%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU970^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:52 AM UTC 2026
% Result : Theorem 1.56s 1.33s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 6
% Syntax : Number of formulae : 77 ( 28 unt; 0 typ; 3 def)
% Number of atoms : 513 ( 127 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 578 ( 29 ~; 65 |; 33 &; 371 @)
% ( 3 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 9 con; 0-2 aty)
% ( 28 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 92 ( 48 ^; 35 !; 9 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
s: $i > $i ).
thf(func_def_1,type,
cCKB_E2: $i > $i > $o ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK4: $i > $o ).
thf(func_def_18,type,
sK5: ( $i > $o ) > $i ).
thf(func_def_19,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_20,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f125,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f65,f88,f110,f124]) ).
thf(f124,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[status(thm)],[f123]) ).
thf(f123,plain,
( $false
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
( ( $false = $true )
| ~ spl3_5 ),
inference(backward_demodulation,[status(thm)],[f26,f108]) ).
thf(f108,plain,
( ( $false
= ( sK4 @ sK2 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f106]) ).
thf(f106,definition,
( spl3_5
<=> ( $false
= ( sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f26,plain,
( $true
= ( sK4 @ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( sK4 @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ ( s @ Y0 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( ( sK4 @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ ( s @ Y0 ) ) ) ) ) )
=> ( sK4 @ sK0 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ sK2 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK0 ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ sK2 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK0 ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ sK2
@ sK0 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f15,f16]) ).
thf(f16,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) )
& ( X2 @ X0 ) )
=> ( X2 @ X1 ) ) )
= cCKB_E2 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) )
& ( X2 @ X0 ) )
=> ( X2 @ X1 ) ) )
= cCKB_E2 ),
file('/export/starexec/sandbox2/tmp/tmp.LZ9nFtwbHO/DTF2THF_27547.p',cCKB_E2_def) ).
thf(f15,plain,
( ( cCKB_E2 @ sK2 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( cCKB_E2 @ sK2 @ sK0 )
!= $true )
& ( $true
= ( cCKB_E2 @ sK2 @ sK1 ) )
& ( ( cCKB_E2 @ sK1 @ sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( cCKB_E2 @ X2 @ X0 )
!= $true )
& ( ( cCKB_E2 @ X2 @ X1 )
= $true )
& ( ( cCKB_E2 @ X1 @ X0 )
= $true ) )
=> ( ( ( cCKB_E2 @ sK2 @ sK0 )
!= $true )
& ( $true
= ( cCKB_E2 @ sK2 @ sK1 ) )
& ( ( cCKB_E2 @ sK1 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( ( cCKB_E2 @ X2 @ X0 )
!= $true )
& ( ( cCKB_E2 @ X2 @ X1 )
= $true )
& ( ( cCKB_E2 @ X1 @ X0 )
= $true ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( ( cCKB_E2 @ X2 @ X0 )
!= $true )
& ( ( cCKB_E2 @ X1 @ X0 )
= $true )
& ( ( cCKB_E2 @ X2 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( cCKB_E2 @ X1 @ X0 )
= $true )
& ( ( cCKB_E2 @ X2 @ X1 )
= $true ) )
=> ( ( cCKB_E2 @ X2 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( ( cCKB_E2 @ X2 @ X1 )
& ( cCKB_E2 @ X1 @ X0 ) )
=> ( cCKB_E2 @ X2 @ X0 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X4: $i,X1: $i,X0: $i] :
( ( ( cCKB_E2 @ X0 @ X1 )
& ( cCKB_E2 @ X1 @ X4 ) )
=> ( cCKB_E2 @ X0 @ X4 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X4: $i,X1: $i,X0: $i] :
( ( ( cCKB_E2 @ X0 @ X1 )
& ( cCKB_E2 @ X1 @ X4 ) )
=> ( cCKB_E2 @ X0 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.LZ9nFtwbHO/DTF2THF_27547.p',cCKB_L34000_pme) ).
thf(f110,plain,
( spl3_5
| spl3_2
| ~ spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f103,f55,f59,f106]) ).
thf(f59,definition,
( spl3_2
<=> ( ( sK4 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f55,definition,
( spl3_1
<=> ( $false
= ( sK4 @ ( sK5 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f103,plain,
( ( $false
= ( sK4 @ sK2 ) )
| ( ( sK4 @ sK1 )
= $true )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
( ( $false
= ( sK4 @ sK2 ) )
| ( $false = $true )
| ( ( sK4 @ sK1 )
= $true )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f38,f57]) ).
