%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV289^5 : 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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:45 AM UTC 2026
% Result : Theorem 1.42s 1.22s
% Output : Refutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 71 ( 33 unt; 0 typ; 4 def)
% Number of atoms : 445 ( 117 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 715 ( 81 ~; 39 |; 75 &; 404 @)
% ( 4 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 249 ( 249 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 12 usr; 8 con; 0-2 aty)
% ( 22 !!; 51 ??; 0 @@+; 0 @@-)
% Number of variables : 180 ( 155 ^; 19 !; 6 ?; 180 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cNAT: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_1,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(func_def_2,type,
cZERO: ( $i > $o ) > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK0: ( $i > $o ) > $o ).
thf(func_def_19,type,
sK2: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_20,type,
sK3: ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).
thf(func_def_21,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f91,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f58,f69,f84,f87,f90]) ).
thf(f90,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f89]) ).
thf(f89,plain,
( $false
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_3 ),
inference(backward_demodulation,[status(thm)],[f52,f75]) ).
thf(f75,plain,
( ( $false
= ( sK2 @ ( sK3 @ sK2 ) ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f73]) ).
thf(f73,definition,
( spl1_3
<=> ( $false
= ( sK2 @ ( sK3 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f52,plain,
( ( $true
= ( sK2 @ ( sK3 @ sK2 ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl1_1
<=> ( $true
= ( sK2 @ ( sK3 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f87,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[status(thm)],[f86]) ).
thf(f86,plain,
( $false
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $true = $false )
| ~ spl1_4 ),
inference(backward_demodulation,[status(thm)],[f31,f79]) ).
thf(f79,plain,
( ( ( sK2
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $false )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
thf(f77,definition,
( spl1_4
<=> ( ( sK2
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f31,plain,
( ( sK2
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( sK2
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( sK2
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( sK2
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( sK2
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) )
=> ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( sK0
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( $false
= ( ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( sK0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( $true
!= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( sK0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ( ^ [Y3: ( $i > $o ) > $o,Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
& ( Y3
@ ^ [Y6: $i] :
( ( Y5 != Y6 )
& ( Y4 @ Y6 ) ) ) ) )
@ Y2 ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) )
@ sK0 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f19,f23,f22]) ).
thf(f22,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( cSUCC
= ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X0
@ ^ [X3: $i] :
( ( X1 @ X3 )
& ( X2 != X3 ) ) )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( cSUCC
= ( ^ [X2: ( $i > $o ) > $o,X0: $i > $o] :
? [X1: $i] :
( ( X2
@ ^ [X3: $i] :
( ( X0 @ X3 )
& ( X1 != X3 ) ) )
& ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Gg8lLGlouV/DTF2THF_28827.p',cSUCC_def) ).
thf(f23,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ( ^ [Y3: ( $i > $o ) > $o,Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
& ( Y3
@ ^ [Y6: $i] :
( ( Y5 != Y6 )
& ( Y4 @ Y6 ) ) ) ) )
@ Y2 ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f21,f22,f18]) ).
thf(f18,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,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.Gg8lLGlouV/DTF2THF_28827.p',cZERO_def) ).
thf(f21,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ^ [X0: ( $i > $o ) > $o] :
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ( X1 @ cZERO )
& ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( cSUCC @ X2 ) ) ) )
=> ( X1 @ X0 ) ) )
= cNAT ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X2: ( $i > $o ) > $o] :
! [X0: ( ( $i > $o ) > $o ) > $o] :
( ( ( X0 @ cZERO )
& ! [X1: ( $i > $o ) > $o] :
( ( X0 @ X1 )
=> ( X0 @ ( cSUCC @ X1 ) ) ) )
=> ( X0 @ X2 ) ) )
= cNAT ),
file('/export/starexec/sandbox/tmp/tmp.Gg8lLGlouV/DTF2THF_28827.p',cNAT_def) ).
thf(f19,plain,
( $true
!= ( cNAT @ ( cSUCC @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $true
= ( cNAT @ sK0 ) )
& ( $true
!= ( cNAT @ ( cSUCC @ sK0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f16]) ).
