%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM825^5 : 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 : n021.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 09:24:51 AM UTC 2026
% Result : Theorem 9.20s 2.32s
% Output : Refutation 9.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of formulae : 75 ( 35 unt; 0 typ; 2 def)
% Number of atoms : 637 ( 113 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 1283 ( 43 ~; 35 |; 140 &; 757 @)
% ( 2 <=>; 156 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 10 usr; 10 con; 0-2 aty)
% ( 115 !!; 35 ??; 0 @@+; 0 @@-)
% Number of variables : 211 ( 164 ^; 44 !; 3 ?; 211 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cS: $i > $i ).
thf(func_def_1,type,
cEVEN: $i > $o ).
thf(func_def_2,type,
cODD: $i > $o ).
thf(func_def_18,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f798,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f539,f684,f794]) ).
thf(f794,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f793]) ).
thf(f793,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f792]) ).
thf(f792,plain,
( ( $true = $false )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f791]) ).
thf(f791,plain,
( ( ( ( cS @ sK6 )
= ( cS @ sK6 ) )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f786]) ).
thf(f786,plain,
( ( $false
= ( ( ( cS @ sK6 )
= ( cS @ sK6 ) )
& $true ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f772,f722]) ).
thf(f722,plain,
( ( ( cEVEN @ sK6 )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f720]) ).
thf(f720,plain,
( ( ( ( cEVEN @ sK6 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( cS @ Y0 )
= ( cS @ sK6 ) )
& ( cEVEN @ Y0 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f709]) ).
thf(f709,plain,
( ( ( ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= ( cS @ Y0 ) )
& ( cEVEN @ Y1 ) ) ) )
@ sK6 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f538]) ).
thf(f538,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= ( cS @ Y0 ) )
& ( cEVEN @ Y1 ) ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f536]) ).
thf(f536,definition,
( spl0_4
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= ( cS @ Y0 ) )
& ( cEVEN @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f772,plain,
( ! [X1: $i] :
( ( ( ( cS @ X1 )
= ( cS @ sK6 ) )
& ( cEVEN @ X1 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f770]) ).
thf(f770,plain,
( ! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( ( cS @ Y0 )
= ( cS @ sK6 ) )
& ( cEVEN @ Y0 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f741]) ).
thf(f741,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( cS @ Y0 )
= ( cS @ sK6 ) )
& ( cEVEN @ Y0 ) ) )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f723]) ).
thf(f723,plain,
( ( ( $true
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( cS @ Y0 )
= ( cS @ sK6 ) )
& ( cEVEN @ Y0 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f720,f722]) ).
thf(f684,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f683]) ).
thf(f683,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f682]) ).
thf(f682,plain,
( ( $true = $false )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f681,f589]) ).
thf(f589,plain,
( ( $false
= ( cODD @ sK4 ) )
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f583]) ).
thf(f583,plain,
( ( $true
= ( ~ ( cODD @ sK4 ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f579]) ).
thf(f579,plain,
( ( $true
= ( ( cODD @ sK4 )
=> $false ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f83,f576]) ).
thf(f576,plain,
( ( ( cEVEN @ ( cS @ sK4 ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f552]) ).
thf(f552,plain,
( ( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( cS @ Y0 )
= sK4 )
& ( cEVEN @ Y0 ) ) )
=> ( cEVEN @ ( cS @ sK4 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f545]) ).
thf(f545,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) )
=> ( cEVEN @ ( cS @ Y0 ) ) )
@ sK4 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f534]) ).
thf(f534,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) )
=> ( cEVEN @ ( cS @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f532]) ).
thf(f532,definition,
( spl0_3
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) )
=> ( cEVEN @ ( cS @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f83,plain,
! [X1: $i] :
( $true
= ( ( cODD @ X1 )
=> ( cEVEN @ ( cS @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( cEVEN @ ( cS @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( cEVEN @ ( cS @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( cODD @ ( cS @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( cEVEN @ ( cS @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( cODD @ ( cS @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( cEVEN @ ( cS @ Y0 ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f23,f29]) ).
thf(f29,plain,
( ( cEVEN @ c0 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( cODD @ ( cS @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( cEVEN @ ( cS @ Y0 ) ) ) )
& ( cEVEN @ c0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( cODD @ ( cS @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( cEVEN @ ( cS @ Y0 ) ) ) )
& ( cEVEN @ c0 )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ ( cS @ Y2 ) ) ) )
& ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ ( cS @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( cEVEN @ Y2 )
=> ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( cODD @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( cODD @ ( cS @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( cEVEN @ ( cS @ Y0 ) ) ) )
& ( cEVEN @ c0 )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ ( cS @ Y2 ) ) ) )
& ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ ( cS @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( cEVEN @ Y2 )
=> ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( cODD @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( cODD @ ( cS @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( cEVEN @ ( cS @ Y0 ) ) ) )
& ( cEVEN @ c0 )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ ( cS @ Y2 ) ) ) )
& ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ ( cS @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( cEVEN @ Y2 )
=> ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( cODD @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) )
=> $false )
= $false ),
inference(backward_demodulation,[status(thm)],[f7,f9]) ).
thf(f9,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( cODD @ ( cS @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( cEVEN @ ( cS @ Y0 ) ) ) )
& ( cEVEN @ c0 )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ ( cS @ Y2 ) ) ) )
& ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ ( cS @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( cEVEN @ Y2 )
=> ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( cODD @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( cODD @ ( cS @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( cEVEN @ ( cS @ Y0 ) ) ) )
& ( cEVEN @ c0 )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ ( cS @ Y2 ) ) ) )
& ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ ( cS @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( cEVEN @ Y2 )
=> ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( cODD @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( cODD @ ( cS @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( cEVEN @ ( cS @ Y0 ) ) ) )
& ( cEVEN @ c0 )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ ( cS @ Y2 ) ) ) )
& ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ ( cS @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( cEVEN @ Y2 )
=> ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( cODD @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i > $o,X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X0 @ ( cS @ X2 ) ) )
& ( X1 @ c0 )
& ! [X3: $i] :
( ( X0 @ X3 )
=> ( X1 @ ( cS @ X3 ) ) ) )
=> ( ! [X4: $i] :
( ( cODD @ X4 )
=> ( X0 @ X4 ) )
& ! [X5: $i] :
( ( cEVEN @ X5 )
=> ( X1 @ X5 ) ) ) )
& ( cEVEN @ c0 )
& ! [X6: $i] :
( ( cODD @ X6 )
=> ( cEVEN @ ( cS @ X6 ) ) )
& ! [X7: $i] :
( ( cEVEN @ X7 )
=> ( cODD @ ( cS @ X7 ) ) ) )
=> ! [X8: $i] :
( ( cODD @ X8 )
=> ? [X9: $i] :
( ( cEVEN @ X9 )
& ( ( cS @ X9 )
= X8 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: $i > $o,X2: $i > $o] :
( ( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ ( cS @ X4 ) ) )
& ( X2 @ c0 )
& ! [X5: $i] :
( ( X3 @ X5 )
=> ( X2 @ ( cS @ X5 ) ) ) )
=> ( ! [X0: $i] :
( ( cODD @ X0 )
=> ( X3 @ X0 ) )
& ! [X0: $i] :
( ( cEVEN @ X0 )
=> ( X2 @ X0 ) ) ) )
& ( cEVEN @ c0 )
& ! [X1: $i] :
( ( cODD @ X1 )
=> ( cEVEN @ ( cS @ X1 ) ) )
& ! [X0: $i] :
( ( cEVEN @ X0 )
=> ( cODD @ ( cS @ X0 ) ) ) )
=> ! [X6: $i] :
( ( cODD @ X6 )
=> ? [X7: $i] :
( ( cEVEN @ X7 )
& ( ( cS @ X7 )
= X6 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X3: $i > $o,X2: $i > $o] :
( ( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ ( cS @ X4 ) ) )
& ( X2 @ c0 )
& ! [X5: $i] :
( ( X3 @ X5 )
=> ( X2 @ ( cS @ X5 ) ) ) )
=> ( ! [X0: $i] :
( ( cODD @ X0 )
=> ( X3 @ X0 ) )
& ! [X0: $i] :
( ( cEVEN @ X0 )
=> ( X2 @ X0 ) ) ) )
& ( cEVEN @ c0 )
& ! [X1: $i] :
( ( cODD @ X1 )
=> ( cEVEN @ ( cS @ X1 ) ) )
& ! [X0: $i] :
( ( cEVEN @ X0 )
=> ( cODD @ ( cS @ X0 ) ) ) )
=> ! [X6: $i] :
( ( cODD @ X6 )
=> ? [X7: $i] :
( ( cEVEN @ X7 )
& ( ( cS @ X7 )
= X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oV3DFLKGde/DTF2THF_20274.p',cTHM624_pme) ).
thf(f681,plain,
( ( $true
= ( cODD @ sK4 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f680]) ).
thf(f680,plain,
( ( $true
= ( $true
=> ( cODD @ sK4 ) ) )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f670,f616]) ).
thf(f616,plain,
( ( $true
= ( cEVEN @ sK5 ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f592]) ).
thf(f592,plain,
( ( $true
= ( ( ( cS @ sK5 )
= sK4 )
& ( cEVEN @ sK5 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f591]) ).
thf(f591,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( ( cS @ Y0 )
= sK4 )
& ( cEVEN @ Y0 ) )
@ sK5 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f588]) ).
thf(f588,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( cS @ Y0 )
= sK4 )
& ( cEVEN @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f584]) ).
thf(f584,plain,
( ( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( cS @ Y0 )
= sK4 )
& ( cEVEN @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f578]) ).
thf(f578,plain,
( ( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( cS @ Y0 )
= sK4 )
& ( cEVEN @ Y0 ) ) )
=> $false )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f552,f576]) ).
thf(f670,plain,
( ( $true
= ( ( cEVEN @ sK5 )
=> ( cODD @ sK4 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f97,f665]) ).
thf(f665,plain,
( ( sK4
= ( cS @ sK5 ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f626]) ).
thf(f626,plain,
( ( $true
= ( ( cS @ sK5 )
= sK4 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f618]) ).
thf(f618,plain,
( ( $true
= ( ( ( cS @ sK5 )
= sK4 )
& $true ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f592,f616]) ).
thf(f97,plain,
! [X1: $i] :
( $true
= ( ( cEVEN @ X1 )
=> ( cODD @ ( cS @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( cODD @ ( cS @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( cODD @ ( cS @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f71]) ).
thf(f71,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( cODD @ ( cS @ Y0 ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f34,f66]) ).
thf(f539,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f527,f536,f532]) ).
thf(f527,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) )
=> ( cEVEN @ ( cS @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= ( cS @ Y0 ) )
& ( cEVEN @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f259]) ).
thf(f259,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) )
=> ( cEVEN @ ( cS @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= ( cS @ Y0 ) )
& ( cEVEN @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f258]) ).
thf(f258,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) )
=> ( cEVEN @ ( cS @ Y0 ) ) ) )
& $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= ( cS @ Y0 ) )
& ( cEVEN @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f253]) ).
thf(f253,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) )
=> ( ^ [Y1: $i] :
( cEVEN
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ ( cS @ Y0 ) ) ) )
& $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( cEVEN
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= ( cS @ Y0 ) )
& ( cEVEN @ Y1 ) ) ) ) ) )
= $false ),
inference(superposition,[status(thm)],[f199,f29]) ).
thf(f199,plain,
! [X0: $i > $o] :
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) )
=> ( X0 @ ( cS @ Y0 ) ) ) )
& ( X0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= ( cS @ Y0 ) )
& ( cEVEN @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X0: $i > $o] :
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) )
=> ( X0 @ ( cS @ Y0 ) ) ) )
& ( X0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= ( cS @ Y0 ) )
& ( cEVEN @ Y1 ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: $i > $o] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) )
=> ( X0 @ ( cS @ Y0 ) ) ) )
& ( X0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= ( cS @ Y0 ) )
& ( cEVEN @ Y1 ) ) ) ) ) )
=> $false ) ),
inference(boolean_simplification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X0: $i > $o] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= Y0 )
& ( cEVEN @ Y1 ) ) )
=> ( X0 @ ( cS @ Y0 ) ) ) )
& ( X0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( cS @ Y1 )
= ( cS @ Y0 ) )
& ( cEVEN @ Y1 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( X0 @ Y0 ) ) )
& $false ) ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: $i > $o] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( cS @ Y2 )
= Y1 )
& ( cEVEN @ Y2 ) ) )
@ Y0 )
=> ( X0 @ ( cS @ Y0 ) ) ) )
& ( X0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
=> ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( cS @ Y2 )
= Y1 )
& ( cEVEN @ Y2 ) ) )
@ ( cS @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( X0 @ Y0 ) ) )
& $false ) ) ),
inference(superposition,[status(thm)],[f42,f9]) ).
thf(f42,plain,
! [X2: $i > $o,X1: $i > $o] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) )
& ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X2 @ ( cS @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cEVEN @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cODD @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i > $o,X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( X1 @ ( cS @ Y1 ) ) ) )
& ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( cEVEN @ Y1 )
=> ( X1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( cODD @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i > $o] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( X1 @ ( cS @ Y1 ) ) ) )
& ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( cEVEN @ Y1 )
=> ( X1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( cODD @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ ( cS @ Y2 ) ) ) )
& ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ ( cS @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( cEVEN @ Y2 )
=> ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( cODD @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ ( cS @ Y2 ) ) ) )
& ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ ( cS @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( cEVEN @ Y2 )
=> ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( cODD @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
= ( $true
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ ( cS @ Y2 ) ) ) )
& ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ ( cS @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( cEVEN @ Y2 )
=> ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( cODD @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f18,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM825^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n021.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 11:14:53 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : NUM825^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Number Theory (Induction on naturals)
% 0.16/0.39 % Problem : TPS problem from IND-THMS
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_1036 [Bro09]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.89 v9.1.0, 0.88 v9.0.0, 1.00 v5.5.0, 0.83 v5.4.0, 0.80 v5.3.0, 1.00 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.16/0.39 % Number of atoms : 10 ( 1 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 10 ( 10 avg)
% 0.16/0.39 % Number of connectives : 37 ( 0 ~; 0 |; 7 &; 21 @)
% 0.16/0.39 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 14 ( 14 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 10 ( 0 ^; 9 !; 1 ?; 10 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 % :
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(cS,type,
% 0.16/0.39 cS: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(cEVEN,type,
% 0.16/0.39 cEVEN: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(cODD,type,
% 0.16/0.39 cODD: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(c0,type,
% 0.16/0.39 c0: $i ).