thf(f57,plain,
( ( $false
= ( sK4 @ ( sK5 @ sK4 ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f38,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( X1 @ sK2 ) )
| ( ( X1 @ sK1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i > $o] :
( ( $false
= ( ( X1 @ ( sK5 @ X1 ) )
=> ( X1 @ ( s @ ( s @ ( sK5 @ X1 ) ) ) ) ) )
| ( ( X1 @ sK1 )
= $true )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i > $o] :
( ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) )
@ ( sK5 @ X1 ) ) )
| ( ( X1 @ sK1 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i > $o] :
( ( ( X1 @ sK1 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) ) )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i > $o] :
( ( ( X1 @ sK1 )
= $true )
| ( ( ( X1 @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i > $o] :
( ( ( ( X1 @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) ) )
=> ( X1 @ sK1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( ( Y0 @ sK2 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ sK2 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ sK2
@ sK1 )
= $true ),
inference(definition_unfolding,[status(thm)],[f14,f16]) ).
thf(f14,plain,
( $true
= ( cCKB_E2 @ sK2 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f88,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[status(thm)],[f87]) ).
thf(f87,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
( ( $false = $true )
| ~ spl3_2 ),
inference(backward_demodulation,[status(thm)],[f61,f83]) ).
thf(f83,plain,
( ( ( sK4 @ sK1 )
= $false )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ( sK4 @ sK1 )
= $false )
| ( $false = $true )
| ~ spl3_2 ),
inference(forward_demodulation,[status(thm)],[f81,f23]) ).
thf(f23,plain,
( ( sK4 @ sK0 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f81,plain,
( ( ( sK4 @ sK1 )
= $false )
| ( ( sK4 @ sK0 )
= $true )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $false = $true )
| ( ( sK4 @ sK1 )
= $false )
| ( ( sK4 @ sK0 )
= $true )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f47,f73]) ).
thf(f73,plain,
( ( $false
= ( sK4 @ ( sK6 @ sK4 ) ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $false = $true )
| ( $false
= ( sK4 @ ( sK6 @ sK4 ) ) )
| ~ spl3_2 ),
inference(forward_demodulation,[status(thm)],[f71,f61]) ).
thf(f71,plain,
( ( ( sK4 @ sK1 )
= $false )
| ( $false
= ( sK4 @ ( sK6 @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ( sK4 @ sK1 )
= $false )
| ( $false
= ( sK4 @ ( sK6 @ sK4 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f69,f23]) ).
thf(f69,plain,
( ( ( sK4 @ sK0 )
= $true )
| ( $false
= ( sK4 @ ( sK6 @ sK4 ) ) )
| ( ( sK4 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ( sK4 @ sK1 )
= $false )
| ( $false = $true )
| ( $false
= ( sK4 @ ( sK6 @ sK4 ) ) )
| ( ( sK4 @ sK0 )
= $true ) ),
inference(superposition,[status(thm)],[f29,f46]) ).
thf(f46,plain,
! [X1: $i > $o] :
( ( $false
= ( X1 @ ( s @ ( s @ ( sK6 @ X1 ) ) ) ) )
| ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ sK1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ sK1 )
= $false )
| ( ( ( X1 @ ( sK6 @ X1 ) )
=> ( X1 @ ( s @ ( s @ ( sK6 @ X1 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: $i > $o] :
( ( ( X1 @ sK1 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) )
@ ( sK6 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(sigma_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: $i > $o] :
( ( ( X1 @ sK1 )
= $false )
| ( $true
= ( X1 @ sK0 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: $i > $o] :
( ( $false
= ( ( X1 @ sK1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) ) ) )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X1: $i > $o] :
( $true
= ( ( ( X1 @ sK1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) ) )
=> ( X1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( ( Y0 @ sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ sK1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ sK1
@ sK0 )
= $true ),
inference(definition_unfolding,[status(thm)],[f13,f16]) ).
thf(f13,plain,
( ( cCKB_E2 @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f29,plain,
! [X1: $i] :
( ( ( sK4 @ ( s @ ( s @ X1 ) ) )
= $true )
| ( $false
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( ( ( sK4 @ X1 )
=> ( sK4 @ ( s @ ( s @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ ( s @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ ( s @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f47,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ sK1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f61,plain,
( ( ( sK4 @ sK1 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f65,plain,
( spl3_2
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f64,f55,f59]) ).
thf(f64,plain,
( ( ( sK4 @ sK1 )
= $true )
| ( $false
= ( sK4 @ ( sK5 @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $false
= ( sK4 @ ( sK5 @ sK4 ) ) )
| ( ( sK4 @ sK1 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f50,f26]) ).
thf(f50,plain,
( ( $false
= ( sK4 @ ( sK5 @ sK4 ) ) )
| ( $false
= ( sK4 @ sK2 ) )
| ( ( sK4 @ sK1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false
= ( sK4 @ sK2 ) )
| ( ( sK4 @ sK1 )
= $true )
| ( $false
= ( sK4 @ ( sK5 @ sK4 ) ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f37,f29]) ).
thf(f37,plain,
! [X1: $i > $o] :
( ( $false
= ( X1 @ ( s @ ( s @ ( sK5 @ X1 ) ) ) ) )
| ( $false
= ( X1 @ sK2 ) )
| ( ( X1 @ sK1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU970^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n001.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 12:38:20 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.39 ---- Original DTF file ---
% 0.19/0.39 thf(spec,logic,$$dhol).
