%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO335^5 : 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 : n015.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 09:53:58 AM UTC 2026
% Result : Theorem 1.64s 1.80s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 1
% Syntax : Number of formulae : 64 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 760 ( 67 equ; 0 cnn)
% Maximal formula atoms : 17 ( 11 avg)
% Number of connectives : 1855 ( 11 ~; 68 |; 90 &;1424 @)
% ( 0 <=>; 127 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 8 con; 0-2 aty)
% ( 135 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 271 ( 216 ^; 55 !; 0 ?; 271 :)
% 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(f538,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f537]) ).
thf(f537,plain,
$false = $true,
inference(boolean_simplification,[status(thm)],[f536]) ).
thf(f536,plain,
( ( $false
=> ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ ( cS @ sK4 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ sK3 ) ) @ ( cS @ ( cS @ ( cS @ sK4 ) ) ) ) ) )
= $false ),
inference(forward_demodulation,[status(thm)],[f528,f475]) ).
thf(f475,plain,
( ( cDOUBLE @ sK3 @ sK4 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f474]) ).
thf(f474,plain,
( ( $false = $true )
| ( ( cDOUBLE @ sK3 @ sK4 )
= $false ) ),
inference(boolean_simplification,[status(thm)],[f473]) ).
thf(f473,plain,
( ( ( ( ( cDOUBLE @ sK3 @ sK4 )
| ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) )
=> $true )
= $false )
| ( ( cDOUBLE @ sK3 @ sK4 )
= $false ) ),
inference(boolean_simplification,[status(thm)],[f469]) ).
thf(f469,plain,
( ( ( cDOUBLE @ sK3 @ sK4 )
= $false )
| ( ( ( ( cDOUBLE @ sK3 @ sK4 )
| ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) )
=> ( $true
| ( cDOUBLE @ ( cS @ ( cS @ sK3 ) ) @ ( cS @ ( cS @ ( cS @ sK4 ) ) ) ) ) )
= $false ) ),
inference(superposition,[status(thm)],[f465,f66]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( ( ( cDOUBLE @ ( cS @ X1 ) @ ( cS @ ( cS @ X2 ) ) )
= $true )
| ( ( cDOUBLE @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( cDOUBLE @ X1 @ X2 )
=> ( cDOUBLE @ ( cS @ X1 ) @ ( cS @ ( cS @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( cDOUBLE @ X1 @ Y0 )
=> ( cDOUBLE @ ( cS @ X1 ) @ ( cS @ ( cS @ Y0 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( cDOUBLE @ X1 @ Y0 )
=> ( cDOUBLE @ ( cS @ X1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y0 @ Y1 )
=> ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y0 @ Y1 )
=> ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
& ( !! @ $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] :
( ( cDOUBLE @ Y0 @ Y1 )
=> ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
& ( !! @ $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] :
( ( cDOUBLE @ Y0 @ Y1 )
=> ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y0 @ Y1 )
=> ( ( cDOUBLE @ Y1 @ Y0 )
| ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
& ( !! @ $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] :
( ( cDOUBLE @ Y0 @ Y1 )
=> ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y0 @ Y1 )
=> ( ( cDOUBLE @ Y1 @ Y0 )
| ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
& ( !! @ $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] :
( ( cDOUBLE @ Y0 @ Y1 )
=> ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y0 @ Y1 )
=> ( ( cDOUBLE @ Y1 @ Y0 )
| ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( cDOUBLE @ X1 @ X0 )
=> ( cDOUBLE @ ( cS @ X1 ) @ ( cS @ ( cS @ X0 ) ) ) )
& ! [X2: $i,X3: $i] :
( ( cDOUBLE @ X2 @ X3 )
=> ( cDOUBLE @ ( cS @ X2 ) @ ( cS @ ( cS @ X3 ) ) ) )
& ( cDOUBLE @ c0 @ c0 )
& ! [X4: $i,X5: $i] :
( ( cHALF @ X5 @ X4 )
=> ! [X6: $i > $i > $o] :
( ( ( X6 @ ( cS @ c0 ) @ c0 )
& ! [X7: $i,X8: $i] :
( ( X6 @ X7 @ X8 )
=> ( X6 @ ( cS @ ( cS @ X7 ) ) @ ( cS @ X8 ) ) )
& ( X6 @ c0 @ c0 ) )
=> ( X6 @ X5 @ X4 ) ) )
& ! [X9: $i,X10: $i] :
( ( cDOUBLE @ X9 @ X10 )
=> ( cDOUBLE @ ( cS @ X9 ) @ ( cS @ ( cS @ X10 ) ) ) ) )
=> ! [X11: $i,X12: $i] :
( ( cHALF @ X12 @ X11 )
=> ( ( cDOUBLE @ ( cS @ X11 ) @ ( cS @ X12 ) )
| ( cDOUBLE @ X11 @ X12 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X4: $i,X3: $i] :
( ( cDOUBLE @ X3 @ X4 )
=> ( cDOUBLE @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) ) )
& ! [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 ) ) )
& ! [X3: $i,X4: $i] :
( ( cDOUBLE @ X3 @ X4 )
=> ( cDOUBLE @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) ) ) )
=> ! [X1: $i,X0: $i] :
( ( cHALF @ X0 @ X1 )
=> ( ( cDOUBLE @ ( cS @ X1 ) @ ( cS @ X0 ) )
| ( cDOUBLE @ X1 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X4: $i,X3: $i] :
( ( cDOUBLE @ X3 @ X4 )
=> ( cDOUBLE @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) ) )
& ! [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 ) ) )
& ! [X3: $i,X4: $i] :
( ( cDOUBLE @ X3 @ X4 )
=> ( cDOUBLE @ ( cS @ X3 ) @ ( cS @ ( cS @ X4 ) ) ) ) )
=> ! [X1: $i,X0: $i] :
( ( cHALF @ X0 @ X1 )
=> ( ( cDOUBLE @ ( cS @ X1 ) @ ( cS @ X0 ) )
| ( cDOUBLE @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.s6yvc8IF6f/DTF2THF_2774.p',cTHM300C) ).
thf(f465,plain,
( $false
= ( ( ( cDOUBLE @ sK3 @ sK4 )
| ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) )
=> ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ ( cS @ sK4 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ sK3 ) ) @ ( cS @ ( cS @ ( cS @ sK4 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f464]) ).
thf(f464,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)],[f463]) ).
thf(f463,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)],[f455]) ).
thf(f455,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)],[f450]) ).
thf(f450,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)],[f389]) ).
thf(f389,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)],[f388]) ).
thf(f388,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)],[f387]) ).
thf(f387,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 ) )
| $true ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f386,f124]) ).
thf(f124,plain,
( ( cDOUBLE @ ( cS @ c0 ) @ ( cS @ ( cS @ c0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $true
=> ( cDOUBLE @ ( cS @ c0 ) @ ( cS @ ( cS @ c0 ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f59,f114]) ).
thf(f114,plain,
( ( cDOUBLE @ c0 @ c0 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,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 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f99]) ).
thf(f99,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 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f91]) ).
thf(f91,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 )
& $true )
= $true ),
inference(superposition,[status(thm)],[f26,f71]) ).
thf(f71,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
& ( !! @ $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 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f386,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)],[f385]) ).
thf(f385,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 ) )
| ( cDOUBLE @ ( cS @ c0 ) @ ( cS @ ( cS @ c0 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f384]) ).
thf(f384,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)],[f313,f114]) ).
thf(f313,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 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f312]) ).
thf(f312,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)],[f248]) ).
thf(f248,plain,
( ( ( ( ^ [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 )
= $true ),
inference(superposition,[status(thm)],[f240,f21]) ).
thf(f21,plain,
( ( ( cDOUBLE @ sK2 @ sK1 )
| ( cDOUBLE @ ( cS @ sK2 ) @ ( cS @ sK1 ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( $false
= ( ( cHALF @ sK1 @ sK2 )
=> ( ( cDOUBLE @ sK2 @ sK1 )
| ( cDOUBLE @ ( cS @ sK2 ) @ ( cS @ sK1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: $i] :
( ( cHALF @ sK1 @ Y0 )
=> ( ( cDOUBLE @ Y0 @ sK1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ sK1 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( cHALF @ sK1 @ Y0 )
=> ( ( cDOUBLE @ Y0 @ sK1 )
| ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ sK1 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y0 @ Y1 )
=> ( ( cDOUBLE @ Y1 @ Y0 )
| ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ Y0 ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cHALF @ Y0 @ Y1 )
=> ( ( cDOUBLE @ Y1 @ Y0 )
| ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ Y0 ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f240,plain,
! [X1: $i > $i > $o] :
( ( ( ( X1 @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y1 ) ) @ ( cS @ Y0 ) ) ) ) )
& ( X1 @ ( cS @ c0 ) @ c0 ) )
=> ( X1 @ sK1 @ sK2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f238]) ).
thf(f238,plain,
! [X1: $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 @ sK1 @ sK2 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f233]) ).
thf(f233,plain,
( $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 @ sK1 @ sK2 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f232]) ).
thf(f232,plain,
( ( $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 @ sK1 @ sK2 ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f226,f22]) ).
thf(f22,plain,
( ( cHALF @ sK1 @ sK2 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f226,plain,
! [X2: $i,X1: $i] :
( ( ( 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 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f225]) ).
thf(f225,plain,
! [X2: $i,X1: $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 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f194]) ).
thf(f194,plain,
! [X1: $i] :
( ( !! @ $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 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f185]) ).
thf(f185,plain,
! [X1: $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 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f115]) ).
thf(f115,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 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f528,plain,
( $false
= ( ( cDOUBLE @ sK3 @ sK4 )
=> ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ ( cS @ sK4 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ sK3 ) ) @ ( cS @ ( cS @ ( cS @ sK4 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f516]) ).
thf(f516,plain,
( $false
= ( ( ( cDOUBLE @ sK3 @ sK4 )
| $false )
=> ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ ( cS @ sK4 ) ) )
| ( cDOUBLE @ ( cS @ ( cS @ sK3 ) ) @ ( cS @ ( cS @ ( cS @ sK4 ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f465,f472]) ).
thf(f472,plain,
( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f471]) ).
thf(f471,plain,
( ( $false = $true )
| ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) )
= $false ) ),
inference(boolean_simplification,[status(thm)],[f470]) ).
thf(f470,plain,
( ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) )
= $false )
| ( ( ( ( cDOUBLE @ sK3 @ sK4 )
| ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) )
=> $true )
= $false ) ),
inference(boolean_simplification,[status(thm)],[f468]) ).
thf(f468,plain,
( ( ( ( ( cDOUBLE @ sK3 @ sK4 )
| ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) ) )
=> ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ ( cS @ sK4 ) ) )
| $true ) )
= $false )
| ( ( cDOUBLE @ ( cS @ sK3 ) @ ( cS @ sK4 ) )
= $false ) ),
inference(superposition,[status(thm)],[f465,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO335^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n015.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:29:16 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.25/0.46 ---- Original DTF file ---
% 0.25/0.46 thf(spec,logic,$$dhol).
