%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU649^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 09:35:57 AM UTC 2026
% Result : Theorem 1.70s 1.49s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 8
% Syntax : Number of formulae : 109 ( 70 unt; 0 typ; 2 def)
% Number of atoms : 926 ( 220 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 1376 ( 45 ~; 54 |; 0 &; 959 @)
% ( 2 <=>; 174 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 15 con; 0-2 aty)
% ( 142 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 225 ( 157 ^; 68 !; 0 ?; 225 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_21,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f292,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f176,f242,f290]) ).
thf(f290,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f289]) ).
thf(f289,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f285]) ).
thf(f285,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f51,f282]) ).
thf(f282,plain,
( ( $false
= ( in @ sK2 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f255,f265]) ).
thf(f265,plain,
( ( sK2 = sK5 )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[status(thm)],[f263]) ).
thf(f263,plain,
( ( ( sK5 = sK2 )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f262]) ).
thf(f262,plain,
( ( $true
= ( $true
=> ( sK5 = sK2 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f61,f256]) ).
thf(f256,plain,
( ( $true
= ( in @ sK5 @ ( setadjoin @ sK2 @ emptyset ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f253]) ).
thf(f253,plain,
( ( ( ( in @ sK5 @ ( setadjoin @ sK2 @ emptyset ) )
=> ( in @ sK5 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f248]) ).
thf(f248,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK2 @ emptyset ) )
=> ( in @ Y0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) ) )
@ sK5 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f172]) ).
thf(f172,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK2 @ emptyset ) )
=> ( in @ Y0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f171]) ).
thf(f171,definition,
( spl0_1
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK2 @ emptyset ) )
=> ( in @ Y0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ emptyset )
= ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ emptyset )
= ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ emptyset )
= ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ emptyset )
= ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f21,f24,f22,f23,f25,f26]) ).
thf(f26,plain,
( upairset2E
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( upairset2E
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( upairset2E
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X1 = X2 )
| ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( upairset2E
= ( ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X4 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X3 = X4 )
| ( X2 = X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AjvqUJqO9X/DTF2THF_12488.p',upairset2E) ).
thf(f25,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= eqinunit ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X3: $i,X2: $i] :
( ( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= eqinunit ),
file('/export/starexec/sandbox/tmp/tmp.AjvqUJqO9X/DTF2THF_12488.p',eqinunit) ).
thf(f23,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) )
= uniqinunit ),
file('/export/starexec/sandbox/tmp/tmp.AjvqUJqO9X/DTF2THF_12488.p',uniqinunit) ).
thf(f22,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= setadjoinIL ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X3: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= setadjoinIL ),
file('/export/starexec/sandbox/tmp/tmp.AjvqUJqO9X/DTF2THF_12488.p',setadjoinIL) ).
thf(f24,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( setext
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X0 ) )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setext
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AjvqUJqO9X/DTF2THF_12488.p',setext) ).
thf(f21,plain,
( $true
= ( ~ ( setext
=> ( setadjoinIL
=> ( uniqinunit
=> ( eqinunit
=> ( upairset2E
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ emptyset )
= ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
= ( ~ ( setext
=> ( setadjoinIL
=> ( uniqinunit
=> ( eqinunit
=> ( upairset2E
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ emptyset )
= ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( setext
=> ( setadjoinIL
=> ( uniqinunit
=> ( eqinunit
=> ( upairset2E
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ X0 @ emptyset )
= ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( setext
=> ( setadjoinIL
=> ( uniqinunit
=> ( eqinunit
=> ( upairset2E
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( setext
=> ( setadjoinIL
=> ( uniqinunit
=> ( eqinunit
=> ( upairset2E
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AjvqUJqO9X/DTF2THF_12488.p',setukpairinjR11) ).
thf(f255,plain,
( ( $false
= ( in @ sK5 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f253]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f242,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f241]) ).
thf(f241,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f240]) ).
thf(f240,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f230,f217]) ).
thf(f217,plain,
( ( $false
= ( in @ sK2 @ ( setadjoin @ sK4 @ emptyset ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f215]) ).
thf(f215,plain,
( ( ( ~ ( in @ sK2 @ ( setadjoin @ sK4 @ emptyset ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f210]) ).
thf(f210,plain,
( ( $true
= ( ( in @ sK2 @ ( setadjoin @ sK4 @ emptyset ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f61,f203]) ).
thf(f203,plain,
( ( $false
= ( sK2 = sK4 ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f201]) ).
thf(f201,plain,
( ( ( sK2 != sK4 )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f199]) ).
thf(f199,plain,
( ( ( ( sK2 = sK4 )
=> $false )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f75,f198]) ).
thf(f198,plain,
( ( $false
= ( in @ sK4 @ ( setadjoin @ sK2 @ emptyset ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f197]) ).
thf(f197,plain,
( ( $false
= ( $true
=> ( in @ sK4 @ ( setadjoin @ sK2 @ emptyset ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f194,f196]) ).
thf(f196,plain,
( ( ( in @ sK4 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f194]) ).
thf(f194,plain,
( ( ( ( in @ sK4 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) )
=> ( in @ sK4 @ ( setadjoin @ sK2 @ emptyset ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f188]) ).
thf(f188,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK2 @ emptyset ) ) )
@ sK4 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f183]) ).
thf(f183,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f175]) ).
thf(f175,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f174]) ).
thf(f174,definition,
( spl0_2
<=> ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( ( ( X2 = X1 )
=> ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ emptyset )
= ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f230,plain,
( ( $true
= ( in @ sK2 @ ( setadjoin @ sK4 @ emptyset ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f227]) ).
thf(f227,plain,
( ( $true
= ( $true
=> ( in @ sK2 @ ( setadjoin @ sK4 @ emptyset ) ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f75,f223]) ).
thf(f223,plain,
( ( $true
= ( sK4 = sK2 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f222]) ).
thf(f222,plain,
( ( $true
= ( $false
| ( sK4 = sK2 ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f221,f203]) ).
thf(f221,plain,
( ( $true
= ( ( sK2 = sK4 )
| ( sK4 = sK2 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f220]) ).
thf(f220,plain,
( ( ( $true
=> ( ( sK2 = sK4 )
| ( sK4 = sK2 ) ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f127,f196]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X3 = X2 )
| ( X2 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f126]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y0 = X2 )
| ( X2 = X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y0 = X2 )
| ( X2 = X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f121]) ).
