%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV291^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 09:40:45 AM UTC 2026
% Result : Theorem 1.69s 1.71s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 383 ( 89 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 1067 ( 78 ~; 0 |; 119 &; 671 @)
% ( 0 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 468 ( 468 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 7 usr; 4 con; 0-2 aty)
% ( 50 !!; 76 ??; 0 @@+; 0 @@-)
% Number of variables : 321 ( 292 ^; 22 !; 7 ?; 321 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
r: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(func_def_1,type,
cNAT: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_2,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(func_def_3,type,
cZERO: ( $i > $o ) > $o ).
thf(func_def_18,type,
ph0:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
sK1: ( $i > $o ) > $o ).
thf(func_def_26,type,
sK2: ( $i > $o ) > $o ).
thf(f143,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f141]) ).
thf(f141,plain,
$false = $true,
inference(superposition,[status(thm)],[f137,f107]) ).
thf(f107,plain,
! [X2: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( r @ X1 @ X2 )
=> ( r
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( X1
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) )
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( X2
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f106]) ).
thf(f106,plain,
! [X2: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( r @ X1 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( X1
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X1: ( $i > $o ) > $o] :
( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( r @ X1 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( X1
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
! [X1: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y1 )
=> ( r
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y0
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) )
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y1 )
=> ( r
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y0
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) )
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y1 )
=> ( r
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y0
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) )
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
& ( r
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( $false
= ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y1 )
=> ( r
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y0
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) )
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
& ( r
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( ?? @ ( ( $i > $o ) > $o ) @ ( r @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ~ ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y1 )
=> ( r
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y0
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) )
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
& ( r
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( ?? @ ( ( $i > $o ) > $o ) @ ( r @ Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ~ ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y1 )
=> ( r
@ ( ^ [Y2: ( $i > $o ) > $o,Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) )
@ Y0 )
@ ( ^ [Y2: ( $i > $o ) > $o,Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) )
@ Y1 ) ) ) ) )
& ( r
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( ^ [Y1: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y2: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y3: ( $i > $o ) > $o] :
( ( Y2 @ Y3 )
=> ( Y2
@ ( ^ [Y4: ( $i > $o ) > $o,Y5: $i > $o] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( Y5 @ Y6 )
& ( Y4
@ ^ [Y7: $i] :
( ( Y6 != Y7 )
& ( Y5 @ Y7 ) ) ) ) )
@ Y3 ) ) ) )
& ( Y2
@ ^ [Y3: $i > $o] :
~ ( ?? @ $i
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] : ( r @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f16,f18,f18,f15,f15,f19]) ).
thf(f19,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ( ^ [Y3: ( $i > $o ) > $o,Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
& ( Y3
@ ^ [Y6: $i] :
( ( Y5 != Y6 )
& ( Y4 @ Y6 ) ) ) ) )
@ Y2 ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f17,f18,f15]) ).
thf(f17,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: ( $i > $o ) > $o] :
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ( X1 @ cZERO )
& ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( cSUCC @ X2 ) ) ) )
=> ( X1 @ X0 ) ) )
= cNAT ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X2: ( $i > $o ) > $o] :
! [X0: ( ( $i > $o ) > $o ) > $o] :
( ( ( X0 @ cZERO )
& ! [X1: ( $i > $o ) > $o] :
( ( X0 @ X1 )
=> ( X0 @ ( cSUCC @ X1 ) ) ) )
=> ( X0 @ X2 ) ) )
= cNAT ),
file('/export/starexec/sandbox/tmp/tmp.Ufgz3VaiJ2/DTF2THF_4599.p',cNAT_def) ).
thf(f15,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) )
= cZERO ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) )
= cZERO ),
file('/export/starexec/sandbox/tmp/tmp.Ufgz3VaiJ2/DTF2THF_4599.p',cZERO_def) ).
thf(f18,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X0
@ ^ [X3: $i] :
( ( X1 @ X3 )
& ( X2 != X3 ) ) )
& ( X1 @ X2 ) ) )
= cSUCC ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X2: ( $i > $o ) > $o,X0: $i > $o] :
? [X1: $i] :
( ( X2
@ ^ [X3: $i] :
( ( X0 @ X3 )
& ( X1 != X3 ) ) )
& ( X0 @ X1 ) ) )
= cSUCC ),
file('/export/starexec/sandbox/tmp/tmp.Ufgz3VaiJ2/DTF2THF_4599.p',cSUCC_def) ).
thf(f16,plain,
( ( ~ ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y1 )
=> ( r @ ( cSUCC @ Y0 ) @ ( cSUCC @ Y1 ) ) ) ) )
& ( r @ cZERO @ cZERO ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( cNAT @ Y0 )
=> ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] : ( r @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ~ ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y1 )
=> ( r @ ( cSUCC @ Y0 ) @ ( cSUCC @ Y1 ) ) ) ) )
& ( r @ cZERO @ cZERO ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( cNAT @ Y0 )
=> ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] : ( r @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( ( r @ cZERO @ cZERO )
& ! [X0: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( r @ X1 @ X0 )
=> ( r @ ( cSUCC @ X1 ) @ ( cSUCC @ X0 ) ) ) )
=> ! [X2: ( $i > $o ) > $o] :
( ( cNAT @ X2 )
=> ? [X3: ( $i > $o ) > $o] : ( r @ X2 @ X3 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( ( ( r @ cZERO @ cZERO )
& ! [X4: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( r @ X1 @ X4 )
=> ( r @ ( cSUCC @ X1 ) @ ( cSUCC @ X4 ) ) ) )
=> ! [X1: ( $i > $o ) > $o] :
( ( cNAT @ X1 )
=> ? [X4: ( $i > $o ) > $o] : ( r @ X1 @ X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( ( ( r @ cZERO @ cZERO )
& ! [X4: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( r @ X1 @ X4 )
=> ( r @ ( cSUCC @ X1 ) @ ( cSUCC @ X4 ) ) ) )
=> ! [X1: ( $i > $o ) > $o] :
( ( cNAT @ X1 )
=> ? [X4: ( $i > $o ) > $o] : ( r @ X1 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ufgz3VaiJ2/DTF2THF_4599.p',cTHM130_B) ).
thf(f137,plain,
( ( ( r @ sK2 @ sK2 )
=> ( r
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( sK2
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) )
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( sK2
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f131]) ).
thf(f131,plain,
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
( ( ~ ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> $false )
= $true ),
inference(forward_demodulation,[status(thm)],[f81,f44]) ).
thf(f44,plain,
! [X1: ( $i > $o ) > $o] :
( ( r @ sK1 @ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $false
= ( ?? @ ( ( $i > $o ) > $o ) @ ( r @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
= ( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0 @ sK1 ) ) )
=> ( ?? @ ( ( $i > $o ) > $o ) @ ( r @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( $false
= ( ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( ?? @ ( ( $i > $o ) > $o ) @ ( r @ Y0 ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $false
= ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( ?? @ ( ( $i > $o ) > $o ) @ ( r @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f81,plain,
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( r @ sK1 @ sK1 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
& $true )
=> ( r @ sK1 @ sK1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( ^ [Y1: ( $i > $o ) > $o] :
( r
@ ( ^ [Y2: ( $i > $o ) > $o,Y3: $i > $o] :
( Y2
@ ( ^ [Y4: ( $i > $o ) > $o,Y5: $i > $o,Y6: $i] :
( Y5
@ ( ^ [Y7: ( $i > $o ) > $o,Y8: $i > $o,Y9: $i] : Y9
@ Y4
@ Y5
@ Y6 ) )
@ Y2
@ Y3 ) )
@ Y1 )
@ ( ^ [Y2: ( $i > $o ) > $o,Y3: $i > $o] :
( Y2
@ ( ^ [Y4: ( $i > $o ) > $o,Y5: $i > $o,Y6: $i] :
( Y5
@ ( ^ [Y7: ( $i > $o ) > $o,Y8: $i > $o,Y9: $i] : Y9
@ Y4
@ Y5
@ Y6 ) )
@ Y2
@ Y3 ) )
@ Y1 ) )
@ Y0 )
=> ( ^ [Y1: ( $i > $o ) > $o] :
( r
@ ( ^ [Y2: ( $i > $o ) > $o,Y3: $i > $o] :
( Y2
@ ( ^ [Y4: ( $i > $o ) > $o,Y5: $i > $o,Y6: $i] :
( Y5
@ ( ^ [Y7: ( $i > $o ) > $o,Y8: $i > $o,Y9: $i] : Y9
@ Y4
@ Y5
@ Y6 ) )
@ Y2
@ Y3 ) )
@ Y1 )
@ ( ^ [Y2: ( $i > $o ) > $o,Y3: $i > $o] :
( Y2
@ ( ^ [Y4: ( $i > $o ) > $o,Y5: $i > $o,Y6: $i] :
( Y5
@ ( ^ [Y7: ( $i > $o ) > $o,Y8: $i > $o,Y9: $i] : Y9
@ Y4
@ Y5
@ Y6 ) )
@ Y2
@ Y3 ) )
@ Y1 ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
& $true )
=> ( ^ [Y0: ( $i > $o ) > $o] :
( r
@ ( ^ [Y1: ( $i > $o ) > $o,Y2: $i > $o] :
( Y1
@ ( ^ [Y3: ( $i > $o ) > $o,Y4: $i > $o,Y5: $i] :
( Y4
@ ( ^ [Y6: ( $i > $o ) > $o,Y7: $i > $o,Y8: $i] : Y8
@ Y3
@ Y4
@ Y5 ) )
@ Y1
@ Y2 ) )
@ Y0 )
@ ( ^ [Y1: ( $i > $o ) > $o,Y2: $i > $o] :
( Y1
@ ( ^ [Y3: ( $i > $o ) > $o,Y4: $i > $o,Y5: $i] :
( Y4
@ ( ^ [Y6: ( $i > $o ) > $o,Y7: $i > $o,Y8: $i] : Y8
@ Y3
@ Y4
@ Y5 ) )
@ Y1
@ Y2 ) )
@ Y0 ) )
@ sK1 ) )
= $true ),
inference(superposition,[status(thm)],[f61,f36]) ).
