%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU815^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 09:37:26 AM UTC 2026
% Result : Theorem 1.75s 1.92s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 8
% Syntax : Number of formulae : 118 ( 64 unt; 0 typ; 2 def)
% Number of atoms : 1099 ( 193 equ; 0 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 1952 ( 14 ~; 91 |; 0 &;1350 @)
% ( 2 <=>; 296 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 11 con; 0-3 aty)
% ( 199 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 384 ( 223 ^; 161 !; 0 ?; 384 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setunion: $i > $i ).
thf(func_def_5,type,
subset: $i > $i > $o ).
thf(func_def_7,type,
transitiveset: $i > $o ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: $i > $i > $i ).
thf(func_def_22,type,
sK3: $o > $i > $i > $i ).
thf(func_def_25,type,
sK6: $i > $i ).
thf(f599,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f510,f513,f589]) ).
thf(f589,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f588]) ).
thf(f588,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f573]) ).
thf(f573,plain,
( ( $true = $false )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f271,f505]) ).
thf(f505,plain,
( ! [X0: $o] : ( $true = X0 )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f504]) ).
thf(f504,definition,
( spl0_3
<=> ! [X0: $o] : ( $true = X0 ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f271,plain,
( ( in @ ( setunion @ sK4 ) @ sK4 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f268]) ).
thf(f268,plain,
( ( $true = $false )
| ( ( in @ ( setunion @ sK4 ) @ sK4 )
= $false ) ),
inference(superposition,[status(thm)],[f151,f262]) ).
thf(f262,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) ) )
| ( ( in @ X1 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f261]) ).
thf(f261,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f260]) ).
thf(f260,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f152]) ).
thf(f152,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK4 ) )
=> ( subset @ Y0 @ ( setunion @ sK4 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f149]) ).
thf(f149,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
=> ( subset @ Y1 @ ( setunion @ Y0 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
=> ( subset @ Y1 @ ( setunion @ Y0 ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
=> ( subset @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
=> ( subset @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
=> ( subset @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y0 @ ( setunion @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
=> ( subset @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y0 @ ( setunion @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
=> ( subset @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y0 @ ( setunion @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( subset @ Y3 @ Y2 ) ) )
@ Y1 ) ) )
=> ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ ( setunion @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f23,f22,f21,f24,f27,f26,f26]) ).
thf(f26,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( transitiveset
= ( ^ [X0: $i] :
! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( subset @ X4 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.89llQL148d/DTF2THF_18003.p',transitiveset) ).
thf(f27,plain,
( transitivesetOp2
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f25,f26]) ).
thf(f25,plain,
( transitivesetOp2
= ( !! @ $i
@ ^ [Y0: $i] :
( ( transitiveset @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( transitivesetOp2
= ( !! @ $i
@ ^ [Y0: $i] :
( ( transitiveset @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i] :
( ( ( transitiveset @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) )
= transitivesetOp2 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X4: $i] :
( ( ( transitiveset @ X4 )
=> ! [X1: $i,X0: $i] :
( ( in @ X0 @ X4 )
=> ( ( in @ X1 @ X0 )
=> ( in @ X1 @ X4 ) ) ) )
= transitivesetOp2 ),
file('/export/starexec/sandbox2/tmp/tmp.89llQL148d/DTF2THF_18003.p',transitivesetOp2) ).
thf(f24,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( subsetI1
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( subsetI1
= ( ! [X2: $i,X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ X1 @ X2 ) )
=> ( subset @ X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.89llQL148d/DTF2THF_18003.p',subsetI1) ).
thf(f21,plain,
( setunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( setunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setunion @ X0 ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X3 @ X0 )
=> X2 ) )
=> X2 ) )
= setunionE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setunion @ X0 ) )
=> ! [X3: $o] :
( ! [X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> X3 ) )
=> X3 ) )
= setunionE ),
file('/export/starexec/sandbox2/tmp/tmp.89llQL148d/DTF2THF_18003.p',setunionE) ).
thf(f22,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y0 @ ( setunion @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y0 @ ( setunion @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X2 @ ( setunion @ X1 ) ) ) )
= setunionI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) )
= setunionI ),
file('/export/starexec/sandbox2/tmp/tmp.89llQL148d/DTF2THF_18003.p',setunionI) ).
thf(f23,plain,
( $true
= ( ~ ( setunionI
=> ( setunionE
=> ( subsetI1
=> ( transitivesetOp2
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( transitiveset @ Y1 ) ) )
=> ( transitiveset @ ( setunion @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( $true
= ( ~ ( setunionI
=> ( setunionE
=> ( subsetI1
=> ( transitivesetOp2
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( transitiveset @ Y1 ) ) )
=> ( transitiveset @ ( setunion @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( setunionI
=> ( setunionE
=> ( subsetI1
=> ( transitivesetOp2
=> ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( transitiveset @ X1 ) )
=> ( transitiveset @ ( setunion @ X0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( setunionI
=> ( setunionE
=> ( subsetI1
=> ( transitivesetOp2
=> ! [X4: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( transitiveset @ X1 ) )
=> ( transitiveset @ ( setunion @ X4 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( setunionI
=> ( setunionE
=> ( subsetI1
=> ( transitivesetOp2
=> ! [X4: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( transitiveset @ X1 ) )
=> ( transitiveset @ ( setunion @ X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.89llQL148d/DTF2THF_18003.p',setunionTransitive) ).
thf(f151,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK4 ) )
=> ( subset @ Y0 @ ( setunion @ sK4 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f150]) ).
thf(f513,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f512]) ).
thf(f512,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f511]) ).
thf(f511,plain,
( ( $true = $false )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f160,f509]) ).
thf(f509,plain,
( ( ( in @ sK5 @ ( setunion @ sK4 ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f507]) ).
thf(f507,definition,
( spl0_4
<=> ( ( in @ sK5 @ ( setunion @ sK4 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f160,plain,
( ( in @ sK5 @ ( setunion @ sK4 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f154]) ).
thf(f154,plain,
( ( ( in @ sK5 @ ( setunion @ sK4 ) )
=> ( subset @ sK5 @ ( setunion @ sK4 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f153]) ).
thf(f153,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sK4 ) )
=> ( subset @ Y0 @ ( setunion @ sK4 ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f151]) ).
thf(f510,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f501,f507,f504]) ).
thf(f501,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( in @ sK5 @ ( setunion @ sK4 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f500]) ).
thf(f500,plain,
! [X0: $o] :
( ( ( in @ sK5 @ ( setunion @ sK4 ) )
= $false )
| ( $true = X0 )
| ( $true = $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f497]) ).
thf(f497,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( in @ sK5 @ ( setunion @ sK4 ) )
= $false )
| ( $true = $false )
| ( $true = X0 )
| ( ( in @ sK5 @ ( setunion @ sK4 ) )
= $false ) ),
inference(superposition,[status(thm)],[f106,f472]) ).
thf(f472,plain,
! [X0: $o,X1: $i] :
( ( ( in @ ( sK3 @ X0 @ sK5 @ X1 ) @ sK4 )
= $false )
| ( $true = X0 )
| ( ( in @ sK5 @ ( setunion @ X1 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f457]) ).
thf(f457,plain,
! [X0: $o,X1: $i] :
( ( ( in @ ( sK3 @ X0 @ sK5 @ X1 ) @ sK4 )
= $false )
| ( $true = X0 )
| ( ( in @ sK5 @ ( setunion @ X1 ) )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f452,f104]) ).
thf(f104,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $true
= ( in @ X1 @ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( $true = X3 )
| ( ( in @ X1 @ ( setunion @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ( ( in @ X1 @ ( sK3 @ X3 @ X1 @ X2 ) )
=> ( ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X2 )
=> X3 ) )
= $false )
| ( ( in @ X1 @ ( setunion @ X2 ) )
= $false )
| ( $true = X3 ) ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $true = X3 )
| ( ( in @ X1 @ ( setunion @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ Y0 @ X2 )
=> X3 ) )
@ ( sK3 @ X3 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ Y0 @ X2 )
=> X3 ) ) )
= $false )
| ( ( in @ X1 @ ( setunion @ X2 ) )
= $false )
| ( $true = X3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ Y0 @ X2 )
=> X3 ) ) )
=> X3 ) )
| ( ( in @ X1 @ ( setunion @ X2 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $true
= ( ^ [Y0: $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ Y1 @ X2 )
=> Y0 ) ) )
=> Y0 )
@ X3 ) )
| ( ( in @ X1 @ ( setunion @ X2 ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $o
@ ^ [Y0: $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ Y1 @ X2 )
=> Y0 ) ) )
=> Y0 ) )
= $true )
| ( ( in @ X1 @ ( setunion @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setunion @ X2 ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ Y1 @ X2 )
=> Y0 ) ) )
=> Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setunion @ Y0 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ X1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> Y1 ) ) )
=> Y1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setunion @ Y0 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ X1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> Y1 ) ) )
=> Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f452,plain,
! [X0: $i] :
( ( ( in @ sK5 @ X0 )
= $false )
| ( ( in @ X0 @ sK4 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f451]) ).
thf(f451,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( in @ sK5 @ X0 )
= $false )
| ( ( in @ X0 @ sK4 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f445]) ).
thf(f445,plain,
! [X0: $i] :
( ( ( in @ sK5 @ X0 )
= $false )
| ( ( in @ X0 @ sK4 )
= $false )
| ( ( in @ X0 @ sK4 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f159,f438]) ).
thf(f438,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ ( setunion @ X1 ) ) )
| ( ( in @ X2 @ sK4 )
= $false )
| ( ( in @ X0 @ X2 )
= $false )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f437]) ).
thf(f437,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( in @ X2 @ sK4 )
= $false )
| ( $true
= ( subset @ X0 @ ( setunion @ X1 ) ) )
| ( ( in @ X0 @ X2 )
= $false )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f413]) ).
thf(f413,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ ( setunion @ X1 ) ) )
| ( ( in @ X0 @ X2 )
= $false )
| ( $true
= ( subset @ X0 @ ( setunion @ X1 ) ) )
| ( ( in @ X2 @ sK4 )
= $false )
| ( $true = $false )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(superposition,[status(thm)],[f332,f62]) ).
thf(f62,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X0 @ ( setunion @ X1 ) ) @ X2 )
= $false )
| ( ( in @ X2 @ X1 )
= $false )
| ( $true
= ( subset @ X0 @ ( setunion @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( in @ ( sK2 @ X0 @ ( setunion @ X1 ) ) @ X2 )
= $false )
| ( ( in @ X2 @ X1 )
= $false )
| ( $true
= ( subset @ X0 @ ( setunion @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f46,f57]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( sK2 @ X1 @ X2 ) @ X2 )
= $false )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
| ( ( ( in @ ( sK2 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK2 @ X1 @ X2 ) )
= $false )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( ( in @ X1 @ X3 )
= $false )
| ( ( in @ X3 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ X3 )
= $false )
| ( $true
= ( ( in @ X3 @ X2 )
=> ( in @ X1 @ ( setunion @ X2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ X3 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X1 @ ( setunion @ X2 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ X1 @ ( setunion @ X2 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ X1 @ ( setunion @ X2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ X1 @ ( setunion @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ X1 @ ( setunion @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y0 @ ( setunion @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y0 @ ( setunion @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f332,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X0 @ X1 ) @ X2 ) )
| ( ( in @ X2 @ sK4 )
= $false )
| ( $true
= ( subset @ X0 @ X1 ) )
| ( ( in @ X0 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f314]) ).
thf(f314,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK2 @ X0 @ X1 ) @ X2 ) )
| ( ( in @ X0 @ X2 )
= $false )
| ( ( in @ X2 @ sK4 )
= $false )
| ( $true
= ( subset @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f58,f286]) ).
thf(f286,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( ( in @ X0 @ sK4 )
= $false )
| ( ( in @ X1 @ X0 )
= $false )
| ( ( in @ X2 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f282]) ).
thf(f282,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( in @ X1 @ X0 )
= $false )
| ( ( in @ X0 @ sK4 )
= $false )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(superposition,[status(thm)],[f262,f148]) ).
thf(f148,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( $true
= ( in @ X3 @ X1 ) )
| ( ( in @ X3 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f146]) ).
thf(f146,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ X1 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f145]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f143]) ).
thf(f143,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f133]) ).
thf(f133,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f132]) ).
thf(f132,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( sK2 @ X1 @ X2 ) @ X1 )
= $true )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f159,plain,
( ( subset @ sK5 @ ( setunion @ sK4 ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f154]) ).
thf(f106,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $true
= ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( ( in @ X1 @ ( setunion @ X2 ) )
= $false )
| ( $true = X3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ( in @ X1 @ ( setunion @ X2 ) )
= $false )
| ( ( ( in @ ( sK3 @ X3 @ X1 @ X2 ) @ X2 )
=> X3 )
= $false )
| ( $true = X3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU815^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n002.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:35:03 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.48 ---- Original DTF file ---
% 0.26/0.49 thf(spec,logic,$$dhol).
