%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV295^5 : 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 : n003.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 09:40:46 AM UTC 2026
% Result : Theorem 1.71s 1.91s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 487 ( 107 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 1491 ( 104 ~; 0 |; 169 &; 915 @)
% ( 0 <=>; 115 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 692 ( 692 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 8 usr; 5 con; 0-2 aty)
% ( 86 !!; 102 ??; 0 @@+; 0 @@-)
% Number of variables : 423 ( 388 ^; 28 !; 7 ?; 423 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
r: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(func_def_2,type,
cNAT: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_3,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(func_def_4,type,
cZERO: ( $i > $o ) > $o ).
thf(func_def_19,type,
ph0:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK1: ( $i > $o ) > $o ).
thf(func_def_27,type,
sK2: ( $i > $o ) > $o ).
thf(f212,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f211]) ).
thf(f211,plain,
$false = $true,
inference(superposition,[status(thm)],[f98,f176]) ).
thf(f176,plain,
( ( ( r @ sK2 @ sK2 )
=> ( r
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( sK2
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) ) ) )
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( sK2
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f171]) ).
thf(f171,plain,
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f160]) ).
thf(f160,plain,
( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
( ( ~ ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f140]) ).
thf(f140,plain,
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ) )
=> $false )
= $true ),
inference(forward_demodulation,[status(thm)],[f127,f49]) ).
thf(f49,plain,
! [X1: ( $i > $o ) > $o] :
( ( r @ sK1 @ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( $false
= ( ?? @ ( ( $i > $o ) > $o ) @ ( r @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( $false
= ( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) ) ) ) ) )
=> ( Y0 @ sK1 ) ) )
=> ( ?? @ ( ( $i > $o ) > $o ) @ ( r @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( ?? @ ( ( $i > $o ) > $o ) @ ( r @ Y0 ) ) )
@ sK1 )
= $false ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( ?? @ ( ( $i > $o ) > $o ) @ ( r @ Y0 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( ( r
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
& ( !! @ ( ( ( $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] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y2: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y2
@ ^ [Y3: $i > $o] :
~ ( ?? @ $i @ Y3 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y3: ( $i > $o ) > $o] :
( ( Y2 @ Y3 )
=> ( Y2
@ ^ [Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
& ( Y3
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 != Y6 ) ) ) ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y1 @ Y0 )
=> ( r
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) )
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y0
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) ) ) ) ) ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( ?? @ ( ( $i > $o ) > $o ) @ ( r @ Y0 ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ~ ( ( ( r
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
& ( !! @ ( ( ( $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] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y2: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y2
@ ^ [Y3: $i > $o] :
~ ( ?? @ $i @ Y3 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y3: ( $i > $o ) > $o] :
( ( Y2 @ Y3 )
=> ( Y2
@ ^ [Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
& ( Y3
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 != Y6 ) ) ) ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y1 @ Y0 )
=> ( r
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) )
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y0
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) ) ) ) ) ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( ?? @ ( ( $i > $o ) > $o ) @ ( r @ Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ~ ( ( ( r
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) )
& ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ( ^ [Y2: ( $i > $o ) > $o,Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) ) ) )
@ Y1 ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( ^ [Y2: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y3: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y3
@ ^ [Y4: $i > $o] :
~ ( ?? @ $i
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y4: ( $i > $o ) > $o] :
( ( Y3 @ Y4 )
=> ( Y3
@ ( ^ [Y5: ( $i > $o ) > $o,Y6: $i > $o] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( Y6 @ Y7 )
& ( Y5
@ ^ [Y8: $i] :
( ( Y6 @ Y8 )
& ( Y7 != Y8 ) ) ) ) )
@ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
@ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y1 @ Y0 )
=> ( r
@ ( ^ [Y2: ( $i > $o ) > $o,Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) ) ) )
@ Y1 )
@ ( ^ [Y2: ( $i > $o ) > $o,Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) ) ) )
@ Y0 ) ) ) ) ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( ^ [Y1: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y2: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y2
@ ^ [Y3: $i > $o] :
~ ( ?? @ $i
@ ^ [Y4: $i] : ( Y3 @ Y4 ) ) )
& ( !! @ ( ( $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] :
( ( Y5 @ Y7 )
& ( Y6 != Y7 ) ) ) ) )
@ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] : ( r @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f21,f19,f19,f24,f18,f18,f23]) ).
thf(f23,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
& ( !! @ ( ( $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] :
( ( Y4 @ Y6 )
& ( Y5 != Y6 ) ) ) ) )
@ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f22,f19,f18]) ).
thf(f22,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1 @ cZERO )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1 @ cZERO )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [X0: ( $i > $o ) > $o] :
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( cSUCC @ X2 ) ) )
& ( X1 @ cZERO ) )
=> ( X1 @ X0 ) ) )
= cNAT ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X2: ( $i > $o ) > $o] :
! [X0: ( ( $i > $o ) > $o ) > $o] :
( ( ! [X1: ( $i > $o ) > $o] :
( ( X0 @ X1 )
=> ( X0 @ ( cSUCC @ X1 ) ) )
& ( X0 @ cZERO ) )
=> ( X0 @ X2 ) ) )
= cNAT ),
file('/export/starexec/sandbox/tmp/tmp.Gc2avpieIj/DTF2THF_2206.p',cNAT_def) ).
thf(f18,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X0
@ ^ [X3: $i] :
( ( X2 != X3 )
& ( X1 @ X3 ) ) )
& ( X1 @ X2 ) ) )
= cSUCC ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X2: ( $i > $o ) > $o,X0: $i > $o] :
? [X1: $i] :
( ( X2
@ ^ [X3: $i] :
( ( X1 != X3 )
& ( X0 @ X3 ) ) )
& ( X0 @ X1 ) ) )
= cSUCC ),
file('/export/starexec/sandbox/tmp/tmp.Gc2avpieIj/DTF2THF_2206.p',cSUCC_def) ).
thf(f24,plain,
( cINDUCTION
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ( ^ [Y2: ( $i > $o ) > $o,Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 != Y5 ) ) ) ) )
@ Y1 ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( ^ [Y2: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y3: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y3
@ ^ [Y4: $i > $o] :
~ ( ?? @ $i
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y4: ( $i > $o ) > $o] :
( ( Y3 @ Y4 )
=> ( Y3
@ ( ^ [Y5: ( $i > $o ) > $o,Y6: $i > $o] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( Y6 @ Y7 )
& ( Y5
@ ^ [Y8: $i] :
( ( Y6 @ Y8 )
& ( Y7 != Y8 ) ) ) ) )
@ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
@ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f20,f18,f19,f23]) ).
thf(f20,plain,
( cINDUCTION
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cSUCC @ Y1 ) ) ) )
& ( Y0 @ cZERO ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( cNAT @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( cINDUCTION
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cSUCC @ Y1 ) ) ) )
& ( Y0 @ cZERO ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( cNAT @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( cINDUCTION
= ( ! [X0: ( ( $i > $o ) > $o ) > $o] :
( ( ( X0 @ cZERO )
& ! [X1: ( $i > $o ) > $o] :
( ( X0 @ X1 )
=> ( X0 @ ( cSUCC @ X1 ) ) ) )
=> ! [X2: ( $i > $o ) > $o] :
( ( cNAT @ X2 )
=> ( X0 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( cINDUCTION
= ( ! [X4: ( ( $i > $o ) > $o ) > $o] :
( ( ( X4 @ cZERO )
& ! [X5: ( $i > $o ) > $o] :
( ( X4 @ X5 )
=> ( X4 @ ( cSUCC @ X5 ) ) ) )
=> ! [X6: ( $i > $o ) > $o] :
( ( cNAT @ X6 )
=> ( X4 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Gc2avpieIj/DTF2THF_2206.p',cINDUCTION_def) ).
thf(f19,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,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.Gc2avpieIj/DTF2THF_2206.p',cZERO_def) ).
thf(f21,plain,
( ( ~ ( ( ( r @ cZERO @ cZERO )
& cINDUCTION
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y1 @ Y0 )
=> ( r @ ( cSUCC @ Y1 ) @ ( cSUCC @ Y0 ) ) ) ) ) )
=> ( !! @ ( ( $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)],[f15]) ).
thf(f15,plain,
( ( ~ ( ( ( r @ cZERO @ cZERO )
& cINDUCTION
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y1 @ Y0 )
=> ( r @ ( cSUCC @ Y1 ) @ ( cSUCC @ Y0 ) ) ) ) ) )
=> ( !! @ ( ( $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)],[f14]) ).
thf(f14,plain,
~ ( ( ! [X0: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( r @ X0 @ X1 )
=> ( r @ ( cSUCC @ X0 ) @ ( cSUCC @ X1 ) ) )
& cINDUCTION
& ( r @ cZERO @ cZERO ) )
=> ! [X2: ( $i > $o ) > $o] :
( ( cNAT @ X2 )
=> ? [X3: ( $i > $o ) > $o] : ( r @ X2 @ X3 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( ( ! [X1: ( $i > $o ) > $o,X7: ( $i > $o ) > $o] :
( ( r @ X1 @ X7 )
=> ( r @ ( cSUCC @ X1 ) @ ( cSUCC @ X7 ) ) )
& cINDUCTION
& ( r @ cZERO @ cZERO ) )
=> ! [X1: ( $i > $o ) > $o] :
( ( cNAT @ X1 )
=> ? [X7: ( $i > $o ) > $o] : ( r @ X1 @ X7 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( ( ! [X1: ( $i > $o ) > $o,X7: ( $i > $o ) > $o] :
( ( r @ X1 @ X7 )
=> ( r @ ( cSUCC @ X1 ) @ ( cSUCC @ X7 ) ) )
& cINDUCTION
& ( r @ cZERO @ cZERO ) )
=> ! [X1: ( $i > $o ) > $o] :
( ( cNAT @ X1 )
=> ? [X7: ( $i > $o ) > $o] : ( r @ X1 @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Gc2avpieIj/DTF2THF_2206.p',cTHM130_NAT) ).
