%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU813^2 : 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 : n011.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 09:37:25 AM UTC 2026
% Result : Theorem 1.54s 1.23s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 94 ( 63 unt; 0 typ; 2 def)
% Number of atoms : 632 ( 131 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 765 ( 23 ~; 23 |; 24 &; 553 @)
% ( 2 <=>; 87 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 12 con; 0-2 aty)
% ( 53 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 162 ( 72 ^; 82 !; 8 ?; 162 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
binintersect: $i > $i > $i ).
thf(func_def_7,type,
transitiveset: $i > $o ).
thf(func_def_9,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f120,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f109,f116,f119]) ).
thf(f119,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f118]) ).
thf(f118,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ( $false = $true )
| ~ spl2_1 ),
inference(backward_demodulation,[status(thm)],[f90,f103]) ).
thf(f103,plain,
( ( $false
= ( subset @ sK3 @ sK0 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f101,definition,
( spl2_1
<=> ( $false
= ( subset @ sK3 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f90,plain,
( ( subset @ sK3 @ sK0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ( subset @ sK3 @ sK0 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f48,f86]) ).
thf(f86,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $false = $true )
| ( $true
= ( in @ sK3 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f64,f55]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binintersect @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( binintersect @ X3 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( binintersect @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( binintersect @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f33,f28]) ).
thf(f28,plain,
( binintersectEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( binintersectEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( binintersectEL
= ( ! [X0: $i,X1: $i,X3: $i] :
( ( in @ X3 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X3 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.f1Li3pTZ60/DTF2THF_4331.p',binintersectEL) ).
thf(f33,plain,
binintersectEL = $true,
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $true
!= ( transitiveset @ ( binintersect @ sK0 @ sK1 ) ) )
& ( $true
= ( transitiveset @ sK1 ) )
& ( $true
= ( transitiveset @ sK0 ) )
& ( binintersectEL = $true )
& ( transitivesetOp1 = $true )
& ( binintersectSubset5 = $true )
& ( binintersectER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f22,f24,f23]) ).
thf(f23,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( $true
!= ( transitiveset @ ( binintersect @ X0 @ X1 ) ) )
& ( $true
= ( transitiveset @ X1 ) ) )
& ( $true
= ( transitiveset @ X0 ) ) )
=> ( ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ sK0 @ X1 ) )
!= $true )
& ( $true
= ( transitiveset @ X1 ) ) )
& ( $true
= ( transitiveset @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ sK0 @ X1 ) )
!= $true )
& ( $true
= ( transitiveset @ X1 ) ) )
=> ( ( $true
!= ( transitiveset @ ( binintersect @ sK0 @ sK1 ) ) )
& ( $true
= ( transitiveset @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( $true
!= ( transitiveset @ ( binintersect @ X0 @ X1 ) ) )
& ( $true
= ( transitiveset @ X1 ) ) )
& ( $true
= ( transitiveset @ X0 ) ) )
& ( binintersectEL = $true )
& ( transitivesetOp1 = $true )
& ( binintersectSubset5 = $true )
& ( binintersectER = $true ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( $true
!= ( transitiveset @ ( binintersect @ X0 @ X1 ) ) )
& ( $true
= ( transitiveset @ X1 ) ) )
& ( $true
= ( transitiveset @ X0 ) ) )
& ( transitivesetOp1 = $true )
& ( binintersectER = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
~ ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectER = $true )
=> ( ( transitivesetOp1 = $true )
=> ! [X0: $i] :
( ( $true
= ( transitiveset @ X0 ) )
=> ! [X1: $i] :
( ( $true
= ( transitiveset @ X1 ) )
=> ( $true
= ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
~ ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectER
=> ( transitivesetOp1
=> ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( transitiveset @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectER
=> ( transitivesetOp1
=> ! [X4: $i] :
( ( transitiveset @ X4 )
=> ! [X5: $i] :
( ( transitiveset @ X5 )
=> ( transitiveset @ ( binintersect @ X4 @ X5 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( binintersectSubset5
=> ( binintersectEL
=> ( binintersectER
=> ( transitivesetOp1
=> ! [X4: $i] :
( ( transitiveset @ X4 )
=> ! [X5: $i] :
( ( transitiveset @ X5 )
=> ( transitiveset @ ( binintersect @ X4 @ X5 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.f1Li3pTZ60/DTF2THF_4331.p',binintTransitive) ).
thf(f64,plain,
( $true
= ( in @ sK3 @ ( binintersect @ sK0 @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( $false
= ( ( in @ sK3 @ ( binintersect @ sK0 @ sK1 ) )
=> ( subset @ sK3 @ ( binintersect @ sK0 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ sK0 @ sK1 ) )
=> ( subset @ Y0 @ ( binintersect @ sK0 @ sK1 ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ sK0 @ sK1 ) )
=> ( subset @ Y0 @ ( binintersect @ sK0 @ sK1 ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ ( binintersect @ sK0 @ sK1 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f36,f29]) ).
thf(f29,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitiveset ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: $i] :
! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( subset @ X4 @ X0 ) ) )
= transitiveset ),
file('/export/starexec/sandbox/tmp/tmp.f1Li3pTZ60/DTF2THF_4331.p',transitiveset) ).
thf(f36,plain,
( $true
!= ( transitiveset @ ( binintersect @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f48,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK0 ) )
| ( ( subset @ X1 @ sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( subset @ X1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f34,f29]) ).
thf(f34,plain,
( $true
= ( transitiveset @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f116,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f115]) ).
thf(f115,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f114]) ).
