%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO329^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:53:57 AM UTC 2026
% Result : Theorem 1.61s 1.79s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 1
% Syntax : Number of formulae : 60 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 654 ( 63 equ; 0 cnn)
% Maximal formula atoms : 13 ( 10 avg)
% Number of connectives : 1517 ( 11 ~; 68 |; 62 &;1177 @)
% ( 0 <=>; 101 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 8 con; 0-2 aty)
% ( 98 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 222 ( 179 ^; 43 !; 0 ?; 222 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cS: $i > $i ).
thf(func_def_1,type,
cDOUBLE: $i > $i > $o ).
thf(func_def_2,type,
cHALF: $i > $i > $o ).
thf(func_def_16,type,
ph0:
!>[X0: $tType] : X0 ).
thf(f403,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f402]) ).
thf(f402,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f401]) ).
thf(f401,plain,
( ( $false
=> ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ ( cS @ sK4 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ sK3 ) ) @ ( cS @ ( cS @ ( cS @ sK4 ) ) ) ) ) )
= $false ),
inference(forward_demodulation,[status(thm)],[f397,f354]) ).
thf(f354,plain,
( ( cDOUBLE @ sK3 @ sK4 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f353]) ).
thf(f353,plain,
( ( $true = $false )
| ( ( cDOUBLE @ sK3 @ sK4 )
= $false ) ),
inference(boolean_simplification,[status(thm)],[f352]) ).
thf(f352,plain,
( ( ( cDOUBLE @ sK3 @ sK4 )
= $false )
| ( $false
= ( ( ( cDOUBLE @ sK3 @ sK4 )
| ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) )
=> $true ) ) ),
inference(boolean_simplification,[status(thm)],[f351]) ).
thf(f351,plain,
( ( ( ( ( cDOUBLE @ sK3 @ sK4 )
| ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) )
=> ( $true
| ( cDOUBLE @ ( cS @ ( cS @ sK3 ) ) @ ( cS @ ( cS @ ( cS @ sK4 ) ) ) ) ) )
= $false )
| ( ( cDOUBLE @ sK3 @ sK4 )
= $false ) ),
inference(superposition,[status(thm)],[f347,f66]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( cDOUBLE @ ( cS @ X2 ) @ ( cS @ ( cS @ X1 ) ) ) )
| ( $false
= ( cDOUBLE @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( cDOUBLE @ X2 @ X1 )
=> ( cDOUBLE @ ( cS @ X2 ) @ ( cS @ ( cS @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( cDOUBLE @ Y0 @ X1 )
=> ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( cDOUBLE @ Y0 @ X1 )
=> ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y0 @ Y1 )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y4 ) ) @ ( cS @ Y3 ) ) ) ) )
& ( Y2 @ ( cS @ c0 ) @ c0 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
& ( cDOUBLE @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y0 @ Y1 )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y4 ) ) @ ( cS @ Y3 ) ) ) ) )
& ( Y2 @ ( cS @ c0 ) @ c0 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
& ( cDOUBLE @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y1 @ Y0 )
=> ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y0 @ Y1 )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y4 ) ) @ ( cS @ Y3 ) ) ) ) )
& ( Y2 @ ( cS @ c0 ) @ c0 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
& ( cDOUBLE @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y1 @ Y0 )
=> ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y0 @ Y1 )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y4 ) ) @ ( cS @ Y3 ) ) ) ) )
& ( Y2 @ ( cS @ c0 ) @ c0 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
& ( cDOUBLE @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y1 @ Y0 )
=> ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( cDOUBLE @ X0 @ X1 )
=> ( cDOUBLE @ ( cS @ X0 ) @ ( cS @ ( cS @ X1 ) ) ) )
& ( cDOUBLE @ c0 @ c0 )
& ! [X2: $i,X3: $i] :
( ( cHALF @ X3 @ X2 )
=> ! [X4: $i > $i > $o] :
( ( ( X4 @ ( cS @ c0 ) @ c0 )
& ! [X5: $i,X6: $i] :
( ( X4 @ X5 @ X6 )
=> ( X4 @ ( cS @ ( cS @ X5 ) ) @ ( cS @ X6 ) ) )
& ( X4 @ c0 @ c0 ) )
=> ( X4 @ X3 @ X2 ) ) ) )
=> ! [X7: $i,X8: $i] :
( ( cHALF @ X7 @ X8 )
=> ( ( cDOUBLE @ ( cS @ X8 ) @ ( cS @ X7 ) )
| ( cDOUBLE @ X8 @ X7 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: $i,X4: $i] :
( ( cDOUBLE @ X3 @ X4 )
=> ( cDOUBLE @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) ) )
& ( cDOUBLE @ c0 @ c0 )
& ! [X1: $i,X0: $i] :
( ( cHALF @ X0 @ X1 )
=> ! [X2: $i > $i > $o] :
( ( ( X2 @ ( cS @ c0 ) @ c0 )
& ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X2 @ ( cS @ ( cS @ X3 ) ) @ ( cS @ X4 ) ) )
& ( X2 @ c0 @ c0 ) )
=> ( X2 @ X0 @ X1 ) ) ) )
=> ! [X0: $i,X1: $i] :
( ( cHALF @ X0 @ X1 )
=> ( ( cDOUBLE @ ( cS @ X1 ) @ ( cS @ X0 ) )
| ( cDOUBLE @ X1 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X3: $i,X4: $i] :
( ( cDOUBLE @ X3 @ X4 )
=> ( cDOUBLE @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) ) )
& ( cDOUBLE @ c0 @ c0 )
& ! [X1: $i,X0: $i] :
( ( cHALF @ X0 @ X1 )
=> ! [X2: $i > $i > $o] :
( ( ( X2 @ ( cS @ c0 ) @ c0 )
& ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X2 @ ( cS @ ( cS @ X3 ) ) @ ( cS @ X4 ) ) )
& ( X2 @ c0 @ c0 ) )
=> ( X2 @ X0 @ X1 ) ) ) )
=> ! [X0: $i,X1: $i] :
( ( cHALF @ X0 @ X1 )
=> ( ( cDOUBLE @ ( cS @ X1 ) @ ( cS @ X0 ) )
| ( cDOUBLE @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8MlOfATr0D/DTF2THF_27150.p',cTHM300B) ).
thf(f347,plain,
( ( ( ( cDOUBLE @ sK3 @ sK4 )
| ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) )
=> ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ ( cS @ sK4 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ sK3 ) ) @ ( cS @ ( cS @ ( cS @ sK4 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f346]) ).
thf(f346,plain,
( $false
= ( ^ [Y0: $i] :
( ( ( cDOUBLE @ sK3 @ Y0 )
| ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ Y0 ) ) )
=> ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ ( cS @ Y0 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ sK3 ) ) @ ( cS @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f340]) ).
thf(f340,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( cDOUBLE @ sK3 @ Y0 )
| ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ Y0 ) ) )
=> ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ ( cS @ Y0 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ sK3 ) ) @ ( cS @ ( cS @ ( cS @ Y0 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f337]) ).
thf(f337,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) )
=> ( ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ Y0 ) ) @ ( cS @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f336]) ).
thf(f336,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) )
=> ( ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ Y0 ) ) @ ( cS @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f310]) ).
thf(f310,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) )
=> ( ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ Y0 ) ) @ ( cS @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f309]) ).
thf(f309,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) )
=> ( ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ Y0 ) ) @ ( cS @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) ) )
& $true ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f308]) ).
thf(f308,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) )
=> ( ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ Y0 ) ) @ ( cS @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) ) )
& ( ( cDOUBLE @ c0 @ ( cS @ c0 ) )
| $true ) ) ) ),
inference(forward_demodulation,[status(thm)],[f307,f91]) ).
thf(f91,plain,
( $true
= ( cDOUBLE @ ( cS @ c0 ) @ ( cS @ ( cS @ c0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f89]) ).
thf(f89,plain,
( $true
= ( $true
=> ( cDOUBLE @ ( cS @ c0 ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(superposition,[status(thm)],[f59,f71]) ).
thf(f71,plain,
( ( cDOUBLE @ c0 @ c0 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y0 @ Y1 )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y4 ) ) @ ( cS @ Y3 ) ) ) ) )
& ( Y2 @ ( cS @ c0 ) @ c0 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
& ( cDOUBLE @ c0 @ c0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f307,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) )
=> ( ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ Y0 ) ) @ ( cS @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) ) )
& ( ( cDOUBLE @ c0 @ ( cS @ c0 ) )
| ( cDOUBLE @ ( cS @ c0 ) @ ( cS @ ( cS @ c0 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f306]) ).
thf(f306,plain,
( $true
= ( ~ ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) )
=> ( ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ Y0 ) ) @ ( cS @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) ) )
& ( ( cDOUBLE @ c0 @ ( cS @ c0 ) )
| ( cDOUBLE @ ( cS @ c0 ) @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f305]) ).
thf(f305,plain,
( $true
= ( ~ ( ( $true
| ( cDOUBLE @ ( cS @ c0 ) @ ( cS @ c0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) )
=> ( ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ Y0 ) ) @ ( cS @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) ) )
& ( ( cDOUBLE @ c0 @ ( cS @ c0 ) )
| ( cDOUBLE @ ( cS @ c0 ) @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f237,f71]) ).
thf(f237,plain,
( $true
= ( ~ ( ( ( cDOUBLE @ c0 @ c0 )
| ( cDOUBLE @ ( cS @ c0 ) @ ( cS @ c0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) )
=> ( ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ Y0 ) ) @ ( cS @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) ) )
& ( ( cDOUBLE @ c0 @ ( cS @ c0 ) )
| ( cDOUBLE @ ( cS @ c0 ) @ ( cS @ ( cS @ c0 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f236]) ).
thf(f236,plain,
( ( ( ( ( cDOUBLE @ c0 @ c0 )
| ( cDOUBLE @ ( cS @ c0 ) @ ( cS @ c0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) )
=> ( ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ Y0 ) ) @ ( cS @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) ) )
& ( ( cDOUBLE @ c0 @ ( cS @ c0 ) )
| ( cDOUBLE @ ( cS @ c0 ) @ ( cS @ ( cS @ c0 ) ) ) ) )
=> $false )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f186]) ).
