%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU969^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 1.72s 1.47s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of formulae : 147 ( 22 unt; 0 typ; 10 def)
% Number of atoms : 1314 ( 264 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 1995 ( 133 ~; 256 |; 91 &;1243 @)
% ( 10 <=>; 141 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 121 ( 121 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 16 con; 0-2 aty)
% ( 121 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 416 ( 346 ^; 70 !; 0 ?; 416 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
cCKB6_BLACK: $i > $i > $o ).
thf(func_def_3,type,
cCKB6_NUM: $i > $o ).
thf(func_def_18,type,
sK3: $i > $o ).
thf(func_def_19,type,
sK4: $i > $o ).
thf(func_def_20,type,
sK5: ( $i > $i > $o ) > $i ).
thf(func_def_21,type,
sK6: ( $i > $i > $o ) > $i ).
thf(func_def_22,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f419,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f47,f52,f57,f71,f73,f75,f84,f87,f91,f201,f266,f300,f392,f397,f418]) ).
thf(f418,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f417]) ).
thf(f417,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f416]) ).
thf(f416,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f415,f83]) ).
thf(f83,plain,
( ( ( sK3 @ sK1 )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f81,definition,
( spl0_6
<=> ( ( sK3 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f415,plain,
( ( ( sK3 @ sK1 )
= $true )
| ~ spl0_1
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f414]) ).
thf(f414,plain,
( ( ( sK3 @ sK1 )
= $true )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f404,f43]) ).
thf(f43,plain,
( ( $true
= ( sK3 @ c1 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl0_1
<=> ( $true
= ( sK3 @ c1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f404,plain,
( ( $false
= ( sK3 @ c1 ) )
| ( ( sK3 @ sK1 )
= $true )
| ~ spl0_17 ),
inference(beta_eta_normalization,[status(thm)],[f403]) ).
thf(f403,plain,
( ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK2
@ sK1 ) )
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f399]) ).
thf(f399,plain,
( ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( $false = $true )
| ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK2
@ sK1 ) )
| ~ spl0_17 ),
inference(superposition,[status(thm)],[f386,f101]) ).
thf(f101,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
= $true )
| ( ( X1 @ sK2 @ sK1 )
= $true )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK2 @ sK1 )
= $true )
| ( ( ( X1 @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
=> ( ( X1 @ ( s @ ( s @ ( sK6 @ X1 ) ) ) @ ( sK5 @ X1 ) )
& ( X1 @ ( s @ ( sK6 @ X1 ) ) @ ( s @ ( sK5 @ X1 ) ) ) ) )
= $false )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f98]) ).
thf(f98,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ c1 @ c1 ) )
| ( ( ^ [Y0: $i] :
( ( X1 @ Y0 @ ( sK5 @ X1 ) )
=> ( ( X1 @ ( s @ ( s @ Y0 ) ) @ ( sK5 @ X1 ) )
& ( X1 @ ( s @ Y0 ) @ ( s @ ( sK5 @ X1 ) ) ) ) )
@ ( sK6 @ X1 ) )
= $false )
| ( ( X1 @ sK2 @ sK1 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ c1 @ c1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 @ ( sK5 @ X1 ) )
=> ( ( X1 @ ( s @ ( s @ Y0 ) ) @ ( sK5 @ X1 ) )
& ( X1 @ ( s @ Y0 ) @ ( s @ ( sK5 @ X1 ) ) ) ) ) )
= $false )
| ( ( X1 @ sK2 @ sK1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f96]) ).
thf(f96,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK2 @ sK1 )
= $true )
| ( $false
= ( X1 @ c1 @ c1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( ( X1 @ ( s @ ( s @ Y1 ) ) @ Y0 )
& ( X1 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) )
@ ( sK5 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK2 @ sK1 )
= $true )
| ( $false
= ( X1 @ c1 @ c1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( ( X1 @ ( s @ ( s @ Y1 ) ) @ Y0 )
& ( X1 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X1: $i > $i > $o] :
( ( ( ( X1 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( ( X1 @ ( s @ ( s @ Y1 ) ) @ Y0 )
& ( X1 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) ) ) )
= $false )
| ( ( X1 @ sK2 @ sK1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X1: $i > $i > $o] :
( $true
= ( ( ( X1 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( ( X1 @ ( s @ ( s @ Y1 ) ) @ Y0 )
& ( X1 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) ) ) )
=> ( X1 @ sK2 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f92]) ).
thf(f92,plain,
! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( Y0 @ ( s @ ( s @ Y2 ) ) @ Y1 )
& ( Y0 @ ( s @ Y2 ) @ ( s @ Y1 ) ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( Y0 @ ( s @ ( s @ Y2 ) ) @ Y1 )
& ( Y0 @ ( s @ Y2 ) @ ( s @ Y1 ) ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK1 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( Y0 @ ( s @ ( s @ Y2 ) ) @ Y1 )
& ( Y0 @ ( s @ Y2 ) @ ( s @ Y1 ) ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK1 ) ) )
=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK2 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK1 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( Y1 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ( ( Y1 @ ( s @ ( s @ Y3 ) ) @ Y2 )
& ( Y1 @ ( s @ Y3 ) @ ( s @ Y2 ) ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK1 ) ) )
=> ( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ sK1 ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( Y1 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ( ( Y1 @ ( s @ ( s @ Y3 ) ) @ Y2 )
& ( Y1 @ ( s @ Y3 ) @ ( s @ Y2 ) ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK1 ) ) )
=> ( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ sK1 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( Y2 @ ( s @ ( s @ Y4 ) ) @ Y3 )
& ( Y2 @ ( s @ Y4 ) @ ( s @ Y3 ) ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ Y3 ) ) ) )
& ( Y2 @ c1 ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ Y3 ) ) ) )
& ( Y2 @ c1 ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( Y2 @ ( s @ ( s @ Y4 ) ) @ Y3 )
& ( Y2 @ ( s @ Y4 ) @ ( s @ Y3 ) ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ Y3 ) ) ) )
& ( Y2 @ c1 ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ Y3 ) ) ) )
& ( Y2 @ c1 ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( Y2 @ ( s @ ( s @ Y4 ) ) @ Y3 )
& ( Y2 @ ( s @ Y4 ) @ ( s @ Y3 ) ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ Y3 ) ) ) )
& ( Y2 @ c1 ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ Y3 ) ) ) )
& ( Y2 @ c1 ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( Y4 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
=> ( ( Y4 @ ( s @ ( s @ Y6 ) ) @ Y5 )
& ( Y4 @ ( s @ Y6 ) @ ( s @ Y5 ) ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y1
@ Y0 )
=> ( ( ^ [Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( s @ Y4 ) ) ) )
& ( Y3 @ c1 ) )
=> ( Y3 @ Y2 ) ) )
@ Y1 )
& ( ^ [Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y3 @ ( s @ Y4 ) ) ) )
& ( Y3 @ c1 ) )
=> ( Y3 @ Y2 ) ) )
@ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f14,f12,f13,f13]) ).
thf(f13,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ( X1 @ c1 )
& ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) ) )
=> ( X1 @ X0 ) ) )
= cCKB6_NUM ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X5: $i] :
! [X6: $i > $o] :
( ( ( X6 @ c1 )
& ! [X2: $i] :
( ( X6 @ X2 )
=> ( X6 @ ( s @ X2 ) ) ) )
=> ( X6 @ X5 ) ) )
= cCKB6_NUM ),
file('/export/starexec/sandbox/tmp/tmp.6uP4k6plCZ/DTF2THF_29139.p',cCKB6_NUM_def) ).
thf(f12,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 @ ( s @ Y4 ) ) @ Y3 )
& ( Y2 @ ( s @ Y4 ) @ ( s @ Y3 ) ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,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 @ ( s @ Y4 ) ) @ Y3 )
& ( Y2 @ ( s @ Y4 ) @ ( s @ Y3 ) ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( cCKB6_BLACK
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $i > $o] :
( ( ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( ( X2 @ ( s @ X3 ) @ ( s @ X4 ) )
& ( X2 @ ( s @ ( s @ X3 ) ) @ X4 ) ) )
& ( X2 @ c1 @ c1 ) )
=> ( X2 @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( cCKB6_BLACK
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $i > $o] :
( ( ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( ( X2 @ ( s @ X3 ) @ ( s @ X4 ) )
& ( X2 @ ( s @ ( s @ X3 ) ) @ X4 ) ) )
& ( X2 @ c1 @ c1 ) )
=> ( X2 @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6uP4k6plCZ/DTF2THF_29139.p',cCKB6_BLACK_def) ).
thf(f14,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cCKB6_BLACK @ Y1 @ Y0 )
=> ( ( cCKB6_NUM @ Y1 )
& ( cCKB6_NUM @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cCKB6_BLACK @ Y1 @ Y0 )
=> ( ( cCKB6_NUM @ Y1 )
& ( cCKB6_NUM @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i] :
( ( cCKB6_BLACK @ X0 @ X1 )
=> ( ( cCKB6_NUM @ X1 )
& ( cCKB6_NUM @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X5: $i,X7: $i] :
( ( cCKB6_BLACK @ X5 @ X7 )
=> ( ( cCKB6_NUM @ X7 )
& ( cCKB6_NUM @ X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X5: $i,X7: $i] :
( ( cCKB6_BLACK @ X5 @ X7 )
=> ( ( cCKB6_NUM @ X7 )
& ( cCKB6_NUM @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6uP4k6plCZ/DTF2THF_29139.p',cCKB6_L6000_pme) ).
thf(f386,plain,
( ( $false
= ( sK3
@ ( sK5
@ ^ [Y0: $i] : sK3 ) ) )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f384]) ).
thf(f384,definition,
( spl0_17
<=> ( $false
= ( sK3
@ ( sK5
@ ^ [Y0: $i] : sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f397,plain,
( spl0_17
| ~ spl0_16 ),
inference(avatar_split_clause,[status(thm)],[f396,f381,f384]) ).
thf(f381,definition,
( spl0_16
<=> ! [X1: $i] :
( ( ( sK5
@ ^ [Y0: $i] : sK3 )
!= X1 )
| ( ( sK3 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f396,plain,
( ( $false
= ( sK3
@ ( sK5
@ ^ [Y0: $i] : sK3 ) ) )
| ~ spl0_16 ),
inference(equality_resolution,[status(thm)],[f382]) ).
thf(f382,plain,
( ! [X1: $i] :
( ( ( sK5
@ ^ [Y0: $i] : sK3 )
!= X1 )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f381]) ).
thf(f392,plain,
( spl0_16
| spl0_17
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f391,f81,f69,f41,f384,f381]) ).
thf(f69,definition,
( spl0_5
<=> ! [X1: $i] :
( ( ( sK3 @ ( s @ X1 ) )
= $true )
| ( ( sK3 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f391,plain,
( ! [X1: $i] :
( ( ( sK3 @ X1 )
= $false )
| ( $false
= ( sK3
@ ( sK5
@ ^ [Y0: $i] : sK3 ) ) )
| ( ( sK5
@ ^ [Y0: $i] : sK3 )
!= X1 ) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f390]) ).
