%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU731^2 : 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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:44 AM UTC 2026
% Result : Theorem 1.77s 1.54s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of formulae : 77 ( 74 unt; 0 typ; 0 def)
% Number of atoms : 842 ( 114 equ; 0 cnn)
% Maximal formula atoms : 6 ( 10 avg)
% Number of connectives : 1875 ( 6 ~; 0 |; 0 &;1386 @)
% ( 0 <=>; 317 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 9 con; 0-2 aty)
% ( 166 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 235 ( 177 ^; 58 !; 0 ?; 235 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
setminus: $i > $i > $i ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f221,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f216,f68]) ).
thf(f68,plain,
( ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) )
!= sK3 ),
inference(equality_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( $false
= ( ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) )
= sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( $false
= ( ( in @ sK3 @ ( powerset @ sK2 ) )
=> ( ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) )
= sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK2 ) )
=> ( ( setminus @ sK2 @ ( setminus @ sK2 @ Y0 ) )
= Y0 ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK2 ) )
=> ( ( setminus @ sK2 @ ( setminus @ sK2 @ Y0 ) )
= Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) )
= Y1 ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f50]) ).
thf(f50,plain,
( $false
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f45,f49]) ).
thf(f49,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f44]) ).
thf(f44,plain,
( $false
= ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f41,f43]) ).
thf(f43,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f40]) ).
thf(f40,plain,
( $false
= ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f27,f39]) ).
thf(f39,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f18,f20,f22,f19,f21]) ).
thf(f21,plain,
( doubleComplementE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( doubleComplementE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) )
=> ( in @ X2 @ X0 ) ) ) )
= doubleComplementE1 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
=> ( in @ X3 @ X1 ) ) ) )
= doubleComplementE1 ),
file('/export/starexec/sandbox/tmp/tmp.g1sG0tvbLl/DTF2THF_10587.p',doubleComplementE1) ).
thf(f19,plain,
( doubleComplementI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( doubleComplementI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) )
= doubleComplementI1 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) )
= doubleComplementI1 ),
file('/export/starexec/sandbox/tmp/tmp.g1sG0tvbLl/DTF2THF_10587.p',doubleComplementI1) ).
thf(f22,plain,
( setextT
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( setextT
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( setextT
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X0 )
=> ( in @ X3 @ X2 ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X0 ) ) )
=> ( X0 = X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setextT
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) )
=> ( X1 = X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.g1sG0tvbLl/DTF2THF_10587.p',setextT) ).
thf(f20,plain,
( complementT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( complementT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
= complementT_lem ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) )
= complementT_lem ),
file('/export/starexec/sandbox/tmp/tmp.g1sG0tvbLl/DTF2THF_10587.p',complementT_lem) ).
thf(f18,plain,
( ( ~ ( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ~ ( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( setminus @ X1 @ X0 ) )
= X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
= X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
= X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.g1sG0tvbLl/DTF2THF_10587.p',doubleComplementEq) ).
thf(f216,plain,
( ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) )
= sK3 ),
inference(equality_proxy_clausification,[status(thm)],[f207]) ).
thf(f207,plain,
( ( sK3
= ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f206]) ).
thf(f206,plain,
( $true
= ( $true
=> ( sK3
= ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f205,f115]) ).
thf(f115,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ Y0 @ ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) )
=> ( in @ Y0 @ sK3 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f105]) ).
thf(f105,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ Y0 @ ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) )
=> ( in @ Y0 @ sK3 ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f97,f57]) ).
thf(f57,plain,
( ( in @ sK3 @ ( powerset @ sK2 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
=> ( in @ Y0 @ X2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ ( setminus @ X1 @ ( setminus @ X1 @ Y0 ) ) )
=> ( in @ Y1 @ Y0 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ ( setminus @ X1 @ ( setminus @ X1 @ Y0 ) ) )
=> ( in @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f205,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ Y0 @ ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) )
=> ( in @ Y0 @ sK3 ) ) ) )
=> ( sK3
= ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f204]) ).
thf(f204,plain,
( ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ Y0 @ ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) )
=> ( in @ Y0 @ sK3 ) ) ) )
=> ( sK3
= ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f203,f80]) ).
thf(f80,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ Y0 @ sK3 )
=> ( in @ Y0 @ ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ Y0 @ sK3 )
=> ( in @ Y0 @ ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f70,f57]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f203,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ Y0 @ sK3 )
=> ( in @ Y0 @ ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ Y0 @ ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) )
=> ( in @ Y0 @ sK3 ) ) ) )
=> ( sK3
= ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f183]) ).
thf(f183,plain,
( ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ Y0 @ sK3 )
=> ( in @ Y0 @ ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ Y0 @ ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) )
=> ( in @ Y0 @ sK3 ) ) ) )
=> ( sK3
= ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f166,f67]) ).
thf(f67,plain,
( ( in @ ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) @ ( powerset @ sK2 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f65]) ).
thf(f65,plain,
( $true
= ( $true
=> ( in @ ( setminus @ sK2 @ ( setminus @ sK2 @ sK3 ) ) @ ( powerset @ sK2 ) ) ) ),
inference(superposition,[status(thm)],[f36,f63]) ).
thf(f63,plain,
( ( in @ ( setminus @ sK2 @ sK3 ) @ ( powerset @ sK2 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true
=> ( in @ ( setminus @ sK2 @ sK3 ) @ ( powerset @ sK2 ) ) )
= $true ),
inference(superposition,[status(thm)],[f36,f57]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ Y0 ) @ ( powerset @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ Y0 ) @ ( powerset @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f166,plain,
! [X1: $i] :
( ( ( in @ X1 @ ( powerset @ sK2 ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ Y0 @ sK3 )
=> ( in @ Y0 @ X1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ sK3 ) ) ) )
=> ( sK3 = X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f164]) ).
thf(f164,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y1 @ sK3 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ sK3 ) ) ) )
=> ( sK3 = Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y1 @ sK3 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ sK3 ) ) ) )
=> ( sK3 = Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y1 @ sK3 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ sK3 ) ) ) )
=> ( sK3 = Y0 ) ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f132,f57]) ).
thf(f132,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ X2 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X2 ) ) ) )
=> ( X2 = Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f131]) ).
thf(f131,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) )
=> ( Y0 = Y1 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f126]) ).
thf(f126,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) )
=> ( Y0 = Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f125]) ).
thf(f125,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU731^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n002.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 12:32:33 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
% 0.29/0.49 ---- Original DTF file ---
% 0.29/0.49 thf(spec,logic,$$dhol).