thf(f127,plain,
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ) )
=> ( r @ sK1 @ sK1 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f126]) ).
thf(f126,plain,
( $true
= ( ( $true
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ Y0 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ) ) )
=> ( r @ sK1 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f121]) ).
thf(f121,plain,
( $true
= ( ( $true
& ( !! @ ( ( $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] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ) ) )
=> ( ^ [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 ) ) ),
inference(superposition,[status(thm)],[f54,f103]) ).
thf(f103,plain,
( ( r
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( r
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
& ( !! @ ( ( ( $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] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y2: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y2
@ ^ [Y3: $i > $o] :
~ ( ?? @ $i @ Y3 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y3: ( $i > $o ) > $o] :
( ( Y2 @ Y3 )
=> ( Y2
@ ^ [Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
& ( Y3
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 != Y6 ) ) ) ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( r
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
& ( !! @ ( ( ( $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] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y2: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y2
@ ^ [Y3: $i > $o] :
~ ( ?? @ $i @ Y3 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y3: ( $i > $o ) > $o] :
( ( Y2 @ Y3 )
=> ( Y2
@ ^ [Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
& ( Y3
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 != Y6 ) ) ) ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y1 @ Y0 )
=> ( r
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) )
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y0
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f54,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( $true
= ( ( ( X1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( X1 @ Y0 )
=> ( X1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ) ) )
=> ( X1 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) ) ) ) ) )
=> ( Y0 @ sK1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( $true
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) ) ) ) ) )
=> ( Y0 @ sK1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f98,plain,
! [X2: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( r @ X2 @ X1 )
=> ( r
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( X2
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) ) ) )
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( X1
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ X1 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( X1
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X1: ( $i > $o ) > $o] :
( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( r @ Y0 @ X1 )
=> ( r
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( X1
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,plain,
! [X1: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y1 @ Y0 )
=> ( r
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) )
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y0
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( r @ Y1 @ Y0 )
=> ( r
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) )
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y0
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV295^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:43:10 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SEV295^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.30/0.45 % Domain : Set Theory
% 0.30/0.45 % Problem : TPS problem THM130-NAT
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Bro09]
% 0.30/0.45 % Names : tps_0548 [Bro09]
% 0.30/0.45 % : THM130-NAT [TPS]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.78 v9.1.0, 0.75 v9.0.0, 0.90 v8.2.0, 0.92 v8.1.0, 0.82 v7.5.0, 0.71 v7.4.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0
% 0.30/0.45 % Syntax : Number of formulae : 10 ( 4 unt; 5 typ; 4 def)
% 0.30/0.45 % Number of atoms : 24 ( 5 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 10 ( 4 avg)
% 0.30/0.45 % Number of connectives : 42 ( 2 ~; 0 |; 6 &; 26 @)
% 0.30/0.45 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 10 ( 3 avg)
% 0.30/0.45 % Number of types : 2 ( 0 usr)
% 0.30/0.45 % Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 6 ( 5 usr; 1 con; 0-2 aty)
% 0.30/0.45 % Number of variables : 16 ( 5 ^; 8 !; 3 ?; 16 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.45 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.30/0.45 % : v6.2.0 - Reordered definitions.
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(r_type,type,
% 0.30/0.45 r: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(cINDUCTION_type,type,
% 0.30/0.45 cINDUCTION: $o ).
% 0.30/0.45
% 0.30/0.45 thf(cNAT_type,type,
% 0.30/0.45 cNAT: ( ( $i > $o ) > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(cSUCC_type,type,
% 0.30/0.45 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(cZERO_type,type,
% 0.30/0.45 cZERO: ( $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(cZERO_def,definition,
% 0.30/0.45 ( cZERO
% 0.30/0.45 = ( ^ [Xp: $i > $o] :
% 0.30/0.45 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(cSUCC_def,definition,
% 0.30/0.45 ( cSUCC
% 0.30/0.45 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 0.30/0.45 ? [Xx: $i] :
% 0.30/0.45 ( ( Xp @ Xx )
% 0.30/0.45 & ( Xn
% 0.30/0.45 @ ^ [Xt: $i] :
% 0.30/0.45 ( ( Xt != Xx )
% 0.30/0.45 & ( Xp @ Xt ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(cNAT_def,definition,
% 0.30/0.45 ( cNAT
% 0.30/0.45 = ( ^ [Xn: ( $i > $o ) > $o] :
% 0.30/0.45 ! [Xp: ( ( $i > $o ) > $o ) > $o] :
% 0.30/0.45 ( ( ( Xp @ cZERO )
% 0.30/0.45 & ! [Xx: ( $i > $o ) > $o] :
% 0.30/0.45 ( ( Xp @ Xx )
% 0.30/0.45 => ( Xp @ ( cSUCC @ Xx ) ) ) )
% 0.30/0.45 => ( Xp @ Xn ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(cINDUCTION_def,definition,
% 0.30/0.45 ( cINDUCTION
% 0.30/0.45 = ( ! [P: ( ( $i > $o ) > $o ) > $o] :
% 0.30/0.45 ( ( ( P @ cZERO )
% 0.30/0.45 & ! [X: ( $i > $o ) > $o] :
% 0.30/0.45 ( ( P @ X )
% 0.30/0.45 => ( P @ ( cSUCC @ X ) ) ) )
% 0.30/0.45 => ! [M: ( $i > $o ) > $o] :
% 0.30/0.45 ( ( cNAT @ M )
% 0.30/0.45 => ( P @ M ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(cTHM130_NAT,conjecture,
% 0.30/0.45 ( ( cINDUCTION
% 0.30/0.45 & ( r @ cZERO @ cZERO )
% 0.30/0.45 & ! [Xx: ( $i > $o ) > $o,Xy: ( $i > $o ) > $o] :
% 0.30/0.45 ( ( r @ Xx @ Xy )
% 0.30/0.45 => ( r @ ( cSUCC @ Xx ) @ ( cSUCC @ Xy ) ) ) )
% 0.30/0.45 => ! [Xx: ( $i > $o ) > $o] :
% 0.30/0.45 ( ( cNAT @ Xx )
% 0.30/0.45 => ? [Xy: ( $i > $o ) > $o] : ( r @ Xx @ Xy ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.50/1.29 ---- Embedded in THF ---
% 1.50/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.29 %%% Generated on Tue Feb 24 12:43:11 EST 2026
% 1.50/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.29 %%% Logic specification used:
% 1.50/1.29 %%% thf(spec, logic, $$dhol).
% 1.50/1.29
% 1.50/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Gc2avpieIj/DTF2DTF2206.p
% See solution above
% 1.50/1.29 ------------------------
% 1.69/1.30 ---- Cleaned THF ---
% 1.69/1.31 thf(r_type,type,
% 1.69/1.31 r: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
% 1.69/1.31
% 1.69/1.31 thf(cINDUCTION_type,type,
% 1.69/1.31 cINDUCTION: $o ).
% 1.69/1.31
% 1.69/1.31 thf(cNAT_type,type,
% 1.69/1.31 cNAT: ( ( $i > $o ) > $o ) > $o ).
% 1.69/1.31
% 1.69/1.31 thf(cSUCC_type,type,
% 1.69/1.31 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 1.69/1.31
% 1.69/1.31 thf(cZERO_type,type,
% 1.69/1.31 cZERO: ( $i > $o ) > $o ).
% 1.69/1.31
% 1.69/1.31 thf(cZERO_def,definition,
% 1.69/1.31 ( cZERO
% 1.69/1.31 = ( ^ [Xp: $i > $o] :
% 1.69/1.31 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 1.69/1.31
% 1.69/1.31 thf(cSUCC_def,definition,
% 1.69/1.31 ( cSUCC
% 1.69/1.31 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 1.69/1.31 ? [Xx: $i] :
% 1.69/1.31 ( ( Xp @ Xx )
% 1.69/1.31 & ( Xn
% 1.69/1.31 @ ^ [Xt: $i] :
% 1.69/1.31 ( ( Xt != Xx )
% 1.69/1.31 & ( Xp @ Xt ) ) ) ) ) ) ).
% 1.69/1.31
% 1.69/1.31 thf(cNAT_def,definition,
% 1.69/1.31 ( cNAT
% 1.69/1.31 = ( ^ [Xn: ( $i > $o ) > $o] :
% 1.69/1.31 ! [Xp: ( ( $i > $o ) > $o ) > $o] :
% 1.69/1.31 ( ( ( Xp @ cZERO )
% 1.69/1.31 & ! [Xx: ( $i > $o ) > $o] :
% 1.69/1.31 ( ( Xp @ Xx )
% 1.69/1.31 => ( Xp @ ( cSUCC @ Xx ) ) ) )
% 1.69/1.31 => ( Xp @ Xn ) ) ) ) ).