thf(f114,plain,
( ( $false = $true )
| ~ spl2_2 ),
inference(backward_demodulation,[status(thm)],[f94,f112]) ).
thf(f112,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f110]) ).
thf(f110,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false = $true )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f107,f83]) ).
thf(f83,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK1 )
=> ( subset @ X1 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( subset @ Y0 @ sK1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( subset @ Y0 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ sK1 )
= $true ),
inference(definition_unfolding,[status(thm)],[f35,f29]) ).
thf(f35,plain,
( $true
= ( transitiveset @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f107,plain,
( ( $false
= ( subset @ sK3 @ sK1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f105]) ).
thf(f105,definition,
( spl2_2
<=> ( $false
= ( subset @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f94,plain,
( ( in @ sK3 @ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
( ( ( in @ sK3 @ sK1 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f71,f64]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( binintersect @ X2 @ X1 ) ) )
| ( ( in @ X3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X3 @ ( binintersect @ X2 @ X1 ) )
=> ( in @ X3 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ X2 @ X1 ) )
=> ( in @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ X2 @ X1 ) )
=> ( in @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( binintersect @ Y0 @ X1 ) )
=> ( in @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( binintersect @ Y0 @ X1 ) )
=> ( in @ Y1 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f30,f27]) ).
thf(f27,plain,
( binintersectER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( binintersectER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binintersect @ Y1 @ Y0 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X0 @ X2 ) )
= binintersectER ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X3 @ X1 ) )
= binintersectER ),
file('/export/starexec/sandbox/tmp/tmp.f1Li3pTZ60/DTF2THF_4331.p',binintersectER) ).
thf(f30,plain,
binintersectER = $true,
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f109,plain,
( spl2_2
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f98,f101,f105]) ).
thf(f98,plain,
( ( $false
= ( subset @ sK3 @ sK0 ) )
| ( $false
= ( subset @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ( $false
= ( subset @ sK3 @ sK1 ) )
| ( $false = $true )
| ( $false
= ( subset @ sK3 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f79,f63]) ).
thf(f63,plain,
( $false
= ( subset @ sK3 @ ( binintersect @ sK0 @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( subset @ X2 @ ( binintersect @ X1 @ X3 ) ) )
| ( ( subset @ X2 @ X1 )
= $false )
| ( ( subset @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( subset @ X2 @ X3 )
=> ( subset @ X2 @ ( binintersect @ X1 @ X3 ) ) )
= $true )
| ( ( subset @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ X2 @ ( binintersect @ X1 @ X3 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ X2 @ X1 )
=> ( ( subset @ X2 @ Y0 )
=> ( subset @ X2 @ ( binintersect @ X1 @ Y0 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X2 @ X1 )
=> ( ( subset @ X2 @ Y0 )
=> ( subset @ X2 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ Y0 @ Y1 )
=> ( subset @ Y0 @ ( binintersect @ X1 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ Y0 @ Y1 )
=> ( subset @ Y0 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y1 @ Y2 )
=> ( subset @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y1 @ Y2 )
=> ( subset @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f31,f26]) ).
thf(f26,plain,
( binintersectSubset5
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y1 @ Y2 )
=> ( subset @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( binintersectSubset5
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y1 @ Y2 )
=> ( subset @ Y1 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
=> ( ( subset @ X1 @ X0 )
=> ( subset @ X1 @ ( binintersect @ X2 @ X0 ) ) ) )
= binintersectSubset5 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X2 @ X0 )
=> ( ( subset @ X2 @ X1 )
=> ( subset @ X2 @ ( binintersect @ X0 @ X1 ) ) ) )
= binintersectSubset5 ),
file('/export/starexec/sandbox/tmp/tmp.f1Li3pTZ60/DTF2THF_4331.p',binintersectSubset5) ).
thf(f31,plain,
binintersectSubset5 = $true,
inference(cnf_transformation,[status(thm)],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU813^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n011.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:34:32 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.48 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : SEU813^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.48 % Domain : Set Theory
% 0.20/0.48 % Problem : Transitive Sets
% 0.20/0.48 % Version : Especial > Reduced > Especial.
% 0.20/0.48 % English : (! X:i.transitiveset X -> (! Y:i.transitiveset Y ->
% 0.20/0.48 % transitiveset (binintersect X Y)))
% 0.20/0.48
% 0.20/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.48 % Source : [Bro08]
% 0.20/0.48 % Names : ZFC315l [Bro08]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.20/0.48 % Syntax : Number of formulae : 14 ( 5 unt; 8 typ; 5 def)
% 0.20/0.48 % Number of atoms : 29 ( 5 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 7 ( 4 avg)
% 0.20/0.48 % Number of connectives : 47 ( 0 ~; 0 |; 0 &; 34 @)
% 0.20/0.48 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 12 ( 3 avg)
% 0.20/0.48 % Number of types : 2 ( 0 usr)
% 0.20/0.48 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 9 ( 8 usr; 4 con; 0-2 aty)
% 0.20/0.48 % Number of variables : 15 ( 1 ^; 14 !; 0 ?; 15 :)
% 0.20/0.48 % SPC : TH0_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : http://mathgate.info/detsetitem.php?id=501
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(in_type,type,
% 0.20/0.48 in: $i > $i > $o ).
% 0.20/0.48
% 0.20/0.48 thf(subset_type,type,
% 0.20/0.48 subset: $i > $i > $o ).
% 0.20/0.48
% 0.20/0.48 thf(binintersect_type,type,
% 0.20/0.48 binintersect: $i > $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(binintersectSubset5_type,type,
% 0.20/0.48 binintersectSubset5: $o ).