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 % File : SEU731^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.49 % Domain : Set Theory
% 0.29/0.49 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.29/0.49 % Version : Especial > Reduced > Especial.
% 0.29/0.49 % English : (! A:i.! X:i.in X (powerset A) -> X = setminus A (setminus A X))
% 0.29/0.49
% 0.29/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.49 % Source : [Bro08]
% 0.29/0.49 % Names : ZFC233l [Bro08]
% 0.29/0.49
% 0.29/0.49 % Status : Theorem
% 0.29/0.49 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.29/0.49 % Syntax : Number of formulae : 12 ( 4 unt; 7 typ; 4 def)
% 0.29/0.49 % Number of atoms : 33 ( 6 equ; 0 cnn)
% 0.29/0.49 % Maximal formula atoms : 6 ( 6 avg)
% 0.29/0.49 % Number of connectives : 79 ( 0 ~; 0 |; 0 &; 59 @)
% 0.29/0.49 % ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% 0.29/0.49 % Maximal formula depth : 10 ( 3 avg)
% 0.29/0.49 % Number of types : 2 ( 0 usr)
% 0.29/0.49 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.29/0.49 % Number of symbols : 8 ( 7 usr; 4 con; 0-2 aty)
% 0.29/0.49 % Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% 0.29/0.49 % SPC : TH0_THM_EQU_NAR
% 0.29/0.49
% 0.29/0.49 % Comments : http://mathgate.info/detsetitem.php?id=291
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 thf(in_type,type,
% 0.29/0.49 in: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(powerset_type,type,
% 0.29/0.49 powerset: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(setminus_type,type,
% 0.29/0.49 setminus: $i > $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(complementT_lem_type,type,
% 0.29/0.49 complementT_lem: $o ).
% 0.29/0.49
% 0.29/0.49 thf(complementT_lem,definition,
% 0.29/0.49 ( complementT_lem
% 0.29/0.49 = ( ! [A: $i,X: $i] :
% 0.29/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.49 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(setextT_type,type,
% 0.29/0.49 setextT: $o ).
% 0.29/0.49
% 0.29/0.49 thf(setextT,definition,
% 0.29/0.49 ( setextT
% 0.29/0.49 = ( ! [A: $i,X: $i] :
% 0.29/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.49 => ! [Y: $i] :
% 0.29/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.49 => ( ! [Xx: $i] :
% 0.29/0.49 ( ( in @ Xx @ A )
% 0.29/0.49 => ( ( in @ Xx @ X )
% 0.29/0.49 => ( in @ Xx @ Y ) ) )
% 0.29/0.49 => ( ! [Xx: $i] :
% 0.29/0.49 ( ( in @ Xx @ A )
% 0.29/0.49 => ( ( in @ Xx @ Y )
% 0.29/0.49 => ( in @ Xx @ X ) ) )
% 0.29/0.49 => ( X = Y ) ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(doubleComplementI1_type,type,
% 0.29/0.49 doubleComplementI1: $o ).
% 0.29/0.49
% 0.29/0.49 thf(doubleComplementI1,definition,
% 0.29/0.49 ( doubleComplementI1
% 0.29/0.49 = ( ! [A: $i,X: $i] :
% 0.29/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.49 => ! [Xx: $i] :
% 0.29/0.49 ( ( in @ Xx @ A )
% 0.29/0.49 => ( ( in @ Xx @ X )
% 0.29/0.49 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(doubleComplementE1_type,type,
% 0.29/0.49 doubleComplementE1: $o ).
% 0.29/0.49
% 0.29/0.49 thf(doubleComplementE1,definition,
% 0.29/0.49 ( doubleComplementE1
% 0.29/0.49 = ( ! [A: $i,X: $i] :
% 0.29/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.49 => ! [Xx: $i] :
% 0.29/0.49 ( ( in @ Xx @ A )
% 0.29/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.29/0.49 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(doubleComplementEq,conjecture,
% 0.29/0.49 ( complementT_lem
% 0.29/0.49 => ( setextT
% 0.29/0.49 => ( doubleComplementI1
% 0.29/0.49 => ( doubleComplementE1
% 0.29/0.49 => ! [A: $i,X: $i] :
% 0.29/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.49 => ( X
% 0.29/0.49 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 ------------------------
% 1.70/1.43 ---- Embedded in THF ---
% 1.70/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.70/1.43 %%% Generated on Tue Feb 24 12:32:34 EST 2026
% 1.70/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.70/1.43 %%% Logic specification used:
% 1.70/1.43 %%% thf(spec, logic, $$dhol).
% 1.70/1.43
% 1.70/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.g1sG0tvbLl/DTF2DTF10587.p
% See solution above
% 1.70/1.43 ------------------------
% 1.70/1.44 ---- Cleaned THF ---
% 1.70/1.44 thf(in_type,type,
% 1.70/1.44 in: $i > $i > $o ).
% 1.70/1.44
% 1.70/1.44 thf(powerset_type,type,
% 1.70/1.44 powerset: $i > $i ).
% 1.70/1.44
% 1.70/1.44 thf(setminus_type,type,
% 1.70/1.44 setminus: $i > $i > $i ).
