%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU703^2 : 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 : n012.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 09:36:31 AM UTC 2026
% Result : Theorem 6.63s 1.85s
% Output : Refutation 6.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 9
% Syntax : Number of formulae : 136 ( 91 unt; 0 typ; 2 def)
% Number of atoms : 1571 ( 402 equ; 0 cnn)
% Maximal formula atoms : 9 ( 11 avg)
% Number of connectives : 2605 ( 130 ~; 122 |; 154 &;1534 @)
% ( 4 <=>; 370 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 19 usr; 18 con; 0-2 aty)
% ( 291 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 488 ( 387 ^; 101 !; 0 ?; 488 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f489,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f326,f419,f488]) ).
thf(f488,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f487]) ).
thf(f487,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f486]) ).
thf(f486,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f485,f483]) ).
thf(f483,plain,
( ( $false
= ( in @ sK3 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f454,f469]) ).
thf(f469,plain,
( ( sK3 = sK9 )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[status(thm)],[f466]) ).
thf(f466,plain,
( ( $true
= ( sK3 = sK9 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f465]) ).
thf(f465,plain,
( ( $true
= ( $false
| ( sK3 = sK9 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f464]) ).
thf(f464,plain,
( ( $true
= ( ( $false
& ( sK5 = sK9 ) )
| ( sK3 = sK9 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f463]) ).
thf(f463,plain,
( ( $true
= ( ( ~ $true
& ( sK5 = sK9 ) )
| ( sK3 = sK9 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f462]) ).
thf(f462,plain,
( ( $true
= ( ( ~ $true
& ( sK5 = sK9 ) )
| ( $true
& ( sK3 = sK9 ) ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f459,f125]) ).
thf(f125,plain,
$true = sK4,
inference(binary_proxy_clausification,[status(thm)],[f123]) ).
thf(f123,plain,
( $false
= ( sK4
=> ( ( dsetconstr @ sK2
@ ^ [Y0: $i] :
( ( ~ sK4
& ( sK5 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) ) )
= ( setadjoin @ sK3 @ emptyset ) ) ) ),
inference(boolean_simplification,[status(thm)],[f122]) ).
thf(f122,plain,
( $false
= ( $true
=> ( sK4
=> ( ( dsetconstr @ sK2
@ ^ [Y0: $i] :
( ( ~ sK4
& ( sK5 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) ) )
= ( setadjoin @ sK3 @ emptyset ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f119,f121]) ).
thf(f121,plain,
( $true
= ( in @ sK5 @ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
( $false
= ( ( in @ sK5 @ sK2 )
=> ( sK4
=> ( ( dsetconstr @ sK2
@ ^ [Y0: $i] :
( ( ~ sK4
& ( sK5 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) ) )
= ( setadjoin @ sK3 @ emptyset ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f118]) ).
thf(f118,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( sK4
=> ( ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( Y0 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) )
= ( setadjoin @ sK3 @ emptyset ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( sK4
=> ( ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( Y0 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) )
= ( setadjoin @ sK3 @ emptyset ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f110]) ).
thf(f110,plain,
( $false
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( sK4
=> ( ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( Y0 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) )
= ( setadjoin @ sK3 @ emptyset ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f107,f109]) ).
thf(f109,plain,
( $true
= ( in @ sK3 @ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
( $false
= ( ( in @ sK3 @ sK2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( sK4
=> ( ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( Y0 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) )
= ( setadjoin @ sK3 @ emptyset ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f106]) ).
thf(f106,plain,
( $false
= ( ^ [Y0: $o] :
( ( in @ sK3 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( Y0
=> ( ( dsetconstr @ sK2
@ ^ [Y2: $i] :
( ( ~ Y0
& ( Y1 = Y2 ) )
| ( Y0
& ( sK3 = Y2 ) ) ) )
= ( setadjoin @ sK3 @ emptyset ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( $false
= ( !! @ $o
@ ^ [Y0: $o] :
( ( in @ sK3 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( Y0
=> ( ( dsetconstr @ sK2
@ ^ [Y2: $i] :
( ( ~ Y0
& ( Y1 = Y2 ) )
| ( Y0
& ( sK3 = Y2 ) ) ) )
= ( setadjoin @ sK3 @ emptyset ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f104]) ).
thf(f104,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( Y1
=> ( ( dsetconstr @ sK2
@ ^ [Y3: $i] :
( ( ~ Y1
& ( Y2 = Y3 ) )
| ( Y1
& ( Y0 = Y3 ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( Y1
=> ( ( dsetconstr @ sK2
@ ^ [Y3: $i] :
( ( ~ Y1
& ( Y2 = Y3 ) )
| ( Y1
& ( Y0 = Y3 ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f102]) ).
thf(f102,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y2 @ Y1 )
= ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f71]) ).
thf(f71,plain,
( $false
= ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y2 @ Y1 )
= ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f55,f70]) ).
thf(f70,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y2 @ Y1 )
= ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y2 @ Y1 )
= ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
= ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y2 @ Y1 )
= ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f36,f50]) ).
thf(f50,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y2 @ Y1 )
= ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y2 @ Y1 )
= ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y2 @ Y1 )
= ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y2 @ Y1 )
= ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f30,f27,f24,f25,f28,f26,f29]) ).
thf(f29,plain,
( iftrueProp1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( iftrueProp1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( X0
=> ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X4: $i] :
( ( ( X1 = X4 )
& X0 )
| ( ( X3 = X4 )
& ~ X0 ) ) ) ) ) ) )
= iftrueProp1 ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X1: $o,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X5: $i] :
( ( ( X2 = X5 )
& X1 )
| ( ( X3 = X5 )
& ~ X1 ) ) ) ) ) ) )
= iftrueProp1 ),
file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',iftrueProp1) ).
thf(f26,plain,
( in__Cong
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y2 @ Y1 )
= ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( in__Cong
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y2 @ Y1 )
= ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( in__Cong
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X3 @ X0 )
<=> ( in @ X2 @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( in__Cong
= ( ! [X0: $i,X4: $i] :
( ( X0 = X4 )
=> ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X0 )
<=> ( in @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',in__Cong) ).
thf(f28,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= eqinunit ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X3: $i,X2: $i] :
( ( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= eqinunit ),
file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',eqinunit) ).
thf(f25,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) )
= uniqinunit ),
file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',uniqinunit) ).
thf(f24,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
( setext
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ X3 @ X1 ) )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setext
= ( ! [X4: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',setext) ).
thf(f27,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X0 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X1: $i > $o,X0: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',dsetconstrER) ).
thf(f30,plain,
( $true
= ( ~ ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( in__Cong
=> ( iftrueProp1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
= ( ~ ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( in__Cong
=> ( iftrueProp1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( in__Cong
=> ( iftrueProp1
=> ! [X0: $o,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( X0
=> ( ( dsetconstr @ X2
@ ^ [X4: $i] :
( ( ( X1 = X4 )
& X0 )
| ( ( X3 = X4 )
& ~ X0 ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( in__Cong
=> ( iftrueProp1
=> ! [X1: $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( ( dsetconstr @ X0
@ ^ [X5: $i] :
( ( ( X2 = X5 )
& X1 )
| ( ( X3 = X5 )
& ~ X1 ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( in__Cong
=> ( iftrueProp1
=> ! [X1: $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( ( dsetconstr @ X0
@ ^ [X5: $i] :
( ( ( X2 = X5 )
& X1 )
| ( ( X3 = X5 )
& ~ X1 ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',iftrueProp2) ).
thf(f459,plain,
( ( $true
= ( ( ~ sK4
& ( sK5 = sK9 ) )
| ( sK4
& ( sK3 = sK9 ) ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f458]) ).
thf(f458,plain,
( ( $true
= ( ( ~ sK4
& ( sK5 = sK9 ) )
| ( sK4
& ( sK3 = sK9 ) ) ) )
| ( $false = $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f457]) ).
thf(f457,plain,
( ( $false
= ( $false
=> ( in @ sK9 @ ( setadjoin @ sK3 @ emptyset ) ) ) )
| ( $true
= ( ( ~ sK4
& ( sK5 = sK9 ) )
| ( sK4
& ( sK3 = sK9 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f456]) ).
thf(f456,plain,
( ( $false
= ( $false
=> ( in @ sK9 @ ( setadjoin @ sK3 @ emptyset ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( ~ sK4
& ( sK5 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) )
@ sK9 ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f450,f48]) ).
thf(f48,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) )
| ( $true
= ( X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ Y0 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( Y0 @ Y1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f450,plain,
( ( $false
= ( ( in @ sK9
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] :
( ( ~ sK4
& ( sK5 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) ) ) )
=> ( in @ sK9 @ ( setadjoin @ sK3 @ emptyset ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f444]) ).
thf(f444,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( sK5 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK3 @ emptyset ) ) )
@ sK9 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f431]) ).
thf(f431,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( sK5 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK3 @ emptyset ) ) ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f322]) ).
thf(f322,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( sK5 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK3 @ emptyset ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f321]) ).
thf(f321,definition,
( spl0_1
<=> ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( sK5 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK3 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f454,plain,
( ( $false
= ( in @ sK9 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f450]) ).
thf(f485,plain,
( ( $true
= ( in @ sK3 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f476,f469]) ).
thf(f476,plain,
( ( $true
= ( in @ sK9 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f471]) ).
thf(f471,plain,
( ( $true
= ( $true
=> ( in @ sK9 @ ( setadjoin @ sK3 @ emptyset ) ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f82,f466]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( X2 = X1 )
=> ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f70]) ).
thf(f419,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f418]) ).
thf(f418,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f417]) ).
thf(f417,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f416]) ).
thf(f416,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f415,f125]) ).
thf(f415,plain,
( ( $true = ( ~ sK4 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f414]) ).
thf(f414,plain,
( ( $true
= ( $true
=> ~ sK4 ) )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f406,f121]) ).
thf(f406,plain,
( ( ( ( in @ sK5 @ sK2 )
=> ~ sK4 )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f400]) ).
thf(f400,plain,
( ( $true
= ( ( in @ sK5 @ sK2 )
=> ( sK4
=> $false ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f216,f397]) ).
thf(f397,plain,
( ( $false
= ( in @ sK3
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] :
( ( ~ sK4
& ( sK5 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f355,f381]) ).
thf(f381,plain,
( ( sK8 = sK3 )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[status(thm)],[f372]) ).
thf(f372,plain,
( ( $true
= ( sK8 = sK3 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f367]) ).
thf(f367,plain,
( ( $true
= ( $true
=> ( sK8 = sK3 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f64,f356]) ).
thf(f356,plain,
( ( $true
= ( in @ sK8 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f343]) ).
thf(f343,plain,
( ( $false
= ( ( in @ sK8 @ ( setadjoin @ sK3 @ emptyset ) )
=> ( in @ sK8
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] :
( ( ~ sK4
& ( sK5 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f340]) ).
thf(f340,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK3 @ emptyset ) )
=> ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( sK5 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) ) ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f325]) ).
thf(f325,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK3 @ emptyset ) )
=> ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( sK5 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f324]) ).
thf(f324,definition,
( spl0_2
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK3 @ emptyset ) )
=> ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( sK5 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f355,plain,
( ( $false
= ( in @ sK8
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] :
( ( ~ sK4
& ( sK5 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f343]) ).
thf(f216,plain,
! [X0: $o,X1: $i] :
( $true
= ( ( in @ X1 @ sK2 )
=> ( X0
=> ( in @ sK3
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] :
( ( ~ X0
& ( X1 = Y0 ) )
| ( X0
& ( sK3 = Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f213]) ).
thf(f213,plain,
! [X0: $o,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( X0
=> ( in @ sK3
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ X0
& ( Y0 = Y1 ) )
| ( X0
& ( sK3 = Y1 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
! [X0: $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( X0
=> ( in @ sK3
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ X0
& ( Y0 = Y1 ) )
| ( X0
& ( sK3 = Y1 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f114]) ).
thf(f114,plain,
! [X0: $o] :
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( X0
=> ( in @ sK3
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ X0
& ( Y0 = Y1 ) )
| ( X0
& ( sK3 = Y1 ) ) ) ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f100,f109]) ).
thf(f100,plain,
! [X2: $i,X3: $o,X1: $i] :
( $true
= ( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( X3
=> ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y1: $i] :
( ( ~ X3
& ( Y0 = Y1 ) )
| ( X3
& ( X2 = Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: $i,X3: $o,X1: $i] :
( $true
= ( ^ [Y0: $o] :
( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( Y0
=> ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y2: $i] :
( ( ~ Y0
& ( Y1 = Y2 ) )
| ( Y0
& ( X2 = Y2 ) ) ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X2: $i,X1: $i] :
( ( !! @ $o
@ ^ [Y0: $o] :
( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( Y0
=> ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y2: $i] :
( ( ~ Y0
& ( Y1 = Y2 ) )
| ( Y0
& ( X2 = Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( Y1
=> ( in @ Y0
@ ( dsetconstr @ X1
@ ^ [Y3: $i] :
( ( ~ Y1
& ( Y2 = Y3 ) )
| ( Y1
& ( Y0 = Y3 ) ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( Y1
=> ( in @ Y0
@ ( dsetconstr @ X1
@ ^ [Y3: $i] :
( ( ~ Y1
& ( Y2 = Y3 ) )
| ( Y1
& ( Y0 = Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f95]) ).
thf(f95,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y2
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ~ Y2
& ( Y3 = Y4 ) )
| ( Y2
& ( Y1 = Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f326,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f319,f324,f321]) ).
thf(f319,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( sK5 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK3 @ emptyset ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK3 @ emptyset ) )
=> ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( sK5 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK3 @ emptyset ) )
=> ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( sK5 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( sK5 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK3 @ emptyset ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f141]) ).
thf(f141,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK3 @ emptyset ) )
=> ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( sK5 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( ( ~ sK4
& ( sK5 = Y1 ) )
| ( sK4
& ( sK3 = Y1 ) ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK3 @ emptyset ) ) ) )
=> $false ) )
= $true ),
inference(superposition,[status(thm)],[f67,f124]) ).
thf(f124,plain,
( $false
= ( ( dsetconstr @ sK2
@ ^ [Y0: $i] :
( ( ~ sK4
& ( sK5 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) ) )
= ( setadjoin @ sK3 @ emptyset ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f123]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( X2 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( Y0 = X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU703^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.25 % Computer : n012.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue Feb 24 12:31:15 EST 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.32 ---- Original DTF file ---
% 0.08/0.32 thf(spec,logic,$$dhol).
% 0.08/0.32 %------------------------------------------------------------------------------
% 0.08/0.32 % File : SEU703^2 : TPTP v9.2.1. Released v3.7.0.
% 0.08/0.32 % Domain : Set Theory
% 0.08/0.32 % Problem : Conditionals
% 0.08/0.32 % Version : Especial > Reduced > Especial.