% 0.16/0.39
% 0.16/0.39 thf(cTHM624_pme,conjecture,
% 0.16/0.39 ( ( ( cEVEN @ c0 )
% 0.16/0.39 & ! [Xx: $i] :
% 0.16/0.39 ( ( cEVEN @ Xx )
% 0.16/0.39 => ( cODD @ ( cS @ Xx ) ) )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( cODD @ Xy )
% 0.16/0.39 => ( cEVEN @ ( cS @ Xy ) ) )
% 0.16/0.39 & ! [Xp: $i > $o,Xq: $i > $o] :
% 0.16/0.39 ( ( ( Xp @ c0 )
% 0.16/0.39 & ! [Xu: $i] :
% 0.16/0.39 ( ( Xp @ Xu )
% 0.16/0.39 => ( Xq @ ( cS @ Xu ) ) )
% 0.16/0.39 & ! [Xv: $i] :
% 0.16/0.39 ( ( Xq @ Xv )
% 0.16/0.39 => ( Xp @ ( cS @ Xv ) ) ) )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( cEVEN @ Xx )
% 0.16/0.39 => ( Xp @ Xx ) )
% 0.16/0.39 & ! [Xx: $i] :
% 0.16/0.39 ( ( cODD @ Xx )
% 0.16/0.39 => ( Xq @ Xx ) ) ) ) )
% 0.16/0.39 => ! [Xn: $i] :
% 0.16/0.39 ( ( cODD @ Xn )
% 0.16/0.39 => ? [Xm: $i] :
% 0.16/0.39 ( ( cEVEN @ Xm )
% 0.16/0.39 & ( ( cS @ Xm )
% 0.16/0.39 = Xn ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.21/1.05 ---- Embedded in THF ---
% 1.21/1.05 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.21/1.05 %%% Generated on Tue Feb 24 11:14:54 EST 2026
% 1.21/1.05 %%% using '$$dhol' embedding, version 1.3.0.
% 1.21/1.05 %%% Logic specification used:
% 1.21/1.05 %%% thf(spec, logic, $$dhol).
% 1.21/1.05
% 1.21/1.05 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oV3DFLKGde/DTF2DTF20274.p
% See solution above
% 1.21/1.05 ------------------------
% 1.21/1.06 ---- Cleaned THF ---
% 1.21/1.06 thf(cS,type,
% 1.21/1.06 cS: $i > $i ).
% 1.21/1.06
% 1.21/1.06 thf(cEVEN,type,
% 1.21/1.06 cEVEN: $i > $o ).
% 1.21/1.06
% 1.21/1.06 thf(cODD,type,
% 1.21/1.06 cODD: $i > $o ).
% 1.21/1.06
% 1.21/1.06 thf(c0,type,
% 1.21/1.06 c0: $i ).
% 1.21/1.06
% 1.21/1.06 thf(cTHM624_pme,conjecture,
% 1.21/1.06 ( ( ( cEVEN @ c0 )
% 1.21/1.06 & ! [Xx: $i] :
% 1.21/1.06 ( ( cEVEN @ Xx )
% 1.21/1.06 => ( cODD @ ( cS @ Xx ) ) )
% 1.21/1.06 & ! [Xy: $i] :
% 1.21/1.06 ( ( cODD @ Xy )
% 1.21/1.06 => ( cEVEN @ ( cS @ Xy ) ) )
% 1.21/1.06 & ! [Xp: $i > $o,Xq: $i > $o] :
% 1.21/1.06 ( ( ( Xp @ c0 )
% 1.21/1.06 & ! [Xu: $i] :
% 1.21/1.06 ( ( Xp @ Xu )
% 1.21/1.06 => ( Xq @ ( cS @ Xu ) ) )
% 1.21/1.06 & ! [Xv: $i] :
% 1.21/1.06 ( ( Xq @ Xv )
% 1.21/1.06 => ( Xp @ ( cS @ Xv ) ) ) )
% 1.21/1.06 => ( ! [Xx: $i] :
% 1.21/1.06 ( ( cEVEN @ Xx )
% 1.21/1.06 => ( Xp @ Xx ) )
% 1.21/1.06 & ! [Xx: $i] :
% 1.21/1.06 ( ( cODD @ Xx )
% 1.21/1.06 => ( Xq @ Xx ) ) ) ) )
% 1.21/1.06 => ! [Xn: $i] :
% 1.21/1.06 ( ( cODD @ Xn )
% 1.21/1.06 => ? [Xm: $i] :
% 1.21/1.06 ( ( cEVEN @ Xm )
% 1.21/1.06 & ( ( cS @ Xm )
% 1.21/1.06 = Xn ) ) ) ) ).
% 1.21/1.06 ------------------------
% 1.21/1.07 % (20389)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20274 for (3000ds/183Mi)
% 1.21/1.08 % (20392)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20274 for (3000ds/2Mi)
% 1.21/1.08 % (20395)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20274 for (3000ds/18Mi)
% 1.21/1.08 % (20390)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_20274 for (3000ds/4Mi)
% 1.21/1.08 % (20393)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_20274 for (3000ds/2Mi)
% 1.21/1.08 % (20394)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_20274 for (3000ds/275Mi)
% 1.21/1.08 % (20391)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_20274 for (3000ds/27Mi)
% 1.21/1.08 % (20392)Instruction limit reached!
% 1.21/1.08 % (20392)------------------------------
% 1.21/1.08 % (20392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.08 % (20392)Termination reason: Unknown
% 1.21/1.08 % (20392)Termination phase: Saturation
% 1.21/1.08 % (20393)Instruction limit reached!
% 1.21/1.08 % (20393)------------------------------
% 1.21/1.08 % (20393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.08 % (20393)Termination reason: Unknown
% 1.21/1.08 % (20393)Termination phase: Property scanning
% 1.21/1.08
% 1.21/1.08 % (20393)Memory used [KB]: 895
% 1.21/1.08 % (20393)Time elapsed: 0.002 s
% 1.21/1.08 % (20393)Instructions burned: 2 (million)
% 1.21/1.08 % (20393)------------------------------
% 1.21/1.08 % (20393)------------------------------
% 1.21/1.08
% 1.21/1.08 % (20392)Memory used [KB]: 5500
% 1.21/1.08 % (20392)Time elapsed: 0.003 s
% 1.21/1.08 % (20392)Instructions burned: 2 (million)
% 1.21/1.08 % (20392)------------------------------
% 1.21/1.08 % (20392)------------------------------
% 1.21/1.08 % (20390)Instruction limit reached!
% 1.21/1.08 % (20390)------------------------------
% 1.21/1.08 % (20390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.08 % (20390)Termination reason: Unknown
% 1.21/1.08 % (20390)Termination phase: Saturation
% 1.21/1.08
% 1.21/1.08 % (20390)Memory used [KB]: 5500
% 1.21/1.08 % (20390)Time elapsed: 0.003 s
% 1.21/1.08 % (20390)Instructions burned: 4 (million)
% 1.21/1.08 % (20390)------------------------------
% 1.21/1.08 % (20390)------------------------------
% 1.21/1.09 % (20395)Instruction limit reached!
% 1.21/1.09 % (20395)------------------------------
% 1.21/1.09 % (20395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.09 % (20395)Termination reason: Unknown
% 1.21/1.09 % (20395)Termination phase: Saturation
% 1.21/1.09
% 1.21/1.09 % (20395)Memory used [KB]: 5628
% 1.21/1.09 % (20395)Time elapsed: 0.012 s
% 1.21/1.09 % (20395)Instructions burned: 19 (million)
% 1.21/1.09 % (20395)------------------------------
% 1.21/1.09 % (20395)------------------------------
% 1.21/1.09 % (20391)Instruction limit reached!
% 1.21/1.09 % (20391)------------------------------
% 1.21/1.09 % (20391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.09 % (20391)Termination reason: Unknown
% 1.21/1.09 % (20391)Termination phase: Saturation
% 1.21/1.09
% 1.21/1.09 % (20391)Memory used [KB]: 5628
% 1.21/1.09 % (20391)Time elapsed: 0.016 s
% 1.21/1.09 % (20391)Instructions burned: 27 (million)
% 1.21/1.09 % (20391)------------------------------
% 1.21/1.09 % (20391)------------------------------
% 1.21/1.09 % (20397)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_20274 for (2999ds/37Mi)
% 1.21/1.09 % (20396)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20274 for (2999ds/3Mi)
% 1.21/1.10 % (20396)Instruction limit reached!
% 1.21/1.10 % (20396)------------------------------
% 1.21/1.10 % (20396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.10 % (20396)Termination reason: Unknown
% 1.21/1.10 % (20396)Termination phase: Saturation
% 1.21/1.10
% 1.21/1.10 % (20396)Memory used [KB]: 5500
% 1.21/1.10 % (20396)Time elapsed: 0.003 s
% 1.21/1.10 % (20396)Instructions burned: 3 (million)
% 1.21/1.10 % (20396)------------------------------
% 1.21/1.10 % (20396)------------------------------
% 1.21/1.10 % (20398)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_20274 for (2999ds/15Mi)
% 1.21/1.11 % (20399)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_20274 for (2999ds/3Mi)
% 1.21/1.11 % (20398)Instruction limit reached!
% 1.21/1.11 % (20398)------------------------------
% 1.21/1.11 % (20398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.11 % (20398)Termination reason: Unknown
% 1.21/1.11 % (20398)Termination phase: Saturation
% 1.21/1.11
% 1.21/1.11 % (20398)Memory used [KB]: 5628
% 1.21/1.11 % (20398)Time elapsed: 0.010 s
% 1.21/1.11 % (20398)Instructions burned: 15 (million)
% 1.21/1.11 % (20398)------------------------------
% 1.21/1.11 % (20398)------------------------------
% 1.21/1.11 % (20399)Instruction limit reached!
% 1.21/1.11 % (20399)------------------------------
% 1.21/1.11 % (20399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.11 % (20399)Termination reason: Unknown
% 1.21/1.11 % (20399)Termination phase: Saturation
% 1.21/1.11
% 1.21/1.11 % (20399)Memory used [KB]: 5500
% 1.21/1.11 % (20399)Time elapsed: 0.004 s
% 1.21/1.11 % (20399)Instructions burned: 4 (million)
% 1.21/1.11 % (20399)------------------------------
% 1.21/1.11 % (20399)------------------------------
% 1.21/1.11 % (20400)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_20274 for (2999ds/1041Mi)
% 1.21/1.11 % (20397)Instruction limit reached!
% 1.21/1.11 % (20397)------------------------------
% 1.21/1.11 % (20397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.11 % (20397)Termination reason: Unknown
% 1.21/1.11 % (20397)Termination phase: Saturation
% 1.21/1.11
% 1.21/1.11 % (20397)Memory used [KB]: 5628
% 1.21/1.11 % (20397)Time elapsed: 0.020 s
% 1.21/1.11 % (20397)Instructions burned: 37 (million)
% 1.21/1.11 % (20397)------------------------------
% 1.21/1.11 % (20397)------------------------------
% 1.21/1.11 % (20401)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20274 for (2999ds/7Mi)
% 1.21/1.12 % (20401)Instruction limit reached!
% 1.21/1.12 % (20401)------------------------------
% 1.21/1.12 % (20401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.12 % (20401)Termination reason: Unknown
% 1.21/1.12 % (20401)Termination phase: Saturation
% 1.21/1.12
% 1.21/1.12 % (20401)Memory used [KB]: 1023
% 1.21/1.12 % (20401)Time elapsed: 0.005 s
% 1.21/1.12 % (20401)Instructions burned: 7 (million)
% 1.21/1.12 % (20401)------------------------------
% 1.21/1.12 % (20401)------------------------------
% 1.27/1.12 % (20403)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_20274 for (2999ds/3Mi)
% 1.27/1.12 % (20403)Instruction limit reached!
% 1.27/1.12 % (20403)------------------------------
% 1.27/1.12 % (20403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.12 % (20403)Termination reason: Unknown
% 1.27/1.12 % (20403)Termination phase: Twee Goal Transformation
% 1.27/1.12
% 1.27/1.12 % (20403)Memory used [KB]: 1023
% 1.27/1.12 % (20403)Time elapsed: 0.003 s
% 1.27/1.12 % (20403)Instructions burned: 3 (million)
% 1.27/1.12 % (20403)------------------------------
% 1.27/1.12 % (20403)------------------------------
% 1.27/1.13 % (20404)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_20274 for (2999ds/3Mi)
% 1.27/1.13 % (20404)Instruction limit reached!