% 1.70/1.44
% 1.70/1.44 thf(complementT_lem_type,type,
% 1.70/1.44 complementT_lem: $o ).
% 1.70/1.44
% 1.70/1.44 thf(complementT_lem,definition,
% 1.70/1.44 ( complementT_lem
% 1.70/1.44 = ( ! [A: $i,X: $i] :
% 1.70/1.44 ( ( in @ X @ ( powerset @ A ) )
% 1.70/1.44 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 1.70/1.44
% 1.70/1.44 thf(setextT_type,type,
% 1.70/1.44 setextT: $o ).
% 1.70/1.44
% 1.70/1.44 thf(setextT,definition,
% 1.70/1.44 ( setextT
% 1.70/1.44 = ( ! [A: $i,X: $i] :
% 1.70/1.44 ( ( in @ X @ ( powerset @ A ) )
% 1.70/1.44 => ! [Y: $i] :
% 1.70/1.44 ( ( in @ Y @ ( powerset @ A ) )
% 1.70/1.44 => ( ! [Xx: $i] :
% 1.70/1.44 ( ( in @ Xx @ A )
% 1.70/1.44 => ( ( in @ Xx @ X )
% 1.70/1.44 => ( in @ Xx @ Y ) ) )
% 1.70/1.44 => ( ! [Xx: $i] :
% 1.70/1.44 ( ( in @ Xx @ A )
% 1.70/1.44 => ( ( in @ Xx @ Y )
% 1.70/1.44 => ( in @ Xx @ X ) ) )
% 1.70/1.44 => ( X = Y ) ) ) ) ) ) ) ).
% 1.70/1.44
% 1.70/1.44 thf(doubleComplementI1_type,type,
% 1.70/1.44 doubleComplementI1: $o ).
% 1.70/1.44
% 1.70/1.44 thf(doubleComplementI1,definition,
% 1.70/1.44 ( doubleComplementI1
% 1.70/1.44 = ( ! [A: $i,X: $i] :
% 1.70/1.44 ( ( in @ X @ ( powerset @ A ) )
% 1.70/1.44 => ! [Xx: $i] :
% 1.70/1.44 ( ( in @ Xx @ A )
% 1.70/1.44 => ( ( in @ Xx @ X )
% 1.70/1.44 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 1.70/1.44
% 1.70/1.44 thf(doubleComplementE1_type,type,
% 1.70/1.44 doubleComplementE1: $o ).
% 1.70/1.44
% 1.70/1.44 thf(doubleComplementE1,definition,
% 1.70/1.44 ( doubleComplementE1
% 1.70/1.44 = ( ! [A: $i,X: $i] :
% 1.70/1.44 ( ( in @ X @ ( powerset @ A ) )
% 1.70/1.44 => ! [Xx: $i] :
% 1.70/1.44 ( ( in @ Xx @ A )
% 1.70/1.44 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 1.70/1.44 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 1.70/1.44
% 1.70/1.44 thf(doubleComplementEq,conjecture,
% 1.70/1.44 ( complementT_lem
% 1.70/1.44 => ( setextT
% 1.70/1.44 => ( doubleComplementI1
% 1.70/1.44 => ( doubleComplementE1
% 1.70/1.44 => ! [A: $i,X: $i] :
% 1.70/1.44 ( ( in @ X @ ( powerset @ A ) )
% 1.70/1.44 => ( X
% 1.70/1.44 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 1.70/1.44 ------------------------
% 1.70/1.46 % (10694)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10587 for (2999ds/2Mi)
% 1.70/1.46 % (10695)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_10587 for (2999ds/2Mi)
% 1.70/1.46 % (10692)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_10587 for (2999ds/4Mi)
% 1.70/1.46 % (10696)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_10587 for (2999ds/275Mi)
% 1.70/1.46 % (10693)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_10587 for (2999ds/27Mi)
% 1.70/1.46 % (10697)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10587 for (2999ds/18Mi)
% 1.70/1.46 % (10691)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10587 for (2999ds/183Mi)
% 1.70/1.47 % (10694)Instruction limit reached!
% 1.70/1.47 % (10694)------------------------------
% 1.70/1.47 % (10694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.47 % (10694)Termination reason: Unknown
% 1.70/1.47 % (10694)Termination phase: Property scanning
% 1.70/1.47 % (10695)Instruction limit reached!
% 1.70/1.47 % (10695)------------------------------
% 1.70/1.47 % (10695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.47 % (10695)Termination reason: Unknown
% 1.70/1.47 % (10695)Termination phase: Property scanning
% 1.70/1.47
% 1.70/1.47 % (10695)Memory used [KB]: 1023
% 1.70/1.47 % (10695)Time elapsed: 0.003 s
% 1.70/1.47 % (10695)Instructions burned: 3 (million)
% 1.70/1.47 % (10695)------------------------------
% 1.70/1.47 % (10695)------------------------------
% 1.70/1.47
% 1.70/1.47 % (10694)Memory used [KB]: 1023
% 1.70/1.47 % (10694)Time elapsed: 0.003 s
% 1.70/1.47 % (10694)Instructions burned: 3 (million)
% 1.70/1.47 % (10694)------------------------------
% 1.70/1.47 % (10694)------------------------------
% 1.70/1.47 % (10692)Instruction limit reached!
% 1.70/1.47 % (10692)------------------------------
% 1.70/1.47 % (10692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.47 % (10692)Termination reason: Unknown
% 1.70/1.47 % (10692)Termination phase: Saturation
% 1.70/1.47
% 1.70/1.47 % (10692)Memory used [KB]: 1023
% 1.70/1.47 % (10692)Time elapsed: 0.004 s
% 1.70/1.47 % (10692)Instructions burned: 4 (million)
% 1.70/1.47 % (10692)------------------------------
% 1.70/1.47 % (10692)------------------------------
% 1.70/1.47 % (10697)Instruction limit reached!