% 0.08/0.32 % English : (! A:i.! phi:o.! x:i.in x A -> (! y:i.in y A -> phi ->
% 0.08/0.32 % dsetconstr A (^ z:i.phi & z = x | ~phi & z = y) =
% 0.08/0.32 % setadjoin x emptyset))
% 0.08/0.32
% 0.08/0.32 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.08/0.32 % Source : [Bro08]
% 0.08/0.32 % Names : ZFC205l [Bro08]
% 0.08/0.32
% 0.08/0.32 % Status : Theorem
% 0.08/0.32 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.70 v8.2.0, 0.77 v8.1.0, 0.73 v7.5.0, 0.57 v7.4.0, 0.44 v7.3.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.57 v6.1.0, 0.71 v5.5.0, 0.67 v5.4.0, 1.00 v5.2.0, 0.80 v5.0.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.08/0.32 % Syntax : Number of formulae : 17 ( 6 unt; 10 typ; 6 def)
% 0.08/0.32 % Number of atoms : 42 ( 16 equ; 0 cnn)
% 0.08/0.32 % Maximal formula atoms : 9 ( 6 avg)
% 0.08/0.32 % Number of connectives : 72 ( 2 ~; 2 |; 4 &; 42 @)
% 0.08/0.32 % ( 1 <=>; 21 =>; 0 <=; 0 <~>)
% 0.08/0.32 % Maximal formula depth : 15 ( 3 avg)
% 0.08/0.32 % Number of types : 2 ( 0 usr)
% 0.08/0.32 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.08/0.32 % Number of symbols : 11 ( 10 usr; 7 con; 0-2 aty)
% 0.08/0.32 % Number of variables : 26 ( 3 ^; 23 !; 0 ?; 26 :)
% 0.08/0.32 % SPC : TH0_THM_EQU_NAR
% 0.08/0.32
% 0.08/0.32 % Comments : http://mathgate.info/detsetitem.php?id=255
% 0.08/0.32 %------------------------------------------------------------------------------
% 0.08/0.32 thf(in_type,type,
% 0.08/0.32 in: $i > $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(emptyset_type,type,
% 0.08/0.32 emptyset: $i ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoin_type,type,
% 0.08/0.32 setadjoin: $i > $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(dsetconstr_type,type,
% 0.08/0.32 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.08/0.32
% 0.08/0.32 thf(dsetconstrER_type,type,
% 0.08/0.32 dsetconstrER: $o ).
% 0.08/0.32
% 0.08/0.32 thf(dsetconstrER,definition,
% 0.08/0.32 ( dsetconstrER
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx
% 0.08/0.32 @ ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.08/0.32 => ( Xphi @ Xx ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setext_type,type,
% 0.08/0.32 setext: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setext,definition,
% 0.08/0.32 ( setext
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ Xx @ B ) )
% 0.08/0.32 => ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ B )
% 0.08/0.32 => ( in @ Xx @ A ) )
% 0.08/0.32 => ( A = B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(uniqinunit_type,type,
% 0.08/0.32 uniqinunit: $o ).
% 0.08/0.32
% 0.08/0.32 thf(uniqinunit,definition,
% 0.08/0.32 ( uniqinunit
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.08/0.32 => ( Xx = Xy ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(eqinunit_type,type,
% 0.08/0.32 eqinunit: $o ).
% 0.08/0.32
% 0.08/0.32 thf(eqinunit,definition,
% 0.08/0.32 ( eqinunit
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xx = Xy )
% 0.08/0.32 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(in__Cong_type,type,
% 0.08/0.32 in__Cong: $o ).
% 0.08/0.32
% 0.08/0.32 thf(in__Cong,definition,
% 0.08/0.32 ( in__Cong
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( A = B )
% 0.08/0.32 => ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xx = Xy )
% 0.08/0.32 => ( ( in @ Xx @ A )
% 0.08/0.32 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(iftrueProp1_type,type,
% 0.08/0.32 iftrueProp1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(iftrueProp1,definition,
% 0.08/0.32 ( iftrueProp1
% 0.08/0.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ A )
% 0.08/0.32 => ( Xphi
% 0.08/0.32 => ( in @ Xx
% 0.08/0.32 @ ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xz: $i] :
% 0.08/0.32 ( ( Xphi
% 0.08/0.32 & ( Xz = Xx ) )
% 0.08/0.32 | ( ~ Xphi
% 0.08/0.32 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(iftrueProp2,conjecture,
% 0.08/0.32 ( dsetconstrER
% 0.08/0.32 => ( setext
% 0.08/0.32 => ( uniqinunit
% 0.08/0.32 => ( eqinunit
% 0.08/0.32 => ( in__Cong
% 0.08/0.32 => ( iftrueProp1
% 0.08/0.32 => ! [A: $i,Xphi: $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ A )
% 0.08/0.32 => ( Xphi
% 0.08/0.32 => ( ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xz: $i] :
% 0.08/0.32 ( ( Xphi
% 0.08/0.32 & ( Xz = Xx ) )
% 0.08/0.32 | ( ~ Xphi
% 0.08/0.32 & ( Xz = Xy ) ) ) )
% 0.08/0.32 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 %------------------------------------------------------------------------------
% 0.08/0.32 ------------------------
% 0.88/0.89 ---- Embedded in THF ---
% 0.88/0.89 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.88/0.89 %%% Generated on Tue Feb 24 12:31:16 EST 2026
% 0.88/0.89 %%% using '$$dhol' embedding, version 1.3.0.
% 0.88/0.89 %%% Logic specification used:
% 0.88/0.89 %%% thf(spec, logic, $$dhol).
% 0.88/0.89
% 0.88/0.89 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2DTF13127.p
% See solution above
% 0.88/0.89 ------------------------
% 0.88/0.89 ---- Cleaned THF ---
% 0.88/0.89 thf(in_type,type,
% 0.88/0.89 in: $i > $i > $o ).
% 0.88/0.89
% 0.88/0.89 thf(emptyset_type,type,
% 0.88/0.89 emptyset: $i ).
% 0.88/0.89
% 0.88/0.89 thf(setadjoin_type,type,
% 0.88/0.89 setadjoin: $i > $i > $i ).
% 0.88/0.89
% 0.88/0.89 thf(dsetconstr_type,type,
% 0.88/0.89 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.88/0.89
% 0.88/0.89 thf(dsetconstrER_type,type,
% 0.88/0.89 dsetconstrER: $o ).
% 0.88/0.89
% 0.88/0.89 thf(dsetconstrER,definition,
% 0.88/0.89 ( dsetconstrER
% 0.88/0.89 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.88/0.89 ( ( in @ Xx
% 0.88/0.89 @ ( dsetconstr @ A
% 0.88/0.89 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.88/0.89 => ( Xphi @ Xx ) ) ) ) ).
% 0.88/0.89
% 0.88/0.89 thf(setext_type,type,
% 0.88/0.89 setext: $o ).
% 0.88/0.89
% 0.88/0.89 thf(setext,definition,
% 0.88/0.89 ( setext
% 0.88/0.89 = ( ! [A: $i,B: $i] :
% 0.88/0.89 ( ! [Xx: $i] :
% 0.88/0.89 ( ( in @ Xx @ A )
% 0.88/0.89 => ( in @ Xx @ B ) )
% 0.88/0.89 => ( ! [Xx: $i] :
% 0.88/0.89 ( ( in @ Xx @ B )
% 0.88/0.89 => ( in @ Xx @ A ) )
% 0.88/0.89 => ( A = B ) ) ) ) ) ).
% 0.88/0.89
% 0.88/0.89 thf(uniqinunit_type,type,
% 0.88/0.89 uniqinunit: $o ).
% 0.88/0.89
% 0.88/0.89 thf(uniqinunit,definition,
% 0.88/0.89 ( uniqinunit
% 0.88/0.89 = ( ! [Xx: $i,Xy: $i] :
% 0.88/0.89 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.88/0.89 => ( Xx = Xy ) ) ) ) ).
% 0.88/0.89
% 0.88/0.89 thf(eqinunit_type,type,
% 0.88/0.89 eqinunit: $o ).
% 0.88/0.89
% 0.88/0.89 thf(eqinunit,definition,
% 0.88/0.89 ( eqinunit
% 0.88/0.89 = ( ! [Xx: $i,Xy: $i] :
% 0.88/0.89 ( ( Xx = Xy )
% 0.88/0.89 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.88/0.89
% 0.88/0.89 thf(in__Cong_type,type,
% 0.88/0.89 in__Cong: $o ).
% 0.88/0.89
% 0.88/0.89 thf(in__Cong,definition,
% 0.88/0.89 ( in__Cong
% 0.88/0.89 = ( ! [A: $i,B: $i] :
% 0.88/0.89 ( ( A = B )
% 0.88/0.89 => ! [Xx: $i,Xy: $i] :
% 0.88/0.89 ( ( Xx = Xy )
% 0.88/0.89 => ( ( in @ Xx @ A )
% 0.88/0.89 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.88/0.89
% 0.88/0.89 thf(iftrueProp1_type,type,
% 0.88/0.89 iftrueProp1: $o ).
% 0.88/0.89
% 0.88/0.89 thf(iftrueProp1,definition,
% 0.88/0.89 ( iftrueProp1
% 0.88/0.89 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.88/0.89 ( ( in @ Xx @ A )
% 0.88/0.89 => ! [Xy: $i] :
% 0.88/0.89 ( ( in @ Xy @ A )
% 0.88/0.89 => ( Xphi
% 0.88/0.89 => ( in @ Xx
% 0.88/0.89 @ ( dsetconstr @ A
% 0.88/0.89 @ ^ [Xz: $i] :
% 0.88/0.89 ( ( Xphi
% 0.88/0.89 & ( Xz = Xx ) )
% 0.88/0.89 | ( ~ Xphi
% 0.88/0.89 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.88/0.89
% 0.88/0.89 thf(iftrueProp2,conjecture,
% 0.88/0.89 ( dsetconstrER
% 0.88/0.89 => ( setext
% 0.88/0.89 => ( uniqinunit
% 0.88/0.89 => ( eqinunit
% 0.88/0.89 => ( in__Cong
% 0.88/0.89 => ( iftrueProp1
% 0.88/0.89 => ! [A: $i,Xphi: $o,Xx: $i] :
% 0.88/0.89 ( ( in @ Xx @ A )
% 0.88/0.89 => ! [Xy: $i] :
% 0.88/0.89 ( ( in @ Xy @ A )
% 0.88/0.89 => ( Xphi
% 0.88/0.89 => ( ( dsetconstr @ A
% 0.88/0.89 @ ^ [Xz: $i] :
% 0.88/0.89 ( ( Xphi
% 0.88/0.89 & ( Xz = Xx ) )
% 0.88/0.89 | ( ~ Xphi
% 0.88/0.89 & ( Xz = Xy ) ) ) )
% 0.88/0.89 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ) ) ) ) ).
% 0.88/0.89 ------------------------
% 1.06/0.91 % (13390)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_13127 for (3000ds/4Mi)
% 1.06/0.91 % (13391)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_13127 for (3000ds/27Mi)
% 1.06/0.91 % (13392)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13127 for (3000ds/2Mi)
% 1.06/0.91 % (13389)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13127 for (3000ds/183Mi)
% 1.06/0.91 % (13393)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_13127 for (3000ds/2Mi)
% 1.06/0.91 % (13394)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_13127 for (3000ds/275Mi)
% 1.06/0.91 % (13395)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13127 for (3000ds/18Mi)
% 1.06/0.91 % (13392)Instruction limit reached!
% 1.06/0.91 % (13392)------------------------------
% 1.06/0.91 % (13392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.91 % (13392)Termination reason: Unknown
% 1.06/0.91 % (13392)Termination phase: Preprocessing 3
% 1.06/0.91
% 1.06/0.91 % (13392)Memory used [KB]: 1023
% 1.06/0.91 % (13392)Time elapsed: 0.002 s
% 1.06/0.91 % (13392)Instructions burned: 3 (million)
% 1.06/0.91 % (13392)------------------------------
% 1.06/0.91 % (13392)------------------------------
% 1.06/0.91 % (13393)Instruction limit reached!
% 1.06/0.91 % (13393)------------------------------
% 1.06/0.91 % (13393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.91 % (13393)Termination reason: Unknown
% 1.06/0.91 % (13393)Termination phase: Property scanning
% 1.06/0.91
% 1.06/0.91 % (13393)Memory used [KB]: 1023
% 1.06/0.91 % (13393)Time elapsed: 0.002 s
% 1.06/0.91 % (13393)Instructions burned: 4 (million)
% 1.06/0.91 % (13393)------------------------------
% 1.06/0.91 % (13393)------------------------------
% 1.06/0.91 % (13390)Instruction limit reached!
% 1.06/0.91 % (13390)------------------------------
% 1.06/0.91 % (13390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.91 % (13390)Termination reason: Unknown
% 1.06/0.91 % (13390)Termination phase: Saturation
% 1.06/0.91
% 1.06/0.91 % (13390)Memory used [KB]: 5500
% 1.06/0.91 % (13390)Time elapsed: 0.003 s
% 1.06/0.91 % (13390)Instructions burned: 6 (million)
% 1.06/0.91 % (13390)------------------------------
% 1.06/0.91 % (13390)------------------------------
% 1.06/0.91 % (13395)Instruction limit reached!
% 1.06/0.91 % (13395)------------------------------
% 1.06/0.91 % (13395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.91 % (13395)Termination reason: Unknown
% 1.06/0.91 % (13395)Termination phase: Saturation
% 1.06/0.91
% 1.06/0.91 % (13395)Memory used [KB]: 5628
% 1.06/0.91 % (13395)Time elapsed: 0.007 s
% 1.06/0.91 % (13395)Instructions burned: 18 (million)
% 1.06/0.91 % (13395)------------------------------
% 1.06/0.91 % (13395)------------------------------
% 1.06/0.92 % (13391)Instruction limit reached!
% 1.06/0.92 % (13391)------------------------------
% 1.06/0.92 % (13391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.92 % (13391)Termination reason: Unknown
% 1.06/0.92 % (13391)Termination phase: Saturation
% 1.06/0.92
% 1.06/0.92 % (13391)Memory used [KB]: 5628
% 1.06/0.92 % (13391)Time elapsed: 0.010 s
% 1.06/0.92 % (13391)Instructions burned: 27 (million)
% 1.06/0.92 % (13391)------------------------------
% 1.06/0.92 % (13391)------------------------------
% 1.06/0.92 % (13396)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/3Mi)
% 1.06/0.92 % (13397)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_13127 for (2999ds/37Mi)
% 1.06/0.92 % (13398)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_13127 for (2999ds/15Mi)
% 1.06/0.92 % (13396)Instruction limit reached!
% 1.06/0.92 % (13396)------------------------------
% 1.06/0.92 % (13396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.92 % (13396)Termination reason: Unknown
% 1.06/0.92 % (13396)Termination phase: Function definition elimination
% 1.06/0.92
% 1.06/0.92 % (13396)Memory used [KB]: 1023
% 1.06/0.92 % (13396)Time elapsed: 0.002 s
% 1.06/0.92 % (13396)Instructions burned: 4 (million)
% 1.06/0.92 % (13396)------------------------------
% 1.06/0.92 % (13396)------------------------------
% 1.06/0.92 % (13399)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_13127 for (2999ds/3Mi)
% 1.06/0.92 % (13398)Instruction limit reached!
% 1.06/0.92 % (13398)------------------------------
% 1.06/0.92 % (13398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.92 % (13398)Termination reason: Unknown
% 1.06/0.92 % (13398)Termination phase: Saturation
% 1.06/0.92
% 1.06/0.92 % (13398)Memory used [KB]: 5628
% 1.06/0.92 % (13398)Time elapsed: 0.006 s
% 1.06/0.92 % (13398)Instructions burned: 15 (million)
% 1.06/0.92 % (13398)------------------------------
% 1.06/0.92 % (13398)------------------------------
% 1.06/0.92 % (13399)Instruction limit reached!
