%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU590^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n031.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 09:35:28 AM UTC 2026
% Result : Theorem 1.29s 1.06s
% Output : Refutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 5
% Syntax : Number of formulae : 83 ( 80 unt; 0 typ; 0 def)
% Number of atoms : 688 ( 79 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 1269 ( 11 ~; 0 |; 0 &; 940 @)
% ( 0 <=>; 186 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 10 con; 0-2 aty)
% ( 132 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 259 ( 198 ^; 61 !; 0 ?; 259 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_6,type,
binintersect: $i > $i > $i ).
thf(func_def_19,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f140,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f139]) ).
thf(f139,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f138]) ).
thf(f138,plain,
( ( ~ $true ) = $true ),
inference(backward_demodulation,[status(thm)],[f137,f129]) ).
thf(f129,plain,
( ( in @ sK5 @ sK3 )
= $true ),
inference(boolean_simplification,[status(thm)],[f123]) ).
thf(f123,plain,
( $true
= ( $true
=> ( in @ sK5 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f69,f103]) ).
thf(f103,plain,
( $true
= ( in @ sK5 @ sK4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( ( in @ sK5 @ sK4 )
=> ( in @ sK5
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( in @ Y0 @ sK2 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] : ( in @ Y1 @ sK2 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] : ( in @ Y1 @ sK2 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] : ( in @ Y1 @ sK2 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f92]) ).
thf(f92,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
=> ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] : ( in @ Y1 @ sK2 ) ) ) ) )
=> $false ) ),
inference(superposition,[status(thm)],[f45,f80]) ).
thf(f80,plain,
( ( subset @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( in @ Y0 @ sK2 ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $true
=> ( subset @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( in @ Y0 @ sK2 ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f60,f78]) ).
thf(f78,plain,
( $true
= ( subset @ sK4 @ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( subset @ sK4 @ sK2 )
=> ( subset @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( in @ Y0 @ sK2 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( subset @ sK4 @ sK3 )
=> ( ( subset @ sK4 @ sK2 )
=> ( subset @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( in @ Y0 @ sK2 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ^ [Y0: $i] :
( ( subset @ Y0 @ sK3 )
=> ( ( subset @ Y0 @ sK2 )
=> ( subset @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] : ( in @ Y1 @ sK2 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ sK3 )
=> ( ( subset @ Y0 @ sK2 )
=> ( subset @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] : ( in @ Y1 @ sK2 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y1 @ sK2 )
=> ( subset @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ sK2 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y1 @ sK2 )
=> ( subset @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ sK2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( subset @ Y2 @ Y0 )
=> ( subset @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( subset @ Y2 @ Y0 )
=> ( subset @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( subset @ Y2 @ Y0 )
=> ( subset @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( subset @ Y2 @ Y0 )
=> ( subset @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f31,f33]) ).
thf(f33,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( subset @ Y2 @ Y0 )
=> ( subset @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( subset @ Y2 @ Y0 )
=> ( subset @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f25,f29]) ).
thf(f29,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( subset @ Y2 @ Y0 )
=> ( subset @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( subset @ Y2 @ Y0 )
=> ( subset @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( subset @ Y2 @ Y0 )
=> ( subset @ Y2
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y1
@ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f17,f18,f20,f22,f19]) ).
thf(f19,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) )
= binintersect ),
file('/export/starexec/sandbox2/tmp/tmp.ZhJl1TIU79/DTF2THF_10477.p',binintersect) ).
thf(f22,plain,
( binintersectI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f21,f19]) ).
thf(f21,plain,
( binintersectI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( binintersect @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( binintersectI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( binintersect @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( binintersectI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( binintersectI
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZhJl1TIU79/DTF2THF_10477.p',binintersectI) ).
thf(f20,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox2/tmp/tmp.ZhJl1TIU79/DTF2THF_10477.p',subsetE) ).
thf(f18,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
file('/export/starexec/sandbox2/tmp/tmp.ZhJl1TIU79/DTF2THF_10477.p',subsetI1) ).
thf(f17,plain,
( $true
= ( ~ ( subsetI1
=> ( subsetE
=> ( binintersectI
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( subset @ Y2 @ Y0 )
=> ( subset @ Y2 @ ( binintersect @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( $true
= ( ~ ( subsetI1
=> ( subsetE
=> ( binintersectI
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( subset @ Y2 @ Y0 )
=> ( subset @ Y2 @ ( binintersect @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( subsetI1
=> ( subsetE
=> ( binintersectI
=> ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X0 @ X2 )
=> ( subset @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( subsetI1
=> ( subsetE
=> ( binintersectI
=> ! [X3: $i,X0: $i,X1: $i] :
( ( subset @ X3 @ X0 )
=> ( ( subset @ X3 @ X1 )
=> ( subset @ X3 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( subsetI1
=> ( subsetE
=> ( binintersectI
=> ! [X3: $i,X0: $i,X1: $i] :
( ( subset @ X3 @ X0 )
=> ( ( subset @ X3 @ X1 )
=> ( subset @ X3 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZhJl1TIU79/DTF2THF_10477.p',binintersectSubset5) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( subset @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f69,plain,
! [X0: $i] :
( $true
= ( ( in @ X0 @ sK4 )
=> ( in @ X0 @ sK3 ) ) ),
inference(boolean_simplification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X0: $i] :
( ( $true
=> ( ( in @ X0 @ sK4 )
=> ( in @ X0 @ sK3 ) ) )
= $true ),
inference(superposition,[status(thm)],[f52,f61]) ).
