ( s @ zero ) ) @ ( X0 @ ( s @ zero ) ) @ ( X4 @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= ( ite @ ( X2 @ zero ) @ ( X0 @ zero ) @ ( X4 @ zero ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f1582]) ).
thf(f1582,plain,
! [X2: $i > $o,X3: $o,X0: $i > $i,X1: $i,X4: $i > $i,X5: $i] :
( ( ( X2 @ ( s @ ( s @ zero ) ) )
= $true )
| ( $true = X3 )
| ( ( s @ zero )
!= ( ite @ ( X2 @ zero ) @ ( X0 @ zero ) @ ( X4 @ zero ) ) )
| ( zero != X5 )
| ( zero
!= ( ite @ ( X2 @ ( s @ zero ) ) @ ( X0 @ ( s @ zero ) ) @ ( X4 @ ( s @ zero ) ) ) )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X5 )
| ( $true = X3 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f1581]) ).
thf(f1581,plain,
! [X2: $i > $o,X3: $o,X0: $i > $i,X1: $i,X4: $i > $i,X5: $i] :
( ( ( s @ zero )
!= ( ite @ ( X2 @ zero ) @ ( X0 @ zero ) @ ( X4 @ zero ) ) )
| ( $true = X3 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X5 )
| ( zero != X5 )
| ( zero
!= ( ite @ ( X2 @ ( s @ zero ) ) @ ( X0 @ ( s @ zero ) ) @ ( X4 @ ( s @ zero ) ) ) )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X3 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f1575]) ).
thf(f1575,plain,
! [X2: $i > $o,X3: $o,X0: $i > $i,X1: $i,X4: $i > $i,X5: $i] :
( ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X3 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X5 )
| ( zero != X5 )
| ( zero
!= ( ^ [Y0: $i] : ( ite @ ( X2 @ Y0 ) @ ( X0 @ Y0 ) @ ( X4 @ Y0 ) )
@ ( s @ zero ) ) )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X1 )
| ( $true = X3 )
| ( ( s @ zero )
!= ( ^ [Y0: $i] : ( ite @ ( X2 @ Y0 ) @ ( X0 @ Y0 ) @ ( X4 @ Y0 ) )
@ zero ) ) ),
inference(constrained_superposition,[status(thm)],[f16,f47]) ).
thf(f47,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ( ite @ X3 @ X1 @ X2 )
= X2 )
| ( $true = X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ( ( ite @ X3 @ X1 @ X2 )
= X2 )
= $true )
| ( $true = X3 ) ),
inference(not_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false = ( ~ X3 ) )
| ( ( ( ite @ X3 @ X1 @ X2 )
= X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ~ X3
=> ( ( ite @ X3 @ X1 @ X2 )
= X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ^ [Y0: $o] :
( ~ Y0
=> ( ( ite @ Y0 @ X1 @ X2 )
= X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( !! @ $o
@ ^ [Y0: $o] :
( ~ Y0
=> ( ( ite @ Y0 @ X1 @ X2 )
= X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ~ Y1
=> ( ( ite @ Y1 @ X1 @ Y0 )
= Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ~ Y1
=> ( ( ite @ Y1 @ X1 @ Y0 )
= Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ~ Y2
=> ( ( ite @ Y2 @ Y0 @ Y1 )
= Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ~ Y2
=> ( ( ite @ Y2 @ Y0 @ Y1 )
= Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( zero
!= ( s @ 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 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f16,plain,
! [X1: $i > $i] :
( ( zero
!= ( X1 @ ( s @ ( s @ zero ) ) ) )
| ( zero
!= ( X1 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X1 @ zero ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: $i > $i] :
( ( zero
!= ( X1 @ ( s @ zero ) ) )
| ( $false
= ( zero
= ( X1 @ ( s @ ( s @ zero ) ) ) ) )
| ( ( s @ zero )
!= ( X1 @ zero ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: $i > $i] :
( ( ( ( s @ zero )
= ( X1 @ zero ) )
= $false )
| ( $false
= ( zero
= ( X1 @ ( s @ ( s @ zero ) ) ) ) )
| ( zero
!= ( X1 @ ( s @ zero ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: $i > $i] :
( ( ( ( ( s @ zero )
= ( X1 @ zero ) )
& ( zero
= ( X1 @ ( s @ ( s @ zero ) ) ) ) )
= $false )
| ( zero
!= ( X1 @ ( s @ zero ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: $i > $i] :
( ( ( zero
= ( X1 @ ( s @ zero ) ) )
= $false )
| ( ( ( ( s @ zero )
= ( X1 @ zero ) )
& ( zero
= ( X1 @ ( s @ ( s @ zero ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: $i > $i] :
( $false
= ( ( ( s @ zero )
= ( X1 @ zero ) )
& ( zero
= ( X1 @ ( s @ ( s @ zero ) ) ) )
& ( zero
= ( X1 @ ( s @ zero ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: $i > $i] :
( ( ^ [Y0: $i > $i] :
( ( ( s @ zero )
= ( Y0 @ zero ) )
& ( zero
= ( Y0 @ ( s @ ( s @ zero ) ) ) )
& ( zero
= ( Y0 @ ( s @ zero ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ?? @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( ( s @ zero )
= ( Y0 @ zero ) )
& ( zero
= ( Y0 @ ( s @ ( s @ zero ) ) ) )
& ( zero
= ( Y0 @ ( s @ zero ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f1561,plain,
~ spl0_114,
inference(avatar_contradiction_clause,[status(thm)],[f1560]) ).
thf(f1560,plain,
( $false
| ~ spl0_114 ),
inference(trivial_inequality_removal,[status(thm)],[f1558]) ).
thf(f1558,plain,
( ( zero != zero )
| ~ spl0_114 ),
inference(superposition,[status(thm)],[f38,f1452]) ).
thf(f1452,plain,
( ( zero
= ( s @ ( s @ zero ) ) )
| ~ spl0_114 ),
inference(avatar_component_clause,[status(thm)],[f1450]) ).
thf(f1450,definition,
( spl0_114
<=> ( zero
= ( s @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_114])],[avatar_definition]) ).
thf(f38,plain,
! [X1: $i] :
( zero
!= ( s @ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( ( zero
= ( s @ X1 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i] :
( ( zero
!= ( s @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( zero
!= ( s @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( zero
!= ( s @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( zero
!= ( s @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( Y2
=> ( ( ite @ Y2 @ Y1 @ Y0 )
= Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f1548,plain,
~ spl0_35,
inference(avatar_contradiction_clause,[status(thm)],[f1547]) ).
thf(f1547,plain,
( $false
| ~ spl0_35 ),
inference(equality_resolution,[status(thm)],[f363]) ).
thf(f363,plain,
( ! [X3: $i] : ( zero != X3 )
| ~ spl0_35 ),
inference(avatar_component_clause,[status(thm)],[f362]) ).
thf(f362,definition,
( spl0_35
<=> ! [X3: $i] : ( zero != X3 ) ),
introduced(definition,[new_symbols(naming,[spl0_35])],[avatar_definition]) ).
thf(f1546,plain,
~ spl0_106,
inference(avatar_contradiction_clause,[status(thm)],[f1545]) ).
thf(f1545,plain,
( $false
| ~ spl0_106 ),
inference(equality_resolution,[status(thm)],[f1278]) ).
thf(f1278,plain,
( ! [X3: $i] :
( ( s @ zero )
!= X3 )
| ~ spl0_106 ),
inference(avatar_component_clause,[status(thm)],[f1277]) ).
thf(f1277,definition,
( spl0_106
<=> ! [X3: $i] :
( ( s @ zero )
!= X3 ) ),
introduced(definition,[new_symbols(naming,[spl0_106])],[avatar_definition]) ).
thf(f1457,plain,
( spl0_114
| spl0_115
| ~ spl0_92 ),
inference(avatar_split_clause,[status(thm)],[f1448,f952,f1454,f1450]) ).
thf(f952,definition,
( spl0_92
<=> ! [X0: $i > $o] :
( ( ( X0 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( X0 @ ( s @ zero ) )
= $true )
| ( ( X0 @ zero )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_92])],[avatar_definition]) ).
thf(f1448,plain,
( ( zero
= ( s @ ( s @ zero ) ) )
| ( zero
= ( s @ zero ) )
| ~ spl0_92 ),
inference(equality_proxy_clausification,[status(thm)],[f1415]) ).
thf(f1415,plain,
( ( zero
= ( s @ ( s @ zero ) ) )
| ( ( zero
= ( s @ zero ) )
= $true )
| ~ spl0_92 ),
inference(leibniz_equality_elimination,[status(thm)],[f953]) ).
thf(f953,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( X0 @ ( s @ zero ) )
= $true )
| ( ( X0 @ zero )
= $false ) )
| ~ spl0_92 ),
inference(avatar_component_clause,[status(thm)],[f952]) ).
thf(f1361,plain,
( spl0_92
| spl0_7
| spl0_77
| spl0_76
| ~ spl0_24 ),
inference(avatar_split_clause,[status(thm)],[f1360,f277,f841,f844,f85,f952]) ).
thf(f85,definition,
( spl0_7
<=> ! [X0: $o] : ( $false = X0 ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f844,definition,
( spl0_77
<=> ! [X5: $i,X4: $i > $i,X7: $i,X6: $i] :
( ( ( X4 @ ( s @ zero ) )
!= X7 )
| ( zero != X6 )
| ( ( X4 @ zero )
!= X5 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 )
| ( zero != X7 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_77])],[avatar_definition]) ).
thf(f841,definition,
( spl0_76
<=> ! [X3: $i,X8: $i,X9: $i,X2: $i > $i] :
( ( ( X2 @ ( s @ zero ) )
!= X9 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X8 )
| ( ( s @ zero )
!= X3 )
| ( ( X2 @ zero )
!= X3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_76])],[avatar_definition]) ).
thf(f277,definition,
( spl0_24
<=> ! [X3: $i,X4: $i > $i,X0: $i > $o,X6: $i,X5: $i,X2: $i > $i,X7: $i] :
( ( ( X0 @ ( s @ zero ) )
= $true )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( X2 @ ( s @ zero ) )
!= X3 )
| ( ( X4 @ ( s @ zero ) )
!= X5 )
| ( ( s @ zero )
!= ( ite @ ( X0 @ zero ) @ ( X2 @ zero ) @ ( X4 @ zero ) ) )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 )
| ( zero != X6 )
| ( zero != X5 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition]) ).
thf(f1360,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 @ ( s @ zero ) ) )
= $true )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 )
| ( ( X0 @ zero )
= $false )
| ( ( s @ zero )
!= X3 )
| ( ( X2 @ ( s @ zero ) )
!= X7 )
| ( ( X2 @ zero )
!= X3 )
| ( ( X4 @ zero )
!= X5 )
| ( $false = X1 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X9 )
| ( ( X0 @ ( s @ zero ) )
= $true )
| ( zero != X6 )
| ( zero != X8 )
| ( ( X4 @ ( s @ zero ) )
!= X8 ) )
| ~ spl0_24 ),
inference(duplicate_literal_removal,[status(thm)],[f1359]) ).
thf(f1359,plain,
( ! [X2: $i > $i,X3: $i,X0: $i > $o,X1: $o,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i > $i,X5: $i] :
( ( ( X4 @ zero )
!= X5 )
| ( ( X0 @ ( s @ zero ) )
= $true )
| ( $false = X1 )
| ( zero != X8 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
= $true )
| ( zero != X6 )
| ( ( X4 @ ( s @ zero ) )
!= X8 )
| ( ( X2 @ ( s @ zero ) )
!= X7 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X9 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 )
| ( ( X0 @ zero )
= $false )
| ( $false = X1 )
| ( ( X2 @ zero )
!= X3 )
| ( ( s @ zero )
!= X3 ) )
| ~ spl0_24 ),
inference(binary_proxy_clausification,[status(thm)],[f1309]) ).
thf(f1309,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 ) )
= $true )
| ( ( X4 @ zero )
!= X5 )
| ( ( X2 @ ( s @ zero ) )
!= X7 )
| ( ( s @ zero )
!= X3 )
| ( ( X2 @ zero )
!= X3 )
| ( ( X4 @ ( s @ zero ) )
!= X8 )
| ( ( X0 @ zero )
!= X1 )
| ( zero != X6 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X9 )
| ( zero != X8 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
= $true )
| ( $false = X1 ) )
| ~ spl0_24 ),
inference(constrained_superposition,[status(thm)],[f278,f34]) ).