thf(f390,plain,
( ! [X1: $i] :
( ( $false = $true )
| ( ( sK5
@ ^ [Y0: $i] : sK3 )
!= X1 )
| ( ( sK3 @ X1 )
= $false )
| ( $false
= ( sK3
@ ( sK5
@ ^ [Y0: $i] : sK3 ) ) ) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f389,f43]) ).
thf(f389,plain,
( ! [X1: $i] :
( ( $false
= ( sK3 @ c1 ) )
| ( $false
= ( sK3
@ ( sK5
@ ^ [Y0: $i] : sK3 ) ) )
| ( ( sK5
@ ^ [Y0: $i] : sK3 )
!= X1 )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f388]) ).
thf(f388,plain,
( ! [X1: $i] :
( ( $false = $true )
| ( $false
= ( sK3 @ c1 ) )
| ( $false
= ( sK3
@ ( sK5
@ ^ [Y0: $i] : sK3 ) ) )
| ( ( sK3 @ X1 )
= $false )
| ( ( sK5
@ ^ [Y0: $i] : sK3 )
!= X1 ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f353,f83]) ).
thf(f353,plain,
( ! [X1: $i] :
( ( ( sK5
@ ^ [Y0: $i] : sK3 )
!= X1 )
| ( ( sK3 @ sK1 )
= $true )
| ( $false
= ( sK3 @ c1 ) )
| ( ( sK3 @ X1 )
= $false )
| ( $false
= ( sK3
@ ( sK5
@ ^ [Y0: $i] : sK3 ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f352]) ).
thf(f352,plain,
( ! [X1: $i] :
( ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( ( sK3 @ X1 )
= $false )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ ( s
@ ( s
@ ( sK6
@ ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) ) )
@ ( sK5
@ ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) ) )
| ( ( sK5
@ ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
!= X1 )
| ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK2
@ sK1 ) ) )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f345]) ).
thf(f345,plain,
( ! [X1: $i] :
( ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ ( s
@ ( s
@ ( sK6
@ ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) ) )
@ ( sK5
@ ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK2
@ sK1 ) )
| ( ( sK3 @ X1 )
= $false )
| ( ( sK5
@ ^ [Y0: $i,Y1: $i] :
( sK3
@ ( ^ [Y2: $i,Y3: $i] : Y3
@ Y0
@ Y1 ) ) )
!= X1 )
| ( $false = $true ) )
| ~ spl0_5 ),
inference(constrained_superposition,[status(thm)],[f70,f102]) ).
thf(f102,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ ( s @ ( sK6 @ X1 ) ) @ ( s @ ( sK5 @ X1 ) ) )
= $false )
| ( ( X1 @ sK2 @ sK1 )
= $true )
| ( $false
= ( X1 @ c1 @ c1 ) )
| ( ( X1 @ ( s @ ( s @ ( sK6 @ X1 ) ) ) @ ( sK5 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK2 @ sK1 )
= $true )
| ( $false
= ( ( X1 @ ( s @ ( s @ ( sK6 @ X1 ) ) ) @ ( sK5 @ X1 ) )
& ( X1 @ ( s @ ( sK6 @ X1 ) ) @ ( s @ ( sK5 @ X1 ) ) ) ) )
| ( $false
= ( X1 @ c1 @ c1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f70,plain,
( ! [X1: $i] :
( ( ( sK3 @ ( s @ X1 ) )
= $true )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f69]) ).
thf(f300,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f299]) ).
thf(f299,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f298]) ).
thf(f298,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[status(thm)],[f297,f56]) ).
thf(f56,plain,
( ( $false
= ( sK4 @ sK2 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f54,definition,
( spl0_4
<=> ( $false
= ( sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f297,plain,
( ( $true
= ( sK4 @ sK2 ) )
| ~ spl0_3
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f296]) ).
thf(f296,plain,
( ( $true
= ( sK4 @ sK2 ) )
| ( $false = $true )
| ~ spl0_3
| ~ spl0_11 ),
inference(forward_demodulation,[status(thm)],[f295,f51]) ).
thf(f51,plain,
( ( ( sK4 @ c1 )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl0_3
<=> ( ( sK4 @ c1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f295,plain,
( ( $false
= ( sK4 @ c1 ) )
| ( $true
= ( sK4 @ sK2 ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f294]) ).
thf(f294,plain,
( ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ sK2
@ sK1 )
= $true )
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f285]) ).
thf(f285,plain,
( ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ sK2
@ sK1 )
= $true )
| ( $false = $true )
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f101,f281]) ).
thf(f281,plain,
( ( ( sK4
@ ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) ) )
= $false )
| ~ spl0_11 ),
inference(equality_resolution,[status(thm)],[f188]) ).
thf(f188,plain,
( ! [X0: $i] :
( ( ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) )
!= X0 )
| ( ( sK4 @ X0 )
= $false ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f187]) ).
thf(f187,definition,
( spl0_11
<=> ! [X0: $i] :
( ( ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) )
!= X0 )
| ( ( sK4 @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f266,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f265]) ).
thf(f265,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f261]) ).
thf(f261,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f51,f258]) ).
thf(f258,plain,
( ( $false
= ( sK4 @ c1 ) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f257]) ).
thf(f257,plain,
( ( $false
= ( sK4 @ c1 ) )
| ( $false = $true )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f256,f56]) ).
thf(f256,plain,
( ( $true
= ( sK4 @ sK2 ) )
| ( $false
= ( sK4 @ c1 ) )
| ~ spl0_2
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f255]) ).
thf(f255,plain,
( ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ sK2
@ sK1 )
= $true )
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f246]) ).
thf(f246,plain,
( ( ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ sK2
@ sK1 )
= $true )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( $false = $true )
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f101,f236]) ).
thf(f236,plain,
( ( ( sK4
@ ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f232]) ).
thf(f232,plain,
( ( $false = $true )
| ( ( sK4
@ ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f227,f46]) ).
thf(f46,plain,
( ! [X1: $i] :
( ( ( sK4 @ ( s @ X1 ) )
= $true )
| ( $false
= ( sK4 @ X1 ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl0_2
<=> ! [X1: $i] :
( ( ( sK4 @ ( s @ X1 ) )
= $true )
| ( $false
= ( sK4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f227,plain,
( ( $false
= ( sK4
@ ( s
@ ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f222]) ).
thf(f222,plain,
( ( $false
= ( sK4
@ ( s
@ ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) ) ) ) )
| ( $false = $true )
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f46,f185]) ).
thf(f185,plain,
( ( $false
= ( sK4
@ ( s
@ ( s
@ ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) ) ) ) ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f183]) ).
thf(f183,definition,
( spl0_10
<=> ( $false
= ( sK4
@ ( s
@ ( s
@ ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f201,plain,
( spl0_11
| spl0_10
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f200,f54,f49,f45,f183,f187]) ).
thf(f200,plain,
( ! [X0: $i] :
( ( ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) )
!= X0 )
| ( $false
= ( sK4
@ ( s
@ ( s
@ ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) ) ) ) ) )
| ( ( sK4 @ X0 )
= $false ) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f199]) ).
thf(f199,plain,
( ! [X0: $i] :
( ( ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) )
!= X0 )
| ( $false = $true )
| ( ( sK4 @ X0 )
= $false )
| ( $false
= ( sK4
@ ( s
@ ( s
@ ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f198,f56]) ).
thf(f198,plain,
( ! [X0: $i] :
( ( $true
= ( sK4 @ sK2 ) )
| ( ( sK4 @ X0 )
= $false )
| ( $false
= ( sK4
@ ( s
@ ( s
@ ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) ) ) ) ) )
| ( ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) )
!= X0 ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f197]) ).
thf(f197,plain,
( ! [X0: $i] :
( ( ( sK4 @ X0 )
= $false )
| ( $false
= ( sK4
@ ( s
@ ( s
@ ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) ) ) ) ) )
| ( ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) )
!= X0 )
| ( $false = $true )
| ( $true
= ( sK4 @ sK2 ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f147,f51]) ).
thf(f147,plain,
( ! [X0: $i] :
( ( $false
= ( sK4
@ ( s
@ ( s
@ ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) ) ) ) ) )
| ( ( sK6
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 ) )
!= X0 )
| ( ( sK4 @ X0 )
= $false )
| ( $false
= ( sK4 @ c1 ) )
| ( $true
= ( sK4 @ sK2 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f146]) ).
thf(f146,plain,
( ! [X0: $i] :
( ( ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ sK2
@ sK1 )
= $true )
| ( ( sK4 @ X0 )
= $false )
| ( ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ ( s
@ ( s
@ ( sK6
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) ) ) )
@ ( sK5
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( ( sK6
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) )
!= X0 ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ! [X0: $i] :
( ( ( sK6
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) )
!= X0 )
| ( ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ sK2
@ sK1 )
= $true )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ c1
@ c1 ) )
| ( ( ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) )
@ ( s
@ ( s
@ ( sK6
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) ) ) )
@ ( sK5
@ ^ [Y0: $i,Y1: $i] :
( sK4
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 ) ) ) )
= $false )
| ( ( sK4 @ X0 )
= $false )
| ( $false = $true ) )
| ~ spl0_2 ),
inference(constrained_superposition,[status(thm)],[f46,f102]) ).
thf(f91,plain,
( spl0_6
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f90,f45,f81]) ).
thf(f90,plain,
! [X1: $i] :
( ( ( sK4 @ ( s @ X1 ) )
= $true )
| ( ( sK3 @ sK1 )
= $false )
| ( $false
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
! [X1: $i] :
( ( ( ( sK4 @ X1 )
=> ( sK4 @ ( s @ X1 ) ) )
= $true )
| ( ( sK3 @ sK1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) )
@ X1 ) )
| ( ( sK3 @ sK1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( ( ( sK3 @ sK1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) )
& ( sK4 @ c1 ) )
= $true )
| ( ( sK3 @ sK1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) )
& ( sK4 @ c1 ) )
=> ( sK4 @ sK2 ) )
= $false )
| ( ( sK3 @ sK1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK2 ) )
@ sK4 )
= $false )
| ( ( sK3 @ sK1 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( sK3 @ sK1 )
= $false )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ Y0 ) ) ) )
& ( sK3 @ c1 ) )
=> ( sK3 @ sK1 ) )
= $false )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK2 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK1 ) )
@ sK3 ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK2 ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK1 ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK2 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK1 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f87,plain,
( spl0_6
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f85,f49,f81]) ).
thf(f85,plain,
( ( ( sK4 @ c1 )
= $true )
| ( ( sK3 @ sK1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f84,plain,
( spl0_4
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f78,f81,f54]) ).
thf(f78,plain,
( ( $false
= ( sK4 @ sK2 ) )
| ( ( sK3 @ sK1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f75,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f74,f69,f54]) ).