% 1.69/1.31
% 1.69/1.31 thf(cINDUCTION_def,definition,
% 1.69/1.31 ( cINDUCTION
% 1.69/1.31 = ( ! [P: ( ( $i > $o ) > $o ) > $o] :
% 1.69/1.31 ( ( ( P @ cZERO )
% 1.69/1.31 & ! [X: ( $i > $o ) > $o] :
% 1.69/1.31 ( ( P @ X )
% 1.69/1.31 => ( P @ ( cSUCC @ X ) ) ) )
% 1.69/1.31 => ! [M: ( $i > $o ) > $o] :
% 1.69/1.31 ( ( cNAT @ M )
% 1.69/1.31 => ( P @ M ) ) ) ) ) ).
% 1.69/1.31
% 1.69/1.31 thf(cTHM130_NAT,conjecture,
% 1.69/1.31 ( ( cINDUCTION
% 1.69/1.31 & ( r @ cZERO @ cZERO )
% 1.69/1.31 & ! [Xx: ( $i > $o ) > $o,Xy: ( $i > $o ) > $o] :
% 1.69/1.31 ( ( r @ Xx @ Xy )
% 1.69/1.31 => ( r @ ( cSUCC @ Xx ) @ ( cSUCC @ Xy ) ) ) )
% 1.69/1.31 => ! [Xx: ( $i > $o ) > $o] :
% 1.69/1.31 ( ( cNAT @ Xx )
% 1.69/1.31 => ? [Xy: ( $i > $o ) > $o] : ( r @ Xx @ Xy ) ) ) ).
% 1.69/1.31 ------------------------
% 1.69/1.32 % (2399)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_2206 for (2999ds/2Mi)
% 1.69/1.32 % (2400)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_2206 for (2999ds/275Mi)
% 1.69/1.32 % (2399)Instruction limit reached!
% 1.69/1.32 % (2399)------------------------------
% 1.69/1.32 % (2399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (2399)Termination reason: Unknown
% 1.69/1.32 % (2399)Termination phase: Property scanning
% 1.69/1.32
% 1.69/1.32 % (2399)Memory used [KB]: 1023
% 1.69/1.32 % (2399)Time elapsed: 0.002 s
% 1.69/1.32 % (2399)Instructions burned: 4 (million)
% 1.69/1.32 % (2399)------------------------------
% 1.69/1.32 % (2399)------------------------------
% 1.69/1.32 % (2396)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_2206 for (2999ds/4Mi)
% 1.69/1.32 % (2396)Instruction limit reached!
% 1.69/1.32 % (2396)------------------------------
% 1.69/1.32 % (2396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (2396)Termination reason: Unknown
% 1.69/1.32 % (2396)Termination phase: Property scanning
% 1.69/1.32
% 1.69/1.32 % (2396)Memory used [KB]: 1023
% 1.69/1.32 % (2396)Time elapsed: 0.003 s
% 1.69/1.32 % (2396)Instructions burned: 4 (million)
% 1.69/1.32 % (2396)------------------------------
% 1.69/1.32 % (2396)------------------------------
% 1.69/1.33 % (2397)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_2206 for (2999ds/27Mi)
% 1.69/1.33 % (2398)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/2Mi)
% 1.69/1.33 % (2401)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/18Mi)
% 1.69/1.33 % (2398)Instruction limit reached!
% 1.69/1.33 % (2398)------------------------------
% 1.69/1.33 % (2398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (2398)Termination reason: Unknown
% 1.69/1.33 % (2398)Termination phase: Property scanning
% 1.69/1.33
% 1.69/1.33 % (2398)Memory used [KB]: 1023
% 1.69/1.33 % (2398)Time elapsed: 0.003 s
% 1.69/1.33 % (2398)Instructions burned: 2 (million)
% 1.69/1.33 % (2398)------------------------------
% 1.69/1.33 % (2398)------------------------------
% 1.69/1.33 % (2402)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/3Mi)
% 1.69/1.33 % (2395)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/183Mi)
% 1.69/1.33 % (2402)Instruction limit reached!
% 1.69/1.33 % (2402)------------------------------
% 1.69/1.33 % (2402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (2402)Termination reason: Unknown
% 1.69/1.33 % (2402)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (2402)Memory used [KB]: 5500
% 1.69/1.33 % (2402)Time elapsed: 0.002 s
% 1.69/1.33 % (2402)Instructions burned: 4 (million)
% 1.69/1.33 % (2402)------------------------------
% 1.69/1.33 % (2402)------------------------------
% 1.69/1.34 % (2403)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_2206 for (2999ds/37Mi)
% 1.69/1.34 % (2401)Instruction limit reached!
% 1.69/1.34 % (2401)------------------------------
% 1.69/1.34 % (2401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (2401)Termination reason: Unknown
% 1.69/1.34 % (2401)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (2401)Memory used [KB]: 5628
% 1.69/1.34 % (2401)Time elapsed: 0.013 s
% 1.69/1.34 % (2401)Instructions burned: 19 (million)
% 1.69/1.34 % (2401)------------------------------
% 1.69/1.34 % (2401)------------------------------
% 1.69/1.34 % (2405)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_2206 for (2999ds/3Mi)
% 1.69/1.34 % (2405)Instruction limit reached!
% 1.69/1.34 % (2405)------------------------------
% 1.69/1.34 % (2405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (2405)Termination reason: Unknown
% 1.69/1.34 % (2405)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (2405)Memory used [KB]: 5500
% 1.69/1.34 % (2405)Time elapsed: 0.002 s
% 1.69/1.34 % (2405)Instructions burned: 4 (million)
% 1.69/1.34 % (2405)------------------------------
% 1.69/1.34 % (2405)------------------------------
% 1.69/1.34 % (2397)Instruction limit reached!
% 1.69/1.34 % (2397)------------------------------
% 1.69/1.34 % (2397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (2397)Termination reason: Unknown
% 1.69/1.34 % (2397)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (2397)Memory used [KB]: 5628
% 1.69/1.34 % (2397)Time elapsed: 0.018 s
% 1.69/1.34 % (2397)Instructions burned: 27 (million)
% 1.69/1.34 % (2397)------------------------------
% 1.69/1.34 % (2397)------------------------------
% 1.69/1.35 % (2404)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_2206 for (2999ds/15Mi)
% 1.69/1.35 % (2407)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/7Mi)
% 1.69/1.35 % (2407)Instruction limit reached!
% 1.69/1.35 % (2407)------------------------------
% 1.69/1.35 % (2407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (2407)Termination reason: Unknown
% 1.69/1.35 % (2407)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (2407)Memory used [KB]: 1023
% 1.69/1.35 % (2407)Time elapsed: 0.003 s
% 1.69/1.35 % (2407)Instructions burned: 8 (million)
% 1.69/1.35 % (2407)------------------------------
% 1.69/1.35 % (2407)------------------------------
% 1.69/1.36 % (2404)Instruction limit reached!
% 1.69/1.36 % (2404)------------------------------
% 1.69/1.36 % (2404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (2404)Termination reason: Unknown
% 1.69/1.36 % (2404)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (2404)Memory used [KB]: 5628
% 1.69/1.36 % (2404)Time elapsed: 0.011 s
% 1.69/1.36 % (2404)Instructions burned: 16 (million)
% 1.69/1.36 % (2404)------------------------------
% 1.69/1.36 % (2404)------------------------------
% 1.69/1.36 % (2403)Instruction limit reached!
% 1.69/1.36 % (2403)------------------------------
% 1.69/1.36 % (2403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (2403)Termination reason: Unknown
% 1.69/1.36 % (2403)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (2403)Memory used [KB]: 5628
% 1.69/1.36 % (2403)Time elapsed: 0.021 s
% 1.69/1.36 % (2403)Instructions burned: 37 (million)
% 1.69/1.36 % (2403)------------------------------
% 1.69/1.36 % (2403)------------------------------
% 1.69/1.36 % (2406)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_2206 for (2999ds/1041Mi)
% 1.69/1.36 % (2408)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/16Mi)
% 1.69/1.36 % (2409)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_2206 for (2999ds/3Mi)
% 1.69/1.36 % (2409)Instruction limit reached!
% 1.69/1.36 % (2409)------------------------------
% 1.69/1.36 % (2409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (2409)Termination reason: Unknown
% 1.69/1.36 % (2409)Termination phase: Twee Goal Transformation
% 1.69/1.36
% 1.69/1.36 % (2409)Memory used [KB]: 1023
% 1.69/1.36 % (2409)Time elapsed: 0.002 s
% 1.69/1.36 % (2409)Instructions burned: 4 (million)
% 1.69/1.36 % (2409)------------------------------
% 1.69/1.36 % (2409)------------------------------
% 1.69/1.37 % (2410)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_2206 for (2999ds/3Mi)
% 1.69/1.37 % (2410)Instruction limit reached!
% 1.69/1.37 % (2410)------------------------------
% 1.69/1.37 % (2410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (2410)Termination reason: Unknown
% 1.69/1.37 % (2410)Termination phase: Property scanning
% 1.69/1.37
% 1.69/1.37 % (2410)Memory used [KB]: 1023
% 1.69/1.37 % (2410)Time elapsed: 0.003 s
% 1.69/1.37 % (2410)Instructions burned: 3 (million)
% 1.69/1.37 % (2410)------------------------------
% 1.69/1.37 % (2410)------------------------------
% 1.69/1.37 % (2408)Instruction limit reached!