thf(f36,plain,
( ( r
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f61,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( $true
= ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( X1 @ Y0 )
=> ( X1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( X1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) )
=> ( X1 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0 @ sK1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( $true
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0 @ sK1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV291^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.32 % Computer : n018.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue Feb 24 12:43:01 EST 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.43 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : SEV291^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.19/0.44 % Domain : Set Theory
% 0.19/0.44 % Problem : TPS problem THM130-B
% 0.19/0.44 % Version : Especial.
% 0.19/0.44 % English :
% 0.19/0.44
% 0.19/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.44 % Source : [Bro09]
% 0.19/0.44 % Names : tps_0296 [Bro09]
% 0.19/0.44 % : THM130-B [TPS]
% 0.19/0.44
% 0.19/0.44 % Status : Theorem
% 0.19/0.44 % Rating : 0.89 v9.1.0, 0.88 v9.0.0, 1.00 v8.1.0, 0.82 v7.5.0, 0.86 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0
% 0.19/0.44 % Syntax : Number of formulae : 8 ( 3 unt; 4 typ; 3 def)
% 0.19/0.44 % Number of atoms : 18 ( 4 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 9 ( 4 avg)
% 0.19/0.44 % Number of connectives : 31 ( 2 ~; 0 |; 4 &; 20 @)
% 0.19/0.44 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 9 ( 3 avg)
% 0.19/0.44 % Number of types : 2 ( 0 usr)
% 0.19/0.44 % Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 5 ( 4 usr; 0 con; 1-2 aty)
% 0.19/0.44 % Number of variables : 13 ( 5 ^; 5 !; 3 ?; 13 :)
% 0.19/0.44 % SPC : TH0_THM_EQU_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.44 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.19/0.44 % : v6.2.0 - Reordered definitions.
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 thf(r_type,type,
% 0.19/0.44 r: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
% 0.19/0.44
% 0.19/0.44 thf(cNAT_type,type,
% 0.19/0.44 cNAT: ( ( $i > $o ) > $o ) > $o ).
% 0.19/0.44
% 0.19/0.44 thf(cSUCC_type,type,
% 0.19/0.44 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 0.19/0.44
% 0.19/0.44 thf(cZERO_type,type,
% 0.19/0.44 cZERO: ( $i > $o ) > $o ).
% 0.19/0.44
% 0.19/0.44 thf(cZERO_def,definition,
% 0.19/0.44 ( cZERO
% 0.19/0.44 = ( ^ [Xp: $i > $o] :
% 0.19/0.44 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cSUCC_def,definition,
% 0.19/0.44 ( cSUCC
% 0.19/0.44 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 0.19/0.44 ? [Xx: $i] :
% 0.19/0.44 ( ( Xp @ Xx )
% 0.19/0.44 & ( Xn
% 0.19/0.44 @ ^ [Xt: $i] :
% 0.19/0.44 ( ( Xt != Xx )
% 0.19/0.44 & ( Xp @ Xt ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cNAT_def,definition,
% 0.19/0.44 ( cNAT
% 0.19/0.44 = ( ^ [Xn: ( $i > $o ) > $o] :
% 0.19/0.44 ! [Xp: ( ( $i > $o ) > $o ) > $o] :
% 0.19/0.44 ( ( ( Xp @ cZERO )
% 0.19/0.44 & ! [Xx: ( $i > $o ) > $o] :
% 0.19/0.44 ( ( Xp @ Xx )
% 0.19/0.44 => ( Xp @ ( cSUCC @ Xx ) ) ) )
% 0.19/0.44 => ( Xp @ Xn ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cTHM130_B,conjecture,
% 0.19/0.44 ( ( ( r @ cZERO @ cZERO )
% 0.19/0.44 & ! [Xx: ( $i > $o ) > $o,Xy: ( $i > $o ) > $o] :
% 0.19/0.44 ( ( r @ Xx @ Xy )
% 0.19/0.44 => ( r @ ( cSUCC @ Xx ) @ ( cSUCC @ Xy ) ) ) )
% 0.19/0.44 => ! [Xx: ( $i > $o ) > $o] :
% 0.19/0.44 ( ( cNAT @ Xx )
% 0.19/0.44 => ? [Xy: ( $i > $o ) > $o] : ( r @ Xx @ Xy ) ) ) ).
% 0.19/0.44
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 ------------------------
% 1.51/1.28 ---- Embedded in THF ---
% 1.51/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.28 %%% Generated on Tue Feb 24 12:43:01 EST 2026
% 1.51/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.28 %%% Logic specification used:
% 1.51/1.28 %%% thf(spec, logic, $$dhol).
% 1.51/1.28
% 1.51/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Ufgz3VaiJ2/DTF2DTF4599.p
% See solution above
% 1.51/1.28 ------------------------
% 1.51/1.29 ---- Cleaned THF ---
% 1.51/1.29 thf(r_type,type,
% 1.51/1.29 r: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
% 1.51/1.29
% 1.51/1.29 thf(cNAT_type,type,
% 1.51/1.29 cNAT: ( ( $i > $o ) > $o ) > $o ).
% 1.51/1.29
% 1.51/1.29 thf(cSUCC_type,type,
% 1.51/1.29 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 1.51/1.29
% 1.51/1.29 thf(cZERO_type,type,
% 1.51/1.29 cZERO: ( $i > $o ) > $o ).
% 1.51/1.29
% 1.51/1.29 thf(cZERO_def,definition,
% 1.51/1.29 ( cZERO
% 1.51/1.29 = ( ^ [Xp: $i > $o] :
% 1.51/1.29 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 1.51/1.29
% 1.51/1.29 thf(cSUCC_def,definition,
% 1.51/1.29 ( cSUCC
% 1.51/1.29 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 1.51/1.29 ? [Xx: $i] :
% 1.51/1.29 ( ( Xp @ Xx )
% 1.51/1.29 & ( Xn
% 1.51/1.29 @ ^ [Xt: $i] :
% 1.51/1.29 ( ( Xt != Xx )
% 1.51/1.29 & ( Xp @ Xt ) ) ) ) ) ) ).
% 1.51/1.29
% 1.51/1.29 thf(cNAT_def,definition,
% 1.51/1.29 ( cNAT
% 1.51/1.29 = ( ^ [Xn: ( $i > $o ) > $o] :
% 1.51/1.29 ! [Xp: ( ( $i > $o ) > $o ) > $o] :
% 1.51/1.29 ( ( ( Xp @ cZERO )
% 1.51/1.29 & ! [Xx: ( $i > $o ) > $o] :
% 1.51/1.29 ( ( Xp @ Xx )
% 1.51/1.29 => ( Xp @ ( cSUCC @ Xx ) ) ) )
% 1.51/1.29 => ( Xp @ Xn ) ) ) ) ).
% 1.51/1.29
% 1.51/1.29 thf(cTHM130_B,conjecture,
% 1.51/1.29 ( ( ( r @ cZERO @ cZERO )
% 1.51/1.29 & ! [Xx: ( $i > $o ) > $o,Xy: ( $i > $o ) > $o] :
% 1.51/1.29 ( ( r @ Xx @ Xy )
% 1.51/1.29 => ( r @ ( cSUCC @ Xx ) @ ( cSUCC @ Xy ) ) ) )
% 1.51/1.29 => ! [Xx: ( $i > $o ) > $o] :
% 1.51/1.29 ( ( cNAT @ Xx )
% 1.51/1.29 => ? [Xy: ( $i > $o ) > $o] : ( r @ Xx @ Xy ) ) ) ).