thf(f34,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ( ite @ X3 @ X2 @ X1 )
= X2 )
| ( $false = X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ( ( ite @ X3 @ X2 @ X1 )
= X2 )
= $true )
| ( $false = X3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( X3
=> ( ( ite @ X3 @ X2 @ X1 )
= X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ^ [Y0: $o] :
( Y0
=> ( ( ite @ Y0 @ X2 @ X1 )
= X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( ( ite @ Y0 @ X2 @ X1 )
= X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( Y1
=> ( ( ite @ Y1 @ Y0 @ X1 )
= Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( Y1
=> ( ( ite @ Y1 @ Y0 @ X1 )
= Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( Y2
=> ( ( ite @ Y2 @ Y1 @ Y0 )
= Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( Y2
=> ( ( ite @ Y2 @ Y1 @ Y0 )
= Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f278,plain,
( ! [X2: $i > $i,X3: $i,X0: $i > $o,X6: $i,X7: $i,X4: $i > $i,X5: $i] :
( ( ( s @ zero )
!= ( ite @ ( X0 @ zero ) @ ( X2 @ zero ) @ ( X4 @ zero ) ) )
| ( zero != X5 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( ( X2 @ ( s @ zero ) )
!= X3 )
| ( ( X4 @ ( s @ zero ) )
!= X5 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( X0 @ ( s @ zero ) )
= $true )
| ( zero != X6 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 ) )
| ~ spl0_24 ),
inference(avatar_component_clause,[status(thm)],[f277]) ).
thf(f1343,plain,
( spl0_35
| spl0_35
| ~ spl0_77 ),
inference(avatar_split_clause,[status(thm)],[f1342,f844,f362,f362]) ).
thf(f1342,plain,
( ! [X0: $i,X1: $i] :
( ( zero != X1 )
| ( zero != X0 ) )
| ~ spl0_77 ),
inference(duplicate_literal_removal,[status(thm)],[f1341]) ).
thf(f1341,plain,
( ! [X0: $i,X1: $i] :
( ( zero != X0 )
| ( zero != X0 )
| ( zero != X1 ) )
| ~ spl0_77 ),
inference(beta_eta_normalization,[status(thm)],[f1338]) ).
thf(f1338,plain,
( ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : zero
@ ( s @ ( s @ zero ) ) )
!= X0 )
| ( ( ^ [Y0: $i] : zero
@ zero )
!= X1 )
| ( zero != X0 ) )
| ~ spl0_77 ),
inference(equality_resolution,[status(thm)],[f1301]) ).
thf(f1301,plain,
( ! [X2: $i,X0: $i,X1: $i > $i] :
( ( zero
!= ( X1 @ ( s @ zero ) ) )
| ( zero != X0 )
| ( ( X1 @ zero )
!= X2 )
| ( ( X1 @ ( s @ ( s @ zero ) ) )
!= X0 ) )
| ~ spl0_77 ),
inference(equality_resolution,[status(thm)],[f845]) ).
thf(f845,plain,
( ! [X6: $i,X7: $i,X4: $i > $i,X5: $i] :
( ( zero != X7 )
| ( ( X4 @ ( s @ zero ) )
!= X7 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 )
| ( ( X4 @ zero )
!= X5 )
| ( zero != X6 ) )
| ~ spl0_77 ),
inference(avatar_component_clause,[status(thm)],[f844]) ).
thf(f1279,plain,
( spl0_106
| spl0_106
| ~ spl0_76 ),
inference(avatar_split_clause,[status(thm)],[f1275,f841,f1277,f1277]) ).
thf(f1275,plain,
( ! [X2: $i,X3: $i] :
( ( ( s @ zero )
!= X2 )
| ( ( s @ zero )
!= X3 ) )
| ~ spl0_76 ),
inference(beta_eta_normalization,[status(thm)],[f1271]) ).
thf(f1271,plain,
( ! [X2: $i,X3: $i] :
( ( ( ^ [Y0: $i] :
( s
@ ( ^ [Y1: $i] : zero
@ Y0 ) )
@ ( s @ zero ) )
!= X3 )
| ( ( ^ [Y0: $i] :
( s
@ ( ^ [Y1: $i] : zero
@ Y0 ) )
@ ( s @ ( s @ zero ) ) )
!= X2 ) )
| ~ spl0_76 ),
inference(equality_resolution,[status(thm)],[f1239]) ).
thf(f1239,plain,
( ! [X2: $i,X0: $i > $i,X1: $i] :
( ( ( s @ zero )
!= ( X0 @ zero ) )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
!= X1 )
| ( ( X0 @ ( s @ zero ) )
!= X2 ) )
| ~ spl0_76 ),
inference(equality_resolution,[status(thm)],[f842]) ).
thf(f842,plain,
( ! [X2: $i > $i,X3: $i,X8: $i,X9: $i] :
( ( ( s @ zero )
!= X3 )
| ( ( X2 @ ( s @ zero ) )
!= X9 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X8 )
| ( ( X2 @ zero )
!= X3 ) )
| ~ spl0_76 ),
inference(avatar_component_clause,[status(thm)],[f841]) ).
thf(f1117,plain,
( spl0_4
| spl0_24
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f1116,f64,f277,f67]) ).
thf(f1116,plain,
( ! [X2: $i > $i,X3: $i,X0: $i > $o,X1: $o,X6: $i,X7: $i,X4: $i > $i,X5: $i] :
( ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 )
| ( ( X0 @ ( s @ zero ) )
= $true )
| ( ( s @ zero )
!= ( ite @ ( X0 @ zero ) @ ( X2 @ zero ) @ ( X4 @ zero ) ) )
| ( ( X2 @ ( s @ zero ) )
!= X3 )
| ( zero != X6 )
| ( $true = X1 )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( ( X4 @ ( s @ zero ) )
!= X5 )
| ( zero != X5 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
= $true ) )
| ~ spl0_3 ),
inference(duplicate_literal_removal,[status(thm)],[f1114]) ).
thf(f1114,plain,
( ! [X2: $i > $i,X3: $i,X0: $i > $o,X1: $o,X6: $i,X7: $i,X4: $i > $i,X5: $i] :
( ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( ( X2 @ ( s @ zero ) )
!= X3 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
= $true )
| ( ( X0 @ ( s @ zero ) )
= $true )
| ( $true = X1 )
| ( $true = X1 )
| ( zero != X6 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 )
| ( ( s @ zero )
!= ( ite @ ( X0 @ zero ) @ ( X2 @ zero ) @ ( X4 @ zero ) ) )
| ( zero != X5 )
| ( ( X4 @ ( s @ zero ) )
!= X5 ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f1099]) ).
thf(f1099,plain,
( ! [X2: $i > $i,X3: $i,X0: $i > $o,X1: $o,X6: $i,X7: $i,X4: $i > $i,X5: $i] :
( ( ( X2 @ ( s @ zero ) )
!= X3 )
| ( zero != X5 )
| ( ( X4 @ ( s @ zero ) )
!= X5 )
| ( ( X0 @ ( s @ ( s @ zero ) ) )
= $true )
| ( zero != X6 )
| ( ( X0 @ ( s @ zero ) )
!= X1 )
| ( $true = X1 )
| ( ( s @ zero )
!= ( ite @ ( X0 @ zero ) @ ( X2 @ zero ) @ ( X4 @ zero ) ) )
| ( ( X2 @ ( s @ ( s @ zero ) ) )
!= X7 )
| ( ( X4 @ ( s @ ( s @ zero ) ) )
!= X6 ) )
| ~ spl0_3 ),
inference(constrained_superposition,[status(thm)],[f65,f47]) ).
thf(f65,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 )
| ( ( X1 @ ( s @ ( s @ zero ) ) )
= $true )
| ( zero != X2 )
| ( ( s @ zero )
!= ( ite @ ( X1 @ zero ) @ ( X5 @ zero ) @ ( X3 @ zero ) ) )
| ( ( X5 @ ( s @ ( s @ zero ) ) )
!= X4 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f571,plain,
( ~ spl0_4
| spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f570]) ).
thf(f570,plain,
( $false
| ~ spl0_4
| spl0_9 ),
inference(equality_resolution,[status(thm)],[f531]) ).
thf(f531,plain,
( ! [X0: $o] : ( $false != X0 )
| ~ spl0_4
| spl0_9 ),
inference(superposition,[status(thm)],[f98,f68]) ).
thf(f68,plain,
( ! [X0: $o] : ( $true = X0 )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f98,plain,
( ( $false != $true )
| spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f96]) ).
thf(f96,definition,
( spl0_9
<=> ( $false = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f229,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[status(thm)],[f228]) ).
thf(f228,plain,
( $false
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $false = $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f96]) ).
thf(f224,plain,
( ~ spl0_7
| spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f223]) ).
thf(f223,plain,
( $false
| ~ spl0_7
| spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f221]) ).
thf(f221,plain,
( ( $false != $false )
| ~ spl0_7
| spl0_9 ),
inference(superposition,[status(thm)],[f98,f86]) ).
thf(f86,plain,
( ! [X0: $o] : ( $false = X0 )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN024^1 : TPTP v9.2.1. Released v6.4.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n020.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 11:19:42 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : NUN024^1 : TPTP v9.2.1. Released v6.4.0.
% 0.31/0.46 % Domain : Number Theory
% 0.31/0.46 % Problem : Function h s.t. h(0) = 1, h(1) = 0, h(2) = 0, no witness
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English : Using an axiomatiztion of if-then-else, find the if-then-else
% 0.31/0.46 % term that expresses the function H.
% 0.31/0.46
% 0.31/0.46 % Refs : [Rie16] Riener (2016), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [TPTP]
% 0.31/0.46 % Names : ntape6-1-without-witness.tptp [Rie16]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.67 v9.1.0, 0.75 v9.0.0, 0.70 v8.2.0, 0.77 v8.1.0, 0.64 v7.5.0, 0.71 v7.4.0, 0.78 v7.3.0, 0.89 v7.2.0, 0.88 v7.0.0, 0.86 v6.4.0
% 0.31/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.31/0.46 % Number of atoms : 7 ( 7 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 7 ( 7 avg)
% 0.31/0.46 % Number of connectives : 26 ( 3 ~; 0 |; 5 &; 15 @)
% 0.31/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 4 ( 3 usr; 1 con; 0-3 aty)
% 0.31/0.46 % Number of variables : 9 ( 0 ^; 8 !; 1 ?; 9 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments :
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(n6,type,
% 0.31/0.46 zero: $i ).
% 0.31/0.46
% 0.31/0.46 thf(n7,type,
% 0.31/0.46 s: $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(n8,type,
% 0.31/0.46 ite: $o > $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(n9,conjecture,
% 0.31/0.46 ( ( ! [X100: $o,U: $i,V: $i] :
% 0.31/0.46 ( X100
% 0.31/0.46 => ( ( ite @ X100 @ U @ V )
% 0.31/0.46 = U ) )
% 0.31/0.46 & ! [X100: $o,U: $i,V: $i] :
% 0.31/0.46 ( ~ X100
% 0.31/0.46 => ( ( ite @ X100 @ U @ V )
% 0.31/0.46 = V ) )
% 0.31/0.46 & ! [X: $i] :
% 0.31/0.46 ( ( s @ X )
% 0.31/0.46 != zero )
% 0.31/0.46 & ! [X: $i] :
% 0.31/0.46 ( ( s @ X )
% 0.31/0.46 != X ) )
% 0.31/0.46 => ? [H: $i > $i] :
% 0.31/0.46 ( ( ( H @ zero )
% 0.31/0.46 = ( s @ zero ) )
% 0.31/0.46 & ( ( H @ ( s @ zero ) )
% 0.31/0.46 = zero )
% 0.31/0.46 & ( ( H @ ( s @ ( s @ zero ) ) )
% 0.31/0.46 = zero ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.64/1.31 ---- Embedded in THF ---
% 1.64/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.32 %%% Generated on Tue Feb 24 11:19:43 EST 2026
% 1.64/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.32 %%% Logic specification used:
% 1.64/1.32 %%% thf(spec, logic, $$dhol).