thf(f186,plain,
( $true
= ( ( ( ^ [Y0: $i,Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] :
( cDOUBLE
@ ( ^ [Y4: $i,Y5: $i] : Y5
@ Y2
@ Y3 )
@ ( ^ [Y4: $i,Y5: $i] : Y4
@ Y2
@ Y3 ) )
@ Y0
@ Y1 )
| ( ^ [Y2: $i,Y3: $i] :
( cDOUBLE
@ ( ^ [Y4: $i,Y5: $i] :
( cS
@ ( ^ [Y6: $i,Y7: $i] : Y7
@ Y4
@ Y5 ) )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i,Y5: $i] :
( cS
@ ( ^ [Y6: $i,Y7: $i] : Y6
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 ) )
@ c0
@ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] :
( ( ^ [Y4: $i,Y5: $i] :
( cDOUBLE
@ ( ^ [Y6: $i,Y7: $i] : Y7
@ Y4
@ Y5 )
@ ( ^ [Y6: $i,Y7: $i] : Y6
@ Y4
@ Y5 ) )
@ Y2
@ Y3 )
| ( ^ [Y4: $i,Y5: $i] :
( cDOUBLE
@ ( ^ [Y6: $i,Y7: $i] :
( cS
@ ( ^ [Y8: $i,Y9: $i] : Y9
@ Y6
@ Y7 ) )
@ Y4
@ Y5 )
@ ( ^ [Y6: $i,Y7: $i] :
( cS
@ ( ^ [Y8: $i,Y9: $i] : Y8
@ Y6
@ Y7 ) )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ Y1
@ Y0 )
=> ( ^ [Y2: $i,Y3: $i] :
( ( ^ [Y4: $i,Y5: $i] :
( cDOUBLE
@ ( ^ [Y6: $i,Y7: $i] : Y7
@ Y4
@ Y5 )
@ ( ^ [Y6: $i,Y7: $i] : Y6
@ Y4
@ Y5 ) )
@ Y2
@ Y3 )
| ( ^ [Y4: $i,Y5: $i] :
( cDOUBLE
@ ( ^ [Y6: $i,Y7: $i] :
( cS
@ ( ^ [Y8: $i,Y9: $i] : Y9
@ Y6
@ Y7 ) )
@ Y4
@ Y5 )
@ ( ^ [Y6: $i,Y7: $i] :
( cS
@ ( ^ [Y8: $i,Y9: $i] : Y8
@ Y6
@ Y7 ) )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ ( cS @ ( cS @ Y1 ) )
@ ( cS @ Y0 ) ) ) ) )
& ( ^ [Y0: $i,Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] :
( cDOUBLE
@ ( ^ [Y4: $i,Y5: $i] : Y5
@ Y2
@ Y3 )
@ ( ^ [Y4: $i,Y5: $i] : Y4
@ Y2
@ Y3 ) )
@ Y0
@ Y1 )
| ( ^ [Y2: $i,Y3: $i] :
( cDOUBLE
@ ( ^ [Y4: $i,Y5: $i] :
( cS
@ ( ^ [Y6: $i,Y7: $i] : Y7
@ Y4
@ Y5 ) )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i,Y5: $i] :
( cS
@ ( ^ [Y6: $i,Y7: $i] : Y6
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 ) )
@ ( cS @ c0 )
@ c0 ) )
=> $false ) ),
inference(superposition,[status(thm)],[f175,f21]) ).
thf(f21,plain,
( $false
= ( ( cDOUBLE @ sK1 @ sK2 )
| ( cDOUBLE @ ( cS @ sK1 ) @ ( cS @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( cHALF @ sK2 @ sK1 )
=> ( ( cDOUBLE @ sK1 @ sK2 )
| ( cDOUBLE @ ( cS @ sK1 ) @ ( cS @ sK2 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: $i] :
( ( cHALF @ Y0 @ sK1 )
=> ( ( cDOUBLE @ sK1 @ Y0 )
| ( cDOUBLE @ ( cS @ sK1 ) @ ( cS @ Y0 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( cHALF @ Y0 @ sK1 )
=> ( ( cDOUBLE @ sK1 @ Y0 )
| ( cDOUBLE @ ( cS @ sK1 ) @ ( cS @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y1 @ Y0 )
=> ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y1 @ Y0 )
=> ( ( cDOUBLE @ Y0 @ Y1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ Y1 ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f175,plain,
! [X1: $i > $i > $o] :
( $true
= ( ( ( X1 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y1 ) ) @ ( cS @ Y0 ) ) ) ) )
& ( X1 @ ( cS @ c0 ) @ c0 ) )
=> ( X1 @ sK2 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f173]) ).
thf(f173,plain,
! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y2 ) ) @ ( cS @ Y1 ) ) ) ) )
& ( Y0 @ ( cS @ c0 ) @ c0 ) )
=> ( Y0 @ sK2 @ sK1 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y2 ) ) @ ( cS @ Y1 ) ) ) ) )
& ( Y0 @ ( cS @ c0 ) @ c0 ) )
=> ( Y0 @ sK2 @ sK1 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f149]) ).
thf(f149,plain,
( $true
= ( $true
=> ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y2 ) ) @ ( cS @ Y1 ) ) ) ) )
& ( Y0 @ ( cS @ c0 ) @ c0 ) )
=> ( Y0 @ sK2 @ sK1 ) ) ) ) ),
inference(superposition,[status(thm)],[f143,f22]) ).
thf(f22,plain,
( $true
= ( cHALF @ sK2 @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f143,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( cHALF @ X1 @ X2 )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y2 ) ) @ ( cS @ Y1 ) ) ) ) )
& ( Y0 @ ( cS @ c0 ) @ c0 ) )
=> ( Y0 @ X1 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f142]) ).
thf(f142,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( cHALF @ X1 @ Y0 )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( Y1 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ ( cS @ ( cS @ Y3 ) ) @ ( cS @ Y2 ) ) ) ) )
& ( Y1 @ ( cS @ c0 ) @ c0 ) )
=> ( Y1 @ X1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( cHALF @ X1 @ Y0 )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( Y1 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ ( cS @ ( cS @ Y3 ) ) @ ( cS @ Y2 ) ) ) ) )
& ( Y1 @ ( cS @ c0 ) @ c0 ) )
=> ( Y1 @ X1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f116]) ).
thf(f116,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y0 @ Y1 )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y4 ) ) @ ( cS @ Y3 ) ) ) ) )
& ( Y2 @ ( cS @ c0 ) @ c0 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y0 @ Y1 )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y4 ) ) @ ( cS @ Y3 ) ) ) ) )
& ( Y2 @ ( cS @ c0 ) @ c0 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f397,plain,
( ( ( cDOUBLE @ sK3 @ sK4 )
=> ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ ( cS @ sK4 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ sK3 ) ) @ ( cS @ ( cS @ ( cS @ sK4 ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f384]) ).
thf(f384,plain,
( $false
= ( ( ( cDOUBLE @ sK3 @ sK4 )
| $false )
=> ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ ( cS @ sK4 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ sK3 ) ) @ ( cS @ ( cS @ ( cS @ sK4 ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f347,f357]) ).
thf(f357,plain,
( $false
= ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f356]) ).
thf(f356,plain,
( ( $true = $false )
| ( $false
= ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f355]) ).
thf(f355,plain,
( ( $false
= ( ( ( cDOUBLE @ sK3 @ sK4 )
| ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) )
=> $true ) )
| ( $false
= ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f350]) ).
thf(f350,plain,
( ( $false
= ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) )
| ( $false
= ( ( ( cDOUBLE @ sK3 @ sK4 )
| ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) )
=> ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ ( cS @ sK4 ) ) )
| $true ) ) ) ),
inference(superposition,[status(thm)],[f347,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO329^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n026.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 14:28:25 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.48 ---- Original DTF file ---
% 0.29/0.48 thf(spec,logic,$$dhol).
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 % File : SYO329^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.48 % Domain : Syntactic
% 0.29/0.48 % Problem : TPS problem from BASIC-HO-THMS
% 0.29/0.48 % Version : Especial.
% 0.29/0.48 % English :
% 0.29/0.48
% 0.29/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.48 % Source : [Bro09]
% 0.29/0.48 % Names : tps_1027 [Bro09]
% 0.29/0.48
% 0.29/0.48 % Status : Theorem
% 0.29/0.48 % Rating : 0.83 v9.1.0, 0.75 v9.0.0, 0.92 v8.2.0, 0.91 v8.1.0, 0.92 v7.4.0, 0.89 v7.3.0, 0.90 v7.2.0, 0.88 v7.1.0, 0.86 v7.0.0, 0.88 v6.4.0, 0.86 v6.3.0, 0.83 v5.5.0, 1.00 v4.0.0
% 0.29/0.48 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.29/0.48 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.29/0.48 % Maximal formula atoms : 7 ( 7 avg)
% 0.29/0.48 % Number of connectives : 44 ( 0 ~; 1 |; 4 &; 33 @)
% 0.29/0.48 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.29/0.48 % Maximal formula depth : 17 ( 17 avg)
% 0.29/0.48 % Number of types : 2 ( 0 usr)
% 0.29/0.48 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.29/0.48 % Number of symbols : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.29/0.48 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.29/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.48
% 0.29/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 thf(cS,type,
% 0.29/0.48 cS: $i > $i ).
% 0.29/0.48
% 0.29/0.48 thf(cDOUBLE,type,
% 0.29/0.48 cDOUBLE: $i > $i > $o ).
% 0.29/0.48
% 0.29/0.48 thf(cHALF,type,
% 0.29/0.48 cHALF: $i > $i > $o ).
% 0.29/0.48
% 0.29/0.48 thf(c0,type,
% 0.29/0.48 c0: $i ).
% 0.29/0.48
% 0.29/0.48 thf(cTHM300B,conjecture,
% 0.29/0.48 ( ( ! [Xu: $i,Xv: $i] :
% 0.29/0.48 ( ( cHALF @ Xu @ Xv )
% 0.29/0.48 => ! [Q: $i > $i > $o] :
% 0.29/0.48 ( ( ( Q @ c0 @ c0 )
% 0.29/0.48 & ( Q @ ( cS @ c0 ) @ c0 )
% 0.29/0.48 & ! [Xx: $i,Xy: $i] :
% 0.29/0.48 ( ( Q @ Xx @ Xy )
% 0.29/0.48 => ( Q @ ( cS @ ( cS @ Xx ) ) @ ( cS @ Xy ) ) ) )
% 0.29/0.48 => ( Q @ Xu @ Xv ) ) )
% 0.29/0.48 & ( cDOUBLE @ c0 @ c0 )
% 0.29/0.48 & ! [Xx: $i,Xy: $i] :
% 0.29/0.48 ( ( cDOUBLE @ Xx @ Xy )
% 0.29/0.48 => ( cDOUBLE @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) ) )
% 0.29/0.48 => ! [Xu: $i,Xv: $i] :
% 0.29/0.48 ( ( cHALF @ Xu @ Xv )
% 0.29/0.48 => ( ( cDOUBLE @ Xv @ Xu )
% 0.29/0.48 | ( cDOUBLE @ ( cS @ Xv ) @ ( cS @ Xu ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 ------------------------
% 1.43/1.28 ---- Embedded in THF ---
% 1.43/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.28 %%% Generated on Tue Feb 24 14:28:26 EST 2026
% 1.43/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.28 %%% Logic specification used:
% 1.43/1.28 %%% thf(spec, logic, $$dhol).
% 1.43/1.28
% 1.43/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8MlOfATr0D/DTF2DTF27150.p
% See solution above
% 1.43/1.28 ------------------------
% 1.43/1.29 ---- Cleaned THF ---
% 1.43/1.29 thf(cS,type,
% 1.43/1.29 cS: $i > $i ).
% 1.43/1.29
% 1.43/1.29 thf(cDOUBLE,type,
% 1.43/1.29 cDOUBLE: $i > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(cHALF,type,
% 1.43/1.29 cHALF: $i > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(c0,type,
% 1.43/1.29 c0: $i ).
% 1.43/1.29
% 1.43/1.29 thf(cTHM300B,conjecture,
% 1.43/1.29 ( ( ! [Xu: $i,Xv: $i] :
% 1.43/1.29 ( ( cHALF @ Xu @ Xv )
% 1.43/1.29 => ! [Q: $i > $i > $o] :
% 1.43/1.29 ( ( ( Q @ c0 @ c0 )
% 1.43/1.29 & ( Q @ ( cS @ c0 ) @ c0 )
% 1.43/1.29 & ! [Xx: $i,Xy: $i] :
% 1.43/1.29 ( ( Q @ Xx @ Xy )
% 1.43/1.29 => ( Q @ ( cS @ ( cS @ Xx ) ) @ ( cS @ Xy ) ) ) )
% 1.43/1.29 => ( Q @ Xu @ Xv ) ) )
% 1.43/1.29 & ( cDOUBLE @ c0 @ c0 )
% 1.43/1.29 & ! [Xx: $i,Xy: $i] :
% 1.43/1.29 ( ( cDOUBLE @ Xx @ Xy )
% 1.43/1.29 => ( cDOUBLE @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) ) )
% 1.43/1.29 => ! [Xu: $i,Xv: $i] :
% 1.43/1.29 ( ( cHALF @ Xu @ Xv )
% 1.43/1.29 => ( ( cDOUBLE @ Xv @ Xu )
% 1.43/1.29 | ( cDOUBLE @ ( cS @ Xv ) @ ( cS @ Xu ) ) ) ) ) ).
