%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU794^2 : 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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:15 AM UTC 2026
% Result : Theorem 0.32s 1.49s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 7
% Syntax : Number of formulae : 92 ( 66 unt; 0 typ; 2 def)
% Number of atoms : 899 ( 229 equ; 0 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 1537 ( 33 ~; 21 |; 76 &;1049 @)
% ( 7 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 15 usr; 13 con; 0-2 aty)
% ( 152 !!; 79 ??; 0 @@+; 0 @@-)
% Number of variables : 330 ( 257 ^; 64 !; 9 ?; 330 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
subset: $i > $i > $o ).
thf(func_def_25,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
sK2: ( $i > $i ) > $i > $i ).
thf(func_def_27,type,
sK3: $i > $i ).
thf(f180,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f94,f132,f179]) ).
thf(f179,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f178]) ).
thf(f178,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f177]) ).
thf(f177,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f176]) ).
thf(f176,plain,
( ( $false
= ( ( in @ sK8 @ sK5 )
=> ( in @ sK8 @ sK5 ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f175,f108]) ).
thf(f108,plain,
! [X0: $i] :
( ( in @ X0 @ sK5 )
= ( in @ X0 @ ( sK2 @ sK3 @ sK4 ) ) ),
inference(superposition,[status(thm)],[f62,f100]) ).
thf(f100,plain,
! [X1: $i] :
( ( in @ X1 @ sK5 )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
& ( ( sK3 @ Y0 )
= X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK4 )
& ( ( sK3 @ Y0 )
= X1 ) ) )
= ( in @ X1 @ sK5 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK4 )
& ( ( sK3 @ Y1 )
= Y0 ) ) )
= ( in @ Y0 @ sK5 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK4 )
& ( ( sK3 @ Y1 )
= Y0 ) ) )
= ( in @ Y0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK4 )
& ( ( sK3 @ Y1 )
= Y0 ) ) )
= ( in @ Y0 @ sK5 ) ) )
=> ( ( sK2 @ sK3 @ sK4 )
= sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK4 )
& ( ( sK3 @ Y2 )
= Y1 ) ) )
= ( in @ Y1 @ Y0 ) ) )
=> ( ( sK2 @ sK3 @ sK4 )
= Y0 ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK4 )
& ( ( sK3 @ Y2 )
= Y1 ) ) )
= ( in @ Y1 @ Y0 ) ) )
=> ( ( sK2 @ sK3 @ sK4 )
= Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK4 )
& ( ( sK3 @ Y2 )
= Y1 ) ) )
= ( in @ Y1 @ Y0 ) ) )
=> ( ( sK2 @ sK3 @ sK4 )
= Y0 ) ) ) )
= $false ),
inference(superposition,[status(thm)],[f70,f59]) ).
thf(f59,plain,
! [X2: $i,X1: $i > $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
& ( ( X1 @ Y1 )
= Y0 ) ) )
= ( in @ Y0 @ ( sK2 @ X1 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X1: $i > $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
& ( ( X1 @ Y2 )
= Y1 ) ) )
= ( in @ Y1 @ Y0 ) ) )
@ ( sK2 @ X1 @ X2 ) ) ),
inference(sigma_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X1: $i > $i] :
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
& ( ( X1 @ Y2 )
= Y1 ) ) )
= ( in @ Y1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X1: $i > $i] :
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ( X1 @ Y3 )
= Y2 ) ) )
= ( in @ Y2 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: $i > $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ( X1 @ Y3 )
= Y2 ) ) )
= ( in @ Y2 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: $i > $i] :
( $true
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( $true
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( $false
= ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) ) ) ) )
=> ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( ( Y0 @ Y5 )
= Y4 ) ) )
= ( in @ Y4 @ Y3 ) ) )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) ) ) ) )
=> ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( ( Y0 @ Y5 )
= Y4 ) ) )
= ( in @ Y4 @ Y3 ) ) )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
= ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) ) ) ) )
=> ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( ( Y0 @ Y5 )
= Y4 ) ) )
= ( in @ Y4 @ Y3 ) ) )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f25,f29]) ).
thf(f29,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) ) ) ) )
=> ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( ( Y0 @ Y5 )
= Y4 ) ) )
= ( in @ Y4 @ Y3 ) ) )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) ) ) ) )
=> ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( ( Y0 @ Y5 )
= Y4 ) ) )
= ( in @ Y4 @ Y3 ) ) )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) ) ) ) )
=> ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 = Y4 ) ) ) ) )
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f22,f18,f19,f21,f20]) ).
thf(f20,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) )
= exu ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) )
= exu ),
file('/export/starexec/sandbox/tmp/tmp.0V7zyvtR6B/DTF2THF_26351.p',exu) ).
thf(f21,plain,
( image1Ex
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( image1Ex
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( image1Ex
= ( ! [X0: $i,X1: $i > $i] :
? [X2: $i] :
! [X3: $i] :
( ? [X4: $i] :
( ( ( X1 @ X4 )
= X3 )
& ( in @ X4 @ X0 ) )
<=> ( in @ X3 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( image1Ex
= ( ! [X3: $i,X5: $i > $i] :
? [X4: $i] :
! [X1: $i] :
( ? [X2: $i] :
( ( ( X5 @ X2 )
= X1 )
& ( in @ X2 @ X3 ) )
<=> ( in @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0V7zyvtR6B/DTF2THF_26351.p',image1Ex) ).
thf(f19,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( subset @ X0 @ X1 )
=> ( X0 = X1 ) ) )
= setextsub ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X4: $i,X3: $i] :
( ( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X3 )
=> ( X3 = X4 ) ) )
= setextsub ),
file('/export/starexec/sandbox/tmp/tmp.0V7zyvtR6B/DTF2THF_26351.p',setextsub) ).
thf(f18,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= subsetI1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X4: $i,X3: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ X4 ) )
=> ( subset @ X3 @ X4 ) )
= subsetI1 ),
file('/export/starexec/sandbox/tmp/tmp.0V7zyvtR6B/DTF2THF_26351.p',subsetI1) ).
thf(f22,plain,
( $true
= ( ~ ( subsetI1
=> ( setextsub
=> ( image1Ex
=> ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( exu
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( $true
= ( ~ ( subsetI1
=> ( setextsub
=> ( image1Ex
=> ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( exu
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( subsetI1
=> ( setextsub
=> ( image1Ex
=> ! [X0: $i,X1: $i > $i] :
( exu
@ ^ [X2: $i] :
! [X3: $i] :
( ? [X4: $i] :
( ( ( X1 @ X4 )
= X3 )
& ( in @ X4 @ X0 ) )
<=> ( in @ X3 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( subsetI1
=> ( setextsub
=> ( image1Ex
=> ! [X3: $i,X5: $i > $i] :
( exu
@ ^ [X4: $i] :
! [X1: $i] :
( ? [X2: $i] :
( ( ( X5 @ X2 )
= X1 )
& ( in @ X2 @ X3 ) )
<=> ( in @ X1 @ X4 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( subsetI1
=> ( setextsub
=> ( image1Ex
=> ! [X3: $i,X5: $i > $i] :
( exu
@ ^ [X4: $i] :
! [X1: $i] :
( ? [X2: $i] :
( ( ( X5 @ X2 )
= X1 )
& ( in @ X2 @ X3 ) )
<=> ( in @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0V7zyvtR6B/DTF2THF_26351.p',image1Ex1) ).