thf(f74,plain,
! [X1: $i] :
( ( $false
= ( sK4 @ sK2 ) )
| ( ( sK3 @ ( s @ X1 ) )
= $true )
| ( ( sK3 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: $i] :
( ( $false
= ( sK4 @ sK2 ) )
| ( ( ( sK3 @ X1 )
=> ( sK3 @ ( s @ X1 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: $i] :
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) )
& ( sK4 @ c1 ) )
=> ( sK4 @ sK2 ) )
= $false )
| ( ( ( sK3 @ X1 )
=> ( sK3 @ ( s @ X1 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: $i] :
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) )
& ( sK4 @ c1 ) )
=> ( sK4 @ sK2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ Y0 ) ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ Y0 ) ) ) )
= $true )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) )
& ( sK4 @ c1 ) )
=> ( sK4 @ sK2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ Y0 ) ) ) )
& ( sK3 @ c1 ) )
= $true )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) )
& ( sK4 @ c1 ) )
=> ( sK4 @ sK2 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ Y0 ) ) ) )
& ( sK3 @ c1 ) )
= $true )
| ( ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK2 ) )
@ sK4 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK2 ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ Y0 ) ) ) )
& ( sK3 @ c1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f73,plain,
( spl0_5
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f72,f49,f69]) ).
thf(f72,plain,
! [X1: $i] :
( ( ( sK4 @ c1 )
= $true )
| ( ( sK3 @ ( s @ X1 ) )
= $true )
| ( ( sK3 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X1: $i] :
( ( ( ( sK3 @ X1 )
=> ( sK3 @ ( s @ X1 ) ) )
= $true )
| ( ( sK4 @ c1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) )
& ( sK4 @ c1 ) )
= $true )
| ( ( ( sK3 @ X1 )
=> ( sK3 @ ( s @ X1 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f71,plain,
( spl0_5
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f67,f45,f69]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK4 @ X2 ) )
| ( ( sK3 @ ( s @ X1 ) )
= $true )
| ( ( sK4 @ ( s @ X2 ) )
= $true )
| ( ( sK3 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK4 @ X2 )
=> ( sK4 @ ( s @ X2 ) ) )
= $true )
| ( ( sK3 @ X1 )
= $false )
| ( ( sK3 @ ( s @ X1 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( ( ( sK3 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) )
@ X2 ) )
| ( ( sK3 @ ( s @ X1 ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X1: $i] :
( ( ( sK3 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) ) )
| ( ( sK3 @ ( s @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X1: $i] :
( ( ( ( sK3 @ X1 )
=> ( sK3 @ ( s @ X1 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f57,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f33,f54,f41]) ).
thf(f33,plain,
( ( $false
= ( sK4 @ sK2 ) )
| ( $true
= ( sK3 @ c1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) )
& ( sK4 @ c1 ) )
=> ( sK4 @ sK2 ) )
= $false )
| ( $true
= ( sK3 @ c1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f52,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f35,f49,f41]) ).
thf(f35,plain,
( ( $true
= ( sK3 @ c1 ) )
| ( ( sK4 @ c1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true
= ( sK3 @ c1 ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) )
& ( sK4 @ c1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f47,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f39,f45,f41]) ).
thf(f39,plain,
! [X1: $i] :
( ( ( sK4 @ ( s @ X1 ) )
= $true )
| ( $true
= ( sK3 @ c1 ) )
| ( $false
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( ( ( ( sK4 @ X1 )
=> ( sK4 @ ( s @ X1 ) ) )
= $true )
| ( $true
= ( sK3 @ c1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ c1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true
= ( sK3 @ c1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU969^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n002.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 12:37:48 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : SEU969^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.31/0.45 % Domain : Set Theory (Relations)
% 0.31/0.45 % Problem : TPS problem from CHECKERBOARD-RELNS
% 0.31/0.45 % Version : Especial.
% 0.31/0.45 % English :
% 0.31/0.45
% 0.31/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.45 % Source : [Bro09]
% 0.31/0.45 % Names : tps_0682 [Bro09]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.29 v7.4.0, 0.56 v7.3.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v5.2.0
% 0.31/0.45 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.31/0.45 % Number of atoms : 7 ( 2 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 3 ( 2 avg)
% 0.31/0.45 % Number of connectives : 32 ( 0 ~; 0 |; 4 &; 23 @)
% 0.31/0.45 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.31/0.45 % Maximal formula depth : 6 ( 3 avg)
% 0.31/0.45 % Number of types : 2 ( 0 usr)
% 0.31/0.45 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.31/0.45 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.31/0.45 % Number of variables : 10 ( 3 ^; 7 !; 0 ?; 10 :)
% 0.31/0.45 % SPC : TH0_THM_EQU_NAR
% 0.31/0.45
% 0.31/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.45 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 thf(c1_type,type,
% 0.31/0.45 c1: $i ).
% 0.31/0.45
% 0.31/0.45 thf(s_type,type,
% 0.31/0.45 s: $i > $i ).
% 0.31/0.45
% 0.31/0.45 thf(cCKB6_BLACK_type,type,
% 0.31/0.45 cCKB6_BLACK: $i > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(cCKB6_NUM_type,type,
% 0.31/0.45 cCKB6_NUM: $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(cCKB6_BLACK_def,definition,
% 0.31/0.45 ( cCKB6_BLACK
% 0.31/0.45 = ( ^ [Xu: $i,Xv: $i] :
% 0.31/0.45 ! [Xw: $i > $i > $o] :
% 0.31/0.45 ( ( ( Xw @ c1 @ c1 )
% 0.31/0.45 & ! [Xj: $i,Xk: $i] :
% 0.31/0.45 ( ( Xw @ Xj @ Xk )
% 0.31/0.45 => ( ( Xw @ ( s @ ( s @ Xj ) ) @ Xk )
% 0.31/0.45 & ( Xw @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
% 0.31/0.45 => ( Xw @ Xu @ Xv ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(cCKB6_NUM_def,definition,
% 0.31/0.45 ( cCKB6_NUM
% 0.31/0.45 = ( ^ [Xx: $i] :
% 0.31/0.45 ! [Xp: $i > $o] :
% 0.31/0.45 ( ( ( Xp @ c1 )
% 0.31/0.45 & ! [Xw: $i] :
% 0.31/0.45 ( ( Xp @ Xw )
% 0.31/0.45 => ( Xp @ ( s @ Xw ) ) ) )
% 0.31/0.45 => ( Xp @ Xx ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(cCKB6_L6000_pme,conjecture,
% 0.31/0.45 ! [Xx: $i,Xy: $i] :
% 0.31/0.45 ( ( cCKB6_BLACK @ Xx @ Xy )
% 0.31/0.45 => ( ( cCKB6_NUM @ Xx )
% 0.31/0.45 & ( cCKB6_NUM @ Xy ) ) ) ).
% 0.31/0.45
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 ------------------------
% 1.67/1.32 ---- Embedded in THF ---
% 1.67/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.32 %%% Generated on Tue Feb 24 12:37:49 EST 2026
% 1.67/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.32 %%% Logic specification used:
% 1.67/1.32 %%% thf(spec, logic, $$dhol).
% 1.67/1.32
% 1.67/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6uP4k6plCZ/DTF2DTF29139.p
% See solution above
% 1.67/1.32 ------------------------
% 1.67/1.32 ---- Cleaned THF ---
% 1.67/1.32 thf(c1_type,type,
% 1.67/1.32 c1: $i ).
% 1.67/1.32
% 1.67/1.32 thf(s_type,type,
% 1.67/1.32 s: $i > $i ).
% 1.67/1.32
% 1.67/1.32 thf(cCKB6_BLACK_type,type,
% 1.67/1.32 cCKB6_BLACK: $i > $i > $o ).
% 1.67/1.32
% 1.67/1.32 thf(cCKB6_NUM_type,type,
% 1.67/1.32 cCKB6_NUM: $i > $o ).
% 1.67/1.32
% 1.67/1.32 thf(cCKB6_BLACK_def,definition,
% 1.67/1.32 ( cCKB6_BLACK
% 1.67/1.32 = ( ^ [Xu: $i,Xv: $i] :
% 1.67/1.32 ! [Xw: $i > $i > $o] :
% 1.67/1.32 ( ( ( Xw @ c1 @ c1 )
% 1.67/1.32 & ! [Xj: $i,Xk: $i] :
% 1.67/1.32 ( ( Xw @ Xj @ Xk )
% 1.67/1.32 => ( ( Xw @ ( s @ ( s @ Xj ) ) @ Xk )
% 1.67/1.32 & ( Xw @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
% 1.67/1.32 => ( Xw @ Xu @ Xv ) ) ) ) ).
% 1.67/1.32
% 1.67/1.32 thf(cCKB6_NUM_def,definition,
% 1.67/1.32 ( cCKB6_NUM
% 1.67/1.32 = ( ^ [Xx: $i] :
% 1.67/1.32 ! [Xp: $i > $o] :
% 1.67/1.32 ( ( ( Xp @ c1 )
% 1.67/1.32 & ! [Xw: $i] :
% 1.67/1.32 ( ( Xp @ Xw )
% 1.67/1.32 => ( Xp @ ( s @ Xw ) ) ) )
% 1.67/1.32 => ( Xp @ Xx ) ) ) ) ).
% 1.67/1.32
% 1.67/1.32 thf(cCKB6_L6000_pme,conjecture,
% 1.67/1.32 ! [Xx: $i,Xy: $i] :
% 1.67/1.32 ( ( cCKB6_BLACK @ Xx @ Xy )
% 1.67/1.32 => ( ( cCKB6_NUM @ Xx )
% 1.67/1.32 & ( cCKB6_NUM @ Xy ) ) ) ).
% 1.67/1.32 ------------------------
% 1.67/1.34 % (29329)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_29139 for (3000ds/27Mi)
% 1.67/1.34 % (29331)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_29139 for (3000ds/2Mi)
% 1.67/1.34 % (29331)Instruction limit reached!
% 1.67/1.34 % (29331)------------------------------
% 1.67/1.34 % (29331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (29331)Termination reason: Unknown
% 1.67/1.34 % (29331)Termination phase: Saturation
% 1.67/1.34
% 1.67/1.34 % (29331)Memory used [KB]: 5500
% 1.67/1.34 % (29331)Time elapsed: 0.002 s
% 1.67/1.34 % (29331)Instructions burned: 3 (million)
% 1.67/1.34 % (29331)------------------------------
% 1.67/1.34 % (29331)------------------------------
% 1.67/1.34 % (29327)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29139 for (3000ds/183Mi)
% 1.67/1.34 % (29329)Refutation not found, incomplete strategy
% 1.67/1.34 % (29329)------------------------------
% 1.67/1.34 % (29329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (29329)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.34
% 1.67/1.34
% 1.67/1.34 % (29329)Memory used [KB]: 5500
% 1.67/1.34 % (29329)Time elapsed: 0.004 s
% 1.67/1.34 % (29329)Instructions burned: 6 (million)
% 1.67/1.34 % (29329)------------------------------
% 1.67/1.34 % (29329)------------------------------
% 1.67/1.34 % (29333)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29139 for (3000ds/18Mi)
% 1.67/1.34 % (29328)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_29139 for (3000ds/4Mi)
% 1.67/1.34 % (29330)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29139 for (3000ds/2Mi)
% 1.67/1.34 % (29332)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_29139 for (3000ds/275Mi)
% 1.67/1.34 % (29330)Instruction limit reached!
