%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV300^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:47 AM UTC 2026
% Result : Theorem 1.53s 1.42s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 123 ( 17 unt; 0 typ; 9 def)
% Number of atoms : 843 ( 316 equ; 37 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 848 ( 205 ~; 199 |; 47 &; 332 @)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 20 usr; 15 con; 0-2 aty)
% ( 0 !!; 47 ??; 0 @@+; 0 @@-)
% Number of variables : 194 ( 105 ^; 80 !; 9 ?; 194 :)
% 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_14,type,
sK0: ( $i > $i ) > ( $i > $i ) > $i ).
thf(func_def_17,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK3: $i > $o ).
thf(func_def_19,type,
sK4: $i > $i ).
thf(func_def_22,type,
sK7: $i > $i ).
thf(func_def_24,type,
sK9: $i > $i ).
thf(f438,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f128,f133,f140,f144,f162,f221,f241,f246,f342,f404,f434]) ).
thf(f434,plain,
( ~ spl1_3
| ~ spl1_5
| ~ spl1_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f433]) ).
thf(f433,plain,
( $false
| ~ spl1_3
| ~ spl1_5
| ~ spl1_13 ),
inference(trivial_inequality_removal,[status(thm)],[f429]) ).
thf(f429,plain,
( ( $true = $false )
| ( sK6 != sK6 )
| ~ spl1_3
| ~ spl1_5
| ~ spl1_13 ),
inference(superposition,[status(thm)],[f132,f425]) ).
thf(f425,plain,
( ! [X0: $i] :
( ( ( sK3 @ X0 )
= $false )
| ( sK6 != X0 ) )
| ~ spl1_5
| ~ spl1_13 ),
inference(trivial_inequality_removal,[status(thm)],[f416]) ).
thf(f416,plain,
( ! [X0: $i] :
( ( sK6 != X0 )
| ( X0 != X0 )
| ( ( sK3 @ X0 )
= $false ) )
| ~ spl1_5
| ~ spl1_13 ),
inference(superposition,[status(thm)],[f346,f402]) ).
thf(f402,plain,
( ! [X0: $i] :
( ( ( sK9 @ X0 )
= X0 )
| ( sK6 != X0 ) )
| ~ spl1_13 ),
inference(avatar_component_clause,[status(thm)],[f401]) ).
thf(f401,definition,
( spl1_13
<=> ! [X0: $i] :
( ( ( sK9 @ X0 )
= X0 )
| ( sK6 != X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_13])],[avatar_definition]) ).
thf(f346,plain,
( ! [X2: $i] :
( ( ( sK3 @ ( sK9 @ X2 ) )
= $false )
| ( ( sK9 @ X2 )
!= X2 ) )
| ~ spl1_5 ),
inference(equality_proxy_clausification,[status(thm)],[f345]) ).
thf(f345,plain,
( ! [X2: $i] :
( ( ( sK3 @ ( sK9 @ X2 ) )
= $false )
| ( ( X2
= ( sK9 @ X2 ) )
= $false ) )
| ~ spl1_5 ),
inference(binary_proxy_clausification,[status(thm)],[f343]) ).
thf(f343,plain,
( ! [X2: $i] :
( ( sK3 @ ( sK9 @ X2 ) )
!= ( X2
= ( sK9 @ X2 ) ) )
| ~ spl1_5 ),
inference(negative_extensionality,[status(thm)],[f139]) ).
thf(f139,plain,
( ! [X2: $i] :
( ( (=) @ X2 )
!= sK3 )
| ~ spl1_5 ),
inference(avatar_component_clause,[status(thm)],[f138]) ).
thf(f138,definition,
( spl1_5
<=> ! [X2: $i] :
( ( (=) @ X2 )
!= sK3 ) ),
introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition]) ).
thf(f132,plain,
( ( $true
= ( sK3 @ sK6 ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f130]) ).
thf(f130,definition,
( spl1_3
<=> ( $true
= ( sK3 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f404,plain,
( spl1_13
| ~ spl1_1
| ~ spl1_5 ),
inference(avatar_split_clause,[status(thm)],[f395,f138,f122,f401]) ).
thf(f122,definition,
( spl1_1
<=> ! [X1: $i] :
( ( sK6 = X1 )
| ( ( sK3 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f395,plain,
( ! [X0: $i] :
( ( ( sK9 @ X0 )
= X0 )
| ( sK6 != X0 ) )
| ~ spl1_1
| ~ spl1_5 ),
inference(equality_factoring,[status(thm)],[f374]) ).
thf(f374,plain,
( ! [X0: $i] :
( ( ( sK9 @ X0 )
= sK6 )
| ( ( sK9 @ X0 )
= X0 ) )
| ~ spl1_1
| ~ spl1_5 ),
inference(trivial_inequality_removal,[status(thm)],[f368]) ).
thf(f368,plain,
( ! [X0: $i] :
( ( ( sK9 @ X0 )
= sK6 )
| ( $true = $false )
| ( ( sK9 @ X0 )
= X0 ) )
| ~ spl1_1
| ~ spl1_5 ),
inference(superposition,[status(thm)],[f347,f123]) ).
thf(f123,plain,
( ! [X1: $i] :
( ( ( sK3 @ X1 )
= $false )
| ( sK6 = X1 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f122]) ).
thf(f347,plain,
( ! [X2: $i] :
( ( $true
= ( sK3 @ ( sK9 @ X2 ) ) )
| ( ( sK9 @ X2 )
= X2 ) )
| ~ spl1_5 ),
inference(equality_proxy_clausification,[status(thm)],[f344]) ).
thf(f344,plain,
( ! [X2: $i] :
( ( $true
= ( sK3 @ ( sK9 @ X2 ) ) )
| ( $true
= ( X2
= ( sK9 @ X2 ) ) ) )
| ~ spl1_5 ),
inference(binary_proxy_clausification,[status(thm)],[f343]) ).
thf(f342,plain,
( ~ spl1_1
| ~ spl1_3
| ~ spl1_4
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f341]) ).
thf(f341,plain,
( $false
| ~ spl1_1
| ~ spl1_3
| ~ spl1_4
| ~ spl1_6 ),
inference(trivial_inequality_removal,[status(thm)],[f331]) ).
thf(f331,plain,
( ( sK6 != sK6 )
| ~ spl1_1
| ~ spl1_3
| ~ spl1_4
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f251,f321]) ).
thf(f321,plain,
( ( ( sK4 @ sK6 )
= sK6 )
| ~ spl1_1
| ~ spl1_3
| ~ spl1_6 ),
inference(trivial_inequality_removal,[status(thm)],[f316]) ).
thf(f316,plain,
( ( $true = $false )
| ( ( sK4 @ sK6 )
= sK6 )
| ~ spl1_1
| ~ spl1_3
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f132,f310]) ).
thf(f310,plain,
( ! [X0: $i] :
( ( ( sK3 @ X0 )
= $false )
| ( ( sK4 @ X0 )
= sK6 ) )
| ~ spl1_1
| ~ spl1_6 ),
inference(trivial_inequality_removal,[status(thm)],[f307]) ).
thf(f307,plain,
( ! [X0: $i] :
( ( ( sK4 @ X0 )
= sK6 )
| ( ( sK3 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl1_1
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f123,f143]) ).
thf(f143,plain,
( ! [X1: $i] :
( ( $true
= ( sK3 @ ( sK4 @ X1 ) ) )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f142]) ).
thf(f142,definition,
( spl1_6
<=> ! [X1: $i] :
( ( $true
= ( sK3 @ ( sK4 @ X1 ) ) )
| ( ( sK3 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition]) ).
thf(f251,plain,
( ( ( sK4 @ sK6 )
!= sK6 )
| ~ spl1_3
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f248]) ).
thf(f248,plain,
( ( ( sK4 @ sK6 )
!= sK6 )
| ( $true = $false )
| ~ spl1_3
| ~ spl1_4 ),
inference(superposition,[status(thm)],[f132,f136]) ).
thf(f136,plain,
( ! [X1: $i] :
( ( ( sK3 @ X1 )
= $false )
| ( ( sK4 @ X1 )
!= X1 ) )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f135]) ).
thf(f135,definition,
( spl1_4
<=> ! [X1: $i] :
( ( ( sK3 @ X1 )
= $false )
| ( ( sK4 @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f246,plain,
( ~ spl1_2
| ~ spl1_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f245]) ).
thf(f245,plain,
( $false
| ~ spl1_2
| ~ spl1_8 ),
inference(equality_resolution,[status(thm)],[f243]) ).
thf(f243,plain,
( ! [X1: $i] : ( sK5 != X1 )
| ~ spl1_2
| ~ spl1_8 ),
inference(trivial_inequality_removal,[status(thm)],[f242]) ).
thf(f242,plain,
( ! [X1: $i] :
( ( $true = $false )
| ( sK5 != X1 ) )
| ~ spl1_2
| ~ spl1_8 ),
inference(backward_demodulation,[status(thm)],[f149,f220]) ).
thf(f220,plain,
( ! [X0: $i] :
( ( sK3 @ X0 )
= $false )
| ~ spl1_8 ),
inference(avatar_component_clause,[status(thm)],[f219]) ).
thf(f219,definition,
( spl1_8
<=> ! [X0: $i] :
( ( sK3 @ X0 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition]) ).
thf(f149,plain,
( ! [X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( sK5 != X1 ) )
| ~ spl1_2 ),
inference(equality_proxy_clausification,[status(thm)],[f146]) ).
thf(f146,plain,
( ! [X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( ( sK5 = X1 )
= $false ) )
| ~ spl1_2 ),
inference(binary_proxy_clausification,[status(thm)],[f145]) ).
thf(f145,plain,
( ! [X1: $i] :
( ( sK3 @ X1 )
= ( sK5 = X1 ) )
| ~ spl1_2 ),
inference(argument_congruence,[status(thm)],[f127]) ).
thf(f127,plain,
( ( sK3
= ( (=) @ sK5 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f125]) ).
thf(f125,definition,
( spl1_2
<=> ( sK3
= ( (=) @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f241,plain,
( ~ spl1_2
| ~ spl1_4
| ~ spl1_6
| ~ spl1_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f240]) ).
