%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ110^5 : 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 : n023.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 09:28:30 AM UTC 2026
% Result : Theorem 1.63s 1.33s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 65 ( 25 unt; 0 typ; 2 def)
% Number of atoms : 517 ( 105 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 861 ( 22 ~; 54 |; 44 &; 660 @)
% ( 2 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 8 con; 0-2 aty)
% ( 38 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 97 ( 56 ^; 37 !; 4 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
cCKB6_BLACK: $i > $i > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK3: ( $i > $i > $o ) > $i ).
thf(func_def_18,type,
sK4: ( $i > $i > $o ) > $i ).
thf(func_def_19,type,
sK5: $i > $i > $o ).
thf(func_def_20,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f87,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f68,f79,f86]) ).
thf(f86,plain,
( spl2_2
| ~ spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f83,f56,f60]) ).
thf(f60,definition,
( spl2_2
<=> ( $false
= ( sK5 @ ( sK4 @ sK5 ) @ ( sK3 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f56,definition,
( spl2_1
<=> ( $false
= ( sK5 @ ( s @ ( s @ ( sK4 @ sK5 ) ) ) @ ( sK3 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f83,plain,
( ( $false
= ( sK5 @ ( sK4 @ sK5 ) @ ( sK3 @ sK5 ) ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $false = $true )
| ( $false
= ( sK5 @ ( sK4 @ sK5 ) @ ( sK3 @ sK5 ) ) )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f58,f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( ( sK5 @ ( s @ ( s @ X2 ) ) @ X1 )
= $true )
| ( $false
= ( sK5 @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK5 @ X2 @ X1 ) )
| ( $true
= ( ( sK5 @ ( s @ X2 ) @ ( s @ X1 ) )
& ( sK5 @ ( s @ ( s @ X2 ) ) @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK5 @ X2 @ X1 )
=> ( ( sK5 @ ( s @ X2 ) @ ( s @ X1 ) )
& ( sK5 @ ( s @ ( s @ X2 ) ) @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( sK5 @ Y0 @ X1 )
=> ( ( sK5 @ ( s @ Y0 ) @ ( s @ X1 ) )
& ( sK5 @ ( s @ ( s @ Y0 ) ) @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 @ X1 )
=> ( ( sK5 @ ( s @ Y0 ) @ ( s @ X1 ) )
& ( sK5 @ ( s @ ( s @ Y0 ) ) @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK5 @ Y1 @ Y0 )
=> ( ( sK5 @ ( s @ Y1 ) @ ( s @ Y0 ) )
& ( sK5 @ ( s @ ( s @ Y1 ) ) @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK5 @ Y1 @ Y0 )
=> ( ( sK5 @ ( s @ Y1 ) @ ( s @ Y0 ) )
& ( sK5 @ ( s @ ( s @ Y1 ) ) @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( ( sK5 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK5 @ Y1 @ Y0 )
=> ( ( sK5 @ ( s @ Y1 ) @ ( s @ Y0 ) )
& ( sK5 @ ( s @ ( s @ Y1 ) ) @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( $false
= ( ( ( sK5 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK5 @ Y1 @ Y0 )
=> ( ( sK5 @ ( s @ Y1 ) @ ( s @ Y0 ) )
& ( sK5 @ ( s @ ( s @ Y1 ) ) @ Y0 ) ) ) ) ) )
=> ( sK5 @ ( s @ ( s @ sK1 ) ) @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
= ( ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( Y0 @ ( s @ Y2 ) @ ( s @ Y1 ) )
& ( Y0 @ ( s @ ( s @ Y2 ) ) @ Y1 ) ) ) ) ) )
=> ( Y0 @ ( s @ ( s @ sK1 ) ) @ sK0 ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( $true
!= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( Y0 @ ( s @ Y2 ) @ ( s @ Y1 ) )
& ( Y0 @ ( s @ ( s @ Y2 ) ) @ Y1 ) ) ) ) ) )
=> ( Y0 @ ( s @ ( s @ sK1 ) ) @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( Y2 @ ( s @ Y4 ) @ ( s @ Y3 ) )
& ( Y2 @ ( s @ ( s @ Y4 ) ) @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ ( s @ ( s @ sK1 ) )
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f13,f14]) ).
thf(f14,plain,
( cCKB6_BLACK
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( Y2 @ ( s @ Y4 ) @ ( s @ Y3 ) )
& ( Y2 @ ( s @ ( s @ Y4 ) ) @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( cCKB6_BLACK
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( Y2 @ ( s @ Y4 ) @ ( s @ Y3 ) )
& ( Y2 @ ( s @ ( s @ Y4 ) ) @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $i > $o] :
( ( ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( ( X2 @ ( s @ ( s @ X3 ) ) @ X4 )
& ( X2 @ ( s @ X3 ) @ ( s @ X4 ) ) ) )
& ( X2 @ c1 @ c1 ) )
=> ( X2 @ X0 @ X1 ) ) )
= cCKB6_BLACK ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $i > $o] :
( ( ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( ( X2 @ ( s @ ( s @ X3 ) ) @ X4 )
& ( X2 @ ( s @ X3 ) @ ( s @ X4 ) ) ) )
& ( X2 @ c1 @ c1 ) )
=> ( X2 @ X0 @ X1 ) ) )
= cCKB6_BLACK ),
file('/export/starexec/sandbox2/tmp/tmp.u8uG9fSAr6/DTF2THF_6718.p',cCKB6_BLACK_def) ).