thf(f61,plain,
( ( subset @ sK4 @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X3 @ X2 )
=> ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X2 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ X2 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X2 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ X2 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ X1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ X1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f137,plain,
( ( ~ ( in @ sK5 @ sK3 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f136]) ).
thf(f136,plain,
( $true
= ( ( in @ sK5 @ sK3 )
=> $false ) ),
inference(boolean_simplification,[status(thm)],[f135]) ).
thf(f135,plain,
( $true
= ( ( in @ sK5 @ sK3 )
=> ~ $true ) ),
inference(backward_demodulation,[status(thm)],[f115,f130]) ).
thf(f130,plain,
( $true
= ( in @ sK5 @ sK2 ) ),
inference(boolean_simplification,[status(thm)],[f122]) ).
thf(f122,plain,
( $true
= ( $true
=> ( in @ sK5 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f85,f103]) ).
thf(f85,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK4 )
=> ( in @ X0 @ sK2 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X0: $i] :
( $true
= ( $true
=> ( ( in @ X0 @ sK4 )
=> ( in @ X0 @ sK2 ) ) ) ),
inference(superposition,[status(thm)],[f52,f78]) ).
thf(f115,plain,
( $true
= ( ( in @ sK5 @ sK3 )
=> ~ ( in @ sK5 @ sK2 ) ) ),
inference(boolean_simplification,[status(thm)],[f110]) ).
thf(f110,plain,
( $true
= ( ( in @ sK5 @ sK3 )
=> ( ( in @ sK5 @ sK2 )
=> $false ) ) ),
inference(superposition,[status(thm)],[f82,f107]) ).
thf(f107,plain,
( ( in @ sK5
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( in @ Y0 @ sK2 ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f106]) ).
thf(f106,plain,
( ( $true
=> ( in @ sK5
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( in @ Y0 @ sK2 ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f100,f103]) ).
thf(f82,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ X3 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2
@ ( dsetconstr @ Y0
@ ^ [Y1: $i] : ( in @ Y1 @ X1 ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2
@ ( dsetconstr @ Y0
@ ^ [Y1: $i] : ( in @ Y1 @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( in @ Y2 @ X1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( in @ Y2 @ X1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU590^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.08 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.26 % Computer : n031.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8042.1875MB
% 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 300
% 0.08/0.26 % DateTime : Tue Feb 24 12:28:48 EST 2026
% 0.08/0.26 % CPUTime :
% 0.08/0.27 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 ---- Original DTF file ---
% 0.08/0.34 thf(spec,logic,$$dhol).
% 0.08/0.34 %------------------------------------------------------------------------------
% 0.08/0.34 % File : SEU590^2 : TPTP v9.2.1. Released v3.7.0.
% 0.08/0.34 % Domain : Set Theory
% 0.08/0.34 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.08/0.34 % Version : Especial > Reduced > Especial.
% 0.08/0.34 % English : (! A:i.! B:i.! C:i.subset C A -> subset C B -> subset C
% 0.08/0.34 % (binintersect A B))
% 0.08/0.34
% 0.08/0.34 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.08/0.34 % Source : [Bro08]
% 0.08/0.34 % Names : ZFC092l [Bro08]
% 0.08/0.34
% 0.08/0.34 % Status : Theorem
% 0.08/0.34 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0, 0.67 v3.7.0
% 0.08/0.34 % Syntax : Number of formulae : 12 ( 4 unt; 7 typ; 4 def)
% 0.08/0.34 % Number of atoms : 23 ( 4 equ; 0 cnn)
% 0.08/0.34 % Maximal formula atoms : 6 ( 4 avg)
% 0.08/0.34 % Number of connectives : 43 ( 0 ~; 0 |; 0 &; 32 @)
% 0.08/0.34 % ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% 0.08/0.34 % Maximal formula depth : 12 ( 3 avg)
% 0.08/0.34 % Number of types : 2 ( 0 usr)
% 0.08/0.34 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.08/0.34 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.08/0.34 % Number of variables : 15 ( 3 ^; 12 !; 0 ?; 15 :)
% 0.08/0.34 % SPC : TH0_THM_EQU_NAR
% 0.08/0.34
% 0.08/0.34 % Comments : http://mathgate.info/detsetitem.php?id=366
% 0.08/0.34 %------------------------------------------------------------------------------
% 0.08/0.34 thf(in_type,type,
% 0.08/0.34 in: $i > $i > $o ).
% 0.08/0.34
% 0.08/0.34 thf(dsetconstr_type,type,
% 0.08/0.34 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.08/0.34
% 0.08/0.34 thf(subset_type,type,
% 0.08/0.34 subset: $i > $i > $o ).
% 0.08/0.34
% 0.08/0.34 thf(subsetI1_type,type,
% 0.08/0.34 subsetI1: $o ).
% 0.08/0.34
% 0.08/0.34 thf(subsetI1,definition,
% 0.08/0.34 ( subsetI1
% 0.08/0.34 = ( ! [A: $i,B: $i] :
% 0.08/0.34 ( ! [Xx: $i] :
% 0.08/0.34 ( ( in @ Xx @ A )
% 0.08/0.34 => ( in @ Xx @ B ) )
% 0.08/0.34 => ( subset @ A @ B ) ) ) ) ).