thf(f70,plain,
! [X1: $i] :
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK4 )
& ( ( sK3 @ Y1 )
= Y0 ) ) )
= ( in @ Y0 @ X1 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK4 )
& ( ( sK3 @ Y2 )
= Y1 ) ) )
= ( in @ Y1 @ Y0 ) ) )
=> ( X1 = Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK4 )
& ( ( sK3 @ Y2 )
= Y1 ) ) )
= ( in @ Y1 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ sK4 )
& ( ( sK3 @ Y3 )
= Y2 ) ) )
= ( in @ Y2 @ Y1 ) ) )
=> ( Y0 = Y1 ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK4 )
& ( ( sK3 @ Y2 )
= Y1 ) ) )
= ( in @ Y1 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ sK4 )
& ( ( sK3 @ Y3 )
= Y2 ) ) )
= ( in @ Y2 @ Y1 ) ) )
=> ( Y0 = Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ( sK3 @ Y3 )
= Y2 ) ) )
= ( in @ Y2 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ( sK3 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) )
=> ( Y1 = Y2 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ( sK3 @ Y3 )
= Y2 ) ) )
= ( in @ Y2 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ( sK3 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) )
=> ( Y1 = Y2 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
( ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( ( Y0 @ Y5 )
= Y4 ) ) )
= ( in @ Y4 @ Y3 ) ) )
=> ( Y2 = Y3 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( $false
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( Y0 @ Y4 )
= Y3 ) ) )
= ( in @ Y3 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( ( Y0 @ Y5 )
= Y4 ) ) )
= ( in @ Y4 @ Y3 ) ) )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i > $i] :
( ( in @ X3 @ ( sK2 @ X1 @ X2 ) )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( ( X1 @ Y0 )
= X3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i > $i] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( ( X1 @ Y0 )
= X3 ) ) )
= ( in @ X3 @ ( sK2 @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i > $i] :
( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
& ( ( X1 @ Y1 )
= Y0 ) ) )
= ( in @ Y0 @ ( sK2 @ X1 @ X2 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f175,plain,
( ( $false
= ( ( in @ sK8 @ sK5 )
=> ( in @ sK8 @ ( sK2 @ sK3 @ sK4 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f172]) ).
thf(f172,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK5 )
=> ( in @ Y0 @ ( sK2 @ sK3 @ sK4 ) ) )
@ sK8 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK5 )
=> ( in @ Y0 @ ( sK2 @ sK3 @ sK4 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK5 )
=> ( in @ Y0 @ ( sK2 @ sK3 @ sK4 ) ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK5 )
=> ( in @ Y0 @ ( sK2 @ sK3 @ sK4 ) ) ) )
=> $false ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f46,f90]) ).
thf(f90,plain,
( ( ( subset @ sK5 @ ( sK2 @ sK3 @ sK4 ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f89,definition,
( spl0_1
<=> ( ( subset @ sK5 @ ( sK2 @ sK3 @ sK4 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f132,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f131]) ).
thf(f131,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f130]) ).
thf(f130,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f129]) ).
thf(f129,plain,
( ( ( ( in @ sK7 @ sK5 )
=> ( in @ sK7 @ sK5 ) )
= $false )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f128,f108]) ).
thf(f128,plain,
( ( $false
= ( ( in @ sK7 @ ( sK2 @ sK3 @ sK4 ) )
=> ( in @ sK7 @ sK5 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f125]) ).
thf(f125,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( sK2 @ sK3 @ sK4 ) )
=> ( in @ Y0 @ sK5 ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f118]) ).
thf(f118,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( sK2 @ sK3 @ sK4 ) )
=> ( in @ Y0 @ sK5 ) ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( sK2 @ sK3 @ sK4 ) )
=> ( in @ Y0 @ sK5 ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f109]) ).
thf(f109,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( sK2 @ sK3 @ sK4 ) )
=> ( in @ Y0 @ sK5 ) ) )
=> $false )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f46,f102]) ).
thf(f102,plain,
( ( $false
= ( subset @ ( sK2 @ sK3 @ sK4 ) @ sK5 ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $true
= ( ~ ( subset @ ( sK2 @ sK3 @ sK4 ) @ sK5 ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f92,definition,
( spl0_2
<=> ( $true
= ( ~ ( subset @ ( sK2 @ sK3 @ sK4 ) @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f94,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f87,f92,f89]) ).
thf(f87,plain,
( ( ( subset @ sK5 @ ( sK2 @ sK3 @ sK4 ) )
= $false )
| ( $true
= ( ~ ( subset @ ( sK2 @ sK3 @ sK4 ) @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( $true
= ( ( subset @ sK5 @ ( sK2 @ sK3 @ sK4 ) )
=> ~ ( subset @ ( sK2 @ sK3 @ sK4 ) @ sK5 ) ) ),
inference(boolean_simplification,[status(thm)],[f85]) ).
thf(f85,plain,
( $true
= ( ( subset @ sK5 @ ( sK2 @ sK3 @ sK4 ) )
=> ( ( subset @ ( sK2 @ sK3 @ sK4 ) @ sK5 )
=> $false ) ) ),
inference(superposition,[status(thm)],[f41,f78]) ).
thf(f78,plain,
( $false
= ( ( sK2 @ sK3 @ sK4 )
= sK5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X1 )
=> ( X2 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( subset @ Y0 @ X1 )
=> ( Y0 = X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( subset @ Y0 @ X1 )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y1 = Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU794^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n026.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:34:25 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
% 0.19/0.48 ---- Original DTF file ---
% 0.19/0.48 thf(spec,logic,$$dhol).
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % File : SEU794^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.48 % Domain : Set Theory
% 0.19/0.48 % Problem : More about Functions - Images of Functions
% 0.19/0.48 % Version : Especial > Reduced > Especial.