% 1.27/1.13 % (20404)------------------------------
% 1.27/1.13 % (20404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.13 % (20389)Instruction limit reached!
% 1.27/1.13 % (20389)------------------------------
% 1.27/1.13 % (20389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.13 % (20389)Termination reason: Unknown
% 1.27/1.13 % (20389)Termination phase: Saturation
% 1.27/1.13
% 1.27/1.13 % (20389)Memory used [KB]: 6396
% 1.27/1.13 % (20389)Time elapsed: 0.058 s
% 1.27/1.13 % (20389)Instructions burned: 183 (million)
% 1.27/1.13 % (20389)------------------------------
% 1.27/1.13 % (20389)------------------------------
% 1.27/1.13 % (20404)Termination reason: Unknown
% 1.27/1.13 % (20404)Termination phase: Property scanning
% 1.27/1.13
% 1.27/1.13 % (20404)Memory used [KB]: 1023
% 1.27/1.13 % (20404)Time elapsed: 0.003 s
% 1.27/1.13 % (20404)Instructions burned: 3 (million)
% 1.27/1.13 % (20402)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20274 for (2999ds/16Mi)
% 1.27/1.13 % (20404)------------------------------
% 1.27/1.13 % (20404)------------------------------
% 1.27/1.13 % (20405)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20274 for (2999ds/7Mi)
% 1.27/1.14 % (20402)Instruction limit reached!
% 1.27/1.14 % (20402)------------------------------
% 1.27/1.14 % (20402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.14 % (20402)Termination reason: Unknown
% 1.27/1.14 % (20402)Termination phase: Saturation
% 1.27/1.14
% 1.27/1.14 % (20402)Memory used [KB]: 5628
% 1.27/1.14 % (20402)Time elapsed: 0.010 s
% 1.27/1.14 % (20402)Instructions burned: 16 (million)
% 1.27/1.14 % (20402)------------------------------
% 1.27/1.14 % (20402)------------------------------
% 1.27/1.14 % (20405)Instruction limit reached!
% 1.27/1.14 % (20405)------------------------------
% 1.27/1.14 % (20405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.14 % (20405)Termination reason: Unknown
% 1.27/1.14 % (20405)Termination phase: Saturation
% 1.27/1.14
% 1.27/1.14 % (20405)Memory used [KB]: 5500
% 1.27/1.14 % (20405)Time elapsed: 0.006 s
% 1.27/1.14 % (20405)Instructions burned: 8 (million)
% 1.27/1.14 % (20405)------------------------------
% 1.27/1.14 % (20405)------------------------------
% 1.27/1.14 % (20407)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20274 for (2999ds/4Mi)
% 1.27/1.14 % (20407)Instruction limit reached!
% 1.27/1.14 % (20407)------------------------------
% 1.27/1.14 % (20407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.14 % (20407)Termination reason: Unknown
% 1.27/1.14 % (20407)Termination phase: Saturation
% 1.27/1.14
% 1.27/1.14 % (20407)Memory used [KB]: 5500
% 1.27/1.14 % (20407)Time elapsed: 0.003 s
% 1.27/1.14 % (20407)Instructions burned: 6 (million)
% 1.27/1.14 % (20407)------------------------------
% 1.27/1.14 % (20407)------------------------------
% 1.27/1.14 % (20406)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20274 for (2999ds/3Mi)
% 1.27/1.14 % (20408)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20274 for (2999ds/18Mi)
% 1.27/1.14 % (20406)Instruction limit reached!
% 1.27/1.14 % (20406)------------------------------
% 1.27/1.14 % (20406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.14 % (20406)Termination reason: Unknown
% 1.27/1.14 % (20406)Termination phase: Saturation
% 1.27/1.14
% 1.27/1.14 % (20406)Memory used [KB]: 5500
% 1.27/1.14 % (20406)Time elapsed: 0.003 s
% 1.27/1.14 % (20406)Instructions burned: 4 (million)
% 1.27/1.14 % (20406)------------------------------
% 1.27/1.14 % (20406)------------------------------
% 1.27/1.15 % (20409)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20274 for (2999ds/710Mi)
% 1.27/1.15 % (20410)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20274 for (2999ds/6Mi)
% 1.27/1.15 % (20408)Instruction limit reached!
% 1.27/1.15 % (20408)------------------------------
% 1.27/1.15 % (20408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.15 % (20408)Termination reason: Unknown
% 1.27/1.15 % (20408)Termination phase: Saturation
% 1.27/1.15
% 1.27/1.15 % (20408)Memory used [KB]: 5628
% 1.27/1.15 % (20408)Time elapsed: 0.012 s
% 1.27/1.15 % (20408)Instructions burned: 19 (million)
% 1.27/1.15 % (20408)------------------------------
% 1.27/1.15 % (20408)------------------------------
% 1.27/1.16 % (20411)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_20274 for (2999ds/902Mi)
% 1.27/1.16 % (20410)Instruction limit reached!
% 1.27/1.16 % (20410)------------------------------
% 1.27/1.16 % (20410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.16 % (20410)Termination reason: Unknown
% 1.27/1.16 % (20410)Termination phase: Saturation
% 1.27/1.16
% 1.27/1.16 % (20410)Memory used [KB]: 5500
% 1.27/1.16 % (20410)Time elapsed: 0.004 s
% 1.27/1.16 % (20410)Instructions burned: 6 (million)
% 1.27/1.16 % (20410)------------------------------
% 1.27/1.16 % (20410)------------------------------
% 1.27/1.16 % (20412)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_20274 for (2999ds/21Mi)
% 1.27/1.16 % (20412)Instruction limit reached!
% 1.27/1.16 % (20412)------------------------------
% 1.27/1.16 % (20412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.16 % (20412)Termination reason: Unknown
% 1.27/1.16 % (20412)Termination phase: Saturation
% 1.27/1.16
% 1.27/1.16 % (20412)Memory used [KB]: 5628
% 1.27/1.16 % (20412)Time elapsed: 0.009 s
% 1.27/1.16 % (20412)Instructions burned: 21 (million)
% 1.27/1.16 % (20412)------------------------------
% 1.27/1.16 % (20412)------------------------------
% 1.27/1.17 % (20414)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_20274 for (2999ds/6Mi)
% 1.27/1.17 % (20413)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20274 for (2999ds/5Mi)
% 1.27/1.17 % (20415)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20274 for (2999ds/377Mi)
% 1.27/1.17 % (20413)Instruction limit reached!
% 1.27/1.17 % (20413)------------------------------
% 1.27/1.17 % (20413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.17 % (20413)Termination reason: Unknown
% 1.27/1.17 % (20413)Termination phase: Saturation
% 1.27/1.17
% 1.27/1.17 % (20413)Memory used [KB]: 5500
% 1.27/1.17 % (20413)Time elapsed: 0.004 s
% 1.27/1.17 % (20413)Instructions burned: 5 (million)
% 1.27/1.17 % (20413)------------------------------
% 1.27/1.17 % (20413)------------------------------
% 1.27/1.17 % (20414)Instruction limit reached!
% 1.27/1.17 % (20414)------------------------------
% 1.27/1.17 % (20414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.17 % (20414)Termination reason: Unknown
% 1.27/1.17 % (20414)Termination phase: Saturation
% 1.27/1.17
% 1.27/1.17 % (20414)Memory used [KB]: 5500
% 1.27/1.17 % (20414)Time elapsed: 0.005 s
% 1.27/1.17 % (20414)Instructions burned: 7 (million)
% 1.27/1.17 % (20414)------------------------------
% 1.27/1.17 % (20414)------------------------------
% 1.27/1.19 % (20416)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_20274 for (2998ds/779Mi)
% 1.27/1.19 % (20417)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_20274 for (2998ds/19Mi)
% 1.27/1.20 % (20417)Instruction limit reached!
% 1.27/1.20 % (20417)------------------------------
% 1.27/1.20 % (20417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.20 % (20417)Termination reason: Unknown
% 1.27/1.20 % (20417)Termination phase: Saturation
% 1.27/1.20
% 1.27/1.20 % (20417)Memory used [KB]: 5500
% 1.27/1.20 % (20417)Time elapsed: 0.011 s
% 1.27/1.20 % (20417)Instructions burned: 19 (million)
% 1.27/1.20 % (20417)------------------------------
% 1.27/1.20 % (20417)------------------------------
% 1.27/1.22 % (20394)Instruction limit reached!
% 1.27/1.22 % (20394)------------------------------
% 1.27/1.22 % (20394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.22 % (20394)Termination reason: Unknown
% 1.27/1.22 % (20394)Termination phase: Saturation
% 1.27/1.22
% 1.27/1.22 % (20394)Memory used [KB]: 6268
% 1.27/1.22 % (20394)Time elapsed: 0.140 s
% 1.27/1.22 % (20394)Instructions burned: 275 (million)
% 1.27/1.22 % (20394)------------------------------
% 1.27/1.22 % (20394)------------------------------
% 1.27/1.22 % (20418)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_20274 for (2998ds/879Mi)
% 1.27/1.23 % (20419)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_20274 for (2998ds/17Mi)
% 1.27/1.24 % (20419)Instruction limit reached!
% 1.27/1.24 % (20419)------------------------------
% 1.27/1.24 % (20419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.24 % (20419)Termination reason: Unknown
% 1.27/1.24 % (20419)Termination phase: Saturation
% 1.27/1.24
% 1.27/1.24 % (20419)Memory used [KB]: 5628
% 1.27/1.24 % (20419)Time elapsed: 0.034 s
% 1.27/1.24 % (20419)Instructions burned: 17 (million)
% 1.27/1.24 % (20419)------------------------------
% 1.27/1.24 % (20419)------------------------------
% 1.27/1.26 % (20420)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20274 for (2998ds/3Mi)
% 1.27/1.26 % (20420)Instruction limit reached!
% 1.27/1.26 % (20420)------------------------------
% 1.27/1.26 % (20420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.26 % (20420)Termination reason: Unknown
% 1.27/1.26 % (20420)Termination phase: Saturation
% 1.27/1.26
% 1.27/1.26 % (20420)Memory used [KB]: 1023
% 1.27/1.26 % (20420)Time elapsed: 0.003 s
% 1.27/1.26 % (20420)Instructions burned: 4 (million)
% 1.27/1.26 % (20420)------------------------------
% 1.27/1.26 % (20420)------------------------------
% 1.27/1.28 % (20421)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_20274 for (2997ds/30Mi)
% 1.27/1.29 % (20415)Instruction limit reached!
% 1.27/1.29 % (20415)------------------------------
% 1.27/1.29 % (20415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.29 % (20415)Termination reason: Unknown
% 1.27/1.29 % (20415)Termination phase: Saturation
% 1.27/1.29
% 1.27/1.29 % (20415)Memory used [KB]: 6396
% 1.27/1.29 % (20415)Time elapsed: 0.115 s
% 1.27/1.29 % (20415)Instructions burned: 377 (million)
% 1.27/1.29 % (20415)------------------------------
% 1.27/1.29 % (20415)------------------------------
% 1.27/1.30 % (20421)Instruction limit reached!
% 1.27/1.30 % (20421)------------------------------
% 1.27/1.30 % (20421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.30 % (20421)Termination reason: Unknown
% 1.27/1.30 % (20421)Termination phase: Saturation
% 1.27/1.30
% 1.27/1.30 % (20421)Memory used [KB]: 5628
% 1.27/1.30 % (20421)Time elapsed: 0.018 s
% 1.27/1.30 % (20421)Instructions burned: 31 (million)
% 1.27/1.30 % (20421)------------------------------
% 1.27/1.30 % (20421)------------------------------
% 1.27/1.30 % (20422)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_20274 for (2997ds/127Mi)
% 1.27/1.31 % (20423)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_20274 for (2997ds/100Mi)
% 1.27/1.34 % (20422)Instruction limit reached!
% 1.27/1.34 % (20422)------------------------------
% 1.27/1.34 % (20422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.34 % (20422)Termination reason: Unknown
% 1.27/1.34 % (20422)Termination phase: Saturation
% 1.27/1.34
% 1.27/1.34 % (20422)Memory used [KB]: 6012
% 1.27/1.34 % (20422)Time elapsed: 0.042 s
% 1.27/1.34 % (20422)Instructions burned: 128 (million)
% 1.27/1.34 % (20422)------------------------------
% 1.27/1.34 % (20422)------------------------------
% 1.27/1.34 % (20423)Refutation not found, incomplete strategy
% 1.27/1.34 % (20423)------------------------------
% 1.27/1.34 % (20423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.34 % (20423)Termination reason: Refutation not found, incomplete strategy
% 1.27/1.34
% 1.27/1.34
% 1.27/1.34 % (20423)Memory used [KB]: 5756
% 1.27/1.34 % (20423)Time elapsed: 0.028 s
% 1.27/1.34 % (20423)Instructions burned: 51 (million)
% 1.27/1.34 % (20423)------------------------------
% 1.27/1.34 % (20423)------------------------------
% 1.27/1.35 % (20424)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_20274 for (2997ds/3Mi)
% 1.27/1.35 % (20424)Instruction limit reached!