thf(f121,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y0 = X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y0 = X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f115]) ).
thf(f115,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ emptyset )
= ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f176,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f169,f174,f171]) ).
thf(f169,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK2 @ emptyset ) )
=> ( in @ Y0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK2 @ emptyset ) )
=> ( in @ Y0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f108]) ).
thf(f108,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK2 @ emptyset ) )
=> ( in @ Y0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK2 @ emptyset ) ) ) )
=> $false ) ) ),
inference(superposition,[status(thm)],[f40,f102]) ).
thf(f102,plain,
( ( ( setadjoin @ sK2 @ emptyset )
= ( setadjoin @ sK2 @ ( setadjoin @ sK2 @ emptyset ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f92,f93]) ).
thf(f93,plain,
sK2 = sK3,
inference(equality_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
( $true
= ( sK3 = sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
( $false
= ( ( sK3 = sK2 )
=> ( ( setadjoin @ sK3 @ emptyset )
= ( setadjoin @ sK3 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f87]) ).
thf(f87,plain,
( $false
= ( ^ [Y0: $i] :
( ( Y0 = sK2 )
=> ( ( setadjoin @ Y0 @ emptyset )
= ( setadjoin @ Y0 @ ( setadjoin @ sK2 @ emptyset ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = sK2 )
=> ( ( setadjoin @ Y0 @ emptyset )
= ( setadjoin @ Y0 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ emptyset )
= ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ emptyset )
= ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f92,plain,
( $false
= ( ( setadjoin @ sK3 @ emptyset )
= ( setadjoin @ sK3 @ ( setadjoin @ sK2 @ emptyset ) ) ) ),
inference(boolean_simplification,[status(thm)],[f91]) ).
thf(f91,plain,
( $false
= ( $true
=> ( ( setadjoin @ sK3 @ emptyset )
= ( setadjoin @ sK3 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f88,f90]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU649^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n019.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 12:29:24 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.40 ---- Original DTF file ---
% 0.16/0.40 thf(spec,logic,$$dhol).
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 % File : SEU649^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.40 % Domain : Set Theory
% 0.16/0.40 % Problem : Ordered Pairs - Properties of Pairs
% 0.16/0.40 % Version : Especial > Reduced > Especial.
% 0.16/0.40 % English : (! x:i.! y:i.x = y -> setadjoin x (setadjoin y emptyset) =
% 0.16/0.40 % setadjoin x emptyset)
% 0.16/0.40
% 0.16/0.40 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.40 % Source : [Bro08]
% 0.16/0.40 % Names : ZFC151l [Bro08]
% 0.16/0.40
% 0.16/0.40 % Status : Theorem
% 0.16/0.40 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.16/0.40 % Syntax : Number of formulae : 14 ( 5 unt; 8 typ; 5 def)
% 0.16/0.40 % Number of atoms : 30 ( 12 equ; 0 cnn)
% 0.16/0.40 % Maximal formula atoms : 7 ( 5 avg)
% 0.16/0.40 % Number of connectives : 46 ( 0 ~; 1 |; 0 &; 32 @)
% 0.16/0.40 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.16/0.40 % Maximal formula depth : 9 ( 2 avg)
% 0.16/0.40 % Number of types : 2 ( 0 usr)
% 0.16/0.40 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.16/0.40 % Number of symbols : 9 ( 8 usr; 6 con; 0-2 aty)
% 0.16/0.40 % Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% 0.16/0.40 % SPC : TH0_THM_EQU_NAR
% 0.16/0.40
% 0.16/0.40 % Comments : http://mathgate.info/detsetitem.php?id=205
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 thf(in_type,type,
% 0.16/0.40 in: $i > $i > $o ).
% 0.16/0.40
% 0.16/0.40 thf(emptyset_type,type,
% 0.16/0.40 emptyset: $i ).
% 0.16/0.40
% 0.16/0.40 thf(setadjoin_type,type,
% 0.16/0.40 setadjoin: $i > $i > $i ).
% 0.16/0.40
% 0.16/0.40 thf(setext_type,type,
% 0.16/0.40 setext: $o ).
% 0.16/0.40
% 0.16/0.40 thf(setext,definition,
% 0.16/0.40 ( setext
% 0.16/0.40 = ( ! [A: $i,B: $i] :
% 0.16/0.40 ( ! [Xx: $i] :
% 0.16/0.40 ( ( in @ Xx @ A )
% 0.16/0.40 => ( in @ Xx @ B ) )
% 0.16/0.40 => ( ! [Xx: $i] :
% 0.16/0.40 ( ( in @ Xx @ B )
% 0.16/0.40 => ( in @ Xx @ A ) )
% 0.16/0.40 => ( A = B ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(setadjoinIL_type,type,
% 0.16/0.40 setadjoinIL: $o ).
% 0.16/0.40
% 0.16/0.40 thf(setadjoinIL,definition,
% 0.16/0.40 ( setadjoinIL
% 0.16/0.40 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(uniqinunit_type,type,
% 0.16/0.40 uniqinunit: $o ).
% 0.16/0.40
% 0.16/0.40 thf(uniqinunit,definition,
% 0.16/0.40 ( uniqinunit
% 0.16/0.40 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.40 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.40 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(eqinunit_type,type,
% 0.16/0.40 eqinunit: $o ).
% 0.16/0.40
% 0.16/0.40 thf(eqinunit,definition,
% 0.16/0.40 ( eqinunit
% 0.16/0.40 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.40 ( ( Xx = Xy )
% 0.16/0.40 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(upairset2E_type,type,
% 0.16/0.40 upairset2E: $o ).
% 0.16/0.40
% 0.16/0.40 thf(upairset2E,definition,
% 0.16/0.40 ( upairset2E
% 0.16/0.40 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.40 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.16/0.40 => ( ( Xz = Xx )
% 0.16/0.40 | ( Xz = Xy ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(setukpairinjR11,conjecture,
% 0.16/0.40 ( setext
% 0.16/0.40 => ( setadjoinIL
% 0.16/0.40 => ( uniqinunit
% 0.16/0.40 => ( eqinunit
% 0.16/0.40 => ( upairset2E
% 0.16/0.40 => ! [Xx: $i,Xy: $i] :
% 0.16/0.40 ( ( Xx = Xy )
% 0.16/0.40 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.40 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 ------------------------
% 1.52/1.39 ---- Embedded in THF ---
% 1.52/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.39 %%% Generated on Tue Feb 24 12:29:25 EST 2026
% 1.52/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.39 %%% Logic specification used:
% 1.52/1.39 %%% thf(spec, logic, $$dhol).