% 1.69/1.37 % (2408)------------------------------
% 1.69/1.37 % (2408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (2408)Termination reason: Unknown
% 1.69/1.37 % (2408)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (2408)Memory used [KB]: 5756
% 1.69/1.37 % (2408)Time elapsed: 0.013 s
% 1.69/1.37 % (2408)Instructions burned: 17 (million)
% 1.69/1.37 % (2408)------------------------------
% 1.69/1.37 % (2408)------------------------------
% 1.69/1.37 % (2412)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/3Mi)
% 1.69/1.37 % (2412)Instruction limit reached!
% 1.69/1.37 % (2412)------------------------------
% 1.69/1.37 % (2412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (2412)Termination reason: Unknown
% 1.69/1.37 % (2412)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (2412)Memory used [KB]: 1023
% 1.69/1.37 % (2412)Time elapsed: 0.002 s
% 1.69/1.37 % (2412)Instructions burned: 4 (million)
% 1.69/1.37 % (2412)------------------------------
% 1.69/1.37 % (2412)------------------------------
% 1.69/1.38 % (2411)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/7Mi)
% 1.69/1.38 % (2411)Refutation not found, incomplete strategy
% 1.69/1.38 % (2411)------------------------------
% 1.69/1.38 % (2411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (2411)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.38
% 1.69/1.38
% 1.69/1.38 % (2411)Memory used [KB]: 5500
% 1.69/1.38 % (2411)Time elapsed: 0.005 s
% 1.69/1.38 % (2411)Instructions burned: 5 (million)
% 1.69/1.38 % (2411)------------------------------
% 1.69/1.38 % (2411)------------------------------
% 1.69/1.38 % (2415)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/710Mi)
% 1.69/1.39 % (2413)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/4Mi)
% 1.69/1.39 % (2413)Instruction limit reached!
% 1.69/1.39 % (2413)------------------------------
% 1.69/1.39 % (2413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (2413)Termination reason: Unknown
% 1.69/1.39 % (2413)Termination phase: Saturation
% 1.69/1.39
% 1.69/1.39 % (2413)Memory used [KB]: 1023
% 1.69/1.39 % (2413)Time elapsed: 0.003 s
% 1.69/1.39 % (2413)Instructions burned: 4 (million)
% 1.69/1.39 % (2413)------------------------------
% 1.69/1.39 % (2413)------------------------------
% 1.69/1.39 % (2414)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/18Mi)
% 1.71/1.40 % (2414)Instruction limit reached!
% 1.71/1.40 % (2414)------------------------------
% 1.71/1.40 % (2414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.40 % (2414)Termination reason: Unknown
% 1.71/1.40 % (2414)Termination phase: Saturation
% 1.71/1.40
% 1.71/1.40 % (2414)Memory used [KB]: 5628
% 1.71/1.40 % (2414)Time elapsed: 0.010 s
% 1.71/1.40 % (2414)Instructions burned: 18 (million)
% 1.71/1.40 % (2414)------------------------------
% 1.71/1.40 % (2414)------------------------------
% 1.71/1.40 % (2417)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_2206 for (2999ds/902Mi)
% 1.71/1.40 % (2400)Instruction limit reached!
% 1.71/1.40 % (2400)------------------------------
% 1.71/1.40 % (2400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.40 % (2400)Termination reason: Unknown
% 1.71/1.40 % (2400)Termination phase: Saturation
% 1.71/1.40
% 1.71/1.40 % (2400)Memory used [KB]: 6012
% 1.71/1.40 % (2400)Time elapsed: 0.081 s
% 1.71/1.40 % (2400)Instructions burned: 277 (million)
% 1.71/1.40 % (2400)------------------------------
% 1.71/1.40 % (2400)------------------------------
% 1.71/1.40 % (2417)Refutation not found, incomplete strategy
% 1.71/1.40 % (2417)------------------------------
% 1.71/1.40 % (2417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.40 % (2417)Termination reason: Refutation not found, incomplete strategy
% 1.71/1.40
% 1.71/1.40
% 1.71/1.40 % (2417)Memory used [KB]: 5500
% 1.71/1.40 % (2417)Time elapsed: 0.003 s
% 1.71/1.40 % (2417)Instructions burned: 4 (million)
% 1.71/1.40 % (2417)------------------------------
% 1.71/1.40 % (2417)------------------------------
% 1.71/1.40 % (2416)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/6Mi)
% 1.71/1.40 % (2416)Instruction limit reached!
% 1.71/1.40 % (2416)------------------------------
% 1.71/1.40 % (2416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.40 % (2416)Termination reason: Unknown
% 1.71/1.40 % (2416)Termination phase: Saturation
% 1.71/1.40
% 1.71/1.40 % (2416)Memory used [KB]: 5500
% 1.71/1.40 % (2416)Time elapsed: 0.006 s
% 1.71/1.40 % (2416)Instructions burned: 7 (million)
% 1.71/1.40 % (2416)------------------------------
% 1.71/1.40 % (2416)------------------------------
% 1.71/1.41 % (2419)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/5Mi)
% 1.71/1.41 % (2418)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_2206 for (2999ds/21Mi)
% 1.71/1.41 % (2420)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_2206 for (2999ds/6Mi)
% 1.71/1.41 % (2419)Instruction limit reached!
% 1.71/1.41 % (2419)------------------------------
% 1.71/1.41 % (2419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.41 % (2419)Termination reason: Unknown
% 1.71/1.41 % (2419)Termination phase: Saturation
% 1.71/1.41
% 1.71/1.41 % (2419)Memory used [KB]: 5500
% 1.71/1.41 % (2419)Time elapsed: 0.003 s
% 1.71/1.41 % (2419)Instructions burned: 6 (million)
% 1.71/1.41 % (2419)------------------------------
% 1.71/1.41 % (2419)------------------------------
% 1.71/1.41 % (2420)Instruction limit reached!
% 1.71/1.41 % (2420)------------------------------
% 1.71/1.41 % (2420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.41 % (2420)Termination reason: Unknown
% 1.71/1.41 % (2420)Termination phase: Saturation
% 1.71/1.41
% 1.71/1.41 % (2420)Memory used [KB]: 5500
% 1.71/1.41 % (2420)Time elapsed: 0.003 s
% 1.71/1.41 % (2420)Instructions burned: 7 (million)
% 1.71/1.41 % (2420)------------------------------
% 1.71/1.41 % (2420)------------------------------
% 1.71/1.42 % (2418)Instruction limit reached!
% 1.71/1.42 % (2418)------------------------------
% 1.71/1.42 % (2418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.42 % (2418)Termination reason: Unknown
% 1.71/1.42 % (2418)Termination phase: Saturation
% 1.71/1.42
% 1.71/1.42 % (2418)Memory used [KB]: 5628
% 1.71/1.42 % (2418)Time elapsed: 0.010 s
% 1.71/1.42 % (2418)Instructions burned: 22 (million)
% 1.71/1.42 % (2418)------------------------------
% 1.71/1.42 % (2418)------------------------------
% 1.71/1.42 % (2421)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/377Mi)
% 1.71/1.42 % (2424)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_2206 for (2999ds/779Mi)
% 1.71/1.42 % (2426)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_2206 for (2999ds/19Mi)
% 1.71/1.43 % (2426)Instruction limit reached!
% 1.71/1.43 % (2426)------------------------------
% 1.71/1.43 % (2426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.43 % (2426)Termination reason: Unknown
% 1.71/1.43 % (2426)Termination phase: Saturation
% 1.71/1.43
% 1.71/1.43 % (2426)Memory used [KB]: 5500
% 1.71/1.43 % (2426)Time elapsed: 0.011 s
% 1.71/1.43 % (2426)Instructions burned: 19 (million)
% 1.71/1.43 % (2426)------------------------------
% 1.71/1.43 % (2426)------------------------------
% 1.71/1.43 % (2430)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_2206 for (2999ds/879Mi)
% 1.71/1.45 % (2439)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_2206 for (2998ds/17Mi)
% 1.71/1.45 % (2395)Instruction limit reached!
% 1.71/1.45 % (2395)------------------------------
% 1.71/1.45 % (2395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.45 % (2395)Termination reason: Unknown
% 1.71/1.45 % (2395)Termination phase: Saturation
% 1.71/1.45
% 1.71/1.45 % (2395)Memory used [KB]: 6524
% 1.71/1.45 % (2395)Time elapsed: 0.123 s
% 1.71/1.45 % (2395)Instructions burned: 183 (million)
% 1.71/1.45 % (2395)------------------------------
% 1.71/1.45 % (2395)------------------------------
% 1.71/1.46 % (2439)Instruction limit reached!
% 1.71/1.46 % (2439)------------------------------
% 1.71/1.46 % (2439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.46 % (2439)Termination reason: Unknown
% 1.71/1.46 % (2439)Termination phase: Saturation
% 1.71/1.46
% 1.71/1.46 % (2439)Memory used [KB]: 5628
% 1.71/1.46 % (2439)Time elapsed: 0.011 s
% 1.71/1.46 % (2439)Instructions burned: 18 (million)
% 1.71/1.46 % (2439)------------------------------
% 1.71/1.46 % (2439)------------------------------
% 1.71/1.47 % (2445)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2206 for (2998ds/3Mi)
% 1.71/1.47 % (2445)Instruction limit reached!