% 0.19/0.48 % English : (! A:i.! f:i>i.exu (^ B:i.! x:i.in x B <->
% 0.19/0.48 % (? y:i.in y A & x = f y)))
% 0.19/0.48
% 0.19/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.48 % Source : [Bro08]
% 0.19/0.48 % Names : ZFC296l [Bro08]
% 0.19/0.48
% 0.19/0.48 % Status : Theorem
% 0.19/0.48 % Rating : 0.67 v9.1.0, 0.62 v9.0.0, 0.80 v8.2.0, 0.92 v8.1.0, 0.82 v7.5.0, 0.57 v7.4.0, 0.67 v7.2.0, 0.62 v7.1.0, 0.75 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.67 v5.4.0, 1.00 v3.7.0
% 0.19/0.48 % Syntax : Number of formulae : 11 ( 4 unt; 6 typ; 4 def)
% 0.19/0.48 % Number of atoms : 25 ( 8 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 7 ( 5 avg)
% 0.19/0.48 % Number of connectives : 36 ( 0 ~; 0 |; 3 &; 23 @)
% 0.19/0.48 % ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 14 ( 4 avg)
% 0.19/0.48 % Number of types : 2 ( 0 usr)
% 0.19/0.48 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% 0.19/0.48 % Number of variables : 18 ( 2 ^; 12 !; 4 ?; 18 :)
% 0.19/0.48 % SPC : TH0_THM_EQU_NAR
% 0.19/0.48
% 0.19/0.48 % Comments : http://mathgate.info/detsetitem.php?id=416
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf(in_type,type,
% 0.19/0.48 in: $i > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(exu_type,type,
% 0.19/0.48 exu: ( $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(exu,definition,
% 0.19/0.48 ( exu
% 0.19/0.48 = ( ^ [Xphi: $i > $o] :
% 0.19/0.48 ? [Xx: $i] :
% 0.19/0.48 ( ( Xphi @ Xx )
% 0.19/0.48 & ! [Xy: $i] :
% 0.19/0.48 ( ( Xphi @ Xy )
% 0.19/0.48 => ( Xx = Xy ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(subset_type,type,
% 0.19/0.48 subset: $i > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(subsetI1_type,type,
% 0.19/0.48 subsetI1: $o ).
% 0.19/0.48
% 0.19/0.48 thf(subsetI1,definition,
% 0.19/0.48 ( subsetI1
% 0.19/0.48 = ( ! [A: $i,B: $i] :
% 0.19/0.48 ( ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( in @ Xx @ B ) )
% 0.19/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(setextsub_type,type,
% 0.19/0.48 setextsub: $o ).
% 0.19/0.48
% 0.19/0.48 thf(setextsub,definition,
% 0.19/0.48 ( setextsub
% 0.19/0.48 = ( ! [A: $i,B: $i] :
% 0.19/0.48 ( ( subset @ A @ B )
% 0.19/0.48 => ( ( subset @ B @ A )
% 0.19/0.48 => ( A = B ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(image1Ex_type,type,
% 0.19/0.48 image1Ex: $o ).
% 0.19/0.48
% 0.19/0.48 thf(image1Ex,definition,
% 0.19/0.48 ( image1Ex
% 0.19/0.48 = ( ! [A: $i,Xf: $i > $i] :
% 0.19/0.48 ? [B: $i] :
% 0.19/0.48 ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ B )
% 0.19/0.48 <=> ? [Xy: $i] :
% 0.19/0.48 ( ( in @ Xy @ A )
% 0.19/0.48 & ( Xx
% 0.19/0.48 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(image1Ex1,conjecture,
% 0.19/0.48 ( subsetI1
% 0.19/0.48 => ( setextsub
% 0.19/0.48 => ( image1Ex
% 0.19/0.48 => ! [A: $i,Xf: $i > $i] :
% 0.19/0.48 ( exu
% 0.19/0.48 @ ^ [B: $i] :
% 0.19/0.48 ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ B )
% 0.19/0.48 <=> ? [Xy: $i] :
% 0.19/0.48 ( ( in @ Xy @ A )
% 0.19/0.48 & ( Xx
% 0.19/0.48 = ( Xf @ Xy ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 ------------------------
% 0.32/1.40 ---- Embedded in THF ---
% 0.32/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.40 %%% Generated on Tue Feb 24 12:34:26 EST 2026
% 0.32/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.40 %%% Logic specification used:
% 0.32/1.40 %%% thf(spec, logic, $$dhol).
% 0.32/1.40
% 0.32/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.0V7zyvtR6B/DTF2DTF26351.p
% See solution above
% 0.32/1.40 ------------------------
% 0.32/1.41 ---- Cleaned THF ---
% 0.32/1.41 thf(in_type,type,
% 0.32/1.41 in: $i > $i > $o ).
% 0.32/1.41
% 0.32/1.41 thf(exu_type,type,
% 0.32/1.41 exu: ( $i > $o ) > $o ).
% 0.32/1.41
% 0.32/1.41 thf(exu,definition,
% 0.32/1.41 ( exu
% 0.32/1.41 = ( ^ [Xphi: $i > $o] :
% 0.32/1.41 ? [Xx: $i] :
% 0.32/1.41 ( ( Xphi @ Xx )
% 0.32/1.41 & ! [Xy: $i] :
% 0.32/1.41 ( ( Xphi @ Xy )
% 0.32/1.41 => ( Xx = Xy ) ) ) ) ) ).
% 0.32/1.41
% 0.32/1.41 thf(subset_type,type,
% 0.32/1.41 subset: $i > $i > $o ).
% 0.32/1.41
% 0.32/1.41 thf(subsetI1_type,type,
% 0.32/1.41 subsetI1: $o ).
% 0.32/1.41
% 0.32/1.41 thf(subsetI1,definition,
% 0.32/1.41 ( subsetI1
% 0.32/1.41 = ( ! [A: $i,B: $i] :
% 0.32/1.41 ( ! [Xx: $i] :
% 0.32/1.41 ( ( in @ Xx @ A )
% 0.32/1.41 => ( in @ Xx @ B ) )
% 0.32/1.41 => ( subset @ A @ B ) ) ) ) ).
% 0.32/1.41
% 0.32/1.41 thf(setextsub_type,type,
% 0.32/1.41 setextsub: $o ).
% 0.32/1.41
% 0.32/1.41 thf(setextsub,definition,
% 0.32/1.41 ( setextsub
% 0.32/1.41 = ( ! [A: $i,B: $i] :
% 0.32/1.41 ( ( subset @ A @ B )
% 0.32/1.41 => ( ( subset @ B @ A )
% 0.32/1.41 => ( A = B ) ) ) ) ) ).
% 0.32/1.41
% 0.32/1.41 thf(image1Ex_type,type,
% 0.32/1.41 image1Ex: $o ).
% 0.32/1.41
% 0.32/1.41 thf(image1Ex,definition,
% 0.32/1.41 ( image1Ex
% 0.32/1.41 = ( ! [A: $i,Xf: $i > $i] :
% 0.32/1.41 ? [B: $i] :
% 0.32/1.41 ! [Xx: $i] :
% 0.32/1.41 ( ( in @ Xx @ B )
% 0.32/1.41 <=> ? [Xy: $i] :
% 0.32/1.41 ( ( in @ Xy @ A )
% 0.32/1.41 & ( Xx
% 0.32/1.41 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.32/1.41
% 0.32/1.41 thf(image1Ex1,conjecture,
% 0.32/1.41 ( subsetI1
% 0.32/1.41 => ( setextsub
% 0.32/1.41 => ( image1Ex
% 0.32/1.41 => ! [A: $i,Xf: $i > $i] :
% 0.32/1.41 ( exu
% 0.32/1.41 @ ^ [B: $i] :
% 0.32/1.41 ! [Xx: $i] :
% 0.32/1.41 ( ( in @ Xx @ B )
% 0.32/1.41 <=> ? [Xy: $i] :
% 0.32/1.41 ( ( in @ Xy @ A )
% 0.32/1.41 & ( Xx
% 0.32/1.41 = ( Xf @ Xy ) ) ) ) ) ) ) ) ).