thf(f13,plain,
( $true
!= ( cCKB6_BLACK @ ( s @ ( s @ sK1 ) ) @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $true
!= ( cCKB6_BLACK @ ( s @ ( s @ sK1 ) ) @ sK0 ) )
& ( $true
= ( cCKB6_BLACK @ sK1 @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( cCKB6_BLACK @ ( s @ ( s @ X1 ) ) @ X0 ) )
& ( ( cCKB6_BLACK @ X1 @ X0 )
= $true ) )
=> ( ( $true
!= ( cCKB6_BLACK @ ( s @ ( s @ sK1 ) ) @ sK0 ) )
& ( $true
= ( cCKB6_BLACK @ sK1 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i,X1: $i] :
( ( $true
!= ( cCKB6_BLACK @ ( s @ ( s @ X1 ) ) @ X0 ) )
& ( ( cCKB6_BLACK @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $i,X1: $i] :
( ( ( cCKB6_BLACK @ X1 @ X0 )
= $true )
=> ( $true
= ( cCKB6_BLACK @ ( s @ ( s @ X1 ) ) @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i,X1: $i] :
( ( cCKB6_BLACK @ X1 @ X0 )
=> ( cCKB6_BLACK @ ( s @ ( s @ X1 ) ) @ X0 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X4: $i,X3: $i] :
( ( cCKB6_BLACK @ X3 @ X4 )
=> ( cCKB6_BLACK @ ( s @ ( s @ X3 ) ) @ X4 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X4: $i,X3: $i] :
( ( cCKB6_BLACK @ X3 @ X4 )
=> ( cCKB6_BLACK @ ( s @ ( s @ X3 ) ) @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.u8uG9fSAr6/DTF2THF_6718.p',cCKB6_L8000) ).
thf(f58,plain,
( ( $false
= ( sK5 @ ( s @ ( s @ ( sK4 @ sK5 ) ) ) @ ( sK3 @ sK5 ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f79,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f78]) ).
thf(f78,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $false = $true )
| ~ spl2_2 ),
inference(forward_demodulation,[status(thm)],[f76,f45]) ).
thf(f45,plain,
( ( sK5 @ sK1 @ sK0 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $false = $true )
| ( ( sK5 @ sK1 @ sK0 )
= $false ) ),
inference(superposition,[status(thm)],[f41,f32]) ).
thf(f32,plain,
( $false
= ( sK5 @ ( s @ ( s @ sK1 ) ) @ sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f76,plain,
( ( ( sK5 @ sK1 @ sK0 )
= $true )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $false = $true )
| ( ( sK5 @ sK1 @ sK0 )
= $true )
| ~ spl2_2 ),
inference(forward_demodulation,[status(thm)],[f71,f35]) ).
thf(f35,plain,
( $true
= ( sK5 @ c1 @ c1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f71,plain,
( ( $false
= ( sK5 @ c1 @ c1 ) )
| ( ( sK5 @ sK1 @ sK0 )
= $true )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $false
= ( sK5 @ c1 @ c1 ) )
| ( $false = $true )
| ( ( sK5 @ sK1 @ sK0 )
= $true )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f27,f62]) ).
thf(f62,plain,
( ( $false
= ( sK5 @ ( sK4 @ sK5 ) @ ( sK3 @ sK5 ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f27,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ ( sK4 @ X1 ) @ ( sK3 @ X1 ) ) )
| ( $false
= ( X1 @ c1 @ c1 ) )
| ( $true
= ( X1 @ sK1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ( X1 @ ( sK4 @ X1 ) @ ( sK3 @ X1 ) )
=> ( ( X1 @ ( s @ ( sK4 @ X1 ) ) @ ( s @ ( sK3 @ X1 ) ) )
& ( X1 @ ( s @ ( s @ ( sK4 @ X1 ) ) ) @ ( sK3 @ X1 ) ) ) ) )
| ( $false
= ( X1 @ c1 @ c1 ) )
| ( $true
= ( X1 @ sK1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 @ ( sK3 @ X1 ) )
=> ( ( X1 @ ( s @ Y0 ) @ ( s @ ( sK3 @ X1 ) ) )
& ( X1 @ ( s @ ( s @ Y0 ) ) @ ( sK3 @ X1 ) ) ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( X1 @ sK1 @ sK0 ) )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(sigma_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 @ ( sK3 @ X1 ) )
=> ( ( X1 @ ( s @ Y0 ) @ ( s @ ( sK3 @ X1 ) ) )
& ( X1 @ ( s @ ( s @ Y0 ) ) @ ( sK3 @ X1 ) ) ) ) ) )
| ( $false
= ( X1 @ c1 @ c1 ) )
| ( $true
= ( X1 @ sK1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $i > $i > $o] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( ( X1 @ ( s @ Y1 ) @ ( s @ Y0 ) )
& ( X1 @ ( s @ ( s @ Y1 ) ) @ Y0 ) ) ) )
@ ( sK3 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK1 @ sK0 ) )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ sK1 @ sK0 ) )
| ( $false
= ( X1 @ c1 @ c1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( ( X1 @ ( s @ Y1 ) @ ( s @ Y0 ) )
& ( X1 @ ( s @ ( s @ Y1 ) ) @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ sK1 @ sK0 ) )
| ( $false
= ( ( X1 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( ( X1 @ ( s @ Y1 ) @ ( s @ Y0 ) )
& ( X1 @ ( s @ ( s @ Y1 ) ) @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i > $i > $o] :
( $true
= ( ( ( X1 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( ( X1 @ ( s @ Y1 ) @ ( s @ Y0 ) )
& ( X1 @ ( s @ ( s @ Y1 ) ) @ Y0 ) ) ) ) ) )
=> ( X1 @ sK1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( Y0 @ ( s @ Y2 ) @ ( s @ Y1 ) )
& ( Y0 @ ( s @ ( s @ Y2 ) ) @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK1 @ sK0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( Y0 @ ( s @ Y2 ) @ ( s @ Y1 ) )
& ( Y0 @ ( s @ ( s @ Y2 ) ) @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK1 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( Y2 @ ( s @ Y4 ) @ ( s @ Y3 ) )
& ( Y2 @ ( s @ ( s @ Y4 ) ) @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f12,f14]) ).