% 0.20/0.48
% 0.20/0.48 thf(binintersectSubset5,definition,
% 0.20/0.48 ( binintersectSubset5
% 0.20/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.48 ( ( subset @ C @ A )
% 0.20/0.48 => ( ( subset @ C @ B )
% 0.20/0.48 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(binintersectEL_type,type,
% 0.20/0.48 binintersectEL: $o ).
% 0.20/0.48
% 0.20/0.48 thf(binintersectEL,definition,
% 0.33/0.48 ( binintersectEL
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.33/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectER_type,type,
% 0.33/0.48 binintersectER: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectER,definition,
% 0.33/0.48 ( binintersectER
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.33/0.48 => ( in @ Xx @ B ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(transitiveset_type,type,
% 0.33/0.48 transitiveset: $i > $o ).
% 0.33/0.48
% 0.33/0.48 thf(transitiveset,definition,
% 0.33/0.48 ( transitiveset
% 0.33/0.48 = ( ^ [A: $i] :
% 0.33/0.48 ! [X: $i] :
% 0.33/0.48 ( ( in @ X @ A )
% 0.33/0.48 => ( subset @ X @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(transitivesetOp1_type,type,
% 0.33/0.48 transitivesetOp1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(transitivesetOp1,definition,
% 0.33/0.48 ( transitivesetOp1
% 0.33/0.48 = ( ! [X: $i] :
% 0.33/0.48 ( ( transitiveset @ X )
% 0.33/0.48 => ! [A: $i] :
% 0.33/0.48 ( ( in @ A @ X )
% 0.33/0.48 => ( subset @ A @ X ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binintTransitive,conjecture,
% 0.33/0.48 ( binintersectSubset5
% 0.33/0.48 => ( binintersectEL
% 0.33/0.48 => ( binintersectER
% 0.33/0.48 => ( transitivesetOp1
% 0.33/0.48 => ! [X: $i] :
% 0.33/0.48 ( ( transitiveset @ X )
% 0.33/0.48 => ! [Y: $i] :
% 0.33/0.48 ( ( transitiveset @ Y )
% 0.33/0.48 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 ------------------------
% 1.39/1.19 ---- Embedded in THF ---
% 1.39/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.20 %%% Generated on Tue Feb 24 12:34:33 EST 2026
% 1.39/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.20 %%% Logic specification used:
% 1.39/1.20 %%% thf(spec, logic, $$dhol).
% 1.39/1.20
% 1.39/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.f1Li3pTZ60/DTF2DTF4331.p
% See solution above
% 1.39/1.20 ------------------------
% 1.54/1.20 ---- Cleaned THF ---
% 1.54/1.20 thf(in_type,type,
% 1.54/1.20 in: $i > $i > $o ).
% 1.54/1.20
% 1.54/1.20 thf(subset_type,type,
% 1.54/1.20 subset: $i > $i > $o ).
% 1.54/1.20
% 1.54/1.20 thf(binintersect_type,type,
% 1.54/1.20 binintersect: $i > $i > $i ).
% 1.54/1.20
% 1.54/1.20 thf(binintersectSubset5_type,type,
% 1.54/1.20 binintersectSubset5: $o ).
% 1.54/1.20
% 1.54/1.20 thf(binintersectSubset5,definition,
% 1.54/1.20 ( binintersectSubset5
% 1.54/1.20 = ( ! [A: $i,B: $i,C: $i] :
% 1.54/1.20 ( ( subset @ C @ A )
% 1.54/1.20 => ( ( subset @ C @ B )
% 1.54/1.20 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 1.54/1.20
% 1.54/1.20 thf(binintersectEL_type,type,
% 1.54/1.20 binintersectEL: $o ).
% 1.54/1.20
% 1.54/1.20 thf(binintersectEL,definition,
% 1.54/1.20 ( binintersectEL
% 1.54/1.20 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.54/1.20 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.54/1.20 => ( in @ Xx @ A ) ) ) ) ).
% 1.54/1.20
% 1.54/1.20 thf(binintersectER_type,type,
% 1.54/1.20 binintersectER: $o ).
% 1.54/1.20
% 1.54/1.20 thf(binintersectER,definition,
% 1.54/1.20 ( binintersectER
% 1.54/1.20 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.54/1.20 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.54/1.20 => ( in @ Xx @ B ) ) ) ) ).
% 1.54/1.20
% 1.54/1.20 thf(transitiveset_type,type,
% 1.54/1.20 transitiveset: $i > $o ).
% 1.54/1.20
% 1.54/1.20 thf(transitiveset,definition,
% 1.54/1.20 ( transitiveset
% 1.54/1.20 = ( ^ [A: $i] :
% 1.54/1.20 ! [X: $i] :
% 1.54/1.20 ( ( in @ X @ A )
% 1.54/1.20 => ( subset @ X @ A ) ) ) ) ).
% 1.54/1.20
% 1.54/1.20 thf(transitivesetOp1_type,type,
% 1.54/1.20 transitivesetOp1: $o ).
% 1.54/1.20
% 1.54/1.20 thf(transitivesetOp1,definition,
% 1.54/1.20 ( transitivesetOp1
% 1.54/1.20 = ( ! [X: $i] :
% 1.54/1.20 ( ( transitiveset @ X )
% 1.54/1.20 => ! [A: $i] :
% 1.54/1.20 ( ( in @ A @ X )
% 1.54/1.20 => ( subset @ A @ X ) ) ) ) ) ).