% 1.64/1.32
% 1.64/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.7Cj4tebpTh/DTF2DTF3149.p
% See solution above
% 1.64/1.32 ------------------------
% 1.64/1.32 ---- Cleaned THF ---
% 1.64/1.32 thf(n6,type,
% 1.64/1.32 zero: $i ).
% 1.64/1.32
% 1.64/1.32 thf(n7,type,
% 1.64/1.32 s: $i > $i ).
% 1.64/1.32
% 1.64/1.32 thf(n8,type,
% 1.64/1.32 ite: $o > $i > $i > $i ).
% 1.64/1.32
% 1.64/1.32 thf(n9,conjecture,
% 1.64/1.32 ( ( ! [X100: $o,U: $i,V: $i] :
% 1.64/1.32 ( X100
% 1.64/1.32 => ( ( ite @ X100 @ U @ V )
% 1.64/1.32 = U ) )
% 1.64/1.32 & ! [X100: $o,U: $i,V: $i] :
% 1.64/1.32 ( ~ X100
% 1.64/1.32 => ( ( ite @ X100 @ U @ V )
% 1.64/1.32 = V ) )
% 1.64/1.32 & ! [X: $i] :
% 1.64/1.32 ( ( s @ X )
% 1.64/1.32 != zero )
% 1.64/1.32 & ! [X: $i] :
% 1.64/1.32 ( ( s @ X )
% 1.64/1.32 != X ) )
% 1.64/1.32 => ? [H: $i > $i] :
% 1.64/1.32 ( ( ( H @ zero )
% 1.64/1.32 = ( s @ zero ) )
% 1.64/1.32 & ( ( H @ ( s @ zero ) )
% 1.64/1.32 = zero )
% 1.64/1.32 & ( ( H @ ( s @ ( s @ zero ) ) )
% 1.64/1.32 = zero ) ) ) ).
% 1.64/1.33 ------------------------
% 1.64/1.34 % (3309)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_3149 for (2999ds/275Mi)
% 1.64/1.34 % (3305)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_3149 for (2999ds/4Mi)
% 1.64/1.34 % (3308)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_3149 for (2999ds/2Mi)
% 1.64/1.34 % (3309)Refutation not found, incomplete strategy
% 1.64/1.34 % (3309)------------------------------
% 1.64/1.34 % (3309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (3309)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.34
% 1.64/1.34
% 1.64/1.34 % (3309)Memory used [KB]: 5500
% 1.64/1.34 % (3309)Time elapsed: 0.002 s
% 1.64/1.34 % (3309)Instructions burned: 2 (million)
% 1.64/1.34 % (3309)------------------------------
% 1.64/1.34 % (3309)------------------------------
% 1.64/1.34 % (3308)Instruction limit reached!
% 1.64/1.34 % (3308)------------------------------
% 1.64/1.34 % (3308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (3308)Termination reason: Unknown
% 1.64/1.34 % (3308)Termination phase: Saturation
% 1.64/1.34
% 1.64/1.34 % (3308)Memory used [KB]: 5500
% 1.64/1.34 % (3308)Time elapsed: 0.002 s
% 1.64/1.34 % (3308)Instructions burned: 3 (million)
% 1.64/1.34 % (3308)------------------------------
% 1.64/1.34 % (3308)------------------------------
% 1.64/1.34 % (3305)Instruction limit reached!
% 1.64/1.34 % (3305)------------------------------
% 1.64/1.34 % (3305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (3305)Termination reason: Unknown
% 1.64/1.34 % (3305)Termination phase: Saturation
% 1.64/1.34
% 1.64/1.34 % (3305)Memory used [KB]: 5500
% 1.64/1.34 % (3305)Time elapsed: 0.003 s
% 1.64/1.34 % (3305)Instructions burned: 5 (million)
% 1.64/1.34 % (3305)------------------------------
% 1.64/1.34 % (3305)------------------------------
% 1.64/1.35 % (3304)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/183Mi)
% 1.64/1.35 % (3307)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/2Mi)
% 1.64/1.35 % (3310)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/18Mi)
% 1.64/1.35 % (3307)Instruction limit reached!
% 1.64/1.35 % (3307)------------------------------
% 1.64/1.35 % (3307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (3307)Termination reason: Unknown
% 1.64/1.35 % (3307)Termination phase: Saturation
% 1.64/1.35
% 1.64/1.35 % (3307)Memory used [KB]: 5500
% 1.64/1.35 % (3307)Time elapsed: 0.004 s
% 1.64/1.35 % (3307)Instructions burned: 2 (million)
% 1.64/1.35 % (3307)------------------------------
% 1.64/1.35 % (3307)------------------------------
% 1.64/1.35 % (3312)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_3149 for (2999ds/37Mi)
% 1.64/1.35 % (3311)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/3Mi)
% 1.64/1.35 % (3306)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_3149 for (2999ds/27Mi)
% 1.64/1.35 % (3313)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_3149 for (2999ds/15Mi)
% 1.64/1.35 % (3311)Instruction limit reached!
% 1.64/1.35 % (3311)------------------------------
% 1.64/1.35 % (3311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (3311)Termination reason: Unknown
% 1.64/1.35 % (3311)Termination phase: Saturation
% 1.64/1.35
% 1.64/1.35 % (3311)Memory used [KB]: 5500
% 1.64/1.35 % (3311)Time elapsed: 0.003 s
% 1.64/1.35 % (3311)Instructions burned: 3 (million)
% 1.64/1.35 % (3311)------------------------------
% 1.64/1.35 % (3311)------------------------------
% 1.64/1.35 % (3313)Refutation not found, incomplete strategy
% 1.64/1.35 % (3313)------------------------------
% 1.64/1.35 % (3313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (3313)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.35
% 1.64/1.35
% 1.64/1.35 % (3313)Memory used [KB]: 5500
% 1.64/1.35 % (3313)Time elapsed: 0.003 s
% 1.64/1.35 % (3313)Instructions burned: 3 (million)
% 1.64/1.35 % (3313)------------------------------
% 1.64/1.35 % (3313)------------------------------
% 1.64/1.36 % (3306)Refutation not found, incomplete strategy
% 1.64/1.36 % (3306)------------------------------
% 1.64/1.36 % (3306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (3306)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.36
% 1.64/1.36
% 1.64/1.36 % (3306)Memory used [KB]: 5500
% 1.64/1.36 % (3306)Time elapsed: 0.007 s
% 1.64/1.36 % (3306)Instructions burned: 4 (million)
% 1.64/1.36 % (3306)------------------------------
% 1.64/1.36 % (3306)------------------------------
% 1.64/1.36 % (3310)Instruction limit reached!
% 1.64/1.36 % (3310)------------------------------
% 1.64/1.36 % (3310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (3310)Termination reason: Unknown
% 1.64/1.36 % (3310)Termination phase: Saturation
% 1.64/1.36
% 1.64/1.36 % (3310)Memory used [KB]: 5628
% 1.64/1.36 % (3310)Time elapsed: 0.014 s
% 1.64/1.36 % (3310)Instructions burned: 19 (million)
% 1.64/1.36 % (3310)------------------------------
% 1.64/1.36 % (3310)------------------------------
% 1.64/1.36 % (3315)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_3149 for (2999ds/1041Mi)
% 1.64/1.36 % (3312)Instruction limit reached!
% 1.64/1.36 % (3312)------------------------------
% 1.64/1.36 % (3312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (3312)Termination reason: Unknown
% 1.64/1.36 % (3312)Termination phase: Saturation
% 1.64/1.36
% 1.64/1.36 % (3312)Memory used [KB]: 5756
% 1.64/1.36 % (3312)Time elapsed: 0.013 s
% 1.64/1.36 % (3312)Instructions burned: 38 (million)
% 1.64/1.36 % (3312)------------------------------
% 1.64/1.36 % (3312)------------------------------
% 1.64/1.36 % (3316)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/7Mi)
% 1.64/1.37 % (3314)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_3149 for (2999ds/3Mi)
% 1.64/1.37 % (3316)Instruction limit reached!
% 1.64/1.37 % (3316)------------------------------
% 1.64/1.37 % (3316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (3316)Termination reason: Unknown
% 1.64/1.37 % (3316)Termination phase: Saturation
% 1.64/1.37
% 1.64/1.37 % (3316)Memory used [KB]: 1023
% 1.64/1.37 % (3316)Time elapsed: 0.005 s
% 1.64/1.37 % (3316)Instructions burned: 9 (million)
% 1.64/1.37 % (3316)------------------------------
% 1.64/1.37 % (3316)------------------------------
% 1.64/1.37 % (3314)Instruction limit reached!
% 1.64/1.37 % (3314)------------------------------
% 1.64/1.37 % (3314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (3314)Termination reason: Unknown
% 1.64/1.37 % (3314)Termination phase: Saturation
% 1.64/1.37
% 1.64/1.37 % (3314)Memory used [KB]: 5500
% 1.64/1.37 % (3314)Time elapsed: 0.004 s
% 1.64/1.37 % (3314)Instructions burned: 3 (million)
% 1.64/1.37 % (3314)------------------------------
% 1.64/1.37 % (3314)------------------------------
% 1.64/1.37 % (3319)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_3149 for (2999ds/3Mi)
% 1.64/1.37 % (3319)Instruction limit reached!
% 1.64/1.37 % (3319)------------------------------
% 1.64/1.37 % (3319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (3319)Termination reason: Unknown
% 1.64/1.37 % (3319)Termination phase: Saturation
% 1.64/1.37
% 1.64/1.37 % (3319)Memory used [KB]: 1023
% 1.64/1.37 % (3319)Time elapsed: 0.002 s
% 1.64/1.37 % (3319)Instructions burned: 3 (million)
% 1.64/1.37 % (3319)------------------------------
% 1.64/1.37 % (3319)------------------------------
% 1.64/1.37 % (3317)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/16Mi)
% 1.64/1.38 % (3320)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/7Mi)
% 1.64/1.38 % (3320)Refutation not found, incomplete strategy
% 1.64/1.38 % (3320)------------------------------
% 1.64/1.38 % (3320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (3320)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.38
% 1.64/1.38
% 1.64/1.38 % (3320)Memory used [KB]: 5500
% 1.64/1.38 % (3320)Time elapsed: 0.002 s
% 1.64/1.38 % (3320)Instructions burned: 1 (million)
% 1.64/1.38 % (3320)------------------------------
% 1.64/1.38 % (3320)------------------------------
% 1.64/1.38 % (3322)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/4Mi)
% 1.64/1.38 % (3322)Instruction limit reached!
% 1.64/1.38 % (3322)------------------------------
% 1.64/1.38 % (3322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (3322)Termination reason: Unknown
% 1.64/1.38 % (3322)Termination phase: Saturation
% 1.64/1.38
% 1.64/1.38 % (3322)Memory used [KB]: 5500
% 1.64/1.38 % (3322)Time elapsed: 0.003 s
% 1.64/1.38 % (3322)Instructions burned: 5 (million)
% 1.64/1.38 % (3322)------------------------------
% 1.64/1.38 % (3322)------------------------------
% 1.64/1.38 % (3317)Instruction limit reached!
% 1.64/1.38 % (3317)------------------------------
% 1.64/1.38 % (3317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (3317)Termination reason: Unknown
% 1.64/1.38 % (3317)Termination phase: Saturation
% 1.64/1.38
% 1.64/1.38 % (3317)Memory used [KB]: 5628
% 1.64/1.38 % (3317)Time elapsed: 0.013 s
% 1.64/1.38 % (3317)Instructions burned: 16 (million)
% 1.64/1.38 % (3317)------------------------------
% 1.64/1.38 % (3317)------------------------------
% 1.64/1.39 % (3321)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/3Mi)
% 1.64/1.39 % (3321)Instruction limit reached!
% 1.64/1.39 % (3321)------------------------------
% 1.64/1.39 % (3321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (3321)Termination reason: Unknown
% 1.64/1.39 % (3321)Termination phase: Saturation
% 1.64/1.39
% 1.64/1.39 % (3321)Memory used [KB]: 5500
% 1.64/1.39 % (3321)Time elapsed: 0.004 s
% 1.64/1.39 % (3321)Instructions burned: 3 (million)
% 1.64/1.39 % (3321)------------------------------
% 1.64/1.39 % (3321)------------------------------
% 1.64/1.39 % (3323)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/18Mi)
% 1.64/1.39 % (3318)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_3149 for (2999ds/3Mi)
% 1.64/1.39 % (3323)Refutation not found, incomplete strategy
% 1.64/1.39 % (3323)------------------------------
% 1.64/1.39 % (3323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (3323)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.39
% 1.64/1.39
% 1.64/1.39 % (3323)Memory used [KB]: 5500
% 1.64/1.39 % (3323)Time elapsed: 0.003 s
% 1.64/1.39 % (3323)Instructions burned: 3 (million)
% 1.64/1.39 % (3323)------------------------------
% 1.64/1.39 % (3323)------------------------------
% 1.64/1.39 % (3318)Instruction limit reached!