% 1.43/1.29 ------------------------
% 1.61/1.30 % (27482)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_27150 for (2999ds/2Mi)
% 1.61/1.30 % (27480)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_27150 for (2999ds/27Mi)
% 1.61/1.30 % (27482)Instruction limit reached!
% 1.61/1.30 % (27482)------------------------------
% 1.61/1.30 % (27482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (27482)Termination reason: Unknown
% 1.61/1.30 % (27482)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (27482)Memory used [KB]: 5500
% 1.61/1.30 % (27482)Time elapsed: 0.002 s
% 1.61/1.30 % (27482)Instructions burned: 3 (million)
% 1.61/1.30 % (27482)------------------------------
% 1.61/1.30 % (27482)------------------------------
% 1.61/1.31 % (27478)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/183Mi)
% 1.61/1.31 % (27479)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_27150 for (2999ds/4Mi)
% 1.61/1.31 % (27481)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/2Mi)
% 1.61/1.31 % (27483)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_27150 for (2999ds/275Mi)
% 1.61/1.31 % (27484)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/18Mi)
% 1.61/1.31 % (27481)Instruction limit reached!
% 1.61/1.31 % (27481)------------------------------
% 1.61/1.31 % (27481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (27481)Termination reason: Unknown
% 1.61/1.31 % (27481)Termination phase: Preprocessing 3
% 1.61/1.31
% 1.61/1.31 % (27481)Memory used [KB]: 895
% 1.61/1.31 % (27481)Time elapsed: 0.003 s
% 1.61/1.31 % (27481)Instructions burned: 2 (million)
% 1.61/1.31 % (27481)------------------------------
% 1.61/1.31 % (27481)------------------------------
% 1.61/1.31 % (27480)Instruction limit reached!
% 1.61/1.31 % (27480)------------------------------
% 1.61/1.31 % (27480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (27480)Termination reason: Unknown
% 1.61/1.31 % (27480)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (27480)Memory used [KB]: 5628
% 1.61/1.31 % (27480)Time elapsed: 0.010 s
% 1.61/1.31 % (27480)Instructions burned: 27 (million)
% 1.61/1.31 % (27480)------------------------------
% 1.61/1.31 % (27480)------------------------------
% 1.61/1.31 % (27485)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/3Mi)
% 1.61/1.31 % (27479)Instruction limit reached!
% 1.61/1.31 % (27479)------------------------------
% 1.61/1.31 % (27479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (27479)Termination reason: Unknown
% 1.61/1.31 % (27479)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (27479)Memory used [KB]: 5500
% 1.61/1.31 % (27479)Time elapsed: 0.005 s
% 1.61/1.31 % (27479)Instructions burned: 4 (million)
% 1.61/1.31 % (27479)------------------------------
% 1.61/1.31 % (27479)------------------------------
% 1.61/1.31 % (27485)Instruction limit reached!
% 1.61/1.31 % (27485)------------------------------
% 1.61/1.31 % (27485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (27485)Termination reason: Unknown
% 1.61/1.31 % (27485)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (27485)Memory used [KB]: 5500
% 1.61/1.31 % (27485)Time elapsed: 0.002 s
% 1.61/1.31 % (27485)Instructions burned: 3 (million)
% 1.61/1.31 % (27485)------------------------------
% 1.61/1.31 % (27485)------------------------------
% 1.61/1.32 % (27484)Instruction limit reached!
% 1.61/1.32 % (27484)------------------------------
% 1.61/1.32 % (27484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (27484)Termination reason: Unknown
% 1.61/1.32 % (27484)Termination phase: Saturation
% 1.61/1.32
% 1.61/1.32 % (27484)Memory used [KB]: 5628
% 1.61/1.32 % (27484)Time elapsed: 0.012 s
% 1.61/1.32 % (27484)Instructions burned: 18 (million)
% 1.61/1.32 % (27484)------------------------------
% 1.61/1.32 % (27484)------------------------------
% 1.61/1.32 % (27487)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_27150 for (2999ds/15Mi)
% 1.61/1.32 % (27489)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_27150 for (2999ds/1041Mi)
% 1.61/1.33 % (27487)Instruction limit reached!
% 1.61/1.33 % (27487)------------------------------
% 1.61/1.33 % (27487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.33 % (27487)Termination reason: Unknown
% 1.61/1.33 % (27487)Termination phase: Saturation
% 1.61/1.33
% 1.61/1.33 % (27487)Memory used [KB]: 5628
% 1.61/1.33 % (27487)Time elapsed: 0.008 s
% 1.61/1.33 % (27487)Instructions burned: 17 (million)
% 1.61/1.33 % (27487)------------------------------
% 1.61/1.33 % (27487)------------------------------
% 1.61/1.33 % (27486)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_27150 for (2999ds/37Mi)
% 1.61/1.33 % (27483)Refutation not found, incomplete strategy
% 1.61/1.33 % (27483)------------------------------
% 1.61/1.33 % (27483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.33 % (27483)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.33
% 1.61/1.33
% 1.61/1.33 % (27483)Memory used [KB]: 5628
% 1.61/1.33 % (27483)Time elapsed: 0.021 s
% 1.61/1.33 % (27483)Instructions burned: 31 (million)
% 1.61/1.33 % (27483)------------------------------
% 1.61/1.33 % (27483)------------------------------
% 1.61/1.33 % (27488)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_27150 for (2999ds/3Mi)
% 1.61/1.33 % (27488)Instruction limit reached!
% 1.61/1.33 % (27488)------------------------------
% 1.61/1.33 % (27488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.33 % (27488)Termination reason: Unknown
% 1.61/1.33 % (27488)Termination phase: Saturation
% 1.61/1.33
% 1.61/1.33 % (27488)Memory used [KB]: 5500
% 1.61/1.33 % (27488)Time elapsed: 0.004 s
% 1.61/1.33 % (27488)Instructions burned: 3 (million)
% 1.61/1.33 % (27488)------------------------------
% 1.61/1.33 % (27488)------------------------------
% 1.61/1.34 % (27491)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/16Mi)
% 1.61/1.34 % (27490)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/7Mi)
% 1.61/1.35 % (27490)Instruction limit reached!
% 1.61/1.35 % (27490)------------------------------
% 1.61/1.35 % (27490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (27490)Termination reason: Unknown
% 1.61/1.35 % (27490)Termination phase: Saturation
% 1.61/1.35
% 1.61/1.35 % (27490)Memory used [KB]: 1023
% 1.61/1.35 % (27490)Time elapsed: 0.007 s
% 1.61/1.35 % (27490)Instructions burned: 8 (million)
% 1.61/1.35 % (27490)------------------------------
% 1.61/1.35 % (27490)------------------------------
% 1.61/1.35 % (27491)Instruction limit reached!
% 1.61/1.35 % (27491)------------------------------
% 1.61/1.35 % (27491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (27491)Termination reason: Unknown
% 1.61/1.35 % (27491)Termination phase: Saturation
% 1.61/1.35
% 1.61/1.35 % (27491)Memory used [KB]: 5756
% 1.61/1.35 % (27491)Time elapsed: 0.008 s
% 1.61/1.35 % (27491)Instructions burned: 17 (million)
% 1.61/1.35 % (27491)------------------------------
% 1.61/1.35 % (27491)------------------------------
% 1.61/1.35 % (27492)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_27150 for (2999ds/3Mi)
% 1.61/1.35 % (27492)Instruction limit reached!
% 1.61/1.35 % (27492)------------------------------
% 1.61/1.35 % (27492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (27492)Termination reason: Unknown
% 1.61/1.35 % (27492)Termination phase: Property scanning
% 1.61/1.35
% 1.61/1.35 % (27492)Memory used [KB]: 1023
% 1.61/1.35 % (27492)Time elapsed: 0.004 s
% 1.61/1.35 % (27492)Instructions burned: 4 (million)
% 1.61/1.35 % (27492)------------------------------
% 1.61/1.35 % (27492)------------------------------
% 1.61/1.35 % (27486)Instruction limit reached!
% 1.61/1.35 % (27486)------------------------------
% 1.61/1.35 % (27486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (27486)Termination reason: Unknown
% 1.61/1.35 % (27486)Termination phase: Saturation
% 1.61/1.35
% 1.61/1.35 % (27486)Memory used [KB]: 5884
% 1.61/1.35 % (27486)Time elapsed: 0.023 s
% 1.61/1.35 % (27486)Instructions burned: 38 (million)
% 1.61/1.35 % (27486)------------------------------
% 1.61/1.35 % (27486)------------------------------
% 1.61/1.35 % (27493)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_27150 for (2999ds/3Mi)
% 1.61/1.35 % (27493)Instruction limit reached!
% 1.61/1.35 % (27493)------------------------------
% 1.61/1.35 % (27493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (27493)Termination reason: Unknown
% 1.61/1.35 % (27493)Termination phase: Saturation
% 1.61/1.35
% 1.61/1.35 % (27493)Memory used [KB]: 1023
% 1.61/1.35 % (27493)Time elapsed: 0.004 s
% 1.61/1.35 % (27493)Instructions burned: 4 (million)
% 1.61/1.35 % (27493)------------------------------
% 1.61/1.35 % (27493)------------------------------
% 1.61/1.36 % (27495)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/3Mi)
% 1.61/1.36 % (27495)Instruction limit reached!
% 1.61/1.36 % (27495)------------------------------
% 1.61/1.36 % (27495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.36 % (27495)Termination reason: Unknown
% 1.61/1.36 % (27495)Termination phase: Saturation
% 1.61/1.36
% 1.61/1.36 % (27495)Memory used [KB]: 5500
% 1.61/1.36 % (27495)Time elapsed: 0.003 s
% 1.61/1.36 % (27495)Instructions burned: 4 (million)
% 1.61/1.36 % (27495)------------------------------
% 1.61/1.36 % (27495)------------------------------
% 1.61/1.36 % (27494)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/7Mi)
% 1.61/1.37 % (27494)Instruction limit reached!
% 1.61/1.37 % (27494)------------------------------
% 1.61/1.37 % (27494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.37 % (27494)Termination reason: Unknown
% 1.61/1.37 % (27494)Termination phase: Saturation
% 1.61/1.37
% 1.61/1.37 % (27494)Memory used [KB]: 5500
% 1.61/1.37 % (27494)Time elapsed: 0.006 s
% 1.61/1.37 % (27494)Instructions burned: 7 (million)
% 1.61/1.37 % (27494)------------------------------
% 1.61/1.37 % (27494)------------------------------
% 1.61/1.37 % (27499)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/6Mi)
% 1.61/1.37 % (27496)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/4Mi)
% 1.61/1.37 % (27497)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/18Mi)
% 1.61/1.37 % (27499)Instruction limit reached!
% 1.61/1.37 % (27499)------------------------------
% 1.61/1.37 % (27499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.37 % (27499)Termination reason: Unknown
% 1.61/1.37 % (27499)Termination phase: Saturation
% 1.61/1.37
% 1.61/1.37 % (27499)Memory used [KB]: 5500
% 1.61/1.37 % (27499)Time elapsed: 0.004 s
% 1.61/1.37 % (27499)Instructions burned: 6 (million)
% 1.61/1.37 % (27499)------------------------------
% 1.61/1.37 % (27499)------------------------------
% 1.61/1.37 % (27498)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/710Mi)
% 1.61/1.37 % (27496)Instruction limit reached!