% 1.27/1.35 % (20424)------------------------------
% 1.27/1.35 % (20424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.35 % (20424)Termination reason: Unknown
% 1.27/1.35 % (20424)Termination phase: Saturation
% 1.27/1.35
% 1.27/1.35 % (20424)Memory used [KB]: 5500
% 1.27/1.35 % (20424)Time elapsed: 0.002 s
% 1.27/1.35 % (20424)Instructions burned: 3 (million)
% 1.27/1.35 % (20424)------------------------------
% 1.27/1.35 % (20424)------------------------------
% 1.27/1.36 % (20425)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_20274 for (2997ds/20Mi)
% 1.27/1.36 % (20426)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_20274 for (2997ds/86Mi)
% 1.27/1.37 % (20425)Instruction limit reached!
% 1.27/1.37 % (20425)------------------------------
% 1.27/1.37 % (20425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.37 % (20425)Termination reason: Unknown
% 1.27/1.37 % (20425)Termination phase: Saturation
% 1.27/1.37
% 1.27/1.37 % (20425)Memory used [KB]: 5628
% 1.27/1.37 % (20425)Time elapsed: 0.013 s
% 1.27/1.37 % (20425)Instructions burned: 20 (million)
% 1.27/1.37 % (20425)------------------------------
% 1.27/1.37 % (20425)------------------------------
% 1.27/1.38 % (20427)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_20274 for (2996ds/107Mi)
% 1.27/1.40 % (20426)Instruction limit reached!
% 1.27/1.40 % (20426)------------------------------
% 1.27/1.40 % (20426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.40 % (20426)Termination reason: Unknown
% 1.27/1.40 % (20426)Termination phase: Saturation
% 1.27/1.40
% 1.27/1.40 % (20426)Memory used [KB]: 6012
% 1.27/1.40 % (20426)Time elapsed: 0.037 s
% 1.27/1.40 % (20426)Instructions burned: 86 (million)
% 1.27/1.40 % (20426)------------------------------
% 1.27/1.40 % (20426)------------------------------
% 1.27/1.41 % (20428)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_20274 for (2996ds/39Mi)
% 1.27/1.42 % (20428)Instruction limit reached!
% 1.27/1.42 % (20428)------------------------------
% 1.27/1.42 % (20428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.42 % (20428)Termination reason: Unknown
% 1.27/1.42 % (20428)Termination phase: Saturation
% 1.27/1.42
% 1.27/1.42 % (20428)Memory used [KB]: 5628
% 1.27/1.42 % (20428)Time elapsed: 0.014 s
% 1.27/1.42 % (20428)Instructions burned: 40 (million)
% 1.27/1.42 % (20428)------------------------------
% 1.27/1.42 % (20428)------------------------------
% 1.27/1.43 % (20427)Instruction limit reached!
% 1.27/1.43 % (20427)------------------------------
% 1.27/1.43 % (20427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.43 % (20427)Termination reason: Unknown
% 1.27/1.43 % (20427)Termination phase: Saturation
% 1.27/1.43
% 1.27/1.43 % (20427)Memory used [KB]: 5884
% 1.27/1.43 % (20427)Time elapsed: 0.051 s
% 1.27/1.43 % (20427)Instructions burned: 108 (million)
% 1.27/1.43 % (20427)------------------------------
% 1.27/1.43 % (20427)------------------------------
% 1.27/1.43 % (20429)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_20274 for (2996ds/448Mi)
% 1.27/1.45 % (20430)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_20274 for (2996ds/46Mi)
% 1.27/1.47 % (20430)Instruction limit reached!
% 1.27/1.47 % (20430)------------------------------
% 1.27/1.47 % (20430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.47 % (20430)Termination reason: Unknown
% 1.27/1.47 % (20430)Termination phase: Saturation
% 1.27/1.47
% 1.27/1.47 % (20430)Memory used [KB]: 5756
% 1.27/1.47 % (20430)Time elapsed: 0.027 s
% 1.27/1.47 % (20430)Instructions burned: 47 (million)
% 1.27/1.47 % (20430)------------------------------
% 1.27/1.47 % (20430)------------------------------
% 1.27/1.49 % (20431)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_20274 for (2995ds/98Mi)
% 1.27/1.49 % (20409)Instruction limit reached!
% 1.27/1.49 % (20409)------------------------------
% 1.27/1.49 % (20409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.49 % (20409)Termination reason: Unknown
% 1.27/1.49 % (20409)Termination phase: Saturation
% 1.27/1.49
% 1.27/1.49 % (20409)Memory used [KB]: 6908
% 1.27/1.49 % (20409)Time elapsed: 0.342 s
% 1.27/1.49 % (20409)Instructions burned: 710 (million)
% 1.27/1.49 % (20409)------------------------------
% 1.27/1.49 % (20409)------------------------------
% 1.27/1.51 % (20432)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_20274 for (2995ds/507Mi)
% 1.27/1.54 % (20431)Instruction limit reached!
% 1.27/1.54 % (20431)------------------------------
% 1.27/1.54 % (20431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.54 % (20431)Termination reason: Unknown
% 1.27/1.54 % (20431)Termination phase: Saturation
% 1.27/1.54
% 1.27/1.54 % (20431)Memory used [KB]: 1151
% 1.27/1.54 % (20431)Time elapsed: 0.050 s
% 1.27/1.54 % (20431)Instructions burned: 99 (million)
% 1.27/1.54 % (20431)------------------------------
% 1.27/1.54 % (20431)------------------------------
% 1.27/1.55 % (20416)Instruction limit reached!
% 1.27/1.55 % (20416)------------------------------
% 1.27/1.55 % (20416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.55 % (20416)Termination reason: Unknown
% 1.27/1.55 % (20416)Termination phase: Saturation
% 1.27/1.55
% 1.27/1.55 % (20416)Memory used [KB]: 6652
% 1.27/1.55 % (20416)Time elapsed: 0.361 s
% 1.27/1.55 % (20416)Instructions burned: 781 (million)
% 1.27/1.55 % (20416)------------------------------
% 1.27/1.55 % (20416)------------------------------
% 1.27/1.56 % (20433)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_20274 for (2995ds/149Mi)
% 1.27/1.56 % (20434)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_20274 for (2995ds/39Mi)
% 1.27/1.57 % (20434)Instruction limit reached!
% 1.27/1.57 % (20434)------------------------------
% 1.27/1.57 % (20434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.57 % (20434)Termination reason: Unknown
% 1.27/1.57 % (20434)Termination phase: Saturation
% 1.27/1.57
% 1.27/1.57 % (20434)Memory used [KB]: 5756
% 1.27/1.57 % (20434)Time elapsed: 0.015 s
% 1.27/1.57 % (20434)Instructions burned: 40 (million)
% 1.27/1.57 % (20434)------------------------------
% 1.27/1.57 % (20434)------------------------------
% 1.27/1.58 % (20435)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_20274 for (2994ds/6Mi)
% 1.27/1.58 % (20400)Instruction limit reached!
% 1.27/1.58 % (20400)------------------------------
% 1.27/1.58 % (20400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.58 % (20400)Termination reason: Unknown
% 1.27/1.58 % (20400)Termination phase: Saturation
% 1.27/1.58
% 1.27/1.58 % (20400)Memory used [KB]: 7547
% 1.27/1.58 % (20400)Time elapsed: 0.474 s
% 1.27/1.58 % (20400)Instructions burned: 1042 (million)
% 1.27/1.58 % (20400)------------------------------
% 1.27/1.58 % (20400)------------------------------
% 1.27/1.59 % (20435)Instruction limit reached!
% 1.27/1.59 % (20435)------------------------------
% 1.27/1.59 % (20435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.59 % (20435)Termination reason: Unknown
% 1.27/1.59 % (20435)Termination phase: Saturation
% 1.27/1.59
% 1.27/1.59 % (20435)Memory used [KB]: 9978
% 1.27/1.59 % (20435)Time elapsed: 0.004 s
% 1.27/1.59 % (20435)Instructions burned: 7 (million)
% 1.27/1.59 % (20435)------------------------------
% 1.27/1.59 % (20435)------------------------------
% 1.27/1.59 % (20429)Instruction limit reached!
% 1.27/1.59 % (20429)------------------------------
% 1.27/1.59 % (20429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.59 % (20429)Termination reason: Unknown
% 1.27/1.59 % (20429)Termination phase: Saturation
% 1.27/1.59
% 1.27/1.59 % (20429)Memory used [KB]: 6140
% 1.27/1.59 % (20429)Time elapsed: 0.162 s
% 1.27/1.59 % (20429)Instructions burned: 449 (million)
% 1.27/1.59 % (20429)------------------------------
% 1.27/1.59 % (20429)------------------------------
% 1.27/1.59 % (20411)Instruction limit reached!
% 1.27/1.59 % (20411)------------------------------
% 1.27/1.59 % (20411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.59 % (20411)Termination reason: Unknown
% 1.27/1.59 % (20411)Termination phase: Saturation
% 1.27/1.59
% 1.27/1.59 % (20411)Memory used [KB]: 8187
% 1.27/1.59 % (20411)Time elapsed: 0.438 s
% 1.27/1.59 % (20411)Instructions burned: 903 (million)
% 1.27/1.59 % (20411)------------------------------
% 1.27/1.59 % (20411)------------------------------
% 1.27/1.60 % (20437)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_20274 for (2994ds/47Mi)
% 1.27/1.60 % (20436)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_20274 for (2994ds/1087Mi)
% 1.27/1.61 % (20438)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_20274 for (2994ds/44Mi)
% 1.27/1.61 % (20439)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_20274 for (2994ds/432Mi)
% 1.27/1.61 % (20433)Instruction limit reached!
% 1.27/1.61 % (20433)------------------------------
% 1.27/1.61 % (20433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.61 % (20433)Termination reason: Unknown
% 1.27/1.61 % (20433)Termination phase: Saturation
% 1.27/1.61
% 1.27/1.61 % (20433)Memory used [KB]: 6012
% 1.27/1.61 % (20433)Time elapsed: 0.060 s
% 1.27/1.61 % (20433)Instructions burned: 151 (million)
% 1.27/1.61 % (20433)------------------------------
% 1.27/1.61 % (20433)------------------------------
% 1.27/1.62 % (20440)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_20274 for (2994ds/62Mi)
% 1.27/1.62 % (20437)Instruction limit reached!
% 1.27/1.62 % (20437)------------------------------
% 1.27/1.62 % (20437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.62 % (20437)Termination reason: Unknown
% 1.27/1.62 % (20437)Termination phase: Saturation
% 1.27/1.62
% 1.27/1.62 % (20437)Memory used [KB]: 5628
% 1.27/1.62 % (20437)Time elapsed: 0.025 s
% 1.27/1.62 % (20437)Instructions burned: 47 (million)
% 1.27/1.62 % (20437)------------------------------
% 1.27/1.62 % (20437)------------------------------
% 1.27/1.63 % (20438)Instruction limit reached!
% 1.27/1.63 % (20438)------------------------------
% 1.27/1.63 % (20438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.63 % (20438)Termination reason: Unknown
% 1.27/1.63 % (20438)Termination phase: Saturation
% 1.27/1.63
% 1.27/1.63 % (20438)Memory used [KB]: 1151
% 1.27/1.63 % (20438)Time elapsed: 0.024 s
% 1.27/1.63 % (20438)Instructions burned: 45 (million)
% 1.27/1.63 % (20438)------------------------------
% 1.27/1.63 % (20438)------------------------------
% 1.27/1.64 % (20441)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_20274 for (2994ds/31Mi)
% 1.27/1.64 % (20436)Refutation not found, incomplete strategy
% 1.27/1.64 % (20436)------------------------------
% 1.27/1.64 % (20436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.64 % (20436)Termination reason: Refutation not found, incomplete strategy
% 1.27/1.64
% 1.27/1.64
% 1.27/1.64 % (20436)Memory used [KB]: 5756
% 1.27/1.64 % (20436)Time elapsed: 0.043 s
% 1.27/1.64 % (20436)Instructions burned: 76 (million)
% 1.27/1.64 % (20436)------------------------------
% 1.27/1.64 % (20436)------------------------------
% 1.27/1.64 % (20440)Instruction limit reached!
% 1.27/1.64 % (20440)------------------------------
% 1.27/1.64 % (20440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.64 % (20440)Termination reason: Unknown
% 1.27/1.64 % (20440)Termination phase: Saturation
% 1.27/1.64
% 1.27/1.64 % (20440)Memory used [KB]: 5884
% 1.27/1.64 % (20440)Time elapsed: 0.020 s
% 1.27/1.64 % (20440)Instructions burned: 65 (million)
% 1.27/1.64 % (20440)------------------------------
% 1.27/1.64 % (20440)------------------------------
% 1.27/1.65 % (20442)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_20274 for (2994ds/96Mi)
% 1.27/1.65 % (20418)Instruction limit reached!
% 1.27/1.65 % (20418)------------------------------
% 1.27/1.65 % (20418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.65 % (20418)Termination reason: Unknown
% 1.27/1.65 % (20418)Termination phase: Saturation
% 1.27/1.65
% 1.27/1.65 % (20418)Memory used [KB]: 7164
% 1.27/1.65 % (20418)Time elapsed: 0.456 s
% 1.27/1.65 % (20418)Instructions burned: 879 (million)
% 1.27/1.65 % (20418)------------------------------
% 1.27/1.65 % (20418)------------------------------
% 1.27/1.65 % (20443)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_20274 for (2994ds/453Mi)
% 1.27/1.66 % (20441)Instruction limit reached!