% 1.71/1.47 % (2445)------------------------------
% 1.71/1.47 % (2445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.47 % (2445)Termination reason: Unknown
% 1.71/1.47 % (2445)Termination phase: Function definition elimination
% 1.71/1.47
% 1.71/1.47 % (2445)Memory used [KB]: 1023
% 1.71/1.47 % (2445)Time elapsed: 0.003 s
% 1.71/1.47 % (2445)Instructions burned: 3 (million)
% 1.71/1.47 % (2445)------------------------------
% 1.71/1.47 % (2445)------------------------------
% 1.71/1.48 % (2447)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_2206 for (2998ds/30Mi)
% 1.71/1.49 % (2450)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_2206 for (2998ds/127Mi)
% 1.71/1.49 % (2447)Instruction limit reached!
% 1.71/1.49 % (2447)------------------------------
% 1.71/1.49 % (2447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.49 % (2447)Termination reason: Unknown
% 1.71/1.49 % (2447)Termination phase: Saturation
% 1.71/1.49
% 1.71/1.49 % (2447)Memory used [KB]: 5628
% 1.71/1.49 % (2447)Time elapsed: 0.039 s
% 1.71/1.49 % (2447)Instructions burned: 31 (million)
% 1.71/1.49 % (2447)------------------------------
% 1.71/1.49 % (2447)------------------------------
% 1.71/1.50 % (2459)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_2206 for (2998ds/100Mi)
% 1.71/1.55 % (2459)Instruction limit reached!
% 1.71/1.55 % (2459)------------------------------
% 1.71/1.55 % (2459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.55 % (2459)Termination reason: Unknown
% 1.71/1.55 % (2459)Termination phase: Saturation
% 1.71/1.55
% 1.71/1.55 % (2459)Memory used [KB]: 5628
% 1.71/1.55 % (2459)Time elapsed: 0.068 s
% 1.71/1.55 % (2459)Instructions burned: 100 (million)
% 1.71/1.55 % (2459)------------------------------
% 1.71/1.55 % (2459)------------------------------
% 1.71/1.55 % (2450)Instruction limit reached!
% 1.71/1.55 % (2450)------------------------------
% 1.71/1.55 % (2450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.55 % (2450)Termination reason: Unknown
% 1.71/1.55 % (2450)Termination phase: Saturation
% 1.71/1.55
% 1.71/1.55 % (2450)Memory used [KB]: 6140
% 1.71/1.55 % (2450)Time elapsed: 0.068 s
% 1.71/1.55 % (2450)Instructions burned: 128 (million)
% 1.71/1.55 % (2450)------------------------------
% 1.71/1.55 % (2450)------------------------------
% 1.71/1.57 % (2469)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_2206 for (2997ds/3Mi)
% 1.71/1.57 % (2469)Instruction limit reached!
% 1.71/1.57 % (2469)------------------------------
% 1.71/1.57 % (2469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.57 % (2469)Termination reason: Unknown
% 1.71/1.57 % (2469)Termination phase: Saturation
% 1.71/1.57
% 1.71/1.57 % (2469)Memory used [KB]: 5500
% 1.71/1.57 % (2469)Time elapsed: 0.004 s
% 1.71/1.57 % (2469)Instructions burned: 4 (million)
% 1.71/1.57 % (2469)------------------------------
% 1.71/1.57 % (2469)------------------------------
% 1.71/1.57 % (2470)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_2206 for (2997ds/20Mi)
% 1.71/1.58 % (2470)Instruction limit reached!
% 1.71/1.58 % (2470)------------------------------
% 1.71/1.58 % (2470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.58 % (2470)Termination reason: Unknown
% 1.71/1.58 % (2470)Termination phase: Saturation
% 1.71/1.58
% 1.71/1.58 % (2470)Memory used [KB]: 5628
% 1.71/1.58 % (2470)Time elapsed: 0.014 s
% 1.71/1.58 % (2470)Instructions burned: 21 (million)
% 1.71/1.58 % (2470)------------------------------
% 1.71/1.58 % (2470)------------------------------
% 1.71/1.59 % (2475)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_2206 for (2997ds/86Mi)
% 1.71/1.60 % (2477)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_2206 for (2997ds/107Mi)
% 1.71/1.62 % (2475)Instruction limit reached!
% 1.71/1.62 % (2475)------------------------------
% 1.71/1.62 % (2475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.62 % (2475)Termination reason: Unknown
% 1.71/1.62 % (2475)Termination phase: Saturation
% 1.71/1.62
% 1.71/1.62 % (2475)Memory used [KB]: 6140
% 1.71/1.62 % (2475)Time elapsed: 0.036 s
% 1.71/1.62 % (2475)Instructions burned: 87 (million)
% 1.71/1.62 % (2475)------------------------------
% 1.71/1.62 % (2475)------------------------------
% 1.71/1.63 % (2421)Instruction limit reached!
% 1.71/1.63 % (2421)------------------------------
% 1.71/1.63 % (2421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.63 % (2421)Termination reason: Unknown
% 1.71/1.63 % (2421)Termination phase: Saturation
% 1.71/1.63
% 1.71/1.63 % (2421)Memory used [KB]: 6524
% 1.71/1.63 % (2421)Time elapsed: 0.207 s
% 1.71/1.63 % (2421)Instructions burned: 377 (million)
% 1.71/1.63 % (2421)------------------------------
% 1.71/1.63 % (2421)------------------------------
% 1.71/1.64 % (2483)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_2206 for (2996ds/39Mi)
% 1.71/1.64 % (2486)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_2206 for (2996ds/448Mi)
% 1.71/1.65 % (2483)Instruction limit reached!
% 1.71/1.65 % (2483)------------------------------
% 1.71/1.65 % (2483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.65 % (2483)Termination reason: Unknown
% 1.71/1.65 % (2483)Termination phase: Saturation
% 1.71/1.65
% 1.71/1.65 % (2483)Memory used [KB]: 5756
% 1.71/1.65 % (2483)Time elapsed: 0.014 s
% 1.71/1.65 % (2483)Instructions burned: 40 (million)
% 1.71/1.65 % (2483)------------------------------
% 1.71/1.65 % (2483)------------------------------
% 1.71/1.65 % (2477)Instruction limit reached!
% 1.71/1.65 % (2477)------------------------------
% 1.71/1.65 % (2477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.65 % (2477)Termination reason: Unknown
% 1.71/1.65 % (2477)Termination phase: Saturation
% 1.71/1.65
% 1.71/1.65 % (2477)Memory used [KB]: 5756
% 1.71/1.65 % (2477)Time elapsed: 0.055 s
% 1.71/1.65 % (2477)Instructions burned: 107 (million)
% 1.71/1.65 % (2477)------------------------------
% 1.71/1.65 % (2477)------------------------------
% 1.71/1.66 % (2489)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_2206 for (2996ds/46Mi)
% 1.71/1.67 % (2491)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_2206 for (2996ds/98Mi)
% 1.71/1.67 % (2489)Instruction limit reached!
% 1.71/1.67 % (2489)------------------------------
% 1.71/1.67 % (2489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.67 % (2489)Termination reason: Unknown
% 1.71/1.67 % (2489)Termination phase: Saturation
% 1.71/1.67
% 1.71/1.67 % (2489)Memory used [KB]: 5628
% 1.71/1.67 % (2489)Time elapsed: 0.018 s
% 1.71/1.67 % (2489)Instructions burned: 47 (million)
% 1.71/1.67 % (2489)------------------------------
% 1.71/1.67 % (2489)------------------------------
% 1.71/1.68 % (2415)Instruction limit reached!
% 1.71/1.68 % (2415)------------------------------
% 1.71/1.68 % (2415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.68 % (2415)Termination reason: Unknown
% 1.71/1.68 % (2415)Termination phase: Saturation
% 1.71/1.68
% 1.71/1.68 % (2415)Memory used [KB]: 7036
% 1.71/1.68 % (2415)Time elapsed: 0.296 s
% 1.71/1.68 % (2415)Instructions burned: 710 (million)
% 1.71/1.68 % (2415)------------------------------
% 1.71/1.68 % (2415)------------------------------
% 1.71/1.68 % (2495)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_2206 for (2996ds/507Mi)
% 1.71/1.70 % (2496)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_2206 for (2996ds/149Mi)
% 1.71/1.72 % (2491)Instruction limit reached!
% 1.71/1.72 % (2491)------------------------------
% 1.71/1.72 % (2491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.72 % (2491)Termination reason: Unknown
% 1.71/1.72 % (2491)Termination phase: Saturation
% 1.71/1.72
% 1.71/1.72 % (2491)Memory used [KB]: 1151
% 1.71/1.72 % (2491)Time elapsed: 0.051 s
% 1.71/1.72 % (2491)Instructions burned: 100 (million)
% 1.71/1.72 % (2491)------------------------------
% 1.71/1.72 % (2491)------------------------------
% 1.71/1.74 % (2503)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_2206 for (2995ds/39Mi)
% 1.71/1.76 % (2503)Instruction limit reached!
% 1.71/1.76 % (2503)------------------------------
% 1.71/1.76 % (2503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.76 % (2503)Termination reason: Unknown
% 1.71/1.76 % (2503)Termination phase: Saturation
% 1.71/1.76
% 1.71/1.76 % (2503)Memory used [KB]: 5628
% 1.71/1.76 % (2503)Time elapsed: 0.022 s
% 1.71/1.76 % (2503)Instructions burned: 39 (million)
% 1.71/1.76 % (2503)------------------------------
% 1.71/1.76 % (2503)------------------------------
% 1.71/1.76 % (2406)Instruction limit reached!