% 1.52/1.39
% 1.52/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.AjvqUJqO9X/DTF2DTF12488.p
% See solution above
% 1.52/1.39 ------------------------
% 1.70/1.40 ---- Cleaned THF ---
% 1.70/1.40 thf(in_type,type,
% 1.70/1.40 in: $i > $i > $o ).
% 1.70/1.40
% 1.70/1.40 thf(emptyset_type,type,
% 1.70/1.40 emptyset: $i ).
% 1.70/1.40
% 1.70/1.40 thf(setadjoin_type,type,
% 1.70/1.40 setadjoin: $i > $i > $i ).
% 1.70/1.40
% 1.70/1.40 thf(setext_type,type,
% 1.70/1.40 setext: $o ).
% 1.70/1.40
% 1.70/1.40 thf(setext,definition,
% 1.70/1.40 ( setext
% 1.70/1.40 = ( ! [A: $i,B: $i] :
% 1.70/1.40 ( ! [Xx: $i] :
% 1.70/1.40 ( ( in @ Xx @ A )
% 1.70/1.40 => ( in @ Xx @ B ) )
% 1.70/1.40 => ( ! [Xx: $i] :
% 1.70/1.40 ( ( in @ Xx @ B )
% 1.70/1.40 => ( in @ Xx @ A ) )
% 1.70/1.40 => ( A = B ) ) ) ) ) ).
% 1.70/1.40
% 1.70/1.40 thf(setadjoinIL_type,type,
% 1.70/1.40 setadjoinIL: $o ).
% 1.70/1.40
% 1.70/1.40 thf(setadjoinIL,definition,
% 1.70/1.40 ( setadjoinIL
% 1.70/1.40 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.70/1.40
% 1.70/1.40 thf(uniqinunit_type,type,
% 1.70/1.40 uniqinunit: $o ).
% 1.70/1.40
% 1.70/1.40 thf(uniqinunit,definition,
% 1.70/1.40 ( uniqinunit
% 1.70/1.40 = ( ! [Xx: $i,Xy: $i] :
% 1.70/1.40 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.70/1.40 => ( Xx = Xy ) ) ) ) ).
% 1.70/1.40
% 1.70/1.40 thf(eqinunit_type,type,
% 1.70/1.40 eqinunit: $o ).
% 1.70/1.40
% 1.70/1.40 thf(eqinunit,definition,
% 1.70/1.40 ( eqinunit
% 1.70/1.40 = ( ! [Xx: $i,Xy: $i] :
% 1.70/1.40 ( ( Xx = Xy )
% 1.70/1.40 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.70/1.40
% 1.70/1.40 thf(upairset2E_type,type,
% 1.70/1.40 upairset2E: $o ).
% 1.70/1.40
% 1.70/1.40 thf(upairset2E,definition,
% 1.70/1.40 ( upairset2E
% 1.70/1.40 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.70/1.40 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 1.70/1.40 => ( ( Xz = Xx )
% 1.70/1.40 | ( Xz = Xy ) ) ) ) ) ).
% 1.70/1.40
% 1.70/1.40 thf(setukpairinjR11,conjecture,
% 1.70/1.40 ( setext
% 1.70/1.40 => ( setadjoinIL
% 1.70/1.40 => ( uniqinunit
% 1.70/1.40 => ( eqinunit
% 1.70/1.40 => ( upairset2E
% 1.70/1.40 => ! [Xx: $i,Xy: $i] :
% 1.70/1.40 ( ( Xx = Xy )
% 1.70/1.40 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.70/1.40 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ) ).
% 1.70/1.40 ------------------------
% 1.70/1.42 % (12586)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_12488 for (2999ds/4Mi)
% 1.70/1.42 % (12590)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_12488 for (2999ds/275Mi)
% 1.70/1.42 % (12585)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12488 for (2999ds/183Mi)
% 1.70/1.42 % (12588)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12488 for (2999ds/2Mi)
% 1.70/1.42 % (12589)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_12488 for (2999ds/2Mi)
% 1.70/1.42 % (12591)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12488 for (2999ds/18Mi)
% 1.70/1.42 % (12588)Instruction limit reached!
% 1.70/1.42 % (12588)------------------------------
% 1.70/1.42 % (12588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.42 % (12588)Termination reason: Unknown
% 1.70/1.42 % (12588)Termination phase: Saturation
% 1.70/1.42 % (12589)Instruction limit reached!
% 1.70/1.42 % (12589)------------------------------
% 1.70/1.42 % (12589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.42 % (12589)Termination reason: Unknown
% 1.70/1.42 % (12589)Termination phase: Property scanning
% 1.70/1.42
% 1.70/1.42 % (12589)Memory used [KB]: 1023
% 1.70/1.42 % (12589)Time elapsed: 0.003 s
% 1.70/1.42 % (12589)Instructions burned: 4 (million)
% 1.70/1.42 % (12589)------------------------------
% 1.70/1.42 % (12589)------------------------------
% 1.70/1.42
% 1.70/1.42 % (12588)Memory used [KB]: 1023
% 1.70/1.42 % (12588)Time elapsed: 0.003 s
% 1.70/1.42 % (12588)Instructions burned: 3 (million)
% 1.70/1.42 % (12588)------------------------------
% 1.70/1.42 % (12588)------------------------------
% 1.70/1.42 % (12586)Instruction limit reached!
% 1.70/1.42 % (12586)------------------------------
% 1.70/1.42 % (12586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.42 % (12586)Termination reason: Unknown
% 1.70/1.42 % (12586)Termination phase: Saturation
% 1.70/1.42
% 1.70/1.42 % (12586)Memory used [KB]: 5500
% 1.70/1.42 % (12586)Time elapsed: 0.005 s
% 1.70/1.42 % (12586)Instructions burned: 5 (million)
% 1.70/1.42 % (12586)------------------------------
% 1.70/1.42 % (12586)------------------------------
% 1.70/1.42 % (12587)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_12488 for (2999ds/27Mi)
% 1.70/1.43 % (12591)Instruction limit reached!