% 1.06/0.92 % (13399)------------------------------
% 1.06/0.92 % (13399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.92 % (13399)Termination reason: Unknown
% 1.06/0.92 % (13399)Termination phase: Function definition elimination
% 1.06/0.92
% 1.06/0.92 % (13399)Memory used [KB]: 1023
% 1.06/0.92 % (13399)Time elapsed: 0.002 s
% 1.06/0.92 % (13399)Instructions burned: 4 (million)
% 1.06/0.92 % (13399)------------------------------
% 1.06/0.92 % (13399)------------------------------
% 1.06/0.92 % (13400)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_13127 for (2999ds/1041Mi)
% 1.06/0.93 % (13401)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/7Mi)
% 1.06/0.93 % (13397)Instruction limit reached!
% 1.06/0.93 % (13397)------------------------------
% 1.06/0.93 % (13397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.93 % (13397)Termination reason: Unknown
% 1.06/0.93 % (13397)Termination phase: Saturation
% 1.06/0.93
% 1.06/0.93 % (13397)Memory used [KB]: 5756
% 1.06/0.93 % (13397)Time elapsed: 0.012 s
% 1.06/0.93 % (13397)Instructions burned: 37 (million)
% 1.06/0.93 % (13397)------------------------------
% 1.06/0.93 % (13397)------------------------------
% 1.06/0.93 % (13401)Instruction limit reached!
% 1.06/0.93 % (13401)------------------------------
% 1.06/0.93 % (13401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.93 % (13401)Termination reason: Unknown
% 1.06/0.93 % (13401)Termination phase: Saturation
% 1.06/0.93
% 1.06/0.93 % (13401)Memory used [KB]: 1023
% 1.06/0.93 % (13401)Time elapsed: 0.003 s
% 1.06/0.93 % (13401)Instructions burned: 8 (million)
% 1.06/0.93 % (13401)------------------------------
% 1.06/0.93 % (13401)------------------------------
% 1.06/0.93 % (13402)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/16Mi)
% 1.06/0.93 % (13403)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_13127 for (2999ds/3Mi)
% 1.06/0.93 % (13403)Instruction limit reached!
% 1.06/0.93 % (13403)------------------------------
% 1.06/0.93 % (13403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.93 % (13403)Termination reason: Unknown
% 1.06/0.93 % (13403)Termination phase: Property scanning
% 1.06/0.93
% 1.06/0.93 % (13403)Memory used [KB]: 1023
% 1.06/0.93 % (13403)Time elapsed: 0.002 s
% 1.06/0.93 % (13403)Instructions burned: 4 (million)
% 1.06/0.93 % (13403)------------------------------
% 1.06/0.93 % (13403)------------------------------
% 1.06/0.94 % (13402)Instruction limit reached!
% 1.06/0.94 % (13402)------------------------------
% 1.06/0.94 % (13402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.94 % (13402)Termination reason: Unknown
% 1.06/0.94 % (13402)Termination phase: Saturation
% 1.06/0.94
% 1.06/0.94 % (13402)Memory used [KB]: 5884
% 1.06/0.94 % (13402)Time elapsed: 0.006 s
% 1.06/0.94 % (13402)Instructions burned: 16 (million)
% 1.06/0.94 % (13402)------------------------------
% 1.06/0.94 % (13402)------------------------------
% 1.06/0.94 % (13404)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_13127 for (2999ds/3Mi)
% 1.06/0.94 % (13404)Instruction limit reached!
% 1.06/0.94 % (13404)------------------------------
% 1.06/0.94 % (13404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.94 % (13404)Termination reason: Unknown
% 1.06/0.94 % (13404)Termination phase: Property scanning
% 1.06/0.94
% 1.06/0.94 % (13404)Memory used [KB]: 1023
% 1.06/0.94 % (13404)Time elapsed: 0.002 s
% 1.06/0.94 % (13404)Instructions burned: 4 (million)
% 1.06/0.94 % (13404)------------------------------
% 1.06/0.94 % (13404)------------------------------
% 1.06/0.94 % (13405)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/7Mi)
% 1.06/0.94 % (13405)Refutation not found, incomplete strategy
% 1.06/0.94 % (13405)------------------------------
% 1.06/0.94 % (13405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.94 % (13405)Termination reason: Refutation not found, incomplete strategy
% 1.06/0.94
% 1.06/0.94
% 1.06/0.94 % (13405)Memory used [KB]: 5500
% 1.06/0.94 % (13405)Time elapsed: 0.002 s
% 1.06/0.94 % (13405)Instructions burned: 4 (million)
% 1.06/0.94 % (13405)------------------------------
% 1.06/0.94 % (13405)------------------------------
% 1.06/0.94 % (13406)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/3Mi)
% 1.06/0.94 % (13406)Instruction limit reached!
% 1.06/0.94 % (13406)------------------------------
% 1.06/0.94 % (13406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.94 % (13406)Termination reason: Unknown
% 1.06/0.94 % (13406)Termination phase: Property scanning
% 1.06/0.94
% 1.06/0.94 % (13406)Memory used [KB]: 1023
% 1.06/0.94 % (13406)Time elapsed: 0.002 s
% 1.06/0.94 % (13406)Instructions burned: 5 (million)
% 1.06/0.94 % (13406)------------------------------
% 1.06/0.94 % (13406)------------------------------
% 1.06/0.95 % (13407)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/4Mi)
% 1.06/0.95 % (13407)Instruction limit reached!
% 1.06/0.95 % (13407)------------------------------
% 1.06/0.95 % (13407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.95 % (13407)Termination reason: Unknown
% 1.06/0.95 % (13407)Termination phase: Function definition elimination
% 1.06/0.95
% 1.06/0.95 % (13407)Memory used [KB]: 1023
% 1.06/0.95 % (13407)Time elapsed: 0.002 s
% 1.06/0.95 % (13407)Instructions burned: 4 (million)
% 1.06/0.95 % (13407)------------------------------
% 1.06/0.95 % (13407)------------------------------
% 1.06/0.95 % (13408)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/18Mi)
% 1.06/0.95 % (13409)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/710Mi)
% 1.06/0.95 % (13408)Instruction limit reached!
% 1.06/0.95 % (13408)------------------------------
% 1.06/0.95 % (13408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.95 % (13408)Termination reason: Unknown
% 1.06/0.95 % (13408)Termination phase: Saturation
% 1.06/0.95
% 1.06/0.95 % (13408)Memory used [KB]: 5628
% 1.06/0.95 % (13408)Time elapsed: 0.006 s
% 1.06/0.95 % (13408)Instructions burned: 18 (million)
% 1.06/0.95 % (13408)------------------------------
% 1.06/0.95 % (13408)------------------------------
% 1.06/0.95 % (13410)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/6Mi)
% 1.06/0.95 % (13410)Instruction limit reached!
% 1.06/0.95 % (13410)------------------------------
% 1.06/0.95 % (13410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.95 % (13410)Termination reason: Unknown
% 1.06/0.95 % (13410)Termination phase: Saturation
% 1.06/0.95
% 1.06/0.95 % (13410)Memory used [KB]: 5500
% 1.06/0.95 % (13410)Time elapsed: 0.003 s
% 1.06/0.95 % (13410)Instructions burned: 8 (million)
% 1.06/0.95 % (13410)------------------------------
% 1.06/0.95 % (13410)------------------------------
% 1.06/0.96 % (13411)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/902Mi)
% 1.06/0.96 % (13411)Refutation not found, incomplete strategy
% 1.06/0.96 % (13411)------------------------------
% 1.06/0.96 % (13411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.96 % (13411)Termination reason: Refutation not found, incomplete strategy
% 1.06/0.96
% 1.06/0.96
% 1.06/0.96 % (13411)Memory used [KB]: 5500
% 1.06/0.96 % (13411)Time elapsed: 0.003 s
% 1.06/0.96 % (13411)Instructions burned: 7 (million)
% 1.06/0.96 % (13411)------------------------------
% 1.06/0.96 % (13411)------------------------------
% 1.06/0.96 % (13412)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/21Mi)
% 1.06/0.96 % (13389)Instruction limit reached!
% 1.06/0.96 % (13389)------------------------------
% 1.06/0.96 % (13389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.96 % (13389)Termination reason: Unknown
% 1.06/0.96 % (13389)Termination phase: Saturation
% 1.06/0.96
% 1.06/0.96 % (13389)Memory used [KB]: 6012
% 1.06/0.96 % (13389)Time elapsed: 0.058 s
% 1.06/0.96 % (13389)Instructions burned: 184 (million)
% 1.06/0.96 % (13389)------------------------------
% 1.06/0.96 % (13389)------------------------------
% 1.06/0.96 % (13413)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/5Mi)
% 1.06/0.96 % (13413)Instruction limit reached!
% 1.06/0.96 % (13413)------------------------------
% 1.06/0.96 % (13413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.96 % (13413)Termination reason: Unknown
% 1.06/0.96 % (13413)Termination phase: Property scanning
% 1.06/0.96
% 1.06/0.96 % (13413)Memory used [KB]: 1023
% 1.06/0.96 % (13413)Time elapsed: 0.002 s
% 1.06/0.96 % (13413)Instructions burned: 5 (million)
% 1.06/0.96 % (13413)------------------------------
% 1.06/0.96 % (13413)------------------------------
% 1.06/0.97 % (13414)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/6Mi)
% 1.06/0.97 % (13412)Instruction limit reached!
% 1.06/0.97 % (13412)------------------------------
% 1.06/0.97 % (13412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.97 % (13412)Termination reason: Unknown
% 1.06/0.97 % (13412)Termination phase: Saturation
% 1.06/0.97
% 1.06/0.97 % (13412)Memory used [KB]: 5628
% 1.06/0.97 % (13412)Time elapsed: 0.008 s
% 1.06/0.97 % (13412)Instructions burned: 22 (million)
% 1.06/0.97 % (13412)------------------------------
% 1.06/0.97 % (13412)------------------------------
% 1.06/0.97 % (13414)Instruction limit reached!
% 1.06/0.97 % (13414)------------------------------
% 1.06/0.97 % (13414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.97 % (13414)Termination reason: Unknown
% 1.06/0.97 % (13414)Termination phase: Saturation
% 1.06/0.97
% 1.06/0.97 % (13414)Memory used [KB]: 5500
% 1.06/0.97 % (13414)Time elapsed: 0.003 s
% 1.06/0.97 % (13414)Instructions burned: 8 (million)
% 1.06/0.97 % (13414)------------------------------
% 1.06/0.97 % (13414)------------------------------
% 1.06/0.97 % (13415)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/377Mi)
% 1.06/0.97 % (13416)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/779Mi)
% 1.06/0.98 % (13417)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/19Mi)
% 1.06/0.98 % (13418)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/879Mi)
% 1.06/0.98 % (13417)Instruction limit reached!
% 1.06/0.98 % (13417)------------------------------
% 1.06/0.98 % (13417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.98 % (13417)Termination reason: Unknown
% 1.06/0.98 % (13417)Termination phase: Saturation
% 1.06/0.98
% 1.06/0.98 % (13417)Memory used [KB]: 5628
% 1.06/0.98 % (13417)Time elapsed: 0.007 s
% 1.06/0.98 % (13417)Instructions burned: 21 (million)
% 1.06/0.98 % (13417)------------------------------
% 1.06/0.98 % (13417)------------------------------
% 1.06/0.99 % (13394)Instruction limit reached!
% 1.06/0.99 % (13394)------------------------------
% 1.06/0.99 % (13394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/0.99 % (13394)Termination reason: Unknown
% 1.06/0.99 % (13394)Termination phase: Saturation
% 1.06/0.99
% 1.06/0.99 % (13394)Memory used [KB]: 6012
% 1.06/0.99 % (13394)Time elapsed: 0.083 s
% 1.06/0.99 % (13394)Instructions burned: 277 (million)
% 1.06/0.99 % (13394)------------------------------
% 1.06/0.99 % (13394)------------------------------
% 1.06/0.99 % (13419)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/17Mi)
% 1.06/1.00 % (13420)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13127 for (2999ds/3Mi)
% 1.06/1.00 % (13420)Instruction limit reached!
% 1.06/1.00 % (13420)------------------------------
% 1.06/1.00 % (13420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/1.00 % (13420)Termination reason: Unknown
% 1.06/1.00 % (13420)Termination phase: Property scanning
% 1.06/1.00
% 1.06/1.00 % (13420)Memory used [KB]: 1023
% 1.06/1.00 % (13420)Time elapsed: 0.002 s
% 1.06/1.00 % (13420)Instructions burned: 4 (million)
% 1.06/1.00 % (13420)------------------------------
% 1.06/1.00 % (13420)------------------------------
% 1.06/1.00 % (13419)Instruction limit reached!
% 1.06/1.00 % (13419)------------------------------
% 1.06/1.00 % (13419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.06/1.00 % (13419)Termination reason: Unknown
% 1.06/1.00 % (13419)Termination phase: Saturation
% 1.06/1.00
% 1.06/1.00 % (13419)Memory used [KB]: 5628
% 1.06/1.00 % (13419)Time elapsed: 0.029 s
% 1.06/1.00 % (13419)Instructions burned: 19 (million)
% 1.06/1.00 % (13419)------------------------------
% 1.06/1.00 % (13419)------------------------------
% 1.06/1.01 % (13421)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13127 for (2998ds/30Mi)
% 1.06/1.01 % (13422)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13127 for (2998ds/127Mi)
% 1.79/1.01 % (13421)Refutation not found, incomplete strategy
% 1.79/1.01 % (13421)------------------------------
% 1.79/1.01 % (13421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.01 % (13421)Termination reason: Refutation not found, incomplete strategy
% 1.79/1.01
% 1.79/1.01
% 1.79/1.01 % (13421)Memory used [KB]: 5500
% 1.79/1.01 % (13421)Time elapsed: 0.005 s
% 1.79/1.01 % (13421)Instructions burned: 14 (million)
% 1.79/1.01 % (13421)------------------------------
% 1.79/1.01 % (13421)------------------------------
% 1.79/1.02 % (13423)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13127 for (2998ds/100Mi)
% 1.79/1.05 % (13422)Instruction limit reached!
% 1.79/1.05 % (13422)------------------------------
% 1.79/1.05 % (13422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.05 % (13422)Termination reason: Unknown
% 1.79/1.05 % (13422)Termination phase: Saturation
% 1.79/1.05
% 1.79/1.05 % (13422)Memory used [KB]: 5756
% 1.79/1.05 % (13422)Time elapsed: 0.041 s
% 1.79/1.05 % (13422)Instructions burned: 128 (million)
% 1.79/1.05 % (13422)------------------------------
% 1.79/1.05 % (13422)------------------------------
% 1.79/1.05 % (13423)Instruction limit reached!
% 1.79/1.05 % (13423)------------------------------
% 1.79/1.05 % (13423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.05 % (13423)Termination reason: Unknown
% 1.79/1.05 % (13423)Termination phase: Saturation
% 1.79/1.05
% 1.79/1.05 % (13423)Memory used [KB]: 5884
% 1.79/1.05 % (13423)Time elapsed: 0.032 s
% 1.79/1.05 % (13423)Instructions burned: 100 (million)
% 1.79/1.05 % (13423)------------------------------
% 1.79/1.05 % (13423)------------------------------
% 1.79/1.06 % (13424)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_13127 for (2998ds/3Mi)
% 1.79/1.06 % (13424)Instruction limit reached!