% 0.26/0.49 %------------------------------------------------------------------------------
% 0.26/0.49 % File : SEU815^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.49 % Domain : Set Theory
% 0.26/0.49 % Problem : Transitive Sets
% 0.26/0.49 % Version : Especial > Reduced > Especial.
% 0.26/0.49 % English : (! X:i.(! x:i.in x X -> transitiveset x) ->
% 0.26/0.49 % transitiveset (setunion X))
% 0.26/0.49
% 0.26/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.49 % Source : [Bro08]
% 0.26/0.49 % Names : ZFC317l [Bro08]
% 0.26/0.49
% 0.26/0.49 % Status : Theorem
% 0.26/0.49 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.60 v5.3.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v3.7.0
% 0.26/0.49 % Syntax : Number of formulae : 14 ( 5 unt; 8 typ; 5 def)
% 0.26/0.49 % Number of atoms : 32 ( 5 equ; 0 cnn)
% 0.26/0.49 % Maximal formula atoms : 7 ( 5 avg)
% 0.26/0.49 % Number of connectives : 54 ( 0 ~; 0 |; 0 &; 36 @)
% 0.26/0.49 % ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% 0.26/0.49 % Maximal formula depth : 11 ( 3 avg)
% 0.26/0.49 % Number of types : 2 ( 0 usr)
% 0.26/0.49 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.26/0.49 % Number of symbols : 9 ( 8 usr; 4 con; 0-2 aty)
% 0.26/0.49 % Number of variables : 17 ( 1 ^; 16 !; 0 ?; 17 :)
% 0.26/0.49 % SPC : TH0_THM_EQU_NAR
% 0.26/0.49
% 0.26/0.49 % Comments : http://mathgate.info/detsetitem.php?id=503
% 0.26/0.49 %------------------------------------------------------------------------------
% 0.26/0.49 thf(in_type,type,
% 0.26/0.49 in: $i > $i > $o ).
% 0.26/0.49
% 0.26/0.49 thf(setunion_type,type,
% 0.26/0.49 setunion: $i > $i ).
% 0.26/0.49
% 0.26/0.49 thf(setunionI_type,type,
% 0.26/0.49 setunionI: $o ).
% 0.26/0.49
% 0.26/0.49 thf(setunionI,definition,
% 0.26/0.49 ( setunionI
% 0.26/0.49 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.26/0.49 ( ( in @ Xx @ B )
% 0.26/0.49 => ( ( in @ B @ A )
% 0.26/0.49 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(setunionE_type,type,
% 0.26/0.49 setunionE: $o ).
% 0.26/0.49
% 0.26/0.49 thf(setunionE,definition,
% 0.26/0.49 ( setunionE
% 0.26/0.49 = ( ! [A: $i,Xx: $i] :
% 0.26/0.49 ( ( in @ Xx @ ( setunion @ A ) )
% 0.26/0.49 => ! [Xphi: $o] :
% 0.26/0.49 ( ! [B: $i] :
% 0.26/0.49 ( ( in @ Xx @ B )
% 0.26/0.49 => ( ( in @ B @ A )
% 0.26/0.49 => Xphi ) )
% 0.26/0.49 => Xphi ) ) ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(subset_type,type,
% 0.26/0.49 subset: $i > $i > $o ).
% 0.26/0.49
% 0.26/0.49 thf(subsetI1_type,type,
% 0.26/0.49 subsetI1: $o ).
% 0.26/0.49
% 0.26/0.49 thf(subsetI1,definition,
% 0.26/0.49 ( subsetI1
% 0.26/0.49 = ( ! [A: $i,B: $i] :
% 0.26/0.49 ( ! [Xx: $i] :
% 0.26/0.49 ( ( in @ Xx @ A )
% 0.26/0.49 => ( in @ Xx @ B ) )
% 0.26/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(transitiveset_type,type,
% 0.26/0.49 transitiveset: $i > $o ).
% 0.26/0.49
% 0.26/0.49 thf(transitiveset,definition,
% 0.26/0.49 ( transitiveset
% 0.26/0.49 = ( ^ [A: $i] :
% 0.26/0.49 ! [X: $i] :
% 0.26/0.49 ( ( in @ X @ A )
% 0.26/0.49 => ( subset @ X @ A ) ) ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(transitivesetOp2_type,type,
% 0.26/0.49 transitivesetOp2: $o ).
% 0.26/0.49
% 0.26/0.49 thf(transitivesetOp2,definition,
% 0.26/0.49 ( transitivesetOp2
% 0.26/0.49 = ( ! [X: $i] :
% 0.26/0.49 ( ( transitiveset @ X )
% 0.26/0.49 => ! [A: $i,Xx: $i] :
% 0.26/0.49 ( ( in @ A @ X )
% 0.26/0.49 => ( ( in @ Xx @ A )
% 0.26/0.49 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(setunionTransitive,conjecture,
% 0.26/0.49 ( setunionI
% 0.26/0.49 => ( setunionE
% 0.26/0.49 => ( subsetI1
% 0.26/0.49 => ( transitivesetOp2
% 0.26/0.49 => ! [X: $i] :
% 0.26/0.49 ( ! [Xx: $i] :
% 0.26/0.49 ( ( in @ Xx @ X )
% 0.26/0.49 => ( transitiveset @ Xx ) )
% 0.26/0.49 => ( transitiveset @ ( setunion @ X ) ) ) ) ) ) ) ).
% 0.26/0.49
% 0.26/0.49 %------------------------------------------------------------------------------
% 0.26/0.49 ------------------------
% 1.64/1.35 ---- Embedded in THF ---
% 1.64/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.35 %%% Generated on Tue Feb 24 12:35:04 EST 2026
% 1.64/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.35 %%% Logic specification used:
% 1.64/1.35 %%% thf(spec, logic, $$dhol).
% 1.64/1.35
% 1.64/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.89llQL148d/DTF2DTF18003.p
% See solution above
% 1.64/1.35 ------------------------
% 1.64/1.36 ---- Cleaned THF ---
% 1.64/1.36 thf(in_type,type,
% 1.64/1.36 in: $i > $i > $o ).
% 1.64/1.36
% 1.64/1.36 thf(setunion_type,type,
% 1.64/1.36 setunion: $i > $i ).
% 1.64/1.36
% 1.64/1.36 thf(setunionI_type,type,
% 1.64/1.36 setunionI: $o ).
% 1.64/1.36
% 1.64/1.36 thf(setunionI,definition,
% 1.64/1.36 ( setunionI
% 1.64/1.36 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.64/1.36 ( ( in @ Xx @ B )
% 1.64/1.36 => ( ( in @ B @ A )
% 1.64/1.36 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.64/1.36
% 1.64/1.36 thf(setunionE_type,type,
% 1.64/1.36 setunionE: $o ).
% 1.64/1.36
% 1.64/1.36 thf(setunionE,definition,
% 1.64/1.36 ( setunionE
% 1.64/1.36 = ( ! [A: $i,Xx: $i] :
% 1.64/1.36 ( ( in @ Xx @ ( setunion @ A ) )
% 1.64/1.36 => ! [Xphi: $o] :
% 1.64/1.36 ( ! [B: $i] :
% 1.64/1.36 ( ( in @ Xx @ B )
% 1.64/1.36 => ( ( in @ B @ A )
% 1.64/1.36 => Xphi ) )
% 1.64/1.36 => Xphi ) ) ) ) ).
% 1.64/1.36
% 1.64/1.36 thf(subset_type,type,
% 1.64/1.36 subset: $i > $i > $o ).
% 1.64/1.36
% 1.64/1.36 thf(subsetI1_type,type,
% 1.64/1.36 subsetI1: $o ).
% 1.64/1.36
% 1.64/1.36 thf(subsetI1,definition,
% 1.64/1.36 ( subsetI1
% 1.64/1.36 = ( ! [A: $i,B: $i] :
% 1.64/1.36 ( ! [Xx: $i] :
% 1.64/1.36 ( ( in @ Xx @ A )
% 1.64/1.36 => ( in @ Xx @ B ) )
% 1.64/1.36 => ( subset @ A @ B ) ) ) ) ).
% 1.64/1.36
% 1.64/1.36 thf(transitiveset_type,type,
% 1.64/1.36 transitiveset: $i > $o ).
% 1.64/1.36
% 1.64/1.36 thf(transitiveset,definition,
% 1.64/1.36 ( transitiveset
% 1.64/1.36 = ( ^ [A: $i] :
% 1.64/1.36 ! [X: $i] :
% 1.64/1.36 ( ( in @ X @ A )
% 1.64/1.36 => ( subset @ X @ A ) ) ) ) ).
% 1.64/1.36
% 1.64/1.36 thf(transitivesetOp2_type,type,
% 1.64/1.36 transitivesetOp2: $o ).
% 1.64/1.36
% 1.64/1.36 thf(transitivesetOp2,definition,
% 1.64/1.36 ( transitivesetOp2
% 1.64/1.36 = ( ! [X: $i] :
% 1.64/1.36 ( ( transitiveset @ X )
% 1.64/1.36 => ! [A: $i,Xx: $i] :
% 1.64/1.36 ( ( in @ A @ X )
% 1.64/1.36 => ( ( in @ Xx @ A )
% 1.64/1.36 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 1.64/1.36
% 1.64/1.36 thf(setunionTransitive,conjecture,
% 1.64/1.36 ( setunionI
% 1.64/1.36 => ( setunionE
% 1.64/1.36 => ( subsetI1
% 1.64/1.36 => ( transitivesetOp2
% 1.64/1.36 => ! [X: $i] :
% 1.64/1.36 ( ! [Xx: $i] :
% 1.64/1.36 ( ( in @ Xx @ X )
% 1.64/1.36 => ( transitiveset @ Xx ) )
% 1.64/1.36 => ( transitiveset @ ( setunion @ X ) ) ) ) ) ) ) ).