% 1.51/1.29 ------------------------
% 1.69/1.30 % (4792)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_4599 for (2999ds/2Mi)
% 1.69/1.30 % (4789)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_4599 for (2999ds/4Mi)
% 1.69/1.30 % (4792)Instruction limit reached!
% 1.69/1.30 % (4792)------------------------------
% 1.69/1.30 % (4792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.30 % (4792)Termination reason: Unknown
% 1.69/1.30 % (4792)Termination phase: Property scanning
% 1.69/1.30
% 1.69/1.30 % (4792)Memory used [KB]: 1023
% 1.69/1.30 % (4792)Time elapsed: 0.002 s
% 1.69/1.30 % (4792)Instructions burned: 3 (million)
% 1.69/1.30 % (4792)------------------------------
% 1.69/1.30 % (4792)------------------------------
% 1.69/1.31 % (4789)Instruction limit reached!
% 1.69/1.31 % (4789)------------------------------
% 1.69/1.31 % (4789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.31 % (4789)Termination reason: Unknown
% 1.69/1.31 % (4789)Termination phase: Saturation
% 1.69/1.31
% 1.69/1.31 % (4789)Memory used [KB]: 5500
% 1.69/1.31 % (4789)Time elapsed: 0.003 s
% 1.69/1.31 % (4789)Instructions burned: 5 (million)
% 1.69/1.31 % (4789)------------------------------
% 1.69/1.31 % (4789)------------------------------
% 1.69/1.31 % (4788)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/183Mi)
% 1.69/1.31 % (4791)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/2Mi)
% 1.69/1.31 % (4793)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_4599 for (2999ds/275Mi)
% 1.69/1.31 % (4790)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_4599 for (2999ds/27Mi)
% 1.69/1.31 % (4791)Instruction limit reached!
% 1.69/1.31 % (4791)------------------------------
% 1.69/1.31 % (4791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.31 % (4791)Termination reason: Unknown
% 1.69/1.31 % (4791)Termination phase: Unused predicate definition removal
% 1.69/1.31
% 1.69/1.31 % (4791)Memory used [KB]: 895
% 1.69/1.31 % (4791)Time elapsed: 0.003 s
% 1.69/1.31 % (4791)Instructions burned: 2 (million)
% 1.69/1.31 % (4791)------------------------------
% 1.69/1.31 % (4791)------------------------------
% 1.69/1.31 % (4794)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/18Mi)
% 1.69/1.31 % (4795)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/3Mi)
% 1.69/1.31 % (4793)Refutation not found, incomplete strategy
% 1.69/1.31 % (4793)------------------------------
% 1.69/1.31 % (4793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.31 % (4793)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.31
% 1.69/1.31
% 1.69/1.31 % (4793)Memory used [KB]: 5500
% 1.69/1.31 % (4793)Time elapsed: 0.003 s
% 1.69/1.31 % (4793)Instructions burned: 2 (million)
% 1.69/1.31 % (4793)------------------------------
% 1.69/1.31 % (4793)------------------------------
% 1.69/1.32 % (4795)Instruction limit reached!
% 1.69/1.32 % (4795)------------------------------
% 1.69/1.32 % (4795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (4795)Termination reason: Unknown
% 1.69/1.32 % (4795)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (4795)Memory used [KB]: 5500
% 1.69/1.32 % (4795)Time elapsed: 0.002 s
% 1.69/1.32 % (4795)Instructions burned: 4 (million)
% 1.69/1.32 % (4795)------------------------------
% 1.69/1.32 % (4795)------------------------------
% 1.69/1.32 % (4796)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_4599 for (2999ds/37Mi)
% 1.69/1.32 % (4794)Instruction limit reached!
% 1.69/1.32 % (4794)------------------------------
% 1.69/1.32 % (4794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (4794)Termination reason: Unknown
% 1.69/1.32 % (4794)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (4794)Memory used [KB]: 5628
% 1.69/1.32 % (4794)Time elapsed: 0.013 s
% 1.69/1.32 % (4794)Instructions burned: 18 (million)
% 1.69/1.32 % (4794)------------------------------
% 1.69/1.32 % (4794)------------------------------
% 1.69/1.32 % (4799)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_4599 for (2999ds/1041Mi)
% 1.69/1.33 % (4796)Instruction limit reached!
% 1.69/1.33 % (4796)------------------------------
% 1.69/1.33 % (4796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (4796)Termination reason: Unknown
% 1.69/1.33 % (4796)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (4796)Memory used [KB]: 5884
% 1.69/1.33 % (4796)Time elapsed: 0.014 s
% 1.69/1.33 % (4796)Instructions burned: 38 (million)
% 1.69/1.33 % (4796)------------------------------
% 1.69/1.33 % (4796)------------------------------
% 1.69/1.33 % (4790)Instruction limit reached!
% 1.69/1.33 % (4790)------------------------------
% 1.69/1.33 % (4790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (4790)Termination reason: Unknown
% 1.69/1.33 % (4790)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (4790)Memory used [KB]: 5628
% 1.69/1.33 % (4790)Time elapsed: 0.020 s
% 1.69/1.33 % (4790)Instructions burned: 27 (million)
% 1.69/1.33 % (4790)------------------------------
% 1.69/1.33 % (4790)------------------------------
% 1.69/1.33 % (4797)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_4599 for (2999ds/15Mi)
% 1.69/1.33 % (4798)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_4599 for (2999ds/3Mi)
% 1.69/1.33 % (4798)Instruction limit reached!
% 1.69/1.33 % (4798)------------------------------
% 1.69/1.33 % (4798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (4798)Termination reason: Unknown
% 1.69/1.33 % (4798)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (4798)Memory used [KB]: 5500
% 1.69/1.33 % (4798)Time elapsed: 0.004 s
% 1.69/1.33 % (4798)Instructions burned: 3 (million)
% 1.69/1.33 % (4798)------------------------------
% 1.69/1.33 % (4798)------------------------------
% 1.69/1.34 % (4797)Instruction limit reached!
% 1.69/1.34 % (4797)------------------------------
% 1.69/1.34 % (4797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (4797)Termination reason: Unknown
% 1.69/1.34 % (4797)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (4797)Memory used [KB]: 5628
% 1.69/1.34 % (4797)Time elapsed: 0.009 s
% 1.69/1.34 % (4797)Instructions burned: 16 (million)
% 1.69/1.34 % (4797)------------------------------
% 1.69/1.34 % (4797)------------------------------
% 1.69/1.34 % (4800)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/7Mi)
% 1.69/1.34 % (4800)Instruction limit reached!
% 1.69/1.34 % (4800)------------------------------
% 1.69/1.34 % (4800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (4800)Termination reason: Unknown
% 1.69/1.34 % (4800)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (4800)Memory used [KB]: 1023
% 1.69/1.34 % (4800)Time elapsed: 0.004 s
% 1.69/1.34 % (4800)Instructions burned: 7 (million)
% 1.69/1.34 % (4800)------------------------------
% 1.69/1.34 % (4800)------------------------------
% 1.69/1.34 % (4802)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_4599 for (2999ds/3Mi)
% 1.69/1.34 % (4802)Instruction limit reached!
% 1.69/1.34 % (4802)------------------------------
% 1.69/1.34 % (4802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (4802)Termination reason: Unknown
% 1.69/1.34 % (4802)Termination phase: Twee Goal Transformation
% 1.69/1.34
% 1.69/1.34 % (4802)Memory used [KB]: 1023
% 1.69/1.34 % (4802)Time elapsed: 0.002 s
% 1.69/1.34 % (4802)Instructions burned: 3 (million)
% 1.69/1.34 % (4802)------------------------------
% 1.69/1.34 % (4802)------------------------------
% 1.69/1.35 % (4807)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/7Mi)
% 1.69/1.35 % (4801)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/16Mi)
% 1.69/1.35 % (4807)Refutation not found, incomplete strategy
% 1.69/1.35 % (4807)------------------------------
% 1.69/1.35 % (4807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (4807)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.35
% 1.69/1.35
% 1.69/1.35 % (4807)Memory used [KB]: 5500
% 1.69/1.35 % (4807)Time elapsed: 0.003 s
% 1.69/1.35 % (4807)Instructions burned: 4 (million)
% 1.69/1.35 % (4807)------------------------------
% 1.69/1.35 % (4807)------------------------------
% 1.69/1.35 % (4804)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_4599 for (2999ds/3Mi)
% 1.69/1.35 % (4811)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/4Mi)
% 1.69/1.36 % (4804)Instruction limit reached!
