%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV293^5 : 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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:46 AM UTC 2026
% Result : Theorem 1.64s 1.32s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 110 ( 22 unt; 0 typ; 7 def)
% Number of atoms : 756 ( 291 equ; 37 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 746 ( 183 ~; 176 |; 47 &; 289 @)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 16 usr; 13 con; 0-2 aty)
% ( 0 !!; 44 ??; 0 @@+; 0 @@-)
% Number of variables : 173 ( 99 ^; 67 !; 7 ?; 173 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cONE: ( $i > $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_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK2: $i > $o ).
thf(func_def_18,type,
sK3: $i > $i ).
thf(func_def_22,type,
sK7: $i > $i ).
thf(f219,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f61,f65,f72,f76,f78,f113,f168,f196,f214]) ).
thf(f214,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f213]) ).
thf(f213,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f207]) ).
thf(f207,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f56,f202]) ).
thf(f202,plain,
( ! [X0: $i] :
( ( sK2 @ X0 )
= $false )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f201,f64]) ).
thf(f64,plain,
( ! [X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( sK5 = X1 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl0_3
<=> ! [X1: $i] :
( ( sK5 = X1 )
| ( ( sK2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f201,plain,
( ! [X0: $i] :
( ( sK5 != X0 )
| ( ( sK2 @ X0 )
= $false ) )
| ~ spl0_4
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f200]) ).
thf(f200,plain,
( ! [X0: $i] :
( ( X0 != X0 )
| ( ( sK2 @ X0 )
= $false )
| ( sK5 != X0 ) )
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f173,f190]) ).
thf(f190,plain,
( ! [X0: $i] :
( ( ( sK7 @ X0 )
= X0 )
| ( sK5 != X0 ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f189]) ).
thf(f189,definition,
( spl0_10
<=> ! [X0: $i] :
( ( sK5 != X0 )
| ( ( sK7 @ X0 )
= X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f173,plain,
( ! [X2: $i] :
( ( $false
= ( sK2 @ ( sK7 @ X2 ) ) )
| ( ( sK7 @ X2 )
!= X2 ) )
| ~ spl0_4 ),
inference(equality_proxy_clausification,[status(thm)],[f172]) ).
thf(f172,plain,
( ! [X2: $i] :
( ( $false
= ( sK2 @ ( sK7 @ X2 ) ) )
| ( ( X2
= ( sK7 @ X2 ) )
= $false ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f170]) ).
thf(f170,plain,
( ! [X2: $i] :
( ( X2
= ( sK7 @ X2 ) )
!= ( sK2 @ ( sK7 @ X2 ) ) )
| ~ spl0_4 ),
inference(negative_extensionality,[status(thm)],[f68]) ).
thf(f68,plain,
( ! [X2: $i] :
( ( (=) @ X2 )
!= sK2 )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f67,definition,
( spl0_4
<=> ! [X2: $i] :
( ( (=) @ X2 )
!= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f56,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f54,definition,
( spl0_1
<=> ( $true
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f196,plain,
( spl0_10
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f187,f67,f63,f189]) ).
thf(f187,plain,
( ! [X0: $i] :
( ( sK5 != X0 )
| ( ( sK7 @ X0 )
= X0 ) )
| ~ spl0_3
| ~ spl0_4 ),
inference(equality_factoring,[status(thm)],[f182]) ).
thf(f182,plain,
( ! [X0: $i] :
( ( sK5
= ( sK7 @ X0 ) )
| ( ( sK7 @ X0 )
= X0 ) )
| ~ spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f176]) ).
thf(f176,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( sK5
= ( sK7 @ X0 ) )
| ( ( sK7 @ X0 )
= X0 ) )
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f174,f64]) ).
thf(f174,plain,
( ! [X2: $i] :
( ( ( sK2 @ ( sK7 @ X2 ) )
= $true )
| ( ( sK7 @ X2 )
= X2 ) )
| ~ spl0_4 ),
inference(equality_proxy_clausification,[status(thm)],[f171]) ).
thf(f171,plain,
( ! [X2: $i] :
( ( ( sK2 @ ( sK7 @ X2 ) )
= $true )
| ( ( X2
= ( sK7 @ X2 ) )
= $true ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f170]) ).
thf(f168,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f167]) ).
thf(f167,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(subsumption_resolution,[status(thm)],[f162,f117]) ).
thf(f117,plain,
( ( ( sK3 @ sK5 )
!= sK5 )
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f114]) ).
thf(f114,plain,
( ( $false = $true )
| ( ( sK3 @ sK5 )
!= sK5 )
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f56,f71]) ).
thf(f71,plain,
( ! [X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( ( sK3 @ X1 )
!= X1 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f70,definition,
( spl0_5
<=> ! [X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( ( sK3 @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f162,plain,
( ( ( sK3 @ sK5 )
= sK5 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f157]) ).
thf(f157,plain,
( ( $false = $true )
| ( ( sK3 @ sK5 )
= sK5 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f56,f123]) ).
thf(f123,plain,
( ! [X0: $i] :
( ( ( sK2 @ X0 )
= $false )
| ( ( sK3 @ X0 )
= sK5 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ! [X0: $i] :
( ( ( sK2 @ X0 )
= $false )
| ( $false = $true )
| ( ( sK3 @ X0 )
= sK5 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f75,f64]) ).
thf(f75,plain,
( ! [X1: $i] :
( ( $true
= ( sK2 @ ( sK3 @ X1 ) ) )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f74]) ).
thf(f74,definition,
( spl0_6
<=> ! [X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( $true
= ( sK2 @ ( sK3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f113,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f112]) ).
thf(f112,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(equality_resolution,[status(thm)],[f108]) ).
thf(f108,plain,
( ! [X0: $i] : ( sK4 != X0 )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(duplicate_literal_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ! [X0: $i] :
( ( sK4 != X0 )
| ( sK4 != X0 )
| ( sK4 != X0 ) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f89,f103]) ).
thf(f103,plain,
( ! [X0: $i] :
( ( ( sK3 @ X0 )
= sK4 )
| ( sK4 != X0 ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ! [X0: $i] :
( ( ( sK3 @ X0 )
= sK4 )
| ( $false = $true )
| ( sK4 != X0 ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f97,f82]) ).