thf(f240,plain,
( $false
| ~ spl1_2
| ~ spl1_4
| ~ spl1_6
| ~ spl1_7 ),
inference(trivial_inequality_removal,[status(thm)],[f239]) ).
thf(f239,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_4
| ~ spl1_6
| ~ spl1_7 ),
inference(backward_demodulation,[status(thm)],[f217,f238]) ).
thf(f238,plain,
( ( ( sK3 @ sK5 )
= $false )
| ~ spl1_2
| ~ spl1_4
| ~ spl1_6
| ~ spl1_7 ),
inference(trivial_inequality_removal,[status(thm)],[f229]) ).
thf(f229,plain,
( ( ( sK3 @ sK5 )
= $false )
| ( sK5 != sK5 )
| ~ spl1_2
| ~ spl1_4
| ~ spl1_6
| ~ spl1_7 ),
inference(superposition,[status(thm)],[f228,f193]) ).
thf(f193,plain,
( ! [X0: $i] :
( ( sK5
= ( sK4 @ X0 ) )
| ( ( sK3 @ X0 )
= $false ) )
| ~ spl1_2
| ~ spl1_6 ),
inference(trivial_inequality_removal,[status(thm)],[f187]) ).
thf(f187,plain,
( ! [X0: $i] :
( ( ( sK3 @ X0 )
= $false )
| ( $true = $false )
| ( sK5
= ( sK4 @ X0 ) ) )
| ~ spl1_2
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f143,f148]) ).
thf(f148,plain,
( ! [X1: $i] :
( ( ( sK3 @ X1 )
= $false )
| ( sK5 = X1 ) )
| ~ spl1_2 ),
inference(equality_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
( ! [X1: $i] :
( ( $true
= ( sK5 = X1 ) )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl1_2 ),
inference(binary_proxy_clausification,[status(thm)],[f145]) ).
thf(f228,plain,
( ( ( sK4 @ sK5 )
!= sK5 )
| ~ spl1_4
| ~ spl1_7 ),
inference(trivial_inequality_removal,[status(thm)],[f223]) ).
thf(f223,plain,
( ( $true = $false )
| ( ( sK4 @ sK5 )
!= sK5 )
| ~ spl1_4
| ~ spl1_7 ),
inference(superposition,[status(thm)],[f217,f136]) ).
thf(f217,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ~ spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f215]) ).
thf(f215,definition,
( spl1_7
<=> ( $true
= ( sK3 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition]) ).
thf(f221,plain,
( spl1_7
| spl1_8
| ~ spl1_2
| ~ spl1_6 ),
inference(avatar_split_clause,[status(thm)],[f212,f142,f125,f219,f215]) ).
thf(f212,plain,
( ! [X0: $i] :
( ( $true
= ( sK3 @ sK5 ) )
| ( ( sK3 @ X0 )
= $false ) )
| ~ spl1_2
| ~ spl1_6 ),
inference(duplicate_literal_removal,[status(thm)],[f202]) ).
thf(f202,plain,
( ! [X0: $i] :
( ( ( sK3 @ X0 )
= $false )
| ( $true
= ( sK3 @ sK5 ) )
| ( ( sK3 @ X0 )
= $false ) )
| ~ spl1_2
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f143,f193]) ).
thf(f162,plain,
( ~ spl1_2
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f161]) ).
thf(f161,plain,
( $false
| ~ spl1_2
| ~ spl1_5 ),
inference(trivial_inequality_removal,[status(thm)],[f156]) ).
thf(f156,plain,
( ( sK3 != sK3 )
| ~ spl1_2
| ~ spl1_5 ),
inference(superposition,[status(thm)],[f139,f127]) ).
thf(f144,plain,
( spl1_6
| spl1_5 ),
inference(avatar_split_clause,[status(thm)],[f103,f138,f142]) ).
thf(f103,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ ( sK4 @ X1 ) ) )
| ( ( (=) @ X2 )
!= sK3 )
| ( ( sK3 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ ( sK4 @ X1 ) ) )
| ( ( sK3 @ X1 )
= $false )
| ( ( sK3
= ( (=) @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X2: $i,X1: $i] :
( ( ( sK3 @ X1 )
= $false )
| ( $true
= ( ( sK3 @ ( sK4 @ X1 ) )
& ( X1
!= ( sK4 @ X1 ) ) ) )
| ( ( sK3
= ( (=) @ X2 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( sK3
= ( (=) @ Y0 ) )
@ X2 )
= $false )
| ( $true
= ( ( sK3 @ ( sK4 @ X1 ) )
& ( X1
!= ( sK4 @ X1 ) ) ) )
| ( ( sK3 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X1: $i] :
( ( ( sK3 @ X1 )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( sK3
= ( (=) @ Y0 ) ) )
= $false )
| ( $true
= ( ( sK3 @ ( sK4 @ X1 ) )
& ( X1
!= ( sK4 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ( X1 != Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( ( sK3 @ X1 )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( sK3
= ( (=) @ Y0 ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X1: $i] :
( ( ( sK3 @ X1 )
= $false )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ( X1 != Y0 ) ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( sK3
= ( (=) @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X1: $i] :
( ( ( sK3 @ X1 )
= $false )
| ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ( X1 != Y0 ) ) ) )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( sK3
= ( (=) @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X1: $i] :
( ( ( ( sK3 @ X1 )
& ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ( X1 != Y0 ) ) ) )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( sK3
= ( (=) @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f93]) ).
thf(f93,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( sK3
= ( (=) @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
& ( Y0 != Y1 ) ) ) )
@ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
& ( Y0 != Y1 ) ) ) ) )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( sK3
= ( (=) @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
& ( Y0 != Y1 ) ) ) ) )
!= ( ?? @ $i
@ ^ [Y0: $i] :
( sK3
= ( (=) @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) ) ) )
@ sK3 )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( (=) @ Y1 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( (=) @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) ) )
!= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f19,f21]) ).
thf(f21,plain,
( cONE
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f17,f18,f16]) ).
thf(f16,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.9qmM38glqc/DTF2THF_5999.p',cZERO_def) ).
thf(f18,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( cSUCC
= ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X0
@ ^ [X3: $i] :
( ( X2 != X3 )
& ( X1 @ X3 ) ) )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( cSUCC
= ( ^ [X2: ( $i > $o ) > $o,X0: $i > $o] :
? [X1: $i] :
( ( X2
@ ^ [X3: $i] :
( ( X1 != X3 )
& ( X0 @ X3 ) ) )
& ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9qmM38glqc/DTF2THF_5999.p',cSUCC_def) ).
thf(f17,plain,
( cONE
= ( cSUCC @ cZERO ) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
thf(f3,axiom,
( cONE
= ( cSUCC @ cZERO ) ),
file('/export/starexec/sandbox/tmp/tmp.9qmM38glqc/DTF2THF_5999.p',cONE_def) ).
thf(f19,plain,
( cONE
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: $i > $i,X1: $i > $i] :
( ( X0 = X1 )
| ( ( X0 @ ( sK0 @ X1 @ X0 ) )
!= ( X1 @ ( sK0 @ X1 @ X0 ) ) ) )
& ( cONE
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).
thf(f14,plain,
! [X0: $i > $i,X1: $i > $i] :
( ? [X2: $i] :
( ( X0 @ X2 )
!= ( X1 @ X2 ) )
=> ( ( X0 @ ( sK0 @ X1 @ X0 ) )
!= ( X1 @ ( sK0 @ X1 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ! [X0: $i > $i,X1: $i > $i] :
( ( X0 = X1 )
| ? [X2: $i] :
( ( X0 @ X2 )
!= ( X1 @ X2 ) ) )
& ( cONE
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ! [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
= ( X1 @ X2 ) )
=> ( X0 = X1 ) )
=> ( cONE
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ! [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
= ( X1 @ X2 ) )
=> ( X0 = X1 ) )
=> ( ( ^ [X3: $i > $o] :
? [X4: $i] :
( X3
= ( ^ [X5: $i,X6: $i] : ( X5 = X6 )
@ X4 ) ) )
= cONE ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( ! [X5: $i > $i,X4: $i > $i] :
( ! [X1: $i] :
( ( X4 @ X1 )
= ( X5 @ X1 ) )
=> ( X4 = X5 ) )
=> ( ( ^ [X6: $i > $o] :
? [X7: $i] :
( X6
= ( ^ [X1: $i,X7: $i] : ( X1 = X7 )
@ X7 ) ) )
= cONE ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( ! [X5: $i > $i,X4: $i > $i] :
( ! [X1: $i] :
( ( X4 @ X1 )
= ( X5 @ X1 ) )
=> ( X4 = X5 ) )
=> ( ( ^ [X6: $i > $o] :
? [X7: $i] :
( X6
= ( ^ [X1: $i,X7: $i] : ( X1 = X7 )
@ X7 ) ) )
= cONE ) ),
file('/export/starexec/sandbox/tmp/tmp.9qmM38glqc/DTF2THF_5999.p',cX6101_EXT_pme) ).
thf(f140,plain,
( spl1_4
| spl1_5 ),
inference(avatar_split_clause,[status(thm)],[f106,f138,f135]) ).
thf(f106,plain,
! [X2: $i,X1: $i] :
( ( ( (=) @ X2 )
!= sK3 )
| ( ( sK3 @ X1 )
= $false )
| ( ( sK4 @ X1 )
!= X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
! [X2: $i,X1: $i] :
( ( ( X1
= ( sK4 @ X1 ) )
= $false )
| ( ( (=) @ X2 )
!= sK3 )
| ( ( sK3 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
! [X2: $i,X1: $i] :
( ( ( sK3
= ( (=) @ X2 ) )
= $false )
| ( ( X1
= ( sK4 @ X1 ) )
= $false )
| ( ( sK3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X2: $i,X1: $i] :
( ( ( X1
!= ( sK4 @ X1 ) )
= $true )
| ( ( sK3 @ X1 )
= $false )
| ( ( sK3
= ( (=) @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f133,plain,
( spl1_2
| spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f113,f130,f125]) ).