% 1.67/1.34 % (29330)------------------------------
% 1.67/1.34 % (29330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (29330)Termination reason: Unknown
% 1.67/1.34 % (29330)Termination phase: Property scanning
% 1.67/1.34
% 1.67/1.34 % (29330)Memory used [KB]: 895
% 1.67/1.34 % (29330)Time elapsed: 0.003 s
% 1.67/1.34 % (29330)Instructions burned: 2 (million)
% 1.67/1.34 % (29330)------------------------------
% 1.67/1.34 % (29330)------------------------------
% 1.67/1.35 % (29333)Instruction limit reached!
% 1.67/1.35 % (29333)------------------------------
% 1.67/1.35 % (29333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (29333)Termination reason: Unknown
% 1.67/1.35 % (29333)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (29333)Memory used [KB]: 5628
% 1.67/1.35 % (29333)Time elapsed: 0.008 s
% 1.67/1.35 % (29333)Instructions burned: 18 (million)
% 1.67/1.35 % (29333)------------------------------
% 1.67/1.35 % (29333)------------------------------
% 1.67/1.35 % (29328)Instruction limit reached!
% 1.67/1.35 % (29328)------------------------------
% 1.67/1.35 % (29328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (29328)Termination reason: Unknown
% 1.67/1.35 % (29328)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (29328)Memory used [KB]: 5500
% 1.67/1.35 % (29328)Time elapsed: 0.005 s
% 1.67/1.35 % (29328)Instructions burned: 5 (million)
% 1.67/1.35 % (29328)------------------------------
% 1.67/1.35 % (29328)------------------------------
% 1.67/1.35 % (29332)Refutation not found, incomplete strategy
% 1.67/1.35 % (29332)------------------------------
% 1.67/1.35 % (29332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (29332)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.35
% 1.67/1.35
% 1.67/1.35 % (29332)Memory used [KB]: 5500
% 1.67/1.35 % (29332)Time elapsed: 0.006 s
% 1.67/1.35 % (29332)Instructions burned: 5 (million)
% 1.67/1.35 % (29332)------------------------------
% 1.67/1.35 % (29332)------------------------------
% 1.67/1.35 % (29334)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29139 for (2999ds/3Mi)
% 1.67/1.35 % (29335)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_29139 for (2999ds/37Mi)
% 1.67/1.35 % (29334)Instruction limit reached!
% 1.67/1.35 % (29334)------------------------------
% 1.67/1.35 % (29334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (29334)Termination reason: Unknown
% 1.67/1.35 % (29334)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (29334)Memory used [KB]: 5500
% 1.67/1.35 % (29334)Time elapsed: 0.003 s
% 1.67/1.35 % (29334)Instructions burned: 3 (million)
% 1.67/1.35 % (29334)------------------------------
% 1.67/1.35 % (29334)------------------------------
% 1.67/1.36 % (29338)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_29139 for (2999ds/1041Mi)
% 1.67/1.36 % (29340)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29139 for (2999ds/16Mi)
% 1.67/1.36 % (29335)Instruction limit reached!
% 1.67/1.36 % (29335)------------------------------
% 1.67/1.36 % (29335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.36 % (29335)Termination reason: Unknown
% 1.67/1.36 % (29335)Termination phase: Saturation
% 1.67/1.36
% 1.67/1.36 % (29335)Memory used [KB]: 5884
% 1.67/1.36 % (29335)Time elapsed: 0.012 s
% 1.67/1.36 % (29335)Instructions burned: 38 (million)
% 1.67/1.36 % (29335)------------------------------
% 1.67/1.36 % (29335)------------------------------
% 1.67/1.36 % (29336)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_29139 for (2999ds/15Mi)
% 1.67/1.36 % (29337)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_29139 for (2999ds/3Mi)
% 1.67/1.37 % (29340)Instruction limit reached!
% 1.67/1.37 % (29340)------------------------------
% 1.67/1.37 % (29340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (29340)Termination reason: Unknown
% 1.67/1.37 % (29340)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (29340)Memory used [KB]: 5756
% 1.67/1.37 % (29340)Time elapsed: 0.008 s
% 1.67/1.37 % (29340)Instructions burned: 16 (million)
% 1.67/1.37 % (29340)------------------------------
% 1.67/1.37 % (29340)------------------------------
% 1.67/1.37 % (29337)Instruction limit reached!
% 1.67/1.37 % (29337)------------------------------
% 1.67/1.37 % (29337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (29339)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29139 for (2999ds/7Mi)
% 1.67/1.37 % (29337)Termination reason: Unknown
% 1.67/1.37 % (29337)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (29337)Memory used [KB]: 5500
% 1.67/1.37 % (29337)Time elapsed: 0.004 s
% 1.67/1.37 % (29337)Instructions burned: 3 (million)
% 1.67/1.37 % (29337)------------------------------
% 1.67/1.37 % (29337)------------------------------
% 1.67/1.37 % (29346)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_29139 for (2999ds/3Mi)
% 1.67/1.37 % (29339)Instruction limit reached!
% 1.67/1.37 % (29339)------------------------------
% 1.67/1.37 % (29339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (29339)Termination reason: Unknown
% 1.67/1.37 % (29339)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (29339)Memory used [KB]: 1023
% 1.67/1.37 % (29339)Time elapsed: 0.008 s
% 1.67/1.37 % (29339)Instructions burned: 7 (million)
% 1.67/1.37 % (29339)------------------------------
% 1.67/1.37 % (29339)------------------------------
% 1.67/1.37 % (29346)Instruction limit reached!
% 1.67/1.37 % (29346)------------------------------
% 1.67/1.37 % (29346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (29346)Termination reason: Unknown
% 1.67/1.37 % (29346)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (29346)Memory used [KB]: 5500
% 1.67/1.37 % (29346)Time elapsed: 0.004 s
% 1.67/1.37 % (29346)Instructions burned: 4 (million)
% 1.67/1.37 % (29346)------------------------------
% 1.67/1.37 % (29346)------------------------------
% 1.67/1.37 % (29336)Instruction limit reached!
% 1.67/1.37 % (29336)------------------------------
% 1.67/1.37 % (29336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (29336)Termination reason: Unknown
% 1.67/1.37 % (29336)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (29336)Memory used [KB]: 5628
% 1.67/1.37 % (29336)Time elapsed: 0.013 s
% 1.67/1.37 % (29336)Instructions burned: 15 (million)
% 1.67/1.37 % (29336)------------------------------
% 1.67/1.37 % (29336)------------------------------
% 1.67/1.38 % (29349)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_29139 for (2999ds/3Mi)
% 1.67/1.38 % (29349)Instruction limit reached!
% 1.67/1.38 % (29349)------------------------------
% 1.67/1.38 % (29349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.38 % (29349)Termination reason: Unknown
% 1.67/1.38 % (29349)Termination phase: Property scanning
% 1.67/1.38
% 1.67/1.38 % (29349)Memory used [KB]: 1023
% 1.67/1.38 % (29349)Time elapsed: 0.003 s
% 1.67/1.38 % (29349)Instructions burned: 3 (million)
% 1.67/1.38 % (29349)------------------------------
% 1.67/1.38 % (29349)------------------------------
% 1.67/1.38 % (29350)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29139 for (2999ds/7Mi)
% 1.67/1.39 % (29350)Refutation not found, incomplete strategy
% 1.67/1.39 % (29350)------------------------------
% 1.67/1.39 % (29350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (29350)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.39
% 1.67/1.39
% 1.67/1.39 % (29350)Memory used [KB]: 5500
% 1.67/1.39 % (29350)Time elapsed: 0.004 s
% 1.67/1.39 % (29350)Instructions burned: 3 (million)
% 1.67/1.39 % (29350)------------------------------
% 1.67/1.39 % (29350)------------------------------
% 1.67/1.39 % (29359)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29139 for (2999ds/4Mi)
% 1.67/1.39 % (29359)Instruction limit reached!
% 1.67/1.39 % (29359)------------------------------
% 1.67/1.39 % (29359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (29359)Termination reason: Unknown
% 1.67/1.39 % (29359)Termination phase: Saturation
% 1.67/1.39
% 1.67/1.39 % (29359)Memory used [KB]: 5500
% 1.67/1.39 % (29359)Time elapsed: 0.002 s
% 1.67/1.39 % (29359)Instructions burned: 4 (million)
% 1.67/1.39 % (29359)------------------------------
% 1.67/1.39 % (29359)------------------------------
% 1.67/1.39 % (29360)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29139 for (2999ds/18Mi)
% 1.72/1.40 % (29364)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29139 for (2999ds/6Mi)
% 1.72/1.40 % (29361)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29139 for (2999ds/710Mi)
% 1.72/1.40 % (29364)Instruction limit reached!
% 1.72/1.40 % (29364)------------------------------
% 1.72/1.40 % (29364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.40 % (29364)Termination reason: Unknown
% 1.72/1.40 % (29364)Termination phase: Saturation
% 1.72/1.40
% 1.72/1.40 % (29364)Memory used [KB]: 5500
% 1.72/1.40 % (29364)Time elapsed: 0.005 s
% 1.72/1.40 % (29364)Instructions burned: 7 (million)
% 1.72/1.40 % (29364)------------------------------
% 1.72/1.40 % (29364)------------------------------
% 1.72/1.40 % (29360)Instruction limit reached!
% 1.72/1.40 % (29360)------------------------------
% 1.72/1.40 % (29360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.40 % (29360)Termination reason: Unknown
% 1.72/1.40 % (29360)Termination phase: Saturation
% 1.72/1.40
% 1.72/1.40 % (29360)Memory used [KB]: 5628
% 1.72/1.40 % (29360)Time elapsed: 0.012 s
% 1.72/1.40 % (29360)Instructions burned: 18 (million)
% 1.72/1.40 % (29360)------------------------------
% 1.72/1.40 % (29360)------------------------------
% 1.72/1.40 % (29365)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_29139 for (2999ds/902Mi)
% 1.72/1.40 % (29365)Refutation not found, incomplete strategy
% 1.72/1.40 % (29365)------------------------------
% 1.72/1.40 % (29365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.40 % (29365)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.40
% 1.72/1.40
% 1.72/1.40 % (29365)Memory used [KB]: 5500
% 1.72/1.40 % (29365)Time elapsed: 0.023 s
% 1.72/1.40 % (29365)Instructions burned: 1 (million)
% 1.72/1.40 % (29365)------------------------------
% 1.72/1.40 % (29365)------------------------------
% 1.72/1.41 % (29358)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29139 for (2999ds/3Mi)
% 1.72/1.41 % (29358)Instruction limit reached!