thf(f16,plain,
( ? [X0: ( $i > $o ) > $o] :
( ( $true
= ( cNAT @ X0 ) )
& ( ( cNAT @ ( cSUCC @ X0 ) )
!= $true ) )
=> ( ( $true
= ( cNAT @ sK0 ) )
& ( $true
!= ( cNAT @ ( cSUCC @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
? [X0: ( $i > $o ) > $o] :
( ( $true
= ( cNAT @ X0 ) )
& ( ( cNAT @ ( cSUCC @ X0 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: ( $i > $o ) > $o] :
( ( $true
= ( cNAT @ X0 ) )
=> ( ( cNAT @ ( cSUCC @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: ( $i > $o ) > $o] :
( ( cNAT @ X0 )
=> ( cNAT @ ( cSUCC @ X0 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X1: ( $i > $o ) > $o] :
( ( cNAT @ X1 )
=> ( cNAT @ ( cSUCC @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X1: ( $i > $o ) > $o] :
( ( cNAT @ X1 )
=> ( cNAT @ ( cSUCC @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Gg8lLGlouV/DTF2THF_28827.p',cTTTP6101) ).
thf(f84,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f83,f77,f73]) ).
thf(f83,plain,
( ( ( sK2
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $false )
| ( $false
= ( sK2 @ ( sK3 @ sK2 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( $true = $false )
| ( ( sK2
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $false )
| ( $false
= ( sK2 @ ( sK3 @ sK2 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f66,f61]) ).
thf(f61,plain,
( $false
= ( sK2 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $false
= ( sK2 @ sK0 ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f29,f35]) ).
thf(f35,plain,
! [X1: ( $i > $o ) > $o] :
( ( $true
= ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( X1
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: ( $i > $o ) > $o] :
( ( ( sK2 @ X1 )
=> ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( X1
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( sK2
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( sK2
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f29,plain,
( $false
= ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( sK0
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f66,plain,
( ( ( sK2
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $false )
| ( $true
= ( sK2 @ sK0 ) )
| ( $false
= ( sK2 @ ( sK3 @ sK2 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $true = $false )
| ( $true
= ( sK2 @ sK0 ) )
| ( ( sK2
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $false )
| ( $false
= ( sK2 @ ( sK3 @ sK2 ) ) ) ),
inference(superposition,[status(thm)],[f35,f43]) ).
thf(f43,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ( X1
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( sK3 @ X1
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( ( X1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $false )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ( X1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $false )
| ( ( ( X1 @ ( sK3 @ X1 ) )
=> ( X1
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( sK3 @ X1
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ( ^ [Y0: ( $i > $o ) > $o] :
( ( X1 @ Y0 )
=> ( X1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
@ ( sK3 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK0 ) )
| ( ( X1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( X1 @ Y0 )
=> ( X1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
= $false )
| ( ( X1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $false )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( $true
= ( X1 @ sK0 ) )
| ( $false
= ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( X1 @ Y0 )
=> ( X1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( X1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( X1 @ Y0 )
=> ( X1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( X1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) )
=> ( X1 @ sK0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0 @ sK0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( $true
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ( ^ [Y3: ( $i > $o ) > $o,Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
& ( Y3
@ ^ [Y6: $i] :
( ( Y5 != Y6 )
& ( Y4 @ Y6 ) ) ) ) )
@ Y2 ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f20,f23]) ).
thf(f20,plain,
( $true
= ( cNAT @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f69,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[status(thm)],[f68]) ).
thf(f68,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( $true = $false )
| ~ spl1_2 ),
inference(backward_demodulation,[status(thm)],[f56,f61]) ).
thf(f56,plain,
( ( $true
= ( sK2 @ sK0 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f54,definition,
( spl1_2
<=> ( $true
= ( sK2 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f58,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f47,f54,f50]) ).
thf(f47,plain,
( ( $true
= ( sK2 @ ( sK3 @ sK2 ) ) )
| ( $true
= ( sK2 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $true
= ( sK2 @ ( sK3 @ sK2 ) ) )
| ( $true = $false )
| ( $true
= ( sK2 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f44,f31]) ).
thf(f44,plain,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ( X1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $false )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV289^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n011.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 12:42:47 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SEV289^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.16/0.42 % Domain : Set Theory
% 0.16/0.42 % Problem : TPS problem TTTP6101
% 0.16/0.42 % Version : Especial.