% 1.71/1.76 % (2406)------------------------------
% 1.71/1.76 % (2406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.76 % (2406)Termination reason: Unknown
% 1.71/1.76 % (2406)Termination phase: Saturation
% 1.71/1.76
% 1.71/1.76 % (2406)Memory used [KB]: 6140
% 1.71/1.76 % (2406)Time elapsed: 0.406 s
% 1.71/1.76 % (2406)Instructions burned: 1042 (million)
% 1.71/1.76 % (2406)------------------------------
% 1.71/1.76 % (2406)------------------------------
% 1.71/1.77 % (2496)Instruction limit reached!
% 1.71/1.77 % (2496)------------------------------
% 1.71/1.77 % (2496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.77 % (2496)Termination reason: Unknown
% 1.71/1.77 % (2496)Termination phase: Saturation
% 1.71/1.77
% 1.71/1.77 % (2496)Memory used [KB]: 6140
% 1.71/1.77 % (2496)Time elapsed: 0.077 s
% 1.71/1.77 % (2496)Instructions burned: 150 (million)
% 1.71/1.77 % (2496)------------------------------
% 1.71/1.77 % (2496)------------------------------
% 1.71/1.78 % (2508)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_2206 for (2995ds/6Mi)
% 1.71/1.78 % (2509)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_2206 for (2995ds/1087Mi)
% 1.71/1.78 % (2508)Instruction limit reached!
% 1.71/1.78 % (2508)------------------------------
% 1.71/1.78 % (2508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.78 % (2508)Termination reason: Unknown
% 1.71/1.78 % (2508)Termination phase: Saturation
% 1.71/1.78
% 1.71/1.78 % (2508)Memory used [KB]: 9978
% 1.71/1.78 % (2508)Time elapsed: 0.005 s
% 1.71/1.78 % (2508)Instructions burned: 6 (million)
% 1.71/1.78 % (2508)------------------------------
% 1.71/1.78 % (2508)------------------------------
% 1.71/1.79 % (2510)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_2206 for (2995ds/47Mi)
% 1.71/1.79 % (2424)Instruction limit reached!
% 1.71/1.79 % (2424)------------------------------
% 1.71/1.79 % (2424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.79 % (2424)Termination reason: Unknown
% 1.71/1.79 % (2424)Termination phase: Saturation
% 1.71/1.79
% 1.71/1.79 % (2424)Memory used [KB]: 7036
% 1.71/1.79 % (2424)Time elapsed: 0.373 s
% 1.71/1.79 % (2424)Instructions burned: 781 (million)
% 1.71/1.79 % (2424)------------------------------
% 1.71/1.79 % (2424)------------------------------
% 1.71/1.80 % (2513)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_2206 for (2995ds/44Mi)
% 1.71/1.80 % (2518)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_2206 for (2995ds/432Mi)
% 1.71/1.81 % (2510)Instruction limit reached!
% 1.71/1.81 % (2510)------------------------------
% 1.71/1.81 % (2510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.81 % (2510)Termination reason: Unknown
% 1.71/1.81 % (2510)Termination phase: Saturation
% 1.71/1.81
% 1.71/1.81 % (2510)Memory used [KB]: 5628
% 1.71/1.81 % (2510)Time elapsed: 0.023 s
% 1.71/1.81 % (2510)Instructions burned: 48 (million)
% 1.71/1.81 % (2510)------------------------------
% 1.71/1.81 % (2510)------------------------------
% 1.71/1.82 % (2513)Instruction limit reached!
% 1.71/1.82 % (2513)------------------------------
% 1.71/1.82 % (2513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.82 % (2513)Termination reason: Unknown
% 1.71/1.82 % (2513)Termination phase: Saturation
% 1.71/1.82
% 1.71/1.82 % (2513)Memory used [KB]: 1151
% 1.71/1.82 % (2513)Time elapsed: 0.023 s
% 1.71/1.82 % (2513)Instructions burned: 44 (million)
% 1.71/1.82 % (2513)------------------------------
% 1.71/1.82 % (2513)------------------------------
% 1.71/1.82 % (2430)Instruction limit reached!
% 1.71/1.82 % (2430)------------------------------
% 1.71/1.82 % (2430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.82 % (2430)Termination reason: Unknown
% 1.71/1.82 % (2430)Termination phase: Saturation
% 1.71/1.82
% 1.71/1.82 % (2430)Memory used [KB]: 7036
% 1.71/1.82 % (2430)Time elapsed: 0.387 s
% 1.71/1.82 % (2430)Instructions burned: 882 (million)
% 1.71/1.82 % (2430)------------------------------
% 1.71/1.82 % (2430)------------------------------
% 1.71/1.83 % (2521)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_2206 for (2995ds/62Mi)
% 1.71/1.83 % (2525)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_2206 for (2994ds/96Mi)
% 1.71/1.83 % (2524)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_2206 for (2994ds/31Mi)
% 1.71/1.84 % (2486)Instruction limit reached!
% 1.71/1.84 % (2486)------------------------------
% 1.71/1.84 % (2486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.84 % (2486)Termination reason: Unknown
% 1.71/1.84 % (2486)Termination phase: Saturation
% 1.71/1.84
% 1.71/1.84 % (2486)Memory used [KB]: 6908
% 1.71/1.84 % (2486)Time elapsed: 0.202 s
% 1.71/1.84 % (2486)Instructions burned: 449 (million)
% 1.71/1.84 % (2486)------------------------------
% 1.71/1.84 % (2486)------------------------------
% 1.71/1.85 % (2524)Instruction limit reached!
% 1.71/1.85 % (2524)------------------------------
% 1.71/1.85 % (2524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.85 % (2524)Termination reason: Unknown
% 1.71/1.85 % (2524)Termination phase: Saturation
% 1.71/1.85
% 1.71/1.85 % (2524)Memory used [KB]: 5756
% 1.71/1.85 % (2524)Time elapsed: 0.016 s
% 1.71/1.85 % (2524)Instructions burned: 31 (million)
% 1.71/1.85 % (2524)------------------------------
% 1.71/1.85 % (2524)------------------------------
% 1.71/1.86 % (2521)Instruction limit reached!
% 1.71/1.86 % (2521)------------------------------
% 1.71/1.86 % (2521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.86 % (2521)Termination reason: Unknown
% 1.71/1.86 % (2521)Termination phase: Saturation
% 1.71/1.86
% 1.71/1.86 % (2521)Memory used [KB]: 5884
% 1.71/1.86 % (2521)Time elapsed: 0.030 s
% 1.71/1.86 % (2521)Instructions burned: 63 (million)
% 1.71/1.86 % (2521)------------------------------
% 1.71/1.86 % (2521)------------------------------
% 1.71/1.86 % (2529)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_2206 for (2994ds/453Mi)
% 1.71/1.86 % (2525)Instruction limit reached!
% 1.71/1.86 % (2525)------------------------------
% 1.71/1.86 % (2525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.86 % (2525)Termination reason: Unknown
% 1.71/1.86 % (2525)Termination phase: Saturation
% 1.71/1.86
% 1.71/1.86 % (2525)Memory used [KB]: 5628
% 1.71/1.86 % (2525)Time elapsed: 0.034 s
% 1.71/1.86 % (2525)Instructions burned: 96 (million)
% 1.71/1.86 % (2525)------------------------------
% 1.71/1.86 % (2525)------------------------------
% 1.71/1.86 % (2530)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_2206 for (2994ds/71Mi)
% 1.71/1.87 % (2531)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_2206 for (2994ds/83Mi)
% 1.71/1.88 % (2533)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_2206 for (2994ds/11Mi)
% 1.71/1.88 % (2495)Instruction limit reached!
% 1.71/1.88 % (2495)------------------------------
% 1.71/1.88 % (2495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.88 % (2495)Termination reason: Unknown
% 1.71/1.88 % (2495)Termination phase: Saturation
% 1.71/1.88
% 1.71/1.88 % (2495)Memory used [KB]: 6524
% 1.71/1.88 % (2495)Time elapsed: 0.201 s
% 1.71/1.88 % (2495)Instructions burned: 508 (million)
% 1.71/1.88 % (2495)------------------------------
% 1.71/1.88 % (2495)------------------------------
% 1.71/1.89 % (2533)Instruction limit reached!
% 1.71/1.89 % (2533)------------------------------
% 1.71/1.89 % (2533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.89 % (2533)Termination reason: Unknown
% 1.71/1.89 % (2533)Termination phase: Saturation
% 1.71/1.89
% 1.71/1.89 % (2533)Memory used [KB]: 5500
% 1.71/1.89 % (2533)Time elapsed: 0.007 s
% 1.71/1.89 % (2533)Instructions burned: 12 (million)
% 1.71/1.89 % (2533)------------------------------
% 1.71/1.89 % (2533)------------------------------
% 1.71/1.89 % (2530)Instruction limit reached!
% 1.71/1.89 % (2530)------------------------------
% 1.71/1.89 % (2530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.89 % (2530)Termination reason: Unknown
% 1.71/1.89 % (2530)Termination phase: Saturation
% 1.71/1.89
% 1.71/1.89 % (2530)Memory used [KB]: 5756
% 1.71/1.89 % (2530)Time elapsed: 0.027 s
% 1.71/1.89 % (2530)Instructions burned: 73 (million)
% 1.71/1.89 % (2530)------------------------------
% 1.71/1.89 % (2530)------------------------------
% 1.71/1.90 % (2537)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_2206 for (2994ds/150Mi)
% 1.71/1.90 % (2535)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_2206 for (2994ds/41Mi)
% 1.71/1.90 % (2536)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2206 for (2994ds/6Mi)
% 1.71/1.90 % (2536)Instruction limit reached!