% 0.08/0.34
% 0.08/0.34 thf(subsetE_type,type,
% 0.08/0.34 subsetE: $o ).
% 0.08/0.34
% 0.08/0.34 thf(subsetE,definition,
% 0.08/0.34 ( subsetE
% 0.08/0.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.34 ( ( subset @ A @ B )
% 0.08/0.34 => ( ( in @ Xx @ A )
% 0.08/0.34 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.08/0.34
% 0.08/0.34 thf(binintersect_type,type,
% 0.08/0.34 binintersect: $i > $i > $i ).
% 0.08/0.34
% 0.08/0.34 thf(binintersect,definition,
% 0.08/0.34 ( binintersect
% 0.08/0.34 = ( ^ [A: $i,B: $i] :
% 0.08/0.34 ( dsetconstr @ A
% 0.08/0.34 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 0.08/0.34
% 0.08/0.34 thf(binintersectI_type,type,
% 0.08/0.34 binintersectI: $o ).
% 0.08/0.34
% 0.08/0.34 thf(binintersectI,definition,
% 0.08/0.34 ( binintersectI
% 0.08/0.34 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.34 ( ( in @ Xx @ A )
% 0.08/0.34 => ( ( in @ Xx @ B )
% 0.08/0.34 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.08/0.34
% 0.08/0.34 thf(binintersectSubset5,conjecture,
% 0.08/0.34 ( subsetI1
% 0.08/0.34 => ( subsetE
% 0.08/0.34 => ( binintersectI
% 0.08/0.34 => ! [A: $i,B: $i,C: $i] :
% 0.08/0.34 ( ( subset @ C @ A )
% 0.08/0.34 => ( ( subset @ C @ B )
% 0.08/0.34 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ) ).
% 0.08/0.34
% 0.08/0.34 %------------------------------------------------------------------------------
% 0.08/0.34 ------------------------
% 1.09/1.00 ---- Embedded in THF ---
% 1.09/1.00 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.09/1.00 %%% Generated on Tue Feb 24 12:28:48 EST 2026
% 1.09/1.00 %%% using '$$dhol' embedding, version 1.3.0.
% 1.09/1.00 %%% Logic specification used:
% 1.09/1.00 %%% thf(spec, logic, $$dhol).
% 1.09/1.00
% 1.09/1.00 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ZhJl1TIU79/DTF2DTF10477.p
% See solution above
% 1.09/1.00 ------------------------
% 1.09/1.01 ---- Cleaned THF ---
% 1.09/1.01 thf(in_type,type,
% 1.09/1.01 in: $i > $i > $o ).
% 1.09/1.01
% 1.09/1.01 thf(dsetconstr_type,type,
% 1.09/1.01 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.09/1.01
% 1.09/1.01 thf(subset_type,type,
% 1.09/1.01 subset: $i > $i > $o ).
% 1.09/1.01
% 1.09/1.01 thf(subsetI1_type,type,
% 1.09/1.01 subsetI1: $o ).
% 1.09/1.01
% 1.09/1.01 thf(subsetI1,definition,
% 1.09/1.01 ( subsetI1
% 1.09/1.01 = ( ! [A: $i,B: $i] :
% 1.09/1.01 ( ! [Xx: $i] :
% 1.09/1.01 ( ( in @ Xx @ A )
% 1.09/1.01 => ( in @ Xx @ B ) )
% 1.09/1.01 => ( subset @ A @ B ) ) ) ) ).
% 1.09/1.01
% 1.09/1.01 thf(subsetE_type,type,
% 1.09/1.01 subsetE: $o ).
% 1.09/1.01
% 1.09/1.01 thf(subsetE,definition,
% 1.09/1.01 ( subsetE
% 1.09/1.01 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.09/1.01 ( ( subset @ A @ B )
% 1.09/1.01 => ( ( in @ Xx @ A )
% 1.09/1.01 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.09/1.01
% 1.09/1.01 thf(binintersect_type,type,
% 1.09/1.01 binintersect: $i > $i > $i ).
% 1.09/1.01
% 1.09/1.01 thf(binintersect,definition,
% 1.09/1.01 ( binintersect
% 1.09/1.01 = ( ^ [A: $i,B: $i] :
% 1.09/1.01 ( dsetconstr @ A
% 1.09/1.01 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 1.09/1.01
% 1.09/1.01 thf(binintersectI_type,type,
% 1.09/1.01 binintersectI: $o ).
% 1.09/1.01
% 1.09/1.01 thf(binintersectI,definition,
% 1.09/1.01 ( binintersectI
% 1.09/1.01 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.09/1.01 ( ( in @ Xx @ A )
% 1.09/1.01 => ( ( in @ Xx @ B )
% 1.09/1.01 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 1.09/1.01
% 1.09/1.01 thf(binintersectSubset5,conjecture,
% 1.09/1.01 ( subsetI1
% 1.09/1.01 => ( subsetE
% 1.09/1.01 => ( binintersectI
% 1.09/1.01 => ! [A: $i,B: $i,C: $i] :
% 1.09/1.01 ( ( subset @ C @ A )
% 1.09/1.01 => ( ( subset @ C @ B )
% 1.09/1.01 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ) ).