% 1.54/1.20
% 1.54/1.20 thf(binintTransitive,conjecture,
% 1.54/1.20 ( binintersectSubset5
% 1.54/1.20 => ( binintersectEL
% 1.54/1.20 => ( binintersectER
% 1.54/1.20 => ( transitivesetOp1
% 1.54/1.20 => ! [X: $i] :
% 1.54/1.20 ( ( transitiveset @ X )
% 1.54/1.20 => ! [Y: $i] :
% 1.54/1.20 ( ( transitiveset @ Y )
% 1.54/1.20 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 1.54/1.20 ------------------------
% 1.54/1.22 % (4428)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4331 for (3000ds/183Mi)
% 1.54/1.22 % (4430)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_4331 for (3000ds/27Mi)
% 1.54/1.22 % (4432)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_4331 for (3000ds/2Mi)
% 1.54/1.22 % (4432)Instruction limit reached!
% 1.54/1.22 % (4432)------------------------------
% 1.54/1.22 % (4432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.22 % (4432)Termination reason: Unknown
% 1.54/1.22 % (4432)Termination phase: Property scanning
% 1.54/1.22
% 1.54/1.22 % (4432)Memory used [KB]: 1023
% 1.54/1.22 % (4432)Time elapsed: 0.002 s
% 1.54/1.22 % (4432)Instructions burned: 3 (million)
% 1.54/1.22 % (4432)------------------------------
% 1.54/1.22 % (4432)------------------------------
% 1.54/1.22 % (4433)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_4331 for (3000ds/275Mi)
% 1.54/1.22 % (4433)Refutation not found, incomplete strategy
% 1.54/1.22 % (4433)------------------------------
% 1.54/1.22 % (4433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.22 % (4433)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.22
% 1.54/1.22
% 1.54/1.22 % (4433)Memory used [KB]: 5500
% 1.54/1.22 % (4433)Time elapsed: 0.003 s
% 1.54/1.22 % (4433)Instructions burned: 5 (million)
% 1.54/1.22 % (4433)------------------------------
% 1.54/1.22 % (4433)------------------------------
% 1.54/1.22 % (4434)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4331 for (3000ds/18Mi)
% 1.54/1.23 % (4429)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_4331 for (3000ds/4Mi)
% 1.54/1.23 % (4431)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4331 for (3000ds/2Mi)
% 1.54/1.23 % (4430)First to succeed.
% 1.54/1.23 % (4431)Instruction limit reached!
% 1.54/1.23 % (4431)------------------------------
% 1.54/1.23 % (4431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.23 % (4431)Termination reason: Unknown
% 1.54/1.23 % (4431)Termination phase: Property scanning
% 1.54/1.23
% 1.54/1.23 % (4431)Memory used [KB]: 1023
% 1.54/1.23 % (4431)Time elapsed: 0.002 s
% 1.54/1.23 % (4431)Instructions burned: 3 (million)
% 1.54/1.23 % (4431)------------------------------
% 1.54/1.23 % (4431)------------------------------
% 1.54/1.23 % (4429)Instruction limit reached!
% 1.54/1.23 % (4429)------------------------------
% 1.54/1.23 % (4429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.23 % (4429)Termination reason: Unknown
% 1.54/1.23 % (4429)Termination phase: Saturation
% 1.54/1.23
% 1.54/1.23 % (4429)Memory used [KB]: 5500
% 1.54/1.23 % (4429)Time elapsed: 0.003 s
% 1.54/1.23 % (4429)Instructions burned: 5 (million)
% 1.54/1.23 % (4429)------------------------------
% 1.54/1.23 % (4429)------------------------------
% 1.54/1.23 % (4435)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4331 for (2999ds/3Mi)
% 1.54/1.23 % (4430)Refutation found. Thanks to Tanya!
% 1.54/1.23 % SZS status Theorem for DTF2THF_4331
% 1.54/1.23 % SZS output start Proof for DTF2THF_4331
% 1.54/1.23 thf(func_def_0, type, in: $i > $i > $o).
% 1.54/1.23 thf(func_def_1, type, subset: $i > $i > $o).
% 1.54/1.23 thf(func_def_2, type, binintersect: $i > $i > $i).
% 1.54/1.23 thf(func_def_7, type, transitiveset: $i > $o).
% 1.54/1.23 thf(func_def_9, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.54/1.23 thf(f120,plain,(
% 1.54/1.23 $false),
% 1.54/1.23 inference(avatar_sat_refutation,[status(thm)],[f109,f116,f119])).
% 1.54/1.23 thf(f119,plain,(
% 1.54/1.23 ~spl2_1),
% 1.54/1.23 inference(avatar_contradiction_clause,[status(thm)],[f118])).
% 1.54/1.23 thf(f118,plain,(
% 1.54/1.23 $false | ~spl2_1),
% 1.54/1.23 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.54/1.23 thf(f117,plain,(
% 1.54/1.23 ($false = $true) | ~spl2_1),
% 1.54/1.23 inference(backward_demodulation,[status(thm)],[f90,f103])).
% 1.54/1.23 thf(f103,plain,(
% 1.54/1.23 ($false = (subset @ sK3 @ sK0)) | ~spl2_1),
% 1.54/1.23 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.54/1.23 thf(f101,definition,(
% 1.54/1.23 spl2_1 <=> ($false = (subset @ sK3 @ sK0))),
% 1.54/1.23 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.54/1.23 thf(f90,plain,(
% 1.54/1.23 ((subset @ sK3 @ sK0) = $true)),
% 1.54/1.23 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.54/1.23 thf(f89,plain,(
% 1.54/1.23 ((subset @ sK3 @ sK0) = $true) | ($false = $true)),
% 1.54/1.23 inference(superposition,[status(thm)],[f48,f86])).