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 % File : SEU970^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.19/0.39 % Domain : Set Theory (Relations)
% 0.19/0.39 % Problem : TPS problem from CHECKERBOARD-RELNS
% 0.19/0.39 % Version : Especial.
% 0.19/0.39 % English :
% 0.19/0.39
% 0.19/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.39 % Source : [Bro09]
% 0.19/0.39 % Names : tps_0745 [Bro09]
% 0.19/0.39
% 0.19/0.39 % Status : Theorem
% 0.19/0.39 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
% 0.19/0.39 % Syntax : Number of formulae : 4 ( 1 unt; 2 typ; 1 def)
% 0.19/0.39 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.19/0.39 % Maximal formula atoms : 3 ( 2 avg)
% 0.19/0.39 % Number of connectives : 17 ( 0 ~; 0 |; 2 &; 12 @)
% 0.19/0.39 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.39 % Maximal formula depth : 8 ( 5 avg)
% 0.19/0.39 % Number of types : 2 ( 0 usr)
% 0.19/0.39 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.39 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.19/0.39 % Number of variables : 7 ( 2 ^; 5 !; 0 ?; 7 :)
% 0.19/0.39 % SPC : TH0_THM_EQU_NAR
% 0.19/0.39
% 0.19/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.39 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 thf(s_type,type,
% 0.19/0.39 s: $i > $i ).
% 0.19/0.39
% 0.19/0.39 thf(cCKB_E2_type,type,
% 0.19/0.39 cCKB_E2: $i > $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(cCKB_E2_def,definition,
% 0.19/0.39 ( cCKB_E2
% 0.19/0.39 = ( ^ [Xx: $i,Xy: $i] :
% 0.19/0.39 ! [Xp: $i > $o] :
% 0.19/0.39 ( ( ( Xp @ Xx )
% 0.19/0.39 & ! [Xu: $i] :
% 0.19/0.39 ( ( Xp @ Xu )
% 0.19/0.39 => ( Xp @ ( s @ ( s @ Xu ) ) ) ) )
% 0.19/0.39 => ( Xp @ Xy ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(cCKB_L34000_pme,conjecture,
% 0.19/0.39 ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.19/0.39 ( ( ( cCKB_E2 @ Xx @ Xy )
% 0.19/0.39 & ( cCKB_E2 @ Xy @ Xz ) )
% 0.19/0.39 => ( cCKB_E2 @ Xx @ Xz ) ) ).
% 0.19/0.39
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 ------------------------
% 1.36/1.29 ---- Embedded in THF ---
% 1.36/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.30 %%% Generated on Tue Feb 24 12:38:21 EST 2026
% 1.36/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.30 %%% Logic specification used:
% 1.36/1.30 %%% thf(spec, logic, $$dhol).
% 1.36/1.30
% 1.36/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.LZ9nFtwbHO/DTF2DTF27547.p
% See solution above
% 1.36/1.30 ------------------------
% 1.56/1.30 ---- Cleaned THF ---
% 1.56/1.31 thf(s_type,type,
% 1.56/1.31 s: $i > $i ).
% 1.56/1.31
% 1.56/1.31 thf(cCKB_E2_type,type,
% 1.56/1.31 cCKB_E2: $i > $i > $o ).
% 1.56/1.31
% 1.56/1.31 thf(cCKB_E2_def,definition,
% 1.56/1.31 ( cCKB_E2
% 1.56/1.31 = ( ^ [Xx: $i,Xy: $i] :
% 1.56/1.31 ! [Xp: $i > $o] :
% 1.56/1.31 ( ( ( Xp @ Xx )
% 1.56/1.31 & ! [Xu: $i] :
% 1.56/1.31 ( ( Xp @ Xu )
% 1.56/1.31 => ( Xp @ ( s @ ( s @ Xu ) ) ) ) )
% 1.56/1.31 => ( Xp @ Xy ) ) ) ) ).