% 0.25/0.46 %------------------------------------------------------------------------------
% 0.25/0.46 % File : SYO335^5 : TPTP v9.2.1. Released v4.0.0.
% 0.25/0.46 % Domain : Syntactic
% 0.25/0.46 % Problem : TPS problem from BASIC-HO-THMS
% 0.25/0.46 % Version : Especial.
% 0.25/0.46 % English :
% 0.25/0.46
% 0.25/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.25/0.46 % Source : [Bro09]
% 0.25/0.46 % Names : tps_1104 [Bro09]
% 0.25/0.46
% 0.25/0.46 % Status : Theorem
% 0.25/0.46 % Rating : 0.92 v9.1.0, 0.88 v9.0.0, 1.00 v5.3.0, 0.75 v4.1.0, 0.67 v4.0.0
% 0.25/0.46 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.25/0.46 % Number of atoms : 11 ( 0 equ; 0 cnn)
% 0.25/0.46 % Maximal formula atoms : 11 ( 11 avg)
% 0.25/0.46 % Number of connectives : 62 ( 0 ~; 1 |; 6 &; 47 @)
% 0.25/0.46 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.25/0.46 % Maximal formula depth : 17 ( 17 avg)
% 0.25/0.46 % Number of types : 2 ( 0 usr)
% 0.25/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.25/0.46 % Number of symbols : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.25/0.46 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.25/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.25/0.46
% 0.25/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.25/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.25/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.25/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.25/0.46 %------------------------------------------------------------------------------
% 0.25/0.46 thf(cS,type,
% 0.25/0.46 cS: $i > $i ).
% 0.25/0.46
% 0.25/0.46 thf(cDOUBLE,type,
% 0.25/0.46 cDOUBLE: $i > $i > $o ).
% 0.25/0.46
% 0.25/0.46 thf(cHALF,type,
% 0.25/0.46 cHALF: $i > $i > $o ).
% 0.25/0.46
% 0.25/0.46 thf(c0,type,
% 0.25/0.46 c0: $i ).
% 0.25/0.46
% 0.25/0.46 thf(cTHM300C,conjecture,
% 0.25/0.46 ( ( ! [Xu: $i,Xv: $i] :
% 0.25/0.46 ( ( cHALF @ Xu @ Xv )
% 0.25/0.46 => ! [Q: $i > $i > $o] :
% 0.25/0.46 ( ( ( Q @ c0 @ c0 )
% 0.25/0.46 & ( Q @ ( cS @ c0 ) @ c0 )
% 0.25/0.46 & ! [Xx: $i,Xy: $i] :
% 0.25/0.46 ( ( Q @ Xx @ Xy )
% 0.25/0.46 => ( Q @ ( cS @ ( cS @ Xx ) ) @ ( cS @ Xy ) ) ) )
% 0.25/0.46 => ( Q @ Xu @ Xv ) ) )
% 0.25/0.46 & ( cDOUBLE @ c0 @ c0 )
% 0.25/0.46 & ! [Xx: $i,Xy: $i] :
% 0.25/0.46 ( ( cDOUBLE @ Xx @ Xy )
% 0.25/0.46 => ( cDOUBLE @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) )
% 0.25/0.46 & ! [Xx: $i,Xy: $i] :
% 0.25/0.46 ( ( cDOUBLE @ Xx @ Xy )
% 0.25/0.46 => ( cDOUBLE @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) )
% 0.25/0.46 & ! [Xx: $i,Xy: $i] :
% 0.25/0.46 ( ( cDOUBLE @ Xx @ Xy )
% 0.25/0.46 => ( cDOUBLE @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) ) )
% 0.25/0.46 => ! [Xu: $i,Xv: $i] :
% 0.25/0.46 ( ( cHALF @ Xu @ Xv )
% 0.25/0.46 => ( ( cDOUBLE @ Xv @ Xu )
% 0.25/0.46 | ( cDOUBLE @ ( cS @ Xv ) @ ( cS @ Xu ) ) ) ) ) ).
% 0.25/0.46
% 0.25/0.46 %------------------------------------------------------------------------------
% 0.25/0.46 ------------------------
% 1.49/1.26 ---- Embedded in THF ---
% 1.49/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.26 %%% Generated on Tue Feb 24 14:29:17 EST 2026
% 1.49/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.26 %%% Logic specification used:
% 1.49/1.26 %%% thf(spec, logic, $$dhol).
% 1.49/1.26
% 1.49/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.s6yvc8IF6f/DTF2DTF2774.p
% See solution above
% 1.49/1.26 ------------------------
% 1.49/1.27 ---- Cleaned THF ---
% 1.49/1.28 thf(cS,type,
% 1.49/1.28 cS: $i > $i ).
% 1.49/1.28
% 1.49/1.28 thf(cDOUBLE,type,
% 1.49/1.28 cDOUBLE: $i > $i > $o ).
% 1.49/1.28
% 1.49/1.28 thf(cHALF,type,
% 1.49/1.28 cHALF: $i > $i > $o ).
% 1.49/1.28
% 1.49/1.28 thf(c0,type,
% 1.49/1.28 c0: $i ).
% 1.49/1.28
% 1.49/1.28 thf(cTHM300C,conjecture,
% 1.49/1.28 ( ( ! [Xu: $i,Xv: $i] :
% 1.49/1.28 ( ( cHALF @ Xu @ Xv )
% 1.49/1.28 => ! [Q: $i > $i > $o] :
% 1.49/1.28 ( ( ( Q @ c0 @ c0 )
% 1.49/1.28 & ( Q @ ( cS @ c0 ) @ c0 )
% 1.49/1.28 & ! [Xx: $i,Xy: $i] :
% 1.49/1.28 ( ( Q @ Xx @ Xy )
% 1.49/1.28 => ( Q @ ( cS @ ( cS @ Xx ) ) @ ( cS @ Xy ) ) ) )
% 1.49/1.28 => ( Q @ Xu @ Xv ) ) )
% 1.49/1.28 & ( cDOUBLE @ c0 @ c0 )
% 1.49/1.28 & ! [Xx: $i,Xy: $i] :
% 1.49/1.28 ( ( cDOUBLE @ Xx @ Xy )
% 1.49/1.28 => ( cDOUBLE @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) )
% 1.49/1.28 & ! [Xx: $i,Xy: $i] :
% 1.49/1.28 ( ( cDOUBLE @ Xx @ Xy )
% 1.49/1.28 => ( cDOUBLE @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) )
% 1.49/1.28 & ! [Xx: $i,Xy: $i] :
% 1.49/1.28 ( ( cDOUBLE @ Xx @ Xy )
% 1.49/1.28 => ( cDOUBLE @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) ) )
% 1.49/1.28 => ! [Xu: $i,Xv: $i] :
% 1.49/1.28 ( ( cHALF @ Xu @ Xv )
% 1.49/1.28 => ( ( cDOUBLE @ Xv @ Xu )
% 1.49/1.28 | ( cDOUBLE @ ( cS @ Xv ) @ ( cS @ Xu ) ) ) ) ) ).
% 1.49/1.28 ------------------------
% 1.49/1.29 % (3045)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2774 for (3000ds/2Mi)
% 1.49/1.29 % (3045)Instruction limit reached!
% 1.49/1.29 % (3045)------------------------------
% 1.49/1.29 % (3045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (3045)Termination reason: Unknown
% 1.49/1.29 % (3045)Termination phase: Property scanning
% 1.49/1.29
% 1.49/1.29 % (3045)Memory used [KB]: 1023
% 1.49/1.29 % (3045)Time elapsed: 0.002 s
% 1.49/1.29 % (3045)Instructions burned: 3 (million)
% 1.49/1.29 % (3045)------------------------------
% 1.49/1.29 % (3045)------------------------------
% 1.49/1.30 % (3042)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2774 for (3000ds/183Mi)
% 1.49/1.30 % (3043)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_2774 for (3000ds/4Mi)
% 1.49/1.30 % (3044)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_2774 for (3000ds/27Mi)
% 1.49/1.30 % (3046)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_2774 for (3000ds/2Mi)
% 1.49/1.30 % (3047)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_2774 for (3000ds/275Mi)
% 1.64/1.30 % (3048)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2774 for (3000ds/18Mi)
% 1.64/1.30 % (3046)Instruction limit reached!
% 1.64/1.30 % (3046)------------------------------
% 1.64/1.30 % (3046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (3046)Termination reason: Unknown
% 1.64/1.30 % (3046)Termination phase: Property scanning
% 1.64/1.30
% 1.64/1.30 % (3046)Memory used [KB]: 895
% 1.64/1.30 % (3046)Time elapsed: 0.003 s
% 1.64/1.30 % (3046)Instructions burned: 2 (million)
% 1.64/1.30 % (3046)------------------------------
% 1.64/1.30 % (3046)------------------------------
% 1.64/1.30 % (3043)Instruction limit reached!