% 1.54/1.23 thf(f86,plain,(
% 1.54/1.23 ($true = (in @ sK3 @ sK0))),
% 1.54/1.23 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.54/1.23 thf(f85,plain,(
% 1.54/1.23 ($false = $true) | ($true = (in @ sK3 @ sK0))),
% 1.54/1.23 inference(superposition,[status(thm)],[f64,f55])).
% 1.54/1.23 thf(f55,plain,(
% 1.54/1.23 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X1 @ (binintersect @ X3 @ X2))) | ($true = (in @ X1 @ X3))) )),
% 1.54/1.23 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.54/1.23 thf(f54,plain,(
% 1.54/1.23 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X1 @ (binintersect @ X3 @ X2)) => (in @ X1 @ X3)))) )),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.54/1.23 thf(f53,plain,(
% 1.54/1.23 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X1 @ (binintersect @ Y0 @ X2)) => (in @ X1 @ Y0))) @ X3))) )),
% 1.54/1.23 inference(pi_clausification,[status(thm)],[f52])).
% 1.54/1.23 thf(f52,plain,(
% 1.54/1.23 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (binintersect @ Y0 @ X2)) => (in @ X1 @ Y0)))))) )),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.54/1.23 thf(f51,plain,(
% 1.54/1.23 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (binintersect @ Y1 @ Y0)) => (in @ X1 @ Y1))))) @ X2))) )),
% 1.54/1.23 inference(pi_clausification,[status(thm)],[f50])).
% 1.54/1.23 thf(f50,plain,(
% 1.54/1.23 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (binintersect @ Y1 @ Y0)) => (in @ X1 @ Y1)))))))) )),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.54/1.23 thf(f49,plain,(
% 1.54/1.23 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y2))))))) @ X1))) )),
% 1.54/1.23 inference(pi_clausification,[status(thm)],[f41])).
% 1.54/1.23 thf(f41,plain,(
% 1.54/1.23 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))))),
% 1.54/1.23 inference(definition_unfolding,[status(thm)],[f33,f28])).
% 1.54/1.23 thf(f28,plain,(
% 1.54/1.23 (binintersectEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))))),
% 1.54/1.23 inference(cnf_transformation,[status(thm)],[f14])).
% 1.54/1.23 thf(f14,plain,(
% 1.54/1.23 (binintersectEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))))),
% 1.54/1.23 inference(fool_elimination,[status(thm)],[f13])).
% 1.54/1.23 thf(f13,plain,(
% 1.54/1.23 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 1.54/1.23 inference(rectify,[status(thm)],[f2])).
% 1.54/1.23 thf(f2,axiom,(
% 1.54/1.23 (binintersectEL = ! [X0 : $i,X1 : $i,X3 : $i] : ((in @ X3 @ (binintersect @ X0 @ X1)) => (in @ X3 @ X0)))),
% 1.54/1.23 file('/export/starexec/sandbox/tmp/tmp.f1Li3pTZ60/DTF2THF_4331.p',binintersectEL)).
% 1.54/1.23 thf(f33,plain,(
% 1.54/1.23 (binintersectEL = $true)),
% 1.54/1.23 inference(cnf_transformation,[status(thm)],[f25])).
% 1.54/1.23 thf(f25,plain,(
% 1.54/1.23 ((($true != (transitiveset @ (binintersect @ sK0 @ sK1))) & ($true = (transitiveset @ sK1))) & ($true = (transitiveset @ sK0))) & (binintersectEL = $true) & (transitivesetOp1 = $true) & (binintersectSubset5 = $true) & (binintersectER = $true)),
% 1.54/1.23 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f22,f24,f23])).
% 1.54/1.23 thf(f23,plain,(
% 1.54/1.23 ? [X0 : $i] : (? [X1 : $i] : (($true != (transitiveset @ (binintersect @ X0 @ X1))) & ($true = (transitiveset @ X1))) & ($true = (transitiveset @ X0))) => (? [X1 : $i] : (((transitiveset @ (binintersect @ sK0 @ X1)) != $true) & ($true = (transitiveset @ X1))) & ($true = (transitiveset @ sK0)))),
% 1.54/1.23 introduced(definition,[],[choice_axiom])).
% 1.54/1.23 thf(f24,plain,(
% 1.54/1.23 ? [X1 : $i] : (((transitiveset @ (binintersect @ sK0 @ X1)) != $true) & ($true = (transitiveset @ X1))) => (($true != (transitiveset @ (binintersect @ sK0 @ sK1))) & ($true = (transitiveset @ sK1)))),
% 1.54/1.23 introduced(definition,[],[choice_axiom])).
% 1.54/1.23 thf(f22,plain,(
% 1.54/1.23 ? [X0 : $i] : (? [X1 : $i] : (($true != (transitiveset @ (binintersect @ X0 @ X1))) & ($true = (transitiveset @ X1))) & ($true = (transitiveset @ X0))) & (binintersectEL = $true) & (transitivesetOp1 = $true) & (binintersectSubset5 = $true) & (binintersectER = $true)),
% 1.54/1.23 inference(flattening,[status(thm)],[f21])).
% 1.54/1.23 thf(f21,plain,(
% 1.54/1.23 (((? [X0 : $i] : (? [X1 : $i] : (($true != (transitiveset @ (binintersect @ X0 @ X1))) & ($true = (transitiveset @ X1))) & ($true = (transitiveset @ X0))) & (transitivesetOp1 = $true)) & (binintersectER = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)),
% 1.54/1.23 inference(ennf_transformation,[status(thm)],[f20])).