thf(f12,plain,
( $true
= ( cCKB6_BLACK @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f68,plain,
( spl2_2
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f67,f56,f60]) ).
thf(f67,plain,
( ( $false
= ( sK5 @ ( s @ ( s @ ( sK4 @ sK5 ) ) ) @ ( sK3 @ sK5 ) ) )
| ( $false
= ( sK5 @ ( sK4 @ sK5 ) @ ( sK3 @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $false = $true )
| ( $false
= ( sK5 @ ( sK4 @ sK5 ) @ ( sK3 @ sK5 ) ) )
| ( $false
= ( sK5 @ ( s @ ( s @ ( sK4 @ sK5 ) ) ) @ ( sK3 @ sK5 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f65,f35]) ).
thf(f65,plain,
( ( $false
= ( sK5 @ ( s @ ( s @ ( sK4 @ sK5 ) ) ) @ ( sK3 @ sK5 ) ) )
| ( $false
= ( sK5 @ ( sK4 @ sK5 ) @ ( sK3 @ sK5 ) ) )
| ( $false
= ( sK5 @ c1 @ c1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $false = $true )
| ( $false
= ( sK5 @ ( sK4 @ sK5 ) @ ( sK3 @ sK5 ) ) )
| ( $false
= ( sK5 @ ( s @ ( s @ ( sK4 @ sK5 ) ) ) @ ( sK3 @ sK5 ) ) )
| ( $false
= ( sK5 @ c1 @ c1 ) ) ),
inference(forward_demodulation,[status(thm)],[f49,f45]) ).
thf(f49,plain,
( ( ( sK5 @ sK1 @ sK0 )
= $true )
| ( $false
= ( sK5 @ ( sK4 @ sK5 ) @ ( sK3 @ sK5 ) ) )
| ( $false
= ( sK5 @ ( s @ ( s @ ( sK4 @ sK5 ) ) ) @ ( sK3 @ sK5 ) ) )
| ( $false
= ( sK5 @ c1 @ c1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( sK5 @ sK1 @ sK0 )
= $true )
| ( $false
= ( sK5 @ ( sK4 @ sK5 ) @ ( sK3 @ sK5 ) ) )
| ( $false
= ( sK5 @ ( s @ ( s @ ( sK4 @ sK5 ) ) ) @ ( sK3 @ sK5 ) ) )
| ( $false
= ( sK5 @ c1 @ c1 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f42,f28]) ).
thf(f28,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( s @ ( sK4 @ X1 ) ) @ ( s @ ( sK3 @ X1 ) ) ) )
| ( $true
= ( X1 @ sK1 @ sK0 ) )
| ( $false
= ( X1 @ ( s @ ( s @ ( sK4 @ X1 ) ) ) @ ( sK3 @ X1 ) ) )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ( X1 @ ( s @ ( sK4 @ X1 ) ) @ ( s @ ( sK3 @ X1 ) ) )
& ( X1 @ ( s @ ( s @ ( sK4 @ X1 ) ) ) @ ( sK3 @ X1 ) ) ) )
| ( $true
= ( X1 @ sK1 @ sK0 ) )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( ( sK5 @ ( s @ X2 ) @ ( s @ X1 ) )
= $true )
| ( $false
= ( sK5 @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PUZ110^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n023.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 11:33:49 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : PUZ110^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.29/0.45 % Domain : Puzzles
% 0.29/0.45 % Problem : TPS problem from CHECKERBOARD-THMS
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : tps_0681 [Bro09]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
% 0.29/0.45 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.29/0.45 % Number of atoms : 4 ( 1 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 2 ( 2 avg)
% 0.29/0.45 % Number of connectives : 25 ( 0 ~; 0 |; 2 &; 20 @)
% 0.29/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 8 ( 5 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.29/0.45 % Number of variables : 7 ( 2 ^; 5 !; 0 ?; 7 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.45 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(c1_type,type,
% 0.29/0.45 c1: $i ).
% 0.29/0.45
% 0.29/0.45 thf(s_type,type,
% 0.29/0.45 s: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(cCKB6_BLACK_type,type,
% 0.29/0.45 cCKB6_BLACK: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(cCKB6_BLACK_def,definition,
% 0.29/0.45 ( cCKB6_BLACK
% 0.29/0.45 = ( ^ [Xu: $i,Xv: $i] :
% 0.29/0.45 ! [Xw: $i > $i > $o] :
% 0.29/0.45 ( ( ( Xw @ c1 @ c1 )
% 0.29/0.45 & ! [Xj: $i,Xk: $i] :
% 0.29/0.45 ( ( Xw @ Xj @ Xk )
% 0.29/0.45 => ( ( Xw @ ( s @ ( s @ Xj ) ) @ Xk )
% 0.29/0.45 & ( Xw @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
% 0.29/0.45 => ( Xw @ Xu @ Xv ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(cCKB6_L8000,conjecture,
% 0.29/0.45 ! [Xj: $i,Xk: $i] :
% 0.29/0.45 ( ( cCKB6_BLACK @ Xj @ Xk )
% 0.29/0.45 => ( cCKB6_BLACK @ ( s @ ( s @ Xj ) ) @ Xk ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.44/1.28 ---- Embedded in THF ---
% 1.44/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.28 %%% Generated on Tue Feb 24 11:33:50 EST 2026
% 1.44/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.28 %%% Logic specification used:
% 1.44/1.28 %%% thf(spec, logic, $$dhol).