% 1.09/1.01 ------------------------
% 1.29/1.03 % (10680)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_10477 for (2999ds/2Mi)
% 1.29/1.03 % (10680)Instruction limit reached!
% 1.29/1.03 % (10680)------------------------------
% 1.29/1.03 % (10680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.03 % (10680)Termination reason: Unknown
% 1.29/1.03 % (10680)Termination phase: Unused predicate definition removal
% 1.29/1.03
% 1.29/1.03 % (10680)Memory used [KB]: 895
% 1.29/1.03 % (10680)Time elapsed: 0.002 s
% 1.29/1.03 % (10680)Instructions burned: 2 (million)
% 1.29/1.03 % (10680)------------------------------
% 1.29/1.03 % (10680)------------------------------
% 1.29/1.03 % (10678)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_10477 for (2999ds/27Mi)
% 1.29/1.03 % (10676)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10477 for (2999ds/183Mi)
% 1.29/1.03 % (10677)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_10477 for (2999ds/4Mi)
% 1.29/1.03 % (10679)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10477 for (2999ds/2Mi)
% 1.29/1.04 % (10682)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10477 for (2999ds/18Mi)
% 1.29/1.04 % (10681)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_10477 for (2999ds/275Mi)
% 1.29/1.04 % (10679)Instruction limit reached!
% 1.29/1.04 % (10679)------------------------------
% 1.29/1.04 % (10679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.04 % (10679)Termination reason: Unknown
% 1.29/1.04 % (10679)Termination phase: Preprocessing 1
% 1.29/1.04
% 1.29/1.04 % (10679)Memory used [KB]: 895
% 1.29/1.04 % (10679)Time elapsed: 0.003 s
% 1.29/1.04 % (10679)Instructions burned: 2 (million)
% 1.29/1.04 % (10679)------------------------------
% 1.29/1.04 % (10679)------------------------------
% 1.29/1.04 % (10683)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10477 for (2999ds/3Mi)
% 1.29/1.04 % (10677)Instruction limit reached!
% 1.29/1.04 % (10677)------------------------------
% 1.29/1.04 % (10677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.04 % (10677)Termination reason: Unknown
% 1.29/1.04 % (10677)Termination phase: Saturation
% 1.29/1.04
% 1.29/1.04 % (10677)Memory used [KB]: 5500
% 1.29/1.04 % (10677)Time elapsed: 0.005 s
% 1.29/1.04 % (10677)Instructions burned: 5 (million)
% 1.29/1.04 % (10677)------------------------------
% 1.29/1.04 % (10677)------------------------------
% 1.29/1.04 % (10678)Instruction limit reached!
% 1.29/1.04 % (10678)------------------------------
% 1.29/1.04 % (10678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.04 % (10678)Termination reason: Unknown
% 1.29/1.04 % (10678)Termination phase: Saturation
% 1.29/1.04
% 1.29/1.04 % (10678)Memory used [KB]: 5628
% 1.29/1.04 % (10678)Time elapsed: 0.011 s
% 1.29/1.04 % (10678)Instructions burned: 28 (million)
% 1.29/1.04 % (10678)------------------------------
% 1.29/1.04 % (10678)------------------------------
% 1.29/1.04 % (10683)Instruction limit reached!
% 1.29/1.04 % (10683)------------------------------
% 1.29/1.04 % (10683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.04 % (10683)Termination reason: Unknown
% 1.29/1.04 % (10683)Termination phase: Saturation
% 1.29/1.04
% 1.29/1.04 % (10683)Memory used [KB]: 5500
% 1.29/1.04 % (10683)Time elapsed: 0.002 s
% 1.29/1.04 % (10683)Instructions burned: 4 (million)
% 1.29/1.04 % (10683)------------------------------
% 1.29/1.04 % (10683)------------------------------
% 1.29/1.05 % (10682)Instruction limit reached!
% 1.29/1.05 % (10682)------------------------------
% 1.29/1.05 % (10682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.05 % (10682)Termination reason: Unknown
% 1.29/1.05 % (10682)Termination phase: Saturation
% 1.29/1.05
% 1.29/1.05 % (10682)Memory used [KB]: 5628
% 1.29/1.05 % (10682)Time elapsed: 0.014 s
% 1.29/1.05 % (10682)Instructions burned: 19 (million)
% 1.29/1.05 % (10682)------------------------------
% 1.29/1.05 % (10682)------------------------------
% 1.29/1.05 % (10687)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_10477 for (2999ds/1041Mi)
% 1.29/1.05 % (10686)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_10477 for (2999ds/3Mi)
% 1.29/1.05 % (10686)Instruction limit reached!
% 1.29/1.05 % (10686)------------------------------
% 1.29/1.05 % (10686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.05 % (10686)Termination reason: Unknown
% 1.29/1.05 % (10686)Termination phase: Saturation
% 1.29/1.05
% 1.29/1.05 % (10686)Memory used [KB]: 5500
% 1.29/1.05 % (10686)Time elapsed: 0.003 s
% 1.29/1.05 % (10686)Instructions burned: 4 (million)
% 1.29/1.05 % (10686)------------------------------
% 1.29/1.05 % (10686)------------------------------
% 1.29/1.05 % (10684)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_10477 for (2999ds/37Mi)
% 1.29/1.06 % (10685)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_10477 for (2999ds/15Mi)
% 1.29/1.06 % (10687)First to succeed.