% 1.64/1.30 % (3043)------------------------------
% 1.64/1.30 % (3043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (3043)Termination reason: Unknown
% 1.64/1.30 % (3043)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (3043)Memory used [KB]: 5500
% 1.64/1.30 % (3043)Time elapsed: 0.005 s
% 1.64/1.30 % (3043)Instructions burned: 4 (million)
% 1.64/1.30 % (3043)------------------------------
% 1.64/1.30 % (3043)------------------------------
% 1.64/1.30 % (3049)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2774 for (2999ds/3Mi)
% 1.64/1.30 % (3049)Instruction limit reached!
% 1.64/1.30 % (3049)------------------------------
% 1.64/1.30 % (3049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (3049)Termination reason: Unknown
% 1.64/1.30 % (3049)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (3049)Memory used [KB]: 5500
% 1.64/1.30 % (3049)Time elapsed: 0.003 s
% 1.64/1.30 % (3049)Instructions burned: 4 (million)
% 1.64/1.30 % (3049)------------------------------
% 1.64/1.30 % (3049)------------------------------
% 1.64/1.31 % (3048)Instruction limit reached!
% 1.64/1.31 % (3048)------------------------------
% 1.64/1.31 % (3048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (3048)Termination reason: Unknown
% 1.64/1.31 % (3048)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (3048)Memory used [KB]: 5628
% 1.64/1.31 % (3048)Time elapsed: 0.013 s
% 1.64/1.31 % (3048)Instructions burned: 18 (million)
% 1.64/1.31 % (3048)------------------------------
% 1.64/1.31 % (3048)------------------------------
% 1.64/1.31 % (3052)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_2774 for (2999ds/3Mi)
% 1.64/1.31 % (3044)Instruction limit reached!
% 1.64/1.31 % (3044)------------------------------
% 1.64/1.31 % (3044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (3044)Termination reason: Unknown
% 1.64/1.31 % (3044)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (3044)Memory used [KB]: 5628
% 1.64/1.31 % (3044)Time elapsed: 0.018 s
% 1.64/1.31 % (3044)Instructions burned: 27 (million)
% 1.64/1.31 % (3044)------------------------------
% 1.64/1.31 % (3044)------------------------------
% 1.64/1.31 % (3052)Instruction limit reached!
% 1.64/1.31 % (3052)------------------------------
% 1.64/1.31 % (3052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (3052)Termination reason: Unknown
% 1.64/1.31 % (3052)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (3052)Memory used [KB]: 5500
% 1.64/1.31 % (3052)Time elapsed: 0.003 s
% 1.64/1.31 % (3052)Instructions burned: 3 (million)
% 1.64/1.31 % (3052)------------------------------
% 1.64/1.31 % (3052)------------------------------
% 1.64/1.31 % (3050)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_2774 for (2999ds/37Mi)
% 1.64/1.32 % (3047)Refutation not found, incomplete strategy
% 1.64/1.32 % (3047)------------------------------
% 1.64/1.32 % (3047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (3047)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.32
% 1.64/1.32
% 1.64/1.32 % (3047)Memory used [KB]: 5628
% 1.64/1.32 % (3047)Time elapsed: 0.021 s
% 1.64/1.32 % (3047)Instructions burned: 31 (million)
% 1.64/1.32 % (3047)------------------------------
% 1.64/1.32 % (3047)------------------------------
% 1.64/1.32 % (3051)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_2774 for (2999ds/15Mi)
% 1.64/1.32 % (3055)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2774 for (2999ds/16Mi)
% 1.64/1.32 % (3053)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_2774 for (2999ds/1041Mi)
% 1.64/1.33 % (3051)Instruction limit reached!
% 1.64/1.33 % (3051)------------------------------
% 1.64/1.33 % (3051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (3051)Termination reason: Unknown
% 1.64/1.33 % (3051)Termination phase: Saturation
% 1.64/1.33
% 1.64/1.33 % (3051)Memory used [KB]: 5628
% 1.64/1.33 % (3051)Time elapsed: 0.011 s
% 1.64/1.33 % (3051)Instructions burned: 15 (million)
% 1.64/1.33 % (3051)------------------------------
% 1.64/1.33 % (3051)------------------------------
% 1.64/1.33 % (3055)Instruction limit reached!
% 1.64/1.33 % (3055)------------------------------
% 1.64/1.33 % (3055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (3055)Termination reason: Unknown
% 1.64/1.33 % (3055)Termination phase: Saturation
% 1.64/1.33
% 1.64/1.33 % (3055)Memory used [KB]: 5756
% 1.64/1.33 % (3055)Time elapsed: 0.008 s
% 1.64/1.33 % (3055)Instructions burned: 18 (million)
% 1.64/1.33 % (3055)------------------------------
% 1.64/1.33 % (3055)------------------------------
% 1.64/1.33 % (3054)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2774 for (2999ds/7Mi)
% 1.64/1.33 % (3056)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_2774 for (2999ds/3Mi)
% 1.64/1.33 % (3054)Instruction limit reached!
% 1.64/1.33 % (3054)------------------------------
% 1.64/1.33 % (3054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (3054)Termination reason: Unknown
% 1.64/1.33 % (3054)Termination phase: Saturation
% 1.64/1.33
% 1.64/1.33 % (3054)Memory used [KB]: 1023
% 1.64/1.33 % (3054)Time elapsed: 0.007 s
% 1.64/1.33 % (3054)Instructions burned: 8 (million)
% 1.64/1.33 % (3054)------------------------------
% 1.64/1.33 % (3054)------------------------------
% 1.64/1.34 % (3050)Instruction limit reached!
% 1.64/1.34 % (3050)------------------------------
% 1.64/1.34 % (3050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (3050)Termination reason: Unknown
% 1.64/1.34 % (3050)Termination phase: Saturation
% 1.64/1.34
% 1.64/1.34 % (3050)Memory used [KB]: 5756
% 1.64/1.34 % (3050)Time elapsed: 0.023 s
% 1.64/1.34 % (3050)Instructions burned: 38 (million)
% 1.64/1.34 % (3050)------------------------------
% 1.64/1.34 % (3050)------------------------------
% 1.64/1.34 % (3056)Instruction limit reached!
% 1.64/1.34 % (3056)------------------------------
% 1.64/1.34 % (3056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (3056)Termination reason: Unknown
% 1.64/1.34 % (3056)Termination phase: Twee Goal Transformation
% 1.64/1.34
% 1.64/1.34 % (3056)Memory used [KB]: 1023
% 1.64/1.34 % (3056)Time elapsed: 0.004 s
% 1.64/1.34 % (3056)Instructions burned: 4 (million)
% 1.64/1.34 % (3056)------------------------------
% 1.64/1.34 % (3056)------------------------------
% 1.64/1.34 % (3058)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2774 for (2999ds/7Mi)
% 1.64/1.34 % (3057)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_2774 for (2999ds/3Mi)
% 1.64/1.34 % (3057)Instruction limit reached!
% 1.64/1.34 % (3057)------------------------------
% 1.64/1.34 % (3057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (3057)Termination reason: Unknown
% 1.64/1.34 % (3057)Termination phase: Saturation
% 1.64/1.34
% 1.64/1.34 % (3057)Memory used [KB]: 1023
% 1.64/1.34 % (3057)Time elapsed: 0.003 s
% 1.64/1.34 % (3057)Instructions burned: 4 (million)
% 1.64/1.34 % (3057)------------------------------
% 1.64/1.34 % (3057)------------------------------
% 1.64/1.34 % (3058)Instruction limit reached!
% 1.64/1.34 % (3058)------------------------------
% 1.64/1.34 % (3058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (3058)Termination reason: Unknown
% 1.64/1.34 % (3058)Termination phase: Saturation
% 1.64/1.34
% 1.64/1.34 % (3058)Memory used [KB]: 5500
% 1.64/1.34 % (3058)Time elapsed: 0.004 s
% 1.64/1.34 % (3058)Instructions burned: 7 (million)
% 1.64/1.34 % (3058)------------------------------
% 1.64/1.34 % (3058)------------------------------
% 1.64/1.35 % (3063)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2774 for (2999ds/6Mi)
% 1.64/1.35 % (3062)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2774 for (2999ds/710Mi)
% 1.64/1.35 % (3059)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2774 for (2999ds/3Mi)
% 1.64/1.35 % (3060)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2774 for (2999ds/4Mi)
% 1.64/1.35 % (3059)Instruction limit reached!
% 1.64/1.35 % (3059)------------------------------
% 1.64/1.35 % (3059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (3059)Termination reason: Unknown
% 1.64/1.35 % (3059)Termination phase: Property scanning
% 1.64/1.35
% 1.64/1.35 % (3059)Memory used [KB]: 1023
% 1.64/1.35 % (3059)Time elapsed: 0.003 s
% 1.64/1.35 % (3059)Instructions burned: 3 (million)
% 1.64/1.35 % (3059)------------------------------
% 1.64/1.35 % (3059)------------------------------
% 1.64/1.35 % (3061)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2774 for (2999ds/18Mi)
% 1.64/1.35 % (3063)Instruction limit reached!
% 1.64/1.35 % (3063)------------------------------
% 1.64/1.35 % (3063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (3063)Termination reason: Unknown
% 1.64/1.35 % (3063)Termination phase: Saturation
% 1.64/1.35
% 1.64/1.35 % (3063)Memory used [KB]: 5500
% 1.64/1.35 % (3063)Time elapsed: 0.004 s
% 1.64/1.35 % (3063)Instructions burned: 6 (million)
% 1.64/1.35 % (3063)------------------------------
% 1.64/1.35 % (3063)------------------------------
% 1.64/1.35 % (3060)Instruction limit reached!