thf(f113,plain,
( ( sK3
= ( (=) @ sK5 ) )
| ( $true
= ( sK3 @ sK6 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
( ( $true
= ( sK3
= ( (=) @ sK5 ) ) )
| ( $true
= ( sK3 @ sK6 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( ( $true
= ( ( sK3 @ sK6 )
& ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ( sK6 != Y0 ) ) ) ) )
| ( $true
= ( sK3
= ( (=) @ sK5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f109]) ).
thf(f109,plain,
( ( $true
= ( sK3
= ( (=) @ sK5 ) ) )
| ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
& ( Y0 != Y1 ) ) ) )
@ sK6 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
& ( Y0 != Y1 ) ) ) ) ) )
| ( $true
= ( sK3
= ( (=) @ sK5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f107]) ).
thf(f107,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
& ( Y0 != Y1 ) ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( sK3
= ( (=) @ Y0 ) )
@ sK5 ) ) ),
inference(sigma_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( sK3
= ( (=) @ Y0 ) ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
& ( Y0 != Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f90]) ).
thf(f128,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f120,f125,f122]) ).
thf(f120,plain,
! [X1: $i] :
( ( sK6 = X1 )
| ( ( sK3 @ X1 )
= $false )
| ( sK3
= ( (=) @ sK5 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
! [X1: $i] :
( ( $true
= ( sK6 = X1 ) )
| ( ( sK3 @ X1 )
= $false )
| ( sK3
= ( (=) @ sK5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f118]) ).
thf(f118,plain,
! [X1: $i] :
( ( ( sK3 @ X1 )
= $false )
| ( sK3
= ( (=) @ sK5 ) )
| ( ( sK6 != X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
! [X1: $i] :
( ( ( ( sK3 @ X1 )
& ( sK6 != X1 ) )
= $false )
| ( sK3
= ( (=) @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f116]) ).
thf(f116,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ( sK6 != Y0 ) )
@ X1 ) )
| ( sK3
= ( (=) @ sK5 ) ) ),
inference(pi_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
( ( sK3
= ( (=) @ sK5 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ( sK6 != Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
( ( sK3
= ( (=) @ sK5 ) )
| ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ( sK6 != Y0 ) ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
( ( $true
= ( sK3
= ( (=) @ sK5 ) ) )
| ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
& ( sK6 != Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV300^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:43:16 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEV300^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : TPS problem from TTTP-NATS-THMS
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0824 [Bro09]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.50 v8.2.0, 0.46 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0
% 0.19/0.45 % Syntax : Number of formulae : 7 ( 3 unt; 3 typ; 3 def)
% 0.19/0.45 % Number of atoms : 15 ( 9 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 3 ( 3 avg)
% 0.19/0.45 % Number of connectives : 14 ( 2 ~; 0 |; 2 &; 8 @)
% 0.19/0.45 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 6 ( 2 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.19/0.45 % Number of variables : 13 ( 7 ^; 3 !; 3 ?; 13 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.19/0.45 % : v6.2.0 - Reordered definitions.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(cONE_type,type,
% 0.19/0.45 cONE: ( $i > $o ) > $o ).
% 0.19/0.45
% 0.19/0.45 thf(cSUCC_type,type,
% 0.19/0.45 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 0.19/0.45
% 0.19/0.45 thf(cZERO_type,type,
% 0.19/0.45 cZERO: ( $i > $o ) > $o ).
% 0.19/0.45
% 0.19/0.45 thf(cZERO_def,definition,
% 0.19/0.45 ( cZERO
% 0.19/0.45 = ( ^ [Xp: $i > $o] :
% 0.19/0.45 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(cSUCC_def,definition,
% 0.19/0.45 ( cSUCC
% 0.19/0.45 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 0.19/0.45 ? [Xx: $i] :
% 0.19/0.45 ( ( Xp @ Xx )
% 0.19/0.45 & ( Xn
% 0.19/0.45 @ ^ [Xt: $i] :
% 0.19/0.45 ( ( Xt != Xx )
% 0.19/0.45 & ( Xp @ Xt ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(cONE_def,definition,
% 0.19/0.45 ( cONE
% 0.19/0.45 = ( cSUCC @ cZERO ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(cX6101_EXT_pme,conjecture,
% 0.19/0.45 ( ! [Xf: $i > $i,Xg: $i > $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( Xf @ Xx )
% 0.19/0.45 = ( Xg @ Xx ) )
% 0.19/0.45 => ( Xf = Xg ) )
% 0.19/0.45 => ( cONE
% 0.19/0.45 = ( ^ [P: $i > $o] :
% 0.19/0.45 ? [Xy: $i] :
% 0.19/0.45 ( P
% 0.19/0.45 = ( ^ [Xx: $i,Xy: $i] : ( Xx = Xy )
% 0.19/0.45 @ Xy ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.43/1.25 ---- Embedded in THF ---
% 1.43/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.25 %%% Generated on Tue Feb 24 12:43:16 EST 2026
% 1.43/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.25 %%% Logic specification used:
% 1.43/1.25 %%% thf(spec, logic, $$dhol).
% 1.43/1.25
% 1.43/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.9qmM38glqc/DTF2DTF5999.p
% See solution above
% 1.43/1.25 ------------------------
% 1.43/1.25 ---- Cleaned THF ---
% 1.43/1.25 thf(cONE_type,type,
% 1.43/1.25 cONE: ( $i > $o ) > $o ).
% 1.43/1.25
% 1.43/1.25 thf(cSUCC_type,type,
% 1.43/1.25 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 1.43/1.25
% 1.43/1.25 thf(cZERO_type,type,
% 1.43/1.25 cZERO: ( $i > $o ) > $o ).
% 1.43/1.25
% 1.43/1.25 thf(cZERO_def,definition,
% 1.43/1.25 ( cZERO
% 1.43/1.25 = ( ^ [Xp: $i > $o] :
% 1.43/1.25 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 1.43/1.25
% 1.43/1.25 thf(cSUCC_def,definition,
% 1.43/1.25 ( cSUCC
% 1.43/1.25 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 1.43/1.25 ? [Xx: $i] :
% 1.43/1.25 ( ( Xp @ Xx )
% 1.43/1.25 & ( Xn
% 1.43/1.25 @ ^ [Xt: $i] :
% 1.43/1.25 ( ( Xt != Xx )
% 1.43/1.25 & ( Xp @ Xt ) ) ) ) ) ) ).
% 1.43/1.25
% 1.43/1.25 thf(cONE_def,definition,
% 1.43/1.25 ( cONE
% 1.43/1.25 = ( cSUCC @ cZERO ) ) ).
% 1.43/1.25
% 1.43/1.25 thf(cX6101_EXT_pme,conjecture,
% 1.43/1.25 ( ! [Xf: $i > $i,Xg: $i > $i] :
% 1.43/1.25 ( ! [Xx: $i] :
% 1.43/1.25 ( ( Xf @ Xx )
% 1.43/1.25 = ( Xg @ Xx ) )
% 1.43/1.25 => ( Xf = Xg ) )
% 1.43/1.25 => ( cONE
% 1.43/1.25 = ( ^ [P: $i > $o] :
% 1.43/1.25 ? [Xy: $i] :
% 1.43/1.25 ( P
% 1.43/1.25 = ( ^ [Xx: $i,Xy: $i] : ( Xx = Xy )
% 1.43/1.25 @ Xy ) ) ) ) ) ).
% 1.43/1.26 ------------------------
% 1.43/1.27 % (6174)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_5999 for (3000ds/4Mi)
% 1.43/1.27 % (6176)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5999 for (3000ds/2Mi)
% 1.43/1.27 % (6177)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_5999 for (3000ds/2Mi)
% 1.43/1.27 % (6177)Instruction limit reached!
% 1.43/1.27 % (6177)------------------------------
% 1.43/1.27 % (6177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.27 % (6177)Termination reason: Unknown
% 1.43/1.27 % (6177)Termination phase: Saturation
% 1.43/1.27
% 1.43/1.27 % (6177)Memory used [KB]: 5500
% 1.43/1.27 % (6177)Time elapsed: 0.002 s
% 1.43/1.27 % (6177)Instructions burned: 3 (million)
% 1.43/1.27 % (6177)------------------------------
% 1.43/1.27 % (6177)------------------------------
% 1.43/1.27 % (6174)Instruction limit reached!
% 1.43/1.27 % (6174)------------------------------
% 1.43/1.27 % (6174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.27 % (6174)Termination reason: Unknown
% 1.43/1.27 % (6174)Termination phase: Saturation
% 1.43/1.27
% 1.43/1.27 % (6174)Memory used [KB]: 5500
% 1.43/1.27 % (6174)Time elapsed: 0.004 s
% 1.43/1.27 % (6174)Instructions burned: 5 (million)
% 1.43/1.27 % (6174)------------------------------
% 1.43/1.27 % (6174)------------------------------
% 1.43/1.27 % (6178)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_5999 for (3000ds/275Mi)
% 1.43/1.27 % (6179)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5999 for (3000ds/18Mi)
% 1.43/1.27 % (6175)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_5999 for (3000ds/27Mi)
% 1.43/1.28 % (6173)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5999 for (3000ds/183Mi)
% 1.43/1.28 % (6180)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/3Mi)
% 1.43/1.28 % (6181)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/37Mi)
% 1.43/1.28 % (6180)Instruction limit reached!
% 1.43/1.28 % (6180)------------------------------
% 1.43/1.28 % (6180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.28 % (6180)Termination reason: Unknown
% 1.43/1.28 % (6180)Termination phase: Saturation
% 1.43/1.28
% 1.43/1.28 % (6180)Memory used [KB]: 5500
% 1.43/1.28 % (6180)Time elapsed: 0.003 s
% 1.43/1.28 % (6180)Instructions burned: 3 (million)
% 1.43/1.28 % (6180)------------------------------
% 1.43/1.28 % (6180)------------------------------
% 1.43/1.28 % (6176)Instruction limit reached!