% 1.29/1.06 % (10689)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10477 for (2999ds/16Mi)
% 1.29/1.06 % (10687)Refutation found. Thanks to Tanya!
% 1.29/1.06 % SZS status Theorem for DTF2THF_10477
% 1.29/1.06 % SZS output start Proof for DTF2THF_10477
% 1.29/1.06 thf(func_def_0, type, in: $i > $i > $o).
% 1.29/1.06 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.29/1.06 thf(func_def_2, type, subset: $i > $i > $o).
% 1.29/1.06 thf(func_def_6, type, binintersect: $i > $i > $i).
% 1.29/1.06 thf(func_def_19, type, ph1: !>[X0: $tType]:(X0)).
% 1.29/1.06 thf(f140,plain,(
% 1.29/1.06 $false),
% 1.29/1.06 inference(trivial_inequality_removal,[status(thm)],[f139])).
% 1.29/1.06 thf(f139,plain,(
% 1.29/1.06 ($true = $false)),
% 1.29/1.06 inference(boolean_simplification,[status(thm)],[f138])).
% 1.29/1.06 thf(f138,plain,(
% 1.29/1.06 ((~ $true) = $true)),
% 1.29/1.06 inference(backward_demodulation,[status(thm)],[f137,f129])).
% 1.29/1.06 thf(f129,plain,(
% 1.29/1.06 ((in @ sK5 @ sK3) = $true)),
% 1.29/1.06 inference(boolean_simplification,[status(thm)],[f123])).
% 1.29/1.06 thf(f123,plain,(
% 1.29/1.06 ($true = ($true => (in @ sK5 @ sK3)))),
% 1.29/1.06 inference(superposition,[status(thm)],[f69,f103])).
% 1.29/1.06 thf(f103,plain,(
% 1.29/1.06 ($true = (in @ sK5 @ sK4))),
% 1.29/1.06 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.29/1.06 thf(f100,plain,(
% 1.29/1.06 (((in @ sK5 @ sK4) => (in @ sK5 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (in @ Y0 @ sK2))))) = $false)),
% 1.29/1.06 inference(beta_eta_normalization,[status(thm)],[f98])).
% 1.29/1.06 thf(f98,plain,(
% 1.29/1.06 (((^[Y0 : $i]: ((in @ Y0 @ sK4) => (in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (in @ Y1 @ sK2)))))) @ sK5) = $false)),
% 1.29/1.06 inference(sigma_clausification,[status(thm)],[f95])).
% 1.29/1.06 thf(f95,plain,(
% 1.29/1.06 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => (in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (in @ Y1 @ sK2))))))))),
% 1.29/1.06 inference(not_proxy_clausification,[status(thm)],[f93])).
% 1.29/1.06 thf(f93,plain,(
% 1.29/1.06 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => (in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (in @ Y1 @ sK2)))))))) = $true)),
% 1.29/1.06 inference(boolean_simplification,[status(thm)],[f92])).
% 1.29/1.06 thf(f92,plain,(
% 1.29/1.06 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => (in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (in @ Y1 @ sK2))))))) => $false))),
% 1.29/1.06 inference(superposition,[status(thm)],[f45,f80])).
% 1.29/1.06 thf(f80,plain,(
% 1.29/1.06 ((subset @ sK4 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (in @ Y0 @ sK2)))) = $false)),
% 1.29/1.06 inference(boolean_simplification,[status(thm)],[f79])).
% 1.29/1.06 thf(f79,plain,(
% 1.29/1.06 (($true => (subset @ sK4 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (in @ Y0 @ sK2))))) = $false)),
% 1.29/1.06 inference(backward_demodulation,[status(thm)],[f60,f78])).
% 1.29/1.06 thf(f78,plain,(
% 1.29/1.06 ($true = (subset @ sK4 @ sK2))),
% 1.29/1.06 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.29/1.06 thf(f60,plain,(
% 1.29/1.06 (((subset @ sK4 @ sK2) => (subset @ sK4 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (in @ Y0 @ sK2))))) = $false)),
% 1.29/1.06 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.29/1.06 thf(f59,plain,(
% 1.29/1.06 (((subset @ sK4 @ sK3) => ((subset @ sK4 @ sK2) => (subset @ sK4 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (in @ Y0 @ sK2)))))) = $false)),
% 1.29/1.06 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.29/1.06 thf(f58,plain,(
% 1.29/1.06 (((^[Y0 : $i]: ((subset @ Y0 @ sK3) => ((subset @ Y0 @ sK2) => (subset @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (in @ Y1 @ sK2))))))) @ sK4) = $false)),
% 1.29/1.06 inference(sigma_clausification,[status(thm)],[f57])).
% 1.29/1.06 thf(f57,plain,(
% 1.29/1.06 ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ sK3) => ((subset @ Y0 @ sK2) => (subset @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (in @ Y1 @ sK2)))))))) = $false)),
% 1.29/1.06 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.29/1.06 thf(f56,plain,(
% 1.29/1.06 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ sK2) => (subset @ Y1 @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ sK2))))))))) @ sK3) = $false)),
% 1.29/1.06 inference(sigma_clausification,[status(thm)],[f55])).