% 1.56/1.31
% 1.56/1.31 thf(cCKB_L34000_pme,conjecture,
% 1.56/1.31 ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.56/1.31 ( ( ( cCKB_E2 @ Xx @ Xy )
% 1.56/1.31 & ( cCKB_E2 @ Xy @ Xz ) )
% 1.56/1.31 => ( cCKB_E2 @ Xx @ Xz ) ) ).
% 1.56/1.31 ------------------------
% 1.56/1.32 % (27649)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_27547 for (2999ds/2Mi)
% 1.56/1.32 % (27648)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27547 for (2999ds/2Mi)
% 1.56/1.32 % (27647)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_27547 for (2999ds/27Mi)
% 1.56/1.32 % (27646)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_27547 for (2999ds/4Mi)
% 1.56/1.32 % (27650)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_27547 for (2999ds/275Mi)
% 1.56/1.33 % (27645)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27547 for (2999ds/183Mi)
% 1.56/1.33 % (27651)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27547 for (2999ds/18Mi)
% 1.56/1.33 % (27648)Instruction limit reached!
% 1.56/1.33 % (27648)------------------------------
% 1.56/1.33 % (27648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (27648)Termination reason: Unknown
% 1.56/1.33 % (27648)Termination phase: Saturation
% 1.56/1.33 % (27649)Instruction limit reached!
% 1.56/1.33 % (27649)------------------------------
% 1.56/1.33 % (27649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (27649)Termination reason: Unknown
% 1.56/1.33 % (27649)Termination phase: Saturation
% 1.56/1.33
% 1.56/1.33 % (27649)Memory used [KB]: 5500
% 1.56/1.33 % (27649)Time elapsed: 0.003 s
% 1.56/1.33 % (27649)Instructions burned: 2 (million)
% 1.56/1.33 % (27649)------------------------------
% 1.56/1.33 % (27649)------------------------------
% 1.56/1.33
% 1.56/1.33 % (27648)Memory used [KB]: 5373
% 1.56/1.33 % (27648)Time elapsed: 0.003 s
% 1.56/1.33 % (27648)Instructions burned: 2 (million)
% 1.56/1.33 % (27648)------------------------------
% 1.56/1.33 % (27648)------------------------------
% 1.56/1.33 % (27650)Refutation not found, incomplete strategy
% 1.56/1.33 % (27650)------------------------------
% 1.56/1.33 % (27650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (27650)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.33
% 1.56/1.33
% 1.56/1.33 % (27650)Memory used [KB]: 5500
% 1.56/1.33 % (27650)Time elapsed: 0.003 s
% 1.56/1.33 % (27650)Instructions burned: 2 (million)
% 1.56/1.33 % (27650)------------------------------
% 1.56/1.33 % (27650)------------------------------
% 1.56/1.33 % (27646)Instruction limit reached!
% 1.56/1.33 % (27646)------------------------------
% 1.56/1.33 % (27646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (27646)Termination reason: Unknown
% 1.56/1.33 % (27646)Termination phase: Saturation
% 1.56/1.33
% 1.56/1.33 % (27646)Memory used [KB]: 5500
% 1.56/1.33 % (27646)Time elapsed: 0.005 s
% 1.56/1.33 % (27646)Instructions burned: 5 (million)
% 1.56/1.33 % (27646)------------------------------
% 1.56/1.33 % (27646)------------------------------
% 1.56/1.33 % (27647)First to succeed.
% 1.56/1.33 % (27647)Refutation found. Thanks to Tanya!
% 1.56/1.33 % SZS status Theorem for DTF2THF_27547
% 1.56/1.33 % SZS output start Proof for DTF2THF_27547
% 1.56/1.33 thf(func_def_0, type, s: $i > $i).
% 1.56/1.33 thf(func_def_1, type, cCKB_E2: $i > $i > $o).
% 1.56/1.33 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.56/1.33 thf(func_def_17, type, sK4: $i > $o).
% 1.56/1.33 thf(func_def_18, type, sK5: ($i > $o) > $i).
% 1.56/1.33 thf(func_def_19, type, sK6: ($i > $o) > $i).
% 1.56/1.33 thf(func_def_20, type, ph7: !>[X0: $tType]:(X0)).
% 1.56/1.33 thf(f125,plain,(
% 1.56/1.33 $false),
% 1.56/1.33 inference(avatar_sat_refutation,[status(thm)],[f65,f88,f110,f124])).
% 1.56/1.33 thf(f124,plain,(
% 1.56/1.33 ~spl3_5),
% 1.56/1.33 inference(avatar_contradiction_clause,[status(thm)],[f123])).