% 1.72/1.41 % (29358)------------------------------
% 1.72/1.41 % (29358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.41 % (29358)Termination reason: Unknown
% 1.72/1.41 % (29358)Termination phase: Saturation
% 1.72/1.41
% 1.72/1.41 % (29358)Memory used [KB]: 5500
% 1.72/1.41 % (29358)Time elapsed: 0.025 s
% 1.72/1.41 % (29358)Instructions burned: 4 (million)
% 1.72/1.41 % (29358)------------------------------
% 1.72/1.41 % (29358)------------------------------
% 1.72/1.41 % (29327)Instruction limit reached!
% 1.72/1.41 % (29327)------------------------------
% 1.72/1.41 % (29327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.41 % (29327)Termination reason: Unknown
% 1.72/1.41 % (29327)Termination phase: Saturation
% 1.72/1.41
% 1.72/1.41 % (29327)Memory used [KB]: 6396
% 1.72/1.41 % (29327)Time elapsed: 0.075 s
% 1.72/1.41 % (29327)Instructions burned: 185 (million)
% 1.72/1.41 % (29327)------------------------------
% 1.72/1.41 % (29327)------------------------------
% 1.72/1.42 % (29370)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29139 for (2999ds/5Mi)
% 1.72/1.42 % (29370)Instruction limit reached!
% 1.72/1.42 % (29370)------------------------------
% 1.72/1.42 % (29370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (29370)Termination reason: Unknown
% 1.72/1.42 % (29370)Termination phase: Saturation
% 1.72/1.42
% 1.72/1.42 % (29370)Memory used [KB]: 5500
% 1.72/1.42 % (29370)Time elapsed: 0.004 s
% 1.72/1.42 % (29370)Instructions burned: 8 (million)
% 1.72/1.42 % (29370)------------------------------
% 1.72/1.42 % (29370)------------------------------
% 1.72/1.42 % (29372)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_29139 for (2999ds/6Mi)
% 1.72/1.42 % (29372)Instruction limit reached!
% 1.72/1.42 % (29372)------------------------------
% 1.72/1.42 % (29372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (29372)Termination reason: Unknown
% 1.72/1.42 % (29372)Termination phase: Saturation
% 1.72/1.42
% 1.72/1.42 % (29372)Memory used [KB]: 5500
% 1.72/1.42 % (29372)Time elapsed: 0.005 s
% 1.72/1.42 % (29372)Instructions burned: 7 (million)
% 1.72/1.42 % (29372)------------------------------
% 1.72/1.42 % (29372)------------------------------
% 1.72/1.43 % (29375)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_29139 for (2999ds/779Mi)
% 1.72/1.43 % (29377)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_29139 for (2999ds/19Mi)
% 1.72/1.44 % (29373)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29139 for (2999ds/377Mi)
% 1.72/1.44 % (29377)Refutation not found, incomplete strategy
% 1.72/1.44 % (29377)------------------------------
% 1.72/1.44 % (29377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.44 % (29377)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.44
% 1.72/1.44
% 1.72/1.44 % (29377)Memory used [KB]: 5500
% 1.72/1.44 % (29377)Time elapsed: 0.005 s
% 1.72/1.44 % (29377)Instructions burned: 7 (million)
% 1.72/1.44 % (29377)------------------------------
% 1.72/1.44 % (29377)------------------------------
% 1.72/1.44 % (29369)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_29139 for (2999ds/21Mi)
% 1.72/1.44 % (29380)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_29139 for (2999ds/879Mi)
% 1.72/1.45 % (29385)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_29139 for (2999ds/17Mi)
% 1.72/1.45 % (29380)Refutation not found, incomplete strategy
% 1.72/1.45 % (29380)------------------------------
% 1.72/1.45 % (29380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (29380)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.45
% 1.72/1.45
% 1.72/1.45 % (29380)Memory used [KB]: 5628
% 1.72/1.45 % (29380)Time elapsed: 0.012 s
% 1.72/1.45 % (29380)Instructions burned: 19 (million)
% 1.72/1.45 % (29380)------------------------------
% 1.72/1.45 % (29380)------------------------------
% 1.72/1.46 % (29385)Instruction limit reached!
% 1.72/1.46 % (29385)------------------------------
% 1.72/1.46 % (29385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (29385)Termination reason: Unknown
% 1.72/1.46 % (29385)Termination phase: Saturation
% 1.72/1.46
% 1.72/1.46 % (29385)Memory used [KB]: 5628
% 1.72/1.46 % (29385)Time elapsed: 0.034 s
% 1.72/1.46 % (29385)Instructions burned: 18 (million)
% 1.72/1.46 % (29385)------------------------------
% 1.72/1.46 % (29385)------------------------------
% 1.72/1.46 % (29369)Instruction limit reached!
% 1.72/1.46 % (29369)------------------------------
% 1.72/1.46 % (29369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (29369)Termination reason: Unknown
% 1.72/1.46 % (29369)Termination phase: Saturation
% 1.72/1.46
% 1.72/1.46 % (29369)Memory used [KB]: 5628
% 1.72/1.46 % (29369)Time elapsed: 0.049 s
% 1.72/1.46 % (29369)Instructions burned: 21 (million)
% 1.72/1.46 % (29369)------------------------------
% 1.72/1.46 % (29369)------------------------------
% 1.72/1.46 % (29375)First to succeed.
% 1.72/1.47 % (29375)Refutation found. Thanks to Tanya!
% 1.72/1.47 % SZS status Theorem for DTF2THF_29139
% 1.72/1.47 % SZS output start Proof for DTF2THF_29139
% 1.72/1.47 thf(func_def_1, type, s: $i > $i).
% 1.72/1.47 thf(func_def_2, type, cCKB6_BLACK: $i > $i > $o).
% 1.72/1.47 thf(func_def_3, type, cCKB6_NUM: $i > $o).
% 1.72/1.47 thf(func_def_18, type, sK3: $i > $o).
% 1.72/1.47 thf(func_def_19, type, sK4: $i > $o).
% 1.72/1.47 thf(func_def_20, type, sK5: ($i > $i > $o) > $i).
% 1.72/1.47 thf(func_def_21, type, sK6: ($i > $i > $o) > $i).
% 1.72/1.47 thf(func_def_22, type, ph7: !>[X0: $tType]:(X0)).
% 1.72/1.47 thf(f419,plain,(
% 1.72/1.47 $false),
% 1.72/1.47 inference(avatar_sat_refutation,[status(thm)],[f47,f52,f57,f71,f73,f75,f84,f87,f91,f201,f266,f300,f392,f397,f418])).
% 1.72/1.47 thf(f418,plain,(
% 1.72/1.47 ~spl0_1 | ~spl0_6 | ~spl0_17),
% 1.72/1.47 inference(avatar_contradiction_clause,[status(thm)],[f417])).
% 1.72/1.47 thf(f417,plain,(
% 1.72/1.47 $false | (~spl0_1 | ~spl0_6 | ~spl0_17)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f416])).
% 1.72/1.47 thf(f416,plain,(
% 1.72/1.47 ($false = $true) | (~spl0_1 | ~spl0_6 | ~spl0_17)),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f415,f83])).
% 1.72/1.47 thf(f83,plain,(
% 1.72/1.47 ((sK3 @ sK1) = $false) | ~spl0_6),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.72/1.47 thf(f81,definition,(
% 1.72/1.47 spl0_6 <=> ((sK3 @ sK1) = $false)),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.72/1.47 thf(f415,plain,(
% 1.72/1.47 ((sK3 @ sK1) = $true) | (~spl0_1 | ~spl0_17)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f414])).
% 1.72/1.47 thf(f414,plain,(
% 1.72/1.47 ((sK3 @ sK1) = $true) | ($false = $true) | (~spl0_1 | ~spl0_17)),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f404,f43])).
% 1.72/1.47 thf(f43,plain,(
% 1.72/1.47 ($true = (sK3 @ c1)) | ~spl0_1),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.72/1.47 thf(f41,definition,(
% 1.72/1.47 spl0_1 <=> ($true = (sK3 @ c1))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.72/1.47 thf(f404,plain,(
% 1.72/1.47 ($false = (sK3 @ c1)) | ((sK3 @ sK1) = $true) | ~spl0_17),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f403])).
% 1.72/1.47 thf(f403,plain,(
% 1.72/1.47 ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ c1 @ c1)) | ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ sK2 @ sK1)) | ~spl0_17),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f399])).
% 1.72/1.47 thf(f399,plain,(
% 1.72/1.47 ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ c1 @ c1)) | ($false = $true) | ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ sK2 @ sK1)) | ~spl0_17),
% 1.72/1.47 inference(superposition,[status(thm)],[f386,f101])).
% 1.72/1.47 thf(f101,plain,(
% 1.72/1.47 ( ! [X1 : $i > $i > $o] : (((X1 @ (sK6 @ X1) @ (sK5 @ X1)) = $true) | ((X1 @ sK2 @ sK1) = $true) | ($false = (X1 @ c1 @ c1))) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.72/1.47 thf(f99,plain,(
% 1.72/1.47 ( ! [X1 : $i > $i > $o] : (((X1 @ sK2 @ sK1) = $true) | (((X1 @ (sK6 @ X1) @ (sK5 @ X1)) => ((X1 @ (s @ (s @ (sK6 @ X1))) @ (sK5 @ X1)) & (X1 @ (s @ (sK6 @ X1)) @ (s @ (sK5 @ X1))))) = $false) | ($false = (X1 @ c1 @ c1))) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f98])).
% 1.72/1.47 thf(f98,plain,(
% 1.72/1.47 ( ! [X1 : $i > $i > $o] : (($false = (X1 @ c1 @ c1)) | (((^[Y0 : $i]: ((X1 @ Y0 @ (sK5 @ X1)) => ((X1 @ (s @ (s @ Y0)) @ (sK5 @ X1)) & (X1 @ (s @ Y0) @ (s @ (sK5 @ X1)))))) @ (sK6 @ X1)) = $false) | ((X1 @ sK2 @ sK1) = $true)) )),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f97])).
% 1.72/1.47 thf(f97,plain,(
% 1.72/1.47 ( ! [X1 : $i > $i > $o] : (($false = (X1 @ c1 @ c1)) | ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0 @ (sK5 @ X1)) => ((X1 @ (s @ (s @ Y0)) @ (sK5 @ X1)) & (X1 @ (s @ Y0) @ (s @ (sK5 @ X1))))))) = $false) | ((X1 @ sK2 @ sK1) = $true)) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f96])).
% 1.72/1.47 thf(f96,plain,(
% 1.72/1.47 ( ! [X1 : $i > $i > $o] : (((X1 @ sK2 @ sK1) = $true) | ($false = (X1 @ c1 @ c1)) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => ((X1 @ (s @ (s @ Y1)) @ Y0) & (X1 @ (s @ Y1) @ (s @ Y0))))))) @ (sK5 @ X1)))) )),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f95])).