% 1.61/1.37 % (27496)------------------------------
% 1.61/1.37 % (27496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.37 % (27496)Termination reason: Unknown
% 1.61/1.37 % (27496)Termination phase: Saturation
% 1.61/1.37
% 1.61/1.37 % (27496)Memory used [KB]: 5500
% 1.61/1.37 % (27496)Time elapsed: 0.005 s
% 1.61/1.37 % (27496)Instructions burned: 5 (million)
% 1.61/1.37 % (27496)------------------------------
% 1.61/1.37 % (27496)------------------------------
% 1.61/1.37 % (27497)Refutation not found, incomplete strategy
% 1.61/1.37 % (27497)------------------------------
% 1.61/1.37 % (27497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.37 % (27497)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.37
% 1.61/1.37
% 1.61/1.37 % (27497)Memory used [KB]: 5500
% 1.61/1.37 % (27497)Time elapsed: 0.005 s
% 1.61/1.37 % (27497)Instructions burned: 4 (million)
% 1.61/1.37 % (27497)------------------------------
% 1.61/1.37 % (27497)------------------------------
% 1.61/1.38 % (27501)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_27150 for (2999ds/21Mi)
% 1.61/1.38 % (27500)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_27150 for (2999ds/902Mi)
% 1.61/1.39 % (27501)Instruction limit reached!
% 1.61/1.39 % (27501)------------------------------
% 1.61/1.39 % (27501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.39 % (27501)Termination reason: Unknown
% 1.61/1.39 % (27501)Termination phase: Saturation
% 1.61/1.39
% 1.61/1.39 % (27501)Memory used [KB]: 5628
% 1.61/1.39 % (27501)Time elapsed: 0.009 s
% 1.61/1.39 % (27501)Instructions burned: 22 (million)
% 1.61/1.39 % (27501)------------------------------
% 1.61/1.39 % (27501)------------------------------
% 1.61/1.39 % (27502)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/5Mi)
% 1.61/1.39 % (27503)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_27150 for (2999ds/6Mi)
% 1.61/1.39 % (27503)Instruction limit reached!
% 1.61/1.39 % (27503)------------------------------
% 1.61/1.39 % (27503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.39 % (27503)Termination reason: Unknown
% 1.61/1.39 % (27503)Termination phase: Saturation
% 1.61/1.39
% 1.61/1.39 % (27503)Memory used [KB]: 5500
% 1.61/1.39 % (27503)Time elapsed: 0.004 s
% 1.61/1.39 % (27503)Instructions burned: 8 (million)
% 1.61/1.39 % (27503)------------------------------
% 1.61/1.39 % (27503)------------------------------
% 1.61/1.39 % (27502)Instruction limit reached!
% 1.61/1.39 % (27502)------------------------------
% 1.61/1.39 % (27502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.39 % (27502)Termination reason: Unknown
% 1.61/1.39 % (27502)Termination phase: Saturation
% 1.61/1.39
% 1.61/1.39 % (27502)Memory used [KB]: 5500
% 1.61/1.39 % (27502)Time elapsed: 0.005 s
% 1.61/1.39 % (27502)Instructions burned: 5 (million)
% 1.61/1.39 % (27502)------------------------------
% 1.61/1.39 % (27502)------------------------------
% 1.61/1.40 % (27504)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27150 for (2999ds/377Mi)
% 1.61/1.40 % (27505)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_27150 for (2999ds/779Mi)
% 1.61/1.41 % (27506)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_27150 for (2999ds/19Mi)
% 1.61/1.41 % (27478)Instruction limit reached!
% 1.61/1.41 % (27478)------------------------------
% 1.61/1.41 % (27478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.41 % (27478)Termination reason: Unknown
% 1.61/1.41 % (27478)Termination phase: Saturation
% 1.61/1.41
% 1.61/1.41 % (27478)Memory used [KB]: 6524
% 1.61/1.41 % (27478)Time elapsed: 0.101 s
% 1.61/1.41 % (27478)Instructions burned: 185 (million)
% 1.61/1.41 % (27478)------------------------------
% 1.61/1.41 % (27478)------------------------------
% 1.61/1.42 % (27506)Instruction limit reached!
% 1.61/1.42 % (27506)------------------------------
% 1.61/1.42 % (27506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.42 % (27506)Termination reason: Unknown
% 1.61/1.42 % (27506)Termination phase: Saturation
% 1.61/1.42
% 1.61/1.42 % (27506)Memory used [KB]: 5628
% 1.61/1.42 % (27506)Time elapsed: 0.031 s
% 1.61/1.42 % (27506)Instructions burned: 20 (million)
% 1.61/1.42 % (27506)------------------------------
% 1.61/1.42 % (27506)------------------------------
% 1.61/1.42 % (27507)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27150 for (2998ds/879Mi)
% 1.61/1.43 % (27508)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27150 for (2998ds/17Mi)
% 1.61/1.43 % (27508)Instruction limit reached!
% 1.61/1.43 % (27508)------------------------------
% 1.61/1.43 % (27508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.43 % (27508)Termination reason: Unknown
% 1.61/1.43 % (27508)Termination phase: Saturation
% 1.61/1.43
% 1.61/1.43 % (27508)Memory used [KB]: 5628
% 1.61/1.43 % (27508)Time elapsed: 0.008 s
% 1.61/1.43 % (27508)Instructions burned: 18 (million)
% 1.61/1.43 % (27508)------------------------------
% 1.61/1.43 % (27508)------------------------------
% 1.61/1.44 % (27509)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27150 for (2998ds/3Mi)
% 1.61/1.44 % (27509)Instruction limit reached!
% 1.61/1.44 % (27509)------------------------------
% 1.61/1.44 % (27509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.44 % (27509)Termination reason: Unknown
% 1.61/1.44 % (27509)Termination phase: Saturation
% 1.61/1.44
% 1.61/1.45 % (27509)Memory used [KB]: 1023
% 1.61/1.45 % (27509)Time elapsed: 0.003 s
% 1.61/1.45 % (27509)Instructions burned: 4 (million)
% 1.61/1.45 % (27509)------------------------------
% 1.61/1.45 % (27509)------------------------------
% 1.61/1.46 % (27510)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27150 for (2998ds/30Mi)
% 1.61/1.47 % (27510)Instruction limit reached!
% 1.61/1.47 % (27510)------------------------------
% 1.61/1.47 % (27510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.47 % (27510)Termination reason: Unknown
% 1.61/1.47 % (27510)Termination phase: Saturation
% 1.61/1.47
% 1.61/1.47 % (27510)Memory used [KB]: 5628
% 1.61/1.47 % (27510)Time elapsed: 0.012 s
% 1.61/1.47 % (27510)Instructions burned: 31 (million)
% 1.61/1.47 % (27510)------------------------------
% 1.61/1.47 % (27510)------------------------------
% 1.61/1.48 % (27511)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_27150 for (2998ds/127Mi)
% 1.61/1.51 % (27504)Instruction limit reached!
% 1.61/1.51 % (27504)------------------------------
% 1.61/1.51 % (27504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.51 % (27504)Termination reason: Unknown
% 1.61/1.51 % (27504)Termination phase: Saturation
% 1.61/1.51
% 1.61/1.51 % (27504)Memory used [KB]: 6140
% 1.61/1.51 % (27504)Time elapsed: 0.116 s
% 1.61/1.51 % (27504)Instructions burned: 377 (million)
% 1.61/1.51 % (27504)------------------------------
% 1.61/1.51 % (27504)------------------------------
% 1.61/1.52 % (27511)Instruction limit reached!
% 1.61/1.52 % (27511)------------------------------
% 1.61/1.52 % (27511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.52 % (27511)Termination reason: Unknown
% 1.61/1.52 % (27511)Termination phase: Saturation
% 1.61/1.52
% 1.61/1.52 % (27511)Memory used [KB]: 6012
% 1.61/1.52 % (27511)Time elapsed: 0.043 s
% 1.61/1.52 % (27511)Instructions burned: 127 (million)
% 1.61/1.52 % (27511)------------------------------
% 1.61/1.52 % (27511)------------------------------
% 1.61/1.52 % (27512)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_27150 for (2997ds/100Mi)
% 1.61/1.52 % (27512)Refutation not found, incomplete strategy
% 1.61/1.52 % (27512)------------------------------
% 1.61/1.52 % (27512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.52 % (27512)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.52
% 1.61/1.52
% 1.61/1.52 % (27512)Memory used [KB]: 5500
% 1.61/1.52 % (27512)Time elapsed: 0.004 s
% 1.61/1.52 % (27512)Instructions burned: 6 (million)
% 1.61/1.52 % (27512)------------------------------
% 1.61/1.52 % (27512)------------------------------
% 1.61/1.53 % (27513)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_27150 for (2997ds/3Mi)
% 1.61/1.53 % (27513)Instruction limit reached!
% 1.61/1.53 % (27513)------------------------------
% 1.61/1.53 % (27513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.53 % (27513)Termination reason: Unknown
% 1.61/1.53 % (27513)Termination phase: Saturation
% 1.61/1.53
% 1.61/1.53 % (27513)Memory used [KB]: 5500
% 1.61/1.53 % (27513)Time elapsed: 0.003 s
% 1.61/1.53 % (27513)Instructions burned: 4 (million)
% 1.61/1.53 % (27513)------------------------------
% 1.61/1.53 % (27513)------------------------------
% 1.61/1.53 % (27514)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_27150 for (2997ds/20Mi)
% 1.61/1.54 % (27515)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_27150 for (2997ds/86Mi)
% 1.61/1.54 % (27514)Instruction limit reached!
% 1.61/1.54 % (27514)------------------------------
% 1.61/1.54 % (27514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.54 % (27514)Termination reason: Unknown
% 1.61/1.54 % (27514)Termination phase: Saturation
% 1.61/1.54
% 1.61/1.54 % (27514)Memory used [KB]: 5628
% 1.61/1.54 % (27514)Time elapsed: 0.009 s
% 1.61/1.54 % (27514)Instructions burned: 21 (million)
% 1.61/1.54 % (27514)------------------------------
% 1.61/1.54 % (27514)------------------------------
% 1.61/1.55 % (27516)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_27150 for (2997ds/107Mi)
% 1.61/1.57 % (27515)Instruction limit reached!
% 1.61/1.57 % (27515)------------------------------
% 1.61/1.57 % (27515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.57 % (27515)Termination reason: Unknown
% 1.61/1.57 % (27515)Termination phase: Saturation
% 1.61/1.57
% 1.61/1.57 % (27515)Memory used [KB]: 6012
% 1.61/1.57 % (27515)Time elapsed: 0.029 s
% 1.61/1.57 % (27515)Instructions burned: 86 (million)
% 1.61/1.57 % (27515)------------------------------
% 1.61/1.57 % (27515)------------------------------
% 1.61/1.58 % (27517)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_27150 for (2997ds/39Mi)
% 1.61/1.58 % (27516)Instruction limit reached!
% 1.61/1.58 % (27516)------------------------------
% 1.61/1.58 % (27516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.58 % (27516)Termination reason: Unknown
% 1.61/1.58 % (27516)Termination phase: Saturation
% 1.61/1.58
% 1.61/1.58 % (27516)Memory used [KB]: 5756
% 1.61/1.58 % (27516)Time elapsed: 0.031 s
% 1.61/1.58 % (27516)Instructions burned: 110 (million)
% 1.61/1.58 % (27516)------------------------------
% 1.61/1.58 % (27516)------------------------------
% 1.61/1.59 % (27517)Instruction limit reached!