% 1.54/1.23 thf(f20,plain,(
% 1.54/1.23 ~((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectER = $true) => ((transitivesetOp1 = $true) => ! [X0 : $i] : (($true = (transitiveset @ X0)) => ! [X1 : $i] : (($true = (transitiveset @ X1)) => ($true = (transitiveset @ (binintersect @ X0 @ X1)))))))))),
% 1.54/1.23 inference(fool_elimination,[status(thm)],[f19])).
% 1.54/1.23 thf(f19,plain,(
% 1.54/1.23 ~(binintersectSubset5 => (binintersectEL => (binintersectER => (transitivesetOp1 => ! [X0 : $i] : ((transitiveset @ X0) => ! [X1 : $i] : ((transitiveset @ X1) => (transitiveset @ (binintersect @ X0 @ X1))))))))),
% 1.54/1.23 inference(rectify,[status(thm)],[f7])).
% 1.54/1.23 thf(f7,negated_conjecture,(
% 1.54/1.23 ~(binintersectSubset5 => (binintersectEL => (binintersectER => (transitivesetOp1 => ! [X4 : $i] : ((transitiveset @ X4) => ! [X5 : $i] : ((transitiveset @ X5) => (transitiveset @ (binintersect @ X4 @ X5))))))))),
% 1.54/1.23 inference(negated_conjecture,[status(cth)],[f6])).
% 1.54/1.23 thf(f6,conjecture,(
% 1.54/1.23 binintersectSubset5 => (binintersectEL => (binintersectER => (transitivesetOp1 => ! [X4 : $i] : ((transitiveset @ X4) => ! [X5 : $i] : ((transitiveset @ X5) => (transitiveset @ (binintersect @ X4 @ X5)))))))),
% 1.54/1.23 file('/export/starexec/sandbox/tmp/tmp.f1Li3pTZ60/DTF2THF_4331.p',binintTransitive)).
% 1.54/1.23 thf(f64,plain,(
% 1.54/1.23 ($true = (in @ sK3 @ (binintersect @ sK0 @ sK1)))),
% 1.54/1.23 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.54/1.23 thf(f62,plain,(
% 1.54/1.23 ($false = ((in @ sK3 @ (binintersect @ sK0 @ sK1)) => (subset @ sK3 @ (binintersect @ sK0 @ sK1))))),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.54/1.23 thf(f61,plain,(
% 1.54/1.23 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (binintersect @ sK0 @ sK1)) => (subset @ Y0 @ (binintersect @ sK0 @ sK1)))) @ sK3))),
% 1.54/1.23 inference(sigma_clausification,[status(thm)],[f60])).
% 1.54/1.23 thf(f60,plain,(
% 1.54/1.23 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (binintersect @ sK0 @ sK1)) => (subset @ Y0 @ (binintersect @ sK0 @ sK1))))) != $true)),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.54/1.23 thf(f38,plain,(
% 1.54/1.23 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))) @ (binintersect @ sK0 @ sK1)) != $true)),
% 1.54/1.23 inference(definition_unfolding,[status(thm)],[f36,f29])).
% 1.54/1.23 thf(f29,plain,(
% 1.54/1.23 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 1.54/1.23 inference(cnf_transformation,[status(thm)],[f10])).
% 1.54/1.23 thf(f10,plain,(
% 1.54/1.23 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 1.54/1.23 inference(fool_elimination,[status(thm)],[f9])).
% 1.54/1.23 thf(f9,plain,(
% 1.54/1.23 ((^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))) = transitiveset)),
% 1.54/1.23 inference(rectify,[status(thm)],[f4])).
% 1.54/1.23 thf(f4,axiom,(
% 1.54/1.23 ((^[X0 : $i] : (! [X4 : $i] : ((in @ X4 @ X0) => (subset @ X4 @ X0)))) = transitiveset)),
% 1.54/1.23 file('/export/starexec/sandbox/tmp/tmp.f1Li3pTZ60/DTF2THF_4331.p',transitiveset)).
% 1.54/1.23 thf(f36,plain,(
% 1.54/1.23 ($true != (transitiveset @ (binintersect @ sK0 @ sK1)))),
% 1.54/1.23 inference(cnf_transformation,[status(thm)],[f25])).
% 1.54/1.23 thf(f48,plain,(
% 1.54/1.23 ( ! [X1 : $i] : (($false = (in @ X1 @ sK0)) | ((subset @ X1 @ sK0) = $true)) )),
% 1.54/1.23 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.54/1.23 thf(f47,plain,(
% 1.54/1.23 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK0) => (subset @ X1 @ sK0)))) )),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.54/1.23 thf(f46,plain,(
% 1.54/1.23 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK0) => (subset @ Y0 @ sK0))) @ X1))) )),
% 1.54/1.23 inference(pi_clausification,[status(thm)],[f45])).
% 1.54/1.23 thf(f45,plain,(
% 1.54/1.23 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (subset @ Y0 @ sK0)))))),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.54/1.23 thf(f40,plain,(
% 1.54/1.23 ($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))) @ sK0))),
% 1.54/1.23 inference(definition_unfolding,[status(thm)],[f34,f29])).
% 1.54/1.23 thf(f34,plain,(
% 1.54/1.23 ($true = (transitiveset @ sK0))),
% 1.54/1.23 inference(cnf_transformation,[status(thm)],[f25])).