% 0.32/1.41 ------------------------
% 0.32/1.43 % (26451)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26351 for (2999ds/2Mi)
% 0.32/1.43 % (26454)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26351 for (2999ds/18Mi)
% 0.32/1.43 % (26453)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_26351 for (2999ds/275Mi)
% 0.32/1.43 % (26449)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_26351 for (2999ds/4Mi)
% 0.32/1.43 % (26448)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26351 for (2999ds/183Mi)
% 0.32/1.43 % (26452)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_26351 for (2999ds/2Mi)
% 0.32/1.43 % (26450)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_26351 for (2999ds/27Mi)
% 0.32/1.43 % (26451)Instruction limit reached!
% 0.32/1.43 % (26451)------------------------------
% 0.32/1.43 % (26451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (26451)Termination reason: Unknown
% 0.32/1.43 % (26451)Termination phase: Property scanning
% 0.32/1.43
% 0.32/1.43 % (26451)Memory used [KB]: 1023
% 0.32/1.43 % (26451)Time elapsed: 0.003 s
% 0.32/1.43 % (26451)Instructions burned: 2 (million)
% 0.32/1.43 % (26451)------------------------------
% 0.32/1.43 % (26451)------------------------------
% 0.32/1.43 % (26452)Instruction limit reached!
% 0.32/1.43 % (26452)------------------------------
% 0.32/1.43 % (26452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (26452)Termination reason: Unknown
% 0.32/1.43 % (26452)Termination phase: Property scanning
% 0.32/1.43
% 0.32/1.43 % (26452)Memory used [KB]: 1023
% 0.32/1.43 % (26452)Time elapsed: 0.003 s
% 0.32/1.43 % (26452)Instructions burned: 3 (million)
% 0.32/1.43 % (26452)------------------------------
% 0.32/1.43 % (26452)------------------------------
% 0.32/1.43 % (26449)Instruction limit reached!
% 0.32/1.43 % (26449)------------------------------
% 0.32/1.43 % (26449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (26449)Termination reason: Unknown
% 0.32/1.43 % (26449)Termination phase: Saturation
% 0.32/1.43
% 0.32/1.43 % (26449)Memory used [KB]: 5500
% 0.32/1.43 % (26449)Time elapsed: 0.004 s
% 0.32/1.43 % (26449)Instructions burned: 4 (million)
% 0.32/1.43 % (26449)------------------------------
% 0.32/1.43 % (26449)------------------------------
% 0.32/1.44 % (26454)Instruction limit reached!
% 0.32/1.44 % (26454)------------------------------
% 0.32/1.44 % (26454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.44 % (26454)Termination reason: Unknown
% 0.32/1.44 % (26454)Termination phase: Saturation
% 0.32/1.44
% 0.32/1.44 % (26454)Memory used [KB]: 5628
% 0.32/1.44 % (26454)Time elapsed: 0.011 s
% 0.32/1.44 % (26454)Instructions burned: 18 (million)
% 0.32/1.44 % (26454)------------------------------
% 0.32/1.44 % (26454)------------------------------
% 0.32/1.44 % (26450)Instruction limit reached!
% 0.32/1.44 % (26450)------------------------------
% 0.32/1.44 % (26450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.44 % (26450)Termination reason: Unknown
% 0.32/1.44 % (26450)Termination phase: Saturation
% 0.32/1.44
% 0.32/1.44 % (26450)Memory used [KB]: 5628
% 0.32/1.44 % (26450)Time elapsed: 0.016 s
% 0.32/1.44 % (26450)Instructions burned: 27 (million)
% 0.32/1.44 % (26450)------------------------------
% 0.32/1.44 % (26450)------------------------------
% 0.32/1.45 % (26455)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26351 for (2999ds/3Mi)
% 0.32/1.45 % (26456)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_26351 for (2999ds/37Mi)
% 0.32/1.45 % (26457)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_26351 for (2999ds/15Mi)
% 0.32/1.45 % (26455)Instruction limit reached!
% 0.32/1.45 % (26455)------------------------------
% 0.32/1.45 % (26455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.45 % (26455)Termination reason: Unknown
% 0.32/1.45 % (26455)Termination phase: Saturation
% 0.32/1.45
% 0.32/1.45 % (26455)Memory used [KB]: 1023
% 0.32/1.45 % (26455)Time elapsed: 0.003 s
% 0.32/1.45 % (26455)Instructions burned: 3 (million)
% 0.32/1.45 % (26455)------------------------------
% 0.32/1.45 % (26455)------------------------------
% 0.32/1.45 % (26457)Instruction limit reached!
% 0.32/1.45 % (26457)------------------------------
% 0.32/1.45 % (26457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.45 % (26457)Termination reason: Unknown
% 0.32/1.45 % (26457)Termination phase: Saturation
% 0.32/1.45
% 0.32/1.45 % (26457)Memory used [KB]: 5628
% 0.32/1.45 % (26457)Time elapsed: 0.009 s
% 0.32/1.45 % (26457)Instructions burned: 15 (million)
% 0.32/1.45 % (26457)------------------------------
% 0.32/1.45 % (26457)------------------------------
% 0.32/1.45 % (26458)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_26351 for (2999ds/3Mi)
% 0.32/1.46 % (26458)Instruction limit reached!
% 0.32/1.46 % (26458)------------------------------
% 0.32/1.46 % (26458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.46 % (26458)Termination reason: Unknown
% 0.32/1.46 % (26458)Termination phase: Saturation
% 0.32/1.46
% 0.32/1.46 % (26458)Memory used [KB]: 1023
% 0.32/1.46 % (26458)Time elapsed: 0.003 s
% 0.32/1.46 % (26458)Instructions burned: 3 (million)
% 0.32/1.46 % (26458)------------------------------
% 0.32/1.46 % (26458)------------------------------
% 0.32/1.46 % (26459)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_26351 for (2999ds/1041Mi)
% 0.32/1.46 % (26460)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26351 for (2999ds/7Mi)
% 0.32/1.46 % (26456)Instruction limit reached!
% 0.32/1.46 % (26456)------------------------------
% 0.32/1.46 % (26456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.46 % (26456)Termination reason: Unknown
% 0.32/1.46 % (26456)Termination phase: Saturation
% 0.32/1.46
% 0.32/1.46 % (26456)Memory used [KB]: 5756
% 0.32/1.46 % (26456)Time elapsed: 0.020 s
% 0.32/1.46 % (26456)Instructions burned: 38 (million)
% 0.32/1.46 % (26456)------------------------------
% 0.32/1.46 % (26456)------------------------------
% 0.32/1.47 % (26460)Instruction limit reached!