% 1.43/1.28 % (6176)------------------------------
% 1.43/1.28 % (6176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.28 % (6176)Termination reason: Unknown
% 1.43/1.28 % (6176)Termination phase: Saturation
% 1.43/1.28
% 1.43/1.28 % (6176)Memory used [KB]: 5500
% 1.43/1.28 % (6176)Time elapsed: 0.002 s
% 1.43/1.28 % (6176)Instructions burned: 2 (million)
% 1.43/1.28 % (6176)------------------------------
% 1.43/1.28 % (6176)------------------------------
% 1.43/1.28 % (6179)Instruction limit reached!
% 1.43/1.28 % (6179)------------------------------
% 1.43/1.28 % (6179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.28 % (6179)Termination reason: Unknown
% 1.43/1.28 % (6179)Termination phase: Saturation
% 1.43/1.28
% 1.43/1.28 % (6179)Memory used [KB]: 5500
% 1.43/1.28 % (6179)Time elapsed: 0.010 s
% 1.43/1.28 % (6179)Instructions burned: 18 (million)
% 1.43/1.28 % (6179)------------------------------
% 1.43/1.28 % (6179)------------------------------
% 1.43/1.29 % (6175)Instruction limit reached!
% 1.43/1.29 % (6175)------------------------------
% 1.43/1.29 % (6175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.29 % (6175)Termination reason: Unknown
% 1.43/1.29 % (6175)Termination phase: Saturation
% 1.43/1.29
% 1.43/1.29 % (6175)Memory used [KB]: 5628
% 1.43/1.29 % (6175)Time elapsed: 0.015 s
% 1.43/1.29 % (6175)Instructions burned: 27 (million)
% 1.43/1.29 % (6175)------------------------------
% 1.43/1.29 % (6175)------------------------------
% 1.43/1.29 % (6182)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/15Mi)
% 1.43/1.29 % (6181)Instruction limit reached!
% 1.43/1.29 % (6181)------------------------------
% 1.43/1.29 % (6181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.29 % (6181)Termination reason: Unknown
% 1.43/1.29 % (6181)Termination phase: Saturation
% 1.43/1.29
% 1.43/1.29 % (6181)Memory used [KB]: 5628
% 1.43/1.29 % (6181)Time elapsed: 0.014 s
% 1.43/1.29 % (6181)Instructions burned: 37 (million)
% 1.43/1.29 % (6181)------------------------------
% 1.43/1.29 % (6181)------------------------------
% 1.53/1.30 % (6182)Instruction limit reached!
% 1.53/1.30 % (6182)------------------------------
% 1.53/1.30 % (6182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.30 % (6182)Termination reason: Unknown
% 1.53/1.30 % (6182)Termination phase: Saturation
% 1.53/1.30
% 1.53/1.30 % (6182)Memory used [KB]: 5628
% 1.53/1.30 % (6182)Time elapsed: 0.007 s
% 1.53/1.30 % (6182)Instructions burned: 16 (million)
% 1.53/1.30 % (6182)------------------------------
% 1.53/1.30 % (6182)------------------------------
% 1.53/1.30 % (6183)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/3Mi)
% 1.53/1.30 % (6184)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/1041Mi)
% 1.53/1.30 % (6183)Instruction limit reached!
% 1.53/1.30 % (6183)------------------------------
% 1.53/1.30 % (6183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.30 % (6183)Termination reason: Unknown
% 1.53/1.30 % (6183)Termination phase: Saturation
% 1.53/1.30
% 1.53/1.30 % (6183)Memory used [KB]: 5500
% 1.53/1.30 % (6183)Time elapsed: 0.003 s
% 1.53/1.30 % (6183)Instructions burned: 3 (million)
% 1.53/1.30 % (6183)------------------------------
% 1.53/1.30 % (6183)------------------------------
% 1.53/1.30 % (6186)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/16Mi)
% 1.53/1.30 % (6185)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/7Mi)
% 1.53/1.31 % (6187)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/3Mi)
% 1.53/1.31 % (6185)Instruction limit reached!
% 1.53/1.31 % (6185)------------------------------
% 1.53/1.31 % (6185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.31 % (6185)Termination reason: Unknown
% 1.53/1.31 % (6185)Termination phase: Saturation
% 1.53/1.31
% 1.53/1.31 % (6185)Memory used [KB]: 1023
% 1.53/1.31 % (6185)Time elapsed: 0.005 s
% 1.53/1.31 % (6185)Instructions burned: 7 (million)
% 1.53/1.31 % (6185)------------------------------
% 1.53/1.31 % (6185)------------------------------
% 1.53/1.31 % (6187)Instruction limit reached!
% 1.53/1.31 % (6187)------------------------------
% 1.53/1.31 % (6187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.31 % (6187)Termination reason: Unknown
% 1.53/1.31 % (6187)Termination phase: Saturation
% 1.53/1.31
% 1.53/1.31 % (6187)Memory used [KB]: 5500
% 1.53/1.31 % (6187)Time elapsed: 0.003 s
% 1.53/1.31 % (6187)Instructions burned: 3 (million)
% 1.53/1.31 % (6187)------------------------------
% 1.53/1.31 % (6187)------------------------------
% 1.53/1.31 % (6186)Instruction limit reached!
% 1.53/1.31 % (6186)------------------------------
% 1.53/1.31 % (6186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.31 % (6186)Termination reason: Unknown
% 1.53/1.31 % (6186)Termination phase: Saturation
% 1.53/1.31
% 1.53/1.31 % (6186)Memory used [KB]: 5756
% 1.53/1.31 % (6186)Time elapsed: 0.008 s
% 1.53/1.31 % (6186)Instructions burned: 16 (million)
% 1.53/1.31 % (6186)------------------------------
% 1.53/1.31 % (6186)------------------------------
% 1.53/1.31 % (6188)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/3Mi)
% 1.53/1.32 % (6188)Instruction limit reached!
% 1.53/1.32 % (6188)------------------------------
% 1.53/1.32 % (6188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.32 % (6188)Termination reason: Unknown
% 1.53/1.32 % (6188)Termination phase: Saturation
% 1.53/1.32
% 1.53/1.32 % (6188)Memory used [KB]: 1023
% 1.53/1.32 % (6188)Time elapsed: 0.003 s
% 1.53/1.32 % (6188)Instructions burned: 3 (million)
% 1.53/1.32 % (6188)------------------------------
% 1.53/1.32 % (6188)------------------------------
% 1.53/1.32 % (6190)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/3Mi)
% 1.53/1.32 % (6190)Instruction limit reached!
% 1.53/1.32 % (6190)------------------------------
% 1.53/1.32 % (6190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.32 % (6190)Termination reason: Unknown
% 1.53/1.32 % (6190)Termination phase: Saturation
% 1.53/1.32
% 1.53/1.32 % (6190)Memory used [KB]: 5500
% 1.53/1.32 % (6190)Time elapsed: 0.003 s
% 1.53/1.32 % (6190)Instructions burned: 4 (million)
% 1.53/1.32 % (6190)------------------------------
% 1.53/1.32 % (6190)------------------------------
% 1.53/1.32 % (6191)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/4Mi)
% 1.53/1.32 % (6191)Instruction limit reached!
% 1.53/1.32 % (6191)------------------------------
% 1.53/1.32 % (6191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.32 % (6191)Termination reason: Unknown
% 1.53/1.32 % (6191)Termination phase: Saturation
% 1.53/1.32
% 1.53/1.32 % (6191)Memory used [KB]: 5500
% 1.53/1.32 % (6191)Time elapsed: 0.004 s
% 1.53/1.32 % (6191)Instructions burned: 6 (million)
% 1.53/1.32 % (6191)------------------------------
% 1.53/1.32 % (6191)------------------------------
% 1.53/1.32 % (6189)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/7Mi)
% 1.53/1.33 % (6189)Refutation not found, incomplete strategy
% 1.53/1.33 % (6189)------------------------------
% 1.53/1.33 % (6189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.33 % (6189)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.33
% 1.53/1.33
% 1.53/1.33 % (6189)Memory used [KB]: 5500
% 1.53/1.33 % (6189)Time elapsed: 0.004 s
% 1.53/1.33 % (6189)Instructions burned: 5 (million)
% 1.53/1.33 % (6189)------------------------------
% 1.53/1.33 % (6189)------------------------------
% 1.53/1.33 % (6173)Instruction limit reached!
% 1.53/1.33 % (6173)------------------------------
% 1.53/1.33 % (6173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.33 % (6173)Termination reason: Unknown
% 1.53/1.33 % (6173)Termination phase: Saturation
% 1.53/1.33
% 1.53/1.33 % (6173)Memory used [KB]: 5628
% 1.53/1.33 % (6173)Time elapsed: 0.052 s
% 1.53/1.33 % (6173)Instructions burned: 183 (million)
% 1.53/1.33 % (6173)------------------------------
% 1.53/1.33 % (6173)------------------------------
% 1.53/1.33 % (6193)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/710Mi)
% 1.53/1.33 % (6194)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/6Mi)
% 1.53/1.33 % (6192)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/18Mi)
% 1.53/1.33 % (6194)Instruction limit reached!
% 1.53/1.33 % (6194)------------------------------
% 1.53/1.33 % (6194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.33 % (6194)Termination reason: Unknown
% 1.53/1.33 % (6194)Termination phase: Saturation
% 1.53/1.33
% 1.53/1.33 % (6194)Memory used [KB]: 5500
% 1.53/1.33 % (6194)Time elapsed: 0.004 s
% 1.53/1.33 % (6194)Instructions burned: 6 (million)
% 1.53/1.33 % (6194)------------------------------
% 1.53/1.33 % (6194)------------------------------
% 1.53/1.34 % (6195)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/902Mi)
% 1.53/1.34 % (6192)Instruction limit reached!
% 1.53/1.34 % (6192)------------------------------
% 1.53/1.34 % (6192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.34 % (6192)Termination reason: Unknown
% 1.53/1.34 % (6192)Termination phase: Saturation
% 1.53/1.34
% 1.53/1.34 % (6192)Memory used [KB]: 5628
% 1.53/1.34 % (6192)Time elapsed: 0.012 s
% 1.53/1.34 % (6192)Instructions burned: 19 (million)
% 1.53/1.34 % (6192)------------------------------
% 1.53/1.34 % (6192)------------------------------
% 1.53/1.34 % (6197)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/5Mi)
% 1.53/1.34 % (6196)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/21Mi)
% 1.53/1.35 % (6197)Instruction limit reached!