% 1.64/1.35 % (3060)------------------------------
% 1.64/1.35 % (3060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (3060)Termination reason: Unknown
% 1.64/1.35 % (3060)Termination phase: Saturation
% 1.64/1.35
% 1.64/1.35 % (3060)Memory used [KB]: 5500
% 1.64/1.35 % (3060)Time elapsed: 0.004 s
% 1.64/1.35 % (3060)Instructions burned: 4 (million)
% 1.64/1.35 % (3060)------------------------------
% 1.64/1.35 % (3060)------------------------------
% 1.64/1.36 % (3061)Refutation not found, incomplete strategy
% 1.64/1.36 % (3061)------------------------------
% 1.64/1.36 % (3061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (3061)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.36
% 1.64/1.36
% 1.64/1.36 % (3061)Memory used [KB]: 5500
% 1.64/1.36 % (3061)Time elapsed: 0.006 s
% 1.64/1.36 % (3061)Instructions burned: 6 (million)
% 1.64/1.36 % (3061)------------------------------
% 1.64/1.36 % (3061)------------------------------
% 1.64/1.36 % (3065)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_2774 for (2999ds/21Mi)
% 1.64/1.37 % (3066)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2774 for (2999ds/5Mi)
% 1.64/1.37 % (3064)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_2774 for (2999ds/902Mi)
% 1.64/1.37 % (3066)Instruction limit reached!
% 1.64/1.37 % (3066)------------------------------
% 1.64/1.37 % (3066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (3066)Termination reason: Unknown
% 1.64/1.37 % (3066)Termination phase: Saturation
% 1.64/1.37
% 1.64/1.37 % (3066)Memory used [KB]: 5500
% 1.64/1.37 % (3066)Time elapsed: 0.003 s
% 1.64/1.37 % (3066)Instructions burned: 7 (million)
% 1.64/1.37 % (3066)------------------------------
% 1.64/1.37 % (3066)------------------------------
% 1.64/1.37 % (3065)Instruction limit reached!
% 1.64/1.37 % (3065)------------------------------
% 1.64/1.37 % (3065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (3065)Termination reason: Unknown
% 1.64/1.37 % (3065)Termination phase: Saturation
% 1.64/1.37
% 1.64/1.37 % (3065)Memory used [KB]: 5628
% 1.64/1.37 % (3065)Time elapsed: 0.009 s
% 1.64/1.37 % (3065)Instructions burned: 22 (million)
% 1.64/1.37 % (3065)------------------------------
% 1.64/1.37 % (3065)------------------------------
% 1.64/1.38 % (3067)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_2774 for (2999ds/6Mi)
% 1.64/1.38 % (3067)Instruction limit reached!
% 1.64/1.38 % (3067)------------------------------
% 1.64/1.38 % (3067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (3067)Termination reason: Unknown
% 1.64/1.38 % (3067)Termination phase: Saturation
% 1.64/1.38
% 1.64/1.38 % (3067)Memory used [KB]: 5500
% 1.64/1.38 % (3067)Time elapsed: 0.005 s
% 1.64/1.38 % (3067)Instructions burned: 6 (million)
% 1.64/1.38 % (3067)------------------------------
% 1.64/1.38 % (3067)------------------------------
% 1.64/1.38 % (3068)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_2774 for (2999ds/377Mi)
% 1.64/1.38 % (3069)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_2774 for (2999ds/779Mi)
% 1.64/1.39 % (3042)Instruction limit reached!
% 1.64/1.39 % (3042)------------------------------
% 1.64/1.39 % (3042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (3042)Termination reason: Unknown
% 1.64/1.39 % (3042)Termination phase: Saturation
% 1.64/1.39
% 1.64/1.39 % (3042)Memory used [KB]: 6524
% 1.64/1.39 % (3042)Time elapsed: 0.101 s
% 1.64/1.39 % (3042)Instructions burned: 185 (million)
% 1.64/1.39 % (3042)------------------------------
% 1.64/1.39 % (3042)------------------------------
% 1.64/1.40 % (3070)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_2774 for (2999ds/19Mi)
% 1.64/1.41 % (3070)Instruction limit reached!
% 1.64/1.41 % (3070)------------------------------
% 1.64/1.41 % (3070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.41 % (3070)Termination reason: Unknown
% 1.64/1.41 % (3070)Termination phase: Saturation
% 1.64/1.41
% 1.64/1.41 % (3070)Memory used [KB]: 5500
% 1.64/1.41 % (3070)Time elapsed: 0.013 s
% 1.64/1.41 % (3070)Instructions burned: 20 (million)
% 1.64/1.41 % (3070)------------------------------
% 1.64/1.41 % (3070)------------------------------
% 1.64/1.41 % (3071)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_2774 for (2998ds/879Mi)
% 1.64/1.42 % (3072)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_2774 for (2998ds/17Mi)
% 1.64/1.43 % (3072)Instruction limit reached!
% 1.64/1.43 % (3072)------------------------------
% 1.64/1.43 % (3072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.43 % (3072)Termination reason: Unknown
% 1.64/1.43 % (3072)Termination phase: Saturation
% 1.64/1.43
% 1.64/1.43 % (3072)Memory used [KB]: 5628
% 1.64/1.43 % (3072)Time elapsed: 0.009 s
% 1.64/1.43 % (3072)Instructions burned: 19 (million)
% 1.64/1.43 % (3072)------------------------------
% 1.64/1.43 % (3072)------------------------------
% 1.64/1.44 % (3073)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2774 for (2998ds/3Mi)
% 1.64/1.44 % (3073)Instruction limit reached!
% 1.64/1.44 % (3073)------------------------------
% 1.64/1.44 % (3073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.44 % (3073)Termination reason: Unknown
% 1.64/1.44 % (3073)Termination phase: Saturation
% 1.64/1.44
% 1.64/1.44 % (3073)Memory used [KB]: 1023
% 1.64/1.44 % (3073)Time elapsed: 0.003 s
% 1.64/1.44 % (3073)Instructions burned: 4 (million)
% 1.64/1.44 % (3073)------------------------------
% 1.64/1.44 % (3073)------------------------------
% 1.64/1.45 % (3074)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_2774 for (2998ds/30Mi)
% 1.64/1.46 % (3074)Instruction limit reached!
% 1.64/1.46 % (3074)------------------------------
% 1.64/1.46 % (3074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.46 % (3074)Termination reason: Unknown
% 1.64/1.46 % (3074)Termination phase: Saturation
% 1.64/1.46
% 1.64/1.46 % (3074)Memory used [KB]: 5628
% 1.64/1.46 % (3074)Time elapsed: 0.012 s
% 1.64/1.46 % (3074)Instructions burned: 31 (million)
% 1.64/1.46 % (3074)------------------------------
% 1.64/1.46 % (3074)------------------------------
% 1.64/1.47 % (3075)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_2774 for (2998ds/127Mi)
% 1.64/1.49 % (3068)Instruction limit reached!
% 1.64/1.49 % (3068)------------------------------
% 1.64/1.49 % (3068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.49 % (3068)Termination reason: Unknown
% 1.64/1.49 % (3068)Termination phase: Saturation
% 1.64/1.49
% 1.64/1.49 % (3068)Memory used [KB]: 6140
% 1.64/1.49 % (3068)Time elapsed: 0.116 s
% 1.64/1.49 % (3068)Instructions burned: 378 (million)
% 1.64/1.49 % (3068)------------------------------
% 1.64/1.49 % (3068)------------------------------
% 1.64/1.50 % (3076)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_2774 for (2997ds/100Mi)
% 1.64/1.51 % (3076)Refutation not found, incomplete strategy
% 1.64/1.51 % (3076)------------------------------
% 1.64/1.51 % (3076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.51 % (3076)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.51
% 1.64/1.51
% 1.64/1.51 % (3076)Memory used [KB]: 5500
% 1.64/1.51 % (3076)Time elapsed: 0.004 s
% 1.64/1.51 % (3076)Instructions burned: 6 (million)
% 1.64/1.51 % (3076)------------------------------
% 1.64/1.51 % (3076)------------------------------
% 1.64/1.51 % (3075)Instruction limit reached!
% 1.64/1.51 % (3075)------------------------------
% 1.64/1.51 % (3075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.51 % (3075)Termination reason: Unknown
% 1.64/1.51 % (3075)Termination phase: Saturation
% 1.64/1.51
% 1.64/1.51 % (3075)Memory used [KB]: 6012
% 1.64/1.51 % (3075)Time elapsed: 0.043 s
% 1.64/1.51 % (3075)Instructions burned: 128 (million)
% 1.64/1.51 % (3075)------------------------------
% 1.64/1.51 % (3075)------------------------------
% 1.64/1.52 % (3077)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_2774 for (2997ds/3Mi)
% 1.64/1.52 % (3077)Instruction limit reached!
% 1.64/1.52 % (3077)------------------------------
% 1.64/1.52 % (3077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.52 % (3077)Termination reason: Unknown
% 1.64/1.52 % (3077)Termination phase: Saturation
% 1.64/1.52
% 1.64/1.52 % (3077)Memory used [KB]: 5500
% 1.64/1.52 % (3077)Time elapsed: 0.003 s
% 1.64/1.52 % (3077)Instructions burned: 4 (million)
% 1.64/1.52 % (3077)------------------------------
% 1.64/1.52 % (3077)------------------------------
% 1.64/1.52 % (3078)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_2774 for (2997ds/20Mi)
% 1.64/1.53 % (3078)Instruction limit reached!
% 1.64/1.53 % (3078)------------------------------
% 1.64/1.53 % (3078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.53 % (3078)Termination reason: Unknown
% 1.64/1.53 % (3078)Termination phase: Saturation
% 1.64/1.53
% 1.64/1.53 % (3078)Memory used [KB]: 5628
% 1.64/1.53 % (3078)Time elapsed: 0.030 s
% 1.64/1.53 % (3078)Instructions burned: 21 (million)
% 1.64/1.53 % (3078)------------------------------
% 1.64/1.53 % (3078)------------------------------
% 1.64/1.53 % (3079)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_2774 for (2997ds/86Mi)
% 1.64/1.54 % (3080)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_2774 for (2997ds/107Mi)
% 1.64/1.56 % (3079)Instruction limit reached!