% 1.64/1.36 ------------------------
% 1.64/1.37 % (18154)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_18003 for (3000ds/4Mi)
% 1.64/1.37 % (18159)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18003 for (3000ds/18Mi)
% 1.64/1.37 % (18156)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18003 for (3000ds/2Mi)
% 1.64/1.38 % (18156)Instruction limit reached!
% 1.64/1.38 % (18156)------------------------------
% 1.64/1.38 % (18156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (18156)Termination reason: Unknown
% 1.64/1.38 % (18156)Termination phase: Property scanning
% 1.64/1.38
% 1.64/1.38 % (18156)Memory used [KB]: 1023
% 1.64/1.38 % (18156)Time elapsed: 0.002 s
% 1.64/1.38 % (18156)Instructions burned: 3 (million)
% 1.64/1.38 % (18156)------------------------------
% 1.64/1.38 % (18156)------------------------------
% 1.64/1.38 % (18159)Instruction limit reached!
% 1.64/1.38 % (18159)------------------------------
% 1.64/1.38 % (18159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (18159)Termination reason: Unknown
% 1.64/1.38 % (18159)Termination phase: Saturation
% 1.64/1.38
% 1.64/1.38 % (18159)Memory used [KB]: 5628
% 1.64/1.38 % (18159)Time elapsed: 0.008 s
% 1.64/1.38 % (18159)Instructions burned: 18 (million)
% 1.64/1.38 % (18159)------------------------------
% 1.64/1.38 % (18159)------------------------------
% 1.64/1.38 % (18157)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_18003 for (3000ds/2Mi)
% 1.64/1.38 % (18157)Instruction limit reached!
% 1.64/1.38 % (18157)------------------------------
% 1.64/1.38 % (18157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (18157)Termination reason: Unknown
% 1.64/1.38 % (18157)Termination phase: Property scanning
% 1.64/1.38
% 1.64/1.38 % (18157)Memory used [KB]: 1023
% 1.64/1.38 % (18157)Time elapsed: 0.003 s
% 1.64/1.38 % (18157)Instructions burned: 3 (million)
% 1.64/1.38 % (18157)------------------------------
% 1.64/1.38 % (18157)------------------------------
% 1.64/1.38 % (18155)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_18003 for (3000ds/27Mi)
% 1.64/1.38 % (18158)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_18003 for (3000ds/275Mi)
% 1.64/1.38 % (18154)Instruction limit reached!
% 1.64/1.38 % (18154)------------------------------
% 1.64/1.38 % (18154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (18154)Termination reason: Unknown
% 1.64/1.38 % (18154)Termination phase: Saturation
% 1.64/1.38
% 1.64/1.38 % (18154)Memory used [KB]: 5500
% 1.64/1.38 % (18154)Time elapsed: 0.005 s
% 1.64/1.38 % (18154)Instructions burned: 4 (million)
% 1.64/1.38 % (18154)------------------------------
% 1.64/1.38 % (18154)------------------------------
% 1.64/1.38 % (18153)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18003 for (3000ds/183Mi)
% 1.64/1.39 % (18161)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_18003 for (2999ds/37Mi)
% 1.64/1.39 % (18155)Instruction limit reached!
% 1.64/1.39 % (18155)------------------------------
% 1.64/1.39 % (18155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (18155)Termination reason: Unknown
% 1.64/1.39 % (18155)Termination phase: Saturation
% 1.64/1.39
% 1.64/1.39 % (18155)Memory used [KB]: 5628
% 1.64/1.39 % (18155)Time elapsed: 0.011 s
% 1.64/1.39 % (18155)Instructions burned: 29 (million)
% 1.64/1.39 % (18155)------------------------------
% 1.64/1.39 % (18155)------------------------------
% 1.75/1.40 % (18162)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_18003 for (2999ds/15Mi)
% 1.75/1.40 % (18161)Instruction limit reached!
% 1.75/1.40 % (18161)------------------------------
% 1.75/1.40 % (18161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.40 % (18161)Termination reason: Unknown
% 1.75/1.40 % (18161)Termination phase: Saturation
% 1.75/1.40
% 1.75/1.40 % (18161)Memory used [KB]: 5628
% 1.75/1.40 % (18161)Time elapsed: 0.012 s
% 1.75/1.40 % (18161)Instructions burned: 38 (million)
% 1.75/1.40 % (18161)------------------------------
% 1.75/1.40 % (18161)------------------------------
% 1.75/1.40 % (18164)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_18003 for (2999ds/1041Mi)
% 1.75/1.40 % (18163)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_18003 for (2999ds/3Mi)
% 1.75/1.40 % (18163)Instruction limit reached!
% 1.75/1.40 % (18163)------------------------------
% 1.75/1.40 % (18163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.40 % (18163)Termination reason: Unknown
% 1.75/1.40 % (18163)Termination phase: Function definition elimination
% 1.75/1.40
% 1.75/1.40 % (18163)Memory used [KB]: 1023
% 1.75/1.40 % (18163)Time elapsed: 0.003 s
% 1.75/1.40 % (18163)Instructions burned: 3 (million)
% 1.75/1.40 % (18163)------------------------------
% 1.75/1.40 % (18163)------------------------------
% 1.75/1.41 % (18160)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18003 for (2999ds/3Mi)
% 1.75/1.41 % (18162)Instruction limit reached!
% 1.75/1.41 % (18162)------------------------------
% 1.75/1.41 % (18162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.41 % (18162)Termination reason: Unknown
% 1.75/1.41 % (18162)Termination phase: Saturation
% 1.75/1.41
% 1.75/1.41 % (18162)Memory used [KB]: 5628
% 1.75/1.41 % (18162)Time elapsed: 0.011 s
% 1.75/1.41 % (18162)Instructions burned: 15 (million)
% 1.75/1.41 % (18162)------------------------------
% 1.75/1.41 % (18162)------------------------------
% 1.75/1.41 % (18160)Instruction limit reached!
% 1.75/1.41 % (18160)------------------------------
% 1.75/1.41 % (18160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.41 % (18160)Termination reason: Unknown
% 1.75/1.41 % (18160)Termination phase: Function definition elimination
% 1.75/1.41
% 1.75/1.41 % (18160)Memory used [KB]: 1023
% 1.75/1.41 % (18160)Time elapsed: 0.005 s
% 1.75/1.41 % (18160)Instructions burned: 3 (million)
% 1.75/1.41 % (18160)------------------------------
% 1.75/1.41 % (18160)------------------------------
% 1.75/1.41 % (18165)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_18003 for (2999ds/7Mi)
% 1.75/1.41 % (18165)Instruction limit reached!
% 1.75/1.41 % (18165)------------------------------
% 1.75/1.41 % (18165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.41 % (18165)Termination reason: Unknown
% 1.75/1.41 % (18165)Termination phase: Saturation
% 1.75/1.41
% 1.75/1.41 % (18165)Memory used [KB]: 1023
% 1.75/1.41 % (18165)Time elapsed: 0.004 s
% 1.75/1.41 % (18165)Instructions burned: 9 (million)
% 1.75/1.41 % (18165)------------------------------
% 1.75/1.41 % (18165)------------------------------
% 1.75/1.42 % (18169)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_18003 for (2999ds/7Mi)
% 1.75/1.42 % (18166)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_18003 for (2999ds/16Mi)
% 1.75/1.42 % (18169)Refutation not found, incomplete strategy
% 1.75/1.42 % (18169)------------------------------
% 1.75/1.42 % (18169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.42 % (18169)Termination reason: Refutation not found, incomplete strategy
% 1.75/1.42
% 1.75/1.42
% 1.75/1.42 % (18169)Memory used [KB]: 5500
% 1.75/1.42 % (18169)Time elapsed: 0.002 s
% 1.75/1.42 % (18169)Instructions burned: 3 (million)
% 1.75/1.42 % (18167)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_18003 for (2999ds/3Mi)
% 1.75/1.42 % (18169)------------------------------
% 1.75/1.42 % (18169)------------------------------
% 1.75/1.43 % (18167)Instruction limit reached!
% 1.75/1.43 % (18167)------------------------------
% 1.75/1.43 % (18167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.43 % (18167)Termination reason: Unknown
% 1.75/1.43 % (18167)Termination phase: Twee Goal Transformation
% 1.75/1.43
% 1.75/1.43 % (18167)Memory used [KB]: 1023
% 1.75/1.43 % (18167)Time elapsed: 0.004 s
% 1.75/1.43 % (18167)Instructions burned: 4 (million)
% 1.75/1.43 % (18167)------------------------------
% 1.75/1.43 % (18167)------------------------------
% 1.75/1.43 % (18166)Instruction limit reached!
% 1.75/1.43 % (18166)------------------------------
% 1.75/1.43 % (18166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.43 % (18166)Termination reason: Unknown
% 1.75/1.43 % (18166)Termination phase: Saturation
% 1.75/1.43
% 1.75/1.43 % (18166)Memory used [KB]: 5756
% 1.75/1.43 % (18166)Time elapsed: 0.010 s
% 1.75/1.43 % (18166)Instructions burned: 16 (million)
% 1.75/1.43 % (18166)------------------------------
% 1.75/1.43 % (18166)------------------------------
% 1.75/1.43 % (18168)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_18003 for (2999ds/3Mi)
% 1.75/1.43 % (18170)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_18003 for (2999ds/3Mi)
% 1.75/1.43 % (18168)Instruction limit reached!
% 1.75/1.43 % (18168)------------------------------
% 1.75/1.43 % (18168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.43 % (18168)Termination reason: Unknown
% 1.75/1.43 % (18168)Termination phase: Function definition elimination
% 1.75/1.43
% 1.75/1.43 % (18168)Memory used [KB]: 1023
% 1.75/1.43 % (18168)Time elapsed: 0.003 s
% 1.75/1.43 % (18168)Instructions burned: 4 (million)
% 1.75/1.43 % (18168)------------------------------
% 1.75/1.43 % (18168)------------------------------
% 1.75/1.43 % (18170)Instruction limit reached!
% 1.75/1.43 % (18170)------------------------------
% 1.75/1.43 % (18170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.43 % (18170)Termination reason: Unknown
% 1.75/1.43 % (18170)Termination phase: Saturation
% 1.75/1.43
% 1.75/1.43 % (18170)Memory used [KB]: 1023
% 1.75/1.43 % (18170)Time elapsed: 0.002 s
% 1.75/1.43 % (18170)Instructions burned: 4 (million)
% 1.75/1.43 % (18170)------------------------------
% 1.75/1.43 % (18170)------------------------------
% 1.75/1.44 % (18171)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_18003 for (2999ds/4Mi)
% 1.75/1.44 % (18171)Instruction limit reached!
% 1.75/1.44 % (18171)------------------------------
% 1.75/1.44 % (18171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.44 % (18171)Termination reason: Unknown
% 1.75/1.44 % (18171)Termination phase: Saturation
% 1.75/1.44
% 1.75/1.44 % (18171)Memory used [KB]: 5500
% 1.75/1.44 % (18171)Time elapsed: 0.003 s
% 1.75/1.44 % (18171)Instructions burned: 6 (million)
% 1.75/1.44 % (18171)------------------------------
% 1.75/1.44 % (18171)------------------------------
% 1.75/1.44 % (18172)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_18003 for (2999ds/18Mi)
% 1.75/1.44 % (18174)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18003 for (2999ds/6Mi)
% 1.75/1.44 % (18173)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_18003 for (2999ds/710Mi)
% 1.75/1.45 % (18174)Instruction limit reached!