% 1.53/1.35 % (6197)------------------------------
% 1.53/1.35 % (6197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.35 % (6197)Termination reason: Unknown
% 1.53/1.35 % (6197)Termination phase: Saturation
% 1.53/1.35
% 1.53/1.35 % (6197)Memory used [KB]: 5500
% 1.53/1.35 % (6197)Time elapsed: 0.004 s
% 1.53/1.35 % (6197)Instructions burned: 6 (million)
% 1.53/1.35 % (6197)------------------------------
% 1.53/1.35 % (6197)------------------------------
% 1.53/1.35 % (6196)Instruction limit reached!
% 1.53/1.35 % (6196)------------------------------
% 1.53/1.35 % (6196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.35 % (6196)Termination reason: Unknown
% 1.53/1.35 % (6196)Termination phase: Saturation
% 1.53/1.35
% 1.53/1.35 % (6196)Memory used [KB]: 5628
% 1.53/1.35 % (6196)Time elapsed: 0.009 s
% 1.53/1.35 % (6196)Instructions burned: 22 (million)
% 1.53/1.35 % (6196)------------------------------
% 1.53/1.35 % (6196)------------------------------
% 1.53/1.36 % (6199)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/377Mi)
% 1.53/1.36 % (6198)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/6Mi)
% 1.53/1.36 % (6200)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/779Mi)
% 1.53/1.36 % (6198)Instruction limit reached!
% 1.53/1.36 % (6198)------------------------------
% 1.53/1.36 % (6198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.36 % (6198)Termination reason: Unknown
% 1.53/1.36 % (6198)Termination phase: Saturation
% 1.53/1.36
% 1.53/1.36 % (6198)Memory used [KB]: 5500
% 1.53/1.36 % (6198)Time elapsed: 0.005 s
% 1.53/1.36 % (6198)Instructions burned: 6 (million)
% 1.53/1.36 % (6198)------------------------------
% 1.53/1.36 % (6198)------------------------------
% 1.53/1.37 % (6201)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_5999 for (2999ds/19Mi)
% 1.53/1.38 % (6201)Refutation not found, incomplete strategy
% 1.53/1.38 % (6201)------------------------------
% 1.53/1.38 % (6201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.38 % (6201)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.38
% 1.53/1.38
% 1.53/1.38 % (6201)Memory used [KB]: 5500
% 1.53/1.38 % (6201)Time elapsed: 0.003 s
% 1.53/1.38 % (6201)Instructions burned: 5 (million)
% 1.53/1.38 % (6201)------------------------------
% 1.53/1.38 % (6201)------------------------------
% 1.53/1.38 % (6178)Instruction limit reached!
% 1.53/1.38 % (6178)------------------------------
% 1.53/1.38 % (6178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.38 % (6178)Termination reason: Unknown
% 1.53/1.38 % (6178)Termination phase: Saturation
% 1.53/1.38
% 1.53/1.38 % (6178)Memory used [KB]: 5500
% 1.53/1.38 % (6178)Time elapsed: 0.106 s
% 1.53/1.38 % (6178)Instructions burned: 276 (million)
% 1.53/1.38 % (6178)------------------------------
% 1.53/1.38 % (6178)------------------------------
% 1.53/1.39 % (6202)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_5999 for (2998ds/879Mi)
% 1.53/1.40 % (6203)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_5999 for (2998ds/17Mi)
% 1.53/1.41 % (6203)Instruction limit reached!
% 1.53/1.41 % (6203)------------------------------
% 1.53/1.41 % (6203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.41 % (6203)Termination reason: Unknown
% 1.53/1.41 % (6203)Termination phase: Saturation
% 1.53/1.41
% 1.53/1.41 % (6203)Memory used [KB]: 5628
% 1.53/1.41 % (6203)Time elapsed: 0.010 s
% 1.53/1.41 % (6203)Instructions burned: 18 (million)
% 1.53/1.41 % (6203)------------------------------
% 1.53/1.41 % (6203)------------------------------
% 1.53/1.42 % (6199)First to succeed.
% 1.53/1.42 % (6199)Refutation found. Thanks to Tanya!
% 1.53/1.42 % SZS status Theorem for DTF2THF_5999
% 1.53/1.42 % SZS output start Proof for DTF2THF_5999
% 1.53/1.42 thf(func_def_0, type, cONE: ($i > $o) > $o).
% 1.53/1.42 thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 1.53/1.42 thf(func_def_2, type, cZERO: ($i > $o) > $o).
% 1.53/1.42 thf(func_def_14, type, sK0: ($i > $i) > ($i > $i) > $i).
% 1.53/1.42 thf(func_def_17, type, ph2: !>[X0: $tType]:(X0)).
% 1.53/1.42 thf(func_def_18, type, sK3: $i > $o).
% 1.53/1.42 thf(func_def_19, type, sK4: $i > $i).
% 1.53/1.42 thf(func_def_22, type, sK7: $i > $i).
% 1.53/1.42 thf(func_def_24, type, sK9: $i > $i).
% 1.53/1.42 thf(f438,plain,(
% 1.53/1.42 $false),
% 1.53/1.42 inference(avatar_sat_refutation,[status(thm)],[f128,f133,f140,f144,f162,f221,f241,f246,f342,f404,f434])).
% 1.53/1.42 thf(f434,plain,(
% 1.53/1.42 ~spl1_3 | ~spl1_5 | ~spl1_13),
% 1.53/1.42 inference(avatar_contradiction_clause,[status(thm)],[f433])).
% 1.53/1.42 thf(f433,plain,(
% 1.53/1.42 $false | (~spl1_3 | ~spl1_5 | ~spl1_13)),
% 1.53/1.42 inference(trivial_inequality_removal,[status(thm)],[f429])).
% 1.53/1.42 thf(f429,plain,(
% 1.53/1.42 ($true = $false) | (sK6 != sK6) | (~spl1_3 | ~spl1_5 | ~spl1_13)),
% 1.53/1.42 inference(superposition,[status(thm)],[f132,f425])).
% 1.53/1.42 thf(f425,plain,(
% 1.53/1.42 ( ! [X0 : $i] : (((sK3 @ X0) = $false) | (sK6 != X0)) ) | (~spl1_5 | ~spl1_13)),
% 1.53/1.42 inference(trivial_inequality_removal,[status(thm)],[f416])).
% 1.53/1.42 thf(f416,plain,(
% 1.53/1.42 ( ! [X0 : $i] : ((sK6 != X0) | (X0 != X0) | ((sK3 @ X0) = $false)) ) | (~spl1_5 | ~spl1_13)),
% 1.53/1.42 inference(superposition,[status(thm)],[f346,f402])).
% 1.53/1.42 thf(f402,plain,(
% 1.53/1.42 ( ! [X0 : $i] : (((sK9 @ X0) = X0) | (sK6 != X0)) ) | ~spl1_13),
% 1.53/1.42 inference(avatar_component_clause,[status(thm)],[f401])).
% 1.53/1.42 thf(f401,definition,(
% 1.53/1.42 spl1_13 <=> ! [X0 : $i] : (((sK9 @ X0) = X0) | (sK6 != X0))),
% 1.53/1.42 introduced(definition,[new_symbols(naming,[spl1_13])],[avatar_definition])).
% 1.53/1.42 thf(f346,plain,(
% 1.53/1.42 ( ! [X2 : $i] : (((sK3 @ (sK9 @ X2)) = $false) | ((sK9 @ X2) != X2)) ) | ~spl1_5),
% 1.53/1.42 inference(equality_proxy_clausification,[status(thm)],[f345])).
% 1.53/1.42 thf(f345,plain,(
% 1.53/1.42 ( ! [X2 : $i] : (((sK3 @ (sK9 @ X2)) = $false) | ((X2 = (sK9 @ X2)) = $false)) ) | ~spl1_5),
% 1.53/1.42 inference(binary_proxy_clausification,[status(thm)],[f343])).
% 1.53/1.42 thf(f343,plain,(
% 1.53/1.42 ( ! [X2 : $i] : (((sK3 @ (sK9 @ X2)) != (X2 = (sK9 @ X2)))) ) | ~spl1_5),
% 1.53/1.42 inference(negative_extensionality,[status(thm)],[f139])).
% 1.53/1.42 thf(f139,plain,(
% 1.53/1.42 ( ! [X2 : $i] : (((= @ X2) != sK3)) ) | ~spl1_5),
% 1.53/1.42 inference(avatar_component_clause,[status(thm)],[f138])).
% 1.53/1.42 thf(f138,definition,(
% 1.53/1.42 spl1_5 <=> ! [X2 : $i] : ((= @ X2) != sK3)),
% 1.53/1.42 introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition])).
% 1.53/1.42 thf(f132,plain,(
% 1.53/1.42 ($true = (sK3 @ sK6)) | ~spl1_3),
% 1.53/1.42 inference(avatar_component_clause,[status(thm)],[f130])).
% 1.53/1.42 thf(f130,definition,(
% 1.53/1.42 spl1_3 <=> ($true = (sK3 @ sK6))),
% 1.53/1.42 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.53/1.42 thf(f404,plain,(
% 1.53/1.42 spl1_13 | ~spl1_1 | ~spl1_5),
% 1.53/1.42 inference(avatar_split_clause,[status(thm)],[f395,f138,f122,f401])).
% 1.53/1.42 thf(f122,definition,(
% 1.53/1.42 spl1_1 <=> ! [X1 : $i] : ((sK6 = X1) | ((sK3 @ X1) = $false))),
% 1.53/1.42 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.53/1.42 thf(f395,plain,(
% 1.53/1.42 ( ! [X0 : $i] : (((sK9 @ X0) = X0) | (sK6 != X0)) ) | (~spl1_1 | ~spl1_5)),
% 1.53/1.42 inference(equality_factoring,[status(thm)],[f374])).