thf(f82,plain,
( ! [X1: $i] :
( ( ( sK2 @ X1 )
= $true )
| ( sK4 != X1 ) )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( ! [X1: $i] :
( ( ( sK4 = X1 )
= $false )
| ( ( sK2 @ X1 )
= $true ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( ! [X1: $i] :
( ( sK4 = X1 )
= ( sK2 @ X1 ) )
| ~ spl0_2 ),
inference(argument_congruence,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( (=) @ sK4 )
= sK2 )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl0_2
<=> ( ( (=) @ sK4 )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f97,plain,
( ! [X0: $i] :
( ( ( sK2 @ X0 )
= $false )
| ( ( sK3 @ X0 )
= sK4 ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
( ! [X0: $i] :
( ( ( sK2 @ X0 )
= $false )
| ( $false = $true )
| ( ( sK3 @ X0 )
= sK4 ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f75,f83]) ).
thf(f83,plain,
( ! [X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( sK4 = X1 ) )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ! [X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( ( sK4 = X1 )
= $true ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f89,plain,
( ! [X0: $i] :
( ( ( sK3 @ X0 )
!= X0 )
| ( sK4 != X0 ) )
| ~ spl0_2
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( sK3 @ X0 )
!= X0 )
| ( sK4 != X0 ) )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f82,f71]) ).
thf(f78,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f77]) ).
thf(f77,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f60,f68]) ).
thf(f76,plain,
( spl0_6
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f35,f67,f74]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( ( (=) @ X2 )
!= sK2 )
| ( $true
= ( sK2 @ ( sK3 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK2 @ ( sK3 @ X1 ) ) )
| ( ( sK2 @ X1 )
= $false )
| ( ( ( (=) @ X2 )
= sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK2 @ ( sK3 @ X1 ) )
& ( X1
!= ( sK3 @ X1 ) ) )
= $true )
| ( ( ( (=) @ X2 )
= sK2 )
= $false )
| ( ( sK2 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( ( ( ( (=) @ X2 )
= sK2 )
= $false )
| ( ( sK2 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( X1 != Y0 ) )
@ ( sK3 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( X1 != Y0 ) ) ) )
| ( ( ( (=) @ X2 )
= sK2 )
= $false )
| ( ( sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( X1 != Y0 ) ) ) )
= $false )
| ( ( ( (=) @ X2 )
= sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( X1 != Y0 ) ) )
& ( sK2 @ X1 ) )
= $false )
| ( ( ( (=) @ X2 )
= sK2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( (=) @ Y0 )
= sK2 )
@ X2 )
= $false )
| ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( X1 != Y0 ) ) )
& ( sK2 @ X1 ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( (=) @ Y0 )
= sK2 ) ) )
| ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( X1 != Y0 ) ) )
& ( sK2 @ X1 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( (=) @ Y0 )
= sK2 ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
& ( Y0 != Y1 ) ) )
& ( sK2 @ Y0 ) )
@ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
& ( Y0 != Y1 ) ) )
& ( sK2 @ Y0 ) ) ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( (=) @ Y0 )
= sK2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( (=) @ Y0 )
= sK2 ) )
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
& ( Y0 != Y1 ) ) )
& ( sK2 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) )
& ( Y0 @ Y1 ) ) )
@ sK2 )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( (=) @ Y1 )
= Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( (=) @ Y1 )
= Y0 ) ) )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 )
= Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f15,f18]) ).
thf(f18,plain,
( cONE
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f17,f16,f14]) ).
thf(f14,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,
( cZERO
= ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( cZERO
= ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PJMs0MIlMx/DTF2THF_23687.p',cZERO_def) ).
thf(f16,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ( X0
@ ^ [X3: $i] :
( ( X2 != X3 )
& ( X1 @ X3 ) ) ) ) )
= cSUCC ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X2: ( $i > $o ) > $o,X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ( X2
@ ^ [X3: $i] :
( ( X1 != X3 )
& ( X0 @ X3 ) ) ) ) )
= cSUCC ),
file('/export/starexec/sandbox/tmp/tmp.PJMs0MIlMx/DTF2THF_23687.p',cSUCC_def) ).
thf(f17,plain,
( cONE
= ( cSUCC @ cZERO ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
( cONE
= ( cSUCC @ cZERO ) ),
file('/export/starexec/sandbox/tmp/tmp.PJMs0MIlMx/DTF2THF_23687.p',cONE_def) ).
thf(f15,plain,
( cONE
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 )
= Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( cONE
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 )
= Y0 ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( cONE
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 )
= Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( cONE
!= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( ^ [X2: $i,X3: $i] : ( X2 = X3 )
@ X1 )
= X0 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
( cONE
!= ( ^ [X4: $i > $o] :
? [X5: $i] :
( ( ^ [X1: $i,X5: $i] : ( X1 = X5 )
@ X5 )
= X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( cONE
= ( ^ [X4: $i > $o] :
? [X5: $i] :
( ( ^ [X1: $i,X5: $i] : ( X1 = X5 )
@ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PJMs0MIlMx/DTF2THF_23687.p',cX6101_pme) ).
thf(f72,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f38,f70,f67]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( ( (=) @ X2 )
!= sK2 )
| ( ( sK3 @ X1 )
!= X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( $false
= ( X1
= ( sK3 @ X1 ) ) )
| ( ( (=) @ X2 )
!= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( ( ( (=) @ X2 )
= sK2 )
= $false )
| ( $false
= ( X1
= ( sK3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( ( X1
!= ( sK3 @ X1 ) )
= $true )
| ( ( ( (=) @ X2 )
= sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f65,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f51,f58,f63]) ).