% 1.71/1.90 % (2536)------------------------------
% 1.71/1.90 % (2536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.90 % (2536)Termination reason: Unknown
% 1.71/1.90 % (2536)Termination phase: Saturation
% 1.71/1.90
% 1.71/1.90 % (2536)Memory used [KB]: 5500
% 1.71/1.90 % (2536)Time elapsed: 0.004 s
% 1.71/1.90 % (2536)Instructions burned: 6 (million)
% 1.71/1.90 % (2536)------------------------------
% 1.71/1.90 % (2536)------------------------------
% 1.71/1.91 % (2518)First to succeed.
% 1.71/1.91 % (2518)Refutation found. Thanks to Tanya!
% 1.71/1.91 % SZS status Theorem for DTF2THF_2206
% 1.71/1.91 % SZS output start Proof for DTF2THF_2206
% 1.71/1.91 thf(func_def_0, type, r: (($i > $o) > $o) > (($i > $o) > $o) > $o).
% 1.71/1.91 thf(func_def_2, type, cNAT: (($i > $o) > $o) > $o).
% 1.71/1.91 thf(func_def_3, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 1.71/1.91 thf(func_def_4, type, cZERO: ($i > $o) > $o).
% 1.71/1.91 thf(func_def_19, type, ph0: !>[X0: $tType]:(X0)).
% 1.71/1.91 thf(func_def_20, type, sK1: ($i > $o) > $o).
% 1.71/1.91 thf(func_def_27, type, sK2: ($i > $o) > $o).
% 1.71/1.91 thf(f212,plain,(
% 1.71/1.91 $false),
% 1.71/1.91 inference(trivial_inequality_removal,[status(thm)],[f211])).
% 1.71/1.91 thf(f211,plain,(
% 1.71/1.91 ($false = $true)),
% 1.71/1.91 inference(superposition,[status(thm)],[f98,f176])).
% 1.71/1.91 thf(f176,plain,(
% 1.71/1.91 (((r @ sK2 @ sK2) => (r @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK2 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK2 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))) = $false)),
% 1.71/1.91 inference(beta_eta_normalization,[status(thm)],[f171])).
% 1.71/1.91 thf(f171,plain,(
% 1.71/1.91 (((^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))) @ sK2) = $false)),
% 1.71/1.91 inference(sigma_clausification,[status(thm)],[f160])).
% 1.71/1.91 thf(f160,plain,(
% 1.71/1.91 ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) = $false)),
% 1.71/1.91 inference(not_proxy_clausification,[status(thm)],[f141])).
% 1.71/1.91 thf(f141,plain,(
% 1.71/1.91 ((~ (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) = $true)),
% 1.71/1.91 inference(boolean_simplification,[status(thm)],[f140])).
% 1.71/1.91 thf(f140,plain,(
% 1.71/1.91 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) => $false) = $true)),
% 1.71/1.91 inference(forward_demodulation,[status(thm)],[f127,f49])).
% 1.71/1.91 thf(f49,plain,(
% 1.71/1.91 ( ! [X1 : ($i > $o) > $o] : (((r @ sK1 @ X1) = $false)) )),
% 1.71/1.91 inference(pi_clausification,[status(thm)],[f39])).
% 1.71/1.91 thf(f39,plain,(
% 1.71/1.91 ($false = (?? @ (($i > $o) > $o) @ (r @ sK1)))),
% 1.71/1.91 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.71/1.91 thf(f35,plain,(
% 1.71/1.91 ($false = ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) => (Y0 @ sK1)))) => (?? @ (($i > $o) > $o) @ (r @ sK1))))),
% 1.71/1.91 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.71/1.91 thf(f32,plain,(
% 1.71/1.91 (((^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ Y0)))) => (?? @ (($i > $o) > $o) @ (r @ Y0)))) @ sK1) = $false)),
% 1.71/1.91 inference(sigma_clausification,[status(thm)],[f28])).
% 1.71/1.91 thf(f28,plain,(
% 1.71/1.91 ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ Y0)))) => (?? @ (($i > $o) > $o) @ (r @ Y0))))) = $false)),
% 1.71/1.91 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.71/1.91 thf(f27,plain,(
% 1.71/1.91 (((((r @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ ((($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]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6)))))))))))))) => (Y2 @ Y1)))) => (Y0 @ Y1)))))))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y1 @ Y0) => (r @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))) @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ Y0)))) => (?? @ (($i > $o) > $o) @ (r @ Y0)))))) = $false)),
% 1.71/1.91 inference(not_proxy_clausification,[status(thm)],[f26])).
% 1.71/1.91 thf(f26,plain,(
% 1.71/1.91 ((~ ((((r @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ ((($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]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6)))))))))))))) => (Y2 @ Y1)))) => (Y0 @ Y1)))))))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y1 @ Y0) => (r @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))) @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ Y0)))) => (?? @ (($i > $o) > $o) @ (r @ Y0))))))) = $true)),
% 1.71/1.91 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.71/1.91 thf(f25,plain,(
% 1.71/1.91 ((~ ((((r @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ ((^[Y2 : ($i > $o) > $o]: ((^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))) @ Y1))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((^[Y2 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ (^[Y5 : $i]: (Y4 @ Y5)))))) & (!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ ((^[Y5 : ($i > $o) > $o]: ((^[Y6 : $i > $o]: (?? @ $i @ (^[Y7 : $i]: ((Y6 @ Y7) & (Y5 @ (^[Y8 : $i]: ((Y6 @ Y8) & (~ (Y7 = Y8))))))))))) @ Y4)))))) => (Y3 @ Y2))))) @ Y1) => (Y0 @ Y1)))))))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y1 @ Y0) => (r @ ((^[Y2 : ($i > $o) > $o]: ((^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))) @ Y1) @ ((^[Y2 : ($i > $o) > $o]: ((^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))) @ Y0)))))))) => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((^[Y1 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ (^[Y4 : $i]: (Y3 @ Y4)))))) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ ((^[Y4 : ($i > $o) > $o]: ((^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7))))))))))) @ Y3)))))) => (Y2 @ Y1))))) @ Y0) => (?? @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (r @ Y0 @ Y1)))))))) = $true)),
% 1.71/1.91 inference(definition_unfolding,[status(thm)],[f21,f19,f19,f24,f18,f18,f23])).
% 1.71/1.91 thf(f23,plain,(
% 1.71/1.91 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3)))))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))) @ Y2)))))) => (Y1 @ Y0))))))),
% 1.71/1.91 inference(definition_unfolding,[status(thm)],[f22,f19,f18])).
% 1.71/1.91 thf(f22,plain,(
% 1.71/1.91 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ cZERO) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2)))))) => (Y1 @ Y0))))))),
% 1.71/1.91 inference(cnf_transformation,[status(thm)],[f17])).
% 1.71/1.91 thf(f17,plain,(
% 1.71/1.91 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ cZERO) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2)))))) => (Y1 @ Y0))))))),
% 1.71/1.91 inference(fool_elimination,[status(thm)],[f16])).
% 1.71/1.91 thf(f16,plain,(
% 1.71/1.91 ((^[X0 : ($i > $o) > $o] : (! [X1 : (($i > $o) > $o) > $o] : ((! [X2 : ($i > $o) > $o] : ((X1 @ X2) => (X1 @ (cSUCC @ X2))) & (X1 @ cZERO)) => (X1 @ X0)))) = cNAT)),
% 1.71/1.91 inference(rectify,[status(thm)],[f3])).
% 1.71/1.91 thf(f3,axiom,(
% 1.71/1.91 ((^[X2 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : ((! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1))) & (X0 @ cZERO)) => (X0 @ X2)))) = cNAT)),
% 1.71/1.91 file('/export/starexec/sandbox/tmp/tmp.Gc2avpieIj/DTF2THF_2206.p',cNAT_def)).
% 1.71/1.91 thf(f18,plain,(
% 1.71/1.91 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))),
% 1.71/1.91 inference(cnf_transformation,[status(thm)],[f11])).
% 1.71/1.91 thf(f11,plain,(
% 1.71/1.91 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))),
% 1.71/1.91 inference(fool_elimination,[status(thm)],[f10])).
% 1.71/1.91 thf(f10,plain,(
% 1.71/1.91 ((^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2 : $i] : ((X0 @ (^[X3 : $i] : ((X2 != X3) & (X1 @ X3)))) & (X1 @ X2)))) = cSUCC)),
% 1.71/1.91 inference(rectify,[status(thm)],[f2])).
% 1.71/1.91 thf(f2,axiom,(
% 1.71/1.91 ((^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1 : $i] : ((X2 @ (^[X3 : $i] : ((X1 != X3) & (X0 @ X3)))) & (X0 @ X1)))) = cSUCC)),
% 1.71/1.91 file('/export/starexec/sandbox/tmp/tmp.Gc2avpieIj/DTF2THF_2206.p',cSUCC_def)).