% 1.29/1.06 thf(f55,plain,(
% 1.29/1.06 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ sK2) => (subset @ Y1 @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ sK2)))))))))))),
% 1.29/1.06 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.29/1.06 thf(f54,plain,(
% 1.29/1.06 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (in @ Y3 @ Y0))))))))))) @ sK2) = $false)),
% 1.29/1.06 inference(sigma_clausification,[status(thm)],[f38])).
% 1.29/1.06 thf(f38,plain,(
% 1.29/1.06 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (in @ Y3 @ Y0)))))))))))) = $false)),
% 1.29/1.06 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.29/1.06 thf(f35,plain,(
% 1.29/1.06 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (in @ Y3 @ Y0)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (in @ Y3 @ Y0))))))))))))) = $false)),
% 1.29/1.06 inference(boolean_simplification,[status(thm)],[f34])).
% 1.29/1.06 thf(f34,plain,(
% 1.29/1.06 (($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (in @ Y3 @ Y0)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (in @ Y3 @ Y0)))))))))))))) = $false)),
% 1.29/1.06 inference(backward_demodulation,[status(thm)],[f31,f33])).
% 1.29/1.06 thf(f33,plain,(
% 1.29/1.06 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))))),
% 1.29/1.06 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.29/1.06 thf(f31,plain,(
% 1.29/1.06 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (in @ Y3 @ Y0)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (in @ Y3 @ Y0)))))))))))))) = $false)),
% 1.29/1.06 inference(boolean_simplification,[status(thm)],[f30])).
% 1.29/1.06 thf(f30,plain,(
% 1.29/1.06 (($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (in @ Y3 @ Y0)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (in @ Y3 @ Y0))))))))))))))) = $false)),
% 1.29/1.06 inference(backward_demodulation,[status(thm)],[f25,f29])).
% 1.29/1.06 thf(f29,plain,(
% 1.29/1.06 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))))),
% 1.29/1.06 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.29/1.06 thf(f25,plain,(
% 1.29/1.06 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (in @ Y3 @ Y0)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (in @ Y3 @ Y0))))))))))))))) = $false)),
% 1.29/1.06 inference(not_proxy_clausification,[status(thm)],[f24])).
% 1.29/1.06 thf(f24,plain,(
% 1.29/1.06 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (in @ Y3 @ Y0)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (in @ Y3 @ Y0)))))))))))))))))),
% 1.29/1.06 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.29/1.06 thf(f23,plain,(
% 1.29/1.06 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ ((^[Y3 : $i]: ((^[Y4 : $i]: (dsetconstr @ Y3 @ (^[Y5 : $i]: (in @ Y5 @ Y4)))))) @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ ((^[Y3 : $i]: ((^[Y4 : $i]: (dsetconstr @ Y3 @ (^[Y5 : $i]: (in @ Y5 @ Y4)))))) @ Y1 @ Y0)))))))))))))))),
% 1.29/1.06 inference(definition_unfolding,[status(thm)],[f17,f18,f20,f22,f19])).
% 1.29/1.06 thf(f19,plain,(
% 1.29/1.06 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 1.29/1.06 inference(cnf_transformation,[status(thm)],[f10])).
% 1.29/1.06 thf(f10,plain,(
% 1.29/1.06 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 1.29/1.06 inference(fool_elimination,[status(thm)],[f3])).
% 1.29/1.06 thf(f3,axiom,(
% 1.29/1.06 ((^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (in @ X2 @ X1)))) = binintersect)),
% 1.29/1.06 file('/export/starexec/sandbox2/tmp/tmp.ZhJl1TIU79/DTF2THF_10477.p',binintersect)).
% 1.29/1.06 thf(f22,plain,(
% 1.29/1.06 (binintersectI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ ((^[Y3 : $i]: ((^[Y4 : $i]: (dsetconstr @ Y3 @ (^[Y5 : $i]: (in @ Y5 @ Y4)))))) @ Y2 @ Y0)))))))))))),
% 1.29/1.06 inference(definition_unfolding,[status(thm)],[f21,f19])).
% 1.29/1.06 thf(f21,plain,(
% 1.29/1.06 (binintersectI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ (binintersect @ Y2 @ Y0)))))))))))),
% 1.29/1.06 inference(cnf_transformation,[status(thm)],[f9])).
% 1.29/1.06 thf(f9,plain,(
% 1.29/1.06 (binintersectI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ (binintersect @ Y2 @ Y0)))))))))))),
% 1.29/1.06 inference(fool_elimination,[status(thm)],[f8])).
% 1.29/1.06 thf(f8,plain,(
% 1.29/1.06 (binintersectI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X1 @ X2) => (in @ X1 @ (binintersect @ X0 @ X2)))))),
% 1.29/1.06 inference(rectify,[status(thm)],[f4])).
% 1.29/1.06 thf(f4,axiom,(
% 1.29/1.06 (binintersectI = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))))),
% 1.29/1.06 file('/export/starexec/sandbox2/tmp/tmp.ZhJl1TIU79/DTF2THF_10477.p',binintersectI)).
% 1.29/1.06 thf(f20,plain,(
% 1.29/1.06 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))))),
% 1.29/1.06 inference(cnf_transformation,[status(thm)],[f16])).
% 1.29/1.06 thf(f16,plain,(
% 1.29/1.06 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))))),
% 1.29/1.06 inference(fool_elimination,[status(thm)],[f15])).
% 1.29/1.06 thf(f15,plain,(
% 1.29/1.06 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.29/1.06 inference(rectify,[status(thm)],[f2])).