% 0.16/0.42 % English :
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Bro09]
% 0.16/0.42 % Names : tps_0168 [Bro09]
% 0.16/0.42 % : TTTP6101 [TPS]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0
% 0.16/0.42 % Syntax : Number of formulae : 7 ( 3 unt; 3 typ; 3 def)
% 0.16/0.42 % Number of atoms : 12 ( 4 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 3 ( 3 avg)
% 0.16/0.42 % Number of connectives : 20 ( 2 ~; 0 |; 3 &; 12 @)
% 0.16/0.42 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 5 ( 2 avg)
% 0.16/0.42 % Number of types : 2 ( 0 usr)
% 0.16/0.42 % Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.16/0.42 % Number of variables : 10 ( 5 ^; 3 !; 2 ?; 10 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.42 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.16/0.42 % : v6.2.0 - Reordered definitions.
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(cNAT_type,type,
% 0.16/0.42 cNAT: ( ( $i > $o ) > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(cSUCC_type,type,
% 0.16/0.42 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(cZERO_type,type,
% 0.16/0.42 cZERO: ( $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(cZERO_def,definition,
% 0.16/0.42 ( cZERO
% 0.16/0.42 = ( ^ [Xp: $i > $o] :
% 0.16/0.42 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(cSUCC_def,definition,
% 0.16/0.42 ( cSUCC
% 0.16/0.42 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 0.16/0.42 ? [Xx: $i] :
% 0.16/0.42 ( ( Xp @ Xx )
% 0.16/0.42 & ( Xn
% 0.16/0.42 @ ^ [Xt: $i] :
% 0.16/0.42 ( ( Xt != Xx )
% 0.16/0.42 & ( Xp @ Xt ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(cNAT_def,definition,
% 0.16/0.42 ( cNAT
% 0.16/0.42 = ( ^ [Xn: ( $i > $o ) > $o] :
% 0.16/0.42 ! [Xp: ( ( $i > $o ) > $o ) > $o] :
% 0.16/0.42 ( ( ( Xp @ cZERO )
% 0.16/0.42 & ! [Xx: ( $i > $o ) > $o] :
% 0.16/0.42 ( ( Xp @ Xx )
% 0.16/0.42 => ( Xp @ ( cSUCC @ Xx ) ) ) )
% 0.16/0.42 => ( Xp @ Xn ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(cTTTP6101,conjecture,
% 0.16/0.42 ! [Xx: ( $i > $o ) > $o] :
% 0.16/0.42 ( ( cNAT @ Xx )
% 0.16/0.42 => ( cNAT @ ( cSUCC @ Xx ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.27/1.18 ---- Embedded in THF ---
% 1.27/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.27/1.18 %%% Generated on Tue Feb 24 12:42:48 EST 2026
% 1.27/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.27/1.18 %%% Logic specification used:
% 1.27/1.18 %%% thf(spec, logic, $$dhol).
% 1.27/1.18
% 1.27/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Gg8lLGlouV/DTF2DTF28827.p
% See solution above
% 1.27/1.18 ------------------------
% 1.27/1.19 ---- Cleaned THF ---
% 1.27/1.19 thf(cNAT_type,type,
% 1.27/1.19 cNAT: ( ( $i > $o ) > $o ) > $o ).
% 1.27/1.19
% 1.27/1.19 thf(cSUCC_type,type,
% 1.27/1.19 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 1.27/1.19
% 1.27/1.19 thf(cZERO_type,type,
% 1.27/1.19 cZERO: ( $i > $o ) > $o ).
% 1.27/1.19
% 1.27/1.19 thf(cZERO_def,definition,
% 1.27/1.19 ( cZERO
% 1.27/1.19 = ( ^ [Xp: $i > $o] :
% 1.27/1.19 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 1.27/1.19
% 1.27/1.19 thf(cSUCC_def,definition,
% 1.27/1.19 ( cSUCC
% 1.27/1.19 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 1.27/1.19 ? [Xx: $i] :
% 1.27/1.19 ( ( Xp @ Xx )
% 1.27/1.19 & ( Xn
% 1.27/1.19 @ ^ [Xt: $i] :
% 1.27/1.19 ( ( Xt != Xx )
% 1.27/1.19 & ( Xp @ Xt ) ) ) ) ) ) ).