% 1.69/1.36 % (4804)------------------------------
% 1.69/1.36 % (4804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (4804)Termination reason: Unknown
% 1.69/1.36 % (4804)Termination phase: Property scanning
% 1.69/1.36
% 1.69/1.36 % (4804)Memory used [KB]: 1023
% 1.69/1.36 % (4804)Time elapsed: 0.005 s
% 1.69/1.36 % (4804)Instructions burned: 3 (million)
% 1.69/1.36 % (4804)------------------------------
% 1.69/1.36 % (4804)------------------------------
% 1.69/1.36 % (4811)Instruction limit reached!
% 1.69/1.36 % (4811)------------------------------
% 1.69/1.36 % (4811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (4811)Termination reason: Unknown
% 1.69/1.36 % (4811)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (4811)Memory used [KB]: 5500
% 1.69/1.36 % (4811)Time elapsed: 0.004 s
% 1.69/1.36 % (4811)Instructions burned: 4 (million)
% 1.69/1.36 % (4811)------------------------------
% 1.69/1.36 % (4811)------------------------------
% 1.69/1.36 % (4801)Instruction limit reached!
% 1.69/1.36 % (4801)------------------------------
% 1.69/1.36 % (4801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (4801)Termination reason: Unknown
% 1.69/1.36 % (4801)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (4801)Memory used [KB]: 5756
% 1.69/1.36 % (4801)Time elapsed: 0.014 s
% 1.69/1.36 % (4801)Instructions burned: 17 (million)
% 1.69/1.36 % (4801)------------------------------
% 1.69/1.36 % (4801)------------------------------
% 1.69/1.36 % (4810)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/3Mi)
% 1.69/1.37 % (4814)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/18Mi)
% 1.69/1.37 % (4810)Instruction limit reached!
% 1.69/1.37 % (4810)------------------------------
% 1.69/1.37 % (4810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (4810)Termination reason: Unknown
% 1.69/1.37 % (4810)Termination phase: Property scanning
% 1.69/1.37
% 1.69/1.37 % (4810)Memory used [KB]: 1023
% 1.69/1.37 % (4810)Time elapsed: 0.004 s
% 1.69/1.37 % (4810)Instructions burned: 3 (million)
% 1.69/1.37 % (4810)------------------------------
% 1.69/1.37 % (4810)------------------------------
% 1.69/1.37 % (4823)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/6Mi)
% 1.69/1.38 % (4823)Instruction limit reached!
% 1.69/1.38 % (4823)------------------------------
% 1.69/1.38 % (4823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (4823)Termination reason: Unknown
% 1.69/1.38 % (4823)Termination phase: Saturation
% 1.69/1.38
% 1.69/1.38 % (4823)Memory used [KB]: 5500
% 1.69/1.38 % (4823)Time elapsed: 0.005 s
% 1.69/1.38 % (4823)Instructions burned: 6 (million)
% 1.69/1.38 % (4823)------------------------------
% 1.69/1.38 % (4823)------------------------------
% 1.69/1.38 % (4814)Instruction limit reached!
% 1.69/1.38 % (4814)------------------------------
% 1.69/1.38 % (4814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (4814)Termination reason: Unknown
% 1.69/1.38 % (4814)Termination phase: Saturation
% 1.69/1.38
% 1.69/1.38 % (4814)Memory used [KB]: 5628
% 1.69/1.38 % (4814)Time elapsed: 0.012 s
% 1.69/1.38 % (4814)Instructions burned: 18 (million)
% 1.69/1.38 % (4814)------------------------------
% 1.69/1.38 % (4814)------------------------------
% 1.69/1.38 % (4822)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/710Mi)
% 1.69/1.38 % (4788)Instruction limit reached!
% 1.69/1.38 % (4788)------------------------------
% 1.69/1.38 % (4788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (4788)Termination reason: Unknown
% 1.69/1.38 % (4788)Termination phase: Saturation
% 1.69/1.38
% 1.69/1.38 % (4788)Memory used [KB]: 6524
% 1.69/1.38 % (4788)Time elapsed: 0.076 s
% 1.69/1.38 % (4788)Instructions burned: 184 (million)
% 1.69/1.38 % (4788)------------------------------
% 1.69/1.38 % (4788)------------------------------
% 1.69/1.38 % (4824)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_4599 for (2999ds/902Mi)
% 1.69/1.39 % (4824)Refutation not found, incomplete strategy
% 1.69/1.39 % (4824)------------------------------
% 1.69/1.39 % (4824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (4824)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.39
% 1.69/1.39
% 1.69/1.39 % (4824)Memory used [KB]: 5500
% 1.69/1.39 % (4824)Time elapsed: 0.006 s
% 1.69/1.39 % (4824)Instructions burned: 3 (million)
% 1.69/1.39 % (4824)------------------------------
% 1.69/1.39 % (4824)------------------------------
% 1.69/1.39 % (4829)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/5Mi)
% 1.69/1.39 % (4830)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_4599 for (2999ds/6Mi)
% 1.69/1.39 % (4825)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_4599 for (2999ds/21Mi)
% 1.69/1.40 % (4829)Instruction limit reached!
% 1.69/1.40 % (4829)------------------------------
% 1.69/1.40 % (4829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.40 % (4829)Termination reason: Unknown
% 1.69/1.40 % (4829)Termination phase: Saturation
% 1.69/1.40
% 1.69/1.40 % (4829)Memory used [KB]: 5500
% 1.69/1.40 % (4829)Time elapsed: 0.004 s
% 1.69/1.40 % (4829)Instructions burned: 5 (million)
% 1.69/1.40 % (4829)------------------------------
% 1.69/1.40 % (4829)------------------------------
% 1.69/1.40 % (4830)Instruction limit reached!
% 1.69/1.40 % (4830)------------------------------
% 1.69/1.40 % (4830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.40 % (4830)Termination reason: Unknown
% 1.69/1.40 % (4830)Termination phase: Saturation
% 1.69/1.40
% 1.69/1.40 % (4830)Memory used [KB]: 5500
% 1.69/1.40 % (4830)Time elapsed: 0.005 s
% 1.69/1.40 % (4830)Instructions burned: 6 (million)
% 1.69/1.40 % (4830)------------------------------
% 1.69/1.40 % (4830)------------------------------
% 1.69/1.40 % (4833)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/377Mi)
% 1.69/1.41 % (4838)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/879Mi)
% 1.69/1.41 % (4825)Instruction limit reached!
% 1.69/1.41 % (4825)------------------------------
% 1.69/1.41 % (4825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.41 % (4825)Termination reason: Unknown
% 1.69/1.41 % (4825)Termination phase: Saturation
% 1.69/1.41
% 1.69/1.41 % (4825)Memory used [KB]: 5628
% 1.69/1.41 % (4825)Time elapsed: 0.023 s
% 1.69/1.41 % (4825)Instructions burned: 22 (million)
% 1.69/1.41 % (4825)------------------------------
% 1.69/1.41 % (4825)------------------------------
% 1.69/1.42 % (4835)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_4599 for (2999ds/779Mi)
% 1.69/1.42 % (4837)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_4599 for (2999ds/19Mi)
% 1.69/1.43 % (4843)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_4599 for (2999ds/17Mi)
% 1.69/1.43 % (4837)Instruction limit reached!
% 1.69/1.43 % (4837)------------------------------
% 1.69/1.43 % (4837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.43 % (4837)Termination reason: Unknown
% 1.69/1.43 % (4837)Termination phase: Saturation
% 1.69/1.43
% 1.69/1.43 % (4837)Memory used [KB]: 5628
% 1.69/1.43 % (4837)Time elapsed: 0.032 s
% 1.69/1.43 % (4837)Instructions burned: 19 (million)
% 1.69/1.43 % (4837)------------------------------
% 1.69/1.43 % (4837)------------------------------
% 1.69/1.43 % (4843)Instruction limit reached!
% 1.69/1.43 % (4843)------------------------------
% 1.69/1.43 % (4843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.43 % (4843)Termination reason: Unknown
% 1.69/1.43 % (4843)Termination phase: Saturation
% 1.69/1.43
% 1.69/1.43 % (4843)Memory used [KB]: 5628
% 1.69/1.43 % (4843)Time elapsed: 0.007 s
% 1.69/1.43 % (4843)Instructions burned: 17 (million)
% 1.69/1.43 % (4843)------------------------------
% 1.69/1.43 % (4843)------------------------------
% 1.69/1.44 % (4844)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4599 for (2998ds/3Mi)
% 1.69/1.44 % (4844)Instruction limit reached!