% 1.27/1.66 % (20441)------------------------------
% 1.27/1.66 % (20441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.66 % (20441)Termination reason: Unknown
% 1.27/1.66 % (20441)Termination phase: Saturation
% 1.27/1.66
% 1.27/1.66 % (20441)Memory used [KB]: 5628
% 1.27/1.66 % (20441)Time elapsed: 0.018 s
% 1.27/1.66 % (20441)Instructions burned: 32 (million)
% 1.27/1.66 % (20441)------------------------------
% 1.27/1.66 % (20441)------------------------------
% 1.27/1.67 % (20445)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_20274 for (2994ds/83Mi)
% 1.27/1.67 % (20444)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_20274 for (2994ds/71Mi)
% 1.27/1.68 % (20446)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_20274 for (2994ds/11Mi)
% 1.27/1.68 % (20446)Instruction limit reached!
% 1.27/1.68 % (20446)------------------------------
% 1.27/1.68 % (20446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.68 % (20446)Termination reason: Unknown
% 1.27/1.68 % (20446)Termination phase: Saturation
% 1.27/1.68
% 1.27/1.68 % (20446)Memory used [KB]: 5500
% 1.27/1.68 % (20446)Time elapsed: 0.008 s
% 1.27/1.68 % (20446)Instructions burned: 12 (million)
% 1.27/1.68 % (20446)------------------------------
% 1.27/1.68 % (20446)------------------------------
% 1.27/1.69 % (20442)Instruction limit reached!
% 1.27/1.69 % (20442)------------------------------
% 1.27/1.69 % (20442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.69 % (20442)Termination reason: Unknown
% 1.27/1.69 % (20442)Termination phase: Saturation
% 1.27/1.69
% 1.27/1.69 % (20442)Memory used [KB]: 5756
% 1.27/1.69 % (20442)Time elapsed: 0.048 s
% 1.27/1.69 % (20442)Instructions burned: 96 (million)
% 1.27/1.69 % (20442)------------------------------
% 1.27/1.69 % (20442)------------------------------
% 1.27/1.70 % (20447)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_20274 for (2993ds/41Mi)
% 1.27/1.70 % (20444)Instruction limit reached!
% 1.27/1.70 % (20444)------------------------------
% 1.27/1.70 % (20444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.70 % (20444)Termination reason: Unknown
% 1.27/1.70 % (20444)Termination phase: Saturation
% 1.27/1.70
% 1.27/1.70 % (20444)Memory used [KB]: 5756
% 1.27/1.70 % (20444)Time elapsed: 0.037 s
% 1.27/1.70 % (20444)Instructions burned: 73 (million)
% 1.27/1.70 % (20444)------------------------------
% 1.27/1.70 % (20444)------------------------------
% 1.27/1.71 % (20445)Instruction limit reached!
% 1.27/1.71 % (20445)------------------------------
% 1.27/1.71 % (20445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.71 % (20445)Termination reason: Unknown
% 1.27/1.71 % (20445)Termination phase: Saturation
% 1.27/1.71
% 1.27/1.71 % (20445)Memory used [KB]: 5884
% 1.27/1.71 % (20445)Time elapsed: 0.044 s
% 1.27/1.71 % (20445)Instructions burned: 83 (million)
% 1.27/1.71 % (20445)------------------------------
% 1.27/1.71 % (20445)------------------------------
% 1.27/1.71 % (20448)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20274 for (2993ds/6Mi)
% 1.27/1.71 % (20448)Instruction limit reached!
% 1.27/1.71 % (20448)------------------------------
% 1.27/1.71 % (20448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.71 % (20448)Termination reason: Unknown
% 1.27/1.71 % (20448)Termination phase: Saturation
% 1.27/1.71
% 1.27/1.71 % (20448)Memory used [KB]: 5500
% 1.27/1.71 % (20448)Time elapsed: 0.004 s
% 1.27/1.71 % (20448)Instructions burned: 6 (million)
% 1.27/1.71 % (20448)------------------------------
% 1.27/1.71 % (20448)------------------------------
% 1.27/1.72 % (20447)Instruction limit reached!
% 1.27/1.72 % (20447)------------------------------
% 1.27/1.72 % (20447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.72 % (20447)Termination reason: Unknown
% 1.27/1.72 % (20447)Termination phase: Saturation
% 1.27/1.72
% 1.27/1.72 % (20447)Memory used [KB]: 5628
% 1.27/1.72 % (20447)Time elapsed: 0.023 s
% 1.27/1.72 % (20447)Instructions burned: 42 (million)
% 1.27/1.72 % (20447)------------------------------
% 1.27/1.72 % (20447)------------------------------
% 1.27/1.72 % (20449)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_20274 for (2993ds/150Mi)
% 1.27/1.72 % (20450)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_20274 for (2993ds/343Mi)
% 1.27/1.73 % (20451)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_20274 for (2993ds/109Mi)
% 1.27/1.74 % (20452)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_20274 for (2993ds/253Mi)
% 1.27/1.75 % (20443)Refutation not found, incomplete strategy
% 1.27/1.75 % (20443)------------------------------
% 1.27/1.75 % (20443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.75 % (20443)Termination reason: Refutation not found, incomplete strategy
% 1.27/1.75
% 1.27/1.75
% 1.27/1.75 % (20443)Memory used [KB]: 6012
% 1.27/1.75 % (20443)Time elapsed: 0.104 s
% 1.27/1.75 % (20443)Instructions burned: 251 (million)
% 1.27/1.75 % (20443)------------------------------
% 1.27/1.75 % (20443)------------------------------
% 1.27/1.76 % (20432)Instruction limit reached!
% 1.27/1.76 % (20432)------------------------------
% 1.27/1.76 % (20432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.76 % (20432)Termination reason: Unknown
% 1.27/1.76 % (20432)Termination phase: Saturation
% 1.27/1.76
% 1.27/1.76 % (20432)Memory used [KB]: 6524
% 1.27/1.76 % (20432)Time elapsed: 0.252 s
% 1.27/1.76 % (20432)Instructions burned: 508 (million)
% 1.27/1.76 % (20432)------------------------------
% 1.27/1.76 % (20432)------------------------------
% 1.27/1.76 % (20439)Instruction limit reached!
% 1.27/1.76 % (20439)------------------------------
% 1.27/1.76 % (20439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.76 % (20439)Termination reason: Unknown
% 1.27/1.76 % (20439)Termination phase: Saturation
% 1.27/1.76
% 1.27/1.76 % (20439)Memory used [KB]: 2942
% 1.27/1.76 % (20439)Time elapsed: 0.157 s
% 1.27/1.76 % (20439)Instructions burned: 433 (million)
% 1.27/1.76 % (20439)------------------------------
% 1.27/1.76 % (20439)------------------------------
% 1.27/1.77 % (20453)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_20274 for (2993ds/140Mi)
% 1.27/1.77 % (20454)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_20274 for (2993ds/614Mi)
% 1.27/1.77 % (20455)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_20274 for (2993ds/202Mi)
% 1.27/1.78 % (20451)Instruction limit reached!
% 1.27/1.78 % (20451)------------------------------
% 1.27/1.78 % (20451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.78 % (20451)Termination reason: Unknown
% 1.27/1.78 % (20451)Termination phase: Saturation
% 1.27/1.78
% 1.27/1.78 % (20451)Memory used [KB]: 5756
% 1.27/1.78 % (20451)Time elapsed: 0.055 s
% 1.27/1.78 % (20451)Instructions burned: 110 (million)
% 1.27/1.78 % (20451)------------------------------
% 1.27/1.78 % (20451)------------------------------
% 1.27/1.79 % (20449)Instruction limit reached!
% 1.27/1.79 % (20449)------------------------------
% 1.27/1.79 % (20449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.79 % (20449)Termination reason: Unknown
% 1.27/1.79 % (20449)Termination phase: Saturation
% 1.27/1.79
% 1.27/1.79 % (20449)Memory used [KB]: 6012
% 1.27/1.79 % (20449)Time elapsed: 0.074 s
% 1.27/1.79 % (20449)Instructions burned: 150 (million)
% 1.27/1.79 % (20449)------------------------------
% 1.27/1.79 % (20449)------------------------------
% 1.27/1.80 % (20456)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_20274 for (2992ds/339Mi)
% 1.27/1.81 % (20457)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_20274 for (2992ds/283Mi)
% 1.27/1.84 % (20455)Instruction limit reached!
% 1.27/1.84 % (20455)------------------------------
% 1.27/1.84 % (20455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.84 % (20455)Termination reason: Unknown
% 1.27/1.84 % (20455)Termination phase: Saturation
% 1.27/1.84
% 1.27/1.84 % (20455)Memory used [KB]: 6140
% 1.27/1.84 % (20455)Time elapsed: 0.064 s
% 1.27/1.84 % (20455)Instructions burned: 203 (million)
% 1.27/1.84 % (20455)------------------------------
% 1.27/1.84 % (20455)------------------------------
% 1.27/1.84 % (20453)Instruction limit reached!
% 1.27/1.84 % (20453)------------------------------
% 1.27/1.84 % (20453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.84 % (20453)Termination reason: Unknown
% 1.27/1.84 % (20453)Termination phase: Saturation
% 1.27/1.84
% 1.27/1.84 % (20453)Memory used [KB]: 6012
% 1.27/1.84 % (20453)Time elapsed: 0.073 s
% 1.27/1.84 % (20453)Instructions burned: 140 (million)
% 1.27/1.84 % (20453)------------------------------
% 1.27/1.84 % (20453)------------------------------
% 1.27/1.85 % (20458)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_20274 for (2992ds/134Mi)
% 1.27/1.86 % (20459)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_20274 for (2992ds/298Mi)
% 1.27/1.87 % (20452)Instruction limit reached!
% 1.27/1.87 % (20452)------------------------------
% 1.27/1.87 % (20452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.87 % (20452)Termination reason: Unknown
% 1.27/1.87 % (20452)Termination phase: Saturation
% 1.27/1.87
% 1.27/1.87 % (20452)Memory used [KB]: 6268
% 1.27/1.87 % (20452)Time elapsed: 0.152 s
% 1.27/1.87 % (20452)Instructions burned: 254 (million)
% 1.27/1.87 % (20452)------------------------------
% 1.27/1.87 % (20452)------------------------------
% 1.27/1.89 % (20458)Instruction limit reached!
% 1.27/1.89 % (20458)------------------------------
% 1.27/1.89 % (20458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.89 % (20458)Termination reason: Unknown
% 1.27/1.89 % (20458)Termination phase: Saturation
% 1.27/1.89
% 1.27/1.89 % (20458)Memory used [KB]: 6012
% 1.27/1.89 % (20458)Time elapsed: 0.065 s
% 1.27/1.89 % (20458)Instructions burned: 134 (million)
% 1.27/1.89 % (20458)------------------------------
% 1.27/1.89 % (20458)------------------------------
% 1.27/1.89 % (20460)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_20274 for (2991ds/192Mi)
% 1.27/1.90 % (20450)Instruction limit reached!
% 1.27/1.90 % (20450)------------------------------
% 1.27/1.90 % (20450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.90 % (20450)Termination reason: Unknown
% 1.27/1.90 % (20450)Termination phase: Saturation
% 1.27/1.90
% 1.27/1.90 % (20450)Memory used [KB]: 6396
% 1.27/1.90 % (20450)Time elapsed: 0.172 s
% 1.27/1.90 % (20450)Instructions burned: 343 (million)
% 1.27/1.90 % (20450)------------------------------
% 1.27/1.90 % (20450)------------------------------
% 1.27/1.90 % (20461)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_20274 for (2991ds/258Mi)
% 1.27/1.91 % (20462)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_20274 for (2991ds/90Mi)
% 1.27/1.94 % (20457)Instruction limit reached!
% 1.27/1.94 % (20457)------------------------------
% 1.27/1.94 % (20457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.94 % (20457)Termination reason: Unknown
% 1.27/1.94 % (20457)Termination phase: Saturation
% 1.27/1.94
% 1.27/1.94 % (20457)Memory used [KB]: 6780
% 1.27/1.94 % (20457)Time elapsed: 0.156 s
% 1.27/1.94 % (20457)Instructions burned: 284 (million)
% 1.27/1.94 % (20457)------------------------------
% 1.27/1.94 % (20457)------------------------------
% 1.27/1.96 % (20462)Instruction limit reached!
% 1.27/1.96 % (20462)------------------------------
% 1.27/1.96 % (20462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.96 % (20462)Termination reason: Unknown
% 1.27/1.96 % (20462)Termination phase: Saturation
% 1.27/1.96
% 1.27/1.96 % (20462)Memory used [KB]: 5884
% 1.27/1.96 % (20462)Time elapsed: 0.047 s
% 1.27/1.96 % (20462)Instructions burned: 91 (million)
% 1.27/1.96 % (20462)------------------------------
% 1.27/1.96 % (20462)------------------------------
% 1.27/1.96 % (20463)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_20274 for (2991ds/231Mi)
% 1.27/1.97 % (20456)Instruction limit reached!
% 1.27/1.97 % (20456)------------------------------
% 1.27/1.97 % (20456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.97 % (20456)Termination reason: Unknown
% 1.27/1.97 % (20456)Termination phase: Saturation
% 1.27/1.97
% 1.27/1.97 % (20456)Memory used [KB]: 6396
% 1.27/1.97 % (20456)Time elapsed: 0.192 s
% 1.27/1.97 % (20456)Instructions burned: 340 (million)
% 1.27/1.97 % (20456)------------------------------
% 1.27/1.97 % (20456)------------------------------
% 1.27/1.98 % (20464)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_20274 for (2990ds/458Mi)
% 1.27/1.98 % (20461)Instruction limit reached!