% 1.61/1.59 % (27517)------------------------------
% 1.61/1.59 % (27517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.59 % (27517)Termination reason: Unknown
% 1.61/1.59 % (27517)Termination phase: Saturation
% 1.61/1.59
% 1.61/1.59 % (27517)Memory used [KB]: 5628
% 1.61/1.59 % (27517)Time elapsed: 0.015 s
% 1.61/1.59 % (27517)Instructions burned: 41 (million)
% 1.61/1.59 % (27517)------------------------------
% 1.61/1.59 % (27517)------------------------------
% 1.61/1.59 % (27518)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_27150 for (2997ds/448Mi)
% 1.61/1.59 % (27489)Instruction limit reached!
% 1.61/1.59 % (27489)------------------------------
% 1.61/1.59 % (27489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.59 % (27489)Termination reason: Unknown
% 1.61/1.59 % (27489)Termination phase: Saturation
% 1.61/1.59
% 1.61/1.59 % (27489)Memory used [KB]: 6908
% 1.61/1.59 % (27489)Time elapsed: 0.268 s
% 1.61/1.59 % (27489)Instructions burned: 1044 (million)
% 1.61/1.59 % (27489)------------------------------
% 1.61/1.59 % (27489)------------------------------
% 1.61/1.60 % (27498)Instruction limit reached!
% 1.61/1.60 % (27498)------------------------------
% 1.61/1.60 % (27498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.60 % (27498)Termination reason: Unknown
% 1.61/1.60 % (27498)Termination phase: Saturation
% 1.61/1.60
% 1.61/1.60 % (27498)Memory used [KB]: 7419
% 1.61/1.60 % (27498)Time elapsed: 0.230 s
% 1.61/1.60 % (27498)Instructions burned: 712 (million)
% 1.61/1.60 % (27498)------------------------------
% 1.61/1.60 % (27498)------------------------------
% 1.61/1.60 % (27519)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_27150 for (2997ds/46Mi)
% 1.61/1.60 % (27520)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_27150 for (2997ds/98Mi)
% 1.61/1.61 % (27521)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_27150 for (2996ds/507Mi)
% 1.61/1.62 % (27519)Instruction limit reached!
% 1.61/1.62 % (27519)------------------------------
% 1.61/1.62 % (27519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.62 % (27519)Termination reason: Unknown
% 1.61/1.62 % (27519)Termination phase: Saturation
% 1.61/1.62
% 1.61/1.62 % (27519)Memory used [KB]: 5756
% 1.61/1.62 % (27519)Time elapsed: 0.019 s
% 1.61/1.62 % (27519)Instructions burned: 48 (million)
% 1.61/1.62 % (27519)------------------------------
% 1.61/1.62 % (27519)------------------------------
% 1.61/1.63 % (27522)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_27150 for (2996ds/149Mi)
% 1.61/1.63 % (27520)Instruction limit reached!
% 1.61/1.63 % (27520)------------------------------
% 1.61/1.63 % (27520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.63 % (27520)Termination reason: Unknown
% 1.61/1.63 % (27520)Termination phase: Saturation
% 1.61/1.63
% 1.61/1.63 % (27520)Memory used [KB]: 1151
% 1.61/1.63 % (27520)Time elapsed: 0.031 s
% 1.61/1.63 % (27520)Instructions burned: 99 (million)
% 1.61/1.63 % (27520)------------------------------
% 1.61/1.63 % (27520)------------------------------
% 1.61/1.64 % (27523)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_27150 for (2996ds/39Mi)
% 1.61/1.65 % (27505)Instruction limit reached!
% 1.61/1.65 % (27505)------------------------------
% 1.61/1.65 % (27505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.65 % (27505)Termination reason: Unknown
% 1.61/1.65 % (27505)Termination phase: Saturation
% 1.61/1.65
% 1.61/1.65 % (27505)Memory used [KB]: 7164
% 1.61/1.65 % (27505)Time elapsed: 0.247 s
% 1.61/1.65 % (27505)Instructions burned: 781 (million)
% 1.61/1.65 % (27505)------------------------------
% 1.61/1.65 % (27505)------------------------------
% 1.61/1.65 % (27523)Instruction limit reached!
% 1.61/1.65 % (27523)------------------------------
% 1.61/1.65 % (27523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.65 % (27523)Termination reason: Unknown
% 1.61/1.65 % (27523)Termination phase: Saturation
% 1.61/1.65
% 1.61/1.65 % (27523)Memory used [KB]: 5628
% 1.61/1.65 % (27523)Time elapsed: 0.013 s
% 1.61/1.65 % (27523)Instructions burned: 39 (million)
% 1.61/1.65 % (27523)------------------------------
% 1.61/1.65 % (27523)------------------------------
% 1.61/1.66 % (27507)Instruction limit reached!
% 1.61/1.66 % (27507)------------------------------
% 1.61/1.66 % (27507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.66 % (27507)Termination reason: Unknown
% 1.61/1.66 % (27507)Termination phase: Saturation
% 1.61/1.66
% 1.61/1.66 % (27507)Memory used [KB]: 6652
% 1.61/1.66 % (27507)Time elapsed: 0.259 s
% 1.61/1.66 % (27507)Instructions burned: 881 (million)
% 1.61/1.66 % (27507)------------------------------
% 1.61/1.66 % (27507)------------------------------
% 1.61/1.66 % (27524)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_27150 for (2996ds/6Mi)
% 1.61/1.66 % (27524)Instruction limit reached!
% 1.61/1.66 % (27524)------------------------------
% 1.61/1.66 % (27524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.66 % (27524)Termination reason: Unknown
% 1.61/1.66 % (27524)Termination phase: Saturation
% 1.61/1.66
% 1.61/1.66 % (27524)Memory used [KB]: 9978
% 1.61/1.66 % (27524)Time elapsed: 0.005 s
% 1.61/1.66 % (27524)Instructions burned: 8 (million)
% 1.61/1.66 % (27524)------------------------------
% 1.61/1.66 % (27524)------------------------------
% 1.61/1.66 % (27525)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_27150 for (2996ds/1087Mi)
% 1.61/1.67 % (27526)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_27150 for (2996ds/47Mi)
% 1.61/1.67 % (27500)Instruction limit reached!
% 1.61/1.67 % (27500)------------------------------
% 1.61/1.67 % (27500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.67 % (27500)Termination reason: Unknown
% 1.61/1.67 % (27500)Termination phase: Saturation
% 1.61/1.67
% 1.61/1.67 % (27500)Memory used [KB]: 6396
% 1.61/1.67 % (27500)Time elapsed: 0.285 s
% 1.61/1.67 % (27500)Instructions burned: 905 (million)
% 1.61/1.67 % (27500)------------------------------
% 1.61/1.67 % (27500)------------------------------
% 1.61/1.67 % (27527)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_27150 for (2996ds/44Mi)
% 1.61/1.67 % (27525)Refutation not found, incomplete strategy
% 1.61/1.67 % (27525)------------------------------
% 1.61/1.67 % (27525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.67 % (27525)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.67
% 1.61/1.67
% 1.61/1.67 % (27525)Memory used [KB]: 5756
% 1.61/1.67 % (27525)Time elapsed: 0.013 s
% 1.61/1.67 % (27525)Instructions burned: 37 (million)
% 1.61/1.67 % (27525)------------------------------
% 1.61/1.67 % (27525)------------------------------
% 1.61/1.68 % (27522)Instruction limit reached!
% 1.61/1.68 % (27522)------------------------------
% 1.61/1.68 % (27522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.68 % (27522)Termination reason: Unknown
% 1.61/1.68 % (27522)Termination phase: Saturation
% 1.61/1.68
% 1.61/1.68 % (27522)Memory used [KB]: 6268
% 1.61/1.68 % (27522)Time elapsed: 0.051 s
% 1.61/1.68 % (27522)Instructions burned: 150 (million)
% 1.61/1.68 % (27522)------------------------------
% 1.61/1.68 % (27522)------------------------------
% 1.61/1.68 % (27528)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_27150 for (2996ds/432Mi)
% 1.61/1.68 % (27526)Instruction limit reached!
% 1.61/1.68 % (27526)------------------------------
% 1.61/1.68 % (27526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.68 % (27526)Termination reason: Unknown
% 1.61/1.68 % (27526)Termination phase: Saturation
% 1.61/1.68
% 1.61/1.68 % (27526)Memory used [KB]: 5628
% 1.61/1.68 % (27526)Time elapsed: 0.017 s
% 1.61/1.68 % (27526)Instructions burned: 47 (million)
% 1.61/1.68 % (27526)------------------------------
% 1.61/1.68 % (27526)------------------------------
% 1.61/1.68 % (27529)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_27150 for (2996ds/62Mi)
% 1.61/1.68 % (27527)Instruction limit reached!
% 1.61/1.68 % (27527)------------------------------
% 1.61/1.68 % (27527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.68 % (27527)Termination reason: Unknown
% 1.61/1.68 % (27527)Termination phase: Saturation
% 1.61/1.68
% 1.61/1.68 % (27527)Memory used [KB]: 1279
% 1.61/1.68 % (27527)Time elapsed: 0.016 s
% 1.61/1.68 % (27527)Instructions burned: 44 (million)
% 1.61/1.68 % (27527)------------------------------
% 1.61/1.68 % (27527)------------------------------
% 1.61/1.69 % (27530)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_27150 for (2996ds/31Mi)
% 1.61/1.69 % (27531)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_27150 for (2996ds/96Mi)
% 1.61/1.69 % (27532)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_27150 for (2996ds/453Mi)
% 1.61/1.70 % (27530)Instruction limit reached!
% 1.61/1.70 % (27530)------------------------------
% 1.61/1.70 % (27530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.70 % (27530)Termination reason: Unknown
% 1.61/1.70 % (27530)Termination phase: Saturation
% 1.61/1.70
% 1.61/1.70 % (27530)Memory used [KB]: 5756
% 1.61/1.70 % (27530)Time elapsed: 0.012 s
% 1.61/1.70 % (27530)Instructions burned: 32 (million)
% 1.61/1.70 % (27530)------------------------------
% 1.61/1.70 % (27530)------------------------------
% 1.61/1.70 % (27529)Instruction limit reached!
% 1.61/1.70 % (27529)------------------------------
% 1.61/1.70 % (27529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.70 % (27529)Termination reason: Unknown
% 1.61/1.70 % (27529)Termination phase: Saturation
% 1.61/1.70
% 1.61/1.70 % (27529)Memory used [KB]: 5884
% 1.61/1.70 % (27529)Time elapsed: 0.019 s
% 1.61/1.70 % (27529)Instructions burned: 62 (million)
% 1.61/1.70 % (27529)------------------------------
% 1.61/1.70 % (27529)------------------------------
% 1.61/1.70 % (27532)Refutation not found, incomplete strategy
% 1.61/1.70 % (27532)------------------------------
% 1.61/1.70 % (27532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.70 % (27532)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.70
% 1.61/1.70
% 1.61/1.70 % (27532)Memory used [KB]: 5628
% 1.61/1.70 % (27532)Time elapsed: 0.008 s
% 1.61/1.70 % (27532)Instructions burned: 18 (million)
% 1.61/1.70 % (27532)------------------------------
% 1.61/1.70 % (27532)------------------------------
% 1.61/1.71 % (27533)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_27150 for (2996ds/71Mi)
% 1.61/1.71 % (27534)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_27150 for (2996ds/83Mi)
% 1.61/1.71 % (27535)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_27150 for (2996ds/11Mi)
% 1.61/1.72 % (27535)Instruction limit reached!
% 1.61/1.72 % (27535)------------------------------
% 1.61/1.72 % (27535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.72 % (27535)Termination reason: Unknown
% 1.61/1.72 % (27535)Termination phase: Saturation
% 1.61/1.72
% 1.61/1.72 % (27535)Memory used [KB]: 5500
% 1.61/1.72 % (27535)Time elapsed: 0.006 s
% 1.61/1.72 % (27535)Instructions burned: 13 (million)
% 1.61/1.72 % (27535)------------------------------
% 1.61/1.72 % (27535)------------------------------
% 1.61/1.72 % (27518)Instruction limit reached!