% 1.27/1.19
% 1.27/1.19 thf(cNAT_def,definition,
% 1.27/1.19 ( cNAT
% 1.27/1.19 = ( ^ [Xn: ( $i > $o ) > $o] :
% 1.27/1.19 ! [Xp: ( ( $i > $o ) > $o ) > $o] :
% 1.27/1.19 ( ( ( Xp @ cZERO )
% 1.27/1.19 & ! [Xx: ( $i > $o ) > $o] :
% 1.27/1.19 ( ( Xp @ Xx )
% 1.27/1.19 => ( Xp @ ( cSUCC @ Xx ) ) ) )
% 1.27/1.19 => ( Xp @ Xn ) ) ) ) ).
% 1.27/1.19
% 1.27/1.19 thf(cTTTP6101,conjecture,
% 1.27/1.19 ! [Xx: ( $i > $o ) > $o] :
% 1.27/1.19 ( ( cNAT @ Xx )
% 1.27/1.19 => ( cNAT @ ( cSUCC @ Xx ) ) ) ).
% 1.27/1.19 ------------------------
% 1.42/1.21 % (28929)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28827 for (2999ds/2Mi)
% 1.42/1.21 % (28926)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28827 for (2999ds/183Mi)
% 1.42/1.21 % (28928)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_28827 for (2999ds/27Mi)
% 1.42/1.21 % (28927)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_28827 for (2999ds/4Mi)
% 1.42/1.21 % (28932)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28827 for (2999ds/18Mi)
% 1.42/1.21 % (28931)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_28827 for (2999ds/275Mi)
% 1.42/1.21 % (28930)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_28827 for (2999ds/2Mi)
% 1.42/1.21 % (28929)Instruction limit reached!
% 1.42/1.21 % (28929)------------------------------
% 1.42/1.21 % (28929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.42/1.21 % (28929)Termination reason: Unknown
% 1.42/1.21 % (28929)Termination phase: Saturation
% 1.42/1.21
% 1.42/1.21 % (28929)Memory used [KB]: 1023
% 1.42/1.21 % (28929)Time elapsed: 0.003 s
% 1.42/1.21 % (28929)Instructions burned: 3 (million)
% 1.42/1.21 % (28929)------------------------------
% 1.42/1.21 % (28929)------------------------------
% 1.42/1.21 % (28930)Instruction limit reached!
% 1.42/1.21 % (28930)------------------------------
% 1.42/1.21 % (28930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.42/1.21 % (28930)Termination reason: Unknown
% 1.42/1.21 % (28930)Termination phase: Saturation
% 1.42/1.21
% 1.42/1.21 % (28930)Memory used [KB]: 1023
% 1.42/1.21 % (28930)Time elapsed: 0.003 s
% 1.42/1.21 % (28930)Instructions burned: 3 (million)
% 1.42/1.21 % (28930)------------------------------
% 1.42/1.21 % (28930)------------------------------
% 1.42/1.21 % (28931)Refutation not found, incomplete strategy
% 1.42/1.21 % (28931)------------------------------
% 1.42/1.21 % (28931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.42/1.21 % (28931)Termination reason: Refutation not found, incomplete strategy
% 1.42/1.21
% 1.42/1.21
% 1.42/1.21 % (28931)Memory used [KB]: 5500
% 1.42/1.21 % (28931)Time elapsed: 0.003 s
% 1.42/1.21 % (28931)Instructions burned: 1 (million)
% 1.42/1.21 % (28931)------------------------------
% 1.42/1.21 % (28931)------------------------------
% 1.42/1.21 % (28927)Instruction limit reached!
% 1.42/1.21 % (28927)------------------------------
% 1.42/1.21 % (28927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.42/1.21 % (28927)Termination reason: Unknown
% 1.42/1.21 % (28927)Termination phase: Saturation
% 1.42/1.21
% 1.42/1.21 % (28927)Memory used [KB]: 5500
% 1.42/1.21 % (28927)Time elapsed: 0.004 s
% 1.42/1.21 % (28927)Instructions burned: 4 (million)
% 1.42/1.21 % (28927)------------------------------
% 1.42/1.21 % (28927)------------------------------
% 1.42/1.22 % (28928)First to succeed.