% 1.79/1.06 % (13424)------------------------------
% 1.79/1.06 % (13424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.06 % (13424)Termination reason: Unknown
% 1.79/1.06 % (13424)Termination phase: Property scanning
% 1.79/1.06
% 1.79/1.06 % (13424)Memory used [KB]: 1023
% 1.79/1.06 % (13424)Time elapsed: 0.002 s
% 1.79/1.06 % (13424)Instructions burned: 5 (million)
% 1.79/1.06 % (13424)------------------------------
% 1.79/1.06 % (13424)------------------------------
% 1.79/1.06 % (13425)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_13127 for (2998ds/20Mi)
% 1.79/1.07 % (13426)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_13127 for (2998ds/86Mi)
% 1.79/1.07 % (13425)Instruction limit reached!
% 1.79/1.07 % (13425)------------------------------
% 1.79/1.07 % (13425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.07 % (13425)Termination reason: Unknown
% 1.79/1.07 % (13425)Termination phase: Saturation
% 1.79/1.07
% 1.79/1.07 % (13425)Memory used [KB]: 5628
% 1.79/1.07 % (13425)Time elapsed: 0.008 s
% 1.79/1.07 % (13425)Instructions burned: 22 (million)
% 1.79/1.07 % (13425)------------------------------
% 1.79/1.07 % (13425)------------------------------
% 1.79/1.08 % (13427)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_13127 for (2998ds/107Mi)
% 1.79/1.09 % (13415)Instruction limit reached!
% 1.79/1.09 % (13415)------------------------------
% 1.79/1.09 % (13415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.09 % (13415)Termination reason: Unknown
% 1.79/1.09 % (13415)Termination phase: Saturation
% 1.79/1.09
% 1.79/1.09 % (13415)Memory used [KB]: 5884
% 1.79/1.09 % (13415)Time elapsed: 0.119 s
% 1.79/1.09 % (13415)Instructions burned: 378 (million)
% 1.79/1.09 % (13415)------------------------------
% 1.79/1.09 % (13415)------------------------------
% 1.79/1.09 % (13426)Instruction limit reached!
% 1.79/1.09 % (13426)------------------------------
% 1.79/1.09 % (13426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.09 % (13426)Termination reason: Unknown
% 1.79/1.09 % (13426)Termination phase: Saturation
% 1.79/1.09
% 1.79/1.09 % (13426)Memory used [KB]: 5884
% 1.79/1.09 % (13426)Time elapsed: 0.028 s
% 1.79/1.09 % (13426)Instructions burned: 87 (million)
% 1.79/1.09 % (13426)------------------------------
% 1.79/1.09 % (13426)------------------------------
% 1.79/1.10 % (13428)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_13127 for (2998ds/39Mi)
% 1.79/1.10 % (13429)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_13127 for (2997ds/448Mi)
% 1.79/1.11 % (13428)Instruction limit reached!
% 1.79/1.11 % (13428)------------------------------
% 1.79/1.11 % (13428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.11 % (13428)Termination reason: Unknown
% 1.79/1.11 % (13428)Termination phase: Saturation
% 1.79/1.11
% 1.79/1.11 % (13428)Memory used [KB]: 5884
% 1.79/1.11 % (13428)Time elapsed: 0.012 s
% 1.79/1.11 % (13428)Instructions burned: 40 (million)
% 1.79/1.11 % (13428)------------------------------
% 1.79/1.11 % (13428)------------------------------
% 2.45/1.11 % (13427)Instruction limit reached!
% 2.45/1.11 % (13427)------------------------------
% 2.45/1.11 % (13427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.11 % (13427)Termination reason: Unknown
% 2.45/1.11 % (13427)Termination phase: Saturation
% 2.45/1.11
% 2.45/1.11 % (13427)Memory used [KB]: 5884
% 2.45/1.11 % (13427)Time elapsed: 0.035 s
% 2.45/1.11 % (13427)Instructions burned: 108 (million)
% 2.45/1.11 % (13427)------------------------------
% 2.45/1.11 % (13427)------------------------------
% 2.45/1.12 % (13430)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_13127 for (2997ds/46Mi)
% 2.45/1.12 % (13431)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_13127 for (2997ds/98Mi)
% 2.45/1.13 % (13430)Instruction limit reached!
% 2.45/1.13 % (13430)------------------------------
% 2.45/1.13 % (13430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.13 % (13430)Termination reason: Unknown
% 2.45/1.13 % (13430)Termination phase: Saturation
% 2.45/1.13
% 2.45/1.13 % (13430)Memory used [KB]: 5884
% 2.45/1.13 % (13430)Time elapsed: 0.016 s
% 2.45/1.13 % (13430)Instructions burned: 47 (million)
% 2.45/1.13 % (13430)------------------------------
% 2.45/1.13 % (13430)------------------------------
% 2.45/1.14 % (13432)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_13127 for (2997ds/507Mi)
% 2.45/1.15 % (13431)Instruction limit reached!
% 2.45/1.15 % (13431)------------------------------
% 2.45/1.15 % (13431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.15 % (13431)Termination reason: Unknown
% 2.45/1.15 % (13431)Termination phase: Saturation
% 2.45/1.15
% 2.45/1.15 % (13431)Memory used [KB]: 1279
% 2.45/1.15 % (13431)Time elapsed: 0.033 s
% 2.45/1.15 % (13431)Instructions burned: 99 (million)
% 2.45/1.15 % (13431)------------------------------
% 2.45/1.15 % (13431)------------------------------
% 2.45/1.16 % (13409)Instruction limit reached!
% 2.45/1.16 % (13409)------------------------------
% 2.45/1.16 % (13409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.16 % (13409)Termination reason: Unknown
% 2.45/1.16 % (13409)Termination phase: Saturation
% 2.45/1.16
% 2.45/1.16 % (13409)Memory used [KB]: 7164
% 2.45/1.16 % (13409)Time elapsed: 0.213 s
% 2.45/1.16 % (13409)Instructions burned: 712 (million)
% 2.45/1.16 % (13409)------------------------------
% 2.45/1.16 % (13409)------------------------------
% 2.45/1.16 % (13433)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_13127 for (2997ds/149Mi)
% 2.45/1.17 % (13434)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_13127 for (2997ds/39Mi)
% 2.45/1.18 % (13434)Instruction limit reached!
% 2.45/1.18 % (13434)------------------------------
% 2.45/1.18 % (13434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.18 % (13434)Termination reason: Unknown
% 2.45/1.18 % (13434)Termination phase: Saturation
% 2.45/1.18
% 2.45/1.18 % (13434)Memory used [KB]: 5628
% 2.45/1.18 % (13434)Time elapsed: 0.013 s
% 2.45/1.18 % (13434)Instructions burned: 39 (million)
% 2.45/1.18 % (13434)------------------------------
% 2.45/1.18 % (13434)------------------------------
% 2.45/1.19 % (13435)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_13127 for (2997ds/6Mi)
% 2.45/1.20 % (13435)Instruction limit reached!
% 2.45/1.20 % (13435)------------------------------
% 2.45/1.20 % (13435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.20 % (13435)Termination reason: Unknown
% 2.45/1.20 % (13435)Termination phase: Saturation
% 2.45/1.20
% 2.45/1.20 % (13435)Memory used [KB]: 9978
% 2.45/1.20 % (13435)Time elapsed: 0.004 s
% 2.45/1.20 % (13435)Instructions burned: 8 (million)
% 2.45/1.20 % (13435)------------------------------
% 2.45/1.20 % (13435)------------------------------
% 2.91/1.20 % (13436)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_13127 for (2997ds/1087Mi)
% 2.91/1.21 % (13416)Instruction limit reached!
% 2.91/1.21 % (13416)------------------------------
% 2.91/1.21 % (13416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.21 % (13416)Termination reason: Unknown
% 2.91/1.21 % (13416)Termination phase: Saturation
% 2.91/1.21
% 2.91/1.21 % (13416)Memory used [KB]: 6268
% 2.91/1.21 % (13416)Time elapsed: 0.258 s
% 2.91/1.21 % (13416)Instructions burned: 780 (million)
% 2.91/1.21 % (13416)------------------------------
% 2.91/1.21 % (13416)------------------------------
% 2.91/1.21 % (13433)Instruction limit reached!
% 2.91/1.21 % (13433)------------------------------
% 2.91/1.21 % (13433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.21 % (13433)Termination reason: Unknown
% 2.91/1.21 % (13433)Termination phase: Saturation
% 2.91/1.21
% 2.91/1.21 % (13433)Memory used [KB]: 5884
% 2.91/1.21 % (13433)Time elapsed: 0.048 s
% 2.91/1.21 % (13433)Instructions burned: 151 (million)
% 2.91/1.21 % (13433)------------------------------
% 2.91/1.21 % (13433)------------------------------
% 2.91/1.22 % (13437)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/47Mi)
% 2.91/1.22 % (13438)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/44Mi)
% 2.91/1.23 % (13400)Instruction limit reached!
% 2.91/1.23 % (13400)------------------------------
% 2.91/1.23 % (13400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.23 % (13400)Termination reason: Unknown
% 2.91/1.23 % (13400)Termination phase: Saturation
% 2.91/1.23
% 2.91/1.23 % (13400)Memory used [KB]: 7291
% 2.91/1.23 % (13400)Time elapsed: 0.308 s
% 2.91/1.23 % (13400)Instructions burned: 1041 (million)
% 2.91/1.23 % (13400)------------------------------
% 2.91/1.23 % (13400)------------------------------
% 2.91/1.23 % (13438)Instruction limit reached!
% 2.91/1.23 % (13438)------------------------------
% 2.91/1.23 % (13438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.23 % (13438)Termination reason: Unknown
% 2.91/1.23 % (13438)Termination phase: Saturation
% 2.91/1.23
% 2.91/1.23 % (13438)Memory used [KB]: 1279
% 2.91/1.23 % (13438)Time elapsed: 0.015 s
% 2.91/1.23 % (13438)Instructions burned: 44 (million)
% 2.91/1.23 % (13438)------------------------------
% 2.91/1.23 % (13438)------------------------------
% 2.91/1.23 % (13437)Instruction limit reached!
% 2.91/1.23 % (13437)------------------------------
% 2.91/1.23 % (13437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.23 % (13437)Termination reason: Unknown
% 2.91/1.23 % (13437)Termination phase: Saturation
% 2.91/1.23
% 2.91/1.23 % (13437)Memory used [KB]: 5884
% 2.91/1.23 % (13437)Time elapsed: 0.016 s
% 2.91/1.23 % (13437)Instructions burned: 50 (million)
% 2.91/1.23 % (13437)------------------------------
% 2.91/1.23 % (13437)------------------------------
% 2.91/1.24 % (13429)Instruction limit reached!
% 2.91/1.24 % (13429)------------------------------
% 2.91/1.24 % (13429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.24 % (13429)Termination reason: Unknown
% 2.91/1.24 % (13429)Termination phase: Saturation
% 2.91/1.24
% 2.91/1.24 % (13429)Memory used [KB]: 6524
% 2.91/1.24 % (13429)Time elapsed: 0.134 s
% 2.91/1.24 % (13429)Instructions burned: 448 (million)
% 2.91/1.24 % (13429)------------------------------
% 2.91/1.24 % (13429)------------------------------
% 2.91/1.24 % (13439)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/432Mi)
% 2.91/1.24 % (13441)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/62Mi)
% 2.91/1.24 % (13442)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/31Mi)
% 2.91/1.25 % (13443)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/96Mi)
% 2.91/1.25 % (13442)Instruction limit reached!
% 2.91/1.25 % (13442)------------------------------
% 2.91/1.25 % (13442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.25 % (13442)Termination reason: Unknown
% 2.91/1.25 % (13442)Termination phase: Saturation
% 2.91/1.25
% 2.91/1.25 % (13442)Memory used [KB]: 5628
% 2.91/1.25 % (13442)Time elapsed: 0.011 s
% 2.91/1.25 % (13442)Instructions burned: 31 (million)
% 2.91/1.25 % (13442)------------------------------
% 2.91/1.25 % (13442)------------------------------
% 2.91/1.25 % (13418)Instruction limit reached!
% 2.91/1.25 % (13418)------------------------------
% 2.91/1.25 % (13418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.25 % (13418)Termination reason: Unknown
% 2.91/1.25 % (13418)Termination phase: Saturation
% 2.91/1.25
% 2.91/1.25 % (13418)Memory used [KB]: 6396
% 2.91/1.25 % (13418)Time elapsed: 0.298 s
% 2.91/1.25 % (13418)Instructions burned: 880 (million)
% 2.91/1.25 % (13418)------------------------------
% 2.91/1.25 % (13418)------------------------------
% 2.91/1.26 % (13441)Instruction limit reached!
% 2.91/1.26 % (13441)------------------------------
% 2.91/1.26 % (13441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.26 % (13441)Termination reason: Unknown
% 2.91/1.26 % (13441)Termination phase: Saturation
% 2.91/1.26
% 2.91/1.26 % (13441)Memory used [KB]: 5884
% 2.91/1.26 % (13441)Time elapsed: 0.020 s
% 2.91/1.26 % (13441)Instructions burned: 63 (million)
% 2.91/1.26 % (13441)------------------------------
% 2.91/1.26 % (13441)------------------------------
% 2.91/1.26 % (13444)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/453Mi)
% 2.91/1.26 % (13445)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/71Mi)
% 2.91/1.27 % (13446)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/83Mi)
% 2.91/1.28 % (13443)Instruction limit reached!
% 2.91/1.28 % (13443)------------------------------
% 2.91/1.28 % (13443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.28 % (13443)Termination reason: Unknown
% 2.91/1.28 % (13443)Termination phase: Saturation
% 2.91/1.28
% 2.91/1.28 % (13443)Memory used [KB]: 5628
% 2.91/1.28 % (13443)Time elapsed: 0.033 s
% 2.91/1.28 % (13443)Instructions burned: 99 (million)
% 2.91/1.28 % (13443)------------------------------
% 2.91/1.28 % (13443)------------------------------
% 2.91/1.29 % (13445)Instruction limit reached!
% 2.91/1.29 % (13445)------------------------------
% 2.91/1.29 % (13445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.29 % (13445)Termination reason: Unknown
% 2.91/1.29 % (13445)Termination phase: Saturation
% 2.91/1.29
% 2.91/1.29 % (13445)Memory used [KB]: 5756
% 2.91/1.29 % (13445)Time elapsed: 0.024 s
% 2.91/1.29 % (13445)Instructions burned: 72 (million)
% 2.91/1.29 % (13445)------------------------------
% 2.91/1.29 % (13445)------------------------------
% 2.91/1.29 % (13447)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/11Mi)
% 2.91/1.29 % (13447)Instruction limit reached!
% 2.91/1.29 % (13447)------------------------------
% 2.91/1.29 % (13447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.29 % (13447)Termination reason: Unknown
% 2.91/1.29 % (13447)Termination phase: Saturation
% 2.91/1.29
% 2.91/1.29 % (13447)Memory used [KB]: 5500
% 2.91/1.29 % (13447)Time elapsed: 0.004 s
% 2.91/1.29 % (13447)Instructions burned: 11 (million)
% 2.91/1.29 % (13447)------------------------------
% 2.91/1.29 % (13447)------------------------------
% 2.91/1.30 % (13448)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/41Mi)
% 3.42/1.30 % (13446)Instruction limit reached!