% 1.70/1.47 % (10697)------------------------------
% 1.70/1.47 % (10697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.47 % (10697)Termination reason: Unknown
% 1.70/1.47 % (10697)Termination phase: Saturation
% 1.70/1.47
% 1.70/1.47 % (10697)Memory used [KB]: 5628
% 1.70/1.47 % (10697)Time elapsed: 0.012 s
% 1.70/1.47 % (10697)Instructions burned: 19 (million)
% 1.70/1.47 % (10697)------------------------------
% 1.70/1.47 % (10697)------------------------------
% 1.70/1.48 % (10693)Instruction limit reached!
% 1.70/1.48 % (10693)------------------------------
% 1.70/1.48 % (10693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.48 % (10693)Termination reason: Unknown
% 1.70/1.48 % (10693)Termination phase: Saturation
% 1.70/1.48
% 1.70/1.48 % (10693)Memory used [KB]: 5628
% 1.70/1.48 % (10693)Time elapsed: 0.016 s
% 1.70/1.48 % (10693)Instructions burned: 28 (million)
% 1.70/1.48 % (10693)------------------------------
% 1.70/1.48 % (10693)------------------------------
% 1.70/1.48 % (10698)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10587 for (2999ds/3Mi)
% 1.70/1.48 % (10699)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_10587 for (2999ds/37Mi)
% 1.70/1.48 % (10700)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_10587 for (2999ds/15Mi)
% 1.70/1.48 % (10698)Instruction limit reached!
% 1.70/1.48 % (10698)------------------------------
% 1.70/1.48 % (10698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.48 % (10698)Termination reason: Unknown
% 1.70/1.48 % (10698)Termination phase: Saturation
% 1.70/1.48
% 1.70/1.48 % (10698)Memory used [KB]: 1023
% 1.70/1.48 % (10698)Time elapsed: 0.004 s
% 1.70/1.48 % (10698)Instructions burned: 4 (million)
% 1.70/1.48 % (10698)------------------------------
% 1.70/1.48 % (10698)------------------------------
% 1.70/1.49 % (10700)Instruction limit reached!
% 1.70/1.49 % (10700)------------------------------
% 1.70/1.49 % (10700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.49 % (10700)Termination reason: Unknown
% 1.70/1.49 % (10700)Termination phase: Saturation
% 1.70/1.49
% 1.70/1.49 % (10700)Memory used [KB]: 5628
% 1.70/1.49 % (10700)Time elapsed: 0.009 s
% 1.70/1.49 % (10700)Instructions burned: 15 (million)
% 1.70/1.49 % (10700)------------------------------
% 1.70/1.49 % (10700)------------------------------
% 1.70/1.49 % (10701)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_10587 for (2999ds/3Mi)
% 1.70/1.49 % (10701)Instruction limit reached!
% 1.70/1.49 % (10701)------------------------------
% 1.70/1.49 % (10701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.49 % (10701)Termination reason: Unknown
% 1.70/1.49 % (10701)Termination phase: Preprocessing 3
% 1.70/1.49
% 1.70/1.49 % (10701)Memory used [KB]: 1023
% 1.70/1.49 % (10701)Time elapsed: 0.003 s
% 1.70/1.49 % (10701)Instructions burned: 3 (million)
% 1.70/1.49 % (10701)------------------------------
% 1.70/1.49 % (10701)------------------------------
% 1.70/1.49 % (10702)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_10587 for (2999ds/1041Mi)
% 1.77/1.50 % (10699)Instruction limit reached!
% 1.77/1.50 % (10699)------------------------------
% 1.77/1.50 % (10699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.50 % (10699)Termination reason: Unknown
% 1.77/1.50 % (10699)Termination phase: Saturation
% 1.77/1.50
% 1.77/1.50 % (10699)Memory used [KB]: 5628
% 1.77/1.50 % (10699)Time elapsed: 0.019 s
% 1.77/1.50 % (10699)Instructions burned: 37 (million)
% 1.77/1.50 % (10699)------------------------------
% 1.77/1.50 % (10699)------------------------------
% 1.77/1.50 % (10703)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10587 for (2999ds/7Mi)
% 1.77/1.50 % (10703)Instruction limit reached!
% 1.77/1.50 % (10703)------------------------------
% 1.77/1.50 % (10703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.50 % (10703)Termination reason: Unknown
% 1.77/1.50 % (10703)Termination phase: Saturation
% 1.77/1.50
% 1.77/1.50 % (10703)Memory used [KB]: 1023
% 1.77/1.50 % (10703)Time elapsed: 0.005 s
% 1.77/1.50 % (10703)Instructions burned: 7 (million)
% 1.77/1.50 % (10703)------------------------------
% 1.77/1.50 % (10703)------------------------------
% 1.77/1.51 % (10704)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10587 for (2999ds/16Mi)
% 1.77/1.51 % (10705)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_10587 for (2999ds/3Mi)
% 1.77/1.51 % (10705)Instruction limit reached!
% 1.77/1.51 % (10705)------------------------------
% 1.77/1.51 % (10705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.51 % (10705)Termination reason: Unknown
% 1.77/1.51 % (10705)Termination phase: Property scanning
% 1.77/1.51
% 1.77/1.51 % (10705)Memory used [KB]: 1023
% 1.77/1.51 % (10705)Time elapsed: 0.003 s
% 1.77/1.51 % (10705)Instructions burned: 3 (million)
% 1.77/1.51 % (10705)------------------------------
% 1.77/1.51 % (10705)------------------------------
% 1.77/1.52 % (10706)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10587 for (2999ds/3Mi)
% 1.77/1.52 % (10704)Instruction limit reached!