% 1.64/1.56 % (3079)------------------------------
% 1.64/1.56 % (3079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.56 % (3079)Termination reason: Unknown
% 1.64/1.56 % (3079)Termination phase: Saturation
% 1.64/1.56
% 1.64/1.56 % (3079)Memory used [KB]: 6012
% 1.64/1.56 % (3079)Time elapsed: 0.051 s
% 1.64/1.56 % (3079)Instructions burned: 86 (million)
% 1.64/1.56 % (3079)------------------------------
% 1.64/1.56 % (3079)------------------------------
% 1.64/1.57 % (3081)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_2774 for (2997ds/39Mi)
% 1.64/1.57 % (3080)Instruction limit reached!
% 1.64/1.57 % (3080)------------------------------
% 1.64/1.57 % (3080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.57 % (3080)Termination reason: Unknown
% 1.64/1.57 % (3080)Termination phase: Saturation
% 1.64/1.57
% 1.64/1.57 % (3080)Memory used [KB]: 5756
% 1.64/1.57 % (3080)Time elapsed: 0.056 s
% 1.64/1.57 % (3080)Instructions burned: 109 (million)
% 1.64/1.57 % (3080)------------------------------
% 1.64/1.57 % (3080)------------------------------
% 1.64/1.58 % (3062)Instruction limit reached!
% 1.64/1.58 % (3062)------------------------------
% 1.64/1.58 % (3062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.58 % (3062)Termination reason: Unknown
% 1.64/1.58 % (3062)Termination phase: Saturation
% 1.64/1.58
% 1.64/1.58 % (3062)Memory used [KB]: 7419
% 1.64/1.58 % (3062)Time elapsed: 0.226 s
% 1.64/1.58 % (3062)Instructions burned: 710 (million)
% 1.64/1.58 % (3062)------------------------------
% 1.64/1.58 % (3062)------------------------------
% 1.64/1.58 % (3081)Instruction limit reached!
% 1.64/1.58 % (3081)------------------------------
% 1.64/1.58 % (3081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.58 % (3081)Termination reason: Unknown
% 1.64/1.58 % (3081)Termination phase: Saturation
% 1.64/1.58
% 1.64/1.58 % (3081)Memory used [KB]: 5884
% 1.64/1.58 % (3081)Time elapsed: 0.014 s
% 1.64/1.58 % (3081)Instructions burned: 39 (million)
% 1.64/1.58 % (3081)------------------------------
% 1.64/1.58 % (3081)------------------------------
% 1.64/1.58 % (3082)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_2774 for (2997ds/448Mi)
% 1.64/1.59 % (3083)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_2774 for (2997ds/46Mi)
% 1.64/1.59 % (3084)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_2774 for (2996ds/98Mi)
% 1.64/1.60 % (3083)Instruction limit reached!
% 1.64/1.60 % (3083)------------------------------
% 1.64/1.60 % (3083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.60 % (3083)Termination reason: Unknown
% 1.64/1.60 % (3083)Termination phase: Saturation
% 1.64/1.60
% 1.64/1.60 % (3083)Memory used [KB]: 5756
% 1.64/1.60 % (3083)Time elapsed: 0.019 s
% 1.64/1.60 % (3083)Instructions burned: 48 (million)
% 1.64/1.60 % (3083)------------------------------
% 1.64/1.60 % (3083)------------------------------
% 1.64/1.61 % (3085)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_2774 for (2996ds/507Mi)
% 1.64/1.62 % (3084)Instruction limit reached!
% 1.64/1.62 % (3084)------------------------------
% 1.64/1.62 % (3084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.62 % (3084)Termination reason: Unknown
% 1.64/1.62 % (3084)Termination phase: Saturation
% 1.64/1.62
% 1.64/1.62 % (3084)Memory used [KB]: 1151
% 1.64/1.62 % (3084)Time elapsed: 0.034 s
% 1.64/1.62 % (3084)Instructions burned: 99 (million)
% 1.64/1.62 % (3084)------------------------------
% 1.64/1.62 % (3084)------------------------------
% 1.64/1.63 % (3069)Instruction limit reached!
% 1.64/1.63 % (3069)------------------------------
% 1.64/1.63 % (3069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.63 % (3069)Termination reason: Unknown
% 1.64/1.63 % (3069)Termination phase: Saturation
% 1.64/1.63
% 1.64/1.63 % (3069)Memory used [KB]: 7931
% 1.64/1.63 % (3069)Time elapsed: 0.250 s
% 1.64/1.63 % (3069)Instructions burned: 782 (million)
% 1.64/1.63 % (3069)------------------------------
% 1.64/1.63 % (3069)------------------------------
% 1.64/1.63 % (3086)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_2774 for (2996ds/149Mi)
% 1.64/1.63 % (3053)Instruction limit reached!
% 1.64/1.63 % (3053)------------------------------
% 1.64/1.63 % (3053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.63 % (3053)Termination reason: Unknown
% 1.64/1.63 % (3053)Termination phase: Saturation
% 1.64/1.63
% 1.64/1.63 % (3053)Memory used [KB]: 6652
% 1.64/1.63 % (3053)Time elapsed: 0.310 s
% 1.64/1.63 % (3053)Instructions burned: 1043 (million)
% 1.64/1.63 % (3053)------------------------------
% 1.64/1.63 % (3053)------------------------------
% 1.64/1.64 % (3087)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_2774 for (2996ds/39Mi)
% 1.64/1.64 % (3088)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_2774 for (2996ds/6Mi)
% 1.64/1.64 % (3071)Instruction limit reached!
% 1.64/1.64 % (3071)------------------------------
% 1.64/1.64 % (3071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.64 % (3071)Termination reason: Unknown
% 1.64/1.64 % (3071)Termination phase: Saturation
% 1.64/1.64
% 1.64/1.64 % (3071)Memory used [KB]: 6652
% 1.64/1.64 % (3071)Time elapsed: 0.237 s
% 1.64/1.64 % (3071)Instructions burned: 879 (million)
% 1.64/1.64 % (3071)------------------------------
% 1.64/1.64 % (3071)------------------------------
% 1.64/1.65 % (3088)Instruction limit reached!
% 1.64/1.65 % (3088)------------------------------
% 1.64/1.65 % (3088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.65 % (3088)Termination reason: Unknown
% 1.64/1.65 % (3088)Termination phase: Saturation
% 1.64/1.65
% 1.64/1.65 % (3088)Memory used [KB]: 9978
% 1.64/1.65 % (3088)Time elapsed: 0.005 s
% 1.64/1.65 % (3088)Instructions burned: 8 (million)
% 1.64/1.65 % (3088)------------------------------
% 1.64/1.65 % (3088)------------------------------
% 1.64/1.65 % (3087)Instruction limit reached!
% 1.64/1.65 % (3087)------------------------------
% 1.64/1.65 % (3087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.65 % (3087)Termination reason: Unknown
% 1.64/1.65 % (3087)Termination phase: Saturation
% 1.64/1.65
% 1.64/1.65 % (3087)Memory used [KB]: 5628
% 1.64/1.65 % (3087)Time elapsed: 0.013 s
% 1.64/1.65 % (3087)Instructions burned: 40 (million)
% 1.64/1.65 % (3087)------------------------------
% 1.64/1.65 % (3087)------------------------------
% 1.64/1.65 % (3089)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_2774 for (2996ds/1087Mi)
% 1.64/1.66 % (3090)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_2774 for (2996ds/47Mi)
% 1.64/1.66 % (3091)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_2774 for (2996ds/44Mi)
% 1.64/1.67 % (3089)Refutation not found, incomplete strategy
% 1.64/1.67 % (3089)------------------------------
% 1.64/1.67 % (3089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.67 % (3089)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.67
% 1.64/1.67
% 1.64/1.67 % (3089)Memory used [KB]: 5756
% 1.64/1.67 % (3089)Time elapsed: 0.014 s
% 1.64/1.67 % (3089)Instructions burned: 35 (million)
% 1.64/1.67 % (3089)------------------------------
% 1.64/1.67 % (3089)------------------------------
% 1.64/1.67 % (3064)Instruction limit reached!
% 1.64/1.67 % (3064)------------------------------
% 1.64/1.67 % (3064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.67 % (3064)Termination reason: Unknown
% 1.64/1.67 % (3064)Termination phase: Saturation
% 1.64/1.67
% 1.64/1.67 % (3064)Memory used [KB]: 6396
% 1.64/1.67 % (3064)Time elapsed: 0.300 s
% 1.64/1.67 % (3064)Instructions burned: 903 (million)
% 1.64/1.67 % (3064)------------------------------
% 1.64/1.67 % (3064)------------------------------
% 1.64/1.67 % (3090)Instruction limit reached!
% 1.64/1.67 % (3090)------------------------------
% 1.64/1.67 % (3090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.67 % (3090)Termination reason: Unknown
% 1.64/1.67 % (3090)Termination phase: Saturation
% 1.64/1.67
% 1.64/1.67 % (3090)Memory used [KB]: 5628
% 1.64/1.67 % (3090)Time elapsed: 0.017 s
% 1.64/1.67 % (3090)Instructions burned: 47 (million)
% 1.64/1.67 % (3090)------------------------------
% 1.64/1.67 % (3090)------------------------------
% 1.64/1.67 % (3091)Instruction limit reached!
% 1.64/1.67 % (3091)------------------------------
% 1.64/1.67 % (3091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.67 % (3091)Termination reason: Unknown
% 1.64/1.67 % (3091)Termination phase: Saturation
% 1.64/1.67
% 1.64/1.67 % (3091)Memory used [KB]: 1279
% 1.64/1.67 % (3091)Time elapsed: 0.014 s
% 1.64/1.67 % (3091)Instructions burned: 45 (million)
% 1.64/1.67 % (3091)------------------------------
% 1.64/1.67 % (3091)------------------------------
% 1.64/1.68 % (3092)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_2774 for (2996ds/432Mi)
% 1.64/1.68 % (3093)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_2774 for (2996ds/62Mi)
% 1.64/1.68 % (3094)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_2774 for (2996ds/31Mi)
% 1.64/1.68 % (3095)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_2774 for (2996ds/96Mi)
% 1.64/1.68 % (3086)Instruction limit reached!