% 1.69/1.44 % (4844)------------------------------
% 1.69/1.44 % (4844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.44 % (4844)Termination reason: Unknown
% 1.69/1.44 % (4844)Termination phase: Saturation
% 1.69/1.44
% 1.69/1.44 % (4844)Memory used [KB]: 5500
% 1.69/1.44 % (4844)Time elapsed: 0.003 s
% 1.69/1.44 % (4844)Instructions burned: 5 (million)
% 1.69/1.44 % (4844)------------------------------
% 1.69/1.44 % (4844)------------------------------
% 1.69/1.44 % (4845)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_4599 for (2998ds/30Mi)
% 1.69/1.45 % (4846)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_4599 for (2998ds/127Mi)
% 1.69/1.45 % (4845)Instruction limit reached!
% 1.69/1.45 % (4845)------------------------------
% 1.69/1.45 % (4845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.45 % (4845)Termination reason: Unknown
% 1.69/1.45 % (4845)Termination phase: Saturation
% 1.69/1.45
% 1.69/1.45 % (4845)Memory used [KB]: 5628
% 1.69/1.45 % (4845)Time elapsed: 0.036 s
% 1.69/1.45 % (4845)Instructions burned: 30 (million)
% 1.69/1.45 % (4845)------------------------------
% 1.69/1.45 % (4845)------------------------------
% 1.69/1.46 % (4847)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_4599 for (2998ds/100Mi)
% 1.69/1.47 % (4847)Refutation not found, incomplete strategy
% 1.69/1.47 % (4847)------------------------------
% 1.69/1.47 % (4847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.47 % (4847)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.47
% 1.69/1.47
% 1.69/1.47 % (4847)Memory used [KB]: 5500
% 1.69/1.47 % (4847)Time elapsed: 0.029 s
% 1.69/1.47 % (4847)Instructions burned: 11 (million)
% 1.69/1.47 % (4847)------------------------------
% 1.69/1.47 % (4847)------------------------------
% 1.69/1.48 % (4848)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_4599 for (2998ds/3Mi)
% 1.69/1.48 % (4848)Instruction limit reached!
% 1.69/1.48 % (4848)------------------------------
% 1.69/1.48 % (4848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.48 % (4848)Termination reason: Unknown
% 1.69/1.48 % (4848)Termination phase: Saturation
% 1.69/1.48
% 1.69/1.48 % (4848)Memory used [KB]: 5500
% 1.69/1.48 % (4848)Time elapsed: 0.003 s
% 1.69/1.48 % (4848)Instructions burned: 3 (million)
% 1.69/1.48 % (4848)------------------------------
% 1.69/1.48 % (4848)------------------------------
% 1.69/1.49 % (4849)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_4599 for (2998ds/20Mi)
% 1.69/1.49 % (4846)Instruction limit reached!
% 1.69/1.49 % (4846)------------------------------
% 1.69/1.49 % (4846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.49 % (4846)Termination reason: Unknown
% 1.69/1.49 % (4846)Termination phase: Saturation
% 1.69/1.49
% 1.69/1.49 % (4846)Memory used [KB]: 6140
% 1.69/1.49 % (4846)Time elapsed: 0.068 s
% 1.69/1.49 % (4846)Instructions burned: 129 (million)
% 1.69/1.49 % (4846)------------------------------
% 1.69/1.49 % (4846)------------------------------
% 1.69/1.50 % (4849)Instruction limit reached!
% 1.69/1.50 % (4849)------------------------------
% 1.69/1.50 % (4849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.50 % (4849)Termination reason: Unknown
% 1.69/1.50 % (4849)Termination phase: Saturation
% 1.69/1.50
% 1.69/1.50 % (4849)Memory used [KB]: 5500
% 1.69/1.50 % (4849)Time elapsed: 0.034 s
% 1.69/1.50 % (4849)Instructions burned: 22 (million)
% 1.69/1.50 % (4849)------------------------------
% 1.69/1.50 % (4849)------------------------------
% 1.69/1.50 % (4850)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_4599 for (2998ds/86Mi)
% 1.69/1.51 % (4851)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_4599 for (2997ds/107Mi)
% 1.69/1.52 % (4833)Instruction limit reached!
% 1.69/1.52 % (4833)------------------------------
% 1.69/1.52 % (4833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.52 % (4833)Termination reason: Unknown
% 1.69/1.52 % (4833)Termination phase: Saturation
% 1.69/1.52
% 1.69/1.52 % (4833)Memory used [KB]: 6652
% 1.69/1.52 % (4833)Time elapsed: 0.145 s
% 1.69/1.52 % (4833)Instructions burned: 377 (million)
% 1.69/1.52 % (4833)------------------------------
% 1.69/1.52 % (4833)------------------------------
% 1.69/1.53 % (4850)Instruction limit reached!
% 1.69/1.53 % (4850)------------------------------
% 1.69/1.53 % (4850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.53 % (4850)Termination reason: Unknown
% 1.69/1.53 % (4850)Termination phase: Saturation
% 1.69/1.53
% 1.69/1.53 % (4850)Memory used [KB]: 6012
% 1.69/1.53 % (4850)Time elapsed: 0.030 s
% 1.69/1.53 % (4850)Instructions burned: 88 (million)
% 1.69/1.53 % (4850)------------------------------
% 1.69/1.53 % (4850)------------------------------
% 1.69/1.53 % (4852)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_4599 for (2997ds/39Mi)
% 1.69/1.54 % (4851)Instruction limit reached!
% 1.69/1.54 % (4851)------------------------------
% 1.69/1.54 % (4851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.54 % (4851)Termination reason: Unknown
% 1.69/1.54 % (4851)Termination phase: Saturation
% 1.69/1.54
% 1.69/1.54 % (4851)Memory used [KB]: 5628
% 1.69/1.54 % (4851)Time elapsed: 0.033 s
% 1.69/1.54 % (4851)Instructions burned: 110 (million)
% 1.69/1.54 % (4851)------------------------------
% 1.69/1.54 % (4851)------------------------------
% 1.69/1.54 % (4853)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_4599 for (2997ds/448Mi)
% 1.69/1.54 % (4852)Instruction limit reached!
% 1.69/1.54 % (4852)------------------------------
% 1.69/1.54 % (4852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.54 % (4852)Termination reason: Unknown
% 1.69/1.54 % (4852)Termination phase: Saturation
% 1.69/1.54
% 1.69/1.54 % (4852)Memory used [KB]: 5884
% 1.69/1.54 % (4852)Time elapsed: 0.014 s
% 1.69/1.54 % (4852)Instructions burned: 40 (million)
% 1.69/1.54 % (4852)------------------------------
% 1.69/1.54 % (4852)------------------------------
% 1.69/1.55 % (4854)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_4599 for (2997ds/46Mi)
% 1.69/1.55 % (4855)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_4599 for (2997ds/98Mi)
% 1.69/1.56 % (4855)Refutation not found, incomplete strategy
% 1.69/1.56 % (4855)------------------------------
% 1.69/1.56 % (4855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.56 % (4855)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.56
% 1.69/1.56
% 1.69/1.56 % (4855)Memory used [KB]: 1151
% 1.69/1.56 % (4855)Time elapsed: 0.008 s
% 1.69/1.56 % (4855)Instructions burned: 18 (million)
% 1.69/1.56 % (4855)------------------------------
% 1.69/1.56 % (4855)------------------------------
% 1.69/1.57 % (4854)Instruction limit reached!
% 1.69/1.57 % (4854)------------------------------
% 1.69/1.57 % (4854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.57 % (4854)Termination reason: Unknown
% 1.69/1.57 % (4854)Termination phase: Saturation
% 1.69/1.57
% 1.69/1.57 % (4854)Memory used [KB]: 5756
% 1.69/1.57 % (4854)Time elapsed: 0.019 s
% 1.69/1.57 % (4854)Instructions burned: 48 (million)
% 1.69/1.57 % (4854)------------------------------
% 1.69/1.57 % (4854)------------------------------
% 1.69/1.57 % (4860)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_4599 for (2997ds/507Mi)
% 1.69/1.58 % (4864)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_4599 for (2997ds/149Mi)
% 1.69/1.59 % (4799)Instruction limit reached!
% 1.69/1.59 % (4799)------------------------------
% 1.69/1.59 % (4799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.59 % (4799)Termination reason: Unknown
% 1.69/1.59 % (4799)Termination phase: Saturation
% 1.69/1.59
% 1.69/1.59 % (4799)Memory used [KB]: 6140
% 1.69/1.59 % (4799)Time elapsed: 0.267 s
% 1.69/1.59 % (4799)Instructions burned: 1043 (million)
% 1.69/1.59 % (4799)------------------------------
% 1.69/1.59 % (4799)------------------------------
% 1.69/1.60 % (4875)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_4599 for (2997ds/39Mi)
% 1.69/1.61 % (4875)Instruction limit reached!