% 1.61/1.72 % (27518)------------------------------
% 1.61/1.72 % (27518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.72 % (27518)Termination reason: Unknown
% 1.61/1.72 % (27518)Termination phase: Saturation
% 1.61/1.72
% 1.61/1.72 % (27518)Memory used [KB]: 6396
% 1.61/1.72 % (27518)Time elapsed: 0.134 s
% 1.61/1.72 % (27518)Instructions burned: 450 (million)
% 1.61/1.72 % (27518)------------------------------
% 1.61/1.72 % (27518)------------------------------
% 1.61/1.72 % (27531)Instruction limit reached!
% 1.61/1.72 % (27531)------------------------------
% 1.61/1.72 % (27531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.72 % (27531)Termination reason: Unknown
% 1.61/1.72 % (27531)Termination phase: Saturation
% 1.61/1.72
% 1.61/1.72 % (27531)Memory used [KB]: 5756
% 1.61/1.72 % (27531)Time elapsed: 0.033 s
% 1.61/1.72 % (27531)Instructions burned: 99 (million)
% 1.61/1.72 % (27531)------------------------------
% 1.61/1.72 % (27531)------------------------------
% 1.61/1.73 % (27536)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_27150 for (2995ds/41Mi)
% 1.61/1.73 % (27533)Instruction limit reached!
% 1.61/1.73 % (27533)------------------------------
% 1.61/1.73 % (27533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.73 % (27533)Termination reason: Unknown
% 1.61/1.73 % (27533)Termination phase: Saturation
% 1.61/1.73
% 1.61/1.73 % (27533)Memory used [KB]: 5756
% 1.61/1.73 % (27533)Time elapsed: 0.027 s
% 1.61/1.73 % (27533)Instructions burned: 73 (million)
% 1.61/1.73 % (27533)------------------------------
% 1.61/1.73 % (27533)------------------------------
% 1.61/1.73 % (27537)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27150 for (2995ds/6Mi)
% 1.61/1.73 % (27538)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_27150 for (2995ds/150Mi)
% 1.61/1.73 % (27536)Refutation not found, incomplete strategy
% 1.61/1.73 % (27536)------------------------------
% 1.61/1.73 % (27536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.73 % (27536)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.73
% 1.61/1.73
% 1.61/1.73 % (27536)Memory used [KB]: 5628
% 1.61/1.73 % (27536)Time elapsed: 0.009 s
% 1.61/1.73 % (27536)Instructions burned: 19 (million)
% 1.61/1.73 % (27536)------------------------------
% 1.61/1.73 % (27536)------------------------------
% 1.61/1.73 % (27537)Instruction limit reached!
% 1.61/1.73 % (27537)------------------------------
% 1.61/1.73 % (27537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.73 % (27537)Termination reason: Unknown
% 1.61/1.73 % (27537)Termination phase: Saturation
% 1.61/1.73
% 1.61/1.73 % (27537)Memory used [KB]: 5500
% 1.61/1.73 % (27537)Time elapsed: 0.003 s
% 1.61/1.73 % (27537)Instructions burned: 6 (million)
% 1.61/1.73 % (27537)------------------------------
% 1.61/1.73 % (27537)------------------------------
% 1.61/1.74 % (27534)Instruction limit reached!
% 1.61/1.74 % (27534)------------------------------
% 1.61/1.74 % (27534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.74 % (27534)Termination reason: Unknown
% 1.61/1.74 % (27534)Termination phase: Saturation
% 1.61/1.74
% 1.61/1.74 % (27534)Memory used [KB]: 5884
% 1.61/1.74 % (27534)Time elapsed: 0.026 s
% 1.61/1.74 % (27534)Instructions burned: 84 (million)
% 1.61/1.74 % (27534)------------------------------
% 1.61/1.74 % (27534)------------------------------
% 1.61/1.74 % (27539)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_27150 for (2995ds/343Mi)
% 1.61/1.74 % (27540)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_27150 for (2995ds/109Mi)
% 1.61/1.74 % (27541)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_27150 for (2995ds/253Mi)
% 1.61/1.74 % (27542)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_27150 for (2995ds/140Mi)
% 1.61/1.77 % (27521)Instruction limit reached!
% 1.61/1.77 % (27521)------------------------------
% 1.61/1.77 % (27521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.77 % (27521)Termination reason: Unknown
% 1.61/1.77 % (27521)Termination phase: Saturation
% 1.61/1.77
% 1.61/1.77 % (27521)Memory used [KB]: 6652
% 1.61/1.77 % (27521)Time elapsed: 0.168 s
% 1.61/1.77 % (27521)Instructions burned: 509 (million)
% 1.61/1.77 % (27521)------------------------------
% 1.61/1.77 % (27521)------------------------------
% 1.61/1.78 % (27540)Instruction limit reached!
% 1.61/1.78 % (27540)------------------------------
% 1.61/1.78 % (27540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.78 % (27540)Termination reason: Unknown
% 1.61/1.78 % (27540)Termination phase: Saturation
% 1.61/1.78
% 1.61/1.78 % (27540)Memory used [KB]: 6140
% 1.61/1.78 % (27540)Time elapsed: 0.034 s
% 1.61/1.78 % (27540)Instructions burned: 109 (million)
% 1.61/1.78 % (27540)------------------------------
% 1.61/1.78 % (27540)------------------------------
% 1.61/1.78 % (27538)Instruction limit reached!
% 1.61/1.78 % (27538)------------------------------
% 1.61/1.78 % (27538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.78 % (27538)Termination reason: Unknown
% 1.61/1.78 % (27538)Termination phase: Saturation
% 1.61/1.78
% 1.61/1.78 % (27538)Memory used [KB]: 6012
% 1.61/1.78 % (27538)Time elapsed: 0.049 s
% 1.61/1.78 % (27538)Instructions burned: 152 (million)
% 1.61/1.78 % (27538)------------------------------
% 1.61/1.78 % (27538)------------------------------
% 1.61/1.78 % (27542)Instruction limit reached!
% 1.61/1.78 % (27542)------------------------------
% 1.61/1.78 % (27542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.78 % (27542)Termination reason: Unknown
% 1.61/1.78 % (27542)Termination phase: Saturation
% 1.61/1.78
% 1.61/1.78 % (27542)Memory used [KB]: 5884
% 1.61/1.78 % (27542)Time elapsed: 0.059 s
% 1.61/1.78 % (27542)Instructions burned: 140 (million)
% 1.61/1.78 % (27542)------------------------------
% 1.61/1.78 % (27542)------------------------------
% 1.61/1.78 % (27543)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_27150 for (2995ds/614Mi)
% 1.61/1.79 % (27544)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_27150 for (2995ds/202Mi)
% 1.61/1.79 % (27528)First to succeed.
% 1.61/1.79 % (27545)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_27150 for (2995ds/339Mi)
% 1.61/1.79 % (27546)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_27150 for (2995ds/283Mi)
% 1.61/1.79 % (27528)Refutation found. Thanks to Tanya!
% 1.61/1.79 % SZS status Theorem for DTF2THF_27150
% 1.61/1.79 % SZS output start Proof for DTF2THF_27150
% 1.61/1.79 thf(func_def_0, type, cS: $i > $i).
% 1.61/1.79 thf(func_def_1, type, cDOUBLE: $i > $i > $o).
% 1.61/1.79 thf(func_def_2, type, cHALF: $i > $i > $o).
% 1.61/1.79 thf(func_def_16, type, ph0: !>[X0: $tType]:(X0)).
% 1.61/1.79 thf(f403,plain,(
% 1.61/1.79 $false),
% 1.61/1.79 inference(trivial_inequality_removal,[status(thm)],[f402])).
% 1.61/1.79 thf(f402,plain,(
% 1.61/1.79 ($true = $false)),
% 1.61/1.79 inference(boolean_simplification,[status(thm)],[f401])).
% 1.61/1.79 thf(f401,plain,(
% 1.61/1.79 (($false => ((cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ sK4))) | (cDOUBLE @ (cS @ (cS @ sK3)) @ (cS @ (cS @ (cS @ sK4)))))) = $false)),
% 1.61/1.79 inference(forward_demodulation,[status(thm)],[f397,f354])).
% 1.61/1.79 thf(f354,plain,(
% 1.61/1.79 ((cDOUBLE @ sK3 @ sK4) = $false)),
% 1.61/1.79 inference(trivial_inequality_removal,[status(thm)],[f353])).
% 1.61/1.79 thf(f353,plain,(
% 1.61/1.79 ($true = $false) | ((cDOUBLE @ sK3 @ sK4) = $false)),
% 1.61/1.79 inference(boolean_simplification,[status(thm)],[f352])).
% 1.61/1.79 thf(f352,plain,(
% 1.61/1.79 ((cDOUBLE @ sK3 @ sK4) = $false) | ($false = (((cDOUBLE @ sK3 @ sK4) | (cDOUBLE @ (cS @ sK3) @ (cS @ sK4))) => $true))),
% 1.61/1.79 inference(boolean_simplification,[status(thm)],[f351])).
% 1.61/1.79 thf(f351,plain,(
% 1.61/1.79 ((((cDOUBLE @ sK3 @ sK4) | (cDOUBLE @ (cS @ sK3) @ (cS @ sK4))) => ($true | (cDOUBLE @ (cS @ (cS @ sK3)) @ (cS @ (cS @ (cS @ sK4)))))) = $false) | ((cDOUBLE @ sK3 @ sK4) = $false)),
% 1.61/1.79 inference(superposition,[status(thm)],[f347,f66])).
% 1.61/1.79 thf(f66,plain,(
% 1.61/1.79 ( ! [X2 : $i,X1 : $i] : (($true = (cDOUBLE @ (cS @ X2) @ (cS @ (cS @ X1)))) | ($false = (cDOUBLE @ X2 @ X1))) )),
% 1.61/1.79 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.61/1.79 thf(f59,plain,(
% 1.61/1.79 ( ! [X2 : $i,X1 : $i] : (($true = ((cDOUBLE @ X2 @ X1) => (cDOUBLE @ (cS @ X2) @ (cS @ (cS @ X1)))))) )),
% 1.61/1.79 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.61/1.79 thf(f58,plain,(
% 1.61/1.79 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((cDOUBLE @ Y0 @ X1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ X1))))) @ X2))) )),
% 1.61/1.79 inference(pi_clausification,[status(thm)],[f46])).
% 1.61/1.79 thf(f46,plain,(
% 1.61/1.79 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((cDOUBLE @ Y0 @ X1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ X1)))))))) )),
% 1.61/1.79 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.61/1.79 thf(f39,plain,(
% 1.61/1.79 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))) @ X1) = $true)) )),
% 1.61/1.79 inference(pi_clausification,[status(thm)],[f25])).
% 1.61/1.79 thf(f25,plain,(
% 1.61/1.79 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0)))))))))),
% 1.61/1.79 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.61/1.79 thf(f9,plain,(
% 1.61/1.79 ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y0 @ Y1) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((((Y2 @ c0 @ c0) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => (Y2 @ (cS @ (cS @ Y4)) @ (cS @ Y3)))))))) & (Y2 @ (cS @ c0) @ c0)) => (Y2 @ Y0 @ Y1))))))))) & (cDOUBLE @ c0 @ c0)) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))))))),
% 1.61/1.79 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.61/1.79 thf(f7,plain,(
% 1.61/1.79 (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y0 @ Y1) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((((Y2 @ c0 @ c0) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => (Y2 @ (cS @ (cS @ Y4)) @ (cS @ Y3)))))))) & (Y2 @ (cS @ c0) @ c0)) => (Y2 @ Y0 @ Y1))))))))) & (cDOUBLE @ c0 @ c0)) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y1 @ Y0) => ((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1))))))))) = $false)),
% 1.61/1.79 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.61/1.79 thf(f6,plain,(
% 1.61/1.79 ((~ ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y0 @ Y1) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((((Y2 @ c0 @ c0) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => (Y2 @ (cS @ (cS @ Y4)) @ (cS @ Y3)))))))) & (Y2 @ (cS @ c0) @ c0)) => (Y2 @ Y0 @ Y1))))))))) & (cDOUBLE @ c0 @ c0)) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y1 @ Y0) => ((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1)))))))))) = $true)),
% 1.61/1.79 inference(cnf_transformation,[status(thm)],[f5])).