% 0.32/1.47 % (26460)------------------------------
% 0.32/1.47 % (26460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.47 % (26460)Termination reason: Unknown
% 0.32/1.47 % (26460)Termination phase: Saturation
% 0.32/1.47
% 0.32/1.47 % (26460)Memory used [KB]: 1023
% 0.32/1.47 % (26460)Time elapsed: 0.005 s
% 0.32/1.47 % (26460)Instructions burned: 8 (million)
% 0.32/1.47 % (26460)------------------------------
% 0.32/1.47 % (26460)------------------------------
% 0.32/1.47 % (26461)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26351 for (2999ds/16Mi)
% 0.32/1.47 % (26462)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_26351 for (2999ds/3Mi)
% 0.32/1.47 % (26462)Instruction limit reached!
% 0.32/1.47 % (26462)------------------------------
% 0.32/1.47 % (26462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.47 % (26462)Termination reason: Unknown
% 0.32/1.47 % (26462)Termination phase: Twee Goal Transformation
% 0.32/1.47
% 0.32/1.47 % (26462)Memory used [KB]: 1023
% 0.32/1.47 % (26462)Time elapsed: 0.003 s
% 0.32/1.47 % (26462)Instructions burned: 4 (million)
% 0.32/1.47 % (26462)------------------------------
% 0.32/1.47 % (26462)------------------------------
% 0.32/1.48 % (26461)Instruction limit reached!
% 0.32/1.48 % (26461)------------------------------
% 0.32/1.48 % (26461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.48 % (26461)Termination reason: Unknown
% 0.32/1.48 % (26461)Termination phase: Saturation
% 0.32/1.48
% 0.32/1.48 % (26461)Memory used [KB]: 5756
% 0.32/1.48 % (26461)Time elapsed: 0.010 s
% 0.32/1.48 % (26461)Instructions burned: 16 (million)
% 0.32/1.48 % (26461)------------------------------
% 0.32/1.48 % (26461)------------------------------
% 0.32/1.48 % (26463)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_26351 for (2999ds/3Mi)
% 0.32/1.48 % (26459)First to succeed.
% 0.32/1.48 % (26463)Instruction limit reached!
% 0.32/1.48 % (26463)------------------------------
% 0.32/1.48 % (26463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.48 % (26463)Termination reason: Unknown
% 0.32/1.48 % (26463)Termination phase: Property scanning
% 0.32/1.48
% 0.32/1.48 % (26463)Memory used [KB]: 1023
% 0.32/1.48 % (26463)Time elapsed: 0.003 s
% 0.32/1.48 % (26463)Instructions burned: 4 (million)
% 0.32/1.48 % (26463)------------------------------
% 0.32/1.48 % (26463)------------------------------
% 0.32/1.48 % (26464)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26351 for (2999ds/7Mi)
% 0.32/1.48 % (26464)Refutation not found, incomplete strategy
% 0.32/1.48 % (26464)------------------------------
% 0.32/1.48 % (26464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.48 % (26464)Termination reason: Refutation not found, incomplete strategy
% 0.32/1.48
% 0.32/1.48
% 0.32/1.48 % (26464)Memory used [KB]: 5500
% 0.32/1.48 % (26464)Time elapsed: 0.003 s
% 0.32/1.48 % (26464)Instructions burned: 4 (million)
% 0.32/1.48 % (26464)------------------------------
% 0.32/1.48 % (26464)------------------------------
% 0.32/1.49 % (26459)Refutation found. Thanks to Tanya!
% 0.32/1.49 % SZS status Theorem for DTF2THF_26351
% 0.32/1.49 % SZS output start Proof for DTF2THF_26351
% 0.32/1.49 thf(func_def_0, type, in: $i > $i > $o).
% 0.32/1.49 thf(func_def_1, type, exu: ($i > $o) > $o).
% 0.32/1.49 thf(func_def_3, type, subset: $i > $i > $o).
% 0.32/1.49 thf(func_def_25, type, ph1: !>[X0: $tType]:(X0)).
% 0.32/1.49 thf(func_def_26, type, sK2: ($i > $i) > $i > $i).
% 0.32/1.49 thf(func_def_27, type, sK3: $i > $i).
% 0.32/1.49 thf(f180,plain,(
% 0.32/1.49 $false),
% 0.32/1.49 inference(avatar_sat_refutation,[status(thm)],[f94,f132,f179])).
% 0.32/1.49 thf(f179,plain,(
% 0.32/1.49 ~spl0_1),
% 0.32/1.49 inference(avatar_contradiction_clause,[status(thm)],[f178])).
% 0.32/1.49 thf(f178,plain,(
% 0.32/1.49 $false | ~spl0_1),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f177])).
% 0.32/1.49 thf(f177,plain,(
% 0.32/1.49 ($true = $false) | ~spl0_1),
% 0.32/1.49 inference(boolean_simplification,[status(thm)],[f176])).
% 0.32/1.49 thf(f176,plain,(
% 0.32/1.49 ($false = ((in @ sK8 @ sK5) => (in @ sK8 @ sK5))) | ~spl0_1),
% 0.32/1.49 inference(forward_demodulation,[status(thm)],[f175,f108])).
% 0.32/1.49 thf(f108,plain,(
% 0.32/1.49 ( ! [X0 : $i] : (((in @ X0 @ sK5) = (in @ X0 @ (sK2 @ sK3 @ sK4)))) )),
% 0.32/1.49 inference(superposition,[status(thm)],[f62,f100])).
% 0.32/1.49 thf(f100,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (((in @ X1 @ sK5) = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) & ((sK3 @ Y0) = X1)))))) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 0.32/1.49 thf(f99,plain,(
% 0.32/1.49 ( ! [X1 : $i] : ((((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) & ((sK3 @ Y0) = X1)))) = (in @ X1 @ sK5)) = $true)) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f97])).
% 0.32/1.49 thf(f97,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) & ((sK3 @ Y1) = Y0)))) = (in @ Y0 @ sK5))) @ X1))) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f79])).
% 0.32/1.49 thf(f79,plain,(
% 0.32/1.49 ($true = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) & ((sK3 @ Y1) = Y0)))) = (in @ Y0 @ sK5)))))),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 0.32/1.49 thf(f77,plain,(
% 0.32/1.49 ($false = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) & ((sK3 @ Y1) = Y0)))) = (in @ Y0 @ sK5)))) => ((sK2 @ sK3 @ sK4) = sK5)))),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f74])).
% 0.32/1.49 thf(f74,plain,(
% 0.32/1.49 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) & ((sK3 @ Y2) = Y1)))) = (in @ Y1 @ Y0)))) => ((sK2 @ sK3 @ sK4) = Y0))) @ sK5) = $false)),
% 0.32/1.49 inference(sigma_clausification,[status(thm)],[f73])).