% 1.75/1.45 % (18174)------------------------------
% 1.75/1.45 % (18174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.45 % (18174)Termination reason: Unknown
% 1.75/1.45 % (18174)Termination phase: Saturation
% 1.75/1.45
% 1.75/1.45 % (18174)Memory used [KB]: 5500
% 1.75/1.45 % (18174)Time elapsed: 0.003 s
% 1.75/1.45 % (18174)Instructions burned: 7 (million)
% 1.75/1.45 % (18174)------------------------------
% 1.75/1.45 % (18174)------------------------------
% 1.75/1.45 % (18153)Instruction limit reached!
% 1.75/1.45 % (18153)------------------------------
% 1.75/1.45 % (18153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.45 % (18153)Termination reason: Unknown
% 1.75/1.45 % (18153)Termination phase: Saturation
% 1.75/1.45
% 1.75/1.45 % (18153)Memory used [KB]: 6140
% 1.75/1.45 % (18153)Time elapsed: 0.063 s
% 1.75/1.45 % (18153)Instructions burned: 185 (million)
% 1.75/1.45 % (18153)------------------------------
% 1.75/1.45 % (18153)------------------------------
% 1.75/1.45 % (18172)Instruction limit reached!
% 1.75/1.45 % (18172)------------------------------
% 1.75/1.45 % (18172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.45 % (18172)Termination reason: Unknown
% 1.75/1.45 % (18172)Termination phase: Saturation
% 1.75/1.45
% 1.75/1.45 % (18172)Memory used [KB]: 5628
% 1.75/1.45 % (18172)Time elapsed: 0.008 s
% 1.75/1.45 % (18172)Instructions burned: 18 (million)
% 1.75/1.45 % (18172)------------------------------
% 1.75/1.45 % (18172)------------------------------
% 1.75/1.45 % (18175)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_18003 for (2999ds/902Mi)
% 1.75/1.45 % (18175)Refutation not found, incomplete strategy
% 1.75/1.45 % (18175)------------------------------
% 1.75/1.45 % (18175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.45 % (18175)Termination reason: Refutation not found, incomplete strategy
% 1.75/1.45
% 1.75/1.45
% 1.75/1.45 % (18175)Memory used [KB]: 5500
% 1.75/1.45 % (18175)Time elapsed: 0.004 s
% 1.75/1.45 % (18175)Instructions burned: 6 (million)
% 1.75/1.45 % (18175)------------------------------
% 1.75/1.45 % (18175)------------------------------
% 1.75/1.46 % (18176)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_18003 for (2999ds/21Mi)
% 1.75/1.46 % (18177)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_18003 for (2999ds/5Mi)
% 1.75/1.46 % (18177)Instruction limit reached!
% 1.75/1.46 % (18177)------------------------------
% 1.75/1.46 % (18177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.46 % (18177)Termination reason: Unknown
% 1.75/1.46 % (18177)Termination phase: Saturation
% 1.75/1.46
% 1.75/1.46 % (18177)Memory used [KB]: 5500
% 1.75/1.46 % (18177)Time elapsed: 0.003 s
% 1.75/1.46 % (18177)Instructions burned: 6 (million)
% 1.75/1.46 % (18177)------------------------------
% 1.75/1.46 % (18177)------------------------------
% 1.75/1.46 % (18176)Instruction limit reached!
% 1.75/1.46 % (18176)------------------------------
% 1.75/1.46 % (18176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.46 % (18176)Termination reason: Unknown
% 1.75/1.46 % (18176)Termination phase: Saturation
% 1.75/1.46
% 1.75/1.46 % (18176)Memory used [KB]: 5628
% 1.75/1.46 % (18176)Time elapsed: 0.008 s
% 1.75/1.46 % (18176)Instructions burned: 21 (million)
% 1.75/1.46 % (18176)------------------------------
% 1.75/1.46 % (18176)------------------------------
% 1.75/1.46 % (18179)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_18003 for (2999ds/377Mi)
% 1.75/1.47 % (18178)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_18003 for (2999ds/6Mi)
% 1.75/1.47 % (18178)Instruction limit reached!
% 1.75/1.47 % (18178)------------------------------
% 1.75/1.47 % (18178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.47 % (18178)Termination reason: Unknown
% 1.75/1.47 % (18178)Termination phase: Saturation
% 1.75/1.47
% 1.75/1.47 % (18178)Memory used [KB]: 5500
% 1.75/1.47 % (18178)Time elapsed: 0.004 s
% 1.75/1.47 % (18178)Instructions burned: 6 (million)
% 1.75/1.47 % (18178)------------------------------
% 1.75/1.47 % (18178)------------------------------
% 1.75/1.47 % (18180)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_18003 for (2999ds/779Mi)
% 1.75/1.47 % (18181)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_18003 for (2999ds/19Mi)
% 1.75/1.48 % (18182)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_18003 for (2999ds/879Mi)
% 1.75/1.48 % (18181)Instruction limit reached!
% 1.75/1.48 % (18181)------------------------------
% 1.75/1.48 % (18181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.48 % (18181)Termination reason: Unknown
% 1.75/1.48 % (18181)Termination phase: Saturation
% 1.75/1.48
% 1.75/1.48 % (18181)Memory used [KB]: 5628
% 1.75/1.48 % (18181)Time elapsed: 0.008 s
% 1.75/1.48 % (18181)Instructions burned: 21 (million)
% 1.75/1.48 % (18181)------------------------------
% 1.75/1.48 % (18181)------------------------------
% 1.75/1.49 % (18183)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_18003 for (2998ds/17Mi)
% 1.75/1.49 % (18158)Instruction limit reached!
% 1.75/1.49 % (18158)------------------------------
% 1.75/1.49 % (18158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.49 % (18158)Termination reason: Unknown
% 1.75/1.49 % (18158)Termination phase: Saturation
% 1.75/1.49
% 1.75/1.49 % (18158)Memory used [KB]: 5884
% 1.75/1.49 % (18158)Time elapsed: 0.111 s
% 1.75/1.49 % (18158)Instructions burned: 276 (million)
% 1.75/1.49 % (18158)------------------------------
% 1.75/1.49 % (18158)------------------------------
% 1.75/1.49 % (18183)Instruction limit reached!
% 1.75/1.49 % (18183)------------------------------
% 1.75/1.49 % (18183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.49 % (18183)Termination reason: Unknown
% 1.75/1.49 % (18183)Termination phase: Saturation
% 1.75/1.49
% 1.75/1.49 % (18183)Memory used [KB]: 5628
% 1.75/1.49 % (18183)Time elapsed: 0.007 s
% 1.75/1.49 % (18183)Instructions burned: 18 (million)
% 1.75/1.49 % (18183)------------------------------
% 1.75/1.49 % (18183)------------------------------
% 1.75/1.50 % (18190)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_18003 for (2998ds/30Mi)
% 1.75/1.50 % (18189)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_18003 for (2998ds/3Mi)
% 1.75/1.50 % (18189)Instruction limit reached!
% 1.75/1.50 % (18189)------------------------------
% 1.75/1.50 % (18189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.50 % (18189)Termination reason: Unknown
% 1.75/1.50 % (18189)Termination phase: Property scanning
% 1.75/1.50
% 1.75/1.50 % (18189)Memory used [KB]: 1023
% 1.75/1.50 % (18189)Time elapsed: 0.002 s
% 1.75/1.50 % (18189)Instructions burned: 4 (million)
% 1.75/1.50 % (18189)------------------------------
% 1.75/1.50 % (18189)------------------------------
% 1.75/1.51 % (18190)Refutation not found, incomplete strategy
% 1.75/1.51 % (18190)------------------------------
% 1.75/1.51 % (18190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.51 % (18190)Termination reason: Refutation not found, incomplete strategy
% 1.75/1.51
% 1.75/1.51
% 1.75/1.51 % (18190)Memory used [KB]: 5628
% 1.75/1.51 % (18190)Time elapsed: 0.033 s
% 1.75/1.51 % (18190)Instructions burned: 26 (million)
% 1.75/1.51 % (18190)------------------------------
% 1.75/1.51 % (18190)------------------------------
% 1.75/1.51 % (18191)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_18003 for (2998ds/127Mi)
% 1.75/1.52 % (18192)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_18003 for (2998ds/100Mi)
% 1.75/1.55 % (18192)Instruction limit reached!
% 1.75/1.55 % (18192)------------------------------
% 1.75/1.55 % (18192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.55 % (18192)Termination reason: Unknown
% 1.75/1.55 % (18192)Termination phase: Saturation
% 1.75/1.55
% 1.75/1.55 % (18192)Memory used [KB]: 5756
% 1.75/1.55 % (18192)Time elapsed: 0.055 s
% 1.75/1.55 % (18192)Instructions burned: 100 (million)
% 1.75/1.55 % (18192)------------------------------
% 1.75/1.55 % (18192)------------------------------
% 1.75/1.56 % (18191)Instruction limit reached!
% 1.75/1.56 % (18191)------------------------------
% 1.75/1.56 % (18191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.56 % (18191)Termination reason: Unknown
% 1.75/1.56 % (18191)Termination phase: Saturation
% 1.75/1.56
% 1.75/1.56 % (18191)Memory used [KB]: 5884
% 1.75/1.56 % (18191)Time elapsed: 0.067 s
% 1.75/1.56 % (18191)Instructions burned: 128 (million)
% 1.75/1.56 % (18191)------------------------------
% 1.75/1.56 % (18191)------------------------------
% 1.75/1.56 % (18193)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_18003 for (2998ds/3Mi)
% 1.75/1.56 % (18193)Instruction limit reached!
% 1.75/1.56 % (18193)------------------------------
% 1.75/1.56 % (18193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.56 % (18193)Termination reason: Unknown
% 1.75/1.56 % (18193)Termination phase: Property scanning
% 1.75/1.56
% 1.75/1.56 % (18193)Memory used [KB]: 1023
% 1.75/1.56 % (18193)Time elapsed: 0.002 s
% 1.75/1.56 % (18193)Instructions burned: 3 (million)
% 1.75/1.56 % (18193)------------------------------
% 1.75/1.56 % (18193)------------------------------
% 1.75/1.57 % (18194)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_18003 for (2998ds/20Mi)
% 1.75/1.57 % (18195)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_18003 for (2997ds/86Mi)
% 1.75/1.58 % (18194)Instruction limit reached!
% 1.75/1.58 % (18194)------------------------------
% 1.75/1.58 % (18194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.58 % (18194)Termination reason: Unknown
% 1.75/1.58 % (18194)Termination phase: Saturation
% 1.75/1.58
% 1.75/1.58 % (18194)Memory used [KB]: 5628
% 1.75/1.58 % (18194)Time elapsed: 0.009 s
% 1.75/1.58 % (18194)Instructions burned: 20 (million)
% 1.75/1.58 % (18194)------------------------------
% 1.75/1.58 % (18194)------------------------------
% 1.75/1.59 % (18197)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_18003 for (2997ds/107Mi)
% 1.75/1.60 % (18195)Instruction limit reached!