% 1.29/1.06 thf(f2,axiom,(
% 1.29/1.06 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.29/1.06 file('/export/starexec/sandbox2/tmp/tmp.ZhJl1TIU79/DTF2THF_10477.p',subsetE)).
% 1.29/1.06 thf(f18,plain,(
% 1.29/1.06 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))))),
% 1.29/1.06 inference(cnf_transformation,[status(thm)],[f12])).
% 1.29/1.06 thf(f12,plain,(
% 1.29/1.06 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))))),
% 1.29/1.06 inference(fool_elimination,[status(thm)],[f11])).
% 1.29/1.06 thf(f11,plain,(
% 1.29/1.06 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 1.29/1.06 inference(rectify,[status(thm)],[f1])).
% 1.29/1.06 thf(f1,axiom,(
% 1.29/1.06 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 1.29/1.06 file('/export/starexec/sandbox2/tmp/tmp.ZhJl1TIU79/DTF2THF_10477.p',subsetI1)).
% 1.29/1.06 thf(f17,plain,(
% 1.29/1.06 ($true = (~ (subsetI1 => (subsetE => (binintersectI => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))))))))),
% 1.29/1.06 inference(cnf_transformation,[status(thm)],[f14])).
% 1.29/1.06 thf(f14,plain,(
% 1.29/1.06 ($true = (~ (subsetI1 => (subsetE => (binintersectI => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))))))))),
% 1.29/1.06 inference(fool_elimination,[status(thm)],[f13])).
% 1.29/1.06 thf(f13,plain,(
% 1.29/1.06 ~(subsetI1 => (subsetE => (binintersectI => ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((subset @ X0 @ X2) => (subset @ X0 @ (binintersect @ X1 @ X2)))))))),
% 1.29/1.06 inference(rectify,[status(thm)],[f6])).
% 1.29/1.06 thf(f6,negated_conjecture,(
% 1.29/1.06 ~(subsetI1 => (subsetE => (binintersectI => ! [X3 : $i,X0 : $i,X1 : $i] : ((subset @ X3 @ X0) => ((subset @ X3 @ X1) => (subset @ X3 @ (binintersect @ X0 @ X1)))))))),
% 1.29/1.06 inference(negated_conjecture,[status(cth)],[f5])).
% 1.29/1.06 thf(f5,conjecture,(
% 1.29/1.06 subsetI1 => (subsetE => (binintersectI => ! [X3 : $i,X0 : $i,X1 : $i] : ((subset @ X3 @ X0) => ((subset @ X3 @ X1) => (subset @ X3 @ (binintersect @ X0 @ X1))))))),
% 1.29/1.06 file('/export/starexec/sandbox2/tmp/tmp.ZhJl1TIU79/DTF2THF_10477.p',binintersectSubset5)).
% 1.29/1.06 thf(f45,plain,(
% 1.29/1.06 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => (subset @ X2 @ X1)))) )),
% 1.29/1.06 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.29/1.06 thf(f44,plain,(
% 1.29/1.06 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1))) @ X2))) )),
% 1.29/1.06 inference(pi_clausification,[status(thm)],[f37])).
% 1.29/1.06 thf(f37,plain,(
% 1.29/1.06 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1)))) = $true)) )),
% 1.29/1.06 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.29/1.06 thf(f36,plain,(
% 1.29/1.06 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))) @ X1) = $true)) )),
% 1.29/1.06 inference(pi_clausification,[status(thm)],[f29])).
% 1.29/1.06 thf(f69,plain,(
% 1.29/1.06 ( ! [X0 : $i] : (($true = ((in @ X0 @ sK4) => (in @ X0 @ sK3)))) )),
% 1.29/1.06 inference(boolean_simplification,[status(thm)],[f66])).
% 1.29/1.06 thf(f66,plain,(
% 1.29/1.06 ( ! [X0 : $i] : ((($true => ((in @ X0 @ sK4) => (in @ X0 @ sK3))) = $true)) )),
% 1.29/1.06 inference(superposition,[status(thm)],[f52,f61])).
% 1.29/1.06 thf(f61,plain,(
% 1.29/1.06 ((subset @ sK4 @ sK3) = $true)),
% 1.29/1.06 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.29/1.06 thf(f52,plain,(
% 1.29/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X3 @ X2) => ((in @ X1 @ X3) => (in @ X1 @ X2))))) )),
% 1.29/1.06 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.29/1.06 thf(f51,plain,(
% 1.29/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ Y0 @ X2) => ((in @ X1 @ Y0) => (in @ X1 @ X2)))) @ X3))) )),
% 1.29/1.06 inference(pi_clausification,[status(thm)],[f50])).
% 1.29/1.06 thf(f50,plain,(
% 1.29/1.06 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ X2) => ((in @ X1 @ Y0) => (in @ X1 @ X2))))) = $true)) )),
% 1.29/1.06 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.29/1.06 thf(f49,plain,(
% 1.29/1.06 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((in @ X1 @ Y1) => (in @ X1 @ Y0)))))) @ X2))) )),
% 1.29/1.06 inference(pi_clausification,[status(thm)],[f48])).