% 1.64/1.68 % (3086)------------------------------
% 1.64/1.68 % (3086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.68 % (3086)Termination reason: Unknown
% 1.64/1.68 % (3086)Termination phase: Saturation
% 1.64/1.68
% 1.64/1.68 % (3086)Memory used [KB]: 6268
% 1.64/1.68 % (3086)Time elapsed: 0.054 s
% 1.64/1.68 % (3086)Instructions burned: 149 (million)
% 1.64/1.68 % (3086)------------------------------
% 1.64/1.68 % (3086)------------------------------
% 1.64/1.69 % (3094)Instruction limit reached!
% 1.64/1.69 % (3094)------------------------------
% 1.64/1.69 % (3094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.69 % (3094)Termination reason: Unknown
% 1.64/1.69 % (3094)Termination phase: Saturation
% 1.64/1.69
% 1.64/1.69 % (3094)Memory used [KB]: 5756
% 1.64/1.69 % (3094)Time elapsed: 0.012 s
% 1.64/1.69 % (3094)Instructions burned: 31 (million)
% 1.64/1.69 % (3094)------------------------------
% 1.64/1.69 % (3094)------------------------------
% 1.64/1.69 % (3096)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_2774 for (2996ds/453Mi)
% 1.64/1.70 % (3093)Instruction limit reached!
% 1.64/1.70 % (3093)------------------------------
% 1.64/1.70 % (3093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.70 % (3093)Termination reason: Unknown
% 1.64/1.70 % (3093)Termination phase: Saturation
% 1.64/1.70
% 1.64/1.70 % (3093)Memory used [KB]: 5884
% 1.64/1.70 % (3093)Time elapsed: 0.022 s
% 1.64/1.70 % (3093)Instructions burned: 63 (million)
% 1.64/1.70 % (3093)------------------------------
% 1.64/1.70 % (3093)------------------------------
% 1.64/1.70 % (3096)Refutation not found, incomplete strategy
% 1.64/1.70 % (3096)------------------------------
% 1.64/1.70 % (3096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.70 % (3096)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.70
% 1.64/1.70
% 1.64/1.70 % (3096)Memory used [KB]: 5628
% 1.64/1.70 % (3096)Time elapsed: 0.009 s
% 1.64/1.70 % (3096)Instructions burned: 21 (million)
% 1.64/1.70 % (3096)------------------------------
% 1.64/1.70 % (3096)------------------------------
% 1.64/1.70 % (3097)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_2774 for (2995ds/71Mi)
% 1.64/1.71 % (3098)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_2774 for (2995ds/83Mi)
% 1.64/1.71 % (3099)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_2774 for (2995ds/11Mi)
% 1.64/1.71 % (3095)Instruction limit reached!
% 1.64/1.71 % (3095)------------------------------
% 1.64/1.71 % (3095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.71 % (3095)Termination reason: Unknown
% 1.64/1.71 % (3095)Termination phase: Saturation
% 1.64/1.71
% 1.64/1.71 % (3095)Memory used [KB]: 5756
% 1.64/1.71 % (3095)Time elapsed: 0.030 s
% 1.64/1.71 % (3095)Instructions burned: 98 (million)
% 1.64/1.71 % (3095)------------------------------
% 1.64/1.71 % (3095)------------------------------
% 1.64/1.71 % (3099)Instruction limit reached!
% 1.64/1.71 % (3099)------------------------------
% 1.64/1.71 % (3099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.71 % (3099)Termination reason: Unknown
% 1.64/1.71 % (3099)Termination phase: Saturation
% 1.64/1.71
% 1.64/1.71 % (3099)Memory used [KB]: 5500
% 1.64/1.71 % (3099)Time elapsed: 0.005 s
% 1.64/1.71 % (3099)Instructions burned: 12 (million)
% 1.64/1.71 % (3099)------------------------------
% 1.64/1.71 % (3099)------------------------------
% 1.64/1.72 % (3100)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_2774 for (2995ds/41Mi)
% 1.64/1.72 % (3082)Instruction limit reached!
% 1.64/1.72 % (3082)------------------------------
% 1.64/1.72 % (3082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.72 % (3082)Termination reason: Unknown
% 1.64/1.72 % (3082)Termination phase: Saturation
% 1.64/1.72
% 1.64/1.72 % (3082)Memory used [KB]: 6396
% 1.64/1.72 % (3082)Time elapsed: 0.144 s
% 1.64/1.72 % (3082)Instructions burned: 450 (million)
% 1.64/1.72 % (3082)------------------------------
% 1.64/1.72 % (3082)------------------------------
% 1.64/1.72 % (3101)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2774 for (2995ds/6Mi)
% 1.64/1.73 % (3101)Instruction limit reached!
% 1.64/1.73 % (3101)------------------------------
% 1.64/1.73 % (3101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.73 % (3101)Termination reason: Unknown
% 1.64/1.73 % (3101)Termination phase: Saturation
% 1.64/1.73
% 1.64/1.73 % (3101)Memory used [KB]: 5500
% 1.64/1.73 % (3101)Time elapsed: 0.003 s
% 1.64/1.73 % (3101)Instructions burned: 6 (million)
% 1.64/1.73 % (3101)------------------------------
% 1.64/1.73 % (3101)------------------------------
% 1.64/1.73 % (3097)Instruction limit reached!
% 1.64/1.73 % (3097)------------------------------
% 1.64/1.73 % (3097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.73 % (3097)Termination reason: Unknown
% 1.64/1.73 % (3097)Termination phase: Saturation
% 1.64/1.73
% 1.64/1.73 % (3097)Memory used [KB]: 5756
% 1.64/1.73 % (3097)Time elapsed: 0.026 s
% 1.64/1.73 % (3097)Instructions burned: 73 (million)
% 1.64/1.73 % (3097)------------------------------
% 1.64/1.73 % (3097)------------------------------
% 1.64/1.73 % (3100)Refutation not found, incomplete strategy
% 1.64/1.73 % (3100)------------------------------
% 1.64/1.73 % (3100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.73 % (3100)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.73
% 1.64/1.73
% 1.64/1.73 % (3100)Memory used [KB]: 5628
% 1.64/1.73 % (3100)Time elapsed: 0.008 s
% 1.64/1.73 % (3100)Instructions burned: 23 (million)
% 1.64/1.73 % (3100)------------------------------
% 1.64/1.73 % (3100)------------------------------
% 1.64/1.73 % (3102)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_2774 for (2995ds/150Mi)
% 1.64/1.74 % (3103)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_2774 for (2995ds/343Mi)
% 1.64/1.74 % (3098)Instruction limit reached!
% 1.64/1.74 % (3098)------------------------------
% 1.64/1.74 % (3098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.74 % (3098)Termination reason: Unknown
% 1.64/1.74 % (3098)Termination phase: Saturation
% 1.64/1.74
% 1.64/1.74 % (3098)Memory used [KB]: 5884
% 1.64/1.74 % (3098)Time elapsed: 0.029 s
% 1.64/1.74 % (3098)Instructions burned: 85 (million)
% 1.64/1.74 % (3098)------------------------------
% 1.64/1.74 % (3098)------------------------------
% 1.64/1.74 % (3104)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_2774 for (2995ds/109Mi)
% 1.64/1.74 % (3105)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_2774 for (2995ds/253Mi)
% 1.64/1.75 % (3106)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_2774 for (2995ds/140Mi)
% 1.64/1.77 % (3104)Instruction limit reached!
% 1.64/1.77 % (3104)------------------------------
% 1.64/1.77 % (3104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.77 % (3104)Termination reason: Unknown
% 1.64/1.77 % (3104)Termination phase: Saturation
% 1.64/1.77
% 1.64/1.77 % (3104)Memory used [KB]: 6268
% 1.64/1.77 % (3104)Time elapsed: 0.036 s
% 1.64/1.77 % (3104)Instructions burned: 111 (million)
% 1.64/1.77 % (3104)------------------------------
% 1.64/1.77 % (3104)------------------------------
% 1.64/1.78 % (3085)Instruction limit reached!
% 1.64/1.78 % (3085)------------------------------
% 1.64/1.78 % (3085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.78 % (3085)Termination reason: Unknown
% 1.64/1.78 % (3085)Termination phase: Saturation
% 1.64/1.78
% 1.64/1.78 % (3085)Memory used [KB]: 6524
% 1.64/1.78 % (3085)Time elapsed: 0.166 s
% 1.64/1.78 % (3085)Instructions burned: 507 (million)
% 1.64/1.78 % (3085)------------------------------
% 1.64/1.78 % (3085)------------------------------
% 1.64/1.78 % (3102)Instruction limit reached!
% 1.64/1.78 % (3102)------------------------------
% 1.64/1.78 % (3102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.78 % (3102)Termination reason: Unknown
% 1.64/1.78 % (3102)Termination phase: Saturation
% 1.64/1.78
% 1.64/1.78 % (3102)Memory used [KB]: 6012
% 1.64/1.78 % (3102)Time elapsed: 0.049 s
% 1.64/1.78 % (3102)Instructions burned: 150 (million)
% 1.64/1.78 % (3102)------------------------------
% 1.64/1.78 % (3102)------------------------------
% 1.64/1.78 % (3107)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_2774 for (2995ds/614Mi)
% 1.64/1.79 % (3106)Instruction limit reached!