% 1.44/1.28
% 1.44/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.u8uG9fSAr6/DTF2DTF6718.p
% See solution above
% 1.44/1.28 ------------------------
% 1.44/1.29 ---- Cleaned THF ---
% 1.44/1.29 thf(c1_type,type,
% 1.44/1.29 c1: $i ).
% 1.44/1.29
% 1.44/1.29 thf(s_type,type,
% 1.44/1.29 s: $i > $i ).
% 1.44/1.29
% 1.44/1.29 thf(cCKB6_BLACK_type,type,
% 1.44/1.29 cCKB6_BLACK: $i > $i > $o ).
% 1.44/1.29
% 1.44/1.29 thf(cCKB6_BLACK_def,definition,
% 1.44/1.29 ( cCKB6_BLACK
% 1.44/1.29 = ( ^ [Xu: $i,Xv: $i] :
% 1.44/1.29 ! [Xw: $i > $i > $o] :
% 1.44/1.29 ( ( ( Xw @ c1 @ c1 )
% 1.44/1.29 & ! [Xj: $i,Xk: $i] :
% 1.44/1.29 ( ( Xw @ Xj @ Xk )
% 1.44/1.29 => ( ( Xw @ ( s @ ( s @ Xj ) ) @ Xk )
% 1.44/1.29 & ( Xw @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
% 1.44/1.29 => ( Xw @ Xu @ Xv ) ) ) ) ).
% 1.44/1.29
% 1.44/1.29 thf(cCKB6_L8000,conjecture,
% 1.44/1.29 ! [Xj: $i,Xk: $i] :
% 1.44/1.29 ( ( cCKB6_BLACK @ Xj @ Xk )
% 1.44/1.29 => ( cCKB6_BLACK @ ( s @ ( s @ Xj ) ) @ Xk ) ) ).
% 1.44/1.29 ------------------------
% 1.63/1.31 % (6825)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_6718 for (2999ds/2Mi)
% 1.63/1.31 % (6825)Instruction limit reached!
% 1.63/1.31 % (6825)------------------------------
% 1.63/1.31 % (6825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (6825)Termination reason: Unknown
% 1.63/1.31 % (6825)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (6825)Memory used [KB]: 895
% 1.63/1.31 % (6825)Time elapsed: 0.002 s
% 1.63/1.31 % (6825)Instructions burned: 2 (million)
% 1.63/1.31 % (6825)------------------------------
% 1.63/1.31 % (6825)------------------------------
% 1.63/1.31 % (6822)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_6718 for (2999ds/4Mi)
% 1.63/1.31 % (6821)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6718 for (2999ds/183Mi)
% 1.63/1.31 % (6823)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_6718 for (2999ds/27Mi)
% 1.63/1.31 % (6824)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6718 for (2999ds/2Mi)
% 1.63/1.31 % (6826)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_6718 for (2999ds/275Mi)
% 1.63/1.31 % (6827)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6718 for (2999ds/18Mi)
% 1.63/1.32 % (6824)Instruction limit reached!
% 1.63/1.32 % (6824)------------------------------
% 1.63/1.32 % (6824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (6824)Termination reason: Unknown
% 1.63/1.32 % (6824)Termination phase: Property scanning
% 1.63/1.32
% 1.63/1.32 % (6824)Memory used [KB]: 895
% 1.63/1.32 % (6824)Time elapsed: 0.003 s
% 1.63/1.32 % (6824)Instructions burned: 2 (million)
% 1.63/1.32 % (6824)------------------------------
% 1.63/1.32 % (6824)------------------------------
% 1.63/1.32 % (6826)Refutation not found, incomplete strategy
% 1.63/1.32 % (6826)------------------------------
% 1.63/1.32 % (6826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (6826)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.32
% 1.63/1.32
% 1.63/1.32 % (6826)Memory used [KB]: 5500
% 1.63/1.32 % (6826)Time elapsed: 0.003 s
% 1.63/1.32 % (6826)Instructions burned: 2 (million)
% 1.63/1.32 % (6826)------------------------------
% 1.63/1.32 % (6826)------------------------------
% 1.63/1.32 % (6822)Instruction limit reached!
% 1.63/1.32 % (6822)------------------------------
% 1.63/1.32 % (6822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (6822)Termination reason: Unknown
% 1.63/1.32 % (6822)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (6822)Memory used [KB]: 5500
% 1.63/1.32 % (6822)Time elapsed: 0.005 s
% 1.63/1.32 % (6822)Instructions burned: 5 (million)
% 1.63/1.32 % (6822)------------------------------
% 1.63/1.32 % (6822)------------------------------
% 1.63/1.32 % (6828)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6718 for (2999ds/3Mi)
% 1.63/1.32 % (6828)Instruction limit reached!
% 1.63/1.32 % (6828)------------------------------
% 1.63/1.32 % (6828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (6828)Termination reason: Unknown
% 1.63/1.32 % (6828)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (6828)Memory used [KB]: 5500
% 1.63/1.32 % (6828)Time elapsed: 0.003 s
% 1.63/1.32 % (6828)Instructions burned: 4 (million)
% 1.63/1.32 % (6828)------------------------------
% 1.63/1.32 % (6828)------------------------------
% 1.63/1.32 % (6823)First to succeed.
% 1.63/1.33 % (6823)Refutation found. Thanks to Tanya!
% 1.63/1.33 % SZS status Theorem for DTF2THF_6718
% 1.63/1.33 % SZS output start Proof for DTF2THF_6718
% 1.63/1.33 thf(func_def_1, type, s: $i > $i).