% 1.53/1.42 thf(f374,plain,(
% 1.53/1.42 ( ! [X0 : $i] : (((sK9 @ X0) = sK6) | ((sK9 @ X0) = X0)) ) | (~spl1_1 | ~spl1_5)),
% 1.53/1.42 inference(trivial_inequality_removal,[status(thm)],[f368])).
% 1.53/1.42 thf(f368,plain,(
% 1.53/1.42 ( ! [X0 : $i] : (((sK9 @ X0) = sK6) | ($true = $false) | ((sK9 @ X0) = X0)) ) | (~spl1_1 | ~spl1_5)),
% 1.53/1.42 inference(superposition,[status(thm)],[f347,f123])).
% 1.53/1.42 thf(f123,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (((sK3 @ X1) = $false) | (sK6 = X1)) ) | ~spl1_1),
% 1.53/1.42 inference(avatar_component_clause,[status(thm)],[f122])).
% 1.53/1.42 thf(f347,plain,(
% 1.53/1.42 ( ! [X2 : $i] : (($true = (sK3 @ (sK9 @ X2))) | ((sK9 @ X2) = X2)) ) | ~spl1_5),
% 1.53/1.42 inference(equality_proxy_clausification,[status(thm)],[f344])).
% 1.53/1.42 thf(f344,plain,(
% 1.53/1.42 ( ! [X2 : $i] : (($true = (sK3 @ (sK9 @ X2))) | ($true = (X2 = (sK9 @ X2)))) ) | ~spl1_5),
% 1.53/1.42 inference(binary_proxy_clausification,[status(thm)],[f343])).
% 1.53/1.42 thf(f342,plain,(
% 1.53/1.42 ~spl1_1 | ~spl1_3 | ~spl1_4 | ~spl1_6),
% 1.53/1.42 inference(avatar_contradiction_clause,[status(thm)],[f341])).
% 1.53/1.42 thf(f341,plain,(
% 1.53/1.42 $false | (~spl1_1 | ~spl1_3 | ~spl1_4 | ~spl1_6)),
% 1.53/1.42 inference(trivial_inequality_removal,[status(thm)],[f331])).
% 1.53/1.42 thf(f331,plain,(
% 1.53/1.42 (sK6 != sK6) | (~spl1_1 | ~spl1_3 | ~spl1_4 | ~spl1_6)),
% 1.53/1.42 inference(superposition,[status(thm)],[f251,f321])).
% 1.53/1.42 thf(f321,plain,(
% 1.53/1.42 ((sK4 @ sK6) = sK6) | (~spl1_1 | ~spl1_3 | ~spl1_6)),
% 1.53/1.42 inference(trivial_inequality_removal,[status(thm)],[f316])).
% 1.53/1.42 thf(f316,plain,(
% 1.53/1.42 ($true = $false) | ((sK4 @ sK6) = sK6) | (~spl1_1 | ~spl1_3 | ~spl1_6)),
% 1.53/1.42 inference(superposition,[status(thm)],[f132,f310])).
% 1.53/1.42 thf(f310,plain,(
% 1.53/1.42 ( ! [X0 : $i] : (((sK3 @ X0) = $false) | ((sK4 @ X0) = sK6)) ) | (~spl1_1 | ~spl1_6)),
% 1.53/1.42 inference(trivial_inequality_removal,[status(thm)],[f307])).
% 1.53/1.42 thf(f307,plain,(
% 1.53/1.42 ( ! [X0 : $i] : (((sK4 @ X0) = sK6) | ((sK3 @ X0) = $false) | ($true = $false)) ) | (~spl1_1 | ~spl1_6)),
% 1.53/1.42 inference(superposition,[status(thm)],[f123,f143])).
% 1.53/1.42 thf(f143,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (($true = (sK3 @ (sK4 @ X1))) | ((sK3 @ X1) = $false)) ) | ~spl1_6),
% 1.53/1.42 inference(avatar_component_clause,[status(thm)],[f142])).
% 1.53/1.42 thf(f142,definition,(
% 1.53/1.42 spl1_6 <=> ! [X1 : $i] : (($true = (sK3 @ (sK4 @ X1))) | ((sK3 @ X1) = $false))),
% 1.53/1.42 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 1.53/1.42 thf(f251,plain,(
% 1.53/1.42 ((sK4 @ sK6) != sK6) | (~spl1_3 | ~spl1_4)),
% 1.53/1.42 inference(trivial_inequality_removal,[status(thm)],[f248])).
% 1.53/1.42 thf(f248,plain,(
% 1.53/1.42 ((sK4 @ sK6) != sK6) | ($true = $false) | (~spl1_3 | ~spl1_4)),
% 1.53/1.42 inference(superposition,[status(thm)],[f132,f136])).
% 1.53/1.42 thf(f136,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (((sK3 @ X1) = $false) | ((sK4 @ X1) != X1)) ) | ~spl1_4),
% 1.53/1.42 inference(avatar_component_clause,[status(thm)],[f135])).
% 1.53/1.42 thf(f135,definition,(
% 1.53/1.42 spl1_4 <=> ! [X1 : $i] : (((sK3 @ X1) = $false) | ((sK4 @ X1) != X1))),
% 1.53/1.42 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.53/1.42 thf(f246,plain,(
% 1.53/1.42 ~spl1_2 | ~spl1_8),
% 1.53/1.42 inference(avatar_contradiction_clause,[status(thm)],[f245])).
% 1.53/1.42 thf(f245,plain,(
% 1.53/1.42 $false | (~spl1_2 | ~spl1_8)),
% 1.53/1.42 inference(equality_resolution,[status(thm)],[f243])).
% 1.53/1.42 thf(f243,plain,(
% 1.53/1.42 ( ! [X1 : $i] : ((sK5 != X1)) ) | (~spl1_2 | ~spl1_8)),
% 1.53/1.42 inference(trivial_inequality_removal,[status(thm)],[f242])).
% 1.53/1.42 thf(f242,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (($true = $false) | (sK5 != X1)) ) | (~spl1_2 | ~spl1_8)),
% 1.53/1.42 inference(backward_demodulation,[status(thm)],[f149,f220])).
% 1.53/1.42 thf(f220,plain,(
% 1.53/1.42 ( ! [X0 : $i] : (((sK3 @ X0) = $false)) ) | ~spl1_8),
% 1.53/1.42 inference(avatar_component_clause,[status(thm)],[f219])).
% 1.53/1.42 thf(f219,definition,(
% 1.53/1.42 spl1_8 <=> ! [X0 : $i] : ((sK3 @ X0) = $false)),
% 1.53/1.42 introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition])).
% 1.53/1.42 thf(f149,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (((sK3 @ X1) = $true) | (sK5 != X1)) ) | ~spl1_2),
% 1.53/1.42 inference(equality_proxy_clausification,[status(thm)],[f146])).
% 1.53/1.42 thf(f146,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (((sK3 @ X1) = $true) | ((sK5 = X1) = $false)) ) | ~spl1_2),
% 1.53/1.42 inference(binary_proxy_clausification,[status(thm)],[f145])).
% 1.53/1.42 thf(f145,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (((sK3 @ X1) = (sK5 = X1))) ) | ~spl1_2),
% 1.53/1.42 inference(argument_congruence,[status(thm)],[f127])).
% 1.53/1.42 thf(f127,plain,(
% 1.53/1.42 (sK3 = (= @ sK5)) | ~spl1_2),
% 1.53/1.42 inference(avatar_component_clause,[status(thm)],[f125])).
% 1.53/1.42 thf(f125,definition,(
% 1.53/1.42 spl1_2 <=> (sK3 = (= @ sK5))),
% 1.53/1.42 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.53/1.42 thf(f241,plain,(
% 1.53/1.42 ~spl1_2 | ~spl1_4 | ~spl1_6 | ~spl1_7),
% 1.53/1.42 inference(avatar_contradiction_clause,[status(thm)],[f240])).
% 1.53/1.42 thf(f240,plain,(
% 1.53/1.42 $false | (~spl1_2 | ~spl1_4 | ~spl1_6 | ~spl1_7)),
% 1.53/1.42 inference(trivial_inequality_removal,[status(thm)],[f239])).
% 1.53/1.42 thf(f239,plain,(
% 1.53/1.42 ($true = $false) | (~spl1_2 | ~spl1_4 | ~spl1_6 | ~spl1_7)),
% 1.53/1.42 inference(backward_demodulation,[status(thm)],[f217,f238])).
% 1.53/1.42 thf(f238,plain,(
% 1.53/1.42 ((sK3 @ sK5) = $false) | (~spl1_2 | ~spl1_4 | ~spl1_6 | ~spl1_7)),
% 1.53/1.42 inference(trivial_inequality_removal,[status(thm)],[f229])).
% 1.53/1.42 thf(f229,plain,(
% 1.53/1.42 ((sK3 @ sK5) = $false) | (sK5 != sK5) | (~spl1_2 | ~spl1_4 | ~spl1_6 | ~spl1_7)),
% 1.53/1.42 inference(superposition,[status(thm)],[f228,f193])).
% 1.53/1.42 thf(f193,plain,(
% 1.53/1.42 ( ! [X0 : $i] : ((sK5 = (sK4 @ X0)) | ((sK3 @ X0) = $false)) ) | (~spl1_2 | ~spl1_6)),
% 1.53/1.42 inference(trivial_inequality_removal,[status(thm)],[f187])).
% 1.53/1.42 thf(f187,plain,(
% 1.53/1.42 ( ! [X0 : $i] : (((sK3 @ X0) = $false) | ($true = $false) | (sK5 = (sK4 @ X0))) ) | (~spl1_2 | ~spl1_6)),
% 1.53/1.42 inference(superposition,[status(thm)],[f143,f148])).
% 1.53/1.42 thf(f148,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (((sK3 @ X1) = $false) | (sK5 = X1)) ) | ~spl1_2),
% 1.53/1.42 inference(equality_proxy_clausification,[status(thm)],[f147])).
% 1.53/1.42 thf(f147,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (($true = (sK5 = X1)) | ((sK3 @ X1) = $false)) ) | ~spl1_2),
% 1.53/1.42 inference(binary_proxy_clausification,[status(thm)],[f145])).