% 1.75/1.60 % (18195)------------------------------
% 1.75/1.60 % (18195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.60 % (18195)Termination reason: Unknown
% 1.75/1.60 % (18195)Termination phase: Saturation
% 1.75/1.60
% 1.75/1.60 % (18195)Memory used [KB]: 5884
% 1.75/1.60 % (18195)Time elapsed: 0.028 s
% 1.75/1.60 % (18195)Instructions burned: 86 (million)
% 1.75/1.60 % (18195)------------------------------
% 1.75/1.60 % (18195)------------------------------
% 1.75/1.61 % (18199)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_18003 for (2997ds/39Mi)
% 1.75/1.62 % (18199)Instruction limit reached!
% 1.75/1.62 % (18199)------------------------------
% 1.75/1.62 % (18199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.62 % (18199)Termination reason: Unknown
% 1.75/1.62 % (18199)Termination phase: Saturation
% 1.75/1.62
% 1.75/1.62 % (18199)Memory used [KB]: 5628
% 1.75/1.62 % (18199)Time elapsed: 0.013 s
% 1.75/1.62 % (18199)Instructions burned: 39 (million)
% 1.75/1.62 % (18199)------------------------------
% 1.75/1.62 % (18199)------------------------------
% 1.75/1.62 % (18179)Instruction limit reached!
% 1.75/1.62 % (18179)------------------------------
% 1.75/1.62 % (18179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.62 % (18179)Termination reason: Unknown
% 1.75/1.62 % (18179)Termination phase: Saturation
% 1.75/1.62
% 1.75/1.62 % (18179)Memory used [KB]: 6268
% 1.75/1.62 % (18179)Time elapsed: 0.161 s
% 1.75/1.62 % (18179)Instructions burned: 377 (million)
% 1.75/1.62 % (18179)------------------------------
% 1.75/1.62 % (18179)------------------------------
% 1.75/1.63 % (18197)Instruction limit reached!
% 1.75/1.63 % (18197)------------------------------
% 1.75/1.63 % (18197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.63 % (18197)Termination reason: Unknown
% 1.75/1.63 % (18197)Termination phase: Saturation
% 1.75/1.63
% 1.75/1.63 % (18197)Memory used [KB]: 5884
% 1.75/1.63 % (18197)Time elapsed: 0.045 s
% 1.75/1.63 % (18197)Instructions burned: 108 (million)
% 1.75/1.63 % (18197)------------------------------
% 1.75/1.63 % (18197)------------------------------
% 1.75/1.63 % (18211)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_18003 for (2997ds/46Mi)
% 1.75/1.64 % (18207)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_18003 for (2997ds/448Mi)
% 1.75/1.64 % (18212)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_18003 for (2997ds/98Mi)
% 1.75/1.65 % (18211)Instruction limit reached!
% 1.75/1.65 % (18211)------------------------------
% 1.75/1.65 % (18211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.65 % (18211)Termination reason: Unknown
% 1.75/1.65 % (18211)Termination phase: Saturation
% 1.75/1.65
% 1.75/1.65 % (18211)Memory used [KB]: 5756
% 1.75/1.65 % (18211)Time elapsed: 0.017 s
% 1.75/1.65 % (18211)Instructions burned: 48 (million)
% 1.75/1.65 % (18211)------------------------------
% 1.75/1.65 % (18211)------------------------------
% 1.75/1.66 % (18218)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_18003 for (2997ds/507Mi)
% 1.75/1.69 % (18212)Instruction limit reached!
% 1.75/1.69 % (18212)------------------------------
% 1.75/1.69 % (18212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.69 % (18212)Termination reason: Unknown
% 1.75/1.69 % (18212)Termination phase: Saturation
% 1.75/1.69
% 1.75/1.69 % (18212)Memory used [KB]: 1279
% 1.75/1.69 % (18212)Time elapsed: 0.046 s
% 1.75/1.69 % (18212)Instructions burned: 98 (million)
% 1.75/1.69 % (18212)------------------------------
% 1.75/1.69 % (18212)------------------------------
% 1.75/1.70 % (18173)Refutation not found, non-redundant clauses discarded% (18173)------------------------------
% 1.75/1.70 % (18173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.70 % (18173)Termination reason: Refutation not found, non-redundant clauses discarded
% 1.75/1.70
% 1.75/1.70 % (18173)Memory used [KB]: 7036
% 1.75/1.70 % (18173)Time elapsed: 0.254 s
% 1.75/1.70 % (18173)Instructions burned: 649 (million)
% 1.75/1.70 % (18173)------------------------------
% 1.75/1.70 % (18173)------------------------------
% 1.75/1.71 % (18229)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_18003 for (2996ds/149Mi)
% 1.75/1.72 % (18231)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_18003 for (2996ds/39Mi)
% 1.75/1.74 % (18231)Instruction limit reached!
% 1.75/1.74 % (18231)------------------------------
% 1.75/1.74 % (18231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.74 % (18231)Termination reason: Unknown
% 1.75/1.74 % (18231)Termination phase: Saturation
% 1.75/1.74
% 1.75/1.74 % (18231)Memory used [KB]: 5628
% 1.75/1.74 % (18231)Time elapsed: 0.024 s
% 1.75/1.74 % (18231)Instructions burned: 40 (million)
% 1.75/1.74 % (18231)------------------------------
% 1.75/1.74 % (18231)------------------------------
% 1.75/1.76 % (18236)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_18003 for (2996ds/6Mi)
% 1.75/1.76 % (18236)Instruction limit reached!
% 1.75/1.76 % (18236)------------------------------
% 1.75/1.76 % (18236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.76 % (18236)Termination reason: Unknown
% 1.75/1.76 % (18236)Termination phase: Saturation
% 1.75/1.76
% 1.75/1.76 % (18236)Memory used [KB]: 9978
% 1.75/1.76 % (18236)Time elapsed: 0.006 s
% 1.75/1.76 % (18236)Instructions burned: 6 (million)
% 1.75/1.76 % (18236)------------------------------
% 1.75/1.76 % (18236)------------------------------
% 1.75/1.78 % (18238)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_18003 for (2996ds/1087Mi)
% 1.75/1.78 % (18229)Instruction limit reached!
% 1.75/1.78 % (18229)------------------------------
% 1.75/1.78 % (18229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.78 % (18229)Termination reason: Unknown
% 1.75/1.78 % (18229)Termination phase: Saturation
% 1.75/1.78
% 1.75/1.78 % (18229)Memory used [KB]: 5884
% 1.75/1.78 % (18229)Time elapsed: 0.075 s
% 1.75/1.78 % (18229)Instructions burned: 149 (million)
% 1.75/1.78 % (18229)------------------------------
% 1.75/1.78 % (18229)------------------------------
% 1.75/1.78 % (18180)Instruction limit reached!
% 1.75/1.78 % (18180)------------------------------
% 1.75/1.78 % (18180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.78 % (18180)Termination reason: Unknown
% 1.75/1.78 % (18180)Termination phase: Saturation
% 1.75/1.78
% 1.75/1.78 % (18180)Memory used [KB]: 6396
% 1.75/1.78 % (18180)Time elapsed: 0.332 s
% 1.75/1.78 % (18180)Instructions burned: 780 (million)
% 1.75/1.78 % (18180)------------------------------
% 1.75/1.78 % (18180)------------------------------
% 1.75/1.79 % (18164)Instruction limit reached!
% 1.75/1.79 % (18164)------------------------------
% 1.75/1.79 % (18164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.79 % (18164)Termination reason: Unknown
% 1.75/1.79 % (18164)Termination phase: Saturation
% 1.75/1.79
% 1.75/1.79 % (18164)Memory used [KB]: 7419
% 1.75/1.79 % (18164)Time elapsed: 0.389 s
% 1.75/1.79 % (18164)Instructions burned: 1041 (million)
% 1.75/1.79 % (18164)------------------------------
% 1.75/1.79 % (18164)------------------------------
% 1.75/1.79 % (18240)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_18003 for (2995ds/47Mi)
% 1.75/1.80 % (18241)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_18003 for (2995ds/44Mi)
% 1.75/1.81 % (18242)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_18003 for (2995ds/432Mi)
% 1.75/1.82 % (18241)Instruction limit reached!
% 1.75/1.82 % (18241)------------------------------
% 1.75/1.82 % (18241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.82 % (18241)Termination reason: Unknown
% 1.75/1.82 % (18241)Termination phase: Saturation
% 1.75/1.82
% 1.75/1.82 % (18241)Memory used [KB]: 1151
% 1.75/1.82 % (18241)Time elapsed: 0.023 s
% 1.75/1.82 % (18241)Instructions burned: 44 (million)
% 1.75/1.82 % (18241)------------------------------
% 1.75/1.82 % (18241)------------------------------
% 1.75/1.82 % (18240)Instruction limit reached!
% 1.75/1.82 % (18240)------------------------------
% 1.75/1.82 % (18240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.82 % (18240)Termination reason: Unknown
% 1.75/1.82 % (18240)Termination phase: Saturation
% 1.75/1.82
% 1.75/1.82 % (18240)Memory used [KB]: 5756
% 1.75/1.82 % (18240)Time elapsed: 0.024 s
% 1.75/1.82 % (18240)Instructions burned: 47 (million)
% 1.75/1.82 % (18240)------------------------------
% 1.75/1.82 % (18240)------------------------------
% 1.75/1.82 % (18218)Instruction limit reached!
% 1.75/1.82 % (18218)------------------------------
% 1.75/1.82 % (18218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.82 % (18218)Termination reason: Unknown
% 1.75/1.82 % (18218)Termination phase: Saturation
% 1.75/1.82
% 1.75/1.82 % (18218)Memory used [KB]: 6396
% 1.75/1.82 % (18218)Time elapsed: 0.168 s
% 1.75/1.82 % (18218)Instructions burned: 507 (million)
% 1.75/1.82 % (18218)------------------------------
% 1.75/1.82 % (18218)------------------------------
% 1.75/1.83 % (18182)Refutation not found, non-redundant clauses discarded% (18182)------------------------------
% 1.75/1.83 % (18182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.83 % (18182)Termination reason: Refutation not found, non-redundant clauses discarded
% 1.75/1.83
% 1.75/1.83 % (18182)Memory used [KB]: 6908
% 1.75/1.83 % (18182)Time elapsed: 0.371 s
% 1.75/1.83 % (18182)Instructions burned: 868 (million)
% 1.75/1.83 % (18182)------------------------------
% 1.75/1.83 % (18182)------------------------------
% 1.75/1.83 % (18245)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_18003 for (2995ds/31Mi)
% 1.75/1.83 % (18246)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_18003 for (2995ds/96Mi)
% 1.75/1.84 % (18244)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_18003 for (2995ds/62Mi)
% 1.75/1.84 % (18248)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_18003 for (2995ds/453Mi)
% 1.75/1.85 % (18207)Instruction limit reached!
% 1.75/1.85 % (18207)------------------------------
% 1.75/1.85 % (18207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.85 % (18207)Termination reason: Unknown
% 1.75/1.85 % (18207)Termination phase: Saturation
% 1.75/1.85
% 1.75/1.85 % (18207)Memory used [KB]: 6140
% 1.75/1.85 % (18207)Time elapsed: 0.211 s
% 1.75/1.85 % (18207)Instructions burned: 448 (million)
% 1.75/1.85 % (18207)------------------------------
% 1.75/1.85 % (18207)------------------------------
% 1.75/1.85 % (18245)Instruction limit reached!