% 1.29/1.06 thf(f48,plain,(
% 1.29/1.06 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((in @ X1 @ Y1) => (in @ X1 @ Y0))))))) = $true)) )),
% 1.29/1.06 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.29/1.06 thf(f47,plain,(
% 1.29/1.06 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1)))))))) @ X1))) )),
% 1.29/1.06 inference(pi_clausification,[status(thm)],[f33])).
% 1.29/1.06 thf(f137,plain,(
% 1.29/1.06 ((~ (in @ sK5 @ sK3)) = $true)),
% 1.29/1.06 inference(boolean_simplification,[status(thm)],[f136])).
% 1.29/1.06 thf(f136,plain,(
% 1.29/1.06 ($true = ((in @ sK5 @ sK3) => $false))),
% 1.29/1.06 inference(boolean_simplification,[status(thm)],[f135])).
% 1.29/1.06 thf(f135,plain,(
% 1.29/1.06 ($true = ((in @ sK5 @ sK3) => (~ $true)))),
% 1.29/1.06 inference(backward_demodulation,[status(thm)],[f115,f130])).
% 1.29/1.06 thf(f130,plain,(
% 1.29/1.06 ($true = (in @ sK5 @ sK2))),
% 1.29/1.06 inference(boolean_simplification,[status(thm)],[f122])).
% 1.29/1.06 thf(f122,plain,(
% 1.29/1.06 ($true = ($true => (in @ sK5 @ sK2)))),
% 1.29/1.06 inference(superposition,[status(thm)],[f85,f103])).
% 1.29/1.06 thf(f85,plain,(
% 1.29/1.06 ( ! [X0 : $i] : ((((in @ X0 @ sK4) => (in @ X0 @ sK2)) = $true)) )),
% 1.29/1.06 inference(boolean_simplification,[status(thm)],[f83])).
% 1.29/1.06 thf(f83,plain,(
% 1.29/1.06 ( ! [X0 : $i] : (($true = ($true => ((in @ X0 @ sK4) => (in @ X0 @ sK2))))) )),
% 1.29/1.06 inference(superposition,[status(thm)],[f52,f78])).
% 1.29/1.06 thf(f115,plain,(
% 1.29/1.06 ($true = ((in @ sK5 @ sK3) => (~ (in @ sK5 @ sK2))))),
% 1.29/1.06 inference(boolean_simplification,[status(thm)],[f110])).
% 1.29/1.06 thf(f110,plain,(
% 1.29/1.06 ($true = ((in @ sK5 @ sK3) => ((in @ sK5 @ sK2) => $false)))),
% 1.29/1.06 inference(superposition,[status(thm)],[f82,f107])).
% 1.29/1.06 thf(f107,plain,(
% 1.29/1.06 ((in @ sK5 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (in @ Y0 @ sK2)))) = $false)),
% 1.29/1.06 inference(boolean_simplification,[status(thm)],[f106])).
% 1.29/1.06 thf(f106,plain,(
% 1.29/1.06 (($true => (in @ sK5 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (in @ Y0 @ sK2))))) = $false)),
% 1.29/1.06 inference(backward_demodulation,[status(thm)],[f100,f103])).
% 1.29/1.06 thf(f82,plain,(
% 1.29/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X3) => ((in @ X2 @ X1) => (in @ X2 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (in @ Y0 @ X1)))))))) )),
% 1.29/1.06 inference(beta_eta_normalization,[status(thm)],[f81])).
% 1.29/1.06 thf(f81,plain,(
% 1.29/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X2 @ Y0) => ((in @ X2 @ X1) => (in @ X2 @ (dsetconstr @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ X1))))))) @ X3) = $true)) )),
% 1.29/1.06 inference(pi_clausification,[status(thm)],[f76])).
% 1.29/1.06 thf(f76,plain,(
% 1.29/1.06 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ Y0) => ((in @ X2 @ X1) => (in @ X2 @ (dsetconstr @ Y0 @ (^[Y1 : $i]: (in @ Y1 @ X1)))))))))) )),
% 1.29/1.06 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.29/1.06 thf(f75,plain,(
% 1.29/1.06 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ X1) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ X1))))))))) @ X2))) )),
% 1.29/1.06 inference(pi_clausification,[status(thm)],[f71])).
% 1.29/1.06 thf(f71,plain,(
% 1.29/1.06 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ X1) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (in @ Y2 @ X1)))))))))))) )),
% 1.29/1.06 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.29/1.06 thf(f70,plain,(
% 1.29/1.06 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (in @ Y3 @ Y0))))))))))) @ X1) = $true)) )),
% 1.29/1.06 inference(pi_clausification,[status(thm)],[f39])).
% 1.29/1.06 thf(f39,plain,(
% 1.29/1.06 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (in @ Y3 @ Y0)))))))))))))),
% 1.29/1.06 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.29/1.06 % SZS output end Proof for DTF2THF_10477
% 1.29/1.06 % (10687)------------------------------
% 1.29/1.06 % (10687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.06 % (10687)Termination reason: Refutation
% 1.29/1.06
% 1.29/1.06 % (10687)Memory used [KB]: 5756
% 1.29/1.06 % (10687)Time elapsed: 0.013 s
% 1.29/1.06 % (10687)Instructions burned: 31 (million)
% 1.29/1.06 % (10687)------------------------------
% 1.29/1.06 % (10687)------------------------------
% 1.29/1.06 % (10675)Success in time 0.037 s
%------------------------------------------------------------------------------