% 1.64/1.39 % (3318)------------------------------
% 1.64/1.39 % (3318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (3318)Termination reason: Unknown
% 1.64/1.39 % (3318)Termination phase: Saturation
% 1.64/1.39
% 1.64/1.39 % (3318)Memory used [KB]: 5500
% 1.64/1.39 % (3318)Time elapsed: 0.004 s
% 1.64/1.39 % (3318)Instructions burned: 3 (million)
% 1.64/1.39 % (3318)------------------------------
% 1.64/1.39 % (3318)------------------------------
% 1.64/1.39 % (3324)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/710Mi)
% 1.67/1.40 % (3327)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_3149 for (2999ds/21Mi)
% 1.67/1.40 % (3325)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/6Mi)
% 1.67/1.41 % (3326)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_3149 for (2999ds/902Mi)
% 1.67/1.41 % (3325)Instruction limit reached!
% 1.67/1.41 % (3325)------------------------------
% 1.67/1.41 % (3325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.41 % (3325)Termination reason: Unknown
% 1.67/1.41 % (3325)Termination phase: Saturation
% 1.67/1.41
% 1.67/1.41 % (3325)Memory used [KB]: 5500
% 1.67/1.41 % (3325)Time elapsed: 0.006 s
% 1.67/1.41 % (3325)Instructions burned: 6 (million)
% 1.67/1.41 % (3325)------------------------------
% 1.67/1.41 % (3325)------------------------------
% 1.67/1.41 % (3326)Refutation not found, incomplete strategy
% 1.67/1.41 % (3326)------------------------------
% 1.67/1.41 % (3326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.41 % (3326)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.41
% 1.67/1.41
% 1.67/1.41 % (3326)Memory used [KB]: 5500
% 1.67/1.41 % (3326)Time elapsed: 0.004 s
% 1.67/1.41 % (3326)Instructions burned: 3 (million)
% 1.67/1.41 % (3326)------------------------------
% 1.67/1.41 % (3326)------------------------------
% 1.67/1.41 % (3327)Instruction limit reached!
% 1.67/1.41 % (3327)------------------------------
% 1.67/1.41 % (3327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.41 % (3327)Termination reason: Unknown
% 1.67/1.41 % (3327)Termination phase: Saturation
% 1.67/1.41
% 1.67/1.41 % (3327)Memory used [KB]: 5628
% 1.67/1.41 % (3327)Time elapsed: 0.010 s
% 1.67/1.41 % (3327)Instructions burned: 21 (million)
% 1.67/1.41 % (3327)------------------------------
% 1.67/1.41 % (3327)------------------------------
% 1.67/1.42 % (3328)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/5Mi)
% 1.67/1.42 % (3330)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/377Mi)
% 1.67/1.42 % (3330)Refutation not found, incomplete strategy
% 1.67/1.42 % (3330)------------------------------
% 1.67/1.42 % (3330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.42 % (3330)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.42
% 1.67/1.42
% 1.67/1.42 % (3330)Memory used [KB]: 5500
% 1.67/1.42 % (3330)Time elapsed: 0.003 s
% 1.67/1.42 % (3330)Instructions burned: 3 (million)
% 1.67/1.42 % (3330)------------------------------
% 1.67/1.42 % (3330)------------------------------
% 1.67/1.42 % (3328)Instruction limit reached!
% 1.67/1.42 % (3328)------------------------------
% 1.67/1.42 % (3328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.42 % (3328)Termination reason: Unknown
% 1.67/1.42 % (3328)Termination phase: Saturation
% 1.67/1.42
% 1.67/1.42 % (3328)Memory used [KB]: 5500
% 1.67/1.42 % (3328)Time elapsed: 0.006 s
% 1.67/1.42 % (3328)Instructions burned: 6 (million)
% 1.67/1.42 % (3328)------------------------------
% 1.67/1.42 % (3328)------------------------------
% 1.67/1.42 % (3329)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_3149 for (2999ds/6Mi)
% 1.67/1.43 % (3331)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_3149 for (2999ds/779Mi)
% 1.67/1.43 % (3329)Instruction limit reached!
% 1.67/1.43 % (3329)------------------------------
% 1.67/1.43 % (3329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.43 % (3329)Termination reason: Unknown
% 1.67/1.43 % (3329)Termination phase: Saturation
% 1.67/1.43
% 1.67/1.43 % (3329)Memory used [KB]: 5500
% 1.67/1.43 % (3329)Time elapsed: 0.005 s
% 1.67/1.43 % (3329)Instructions burned: 6 (million)
% 1.67/1.43 % (3329)------------------------------
% 1.67/1.43 % (3329)------------------------------
% 1.67/1.43 % (3333)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/879Mi)
% 1.67/1.43 % (3333)Refutation not found, incomplete strategy
% 1.67/1.43 % (3333)------------------------------
% 1.67/1.43 % (3333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.43 % (3333)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.43
% 1.67/1.43
% 1.67/1.43 % (3333)Memory used [KB]: 5500
% 1.67/1.43 % (3333)Time elapsed: 0.003 s
% 1.67/1.43 % (3333)Instructions burned: 3 (million)
% 1.67/1.43 % (3333)------------------------------
% 1.67/1.43 % (3333)------------------------------
% 1.67/1.44 % (3332)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_3149 for (2999ds/19Mi)
% 1.67/1.44 % (3336)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/3Mi)
% 1.67/1.44 % (3332)Refutation not found, incomplete strategy
% 1.67/1.44 % (3332)------------------------------
% 1.67/1.44 % (3332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (3332)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.44
% 1.67/1.44
% 1.67/1.44 % (3332)Memory used [KB]: 5500
% 1.67/1.44 % (3332)Time elapsed: 0.007 s
% 1.67/1.44 % (3332)Instructions burned: 8 (million)
% 1.67/1.44 % (3332)------------------------------
% 1.67/1.44 % (3332)------------------------------
% 1.67/1.44 % (3336)Instruction limit reached!
% 1.67/1.44 % (3336)------------------------------
% 1.67/1.44 % (3336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (3336)Termination reason: Unknown
% 1.67/1.44 % (3336)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (3336)Memory used [KB]: 5500
% 1.67/1.44 % (3336)Time elapsed: 0.003 s
% 1.67/1.44 % (3336)Instructions burned: 4 (million)
% 1.67/1.44 % (3336)------------------------------
% 1.67/1.44 % (3336)------------------------------
% 1.67/1.44 % (3334)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3149 for (2999ds/17Mi)
% 1.67/1.45 % (3304)Instruction limit reached!
% 1.67/1.45 % (3304)------------------------------
% 1.67/1.45 % (3304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (3304)Termination reason: Unknown
% 1.67/1.45 % (3304)Termination phase: Saturation
% 1.67/1.45
% 1.67/1.45 % (3304)Memory used [KB]: 6140
% 1.67/1.45 % (3304)Time elapsed: 0.107 s
% 1.67/1.45 % (3304)Instructions burned: 183 (million)
% 1.67/1.45 % (3304)------------------------------
% 1.67/1.45 % (3304)------------------------------
% 1.67/1.45 % (3342)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3149 for (2998ds/127Mi)
% 1.67/1.46 % (3334)Instruction limit reached!
% 1.67/1.46 % (3334)------------------------------
% 1.67/1.46 % (3334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.46 % (3334)Termination reason: Unknown
% 1.67/1.46 % (3334)Termination phase: Saturation
% 1.67/1.46
% 1.67/1.46 % (3334)Memory used [KB]: 5628
% 1.67/1.46 % (3334)Time elapsed: 0.013 s
% 1.67/1.46 % (3334)Instructions burned: 17 (million)
% 1.67/1.46 % (3334)------------------------------
% 1.67/1.46 % (3334)------------------------------
% 1.67/1.46 % (3331)Refutation not found, incomplete strategy
% 1.67/1.46 % (3331)------------------------------
% 1.67/1.46 % (3331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.46 % (3331)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.46
% 1.67/1.46
% 1.67/1.46 % (3331)Memory used [KB]: 5628
% 1.67/1.46 % (3331)Time elapsed: 0.032 s
% 1.67/1.46 % (3331)Instructions burned: 51 (million)
% 1.67/1.46 % (3331)------------------------------
% 1.67/1.46 % (3331)------------------------------
% 1.67/1.46 % (3341)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3149 for (2998ds/30Mi)
% 1.67/1.46 % (3347)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3149 for (2998ds/100Mi)
% 1.67/1.46 % (3347)Refutation not found, incomplete strategy
% 1.67/1.46 % (3347)------------------------------
% 1.67/1.46 % (3347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.46 % (3347)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.46
% 1.67/1.46
% 1.67/1.46 % (3347)Memory used [KB]: 5500
% 1.67/1.46 % (3347)Time elapsed: 0.002 s
% 1.67/1.46 % (3347)Instructions burned: 3 (million)
% 1.67/1.46 % (3347)------------------------------
% 1.67/1.46 % (3347)------------------------------
% 1.67/1.47 % (3350)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_3149 for (2998ds/20Mi)
% 1.67/1.47 % (3350)Refutation not found, incomplete strategy
% 1.67/1.47 % (3350)------------------------------
% 1.67/1.47 % (3350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.47 % (3350)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.47
% 1.67/1.47
% 1.67/1.47 % (3350)Memory used [KB]: 5500
% 1.67/1.47 % (3350)Time elapsed: 0.003 s
% 1.67/1.47 % (3350)Instructions burned: 2 (million)
% 1.67/1.47 % (3350)------------------------------
% 1.67/1.47 % (3350)------------------------------
% 1.67/1.47 % (3349)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_3149 for (2998ds/3Mi)
% 1.67/1.47 % (3349)Instruction limit reached!
% 1.67/1.47 % (3349)------------------------------
% 1.67/1.47 % (3349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.47 % (3349)Termination reason: Unknown
% 1.67/1.47 % (3349)Termination phase: Saturation
% 1.67/1.47
% 1.67/1.47 % (3349)Memory used [KB]: 5500
% 1.67/1.47 % (3349)Time elapsed: 0.003 s
% 1.67/1.47 % (3349)Instructions burned: 3 (million)
% 1.67/1.47 % (3349)------------------------------
% 1.67/1.47 % (3349)------------------------------
% 1.67/1.47 % (3341)Instruction limit reached!
% 1.67/1.47 % (3341)------------------------------
% 1.67/1.47 % (3341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.47 % (3341)Termination reason: Unknown
% 1.67/1.47 % (3341)Termination phase: Saturation
% 1.67/1.47
% 1.67/1.47 % (3341)Memory used [KB]: 5628
% 1.67/1.47 % (3341)Time elapsed: 0.015 s
% 1.67/1.47 % (3341)Instructions burned: 30 (million)
% 1.67/1.47 % (3341)------------------------------
% 1.67/1.47 % (3341)------------------------------
% 1.67/1.47 % (3354)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_3149 for (2998ds/86Mi)
% 1.67/1.48 % (3357)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_3149 for (2998ds/107Mi)
% 1.67/1.48 % (3357)Refutation not found, incomplete strategy
% 1.67/1.48 % (3357)------------------------------
% 1.67/1.48 % (3357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.48 % (3357)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.48
% 1.67/1.48
% 1.67/1.48 % (3357)Memory used [KB]: 5500
% 1.67/1.48 % (3357)Time elapsed: 0.003 s
% 1.67/1.48 % (3357)Instructions burned: 3 (million)
% 1.67/1.48 % (3357)------------------------------
% 1.67/1.48 % (3357)------------------------------
% 1.67/1.48 % (3362)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_3149 for (2998ds/448Mi)
% 1.67/1.48 % (3360)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_3149 for (2998ds/39Mi)
% 1.67/1.49 % (3366)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_3149 for (2998ds/46Mi)
% 1.67/1.50 % (3342)Instruction limit reached!