% 1.56/1.33 thf(f123,plain,(
% 1.56/1.33 $false | ~spl3_5),
% 1.56/1.33 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.56/1.33 thf(f122,plain,(
% 1.56/1.33 ($false = $true) | ~spl3_5),
% 1.56/1.33 inference(backward_demodulation,[status(thm)],[f26,f108])).
% 1.56/1.33 thf(f108,plain,(
% 1.56/1.33 ($false = (sK4 @ sK2)) | ~spl3_5),
% 1.56/1.33 inference(avatar_component_clause,[status(thm)],[f106])).
% 1.56/1.33 thf(f106,definition,(
% 1.56/1.33 spl3_5 <=> ($false = (sK4 @ sK2))),
% 1.56/1.33 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.56/1.33 thf(f26,plain,(
% 1.56/1.33 ($true = (sK4 @ sK2))),
% 1.56/1.33 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.56/1.33 thf(f24,plain,(
% 1.56/1.33 (((sK4 @ sK2) & (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ (s @ Y0))))))) = $true)),
% 1.56/1.33 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.56/1.33 thf(f22,plain,(
% 1.56/1.33 ((((sK4 @ sK2) & (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ (s @ Y0))))))) => (sK4 @ sK0)) = $false)),
% 1.56/1.33 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.56/1.33 thf(f21,plain,(
% 1.56/1.33 ($false = ((^[Y0 : $i > $o]: (((Y0 @ sK2) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1))))))) => (Y0 @ sK0))) @ sK4))),
% 1.56/1.33 inference(sigma_clausification,[status(thm)],[f20])).
% 1.56/1.33 thf(f20,plain,(
% 1.56/1.33 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ sK2) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1))))))) => (Y0 @ sK0)))) != $true)),
% 1.56/1.33 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.56/1.33 thf(f17,plain,(
% 1.56/1.33 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ Y0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3))))))) => (Y2 @ Y1))))))) @ sK2 @ sK0) != $true)),
% 1.56/1.33 inference(definition_unfolding,[status(thm)],[f15,f16])).
% 1.56/1.33 thf(f16,plain,(
% 1.56/1.33 (cCKB_E2 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ Y0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3))))))) => (Y2 @ Y1))))))))),
% 1.56/1.33 inference(cnf_transformation,[status(thm)],[f8])).
% 1.56/1.33 thf(f8,plain,(
% 1.56/1.33 (cCKB_E2 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ Y0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3))))))) => (Y2 @ Y1))))))))),
% 1.56/1.33 inference(fool_elimination,[status(thm)],[f7])).
% 1.56/1.33 thf(f7,plain,(
% 1.56/1.33 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((! [X3 : $i] : ((X2 @ X3) => (X2 @ (s @ (s @ X3)))) & (X2 @ X0)) => (X2 @ X1)))) = cCKB_E2)),
% 1.56/1.33 inference(rectify,[status(thm)],[f1])).
% 1.56/1.33 thf(f1,axiom,(
% 1.56/1.33 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((! [X3 : $i] : ((X2 @ X3) => (X2 @ (s @ (s @ X3)))) & (X2 @ X0)) => (X2 @ X1)))) = cCKB_E2)),
% 1.56/1.33 file('/export/starexec/sandbox2/tmp/tmp.LZ9nFtwbHO/DTF2THF_27547.p',cCKB_E2_def)).
% 1.56/1.33 thf(f15,plain,(
% 1.56/1.33 ((cCKB_E2 @ sK2 @ sK0) != $true)),
% 1.56/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.33 thf(f12,plain,(
% 1.56/1.33 ((cCKB_E2 @ sK2 @ sK0) != $true) & ($true = (cCKB_E2 @ sK2 @ sK1)) & ((cCKB_E2 @ sK1 @ sK0) = $true)),
% 1.56/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11])).
% 1.56/1.33 thf(f11,plain,(
% 1.56/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (((cCKB_E2 @ X2 @ X0) != $true) & ((cCKB_E2 @ X2 @ X1) = $true) & ((cCKB_E2 @ X1 @ X0) = $true)) => (((cCKB_E2 @ sK2 @ sK0) != $true) & ($true = (cCKB_E2 @ sK2 @ sK1)) & ((cCKB_E2 @ sK1 @ sK0) = $true))),
% 1.56/1.33 introduced(definition,[],[choice_axiom])).
% 1.56/1.33 thf(f10,plain,(
% 1.56/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (((cCKB_E2 @ X2 @ X0) != $true) & ((cCKB_E2 @ X2 @ X1) = $true) & ((cCKB_E2 @ X1 @ X0) = $true))),
% 1.56/1.33 inference(flattening,[status(thm)],[f9])).