thf(f51,plain,
! [X1: $i] :
( ( sK5 = X1 )
| ( ( (=) @ sK4 )
= sK2 )
| ( ( sK2 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: $i] :
( ( ( (=) @ sK4 )
= sK2 )
| ( ( sK2 @ X1 )
= $false )
| ( ( sK5 = X1 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( ( sK5 != X1 )
= $false )
| ( ( (=) @ sK4 )
= sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: $i] :
( ( $false
= ( ( sK2 @ X1 )
& ( sK5 != X1 ) ) )
| ( ( (=) @ sK4 )
= sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: $i] :
( ( ( (=) @ sK4 )
= sK2 )
| ( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK5 != Y0 ) )
@ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK5 != Y0 ) ) ) )
| ( ( (=) @ sK4 )
= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( ( (=) @ sK4 )
= sK2 )
= $true )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK5 != Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK5 != Y0 ) ) ) )
= $true )
| ( ( ( (=) @ sK4 )
= sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK5 != Y0 ) ) )
& ( sK2 @ sK5 ) )
= $true )
| ( ( ( (=) @ sK4 )
= sK2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( ^ [Y0: $i] :
( ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
& ( Y0 != Y1 ) ) )
& ( sK2 @ Y0 ) )
@ sK5 )
= $true )
| ( ( ( (=) @ sK4 )
= sK2 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
& ( Y0 != Y1 ) ) )
& ( sK2 @ Y0 ) ) ) )
| ( ( ( (=) @ sK4 )
= sK2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
& ( Y0 != Y1 ) ) )
& ( sK2 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( (=) @ Y0 )
= sK2 )
@ sK4 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( (=) @ Y0 )
= sK2 ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
& ( Y0 != Y1 ) ) )
& ( sK2 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f61,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f52,f58,f54]) ).
thf(f52,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( (=) @ sK4 )
= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( ( (=) @ sK4 )
= sK2 )
= $true )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV293^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n015.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:43:31 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
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEV293^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : TPS problem X6101
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0455 [Bro09]
% 0.29/0.46 % : X6101 [TPS]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.60 v8.2.0, 0.46 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.60 v6.2.0
% 0.29/0.46 % Syntax : Number of formulae : 7 ( 4 unt; 3 typ; 3 def)
% 0.29/0.46 % Number of atoms : 13 ( 7 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 1 ( 3 avg)
% 0.29/0.46 % Number of connectives : 10 ( 2 ~; 0 |; 2 &; 6 @)
% 0.29/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 1 ( 1 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.29/0.46 % Number of variables : 10 ( 7 ^; 0 !; 3 ?; 10 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 % : Polymorphic definitions expanded.
% 0.29/0.46 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.29/0.46 % : v6.2.0 - Reordered definitions.
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(cONE_type,type,
% 0.29/0.46 cONE: ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(cSUCC_type,type,
% 0.29/0.46 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(cZERO_type,type,
% 0.29/0.46 cZERO: ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(cZERO_def,definition,
% 0.29/0.46 ( cZERO
% 0.29/0.46 = ( ^ [Xp: $i > $o] :
% 0.29/0.46 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cONE_def,definition,
% 0.29/0.46 ( cONE
% 0.29/0.46 = ( cSUCC @ cZERO ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cSUCC_def,definition,
% 0.29/0.46 ( cSUCC
% 0.29/0.46 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 0.29/0.46 ? [Xx: $i] :
% 0.29/0.46 ( ( Xp @ Xx )
% 0.29/0.46 & ( Xn
% 0.29/0.46 @ ^ [Xt: $i] :
% 0.29/0.46 ( ( Xt != Xx )
% 0.29/0.46 & ( Xp @ Xt ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cX6101_pme,conjecture,
% 0.29/0.46 ( cONE
% 0.29/0.46 = ( ^ [P: $i > $o] :
% 0.29/0.46 ? [Xy: $i] :
% 0.29/0.46 ( P
% 0.29/0.46 = ( ^ [Xx: $i,Xy: $i] : ( Xx = Xy )
% 0.29/0.46 @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.48/1.28 ---- Embedded in THF ---
% 1.48/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.28 %%% Generated on Tue Feb 24 12:43:32 EST 2026
% 1.48/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.28 %%% Logic specification used:
% 1.48/1.28 %%% thf(spec, logic, $$dhol).
% 1.48/1.28
% 1.48/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.PJMs0MIlMx/DTF2DTF23687.p
% See solution above
% 1.48/1.28 ------------------------
% 1.48/1.29 ---- Cleaned THF ---
% 1.48/1.29 thf(cONE_type,type,
% 1.48/1.29 cONE: ( $i > $o ) > $o ).
% 1.48/1.29
% 1.48/1.29 thf(cSUCC_type,type,
% 1.48/1.29 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 1.48/1.29
% 1.48/1.29 thf(cZERO_type,type,
% 1.48/1.29 cZERO: ( $i > $o ) > $o ).
% 1.48/1.29
% 1.48/1.29 thf(cZERO_def,definition,
% 1.48/1.29 ( cZERO
% 1.48/1.29 = ( ^ [Xp: $i > $o] :
% 1.48/1.29 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 1.48/1.29
% 1.48/1.29 thf(cONE_def,definition,
% 1.48/1.29 ( cONE
% 1.48/1.29 = ( cSUCC @ cZERO ) ) ).
% 1.48/1.29
% 1.48/1.29 thf(cSUCC_def,definition,
% 1.48/1.29 ( cSUCC
% 1.48/1.29 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 1.48/1.29 ? [Xx: $i] :
% 1.48/1.29 ( ( Xp @ Xx )
% 1.48/1.29 & ( Xn
% 1.48/1.29 @ ^ [Xt: $i] :
% 1.48/1.29 ( ( Xt != Xx )
% 1.48/1.29 & ( Xp @ Xt ) ) ) ) ) ) ).
% 1.48/1.29
% 1.48/1.29 thf(cX6101_pme,conjecture,
% 1.48/1.29 ( cONE
% 1.48/1.29 = ( ^ [P: $i > $o] :
% 1.48/1.29 ? [Xy: $i] :
% 1.48/1.29 ( P
% 1.48/1.29 = ( ^ [Xx: $i,Xy: $i] : ( Xx = Xy )
% 1.48/1.29 @ Xy ) ) ) ) ).
% 1.48/1.29 ------------------------
% 1.64/1.30 % (23963)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_23687 for (3000ds/4Mi)
% 1.64/1.30 % (23963)Instruction limit reached!
% 1.64/1.30 % (23963)------------------------------
% 1.64/1.30 % (23963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (23963)Termination reason: Unknown
% 1.64/1.30 % (23963)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (23963)Memory used [KB]: 5500
% 1.64/1.30 % (23963)Time elapsed: 0.004 s
% 1.64/1.30 % (23963)Instructions burned: 6 (million)
% 1.64/1.30 % (23963)------------------------------
% 1.64/1.30 % (23963)------------------------------
% 1.64/1.31 % (23962)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23687 for (3000ds/183Mi)
% 1.64/1.31 % (23964)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_23687 for (3000ds/27Mi)
% 1.64/1.31 % (23965)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23687 for (3000ds/2Mi)
% 1.64/1.31 % (23966)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_23687 for (3000ds/2Mi)
% 1.64/1.31 % (23968)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23687 for (3000ds/18Mi)
% 1.64/1.31 % (23967)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_23687 for (3000ds/275Mi)
% 1.64/1.31 % (23965)Instruction limit reached!