% 1.63/1.33 thf(func_def_2, type, cCKB6_BLACK: $i > $i > $o).
% 1.63/1.33 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.63/1.33 thf(func_def_17, type, sK3: ($i > $i > $o) > $i).
% 1.63/1.33 thf(func_def_18, type, sK4: ($i > $i > $o) > $i).
% 1.63/1.33 thf(func_def_19, type, sK5: $i > $i > $o).
% 1.63/1.33 thf(func_def_20, type, ph6: !>[X0: $tType]:(X0)).
% 1.63/1.33 thf(f87,plain,(
% 1.63/1.33 $false),
% 1.63/1.33 inference(avatar_sat_refutation,[status(thm)],[f68,f79,f86])).
% 1.63/1.33 thf(f86,plain,(
% 1.63/1.33 spl2_2 | ~spl2_1),
% 1.63/1.33 inference(avatar_split_clause,[status(thm)],[f83,f56,f60])).
% 1.63/1.33 thf(f60,definition,(
% 1.63/1.33 spl2_2 <=> ($false = (sK5 @ (sK4 @ sK5) @ (sK3 @ sK5)))),
% 1.63/1.33 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.63/1.33 thf(f56,definition,(
% 1.63/1.33 spl2_1 <=> ($false = (sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5)))),
% 1.63/1.33 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.63/1.33 thf(f83,plain,(
% 1.63/1.33 ($false = (sK5 @ (sK4 @ sK5) @ (sK3 @ sK5))) | ~spl2_1),
% 1.63/1.33 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.63/1.33 thf(f81,plain,(
% 1.63/1.33 ($false = $true) | ($false = (sK5 @ (sK4 @ sK5) @ (sK3 @ sK5))) | ~spl2_1),
% 1.63/1.33 inference(superposition,[status(thm)],[f58,f41])).
% 1.63/1.33 thf(f41,plain,(
% 1.63/1.33 ( ! [X2 : $i,X1 : $i] : (((sK5 @ (s @ (s @ X2)) @ X1) = $true) | ($false = (sK5 @ X2 @ X1))) )),
% 1.63/1.33 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.63/1.33 thf(f40,plain,(
% 1.63/1.33 ( ! [X2 : $i,X1 : $i] : (($false = (sK5 @ X2 @ X1)) | ($true = ((sK5 @ (s @ X2) @ (s @ X1)) & (sK5 @ (s @ (s @ X2)) @ X1)))) )),
% 1.63/1.33 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.63/1.33 thf(f39,plain,(
% 1.63/1.33 ( ! [X2 : $i,X1 : $i] : (($true = ((sK5 @ X2 @ X1) => ((sK5 @ (s @ X2) @ (s @ X1)) & (sK5 @ (s @ (s @ X2)) @ X1))))) )),
% 1.63/1.33 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.63/1.33 thf(f38,plain,(
% 1.63/1.33 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((sK5 @ Y0 @ X1) => ((sK5 @ (s @ Y0) @ (s @ X1)) & (sK5 @ (s @ (s @ Y0)) @ X1)))) @ X2) = $true)) )),
% 1.63/1.33 inference(pi_clausification,[status(thm)],[f37])).
% 1.63/1.33 thf(f37,plain,(
% 1.63/1.33 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0 @ X1) => ((sK5 @ (s @ Y0) @ (s @ X1)) & (sK5 @ (s @ (s @ Y0)) @ X1))))))) )),
% 1.63/1.33 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.63/1.33 thf(f36,plain,(
% 1.63/1.33 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1 @ Y0) => ((sK5 @ (s @ Y1) @ (s @ Y0)) & (sK5 @ (s @ (s @ Y1)) @ Y0)))))) @ X1))) )),
% 1.63/1.33 inference(pi_clausification,[status(thm)],[f34])).
% 1.63/1.33 thf(f34,plain,(
% 1.63/1.33 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1 @ Y0) => ((sK5 @ (s @ Y1) @ (s @ Y0)) & (sK5 @ (s @ (s @ Y1)) @ Y0))))))))),
% 1.63/1.33 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.63/1.33 thf(f33,plain,(
% 1.63/1.33 ($true = ((sK5 @ c1 @ c1) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1 @ Y0) => ((sK5 @ (s @ Y1) @ (s @ Y0)) & (sK5 @ (s @ (s @ Y1)) @ Y0)))))))))),
% 1.63/1.33 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.63/1.33 thf(f31,plain,(
% 1.63/1.33 ($false = (((sK5 @ c1 @ c1) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1 @ Y0) => ((sK5 @ (s @ Y1) @ (s @ Y0)) & (sK5 @ (s @ (s @ Y1)) @ Y0)))))))) => (sK5 @ (s @ (s @ sK1)) @ sK0)))),
% 1.63/1.33 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.63/1.33 thf(f30,plain,(
% 1.63/1.33 ($false = ((^[Y0 : $i > $i > $o]: (((Y0 @ c1 @ c1) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => ((Y0 @ (s @ Y2) @ (s @ Y1)) & (Y0 @ (s @ (s @ Y2)) @ Y1)))))))) => (Y0 @ (s @ (s @ sK1)) @ sK0))) @ sK5))),
% 1.63/1.33 inference(sigma_clausification,[status(thm)],[f29])).