% 1.71/1.91 thf(f24,plain,(
% 1.71/1.91 (cINDUCTION = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ ((^[Y2 : ($i > $o) > $o]: ((^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))) @ Y1))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((^[Y2 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ (^[Y5 : $i]: (Y4 @ Y5)))))) & (!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ ((^[Y5 : ($i > $o) > $o]: ((^[Y6 : $i > $o]: (?? @ $i @ (^[Y7 : $i]: ((Y6 @ Y7) & (Y5 @ (^[Y8 : $i]: ((Y6 @ Y8) & (~ (Y7 = Y8))))))))))) @ Y4)))))) => (Y3 @ Y2))))) @ Y1) => (Y0 @ Y1))))))))),
% 1.71/1.91 inference(definition_unfolding,[status(thm)],[f20,f18,f19,f23])).
% 1.71/1.91 thf(f20,plain,(
% 1.71/1.91 (cINDUCTION = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))) & (Y0 @ cZERO)) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((cNAT @ Y1) => (Y0 @ Y1))))))))),
% 1.71/1.91 inference(cnf_transformation,[status(thm)],[f13])).
% 1.71/1.91 thf(f13,plain,(
% 1.71/1.91 (cINDUCTION = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))) & (Y0 @ cZERO)) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((cNAT @ Y1) => (Y0 @ Y1))))))))),
% 1.71/1.91 inference(fool_elimination,[status(thm)],[f12])).
% 1.71/1.91 thf(f12,plain,(
% 1.71/1.91 (cINDUCTION = ! [X0 : (($i > $o) > $o) > $o] : (((X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) => ! [X2 : ($i > $o) > $o] : ((cNAT @ X2) => (X0 @ X2))))),
% 1.71/1.91 inference(rectify,[status(thm)],[f4])).
% 1.71/1.91 thf(f4,axiom,(
% 1.71/1.91 (cINDUCTION = ! [X4 : (($i > $o) > $o) > $o] : (((X4 @ cZERO) & ! [X5 : ($i > $o) > $o] : ((X4 @ X5) => (X4 @ (cSUCC @ X5)))) => ! [X6 : ($i > $o) > $o] : ((cNAT @ X6) => (X4 @ X6))))),
% 1.71/1.91 file('/export/starexec/sandbox/tmp/tmp.Gc2avpieIj/DTF2THF_2206.p',cINDUCTION_def)).
% 1.71/1.91 thf(f19,plain,(
% 1.71/1.91 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.71/1.91 inference(cnf_transformation,[status(thm)],[f9])).
% 1.71/1.91 thf(f9,plain,(
% 1.71/1.91 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.71/1.91 inference(fool_elimination,[status(thm)],[f8])).
% 1.71/1.91 thf(f8,plain,(
% 1.71/1.91 ((^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))) = cZERO)),
% 1.71/1.91 inference(rectify,[status(thm)],[f1])).
% 1.71/1.91 thf(f1,axiom,(
% 1.71/1.91 ((^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))) = cZERO)),
% 1.71/1.91 file('/export/starexec/sandbox/tmp/tmp.Gc2avpieIj/DTF2THF_2206.p',cZERO_def)).
% 1.71/1.91 thf(f21,plain,(
% 1.71/1.91 ((~ ((((r @ cZERO @ cZERO) & cINDUCTION) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y1 @ Y0) => (r @ (cSUCC @ Y1) @ (cSUCC @ Y0)))))))) => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((cNAT @ Y0) => (?? @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (r @ Y0 @ Y1)))))))) = $true)),
% 1.71/1.91 inference(cnf_transformation,[status(thm)],[f15])).
% 1.71/1.91 thf(f15,plain,(
% 1.71/1.91 ((~ ((((r @ cZERO @ cZERO) & cINDUCTION) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y1 @ Y0) => (r @ (cSUCC @ Y1) @ (cSUCC @ Y0)))))))) => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((cNAT @ Y0) => (?? @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (r @ Y0 @ Y1)))))))) = $true)),
% 1.71/1.91 inference(fool_elimination,[status(thm)],[f14])).
% 1.71/1.91 thf(f14,plain,(
% 1.71/1.91 ~((! [X0 : ($i > $o) > $o,X1 : ($i > $o) > $o] : ((r @ X0 @ X1) => (r @ (cSUCC @ X0) @ (cSUCC @ X1))) & cINDUCTION & (r @ cZERO @ cZERO)) => ! [X2 : ($i > $o) > $o] : ((cNAT @ X2) => ? [X3 : ($i > $o) > $o] : (r @ X2 @ X3)))),
% 1.71/1.91 inference(rectify,[status(thm)],[f6])).
% 1.71/1.91 thf(f6,negated_conjecture,(
% 1.71/1.91 ~((! [X1 : ($i > $o) > $o,X7 : ($i > $o) > $o] : ((r @ X1 @ X7) => (r @ (cSUCC @ X1) @ (cSUCC @ X7))) & cINDUCTION & (r @ cZERO @ cZERO)) => ! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => ? [X7 : ($i > $o) > $o] : (r @ X1 @ X7)))),
% 1.71/1.91 inference(negated_conjecture,[status(cth)],[f5])).
% 1.71/1.91 thf(f5,conjecture,(
% 1.71/1.91 (! [X1 : ($i > $o) > $o,X7 : ($i > $o) > $o] : ((r @ X1 @ X7) => (r @ (cSUCC @ X1) @ (cSUCC @ X7))) & cINDUCTION & (r @ cZERO @ cZERO)) => ! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => ? [X7 : ($i > $o) > $o] : (r @ X1 @ X7))),
% 1.71/1.91 file('/export/starexec/sandbox/tmp/tmp.Gc2avpieIj/DTF2THF_2206.p',cTHM130_NAT)).
% 1.71/1.91 thf(f127,plain,(
% 1.71/1.91 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) => (r @ sK1 @ sK1)) = $true)),
% 1.71/1.91 inference(boolean_simplification,[status(thm)],[f126])).
% 1.71/1.91 thf(f126,plain,(
% 1.71/1.91 ($true = (($true & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ Y0) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) => (r @ sK1 @ sK1)))),
% 1.71/1.91 inference(beta_eta_normalization,[status(thm)],[f121])).
% 1.71/1.91 thf(f121,plain,(
% 1.71/1.91 ($true = (($true & (!! @ (($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 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) => ((^[Y0 : ($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)))),
% 1.71/1.91 inference(superposition,[status(thm)],[f54,f103])).
% 1.71/1.91 thf(f103,plain,(
% 1.71/1.91 ((r @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $true)),
% 1.71/1.91 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.71/1.91 thf(f42,plain,(
% 1.71/1.91 (((r @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ ((($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]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6)))))))))))))) => (Y2 @ Y1)))) => (Y0 @ Y1)))))))) = $true)),
% 1.71/1.91 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.71/1.91 thf(f29,plain,(
% 1.71/1.91 ((((r @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ ((($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]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6)))))))))))))) => (Y2 @ Y1)))) => (Y0 @ Y1)))))))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y1 @ Y0) => (r @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))) @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))))) = $true)),
% 1.71/1.91 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.71/1.91 thf(f54,plain,(
% 1.71/1.91 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = (((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) => (X1 @ sK1)))) )),
% 1.71/1.91 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.71/1.91 thf(f52,plain,(
% 1.71/1.91 ( ! [X1 : (($i > $o) > $o) > $o] : ((((^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) => (Y0 @ sK1))) @ X1) = $true)) )),
% 1.71/1.91 inference(pi_clausification,[status(thm)],[f40])).
% 1.71/1.91 thf(f40,plain,(
% 1.71/1.91 ($true = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) => (Y0 @ sK1)))))),
% 1.71/1.91 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.71/1.91 thf(f98,plain,(
% 1.71/1.91 ( ! [X2 : ($i > $o) > $o,X1 : ($i > $o) > $o] : ((((r @ X2 @ X1) => (r @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X2 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))) = $true)) )),
% 1.71/1.91 inference(beta_eta_normalization,[status(thm)],[f97])).
% 1.71/1.91 thf(f97,plain,(
% 1.71/1.91 ( ! [X2 : ($i > $o) > $o,X1 : ($i > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ X1) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (X1 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))) @ X2) = $true)) )),
% 1.71/1.91 inference(pi_clausification,[status(thm)],[f83])).
% 1.71/1.91 thf(f83,plain,(
% 1.71/1.91 ( ! [X1 : ($i > $o) > $o] : (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((r @ Y0 @ X1) => (r @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (X1 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) = $true)) )),
% 1.71/1.91 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.71/1.91 thf(f78,plain,(
% 1.71/1.91 ( ! [X1 : ($i > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y1 @ Y0) => (r @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))) @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) @ X1) = $true)) )),
% 1.71/1.91 inference(pi_clausification,[status(thm)],[f41])).
% 1.71/1.91 thf(f41,plain,(
% 1.71/1.91 ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((r @ Y1 @ Y0) => (r @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))) @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))))) = $true)),
% 1.71/1.91 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.71/1.91 % SZS output end Proof for DTF2THF_2206
% 1.71/1.91 % (2518)------------------------------
% 1.71/1.91 % (2518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.91 % (2518)Termination reason: Refutation
% 1.71/1.91
% 1.71/1.91 % (2518)Memory used [KB]: 3198
% 1.71/1.91 % (2518)Time elapsed: 0.108 s
% 1.71/1.91 % (2518)Instructions burned: 234 (million)
% 1.71/1.91 % (2518)------------------------------
% 1.71/1.91 % (2518)------------------------------
% 1.71/1.91 % (2394)Success in time 0.592 s
%------------------------------------------------------------------------------