% 1.64/1.31 % (23965)------------------------------
% 1.64/1.31 % (23965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (23965)Termination reason: Unknown
% 1.64/1.31 % (23965)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (23965)Memory used [KB]: 5500
% 1.64/1.31 % (23965)Time elapsed: 0.004 s
% 1.64/1.31 % (23965)Instructions burned: 2 (million)
% 1.64/1.31 % (23965)------------------------------
% 1.64/1.31 % (23965)------------------------------
% 1.64/1.31 % (23966)Instruction limit reached!
% 1.64/1.31 % (23966)------------------------------
% 1.64/1.31 % (23966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (23966)Termination reason: Unknown
% 1.64/1.31 % (23966)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (23966)Memory used [KB]: 5500
% 1.64/1.31 % (23966)Time elapsed: 0.004 s
% 1.64/1.31 % (23966)Instructions burned: 3 (million)
% 1.64/1.31 % (23966)------------------------------
% 1.64/1.31 % (23966)------------------------------
% 1.64/1.31 % (23967)Refutation not found, incomplete strategy
% 1.64/1.31 % (23967)------------------------------
% 1.64/1.31 % (23967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (23967)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.31
% 1.64/1.31
% 1.64/1.31 % (23967)Memory used [KB]: 5500
% 1.64/1.31 % (23967)Time elapsed: 0.004 s
% 1.64/1.31 % (23967)Instructions burned: 3 (million)
% 1.64/1.31 % (23967)------------------------------
% 1.64/1.31 % (23967)------------------------------
% 1.64/1.31 % (23969)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23687 for (2999ds/3Mi)
% 1.64/1.31 % (23969)Instruction limit reached!
% 1.64/1.31 % (23969)------------------------------
% 1.64/1.31 % (23969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (23969)Termination reason: Unknown
% 1.64/1.31 % (23969)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (23969)Memory used [KB]: 5500
% 1.64/1.31 % (23969)Time elapsed: 0.002 s
% 1.64/1.31 % (23969)Instructions burned: 3 (million)
% 1.64/1.31 % (23969)------------------------------
% 1.64/1.31 % (23969)------------------------------
% 1.64/1.32 % (23962)First to succeed.
% 1.64/1.32 % (23964)Also succeeded, but the first one will report.
% 1.64/1.32 % (23962)Refutation found. Thanks to Tanya!
% 1.64/1.32 % SZS status Theorem for DTF2THF_23687
% 1.64/1.32 % SZS output start Proof for DTF2THF_23687
% 1.64/1.32 thf(func_def_0, type, cONE: ($i > $o) > $o).
% 1.64/1.32 thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 1.64/1.32 thf(func_def_2, type, cZERO: ($i > $o) > $o).
% 1.64/1.32 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 1.64/1.32 thf(func_def_17, type, sK2: $i > $o).
% 1.64/1.32 thf(func_def_18, type, sK3: $i > $i).
% 1.64/1.32 thf(func_def_22, type, sK7: $i > $i).
% 1.64/1.32 thf(f219,plain,(
% 1.64/1.32 $false),
% 1.64/1.32 inference(avatar_sat_refutation,[status(thm)],[f61,f65,f72,f76,f78,f113,f168,f196,f214])).
% 1.64/1.32 thf(f214,plain,(
% 1.64/1.32 ~spl0_1 | ~spl0_3 | ~spl0_4 | ~spl0_10),
% 1.64/1.32 inference(avatar_contradiction_clause,[status(thm)],[f213])).
% 1.64/1.32 thf(f213,plain,(
% 1.64/1.32 $false | (~spl0_1 | ~spl0_3 | ~spl0_4 | ~spl0_10)),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f207])).
% 1.64/1.32 thf(f207,plain,(
% 1.64/1.32 ($false = $true) | (~spl0_1 | ~spl0_3 | ~spl0_4 | ~spl0_10)),
% 1.64/1.32 inference(superposition,[status(thm)],[f56,f202])).
% 1.64/1.32 thf(f202,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (((sK2 @ X0) = $false)) ) | (~spl0_3 | ~spl0_4 | ~spl0_10)),
% 1.64/1.32 inference(subsumption_resolution,[status(thm)],[f201,f64])).
% 1.64/1.32 thf(f64,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (((sK2 @ X1) = $false) | (sK5 = X1)) ) | ~spl0_3),
% 1.64/1.32 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.64/1.32 thf(f63,definition,(
% 1.64/1.32 spl0_3 <=> ! [X1 : $i] : ((sK5 = X1) | ((sK2 @ X1) = $false))),
% 1.64/1.32 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.64/1.32 thf(f201,plain,(
% 1.64/1.32 ( ! [X0 : $i] : ((sK5 != X0) | ((sK2 @ X0) = $false)) ) | (~spl0_4 | ~spl0_10)),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f200])).
% 1.64/1.32 thf(f200,plain,(
% 1.64/1.32 ( ! [X0 : $i] : ((X0 != X0) | ((sK2 @ X0) = $false) | (sK5 != X0)) ) | (~spl0_4 | ~spl0_10)),
% 1.64/1.32 inference(superposition,[status(thm)],[f173,f190])).
% 1.64/1.32 thf(f190,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (((sK7 @ X0) = X0) | (sK5 != X0)) ) | ~spl0_10),
% 1.64/1.32 inference(avatar_component_clause,[status(thm)],[f189])).
% 1.64/1.32 thf(f189,definition,(
% 1.64/1.32 spl0_10 <=> ! [X0 : $i] : ((sK5 != X0) | ((sK7 @ X0) = X0))),
% 1.64/1.32 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.64/1.32 thf(f173,plain,(
% 1.64/1.32 ( ! [X2 : $i] : (($false = (sK2 @ (sK7 @ X2))) | ((sK7 @ X2) != X2)) ) | ~spl0_4),
% 1.64/1.32 inference(equality_proxy_clausification,[status(thm)],[f172])).