% 1.56/1.33 thf(f9,plain,(
% 1.56/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (((cCKB_E2 @ X2 @ X0) != $true) & (((cCKB_E2 @ X1 @ X0) = $true) & ((cCKB_E2 @ X2 @ X1) = $true)))),
% 1.56/1.33 inference(ennf_transformation,[status(thm)],[f6])).
% 1.56/1.33 thf(f6,plain,(
% 1.56/1.33 ~! [X0 : $i,X1 : $i,X2 : $i] : ((((cCKB_E2 @ X1 @ X0) = $true) & ((cCKB_E2 @ X2 @ X1) = $true)) => ((cCKB_E2 @ X2 @ X0) = $true))),
% 1.56/1.33 inference(fool_elimination,[status(thm)],[f5])).
% 1.56/1.33 thf(f5,plain,(
% 1.56/1.33 ~! [X0 : $i,X1 : $i,X2 : $i] : (((cCKB_E2 @ X2 @ X1) & (cCKB_E2 @ X1 @ X0)) => (cCKB_E2 @ X2 @ X0))),
% 1.56/1.33 inference(rectify,[status(thm)],[f3])).
% 1.56/1.33 thf(f3,negated_conjecture,(
% 1.56/1.33 ~! [X4 : $i,X1 : $i,X0 : $i] : (((cCKB_E2 @ X0 @ X1) & (cCKB_E2 @ X1 @ X4)) => (cCKB_E2 @ X0 @ X4))),
% 1.56/1.33 inference(negated_conjecture,[status(cth)],[f2])).
% 1.56/1.33 thf(f2,conjecture,(
% 1.56/1.33 ! [X4 : $i,X1 : $i,X0 : $i] : (((cCKB_E2 @ X0 @ X1) & (cCKB_E2 @ X1 @ X4)) => (cCKB_E2 @ X0 @ X4))),
% 1.56/1.33 file('/export/starexec/sandbox2/tmp/tmp.LZ9nFtwbHO/DTF2THF_27547.p',cCKB_L34000_pme)).
% 1.56/1.33 thf(f110,plain,(
% 1.56/1.33 spl3_5 | spl3_2 | ~spl3_1),
% 1.56/1.33 inference(avatar_split_clause,[status(thm)],[f103,f55,f59,f106])).
% 1.56/1.33 thf(f59,definition,(
% 1.56/1.33 spl3_2 <=> ((sK4 @ sK1) = $true)),
% 1.56/1.33 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.56/1.33 thf(f55,definition,(
% 1.56/1.33 spl3_1 <=> ($false = (sK4 @ (sK5 @ sK4)))),
% 1.56/1.33 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.56/1.33 thf(f103,plain,(
% 1.56/1.33 ($false = (sK4 @ sK2)) | ((sK4 @ sK1) = $true) | ~spl3_1),
% 1.56/1.33 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.56/1.33 thf(f102,plain,(
% 1.56/1.33 ($false = (sK4 @ sK2)) | ($false = $true) | ((sK4 @ sK1) = $true) | ~spl3_1),
% 1.56/1.33 inference(superposition,[status(thm)],[f38,f57])).
% 1.56/1.33 thf(f57,plain,(
% 1.56/1.33 ($false = (sK4 @ (sK5 @ sK4))) | ~spl3_1),
% 1.56/1.33 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.56/1.33 thf(f38,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (((X1 @ (sK5 @ X1)) = $true) | ($false = (X1 @ sK2)) | ((X1 @ sK1) = $true)) )),
% 1.56/1.33 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.56/1.33 thf(f36,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (($false = ((X1 @ (sK5 @ X1)) => (X1 @ (s @ (s @ (sK5 @ X1)))))) | ((X1 @ sK1) = $true) | ($false = (X1 @ sK2))) )),
% 1.56/1.33 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.56/1.33 thf(f35,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (($false = (X1 @ sK2)) | ($false = ((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0))))) @ (sK5 @ X1))) | ((X1 @ sK1) = $true)) )),
% 1.56/1.33 inference(sigma_clausification,[status(thm)],[f34])).
% 1.56/1.33 thf(f34,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (((X1 @ sK1) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0))))))) | ($false = (X1 @ sK2))) )),
% 1.56/1.33 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.56/1.33 thf(f33,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (((X1 @ sK1) = $true) | (((X1 @ sK2) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0))))))) = $false)) )),
% 1.56/1.33 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.56/1.33 thf(f32,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (((((X1 @ sK2) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0))))))) => (X1 @ sK1)) = $true)) )),
% 1.56/1.33 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.56/1.33 thf(f31,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (((Y0 @ sK2) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1))))))) => (Y0 @ sK1))) @ X1) = $true)) )),
% 1.56/1.33 inference(pi_clausification,[status(thm)],[f30])).