% 1.70/1.43 % (12591)------------------------------
% 1.70/1.43 % (12591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.43 % (12591)Termination reason: Unknown
% 1.70/1.43 % (12591)Termination phase: Saturation
% 1.70/1.43
% 1.70/1.43 % (12591)Memory used [KB]: 5628
% 1.70/1.43 % (12591)Time elapsed: 0.011 s
% 1.70/1.43 % (12591)Instructions burned: 19 (million)
% 1.70/1.43 % (12591)------------------------------
% 1.70/1.43 % (12591)------------------------------
% 1.70/1.43 % (12594)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_12488 for (2999ds/15Mi)
% 1.70/1.43 % (12592)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12488 for (2999ds/3Mi)
% 1.70/1.43 % (12593)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_12488 for (2999ds/37Mi)
% 1.70/1.44 % (12592)Instruction limit reached!
% 1.70/1.44 % (12592)------------------------------
% 1.70/1.44 % (12592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (12592)Termination reason: Unknown
% 1.70/1.44 % (12592)Termination phase: Saturation
% 1.70/1.44
% 1.70/1.44 % (12592)Memory used [KB]: 1023
% 1.70/1.44 % (12592)Time elapsed: 0.003 s
% 1.70/1.44 % (12592)Instructions burned: 4 (million)
% 1.70/1.44 % (12592)------------------------------
% 1.70/1.44 % (12592)------------------------------
% 1.70/1.44 % (12587)Instruction limit reached!
% 1.70/1.44 % (12587)------------------------------
% 1.70/1.44 % (12587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (12587)Termination reason: Unknown
% 1.70/1.44 % (12587)Termination phase: Saturation
% 1.70/1.44
% 1.70/1.44 % (12587)Memory used [KB]: 5628
% 1.70/1.44 % (12587)Time elapsed: 0.018 s
% 1.70/1.44 % (12587)Instructions burned: 28 (million)
% 1.70/1.44 % (12587)------------------------------
% 1.70/1.44 % (12587)------------------------------
% 1.70/1.44 % (12594)Instruction limit reached!
% 1.70/1.44 % (12594)------------------------------
% 1.70/1.44 % (12594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (12594)Termination reason: Unknown
% 1.70/1.44 % (12594)Termination phase: Saturation
% 1.70/1.44
% 1.70/1.44 % (12594)Memory used [KB]: 5628
% 1.70/1.44 % (12594)Time elapsed: 0.010 s
% 1.70/1.44 % (12594)Instructions burned: 16 (million)
% 1.70/1.44 % (12594)------------------------------
% 1.70/1.44 % (12594)------------------------------
% 1.70/1.44 % (12595)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_12488 for (2999ds/3Mi)
% 1.70/1.45 % (12595)Instruction limit reached!
% 1.70/1.45 % (12595)------------------------------
% 1.70/1.45 % (12595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.45 % (12595)Termination reason: Unknown
% 1.70/1.45 % (12595)Termination phase: Saturation
% 1.70/1.45
% 1.70/1.45 % (12595)Memory used [KB]: 5500
% 1.70/1.45 % (12595)Time elapsed: 0.004 s
% 1.70/1.45 % (12595)Instructions burned: 4 (million)
% 1.70/1.45 % (12595)------------------------------
% 1.70/1.45 % (12595)------------------------------
% 1.70/1.45 % (12596)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_12488 for (2999ds/1041Mi)
% 1.70/1.45 % (12593)Instruction limit reached!
% 1.70/1.45 % (12593)------------------------------
% 1.70/1.45 % (12593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.45 % (12593)Termination reason: Unknown
% 1.70/1.45 % (12593)Termination phase: Saturation
% 1.70/1.45
% 1.70/1.45 % (12593)Memory used [KB]: 5756
% 1.70/1.45 % (12593)Time elapsed: 0.020 s
% 1.70/1.45 % (12593)Instructions burned: 38 (million)
% 1.70/1.45 % (12593)------------------------------
% 1.70/1.45 % (12593)------------------------------
% 1.70/1.46 % (12597)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_12488 for (2999ds/7Mi)
% 1.70/1.46 % (12598)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_12488 for (2999ds/16Mi)
% 1.70/1.46 % (12597)Instruction limit reached!
% 1.70/1.46 % (12597)------------------------------
% 1.70/1.46 % (12597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.46 % (12597)Termination reason: Unknown
% 1.70/1.46 % (12597)Termination phase: Saturation
% 1.70/1.46
% 1.70/1.46 % (12597)Memory used [KB]: 1023
% 1.70/1.46 % (12597)Time elapsed: 0.006 s
% 1.70/1.46 % (12597)Instructions burned: 7 (million)
% 1.70/1.46 % (12597)------------------------------
% 1.70/1.46 % (12597)------------------------------
% 1.70/1.46 % (12599)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_12488 for (2999ds/3Mi)
% 1.70/1.46 % (12599)Instruction limit reached!
% 1.70/1.46 % (12599)------------------------------
% 1.70/1.46 % (12599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.46 % (12599)Termination reason: Unknown
% 1.70/1.46 % (12599)Termination phase: Twee Goal Transformation
% 1.70/1.46
% 1.70/1.46 % (12599)Memory used [KB]: 1023
% 1.70/1.46 % (12599)Time elapsed: 0.003 s
% 1.70/1.46 % (12599)Instructions burned: 3 (million)
% 1.70/1.46 % (12599)------------------------------
% 1.70/1.46 % (12599)------------------------------
% 1.70/1.47 % (12598)Instruction limit reached!
% 1.70/1.47 % (12598)------------------------------
% 1.70/1.47 % (12598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.47 % (12598)Termination reason: Unknown
% 1.70/1.47 % (12598)Termination phase: Saturation
% 1.70/1.47
% 1.70/1.47 % (12598)Memory used [KB]: 5756
% 1.70/1.47 % (12598)Time elapsed: 0.011 s
% 1.70/1.47 % (12598)Instructions burned: 17 (million)
% 1.70/1.47 % (12598)------------------------------
% 1.70/1.47 % (12598)------------------------------
% 1.70/1.47 % (12600)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_12488 for (2999ds/3Mi)
% 1.70/1.47 % (12600)Instruction limit reached!