% 1.27/1.98 % (20461)------------------------------
% 1.27/1.98 % (20461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.98 % (20461)Termination reason: Unknown
% 1.27/1.98 % (20461)Termination phase: Saturation
% 1.27/1.98
% 1.27/1.98 % (20461)Memory used [KB]: 6140
% 1.27/1.98 % (20461)Time elapsed: 0.081 s
% 1.27/1.98 % (20461)Instructions burned: 259 (million)
% 1.27/1.98 % (20461)------------------------------
% 1.27/1.98 % (20461)------------------------------
% 1.27/1.98 % (20460)Instruction limit reached!
% 1.27/1.98 % (20460)------------------------------
% 1.27/1.98 % (20460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.98 % (20460)Termination reason: Unknown
% 1.27/1.98 % (20460)Termination phase: Saturation
% 1.27/1.98
% 1.27/1.98 % (20460)Memory used [KB]: 6140
% 1.27/1.98 % (20460)Time elapsed: 0.096 s
% 1.27/1.98 % (20460)Instructions burned: 192 (million)
% 1.27/1.98 % (20460)------------------------------
% 1.27/1.98 % (20460)------------------------------
% 1.27/1.99 % (20466)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_20274 for (2990ds/297Mi)
% 1.27/1.99 % (20465)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_20274 for (2990ds/31Mi)
% 1.27/2.00 % (20467)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_20274 for (2990ds/987Mi)
% 1.27/2.01 % (20465)Instruction limit reached!
% 1.27/2.01 % (20465)------------------------------
% 1.27/2.01 % (20465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/2.01 % (20465)Termination reason: Unknown
% 1.27/2.01 % (20465)Termination phase: Saturation
% 1.27/2.01
% 1.27/2.01 % (20465)Memory used [KB]: 5628
% 1.27/2.01 % (20465)Time elapsed: 0.017 s
% 1.27/2.01 % (20465)Instructions burned: 31 (million)
% 1.27/2.01 % (20465)------------------------------
% 1.27/2.01 % (20465)------------------------------
% 1.27/2.01 % (20459)Instruction limit reached!
% 1.27/2.01 % (20459)------------------------------
% 1.27/2.01 % (20459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/2.01 % (20459)Termination reason: Unknown
% 1.27/2.01 % (20459)Termination phase: Saturation
% 1.27/2.01
% 1.27/2.01 % (20459)Memory used [KB]: 6268
% 1.27/2.01 % (20459)Time elapsed: 0.148 s
% 1.27/2.01 % (20459)Instructions burned: 298 (million)
% 1.27/2.01 % (20459)------------------------------
% 1.27/2.01 % (20459)------------------------------
% 1.27/2.02 % (20468)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_20274 for (2990ds/182Mi)
% 1.27/2.02 % (20469)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_20274 for (2990ds/182Mi)
% 7.81/2.07 % (20454)Instruction limit reached!
% 7.81/2.07 % (20454)------------------------------
% 7.81/2.07 % (20454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.07 % (20454)Termination reason: Unknown
% 7.81/2.07 % (20454)Termination phase: Saturation
% 7.81/2.07
% 7.81/2.07 % (20454)Memory used [KB]: 7164
% 7.81/2.07 % (20454)Time elapsed: 0.301 s
% 7.81/2.07 % (20454)Instructions burned: 615 (million)
% 7.81/2.07 % (20454)------------------------------
% 7.81/2.07 % (20454)------------------------------
% 7.81/2.08 % (20466)Instruction limit reached!
% 7.81/2.08 % (20466)------------------------------
% 7.81/2.08 % (20466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.08 % (20466)Termination reason: Unknown
% 7.81/2.08 % (20466)Termination phase: Saturation
% 7.81/2.08
% 7.81/2.08 % (20466)Memory used [KB]: 6524
% 7.81/2.08 % (20466)Time elapsed: 0.090 s
% 7.81/2.08 % (20466)Instructions burned: 297 (million)
% 7.81/2.08 % (20466)------------------------------
% 7.81/2.08 % (20466)------------------------------
% 7.81/2.08 % (20463)Instruction limit reached!
% 7.81/2.08 % (20463)------------------------------
% 7.81/2.08 % (20463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.08 % (20463)Termination reason: Unknown
% 7.81/2.08 % (20463)Termination phase: Saturation
% 7.81/2.08
% 7.81/2.08 % (20463)Memory used [KB]: 6652
% 7.81/2.08 % (20463)Time elapsed: 0.122 s
% 7.81/2.08 % (20463)Instructions burned: 231 (million)
% 7.81/2.08 % (20463)------------------------------
% 7.81/2.08 % (20463)------------------------------
% 7.81/2.08 % (20470)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_20274 for (2989ds/154Mi)
% 7.81/2.09 % (20471)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_20274 for (2989ds/79Mi)
% 7.81/2.10 % (20472)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_20274 for (2989ds/216Mi)
% 7.81/2.11 % (20468)Instruction limit reached!
% 7.81/2.11 % (20468)------------------------------
% 7.81/2.11 % (20468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.11 % (20468)Termination reason: Unknown
% 7.81/2.11 % (20468)Termination phase: Saturation
% 7.81/2.11
% 7.81/2.11 % (20468)Memory used [KB]: 6012
% 7.81/2.11 % (20468)Time elapsed: 0.087 s
% 7.81/2.11 % (20468)Instructions burned: 183 (million)
% 7.81/2.11 % (20468)------------------------------
% 7.81/2.11 % (20468)------------------------------
% 7.81/2.12 % (20469)Instruction limit reached!
% 7.81/2.12 % (20469)------------------------------
% 7.81/2.12 % (20469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.12 % (20469)Termination reason: Unknown
% 7.81/2.12 % (20469)Termination phase: Saturation
% 7.81/2.12
% 7.81/2.12 % (20469)Memory used [KB]: 6012
% 7.81/2.12 % (20469)Time elapsed: 0.096 s
% 7.81/2.12 % (20469)Instructions burned: 183 (million)
% 7.81/2.12 % (20469)------------------------------
% 7.81/2.12 % (20469)------------------------------
% 7.81/2.12 % (20473)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_20274 for (2989ds/114Mi)
% 8.42/2.13 % (20470)Instruction limit reached!
% 8.42/2.13 % (20470)------------------------------
% 8.42/2.13 % (20470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.13 % (20470)Termination reason: Unknown
% 8.42/2.13 % (20470)Termination phase: Saturation
% 8.42/2.13
% 8.42/2.13 % (20470)Memory used [KB]: 6012
% 8.42/2.13 % (20470)Time elapsed: 0.048 s
% 8.42/2.13 % (20470)Instructions burned: 154 (million)
% 8.42/2.13 % (20470)------------------------------
% 8.42/2.13 % (20470)------------------------------
% 8.42/2.13 % (20471)Instruction limit reached!
% 8.42/2.13 % (20471)------------------------------
% 8.42/2.13 % (20471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.13 % (20471)Termination reason: Unknown
% 8.42/2.13 % (20471)Termination phase: Saturation
% 8.42/2.13
% 8.42/2.13 % (20471)Memory used [KB]: 5884
% 8.42/2.13 % (20471)Time elapsed: 0.042 s
% 8.42/2.13 % (20471)Instructions burned: 79 (million)
% 8.42/2.13 % (20471)------------------------------
% 8.42/2.13 % (20471)------------------------------
% 8.42/2.13 % (20474)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_20274 for (2989ds/922Mi)
% 8.42/2.14 % (20475)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_20274 for (2989ds/182Mi)
% 8.42/2.15 % (20476)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_20274 for (2989ds/164Mi)
% 8.42/2.18 % (20473)Instruction limit reached!
% 8.42/2.18 % (20473)------------------------------
% 8.42/2.18 % (20473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.18 % (20473)Termination reason: Unknown
% 8.42/2.18 % (20473)Termination phase: Saturation
% 8.42/2.18
% 8.42/2.18 % (20473)Memory used [KB]: 6012
% 8.42/2.18 % (20473)Time elapsed: 0.057 s
% 8.42/2.18 % (20473)Instructions burned: 114 (million)
% 8.42/2.18 % (20473)------------------------------
% 8.42/2.18 % (20473)------------------------------
% 8.42/2.19 % (20477)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_20274 for (2988ds/50Mi)
% 8.42/2.20 % (20475)Instruction limit reached!
% 8.42/2.20 % (20475)------------------------------
% 8.42/2.20 % (20475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.20 % (20475)Termination reason: Unknown
% 8.42/2.20 % (20475)Termination phase: Saturation
% 8.42/2.20
% 8.42/2.20 % (20475)Memory used [KB]: 5884
% 8.75/2.20 % (20475)Time elapsed: 0.056 s
% 8.75/2.20 % (20475)Instructions burned: 183 (million)
% 8.75/2.20 % (20475)------------------------------
% 8.75/2.20 % (20475)------------------------------
% 8.75/2.20 % (20472)Instruction limit reached!
% 8.75/2.20 % (20472)------------------------------
% 8.75/2.20 % (20472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.20 % (20472)Termination reason: Unknown
% 8.75/2.20 % (20472)Termination phase: Saturation
% 8.75/2.20
% 8.75/2.20 % (20472)Memory used [KB]: 5756
% 8.75/2.20 % (20472)Time elapsed: 0.103 s
% 8.75/2.20 % (20472)Instructions burned: 216 (million)
% 8.75/2.20 % (20472)------------------------------
% 8.75/2.20 % (20472)------------------------------
% 8.75/2.20 % (20464)Instruction limit reached!
% 8.75/2.20 % (20464)------------------------------
% 8.75/2.20 % (20464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.20 % (20464)Termination reason: Unknown
% 8.75/2.20 % (20464)Termination phase: Saturation
% 8.75/2.20
% 8.75/2.20 % (20464)Memory used [KB]: 6524
% 8.75/2.20 % (20464)Time elapsed: 0.230 s
% 8.75/2.20 % (20464)Instructions burned: 458 (million)
% 8.75/2.20 % (20464)------------------------------
% 8.75/2.20 % (20464)------------------------------
% 8.75/2.21 % (20478)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_20274 for (2988ds/368Mi)
% 8.75/2.21 % (20479)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_20274 for (2988ds/1021Mi)
% 8.75/2.22 % (20477)Instruction limit reached!
% 8.75/2.22 % (20477)------------------------------
% 8.75/2.22 % (20477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.22 % (20477)Termination reason: Unknown
% 8.75/2.22 % (20477)Termination phase: Saturation
% 8.75/2.22
% 8.75/2.22 % (20477)Memory used [KB]: 10234
% 8.75/2.22 % (20477)Time elapsed: 0.028 s
% 8.75/2.22 % (20477)Instructions burned: 51 (million)
% 8.75/2.22 % (20477)------------------------------
% 8.75/2.22 % (20477)------------------------------
% 8.75/2.22 % (20480)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_20274 for (2988ds/267Mi)
% 8.75/2.22 % (20476)Instruction limit reached!
% 8.75/2.22 % (20476)------------------------------
% 8.75/2.22 % (20476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.22 % (20476)Termination reason: Unknown
% 8.75/2.22 % (20476)Termination phase: Saturation
% 8.75/2.22
% 8.75/2.22 % (20476)Memory used [KB]: 1407
% 8.75/2.22 % (20476)Time elapsed: 0.078 s
% 8.75/2.22 % (20476)Instructions burned: 164 (million)
% 8.75/2.22 % (20476)------------------------------
% 8.75/2.22 % (20476)------------------------------
% 8.75/2.24 % (20481)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_20274 for (2988ds/204Mi)
% 8.75/2.24 % (20482)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_20274 for (2988ds/26Mi)
% 8.75/2.25 % (20482)Instruction limit reached!
% 8.75/2.25 % (20482)------------------------------
% 8.75/2.25 % (20482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.75/2.25 % (20482)Termination reason: Unknown
% 8.75/2.25 % (20482)Termination phase: Saturation
% 8.75/2.25
% 8.75/2.25 % (20482)Memory used [KB]: 5628
% 8.75/2.25 % (20482)Time elapsed: 0.014 s
% 8.75/2.25 % (20482)Instructions burned: 26 (million)
% 8.75/2.25 % (20482)------------------------------
% 8.75/2.25 % (20482)------------------------------
% 8.75/2.27 % (20483)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_20274 for (2988ds/53Mi)
% 9.20/2.30 % (20483)Instruction limit reached!
% 9.20/2.30 % (20483)------------------------------
% 9.20/2.30 % (20483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.20/2.30 % (20483)Termination reason: Unknown
% 9.20/2.30 % (20483)Termination phase: Saturation
% 9.20/2.30
% 9.20/2.30 % (20483)Memory used [KB]: 5628
% 9.20/2.30 % (20483)Time elapsed: 0.027 s
% 9.20/2.30 % (20483)Instructions burned: 54 (million)
% 9.20/2.30 % (20483)------------------------------
% 9.20/2.30 % (20483)------------------------------
% 9.20/2.31 % (20480)First to succeed.
% 9.20/2.32 % (20484)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_20274 for (2987ds/4436Mi)
% 9.20/2.32 % (20480)Refutation found. Thanks to Tanya!