% 1.63/1.33 thf(f29,plain,(
% 1.63/1.33 ($true != (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ c1 @ c1) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => ((Y0 @ (s @ Y2) @ (s @ Y1)) & (Y0 @ (s @ (s @ Y2)) @ Y1)))))))) => (Y0 @ (s @ (s @ sK1)) @ sK0)))))),
% 1.63/1.33 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.63/1.33 thf(f15,plain,(
% 1.63/1.33 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ c1 @ c1) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => ((Y2 @ (s @ Y4) @ (s @ Y3)) & (Y2 @ (s @ (s @ Y4)) @ Y3)))))))) => (Y2 @ Y0 @ Y1))))))) @ (s @ (s @ sK1)) @ sK0))),
% 1.63/1.33 inference(definition_unfolding,[status(thm)],[f13,f14])).
% 1.63/1.33 thf(f14,plain,(
% 1.63/1.33 (cCKB6_BLACK = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ c1 @ c1) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => ((Y2 @ (s @ Y4) @ (s @ Y3)) & (Y2 @ (s @ (s @ Y4)) @ Y3)))))))) => (Y2 @ Y0 @ Y1))))))))),
% 1.63/1.33 inference(cnf_transformation,[status(thm)],[f6])).
% 1.63/1.33 thf(f6,plain,(
% 1.63/1.33 (cCKB6_BLACK = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ c1 @ c1) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => ((Y2 @ (s @ Y4) @ (s @ Y3)) & (Y2 @ (s @ (s @ Y4)) @ Y3)))))))) => (Y2 @ Y0 @ Y1))))))))),
% 1.63/1.33 inference(fool_elimination,[status(thm)],[f5])).
% 1.63/1.33 thf(f5,plain,(
% 1.63/1.33 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $i > $o] : ((! [X3 : $i,X4 : $i] : ((X2 @ X3 @ X4) => ((X2 @ (s @ (s @ X3)) @ X4) & (X2 @ (s @ X3) @ (s @ X4)))) & (X2 @ c1 @ c1)) => (X2 @ X0 @ X1)))) = cCKB6_BLACK)),
% 1.63/1.33 inference(rectify,[status(thm)],[f1])).
% 1.63/1.33 thf(f1,axiom,(
% 1.63/1.33 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $i > $o] : ((! [X3 : $i,X4 : $i] : ((X2 @ X3 @ X4) => ((X2 @ (s @ (s @ X3)) @ X4) & (X2 @ (s @ X3) @ (s @ X4)))) & (X2 @ c1 @ c1)) => (X2 @ X0 @ X1)))) = cCKB6_BLACK)),
% 1.63/1.33 file('/export/starexec/sandbox2/tmp/tmp.u8uG9fSAr6/DTF2THF_6718.p',cCKB6_BLACK_def)).
% 1.63/1.33 thf(f13,plain,(
% 1.63/1.33 ($true != (cCKB6_BLACK @ (s @ (s @ sK1)) @ sK0))),
% 1.63/1.33 inference(cnf_transformation,[status(thm)],[f11])).
% 1.63/1.33 thf(f11,plain,(
% 1.63/1.33 ($true != (cCKB6_BLACK @ (s @ (s @ sK1)) @ sK0)) & ($true = (cCKB6_BLACK @ sK1 @ sK0))),
% 1.63/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10])).
% 1.63/1.33 thf(f10,plain,(
% 1.63/1.33 ? [X0 : $i,X1 : $i] : (($true != (cCKB6_BLACK @ (s @ (s @ X1)) @ X0)) & ((cCKB6_BLACK @ X1 @ X0) = $true)) => (($true != (cCKB6_BLACK @ (s @ (s @ sK1)) @ sK0)) & ($true = (cCKB6_BLACK @ sK1 @ sK0)))),
% 1.63/1.33 introduced(definition,[],[choice_axiom])).
% 1.63/1.33 thf(f9,plain,(
% 1.63/1.33 ? [X0 : $i,X1 : $i] : (($true != (cCKB6_BLACK @ (s @ (s @ X1)) @ X0)) & ((cCKB6_BLACK @ X1 @ X0) = $true))),
% 1.63/1.33 inference(ennf_transformation,[status(thm)],[f8])).
% 1.63/1.33 thf(f8,plain,(
% 1.63/1.33 ~! [X0 : $i,X1 : $i] : (((cCKB6_BLACK @ X1 @ X0) = $true) => ($true = (cCKB6_BLACK @ (s @ (s @ X1)) @ X0)))),
% 1.63/1.33 inference(fool_elimination,[status(thm)],[f7])).
% 1.63/1.33 thf(f7,plain,(
% 1.63/1.33 ~! [X0 : $i,X1 : $i] : ((cCKB6_BLACK @ X1 @ X0) => (cCKB6_BLACK @ (s @ (s @ X1)) @ X0))),
% 1.63/1.33 inference(rectify,[status(thm)],[f3])).
% 1.63/1.33 thf(f3,negated_conjecture,(
% 1.63/1.33 ~! [X4 : $i,X3 : $i] : ((cCKB6_BLACK @ X3 @ X4) => (cCKB6_BLACK @ (s @ (s @ X3)) @ X4))),
% 1.63/1.33 inference(negated_conjecture,[status(cth)],[f2])).
% 1.63/1.33 thf(f2,conjecture,(
% 1.63/1.33 ! [X4 : $i,X3 : $i] : ((cCKB6_BLACK @ X3 @ X4) => (cCKB6_BLACK @ (s @ (s @ X3)) @ X4))),
% 1.63/1.33 file('/export/starexec/sandbox2/tmp/tmp.u8uG9fSAr6/DTF2THF_6718.p',cCKB6_L8000)).
% 1.63/1.33 thf(f58,plain,(
% 1.63/1.33 ($false = (sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5))) | ~spl2_1),
% 1.63/1.33 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.63/1.33 thf(f79,plain,(
% 1.63/1.33 ~spl2_2),
% 1.63/1.33 inference(avatar_contradiction_clause,[status(thm)],[f78])).