% 1.77/1.52 % (10704)------------------------------
% 1.77/1.52 % (10704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.52 % (10704)Termination reason: Unknown
% 1.77/1.52 % (10704)Termination phase: Saturation
% 1.77/1.52
% 1.77/1.52 % (10704)Memory used [KB]: 5884
% 1.77/1.52 % (10704)Time elapsed: 0.011 s
% 1.77/1.52 % (10704)Instructions burned: 17 (million)
% 1.77/1.52 % (10704)------------------------------
% 1.77/1.52 % (10704)------------------------------
% 1.77/1.52 % (10706)Instruction limit reached!
% 1.77/1.52 % (10706)------------------------------
% 1.77/1.52 % (10706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.52 % (10706)Termination reason: Unknown
% 1.77/1.52 % (10706)Termination phase: Property scanning
% 1.77/1.52
% 1.77/1.52 % (10706)Memory used [KB]: 1023
% 1.77/1.52 % (10706)Time elapsed: 0.003 s
% 1.77/1.52 % (10706)Instructions burned: 3 (million)
% 1.77/1.52 % (10706)------------------------------
% 1.77/1.52 % (10706)------------------------------
% 1.77/1.52 % (10707)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10587 for (2999ds/7Mi)
% 1.77/1.52 % (10707)Refutation not found, incomplete strategy
% 1.77/1.52 % (10707)------------------------------
% 1.77/1.52 % (10707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.52 % (10707)Termination reason: Refutation not found, incomplete strategy
% 1.77/1.52
% 1.77/1.52
% 1.77/1.52 % (10707)Memory used [KB]: 5500
% 1.77/1.52 % (10707)Time elapsed: 0.004 s
% 1.77/1.52 % (10707)Instructions burned: 5 (million)
% 1.77/1.52 % (10707)------------------------------
% 1.77/1.52 % (10707)------------------------------
% 1.77/1.53 % (10708)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10587 for (2999ds/3Mi)
% 1.77/1.53 % (10708)Instruction limit reached!
% 1.77/1.53 % (10708)------------------------------
% 1.77/1.53 % (10708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.53 % (10708)Termination reason: Unknown
% 1.77/1.53 % (10708)Termination phase: Function definition elimination
% 1.77/1.53
% 1.77/1.53 % (10708)Memory used [KB]: 1023
% 1.77/1.53 % (10708)Time elapsed: 0.003 s
% 1.77/1.53 % (10708)Instructions burned: 4 (million)
% 1.77/1.53 % (10708)------------------------------
% 1.77/1.53 % (10708)------------------------------
% 1.77/1.53 % (10702)First to succeed.
% 1.77/1.53 % (10709)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10587 for (2999ds/4Mi)
% 1.77/1.53 % (10710)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10587 for (2999ds/18Mi)
% 1.77/1.53 % (10709)Instruction limit reached!
% 1.77/1.53 % (10709)------------------------------
% 1.77/1.53 % (10709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.53 % (10709)Termination reason: Unknown
% 1.77/1.53 % (10709)Termination phase: Saturation
% 1.77/1.53
% 1.77/1.53 % (10709)Memory used [KB]: 5500
% 1.77/1.53 % (10709)Time elapsed: 0.004 s
% 1.77/1.53 % (10709)Instructions burned: 5 (million)
% 1.77/1.53 % (10709)------------------------------
% 1.77/1.53 % (10709)------------------------------
% 1.77/1.54 % (10702)Refutation found. Thanks to Tanya!
% 1.77/1.54 % SZS status Theorem for DTF2THF_10587
% 1.77/1.54 % SZS output start Proof for DTF2THF_10587
% 1.77/1.54 thf(func_def_0, type, in: $i > $i > $o).
% 1.77/1.54 thf(func_def_1, type, powerset: $i > $i).
% 1.77/1.54 thf(func_def_2, type, setminus: $i > $i > $i).
% 1.77/1.54 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)).
% 1.77/1.54 thf(f221,plain,(
% 1.77/1.54 $false),
% 1.77/1.54 inference(subsumption_resolution,[status(thm)],[f216,f68])).
% 1.77/1.54 thf(f68,plain,(
% 1.77/1.54 ((setminus @ sK2 @ (setminus @ sK2 @ sK3)) != sK3)),
% 1.77/1.54 inference(equality_proxy_clausification,[status(thm)],[f56])).
% 1.77/1.54 thf(f56,plain,(
% 1.77/1.54 ($false = ((setminus @ sK2 @ (setminus @ sK2 @ sK3)) = sK3))),
% 1.77/1.54 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.77/1.54 thf(f55,plain,(
% 1.77/1.54 ($false = ((in @ sK3 @ (powerset @ sK2)) => ((setminus @ sK2 @ (setminus @ sK2 @ sK3)) = sK3)))),
% 1.77/1.54 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.77/1.54 thf(f54,plain,(
% 1.77/1.54 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((setminus @ sK2 @ (setminus @ sK2 @ Y0)) = Y0))) @ sK3))),
% 1.77/1.54 inference(sigma_clausification,[status(thm)],[f53])).
% 1.77/1.54 thf(f53,plain,(
% 1.77/1.54 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((setminus @ sK2 @ (setminus @ sK2 @ Y0)) = Y0)))))),
% 1.77/1.54 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.77/1.54 thf(f52,plain,(
% 1.77/1.54 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))) @ sK2))),
% 1.77/1.54 inference(sigma_clausification,[status(thm)],[f51])).
% 1.77/1.54 thf(f51,plain,(
% 1.77/1.54 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1)))))))),
% 1.77/1.54 inference(boolean_simplification,[status(thm)],[f50])).
% 1.77/1.54 thf(f50,plain,(
% 1.77/1.54 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))),
% 1.77/1.54 inference(backward_demodulation,[status(thm)],[f45,f49])).
% 1.77/1.54 thf(f49,plain,(
% 1.77/1.54 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))) => (in @ Y2 @ Y1)))))))))) = $true)),
% 1.77/1.54 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.77/1.54 thf(f45,plain,(
% 1.77/1.54 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))) => (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))),
% 1.77/1.54 inference(boolean_simplification,[status(thm)],[f44])).