% 9.20/2.32 % SZS status Theorem for DTF2THF_20274
% 9.20/2.32 % SZS output start Proof for DTF2THF_20274
% 9.20/2.32 thf(func_def_0, type, cS: $i > $i).
% 9.20/2.32 thf(func_def_1, type, cEVEN: $i > $o).
% 9.20/2.32 thf(func_def_2, type, cODD: $i > $o).
% 9.20/2.32 thf(func_def_18, type, ph1: !>[X0: $tType]:(X0)).
% 9.20/2.32 thf(f798,plain,(
% 9.20/2.32 $false),
% 9.20/2.32 inference(avatar_sat_refutation,[status(thm)],[f539,f684,f794])).
% 9.20/2.32 thf(f794,plain,(
% 9.20/2.32 ~spl0_4),
% 9.20/2.32 inference(avatar_contradiction_clause,[status(thm)],[f793])).
% 9.20/2.32 thf(f793,plain,(
% 9.20/2.32 $false | ~spl0_4),
% 9.20/2.32 inference(trivial_inequality_removal,[status(thm)],[f792])).
% 9.20/2.32 thf(f792,plain,(
% 9.20/2.32 ($true = $false) | ~spl0_4),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f791])).
% 9.20/2.32 thf(f791,plain,(
% 9.20/2.32 (((cS @ sK6) = (cS @ sK6)) = $false) | ~spl0_4),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f786])).
% 9.20/2.32 thf(f786,plain,(
% 9.20/2.32 ($false = (((cS @ sK6) = (cS @ sK6)) & $true)) | ~spl0_4),
% 9.20/2.32 inference(superposition,[status(thm)],[f772,f722])).
% 9.20/2.32 thf(f722,plain,(
% 9.20/2.32 ((cEVEN @ sK6) = $true) | ~spl0_4),
% 9.20/2.32 inference(binary_proxy_clausification,[status(thm)],[f720])).
% 9.20/2.32 thf(f720,plain,(
% 9.20/2.32 (((cEVEN @ sK6) => (?? @ $i @ (^[Y0 : $i]: (((cS @ Y0) = (cS @ sK6)) & (cEVEN @ Y0))))) = $false) | ~spl0_4),
% 9.20/2.32 inference(beta_eta_normalization,[status(thm)],[f709])).
% 9.20/2.32 thf(f709,plain,(
% 9.20/2.32 (((^[Y0 : $i]: ((cEVEN @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = (cS @ Y0)) & (cEVEN @ Y1)))))) @ sK6) = $false) | ~spl0_4),
% 9.20/2.32 inference(sigma_clausification,[status(thm)],[f538])).
% 9.20/2.32 thf(f538,plain,(
% 9.20/2.32 ($false = (!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = (cS @ Y0)) & (cEVEN @ Y1)))))))) | ~spl0_4),
% 9.20/2.32 inference(avatar_component_clause,[status(thm)],[f536])).
% 9.20/2.32 thf(f536,definition,(
% 9.20/2.32 spl0_4 <=> ($false = (!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = (cS @ Y0)) & (cEVEN @ Y1))))))))),
% 9.20/2.32 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 9.20/2.32 thf(f772,plain,(
% 9.20/2.32 ( ! [X1 : $i] : (((((cS @ X1) = (cS @ sK6)) & (cEVEN @ X1)) = $false)) ) | ~spl0_4),
% 9.20/2.32 inference(beta_eta_normalization,[status(thm)],[f770])).
% 9.20/2.32 thf(f770,plain,(
% 9.20/2.32 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (((cS @ Y0) = (cS @ sK6)) & (cEVEN @ Y0))) @ X1))) ) | ~spl0_4),
% 9.20/2.32 inference(pi_clausification,[status(thm)],[f741])).
% 9.20/2.32 thf(f741,plain,(
% 9.20/2.32 ((?? @ $i @ (^[Y0 : $i]: (((cS @ Y0) = (cS @ sK6)) & (cEVEN @ Y0)))) = $false) | ~spl0_4),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f723])).
% 9.20/2.32 thf(f723,plain,(
% 9.20/2.32 (($true => (?? @ $i @ (^[Y0 : $i]: (((cS @ Y0) = (cS @ sK6)) & (cEVEN @ Y0))))) = $false) | ~spl0_4),
% 9.20/2.32 inference(backward_demodulation,[status(thm)],[f720,f722])).
% 9.20/2.32 thf(f684,plain,(
% 9.20/2.32 ~spl0_3),
% 9.20/2.32 inference(avatar_contradiction_clause,[status(thm)],[f683])).
% 9.20/2.32 thf(f683,plain,(
% 9.20/2.32 $false | ~spl0_3),
% 9.20/2.32 inference(trivial_inequality_removal,[status(thm)],[f682])).
% 9.20/2.32 thf(f682,plain,(
% 9.20/2.32 ($true = $false) | ~spl0_3),
% 9.20/2.32 inference(forward_demodulation,[status(thm)],[f681,f589])).
% 9.20/2.32 thf(f589,plain,(
% 9.20/2.32 ($false = (cODD @ sK4)) | ~spl0_3),
% 9.20/2.32 inference(not_proxy_clausification,[status(thm)],[f583])).
% 9.20/2.32 thf(f583,plain,(
% 9.20/2.32 ($true = (~ (cODD @ sK4))) | ~spl0_3),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f579])).
% 9.20/2.32 thf(f579,plain,(
% 9.20/2.32 ($true = ((cODD @ sK4) => $false)) | ~spl0_3),
% 9.20/2.32 inference(superposition,[status(thm)],[f83,f576])).
% 9.20/2.32 thf(f576,plain,(
% 9.20/2.32 ((cEVEN @ (cS @ sK4)) = $false) | ~spl0_3),
% 9.20/2.32 inference(binary_proxy_clausification,[status(thm)],[f552])).
% 9.20/2.32 thf(f552,plain,(
% 9.20/2.32 ($false = ((?? @ $i @ (^[Y0 : $i]: (((cS @ Y0) = sK4) & (cEVEN @ Y0)))) => (cEVEN @ (cS @ sK4)))) | ~spl0_3),
% 9.20/2.32 inference(beta_eta_normalization,[status(thm)],[f545])).
% 9.20/2.32 thf(f545,plain,(
% 9.20/2.32 ($false = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1)))) => (cEVEN @ (cS @ Y0)))) @ sK4)) | ~spl0_3),
% 9.20/2.32 inference(sigma_clausification,[status(thm)],[f534])).
% 9.20/2.32 thf(f534,plain,(
% 9.20/2.32 ($false = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1)))) => (cEVEN @ (cS @ Y0)))))) | ~spl0_3),
% 9.20/2.32 inference(avatar_component_clause,[status(thm)],[f532])).
% 9.20/2.32 thf(f532,definition,(
% 9.20/2.32 spl0_3 <=> ($false = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1)))) => (cEVEN @ (cS @ Y0))))))),
% 9.20/2.32 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 9.20/2.32 thf(f83,plain,(
% 9.20/2.32 ( ! [X1 : $i] : (($true = ((cODD @ X1) => (cEVEN @ (cS @ X1))))) )),
% 9.20/2.32 inference(beta_eta_normalization,[status(thm)],[f72])).
% 9.20/2.32 thf(f72,plain,(
% 9.20/2.32 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((cODD @ Y0) => (cEVEN @ (cS @ Y0)))) @ X1))) )),
% 9.20/2.32 inference(pi_clausification,[status(thm)],[f66])).
% 9.20/2.32 thf(f66,plain,(
% 9.20/2.32 ($true = (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (cEVEN @ (cS @ Y0))))))),
% 9.20/2.32 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 9.20/2.32 thf(f34,plain,(
% 9.20/2.32 ($true = ((!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (cODD @ (cS @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (cEVEN @ (cS @ Y0)))))))),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f32])).
% 9.20/2.32 thf(f32,plain,(
% 9.20/2.32 ($true = (((!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (cODD @ (cS @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (cEVEN @ (cS @ Y0)))))) & $true))),
% 9.20/2.32 inference(backward_demodulation,[status(thm)],[f23,f29])).
% 9.20/2.32 thf(f29,plain,(
% 9.20/2.32 ((cEVEN @ c0) = $true)),
% 9.20/2.32 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 9.20/2.32 thf(f23,plain,(
% 9.20/2.32 ($true = (((!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (cODD @ (cS @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (cEVEN @ (cS @ Y0)))))) & (cEVEN @ c0)))),
% 9.20/2.32 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 9.20/2.32 thf(f18,plain,(
% 9.20/2.32 (((((!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (cODD @ (cS @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (cEVEN @ (cS @ Y0)))))) & (cEVEN @ c0)) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ (cS @ Y2))))) & (Y0 @ c0)) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ (cS @ Y2)))))) => ((!! @ $i @ (^[Y2 : $i]: ((cEVEN @ Y2) => (Y0 @ Y2)))) & (!! @ $i @ (^[Y2 : $i]: ((cODD @ Y2) => (Y1 @ Y2))))))))))) = $true)),
% 9.20/2.32 inference(not_proxy_clausification,[status(thm)],[f15])).
% 9.20/2.32 thf(f15,plain,(
% 9.20/2.32 ($false = (~ ((((!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (cODD @ (cS @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (cEVEN @ (cS @ Y0)))))) & (cEVEN @ c0)) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ (cS @ Y2))))) & (Y0 @ c0)) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ (cS @ Y2)))))) => ((!! @ $i @ (^[Y2 : $i]: ((cEVEN @ Y2) => (Y0 @ Y2)))) & (!! @ $i @ (^[Y2 : $i]: ((cODD @ Y2) => (Y1 @ Y2)))))))))))))),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f12])).
% 9.20/2.32 thf(f12,plain,(
% 9.20/2.32 ((((((!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (cODD @ (cS @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (cEVEN @ (cS @ Y0)))))) & (cEVEN @ c0)) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ (cS @ Y2))))) & (Y0 @ c0)) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ (cS @ Y2)))))) => ((!! @ $i @ (^[Y2 : $i]: ((cEVEN @ Y2) => (Y0 @ Y2)))) & (!! @ $i @ (^[Y2 : $i]: ((cODD @ Y2) => (Y1 @ Y2))))))))))) => $false) = $false)),
% 9.20/2.32 inference(backward_demodulation,[status(thm)],[f7,f9])).
% 9.20/2.32 thf(f9,plain,(
% 9.20/2.32 ($false = (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1))))))))),
% 9.20/2.32 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 9.20/2.32 thf(f7,plain,(
% 9.20/2.32 ((((((!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (cODD @ (cS @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (cEVEN @ (cS @ Y0)))))) & (cEVEN @ c0)) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ (cS @ Y2))))) & (Y0 @ c0)) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ (cS @ Y2)))))) => ((!! @ $i @ (^[Y2 : $i]: ((cEVEN @ Y2) => (Y0 @ Y2)))) & (!! @ $i @ (^[Y2 : $i]: ((cODD @ Y2) => (Y1 @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1)))))))) = $false)),
% 9.20/2.32 inference(not_proxy_clausification,[status(thm)],[f6])).
% 9.20/2.32 thf(f6,plain,(
% 9.20/2.32 ($true = (~ (((((!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (cODD @ (cS @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (cEVEN @ (cS @ Y0)))))) & (cEVEN @ c0)) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ (cS @ Y2))))) & (Y0 @ c0)) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ (cS @ Y2)))))) => ((!! @ $i @ (^[Y2 : $i]: ((cEVEN @ Y2) => (Y0 @ Y2)))) & (!! @ $i @ (^[Y2 : $i]: ((cODD @ Y2) => (Y1 @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1))))))))))),
% 9.20/2.32 inference(cnf_transformation,[status(thm)],[f5])).
% 9.20/2.32 thf(f5,plain,(
% 9.20/2.32 ($true = (~ (((((!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (cODD @ (cS @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (cEVEN @ (cS @ Y0)))))) & (cEVEN @ c0)) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ (cS @ Y2))))) & (Y0 @ c0)) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ (cS @ Y2)))))) => ((!! @ $i @ (^[Y2 : $i]: ((cEVEN @ Y2) => (Y0 @ Y2)))) & (!! @ $i @ (^[Y2 : $i]: ((cODD @ Y2) => (Y1 @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1))))))))))),
% 9.20/2.32 inference(fool_elimination,[status(thm)],[f4])).
% 9.20/2.32 thf(f4,plain,(
% 9.20/2.32 ~((! [X0 : $i > $o,X1 : $i > $o] : ((! [X2 : $i] : ((X1 @ X2) => (X0 @ (cS @ X2))) & (X1 @ c0) & ! [X3 : $i] : ((X0 @ X3) => (X1 @ (cS @ X3)))) => (! [X4 : $i] : ((cODD @ X4) => (X0 @ X4)) & ! [X5 : $i] : ((cEVEN @ X5) => (X1 @ X5)))) & (cEVEN @ c0) & ! [X6 : $i] : ((cODD @ X6) => (cEVEN @ (cS @ X6))) & ! [X7 : $i] : ((cEVEN @ X7) => (cODD @ (cS @ X7)))) => ! [X8 : $i] : ((cODD @ X8) => ? [X9 : $i] : ((cEVEN @ X9) & ((cS @ X9) = X8))))),
% 9.20/2.32 inference(rectify,[status(thm)],[f2])).