% 1.63/1.33 thf(f78,plain,(
% 1.63/1.33 $false | ~spl2_2),
% 1.63/1.33 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.63/1.33 thf(f77,plain,(
% 1.63/1.33 ($false = $true) | ~spl2_2),
% 1.63/1.33 inference(forward_demodulation,[status(thm)],[f76,f45])).
% 1.63/1.33 thf(f45,plain,(
% 1.63/1.33 ((sK5 @ sK1 @ sK0) = $false)),
% 1.63/1.33 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.63/1.33 thf(f43,plain,(
% 1.63/1.33 ($false = $true) | ((sK5 @ sK1 @ sK0) = $false)),
% 1.63/1.33 inference(superposition,[status(thm)],[f41,f32])).
% 1.63/1.33 thf(f32,plain,(
% 1.63/1.33 ($false = (sK5 @ (s @ (s @ sK1)) @ sK0))),
% 1.63/1.33 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.63/1.33 thf(f76,plain,(
% 1.63/1.33 ((sK5 @ sK1 @ sK0) = $true) | ~spl2_2),
% 1.63/1.33 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.63/1.33 thf(f75,plain,(
% 1.63/1.33 ($false = $true) | ((sK5 @ sK1 @ sK0) = $true) | ~spl2_2),
% 1.63/1.33 inference(forward_demodulation,[status(thm)],[f71,f35])).
% 1.63/1.33 thf(f35,plain,(
% 1.63/1.33 ($true = (sK5 @ c1 @ c1))),
% 1.63/1.33 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.63/1.33 thf(f71,plain,(
% 1.63/1.33 ($false = (sK5 @ c1 @ c1)) | ((sK5 @ sK1 @ sK0) = $true) | ~spl2_2),
% 1.63/1.33 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.63/1.33 thf(f70,plain,(
% 1.63/1.33 ($false = (sK5 @ c1 @ c1)) | ($false = $true) | ((sK5 @ sK1 @ sK0) = $true) | ~spl2_2),
% 1.63/1.33 inference(superposition,[status(thm)],[f27,f62])).
% 1.63/1.33 thf(f62,plain,(
% 1.63/1.33 ($false = (sK5 @ (sK4 @ sK5) @ (sK3 @ sK5))) | ~spl2_2),
% 1.63/1.33 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.63/1.33 thf(f27,plain,(
% 1.63/1.33 ( ! [X1 : $i > $i > $o] : (($true = (X1 @ (sK4 @ X1) @ (sK3 @ X1))) | ($false = (X1 @ c1 @ c1)) | ($true = (X1 @ sK1 @ sK0))) )),
% 1.63/1.33 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.63/1.33 thf(f25,plain,(
% 1.63/1.33 ( ! [X1 : $i > $i > $o] : (($false = ((X1 @ (sK4 @ X1) @ (sK3 @ X1)) => ((X1 @ (s @ (sK4 @ X1)) @ (s @ (sK3 @ X1))) & (X1 @ (s @ (s @ (sK4 @ X1))) @ (sK3 @ X1))))) | ($false = (X1 @ c1 @ c1)) | ($true = (X1 @ sK1 @ sK0))) )),
% 1.63/1.33 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.63/1.33 thf(f24,plain,(
% 1.63/1.33 ( ! [X1 : $i > $i > $o] : (($false = ((^[Y0 : $i]: ((X1 @ Y0 @ (sK3 @ X1)) => ((X1 @ (s @ Y0) @ (s @ (sK3 @ X1))) & (X1 @ (s @ (s @ Y0)) @ (sK3 @ X1))))) @ (sK4 @ X1))) | ($true = (X1 @ sK1 @ sK0)) | ($false = (X1 @ c1 @ c1))) )),
% 1.63/1.33 inference(sigma_clausification,[status(thm)],[f23])).
% 1.63/1.33 thf(f23,plain,(
% 1.63/1.33 ( ! [X1 : $i > $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0 @ (sK3 @ X1)) => ((X1 @ (s @ Y0) @ (s @ (sK3 @ X1))) & (X1 @ (s @ (s @ Y0)) @ (sK3 @ X1))))))) | ($false = (X1 @ c1 @ c1)) | ($true = (X1 @ sK1 @ sK0))) )),
% 1.63/1.33 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.63/1.33 thf(f22,plain,(
% 1.63/1.33 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => ((X1 @ (s @ Y1) @ (s @ Y0)) & (X1 @ (s @ (s @ Y1)) @ Y0)))))) @ (sK3 @ X1)) = $false) | ($true = (X1 @ sK1 @ sK0)) | ($false = (X1 @ c1 @ c1))) )),
% 1.63/1.33 inference(sigma_clausification,[status(thm)],[f21])).
% 1.63/1.33 thf(f21,plain,(
% 1.63/1.33 ( ! [X1 : $i > $i > $o] : (($true = (X1 @ sK1 @ sK0)) | ($false = (X1 @ c1 @ c1)) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => ((X1 @ (s @ Y1) @ (s @ Y0)) & (X1 @ (s @ (s @ Y1)) @ Y0))))))))) )),
% 1.63/1.33 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.63/1.33 thf(f20,plain,(
% 1.63/1.33 ( ! [X1 : $i > $i > $o] : (($true = (X1 @ sK1 @ sK0)) | ($false = ((X1 @ c1 @ c1) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => ((X1 @ (s @ Y1) @ (s @ Y0)) & (X1 @ (s @ (s @ Y1)) @ Y0)))))))))) )),
% 1.63/1.33 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.63/1.33 thf(f19,plain,(
% 1.63/1.33 ( ! [X1 : $i > $i > $o] : (($true = (((X1 @ c1 @ c1) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => ((X1 @ (s @ Y1) @ (s @ Y0)) & (X1 @ (s @ (s @ Y1)) @ Y0)))))))) => (X1 @ sK1 @ sK0)))) )),
% 1.63/1.33 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.63/1.33 thf(f18,plain,(
% 1.63/1.33 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (((Y0 @ c1 @ c1) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => ((Y0 @ (s @ Y2) @ (s @ Y1)) & (Y0 @ (s @ (s @ Y2)) @ Y1)))))))) => (Y0 @ sK1 @ sK0))) @ X1) = $true)) )),
% 1.63/1.33 inference(pi_clausification,[status(thm)],[f17])).