% 1.64/1.32 thf(f172,plain,(
% 1.64/1.32 ( ! [X2 : $i] : (($false = (sK2 @ (sK7 @ X2))) | ((X2 = (sK7 @ X2)) = $false)) ) | ~spl0_4),
% 1.64/1.32 inference(binary_proxy_clausification,[status(thm)],[f170])).
% 1.64/1.32 thf(f170,plain,(
% 1.64/1.32 ( ! [X2 : $i] : (((X2 = (sK7 @ X2)) != (sK2 @ (sK7 @ X2)))) ) | ~spl0_4),
% 1.64/1.32 inference(negative_extensionality,[status(thm)],[f68])).
% 1.64/1.32 thf(f68,plain,(
% 1.64/1.32 ( ! [X2 : $i] : (((= @ X2) != sK2)) ) | ~spl0_4),
% 1.64/1.32 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.64/1.32 thf(f67,definition,(
% 1.64/1.32 spl0_4 <=> ! [X2 : $i] : ((= @ X2) != sK2)),
% 1.64/1.32 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.64/1.32 thf(f56,plain,(
% 1.64/1.32 ($true = (sK2 @ sK5)) | ~spl0_1),
% 1.64/1.32 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.64/1.32 thf(f54,definition,(
% 1.64/1.32 spl0_1 <=> ($true = (sK2 @ sK5))),
% 1.64/1.32 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.64/1.32 thf(f196,plain,(
% 1.64/1.32 spl0_10 | ~spl0_3 | ~spl0_4),
% 1.64/1.32 inference(avatar_split_clause,[status(thm)],[f187,f67,f63,f189])).
% 1.64/1.32 thf(f187,plain,(
% 1.64/1.32 ( ! [X0 : $i] : ((sK5 != X0) | ((sK7 @ X0) = X0)) ) | (~spl0_3 | ~spl0_4)),
% 1.64/1.32 inference(equality_factoring,[status(thm)],[f182])).
% 1.64/1.32 thf(f182,plain,(
% 1.64/1.32 ( ! [X0 : $i] : ((sK5 = (sK7 @ X0)) | ((sK7 @ X0) = X0)) ) | (~spl0_3 | ~spl0_4)),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f176])).
% 1.64/1.32 thf(f176,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (($false = $true) | (sK5 = (sK7 @ X0)) | ((sK7 @ X0) = X0)) ) | (~spl0_3 | ~spl0_4)),
% 1.64/1.32 inference(superposition,[status(thm)],[f174,f64])).
% 1.64/1.32 thf(f174,plain,(
% 1.64/1.32 ( ! [X2 : $i] : (((sK2 @ (sK7 @ X2)) = $true) | ((sK7 @ X2) = X2)) ) | ~spl0_4),
% 1.64/1.32 inference(equality_proxy_clausification,[status(thm)],[f171])).
% 1.64/1.32 thf(f171,plain,(
% 1.64/1.32 ( ! [X2 : $i] : (((sK2 @ (sK7 @ X2)) = $true) | ((X2 = (sK7 @ X2)) = $true)) ) | ~spl0_4),
% 1.64/1.32 inference(binary_proxy_clausification,[status(thm)],[f170])).
% 1.64/1.32 thf(f168,plain,(
% 1.64/1.32 ~spl0_1 | ~spl0_3 | ~spl0_5 | ~spl0_6),
% 1.64/1.32 inference(avatar_contradiction_clause,[status(thm)],[f167])).
% 1.64/1.32 thf(f167,plain,(
% 1.64/1.32 $false | (~spl0_1 | ~spl0_3 | ~spl0_5 | ~spl0_6)),
% 1.64/1.32 inference(subsumption_resolution,[status(thm)],[f162,f117])).
% 1.64/1.32 thf(f117,plain,(
% 1.64/1.32 ((sK3 @ sK5) != sK5) | (~spl0_1 | ~spl0_5)),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f114])).
% 1.64/1.32 thf(f114,plain,(
% 1.64/1.32 ($false = $true) | ((sK3 @ sK5) != sK5) | (~spl0_1 | ~spl0_5)),
% 1.64/1.32 inference(superposition,[status(thm)],[f56,f71])).
% 1.64/1.32 thf(f71,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (((sK2 @ X1) = $false) | ((sK3 @ X1) != X1)) ) | ~spl0_5),
% 1.64/1.32 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.64/1.32 thf(f70,definition,(
% 1.64/1.32 spl0_5 <=> ! [X1 : $i] : (((sK2 @ X1) = $false) | ((sK3 @ X1) != X1))),
% 1.64/1.32 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.64/1.32 thf(f162,plain,(
% 1.64/1.32 ((sK3 @ sK5) = sK5) | (~spl0_1 | ~spl0_3 | ~spl0_6)),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f157])).
% 1.64/1.32 thf(f157,plain,(
% 1.64/1.32 ($false = $true) | ((sK3 @ sK5) = sK5) | (~spl0_1 | ~spl0_3 | ~spl0_6)),
% 1.64/1.32 inference(superposition,[status(thm)],[f56,f123])).
% 1.64/1.32 thf(f123,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (((sK2 @ X0) = $false) | ((sK3 @ X0) = sK5)) ) | (~spl0_3 | ~spl0_6)),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.64/1.32 thf(f120,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (((sK2 @ X0) = $false) | ($false = $true) | ((sK3 @ X0) = sK5)) ) | (~spl0_3 | ~spl0_6)),
% 1.64/1.32 inference(superposition,[status(thm)],[f75,f64])).
% 1.64/1.32 thf(f75,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (($true = (sK2 @ (sK3 @ X1))) | ((sK2 @ X1) = $false)) ) | ~spl0_6),
% 1.64/1.32 inference(avatar_component_clause,[status(thm)],[f74])).
% 1.64/1.32 thf(f74,definition,(
% 1.64/1.32 spl0_6 <=> ! [X1 : $i] : (((sK2 @ X1) = $false) | ($true = (sK2 @ (sK3 @ X1))))),
% 1.64/1.32 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.64/1.32 thf(f113,plain,(
% 1.64/1.32 ~spl0_2 | ~spl0_5 | ~spl0_6),
% 1.64/1.32 inference(avatar_contradiction_clause,[status(thm)],[f112])).
% 1.64/1.32 thf(f112,plain,(
% 1.64/1.32 $false | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 1.64/1.32 inference(equality_resolution,[status(thm)],[f108])).