% 0.32/1.49 thf(f73,plain,(
% 0.32/1.49 ($false = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) & ((sK3 @ Y2) = Y1)))) = (in @ Y1 @ Y0)))) => ((sK2 @ sK3 @ sK4) = Y0)))))),
% 0.32/1.49 inference(boolean_simplification,[status(thm)],[f72])).
% 0.32/1.49 thf(f72,plain,(
% 0.32/1.49 (($true & (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) & ((sK3 @ Y2) = Y1)))) = (in @ Y1 @ Y0)))) => ((sK2 @ sK3 @ sK4) = Y0))))) = $false)),
% 0.32/1.49 inference(superposition,[status(thm)],[f70,f59])).
% 0.32/1.49 thf(f59,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i > $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) & ((X1 @ Y1) = Y0)))) = (in @ Y0 @ (sK2 @ X1 @ X2))))))) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f58])).
% 0.32/1.49 thf(f58,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i > $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) & ((X1 @ Y2) = Y1)))) = (in @ Y1 @ Y0))))) @ (sK2 @ X1 @ X2)))) )),
% 0.32/1.49 inference(sigma_clausification,[status(thm)],[f57])).
% 0.32/1.49 thf(f57,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i > $i] : (($true = (?? @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) & ((X1 @ Y2) = Y1)))) = (in @ Y1 @ Y0)))))))) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f56])).
% 0.32/1.49 thf(f56,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i > $i] : (($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & ((X1 @ Y3) = Y2)))) = (in @ Y2 @ Y1))))))) @ X2))) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f55])).
% 0.32/1.49 thf(f55,plain,(
% 0.32/1.49 ( ! [X1 : $i > $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & ((X1 @ Y3) = Y2)))) = (in @ Y2 @ Y1)))))))))) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f54])).
% 0.32/1.49 thf(f54,plain,(
% 0.32/1.49 ( ! [X1 : $i > $i] : (($true = ((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2))))))))) @ X1))) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f49])).
% 0.32/1.49 thf(f49,plain,(
% 0.32/1.49 ($true = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))))))))))),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 0.32/1.49 thf(f32,plain,(
% 0.32/1.49 ($false = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))))))))) => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))) & (!! @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) & ((Y0 @ Y5) = Y4)))) = (in @ Y4 @ Y3)))) => (Y2 = Y3)))))))))))))),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 0.32/1.49 thf(f31,plain,(
% 0.32/1.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))))))))) => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))) & (!! @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) & ((Y0 @ Y5) = Y4)))) = (in @ Y4 @ Y3)))) => (Y2 = Y3))))))))))))) = $false)),
% 0.32/1.49 inference(boolean_simplification,[status(thm)],[f30])).
% 0.32/1.49 thf(f30,plain,(
% 0.32/1.49 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))))))))) => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))) & (!! @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) & ((Y0 @ Y5) = Y4)))) = (in @ Y4 @ Y3)))) => (Y2 = Y3)))))))))))))))),
% 0.32/1.49 inference(backward_demodulation,[status(thm)],[f25,f29])).
% 0.32/1.49 thf(f29,plain,(
% 0.32/1.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) = $true)),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 0.32/1.49 thf(f25,plain,(
% 0.32/1.49 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))))))))) => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))) & (!! @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) & ((Y0 @ Y5) = Y4)))) = (in @ Y4 @ Y3)))) => (Y2 = Y3)))))))))))))))),
% 0.32/1.49 inference(not_proxy_clausification,[status(thm)],[f24])).
% 0.32/1.49 thf(f24,plain,(
% 0.32/1.49 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))))))))) => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))) & (!! @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) & ((Y0 @ Y5) = Y4)))) = (in @ Y4 @ Y3)))) => (Y2 = Y3))))))))))))))))),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f23])).
% 0.32/1.49 thf(f23,plain,(
% 0.32/1.49 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))))))))) => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: ((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))))))) @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))))))))))))))),
% 0.32/1.49 inference(definition_unfolding,[status(thm)],[f22,f18,f19,f21,f20])).
% 0.32/1.49 thf(f20,plain,(
% 0.32/1.49 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.32/1.49 inference(cnf_transformation,[status(thm)],[f17])).
% 0.32/1.49 thf(f17,plain,(
% 0.32/1.49 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.32/1.49 inference(fool_elimination,[status(thm)],[f16])).
% 0.32/1.49 thf(f16,plain,(
% 0.32/1.49 ((^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 0.32/1.49 inference(rectify,[status(thm)],[f1])).
% 0.32/1.49 thf(f1,axiom,(
% 0.32/1.49 ((^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 0.32/1.49 file('/export/starexec/sandbox/tmp/tmp.0V7zyvtR6B/DTF2THF_26351.p',exu)).
% 0.32/1.49 thf(f21,plain,(
% 0.32/1.49 (image1Ex = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))))))))))),
% 0.32/1.49 inference(cnf_transformation,[status(thm)],[f11])).
% 0.32/1.49 thf(f11,plain,(
% 0.32/1.49 (image1Ex = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))))))))))),
% 0.32/1.49 inference(fool_elimination,[status(thm)],[f10])).
% 0.32/1.49 thf(f10,plain,(
% 0.32/1.49 (image1Ex = ! [X0 : $i,X1 : $i > $i] : ? [X2 : $i] : ! [X3 : $i] : (? [X4 : $i] : (((X1 @ X4) = X3) & (in @ X4 @ X0)) <=> (in @ X3 @ X2)))),
% 0.32/1.49 inference(rectify,[status(thm)],[f4])).
% 0.32/1.49 thf(f4,axiom,(
% 0.32/1.49 (image1Ex = ! [X3 : $i,X5 : $i > $i] : ? [X4 : $i] : ! [X1 : $i] : (? [X2 : $i] : (((X5 @ X2) = X1) & (in @ X2 @ X3)) <=> (in @ X1 @ X4)))),
% 0.32/1.49 file('/export/starexec/sandbox/tmp/tmp.0V7zyvtR6B/DTF2THF_26351.p',image1Ex)).
% 0.32/1.49 thf(f19,plain,(
% 0.32/1.49 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))))),
% 0.32/1.49 inference(cnf_transformation,[status(thm)],[f15])).
% 0.32/1.49 thf(f15,plain,(
% 0.32/1.49 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))))),
% 0.32/1.49 inference(fool_elimination,[status(thm)],[f14])).
% 0.32/1.49 thf(f14,plain,(
% 0.32/1.49 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1))) = setextsub)),
% 0.32/1.49 inference(rectify,[status(thm)],[f3])).
% 0.32/1.49 thf(f3,axiom,(
% 0.32/1.49 (! [X4 : $i,X3 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X3) => (X3 = X4))) = setextsub)),
% 0.32/1.49 file('/export/starexec/sandbox/tmp/tmp.0V7zyvtR6B/DTF2THF_26351.p',setextsub)).