% 1.56/1.33 thf(f30,plain,(
% 1.56/1.33 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ sK2) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1))))))) => (Y0 @ sK1)))) = $true)),
% 1.56/1.33 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.56/1.33 thf(f18,plain,(
% 1.56/1.33 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ Y0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3))))))) => (Y2 @ Y1))))))) @ sK2 @ sK1) = $true)),
% 1.56/1.33 inference(definition_unfolding,[status(thm)],[f14,f16])).
% 1.56/1.33 thf(f14,plain,(
% 1.56/1.33 ($true = (cCKB_E2 @ sK2 @ sK1))),
% 1.56/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.33 thf(f88,plain,(
% 1.56/1.33 ~spl3_2),
% 1.56/1.33 inference(avatar_contradiction_clause,[status(thm)],[f87])).
% 1.56/1.33 thf(f87,plain,(
% 1.56/1.33 $false | ~spl3_2),
% 1.56/1.33 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.56/1.33 thf(f86,plain,(
% 1.56/1.33 ($false = $true) | ~spl3_2),
% 1.56/1.33 inference(backward_demodulation,[status(thm)],[f61,f83])).
% 1.56/1.33 thf(f83,plain,(
% 1.56/1.33 ((sK4 @ sK1) = $false) | ~spl3_2),
% 1.56/1.33 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.56/1.33 thf(f82,plain,(
% 1.56/1.33 ((sK4 @ sK1) = $false) | ($false = $true) | ~spl3_2),
% 1.56/1.33 inference(forward_demodulation,[status(thm)],[f81,f23])).
% 1.56/1.33 thf(f23,plain,(
% 1.56/1.33 ((sK4 @ sK0) = $false)),
% 1.56/1.33 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.56/1.33 thf(f81,plain,(
% 1.56/1.33 ((sK4 @ sK1) = $false) | ((sK4 @ sK0) = $true) | ~spl3_2),
% 1.56/1.33 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.56/1.33 thf(f79,plain,(
% 1.56/1.33 ($false = $true) | ((sK4 @ sK1) = $false) | ((sK4 @ sK0) = $true) | ~spl3_2),
% 1.56/1.33 inference(superposition,[status(thm)],[f47,f73])).
% 1.56/1.33 thf(f73,plain,(
% 1.56/1.33 ($false = (sK4 @ (sK6 @ sK4))) | ~spl3_2),
% 1.56/1.33 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.56/1.33 thf(f72,plain,(
% 1.56/1.33 ($false = $true) | ($false = (sK4 @ (sK6 @ sK4))) | ~spl3_2),
% 1.56/1.33 inference(forward_demodulation,[status(thm)],[f71,f61])).
% 1.56/1.33 thf(f71,plain,(
% 1.56/1.33 ((sK4 @ sK1) = $false) | ($false = (sK4 @ (sK6 @ sK4)))),
% 1.56/1.33 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.56/1.33 thf(f70,plain,(
% 1.56/1.33 ((sK4 @ sK1) = $false) | ($false = (sK4 @ (sK6 @ sK4))) | ($false = $true)),
% 1.56/1.33 inference(forward_demodulation,[status(thm)],[f69,f23])).
% 1.56/1.33 thf(f69,plain,(
% 1.56/1.33 ((sK4 @ sK0) = $true) | ($false = (sK4 @ (sK6 @ sK4))) | ((sK4 @ sK1) = $false)),
% 1.56/1.33 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.56/1.33 thf(f67,plain,(
% 1.56/1.33 ((sK4 @ sK1) = $false) | ($false = $true) | ($false = (sK4 @ (sK6 @ sK4))) | ((sK4 @ sK0) = $true)),
% 1.56/1.33 inference(superposition,[status(thm)],[f29,f46])).
% 1.56/1.33 thf(f46,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (($false = (X1 @ (s @ (s @ (sK6 @ X1))))) | ($true = (X1 @ sK0)) | ((X1 @ sK1) = $false)) )),
% 1.56/1.33 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.56/1.33 thf(f45,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (($true = (X1 @ sK0)) | ((X1 @ sK1) = $false) | (((X1 @ (sK6 @ X1)) => (X1 @ (s @ (s @ (sK6 @ X1))))) = $false)) )),
% 1.56/1.33 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.56/1.33 thf(f44,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (((X1 @ sK1) = $false) | ($false = ((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0))))) @ (sK6 @ X1))) | ($true = (X1 @ sK0))) )),
% 1.56/1.33 inference(sigma_clausification,[status(thm)],[f43])).