% 1.64/1.32 thf(f108,plain,(
% 1.64/1.32 ( ! [X0 : $i] : ((sK4 != X0)) ) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 1.64/1.32 inference(duplicate_literal_removal,[status(thm)],[f107])).
% 1.64/1.32 thf(f107,plain,(
% 1.64/1.32 ( ! [X0 : $i] : ((sK4 != X0) | (sK4 != X0) | (sK4 != X0)) ) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 1.64/1.32 inference(superposition,[status(thm)],[f89,f103])).
% 1.64/1.32 thf(f103,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (((sK3 @ X0) = sK4) | (sK4 != X0)) ) | (~spl0_2 | ~spl0_6)),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.64/1.32 thf(f98,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (((sK3 @ X0) = sK4) | ($false = $true) | (sK4 != X0)) ) | (~spl0_2 | ~spl0_6)),
% 1.64/1.32 inference(superposition,[status(thm)],[f97,f82])).
% 1.64/1.32 thf(f82,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (((sK2 @ X1) = $true) | (sK4 != X1)) ) | ~spl0_2),
% 1.64/1.32 inference(equality_proxy_clausification,[status(thm)],[f81])).
% 1.64/1.32 thf(f81,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (((sK4 = X1) = $false) | ((sK2 @ X1) = $true)) ) | ~spl0_2),
% 1.64/1.32 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.64/1.32 thf(f79,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (((sK4 = X1) = (sK2 @ X1))) ) | ~spl0_2),
% 1.64/1.32 inference(argument_congruence,[status(thm)],[f60])).
% 1.64/1.32 thf(f60,plain,(
% 1.64/1.32 ((= @ sK4) = sK2) | ~spl0_2),
% 1.64/1.32 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.64/1.32 thf(f58,definition,(
% 1.64/1.32 spl0_2 <=> ((= @ sK4) = sK2)),
% 1.64/1.32 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.64/1.32 thf(f97,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (((sK2 @ X0) = $false) | ((sK3 @ X0) = sK4)) ) | (~spl0_2 | ~spl0_6)),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.64/1.32 thf(f91,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (((sK2 @ X0) = $false) | ($false = $true) | ((sK3 @ X0) = sK4)) ) | (~spl0_2 | ~spl0_6)),
% 1.64/1.32 inference(superposition,[status(thm)],[f75,f83])).
% 1.64/1.32 thf(f83,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (((sK2 @ X1) = $false) | (sK4 = X1)) ) | ~spl0_2),
% 1.64/1.32 inference(equality_proxy_clausification,[status(thm)],[f80])).
% 1.64/1.32 thf(f80,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (((sK2 @ X1) = $false) | ((sK4 = X1) = $true)) ) | ~spl0_2),
% 1.64/1.32 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.64/1.32 thf(f89,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (((sK3 @ X0) != X0) | (sK4 != X0)) ) | (~spl0_2 | ~spl0_5)),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.64/1.32 thf(f87,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (($false = $true) | ((sK3 @ X0) != X0) | (sK4 != X0)) ) | (~spl0_2 | ~spl0_5)),
% 1.64/1.32 inference(superposition,[status(thm)],[f82,f71])).
% 1.64/1.32 thf(f78,plain,(
% 1.64/1.32 ~spl0_2 | ~spl0_4),
% 1.64/1.32 inference(avatar_contradiction_clause,[status(thm)],[f77])).
% 1.64/1.32 thf(f77,plain,(
% 1.64/1.32 $false | (~spl0_2 | ~spl0_4)),
% 1.64/1.32 inference(subsumption_resolution,[status(thm)],[f60,f68])).
% 1.64/1.32 thf(f76,plain,(
% 1.64/1.32 spl0_6 | spl0_4),
% 1.64/1.32 inference(avatar_split_clause,[status(thm)],[f35,f67,f74])).
% 1.64/1.32 thf(f35,plain,(
% 1.64/1.32 ( ! [X2 : $i,X1 : $i] : (((sK2 @ X1) = $false) | ((= @ X2) != sK2) | ($true = (sK2 @ (sK3 @ X1)))) )),
% 1.64/1.32 inference(equality_proxy_clausification,[status(thm)],[f34])).
% 1.64/1.32 thf(f34,plain,(
% 1.64/1.32 ( ! [X2 : $i,X1 : $i] : (($true = (sK2 @ (sK3 @ X1))) | ((sK2 @ X1) = $false) | (((= @ X2) = sK2) = $false)) )),
% 1.64/1.32 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.64/1.32 thf(f32,plain,(
% 1.64/1.32 ( ! [X2 : $i,X1 : $i] : ((((sK2 @ (sK3 @ X1)) & (~ (X1 = (sK3 @ X1)))) = $true) | (((= @ X2) = sK2) = $false) | ((sK2 @ X1) = $false)) )),
% 1.64/1.32 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.64/1.32 thf(f31,plain,(
% 1.64/1.32 ( ! [X2 : $i,X1 : $i] : ((((= @ X2) = sK2) = $false) | ((sK2 @ X1) = $false) | (((^[Y0 : $i]: ((sK2 @ Y0) & (~ (X1 = Y0)))) @ (sK3 @ X1)) = $true)) )),
% 1.64/1.32 inference(sigma_clausification,[status(thm)],[f30])).
% 1.64/1.32 thf(f30,plain,(
% 1.64/1.32 ( ! [X2 : $i,X1 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (X1 = Y0)))))) | (((= @ X2) = sK2) = $false) | ((sK2 @ X1) = $false)) )),
% 1.64/1.32 inference(not_proxy_clausification,[status(thm)],[f29])).
% 1.64/1.32 thf(f29,plain,(
% 1.64/1.32 ( ! [X2 : $i,X1 : $i] : (((sK2 @ X1) = $false) | ((~ (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (X1 = Y0)))))) = $false) | (((= @ X2) = sK2) = $false)) )),
% 1.64/1.32 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.64/1.32 thf(f28,plain,(
% 1.64/1.32 ( ! [X2 : $i,X1 : $i] : ((((~ (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (X1 = Y0)))))) & (sK2 @ X1)) = $false) | (((= @ X2) = sK2) = $false)) )),
% 1.64/1.32 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.64/1.32 thf(f27,plain,(
% 1.64/1.32 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((= @ Y0) = sK2)) @ X2) = $false) | (((~ (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (X1 = Y0)))))) & (sK2 @ X1)) = $false)) )),
% 1.64/1.32 inference(pi_clausification,[status(thm)],[f26])).