% 1.70/1.47 % (12600)------------------------------
% 1.70/1.47 % (12600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.47 % (12600)Termination reason: Unknown
% 1.70/1.47 % (12600)Termination phase: Property scanning
% 1.70/1.47
% 1.70/1.47 % (12600)Memory used [KB]: 1023
% 1.70/1.47 % (12600)Time elapsed: 0.003 s
% 1.70/1.47 % (12600)Instructions burned: 3 (million)
% 1.70/1.47 % (12600)------------------------------
% 1.70/1.47 % (12600)------------------------------
% 1.70/1.48 % (12601)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_12488 for (2999ds/7Mi)
% 1.70/1.48 % (12602)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_12488 for (2999ds/3Mi)
% 1.70/1.48 % (12602)Instruction limit reached!
% 1.70/1.48 % (12602)------------------------------
% 1.70/1.48 % (12602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.48 % (12602)Termination reason: Unknown
% 1.70/1.48 % (12602)Termination phase: Property scanning
% 1.70/1.48
% 1.70/1.48 % (12602)Memory used [KB]: 1023
% 1.70/1.48 % (12602)Time elapsed: 0.003 s
% 1.70/1.48 % (12602)Instructions burned: 4 (million)
% 1.70/1.48 % (12602)------------------------------
% 1.70/1.48 % (12602)------------------------------
% 1.70/1.48 % (12601)Refutation not found, incomplete strategy
% 1.70/1.48 % (12601)------------------------------
% 1.70/1.48 % (12601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.48 % (12601)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.48
% 1.70/1.48
% 1.70/1.48 % (12601)Memory used [KB]: 5500
% 1.70/1.48 % (12601)Time elapsed: 0.004 s
% 1.70/1.48 % (12601)Instructions burned: 4 (million)
% 1.70/1.48 % (12601)------------------------------
% 1.70/1.48 % (12601)------------------------------
% 1.70/1.48 % (12603)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_12488 for (2999ds/4Mi)
% 1.70/1.49 % (12596)First to succeed.
% 1.70/1.49 % (12603)Instruction limit reached!
% 1.70/1.49 % (12603)------------------------------
% 1.70/1.49 % (12603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.49 % (12603)Termination reason: Unknown
% 1.70/1.49 % (12603)Termination phase: Saturation
% 1.70/1.49
% 1.70/1.49 % (12603)Memory used [KB]: 5500
% 1.70/1.49 % (12603)Time elapsed: 0.004 s
% 1.70/1.49 % (12603)Instructions burned: 4 (million)
% 1.70/1.49 % (12603)------------------------------
% 1.70/1.49 % (12603)------------------------------
% 1.70/1.49 % (12604)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_12488 for (2999ds/18Mi)
% 1.70/1.49 % (12596)Refutation found. Thanks to Tanya!
% 1.70/1.49 % SZS status Theorem for DTF2THF_12488
% 1.70/1.49 % SZS output start Proof for DTF2THF_12488
% 1.70/1.49 thf(func_def_0, type, in: $i > $i > $o).
% 1.70/1.49 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.70/1.49 thf(func_def_21, type, ph1: !>[X0: $tType]:(X0)).
% 1.70/1.49 thf(f292,plain,(
% 1.70/1.49 $false),
% 1.70/1.49 inference(avatar_sat_refutation,[status(thm)],[f176,f242,f290])).
% 1.70/1.49 thf(f290,plain,(
% 1.70/1.49 ~spl0_1),
% 1.70/1.49 inference(avatar_contradiction_clause,[status(thm)],[f289])).
% 1.70/1.49 thf(f289,plain,(
% 1.70/1.49 $false | ~spl0_1),
% 1.70/1.49 inference(trivial_inequality_removal,[status(thm)],[f285])).
% 1.70/1.49 thf(f285,plain,(
% 1.70/1.49 ($true = $false) | ~spl0_1),
% 1.70/1.49 inference(superposition,[status(thm)],[f51,f282])).
% 1.70/1.49 thf(f282,plain,(
% 1.70/1.49 ($false = (in @ sK2 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset)))) | ~spl0_1),
% 1.70/1.49 inference(backward_demodulation,[status(thm)],[f255,f265])).
% 1.70/1.49 thf(f265,plain,(
% 1.70/1.49 (sK2 = sK5) | ~spl0_1),
% 1.70/1.49 inference(equality_proxy_clausification,[status(thm)],[f263])).
% 1.70/1.49 thf(f263,plain,(
% 1.70/1.49 ((sK5 = sK2) = $true) | ~spl0_1),
% 1.70/1.49 inference(boolean_simplification,[status(thm)],[f262])).
% 1.70/1.49 thf(f262,plain,(
% 1.70/1.49 ($true = ($true => (sK5 = sK2))) | ~spl0_1),
% 1.70/1.49 inference(superposition,[status(thm)],[f61,f256])).
% 1.70/1.49 thf(f256,plain,(
% 1.70/1.49 ($true = (in @ sK5 @ (setadjoin @ sK2 @ emptyset))) | ~spl0_1),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f253])).
% 1.70/1.49 thf(f253,plain,(
% 1.70/1.49 (((in @ sK5 @ (setadjoin @ sK2 @ emptyset)) => (in @ sK5 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset)))) = $false) | ~spl0_1),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f248])).
% 1.70/1.49 thf(f248,plain,(
% 1.70/1.49 (((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ emptyset)) => (in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))))) @ sK5) = $false) | ~spl0_1),
% 1.70/1.49 inference(sigma_clausification,[status(thm)],[f172])).
% 1.70/1.49 thf(f172,plain,(
% 1.70/1.49 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ emptyset)) => (in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset)))))) = $false) | ~spl0_1),
% 1.70/1.49 inference(avatar_component_clause,[status(thm)],[f171])).
% 1.70/1.49 thf(f171,definition,(
% 1.70/1.49 spl0_1 <=> ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ emptyset)) => (in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset)))))) = $false)),
% 1.70/1.49 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.70/1.49 thf(f61,plain,(
% 1.70/1.49 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X2 @ (setadjoin @ X1 @ emptyset)) => (X2 = X1)))) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.70/1.49 thf(f60,plain,(
% 1.70/1.49 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1))) @ X2) = $true)) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f59])).
% 1.70/1.49 thf(f59,plain,(
% 1.70/1.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1)))) = $true)) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.70/1.49 thf(f58,plain,(
% 1.70/1.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0))))) @ X1))) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f53])).
% 1.70/1.49 thf(f53,plain,(
% 1.70/1.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.70/1.49 thf(f42,plain,(
% 1.70/1.49 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))))))),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.70/1.49 thf(f31,plain,(
% 1.70/1.49 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))))))),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.70/1.49 thf(f28,plain,(
% 1.70/1.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))))))) = $false)),
% 1.70/1.49 inference(not_proxy_clausification,[status(thm)],[f27])).