% 1.54/1.23 thf(f116,plain,(
% 1.54/1.23 ~spl2_2),
% 1.54/1.23 inference(avatar_contradiction_clause,[status(thm)],[f115])).
% 1.54/1.23 thf(f115,plain,(
% 1.54/1.23 $false | ~spl2_2),
% 1.54/1.23 inference(trivial_inequality_removal,[status(thm)],[f114])).
% 1.54/1.23 thf(f114,plain,(
% 1.54/1.23 ($false = $true) | ~spl2_2),
% 1.54/1.23 inference(backward_demodulation,[status(thm)],[f94,f112])).
% 1.54/1.23 thf(f112,plain,(
% 1.54/1.23 ($false = (in @ sK3 @ sK1)) | ~spl2_2),
% 1.54/1.23 inference(trivial_inequality_removal,[status(thm)],[f110])).
% 1.54/1.23 thf(f110,plain,(
% 1.54/1.23 ($false = (in @ sK3 @ sK1)) | ($false = $true) | ~spl2_2),
% 1.54/1.23 inference(superposition,[status(thm)],[f107,f83])).
% 1.54/1.23 thf(f83,plain,(
% 1.54/1.23 ( ! [X1 : $i] : (($true = (subset @ X1 @ sK1)) | ($false = (in @ X1 @ sK1))) )),
% 1.54/1.23 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.54/1.23 thf(f82,plain,(
% 1.54/1.23 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK1) => (subset @ X1 @ sK1)))) )),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f81])).
% 1.54/1.23 thf(f81,plain,(
% 1.54/1.23 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK1) => (subset @ Y0 @ sK1))) @ X1) = $true)) )),
% 1.54/1.23 inference(pi_clausification,[status(thm)],[f80])).
% 1.54/1.23 thf(f80,plain,(
% 1.54/1.23 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (subset @ Y0 @ sK1)))))),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.54/1.23 thf(f39,plain,(
% 1.54/1.23 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))) @ sK1) = $true)),
% 1.54/1.23 inference(definition_unfolding,[status(thm)],[f35,f29])).
% 1.54/1.23 thf(f35,plain,(
% 1.54/1.23 ($true = (transitiveset @ sK1))),
% 1.54/1.23 inference(cnf_transformation,[status(thm)],[f25])).
% 1.54/1.23 thf(f107,plain,(
% 1.54/1.23 ($false = (subset @ sK3 @ sK1)) | ~spl2_2),
% 1.54/1.23 inference(avatar_component_clause,[status(thm)],[f105])).
% 1.54/1.23 thf(f105,definition,(
% 1.54/1.23 spl2_2 <=> ($false = (subset @ sK3 @ sK1))),
% 1.54/1.23 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.54/1.23 thf(f94,plain,(
% 1.54/1.23 ((in @ sK3 @ sK1) = $true)),
% 1.54/1.23 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.54/1.23 thf(f92,plain,(
% 1.54/1.23 ((in @ sK3 @ sK1) = $true) | ($false = $true)),
% 1.54/1.23 inference(superposition,[status(thm)],[f71,f64])).
% 1.54/1.23 thf(f71,plain,(
% 1.54/1.23 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X3 @ (binintersect @ X2 @ X1))) | ((in @ X3 @ X1) = $true)) )),
% 1.54/1.23 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.54/1.23 thf(f70,plain,(
% 1.54/1.23 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ (binintersect @ X2 @ X1)) => (in @ X3 @ X1)))) )),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.54/1.23 thf(f69,plain,(
% 1.54/1.23 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (binintersect @ X2 @ X1)) => (in @ Y0 @ X1))) @ X3))) )),
% 1.54/1.23 inference(pi_clausification,[status(thm)],[f68])).
% 1.54/1.23 thf(f68,plain,(
% 1.54/1.23 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (binintersect @ X2 @ X1)) => (in @ Y0 @ X1)))))) )),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.54/1.23 thf(f67,plain,(
% 1.54/1.23 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ X1)) => (in @ Y1 @ X1))))) @ X2))) )),
% 1.54/1.23 inference(pi_clausification,[status(thm)],[f66])).
% 1.54/1.23 thf(f66,plain,(
% 1.54/1.23 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ X1)) => (in @ Y1 @ X1)))))) = $true)) )),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f65])).
% 1.54/1.23 thf(f65,plain,(
% 1.54/1.23 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y0))))))) @ X1))) )),
% 1.54/1.23 inference(pi_clausification,[status(thm)],[f43])).
% 1.54/1.23 thf(f43,plain,(
% 1.54/1.23 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y0)))))))) = $true)),
% 1.54/1.23 inference(definition_unfolding,[status(thm)],[f30,f27])).
% 1.54/1.23 thf(f27,plain,(
% 1.54/1.23 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y0)))))))))),
% 1.54/1.23 inference(cnf_transformation,[status(thm)],[f12])).
% 1.54/1.23 thf(f12,plain,(
% 1.54/1.23 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y0)))))))))),
% 1.54/1.23 inference(fool_elimination,[status(thm)],[f11])).
% 1.54/1.23 thf(f11,plain,(
% 1.54/1.23 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binintersect @ X1 @ X2)) => (in @ X0 @ X2)) = binintersectER)),
% 1.54/1.23 inference(rectify,[status(thm)],[f3])).
% 1.54/1.23 thf(f3,axiom,(
% 1.54/1.23 (! [X3 : $i,X0 : $i,X1 : $i] : ((in @ X3 @ (binintersect @ X0 @ X1)) => (in @ X3 @ X1)) = binintersectER)),
% 1.54/1.23 file('/export/starexec/sandbox/tmp/tmp.f1Li3pTZ60/DTF2THF_4331.p',binintersectER)).