% 1.72/1.47 thf(f95,plain,(
% 1.72/1.47 ( ! [X1 : $i > $i > $o] : (((X1 @ sK2 @ sK1) = $true) | ($false = (X1 @ c1 @ c1)) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => ((X1 @ (s @ (s @ Y1)) @ Y0) & (X1 @ (s @ Y1) @ (s @ Y0)))))))))) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.72/1.47 thf(f94,plain,(
% 1.72/1.47 ( ! [X1 : $i > $i > $o] : ((((X1 @ c1 @ c1) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => ((X1 @ (s @ (s @ Y1)) @ Y0) & (X1 @ (s @ Y1) @ (s @ Y0))))))))) = $false) | ((X1 @ sK2 @ sK1) = $true)) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.72/1.47 thf(f93,plain,(
% 1.72/1.47 ( ! [X1 : $i > $i > $o] : (($true = (((X1 @ c1 @ c1) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => ((X1 @ (s @ (s @ Y1)) @ Y0) & (X1 @ (s @ Y1) @ (s @ Y0))))))))) => (X1 @ sK2 @ sK1)))) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f92])).
% 1.72/1.47 thf(f92,plain,(
% 1.72/1.47 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (((Y0 @ c1 @ c1) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => ((Y0 @ (s @ (s @ Y2)) @ Y1) & (Y0 @ (s @ Y2) @ (s @ Y1))))))))) => (Y0 @ sK2 @ sK1))) @ X1) = $true)) )),
% 1.72/1.47 inference(pi_clausification,[status(thm)],[f23])).
% 1.72/1.47 thf(f23,plain,(
% 1.72/1.47 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ c1 @ c1) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => ((Y0 @ (s @ (s @ Y2)) @ Y1) & (Y0 @ (s @ Y2) @ (s @ Y1))))))))) => (Y0 @ sK2 @ sK1)))) = $true)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.72/1.47 thf(f21,plain,(
% 1.72/1.47 (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ c1 @ c1) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => ((Y0 @ (s @ (s @ Y2)) @ Y1) & (Y0 @ (s @ Y2) @ (s @ Y1))))))))) => (Y0 @ sK2 @ sK1)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK2)))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK1)))))) = $false)),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.72/1.47 thf(f20,plain,(
% 1.72/1.47 ($false = ((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ c1 @ c1) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) => ((Y1 @ (s @ (s @ Y3)) @ Y2) & (Y1 @ (s @ Y3) @ (s @ Y2))))))))) => (Y1 @ Y0 @ sK1)))) => ((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2))))) & (Y1 @ c1)) => (Y1 @ Y0)))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2))))) & (Y1 @ c1)) => (Y1 @ sK1))))))) @ sK2))),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f19])).
% 1.72/1.47 thf(f19,plain,(
% 1.72/1.47 ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ c1 @ c1) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) => ((Y1 @ (s @ (s @ Y3)) @ Y2) & (Y1 @ (s @ Y3) @ (s @ Y2))))))))) => (Y1 @ Y0 @ sK1)))) => ((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2))))) & (Y1 @ c1)) => (Y1 @ Y0)))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2))))) & (Y1 @ c1)) => (Y1 @ sK1)))))))) = $false)),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.72/1.47 thf(f18,plain,(
% 1.72/1.47 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ c1 @ c1) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => ((Y2 @ (s @ (s @ Y4)) @ Y3) & (Y2 @ (s @ Y4) @ (s @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) => ((!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ Y3))))) & (Y2 @ c1)) => (Y2 @ Y1)))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ Y3))))) & (Y2 @ c1)) => (Y2 @ Y0))))))))) @ sK1) = $false)),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f17])).
% 1.72/1.47 thf(f17,plain,(
% 1.72/1.47 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ c1 @ c1) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => ((Y2 @ (s @ (s @ Y4)) @ Y3) & (Y2 @ (s @ Y4) @ (s @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) => ((!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ Y3))))) & (Y2 @ c1)) => (Y2 @ Y1)))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ Y3))))) & (Y2 @ c1)) => (Y2 @ Y0)))))))))) = $false)),
% 1.72/1.47 inference(not_proxy_clausification,[status(thm)],[f16])).
% 1.72/1.47 thf(f16,plain,(
% 1.72/1.47 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ c1 @ c1) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => ((Y2 @ (s @ (s @ Y4)) @ Y3) & (Y2 @ (s @ Y4) @ (s @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) => ((!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ Y3))))) & (Y2 @ c1)) => (Y2 @ Y1)))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ Y3))))) & (Y2 @ c1)) => (Y2 @ Y0))))))))))))),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.72/1.47 thf(f15,plain,(
% 1.72/1.47 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ c1 @ c1) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) => ((Y4 @ (s @ (s @ Y6)) @ Y5) & (Y4 @ (s @ Y6) @ (s @ Y5))))))))) => (Y4 @ Y2 @ Y3))))))) @ Y1 @ Y0) => (((^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y3 @ (s @ Y4))))) & (Y3 @ c1)) => (Y3 @ Y2))))) @ Y1) & ((^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y3 @ (s @ Y4))))) & (Y3 @ c1)) => (Y3 @ Y2))))) @ Y0)))))))))),
% 1.72/1.47 inference(definition_unfolding,[status(thm)],[f14,f12,f13,f13])).
% 1.72/1.47 thf(f13,plain,(
% 1.72/1.47 (cCKB6_NUM = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2))))) & (Y1 @ c1)) => (Y1 @ Y0))))))),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f11])).
% 1.72/1.47 thf(f11,plain,(
% 1.72/1.47 (cCKB6_NUM = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2))))) & (Y1 @ c1)) => (Y1 @ Y0))))))),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f10])).
% 1.72/1.47 thf(f10,plain,(
% 1.72/1.47 ((^[X0 : $i] : (! [X1 : $i > $o] : (((X1 @ c1) & ! [X2 : $i] : ((X1 @ X2) => (X1 @ (s @ X2)))) => (X1 @ X0)))) = cCKB6_NUM)),
% 1.72/1.47 inference(rectify,[status(thm)],[f2])).
% 1.72/1.47 thf(f2,axiom,(
% 1.72/1.47 ((^[X5 : $i] : (! [X6 : $i > $o] : (((X6 @ c1) & ! [X2 : $i] : ((X6 @ X2) => (X6 @ (s @ X2)))) => (X6 @ X5)))) = cCKB6_NUM)),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.6uP4k6plCZ/DTF2THF_29139.p',cCKB6_NUM_def)).
% 1.72/1.47 thf(f12,plain,(
% 1.72/1.47 (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 @ (s @ Y4)) @ Y3) & (Y2 @ (s @ Y4) @ (s @ Y3))))))))) => (Y2 @ Y0 @ Y1))))))))),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f9])).
% 1.72/1.47 thf(f9,plain,(
% 1.72/1.47 (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 @ (s @ Y4)) @ Y3) & (Y2 @ (s @ Y4) @ (s @ Y3))))))))) => (Y2 @ Y0 @ Y1))))))))),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f8])).
% 1.72/1.47 thf(f8,plain,(
% 1.72/1.47 (cCKB6_BLACK = (^[X0 : $i, X1 : $i] : (! [X2 : $i > $i > $o] : ((! [X3 : $i,X4 : $i] : ((X2 @ X3 @ X4) => ((X2 @ (s @ X3) @ (s @ X4)) & (X2 @ (s @ (s @ X3)) @ X4))) & (X2 @ c1 @ c1)) => (X2 @ X0 @ X1)))))),
% 1.72/1.47 inference(rectify,[status(thm)],[f1])).
% 1.72/1.47 thf(f1,axiom,(
% 1.72/1.47 (cCKB6_BLACK = (^[X0 : $i, X1 : $i] : (! [X2 : $i > $i > $o] : ((! [X3 : $i,X4 : $i] : ((X2 @ X3 @ X4) => ((X2 @ (s @ X3) @ (s @ X4)) & (X2 @ (s @ (s @ X3)) @ X4))) & (X2 @ c1 @ c1)) => (X2 @ X0 @ X1)))))),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.6uP4k6plCZ/DTF2THF_29139.p',cCKB6_BLACK_def)).
% 1.72/1.47 thf(f14,plain,(
% 1.72/1.47 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cCKB6_BLACK @ Y1 @ Y0) => ((cCKB6_NUM @ Y1) & (cCKB6_NUM @ Y0)))))))))),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.47 thf(f7,plain,(
% 1.72/1.47 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cCKB6_BLACK @ Y1 @ Y0) => ((cCKB6_NUM @ Y1) & (cCKB6_NUM @ Y0)))))))))),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f6])).
% 1.72/1.47 thf(f6,plain,(
% 1.72/1.47 ~! [X0 : $i,X1 : $i] : ((cCKB6_BLACK @ X0 @ X1) => ((cCKB6_NUM @ X1) & (cCKB6_NUM @ X0)))),
% 1.72/1.47 inference(rectify,[status(thm)],[f4])).
% 1.72/1.47 thf(f4,negated_conjecture,(
% 1.72/1.47 ~! [X5 : $i,X7 : $i] : ((cCKB6_BLACK @ X5 @ X7) => ((cCKB6_NUM @ X7) & (cCKB6_NUM @ X5)))),
% 1.72/1.47 inference(negated_conjecture,[status(cth)],[f3])).
% 1.72/1.47 thf(f3,conjecture,(
% 1.72/1.47 ! [X5 : $i,X7 : $i] : ((cCKB6_BLACK @ X5 @ X7) => ((cCKB6_NUM @ X7) & (cCKB6_NUM @ X5)))),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.6uP4k6plCZ/DTF2THF_29139.p',cCKB6_L6000_pme)).
% 1.72/1.47 thf(f386,plain,(
% 1.72/1.47 ($false = (sK3 @ (sK5 @ (^[Y0 : $i]: (sK3))))) | ~spl0_17),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f384])).
% 1.72/1.47 thf(f384,definition,(
% 1.72/1.47 spl0_17 <=> ($false = (sK3 @ (sK5 @ (^[Y0 : $i]: (sK3)))))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 1.72/1.47 thf(f397,plain,(
% 1.72/1.47 spl0_17 | ~spl0_16),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f396,f381,f384])).
% 1.72/1.47 thf(f381,definition,(
% 1.72/1.47 spl0_16 <=> ! [X1 : $i] : (((sK5 @ (^[Y0 : $i]: (sK3))) != X1) | ((sK3 @ X1) = $false))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 1.72/1.47 thf(f396,plain,(
% 1.72/1.47 ($false = (sK3 @ (sK5 @ (^[Y0 : $i]: (sK3))))) | ~spl0_16),
% 1.72/1.47 inference(equality_resolution,[status(thm)],[f382])).