% 1.56/1.33 thf(f43,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (((X1 @ sK1) = $false) | ($true = (X1 @ sK0)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0)))))))) )),
% 1.56/1.33 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.56/1.33 thf(f42,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (($false = ((X1 @ sK1) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0)))))))) | ($true = (X1 @ sK0))) )),
% 1.56/1.33 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.56/1.33 thf(f41,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (($true = (((X1 @ sK1) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0))))))) => (X1 @ sK0)))) )),
% 1.56/1.33 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.56/1.33 thf(f40,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (((Y0 @ sK1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1))))))) => (Y0 @ sK0))) @ X1) = $true)) )),
% 1.56/1.33 inference(pi_clausification,[status(thm)],[f39])).
% 1.56/1.33 thf(f39,plain,(
% 1.56/1.33 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ sK1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1))))))) => (Y0 @ sK0)))) = $true)),
% 1.56/1.33 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.56/1.33 thf(f19,plain,(
% 1.56/1.33 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ Y0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3))))))) => (Y2 @ Y1))))))) @ sK1 @ sK0) = $true)),
% 1.56/1.33 inference(definition_unfolding,[status(thm)],[f13,f16])).
% 1.56/1.33 thf(f13,plain,(
% 1.56/1.33 ((cCKB_E2 @ sK1 @ sK0) = $true)),
% 1.56/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.33 thf(f29,plain,(
% 1.56/1.33 ( ! [X1 : $i] : (((sK4 @ (s @ (s @ X1))) = $true) | ($false = (sK4 @ X1))) )),
% 1.56/1.33 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.56/1.33 thf(f28,plain,(
% 1.56/1.33 ( ! [X1 : $i] : ((((sK4 @ X1) => (sK4 @ (s @ (s @ X1)))) = $true)) )),
% 1.56/1.33 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.56/1.33 thf(f27,plain,(
% 1.56/1.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ (s @ Y0))))) @ X1) = $true)) )),
% 1.56/1.33 inference(pi_clausification,[status(thm)],[f25])).
% 1.56/1.33 thf(f25,plain,(
% 1.56/1.33 ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ (s @ Y0)))))) = $true)),
% 1.56/1.33 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.56/1.33 thf(f47,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (($true = (X1 @ (sK6 @ X1))) | ($true = (X1 @ sK0)) | ((X1 @ sK1) = $false)) )),
% 1.56/1.33 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.56/1.33 thf(f61,plain,(
% 1.56/1.33 ((sK4 @ sK1) = $true) | ~spl3_2),
% 1.56/1.33 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.56/1.33 thf(f65,plain,(
% 1.56/1.33 spl3_2 | spl3_1),
% 1.56/1.33 inference(avatar_split_clause,[status(thm)],[f64,f55,f59])).
% 1.56/1.33 thf(f64,plain,(
% 1.56/1.33 ((sK4 @ sK1) = $true) | ($false = (sK4 @ (sK5 @ sK4)))),
% 1.56/1.33 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.56/1.33 thf(f63,plain,(
% 1.56/1.33 ($false = (sK4 @ (sK5 @ sK4))) | ((sK4 @ sK1) = $true) | ($false = $true)),
% 1.56/1.33 inference(forward_demodulation,[status(thm)],[f50,f26])).
% 1.56/1.33 thf(f50,plain,(
% 1.56/1.33 ($false = (sK4 @ (sK5 @ sK4))) | ($false = (sK4 @ sK2)) | ((sK4 @ sK1) = $true)),
% 1.56/1.33 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.56/1.33 thf(f48,plain,(
% 1.56/1.33 ($false = (sK4 @ sK2)) | ((sK4 @ sK1) = $true) | ($false = (sK4 @ (sK5 @ sK4))) | ($false = $true)),
% 1.56/1.33 inference(superposition,[status(thm)],[f37,f29])).
% 1.56/1.33 thf(f37,plain,(
% 1.56/1.33 ( ! [X1 : $i > $o] : (($false = (X1 @ (s @ (s @ (sK5 @ X1))))) | ($false = (X1 @ sK2)) | ((X1 @ sK1) = $true)) )),
% 1.56/1.33 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.56/1.33 % SZS output end Proof for DTF2THF_27547
% 1.56/1.33 % (27647)------------------------------
% 1.56/1.33 % (27647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (27647)Termination reason: Refutation
% 1.56/1.33
% 1.56/1.33 % (27647)Memory used [KB]: 5500
% 1.56/1.33 % (27647)Time elapsed: 0.010 s
% 1.56/1.33 % (27647)Instructions burned: 10 (million)
% 1.56/1.33 % (27647)------------------------------
% 1.56/1.33 % (27647)------------------------------
% 1.56/1.33 % (27644)Success in time 0.025 s
%------------------------------------------------------------------------------