% 1.63/1.33 thf(f17,plain,(
% 1.63/1.33 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ c1 @ c1) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => ((Y0 @ (s @ Y2) @ (s @ Y1)) & (Y0 @ (s @ (s @ Y2)) @ Y1)))))))) => (Y0 @ sK1 @ sK0)))))),
% 1.63/1.33 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.63/1.33 thf(f16,plain,(
% 1.63/1.33 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ c1 @ c1) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => ((Y2 @ (s @ Y4) @ (s @ Y3)) & (Y2 @ (s @ (s @ Y4)) @ Y3)))))))) => (Y2 @ Y0 @ Y1))))))) @ sK1 @ sK0))),
% 1.63/1.33 inference(definition_unfolding,[status(thm)],[f12,f14])).
% 1.63/1.33 thf(f12,plain,(
% 1.63/1.33 ($true = (cCKB6_BLACK @ sK1 @ sK0))),
% 1.63/1.33 inference(cnf_transformation,[status(thm)],[f11])).
% 1.63/1.33 thf(f68,plain,(
% 1.63/1.33 spl2_2 | spl2_1),
% 1.63/1.33 inference(avatar_split_clause,[status(thm)],[f67,f56,f60])).
% 1.63/1.33 thf(f67,plain,(
% 1.63/1.33 ($false = (sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5))) | ($false = (sK5 @ (sK4 @ sK5) @ (sK3 @ sK5)))),
% 1.63/1.33 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.63/1.33 thf(f66,plain,(
% 1.63/1.33 ($false = $true) | ($false = (sK5 @ (sK4 @ sK5) @ (sK3 @ sK5))) | ($false = (sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5)))),
% 1.63/1.33 inference(forward_demodulation,[status(thm)],[f65,f35])).
% 1.63/1.33 thf(f65,plain,(
% 1.63/1.33 ($false = (sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5))) | ($false = (sK5 @ (sK4 @ sK5) @ (sK3 @ sK5))) | ($false = (sK5 @ c1 @ c1))),
% 1.63/1.33 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.63/1.33 thf(f64,plain,(
% 1.63/1.33 ($false = $true) | ($false = (sK5 @ (sK4 @ sK5) @ (sK3 @ sK5))) | ($false = (sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5))) | ($false = (sK5 @ c1 @ c1))),
% 1.63/1.33 inference(forward_demodulation,[status(thm)],[f49,f45])).
% 1.63/1.33 thf(f49,plain,(
% 1.63/1.33 ((sK5 @ sK1 @ sK0) = $true) | ($false = (sK5 @ (sK4 @ sK5) @ (sK3 @ sK5))) | ($false = (sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5))) | ($false = (sK5 @ c1 @ c1))),
% 1.63/1.33 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.63/1.33 thf(f48,plain,(
% 1.63/1.33 ((sK5 @ sK1 @ sK0) = $true) | ($false = (sK5 @ (sK4 @ sK5) @ (sK3 @ sK5))) | ($false = (sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5))) | ($false = (sK5 @ c1 @ c1)) | ($false = $true)),
% 1.63/1.33 inference(superposition,[status(thm)],[f42,f28])).
% 1.63/1.33 thf(f28,plain,(
% 1.63/1.33 ( ! [X1 : $i > $i > $o] : (($false = (X1 @ (s @ (sK4 @ X1)) @ (s @ (sK3 @ X1)))) | ($true = (X1 @ sK1 @ sK0)) | ($false = (X1 @ (s @ (s @ (sK4 @ X1))) @ (sK3 @ X1))) | ($false = (X1 @ c1 @ c1))) )),
% 1.63/1.33 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.63/1.33 thf(f26,plain,(
% 1.63/1.33 ( ! [X1 : $i > $i > $o] : (($false = ((X1 @ (s @ (sK4 @ X1)) @ (s @ (sK3 @ X1))) & (X1 @ (s @ (s @ (sK4 @ X1))) @ (sK3 @ X1)))) | ($true = (X1 @ sK1 @ sK0)) | ($false = (X1 @ c1 @ c1))) )),
% 1.63/1.33 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.63/1.33 thf(f42,plain,(
% 1.63/1.33 ( ! [X2 : $i,X1 : $i] : (((sK5 @ (s @ X2) @ (s @ X1)) = $true) | ($false = (sK5 @ X2 @ X1))) )),
% 1.63/1.33 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.63/1.33 % SZS output end Proof for DTF2THF_6718
% 1.63/1.33 % (6823)------------------------------
% 1.63/1.33 % (6823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (6823)Termination reason: Refutation
% 1.63/1.33
% 1.63/1.33 % (6823)Memory used [KB]: 5628
% 1.63/1.33 % (6823)Time elapsed: 0.011 s
% 1.63/1.33 % (6823)Instructions burned: 10 (million)
% 1.63/1.33 % (6823)------------------------------
% 1.63/1.33 % (6823)------------------------------
% 1.63/1.33 % (6820)Success in time 0.02 s
%------------------------------------------------------------------------------