% 1.67/1.50 % (3342)------------------------------
% 1.67/1.50 % (3342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.50 % (3342)Termination reason: Unknown
% 1.67/1.50 % (3342)Termination phase: Saturation
% 1.67/1.50
% 1.67/1.50 % (3342)Memory used [KB]: 5884
% 1.67/1.50 % (3342)Time elapsed: 0.046 s
% 1.67/1.50 % (3342)Instructions burned: 127 (million)
% 1.67/1.50 % (3342)------------------------------
% 1.67/1.50 % (3342)------------------------------
% 1.67/1.50 % (3360)Instruction limit reached!
% 1.67/1.50 % (3360)------------------------------
% 1.67/1.50 % (3360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.50 % (3360)Termination reason: Unknown
% 1.67/1.50 % (3360)Termination phase: Saturation
% 1.67/1.50
% 1.67/1.50 % (3360)Memory used [KB]: 5756
% 1.67/1.50 % (3360)Time elapsed: 0.016 s
% 1.67/1.50 % (3360)Instructions burned: 41 (million)
% 1.67/1.50 % (3360)------------------------------
% 1.67/1.50 % (3360)------------------------------
% 1.67/1.50 % (3354)Instruction limit reached!
% 1.67/1.50 % (3354)------------------------------
% 1.67/1.50 % (3354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.50 % (3354)Termination reason: Unknown
% 1.67/1.50 % (3354)Termination phase: Saturation
% 1.67/1.50
% 1.67/1.50 % (3354)Memory used [KB]: 5884
% 1.67/1.50 % (3354)Time elapsed: 0.032 s
% 1.67/1.50 % (3354)Instructions burned: 87 (million)
% 1.67/1.50 % (3354)------------------------------
% 1.67/1.50 % (3354)------------------------------
% 1.67/1.51 % (3366)Refutation not found, incomplete strategy
% 1.67/1.51 % (3366)------------------------------
% 1.67/1.51 % (3366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.51 % (3366)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.51
% 1.67/1.51
% 1.67/1.51 % (3366)Memory used [KB]: 5628
% 1.67/1.51 % (3366)Time elapsed: 0.017 s
% 1.67/1.51 % (3366)Instructions burned: 42 (million)
% 1.67/1.51 % (3366)------------------------------
% 1.67/1.51 % (3366)------------------------------
% 1.67/1.51 % (3373)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_3149 for (2998ds/98Mi)
% 1.67/1.51 % (3373)Refutation not found, incomplete strategy
% 1.67/1.51 % (3373)------------------------------
% 1.67/1.51 % (3373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.51 % (3373)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.51
% 1.67/1.51
% 1.67/1.51 % (3373)Memory used [KB]: 1023
% 1.67/1.51 % (3373)Time elapsed: 0.006 s
% 1.67/1.51 % (3373)Instructions burned: 12 (million)
% 1.67/1.51 % (3373)------------------------------
% 1.67/1.51 % (3373)------------------------------
% 1.67/1.51 % (3377)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_3149 for (2998ds/149Mi)
% 1.67/1.52 % (3374)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_3149 for (2998ds/507Mi)
% 1.67/1.52 % (3380)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3149 for (2998ds/39Mi)
% 1.67/1.52 % (3380)Refutation not found, incomplete strategy
% 1.67/1.52 % (3380)------------------------------
% 1.67/1.52 % (3380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.52 % (3380)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.52
% 1.67/1.52
% 1.67/1.52 % (3380)Memory used [KB]: 5500
% 1.67/1.52 % (3380)Time elapsed: 0.003 s
% 1.67/1.52 % (3380)Instructions burned: 3 (million)
% 1.67/1.52 % (3380)------------------------------
% 1.67/1.52 % (3380)------------------------------
% 1.67/1.52 % (3374)Refutation not found, incomplete strategy
% 1.67/1.52 % (3374)------------------------------
% 1.67/1.52 % (3374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.52 % (3374)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.52
% 1.67/1.52
% 1.67/1.52 % (3374)Memory used [KB]: 5500
% 1.67/1.52 % (3374)Time elapsed: 0.006 s
% 1.67/1.52 % (3374)Instructions burned: 6 (million)
% 1.67/1.52 % (3374)------------------------------
% 1.67/1.52 % (3374)------------------------------
% 1.67/1.52 % (3385)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_3149 for (2998ds/6Mi)
% 1.67/1.53 % (3385)Instruction limit reached!
% 1.67/1.53 % (3385)------------------------------
% 1.67/1.53 % (3385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.53 % (3385)Termination reason: Unknown
% 1.67/1.53 % (3385)Termination phase: Saturation
% 1.67/1.53
% 1.67/1.53 % (3385)Memory used [KB]: 9978
% 1.67/1.53 % (3385)Time elapsed: 0.027 s
% 1.67/1.53 % (3385)Instructions burned: 7 (million)
% 1.67/1.53 % (3385)------------------------------
% 1.67/1.53 % (3385)------------------------------
% 1.67/1.53 % (3389)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_3149 for (2998ds/1087Mi)
% 1.67/1.53 % (3389)Refutation not found, incomplete strategy
% 1.67/1.53 % (3389)------------------------------
% 1.67/1.53 % (3389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.53 % (3389)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.53
% 1.67/1.53
% 1.67/1.53 % (3389)Memory used [KB]: 5500
% 1.67/1.53 % (3389)Time elapsed: 0.003 s
% 1.67/1.53 % (3389)Instructions burned: 3 (million)
% 1.67/1.53 % (3389)------------------------------
% 1.67/1.53 % (3389)------------------------------
% 1.67/1.54 % (3393)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_3149 for (2998ds/44Mi)
% 1.67/1.54 % (3390)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3149 for (2998ds/47Mi)
% 1.67/1.54 % (3395)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_3149 for (2997ds/432Mi)
% 1.67/1.55 % (3393)Instruction limit reached!
% 1.67/1.55 % (3393)------------------------------
% 1.67/1.55 % (3393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.55 % (3393)Termination reason: Unknown
% 1.67/1.55 % (3393)Termination phase: Saturation
% 1.67/1.55
% 1.67/1.55 % (3393)Memory used [KB]: 1279
% 1.67/1.55 % (3393)Time elapsed: 0.017 s
% 1.67/1.55 % (3393)Instructions burned: 46 (million)
% 1.67/1.55 % (3393)------------------------------
% 1.67/1.55 % (3393)------------------------------
% 1.67/1.55 % (3390)Instruction limit reached!
% 1.67/1.55 % (3390)------------------------------
% 1.67/1.55 % (3390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.55 % (3390)Termination reason: Unknown
% 1.67/1.55 % (3390)Termination phase: Saturation
% 1.67/1.55
% 1.67/1.55 % (3390)Memory used [KB]: 5628
% 1.67/1.55 % (3390)Time elapsed: 0.039 s
% 1.67/1.55 % (3390)Instructions burned: 47 (million)
% 1.67/1.55 % (3390)------------------------------
% 1.67/1.55 % (3390)------------------------------
% 1.67/1.56 % (3403)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3149 for (2997ds/62Mi)
% 1.67/1.56 % (3404)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_3149 for (2997ds/31Mi)
% 1.67/1.57 % (3377)Instruction limit reached!
% 1.67/1.57 % (3377)------------------------------
% 1.67/1.57 % (3377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.57 % (3377)Termination reason: Unknown
% 1.67/1.57 % (3377)Termination phase: Saturation
% 1.67/1.57
% 1.67/1.57 % (3377)Memory used [KB]: 5884
% 1.67/1.57 % (3377)Time elapsed: 0.074 s
% 1.67/1.57 % (3377)Instructions burned: 150 (million)
% 1.67/1.57 % (3377)------------------------------
% 1.67/1.57 % (3377)------------------------------
% 1.67/1.57 % (3404)Instruction limit reached!
% 1.67/1.57 % (3404)------------------------------
% 1.67/1.57 % (3404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.57 % (3404)Termination reason: Unknown
% 1.67/1.57 % (3404)Termination phase: Saturation
% 1.67/1.57
% 1.67/1.57 % (3404)Memory used [KB]: 5628
% 1.67/1.57 % (3404)Time elapsed: 0.013 s
% 1.67/1.57 % (3404)Instructions burned: 31 (million)
% 1.67/1.57 % (3404)------------------------------
% 1.67/1.57 % (3404)------------------------------
% 1.67/1.58 % (3411)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3149 for (2997ds/96Mi)
% 1.67/1.58 % (3403)Instruction limit reached!
% 1.67/1.58 % (3403)------------------------------
% 1.67/1.58 % (3403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.58 % (3403)Termination reason: Unknown
% 1.67/1.58 % (3403)Termination phase: Saturation
% 1.67/1.58
% 1.67/1.58 % (3403)Memory used [KB]: 5756
% 1.67/1.58 % (3403)Time elapsed: 0.023 s
% 1.67/1.58 % (3403)Instructions burned: 62 (million)
% 1.67/1.58 % (3403)------------------------------
% 1.67/1.58 % (3403)------------------------------
% 1.67/1.58 % (3415)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_3149 for (2997ds/453Mi)
% 1.67/1.59 % (3415)Refutation not found, incomplete strategy
% 1.67/1.59 % (3415)------------------------------
% 1.67/1.59 % (3415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.59 % (3415)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.59
% 1.67/1.59
% 1.67/1.59 % (3415)Memory used [KB]: 5500
% 1.67/1.59 % (3415)Time elapsed: 0.007 s
% 1.67/1.59 % (3415)Instructions burned: 15 (million)
% 1.67/1.59 % (3415)------------------------------
% 1.67/1.59 % (3415)------------------------------
% 1.67/1.59 % (3417)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_3149 for (2997ds/71Mi)
% 1.67/1.60 % (3362)First to succeed.
% 1.67/1.60 % (3420)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3149 for (2997ds/83Mi)
% 1.67/1.60 % (3362)Refutation found. Thanks to Tanya!
% 1.67/1.60 % SZS status Theorem for DTF2THF_3149
% 1.67/1.60 % SZS output start Proof for DTF2THF_3149
% 1.67/1.60 thf(func_def_1, type, s: $i > $i).
% 1.67/1.60 thf(func_def_2, type, ite: $o > $i > $i > $i).
% 1.67/1.60 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 1.67/1.60 thf(f1600,plain,(
% 1.67/1.60 $false),
% 1.67/1.60 inference(avatar_sat_refutation,[status(thm)],[f224,f229,f571,f1117,f1279,f1343,f1361,f1457,f1546,f1548,f1561,f1585,f1598])).
% 1.67/1.60 thf(f1598,plain,(
% 1.67/1.60 ~spl0_115),
% 1.67/1.60 inference(avatar_contradiction_clause,[status(thm)],[f1597])).
% 1.67/1.60 thf(f1597,plain,(
% 1.67/1.60 $false | ~spl0_115),
% 1.67/1.60 inference(trivial_inequality_removal,[status(thm)],[f1593])).
% 1.67/1.60 thf(f1593,plain,(
% 1.67/1.60 (zero != zero) | ~spl0_115),
% 1.67/1.60 inference(superposition,[status(thm)],[f22,f1456])).
% 1.67/1.60 thf(f1456,plain,(
% 1.67/1.60 (zero = (s @ zero)) | ~spl0_115),
% 1.67/1.60 inference(avatar_component_clause,[status(thm)],[f1454])).
% 1.67/1.60 thf(f1454,definition,(
% 1.67/1.60 spl0_115 <=> (zero = (s @ zero))),
% 1.67/1.60 introduced(definition,[new_symbols(naming,[spl0_115])],[avatar_definition])).
% 1.67/1.60 thf(f22,plain,(
% 1.67/1.60 ( ! [X1 : $i] : (((s @ X1) != X1)) )),
% 1.67/1.60 inference(equality_proxy_clausification,[status(thm)],[f21])).
% 1.67/1.60 thf(f21,plain,(
% 1.67/1.60 ( ! [X1 : $i] : ((((s @ X1) = X1) = $false)) )),
% 1.67/1.60 inference(not_proxy_clausification,[status(thm)],[f20])).