% 1.42/1.22 % (28928)Refutation found. Thanks to Tanya!
% 1.42/1.22 % SZS status Theorem for DTF2THF_28827
% 1.42/1.22 % SZS output start Proof for DTF2THF_28827
% 1.42/1.22 thf(func_def_0, type, cNAT: (($i > $o) > $o) > $o).
% 1.42/1.22 thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 1.42/1.22 thf(func_def_2, type, cZERO: ($i > $o) > $o).
% 1.42/1.22 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.42/1.22 thf(func_def_17, type, sK0: ($i > $o) > $o).
% 1.42/1.22 thf(func_def_19, type, sK2: (($i > $o) > $o) > $o).
% 1.42/1.22 thf(func_def_20, type, sK3: ((($i > $o) > $o) > $o) > ($i > $o) > $o).
% 1.42/1.22 thf(func_def_21, type, ph4: !>[X0: $tType]:(X0)).
% 1.42/1.22 thf(f91,plain,(
% 1.42/1.22 $false),
% 1.42/1.22 inference(avatar_sat_refutation,[status(thm)],[f58,f69,f84,f87,f90])).
% 1.42/1.22 thf(f90,plain,(
% 1.42/1.22 ~spl1_1 | ~spl1_3),
% 1.42/1.22 inference(avatar_contradiction_clause,[status(thm)],[f89])).
% 1.42/1.22 thf(f89,plain,(
% 1.42/1.22 $false | (~spl1_1 | ~spl1_3)),
% 1.42/1.22 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.42/1.22 thf(f88,plain,(
% 1.42/1.22 ($true = $false) | (~spl1_1 | ~spl1_3)),
% 1.42/1.22 inference(backward_demodulation,[status(thm)],[f52,f75])).
% 1.42/1.22 thf(f75,plain,(
% 1.42/1.22 ($false = (sK2 @ (sK3 @ sK2))) | ~spl1_3),
% 1.42/1.22 inference(avatar_component_clause,[status(thm)],[f73])).
% 1.42/1.22 thf(f73,definition,(
% 1.42/1.22 spl1_3 <=> ($false = (sK2 @ (sK3 @ sK2)))),
% 1.42/1.22 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.42/1.22 thf(f52,plain,(
% 1.42/1.22 ($true = (sK2 @ (sK3 @ sK2))) | ~spl1_1),
% 1.42/1.22 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.42/1.22 thf(f50,definition,(
% 1.42/1.22 spl1_1 <=> ($true = (sK2 @ (sK3 @ sK2)))),
% 1.42/1.22 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.42/1.22 thf(f87,plain,(
% 1.42/1.22 ~spl1_4),
% 1.42/1.22 inference(avatar_contradiction_clause,[status(thm)],[f86])).
% 1.42/1.22 thf(f86,plain,(
% 1.42/1.22 $false | ~spl1_4),
% 1.42/1.22 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.42/1.22 thf(f85,plain,(
% 1.42/1.22 ($true = $false) | ~spl1_4),
% 1.42/1.22 inference(backward_demodulation,[status(thm)],[f31,f79])).
% 1.42/1.22 thf(f79,plain,(
% 1.42/1.22 ((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ~spl1_4),
% 1.42/1.22 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.42/1.22 thf(f77,definition,(
% 1.42/1.22 spl1_4 <=> ((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false)),
% 1.42/1.22 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.42/1.22 thf(f31,plain,(
% 1.42/1.22 ((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $true)),
% 1.42/1.22 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.42/1.22 thf(f30,plain,(
% 1.42/1.22 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $true)),
% 1.42/1.22 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.42/1.22 thf(f28,plain,(
% 1.42/1.22 ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $false)),
% 1.42/1.22 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.42/1.22 thf(f27,plain,(
% 1.42/1.22 ($false = ((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ sK2))),
% 1.42/1.22 inference(sigma_clausification,[status(thm)],[f26])).
% 1.42/1.22 thf(f26,plain,(
% 1.42/1.22 ($true != (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))))),
% 1.42/1.22 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.42/1.22 thf(f25,plain,(
% 1.42/1.22 (((^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))) @ ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))) @ sK0)) != $true)),
% 1.42/1.22 inference(definition_unfolding,[status(thm)],[f19,f23,f22])).