% 1.69/1.61 % (4875)------------------------------
% 1.69/1.61 % (4875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.61 % (4875)Termination reason: Unknown
% 1.69/1.61 % (4875)Termination phase: Saturation
% 1.69/1.61
% 1.69/1.61 % (4875)Memory used [KB]: 5628
% 1.69/1.61 % (4875)Time elapsed: 0.014 s
% 1.69/1.61 % (4875)Instructions burned: 41 (million)
% 1.69/1.61 % (4875)------------------------------
% 1.69/1.61 % (4875)------------------------------
% 1.69/1.62 % (4822)Instruction limit reached!
% 1.69/1.62 % (4822)------------------------------
% 1.69/1.62 % (4822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.62 % (4822)Termination reason: Unknown
% 1.69/1.62 % (4822)Termination phase: Saturation
% 1.69/1.62
% 1.69/1.62 % (4822)Memory used [KB]: 7164
% 1.69/1.62 % (4822)Time elapsed: 0.244 s
% 1.69/1.62 % (4822)Instructions burned: 713 (million)
% 1.69/1.62 % (4822)------------------------------
% 1.69/1.62 % (4822)------------------------------
% 1.69/1.62 % (4885)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_4599 for (2996ds/6Mi)
% 1.69/1.63 % (4885)Instruction limit reached!
% 1.69/1.63 % (4885)------------------------------
% 1.69/1.63 % (4885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.63 % (4885)Termination reason: Unknown
% 1.69/1.63 % (4885)Termination phase: Saturation
% 1.69/1.63
% 1.69/1.63 % (4885)Memory used [KB]: 9978
% 1.69/1.63 % (4885)Time elapsed: 0.004 s
% 1.69/1.63 % (4885)Instructions burned: 8 (million)
% 1.69/1.63 % (4885)------------------------------
% 1.69/1.63 % (4885)------------------------------
% 1.69/1.63 % (4864)Instruction limit reached!
% 1.69/1.63 % (4864)------------------------------
% 1.69/1.63 % (4864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.63 % (4864)Termination reason: Unknown
% 1.69/1.63 % (4864)Termination phase: Saturation
% 1.69/1.63
% 1.69/1.63 % (4864)Memory used [KB]: 6012
% 1.69/1.63 % (4864)Time elapsed: 0.053 s
% 1.69/1.63 % (4864)Instructions burned: 149 (million)
% 1.69/1.63 % (4864)------------------------------
% 1.69/1.63 % (4864)------------------------------
% 1.69/1.63 % (4888)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_4599 for (2996ds/1087Mi)
% 1.69/1.63 % (4894)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_4599 for (2996ds/47Mi)
% 1.69/1.64 % (4897)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_4599 for (2996ds/44Mi)
% 1.69/1.65 % (4888)Refutation not found, incomplete strategy
% 1.69/1.65 % (4888)------------------------------
% 1.69/1.65 % (4888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.65 % (4888)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.65
% 1.69/1.65
% 1.69/1.65 % (4888)Memory used [KB]: 5756
% 1.69/1.65 % (4888)Time elapsed: 0.019 s
% 1.69/1.65 % (4888)Instructions burned: 52 (million)
% 1.69/1.65 % (4888)------------------------------
% 1.69/1.65 % (4888)------------------------------
% 1.69/1.65 % (4894)Instruction limit reached!
% 1.69/1.65 % (4894)------------------------------
% 1.69/1.65 % (4894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.65 % (4894)Termination reason: Unknown
% 1.69/1.65 % (4894)Termination phase: Saturation
% 1.69/1.65
% 1.69/1.65 % (4894)Memory used [KB]: 5756
% 1.69/1.65 % (4894)Time elapsed: 0.016 s
% 1.69/1.65 % (4894)Instructions burned: 50 (million)
% 1.69/1.65 % (4894)------------------------------
% 1.69/1.65 % (4894)------------------------------
% 1.69/1.65 % (4838)Instruction limit reached!
% 1.69/1.65 % (4838)------------------------------
% 1.69/1.65 % (4838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.65 % (4838)Termination reason: Unknown
% 1.69/1.65 % (4838)Termination phase: Saturation
% 1.69/1.65
% 1.69/1.65 % (4838)Memory used [KB]: 6652
% 1.69/1.65 % (4838)Time elapsed: 0.267 s
% 1.69/1.65 % (4838)Instructions burned: 881 (million)
% 1.69/1.65 % (4838)------------------------------
% 1.69/1.65 % (4838)------------------------------
% 1.69/1.65 % (4897)Instruction limit reached!
% 1.69/1.65 % (4897)------------------------------
% 1.69/1.65 % (4897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.65 % (4897)Termination reason: Unknown
% 1.69/1.65 % (4897)Termination phase: Saturation
% 1.69/1.65
% 1.69/1.65 % (4897)Memory used [KB]: 1279
% 1.69/1.65 % (4897)Time elapsed: 0.016 s
% 1.69/1.65 % (4897)Instructions burned: 44 (million)
% 1.69/1.65 % (4897)------------------------------
% 1.69/1.65 % (4897)------------------------------
% 1.69/1.66 % (4903)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_4599 for (2996ds/432Mi)
% 1.69/1.66 % (4905)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_4599 for (2996ds/62Mi)
% 1.69/1.66 % (4907)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_4599 for (2996ds/31Mi)
% 1.69/1.66 % (4909)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_4599 for (2996ds/96Mi)
% 1.69/1.67 % (4907)Instruction limit reached!
% 1.69/1.67 % (4907)------------------------------
% 1.69/1.67 % (4907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.67 % (4907)Termination reason: Unknown
% 1.69/1.67 % (4907)Termination phase: Saturation
% 1.69/1.67
% 1.69/1.67 % (4907)Memory used [KB]: 5756
% 1.69/1.67 % (4907)Time elapsed: 0.013 s
% 1.69/1.67 % (4907)Instructions burned: 32 (million)
% 1.69/1.67 % (4907)------------------------------
% 1.69/1.67 % (4907)------------------------------
% 1.69/1.67 % (4835)Instruction limit reached!
% 1.69/1.67 % (4835)------------------------------
% 1.69/1.67 % (4835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.67 % (4835)Termination reason: Unknown
% 1.69/1.67 % (4835)Termination phase: Saturation
% 1.69/1.67
% 1.69/1.67 % (4835)Memory used [KB]: 7803
% 1.69/1.67 % (4835)Time elapsed: 0.283 s
% 1.69/1.67 % (4835)Instructions burned: 780 (million)
% 1.69/1.67 % (4835)------------------------------
% 1.69/1.67 % (4835)------------------------------
% 1.69/1.68 % (4905)Instruction limit reached!
% 1.69/1.68 % (4905)------------------------------
% 1.69/1.68 % (4905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.68 % (4905)Termination reason: Unknown
% 1.69/1.68 % (4905)Termination phase: Saturation
% 1.69/1.68
% 1.69/1.68 % (4905)Memory used [KB]: 5884
% 1.69/1.68 % (4905)Time elapsed: 0.019 s
% 1.69/1.68 % (4905)Instructions burned: 62 (million)
% 1.69/1.68 % (4905)------------------------------
% 1.69/1.68 % (4905)------------------------------
% 1.69/1.68 % (4919)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_4599 for (2996ds/453Mi)
% 1.69/1.69 % (4920)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_4599 for (2996ds/71Mi)
% 1.69/1.69 % (4853)Instruction limit reached!
% 1.69/1.69 % (4853)------------------------------
% 1.69/1.69 % (4853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.69 % (4853)Termination reason: Unknown
% 1.69/1.69 % (4853)Termination phase: Saturation
% 1.69/1.69
% 1.69/1.69 % (4853)Memory used [KB]: 6652
% 1.69/1.69 % (4853)Time elapsed: 0.146 s
% 1.69/1.69 % (4853)Instructions burned: 450 (million)
% 1.69/1.69 % (4853)------------------------------
% 1.69/1.69 % (4853)------------------------------
% 1.69/1.69 % (4922)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_4599 for (2996ds/83Mi)
% 1.69/1.69 % (4919)Refutation not found, incomplete strategy
% 1.69/1.69 % (4919)------------------------------
% 1.69/1.69 % (4919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.69 % (4919)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.69
% 1.69/1.69
% 1.69/1.69 % (4919)Memory used [KB]: 5628
% 1.69/1.69 % (4919)Time elapsed: 0.008 s
% 1.69/1.69 % (4919)Instructions burned: 18 (million)
% 1.69/1.69 % (4919)------------------------------
% 1.69/1.69 % (4919)------------------------------
% 1.69/1.70 % (4909)Instruction limit reached!