% 3.42/1.30 % (13446)------------------------------
% 3.42/1.30 % (13446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.42/1.30 % (13446)Termination reason: Unknown
% 3.42/1.30 % (13446)Termination phase: Saturation
% 3.42/1.30
% 3.42/1.30 % (13446)Memory used [KB]: 5756
% 3.42/1.30 % (13446)Time elapsed: 0.027 s
% 3.42/1.30 % (13446)Instructions burned: 85 (million)
% 3.42/1.30 % (13446)------------------------------
% 3.42/1.30 % (13446)------------------------------
% 3.42/1.30 % (13449)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/6Mi)
% 3.42/1.30 % (13432)Instruction limit reached!
% 3.42/1.30 % (13432)------------------------------
% 3.42/1.30 % (13432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.42/1.30 % (13432)Termination reason: Unknown
% 3.42/1.30 % (13432)Termination phase: Saturation
% 3.42/1.30
% 3.42/1.30 % (13432)Memory used [KB]: 6524
% 3.42/1.30 % (13432)Time elapsed: 0.157 s
% 3.42/1.30 % (13432)Instructions burned: 508 (million)
% 3.42/1.30 % (13432)------------------------------
% 3.42/1.30 % (13432)------------------------------
% 3.42/1.30 % (13449)Instruction limit reached!
% 3.42/1.30 % (13449)------------------------------
% 3.42/1.30 % (13449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.42/1.30 % (13449)Termination reason: Unknown
% 3.42/1.30 % (13449)Termination phase: Saturation
% 3.42/1.30
% 3.42/1.30 % (13449)Memory used [KB]: 5500
% 3.42/1.30 % (13449)Time elapsed: 0.003 s
% 3.42/1.30 % (13449)Instructions burned: 7 (million)
% 3.42/1.30 % (13449)------------------------------
% 3.42/1.30 % (13449)------------------------------
% 3.42/1.31 % (13450)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/150Mi)
% 3.42/1.31 % (13448)Instruction limit reached!
% 3.42/1.31 % (13448)------------------------------
% 3.42/1.31 % (13448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.42/1.31 % (13448)Termination reason: Unknown
% 3.42/1.31 % (13448)Termination phase: Saturation
% 3.42/1.31
% 3.42/1.31 % (13448)Memory used [KB]: 5756
% 3.42/1.31 % (13448)Time elapsed: 0.014 s
% 3.42/1.31 % (13448)Instructions burned: 43 (million)
% 3.42/1.31 % (13448)------------------------------
% 3.42/1.31 % (13448)------------------------------
% 3.42/1.31 % (13451)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/343Mi)
% 3.42/1.31 % (13452)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_13127 for (2996ds/109Mi)
% 3.42/1.32 % (13453)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_13127 for (2995ds/253Mi)
% 3.42/1.35 % (13452)Instruction limit reached!
% 3.42/1.35 % (13452)------------------------------
% 3.42/1.35 % (13452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.42/1.35 % (13452)Termination reason: Unknown
% 3.42/1.35 % (13452)Termination phase: Saturation
% 3.42/1.35
% 3.42/1.35 % (13452)Memory used [KB]: 5756
% 3.42/1.35 % (13452)Time elapsed: 0.060 s
% 3.42/1.35 % (13452)Instructions burned: 110 (million)
% 3.42/1.35 % (13452)------------------------------
% 3.42/1.35 % (13452)------------------------------
% 3.42/1.35 % (13450)Instruction limit reached!
% 3.42/1.35 % (13450)------------------------------
% 3.42/1.35 % (13450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.42/1.35 % (13450)Termination reason: Unknown
% 3.42/1.35 % (13450)Termination phase: Saturation
% 3.42/1.35
% 3.42/1.35 % (13450)Memory used [KB]: 6012
% 3.42/1.35 % (13450)Time elapsed: 0.049 s
% 3.42/1.35 % (13450)Instructions burned: 152 (million)
% 3.42/1.35 % (13450)------------------------------
% 3.42/1.35 % (13450)------------------------------
% 3.42/1.36 % (13454)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_13127 for (2995ds/140Mi)
% 3.42/1.36 % (13454)Refutation not found, incomplete strategy
% 3.42/1.36 % (13454)------------------------------
% 3.42/1.36 % (13454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.42/1.36 % (13454)Termination reason: Refutation not found, incomplete strategy
% 3.42/1.36
% 3.42/1.36
% 3.42/1.36 % (13454)Memory used [KB]: 5500
% 3.42/1.36 % (13454)Time elapsed: 0.003 s
% 3.42/1.36 % (13454)Instructions burned: 7 (million)
% 3.42/1.36 % (13454)------------------------------
% 3.42/1.36 % (13454)------------------------------
% 3.42/1.36 % (13455)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_13127 for (2995ds/614Mi)
% 3.42/1.36 % (13439)Instruction limit reached!
% 3.42/1.36 % (13439)------------------------------
% 3.42/1.36 % (13439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.42/1.36 % (13439)Termination reason: Unknown
% 3.42/1.36 % (13439)Termination phase: Saturation
% 3.42/1.36
% 3.42/1.36 % (13439)Memory used [KB]: 2686
% 3.42/1.36 % (13439)Time elapsed: 0.124 s
% 3.42/1.36 % (13439)Instructions burned: 434 (million)
% 3.42/1.36 % (13439)------------------------------
% 3.42/1.36 % (13439)------------------------------
% 3.42/1.37 % (13456)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_13127 for (2995ds/202Mi)
% 3.42/1.37 % (13457)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_13127 for (2995ds/339Mi)
% 3.90/1.40 % (13453)Instruction limit reached!
% 3.90/1.40 % (13453)------------------------------
% 3.90/1.40 % (13453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.40 % (13453)Termination reason: Unknown
% 3.90/1.40 % (13453)Termination phase: Saturation
% 3.90/1.40
% 3.90/1.40 % (13453)Memory used [KB]: 6268
% 3.90/1.40 % (13453)Time elapsed: 0.103 s
% 3.90/1.40 % (13453)Instructions burned: 255 (million)
% 3.90/1.40 % (13453)------------------------------
% 3.90/1.40 % (13453)------------------------------
% 3.90/1.40 % (13444)Instruction limit reached!
% 3.90/1.40 % (13444)------------------------------
% 3.90/1.40 % (13444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.40 % (13444)Termination reason: Unknown
% 3.90/1.40 % (13444)Termination phase: Saturation
% 3.90/1.40
% 3.90/1.40 % (13444)Memory used [KB]: 6012
% 3.90/1.40 % (13444)Time elapsed: 0.142 s
% 3.90/1.40 % (13444)Instructions burned: 455 (million)
% 3.90/1.40 % (13444)------------------------------
% 3.90/1.40 % (13444)------------------------------
% 3.90/1.41 % (13458)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_13127 for (2994ds/283Mi)
% 3.90/1.41 % (13459)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_13127 for (2994ds/134Mi)
% 3.90/1.42 % (13451)Instruction limit reached!
% 3.90/1.42 % (13451)------------------------------
% 3.90/1.42 % (13451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.42 % (13451)Termination reason: Unknown
% 3.90/1.42 % (13451)Termination phase: Saturation
% 3.90/1.42
% 3.90/1.42 % (13451)Memory used [KB]: 6268
% 3.90/1.42 % (13451)Time elapsed: 0.108 s
% 3.90/1.42 % (13451)Instructions burned: 343 (million)
% 3.90/1.42 % (13451)------------------------------
% 3.90/1.42 % (13451)------------------------------
% 3.90/1.43 % (13460)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_13127 for (2994ds/298Mi)
% 3.90/1.43 % (13456)Instruction limit reached!
% 3.90/1.43 % (13456)------------------------------
% 3.90/1.43 % (13456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.43 % (13456)Termination reason: Unknown
% 3.90/1.43 % (13456)Termination phase: Saturation
% 3.90/1.43
% 3.90/1.43 % (13456)Memory used [KB]: 6140
% 3.90/1.43 % (13456)Time elapsed: 0.088 s
% 3.90/1.43 % (13456)Instructions burned: 203 (million)
% 3.90/1.43 % (13456)------------------------------
% 3.90/1.43 % (13456)------------------------------
% 3.90/1.44 % (13461)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_13127 for (2994ds/192Mi)
% 3.90/1.46 % (13459)Instruction limit reached!
% 3.90/1.46 % (13459)------------------------------
% 3.90/1.46 % (13459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.46 % (13459)Termination reason: Unknown
% 3.90/1.46 % (13459)Termination phase: Saturation
% 3.90/1.46
% 3.90/1.46 % (13459)Memory used [KB]: 6140
% 3.90/1.46 % (13459)Time elapsed: 0.044 s
% 3.90/1.46 % (13459)Instructions burned: 136 (million)
% 3.90/1.46 % (13459)------------------------------
% 3.90/1.46 % (13459)------------------------------
% 3.90/1.47 % (13462)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_13127 for (2994ds/258Mi)
% 3.90/1.48 % (13457)Instruction limit reached!
% 3.90/1.48 % (13457)------------------------------
% 3.90/1.48 % (13457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.48 % (13457)Termination reason: Unknown
% 3.90/1.48 % (13457)Termination phase: Saturation
% 3.90/1.48
% 3.90/1.48 % (13457)Memory used [KB]: 6524
% 3.90/1.48 % (13457)Time elapsed: 0.132 s
% 3.90/1.48 % (13457)Instructions burned: 340 (million)
% 3.90/1.48 % (13457)------------------------------
% 3.90/1.48 % (13457)------------------------------
% 3.90/1.49 % (13463)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_13127 for (2994ds/90Mi)
% 3.90/1.49 % (13458)Instruction limit reached!
% 3.90/1.49 % (13458)------------------------------
% 3.90/1.49 % (13458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.49 % (13458)Termination reason: Unknown
% 3.90/1.49 % (13458)Termination phase: Saturation
% 3.90/1.49
% 3.90/1.49 % (13458)Memory used [KB]: 7675
% 3.90/1.49 % (13458)Time elapsed: 0.083 s
% 3.90/1.49 % (13458)Instructions burned: 286 (million)
% 3.90/1.49 % (13458)------------------------------
% 3.90/1.49 % (13458)------------------------------
% 4.59/1.50 % (13464)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_13127 for (2994ds/231Mi)
% 4.59/1.51 % (13461)Instruction limit reached!
% 4.59/1.51 % (13461)------------------------------
% 4.59/1.51 % (13461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.59/1.51 % (13461)Termination reason: Unknown
% 4.59/1.51 % (13461)Termination phase: Saturation
% 4.59/1.51
% 4.59/1.51 % (13461)Memory used [KB]: 5884
% 4.59/1.51 % (13461)Time elapsed: 0.062 s
% 4.59/1.51 % (13461)Instructions burned: 194 (million)
% 4.59/1.51 % (13461)------------------------------
% 4.59/1.51 % (13461)------------------------------
% 4.59/1.51 % (13465)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_13127 for (2993ds/458Mi)
% 4.59/1.52 % (13463)Instruction limit reached!
% 4.59/1.52 % (13463)------------------------------
% 4.59/1.52 % (13463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.59/1.52 % (13463)Termination reason: Unknown
% 4.59/1.52 % (13463)Termination phase: Saturation
% 4.59/1.52
% 4.59/1.52 % (13463)Memory used [KB]: 5884
% 4.59/1.52 % (13463)Time elapsed: 0.029 s
% 4.59/1.52 % (13463)Instructions burned: 91 (million)
% 4.59/1.52 % (13463)------------------------------
% 4.59/1.52 % (13463)------------------------------
% 4.59/1.52 % (13460)Instruction limit reached!
% 4.59/1.52 % (13460)------------------------------
% 4.59/1.52 % (13460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.59/1.52 % (13460)Termination reason: Unknown
% 4.59/1.52 % (13460)Termination phase: Saturation
% 4.59/1.52
% 4.59/1.52 % (13460)Memory used [KB]: 5884
% 4.59/1.52 % (13460)Time elapsed: 0.097 s
% 4.59/1.52 % (13460)Instructions burned: 300 (million)
% 4.59/1.52 % (13460)------------------------------
% 4.59/1.52 % (13460)------------------------------
% 4.59/1.53 % (13466)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_13127 for (2993ds/31Mi)
% 4.59/1.53 % (13436)Instruction limit reached!
% 4.59/1.53 % (13436)------------------------------
% 4.59/1.53 % (13436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.59/1.53 % (13436)Termination reason: Unknown
% 4.59/1.53 % (13436)Termination phase: Saturation
% 4.59/1.53
% 4.59/1.53 % (13436)Memory used [KB]: 6908
% 4.59/1.53 % (13436)Time elapsed: 0.324 s
% 4.59/1.53 % (13436)Instructions burned: 1088 (million)
% 4.59/1.53 % (13436)------------------------------
% 4.59/1.53 % (13436)------------------------------
% 4.59/1.53 % (13467)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_13127 for (2993ds/297Mi)
% 4.59/1.54 % (13468)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_13127 for (2993ds/987Mi)
% 4.59/1.54 % (13466)Instruction limit reached!
% 4.59/1.54 % (13466)------------------------------
% 4.59/1.54 % (13466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.59/1.54 % (13466)Termination reason: Unknown
% 4.59/1.54 % (13466)Termination phase: Saturation
% 4.59/1.54
% 4.59/1.54 % (13466)Memory used [KB]: 5628
% 4.59/1.54 % (13466)Time elapsed: 0.012 s
% 4.59/1.54 % (13466)Instructions burned: 33 (million)
% 4.59/1.54 % (13466)------------------------------
% 4.59/1.54 % (13466)------------------------------
% 4.59/1.55 % (13462)Instruction limit reached!
% 4.59/1.55 % (13462)------------------------------
% 4.59/1.55 % (13462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.59/1.55 % (13462)Termination reason: Unknown
% 4.59/1.55 % (13462)Termination phase: Saturation
% 4.59/1.55
% 4.59/1.55 % (13462)Memory used [KB]: 6012
% 4.59/1.55 % (13462)Time elapsed: 0.081 s
% 4.59/1.55 % (13462)Instructions burned: 260 (million)
% 4.59/1.55 % (13462)------------------------------
% 4.59/1.55 % (13462)------------------------------
% 4.59/1.55 % (13469)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_13127 for (2993ds/182Mi)
% 4.59/1.55 % (13470)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_13127 for (2993ds/182Mi)
% 4.59/1.56 % (13455)Instruction limit reached!
% 4.59/1.56 % (13455)------------------------------
% 4.59/1.56 % (13455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.59/1.56 % (13455)Termination reason: Unknown
% 4.59/1.56 % (13455)Termination phase: Saturation
% 4.59/1.56
% 4.59/1.56 % (13455)Memory used [KB]: 6396
% 4.59/1.56 % (13455)Time elapsed: 0.219 s
% 4.59/1.56 % (13455)Instructions burned: 615 (million)
% 4.59/1.56 % (13455)------------------------------
% 4.59/1.56 % (13455)------------------------------
% 4.59/1.57 % (13471)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_13127 for (2993ds/154Mi)
% 4.59/1.58 % (13464)Instruction limit reached!
% 4.59/1.58 % (13464)------------------------------
% 4.59/1.58 % (13464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.59/1.58 % (13464)Termination reason: Unknown
% 4.59/1.58 % (13464)Termination phase: Saturation
% 4.59/1.58
% 4.59/1.58 % (13464)Memory used [KB]: 6652
% 4.59/1.58 % (13464)Time elapsed: 0.079 s
% 4.59/1.58 % (13464)Instructions burned: 232 (million)
% 4.59/1.58 % (13464)------------------------------
% 4.59/1.58 % (13464)------------------------------
% 4.59/1.59 % (13472)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_13127 for (2993ds/79Mi)
% 5.54/1.61 % (13469)Instruction limit reached!