% 1.72/1.47 thf(f382,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (((sK5 @ (^[Y0 : $i]: (sK3))) != X1) | ((sK3 @ X1) = $false)) ) | ~spl0_16),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f381])).
% 1.72/1.47 thf(f392,plain,(
% 1.72/1.47 spl0_16 | spl0_17 | ~spl0_1 | ~spl0_5 | ~spl0_6),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f391,f81,f69,f41,f384,f381])).
% 1.72/1.47 thf(f69,definition,(
% 1.72/1.47 spl0_5 <=> ! [X1 : $i] : (((sK3 @ (s @ X1)) = $true) | ((sK3 @ X1) = $false))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.72/1.47 thf(f391,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (((sK3 @ X1) = $false) | ($false = (sK3 @ (sK5 @ (^[Y0 : $i]: (sK3))))) | ((sK5 @ (^[Y0 : $i]: (sK3))) != X1)) ) | (~spl0_1 | ~spl0_5 | ~spl0_6)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f390])).
% 1.72/1.47 thf(f390,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($false = $true) | ((sK5 @ (^[Y0 : $i]: (sK3))) != X1) | ((sK3 @ X1) = $false) | ($false = (sK3 @ (sK5 @ (^[Y0 : $i]: (sK3)))))) ) | (~spl0_1 | ~spl0_5 | ~spl0_6)),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f389,f43])).
% 1.72/1.47 thf(f389,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($false = (sK3 @ c1)) | ($false = (sK3 @ (sK5 @ (^[Y0 : $i]: (sK3))))) | ((sK5 @ (^[Y0 : $i]: (sK3))) != X1) | ((sK3 @ X1) = $false)) ) | (~spl0_5 | ~spl0_6)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f388])).
% 1.72/1.47 thf(f388,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($false = $true) | ($false = (sK3 @ c1)) | ($false = (sK3 @ (sK5 @ (^[Y0 : $i]: (sK3))))) | ((sK3 @ X1) = $false) | ((sK5 @ (^[Y0 : $i]: (sK3))) != X1)) ) | (~spl0_5 | ~spl0_6)),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f353,f83])).
% 1.72/1.47 thf(f353,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (((sK5 @ (^[Y0 : $i]: (sK3))) != X1) | ((sK3 @ sK1) = $true) | ($false = (sK3 @ c1)) | ((sK3 @ X1) = $false) | ($false = (sK3 @ (sK5 @ (^[Y0 : $i]: (sK3)))))) ) | ~spl0_5),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f352])).
% 1.72/1.47 thf(f352,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ c1 @ c1)) | ((sK3 @ X1) = $false) | ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ (s @ (s @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))))) @ (sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))))) | ((sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))) != X1) | ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ sK2 @ sK1))) ) | ~spl0_5),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f345])).
% 1.72/1.47 thf(f345,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ c1 @ c1)) | ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ (s @ (s @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))))) @ (sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))))) | ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ sK2 @ sK1)) | ((sK3 @ X1) = $false) | ((sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))) != X1) | ($false = $true)) ) | ~spl0_5),
% 1.72/1.47 inference(constrained_superposition,[status(thm)],[f70,f102])).
% 1.72/1.47 thf(f102,plain,(
% 1.72/1.47 ( ! [X1 : $i > $i > $o] : (((X1 @ (s @ (sK6 @ X1)) @ (s @ (sK5 @ X1))) = $false) | ((X1 @ sK2 @ sK1) = $true) | ($false = (X1 @ c1 @ c1)) | ((X1 @ (s @ (s @ (sK6 @ X1))) @ (sK5 @ X1)) = $false)) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.72/1.47 thf(f100,plain,(
% 1.72/1.47 ( ! [X1 : $i > $i > $o] : (((X1 @ sK2 @ sK1) = $true) | ($false = ((X1 @ (s @ (s @ (sK6 @ X1))) @ (sK5 @ X1)) & (X1 @ (s @ (sK6 @ X1)) @ (s @ (sK5 @ X1))))) | ($false = (X1 @ c1 @ c1))) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.72/1.47 thf(f70,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (((sK3 @ (s @ X1)) = $true) | ((sK3 @ X1) = $false)) ) | ~spl0_5),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f69])).
% 1.72/1.47 thf(f300,plain,(
% 1.72/1.47 ~spl0_3 | ~spl0_4 | ~spl0_11),
% 1.72/1.47 inference(avatar_contradiction_clause,[status(thm)],[f299])).
% 1.72/1.47 thf(f299,plain,(
% 1.72/1.47 $false | (~spl0_3 | ~spl0_4 | ~spl0_11)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f298])).
% 1.72/1.47 thf(f298,plain,(
% 1.72/1.47 ($false = $true) | (~spl0_3 | ~spl0_4 | ~spl0_11)),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f297,f56])).
% 1.72/1.47 thf(f56,plain,(
% 1.72/1.47 ($false = (sK4 @ sK2)) | ~spl0_4),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.72/1.47 thf(f54,definition,(
% 1.72/1.47 spl0_4 <=> ($false = (sK4 @ sK2))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.72/1.47 thf(f297,plain,(
% 1.72/1.47 ($true = (sK4 @ sK2)) | (~spl0_3 | ~spl0_11)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f296])).
% 1.72/1.47 thf(f296,plain,(
% 1.72/1.47 ($true = (sK4 @ sK2)) | ($false = $true) | (~spl0_3 | ~spl0_11)),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f295,f51])).
% 1.72/1.47 thf(f51,plain,(
% 1.72/1.47 ((sK4 @ c1) = $true) | ~spl0_3),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.72/1.47 thf(f49,definition,(
% 1.72/1.47 spl0_3 <=> ((sK4 @ c1) = $true)),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.72/1.47 thf(f295,plain,(
% 1.72/1.47 ($false = (sK4 @ c1)) | ($true = (sK4 @ sK2)) | ~spl0_11),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f294])).
% 1.72/1.47 thf(f294,plain,(
% 1.72/1.47 ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c1 @ c1)) | (((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ sK2 @ sK1) = $true) | ~spl0_11),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f285])).
% 1.72/1.47 thf(f285,plain,(
% 1.72/1.47 ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c1 @ c1)) | (((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ sK2 @ sK1) = $true) | ($false = $true) | ~spl0_11),
% 1.72/1.47 inference(superposition,[status(thm)],[f101,f281])).
% 1.72/1.47 thf(f281,plain,(
% 1.72/1.47 ((sK4 @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0)))))) = $false) | ~spl0_11),
% 1.72/1.47 inference(equality_resolution,[status(thm)],[f188])).
% 1.72/1.47 thf(f188,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (((sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0))))) != X0) | ((sK4 @ X0) = $false)) ) | ~spl0_11),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f187])).
% 1.72/1.47 thf(f187,definition,(
% 1.72/1.47 spl0_11 <=> ! [X0 : $i] : (((sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0))))) != X0) | ((sK4 @ X0) = $false))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.72/1.47 thf(f266,plain,(
% 1.72/1.47 ~spl0_2 | ~spl0_3 | ~spl0_4 | ~spl0_10),
% 1.72/1.47 inference(avatar_contradiction_clause,[status(thm)],[f265])).
% 1.72/1.47 thf(f265,plain,(
% 1.72/1.47 $false | (~spl0_2 | ~spl0_3 | ~spl0_4 | ~spl0_10)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f261])).
% 1.72/1.47 thf(f261,plain,(
% 1.72/1.47 ($false = $true) | (~spl0_2 | ~spl0_3 | ~spl0_4 | ~spl0_10)),
% 1.72/1.47 inference(backward_demodulation,[status(thm)],[f51,f258])).
% 1.72/1.47 thf(f258,plain,(
% 1.72/1.47 ($false = (sK4 @ c1)) | (~spl0_2 | ~spl0_4 | ~spl0_10)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f257])).
% 1.72/1.47 thf(f257,plain,(
% 1.72/1.47 ($false = (sK4 @ c1)) | ($false = $true) | (~spl0_2 | ~spl0_4 | ~spl0_10)),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f256,f56])).
% 1.72/1.47 thf(f256,plain,(
% 1.72/1.47 ($true = (sK4 @ sK2)) | ($false = (sK4 @ c1)) | (~spl0_2 | ~spl0_10)),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f255])).
% 1.72/1.47 thf(f255,plain,(
% 1.72/1.47 ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c1 @ c1)) | (((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ sK2 @ sK1) = $true) | (~spl0_2 | ~spl0_10)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f246])).
% 1.72/1.47 thf(f246,plain,(
% 1.72/1.47 (((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ sK2 @ sK1) = $true) | ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c1 @ c1)) | ($false = $true) | (~spl0_2 | ~spl0_10)),
% 1.72/1.47 inference(superposition,[status(thm)],[f101,f236])).
% 1.72/1.47 thf(f236,plain,(
% 1.72/1.47 ((sK4 @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0)))))) = $false) | (~spl0_2 | ~spl0_10)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f232])).
% 1.72/1.47 thf(f232,plain,(
% 1.72/1.47 ($false = $true) | ((sK4 @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0)))))) = $false) | (~spl0_2 | ~spl0_10)),
% 1.72/1.47 inference(superposition,[status(thm)],[f227,f46])).
% 1.72/1.47 thf(f46,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (((sK4 @ (s @ X1)) = $true) | ($false = (sK4 @ X1))) ) | ~spl0_2),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.72/1.47 thf(f45,definition,(
% 1.72/1.47 spl0_2 <=> ! [X1 : $i] : (((sK4 @ (s @ X1)) = $true) | ($false = (sK4 @ X1)))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.72/1.47 thf(f227,plain,(
% 1.72/1.47 ($false = (sK4 @ (s @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0)))))))) | (~spl0_2 | ~spl0_10)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f222])).
% 1.72/1.47 thf(f222,plain,(
% 1.72/1.47 ($false = (sK4 @ (s @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0)))))))) | ($false = $true) | (~spl0_2 | ~spl0_10)),
% 1.72/1.47 inference(superposition,[status(thm)],[f46,f185])).
% 1.72/1.47 thf(f185,plain,(
% 1.72/1.47 ($false = (sK4 @ (s @ (s @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0))))))))) | ~spl0_10),
% 1.72/1.47 inference(avatar_component_clause,[status(thm)],[f183])).
% 1.72/1.47 thf(f183,definition,(
% 1.72/1.47 spl0_10 <=> ($false = (sK4 @ (s @ (s @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0)))))))))),
% 1.72/1.47 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.72/1.47 thf(f201,plain,(
% 1.72/1.47 spl0_11 | spl0_10 | ~spl0_2 | ~spl0_3 | ~spl0_4),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f200,f54,f49,f45,f183,f187])).
% 1.72/1.47 thf(f200,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (((sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0))))) != X0) | ($false = (sK4 @ (s @ (s @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0))))))))) | ((sK4 @ X0) = $false)) ) | (~spl0_2 | ~spl0_3 | ~spl0_4)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f199])).