% 1.61/1.79 thf(f5,plain,(
% 1.61/1.79 ((~ ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y0 @ Y1) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((((Y2 @ c0 @ c0) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => (Y2 @ (cS @ (cS @ Y4)) @ (cS @ Y3)))))))) & (Y2 @ (cS @ c0) @ c0)) => (Y2 @ Y0 @ Y1))))))))) & (cDOUBLE @ c0 @ c0)) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y1 @ Y0) => ((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1)))))))))) = $true)),
% 1.61/1.79 inference(fool_elimination,[status(thm)],[f4])).
% 1.61/1.79 thf(f4,plain,(
% 1.61/1.79 ~((! [X0 : $i,X1 : $i] : ((cDOUBLE @ X0 @ X1) => (cDOUBLE @ (cS @ X0) @ (cS @ (cS @ X1)))) & (cDOUBLE @ c0 @ c0) & ! [X2 : $i,X3 : $i] : ((cHALF @ X3 @ X2) => ! [X4 : $i > $i > $o] : (((X4 @ (cS @ c0) @ c0) & ! [X5 : $i,X6 : $i] : ((X4 @ X5 @ X6) => (X4 @ (cS @ (cS @ X5)) @ (cS @ X6))) & (X4 @ c0 @ c0)) => (X4 @ X3 @ X2)))) => ! [X7 : $i,X8 : $i] : ((cHALF @ X7 @ X8) => ((cDOUBLE @ (cS @ X8) @ (cS @ X7)) | (cDOUBLE @ X8 @ X7))))),
% 1.61/1.79 inference(rectify,[status(thm)],[f2])).
% 1.61/1.79 thf(f2,negated_conjecture,(
% 1.61/1.79 ~((! [X3 : $i,X4 : $i] : ((cDOUBLE @ X3 @ X4) => (cDOUBLE @ (cS @ X3) @ (cS @ (cS @ X4)))) & (cDOUBLE @ c0 @ c0) & ! [X1 : $i,X0 : $i] : ((cHALF @ X0 @ X1) => ! [X2 : $i > $i > $o] : (((X2 @ (cS @ c0) @ c0) & ! [X3 : $i,X4 : $i] : ((X2 @ X3 @ X4) => (X2 @ (cS @ (cS @ X3)) @ (cS @ X4))) & (X2 @ c0 @ c0)) => (X2 @ X0 @ X1)))) => ! [X0 : $i,X1 : $i] : ((cHALF @ X0 @ X1) => ((cDOUBLE @ (cS @ X1) @ (cS @ X0)) | (cDOUBLE @ X1 @ X0))))),
% 1.61/1.79 inference(negated_conjecture,[status(cth)],[f1])).
% 1.61/1.79 thf(f1,conjecture,(
% 1.61/1.79 (! [X3 : $i,X4 : $i] : ((cDOUBLE @ X3 @ X4) => (cDOUBLE @ (cS @ X3) @ (cS @ (cS @ X4)))) & (cDOUBLE @ c0 @ c0) & ! [X1 : $i,X0 : $i] : ((cHALF @ X0 @ X1) => ! [X2 : $i > $i > $o] : (((X2 @ (cS @ c0) @ c0) & ! [X3 : $i,X4 : $i] : ((X2 @ X3 @ X4) => (X2 @ (cS @ (cS @ X3)) @ (cS @ X4))) & (X2 @ c0 @ c0)) => (X2 @ X0 @ X1)))) => ! [X0 : $i,X1 : $i] : ((cHALF @ X0 @ X1) => ((cDOUBLE @ (cS @ X1) @ (cS @ X0)) | (cDOUBLE @ X1 @ X0)))),
% 1.61/1.79 file('/export/starexec/sandbox/tmp/tmp.8MlOfATr0D/DTF2THF_27150.p',cTHM300B)).
% 1.61/1.79 thf(f347,plain,(
% 1.61/1.79 ((((cDOUBLE @ sK3 @ sK4) | (cDOUBLE @ (cS @ sK3) @ (cS @ sK4))) => ((cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ sK4))) | (cDOUBLE @ (cS @ (cS @ sK3)) @ (cS @ (cS @ (cS @ sK4)))))) = $false)),
% 1.61/1.79 inference(beta_eta_normalization,[status(thm)],[f346])).
% 1.61/1.79 thf(f346,plain,(
% 1.61/1.79 ($false = ((^[Y0 : $i]: (((cDOUBLE @ sK3 @ Y0) | (cDOUBLE @ (cS @ sK3) @ (cS @ Y0))) => ((cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ Y0))) | (cDOUBLE @ (cS @ (cS @ sK3)) @ (cS @ (cS @ (cS @ Y0))))))) @ sK4))),
% 1.61/1.79 inference(sigma_clausification,[status(thm)],[f340])).
% 1.61/1.79 thf(f340,plain,(
% 1.61/1.79 ((!! @ $i @ (^[Y0 : $i]: (((cDOUBLE @ sK3 @ Y0) | (cDOUBLE @ (cS @ sK3) @ (cS @ Y0))) => ((cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ Y0))) | (cDOUBLE @ (cS @ (cS @ sK3)) @ (cS @ (cS @ (cS @ Y0)))))))) = $false)),
% 1.61/1.79 inference(beta_eta_normalization,[status(thm)],[f337])).
% 1.61/1.79 thf(f337,plain,(
% 1.61/1.79 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1))) => ((cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))) | (cDOUBLE @ (cS @ (cS @ Y0)) @ (cS @ (cS @ (cS @ Y1))))))))) @ sK3) = $false)),
% 1.61/1.79 inference(sigma_clausification,[status(thm)],[f336])).
% 1.61/1.79 thf(f336,plain,(
% 1.61/1.79 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1))) => ((cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))) | (cDOUBLE @ (cS @ (cS @ Y0)) @ (cS @ (cS @ (cS @ Y1)))))))))) = $false)),
% 1.61/1.79 inference(not_proxy_clausification,[status(thm)],[f310])).
% 1.61/1.79 thf(f310,plain,(
% 1.61/1.79 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1))) => ((cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))) | (cDOUBLE @ (cS @ (cS @ Y0)) @ (cS @ (cS @ (cS @ Y1))))))))))))),
% 1.61/1.79 inference(boolean_simplification,[status(thm)],[f309])).
% 1.61/1.79 thf(f309,plain,(
% 1.61/1.79 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1))) => ((cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))) | (cDOUBLE @ (cS @ (cS @ Y0)) @ (cS @ (cS @ (cS @ Y1)))))))))) & $true)) = $true)),
% 1.61/1.79 inference(boolean_simplification,[status(thm)],[f308])).
% 1.61/1.79 thf(f308,plain,(
% 1.61/1.79 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1))) => ((cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))) | (cDOUBLE @ (cS @ (cS @ Y0)) @ (cS @ (cS @ (cS @ Y1)))))))))) & ((cDOUBLE @ c0 @ (cS @ c0)) | $true))))),
% 1.61/1.79 inference(forward_demodulation,[status(thm)],[f307,f91])).
% 1.61/1.79 thf(f91,plain,(
% 1.61/1.79 ($true = (cDOUBLE @ (cS @ c0) @ (cS @ (cS @ c0))))),
% 1.61/1.79 inference(boolean_simplification,[status(thm)],[f89])).
% 1.61/1.79 thf(f89,plain,(
% 1.61/1.79 ($true = ($true => (cDOUBLE @ (cS @ c0) @ (cS @ (cS @ c0)))))),
% 1.61/1.79 inference(superposition,[status(thm)],[f59,f71])).
% 1.61/1.79 thf(f71,plain,(
% 1.61/1.79 ((cDOUBLE @ c0 @ c0) = $true)),
% 1.61/1.79 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.61/1.79 thf(f26,plain,(
% 1.61/1.79 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y0 @ Y1) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((((Y2 @ c0 @ c0) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => (Y2 @ (cS @ (cS @ Y4)) @ (cS @ Y3)))))))) & (Y2 @ (cS @ c0) @ c0)) => (Y2 @ Y0 @ Y1))))))))) & (cDOUBLE @ c0 @ c0)))),
% 1.61/1.79 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.61/1.79 thf(f307,plain,(
% 1.61/1.79 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1))) => ((cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))) | (cDOUBLE @ (cS @ (cS @ Y0)) @ (cS @ (cS @ (cS @ Y1)))))))))) & ((cDOUBLE @ c0 @ (cS @ c0)) | (cDOUBLE @ (cS @ c0) @ (cS @ (cS @ c0)))))) = $true)),
% 1.61/1.79 inference(boolean_simplification,[status(thm)],[f306])).
% 1.61/1.79 thf(f306,plain,(
% 1.61/1.79 ($true = (~ (($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1))) => ((cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))) | (cDOUBLE @ (cS @ (cS @ Y0)) @ (cS @ (cS @ (cS @ Y1))))))))))) & ((cDOUBLE @ c0 @ (cS @ c0)) | (cDOUBLE @ (cS @ c0) @ (cS @ (cS @ c0)))))))),
% 1.61/1.79 inference(boolean_simplification,[status(thm)],[f305])).
% 1.61/1.79 thf(f305,plain,(
% 1.61/1.79 ($true = (~ ((($true | (cDOUBLE @ (cS @ c0) @ (cS @ c0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1))) => ((cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))) | (cDOUBLE @ (cS @ (cS @ Y0)) @ (cS @ (cS @ (cS @ Y1))))))))))) & ((cDOUBLE @ c0 @ (cS @ c0)) | (cDOUBLE @ (cS @ c0) @ (cS @ (cS @ c0)))))))),
% 1.61/1.79 inference(forward_demodulation,[status(thm)],[f237,f71])).
% 1.61/1.79 thf(f237,plain,(
% 1.61/1.79 ($true = (~ ((((cDOUBLE @ c0 @ c0) | (cDOUBLE @ (cS @ c0) @ (cS @ c0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1))) => ((cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))) | (cDOUBLE @ (cS @ (cS @ Y0)) @ (cS @ (cS @ (cS @ Y1))))))))))) & ((cDOUBLE @ c0 @ (cS @ c0)) | (cDOUBLE @ (cS @ c0) @ (cS @ (cS @ c0)))))))),
% 1.61/1.79 inference(boolean_simplification,[status(thm)],[f236])).
% 1.61/1.79 thf(f236,plain,(
% 1.61/1.79 ((((((cDOUBLE @ c0 @ c0) | (cDOUBLE @ (cS @ c0) @ (cS @ c0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1))) => ((cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))) | (cDOUBLE @ (cS @ (cS @ Y0)) @ (cS @ (cS @ (cS @ Y1))))))))))) & ((cDOUBLE @ c0 @ (cS @ c0)) | (cDOUBLE @ (cS @ c0) @ (cS @ (cS @ c0))))) => $false) = $true)),
% 1.61/1.79 inference(beta_eta_normalization,[status(thm)],[f186])).