% 1.69/1.70 % (4909)------------------------------
% 1.69/1.70 % (4909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.70 % (4909)Termination reason: Unknown
% 1.69/1.70 % (4909)Termination phase: Saturation
% 1.69/1.70
% 1.69/1.70 % (4909)Memory used [KB]: 5628
% 1.69/1.70 % (4909)Time elapsed: 0.033 s
% 1.69/1.70 % (4909)Instructions burned: 97 (million)
% 1.69/1.70 % (4909)------------------------------
% 1.69/1.70 % (4909)------------------------------
% 1.69/1.70 % (4927)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_4599 for (2996ds/11Mi)
% 1.69/1.70 % (4927)Instruction limit reached!
% 1.69/1.70 % (4927)------------------------------
% 1.69/1.70 % (4927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.70 % (4927)Termination reason: Unknown
% 1.69/1.70 % (4927)Termination phase: Saturation
% 1.69/1.70
% 1.69/1.70 % (4927)Memory used [KB]: 5500
% 1.69/1.70 % (4927)Time elapsed: 0.006 s
% 1.69/1.70 % (4927)Instructions burned: 12 (million)
% 1.69/1.70 % (4927)------------------------------
% 1.69/1.70 % (4927)------------------------------
% 1.69/1.70 % (4929)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_4599 for (2996ds/41Mi)
% 1.69/1.71 % (4930)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4599 for (2996ds/6Mi)
% 1.69/1.71 % (4903)First to succeed.
% 1.69/1.71 % (4930)Instruction limit reached!
% 1.69/1.71 % (4930)------------------------------
% 1.69/1.71 % (4930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.71 % (4930)Termination reason: Unknown
% 1.69/1.71 % (4930)Termination phase: Saturation
% 1.69/1.71
% 1.69/1.71 % (4930)Memory used [KB]: 5500
% 1.69/1.71 % (4930)Time elapsed: 0.004 s
% 1.69/1.71 % (4930)Instructions burned: 6 (million)
% 1.69/1.71 % (4930)------------------------------
% 1.69/1.71 % (4930)------------------------------
% 1.69/1.71 % (4903)Refutation found. Thanks to Tanya!
% 1.69/1.71 % SZS status Theorem for DTF2THF_4599
% 1.69/1.71 % SZS output start Proof for DTF2THF_4599
% 1.69/1.71 thf(func_def_0, type, r: (($i > $o) > $o) > (($i > $o) > $o) > $o).
% 1.69/1.71 thf(func_def_1, type, cNAT: (($i > $o) > $o) > $o).
% 1.69/1.71 thf(func_def_2, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 1.69/1.71 thf(func_def_3, type, cZERO: ($i > $o) > $o).
% 1.69/1.71 thf(func_def_18, type, ph0: !>[X0: $tType]:(X0)).
% 1.69/1.71 thf(func_def_19, type, sK1: ($i > $o) > $o).
% 1.69/1.71 thf(func_def_26, type, sK2: ($i > $o) > $o).
% 1.69/1.71 thf(f143,plain,(
% 1.69/1.71 $false),
% 1.69/1.71 inference(trivial_inequality_removal,[status(thm)],[f141])).
% 1.69/1.71 thf(f141,plain,(
% 1.69/1.71 ($false = $true)),
% 1.69/1.71 inference(superposition,[status(thm)],[f137,f107])).
% 1.69/1.71 thf(f107,plain,(
% 1.69/1.71 ( ! [X2 : ($i > $o) > $o,X1 : ($i > $o) > $o] : ((((r @ X1 @ X2) => (r @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X2 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true)) )),
% 1.69/1.71 inference(beta_eta_normalization,[status(thm)],[f106])).
% 1.69/1.71 thf(f106,plain,(
% 1.69/1.71 ( ! [X2 : ($i > $o) > $o,X1 : ($i > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: ((r @ X1 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (X1 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X2) = $true)) )),
% 1.69/1.71 inference(pi_clausification,[status(thm)],[f96])).
% 1.69/1.71 thf(f96,plain,(
% 1.69/1.71 ( ! [X1 : ($i > $o) > $o] : (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((r @ X1 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (X1 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) = $true)) )),
% 1.69/1.71 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.69/1.71 thf(f91,plain,(
% 1.69/1.71 ( ! [X1 : ($i > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y0 @ Y1) => (r @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))) @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4))))))))))))) @ X1) = $true)) )),
% 1.69/1.71 inference(pi_clausification,[status(thm)],[f37])).
% 1.69/1.71 thf(f37,plain,(
% 1.69/1.71 ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y0 @ Y1) => (r @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))) @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))))) = $true)),
% 1.69/1.71 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.69/1.71 thf(f24,plain,(
% 1.69/1.71 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y0 @ Y1) => (r @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))) @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))))) & (r @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $true)),
% 1.69/1.71 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.69/1.71 thf(f22,plain,(
% 1.69/1.71 ($false = (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y0 @ Y1) => (r @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))) @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))))) & (r @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => (?? @ (($i > $o) > $o) @ (r @ Y0)))))))),
% 1.69/1.71 inference(not_proxy_clausification,[status(thm)],[f21])).
% 1.69/1.71 thf(f21,plain,(
% 1.69/1.71 ((~ (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y0 @ Y1) => (r @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))) @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))))) & (r @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => (?? @ (($i > $o) > $o) @ (r @ Y0))))))) = $true)),
% 1.69/1.71 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.69/1.71 thf(f20,plain,(
% 1.69/1.71 ((~ (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y0 @ Y1) => (r @ ((^[Y2 : ($i > $o) > $o]: ((^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))) @ Y0) @ ((^[Y2 : ($i > $o) > $o]: ((^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))) @ Y1))))))) & (r @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))) => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((^[Y1 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ ((^[Y4 : ($i > $o) > $o]: ((^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((~ (Y6 = Y7)) & (Y5 @ Y7)))))))))) @ Y3))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ (^[Y4 : $i]: (Y3 @ Y4))))))) => (Y2 @ Y1))))) @ Y0) => (?? @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (r @ Y0 @ Y1)))))))) = $true)),
% 1.69/1.71 inference(definition_unfolding,[status(thm)],[f16,f18,f18,f15,f15,f19])).
% 1.69/1.71 thf(f19,plain,(
% 1.69/1.71 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))))),
% 1.69/1.71 inference(definition_unfolding,[status(thm)],[f17,f18,f15])).
% 1.69/1.71 thf(f17,plain,(
% 1.69/1.71 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 1.69/1.71 inference(cnf_transformation,[status(thm)],[f8])).
% 1.69/1.71 thf(f8,plain,(
% 1.69/1.71 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 1.69/1.71 inference(fool_elimination,[status(thm)],[f7])).
% 1.69/1.71 thf(f7,plain,(
% 1.69/1.71 ((^[X0 : ($i > $o) > $o] : (! [X1 : (($i > $o) > $o) > $o] : (((X1 @ cZERO) & ! [X2 : ($i > $o) > $o] : ((X1 @ X2) => (X1 @ (cSUCC @ X2)))) => (X1 @ X0)))) = cNAT)),
% 1.69/1.71 inference(rectify,[status(thm)],[f3])).
% 1.69/1.71 thf(f3,axiom,(
% 1.69/1.71 ((^[X2 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : (((X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) => (X0 @ X2)))) = cNAT)),
% 1.69/1.71 file('/export/starexec/sandbox/tmp/tmp.Ufgz3VaiJ2/DTF2THF_4599.p',cNAT_def)).
% 1.69/1.71 thf(f15,plain,(
% 1.69/1.71 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.69/1.71 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.71 thf(f14,plain,(
% 1.69/1.71 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.69/1.71 inference(fool_elimination,[status(thm)],[f13])).
% 1.69/1.71 thf(f13,plain,(
% 1.69/1.71 ((^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))) = cZERO)),
% 1.69/1.71 inference(rectify,[status(thm)],[f1])).
% 1.69/1.71 thf(f1,axiom,(
% 1.69/1.71 ((^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))) = cZERO)),
% 1.69/1.71 file('/export/starexec/sandbox/tmp/tmp.Ufgz3VaiJ2/DTF2THF_4599.p',cZERO_def)).
% 1.69/1.71 thf(f18,plain,(
% 1.69/1.71 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 1.69/1.71 inference(cnf_transformation,[status(thm)],[f12])).
% 1.69/1.71 thf(f12,plain,(
% 1.69/1.71 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 1.69/1.71 inference(fool_elimination,[status(thm)],[f11])).
% 1.69/1.71 thf(f11,plain,(
% 1.69/1.71 ((^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2 : $i] : ((X0 @ (^[X3 : $i] : ((X1 @ X3) & (X2 != X3)))) & (X1 @ X2)))) = cSUCC)),
% 1.69/1.71 inference(rectify,[status(thm)],[f2])).
% 1.69/1.71 thf(f2,axiom,(
% 1.69/1.71 ((^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1 : $i] : ((X2 @ (^[X3 : $i] : ((X0 @ X3) & (X1 != X3)))) & (X0 @ X1)))) = cSUCC)),
% 1.69/1.71 file('/export/starexec/sandbox/tmp/tmp.Ufgz3VaiJ2/DTF2THF_4599.p',cSUCC_def)).