% 1.64/1.79 % (3106)------------------------------
% 1.64/1.79 % (3106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.79 % (3106)Termination reason: Unknown
% 1.64/1.79 % (3106)Termination phase: Saturation
% 1.64/1.79
% 1.64/1.79 % (3106)Memory used [KB]: 5884
% 1.64/1.79 % (3106)Time elapsed: 0.041 s
% 1.64/1.79 % (3106)Instructions burned: 141 (million)
% 1.64/1.79 % (3106)------------------------------
% 1.64/1.79 % (3106)------------------------------
% 1.64/1.79 % (3108)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_2774 for (2995ds/202Mi)
% 1.64/1.79 % (3109)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_2774 for (2995ds/339Mi)
% 1.64/1.79 % (3110)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_2774 for (2995ds/283Mi)
% 1.64/1.80 % (3092)First to succeed.
% 1.64/1.80 % (3092)Refutation found. Thanks to Tanya!
% 1.64/1.80 % SZS status Theorem for DTF2THF_2774
% 1.64/1.80 % SZS output start Proof for DTF2THF_2774
% 1.64/1.80 thf(func_def_0, type, cS: $i > $i).
% 1.64/1.80 thf(func_def_1, type, cDOUBLE: $i > $i > $o).
% 1.64/1.80 thf(func_def_2, type, cHALF: $i > $i > $o).
% 1.64/1.80 thf(func_def_16, type, ph0: !>[X0: $tType]:(X0)).
% 1.64/1.80 thf(f538,plain,(
% 1.64/1.80 $false),
% 1.64/1.80 inference(trivial_inequality_removal,[status(thm)],[f537])).
% 1.64/1.80 thf(f537,plain,(
% 1.64/1.80 ($false = $true)),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f536])).
% 1.64/1.80 thf(f536,plain,(
% 1.64/1.80 (($false => ((cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ sK4))) | (cDOUBLE @ (cS @ (cS @ sK3)) @ (cS @ (cS @ (cS @ sK4)))))) = $false)),
% 1.64/1.80 inference(forward_demodulation,[status(thm)],[f528,f475])).
% 1.64/1.80 thf(f475,plain,(
% 1.64/1.80 ((cDOUBLE @ sK3 @ sK4) = $false)),
% 1.64/1.80 inference(trivial_inequality_removal,[status(thm)],[f474])).
% 1.64/1.80 thf(f474,plain,(
% 1.64/1.80 ($false = $true) | ((cDOUBLE @ sK3 @ sK4) = $false)),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f473])).
% 1.64/1.80 thf(f473,plain,(
% 1.64/1.80 ((((cDOUBLE @ sK3 @ sK4) | (cDOUBLE @ (cS @ sK3) @ (cS @ sK4))) => $true) = $false) | ((cDOUBLE @ sK3 @ sK4) = $false)),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f469])).
% 1.64/1.80 thf(f469,plain,(
% 1.64/1.80 ((cDOUBLE @ sK3 @ sK4) = $false) | ((((cDOUBLE @ sK3 @ sK4) | (cDOUBLE @ (cS @ sK3) @ (cS @ sK4))) => ($true | (cDOUBLE @ (cS @ (cS @ sK3)) @ (cS @ (cS @ (cS @ sK4)))))) = $false)),
% 1.64/1.80 inference(superposition,[status(thm)],[f465,f66])).
% 1.64/1.80 thf(f66,plain,(
% 1.64/1.80 ( ! [X2 : $i,X1 : $i] : (((cDOUBLE @ (cS @ X1) @ (cS @ (cS @ X2))) = $true) | ((cDOUBLE @ X1 @ X2) = $false)) )),
% 1.64/1.80 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.64/1.80 thf(f59,plain,(
% 1.64/1.80 ( ! [X2 : $i,X1 : $i] : (($true = ((cDOUBLE @ X1 @ X2) => (cDOUBLE @ (cS @ X1) @ (cS @ (cS @ X2)))))) )),
% 1.64/1.80 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.64/1.80 thf(f58,plain,(
% 1.64/1.80 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((cDOUBLE @ X1 @ Y0) => (cDOUBLE @ (cS @ X1) @ (cS @ (cS @ Y0))))) @ X2) = $true)) )),
% 1.64/1.80 inference(pi_clausification,[status(thm)],[f45])).
% 1.64/1.80 thf(f45,plain,(
% 1.64/1.80 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((cDOUBLE @ X1 @ Y0) => (cDOUBLE @ (cS @ X1) @ (cS @ (cS @ Y0)))))) = $true)) )),
% 1.64/1.80 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.64/1.80 thf(f39,plain,(
% 1.64/1.80 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))) @ X1) = $true)) )),
% 1.64/1.80 inference(pi_clausification,[status(thm)],[f25])).
% 1.64/1.80 thf(f25,plain,(
% 1.64/1.80 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1)))))))) = $true)),
% 1.64/1.80 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.64/1.80 thf(f9,plain,(
% 1.64/1.80 ((((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0)))))))) & (!! @ $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]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))))) = $true)),
% 1.64/1.80 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.64/1.80 thf(f7,plain,(
% 1.64/1.80 ($false = ((((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0)))))))) & (!! @ $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]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y0 @ Y1) => ((cDOUBLE @ Y1 @ Y0) | (cDOUBLE @ (cS @ Y1) @ (cS @ Y0))))))))))),
% 1.64/1.80 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.64/1.80 thf(f6,plain,(
% 1.64/1.80 ((~ ((((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0)))))))) & (!! @ $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]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y0 @ Y1) => ((cDOUBLE @ Y1 @ Y0) | (cDOUBLE @ (cS @ Y1) @ (cS @ Y0)))))))))) = $true)),
% 1.64/1.80 inference(cnf_transformation,[status(thm)],[f5])).
% 1.64/1.80 thf(f5,plain,(
% 1.64/1.80 ((~ ((((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0)))))))) & (!! @ $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]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y0 @ Y1) => ((cDOUBLE @ Y1 @ Y0) | (cDOUBLE @ (cS @ Y1) @ (cS @ Y0)))))))))) = $true)),
% 1.64/1.80 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.80 thf(f4,plain,(
% 1.64/1.80 ~((! [X0 : $i,X1 : $i] : ((cDOUBLE @ X1 @ X0) => (cDOUBLE @ (cS @ X1) @ (cS @ (cS @ X0)))) & ! [X2 : $i,X3 : $i] : ((cDOUBLE @ X2 @ X3) => (cDOUBLE @ (cS @ X2) @ (cS @ (cS @ X3)))) & (cDOUBLE @ c0 @ c0) & ! [X4 : $i,X5 : $i] : ((cHALF @ X5 @ X4) => ! [X6 : $i > $i > $o] : (((X6 @ (cS @ c0) @ c0) & ! [X7 : $i,X8 : $i] : ((X6 @ X7 @ X8) => (X6 @ (cS @ (cS @ X7)) @ (cS @ X8))) & (X6 @ c0 @ c0)) => (X6 @ X5 @ X4))) & ! [X9 : $i,X10 : $i] : ((cDOUBLE @ X9 @ X10) => (cDOUBLE @ (cS @ X9) @ (cS @ (cS @ X10))))) => ! [X11 : $i,X12 : $i] : ((cHALF @ X12 @ X11) => ((cDOUBLE @ (cS @ X11) @ (cS @ X12)) | (cDOUBLE @ X11 @ X12))))),
% 1.64/1.80 inference(rectify,[status(thm)],[f2])).
% 1.64/1.80 thf(f2,negated_conjecture,(
% 1.64/1.80 ~((! [X4 : $i,X3 : $i] : ((cDOUBLE @ X3 @ X4) => (cDOUBLE @ (cS @ X3) @ (cS @ (cS @ X4)))) & ! [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))) & ! [X3 : $i,X4 : $i] : ((cDOUBLE @ X3 @ X4) => (cDOUBLE @ (cS @ X3) @ (cS @ (cS @ X4))))) => ! [X1 : $i,X0 : $i] : ((cHALF @ X0 @ X1) => ((cDOUBLE @ (cS @ X1) @ (cS @ X0)) | (cDOUBLE @ X1 @ X0))))),
% 1.64/1.80 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.80 thf(f1,conjecture,(
% 1.64/1.80 (! [X4 : $i,X3 : $i] : ((cDOUBLE @ X3 @ X4) => (cDOUBLE @ (cS @ X3) @ (cS @ (cS @ X4)))) & ! [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))) & ! [X3 : $i,X4 : $i] : ((cDOUBLE @ X3 @ X4) => (cDOUBLE @ (cS @ X3) @ (cS @ (cS @ X4))))) => ! [X1 : $i,X0 : $i] : ((cHALF @ X0 @ X1) => ((cDOUBLE @ (cS @ X1) @ (cS @ X0)) | (cDOUBLE @ X1 @ X0)))),
% 1.64/1.80 file('/export/starexec/sandbox/tmp/tmp.s6yvc8IF6f/DTF2THF_2774.p',cTHM300C)).
% 1.64/1.80 thf(f465,plain,(
% 1.64/1.80 ($false = (((cDOUBLE @ sK3 @ sK4) | (cDOUBLE @ (cS @ sK3) @ (cS @ sK4))) => ((cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ sK4))) | (cDOUBLE @ (cS @ (cS @ sK3)) @ (cS @ (cS @ (cS @ sK4)))))))),
% 1.64/1.80 inference(beta_eta_normalization,[status(thm)],[f464])).
% 1.64/1.80 thf(f464,plain,(
% 1.64/1.80 ($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))),
% 1.64/1.80 inference(sigma_clausification,[status(thm)],[f463])).
% 1.64/1.80 thf(f463,plain,(
% 1.64/1.80 ((!! @ $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)),
% 1.64/1.80 inference(beta_eta_normalization,[status(thm)],[f455])).
% 1.64/1.80 thf(f455,plain,(
% 1.64/1.80 (((^[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)),
% 1.64/1.80 inference(sigma_clausification,[status(thm)],[f450])).
% 1.64/1.80 thf(f450,plain,(
% 1.64/1.80 ((!! @ $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)))))))))) = $false)),
% 1.64/1.80 inference(not_proxy_clausification,[status(thm)],[f389])).