% 1.53/1.42 thf(f228,plain,(
% 1.53/1.42 ((sK4 @ sK5) != sK5) | (~spl1_4 | ~spl1_7)),
% 1.53/1.42 inference(trivial_inequality_removal,[status(thm)],[f223])).
% 1.53/1.42 thf(f223,plain,(
% 1.53/1.42 ($true = $false) | ((sK4 @ sK5) != sK5) | (~spl1_4 | ~spl1_7)),
% 1.53/1.42 inference(superposition,[status(thm)],[f217,f136])).
% 1.53/1.42 thf(f217,plain,(
% 1.53/1.42 ($true = (sK3 @ sK5)) | ~spl1_7),
% 1.53/1.42 inference(avatar_component_clause,[status(thm)],[f215])).
% 1.53/1.42 thf(f215,definition,(
% 1.53/1.42 spl1_7 <=> ($true = (sK3 @ sK5))),
% 1.53/1.42 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.53/1.42 thf(f221,plain,(
% 1.53/1.42 spl1_7 | spl1_8 | ~spl1_2 | ~spl1_6),
% 1.53/1.42 inference(avatar_split_clause,[status(thm)],[f212,f142,f125,f219,f215])).
% 1.53/1.42 thf(f212,plain,(
% 1.53/1.42 ( ! [X0 : $i] : (($true = (sK3 @ sK5)) | ((sK3 @ X0) = $false)) ) | (~spl1_2 | ~spl1_6)),
% 1.53/1.42 inference(duplicate_literal_removal,[status(thm)],[f202])).
% 1.53/1.42 thf(f202,plain,(
% 1.53/1.42 ( ! [X0 : $i] : (((sK3 @ X0) = $false) | ($true = (sK3 @ sK5)) | ((sK3 @ X0) = $false)) ) | (~spl1_2 | ~spl1_6)),
% 1.53/1.42 inference(superposition,[status(thm)],[f143,f193])).
% 1.53/1.42 thf(f162,plain,(
% 1.53/1.42 ~spl1_2 | ~spl1_5),
% 1.53/1.42 inference(avatar_contradiction_clause,[status(thm)],[f161])).
% 1.53/1.42 thf(f161,plain,(
% 1.53/1.42 $false | (~spl1_2 | ~spl1_5)),
% 1.53/1.42 inference(trivial_inequality_removal,[status(thm)],[f156])).
% 1.53/1.42 thf(f156,plain,(
% 1.53/1.42 (sK3 != sK3) | (~spl1_2 | ~spl1_5)),
% 1.53/1.42 inference(superposition,[status(thm)],[f139,f127])).
% 1.53/1.42 thf(f144,plain,(
% 1.53/1.42 spl1_6 | spl1_5),
% 1.53/1.42 inference(avatar_split_clause,[status(thm)],[f103,f138,f142])).
% 1.53/1.42 thf(f103,plain,(
% 1.53/1.42 ( ! [X2 : $i,X1 : $i] : (($true = (sK3 @ (sK4 @ X1))) | ((= @ X2) != sK3) | ((sK3 @ X1) = $false)) )),
% 1.53/1.42 inference(equality_proxy_clausification,[status(thm)],[f102])).
% 1.53/1.42 thf(f102,plain,(
% 1.53/1.42 ( ! [X2 : $i,X1 : $i] : (($true = (sK3 @ (sK4 @ X1))) | ((sK3 @ X1) = $false) | ((sK3 = (= @ X2)) = $false)) )),
% 1.53/1.42 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.53/1.42 thf(f100,plain,(
% 1.53/1.42 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X1) = $false) | ($true = ((sK3 @ (sK4 @ X1)) & (~ (X1 = (sK4 @ X1))))) | ((sK3 = (= @ X2)) = $false)) )),
% 1.53/1.42 inference(beta_eta_normalization,[status(thm)],[f99])).
% 1.53/1.42 thf(f99,plain,(
% 1.53/1.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (sK3 = (= @ Y0))) @ X2) = $false) | ($true = ((sK3 @ (sK4 @ X1)) & (~ (X1 = (sK4 @ X1))))) | ((sK3 @ X1) = $false)) )),
% 1.53/1.42 inference(pi_clausification,[status(thm)],[f98])).
% 1.53/1.42 thf(f98,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (((sK3 @ X1) = $false) | ((?? @ $i @ (^[Y0 : $i]: (sK3 = (= @ Y0)))) = $false) | ($true = ((sK3 @ (sK4 @ X1)) & (~ (X1 = (sK4 @ X1)))))) )),
% 1.53/1.42 inference(beta_eta_normalization,[status(thm)],[f97])).
% 1.53/1.42 thf(f97,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK3 @ Y0) & (~ (X1 = Y0)))) @ (sK4 @ X1))) | ((sK3 @ X1) = $false) | ((?? @ $i @ (^[Y0 : $i]: (sK3 = (= @ Y0)))) = $false)) )),
% 1.53/1.42 inference(sigma_clausification,[status(thm)],[f96])).
% 1.53/1.42 thf(f96,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (((sK3 @ X1) = $false) | ($true = (?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (~ (X1 = Y0)))))) | ((?? @ $i @ (^[Y0 : $i]: (sK3 = (= @ Y0)))) = $false)) )),
% 1.53/1.42 inference(not_proxy_clausification,[status(thm)],[f95])).
% 1.53/1.42 thf(f95,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (((sK3 @ X1) = $false) | ((~ (?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (~ (X1 = Y0)))))) = $false) | ((?? @ $i @ (^[Y0 : $i]: (sK3 = (= @ Y0)))) = $false)) )),
% 1.53/1.42 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.53/1.42 thf(f94,plain,(
% 1.53/1.42 ( ! [X1 : $i] : ((((sK3 @ X1) & (~ (?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (~ (X1 = Y0))))))) = $false) | ((?? @ $i @ (^[Y0 : $i]: (sK3 = (= @ Y0)))) = $false)) )),
% 1.53/1.42 inference(beta_eta_normalization,[status(thm)],[f93])).
% 1.53/1.42 thf(f93,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: (sK3 = (= @ Y0)))) = $false) | (((^[Y0 : $i]: ((sK3 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) & (~ (Y0 = Y1)))))))) @ X1) = $false)) )),
% 1.53/1.42 inference(pi_clausification,[status(thm)],[f92])).
% 1.53/1.42 thf(f92,plain,(
% 1.53/1.42 ((?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) & (~ (Y0 = Y1))))))))) = $false) | ((?? @ $i @ (^[Y0 : $i]: (sK3 = (= @ Y0)))) = $false)),
% 1.53/1.42 inference(binary_proxy_clausification,[status(thm)],[f90])).
% 1.53/1.42 thf(f90,plain,(
% 1.53/1.42 ((?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) & (~ (Y0 = Y1))))))))) != (?? @ $i @ (^[Y0 : $i]: (sK3 = (= @ Y0)))))),
% 1.53/1.42 inference(beta_eta_normalization,[status(thm)],[f89])).
% 1.53/1.42 thf(f89,plain,(
% 1.53/1.42 (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))))))) @ sK3) != ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = (= @ Y1))))) @ sK3))),
% 1.53/1.42 inference(negative_extensionality,[status(thm)],[f23])).
% 1.53/1.42 thf(f23,plain,(
% 1.53/1.42 ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = (= @ Y1))))) != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))))))))),
% 1.53/1.42 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.53/1.42 thf(f22,plain,(
% 1.53/1.42 ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1))))) != ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.53/1.42 inference(definition_unfolding,[status(thm)],[f19,f21])).
% 1.53/1.42 thf(f21,plain,(
% 1.53/1.42 (cONE = ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.53/1.42 inference(definition_unfolding,[status(thm)],[f17,f18,f16])).
% 1.53/1.42 thf(f16,plain,(
% 1.53/1.42 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.53/1.42 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.42 thf(f10,plain,(
% 1.53/1.42 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.53/1.42 inference(fool_elimination,[status(thm)],[f9])).
% 1.53/1.42 thf(f9,plain,(
% 1.53/1.42 (cZERO = (^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))))),
% 1.53/1.42 inference(rectify,[status(thm)],[f1])).
% 1.53/1.42 thf(f1,axiom,(
% 1.53/1.42 (cZERO = (^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))))),
% 1.53/1.42 file('/export/starexec/sandbox/tmp/tmp.9qmM38glqc/DTF2THF_5999.p',cZERO_def)).
% 1.53/1.42 thf(f18,plain,(
% 1.53/1.42 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))),
% 1.53/1.42 inference(cnf_transformation,[status(thm)],[f8])).
% 1.53/1.42 thf(f8,plain,(
% 1.53/1.42 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))),
% 1.53/1.42 inference(fool_elimination,[status(thm)],[f7])).
% 1.53/1.42 thf(f7,plain,(
% 1.53/1.42 (cSUCC = (^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2 : $i] : ((X0 @ (^[X3 : $i] : ((X2 != X3) & (X1 @ X3)))) & (X1 @ X2)))))),
% 1.53/1.42 inference(rectify,[status(thm)],[f2])).
% 1.53/1.42 thf(f2,axiom,(
% 1.53/1.42 (cSUCC = (^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1 : $i] : ((X2 @ (^[X3 : $i] : ((X1 != X3) & (X0 @ X3)))) & (X0 @ X1)))))),
% 1.53/1.42 file('/export/starexec/sandbox/tmp/tmp.9qmM38glqc/DTF2THF_5999.p',cSUCC_def)).
% 1.53/1.42 thf(f17,plain,(
% 1.53/1.42 (cONE = (cSUCC @ cZERO))),
% 1.53/1.42 inference(cnf_transformation,[status(thm)],[f3])).
% 1.53/1.42 thf(f3,axiom,(
% 1.53/1.42 (cONE = (cSUCC @ cZERO))),
% 1.53/1.42 file('/export/starexec/sandbox/tmp/tmp.9qmM38glqc/DTF2THF_5999.p',cONE_def)).
% 1.53/1.42 thf(f19,plain,(
% 1.53/1.42 (cONE != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1))))))),
% 1.53/1.42 inference(cnf_transformation,[status(thm)],[f15])).