% 1.67/1.60 thf(f20,plain,(
% 1.67/1.60 ( ! [X1 : $i] : (((~ ((s @ X1) = X1)) = $true)) )),
% 1.67/1.60 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.67/1.60 thf(f19,plain,(
% 1.67/1.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (~ ((s @ Y0) = Y0))) @ X1))) )),
% 1.67/1.60 inference(pi_clausification,[status(thm)],[f17])).
% 1.67/1.60 thf(f17,plain,(
% 1.67/1.60 ((!! @ $i @ (^[Y0 : $i]: (~ ((s @ Y0) = Y0)))) = $true)),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.67/1.60 thf(f9,plain,(
% 1.67/1.60 (((((!! @ $i @ (^[Y0 : $i]: (~ (zero = (s @ 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 @ (^[Y0 : $i]: (~ ((s @ Y0) = Y0))))) = $true)),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.67/1.60 thf(f7,plain,(
% 1.67/1.60 ($false = (((((!! @ $i @ (^[Y0 : $i]: (~ (zero = (s @ 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 @ (^[Y0 : $i]: (~ ((s @ Y0) = Y0))))) => (?? @ ($i > $i) @ (^[Y0 : $i > $i]: ((((s @ zero) = (Y0 @ zero)) & (zero = (Y0 @ (s @ (s @ zero))))) & (zero = (Y0 @ (s @ zero))))))))),
% 1.67/1.60 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.67/1.60 thf(f6,plain,(
% 1.67/1.60 ((~ (((((!! @ $i @ (^[Y0 : $i]: (~ (zero = (s @ 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 @ (^[Y0 : $i]: (~ ((s @ Y0) = Y0))))) => (?? @ ($i > $i) @ (^[Y0 : $i > $i]: ((((s @ zero) = (Y0 @ zero)) & (zero = (Y0 @ (s @ (s @ zero))))) & (zero = (Y0 @ (s @ zero)))))))) = $true)),
% 1.67/1.60 inference(cnf_transformation,[status(thm)],[f5])).
% 1.67/1.60 thf(f5,plain,(
% 1.67/1.60 ((~ (((((!! @ $i @ (^[Y0 : $i]: (~ (zero = (s @ 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 @ (^[Y0 : $i]: (~ ((s @ Y0) = Y0))))) => (?? @ ($i > $i) @ (^[Y0 : $i > $i]: ((((s @ zero) = (Y0 @ zero)) & (zero = (Y0 @ (s @ (s @ zero))))) & (zero = (Y0 @ (s @ zero)))))))) = $true)),
% 1.67/1.60 inference(fool_elimination,[status(thm)],[f4])).
% 1.67/1.60 thf(f4,plain,(
% 1.67/1.60 ~((! [X0 : $i] : ((s @ X0) != X0) & ! [X1 : $o,X2 : $i,X3 : $i] : (~X1 => ((ite @ X1 @ X3 @ X2) = X2)) & ! [X4 : $o,X5 : $i,X6 : $i] : (X4 => ((ite @ X4 @ X5 @ X6) = X5)) & ! [X7 : $i] : (zero != (s @ X7))) => ? [X8 : $i > $i] : ((zero = (X8 @ (s @ zero))) & (zero = (X8 @ (s @ (s @ zero)))) & ((s @ zero) = (X8 @ zero))))),
% 1.67/1.60 inference(rectify,[status(thm)],[f2])).
% 1.67/1.60 thf(f2,negated_conjecture,(
% 1.67/1.60 ~((! [X3 : $i] : ((s @ X3) != X3) & ! [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) != zero)) => ? [X4 : $i > $i] : ((zero = (X4 @ (s @ zero))) & (zero = (X4 @ (s @ (s @ zero)))) & ((X4 @ zero) = (s @ zero))))),
% 1.67/1.60 inference(negated_conjecture,[status(cth)],[f1])).
% 1.67/1.60 thf(f1,conjecture,(
% 1.67/1.60 (! [X3 : $i] : ((s @ X3) != X3) & ! [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) != zero)) => ? [X4 : $i > $i] : ((zero = (X4 @ (s @ zero))) & (zero = (X4 @ (s @ (s @ zero)))) & ((X4 @ zero) = (s @ zero)))),
% 1.67/1.60 file('/export/starexec/sandbox2/tmp/tmp.7Cj4tebpTh/DTF2THF_3149.p',n9)).
% 1.67/1.60 thf(f1585,plain,(
% 1.67/1.60 spl0_4 | spl0_3),
% 1.67/1.60 inference(avatar_split_clause,[status(thm)],[f1584,f64,f67])).
% 1.67/1.60 thf(f67,definition,(
% 1.67/1.60 spl0_4 <=> ! [X0 : $o] : ($true = X0)),
% 1.67/1.60 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.67/1.60 thf(f64,definition,(
% 1.67/1.60 spl0_3 <=> ! [X3 : $i > $i,X4 : $i,X5 : $i > $i,X2 : $i,X1 : $i > $o] : ((zero != X2) | ((X5 @ (s @ (s @ zero))) != X4) | ((s @ zero) != (ite @ (X1 @ zero) @ (X5 @ zero) @ (X3 @ zero))) | (zero != (ite @ (X1 @ (s @ zero)) @ (X5 @ (s @ zero)) @ (X3 @ (s @ zero)))) | ((X1 @ (s @ (s @ zero))) = $true) | ((X3 @ (s @ (s @ zero))) != X2))),
% 1.67/1.60 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.67/1.60 thf(f1584,plain,(
% 1.67/1.60 ( ! [X2 : $i > $o,X3 : $o,X0 : $i > $i,X1 : $i,X4 : $i > $i,X5 : $i] : ((zero != X5) | ((X2 @ (s @ (s @ zero))) = $true) | ((X0 @ (s @ (s @ zero))) != X1) | ((X4 @ (s @ (s @ zero))) != X5) | ($true = X3) | (zero != (ite @ (X2 @ (s @ zero)) @ (X0 @ (s @ zero)) @ (X4 @ (s @ zero)))) | ((s @ zero) != (ite @ (X2 @ zero) @ (X0 @ zero) @ (X4 @ zero)))) )),
% 1.67/1.60 inference(duplicate_literal_removal,[status(thm)],[f1582])).
% 1.67/1.60 thf(f1582,plain,(
% 1.67/1.60 ( ! [X2 : $i > $o,X3 : $o,X0 : $i > $i,X1 : $i,X4 : $i > $i,X5 : $i] : (((X2 @ (s @ (s @ zero))) = $true) | ($true = X3) | ((s @ zero) != (ite @ (X2 @ zero) @ (X0 @ zero) @ (X4 @ zero))) | (zero != X5) | (zero != (ite @ (X2 @ (s @ zero)) @ (X0 @ (s @ zero)) @ (X4 @ (s @ zero)))) | ((X4 @ (s @ (s @ zero))) != X5) | ($true = X3) | ((X0 @ (s @ (s @ zero))) != X1)) )),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f1581])).
% 1.67/1.60 thf(f1581,plain,(
% 1.67/1.60 ( ! [X2 : $i > $o,X3 : $o,X0 : $i > $i,X1 : $i,X4 : $i > $i,X5 : $i] : (((s @ zero) != (ite @ (X2 @ zero) @ (X0 @ zero) @ (X4 @ zero))) | ($true = X3) | ((X4 @ (s @ (s @ zero))) != X5) | (zero != X5) | (zero != (ite @ (X2 @ (s @ zero)) @ (X0 @ (s @ zero)) @ (X4 @ (s @ zero)))) | ((X2 @ (s @ (s @ zero))) != X3) | ((X0 @ (s @ (s @ zero))) != X1)) )),
% 1.67/1.60 inference(beta_eta_normalization,[status(thm)],[f1575])).
% 1.67/1.60 thf(f1575,plain,(
% 1.67/1.60 ( ! [X2 : $i > $o,X3 : $o,X0 : $i > $i,X1 : $i,X4 : $i > $i,X5 : $i] : (((X2 @ (s @ (s @ zero))) != X3) | ((X4 @ (s @ (s @ zero))) != X5) | (zero != X5) | (zero != ((^[Y0 : $i]: (ite @ (X2 @ Y0) @ (X0 @ Y0) @ (X4 @ Y0))) @ (s @ zero))) | ((X0 @ (s @ (s @ zero))) != X1) | ($true = X3) | ((s @ zero) != ((^[Y0 : $i]: (ite @ (X2 @ Y0) @ (X0 @ Y0) @ (X4 @ Y0))) @ zero))) )),
% 1.67/1.60 inference(constrained_superposition,[status(thm)],[f16,f47])).
% 1.67/1.60 thf(f47,plain,(
% 1.67/1.60 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((ite @ X3 @ X1 @ X2) = X2) | ($true = X3)) )),
% 1.67/1.60 inference(equality_proxy_clausification,[status(thm)],[f46])).
% 1.67/1.60 thf(f46,plain,(
% 1.67/1.60 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((ite @ X3 @ X1 @ X2) = X2) = $true) | ($true = X3)) )),
% 1.67/1.60 inference(not_proxy_clausification,[status(thm)],[f45])).
% 1.67/1.60 thf(f45,plain,(
% 1.67/1.60 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($false = (~ X3)) | (((ite @ X3 @ X1 @ X2) = X2) = $true)) )),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.67/1.60 thf(f44,plain,(
% 1.67/1.60 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((~ X3) => ((ite @ X3 @ X1 @ X2) = X2)) = $true)) )),
% 1.67/1.60 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.67/1.60 thf(f43,plain,(
% 1.67/1.60 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((^[Y0 : $o]: ((~ Y0) => ((ite @ Y0 @ X1 @ X2) = X2))) @ X3) = $true)) )),
% 1.67/1.60 inference(pi_clausification,[status(thm)],[f42])).
% 1.67/1.60 thf(f42,plain,(
% 1.67/1.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $o @ (^[Y0 : $o]: ((~ Y0) => ((ite @ Y0 @ X1 @ X2) = X2)))) = $true)) )),
% 1.67/1.60 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.67/1.60 thf(f41,plain,(
% 1.67/1.60 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((~ Y1) => ((ite @ Y1 @ X1 @ Y0) = Y0))))) @ X2) = $true)) )),
% 1.67/1.60 inference(pi_clausification,[status(thm)],[f40])).
% 1.67/1.60 thf(f40,plain,(
% 1.67/1.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((~ Y1) => ((ite @ Y1 @ X1 @ Y0) = Y0)))))) = $true)) )),
% 1.67/1.60 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.67/1.60 thf(f39,plain,(
% 1.67/1.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y0 @ Y1) = Y1))))))) @ X1) = $true)) )),
% 1.67/1.60 inference(pi_clausification,[status(thm)],[f23])).
% 1.67/1.60 thf(f23,plain,(
% 1.67/1.60 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y0 @ Y1) = Y1)))))))) = $true)),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.67/1.60 thf(f18,plain,(
% 1.67/1.60 ((((!! @ $i @ (^[Y0 : $i]: (~ (zero = (s @ 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))))))))) = $true)),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.67/1.60 thf(f16,plain,(
% 1.67/1.60 ( ! [X1 : $i > $i] : ((zero != (X1 @ (s @ (s @ zero)))) | (zero != (X1 @ (s @ zero))) | ((s @ zero) != (X1 @ zero))) )),
% 1.67/1.60 inference(equality_proxy_clausification,[status(thm)],[f15])).
% 1.67/1.60 thf(f15,plain,(
% 1.67/1.60 ( ! [X1 : $i > $i] : ((zero != (X1 @ (s @ zero))) | ($false = (zero = (X1 @ (s @ (s @ zero))))) | ((s @ zero) != (X1 @ zero))) )),
% 1.67/1.60 inference(equality_proxy_clausification,[status(thm)],[f14])).
% 1.67/1.60 thf(f14,plain,(
% 1.67/1.60 ( ! [X1 : $i > $i] : ((((s @ zero) = (X1 @ zero)) = $false) | ($false = (zero = (X1 @ (s @ (s @ zero))))) | (zero != (X1 @ (s @ zero)))) )),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.67/1.60 thf(f13,plain,(
% 1.67/1.60 ( ! [X1 : $i > $i] : (((((s @ zero) = (X1 @ zero)) & (zero = (X1 @ (s @ (s @ zero))))) = $false) | (zero != (X1 @ (s @ zero)))) )),
% 1.67/1.60 inference(equality_proxy_clausification,[status(thm)],[f12])).