% 1.70/1.49 thf(f27,plain,(
% 1.70/1.49 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))))))) = $true)),
% 1.70/1.49 inference(definition_unfolding,[status(thm)],[f21,f24,f22,f23,f25,f26])).
% 1.70/1.49 thf(f26,plain,(
% 1.70/1.49 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))))),
% 1.70/1.49 inference(cnf_transformation,[status(thm)],[f10])).
% 1.70/1.49 thf(f10,plain,(
% 1.70/1.49 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))))),
% 1.70/1.49 inference(fool_elimination,[status(thm)],[f9])).
% 1.70/1.49 thf(f9,plain,(
% 1.70/1.49 (upairset2E = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset))) => ((X1 = X2) | (X0 = X1))))),
% 1.70/1.49 inference(rectify,[status(thm)],[f5])).
% 1.70/1.49 thf(f5,axiom,(
% 1.70/1.49 (upairset2E = ! [X2 : $i,X4 : $i,X3 : $i] : ((in @ X4 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))) => ((X3 = X4) | (X2 = X4))))),
% 1.70/1.49 file('/export/starexec/sandbox/tmp/tmp.AjvqUJqO9X/DTF2THF_12488.p',upairset2E)).
% 1.70/1.49 thf(f25,plain,(
% 1.70/1.49 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 1.70/1.49 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.49 thf(f12,plain,(
% 1.70/1.49 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 1.70/1.49 inference(fool_elimination,[status(thm)],[f11])).
% 1.70/1.49 thf(f11,plain,(
% 1.70/1.49 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (in @ X1 @ (setadjoin @ X0 @ emptyset))) = eqinunit)),
% 1.70/1.49 inference(rectify,[status(thm)],[f4])).
% 1.70/1.49 thf(f4,axiom,(
% 1.70/1.49 (! [X3 : $i,X2 : $i] : ((X2 = X3) => (in @ X2 @ (setadjoin @ X3 @ emptyset))) = eqinunit)),
% 1.70/1.49 file('/export/starexec/sandbox/tmp/tmp.AjvqUJqO9X/DTF2THF_12488.p',eqinunit)).
% 1.70/1.49 thf(f23,plain,(
% 1.70/1.49 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 1.70/1.49 inference(cnf_transformation,[status(thm)],[f16])).
% 1.70/1.49 thf(f16,plain,(
% 1.70/1.49 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 1.70/1.49 inference(fool_elimination,[status(thm)],[f15])).
% 1.70/1.49 thf(f15,plain,(
% 1.70/1.49 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 1.70/1.49 inference(rectify,[status(thm)],[f3])).
% 1.70/1.49 thf(f3,axiom,(
% 1.70/1.49 (! [X2 : $i,X3 : $i] : ((in @ X2 @ (setadjoin @ X3 @ emptyset)) => (X2 = X3)) = uniqinunit)),
% 1.70/1.49 file('/export/starexec/sandbox/tmp/tmp.AjvqUJqO9X/DTF2THF_12488.p',uniqinunit)).
% 1.70/1.49 thf(f22,plain,(
% 1.70/1.49 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 1.70/1.49 inference(cnf_transformation,[status(thm)],[f14])).
% 1.70/1.49 thf(f14,plain,(
% 1.70/1.49 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 1.70/1.49 inference(fool_elimination,[status(thm)],[f13])).
% 1.70/1.49 thf(f13,plain,(
% 1.70/1.49 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X0)) = setadjoinIL)),
% 1.70/1.49 inference(rectify,[status(thm)],[f2])).
% 1.70/1.49 thf(f2,axiom,(
% 1.70/1.49 (! [X3 : $i,X2 : $i] : (in @ X2 @ (setadjoin @ X2 @ X3)) = setadjoinIL)),
% 1.70/1.49 file('/export/starexec/sandbox/tmp/tmp.AjvqUJqO9X/DTF2THF_12488.p',setadjoinIL)).
% 1.70/1.49 thf(f24,plain,(
% 1.70/1.49 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 1.70/1.49 inference(cnf_transformation,[status(thm)],[f20])).
% 1.70/1.49 thf(f20,plain,(
% 1.70/1.49 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 1.70/1.49 inference(fool_elimination,[status(thm)],[f19])).
% 1.70/1.49 thf(f19,plain,(
% 1.70/1.49 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))))),
% 1.70/1.49 inference(rectify,[status(thm)],[f1])).
% 1.70/1.49 thf(f1,axiom,(
% 1.70/1.49 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))))),
% 1.70/1.49 file('/export/starexec/sandbox/tmp/tmp.AjvqUJqO9X/DTF2THF_12488.p',setext)).
% 1.70/1.49 thf(f21,plain,(
% 1.70/1.49 ($true = (~ (setext => (setadjoinIL => (uniqinunit => (eqinunit => (upairset2E => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))))))))),
% 1.70/1.49 inference(cnf_transformation,[status(thm)],[f18])).
% 1.70/1.49 thf(f18,plain,(
% 1.70/1.49 ($true = (~ (setext => (setadjoinIL => (uniqinunit => (eqinunit => (upairset2E => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))))))))),
% 1.70/1.49 inference(fool_elimination,[status(thm)],[f17])).
% 1.70/1.49 thf(f17,plain,(
% 1.70/1.49 ~(setext => (setadjoinIL => (uniqinunit => (eqinunit => (upairset2E => ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((setadjoin @ X0 @ emptyset) = (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))))))))),
% 1.70/1.49 inference(rectify,[status(thm)],[f7])).
% 1.70/1.49 thf(f7,negated_conjecture,(
% 1.70/1.49 ~(setext => (setadjoinIL => (uniqinunit => (eqinunit => (upairset2E => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) = (setadjoin @ X2 @ emptyset))))))))),
% 1.70/1.49 inference(negated_conjecture,[status(cth)],[f6])).
% 1.70/1.49 thf(f6,conjecture,(
% 1.70/1.49 setext => (setadjoinIL => (uniqinunit => (eqinunit => (upairset2E => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) = (setadjoin @ X2 @ emptyset)))))))),
% 1.70/1.49 file('/export/starexec/sandbox/tmp/tmp.AjvqUJqO9X/DTF2THF_12488.p',setukpairinjR11)).