% 1.77/1.54 thf(f44,plain,(
% 1.77/1.54 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))) => (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1)))))))))),
% 1.77/1.54 inference(backward_demodulation,[status(thm)],[f41,f43])).
% 1.77/1.54 thf(f43,plain,(
% 1.77/1.54 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) = $true)),
% 1.77/1.54 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.77/1.54 thf(f41,plain,(
% 1.77/1.54 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))) => (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1)))))))))),
% 1.77/1.54 inference(boolean_simplification,[status(thm)],[f40])).
% 1.77/1.54 thf(f40,plain,(
% 1.77/1.54 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))) => (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))))),
% 1.77/1.54 inference(backward_demodulation,[status(thm)],[f27,f39])).
% 1.77/1.54 thf(f39,plain,(
% 1.77/1.54 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2))))))))))) = $true)),
% 1.77/1.54 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.77/1.54 thf(f27,plain,(
% 1.77/1.54 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))) => (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))))),
% 1.77/1.54 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.77/1.54 thf(f24,plain,(
% 1.77/1.54 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))) => (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1)))))))))))),
% 1.77/1.54 inference(not_proxy_clausification,[status(thm)],[f23])).
% 1.77/1.54 thf(f23,plain,(
% 1.77/1.54 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))) => (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))))) = $true)),
% 1.77/1.54 inference(definition_unfolding,[status(thm)],[f18,f20,f22,f19,f21])).
% 1.77/1.54 thf(f21,plain,(
% 1.77/1.54 (doubleComplementE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))) => (in @ Y2 @ Y1)))))))))))),
% 1.77/1.54 inference(cnf_transformation,[status(thm)],[f9])).
% 1.77/1.54 thf(f9,plain,(
% 1.77/1.54 (doubleComplementE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))) => (in @ Y2 @ Y1)))))))))))),
% 1.77/1.54 inference(fool_elimination,[status(thm)],[f8])).
% 1.77/1.54 thf(f8,plain,(
% 1.77/1.54 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ X1) => ((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0))) => (in @ X2 @ X0)))) = doubleComplementE1)),
% 1.77/1.54 inference(rectify,[status(thm)],[f4])).
% 1.77/1.54 thf(f4,axiom,(
% 1.77/1.54 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (setminus @ X0 @ X1))) => (in @ X3 @ X1)))) = doubleComplementE1)),
% 1.77/1.54 file('/export/starexec/sandbox/tmp/tmp.g1sG0tvbLl/DTF2THF_10587.p',doubleComplementE1)).
% 1.77/1.54 thf(f19,plain,(
% 1.77/1.54 (doubleComplementI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))))),
% 1.77/1.54 inference(cnf_transformation,[status(thm)],[f15])).
% 1.77/1.54 thf(f15,plain,(
% 1.77/1.54 (doubleComplementI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))))),
% 1.77/1.54 inference(fool_elimination,[status(thm)],[f14])).
% 1.77/1.54 thf(f14,plain,(
% 1.77/1.54 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))) = doubleComplementI1)),
% 1.77/1.54 inference(rectify,[status(thm)],[f3])).
% 1.77/1.54 thf(f3,axiom,(
% 1.77/1.54 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))) = doubleComplementI1)),
% 1.77/1.54 file('/export/starexec/sandbox/tmp/tmp.g1sG0tvbLl/DTF2THF_10587.p',doubleComplementI1)).
% 1.77/1.54 thf(f22,plain,(
% 1.77/1.54 (setextT = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2))))))))))))),
% 1.77/1.54 inference(cnf_transformation,[status(thm)],[f17])).
% 1.77/1.54 thf(f17,plain,(
% 1.77/1.54 (setextT = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2))))))))))))),
% 1.77/1.54 inference(fool_elimination,[status(thm)],[f16])).
% 1.77/1.54 thf(f16,plain,(
% 1.77/1.54 (setextT = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (! [X4 : $i] : ((in @ X4 @ X1) => ((in @ X4 @ X2) => (in @ X4 @ X0))) => (X0 = X2))))))),
% 1.77/1.54 inference(rectify,[status(thm)],[f2])).
% 1.77/1.54 thf(f2,axiom,(
% 1.77/1.54 (setextT = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) => (in @ X3 @ X1))) => (X1 = X2))))))),
% 1.77/1.54 file('/export/starexec/sandbox/tmp/tmp.g1sG0tvbLl/DTF2THF_10587.p',setextT)).
% 1.77/1.54 thf(f20,plain,(
% 1.77/1.54 (complementT_lem = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ Y0))))))))),
% 1.77/1.54 inference(cnf_transformation,[status(thm)],[f11])).
% 1.77/1.54 thf(f11,plain,(
% 1.77/1.54 (complementT_lem = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ Y0))))))))),
% 1.77/1.54 inference(fool_elimination,[status(thm)],[f10])).
% 1.77/1.54 thf(f10,plain,(
% 1.77/1.54 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = complementT_lem)),
% 1.77/1.54 inference(rectify,[status(thm)],[f1])).
% 1.77/1.54 thf(f1,axiom,(
% 1.77/1.54 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = complementT_lem)),
% 1.77/1.54 file('/export/starexec/sandbox/tmp/tmp.g1sG0tvbLl/DTF2THF_10587.p',complementT_lem)).
% 1.77/1.54 thf(f18,plain,(
% 1.77/1.54 ((~ (complementT_lem => (setextT => (doubleComplementI1 => (doubleComplementE1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))))) = $true)),
% 1.77/1.54 inference(cnf_transformation,[status(thm)],[f13])).
% 1.77/1.54 thf(f13,plain,(
% 1.77/1.54 ((~ (complementT_lem => (setextT => (doubleComplementI1 => (doubleComplementE1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))))) = $true)),
% 1.77/1.54 inference(fool_elimination,[status(thm)],[f12])).