% 1.64/1.32 thf(f26,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: ((= @ Y0) = sK2)))) | (((~ (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (X1 = Y0)))))) & (sK2 @ X1)) = $false)) )),
% 1.64/1.32 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.64/1.32 thf(f25,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: ((= @ Y0) = sK2)))) | (((^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) & (~ (Y0 = Y1)))))) & (sK2 @ Y0))) @ X1) = $false)) )),
% 1.64/1.32 inference(pi_clausification,[status(thm)],[f24])).
% 1.64/1.32 thf(f24,plain,(
% 1.64/1.32 ($false = (?? @ $i @ (^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) & (~ (Y0 = Y1)))))) & (sK2 @ Y0))))) | ($false = (?? @ $i @ (^[Y0 : $i]: ((= @ Y0) = sK2))))),
% 1.64/1.32 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.64/1.32 thf(f22,plain,(
% 1.64/1.32 ((?? @ $i @ (^[Y0 : $i]: ((= @ Y0) = sK2))) != (?? @ $i @ (^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) & (~ (Y0 = Y1)))))) & (sK2 @ Y0)))))),
% 1.64/1.32 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.64/1.32 thf(f21,plain,(
% 1.64/1.32 (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))) & (Y0 @ Y1))))) @ sK2) != ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((= @ Y1) = Y0)))) @ sK2))),
% 1.64/1.32 inference(negative_extensionality,[status(thm)],[f20])).
% 1.64/1.32 thf(f20,plain,(
% 1.64/1.32 ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((= @ Y1) = Y0)))) != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))) & (Y0 @ Y1))))))),
% 1.64/1.32 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.64/1.32 thf(f19,plain,(
% 1.64/1.32 (((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1) = Y0)))))),
% 1.64/1.32 inference(definition_unfolding,[status(thm)],[f15,f18])).
% 1.64/1.32 thf(f18,plain,(
% 1.64/1.32 (cONE = ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.64/1.32 inference(definition_unfolding,[status(thm)],[f17,f16,f14])).
% 1.64/1.32 thf(f14,plain,(
% 1.64/1.32 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.32 thf(f10,plain,(
% 1.64/1.32 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.64/1.32 inference(fool_elimination,[status(thm)],[f9])).
% 1.64/1.32 thf(f9,plain,(
% 1.64/1.32 (cZERO = (^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))))),
% 1.64/1.32 inference(rectify,[status(thm)],[f1])).
% 1.64/1.32 thf(f1,axiom,(
% 1.64/1.32 (cZERO = (^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))))),
% 1.64/1.32 file('/export/starexec/sandbox/tmp/tmp.PJMs0MIlMx/DTF2THF_23687.p',cZERO_def)).
% 1.64/1.32 thf(f16,plain,(
% 1.64/1.32 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f8])).
% 1.64/1.32 thf(f8,plain,(
% 1.64/1.32 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))),
% 1.64/1.32 inference(fool_elimination,[status(thm)],[f7])).
% 1.64/1.32 thf(f7,plain,(
% 1.64/1.32 ((^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2 : $i] : ((X1 @ X2) & (X0 @ (^[X3 : $i] : ((X2 != X3) & (X1 @ X3))))))) = cSUCC)),
% 1.64/1.32 inference(rectify,[status(thm)],[f3])).
% 1.64/1.32 thf(f3,axiom,(
% 1.64/1.32 ((^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & (X2 @ (^[X3 : $i] : ((X1 != X3) & (X0 @ X3))))))) = cSUCC)),
% 1.64/1.32 file('/export/starexec/sandbox/tmp/tmp.PJMs0MIlMx/DTF2THF_23687.p',cSUCC_def)).
% 1.64/1.32 thf(f17,plain,(
% 1.64/1.32 (cONE = (cSUCC @ cZERO))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f2])).
% 1.64/1.32 thf(f2,axiom,(
% 1.64/1.32 (cONE = (cSUCC @ cZERO))),
% 1.64/1.32 file('/export/starexec/sandbox/tmp/tmp.PJMs0MIlMx/DTF2THF_23687.p',cONE_def)).
% 1.64/1.32 thf(f15,plain,(
% 1.64/1.32 (cONE != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1) = Y0)))))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.32 thf(f13,plain,(
% 1.64/1.32 (cONE != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1) = Y0)))))),
% 1.64/1.32 inference(flattening,[status(thm)],[f12])).
% 1.64/1.32 thf(f12,plain,(
% 1.64/1.32 ~(cONE = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1) = Y0)))))),
% 1.64/1.32 inference(fool_elimination,[status(thm)],[f11])).
% 1.64/1.32 thf(f11,plain,(
% 1.64/1.32 ~(cONE = (^[X0 : $i > $o] : (? [X1 : $i] : (((^[X2 : $i, X3 : $i] : ((X2 = X3))) @ X1) = X0))))),
% 1.64/1.32 inference(rectify,[status(thm)],[f5])).
% 1.64/1.32 thf(f5,negated_conjecture,(
% 1.64/1.32 ~(cONE = (^[X4 : $i > $o] : (? [X5 : $i] : (((^[X1 : $i, X5 : $i] : ((X1 = X5))) @ X5) = X4))))),
% 1.64/1.32 inference(negated_conjecture,[status(cth)],[f4])).
% 1.64/1.32 thf(f4,conjecture,(
% 1.64/1.32 (cONE = (^[X4 : $i > $o] : (? [X5 : $i] : (((^[X1 : $i, X5 : $i] : ((X1 = X5))) @ X5) = X4))))),
% 1.64/1.32 file('/export/starexec/sandbox/tmp/tmp.PJMs0MIlMx/DTF2THF_23687.p',cX6101_pme)).
% 1.64/1.32 thf(f72,plain,(
% 1.64/1.32 spl0_4 | spl0_5),
% 1.64/1.32 inference(avatar_split_clause,[status(thm)],[f38,f70,f67])).