% 5.54/1.61 % (13469)------------------------------
% 5.54/1.61 % (13469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/1.61 % (13469)Termination reason: Unknown
% 5.54/1.61 % (13469)Termination phase: Saturation
% 5.54/1.61
% 5.54/1.61 % (13469)Memory used [KB]: 5756
% 5.54/1.61 % (13469)Time elapsed: 0.060 s
% 5.54/1.61 % (13469)Instructions burned: 182 (million)
% 5.54/1.61 % (13469)------------------------------
% 5.54/1.61 % (13469)------------------------------
% 5.54/1.61 % (13472)Instruction limit reached!
% 5.54/1.61 % (13472)------------------------------
% 5.54/1.61 % (13472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/1.61 % (13472)Termination reason: Unknown
% 5.54/1.61 % (13472)Termination phase: Saturation
% 5.54/1.61
% 5.54/1.61 % (13472)Memory used [KB]: 5756
% 5.54/1.61 % (13472)Time elapsed: 0.025 s
% 5.54/1.61 % (13472)Instructions burned: 80 (million)
% 5.54/1.61 % (13472)------------------------------
% 5.54/1.61 % (13472)------------------------------
% 5.54/1.61 % (13470)Instruction limit reached!
% 5.54/1.61 % (13470)------------------------------
% 5.54/1.61 % (13470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/1.61 % (13470)Termination reason: Unknown
% 5.54/1.61 % (13470)Termination phase: Saturation
% 5.54/1.61
% 5.54/1.61 % (13470)Memory used [KB]: 6268
% 5.54/1.61 % (13470)Time elapsed: 0.058 s
% 5.54/1.61 % (13470)Instructions burned: 182 (million)
% 5.54/1.61 % (13470)------------------------------
% 5.54/1.61 % (13470)------------------------------
% 5.54/1.62 % (13473)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_13127 for (2992ds/216Mi)
% 5.54/1.62 % (13471)Instruction limit reached!
% 5.54/1.62 % (13471)------------------------------
% 5.54/1.62 % (13471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/1.62 % (13471)Termination reason: Unknown
% 5.54/1.62 % (13471)Termination phase: Saturation
% 5.54/1.62
% 5.54/1.62 % (13471)Memory used [KB]: 5884
% 5.54/1.62 % (13471)Time elapsed: 0.051 s
% 5.54/1.62 % (13471)Instructions burned: 156 (million)
% 5.54/1.62 % (13471)------------------------------
% 5.54/1.62 % (13471)------------------------------
% 5.54/1.62 % (13474)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_13127 for (2992ds/114Mi)
% 5.54/1.62 % (13475)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_13127 for (2992ds/922Mi)
% 5.54/1.62 % (13467)Instruction limit reached!
% 5.54/1.62 % (13467)------------------------------
% 5.54/1.62 % (13467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/1.62 % (13467)Termination reason: Unknown
% 5.54/1.62 % (13467)Termination phase: Saturation
% 5.54/1.62
% 5.54/1.62 % (13467)Memory used [KB]: 6524
% 5.54/1.62 % (13467)Time elapsed: 0.092 s
% 5.54/1.62 % (13467)Instructions burned: 298 (million)
% 5.54/1.62 % (13467)------------------------------
% 5.54/1.62 % (13467)------------------------------
% 5.54/1.63 % (13476)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_13127 for (2992ds/182Mi)
% 5.54/1.63 % (13477)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_13127 for (2992ds/164Mi)
% 5.54/1.65 % (13474)Instruction limit reached!
% 5.54/1.65 % (13474)------------------------------
% 5.54/1.65 % (13474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/1.65 % (13474)Termination reason: Unknown
% 5.54/1.65 % (13474)Termination phase: Saturation
% 5.54/1.65
% 5.54/1.65 % (13474)Memory used [KB]: 6140
% 5.54/1.65 % (13474)Time elapsed: 0.036 s
% 5.54/1.65 % (13474)Instructions burned: 116 (million)
% 5.54/1.65 % (13474)------------------------------
% 5.54/1.65 % (13474)------------------------------
% 5.54/1.66 % (13465)Instruction limit reached!
% 5.54/1.66 % (13465)------------------------------
% 5.54/1.66 % (13465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/1.66 % (13465)Termination reason: Unknown
% 5.54/1.66 % (13465)Termination phase: Saturation
% 5.54/1.66
% 5.54/1.66 % (13465)Memory used [KB]: 6268
% 5.54/1.66 % (13465)Time elapsed: 0.144 s
% 5.54/1.66 % (13465)Instructions burned: 460 (million)
% 5.54/1.66 % (13465)------------------------------
% 5.54/1.66 % (13465)------------------------------
% 5.54/1.66 % (13478)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_13127 for (2992ds/50Mi)
% 5.54/1.67 % (13479)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_13127 for (2992ds/368Mi)
% 5.54/1.68 % (13473)Instruction limit reached!
% 5.54/1.68 % (13473)------------------------------
% 5.54/1.68 % (13473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/1.68 % (13473)Termination reason: Unknown
% 5.54/1.68 % (13473)Termination phase: Saturation
% 5.54/1.68
% 5.54/1.68 % (13473)Memory used [KB]: 5884
% 5.54/1.68 % (13473)Time elapsed: 0.061 s
% 5.54/1.68 % (13473)Instructions burned: 216 (million)
% 5.54/1.68 % (13473)------------------------------
% 5.54/1.68 % (13473)------------------------------
% 5.54/1.68 % (13478)Instruction limit reached!
% 5.54/1.68 % (13478)------------------------------
% 5.54/1.68 % (13478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/1.68 % (13478)Termination reason: Unknown
% 5.54/1.68 % (13478)Termination phase: Saturation
% 5.54/1.68
% 5.54/1.68 % (13478)Memory used [KB]: 10362
% 5.54/1.68 % (13478)Time elapsed: 0.016 s
% 5.54/1.68 % (13478)Instructions burned: 51 (million)
% 5.54/1.68 % (13478)------------------------------
% 5.54/1.68 % (13478)------------------------------
% 5.54/1.68 % (13477)Instruction limit reached!
% 5.54/1.68 % (13477)------------------------------
% 5.54/1.68 % (13477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/1.68 % (13477)Termination reason: Unknown
% 5.54/1.68 % (13477)Termination phase: Saturation
% 5.54/1.68
% 5.54/1.68 % (13477)Memory used [KB]: 1407
% 5.54/1.68 % (13477)Time elapsed: 0.051 s
% 5.54/1.68 % (13477)Instructions burned: 164 (million)
% 5.54/1.68 % (13477)------------------------------
% 5.54/1.68 % (13477)------------------------------
% 5.54/1.68 % (13476)Instruction limit reached!
% 5.54/1.68 % (13476)------------------------------
% 5.54/1.68 % (13476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/1.68 % (13476)Termination reason: Unknown
% 5.54/1.68 % (13476)Termination phase: Saturation
% 5.54/1.68
% 5.54/1.68 % (13476)Memory used [KB]: 5756
% 5.54/1.68 % (13476)Time elapsed: 0.058 s
% 5.54/1.68 % (13476)Instructions burned: 183 (million)
% 5.54/1.68 % (13476)------------------------------
% 5.54/1.68 % (13476)------------------------------
% 5.54/1.68 % (13480)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_13127 for (2992ds/1021Mi)
% 5.54/1.69 % (13481)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_13127 for (2992ds/267Mi)
% 5.54/1.69 % (13482)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_13127 for (2992ds/204Mi)
% 5.54/1.69 % (13483)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_13127 for (2992ds/26Mi)
% 6.29/1.70 % (13483)Instruction limit reached!
% 6.29/1.70 % (13483)------------------------------
% 6.29/1.70 % (13483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/1.70 % (13483)Termination reason: Unknown
% 6.29/1.70 % (13483)Termination phase: Saturation
% 6.29/1.70
% 6.29/1.70 % (13483)Memory used [KB]: 5628
% 6.29/1.70 % (13483)Time elapsed: 0.009 s
% 6.29/1.70 % (13483)Instructions burned: 26 (million)
% 6.29/1.70 % (13483)------------------------------
% 6.29/1.70 % (13483)------------------------------
% 6.29/1.71 % (13484)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_13127 for (2991ds/53Mi)
% 6.29/1.72 % (13484)Instruction limit reached!
% 6.29/1.72 % (13484)------------------------------
% 6.29/1.72 % (13484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/1.72 % (13484)Termination reason: Unknown
% 6.29/1.72 % (13484)Termination phase: Saturation
% 6.29/1.72
% 6.29/1.72 % (13484)Memory used [KB]: 5628
% 6.29/1.72 % (13484)Time elapsed: 0.015 s
% 6.29/1.72 % (13484)Instructions burned: 53 (million)
% 6.29/1.72 % (13484)------------------------------
% 6.29/1.72 % (13484)------------------------------
% 6.29/1.73 % (13485)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_13127 for (2991ds/4436Mi)
% 6.29/1.76 % (13482)Instruction limit reached!
% 6.29/1.76 % (13482)------------------------------
% 6.29/1.76 % (13482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/1.76 % (13482)Termination reason: Unknown
% 6.29/1.76 % (13482)Termination phase: Saturation
% 6.29/1.76
% 6.29/1.76 % (13482)Memory used [KB]: 5884
% 6.29/1.76 % (13482)Time elapsed: 0.067 s
% 6.29/1.76 % (13482)Instructions burned: 206 (million)
% 6.29/1.76 % (13482)------------------------------
% 6.29/1.76 % (13482)------------------------------
% 6.29/1.77 % (13486)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_13127 for (2991ds/1539Mi)
% 6.29/1.77 % (13481)Instruction limit reached!
% 6.29/1.77 % (13481)------------------------------
% 6.29/1.77 % (13481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/1.77 % (13481)Termination reason: Unknown
% 6.29/1.77 % (13481)Termination phase: Saturation
% 6.29/1.77
% 6.29/1.77 % (13481)Memory used [KB]: 6140
% 6.29/1.77 % (13481)Time elapsed: 0.087 s
% 6.29/1.77 % (13481)Instructions burned: 268 (million)
% 6.29/1.77 % (13481)------------------------------
% 6.29/1.77 % (13481)------------------------------
% 6.29/1.78 % (13487)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_13127 for (2991ds/408Mi)
% 6.29/1.78 % (13479)Instruction limit reached!
% 6.29/1.78 % (13479)------------------------------
% 6.29/1.78 % (13479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/1.78 % (13479)Termination reason: Unknown
% 6.29/1.78 % (13479)Termination phase: Saturation
% 6.29/1.78
% 6.29/1.78 % (13479)Memory used [KB]: 6140
% 6.29/1.78 % (13479)Time elapsed: 0.119 s
% 6.29/1.78 % (13479)Instructions burned: 369 (million)
% 6.29/1.78 % (13479)------------------------------
% 6.29/1.78 % (13479)------------------------------
% 6.29/1.79 % (13488)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_13127 for (2991ds/5205Mi)
% 6.63/1.83 % (13468)Instruction limit reached!
% 6.63/1.83 % (13468)------------------------------
% 6.63/1.83 % (13468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/1.83 % (13468)Termination reason: Unknown
% 6.63/1.83 % (13468)Termination phase: Saturation
% 6.63/1.83
% 6.63/1.83 % (13468)Memory used [KB]: 7419
% 6.63/1.83 % (13468)Time elapsed: 0.299 s
% 6.63/1.83 % (13468)Instructions burned: 988 (million)
% 6.63/1.83 % (13468)------------------------------
% 6.63/1.83 % (13468)------------------------------
% 6.63/1.84 % (13488)First to succeed.
% 6.63/1.84 % (13489)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_13127 for (2990ds/1913Mi)
% 6.63/1.85 % (13488)Refutation found. Thanks to Tanya!
% 6.63/1.85 % SZS status Theorem for DTF2THF_13127
% 6.63/1.85 % SZS output start Proof for DTF2THF_13127
% 6.63/1.85 thf(func_def_0, type, in: $i > $i > $o).
% 6.63/1.85 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 6.63/1.85 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 6.63/1.85 thf(func_def_26, type, ph1: !>[X0: $tType]:(X0)).
% 6.63/1.85 thf(f489,plain,(
% 6.63/1.85 $false),
% 6.63/1.85 inference(avatar_sat_refutation,[status(thm)],[f326,f419,f488])).
% 6.63/1.85 thf(f488,plain,(
% 6.63/1.85 ~spl0_1),
% 6.63/1.85 inference(avatar_contradiction_clause,[status(thm)],[f487])).
% 6.63/1.85 thf(f487,plain,(
% 6.63/1.85 $false | ~spl0_1),
% 6.63/1.85 inference(trivial_inequality_removal,[status(thm)],[f486])).
% 6.63/1.85 thf(f486,plain,(
% 6.63/1.85 ($false = $true) | ~spl0_1),
% 6.63/1.85 inference(forward_demodulation,[status(thm)],[f485,f483])).
% 6.63/1.85 thf(f483,plain,(
% 6.63/1.85 ($false = (in @ sK3 @ (setadjoin @ sK3 @ emptyset))) | ~spl0_1),
% 6.63/1.85 inference(backward_demodulation,[status(thm)],[f454,f469])).
% 6.63/1.85 thf(f469,plain,(
% 6.63/1.85 (sK3 = sK9) | ~spl0_1),
% 6.63/1.85 inference(equality_proxy_clausification,[status(thm)],[f466])).
% 6.63/1.85 thf(f466,plain,(
% 6.63/1.85 ($true = (sK3 = sK9)) | ~spl0_1),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f465])).
% 6.63/1.85 thf(f465,plain,(
% 6.63/1.85 ($true = ($false | (sK3 = sK9))) | ~spl0_1),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f464])).
% 6.63/1.85 thf(f464,plain,(
% 6.63/1.85 ($true = (($false & (sK5 = sK9)) | (sK3 = sK9))) | ~spl0_1),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f463])).
% 6.63/1.85 thf(f463,plain,(
% 6.63/1.85 ($true = (((~ $true) & (sK5 = sK9)) | (sK3 = sK9))) | ~spl0_1),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f462])).
% 6.63/1.85 thf(f462,plain,(
% 6.63/1.85 ($true = (((~ $true) & (sK5 = sK9)) | ($true & (sK3 = sK9)))) | ~spl0_1),
% 6.63/1.85 inference(forward_demodulation,[status(thm)],[f459,f125])).
% 6.63/1.85 thf(f125,plain,(
% 6.63/1.85 ($true = sK4)),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f123])).
% 6.63/1.85 thf(f123,plain,(
% 6.63/1.85 ($false = (sK4 => ((dsetconstr @ sK2 @ (^[Y0 : $i]: (((~ sK4) & (sK5 = Y0)) | (sK4 & (sK3 = Y0))))) = (setadjoin @ sK3 @ emptyset))))),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f122])).
% 6.63/1.85 thf(f122,plain,(
% 6.63/1.85 ($false = ($true => (sK4 => ((dsetconstr @ sK2 @ (^[Y0 : $i]: (((~ sK4) & (sK5 = Y0)) | (sK4 & (sK3 = Y0))))) = (setadjoin @ sK3 @ emptyset)))))),
% 6.63/1.85 inference(backward_demodulation,[status(thm)],[f119,f121])).