% 1.70/1.49 thf(f255,plain,(
% 1.70/1.49 ($false = (in @ sK5 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset)))) | ~spl0_1),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f253])).
% 1.70/1.49 thf(f51,plain,(
% 1.70/1.49 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X1 @ X2)))) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.70/1.49 thf(f50,plain,(
% 1.70/1.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (in @ X1 @ (setadjoin @ X1 @ Y0))) @ X2))) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f49])).
% 1.70/1.49 thf(f49,plain,(
% 1.70/1.49 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ X1 @ (setadjoin @ X1 @ Y0)))))) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.70/1.49 thf(f48,plain,(
% 1.70/1.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1))))) @ X1))) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f43])).
% 1.70/1.49 thf(f43,plain,(
% 1.70/1.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.70/1.49 thf(f242,plain,(
% 1.70/1.49 ~spl0_2),
% 1.70/1.49 inference(avatar_contradiction_clause,[status(thm)],[f241])).
% 1.70/1.49 thf(f241,plain,(
% 1.70/1.49 $false | ~spl0_2),
% 1.70/1.49 inference(trivial_inequality_removal,[status(thm)],[f240])).
% 1.70/1.49 thf(f240,plain,(
% 1.70/1.49 ($true = $false) | ~spl0_2),
% 1.70/1.49 inference(forward_demodulation,[status(thm)],[f230,f217])).
% 1.70/1.49 thf(f217,plain,(
% 1.70/1.49 ($false = (in @ sK2 @ (setadjoin @ sK4 @ emptyset))) | ~spl0_2),
% 1.70/1.49 inference(not_proxy_clausification,[status(thm)],[f215])).
% 1.70/1.49 thf(f215,plain,(
% 1.70/1.49 ((~ (in @ sK2 @ (setadjoin @ sK4 @ emptyset))) = $true) | ~spl0_2),
% 1.70/1.49 inference(boolean_simplification,[status(thm)],[f210])).
% 1.70/1.49 thf(f210,plain,(
% 1.70/1.49 ($true = ((in @ sK2 @ (setadjoin @ sK4 @ emptyset)) => $false)) | ~spl0_2),
% 1.70/1.49 inference(superposition,[status(thm)],[f61,f203])).
% 1.70/1.49 thf(f203,plain,(
% 1.70/1.49 ($false = (sK2 = sK4)) | ~spl0_2),
% 1.70/1.49 inference(not_proxy_clausification,[status(thm)],[f201])).
% 1.70/1.49 thf(f201,plain,(
% 1.70/1.49 ((~ (sK2 = sK4)) = $true) | ~spl0_2),
% 1.70/1.49 inference(boolean_simplification,[status(thm)],[f199])).
% 1.70/1.49 thf(f199,plain,(
% 1.70/1.49 (((sK2 = sK4) => $false) = $true) | ~spl0_2),
% 1.70/1.49 inference(superposition,[status(thm)],[f75,f198])).
% 1.70/1.49 thf(f198,plain,(
% 1.70/1.49 ($false = (in @ sK4 @ (setadjoin @ sK2 @ emptyset))) | ~spl0_2),
% 1.70/1.49 inference(boolean_simplification,[status(thm)],[f197])).
% 1.70/1.49 thf(f197,plain,(
% 1.70/1.49 ($false = ($true => (in @ sK4 @ (setadjoin @ sK2 @ emptyset)))) | ~spl0_2),
% 1.70/1.49 inference(backward_demodulation,[status(thm)],[f194,f196])).
% 1.70/1.49 thf(f196,plain,(
% 1.70/1.49 ((in @ sK4 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) = $true) | ~spl0_2),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f194])).
% 1.70/1.49 thf(f194,plain,(
% 1.70/1.49 (((in @ sK4 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ sK4 @ (setadjoin @ sK2 @ emptyset))) = $false) | ~spl0_2),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f188])).
% 1.70/1.49 thf(f188,plain,(
% 1.70/1.49 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ Y0 @ (setadjoin @ sK2 @ emptyset)))) @ sK4)) | ~spl0_2),
% 1.70/1.49 inference(sigma_clausification,[status(thm)],[f183])).
% 1.70/1.49 thf(f183,plain,(
% 1.70/1.49 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ Y0 @ (setadjoin @ sK2 @ emptyset)))))) | ~spl0_2),
% 1.70/1.49 inference(not_proxy_clausification,[status(thm)],[f175])).
% 1.70/1.49 thf(f175,plain,(
% 1.70/1.49 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ Y0 @ (setadjoin @ sK2 @ emptyset))))))) | ~spl0_2),
% 1.70/1.49 inference(avatar_component_clause,[status(thm)],[f174])).
% 1.70/1.49 thf(f174,definition,(
% 1.70/1.49 spl0_2 <=> ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ Y0 @ (setadjoin @ sK2 @ emptyset)))))))),
% 1.70/1.49 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.70/1.49 thf(f75,plain,(
% 1.70/1.49 ( ! [X2 : $i,X1 : $i] : ((((X2 = X1) => (in @ X1 @ (setadjoin @ X2 @ emptyset))) = $true)) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.70/1.49 thf(f74,plain,(
% 1.70/1.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((Y0 = X1) => (in @ X1 @ (setadjoin @ Y0 @ emptyset)))) @ X2))) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f73])).
% 1.70/1.49 thf(f73,plain,(
% 1.70/1.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((Y0 = X1) => (in @ X1 @ (setadjoin @ Y0 @ emptyset))))) = $true)) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.70/1.49 thf(f72,plain,(
% 1.70/1.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))) @ X1))) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f67])).
% 1.70/1.49 thf(f67,plain,(
% 1.70/1.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.70/1.49 thf(f52,plain,(
% 1.70/1.49 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))))),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.70/1.49 thf(f230,plain,(
% 1.70/1.49 ($true = (in @ sK2 @ (setadjoin @ sK4 @ emptyset))) | ~spl0_2),
% 1.70/1.49 inference(boolean_simplification,[status(thm)],[f227])).
% 1.70/1.49 thf(f227,plain,(
% 1.70/1.49 ($true = ($true => (in @ sK2 @ (setadjoin @ sK4 @ emptyset)))) | ~spl0_2),
% 1.70/1.49 inference(superposition,[status(thm)],[f75,f223])).
% 1.70/1.49 thf(f223,plain,(
% 1.70/1.49 ($true = (sK4 = sK2)) | ~spl0_2),
% 1.70/1.49 inference(boolean_simplification,[status(thm)],[f222])).