% 1.42/1.22 thf(f22,plain,(
% 1.42/1.22 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 1.42/1.22 inference(cnf_transformation,[status(thm)],[f12])).
% 1.42/1.22 thf(f12,plain,(
% 1.42/1.22 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 1.42/1.22 inference(fool_elimination,[status(thm)],[f11])).
% 1.42/1.22 thf(f11,plain,(
% 1.42/1.22 (cSUCC = (^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2 : $i] : ((X0 @ (^[X3 : $i] : ((X1 @ X3) & (X2 != X3)))) & (X1 @ X2)))))),
% 1.42/1.22 inference(rectify,[status(thm)],[f2])).
% 1.42/1.22 thf(f2,axiom,(
% 1.42/1.22 (cSUCC = (^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1 : $i] : ((X2 @ (^[X3 : $i] : ((X0 @ X3) & (X1 != X3)))) & (X0 @ X1)))))),
% 1.42/1.22 file('/export/starexec/sandbox/tmp/tmp.Gg8lLGlouV/DTF2THF_28827.p',cSUCC_def)).
% 1.42/1.22 thf(f23,plain,(
% 1.42/1.22 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))))),
% 1.42/1.22 inference(definition_unfolding,[status(thm)],[f21,f22,f18])).
% 1.42/1.22 thf(f18,plain,(
% 1.42/1.22 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.42/1.22 inference(cnf_transformation,[status(thm)],[f10])).
% 1.42/1.22 thf(f10,plain,(
% 1.42/1.22 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.42/1.22 inference(fool_elimination,[status(thm)],[f9])).
% 1.42/1.22 thf(f9,plain,(
% 1.42/1.22 ((^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))) = cZERO)),
% 1.42/1.22 inference(rectify,[status(thm)],[f1])).
% 1.42/1.22 thf(f1,axiom,(
% 1.42/1.22 ((^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))) = cZERO)),
% 1.42/1.22 file('/export/starexec/sandbox/tmp/tmp.Gg8lLGlouV/DTF2THF_28827.p',cZERO_def)).
% 1.42/1.22 thf(f21,plain,(
% 1.42/1.22 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 1.42/1.22 inference(cnf_transformation,[status(thm)],[f14])).
% 1.42/1.22 thf(f14,plain,(
% 1.42/1.22 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 1.42/1.22 inference(fool_elimination,[status(thm)],[f13])).
% 1.42/1.22 thf(f13,plain,(
% 1.42/1.22 ((^[X0 : ($i > $o) > $o] : (! [X1 : (($i > $o) > $o) > $o] : (((X1 @ cZERO) & ! [X2 : ($i > $o) > $o] : ((X1 @ X2) => (X1 @ (cSUCC @ X2)))) => (X1 @ X0)))) = cNAT)),
% 1.42/1.22 inference(rectify,[status(thm)],[f3])).
% 1.42/1.22 thf(f3,axiom,(
% 1.42/1.22 ((^[X2 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : (((X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) => (X0 @ X2)))) = cNAT)),
% 1.42/1.22 file('/export/starexec/sandbox/tmp/tmp.Gg8lLGlouV/DTF2THF_28827.p',cNAT_def)).
% 1.42/1.22 thf(f19,plain,(
% 1.42/1.22 ($true != (cNAT @ (cSUCC @ sK0)))),
% 1.42/1.22 inference(cnf_transformation,[status(thm)],[f17])).
% 1.42/1.22 thf(f17,plain,(
% 1.42/1.22 ($true = (cNAT @ sK0)) & ($true != (cNAT @ (cSUCC @ sK0)))),
% 1.42/1.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f16])).
% 1.42/1.22 thf(f16,plain,(
% 1.42/1.22 ? [X0 : ($i > $o) > $o] : (($true = (cNAT @ X0)) & ((cNAT @ (cSUCC @ X0)) != $true)) => (($true = (cNAT @ sK0)) & ($true != (cNAT @ (cSUCC @ sK0))))),
% 1.42/1.22 introduced(definition,[],[choice_axiom])).