% 1.67/1.60 thf(f12,plain,(
% 1.67/1.60 ( ! [X1 : $i > $i] : (((zero = (X1 @ (s @ zero))) = $false) | ((((s @ zero) = (X1 @ zero)) & (zero = (X1 @ (s @ (s @ zero))))) = $false)) )),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.67/1.60 thf(f11,plain,(
% 1.67/1.60 ( ! [X1 : $i > $i] : (($false = ((((s @ zero) = (X1 @ zero)) & (zero = (X1 @ (s @ (s @ zero))))) & (zero = (X1 @ (s @ zero)))))) )),
% 1.67/1.60 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.67/1.60 thf(f10,plain,(
% 1.67/1.60 ( ! [X1 : $i > $i] : ((((^[Y0 : $i > $i]: ((((s @ zero) = (Y0 @ zero)) & (zero = (Y0 @ (s @ (s @ zero))))) & (zero = (Y0 @ (s @ zero))))) @ X1) = $false)) )),
% 1.67/1.60 inference(pi_clausification,[status(thm)],[f8])).
% 1.67/1.60 thf(f8,plain,(
% 1.67/1.60 ((?? @ ($i > $i) @ (^[Y0 : $i > $i]: ((((s @ zero) = (Y0 @ zero)) & (zero = (Y0 @ (s @ (s @ zero))))) & (zero = (Y0 @ (s @ zero)))))) = $false)),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.67/1.60 thf(f1561,plain,(
% 1.67/1.60 ~spl0_114),
% 1.67/1.60 inference(avatar_contradiction_clause,[status(thm)],[f1560])).
% 1.67/1.60 thf(f1560,plain,(
% 1.67/1.60 $false | ~spl0_114),
% 1.67/1.60 inference(trivial_inequality_removal,[status(thm)],[f1558])).
% 1.67/1.60 thf(f1558,plain,(
% 1.67/1.60 (zero != zero) | ~spl0_114),
% 1.67/1.60 inference(superposition,[status(thm)],[f38,f1452])).
% 1.67/1.60 thf(f1452,plain,(
% 1.67/1.60 (zero = (s @ (s @ zero))) | ~spl0_114),
% 1.67/1.60 inference(avatar_component_clause,[status(thm)],[f1450])).
% 1.67/1.60 thf(f1450,definition,(
% 1.67/1.60 spl0_114 <=> (zero = (s @ (s @ zero)))),
% 1.67/1.60 introduced(definition,[new_symbols(naming,[spl0_114])],[avatar_definition])).
% 1.67/1.60 thf(f38,plain,(
% 1.67/1.60 ( ! [X1 : $i] : ((zero != (s @ X1))) )),
% 1.67/1.60 inference(equality_proxy_clausification,[status(thm)],[f37])).
% 1.67/1.60 thf(f37,plain,(
% 1.67/1.60 ( ! [X1 : $i] : (((zero = (s @ X1)) = $false)) )),
% 1.67/1.60 inference(not_proxy_clausification,[status(thm)],[f36])).
% 1.67/1.60 thf(f36,plain,(
% 1.67/1.60 ( ! [X1 : $i] : (((~ (zero = (s @ X1))) = $true)) )),
% 1.67/1.60 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.67/1.60 thf(f35,plain,(
% 1.67/1.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: (~ (zero = (s @ Y0)))) @ X1) = $true)) )),
% 1.67/1.60 inference(pi_clausification,[status(thm)],[f26])).
% 1.67/1.60 thf(f26,plain,(
% 1.67/1.60 ((!! @ $i @ (^[Y0 : $i]: (~ (zero = (s @ Y0))))) = $true)),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.67/1.60 thf(f24,plain,(
% 1.67/1.60 (((!! @ $i @ (^[Y0 : $i]: (~ (zero = (s @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1))))))))) = $true)),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.67/1.60 thf(f1548,plain,(
% 1.67/1.60 ~spl0_35),
% 1.67/1.60 inference(avatar_contradiction_clause,[status(thm)],[f1547])).
% 1.67/1.60 thf(f1547,plain,(
% 1.67/1.60 $false | ~spl0_35),
% 1.67/1.60 inference(equality_resolution,[status(thm)],[f363])).
% 1.67/1.60 thf(f363,plain,(
% 1.67/1.60 ( ! [X3 : $i] : ((zero != X3)) ) | ~spl0_35),
% 1.67/1.60 inference(avatar_component_clause,[status(thm)],[f362])).
% 1.67/1.60 thf(f362,definition,(
% 1.67/1.60 spl0_35 <=> ! [X3 : $i] : (zero != X3)),
% 1.67/1.60 introduced(definition,[new_symbols(naming,[spl0_35])],[avatar_definition])).
% 1.67/1.60 thf(f1546,plain,(
% 1.67/1.60 ~spl0_106),
% 1.67/1.60 inference(avatar_contradiction_clause,[status(thm)],[f1545])).
% 1.67/1.60 thf(f1545,plain,(
% 1.67/1.60 $false | ~spl0_106),
% 1.67/1.60 inference(equality_resolution,[status(thm)],[f1278])).
% 1.67/1.60 thf(f1278,plain,(
% 1.67/1.60 ( ! [X3 : $i] : (((s @ zero) != X3)) ) | ~spl0_106),
% 1.67/1.60 inference(avatar_component_clause,[status(thm)],[f1277])).
% 1.67/1.60 thf(f1277,definition,(
% 1.67/1.60 spl0_106 <=> ! [X3 : $i] : ((s @ zero) != X3)),
% 1.67/1.60 introduced(definition,[new_symbols(naming,[spl0_106])],[avatar_definition])).
% 1.67/1.60 thf(f1457,plain,(
% 1.67/1.60 spl0_114 | spl0_115 | ~spl0_92),
% 1.67/1.60 inference(avatar_split_clause,[status(thm)],[f1448,f952,f1454,f1450])).
% 1.67/1.60 thf(f952,definition,(
% 1.67/1.60 spl0_92 <=> ! [X0 : $i > $o] : (((X0 @ (s @ (s @ zero))) = $true) | ((X0 @ (s @ zero)) = $true) | ((X0 @ zero) = $false))),
% 1.67/1.60 introduced(definition,[new_symbols(naming,[spl0_92])],[avatar_definition])).
% 1.67/1.60 thf(f1448,plain,(
% 1.67/1.60 (zero = (s @ (s @ zero))) | (zero = (s @ zero)) | ~spl0_92),
% 1.67/1.60 inference(equality_proxy_clausification,[status(thm)],[f1415])).
% 1.67/1.60 thf(f1415,plain,(
% 1.67/1.60 (zero = (s @ (s @ zero))) | ((zero = (s @ zero)) = $true) | ~spl0_92),
% 1.67/1.60 inference(leibniz_equality_elimination,[status(thm)],[f953])).
% 1.67/1.60 thf(f953,plain,(
% 1.67/1.60 ( ! [X0 : $i > $o] : (((X0 @ (s @ (s @ zero))) = $true) | ((X0 @ (s @ zero)) = $true) | ((X0 @ zero) = $false)) ) | ~spl0_92),
% 1.67/1.60 inference(avatar_component_clause,[status(thm)],[f952])).
% 1.67/1.60 thf(f1361,plain,(
% 1.67/1.60 spl0_92 | spl0_7 | spl0_77 | spl0_76 | ~spl0_24),
% 1.67/1.60 inference(avatar_split_clause,[status(thm)],[f1360,f277,f841,f844,f85,f952])).
% 1.67/1.60 thf(f85,definition,(
% 1.67/1.60 spl0_7 <=> ! [X0 : $o] : ($false = X0)),
% 1.67/1.60 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.67/1.60 thf(f844,definition,(
% 1.67/1.60 spl0_77 <=> ! [X5 : $i,X4 : $i > $i,X7 : $i,X6 : $i] : (((X4 @ (s @ zero)) != X7) | (zero != X6) | ((X4 @ zero) != X5) | ((X4 @ (s @ (s @ zero))) != X6) | (zero != X7))),
% 1.67/1.60 introduced(definition,[new_symbols(naming,[spl0_77])],[avatar_definition])).
% 1.67/1.60 thf(f841,definition,(
% 1.67/1.60 spl0_76 <=> ! [X3 : $i,X8 : $i,X9 : $i,X2 : $i > $i] : (((X2 @ (s @ zero)) != X9) | ((X2 @ (s @ (s @ zero))) != X8) | ((s @ zero) != X3) | ((X2 @ zero) != X3))),
% 1.67/1.60 introduced(definition,[new_symbols(naming,[spl0_76])],[avatar_definition])).
% 1.67/1.60 thf(f277,definition,(
% 1.67/1.60 spl0_24 <=> ! [X3 : $i,X4 : $i > $i,X0 : $i > $o,X6 : $i,X5 : $i,X2 : $i > $i,X7 : $i] : (((X0 @ (s @ zero)) = $true) | ((X0 @ (s @ (s @ zero))) = $true) | ((X2 @ (s @ zero)) != X3) | ((X4 @ (s @ zero)) != X5) | ((s @ zero) != (ite @ (X0 @ zero) @ (X2 @ zero) @ (X4 @ zero))) | ((X2 @ (s @ (s @ zero))) != X7) | ((X4 @ (s @ (s @ zero))) != X6) | (zero != X6) | (zero != X5))),
% 1.67/1.60 introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition])).
% 1.67/1.60 thf(f1360,plain,(
% 1.67/1.60 ( ! [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 @ (s @ zero))) = $true) | ((X4 @ (s @ (s @ zero))) != X6) | ((X0 @ zero) = $false) | ((s @ zero) != X3) | ((X2 @ (s @ zero)) != X7) | ((X2 @ zero) != X3) | ((X4 @ zero) != X5) | ($false = X1) | ((X2 @ (s @ (s @ zero))) != X9) | ((X0 @ (s @ zero)) = $true) | (zero != X6) | (zero != X8) | ((X4 @ (s @ zero)) != X8)) ) | ~spl0_24),
% 1.67/1.60 inference(duplicate_literal_removal,[status(thm)],[f1359])).
% 1.67/1.60 thf(f1359,plain,(
% 1.67/1.60 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $o,X1 : $o,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i > $i,X5 : $i] : (((X4 @ zero) != X5) | ((X0 @ (s @ zero)) = $true) | ($false = X1) | (zero != X8) | ((X0 @ (s @ (s @ zero))) = $true) | (zero != X6) | ((X4 @ (s @ zero)) != X8) | ((X2 @ (s @ zero)) != X7) | ((X2 @ (s @ (s @ zero))) != X9) | ((X4 @ (s @ (s @ zero))) != X6) | ((X0 @ zero) = $false) | ($false = X1) | ((X2 @ zero) != X3) | ((s @ zero) != X3)) ) | ~spl0_24),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f1309])).
% 1.67/1.60 thf(f1309,plain,(
% 1.67/1.60 ( ! [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)) = $true) | ((X4 @ zero) != X5) | ((X2 @ (s @ zero)) != X7) | ((s @ zero) != X3) | ((X2 @ zero) != X3) | ((X4 @ (s @ zero)) != X8) | ((X0 @ zero) != X1) | (zero != X6) | ((X4 @ (s @ (s @ zero))) != X6) | ((X2 @ (s @ (s @ zero))) != X9) | (zero != X8) | ((X0 @ (s @ (s @ zero))) = $true) | ($false = X1)) ) | ~spl0_24),
% 1.67/1.60 inference(constrained_superposition,[status(thm)],[f278,f34])).
% 1.67/1.60 thf(f34,plain,(
% 1.67/1.60 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((ite @ X3 @ X2 @ X1) = X2) | ($false = X3)) )),
% 1.67/1.60 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.67/1.60 thf(f33,plain,(
% 1.67/1.60 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((ite @ X3 @ X2 @ X1) = X2) = $true) | ($false = X3)) )),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.67/1.60 thf(f32,plain,(
% 1.67/1.60 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((X3 => ((ite @ X3 @ X2 @ X1) = X2)) = $true)) )),
% 1.67/1.60 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.67/1.60 thf(f31,plain,(
% 1.67/1.60 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((^[Y0 : $o]: (Y0 => ((ite @ Y0 @ X2 @ X1) = X2))) @ X3) = $true)) )),
% 1.67/1.60 inference(pi_clausification,[status(thm)],[f30])).