% 1.64/1.32 thf(f38,plain,(
% 1.64/1.32 ( ! [X2 : $i,X1 : $i] : (((sK2 @ X1) = $false) | ((= @ X2) != sK2) | ((sK3 @ X1) != X1)) )),
% 1.64/1.32 inference(equality_proxy_clausification,[status(thm)],[f37])).
% 1.64/1.32 thf(f37,plain,(
% 1.64/1.32 ( ! [X2 : $i,X1 : $i] : (((sK2 @ X1) = $false) | ($false = (X1 = (sK3 @ X1))) | ((= @ X2) != sK2)) )),
% 1.64/1.32 inference(equality_proxy_clausification,[status(thm)],[f36])).
% 1.64/1.32 thf(f36,plain,(
% 1.64/1.32 ( ! [X2 : $i,X1 : $i] : (((sK2 @ X1) = $false) | (((= @ X2) = sK2) = $false) | ($false = (X1 = (sK3 @ X1)))) )),
% 1.64/1.32 inference(not_proxy_clausification,[status(thm)],[f33])).
% 1.64/1.32 thf(f33,plain,(
% 1.64/1.32 ( ! [X2 : $i,X1 : $i] : (((sK2 @ X1) = $false) | ((~ (X1 = (sK3 @ X1))) = $true) | (((= @ X2) = sK2) = $false)) )),
% 1.64/1.32 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.64/1.32 thf(f65,plain,(
% 1.64/1.32 spl0_3 | spl0_2),
% 1.64/1.32 inference(avatar_split_clause,[status(thm)],[f51,f58,f63])).
% 1.64/1.32 thf(f51,plain,(
% 1.64/1.32 ( ! [X1 : $i] : ((sK5 = X1) | ((= @ sK4) = sK2) | ((sK2 @ X1) = $false)) )),
% 1.64/1.32 inference(equality_proxy_clausification,[status(thm)],[f50])).
% 1.64/1.32 thf(f50,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (((= @ sK4) = sK2) | ((sK2 @ X1) = $false) | ((sK5 = X1) = $true)) )),
% 1.64/1.32 inference(not_proxy_clausification,[status(thm)],[f49])).
% 1.64/1.32 thf(f49,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (((sK2 @ X1) = $false) | ((~ (sK5 = X1)) = $false) | ((= @ sK4) = sK2)) )),
% 1.64/1.32 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.64/1.32 thf(f48,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (($false = ((sK2 @ X1) & (~ (sK5 = X1)))) | ((= @ sK4) = sK2)) )),
% 1.64/1.32 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.64/1.32 thf(f47,plain,(
% 1.64/1.32 ( ! [X1 : $i] : (((= @ sK4) = sK2) | (((^[Y0 : $i]: ((sK2 @ Y0) & (~ (sK5 = Y0)))) @ X1) = $false)) )),
% 1.64/1.32 inference(pi_clausification,[status(thm)],[f46])).
% 1.64/1.32 thf(f46,plain,(
% 1.64/1.32 ($false = (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (sK5 = Y0)))))) | ((= @ sK4) = sK2)),
% 1.64/1.32 inference(equality_proxy_clausification,[status(thm)],[f45])).
% 1.64/1.32 thf(f45,plain,(
% 1.64/1.32 (((= @ sK4) = sK2) = $true) | ($false = (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (sK5 = Y0))))))),
% 1.64/1.32 inference(not_proxy_clausification,[status(thm)],[f44])).
% 1.64/1.32 thf(f44,plain,(
% 1.64/1.32 ((~ (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (sK5 = Y0)))))) = $true) | (((= @ sK4) = sK2) = $true)),
% 1.64/1.32 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.64/1.32 thf(f42,plain,(
% 1.64/1.32 (((~ (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (sK5 = Y0)))))) & (sK2 @ sK5)) = $true) | (((= @ sK4) = sK2) = $true)),
% 1.64/1.32 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.64/1.32 thf(f41,plain,(
% 1.64/1.32 (((^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) & (~ (Y0 = Y1)))))) & (sK2 @ Y0))) @ sK5) = $true) | (((= @ sK4) = sK2) = $true)),
% 1.64/1.32 inference(sigma_clausification,[status(thm)],[f40])).
% 1.64/1.32 thf(f40,plain,(
% 1.64/1.32 ($true = (?? @ $i @ (^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) & (~ (Y0 = Y1)))))) & (sK2 @ Y0))))) | (((= @ sK4) = sK2) = $true)),
% 1.64/1.32 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.64/1.32 thf(f39,plain,(
% 1.64/1.32 ($true = (?? @ $i @ (^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) & (~ (Y0 = Y1)))))) & (sK2 @ Y0))))) | (((^[Y0 : $i]: ((= @ Y0) = sK2)) @ sK4) = $true)),
% 1.64/1.32 inference(sigma_clausification,[status(thm)],[f23])).
% 1.64/1.32 thf(f23,plain,(
% 1.64/1.32 ($true = (?? @ $i @ (^[Y0 : $i]: ((= @ Y0) = sK2)))) | ($true = (?? @ $i @ (^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) & (~ (Y0 = Y1)))))) & (sK2 @ Y0)))))),
% 1.64/1.32 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.64/1.32 thf(f61,plain,(
% 1.64/1.32 spl0_1 | spl0_2),
% 1.64/1.32 inference(avatar_split_clause,[status(thm)],[f52,f58,f54])).
% 1.64/1.32 thf(f52,plain,(
% 1.64/1.32 ($true = (sK2 @ sK5)) | ((= @ sK4) = sK2)),
% 1.64/1.32 inference(equality_proxy_clausification,[status(thm)],[f43])).
% 1.64/1.32 thf(f43,plain,(
% 1.64/1.32 (((= @ sK4) = sK2) = $true) | ($true = (sK2 @ sK5))),
% 1.64/1.32 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.64/1.32 % SZS output end Proof for DTF2THF_23687
% 1.64/1.32 % (23962)------------------------------
% 1.64/1.32 % (23962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (23962)Termination reason: Refutation
% 1.64/1.32
% 1.64/1.32 % (23962)Memory used [KB]: 5628
% 1.64/1.32 % (23962)Time elapsed: 0.014 s
% 1.64/1.32 % (23962)Instructions burned: 14 (million)
% 1.64/1.32 % (23962)------------------------------
% 1.64/1.32 % (23962)------------------------------
% 1.64/1.32 % (23961)Success in time 0.029 s
%------------------------------------------------------------------------------