% 0.32/1.49 thf(f18,plain,(
% 0.32/1.49 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 0.32/1.49 inference(cnf_transformation,[status(thm)],[f9])).
% 0.32/1.49 thf(f9,plain,(
% 0.32/1.49 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 0.32/1.49 inference(fool_elimination,[status(thm)],[f8])).
% 0.32/1.49 thf(f8,plain,(
% 0.32/1.49 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)),
% 0.32/1.49 inference(rectify,[status(thm)],[f2])).
% 0.32/1.49 thf(f2,axiom,(
% 0.32/1.49 (! [X4 : $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)) = subsetI1)),
% 0.32/1.49 file('/export/starexec/sandbox/tmp/tmp.0V7zyvtR6B/DTF2THF_26351.p',subsetI1)).
% 0.32/1.49 thf(f22,plain,(
% 0.32/1.49 ($true = (~ (subsetI1 => (setextsub => (image1Ex => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (exu @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))))))))))))))),
% 0.32/1.49 inference(cnf_transformation,[status(thm)],[f13])).
% 0.32/1.49 thf(f13,plain,(
% 0.32/1.49 ($true = (~ (subsetI1 => (setextsub => (image1Ex => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (exu @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))))))))))))))),
% 0.32/1.49 inference(fool_elimination,[status(thm)],[f12])).
% 0.32/1.49 thf(f12,plain,(
% 0.32/1.49 ~(subsetI1 => (setextsub => (image1Ex => ! [X0 : $i,X1 : $i > $i] : (exu @ (^[X2 : $i] : (! [X3 : $i] : (? [X4 : $i] : (((X1 @ X4) = X3) & (in @ X4 @ X0)) <=> (in @ X3 @ X2))))))))),
% 0.32/1.49 inference(rectify,[status(thm)],[f6])).
% 0.32/1.49 thf(f6,negated_conjecture,(
% 0.32/1.49 ~(subsetI1 => (setextsub => (image1Ex => ! [X3 : $i,X5 : $i > $i] : (exu @ (^[X4 : $i] : (! [X1 : $i] : (? [X2 : $i] : (((X5 @ X2) = X1) & (in @ X2 @ X3)) <=> (in @ X1 @ X4))))))))),
% 0.32/1.49 inference(negated_conjecture,[status(cth)],[f5])).
% 0.32/1.49 thf(f5,conjecture,(
% 0.32/1.49 subsetI1 => (setextsub => (image1Ex => ! [X3 : $i,X5 : $i > $i] : (exu @ (^[X4 : $i] : (! [X1 : $i] : (? [X2 : $i] : (((X5 @ X2) = X1) & (in @ X2 @ X3)) <=> (in @ X1 @ X4)))))))),
% 0.32/1.49 file('/export/starexec/sandbox/tmp/tmp.0V7zyvtR6B/DTF2THF_26351.p',image1Ex1)).
% 0.32/1.49 thf(f70,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) & ((sK3 @ Y1) = Y0)))) = (in @ Y0 @ X1)))) & (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) & ((sK3 @ Y2) = Y1)))) = (in @ Y1 @ Y0)))) => (X1 = Y0))))))) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f69])).
% 0.32/1.49 thf(f69,plain,(
% 0.32/1.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) & ((sK3 @ Y2) = Y1)))) = (in @ Y1 @ Y0)))) & (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK4) & ((sK3 @ Y3) = Y2)))) = (in @ Y2 @ Y1)))) => (Y0 = Y1)))))) @ X1) = $false)) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f68])).
% 0.32/1.49 thf(f68,plain,(
% 0.32/1.49 ($false = (?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) & ((sK3 @ Y2) = Y1)))) = (in @ Y1 @ Y0)))) & (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK4) & ((sK3 @ Y3) = Y2)))) = (in @ Y2 @ Y1)))) => (Y0 = Y1))))))))),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f67])).
% 0.32/1.49 thf(f67,plain,(
% 0.32/1.49 ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & ((sK3 @ Y3) = Y2)))) = (in @ Y2 @ Y1)))) & (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((sK3 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))) => (Y1 = Y2)))))))) @ sK4))),
% 0.32/1.49 inference(sigma_clausification,[status(thm)],[f66])).
% 0.32/1.49 thf(f66,plain,(
% 0.32/1.49 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & ((sK3 @ Y3) = Y2)))) = (in @ Y2 @ Y1)))) & (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((sK3 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))) => (Y1 = Y2))))))))) = $false)),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f65])).
% 0.32/1.49 thf(f65,plain,(
% 0.32/1.49 (((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))) & (!! @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) & ((Y0 @ Y5) = Y4)))) = (in @ Y4 @ Y3)))) => (Y2 = Y3)))))))))) @ sK3) = $false)),
% 0.32/1.49 inference(sigma_clausification,[status(thm)],[f48])).
% 0.32/1.49 thf(f48,plain,(
% 0.32/1.49 ($false = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((Y0 @ Y4) = Y3)))) = (in @ Y3 @ Y2)))) & (!! @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) & ((Y0 @ Y5) = Y4)))) = (in @ Y4 @ Y3)))) => (Y2 = Y3))))))))))))),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 0.32/1.49 thf(f62,plain,(
% 0.32/1.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $i] : (((in @ X3 @ (sK2 @ X1 @ X2)) = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) & ((X1 @ Y0) = X3)))))) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 0.32/1.49 thf(f61,plain,(
% 0.32/1.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $i] : (($true = ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) & ((X1 @ Y0) = X3)))) = (in @ X3 @ (sK2 @ X1 @ X2))))) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f60])).
% 0.32/1.49 thf(f60,plain,(
% 0.32/1.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $i] : (($true = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) & ((X1 @ Y1) = Y0)))) = (in @ Y0 @ (sK2 @ X1 @ X2)))) @ X3))) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f59])).
% 0.32/1.49 thf(f175,plain,(
% 0.32/1.49 ($false = ((in @ sK8 @ sK5) => (in @ sK8 @ (sK2 @ sK3 @ sK4)))) | ~spl0_1),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f172])).
% 0.32/1.49 thf(f172,plain,(
% 0.32/1.49 (((^[Y0 : $i]: ((in @ Y0 @ sK5) => (in @ Y0 @ (sK2 @ sK3 @ sK4)))) @ sK8) = $false) | ~spl0_1),
% 0.32/1.49 inference(sigma_clausification,[status(thm)],[f142])).
% 0.32/1.49 thf(f142,plain,(
% 0.32/1.49 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK5) => (in @ Y0 @ (sK2 @ sK3 @ sK4))))) = $false) | ~spl0_1),
% 0.32/1.49 inference(not_proxy_clausification,[status(thm)],[f138])).
% 0.32/1.49 thf(f138,plain,(
% 0.32/1.49 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK5) => (in @ Y0 @ (sK2 @ sK3 @ sK4))))))) | ~spl0_1),
% 0.32/1.49 inference(boolean_simplification,[status(thm)],[f135])).