% 1.70/1.49 thf(f222,plain,(
% 1.70/1.49 ($true = ($false | (sK4 = sK2))) | ~spl0_2),
% 1.70/1.49 inference(forward_demodulation,[status(thm)],[f221,f203])).
% 1.70/1.49 thf(f221,plain,(
% 1.70/1.49 ($true = ((sK2 = sK4) | (sK4 = sK2))) | ~spl0_2),
% 1.70/1.49 inference(boolean_simplification,[status(thm)],[f220])).
% 1.70/1.49 thf(f220,plain,(
% 1.70/1.49 (($true => ((sK2 = sK4) | (sK4 = sK2))) = $true) | ~spl0_2),
% 1.70/1.49 inference(superposition,[status(thm)],[f127,f196])).
% 1.70/1.49 thf(f127,plain,(
% 1.70/1.49 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset))) => ((X3 = X2) | (X2 = X1))) = $true)) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f126])).
% 1.70/1.49 thf(f126,plain,(
% 1.70/1.49 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset))) => ((Y0 = X2) | (X2 = X1)))) @ X3))) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f122])).
% 1.70/1.49 thf(f122,plain,(
% 1.70/1.49 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset))) => ((Y0 = X2) | (X2 = X1))))))) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f121])).
% 1.70/1.49 thf(f121,plain,(
% 1.70/1.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ X1 @ emptyset))) => ((Y1 = Y0) | (Y0 = X1)))))) @ X2))) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f116])).
% 1.70/1.49 thf(f116,plain,(
% 1.70/1.49 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ X1 @ emptyset))) => ((Y1 = Y0) | (Y0 = X1))))))))) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f115])).
% 1.70/1.49 thf(f115,plain,(
% 1.70/1.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0)))))))) @ X1) = $true)) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f80])).
% 1.70/1.49 thf(f80,plain,(
% 1.70/1.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))))),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.70/1.49 thf(f66,plain,(
% 1.70/1.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))) = $false)),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.70/1.49 thf(f176,plain,(
% 1.70/1.49 spl0_1 | spl0_2),
% 1.70/1.49 inference(avatar_split_clause,[status(thm)],[f169,f174,f171])).
% 1.70/1.49 thf(f169,plain,(
% 1.70/1.49 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ emptyset)) => (in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset)))))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ Y0 @ (setadjoin @ sK2 @ emptyset)))))))),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f111])).
% 1.70/1.49 thf(f111,plain,(
% 1.70/1.49 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ emptyset)) => (in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset)))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ Y0 @ (setadjoin @ sK2 @ emptyset))))))) = $true)),
% 1.70/1.49 inference(boolean_simplification,[status(thm)],[f108])).
% 1.70/1.49 thf(f108,plain,(
% 1.70/1.49 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ emptyset)) => (in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ Y0 @ (setadjoin @ sK2 @ emptyset))))) => $false)))),
% 1.70/1.49 inference(superposition,[status(thm)],[f40,f102])).
% 1.70/1.49 thf(f102,plain,(
% 1.70/1.49 (((setadjoin @ sK2 @ emptyset) = (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) = $false)),
% 1.70/1.49 inference(backward_demodulation,[status(thm)],[f92,f93])).
% 1.70/1.49 thf(f93,plain,(
% 1.70/1.49 (sK2 = sK3)),
% 1.70/1.49 inference(equality_proxy_clausification,[status(thm)],[f90])).
% 1.70/1.49 thf(f90,plain,(
% 1.70/1.49 ($true = (sK3 = sK2))),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f88])).
% 1.70/1.49 thf(f88,plain,(
% 1.70/1.49 ($false = ((sK3 = sK2) => ((setadjoin @ sK3 @ emptyset) = (setadjoin @ sK3 @ (setadjoin @ sK2 @ emptyset)))))),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f87])).
% 1.70/1.49 thf(f87,plain,(
% 1.70/1.49 ($false = ((^[Y0 : $i]: ((Y0 = sK2) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ sK2 @ emptyset))))) @ sK3))),
% 1.70/1.49 inference(sigma_clausification,[status(thm)],[f86])).
% 1.70/1.49 thf(f86,plain,(
% 1.70/1.49 ($false = (!! @ $i @ (^[Y0 : $i]: ((Y0 = sK2) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ sK2 @ emptyset)))))))),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.70/1.49 thf(f85,plain,(
% 1.70/1.49 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) @ sK2))),
% 1.70/1.49 inference(sigma_clausification,[status(thm)],[f79])).
% 1.70/1.49 thf(f79,plain,(
% 1.70/1.49 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.70/1.49 thf(f92,plain,(
% 1.70/1.49 ($false = ((setadjoin @ sK3 @ emptyset) = (setadjoin @ sK3 @ (setadjoin @ sK2 @ emptyset))))),
% 1.70/1.49 inference(boolean_simplification,[status(thm)],[f91])).
% 1.70/1.49 thf(f91,plain,(
% 1.70/1.49 ($false = ($true => ((setadjoin @ sK3 @ emptyset) = (setadjoin @ sK3 @ (setadjoin @ sK2 @ emptyset)))))),
% 1.70/1.49 inference(backward_demodulation,[status(thm)],[f88,f90])).
% 1.70/1.49 thf(f40,plain,(
% 1.70/1.49 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1))))) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.70/1.49 thf(f39,plain,(
% 1.70/1.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1)))) @ X2))) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f38])).
% 1.70/1.49 thf(f38,plain,(
% 1.70/1.49 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1))))))) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.70/1.49 thf(f37,plain,(
% 1.70/1.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) @ X1))) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f32])).
% 1.70/1.49 thf(f32,plain,(
% 1.70/1.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.70/1.49 % SZS output end Proof for DTF2THF_12488
% 1.70/1.49 % (12596)------------------------------
% 1.70/1.49 % (12596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.49 % (12596)Termination reason: Refutation
% 1.70/1.49
% 1.70/1.49 % (12596)Memory used [KB]: 5884
% 1.70/1.49 % (12596)Time elapsed: 0.038 s
% 1.70/1.49 % (12596)Instructions burned: 64 (million)
% 1.70/1.49 % (12596)------------------------------
% 1.70/1.49 % (12596)------------------------------
% 1.70/1.49 % (12584)Success in time 0.08 s
%------------------------------------------------------------------------------