% 1.77/1.54 thf(f12,plain,(
% 1.77/1.54 ~(complementT_lem => (setextT => (doubleComplementI1 => (doubleComplementE1 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ((setminus @ X1 @ (setminus @ X1 @ X0)) = X0))))))),
% 1.77/1.54 inference(rectify,[status(thm)],[f6])).
% 1.77/1.54 thf(f6,negated_conjecture,(
% 1.77/1.54 ~(complementT_lem => (setextT => (doubleComplementI1 => (doubleComplementE1 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ((setminus @ X0 @ (setminus @ X0 @ X1)) = X1))))))),
% 1.77/1.54 inference(negated_conjecture,[status(cth)],[f5])).
% 1.77/1.54 thf(f5,conjecture,(
% 1.77/1.54 complementT_lem => (setextT => (doubleComplementI1 => (doubleComplementE1 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ((setminus @ X0 @ (setminus @ X0 @ X1)) = X1)))))),
% 1.77/1.54 file('/export/starexec/sandbox/tmp/tmp.g1sG0tvbLl/DTF2THF_10587.p',doubleComplementEq)).
% 1.77/1.54 thf(f216,plain,(
% 1.77/1.54 ((setminus @ sK2 @ (setminus @ sK2 @ sK3)) = sK3)),
% 1.77/1.54 inference(equality_proxy_clausification,[status(thm)],[f207])).
% 1.77/1.54 thf(f207,plain,(
% 1.77/1.54 ((sK3 = (setminus @ sK2 @ (setminus @ sK2 @ sK3))) = $true)),
% 1.77/1.54 inference(boolean_simplification,[status(thm)],[f206])).
% 1.77/1.54 thf(f206,plain,(
% 1.77/1.54 ($true = ($true => (sK3 = (setminus @ sK2 @ (setminus @ sK2 @ sK3)))))),
% 1.77/1.54 inference(forward_demodulation,[status(thm)],[f205,f115])).
% 1.77/1.54 thf(f115,plain,(
% 1.77/1.54 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))) => (in @ Y0 @ sK3))))) = $true)),
% 1.77/1.54 inference(boolean_simplification,[status(thm)],[f105])).
% 1.77/1.54 thf(f105,plain,(
% 1.77/1.54 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))) => (in @ Y0 @ sK3)))))) = $true)),
% 1.77/1.54 inference(superposition,[status(thm)],[f97,f57])).
% 1.77/1.54 thf(f57,plain,(
% 1.77/1.54 ((in @ sK3 @ (powerset @ sK2)) = $true)),
% 1.77/1.54 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.77/1.54 thf(f97,plain,(
% 1.77/1.54 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X2 @ (powerset @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ Y0 @ (setminus @ X1 @ (setminus @ X1 @ X2))) => (in @ Y0 @ X2)))))))) )),
% 1.77/1.54 inference(beta_eta_normalization,[status(thm)],[f96])).
% 1.77/1.54 thf(f96,plain,(
% 1.77/1.54 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ Y1 @ (setminus @ X1 @ (setminus @ X1 @ Y0))) => (in @ Y1 @ Y0))))))) @ X2) = $true)) )),
% 1.77/1.54 inference(pi_clausification,[status(thm)],[f89])).
% 1.77/1.54 thf(f89,plain,(
% 1.77/1.54 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ Y1 @ (setminus @ X1 @ (setminus @ X1 @ Y0))) => (in @ Y1 @ Y0)))))))) = $true)) )),
% 1.77/1.54 inference(beta_eta_normalization,[status(thm)],[f88])).
% 1.77/1.54 thf(f88,plain,(
% 1.77/1.54 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))) => (in @ Y2 @ Y1))))))))) @ X1) = $true)) )),
% 1.77/1.54 inference(pi_clausification,[status(thm)],[f49])).
% 1.77/1.54 thf(f205,plain,(
% 1.77/1.54 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))) => (in @ Y0 @ sK3))))) => (sK3 = (setminus @ sK2 @ (setminus @ sK2 @ sK3)))))),
% 1.77/1.54 inference(boolean_simplification,[status(thm)],[f204])).
% 1.77/1.54 thf(f204,plain,(
% 1.77/1.54 (($true => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))) => (in @ Y0 @ sK3))))) => (sK3 = (setminus @ sK2 @ (setminus @ sK2 @ sK3))))) = $true)),
% 1.77/1.54 inference(forward_demodulation,[status(thm)],[f203,f80])).
% 1.77/1.54 thf(f80,plain,(
% 1.77/1.54 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ sK3) => (in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))))))) = $true)),
% 1.77/1.54 inference(boolean_simplification,[status(thm)],[f76])).
% 1.77/1.54 thf(f76,plain,(
% 1.77/1.54 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ sK3) => (in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3)))))))) = $true)),
% 1.77/1.54 inference(superposition,[status(thm)],[f70,f57])).
% 1.77/1.54 thf(f70,plain,(
% 1.77/1.54 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ (setminus @ X2 @ (setminus @ X2 @ X1)))))))) = $true)) )),
% 1.77/1.54 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.77/1.54 thf(f69,plain,(
% 1.77/1.54 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ X1) => (in @ Y1 @ (setminus @ Y0 @ (setminus @ Y0 @ X1))))))))) @ X2) = $true)) )),
% 1.77/1.54 inference(pi_clausification,[status(thm)],[f47])).
% 1.77/1.54 thf(f47,plain,(
% 1.77/1.54 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ X1) => (in @ Y1 @ (setminus @ Y0 @ (setminus @ Y0 @ X1)))))))))) = $true)) )),
% 1.77/1.54 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.77/1.54 thf(f46,plain,(
% 1.77/1.54 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))))))))))) @ X1) = $true)) )),
% 1.77/1.54 inference(pi_clausification,[status(thm)],[f43])).