% 6.63/1.85 thf(f121,plain,(
% 6.63/1.85 ($true = (in @ sK5 @ sK2))),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f119])).
% 6.63/1.85 thf(f119,plain,(
% 6.63/1.85 ($false = ((in @ sK5 @ sK2) => (sK4 => ((dsetconstr @ sK2 @ (^[Y0 : $i]: (((~ sK4) & (sK5 = Y0)) | (sK4 & (sK3 = Y0))))) = (setadjoin @ sK3 @ emptyset)))))),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f118])).
% 6.63/1.85 thf(f118,plain,(
% 6.63/1.85 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK2) => (sK4 => ((dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (Y0 = Y1)) | (sK4 & (sK3 = Y1))))) = (setadjoin @ sK3 @ emptyset))))) @ sK5))),
% 6.63/1.85 inference(sigma_clausification,[status(thm)],[f112])).
% 6.63/1.85 thf(f112,plain,(
% 6.63/1.85 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (sK4 => ((dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (Y0 = Y1)) | (sK4 & (sK3 = Y1))))) = (setadjoin @ sK3 @ emptyset)))))))),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f110])).
% 6.63/1.85 thf(f110,plain,(
% 6.63/1.85 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (sK4 => ((dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (Y0 = Y1)) | (sK4 & (sK3 = Y1))))) = (setadjoin @ sK3 @ emptyset))))))))),
% 6.63/1.85 inference(backward_demodulation,[status(thm)],[f107,f109])).
% 6.63/1.85 thf(f109,plain,(
% 6.63/1.85 ($true = (in @ sK3 @ sK2))),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 6.63/1.85 thf(f107,plain,(
% 6.63/1.85 ($false = ((in @ sK3 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (sK4 => ((dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (Y0 = Y1)) | (sK4 & (sK3 = Y1))))) = (setadjoin @ sK3 @ emptyset))))))))),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f106])).
% 6.63/1.85 thf(f106,plain,(
% 6.63/1.85 ($false = ((^[Y0 : $o]: ((in @ sK3 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (Y0 => ((dsetconstr @ sK2 @ (^[Y2 : $i]: (((~ Y0) & (Y1 = Y2)) | (Y0 & (sK3 = Y2))))) = (setadjoin @ sK3 @ emptyset)))))))) @ sK4))),
% 6.63/1.85 inference(sigma_clausification,[status(thm)],[f105])).
% 6.63/1.85 thf(f105,plain,(
% 6.63/1.85 ($false = (!! @ $o @ (^[Y0 : $o]: ((in @ sK3 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (Y0 => ((dsetconstr @ sK2 @ (^[Y2 : $i]: (((~ Y0) & (Y1 = Y2)) | (Y0 & (sK3 = Y2))))) = (setadjoin @ sK3 @ emptyset))))))))))),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f104])).
% 6.63/1.85 thf(f104,plain,(
% 6.63/1.85 ($false = ((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (Y1 => ((dsetconstr @ sK2 @ (^[Y3 : $i]: (((~ Y1) & (Y2 = Y3)) | (Y1 & (Y0 = Y3))))) = (setadjoin @ Y0 @ emptyset)))))))))) @ sK3))),
% 6.63/1.85 inference(sigma_clausification,[status(thm)],[f103])).
% 6.63/1.85 thf(f103,plain,(
% 6.63/1.85 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (Y1 => ((dsetconstr @ sK2 @ (^[Y3 : $i]: (((~ Y1) & (Y2 = Y3)) | (Y1 & (Y0 = Y3))))) = (setadjoin @ Y0 @ emptyset))))))))))))),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f102])).
% 6.63/1.85 thf(f102,plain,(
% 6.63/1.85 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset)))))))))))) @ sK2))),
% 6.63/1.85 inference(sigma_clausification,[status(thm)],[f89])).
% 6.63/1.85 thf(f89,plain,(
% 6.63/1.85 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset))))))))))))))),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 6.63/1.85 thf(f75,plain,(
% 6.63/1.85 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset)))))))))))))))),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 6.63/1.85 thf(f72,plain,(
% 6.63/1.85 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset))))))))))))))))),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f71])).
% 6.63/1.85 thf(f71,plain,(
% 6.63/1.85 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset)))))))))))))))))),
% 6.63/1.85 inference(backward_demodulation,[status(thm)],[f55,f70])).
% 6.63/1.85 thf(f70,plain,(
% 6.63/1.85 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 6.63/1.85 thf(f55,plain,(
% 6.63/1.85 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset)))))))))))))))))),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 6.63/1.85 thf(f52,plain,(
% 6.63/1.85 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset))))))))))))))))))),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f51])).
% 6.63/1.85 thf(f51,plain,(
% 6.63/1.85 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset)))))))))))))))))))),
% 6.63/1.85 inference(backward_demodulation,[status(thm)],[f36,f50])).
% 6.63/1.85 thf(f50,plain,(
% 6.63/1.85 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) = $true)),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 6.63/1.85 thf(f36,plain,(
% 6.63/1.85 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset)))))))))))))))))))),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 6.63/1.85 thf(f33,plain,(
% 6.63/1.85 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset))))))))))))))))))))),
% 6.63/1.85 inference(not_proxy_clausification,[status(thm)],[f32])).
% 6.63/1.85 thf(f32,plain,(
% 6.63/1.85 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset)))))))))))))))))))))),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f31])).
% 6.63/1.85 thf(f31,plain,(
% 6.63/1.85 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset)))))))))))))))))))))),
% 6.63/1.85 inference(definition_unfolding,[status(thm)],[f30,f27,f24,f25,f28,f26,f29])).
% 6.63/1.85 thf(f29,plain,(
% 6.63/1.85 (iftrueProp1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))))))))))))))))),
% 6.63/1.85 inference(cnf_transformation,[status(thm)],[f21])).
% 6.63/1.85 thf(f21,plain,(
% 6.63/1.85 (iftrueProp1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))))))))))))))))),
% 6.63/1.85 inference(fool_elimination,[status(thm)],[f20])).
% 6.63/1.85 thf(f20,plain,(
% 6.63/1.85 (! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (X0 => (in @ X1 @ (dsetconstr @ X2 @ (^[X4 : $i] : (((X1 = X4) & X0) | ((X3 = X4) & ~X0)))))))) = iftrueProp1)),
% 6.63/1.85 inference(rectify,[status(thm)],[f6])).
% 6.63/1.85 thf(f6,axiom,(
% 6.63/1.85 (! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => (in @ X2 @ (dsetconstr @ X0 @ (^[X5 : $i] : (((X2 = X5) & X1) | ((X3 = X5) & ~X1)))))))) = iftrueProp1)),
% 6.63/1.85 file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',iftrueProp1)).
% 6.63/1.85 thf(f26,plain,(
% 6.63/1.85 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))))),
% 6.63/1.85 inference(cnf_transformation,[status(thm)],[f13])).
% 6.63/1.85 thf(f13,plain,(
% 6.63/1.85 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))))),
% 6.63/1.85 inference(fool_elimination,[status(thm)],[f12])).
% 6.63/1.85 thf(f12,plain,(
% 6.63/1.85 (in__Cong = ! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X3 @ X0) <=> (in @ X2 @ X1)))))),
% 6.63/1.85 inference(rectify,[status(thm)],[f5])).
% 6.63/1.85 thf(f5,axiom,(
% 6.63/1.85 (in__Cong = ! [X0 : $i,X4 : $i] : ((X0 = X4) => ! [X3 : $i,X2 : $i] : ((X2 = X3) => ((in @ X2 @ X0) <=> (in @ X3 @ X4)))))),
% 6.63/1.85 file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',in__Cong)).
% 6.63/1.85 thf(f28,plain,(
% 6.63/1.85 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 6.63/1.85 inference(cnf_transformation,[status(thm)],[f17])).
% 6.63/1.85 thf(f17,plain,(
% 6.63/1.85 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 6.63/1.85 inference(fool_elimination,[status(thm)],[f16])).
% 6.63/1.85 thf(f16,plain,(
% 6.63/1.85 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (in @ X1 @ (setadjoin @ X0 @ emptyset))) = eqinunit)),
% 6.63/1.85 inference(rectify,[status(thm)],[f4])).
% 6.63/1.85 thf(f4,axiom,(
% 6.63/1.85 (! [X3 : $i,X2 : $i] : ((X2 = X3) => (in @ X2 @ (setadjoin @ X3 @ emptyset))) = eqinunit)),
% 6.63/1.85 file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',eqinunit)).
% 6.63/1.85 thf(f25,plain,(
% 6.63/1.85 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 6.63/1.85 inference(cnf_transformation,[status(thm)],[f11])).
% 6.63/1.85 thf(f11,plain,(
% 6.63/1.85 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 6.63/1.85 inference(fool_elimination,[status(thm)],[f10])).
% 6.63/1.85 thf(f10,plain,(
% 6.63/1.85 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 6.63/1.85 inference(rectify,[status(thm)],[f3])).
% 6.63/1.85 thf(f3,axiom,(
% 6.63/1.85 (! [X2 : $i,X3 : $i] : ((in @ X2 @ (setadjoin @ X3 @ emptyset)) => (X2 = X3)) = uniqinunit)),
% 6.63/1.85 file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',uniqinunit)).
% 6.63/1.85 thf(f24,plain,(
% 6.63/1.85 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))))),
% 6.63/1.85 inference(cnf_transformation,[status(thm)],[f23])).
% 6.63/1.85 thf(f23,plain,(
% 6.63/1.85 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))))),
% 6.63/1.85 inference(fool_elimination,[status(thm)],[f22])).
% 6.63/1.85 thf(f22,plain,(
% 6.63/1.85 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))))),
% 6.63/1.85 inference(rectify,[status(thm)],[f2])).
% 6.63/1.85 thf(f2,axiom,(
% 6.63/1.85 (setext = ! [X4 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X4)) => (! [X2 : $i] : ((in @ X2 @ X4) => (in @ X2 @ X0)) => (X0 = X4))))),
% 6.63/1.85 file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',setext)).
% 6.63/1.85 thf(f27,plain,(
% 6.63/1.85 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y2)))))))))),
% 6.63/1.85 inference(cnf_transformation,[status(thm)],[f19])).
% 6.63/1.85 thf(f19,plain,(
% 6.63/1.85 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y2)))))))))),
% 6.63/1.85 inference(fool_elimination,[status(thm)],[f18])).
% 6.63/1.85 thf(f18,plain,(
% 6.63/1.85 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X0)) = dsetconstrER)),
% 6.63/1.85 inference(rectify,[status(thm)],[f1])).
% 6.63/1.85 thf(f1,axiom,(
% 6.63/1.85 (! [X2 : $i,X1 : $i > $o,X0 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 6.63/1.85 file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',dsetconstrER)).
% 6.63/1.85 thf(f30,plain,(
% 6.63/1.85 ($true = (~ (dsetconstrER => (setext => (uniqinunit => (eqinunit => (in__Cong => (iftrueProp1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset)))))))))))))))))))))),
% 6.63/1.85 inference(cnf_transformation,[status(thm)],[f15])).
% 6.63/1.85 thf(f15,plain,(
% 6.63/1.85 ($true = (~ (dsetconstrER => (setext => (uniqinunit => (eqinunit => (in__Cong => (iftrueProp1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))) = (setadjoin @ Y1 @ emptyset)))))))))))))))))))))),
% 6.63/1.85 inference(fool_elimination,[status(thm)],[f14])).
% 6.63/1.85 thf(f14,plain,(
% 6.63/1.85 ~(dsetconstrER => (setext => (uniqinunit => (eqinunit => (in__Cong => (iftrueProp1 => ! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (X0 => ((dsetconstr @ X2 @ (^[X4 : $i] : (((X1 = X4) & X0) | ((X3 = X4) & ~X0)))) = (setadjoin @ X1 @ emptyset)))))))))))),
% 6.63/1.85 inference(rectify,[status(thm)],[f8])).
% 6.63/1.85 thf(f8,negated_conjecture,(
% 6.63/1.85 ~(dsetconstrER => (setext => (uniqinunit => (eqinunit => (in__Cong => (iftrueProp1 => ! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => ((dsetconstr @ X0 @ (^[X5 : $i] : (((X2 = X5) & X1) | ((X3 = X5) & ~X1)))) = (setadjoin @ X2 @ emptyset)))))))))))),
% 6.63/1.85 inference(negated_conjecture,[status(cth)],[f7])).
% 6.63/1.85 thf(f7,conjecture,(
% 6.63/1.85 dsetconstrER => (setext => (uniqinunit => (eqinunit => (in__Cong => (iftrueProp1 => ! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => ((dsetconstr @ X0 @ (^[X5 : $i] : (((X2 = X5) & X1) | ((X3 = X5) & ~X1)))) = (setadjoin @ X2 @ emptyset))))))))))),
% 6.63/1.85 file('/export/starexec/sandbox/tmp/tmp.0c7W5WdEC7/DTF2THF_13127.p',iftrueProp2)).
% 6.63/1.85 thf(f459,plain,(
% 6.63/1.85 ($true = (((~ sK4) & (sK5 = sK9)) | (sK4 & (sK3 = sK9)))) | ~spl0_1),
% 6.63/1.85 inference(trivial_inequality_removal,[status(thm)],[f458])).
% 6.63/1.85 thf(f458,plain,(
% 6.63/1.85 ($true = (((~ sK4) & (sK5 = sK9)) | (sK4 & (sK3 = sK9)))) | ($false = $true) | ~spl0_1),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f457])).
% 6.63/1.85 thf(f457,plain,(
% 6.63/1.85 ($false = ($false => (in @ sK9 @ (setadjoin @ sK3 @ emptyset)))) | ($true = (((~ sK4) & (sK5 = sK9)) | (sK4 & (sK3 = sK9)))) | ~spl0_1),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f456])).
% 6.63/1.85 thf(f456,plain,(
% 6.63/1.85 ($false = ($false => (in @ sK9 @ (setadjoin @ sK3 @ emptyset)))) | ($true = ((^[Y0 : $i]: (((~ sK4) & (sK5 = Y0)) | (sK4 & (sK3 = Y0)))) @ sK9)) | ~spl0_1),
% 6.63/1.85 inference(superposition,[status(thm)],[f450,f48])).
% 6.63/1.85 thf(f48,plain,(
% 6.63/1.85 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (in @ X3 @ (dsetconstr @ X1 @ X2))) | ($true = (X2 @ X3))) )),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 6.63/1.85 thf(f47,plain,(
% 6.63/1.85 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ (dsetconstr @ X1 @ X2)) => (X2 @ X3)))) )),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f46])).
% 6.63/1.85 thf(f46,plain,(
% 6.63/1.85 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X1 @ X2)) => (X2 @ Y0))) @ X3))) )),
% 6.63/1.85 inference(pi_clausification,[status(thm)],[f45])).
% 6.63/1.85 thf(f45,plain,(
% 6.63/1.85 ( ! [X2 : $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X1 @ X2)) => (X2 @ Y0)))))) )),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f44])).
% 6.63/1.85 thf(f44,plain,(
% 6.63/1.85 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X1 @ Y0)) => (Y0 @ Y1))))) @ X2))) )),
% 6.63/1.85 inference(pi_clausification,[status(thm)],[f43])).