% 1.67/1.60 thf(f30,plain,(
% 1.67/1.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $o @ (^[Y0 : $o]: (Y0 => ((ite @ Y0 @ X2 @ X1) = X2)))) = $true)) )),
% 1.67/1.60 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.67/1.60 thf(f29,plain,(
% 1.67/1.60 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (Y1 => ((ite @ Y1 @ Y0 @ X1) = Y0))))) @ X2) = $true)) )),
% 1.67/1.60 inference(pi_clausification,[status(thm)],[f28])).
% 1.67/1.60 thf(f28,plain,(
% 1.67/1.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (Y1 => ((ite @ Y1 @ Y0 @ X1) = Y0)))))) = $true)) )),
% 1.67/1.60 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.67/1.60 thf(f27,plain,(
% 1.67/1.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1))))))) @ X1) = $true)) )),
% 1.67/1.60 inference(pi_clausification,[status(thm)],[f25])).
% 1.67/1.60 thf(f25,plain,(
% 1.67/1.60 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1)))))))) = $true)),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.67/1.60 thf(f278,plain,(
% 1.67/1.60 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $o,X6 : $i,X7 : $i,X4 : $i > $i,X5 : $i] : (((s @ zero) != (ite @ (X0 @ zero) @ (X2 @ zero) @ (X4 @ zero))) | (zero != X5) | ((X2 @ (s @ (s @ zero))) != X7) | ((X2 @ (s @ zero)) != X3) | ((X4 @ (s @ zero)) != X5) | ((X0 @ (s @ (s @ zero))) = $true) | ((X0 @ (s @ zero)) = $true) | (zero != X6) | ((X4 @ (s @ (s @ zero))) != X6)) ) | ~spl0_24),
% 1.67/1.60 inference(avatar_component_clause,[status(thm)],[f277])).
% 1.67/1.60 thf(f1343,plain,(
% 1.67/1.60 spl0_35 | spl0_35 | ~spl0_77),
% 1.67/1.60 inference(avatar_split_clause,[status(thm)],[f1342,f844,f362,f362])).
% 1.67/1.60 thf(f1342,plain,(
% 1.67/1.60 ( ! [X0 : $i,X1 : $i] : ((zero != X1) | (zero != X0)) ) | ~spl0_77),
% 1.67/1.60 inference(duplicate_literal_removal,[status(thm)],[f1341])).
% 1.67/1.60 thf(f1341,plain,(
% 1.67/1.60 ( ! [X0 : $i,X1 : $i] : ((zero != X0) | (zero != X0) | (zero != X1)) ) | ~spl0_77),
% 1.67/1.60 inference(beta_eta_normalization,[status(thm)],[f1338])).
% 1.67/1.60 thf(f1338,plain,(
% 1.67/1.60 ( ! [X0 : $i,X1 : $i] : ((((^[Y0 : $i]: (zero)) @ (s @ (s @ zero))) != X0) | (((^[Y0 : $i]: (zero)) @ zero) != X1) | (zero != X0)) ) | ~spl0_77),
% 1.67/1.60 inference(equality_resolution,[status(thm)],[f1301])).
% 1.67/1.60 thf(f1301,plain,(
% 1.67/1.60 ( ! [X2 : $i,X0 : $i,X1 : $i > $i] : ((zero != (X1 @ (s @ zero))) | (zero != X0) | ((X1 @ zero) != X2) | ((X1 @ (s @ (s @ zero))) != X0)) ) | ~spl0_77),
% 1.67/1.60 inference(equality_resolution,[status(thm)],[f845])).
% 1.67/1.60 thf(f845,plain,(
% 1.67/1.60 ( ! [X6 : $i,X7 : $i,X4 : $i > $i,X5 : $i] : ((zero != X7) | ((X4 @ (s @ zero)) != X7) | ((X4 @ (s @ (s @ zero))) != X6) | ((X4 @ zero) != X5) | (zero != X6)) ) | ~spl0_77),
% 1.67/1.60 inference(avatar_component_clause,[status(thm)],[f844])).
% 1.67/1.60 thf(f1279,plain,(
% 1.67/1.60 spl0_106 | spl0_106 | ~spl0_76),
% 1.67/1.60 inference(avatar_split_clause,[status(thm)],[f1275,f841,f1277,f1277])).
% 1.67/1.60 thf(f1275,plain,(
% 1.67/1.60 ( ! [X2 : $i,X3 : $i] : (((s @ zero) != X2) | ((s @ zero) != X3)) ) | ~spl0_76),
% 1.67/1.60 inference(beta_eta_normalization,[status(thm)],[f1271])).
% 1.67/1.60 thf(f1271,plain,(
% 1.67/1.60 ( ! [X2 : $i,X3 : $i] : ((((^[Y0 : $i]: (s @ ((^[Y1 : $i]: (zero)) @ Y0))) @ (s @ zero)) != X3) | (((^[Y0 : $i]: (s @ ((^[Y1 : $i]: (zero)) @ Y0))) @ (s @ (s @ zero))) != X2)) ) | ~spl0_76),
% 1.67/1.60 inference(equality_resolution,[status(thm)],[f1239])).
% 1.67/1.60 thf(f1239,plain,(
% 1.67/1.60 ( ! [X2 : $i,X0 : $i > $i,X1 : $i] : (((s @ zero) != (X0 @ zero)) | ((X0 @ (s @ (s @ zero))) != X1) | ((X0 @ (s @ zero)) != X2)) ) | ~spl0_76),
% 1.67/1.60 inference(equality_resolution,[status(thm)],[f842])).
% 1.67/1.60 thf(f842,plain,(
% 1.67/1.60 ( ! [X2 : $i > $i,X3 : $i,X8 : $i,X9 : $i] : (((s @ zero) != X3) | ((X2 @ (s @ zero)) != X9) | ((X2 @ (s @ (s @ zero))) != X8) | ((X2 @ zero) != X3)) ) | ~spl0_76),
% 1.67/1.60 inference(avatar_component_clause,[status(thm)],[f841])).
% 1.67/1.60 thf(f1117,plain,(
% 1.67/1.60 spl0_4 | spl0_24 | ~spl0_3),
% 1.67/1.60 inference(avatar_split_clause,[status(thm)],[f1116,f64,f277,f67])).
% 1.67/1.60 thf(f1116,plain,(
% 1.67/1.60 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $o,X1 : $o,X6 : $i,X7 : $i,X4 : $i > $i,X5 : $i] : (((X4 @ (s @ (s @ zero))) != X6) | ((X0 @ (s @ zero)) = $true) | ((s @ zero) != (ite @ (X0 @ zero) @ (X2 @ zero) @ (X4 @ zero))) | ((X2 @ (s @ zero)) != X3) | (zero != X6) | ($true = X1) | ((X2 @ (s @ (s @ zero))) != X7) | ((X4 @ (s @ zero)) != X5) | (zero != X5) | ((X0 @ (s @ (s @ zero))) = $true)) ) | ~spl0_3),
% 1.67/1.60 inference(duplicate_literal_removal,[status(thm)],[f1114])).
% 1.67/1.60 thf(f1114,plain,(
% 1.67/1.60 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $o,X1 : $o,X6 : $i,X7 : $i,X4 : $i > $i,X5 : $i] : (((X2 @ (s @ (s @ zero))) != X7) | ((X2 @ (s @ zero)) != X3) | ((X0 @ (s @ (s @ zero))) = $true) | ((X0 @ (s @ zero)) = $true) | ($true = X1) | ($true = X1) | (zero != X6) | ((X4 @ (s @ (s @ zero))) != X6) | ((s @ zero) != (ite @ (X0 @ zero) @ (X2 @ zero) @ (X4 @ zero))) | (zero != X5) | ((X4 @ (s @ zero)) != X5)) ) | ~spl0_3),
% 1.67/1.60 inference(binary_proxy_clausification,[status(thm)],[f1099])).
% 1.67/1.60 thf(f1099,plain,(
% 1.67/1.60 ( ! [X2 : $i > $i,X3 : $i,X0 : $i > $o,X1 : $o,X6 : $i,X7 : $i,X4 : $i > $i,X5 : $i] : (((X2 @ (s @ zero)) != X3) | (zero != X5) | ((X4 @ (s @ zero)) != X5) | ((X0 @ (s @ (s @ zero))) = $true) | (zero != X6) | ((X0 @ (s @ zero)) != X1) | ($true = X1) | ((s @ zero) != (ite @ (X0 @ zero) @ (X2 @ zero) @ (X4 @ zero))) | ((X2 @ (s @ (s @ zero))) != X7) | ((X4 @ (s @ (s @ zero))) != X6)) ) | ~spl0_3),
% 1.67/1.60 inference(constrained_superposition,[status(thm)],[f65,f47])).
% 1.67/1.60 thf(f65,plain,(
% 1.67/1.60 ( ! [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) | ((X1 @ (s @ (s @ zero))) = $true) | (zero != X2) | ((s @ zero) != (ite @ (X1 @ zero) @ (X5 @ zero) @ (X3 @ zero))) | ((X5 @ (s @ (s @ zero))) != X4)) ) | ~spl0_3),
% 1.67/1.60 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.67/1.60 thf(f571,plain,(
% 1.67/1.60 ~spl0_4 | spl0_9),
% 1.67/1.60 inference(avatar_contradiction_clause,[status(thm)],[f570])).
% 1.67/1.60 thf(f570,plain,(
% 1.67/1.60 $false | (~spl0_4 | spl0_9)),
% 1.67/1.60 inference(equality_resolution,[status(thm)],[f531])).
% 1.67/1.60 thf(f531,plain,(
% 1.67/1.60 ( ! [X0 : $o] : (($false != X0)) ) | (~spl0_4 | spl0_9)),
% 1.67/1.60 inference(superposition,[status(thm)],[f98,f68])).
% 1.67/1.60 thf(f68,plain,(
% 1.67/1.60 ( ! [X0 : $o] : (($true = X0)) ) | ~spl0_4),
% 1.67/1.60 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.67/1.60 thf(f98,plain,(
% 1.67/1.60 ($false != $true) | spl0_9),
% 1.67/1.60 inference(avatar_component_clause,[status(thm)],[f96])).
% 1.67/1.60 thf(f96,definition,(
% 1.67/1.60 spl0_9 <=> ($false = $true)),
% 1.67/1.60 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.67/1.60 thf(f229,plain,(
% 1.67/1.60 ~spl0_9),
% 1.67/1.60 inference(avatar_contradiction_clause,[status(thm)],[f228])).
% 1.67/1.60 thf(f228,plain,(
% 1.67/1.60 $false | ~spl0_9),
% 1.67/1.60 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.67/1.60 thf(f97,plain,(
% 1.67/1.60 ($false = $true) | ~spl0_9),
% 1.67/1.60 inference(avatar_component_clause,[status(thm)],[f96])).
% 1.67/1.60 thf(f224,plain,(
% 1.67/1.60 ~spl0_7 | spl0_9),
% 1.67/1.60 inference(avatar_contradiction_clause,[status(thm)],[f223])).
% 1.67/1.60 thf(f223,plain,(
% 1.67/1.60 $false | (~spl0_7 | spl0_9)),
% 1.67/1.60 inference(trivial_inequality_removal,[status(thm)],[f221])).
% 1.67/1.60 thf(f221,plain,(
% 1.67/1.60 ($false != $false) | (~spl0_7 | spl0_9)),
% 1.67/1.60 inference(superposition,[status(thm)],[f98,f86])).
% 1.67/1.60 thf(f86,plain,(
% 1.67/1.60 ( ! [X0 : $o] : (($false = X0)) ) | ~spl0_7),
% 1.67/1.60 inference(avatar_component_clause,[status(thm)],[f85])).
% 1.67/1.60 % SZS output end Proof for DTF2THF_3149
% 1.67/1.60 % (3362)------------------------------
% 1.67/1.60 % (3362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.60 % (3362)Termination reason: Refutation
% 1.67/1.60
% 1.67/1.60 % (3362)Memory used [KB]: 6780
% 1.67/1.60 % (3362)Time elapsed: 0.120 s
% 1.67/1.60 % (3362)Instructions burned: 357 (million)
% 1.67/1.60 % (3362)------------------------------
% 1.67/1.60 % (3362)------------------------------
% 1.67/1.60 % (3303)Success in time 0.272 s
%------------------------------------------------------------------------------