% 1.54/1.23 thf(f30,plain,(
% 1.54/1.23 (binintersectER = $true)),
% 1.54/1.23 inference(cnf_transformation,[status(thm)],[f25])).
% 1.54/1.23 thf(f109,plain,(
% 1.54/1.23 spl2_2 | spl2_1),
% 1.54/1.23 inference(avatar_split_clause,[status(thm)],[f98,f101,f105])).
% 1.54/1.23 thf(f98,plain,(
% 1.54/1.23 ($false = (subset @ sK3 @ sK0)) | ($false = (subset @ sK3 @ sK1))),
% 1.54/1.23 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.54/1.23 thf(f96,plain,(
% 1.54/1.23 ($false = (subset @ sK3 @ sK1)) | ($false = $true) | ($false = (subset @ sK3 @ sK0))),
% 1.54/1.23 inference(superposition,[status(thm)],[f79,f63])).
% 1.54/1.23 thf(f63,plain,(
% 1.54/1.23 ($false = (subset @ sK3 @ (binintersect @ sK0 @ sK1)))),
% 1.54/1.23 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.54/1.23 thf(f79,plain,(
% 1.54/1.23 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (subset @ X2 @ (binintersect @ X1 @ X3))) | ((subset @ X2 @ X1) = $false) | ((subset @ X2 @ X3) = $false)) )),
% 1.54/1.23 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.54/1.23 thf(f78,plain,(
% 1.54/1.23 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((subset @ X2 @ X3) => (subset @ X2 @ (binintersect @ X1 @ X3))) = $true) | ((subset @ X2 @ X1) = $false)) )),
% 1.54/1.23 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.54/1.23 thf(f77,plain,(
% 1.54/1.23 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((subset @ X2 @ X1) => ((subset @ X2 @ X3) => (subset @ X2 @ (binintersect @ X1 @ X3)))) = $true)) )),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f76])).
% 1.54/1.23 thf(f76,plain,(
% 1.54/1.23 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ X2 @ X1) => ((subset @ X2 @ Y0) => (subset @ X2 @ (binintersect @ X1 @ Y0))))) @ X3))) )),
% 1.54/1.23 inference(pi_clausification,[status(thm)],[f75])).
% 1.54/1.23 thf(f75,plain,(
% 1.54/1.23 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ X2 @ X1) => ((subset @ X2 @ Y0) => (subset @ X2 @ (binintersect @ X1 @ Y0)))))))) )),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.54/1.23 thf(f74,plain,(
% 1.54/1.23 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ X1) => ((subset @ Y0 @ Y1) => (subset @ Y0 @ (binintersect @ X1 @ Y1))))))) @ X2))) )),
% 1.54/1.23 inference(pi_clausification,[status(thm)],[f73])).
% 1.54/1.23 thf(f73,plain,(
% 1.54/1.23 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ X1) => ((subset @ Y0 @ Y1) => (subset @ Y0 @ (binintersect @ X1 @ Y1)))))))) = $true)) )),
% 1.54/1.23 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.54/1.23 thf(f72,plain,(
% 1.54/1.23 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2))))))))) @ X1))) )),
% 1.54/1.23 inference(pi_clausification,[status(thm)],[f42])).
% 1.54/1.23 thf(f42,plain,(
% 1.54/1.23 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))))),
% 1.54/1.23 inference(definition_unfolding,[status(thm)],[f31,f26])).
% 1.54/1.23 thf(f26,plain,(
% 1.54/1.23 (binintersectSubset5 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))))),
% 1.54/1.23 inference(cnf_transformation,[status(thm)],[f18])).
% 1.54/1.23 thf(f18,plain,(
% 1.54/1.23 (binintersectSubset5 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))))),
% 1.54/1.23 inference(fool_elimination,[status(thm)],[f17])).
% 1.54/1.23 thf(f17,plain,(
% 1.54/1.23 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((subset @ X1 @ X0) => (subset @ X1 @ (binintersect @ X2 @ X0)))) = binintersectSubset5)),
% 1.54/1.23 inference(rectify,[status(thm)],[f1])).
% 1.54/1.23 thf(f1,axiom,(
% 1.54/1.23 (! [X1 : $i,X2 : $i,X0 : $i] : ((subset @ X2 @ X0) => ((subset @ X2 @ X1) => (subset @ X2 @ (binintersect @ X0 @ X1)))) = binintersectSubset5)),
% 1.54/1.23 file('/export/starexec/sandbox/tmp/tmp.f1Li3pTZ60/DTF2THF_4331.p',binintersectSubset5)).
% 1.54/1.23 thf(f31,plain,(
% 1.54/1.23 (binintersectSubset5 = $true)),
% 1.54/1.23 inference(cnf_transformation,[status(thm)],[f25])).
% 1.54/1.23 % SZS output end Proof for DTF2THF_4331
% 1.54/1.23 % (4430)------------------------------
% 1.54/1.23 % (4430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.23 % (4430)Termination reason: Refutation
% 1.54/1.23
% 1.54/1.23 % (4430)Memory used [KB]: 5628
% 1.54/1.23 % (4430)Time elapsed: 0.010 s
% 1.54/1.23 % (4430)Instructions burned: 11 (million)
% 1.54/1.23 % (4430)------------------------------
% 1.54/1.23 % (4430)------------------------------
% 1.54/1.23 % (4427)Success in time 0.02 s
%------------------------------------------------------------------------------