% 1.64/1.80 thf(f389,plain,(
% 1.64/1.80 ($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))))))))))))),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f388])).
% 1.64/1.80 thf(f388,plain,(
% 1.64/1.80 ((~ ((!! @ $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)),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f387])).
% 1.64/1.80 thf(f387,plain,(
% 1.64/1.80 ((~ ((!! @ $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))) = $true)),
% 1.64/1.80 inference(forward_demodulation,[status(thm)],[f386,f124])).
% 1.64/1.80 thf(f124,plain,(
% 1.64/1.80 ((cDOUBLE @ (cS @ c0) @ (cS @ (cS @ c0))) = $true)),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f123])).
% 1.64/1.80 thf(f123,plain,(
% 1.64/1.80 (($true => (cDOUBLE @ (cS @ c0) @ (cS @ (cS @ c0)))) = $true)),
% 1.64/1.80 inference(superposition,[status(thm)],[f59,f114])).
% 1.64/1.80 thf(f114,plain,(
% 1.64/1.80 ((cDOUBLE @ c0 @ c0) = $true)),
% 1.64/1.80 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.64/1.80 thf(f100,plain,(
% 1.64/1.80 (((!! @ $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)) = $true)),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f99])).
% 1.64/1.80 thf(f99,plain,(
% 1.64/1.80 ((($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)) = $true)),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f91])).
% 1.64/1.80 thf(f91,plain,(
% 1.64/1.80 (((($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)) & $true) = $true)),
% 1.64/1.80 inference(superposition,[status(thm)],[f26,f71])).
% 1.64/1.80 thf(f71,plain,(
% 1.64/1.80 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0)))))))))),
% 1.64/1.80 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.64/1.80 thf(f26,plain,(
% 1.64/1.80 (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0)))))))) & (!! @ $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))))))))) = $true)),
% 1.64/1.80 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.64/1.80 thf(f386,plain,(
% 1.64/1.80 ((~ ((!! @ $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)))))) = $true)),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f385])).
% 1.64/1.80 thf(f385,plain,(
% 1.64/1.80 ((~ (($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)))))) = $true)),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f384])).
% 1.64/1.80 thf(f384,plain,(
% 1.64/1.80 ($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)))))))),
% 1.64/1.80 inference(forward_demodulation,[status(thm)],[f313,f114])).
% 1.64/1.80 thf(f313,plain,(
% 1.64/1.80 ((~ ((((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)))))) = $true)),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f312])).
% 1.64/1.80 thf(f312,plain,(
% 1.64/1.80 ((((((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)),
% 1.64/1.80 inference(beta_eta_normalization,[status(thm)],[f248])).
% 1.64/1.80 thf(f248,plain,(
% 1.64/1.80 ((((((^[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) = $true)),
% 1.64/1.80 inference(superposition,[status(thm)],[f240,f21])).
% 1.64/1.80 thf(f21,plain,(
% 1.64/1.80 (((cDOUBLE @ sK2 @ sK1) | (cDOUBLE @ (cS @ sK2) @ (cS @ sK1))) = $false)),
% 1.64/1.80 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.64/1.80 thf(f20,plain,(
% 1.64/1.80 ($false = ((cHALF @ sK1 @ sK2) => ((cDOUBLE @ sK2 @ sK1) | (cDOUBLE @ (cS @ sK2) @ (cS @ sK1)))))),
% 1.64/1.80 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.64/1.80 thf(f19,plain,(
% 1.64/1.80 (((^[Y0 : $i]: ((cHALF @ sK1 @ Y0) => ((cDOUBLE @ Y0 @ sK1) | (cDOUBLE @ (cS @ Y0) @ (cS @ sK1))))) @ sK2) = $false)),
% 1.64/1.80 inference(sigma_clausification,[status(thm)],[f17])).
% 1.64/1.80 thf(f17,plain,(
% 1.64/1.80 ((!! @ $i @ (^[Y0 : $i]: ((cHALF @ sK1 @ Y0) => ((cDOUBLE @ Y0 @ sK1) | (cDOUBLE @ (cS @ Y0) @ (cS @ sK1)))))) = $false)),
% 1.64/1.80 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.64/1.80 thf(f12,plain,(
% 1.64/1.80 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y0 @ Y1) => ((cDOUBLE @ Y1 @ Y0) | (cDOUBLE @ (cS @ Y1) @ (cS @ Y0))))))) @ sK1) = $false)),
% 1.64/1.80 inference(sigma_clausification,[status(thm)],[f8])).
% 1.64/1.80 thf(f8,plain,(
% 1.64/1.80 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cHALF @ Y0 @ Y1) => ((cDOUBLE @ Y1 @ Y0) | (cDOUBLE @ (cS @ Y1) @ (cS @ Y0)))))))) = $false)),
% 1.64/1.80 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.64/1.80 thf(f240,plain,(
% 1.64/1.80 ( ! [X1 : $i > $i > $o] : ((((((X1 @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => (X1 @ (cS @ (cS @ Y1)) @ (cS @ Y0)))))))) & (X1 @ (cS @ c0) @ c0)) => (X1 @ sK1 @ sK2)) = $true)) )),
% 1.64/1.80 inference(beta_eta_normalization,[status(thm)],[f238])).
% 1.64/1.80 thf(f238,plain,(
% 1.64/1.80 ( ! [X1 : $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 @ sK1 @ sK2))) @ X1) = $true)) )),
% 1.64/1.80 inference(pi_clausification,[status(thm)],[f233])).
% 1.64/1.80 thf(f233,plain,(
% 1.64/1.80 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((((Y0 @ c0 @ c0) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ (cS @ (cS @ Y2)) @ (cS @ Y1)))))))) & (Y0 @ (cS @ c0) @ c0)) => (Y0 @ sK1 @ sK2)))))),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f232])).
% 1.64/1.80 thf(f232,plain,(
% 1.64/1.80 (($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 @ sK1 @ sK2))))) = $true)),
% 1.64/1.80 inference(superposition,[status(thm)],[f226,f22])).
% 1.64/1.80 thf(f22,plain,(
% 1.64/1.80 ((cHALF @ sK1 @ sK2) = $true)),
% 1.64/1.80 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.64/1.80 thf(f226,plain,(
% 1.64/1.80 ( ! [X2 : $i,X1 : $i] : ((((cHALF @ X1 @ X2) => (!! @ ($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))))) = $true)) )),
% 1.64/1.80 inference(beta_eta_normalization,[status(thm)],[f225])).
% 1.64/1.80 thf(f225,plain,(
% 1.64/1.80 ( ! [X2 : $i,X1 : $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)))))) @ X2) = $true)) )),
% 1.64/1.80 inference(pi_clausification,[status(thm)],[f194])).
% 1.64/1.80 thf(f194,plain,(
% 1.64/1.80 ( ! [X1 : $i] : (((!! @ $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))))))) = $true)) )),
% 1.64/1.80 inference(beta_eta_normalization,[status(thm)],[f185])).
% 1.64/1.80 thf(f185,plain,(
% 1.64/1.80 ( ! [X1 : $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)))))))) @ X1) = $true)) )),
% 1.64/1.80 inference(pi_clausification,[status(thm)],[f115])).
% 1.64/1.80 thf(f115,plain,(
% 1.64/1.80 ((!! @ $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))))))))) = $true)),
% 1.64/1.80 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.64/1.80 thf(f528,plain,(
% 1.64/1.80 ($false = ((cDOUBLE @ sK3 @ sK4) => ((cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ sK4))) | (cDOUBLE @ (cS @ (cS @ sK3)) @ (cS @ (cS @ (cS @ sK4)))))))),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f516])).
% 1.64/1.80 thf(f516,plain,(
% 1.64/1.80 ($false = (((cDOUBLE @ sK3 @ sK4) | $false) => ((cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ sK4))) | (cDOUBLE @ (cS @ (cS @ sK3)) @ (cS @ (cS @ (cS @ sK4)))))))),
% 1.64/1.80 inference(superposition,[status(thm)],[f465,f472])).
% 1.64/1.80 thf(f472,plain,(
% 1.64/1.80 ((cDOUBLE @ (cS @ sK3) @ (cS @ sK4)) = $false)),
% 1.64/1.80 inference(trivial_inequality_removal,[status(thm)],[f471])).
% 1.64/1.80 thf(f471,plain,(
% 1.64/1.80 ($false = $true) | ((cDOUBLE @ (cS @ sK3) @ (cS @ sK4)) = $false)),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f470])).
% 1.64/1.80 thf(f470,plain,(
% 1.64/1.80 ((cDOUBLE @ (cS @ sK3) @ (cS @ sK4)) = $false) | ((((cDOUBLE @ sK3 @ sK4) | (cDOUBLE @ (cS @ sK3) @ (cS @ sK4))) => $true) = $false)),
% 1.64/1.80 inference(boolean_simplification,[status(thm)],[f468])).
% 1.64/1.80 thf(f468,plain,(
% 1.64/1.80 ((((cDOUBLE @ sK3 @ sK4) | (cDOUBLE @ (cS @ sK3) @ (cS @ sK4))) => ((cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ sK4))) | $true)) = $false) | ((cDOUBLE @ (cS @ sK3) @ (cS @ sK4)) = $false)),
% 1.64/1.80 inference(superposition,[status(thm)],[f465,f66])).
% 1.64/1.80 % SZS output end Proof for DTF2THF_2774
% 1.64/1.80 % (3092)------------------------------
% 1.64/1.80 % (3092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.80 % (3092)Termination reason: Refutation
% 1.64/1.80
% 1.64/1.80 % (3092)Memory used [KB]: 3709
% 1.64/1.80 % (3092)Time elapsed: 0.124 s
% 1.64/1.80 % (3092)Instructions burned: 408 (million)
% 1.64/1.80 % (3092)------------------------------
% 1.64/1.80 % (3092)------------------------------
% 1.64/1.80 % (3041)Success in time 0.508 s
%------------------------------------------------------------------------------