% 1.69/1.71 thf(f16,plain,(
% 1.69/1.71 ((~ (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y0 @ Y1) => (r @ (cSUCC @ Y0) @ (cSUCC @ Y1))))))) & (r @ cZERO @ cZERO)) => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((cNAT @ Y0) => (?? @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (r @ Y0 @ Y1)))))))) = $true)),
% 1.69/1.71 inference(cnf_transformation,[status(thm)],[f10])).
% 1.69/1.71 thf(f10,plain,(
% 1.69/1.71 ((~ (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y0 @ Y1) => (r @ (cSUCC @ Y0) @ (cSUCC @ Y1))))))) & (r @ cZERO @ cZERO)) => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((cNAT @ Y0) => (?? @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (r @ Y0 @ Y1)))))))) = $true)),
% 1.69/1.71 inference(fool_elimination,[status(thm)],[f9])).
% 1.69/1.71 thf(f9,plain,(
% 1.69/1.71 ~(((r @ cZERO @ cZERO) & ! [X0 : ($i > $o) > $o,X1 : ($i > $o) > $o] : ((r @ X1 @ X0) => (r @ (cSUCC @ X1) @ (cSUCC @ X0)))) => ! [X2 : ($i > $o) > $o] : ((cNAT @ X2) => ? [X3 : ($i > $o) > $o] : (r @ X2 @ X3)))),
% 1.69/1.71 inference(rectify,[status(thm)],[f5])).
% 1.69/1.71 thf(f5,negated_conjecture,(
% 1.69/1.71 ~(((r @ cZERO @ cZERO) & ! [X4 : ($i > $o) > $o,X1 : ($i > $o) > $o] : ((r @ X1 @ X4) => (r @ (cSUCC @ X1) @ (cSUCC @ X4)))) => ! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => ? [X4 : ($i > $o) > $o] : (r @ X1 @ X4)))),
% 1.69/1.71 inference(negated_conjecture,[status(cth)],[f4])).
% 1.69/1.71 thf(f4,conjecture,(
% 1.69/1.71 ((r @ cZERO @ cZERO) & ! [X4 : ($i > $o) > $o,X1 : ($i > $o) > $o] : ((r @ X1 @ X4) => (r @ (cSUCC @ X1) @ (cSUCC @ X4)))) => ! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => ? [X4 : ($i > $o) > $o] : (r @ X1 @ X4))),
% 1.69/1.71 file('/export/starexec/sandbox/tmp/tmp.Ufgz3VaiJ2/DTF2THF_4599.p',cTHM130_B)).
% 1.69/1.71 thf(f137,plain,(
% 1.69/1.71 (((r @ sK2 @ sK2) => (r @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK2 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK2 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $false)),
% 1.69/1.71 inference(beta_eta_normalization,[status(thm)],[f131])).
% 1.69/1.71 thf(f131,plain,(
% 1.69/1.71 (((^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ sK2) = $false)),
% 1.69/1.71 inference(sigma_clausification,[status(thm)],[f130])).
% 1.69/1.71 thf(f130,plain,(
% 1.69/1.71 ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) = $false)),
% 1.69/1.71 inference(not_proxy_clausification,[status(thm)],[f90])).
% 1.69/1.71 thf(f90,plain,(
% 1.69/1.71 ((~ (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) = $true)),
% 1.69/1.71 inference(boolean_simplification,[status(thm)],[f89])).
% 1.69/1.71 thf(f89,plain,(
% 1.69/1.71 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) => $false) = $true)),
% 1.69/1.71 inference(forward_demodulation,[status(thm)],[f81,f44])).
% 1.69/1.71 thf(f44,plain,(
% 1.69/1.71 ( ! [X1 : ($i > $o) > $o] : (((r @ sK1 @ X1) = $false)) )),
% 1.69/1.71 inference(pi_clausification,[status(thm)],[f34])).
% 1.69/1.71 thf(f34,plain,(
% 1.69/1.71 ($false = (?? @ (($i > $o) > $o) @ (r @ sK1)))),
% 1.69/1.71 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.69/1.71 thf(f30,plain,(
% 1.69/1.71 ($false = ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK1)))) => (?? @ (($i > $o) > $o) @ (r @ sK1))))),
% 1.69/1.71 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.69/1.71 thf(f27,plain,(
% 1.69/1.71 ($false = ((^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => (?? @ (($i > $o) > $o) @ (r @ Y0)))) @ sK1))),
% 1.69/1.71 inference(sigma_clausification,[status(thm)],[f23])).
% 1.69/1.71 thf(f23,plain,(
% 1.69/1.71 ($false = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => (?? @ (($i > $o) > $o) @ (r @ Y0))))))),
% 1.69/1.71 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.69/1.71 thf(f81,plain,(
% 1.69/1.71 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) => (r @ sK1 @ sK1)) = $true)),
% 1.69/1.71 inference(boolean_simplification,[status(thm)],[f80])).
% 1.69/1.71 thf(f80,plain,(
% 1.69/1.71 ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & $true) => (r @ sK1 @ sK1)) = $true)),
% 1.69/1.71 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.69/1.71 thf(f68,plain,(
% 1.69/1.71 ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((^[Y1 : ($i > $o) > $o]: (r @ ((^[Y2 : ($i > $o) > $o]: ((^[Y3 : $i > $o]: (Y2 @ ((^[Y4 : ($i > $o) > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (Y5 @ ((^[Y7 : ($i > $o) > $o]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (Y9)))))) @ Y4 @ Y5 @ Y6))))))) @ Y2 @ Y3))))) @ Y1) @ ((^[Y2 : ($i > $o) > $o]: ((^[Y3 : $i > $o]: (Y2 @ ((^[Y4 : ($i > $o) > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (Y5 @ ((^[Y7 : ($i > $o) > $o]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (Y9)))))) @ Y4 @ Y5 @ Y6))))))) @ Y2 @ Y3))))) @ Y1))) @ Y0) => ((^[Y1 : ($i > $o) > $o]: (r @ ((^[Y2 : ($i > $o) > $o]: ((^[Y3 : $i > $o]: (Y2 @ ((^[Y4 : ($i > $o) > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (Y5 @ ((^[Y7 : ($i > $o) > $o]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (Y9)))))) @ Y4 @ Y5 @ Y6))))))) @ Y2 @ Y3))))) @ Y1) @ ((^[Y2 : ($i > $o) > $o]: ((^[Y3 : $i > $o]: (Y2 @ ((^[Y4 : ($i > $o) > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (Y5 @ ((^[Y7 : ($i > $o) > $o]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (Y9)))))) @ Y4 @ Y5 @ Y6))))))) @ Y2 @ Y3))))) @ Y1))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & $true) => ((^[Y0 : ($i > $o) > $o]: (r @ ((^[Y1 : ($i > $o) > $o]: ((^[Y2 : $i > $o]: (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (Y4 @ ((^[Y6 : ($i > $o) > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: (Y8)))))) @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ Y0) @ ((^[Y1 : ($i > $o) > $o]: ((^[Y2 : $i > $o]: (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (Y4 @ ((^[Y6 : ($i > $o) > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: (Y8)))))) @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ Y0))) @ sK1)) = $true)),
% 1.69/1.71 inference(superposition,[status(thm)],[f61,f36])).
% 1.69/1.71 thf(f36,plain,(
% 1.69/1.71 ((r @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $true)),
% 1.69/1.71 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.69/1.71 thf(f61,plain,(
% 1.69/1.71 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (X1 @ sK1)))) )),
% 1.69/1.71 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.69/1.71 thf(f58,plain,(
% 1.69/1.71 ( ! [X1 : (($i > $o) > $o) > $o] : ((((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK1))) @ X1) = $true)) )),
% 1.69/1.71 inference(pi_clausification,[status(thm)],[f35])).
% 1.69/1.71 thf(f35,plain,(
% 1.69/1.71 ($true = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK1)))))),
% 1.69/1.71 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.69/1.71 % SZS output end Proof for DTF2THF_4599
% 1.69/1.71 % (4903)------------------------------
% 1.69/1.71 % (4903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.71 % (4903)Termination reason: Refutation
% 1.69/1.71
% 1.69/1.71 % (4903)Memory used [KB]: 2430
% 1.69/1.71 % (4903)Time elapsed: 0.050 s
% 1.69/1.71 % (4903)Instructions burned: 162 (million)
% 1.69/1.71 % (4903)------------------------------
% 1.69/1.71 % (4903)------------------------------
% 1.69/1.71 % (4787)Success in time 0.4 s
%------------------------------------------------------------------------------