% 1.75/1.85 % (18245)------------------------------
% 1.75/1.85 % (18245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.85 % (18245)Termination reason: Unknown
% 1.75/1.85 % (18245)Termination phase: Saturation
% 1.75/1.85
% 1.75/1.85 % (18245)Memory used [KB]: 5756
% 1.75/1.85 % (18245)Time elapsed: 0.018 s
% 1.75/1.85 % (18245)Instructions burned: 31 (million)
% 1.75/1.85 % (18245)------------------------------
% 1.75/1.85 % (18245)------------------------------
% 1.75/1.86 % (18249)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_18003 for (2995ds/71Mi)
% 1.75/1.86 % (18246)Instruction limit reached!
% 1.75/1.86 % (18246)------------------------------
% 1.75/1.86 % (18246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.86 % (18246)Termination reason: Unknown
% 1.75/1.86 % (18246)Termination phase: Saturation
% 1.75/1.86
% 1.75/1.86 % (18244)Instruction limit reached!
% 1.75/1.86 % (18244)------------------------------
% 1.75/1.86 % (18244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.86 % (18244)Termination reason: Unknown
% 1.75/1.86 % (18244)Termination phase: Saturation
% 1.75/1.86
% 1.75/1.86 % (18244)Memory used [KB]: 5628
% 1.75/1.86 % (18244)Time elapsed: 0.031 s
% 1.75/1.86 % (18244)Instructions burned: 62 (million)
% 1.75/1.86 % (18244)------------------------------
% 1.75/1.86 % (18244)------------------------------
% 1.75/1.86 % (18246)Memory used [KB]: 5756
% 1.75/1.86 % (18246)Time elapsed: 0.032 s
% 1.75/1.87 % (18246)Instructions burned: 97 (million)
% 1.75/1.87 % (18246)------------------------------
% 1.75/1.87 % (18246)------------------------------
% 1.75/1.87 % (18250)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_18003 for (2995ds/83Mi)
% 1.75/1.87 % (18251)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_18003 for (2995ds/11Mi)
% 1.75/1.88 % (18251)Instruction limit reached!
% 1.75/1.88 % (18251)------------------------------
% 1.75/1.88 % (18251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.88 % (18251)Termination reason: Unknown
% 1.75/1.88 % (18251)Termination phase: Saturation
% 1.75/1.88
% 1.75/1.88 % (18251)Memory used [KB]: 5500
% 1.75/1.88 % (18251)Time elapsed: 0.005 s
% 1.75/1.88 % (18251)Instructions burned: 13 (million)
% 1.75/1.88 % (18251)------------------------------
% 1.75/1.88 % (18251)------------------------------
% 1.75/1.88 % (18252)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_18003 for (2995ds/41Mi)
% 1.75/1.89 % (18255)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18003 for (2994ds/6Mi)
% 1.75/1.89 % (18255)Instruction limit reached!
% 1.75/1.89 % (18255)------------------------------
% 1.75/1.89 % (18255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.89 % (18255)Termination reason: Unknown
% 1.75/1.89 % (18255)Termination phase: Saturation
% 1.75/1.89
% 1.75/1.89 % (18255)Memory used [KB]: 5500
% 1.75/1.89 % (18255)Time elapsed: 0.003 s
% 1.75/1.89 % (18255)Instructions burned: 7 (million)
% 1.75/1.89 % (18255)------------------------------
% 1.75/1.89 % (18255)------------------------------
% 1.75/1.90 % (18249)Instruction limit reached!
% 1.75/1.90 % (18249)------------------------------
% 1.75/1.90 % (18249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.90 % (18249)Termination reason: Unknown
% 1.75/1.90 % (18249)Termination phase: Saturation
% 1.75/1.90
% 1.75/1.90 % (18249)Memory used [KB]: 5756
% 1.75/1.90 % (18249)Time elapsed: 0.036 s
% 1.75/1.90 % (18249)Instructions burned: 71 (million)
% 1.75/1.90 % (18249)------------------------------
% 1.75/1.90 % (18249)------------------------------
% 1.75/1.90 % (18252)Instruction limit reached!
% 1.75/1.90 % (18252)------------------------------
% 1.75/1.90 % (18252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.90 % (18252)Termination reason: Unknown
% 1.75/1.90 % (18252)Termination phase: Saturation
% 1.75/1.90 % (18256)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_18003 for (2994ds/150Mi)
% 1.75/1.90
% 1.75/1.90 % (18252)Memory used [KB]: 5628
% 1.75/1.90 % (18252)Time elapsed: 0.020 s
% 1.75/1.90 % (18252)Instructions burned: 41 (million)
% 1.75/1.90 % (18252)------------------------------
% 1.75/1.90 % (18252)------------------------------
% 1.75/1.91 % (18250)Instruction limit reached!
% 1.75/1.91 % (18250)------------------------------
% 1.75/1.91 % (18250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.91 % (18250)Termination reason: Unknown
% 1.75/1.91 % (18250)Termination phase: Saturation
% 1.75/1.91
% 1.75/1.91 % (18250)Memory used [KB]: 5756
% 1.75/1.91 % (18250)Time elapsed: 0.042 s
% 1.75/1.91 % (18250)Instructions burned: 83 (million)
% 1.75/1.91 % (18250)------------------------------
% 1.75/1.91 % (18250)------------------------------
% 1.75/1.91 % (18258)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_18003 for (2994ds/343Mi)
% 1.75/1.91 % (18248)First to succeed.
% 1.75/1.92 % (18259)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_18003 for (2994ds/109Mi)
% 1.75/1.92 % (18248)Refutation found. Thanks to Tanya!
% 1.75/1.92 % SZS status Theorem for DTF2THF_18003
% 1.75/1.92 % SZS output start Proof for DTF2THF_18003
% 1.75/1.92 thf(func_def_0, type, in: $i > $i > $o).
% 1.75/1.92 thf(func_def_1, type, setunion: $i > $i).
% 1.75/1.92 thf(func_def_5, type, subset: $i > $i > $o).
% 1.75/1.92 thf(func_def_7, type, transitiveset: $i > $o).
% 1.75/1.92 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)).
% 1.75/1.92 thf(func_def_21, type, sK2: $i > $i > $i).
% 1.75/1.92 thf(func_def_22, type, sK3: $o > $i > $i > $i).
% 1.75/1.92 thf(func_def_25, type, sK6: $i > $i).
% 1.75/1.92 thf(f599,plain,(
% 1.75/1.92 $false),
% 1.75/1.92 inference(avatar_sat_refutation,[status(thm)],[f510,f513,f589])).
% 1.75/1.92 thf(f589,plain,(
% 1.75/1.92 ~spl0_3),
% 1.75/1.92 inference(avatar_contradiction_clause,[status(thm)],[f588])).
% 1.75/1.92 thf(f588,plain,(
% 1.75/1.92 $false | ~spl0_3),
% 1.75/1.92 inference(trivial_inequality_removal,[status(thm)],[f573])).
% 1.75/1.92 thf(f573,plain,(
% 1.75/1.92 ($true = $false) | ~spl0_3),
% 1.75/1.92 inference(superposition,[status(thm)],[f271,f505])).
% 1.75/1.92 thf(f505,plain,(
% 1.75/1.92 ( ! [X0 : $o] : (($true = X0)) ) | ~spl0_3),
% 1.75/1.92 inference(avatar_component_clause,[status(thm)],[f504])).
% 1.75/1.92 thf(f504,definition,(
% 1.75/1.92 spl0_3 <=> ! [X0 : $o] : ($true = X0)),
% 1.75/1.92 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.75/1.92 thf(f271,plain,(
% 1.75/1.92 ((in @ (setunion @ sK4) @ sK4) = $false)),
% 1.75/1.92 inference(trivial_inequality_removal,[status(thm)],[f268])).
% 1.75/1.92 thf(f268,plain,(
% 1.75/1.92 ($true = $false) | ((in @ (setunion @ sK4) @ sK4) = $false)),
% 1.75/1.92 inference(superposition,[status(thm)],[f151,f262])).
% 1.75/1.92 thf(f262,plain,(
% 1.75/1.92 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ Y0 @ X1))))) | ((in @ X1 @ sK4) = $false)) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f261])).
% 1.75/1.92 thf(f261,plain,(
% 1.75/1.92 ( ! [X1 : $i] : ((((in @ X1 @ sK4) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ Y0 @ X1))))) = $true)) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f260])).
% 1.75/1.92 thf(f260,plain,(
% 1.75/1.92 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK4) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0)))))) @ X1) = $true)) )),
% 1.75/1.92 inference(pi_clausification,[status(thm)],[f152])).
% 1.75/1.92 thf(f152,plain,(
% 1.75/1.92 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))) = $true)),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f150])).
% 1.75/1.92 thf(f150,plain,(
% 1.75/1.92 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK4)) => (subset @ Y0 @ (setunion @ sK4)))))) = $false)),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f149])).
% 1.75/1.92 thf(f149,plain,(
% 1.75/1.92 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (subset @ Y1 @ (setunion @ Y0))))))) @ sK4) = $false)),
% 1.75/1.92 inference(sigma_clausification,[status(thm)],[f37])).
% 1.75/1.92 thf(f37,plain,(
% 1.75/1.92 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (subset @ Y1 @ (setunion @ Y0)))))))) = $false)),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.75/1.92 thf(f35,plain,(
% 1.75/1.92 (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (subset @ Y1 @ (setunion @ Y0))))))))) = $false)),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.75/1.92 thf(f33,plain,(
% 1.75/1.92 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (subset @ Y1 @ (setunion @ Y0)))))))))) = $false)),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.75/1.92 thf(f31,plain,(
% 1.75/1.92 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (subset @ Y1 @ (setunion @ Y0))))))))))) = $false)),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.75/1.92 thf(f30,plain,(
% 1.75/1.92 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (subset @ Y1 @ (setunion @ Y0)))))))))))) = $false)),
% 1.75/1.92 inference(not_proxy_clausification,[status(thm)],[f29])).
% 1.75/1.92 thf(f29,plain,(
% 1.75/1.92 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (subset @ Y1 @ (setunion @ Y0))))))))))))) = $true)),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.75/1.92 thf(f28,plain,(
% 1.75/1.92 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))) @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ Y3 @ Y2))))) @ Y1)))) => ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))) @ (setunion @ Y0)))))))))) = $true)),
% 1.75/1.92 inference(definition_unfolding,[status(thm)],[f23,f22,f21,f24,f27,f26,f26])).
% 1.75/1.92 thf(f26,plain,(
% 1.75/1.92 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 1.75/1.92 inference(cnf_transformation,[status(thm)],[f16])).
% 1.75/1.92 thf(f16,plain,(
% 1.75/1.92 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 1.75/1.92 inference(fool_elimination,[status(thm)],[f15])).
% 1.75/1.92 thf(f15,plain,(
% 1.75/1.92 (transitiveset = (^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))))),
% 1.75/1.92 inference(rectify,[status(thm)],[f4])).
% 1.75/1.92 thf(f4,axiom,(
% 1.75/1.92 (transitiveset = (^[X0 : $i] : (! [X4 : $i] : ((in @ X4 @ X0) => (subset @ X4 @ X0)))))),
% 1.75/1.92 file('/export/starexec/sandbox2/tmp/tmp.89llQL148d/DTF2THF_18003.p',transitiveset)).
% 1.75/1.92 thf(f27,plain,(
% 1.75/1.92 (transitivesetOp2 = (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))) @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))))),
% 1.75/1.92 inference(definition_unfolding,[status(thm)],[f25,f26])).