% 9.20/2.32 thf(f2,negated_conjecture,(
% 9.20/2.32 ~((! [X3 : $i > $o,X2 : $i > $o] : ((! [X4 : $i] : ((X2 @ X4) => (X3 @ (cS @ X4))) & (X2 @ c0) & ! [X5 : $i] : ((X3 @ X5) => (X2 @ (cS @ X5)))) => (! [X0 : $i] : ((cODD @ X0) => (X3 @ X0)) & ! [X0 : $i] : ((cEVEN @ X0) => (X2 @ X0)))) & (cEVEN @ c0) & ! [X1 : $i] : ((cODD @ X1) => (cEVEN @ (cS @ X1))) & ! [X0 : $i] : ((cEVEN @ X0) => (cODD @ (cS @ X0)))) => ! [X6 : $i] : ((cODD @ X6) => ? [X7 : $i] : ((cEVEN @ X7) & ((cS @ X7) = X6))))),
% 9.20/2.32 inference(negated_conjecture,[status(cth)],[f1])).
% 9.20/2.32 thf(f1,conjecture,(
% 9.20/2.32 (! [X3 : $i > $o,X2 : $i > $o] : ((! [X4 : $i] : ((X2 @ X4) => (X3 @ (cS @ X4))) & (X2 @ c0) & ! [X5 : $i] : ((X3 @ X5) => (X2 @ (cS @ X5)))) => (! [X0 : $i] : ((cODD @ X0) => (X3 @ X0)) & ! [X0 : $i] : ((cEVEN @ X0) => (X2 @ X0)))) & (cEVEN @ c0) & ! [X1 : $i] : ((cODD @ X1) => (cEVEN @ (cS @ X1))) & ! [X0 : $i] : ((cEVEN @ X0) => (cODD @ (cS @ X0)))) => ! [X6 : $i] : ((cODD @ X6) => ? [X7 : $i] : ((cEVEN @ X7) & ((cS @ X7) = X6)))),
% 9.20/2.32 file('/export/starexec/sandbox/tmp/tmp.oV3DFLKGde/DTF2THF_20274.p',cTHM624_pme)).
% 9.20/2.32 thf(f681,plain,(
% 9.20/2.32 ($true = (cODD @ sK4)) | ~spl0_3),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f680])).
% 9.20/2.32 thf(f680,plain,(
% 9.20/2.32 ($true = ($true => (cODD @ sK4))) | ~spl0_3),
% 9.20/2.32 inference(forward_demodulation,[status(thm)],[f670,f616])).
% 9.20/2.32 thf(f616,plain,(
% 9.20/2.32 ($true = (cEVEN @ sK5)) | ~spl0_3),
% 9.20/2.32 inference(binary_proxy_clausification,[status(thm)],[f592])).
% 9.20/2.32 thf(f592,plain,(
% 9.20/2.32 ($true = (((cS @ sK5) = sK4) & (cEVEN @ sK5))) | ~spl0_3),
% 9.20/2.32 inference(beta_eta_normalization,[status(thm)],[f591])).
% 9.20/2.32 thf(f591,plain,(
% 9.20/2.32 ($true = ((^[Y0 : $i]: (((cS @ Y0) = sK4) & (cEVEN @ Y0))) @ sK5)) | ~spl0_3),
% 9.20/2.32 inference(sigma_clausification,[status(thm)],[f588])).
% 9.20/2.32 thf(f588,plain,(
% 9.20/2.32 ($true = (?? @ $i @ (^[Y0 : $i]: (((cS @ Y0) = sK4) & (cEVEN @ Y0))))) | ~spl0_3),
% 9.20/2.32 inference(not_proxy_clausification,[status(thm)],[f584])).
% 9.20/2.32 thf(f584,plain,(
% 9.20/2.32 ($false = (~ (?? @ $i @ (^[Y0 : $i]: (((cS @ Y0) = sK4) & (cEVEN @ Y0)))))) | ~spl0_3),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f578])).
% 9.20/2.32 thf(f578,plain,(
% 9.20/2.32 (((?? @ $i @ (^[Y0 : $i]: (((cS @ Y0) = sK4) & (cEVEN @ Y0)))) => $false) = $false) | ~spl0_3),
% 9.20/2.32 inference(backward_demodulation,[status(thm)],[f552,f576])).
% 9.20/2.32 thf(f670,plain,(
% 9.20/2.32 ($true = ((cEVEN @ sK5) => (cODD @ sK4))) | ~spl0_3),
% 9.20/2.32 inference(superposition,[status(thm)],[f97,f665])).
% 9.20/2.32 thf(f665,plain,(
% 9.20/2.32 (sK4 = (cS @ sK5)) | ~spl0_3),
% 9.20/2.32 inference(equality_proxy_clausification,[status(thm)],[f626])).
% 9.20/2.32 thf(f626,plain,(
% 9.20/2.32 ($true = ((cS @ sK5) = sK4)) | ~spl0_3),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f618])).
% 9.20/2.32 thf(f618,plain,(
% 9.20/2.32 ($true = (((cS @ sK5) = sK4) & $true)) | ~spl0_3),
% 9.20/2.32 inference(backward_demodulation,[status(thm)],[f592,f616])).
% 9.20/2.32 thf(f97,plain,(
% 9.20/2.32 ( ! [X1 : $i] : (($true = ((cEVEN @ X1) => (cODD @ (cS @ X1))))) )),
% 9.20/2.32 inference(beta_eta_normalization,[status(thm)],[f89])).
% 9.20/2.32 thf(f89,plain,(
% 9.20/2.32 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((cEVEN @ Y0) => (cODD @ (cS @ Y0)))) @ X1) = $true)) )),
% 9.20/2.32 inference(pi_clausification,[status(thm)],[f86])).
% 9.20/2.32 thf(f86,plain,(
% 9.20/2.32 ($true = (!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (cODD @ (cS @ Y0))))))),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f71])).
% 9.20/2.32 thf(f71,plain,(
% 9.20/2.32 ($true = ((!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (cODD @ (cS @ Y0))))) & $true))),
% 9.20/2.32 inference(backward_demodulation,[status(thm)],[f34,f66])).
% 9.20/2.32 thf(f539,plain,(
% 9.20/2.32 spl0_3 | spl0_4),
% 9.20/2.32 inference(avatar_split_clause,[status(thm)],[f527,f536,f532])).
% 9.20/2.32 thf(f527,plain,(
% 9.20/2.32 ($false = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1)))) => (cEVEN @ (cS @ Y0)))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = (cS @ Y0)) & (cEVEN @ Y1))))))))),
% 9.20/2.32 inference(binary_proxy_clausification,[status(thm)],[f259])).
% 9.20/2.32 thf(f259,plain,(
% 9.20/2.32 ($false = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1)))) => (cEVEN @ (cS @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = (cS @ Y0)) & (cEVEN @ Y1)))))))))),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f258])).
% 9.20/2.32 thf(f258,plain,(
% 9.20/2.32 ($false = (((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1)))) => (cEVEN @ (cS @ Y0))))) & $true) & (!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = (cS @ Y0)) & (cEVEN @ Y1)))))))))),
% 9.20/2.32 inference(beta_eta_normalization,[status(thm)],[f253])).
% 9.20/2.32 thf(f253,plain,(
% 9.20/2.32 ((((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1)))) => ((^[Y1 : $i]: (cEVEN @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ (cS @ Y0))))) & $true) & (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (cEVEN @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = (cS @ Y0)) & (cEVEN @ Y1)))))))) = $false)),
% 9.20/2.32 inference(superposition,[status(thm)],[f199,f29])).
% 9.20/2.32 thf(f199,plain,(
% 9.20/2.32 ( ! [X0 : $i > $o] : (($false = (((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1)))) => (X0 @ (cS @ Y0))))) & (X0 @ c0)) & (!! @ $i @ (^[Y0 : $i]: ((X0 @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = (cS @ Y0)) & (cEVEN @ Y1)))))))))) )),
% 9.20/2.32 inference(not_proxy_clausification,[status(thm)],[f52])).
% 9.20/2.32 thf(f52,plain,(
% 9.20/2.32 ( ! [X0 : $i > $o] : (($true = (~ (((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1)))) => (X0 @ (cS @ Y0))))) & (X0 @ c0)) & (!! @ $i @ (^[Y0 : $i]: ((X0 @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = (cS @ Y0)) & (cEVEN @ Y1))))))))))) )),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f51])).
% 9.20/2.32 thf(f51,plain,(
% 9.20/2.32 ( ! [X0 : $i > $o] : (($true = ((((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1)))) => (X0 @ (cS @ Y0))))) & (X0 @ c0)) & (!! @ $i @ (^[Y0 : $i]: ((X0 @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = (cS @ Y0)) & (cEVEN @ Y1)))))))) => $false))) )),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f50])).
% 9.20/2.32 thf(f50,plain,(
% 9.20/2.32 ( ! [X0 : $i > $o] : (($true = ((((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = Y0) & (cEVEN @ Y1)))) => (X0 @ (cS @ Y0))))) & (X0 @ c0)) & (!! @ $i @ (^[Y0 : $i]: ((X0 @ Y0) => (?? @ $i @ (^[Y1 : $i]: (((cS @ Y1) = (cS @ Y0)) & (cEVEN @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (X0 @ Y0)))) & $false)))) )),
% 9.20/2.32 inference(beta_eta_normalization,[status(thm)],[f44])).
% 9.20/2.32 thf(f44,plain,(
% 9.20/2.32 ( ! [X0 : $i > $o] : (($true = ((((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((cS @ Y2) = Y1) & (cEVEN @ Y2))))) @ Y0) => (X0 @ (cS @ Y0))))) & (X0 @ c0)) & (!! @ $i @ (^[Y0 : $i]: ((X0 @ Y0) => ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((cS @ Y2) = Y1) & (cEVEN @ Y2))))) @ (cS @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (X0 @ Y0)))) & $false)))) )),
% 9.20/2.32 inference(superposition,[status(thm)],[f42,f9])).
% 9.20/2.32 thf(f42,plain,(
% 9.20/2.32 ( ! [X2 : $i > $o,X1 : $i > $o] : (($true = ((((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) => (X1 @ (cS @ Y0))))) & (X1 @ c0)) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X2 @ (cS @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: ((cEVEN @ Y0) => (X1 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((cODD @ Y0) => (X2 @ Y0)))))))) )),
% 9.20/2.32 inference(beta_eta_normalization,[status(thm)],[f41])).
% 9.20/2.32 thf(f41,plain,(
% 9.20/2.32 ( ! [X2 : $i > $o,X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: ((((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (X1 @ (cS @ Y1))))) & (X1 @ c0)) & (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) => (Y0 @ (cS @ Y1)))))) => ((!! @ $i @ (^[Y1 : $i]: ((cEVEN @ Y1) => (X1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: ((cODD @ Y1) => (Y0 @ Y1))))))) @ X2))) )),
% 9.20/2.32 inference(pi_clausification,[status(thm)],[f37])).
% 9.20/2.32 thf(f37,plain,(
% 9.20/2.32 ( ! [X1 : $i > $o] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (X1 @ (cS @ Y1))))) & (X1 @ c0)) & (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) => (Y0 @ (cS @ Y1)))))) => ((!! @ $i @ (^[Y1 : $i]: ((cEVEN @ Y1) => (X1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: ((cODD @ Y1) => (Y0 @ Y1)))))))))) )),
% 9.20/2.32 inference(beta_eta_normalization,[status(thm)],[f36])).
% 9.20/2.32 thf(f36,plain,(
% 9.20/2.32 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ (cS @ Y2))))) & (Y0 @ c0)) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ (cS @ Y2)))))) => ((!! @ $i @ (^[Y2 : $i]: ((cEVEN @ Y2) => (Y0 @ Y2)))) & (!! @ $i @ (^[Y2 : $i]: ((cODD @ Y2) => (Y1 @ Y2))))))))) @ X1))) )),
% 9.20/2.32 inference(pi_clausification,[status(thm)],[f31])).
% 9.20/2.32 thf(f31,plain,(
% 9.20/2.32 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ (cS @ Y2))))) & (Y0 @ c0)) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ (cS @ Y2)))))) => ((!! @ $i @ (^[Y2 : $i]: ((cEVEN @ Y2) => (Y0 @ Y2)))) & (!! @ $i @ (^[Y2 : $i]: ((cODD @ Y2) => (Y1 @ Y2)))))))))))),
% 9.20/2.32 inference(boolean_simplification,[status(thm)],[f28])).
% 9.20/2.32 thf(f28,plain,(
% 9.20/2.32 ($true = ($true & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ (cS @ Y2))))) & (Y0 @ c0)) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ (cS @ Y2)))))) => ((!! @ $i @ (^[Y2 : $i]: ((cEVEN @ Y2) => (Y0 @ Y2)))) & (!! @ $i @ (^[Y2 : $i]: ((cODD @ Y2) => (Y1 @ Y2))))))))))))),
% 9.20/2.32 inference(backward_demodulation,[status(thm)],[f18,f23])).
% 9.20/2.32 % SZS output end Proof for DTF2THF_20274
% 9.20/2.32 % (20480)------------------------------
% 9.20/2.32 % (20480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.20/2.32 % (20480)Termination reason: Refutation
% 9.20/2.32
% 9.20/2.32 % (20480)Memory used [KB]: 6268
% 9.20/2.32 % (20480)Time elapsed: 0.096 s
% 9.20/2.32 % (20480)Instructions burned: 184 (million)
% 9.20/2.32 % (20480)------------------------------
% 9.20/2.32 % (20480)------------------------------
% 9.20/2.32 % (20388)Success in time 1.252 s
%------------------------------------------------------------------------------