% 6.63/1.85 thf(f43,plain,(
% 6.63/1.85 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X1 @ Y0)) => (Y0 @ Y1)))))))) )),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f42])).
% 6.63/1.85 thf(f42,plain,(
% 6.63/1.85 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ Y2))))))) @ X1))) )),
% 6.63/1.85 inference(pi_clausification,[status(thm)],[f37])).
% 6.63/1.85 thf(f37,plain,(
% 6.63/1.85 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ Y2)))))))))),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 6.63/1.85 thf(f450,plain,(
% 6.63/1.85 ($false = ((in @ sK9 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (((~ sK4) & (sK5 = Y0)) | (sK4 & (sK3 = Y0)))))) => (in @ sK9 @ (setadjoin @ sK3 @ emptyset)))) | ~spl0_1),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f444])).
% 6.63/1.85 thf(f444,plain,(
% 6.63/1.85 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (sK5 = Y1)) | (sK4 & (sK3 = Y1)))))) => (in @ Y0 @ (setadjoin @ sK3 @ emptyset)))) @ sK9)) | ~spl0_1),
% 6.63/1.85 inference(sigma_clausification,[status(thm)],[f431])).
% 6.63/1.85 thf(f431,plain,(
% 6.63/1.85 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (sK5 = Y1)) | (sK4 & (sK3 = Y1)))))) => (in @ Y0 @ (setadjoin @ sK3 @ emptyset)))))) | ~spl0_1),
% 6.63/1.85 inference(not_proxy_clausification,[status(thm)],[f322])).
% 6.63/1.85 thf(f322,plain,(
% 6.63/1.85 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (sK5 = Y1)) | (sK4 & (sK3 = Y1)))))) => (in @ Y0 @ (setadjoin @ sK3 @ emptyset))))))) | ~spl0_1),
% 6.63/1.85 inference(avatar_component_clause,[status(thm)],[f321])).
% 6.63/1.85 thf(f321,definition,(
% 6.63/1.85 spl0_1 <=> ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (sK5 = Y1)) | (sK4 & (sK3 = Y1)))))) => (in @ Y0 @ (setadjoin @ sK3 @ emptyset)))))))),
% 6.63/1.85 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 6.63/1.85 thf(f454,plain,(
% 6.63/1.85 ($false = (in @ sK9 @ (setadjoin @ sK3 @ emptyset))) | ~spl0_1),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f450])).
% 6.63/1.85 thf(f485,plain,(
% 6.63/1.85 ($true = (in @ sK3 @ (setadjoin @ sK3 @ emptyset))) | ~spl0_1),
% 6.63/1.85 inference(forward_demodulation,[status(thm)],[f476,f469])).
% 6.63/1.85 thf(f476,plain,(
% 6.63/1.85 ($true = (in @ sK9 @ (setadjoin @ sK3 @ emptyset))) | ~spl0_1),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f471])).
% 6.63/1.85 thf(f471,plain,(
% 6.63/1.85 ($true = ($true => (in @ sK9 @ (setadjoin @ sK3 @ emptyset)))) | ~spl0_1),
% 6.63/1.85 inference(superposition,[status(thm)],[f82,f466])).
% 6.63/1.85 thf(f82,plain,(
% 6.63/1.85 ( ! [X2 : $i,X1 : $i] : (($true = ((X2 = X1) => (in @ X1 @ (setadjoin @ X2 @ emptyset))))) )),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f81])).
% 6.63/1.85 thf(f81,plain,(
% 6.63/1.85 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((Y0 = X1) => (in @ X1 @ (setadjoin @ Y0 @ emptyset)))) @ X2))) )),
% 6.63/1.85 inference(pi_clausification,[status(thm)],[f74])).
% 6.63/1.85 thf(f74,plain,(
% 6.63/1.85 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((Y0 = X1) => (in @ X1 @ (setadjoin @ Y0 @ emptyset))))) = $true)) )),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f73])).
% 6.63/1.85 thf(f73,plain,(
% 6.63/1.85 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))) @ X1))) )),
% 6.63/1.85 inference(pi_clausification,[status(thm)],[f70])).
% 6.63/1.85 thf(f419,plain,(
% 6.63/1.85 ~spl0_2),
% 6.63/1.85 inference(avatar_contradiction_clause,[status(thm)],[f418])).
% 6.63/1.85 thf(f418,plain,(
% 6.63/1.85 $false | ~spl0_2),
% 6.63/1.85 inference(trivial_inequality_removal,[status(thm)],[f417])).
% 6.63/1.85 thf(f417,plain,(
% 6.63/1.85 ($false = $true) | ~spl0_2),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f416])).
% 6.63/1.85 thf(f416,plain,(
% 6.63/1.85 ((~ $true) = $true) | ~spl0_2),
% 6.63/1.85 inference(forward_demodulation,[status(thm)],[f415,f125])).
% 6.63/1.85 thf(f415,plain,(
% 6.63/1.85 ($true = (~ sK4)) | ~spl0_2),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f414])).
% 6.63/1.85 thf(f414,plain,(
% 6.63/1.85 ($true = ($true => (~ sK4))) | ~spl0_2),
% 6.63/1.85 inference(forward_demodulation,[status(thm)],[f406,f121])).
% 6.63/1.85 thf(f406,plain,(
% 6.63/1.85 (((in @ sK5 @ sK2) => (~ sK4)) = $true) | ~spl0_2),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f400])).
% 6.63/1.85 thf(f400,plain,(
% 6.63/1.85 ($true = ((in @ sK5 @ sK2) => (sK4 => $false))) | ~spl0_2),
% 6.63/1.85 inference(superposition,[status(thm)],[f216,f397])).
% 6.63/1.85 thf(f397,plain,(
% 6.63/1.85 ($false = (in @ sK3 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (((~ sK4) & (sK5 = Y0)) | (sK4 & (sK3 = Y0))))))) | ~spl0_2),
% 6.63/1.85 inference(backward_demodulation,[status(thm)],[f355,f381])).
% 6.63/1.85 thf(f381,plain,(
% 6.63/1.85 (sK8 = sK3) | ~spl0_2),
% 6.63/1.85 inference(equality_proxy_clausification,[status(thm)],[f372])).
% 6.63/1.85 thf(f372,plain,(
% 6.63/1.85 ($true = (sK8 = sK3)) | ~spl0_2),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f367])).
% 6.63/1.85 thf(f367,plain,(
% 6.63/1.85 ($true = ($true => (sK8 = sK3))) | ~spl0_2),
% 6.63/1.85 inference(superposition,[status(thm)],[f64,f356])).
% 6.63/1.85 thf(f356,plain,(
% 6.63/1.85 ($true = (in @ sK8 @ (setadjoin @ sK3 @ emptyset))) | ~spl0_2),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f343])).
% 6.63/1.85 thf(f343,plain,(
% 6.63/1.85 ($false = ((in @ sK8 @ (setadjoin @ sK3 @ emptyset)) => (in @ sK8 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (((~ sK4) & (sK5 = Y0)) | (sK4 & (sK3 = Y0)))))))) | ~spl0_2),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f340])).
% 6.63/1.85 thf(f340,plain,(
% 6.63/1.85 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK3 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (sK5 = Y1)) | (sK4 & (sK3 = Y1)))))))) @ sK8)) | ~spl0_2),
% 6.63/1.85 inference(sigma_clausification,[status(thm)],[f325])).
% 6.63/1.85 thf(f325,plain,(
% 6.63/1.85 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK3 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (sK5 = Y1)) | (sK4 & (sK3 = Y1)))))))))) | ~spl0_2),
% 6.63/1.85 inference(avatar_component_clause,[status(thm)],[f324])).
% 6.63/1.85 thf(f324,definition,(
% 6.63/1.85 spl0_2 <=> ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK3 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (sK5 = Y1)) | (sK4 & (sK3 = Y1))))))))))),
% 6.63/1.85 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 6.63/1.85 thf(f64,plain,(
% 6.63/1.85 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X2 @ (setadjoin @ X1 @ emptyset)) => (X2 = X1)))) )),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f63])).
% 6.63/1.85 thf(f63,plain,(
% 6.63/1.85 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1))) @ X2))) )),
% 6.63/1.85 inference(pi_clausification,[status(thm)],[f62])).
% 6.63/1.85 thf(f62,plain,(
% 6.63/1.85 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1)))))) )),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f61])).
% 6.63/1.85 thf(f61,plain,(
% 6.63/1.85 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0))))) @ X1))) )),
% 6.63/1.85 inference(pi_clausification,[status(thm)],[f56])).
% 6.63/1.85 thf(f56,plain,(
% 6.63/1.85 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) = $true)),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 6.63/1.85 thf(f355,plain,(
% 6.63/1.85 ($false = (in @ sK8 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (((~ sK4) & (sK5 = Y0)) | (sK4 & (sK3 = Y0))))))) | ~spl0_2),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f343])).
% 6.63/1.85 thf(f216,plain,(
% 6.63/1.85 ( ! [X0 : $o,X1 : $i] : (($true = ((in @ X1 @ sK2) => (X0 => (in @ sK3 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (((~ X0) & (X1 = Y0)) | (X0 & (sK3 = Y0)))))))))) )),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f213])).
% 6.63/1.85 thf(f213,plain,(
% 6.63/1.85 ( ! [X0 : $o,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK2) => (X0 => (in @ sK3 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ X0) & (Y0 = Y1)) | (X0 & (sK3 = Y1))))))))) @ X1))) )),
% 6.63/1.85 inference(pi_clausification,[status(thm)],[f116])).
% 6.63/1.85 thf(f116,plain,(
% 6.63/1.85 ( ! [X0 : $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (X0 => (in @ sK3 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ X0) & (Y0 = Y1)) | (X0 & (sK3 = Y1)))))))))))) )),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f114])).
% 6.63/1.85 thf(f114,plain,(
% 6.63/1.85 ( ! [X0 : $o] : (($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (X0 => (in @ sK3 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ X0) & (Y0 = Y1)) | (X0 & (sK3 = Y1))))))))))))) )),
% 6.63/1.85 inference(superposition,[status(thm)],[f100,f109])).
% 6.63/1.85 thf(f100,plain,(
% 6.63/1.85 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = ((in @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (X3 => (in @ X2 @ (dsetconstr @ X1 @ (^[Y1 : $i]: (((~ X3) & (Y0 = Y1)) | (X3 & (X2 = Y1))))))))))))) )),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f99])).
% 6.63/1.85 thf(f99,plain,(
% 6.63/1.85 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = ((^[Y0 : $o]: ((in @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (Y0 => (in @ X2 @ (dsetconstr @ X1 @ (^[Y2 : $i]: (((~ Y0) & (Y1 = Y2)) | (Y0 & (X2 = Y2)))))))))))) @ X3))) )),
% 6.63/1.85 inference(pi_clausification,[status(thm)],[f98])).
% 6.63/1.85 thf(f98,plain,(
% 6.63/1.85 ( ! [X2 : $i,X1 : $i] : (((!! @ $o @ (^[Y0 : $o]: ((in @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (Y0 => (in @ X2 @ (dsetconstr @ X1 @ (^[Y2 : $i]: (((~ Y0) & (Y1 = Y2)) | (Y0 & (X2 = Y2))))))))))))) = $true)) )),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f97])).
% 6.63/1.85 thf(f97,plain,(
% 6.63/1.85 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (Y1 => (in @ Y0 @ (dsetconstr @ X1 @ (^[Y3 : $i]: (((~ Y1) & (Y2 = Y3)) | (Y1 & (Y0 = Y3)))))))))))))) @ X2))) )),
% 6.63/1.85 inference(pi_clausification,[status(thm)],[f96])).
% 6.63/1.85 thf(f96,plain,(
% 6.63/1.85 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (Y1 => (in @ Y0 @ (dsetconstr @ X1 @ (^[Y3 : $i]: (((~ Y1) & (Y2 = Y3)) | (Y1 & (Y0 = Y3))))))))))))))))) )),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f95])).
% 6.63/1.85 thf(f95,plain,(
% 6.63/1.85 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4)))))))))))))))) @ X1))) )),
% 6.63/1.85 inference(pi_clausification,[status(thm)],[f90])).
% 6.63/1.85 thf(f90,plain,(
% 6.63/1.85 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((~ Y2) & (Y3 = Y4)) | (Y2 & (Y1 = Y4))))))))))))))))))),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 6.63/1.85 thf(f326,plain,(
% 6.63/1.85 spl0_1 | spl0_2),
% 6.63/1.85 inference(avatar_split_clause,[status(thm)],[f319,f324,f321])).
% 6.63/1.85 thf(f319,plain,(
% 6.63/1.85 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (sK5 = Y1)) | (sK4 & (sK3 = Y1)))))) => (in @ Y0 @ (setadjoin @ sK3 @ emptyset))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK3 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (sK5 = Y1)) | (sK4 & (sK3 = Y1))))))))))),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f147])).
% 6.63/1.85 thf(f147,plain,(
% 6.63/1.85 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK3 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (sK5 = Y1)) | (sK4 & (sK3 = Y1))))))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (sK5 = Y1)) | (sK4 & (sK3 = Y1)))))) => (in @ Y0 @ (setadjoin @ sK3 @ emptyset))))))))),
% 6.63/1.85 inference(boolean_simplification,[status(thm)],[f141])).
% 6.63/1.85 thf(f141,plain,(
% 6.63/1.85 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK3 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (sK5 = Y1)) | (sK4 & (sK3 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (((~ sK4) & (sK5 = Y1)) | (sK4 & (sK3 = Y1)))))) => (in @ Y0 @ (setadjoin @ sK3 @ emptyset))))) => $false)) = $true)),
% 6.63/1.85 inference(superposition,[status(thm)],[f67,f124])).
% 6.63/1.85 thf(f124,plain,(
% 6.63/1.85 ($false = ((dsetconstr @ sK2 @ (^[Y0 : $i]: (((~ sK4) & (sK5 = Y0)) | (sK4 & (sK3 = Y0))))) = (setadjoin @ sK3 @ emptyset)))),
% 6.63/1.85 inference(binary_proxy_clausification,[status(thm)],[f123])).
% 6.63/1.85 thf(f67,plain,(
% 6.63/1.85 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => (X2 = X1))))) )),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f66])).
% 6.63/1.85 thf(f66,plain,(
% 6.63/1.85 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (Y0 = X1)))) @ X2))) )),
% 6.63/1.85 inference(pi_clausification,[status(thm)],[f54])).
% 6.63/1.85 thf(f54,plain,(
% 6.63/1.85 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (Y0 = X1))))))) )),
% 6.63/1.85 inference(beta_eta_normalization,[status(thm)],[f53])).
% 6.63/1.85 thf(f53,plain,(
% 6.63/1.85 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) @ X1))) )),
% 6.63/1.85 inference(pi_clausification,[status(thm)],[f50])).
% 6.63/1.85 % SZS output end Proof for DTF2THF_13127
% 6.63/1.85 % (13488)------------------------------
% 6.63/1.85 % (13488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/1.85 % (13488)Termination reason: Refutation
% 6.63/1.85
% 6.63/1.85 % (13488)Memory used [KB]: 6140
% 6.63/1.85 % (13488)Time elapsed: 0.052 s
% 6.63/1.85 % (13488)Instructions burned: 155 (million)
% 6.63/1.85 % (13488)------------------------------
% 6.63/1.85 % (13488)------------------------------
% 6.63/1.85 % (13388)Success in time 0.946 s
%------------------------------------------------------------------------------