% 1.42/1.22 thf(f15,plain,(
% 1.42/1.22 ? [X0 : ($i > $o) > $o] : (($true = (cNAT @ X0)) & ((cNAT @ (cSUCC @ X0)) != $true))),
% 1.42/1.22 inference(ennf_transformation,[status(thm)],[f8])).
% 1.42/1.22 thf(f8,plain,(
% 1.42/1.22 ~! [X0 : ($i > $o) > $o] : (($true = (cNAT @ X0)) => ((cNAT @ (cSUCC @ X0)) = $true))),
% 1.42/1.22 inference(fool_elimination,[status(thm)],[f7])).
% 1.42/1.22 thf(f7,plain,(
% 1.42/1.22 ~! [X0 : ($i > $o) > $o] : ((cNAT @ X0) => (cNAT @ (cSUCC @ X0)))),
% 1.42/1.22 inference(rectify,[status(thm)],[f5])).
% 1.42/1.22 thf(f5,negated_conjecture,(
% 1.42/1.22 ~! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => (cNAT @ (cSUCC @ X1)))),
% 1.42/1.22 inference(negated_conjecture,[status(cth)],[f4])).
% 1.42/1.22 thf(f4,conjecture,(
% 1.42/1.22 ! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => (cNAT @ (cSUCC @ X1)))),
% 1.42/1.22 file('/export/starexec/sandbox/tmp/tmp.Gg8lLGlouV/DTF2THF_28827.p',cTTTP6101)).
% 1.42/1.22 thf(f84,plain,(
% 1.42/1.22 spl1_3 | spl1_4),
% 1.42/1.22 inference(avatar_split_clause,[status(thm)],[f83,f77,f73])).
% 1.42/1.22 thf(f83,plain,(
% 1.42/1.22 ((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($false = (sK2 @ (sK3 @ sK2)))),
% 1.42/1.22 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.42/1.22 thf(f82,plain,(
% 1.42/1.22 ($true = $false) | ((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($false = (sK2 @ (sK3 @ sK2)))),
% 1.42/1.22 inference(forward_demodulation,[status(thm)],[f66,f61])).
% 1.42/1.22 thf(f61,plain,(
% 1.42/1.22 ($false = (sK2 @ sK0))),
% 1.42/1.22 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.42/1.22 thf(f60,plain,(
% 1.42/1.22 ($false = (sK2 @ sK0)) | ($true = $false)),
% 1.42/1.22 inference(superposition,[status(thm)],[f29,f35])).
% 1.42/1.22 thf(f35,plain,(
% 1.42/1.22 ( ! [X1 : ($i > $o) > $o] : (($true = (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) | ($false = (sK2 @ X1))) )),
% 1.42/1.22 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.42/1.22 thf(f34,plain,(
% 1.42/1.22 ( ! [X1 : ($i > $o) > $o] : ((((sK2 @ X1) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true)) )),
% 1.42/1.22 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.42/1.22 thf(f33,plain,(
% 1.42/1.22 ( ! [X1 : ($i > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1) = $true)) )),
% 1.42/1.22 inference(pi_clausification,[status(thm)],[f32])).
% 1.42/1.22 thf(f32,plain,(
% 1.42/1.22 ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) = $true)),
% 1.42/1.22 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.42/1.22 thf(f29,plain,(
% 1.42/1.22 ($false = (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))),
% 1.42/1.22 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.42/1.22 thf(f66,plain,(
% 1.42/1.22 ((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($true = (sK2 @ sK0)) | ($false = (sK2 @ (sK3 @ sK2)))),
% 1.42/1.22 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.42/1.22 thf(f64,plain,(
% 1.42/1.22 ($true = $false) | ($true = (sK2 @ sK0)) | ((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($false = (sK2 @ (sK3 @ sK2)))),
% 1.42/1.22 inference(superposition,[status(thm)],[f35,f43])).
% 1.42/1.22 thf(f43,plain,(
% 1.42/1.22 ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK3 @ X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) = $false) | ((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($true = (X1 @ sK0))) )),
% 1.42/1.22 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.42/1.22 thf(f42,plain,(
% 1.42/1.22 ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | (((X1 @ (sK3 @ X1)) => (X1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK3 @ X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $false) | ($true = (X1 @ sK0))) )),
% 1.42/1.22 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.42/1.22 thf(f41,plain,(
% 1.42/1.22 ( ! [X1 : (($i > $o) > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ (sK3 @ X1)) = $false) | ($true = (X1 @ sK0)) | ((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false)) )),
% 1.42/1.22 inference(sigma_clausification,[status(thm)],[f40])).