% 1.75/1.92 thf(f25,plain,(
% 1.75/1.92 (transitivesetOp2 = (!! @ $i @ (^[Y0 : $i]: ((transitiveset @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))))),
% 1.75/1.92 inference(cnf_transformation,[status(thm)],[f10])).
% 1.75/1.92 thf(f10,plain,(
% 1.75/1.92 (transitivesetOp2 = (!! @ $i @ (^[Y0 : $i]: ((transitiveset @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))))),
% 1.75/1.92 inference(fool_elimination,[status(thm)],[f9])).
% 1.75/1.92 thf(f9,plain,(
% 1.75/1.92 (! [X0 : $i] : ((transitiveset @ X0) => ! [X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ((in @ X1 @ X2) => (in @ X1 @ X0)))) = transitivesetOp2)),
% 1.75/1.92 inference(rectify,[status(thm)],[f5])).
% 1.75/1.92 thf(f5,axiom,(
% 1.75/1.92 (! [X4 : $i] : ((transitiveset @ X4) => ! [X1 : $i,X0 : $i] : ((in @ X0 @ X4) => ((in @ X1 @ X0) => (in @ X1 @ X4)))) = transitivesetOp2)),
% 1.75/1.92 file('/export/starexec/sandbox2/tmp/tmp.89llQL148d/DTF2THF_18003.p',transitivesetOp2)).
% 1.75/1.92 thf(f24,plain,(
% 1.75/1.92 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 1.75/1.92 inference(cnf_transformation,[status(thm)],[f18])).
% 1.75/1.92 thf(f18,plain,(
% 1.75/1.92 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 1.75/1.92 inference(fool_elimination,[status(thm)],[f17])).
% 1.75/1.92 thf(f17,plain,(
% 1.75/1.92 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 1.75/1.92 inference(rectify,[status(thm)],[f3])).
% 1.75/1.92 thf(f3,axiom,(
% 1.75/1.92 (subsetI1 = ! [X2 : $i,X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (in @ X1 @ X2)) => (subset @ X0 @ X2)))),
% 1.75/1.92 file('/export/starexec/sandbox2/tmp/tmp.89llQL148d/DTF2THF_18003.p',subsetI1)).
% 1.75/1.92 thf(f21,plain,(
% 1.75/1.92 (setunionE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))))),
% 1.75/1.92 inference(cnf_transformation,[status(thm)],[f14])).
% 1.75/1.92 thf(f14,plain,(
% 1.75/1.92 (setunionE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))))),
% 1.75/1.92 inference(fool_elimination,[status(thm)],[f13])).
% 1.75/1.92 thf(f13,plain,(
% 1.75/1.92 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)) = setunionE)),
% 1.75/1.92 inference(rectify,[status(thm)],[f2])).
% 1.75/1.92 thf(f2,axiom,(
% 1.75/1.92 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X3 : $o] : (! [X2 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => X3)) => X3)) = setunionE)),
% 1.75/1.92 file('/export/starexec/sandbox2/tmp/tmp.89llQL148d/DTF2THF_18003.p',setunionE)).
% 1.75/1.92 thf(f22,plain,(
% 1.75/1.92 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))))),
% 1.75/1.92 inference(cnf_transformation,[status(thm)],[f20])).
% 1.75/1.92 thf(f20,plain,(
% 1.75/1.92 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))))),
% 1.75/1.92 inference(fool_elimination,[status(thm)],[f19])).
% 1.75/1.92 thf(f19,plain,(
% 1.75/1.92 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ((in @ X0 @ X1) => (in @ X2 @ (setunion @ X1)))) = setunionI)),
% 1.75/1.92 inference(rectify,[status(thm)],[f1])).
% 1.75/1.92 thf(f1,axiom,(
% 1.75/1.92 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))) = setunionI)),
% 1.75/1.92 file('/export/starexec/sandbox2/tmp/tmp.89llQL148d/DTF2THF_18003.p',setunionI)).
% 1.75/1.92 thf(f23,plain,(
% 1.75/1.92 ($true = (~ (setunionI => (setunionE => (subsetI1 => (transitivesetOp2 => (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (transitiveset @ Y1)))) => (transitiveset @ (setunion @ Y0)))))))))))),
% 1.75/1.92 inference(cnf_transformation,[status(thm)],[f12])).
% 1.75/1.92 thf(f12,plain,(
% 1.75/1.92 ($true = (~ (setunionI => (setunionE => (subsetI1 => (transitivesetOp2 => (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (transitiveset @ Y1)))) => (transitiveset @ (setunion @ Y0)))))))))))),
% 1.75/1.92 inference(fool_elimination,[status(thm)],[f11])).
% 1.75/1.92 thf(f11,plain,(
% 1.75/1.92 ~(setunionI => (setunionE => (subsetI1 => (transitivesetOp2 => ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (transitiveset @ X1)) => (transitiveset @ (setunion @ X0)))))))),
% 1.75/1.92 inference(rectify,[status(thm)],[f7])).
% 1.75/1.92 thf(f7,negated_conjecture,(
% 1.75/1.92 ~(setunionI => (setunionE => (subsetI1 => (transitivesetOp2 => ! [X4 : $i] : (! [X1 : $i] : ((in @ X1 @ X4) => (transitiveset @ X1)) => (transitiveset @ (setunion @ X4)))))))),
% 1.75/1.92 inference(negated_conjecture,[status(cth)],[f6])).
% 1.75/1.92 thf(f6,conjecture,(
% 1.75/1.92 setunionI => (setunionE => (subsetI1 => (transitivesetOp2 => ! [X4 : $i] : (! [X1 : $i] : ((in @ X1 @ X4) => (transitiveset @ X1)) => (transitiveset @ (setunion @ X4))))))),
% 1.75/1.92 file('/export/starexec/sandbox2/tmp/tmp.89llQL148d/DTF2THF_18003.p',setunionTransitive)).
% 1.75/1.92 thf(f151,plain,(
% 1.75/1.92 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK4)) => (subset @ Y0 @ (setunion @ sK4))))) = $false)),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f150])).
% 1.75/1.92 thf(f513,plain,(
% 1.75/1.92 ~spl0_4),
% 1.75/1.92 inference(avatar_contradiction_clause,[status(thm)],[f512])).
% 1.75/1.92 thf(f512,plain,(
% 1.75/1.92 $false | ~spl0_4),
% 1.75/1.92 inference(trivial_inequality_removal,[status(thm)],[f511])).
% 1.75/1.92 thf(f511,plain,(
% 1.75/1.92 ($true = $false) | ~spl0_4),
% 1.75/1.92 inference(backward_demodulation,[status(thm)],[f160,f509])).
% 1.75/1.92 thf(f509,plain,(
% 1.75/1.92 ((in @ sK5 @ (setunion @ sK4)) = $false) | ~spl0_4),
% 1.75/1.92 inference(avatar_component_clause,[status(thm)],[f507])).
% 1.75/1.92 thf(f507,definition,(
% 1.75/1.92 spl0_4 <=> ((in @ sK5 @ (setunion @ sK4)) = $false)),
% 1.75/1.92 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.75/1.92 thf(f160,plain,(
% 1.75/1.92 ((in @ sK5 @ (setunion @ sK4)) = $true)),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f154])).
% 1.75/1.92 thf(f154,plain,(
% 1.75/1.92 (((in @ sK5 @ (setunion @ sK4)) => (subset @ sK5 @ (setunion @ sK4))) = $false)),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f153])).
% 1.75/1.92 thf(f153,plain,(
% 1.75/1.92 (((^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK4)) => (subset @ Y0 @ (setunion @ sK4)))) @ sK5) = $false)),
% 1.75/1.92 inference(sigma_clausification,[status(thm)],[f151])).
% 1.75/1.92 thf(f510,plain,(
% 1.75/1.92 spl0_3 | spl0_4),
% 1.75/1.92 inference(avatar_split_clause,[status(thm)],[f501,f507,f504])).
% 1.75/1.92 thf(f501,plain,(
% 1.75/1.92 ( ! [X0 : $o] : (($true = X0) | ((in @ sK5 @ (setunion @ sK4)) = $false)) )),
% 1.75/1.92 inference(trivial_inequality_removal,[status(thm)],[f500])).
% 1.75/1.92 thf(f500,plain,(
% 1.75/1.92 ( ! [X0 : $o] : (((in @ sK5 @ (setunion @ sK4)) = $false) | ($true = X0) | ($true = $false)) )),
% 1.75/1.92 inference(duplicate_literal_removal,[status(thm)],[f497])).
% 1.75/1.92 thf(f497,plain,(
% 1.75/1.92 ( ! [X0 : $o] : (($true = X0) | ((in @ sK5 @ (setunion @ sK4)) = $false) | ($true = $false) | ($true = X0) | ((in @ sK5 @ (setunion @ sK4)) = $false)) )),
% 1.75/1.92 inference(superposition,[status(thm)],[f106,f472])).
% 1.75/1.92 thf(f472,plain,(
% 1.75/1.92 ( ! [X0 : $o,X1 : $i] : (((in @ (sK3 @ X0 @ sK5 @ X1) @ sK4) = $false) | ($true = X0) | ((in @ sK5 @ (setunion @ X1)) = $false)) )),
% 1.75/1.92 inference(trivial_inequality_removal,[status(thm)],[f457])).
% 1.75/1.92 thf(f457,plain,(
% 1.75/1.92 ( ! [X0 : $o,X1 : $i] : (((in @ (sK3 @ X0 @ sK5 @ X1) @ sK4) = $false) | ($true = X0) | ((in @ sK5 @ (setunion @ X1)) = $false) | ($true = $false)) )),
% 1.75/1.92 inference(superposition,[status(thm)],[f452,f104])).
% 1.75/1.92 thf(f104,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = (in @ X1 @ (sK3 @ X3 @ X1 @ X2))) | ($true = X3) | ((in @ X1 @ (setunion @ X2)) = $false)) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f102])).
% 1.75/1.92 thf(f102,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((in @ X1 @ (sK3 @ X3 @ X1 @ X2)) => ((in @ (sK3 @ X3 @ X1 @ X2) @ X2) => X3)) = $false) | ((in @ X1 @ (setunion @ X2)) = $false) | ($true = X3)) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f97])).
% 1.75/1.92 thf(f97,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = X3) | ((in @ X1 @ (setunion @ X2)) = $false) | (((^[Y0 : $i]: ((in @ X1 @ Y0) => ((in @ Y0 @ X2) => X3))) @ (sK3 @ X3 @ X1 @ X2)) = $false)) )),
% 1.75/1.92 inference(sigma_clausification,[status(thm)],[f96])).
% 1.75/1.92 thf(f96,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => ((in @ Y0 @ X2) => X3)))) = $false) | ((in @ X1 @ (setunion @ X2)) = $false) | ($true = X3)) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.75/1.92 thf(f95,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => ((in @ Y0 @ X2) => X3)))) => X3)) | ((in @ X1 @ (setunion @ X2)) = $false)) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f94])).
% 1.75/1.92 thf(f94,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = ((^[Y0 : $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((in @ Y1 @ X2) => Y0)))) => Y0)) @ X3)) | ((in @ X1 @ (setunion @ X2)) = $false)) )),
% 1.75/1.92 inference(pi_clausification,[status(thm)],[f71])).