% 1.72/1.47 thf(f199,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (((sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0))))) != X0) | ($false = $true) | ((sK4 @ X0) = $false) | ($false = (sK4 @ (s @ (s @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0)))))))))) ) | (~spl0_2 | ~spl0_3 | ~spl0_4)),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f198,f56])).
% 1.72/1.47 thf(f198,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (($true = (sK4 @ sK2)) | ((sK4 @ X0) = $false) | ($false = (sK4 @ (s @ (s @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0))))))))) | ((sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0))))) != X0)) ) | (~spl0_2 | ~spl0_3)),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f197])).
% 1.72/1.47 thf(f197,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (((sK4 @ X0) = $false) | ($false = (sK4 @ (s @ (s @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0))))))))) | ((sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0))))) != X0) | ($false = $true) | ($true = (sK4 @ sK2))) ) | (~spl0_2 | ~spl0_3)),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f147,f51])).
% 1.72/1.47 thf(f147,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (($false = (sK4 @ (s @ (s @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0))))))))) | ((sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ Y0))))) != X0) | ((sK4 @ X0) = $false) | ($false = (sK4 @ c1)) | ($true = (sK4 @ sK2))) ) | ~spl0_2),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f146])).
% 1.72/1.47 thf(f146,plain,(
% 1.72/1.47 ( ! [X0 : $i] : ((((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ sK2 @ sK1) = $true) | ((sK4 @ X0) = $false) | (((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ (s @ (s @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))))) @ (sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))) = $false) | ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c1 @ c1)) | ((sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))) != X0)) ) | ~spl0_2),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.72/1.47 thf(f131,plain,(
% 1.72/1.47 ( ! [X0 : $i] : (((sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))) != X0) | (((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ sK2 @ sK1) = $true) | ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c1 @ c1)) | (((^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ (s @ (s @ (sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))))) @ (sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))) = $false) | ((sK4 @ X0) = $false) | ($false = $true)) ) | ~spl0_2),
% 1.72/1.47 inference(constrained_superposition,[status(thm)],[f46,f102])).
% 1.72/1.47 thf(f91,plain,(
% 1.72/1.47 spl0_6 | spl0_2),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f90,f45,f81])).
% 1.72/1.47 thf(f90,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (((sK4 @ (s @ X1)) = $true) | ((sK3 @ sK1) = $false) | ($false = (sK4 @ X1))) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 1.72/1.47 thf(f89,plain,(
% 1.72/1.47 ( ! [X1 : $i] : ((((sK4 @ X1) => (sK4 @ (s @ X1))) = $true) | ((sK3 @ sK1) = $false)) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f88])).
% 1.72/1.47 thf(f88,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0)))) @ X1)) | ((sK3 @ sK1) = $false)) )),
% 1.72/1.47 inference(pi_clausification,[status(thm)],[f86])).
% 1.72/1.47 thf(f86,plain,(
% 1.72/1.47 ((sK3 @ sK1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0))))))),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.72/1.47 thf(f79,plain,(
% 1.72/1.47 (((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0))))) & (sK4 @ c1)) = $true) | ((sK3 @ sK1) = $false)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.72/1.47 thf(f77,plain,(
% 1.72/1.47 ((((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0))))) & (sK4 @ c1)) => (sK4 @ sK2)) = $false) | ((sK3 @ sK1) = $false)),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f76])).
% 1.72/1.47 thf(f76,plain,(
% 1.72/1.47 (((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK2))) @ sK4) = $false) | ((sK3 @ sK1) = $false)),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f27])).
% 1.72/1.47 thf(f27,plain,(
% 1.72/1.47 ((sK3 @ sK1) = $false) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK2)))) = $false)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.72/1.47 thf(f26,plain,(
% 1.72/1.47 ((((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ Y0))))) & (sK3 @ c1)) => (sK3 @ sK1)) = $false) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK2)))) = $false)),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.72/1.47 thf(f25,plain,(
% 1.72/1.47 ($false = ((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK1))) @ sK3)) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK2)))) = $false)),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f24])).
% 1.72/1.47 thf(f24,plain,(
% 1.72/1.47 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK1))))) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK2)))) = $false)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.72/1.47 thf(f22,plain,(
% 1.72/1.47 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK2)))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK1))))) = $false)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.72/1.47 thf(f87,plain,(
% 1.72/1.47 spl0_6 | spl0_3),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f85,f49,f81])).
% 1.72/1.47 thf(f85,plain,(
% 1.72/1.47 ((sK4 @ c1) = $true) | ((sK3 @ sK1) = $false)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.72/1.47 thf(f84,plain,(
% 1.72/1.47 spl0_4 | spl0_6),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f78,f81,f54])).
% 1.72/1.47 thf(f78,plain,(
% 1.72/1.47 ($false = (sK4 @ sK2)) | ((sK3 @ sK1) = $false)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.72/1.47 thf(f75,plain,(
% 1.72/1.47 spl0_4 | spl0_5),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f74,f69,f54])).
% 1.72/1.47 thf(f74,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($false = (sK4 @ sK2)) | ((sK3 @ (s @ X1)) = $true) | ((sK3 @ X1) = $false)) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.72/1.47 thf(f60,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($false = (sK4 @ sK2)) | (((sK3 @ X1) => (sK3 @ (s @ X1))) = $true)) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.72/1.47 thf(f59,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (((((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0))))) & (sK4 @ c1)) => (sK4 @ sK2)) = $false) | (((sK3 @ X1) => (sK3 @ (s @ X1))) = $true)) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.72/1.47 thf(f58,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (((((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0))))) & (sK4 @ c1)) => (sK4 @ sK2)) = $false) | (((^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ Y0)))) @ X1) = $true)) )),
% 1.72/1.47 inference(pi_clausification,[status(thm)],[f32])).
% 1.72/1.47 thf(f32,plain,(
% 1.72/1.47 ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ Y0))))) = $true) | ((((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0))))) & (sK4 @ c1)) => (sK4 @ sK2)) = $false)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.72/1.47 thf(f30,plain,(
% 1.72/1.47 (((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ Y0))))) & (sK3 @ c1)) = $true) | ((((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0))))) & (sK4 @ c1)) => (sK4 @ sK2)) = $false)),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.72/1.47 thf(f29,plain,(
% 1.72/1.47 (((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ Y0))))) & (sK3 @ c1)) = $true) | (((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK2))) @ sK4) = $false)),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f28])).
% 1.72/1.47 thf(f28,plain,(
% 1.72/1.47 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK2)))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ Y0))))) & (sK3 @ c1)) = $true)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.72/1.47 thf(f73,plain,(
% 1.72/1.47 spl0_5 | spl0_3),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f72,f49,f69])).
% 1.72/1.47 thf(f72,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (((sK4 @ c1) = $true) | ((sK3 @ (s @ X1)) = $true) | ((sK3 @ X1) = $false)) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.72/1.47 thf(f62,plain,(
% 1.72/1.47 ( ! [X1 : $i] : ((((sK3 @ X1) => (sK3 @ (s @ X1))) = $true) | ((sK4 @ c1) = $true)) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.72/1.47 thf(f61,plain,(
% 1.72/1.47 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0))))) & (sK4 @ c1)) = $true) | (((sK3 @ X1) => (sK3 @ (s @ X1))) = $true)) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.72/1.47 thf(f71,plain,(
% 1.72/1.47 spl0_5 | spl0_2),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f67,f45,f69])).
% 1.72/1.47 thf(f67,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (($false = (sK4 @ X2)) | ((sK3 @ (s @ X1)) = $true) | ((sK4 @ (s @ X2)) = $true) | ((sK3 @ X1) = $false)) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.72/1.47 thf(f66,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : ((((sK4 @ X2) => (sK4 @ (s @ X2))) = $true) | ((sK3 @ X1) = $false) | ((sK3 @ (s @ X1)) = $true)) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f65])).
% 1.72/1.47 thf(f65,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X1) = $false) | ($true = ((^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0)))) @ X2)) | ((sK3 @ (s @ X1)) = $true)) )),
% 1.72/1.47 inference(pi_clausification,[status(thm)],[f64])).
% 1.72/1.47 thf(f64,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (((sK3 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0)))))) | ((sK3 @ (s @ X1)) = $true)) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.72/1.47 thf(f63,plain,(
% 1.72/1.47 ( ! [X1 : $i] : ((((sK3 @ X1) => (sK3 @ (s @ X1))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0))))))) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.72/1.47 thf(f57,plain,(
% 1.72/1.47 spl0_1 | spl0_4),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f33,f54,f41])).
% 1.72/1.47 thf(f33,plain,(
% 1.72/1.47 ($false = (sK4 @ sK2)) | ($true = (sK3 @ c1))),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.72/1.47 thf(f31,plain,(
% 1.72/1.47 ((((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0))))) & (sK4 @ c1)) => (sK4 @ sK2)) = $false) | ($true = (sK3 @ c1))),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.72/1.47 thf(f52,plain,(
% 1.72/1.47 spl0_1 | spl0_3),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f35,f49,f41])).
% 1.72/1.47 thf(f35,plain,(
% 1.72/1.47 ($true = (sK3 @ c1)) | ((sK4 @ c1) = $true)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.72/1.47 thf(f34,plain,(
% 1.72/1.47 ($true = (sK3 @ c1)) | (((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0))))) & (sK4 @ c1)) = $true)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.72/1.47 thf(f47,plain,(
% 1.72/1.47 spl0_1 | spl0_2),
% 1.72/1.47 inference(avatar_split_clause,[status(thm)],[f39,f45,f41])).
% 1.72/1.47 thf(f39,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (((sK4 @ (s @ X1)) = $true) | ($true = (sK3 @ c1)) | ($false = (sK4 @ X1))) )),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.72/1.47 thf(f38,plain,(
% 1.72/1.47 ( ! [X1 : $i] : ((((sK4 @ X1) => (sK4 @ (s @ X1))) = $true) | ($true = (sK3 @ c1))) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.72/1.47 thf(f37,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($true = (sK3 @ c1)) | ($true = ((^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0)))) @ X1))) )),
% 1.72/1.47 inference(pi_clausification,[status(thm)],[f36])).
% 1.72/1.47 thf(f36,plain,(
% 1.72/1.47 ($true = (sK3 @ c1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK4 @ (s @ Y0))))))),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.72/1.47 % SZS output end Proof for DTF2THF_29139
% 1.72/1.47 % (29375)------------------------------
% 1.72/1.47 % (29375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.47 % (29375)Termination reason: Refutation
% 1.72/1.47
% 1.72/1.47 % (29375)Memory used [KB]: 5884
% 1.72/1.47 % (29375)Time elapsed: 0.057 s
% 1.72/1.47 % (29375)Instructions burned: 65 (million)
% 1.72/1.47 % (29375)------------------------------
% 1.72/1.47 % (29375)------------------------------
% 1.72/1.47 % (29326)Success in time 0.141 s
%------------------------------------------------------------------------------