% 1.42/1.22 thf(f40,plain,(
% 1.42/1.22 ( ! [X1 : (($i > $o) > $o) > $o] : (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) = $false) | ((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($true = (X1 @ sK0))) )),
% 1.42/1.22 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.42/1.22 thf(f39,plain,(
% 1.42/1.22 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = (X1 @ sK0)) | ($false = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))))) )),
% 1.42/1.22 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.42/1.22 thf(f38,plain,(
% 1.42/1.22 ( ! [X1 : (($i > $o) > $o) > $o] : (((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (X1 @ sK0)) = $true)) )),
% 1.42/1.22 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.42/1.22 thf(f37,plain,(
% 1.42/1.22 ( ! [X1 : (($i > $o) > $o) > $o] : ((((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK0))) @ X1) = $true)) )),
% 1.42/1.22 inference(pi_clausification,[status(thm)],[f36])).
% 1.42/1.22 thf(f36,plain,(
% 1.42/1.22 ($true = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK0)))))),
% 1.42/1.22 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.42/1.22 thf(f24,plain,(
% 1.42/1.22 ($true = ((^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))) @ sK0))),
% 1.42/1.22 inference(definition_unfolding,[status(thm)],[f20,f23])).
% 1.42/1.22 thf(f20,plain,(
% 1.42/1.22 ($true = (cNAT @ sK0))),
% 1.42/1.22 inference(cnf_transformation,[status(thm)],[f17])).
% 1.42/1.22 thf(f69,plain,(
% 1.42/1.22 ~spl1_2),
% 1.42/1.22 inference(avatar_contradiction_clause,[status(thm)],[f68])).
% 1.42/1.22 thf(f68,plain,(
% 1.42/1.22 $false | ~spl1_2),
% 1.42/1.22 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.42/1.22 thf(f67,plain,(
% 1.42/1.22 ($true = $false) | ~spl1_2),
% 1.42/1.22 inference(backward_demodulation,[status(thm)],[f56,f61])).
% 1.42/1.22 thf(f56,plain,(
% 1.42/1.22 ($true = (sK2 @ sK0)) | ~spl1_2),
% 1.42/1.22 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.42/1.22 thf(f54,definition,(
% 1.42/1.22 spl1_2 <=> ($true = (sK2 @ sK0))),
% 1.42/1.22 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.42/1.22 thf(f58,plain,(
% 1.42/1.22 spl1_1 | spl1_2),
% 1.42/1.22 inference(avatar_split_clause,[status(thm)],[f47,f54,f50])).
% 1.42/1.22 thf(f47,plain,(
% 1.42/1.22 ($true = (sK2 @ (sK3 @ sK2))) | ($true = (sK2 @ sK0))),
% 1.42/1.22 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.42/1.22 thf(f45,plain,(
% 1.42/1.22 ($true = (sK2 @ (sK3 @ sK2))) | ($true = $false) | ($true = (sK2 @ sK0))),
% 1.42/1.22 inference(superposition,[status(thm)],[f44,f31])).
% 1.42/1.22 thf(f44,plain,(
% 1.42/1.22 ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($true = (X1 @ (sK3 @ X1))) | ($true = (X1 @ sK0))) )),
% 1.42/1.22 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.42/1.22 % SZS output end Proof for DTF2THF_28827
% 1.42/1.22 % (28928)------------------------------
% 1.42/1.22 % (28928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.42/1.22 % (28928)Termination reason: Refutation
% 1.42/1.22
% 1.42/1.22 % (28928)Memory used [KB]: 5628
% 1.42/1.22 % (28928)Time elapsed: 0.010 s
% 1.42/1.22 % (28928)Instructions burned: 10 (million)
% 1.42/1.22 % (28928)------------------------------
% 1.42/1.22 % (28928)------------------------------
% 1.42/1.22 % (28925)Success in time 0.024 s
%------------------------------------------------------------------------------