% 1.61/1.79 thf(f186,plain,(
% 1.61/1.79 ($true = (((((^[Y0 : $i]: ((^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (cDOUBLE @ ((^[Y4 : $i]: ((^[Y5 : $i]: (Y5)))) @ Y2 @ Y3) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (Y4)))) @ Y2 @ Y3))))) @ Y0 @ Y1) | ((^[Y2 : $i]: ((^[Y3 : $i]: (cDOUBLE @ ((^[Y4 : $i]: ((^[Y5 : $i]: (cS @ ((^[Y6 : $i]: ((^[Y7 : $i]: (Y7)))) @ Y4 @ Y5))))) @ Y2 @ Y3) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (cS @ ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6)))) @ Y4 @ Y5))))) @ Y2 @ Y3))))) @ Y0 @ Y1))))) @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i]: (cDOUBLE @ ((^[Y6 : $i]: ((^[Y7 : $i]: (Y7)))) @ Y4 @ Y5) @ ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6)))) @ Y4 @ Y5))))) @ Y2 @ Y3) | ((^[Y4 : $i]: ((^[Y5 : $i]: (cDOUBLE @ ((^[Y6 : $i]: ((^[Y7 : $i]: (cS @ ((^[Y8 : $i]: ((^[Y9 : $i]: (Y9)))) @ Y6 @ Y7))))) @ Y4 @ Y5) @ ((^[Y6 : $i]: ((^[Y7 : $i]: (cS @ ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8)))) @ Y6 @ Y7))))) @ Y4 @ Y5))))) @ Y2 @ Y3))))) @ Y1 @ Y0) => ((^[Y2 : $i]: ((^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i]: (cDOUBLE @ ((^[Y6 : $i]: ((^[Y7 : $i]: (Y7)))) @ Y4 @ Y5) @ ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6)))) @ Y4 @ Y5))))) @ Y2 @ Y3) | ((^[Y4 : $i]: ((^[Y5 : $i]: (cDOUBLE @ ((^[Y6 : $i]: ((^[Y7 : $i]: (cS @ ((^[Y8 : $i]: ((^[Y9 : $i]: (Y9)))) @ Y6 @ Y7))))) @ Y4 @ Y5) @ ((^[Y6 : $i]: ((^[Y7 : $i]: (cS @ ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8)))) @ Y6 @ Y7))))) @ Y4 @ Y5))))) @ Y2 @ Y3))))) @ (cS @ (cS @ Y1)) @ (cS @ Y0)))))))) & ((^[Y0 : $i]: ((^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (cDOUBLE @ ((^[Y4 : $i]: ((^[Y5 : $i]: (Y5)))) @ Y2 @ Y3) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (Y4)))) @ Y2 @ Y3))))) @ Y0 @ Y1) | ((^[Y2 : $i]: ((^[Y3 : $i]: (cDOUBLE @ ((^[Y4 : $i]: ((^[Y5 : $i]: (cS @ ((^[Y6 : $i]: ((^[Y7 : $i]: (Y7)))) @ Y4 @ Y5))))) @ Y2 @ Y3) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (cS @ ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6)))) @ Y4 @ Y5))))) @ Y2 @ Y3))))) @ Y0 @ Y1))))) @ (cS @ c0) @ c0)) => $false))),
% 1.61/1.79 inference(superposition,[status(thm)],[f175,f21])).
% 1.61/1.79 thf(f21,plain,(
% 1.61/1.79 ($false = ((cDOUBLE @ sK1 @ sK2) | (cDOUBLE @ (cS @ sK1) @ (cS @ sK2))))),
% 1.61/1.79 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.61/1.79 thf(f20,plain,(
% 1.61/1.79 (((cHALF @ sK2 @ sK1) => ((cDOUBLE @ sK1 @ sK2) | (cDOUBLE @ (cS @ sK1) @ (cS @ sK2)))) = $false)),
% 1.61/1.79 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.61/1.79 thf(f19,plain,(
% 1.61/1.79 (((^[Y0 : $i]: ((cHALF @ Y0 @ sK1) => ((cDOUBLE @ sK1 @ Y0) | (cDOUBLE @ (cS @ sK1) @ (cS @ Y0))))) @ sK2) = $false)),
% 1.61/1.79 inference(sigma_clausification,[status(thm)],[f15])).
% 1.61/1.79 thf(f15,plain,(
% 1.61/1.79 ($false = (!! @ $i @ (^[Y0 : $i]: ((cHALF @ Y0 @ sK1) => ((cDOUBLE @ sK1 @ Y0) | (cDOUBLE @ (cS @ sK1) @ (cS @ Y0)))))))),
% 1.61/1.79 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.61/1.79 thf(f12,plain,(
% 1.61/1.79 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y1 @ Y0) => ((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1))))))) @ sK1))),
% 1.61/1.79 inference(sigma_clausification,[status(thm)],[f8])).
% 1.61/1.79 thf(f8,plain,(
% 1.61/1.79 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y1 @ Y0) => ((cDOUBLE @ Y0 @ Y1) | (cDOUBLE @ (cS @ Y0) @ (cS @ Y1)))))))) = $false)),
% 1.61/1.79 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.61/1.79 thf(f175,plain,(
% 1.61/1.79 ( ! [X1 : $i > $i > $o] : (($true = ((((X1 @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => (X1 @ (cS @ (cS @ Y1)) @ (cS @ Y0)))))))) & (X1 @ (cS @ c0) @ c0)) => (X1 @ sK2 @ sK1)))) )),
% 1.61/1.79 inference(beta_eta_normalization,[status(thm)],[f173])).
% 1.61/1.79 thf(f173,plain,(
% 1.61/1.79 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: ((((Y0 @ c0 @ c0) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ (cS @ (cS @ Y2)) @ (cS @ Y1)))))))) & (Y0 @ (cS @ c0) @ c0)) => (Y0 @ sK2 @ sK1))) @ X1))) )),
% 1.61/1.79 inference(pi_clausification,[status(thm)],[f150])).
% 1.61/1.79 thf(f150,plain,(
% 1.61/1.79 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((((Y0 @ c0 @ c0) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ (cS @ (cS @ Y2)) @ (cS @ Y1)))))))) & (Y0 @ (cS @ c0) @ c0)) => (Y0 @ sK2 @ sK1)))) = $true)),
% 1.61/1.79 inference(boolean_simplification,[status(thm)],[f149])).
% 1.61/1.79 thf(f149,plain,(
% 1.61/1.79 ($true = ($true => (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((((Y0 @ c0 @ c0) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ (cS @ (cS @ Y2)) @ (cS @ Y1)))))))) & (Y0 @ (cS @ c0) @ c0)) => (Y0 @ sK2 @ sK1))))))),
% 1.61/1.79 inference(superposition,[status(thm)],[f143,f22])).
% 1.61/1.79 thf(f22,plain,(
% 1.61/1.79 ($true = (cHALF @ sK2 @ sK1))),
% 1.61/1.79 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.61/1.79 thf(f143,plain,(
% 1.61/1.79 ( ! [X2 : $i,X1 : $i] : (($true = ((cHALF @ X1 @ X2) => (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((((Y0 @ c0 @ c0) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ (cS @ (cS @ Y2)) @ (cS @ Y1)))))))) & (Y0 @ (cS @ c0) @ c0)) => (Y0 @ X1 @ X2))))))) )),
% 1.61/1.79 inference(beta_eta_normalization,[status(thm)],[f142])).
% 1.61/1.79 thf(f142,plain,(
% 1.61/1.79 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((cHALF @ X1 @ Y0) => (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((((Y1 @ c0 @ c0) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) => (Y1 @ (cS @ (cS @ Y3)) @ (cS @ Y2)))))))) & (Y1 @ (cS @ c0) @ c0)) => (Y1 @ X1 @ Y0)))))) @ X2))) )),
% 1.61/1.79 inference(pi_clausification,[status(thm)],[f122])).
% 1.61/1.79 thf(f122,plain,(
% 1.61/1.79 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((cHALF @ X1 @ Y0) => (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((((Y1 @ c0 @ c0) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) => (Y1 @ (cS @ (cS @ Y3)) @ (cS @ Y2)))))))) & (Y1 @ (cS @ c0) @ c0)) => (Y1 @ X1 @ Y0))))))))) )),
% 1.61/1.79 inference(beta_eta_normalization,[status(thm)],[f116])).
% 1.61/1.79 thf(f116,plain,(
% 1.61/1.79 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y0 @ Y1) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((((Y2 @ c0 @ c0) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => (Y2 @ (cS @ (cS @ Y4)) @ (cS @ Y3)))))))) & (Y2 @ (cS @ c0) @ c0)) => (Y2 @ Y0 @ Y1)))))))) @ X1))) )),
% 1.61/1.79 inference(pi_clausification,[status(thm)],[f72])).
% 1.61/1.79 thf(f72,plain,(
% 1.61/1.79 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y0 @ Y1) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((((Y2 @ c0 @ c0) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => (Y2 @ (cS @ (cS @ Y4)) @ (cS @ Y3)))))))) & (Y2 @ (cS @ c0) @ c0)) => (Y2 @ Y0 @ Y1))))))))))),
% 1.61/1.79 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.61/1.79 thf(f397,plain,(
% 1.61/1.79 (((cDOUBLE @ sK3 @ sK4) => ((cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ sK4))) | (cDOUBLE @ (cS @ (cS @ sK3)) @ (cS @ (cS @ (cS @ sK4)))))) = $false)),
% 1.61/1.79 inference(boolean_simplification,[status(thm)],[f384])).
% 1.61/1.79 thf(f384,plain,(
% 1.61/1.79 ($false = (((cDOUBLE @ sK3 @ sK4) | $false) => ((cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ sK4))) | (cDOUBLE @ (cS @ (cS @ sK3)) @ (cS @ (cS @ (cS @ sK4)))))))),
% 1.61/1.79 inference(superposition,[status(thm)],[f347,f357])).
% 1.61/1.79 thf(f357,plain,(
% 1.61/1.79 ($false = (cDOUBLE @ (cS @ sK3) @ (cS @ sK4)))),
% 1.61/1.79 inference(trivial_inequality_removal,[status(thm)],[f356])).
% 1.61/1.79 thf(f356,plain,(
% 1.61/1.79 ($true = $false) | ($false = (cDOUBLE @ (cS @ sK3) @ (cS @ sK4)))),
% 1.61/1.79 inference(boolean_simplification,[status(thm)],[f355])).
% 1.61/1.79 thf(f355,plain,(
% 1.61/1.79 ($false = (((cDOUBLE @ sK3 @ sK4) | (cDOUBLE @ (cS @ sK3) @ (cS @ sK4))) => $true)) | ($false = (cDOUBLE @ (cS @ sK3) @ (cS @ sK4)))),
% 1.61/1.79 inference(boolean_simplification,[status(thm)],[f350])).
% 1.61/1.79 thf(f350,plain,(
% 1.61/1.79 ($false = (cDOUBLE @ (cS @ sK3) @ (cS @ sK4))) | ($false = (((cDOUBLE @ sK3 @ sK4) | (cDOUBLE @ (cS @ sK3) @ (cS @ sK4))) => ((cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ sK4))) | $true)))),
% 1.61/1.79 inference(superposition,[status(thm)],[f347,f66])).
% 1.61/1.79 % SZS output end Proof for DTF2THF_27150
% 1.61/1.79 % (27528)------------------------------
% 1.61/1.79 % (27528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.79 % (27528)Termination reason: Refutation
% 1.61/1.79
% 1.61/1.79 % (27528)Memory used [KB]: 3454
% 1.61/1.79 % (27528)Time elapsed: 0.115 s
% 1.61/1.79 % (27528)Instructions burned: 374 (million)
% 1.61/1.79 % (27528)------------------------------
% 1.61/1.79 % (27528)------------------------------
% 1.61/1.79 % (27477)Success in time 0.481 s
%------------------------------------------------------------------------------