% 1.77/1.54 thf(f203,plain,(
% 1.77/1.54 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ sK3) => (in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))) => (in @ Y0 @ sK3))))) => (sK3 = (setminus @ sK2 @ (setminus @ sK2 @ sK3))))) = $true)),
% 1.77/1.54 inference(boolean_simplification,[status(thm)],[f183])).
% 1.77/1.54 thf(f183,plain,(
% 1.77/1.54 (($true => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ sK3) => (in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))) => (in @ Y0 @ sK3))))) => (sK3 = (setminus @ sK2 @ (setminus @ sK2 @ sK3)))))) = $true)),
% 1.77/1.54 inference(superposition,[status(thm)],[f166,f67])).
% 1.77/1.54 thf(f67,plain,(
% 1.77/1.54 ((in @ (setminus @ sK2 @ (setminus @ sK2 @ sK3)) @ (powerset @ sK2)) = $true)),
% 1.77/1.54 inference(boolean_simplification,[status(thm)],[f65])).
% 1.77/1.54 thf(f65,plain,(
% 1.77/1.54 ($true = ($true => (in @ (setminus @ sK2 @ (setminus @ sK2 @ sK3)) @ (powerset @ sK2))))),
% 1.77/1.54 inference(superposition,[status(thm)],[f36,f63])).
% 1.77/1.54 thf(f63,plain,(
% 1.77/1.54 ((in @ (setminus @ sK2 @ sK3) @ (powerset @ sK2)) = $true)),
% 1.77/1.54 inference(boolean_simplification,[status(thm)],[f62])).
% 1.77/1.54 thf(f62,plain,(
% 1.77/1.54 (($true => (in @ (setminus @ sK2 @ sK3) @ (powerset @ sK2))) = $true)),
% 1.77/1.54 inference(superposition,[status(thm)],[f36,f57])).
% 1.77/1.54 thf(f36,plain,(
% 1.77/1.54 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X2 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X2) @ (powerset @ X1))))) )),
% 1.77/1.54 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.77/1.54 thf(f35,plain,(
% 1.77/1.54 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ Y0) @ (powerset @ X1)))) @ X2) = $true)) )),
% 1.77/1.54 inference(pi_clausification,[status(thm)],[f34])).
% 1.77/1.54 thf(f34,plain,(
% 1.77/1.54 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ Y0) @ (powerset @ X1))))) = $true)) )),
% 1.77/1.54 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.77/1.54 thf(f33,plain,(
% 1.77/1.54 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ Y0)))))) @ X1) = $true)) )),
% 1.77/1.54 inference(pi_clausification,[status(thm)],[f28])).
% 1.77/1.54 thf(f28,plain,(
% 1.77/1.54 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ Y0))))))) = $true)),
% 1.77/1.54 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.77/1.54 thf(f166,plain,(
% 1.77/1.54 ( ! [X1 : $i] : ((((in @ X1 @ (powerset @ sK2)) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ sK3) => (in @ Y0 @ X1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ X1) => (in @ Y0 @ sK3))))) => (sK3 = X1)))) = $true)) )),
% 1.77/1.54 inference(beta_eta_normalization,[status(thm)],[f164])).
% 1.77/1.54 thf(f164,plain,(
% 1.77/1.54 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y1 @ sK3) => (in @ Y1 @ Y0))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y1 @ Y0) => (in @ Y1 @ sK3))))) => (sK3 = Y0))))) @ X1) = $true)) )),
% 1.77/1.54 inference(pi_clausification,[status(thm)],[f143])).
% 1.77/1.54 thf(f143,plain,(
% 1.77/1.54 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y1 @ sK3) => (in @ Y1 @ Y0))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y1 @ Y0) => (in @ Y1 @ sK3))))) => (sK3 = Y0)))))))),
% 1.77/1.54 inference(boolean_simplification,[status(thm)],[f135])).
% 1.77/1.54 thf(f135,plain,(
% 1.77/1.54 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y1 @ sK3) => (in @ Y1 @ Y0))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y1 @ Y0) => (in @ Y1 @ sK3))))) => (sK3 = Y0))))))) = $true)),
% 1.77/1.54 inference(superposition,[status(thm)],[f132,f57])).
% 1.77/1.54 thf(f132,plain,(
% 1.77/1.54 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ Y1 @ X2) => (in @ Y1 @ Y0))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ Y1 @ Y0) => (in @ Y1 @ X2))))) => (X2 = Y0))))))) = $true)) )),
% 1.77/1.54 inference(beta_eta_normalization,[status(thm)],[f131])).
% 1.77/1.54 thf(f131,plain,(
% 1.77/1.54 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))) => (Y0 = Y1)))))))) @ X2) = $true)) )),
% 1.77/1.54 inference(pi_clausification,[status(thm)],[f126])).
% 1.77/1.54 thf(f126,plain,(
% 1.77/1.54 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))) => (Y0 = Y1))))))))) = $true)) )),
% 1.77/1.54 inference(beta_eta_normalization,[status(thm)],[f125])).
% 1.77/1.54 thf(f125,plain,(
% 1.77/1.54 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2)))))))))) @ X1) = $true)) )),
% 1.77/1.54 inference(pi_clausification,[status(thm)],[f39])).
% 1.77/1.54 % SZS output end Proof for DTF2THF_10587
% 1.77/1.54 % (10702)------------------------------
% 1.77/1.54 % (10702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.54 % (10702)Termination reason: Refutation
% 1.77/1.54
% 1.77/1.54 % (10702)Memory used [KB]: 5884
% 1.77/1.54 % (10702)Time elapsed: 0.042 s
% 1.77/1.54 % (10702)Instructions burned: 73 (million)
% 1.77/1.54 % (10702)------------------------------
% 1.77/1.54 % (10702)------------------------------
% 1.77/1.54 % (10690)Success in time 0.078 s
%------------------------------------------------------------------------------