% 1.53/1.42 thf(f15,plain,(
% 1.53/1.42 ! [X0 : $i > $i,X1 : $i > $i] : ((X0 = X1) | ((X0 @ (sK0 @ X1 @ X0)) != (X1 @ (sK0 @ X1 @ X0)))) & (cONE != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1))))))),
% 1.53/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14])).
% 1.53/1.42 thf(f14,plain,(
% 1.53/1.42 ! [X0 : $i > $i,X1 : $i > $i] : (? [X2 : $i] : ((X0 @ X2) != (X1 @ X2)) => ((X0 @ (sK0 @ X1 @ X0)) != (X1 @ (sK0 @ X1 @ X0))))),
% 1.53/1.42 introduced(definition,[],[choice_axiom])).
% 1.53/1.42 thf(f13,plain,(
% 1.53/1.42 ! [X0 : $i > $i,X1 : $i > $i] : ((X0 = X1) | ? [X2 : $i] : ((X0 @ X2) != (X1 @ X2))) & (cONE != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1))))))),
% 1.53/1.42 inference(ennf_transformation,[status(thm)],[f12])).
% 1.53/1.42 thf(f12,plain,(
% 1.53/1.42 ~(! [X0 : $i > $i,X1 : $i > $i] : (! [X2 : $i] : ((X0 @ X2) = (X1 @ X2)) => (X0 = X1)) => (cONE = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1)))))))),
% 1.53/1.42 inference(fool_elimination,[status(thm)],[f11])).
% 1.53/1.42 thf(f11,plain,(
% 1.53/1.42 ~(! [X0 : $i > $i,X1 : $i > $i] : (! [X2 : $i] : ((X0 @ X2) = (X1 @ X2)) => (X0 = X1)) => ((^[X3 : $i > $o] : (? [X4 : $i] : (X3 = ((^[X5 : $i, X6 : $i] : ((X5 = X6))) @ X4)))) = cONE))),
% 1.53/1.42 inference(rectify,[status(thm)],[f5])).
% 1.53/1.42 thf(f5,negated_conjecture,(
% 1.53/1.42 ~(! [X5 : $i > $i,X4 : $i > $i] : (! [X1 : $i] : ((X4 @ X1) = (X5 @ X1)) => (X4 = X5)) => ((^[X6 : $i > $o] : (? [X7 : $i] : (X6 = ((^[X1 : $i, X7 : $i] : ((X1 = X7))) @ X7)))) = cONE))),
% 1.53/1.42 inference(negated_conjecture,[status(cth)],[f4])).
% 1.53/1.42 thf(f4,conjecture,(
% 1.53/1.42 ! [X5 : $i > $i,X4 : $i > $i] : (! [X1 : $i] : ((X4 @ X1) = (X5 @ X1)) => (X4 = X5)) => ((^[X6 : $i > $o] : (? [X7 : $i] : (X6 = ((^[X1 : $i, X7 : $i] : ((X1 = X7))) @ X7)))) = cONE)),
% 1.53/1.42 file('/export/starexec/sandbox/tmp/tmp.9qmM38glqc/DTF2THF_5999.p',cX6101_EXT_pme)).
% 1.53/1.42 thf(f140,plain,(
% 1.53/1.42 spl1_4 | spl1_5),
% 1.53/1.42 inference(avatar_split_clause,[status(thm)],[f106,f138,f135])).
% 1.53/1.42 thf(f106,plain,(
% 1.53/1.42 ( ! [X2 : $i,X1 : $i] : (((= @ X2) != sK3) | ((sK3 @ X1) = $false) | ((sK4 @ X1) != X1)) )),
% 1.53/1.42 inference(equality_proxy_clausification,[status(thm)],[f105])).
% 1.53/1.42 thf(f105,plain,(
% 1.53/1.42 ( ! [X2 : $i,X1 : $i] : (((X1 = (sK4 @ X1)) = $false) | ((= @ X2) != sK3) | ((sK3 @ X1) = $false)) )),
% 1.53/1.42 inference(equality_proxy_clausification,[status(thm)],[f104])).
% 1.53/1.42 thf(f104,plain,(
% 1.53/1.42 ( ! [X2 : $i,X1 : $i] : (((sK3 = (= @ X2)) = $false) | ((X1 = (sK4 @ X1)) = $false) | ((sK3 @ X1) = $false)) )),
% 1.53/1.42 inference(not_proxy_clausification,[status(thm)],[f101])).
% 1.53/1.42 thf(f101,plain,(
% 1.53/1.42 ( ! [X2 : $i,X1 : $i] : (((~ (X1 = (sK4 @ X1))) = $true) | ((sK3 @ X1) = $false) | ((sK3 = (= @ X2)) = $false)) )),
% 1.53/1.42 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.53/1.42 thf(f133,plain,(
% 1.53/1.42 spl1_2 | spl1_3),
% 1.53/1.42 inference(avatar_split_clause,[status(thm)],[f113,f130,f125])).
% 1.53/1.42 thf(f113,plain,(
% 1.53/1.42 (sK3 = (= @ sK5)) | ($true = (sK3 @ sK6))),
% 1.53/1.42 inference(equality_proxy_clausification,[status(thm)],[f112])).
% 1.53/1.42 thf(f112,plain,(
% 1.53/1.42 ($true = (sK3 = (= @ sK5))) | ($true = (sK3 @ sK6))),
% 1.53/1.42 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 1.53/1.42 thf(f110,plain,(
% 1.53/1.42 ($true = ((sK3 @ sK6) & (~ (?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (~ (sK6 = Y0)))))))) | ($true = (sK3 = (= @ sK5)))),
% 1.53/1.42 inference(beta_eta_normalization,[status(thm)],[f109])).
% 1.53/1.42 thf(f109,plain,(
% 1.53/1.42 ($true = (sK3 = (= @ sK5))) | (((^[Y0 : $i]: ((sK3 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) & (~ (Y0 = Y1)))))))) @ sK6) = $true)),
% 1.53/1.42 inference(sigma_clausification,[status(thm)],[f108])).
% 1.53/1.42 thf(f108,plain,(
% 1.53/1.42 ($true = (?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) & (~ (Y0 = Y1)))))))))) | ($true = (sK3 = (= @ sK5)))),
% 1.53/1.42 inference(beta_eta_normalization,[status(thm)],[f107])).
% 1.53/1.42 thf(f107,plain,(
% 1.53/1.42 ($true = (?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) & (~ (Y0 = Y1)))))))))) | ($true = ((^[Y0 : $i]: (sK3 = (= @ Y0))) @ sK5))),
% 1.53/1.42 inference(sigma_clausification,[status(thm)],[f91])).
% 1.53/1.42 thf(f91,plain,(
% 1.53/1.42 ($true = (?? @ $i @ (^[Y0 : $i]: (sK3 = (= @ Y0))))) | ($true = (?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) & (~ (Y0 = Y1))))))))))),
% 1.53/1.42 inference(binary_proxy_clausification,[status(thm)],[f90])).
% 1.53/1.42 thf(f128,plain,(
% 1.53/1.42 spl1_1 | spl1_2),
% 1.53/1.42 inference(avatar_split_clause,[status(thm)],[f120,f125,f122])).
% 1.53/1.42 thf(f120,plain,(
% 1.53/1.42 ( ! [X1 : $i] : ((sK6 = X1) | ((sK3 @ X1) = $false) | (sK3 = (= @ sK5))) )),
% 1.53/1.42 inference(equality_proxy_clausification,[status(thm)],[f119])).
% 1.53/1.42 thf(f119,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (($true = (sK6 = X1)) | ((sK3 @ X1) = $false) | (sK3 = (= @ sK5))) )),
% 1.53/1.42 inference(not_proxy_clausification,[status(thm)],[f118])).
% 1.53/1.42 thf(f118,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (((sK3 @ X1) = $false) | (sK3 = (= @ sK5)) | ((~ (sK6 = X1)) = $false)) )),
% 1.53/1.42 inference(binary_proxy_clausification,[status(thm)],[f117])).
% 1.53/1.42 thf(f117,plain,(
% 1.53/1.42 ( ! [X1 : $i] : ((((sK3 @ X1) & (~ (sK6 = X1))) = $false) | (sK3 = (= @ sK5))) )),
% 1.53/1.42 inference(beta_eta_normalization,[status(thm)],[f116])).
% 1.53/1.42 thf(f116,plain,(
% 1.53/1.42 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((sK3 @ Y0) & (~ (sK6 = Y0)))) @ X1)) | (sK3 = (= @ sK5))) )),
% 1.53/1.42 inference(pi_clausification,[status(thm)],[f115])).
% 1.53/1.42 thf(f115,plain,(
% 1.53/1.42 (sK3 = (= @ sK5)) | ((?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (~ (sK6 = Y0))))) = $false)),
% 1.53/1.42 inference(not_proxy_clausification,[status(thm)],[f114])).
% 1.53/1.42 thf(f114,plain,(
% 1.53/1.42 (sK3 = (= @ sK5)) | ((~ (?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (~ (sK6 = Y0)))))) = $true)),
% 1.53/1.42 inference(equality_proxy_clausification,[status(thm)],[f111])).
% 1.53/1.42 thf(f111,plain,(
% 1.53/1.42 ($true = (sK3 = (= @ sK5))) | ((~ (?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (~ (sK6 = Y0)))))) = $true)),
% 1.53/1.42 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 1.53/1.42 % SZS output end Proof for DTF2THF_5999
% 1.53/1.42 % (6199)------------------------------
% 1.53/1.42 % (6199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.42 % (6199)Termination reason: Refutation
% 1.53/1.42
% 1.53/1.42 % (6199)Memory used [KB]: 5756
% 1.53/1.42 % (6199)Time elapsed: 0.063 s
% 1.53/1.42 % (6199)Instructions burned: 207 (million)
% 1.53/1.42 % (6199)------------------------------
% 1.53/1.42 % (6199)------------------------------
% 1.53/1.42 % (6172)Success in time 0.147 s
%------------------------------------------------------------------------------