% 1.75/1.92 thf(f71,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : (((!! @ $o @ (^[Y0 : $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((in @ Y1 @ X2) => Y0)))) => Y0))) = $true) | ((in @ X1 @ (setunion @ X2)) = $false)) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.75/1.92 thf(f70,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (setunion @ X2)) => (!! @ $o @ (^[Y0 : $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((in @ Y1 @ X2) => Y0)))) => Y0)))) = $true)) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.75/1.92 thf(f69,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y1 : $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ X1 @ Y2) => ((in @ Y2 @ Y0) => Y1)))) => Y1))))) @ X2))) )),
% 1.75/1.92 inference(pi_clausification,[status(thm)],[f51])).
% 1.75/1.92 thf(f51,plain,(
% 1.75/1.92 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y1 : $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ X1 @ Y2) => ((in @ Y2 @ Y0) => Y1)))) => Y1)))))))) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.75/1.92 thf(f50,plain,(
% 1.75/1.92 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2))))))) @ X1))) )),
% 1.75/1.92 inference(pi_clausification,[status(thm)],[f34])).
% 1.75/1.92 thf(f34,plain,(
% 1.75/1.92 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))))),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.75/1.92 thf(f452,plain,(
% 1.75/1.92 ( ! [X0 : $i] : (((in @ sK5 @ X0) = $false) | ((in @ X0 @ sK4) = $false)) )),
% 1.75/1.92 inference(trivial_inequality_removal,[status(thm)],[f451])).
% 1.75/1.92 thf(f451,plain,(
% 1.75/1.92 ( ! [X0 : $i] : (($true = $false) | ((in @ sK5 @ X0) = $false) | ((in @ X0 @ sK4) = $false)) )),
% 1.75/1.92 inference(duplicate_literal_removal,[status(thm)],[f445])).
% 1.75/1.92 thf(f445,plain,(
% 1.75/1.92 ( ! [X0 : $i] : (((in @ sK5 @ X0) = $false) | ((in @ X0 @ sK4) = $false) | ((in @ X0 @ sK4) = $false) | ($true = $false)) )),
% 1.75/1.92 inference(superposition,[status(thm)],[f159,f438])).
% 1.75/1.92 thf(f438,plain,(
% 1.75/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ X0 @ (setunion @ X1))) | ((in @ X2 @ sK4) = $false) | ((in @ X0 @ X2) = $false) | ((in @ X2 @ X1) = $false)) )),
% 1.75/1.92 inference(trivial_inequality_removal,[status(thm)],[f437])).
% 1.75/1.92 thf(f437,plain,(
% 1.75/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ((in @ X2 @ sK4) = $false) | ($true = (subset @ X0 @ (setunion @ X1))) | ((in @ X0 @ X2) = $false) | ((in @ X2 @ X1) = $false)) )),
% 1.75/1.92 inference(duplicate_literal_removal,[status(thm)],[f413])).
% 1.75/1.92 thf(f413,plain,(
% 1.75/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ X0 @ (setunion @ X1))) | ((in @ X0 @ X2) = $false) | ($true = (subset @ X0 @ (setunion @ X1))) | ((in @ X2 @ sK4) = $false) | ($true = $false) | ((in @ X2 @ X1) = $false)) )),
% 1.75/1.92 inference(superposition,[status(thm)],[f332,f62])).
% 1.75/1.92 thf(f62,plain,(
% 1.75/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK2 @ X0 @ (setunion @ X1)) @ X2) = $false) | ((in @ X2 @ X1) = $false) | ($true = (subset @ X0 @ (setunion @ X1)))) )),
% 1.75/1.92 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.75/1.92 thf(f60,plain,(
% 1.75/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ((in @ (sK2 @ X0 @ (setunion @ X1)) @ X2) = $false) | ((in @ X2 @ X1) = $false) | ($true = (subset @ X0 @ (setunion @ X1)))) )),
% 1.75/1.92 inference(superposition,[status(thm)],[f46,f57])).
% 1.75/1.92 thf(f57,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : (((in @ (sK2 @ X1 @ X2) @ X2) = $false) | ((subset @ X1 @ X2) = $true)) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.75/1.92 thf(f56,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : (((subset @ X1 @ X2) = $true) | (((in @ (sK2 @ X1 @ X2) @ X1) => (in @ (sK2 @ X1 @ X2) @ X2)) = $false)) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.75/1.92 thf(f55,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK2 @ X1 @ X2)) = $false) | ((subset @ X1 @ X2) = $true)) )),
% 1.75/1.92 inference(sigma_clausification,[status(thm)],[f54])).
% 1.75/1.92 thf(f54,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) = $false) | ((subset @ X1 @ X2) = $true)) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.75/1.92 thf(f53,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (subset @ X1 @ X2)))) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.75/1.92 thf(f52,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0))) @ X2))) )),
% 1.75/1.92 inference(pi_clausification,[status(thm)],[f49])).
% 1.75/1.92 thf(f49,plain,(
% 1.75/1.92 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0)))))) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.75/1.92 thf(f48,plain,(
% 1.75/1.92 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))) @ X1) = $true)) )),
% 1.75/1.92 inference(pi_clausification,[status(thm)],[f36])).
% 1.75/1.92 thf(f36,plain,(
% 1.75/1.92 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.75/1.92 thf(f46,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (in @ X1 @ (setunion @ X2))) | ((in @ X1 @ X3) = $false) | ((in @ X3 @ X2) = $false)) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.75/1.92 thf(f45,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X1 @ X3) = $false) | ($true = ((in @ X3 @ X2) => (in @ X1 @ (setunion @ X2))))) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.75/1.92 thf(f44,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ X3) => ((in @ X3 @ X2) => (in @ X1 @ (setunion @ X2)))) = $true)) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.75/1.92 thf(f43,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X1 @ Y0) => ((in @ Y0 @ X2) => (in @ X1 @ (setunion @ X2))))) @ X3))) )),
% 1.75/1.92 inference(pi_clausification,[status(thm)],[f42])).
% 1.75/1.92 thf(f42,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => ((in @ Y0 @ X2) => (in @ X1 @ (setunion @ X2)))))))) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.75/1.92 thf(f41,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((in @ Y1 @ Y0) => (in @ X1 @ (setunion @ Y0))))))) @ X2))) )),
% 1.75/1.92 inference(pi_clausification,[status(thm)],[f40])).
% 1.75/1.92 thf(f40,plain,(
% 1.75/1.92 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((in @ Y1 @ Y0) => (in @ X1 @ (setunion @ Y0)))))))))) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.75/1.92 thf(f39,plain,(
% 1.75/1.92 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1))))))))) @ X1) = $true)) )),
% 1.75/1.92 inference(pi_clausification,[status(thm)],[f32])).
% 1.75/1.92 thf(f32,plain,(
% 1.75/1.92 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))))),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.75/1.92 thf(f332,plain,(
% 1.75/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ (sK2 @ X0 @ X1) @ X2)) | ((in @ X2 @ sK4) = $false) | ($true = (subset @ X0 @ X1)) | ((in @ X0 @ X2) = $false)) )),
% 1.75/1.92 inference(trivial_inequality_removal,[status(thm)],[f314])).
% 1.75/1.92 thf(f314,plain,(
% 1.75/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($true = (in @ (sK2 @ X0 @ X1) @ X2)) | ((in @ X0 @ X2) = $false) | ((in @ X2 @ sK4) = $false) | ($true = (subset @ X0 @ X1))) )),
% 1.75/1.92 inference(superposition,[status(thm)],[f58,f286])).
% 1.75/1.92 thf(f286,plain,(
% 1.75/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) = $false) | ((in @ X0 @ sK4) = $false) | ((in @ X1 @ X0) = $false) | ((in @ X2 @ X0) = $true)) )),
% 1.75/1.92 inference(trivial_inequality_removal,[status(thm)],[f282])).
% 1.75/1.92 thf(f282,plain,(
% 1.75/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ((in @ X1 @ X0) = $false) | ((in @ X0 @ sK4) = $false) | ((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) = $false)) )),
% 1.75/1.92 inference(superposition,[status(thm)],[f262,f148])).
% 1.75/1.92 thf(f148,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ Y0 @ X1))))) | ((in @ X2 @ X1) = $false) | ($true = (in @ X3 @ X1)) | ((in @ X3 @ X2) = $false)) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f147])).
% 1.75/1.92 thf(f147,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ X2) => (in @ X3 @ X1))) | ((in @ X2 @ X1) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ Y0 @ X1)))))) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f146])).
% 1.75/1.92 thf(f146,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X1) => ((in @ X3 @ X2) => (in @ X3 @ X1)))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ Y0 @ X1)))))) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f145])).
% 1.75/1.92 thf(f145,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ X1) => ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) @ X3)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ Y0 @ X1)))))) )),
% 1.75/1.92 inference(pi_clausification,[status(thm)],[f144])).
% 1.75/1.92 thf(f144,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ X1) => ((in @ Y0 @ X2) => (in @ Y0 @ X1))))) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ Y0 @ X1)))))) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f143])).
% 1.75/1.92 thf(f143,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ Y0 @ X1))))) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))))) @ X2) = $true)) )),
% 1.75/1.92 inference(pi_clausification,[status(thm)],[f134])).
% 1.75/1.92 thf(f134,plain,(
% 1.75/1.92 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => ((in @ Y1 @ Y0) => (in @ Y1 @ X1))))))) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ Y0 @ X1)))))) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f133])).
% 1.75/1.92 thf(f133,plain,(
% 1.75/1.92 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ Y0 @ X1)))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))))))))) )),
% 1.75/1.92 inference(beta_eta_normalization,[status(thm)],[f132])).
% 1.75/1.92 thf(f132,plain,(
% 1.75/1.92 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) @ X1) = $true)) )),
% 1.75/1.92 inference(pi_clausification,[status(thm)],[f38])).
% 1.75/1.92 thf(f38,plain,(
% 1.75/1.92 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))))),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.75/1.92 thf(f58,plain,(
% 1.75/1.92 ( ! [X2 : $i,X1 : $i] : (((in @ (sK2 @ X1 @ X2) @ X1) = $true) | ((subset @ X1 @ X2) = $true)) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.75/1.92 thf(f159,plain,(
% 1.75/1.92 ((subset @ sK5 @ (setunion @ sK4)) = $false)),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f154])).
% 1.75/1.92 thf(f106,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = (in @ (sK3 @ X3 @ X1 @ X2) @ X2)) | ((in @ X1 @ (setunion @ X2)) = $false) | ($true = X3)) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.75/1.92 thf(f103,plain,(
% 1.75/1.92 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((in @ X1 @ (setunion @ X2)) = $false) | (((in @ (sK3 @ X3 @ X1 @ X2) @ X2) => X3) = $false) | ($true = X3)) )),
% 1.75/1.92 inference(binary_proxy_clausification,[status(thm)],[f102])).
% 1.75/1.92 % SZS output end Proof for DTF2THF_18003
% 1.75/1.92 % (18248)------------------------------
% 1.75/1.92 % (18248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.92 % (18248)Termination reason: Refutation
% 1.75/1.92
% 1.75/1.92 % (18248)Memory used [KB]: 5884
% 1.75/1.92 % (18248)Time elapsed: 0.077 s
% 1.75/1.92 % (18248)Instructions burned: 143 (million)
% 1.75/1.92 % (18248)------------------------------
% 1.75/1.92 % (18248)------------------------------
% 1.75/1.92 % (18152)Success in time 0.546 s
%------------------------------------------------------------------------------