% 0.32/1.49 thf(f135,plain,(
% 0.32/1.49 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK5) => (in @ Y0 @ (sK2 @ sK3 @ sK4))))) => $false)) | ~spl0_1),
% 0.32/1.49 inference(superposition,[status(thm)],[f46,f90])).
% 0.32/1.49 thf(f90,plain,(
% 0.32/1.49 ((subset @ sK5 @ (sK2 @ sK3 @ sK4)) = $false) | ~spl0_1),
% 0.32/1.49 inference(avatar_component_clause,[status(thm)],[f89])).
% 0.32/1.49 thf(f89,definition,(
% 0.32/1.49 spl0_1 <=> ((subset @ sK5 @ (sK2 @ sK3 @ sK4)) = $false)),
% 0.32/1.49 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 0.32/1.49 thf(f46,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (subset @ X1 @ X2)))) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f45])).
% 0.32/1.49 thf(f45,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0))) @ X2))) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f44])).
% 0.32/1.49 thf(f44,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0)))))) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f43])).
% 0.32/1.49 thf(f43,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))) @ X1))) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f29])).
% 0.32/1.49 thf(f132,plain,(
% 0.32/1.49 ~spl0_2),
% 0.32/1.49 inference(avatar_contradiction_clause,[status(thm)],[f131])).
% 0.32/1.49 thf(f131,plain,(
% 0.32/1.49 $false | ~spl0_2),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f130])).
% 0.32/1.49 thf(f130,plain,(
% 0.32/1.49 ($true = $false) | ~spl0_2),
% 0.32/1.49 inference(boolean_simplification,[status(thm)],[f129])).
% 0.32/1.49 thf(f129,plain,(
% 0.32/1.49 (((in @ sK7 @ sK5) => (in @ sK7 @ sK5)) = $false) | ~spl0_2),
% 0.32/1.49 inference(forward_demodulation,[status(thm)],[f128,f108])).
% 0.32/1.49 thf(f128,plain,(
% 0.32/1.49 ($false = ((in @ sK7 @ (sK2 @ sK3 @ sK4)) => (in @ sK7 @ sK5))) | ~spl0_2),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f125])).
% 0.32/1.49 thf(f125,plain,(
% 0.32/1.49 (((^[Y0 : $i]: ((in @ Y0 @ (sK2 @ sK3 @ sK4)) => (in @ Y0 @ sK5))) @ sK7) = $false) | ~spl0_2),
% 0.32/1.49 inference(sigma_clausification,[status(thm)],[f118])).
% 0.32/1.49 thf(f118,plain,(
% 0.32/1.49 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (sK2 @ sK3 @ sK4)) => (in @ Y0 @ sK5))))) | ~spl0_2),
% 0.32/1.49 inference(not_proxy_clausification,[status(thm)],[f112])).
% 0.32/1.49 thf(f112,plain,(
% 0.32/1.49 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (sK2 @ sK3 @ sK4)) => (in @ Y0 @ sK5)))))) | ~spl0_2),
% 0.32/1.49 inference(boolean_simplification,[status(thm)],[f109])).
% 0.32/1.49 thf(f109,plain,(
% 0.32/1.49 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (sK2 @ sK3 @ sK4)) => (in @ Y0 @ sK5)))) => $false) = $true) | ~spl0_2),
% 0.32/1.49 inference(superposition,[status(thm)],[f46,f102])).
% 0.32/1.49 thf(f102,plain,(
% 0.32/1.49 ($false = (subset @ (sK2 @ sK3 @ sK4) @ sK5)) | ~spl0_2),
% 0.32/1.49 inference(not_proxy_clausification,[status(thm)],[f93])).
% 0.32/1.49 thf(f93,plain,(
% 0.32/1.49 ($true = (~ (subset @ (sK2 @ sK3 @ sK4) @ sK5))) | ~spl0_2),
% 0.32/1.49 inference(avatar_component_clause,[status(thm)],[f92])).
% 0.32/1.49 thf(f92,definition,(
% 0.32/1.49 spl0_2 <=> ($true = (~ (subset @ (sK2 @ sK3 @ sK4) @ sK5)))),
% 0.32/1.49 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 0.32/1.49 thf(f94,plain,(
% 0.32/1.49 spl0_1 | spl0_2),
% 0.32/1.49 inference(avatar_split_clause,[status(thm)],[f87,f92,f89])).
% 0.32/1.49 thf(f87,plain,(
% 0.32/1.49 ((subset @ sK5 @ (sK2 @ sK3 @ sK4)) = $false) | ($true = (~ (subset @ (sK2 @ sK3 @ sK4) @ sK5)))),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f86])).
% 0.32/1.49 thf(f86,plain,(
% 0.32/1.49 ($true = ((subset @ sK5 @ (sK2 @ sK3 @ sK4)) => (~ (subset @ (sK2 @ sK3 @ sK4) @ sK5))))),
% 0.32/1.49 inference(boolean_simplification,[status(thm)],[f85])).
% 0.32/1.49 thf(f85,plain,(
% 0.32/1.49 ($true = ((subset @ sK5 @ (sK2 @ sK3 @ sK4)) => ((subset @ (sK2 @ sK3 @ sK4) @ sK5) => $false)))),
% 0.32/1.49 inference(superposition,[status(thm)],[f41,f78])).
% 0.32/1.49 thf(f78,plain,(
% 0.32/1.49 ($false = ((sK2 @ sK3 @ sK4) = sK5))),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 0.32/1.49 thf(f41,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (($true = ((subset @ X1 @ X2) => ((subset @ X2 @ X1) => (X2 = X1))))) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f40])).
% 0.32/1.49 thf(f40,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((subset @ X1 @ Y0) => ((subset @ Y0 @ X1) => (Y0 = X1)))) @ X2) = $true)) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f39])).
% 0.32/1.49 thf(f39,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ Y0) => ((subset @ Y0 @ X1) => (Y0 = X1))))))) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f38])).
% 0.32/1.49 thf(f38,plain,(
% 0.32/1.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0)))))) @ X1) = $true)) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f33])).
% 0.32/1.49 thf(f33,plain,(
% 0.32/1.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))) = $true)),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 0.32/1.49 % SZS output end Proof for DTF2THF_26351
% 0.32/1.49 % (26459)------------------------------
% 0.32/1.49 % (26459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.49 % (26459)Termination reason: Refutation
% 0.32/1.49
% 0.32/1.49 % (26459)Memory used [KB]: 5756
% 0.32/1.49 % (26459)Time elapsed: 0.027 s
% 0.32/1.49 % (26459)Instructions burned: 42 (million)
% 0.32/1.49 % (26459)------------------------------
% 0.32/1.49 % (26459)------------------------------
% 0.32/1.49 % (26447)Success in time 0.066 s
%------------------------------------------------------------------------------