%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV100^5 : TPTP v9.2.1. Released v4.0.0.
% 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 09:40:17 AM UTC 2026
% Result : Theorem 1.51s 1.32s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 67 ( 3 unt; 0 typ; 1 def)
% Number of atoms : 1188 ( 400 equ; 0 cnn)
% Maximal formula atoms : 12 ( 17 avg)
% Number of connectives : 1644 ( 147 ~; 235 |; 69 &;1184 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 712 ( 712 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 894 ( 680 ^; 178 !; 36 ?; 894 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_8,type,
sK0: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_9,type,
sK1: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_10,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_11,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_12,type,
sK4: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_13,type,
sK5: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_15,type,
ph7:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK9: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_22,type,
sK10: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(f459,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f392,f458]) ).
thf(f458,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[status(thm)],[f457]) ).
thf(f457,plain,
( $false
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f456]) ).
thf(f456,plain,
( ( $false = $true )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f455]) ).
thf(f455,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : $true
@ X1 )
= ( ^ [Y0: $i] : $false
@ X1 ) )
| ~ spl6_1 ),
inference(argument_congruence,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f73]) ).
thf(f73,definition,
( spl6_1
<=> ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f392,plain,
spl6_1,
inference(avatar_contradiction_clause,[status(thm)],[f391]) ).
thf(f391,plain,
( $false
| spl6_1 ),
inference(subsumption_resolution,[status(thm)],[f376,f368]) ).
thf(f368,plain,
( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
!= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| spl6_1 ),
inference(subsumption_resolution,[status(thm)],[f364,f75]) ).
thf(f75,plain,
( ( ( ^ [Y0: $i] : $false )
!= ( ^ [Y0: $i] : $true ) )
| spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f73]) ).
thf(f364,plain,
( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
!= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
| spl6_1 ),
inference(equality_proxy_clausification,[status(thm)],[f363]) ).
thf(f363,plain,
( ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
!= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| spl6_1 ),
inference(equality_proxy_clausification,[status(thm)],[f362]) ).
thf(f362,plain,
( ( $true
!= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f361]) ).
thf(f361,plain,
( ( $true
!= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) ) )
| ( $true != $true )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| spl6_1 ),
inference(boolean_simplification,[status(thm)],[f360]) ).
thf(f360,plain,
( ( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
!= $true )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true
!= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) ) )
| spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f359]) ).
thf(f359,plain,
( ( $false = $true )
| ( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
!= $true )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true
!= ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) ) )
| spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f355]) ).
thf(f355,plain,
( ! [X0: $i] :
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X0 ) )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
!= $true )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X0 ) ) )
| spl6_1 ),
inference(superposition,[status(thm)],[f45,f348]) ).
thf(f348,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f347]) ).
thf(f347,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ( $false = $true )
| spl6_1 ),
inference(duplicate_literal_removal,[status(thm)],[f346]) ).
thf(f346,plain,
( ( $false = $true )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ( $false = $true )
| spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f333]) ).
thf(f333,plain,
( ! [X2: $i,X8: $i] :
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ X8 ) ) )
| spl6_1 ),
inference(primitive_instantiation,[status(thm)],[f215]) ).
thf(f215,plain,
( ! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( X0
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X8 )
= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) ) )
| spl6_1 ),
inference(subsumption_resolution,[status(thm)],[f212,f75]) ).
thf(f212,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
| ( ( X0
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X8 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f211]) ).
thf(f211,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
| ( ( X0
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X8 )
= $true )
| ( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) )
= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f210]) ).
thf(f210,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( X0
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X8 )
= $true )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f209]) ).
thf(f209,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( $true != $true )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) )
= $true )
| ( ( X0
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X8 )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f208]) ).
thf(f208,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) )
!= $true )
| ( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) )
= $true )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( ( X0
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X8 )
= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f190]) ).
thf(f190,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X8 ) )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( X0
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X8 )
= $true ) ),
inference(primitive_instantiation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 )
= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 ) ) ),
inference(boolean_simplification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( $true
= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 ) )
| ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( $true
= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 ) )
| ( $true
= ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 )
= $true )
| ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] : $false
@ X2 ) ) ),
inference(boolean_simplification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 )
= $true )
| ( ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 )
= $true )
| ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( $true
= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 ) )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] : $false
@ X2 ) ) ),
inference(boolean_simplification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X8: $i] :
( ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 )
= $true )
| ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 ) )
| ( ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 )
= $true )
| ( $true
= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 )
= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 ) ) )
| ( ! [X6: $i] :
( ( $true
= ( X0 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) )
| ( $true
= ( X1 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) ) )
& ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) )
!= $true )
& ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) )
& ! [X8: $i] :
( ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 )
= $true )
| ( $true
= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 ) ) ) )
| ( ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f9,f12,f11,f10]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ! [X6: $i] :
( ( ( X0 @ X3 @ X5 @ X6 )
= $true )
| ( $true
= ( X1 @ X3 @ X5 @ X6 ) ) )
& ? [X7: $i] :
( ( ( X0 @ X4 @ X5 @ X7 )
!= $true )
& ( $true
!= ( X1 @ X4 @ X5 @ X7 ) ) )
& ! [X8: $i] :
( ( $true
= ( X0 @ X4 @ X3 @ X8 ) )
| ( $true
= ( X1 @ X4 @ X3 @ X8 ) ) ) )
=> ( ! [X6: $i] :
( ( $true
= ( X0 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) )
| ( $true
= ( X1 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) ) )
& ? [X7: $i] :
( ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X7 )
!= $true )
& ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X7 ) ) )
& ! [X8: $i] :
( ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 )
= $true )
| ( $true
= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) @ X8 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X7: $i] :
( ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X7 )
!= $true )
& ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X7 ) ) )
=> ( ( ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) )
!= $true )
& ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X9: $i,X10: $i > $o] :
( ( ( X1 @ X10 @ X10 @ X9 )
!= $true )
& ( ( X0 @ X10 @ X10 @ X9 )
!= $true ) )
=> ( ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 )
= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 ) ) )
| ? [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ! [X6: $i] :
( ( ( X0 @ X3 @ X5 @ X6 )
= $true )
| ( $true
= ( X1 @ X3 @ X5 @ X6 ) ) )
& ? [X7: $i] :
( ( ( X0 @ X4 @ X5 @ X7 )
!= $true )
& ( $true
!= ( X1 @ X4 @ X5 @ X7 ) ) )
& ! [X8: $i] :
( ( $true
= ( X0 @ X4 @ X3 @ X8 ) )
| ( $true
= ( X1 @ X4 @ X3 @ X8 ) ) ) )
| ? [X9: $i,X10: $i > $o] :
( ( ( X1 @ X10 @ X10 @ X9 )
!= $true )
& ( ( X0 @ X10 @ X10 @ X9 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 )
= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 ) ) )
| ? [X3: $i > $o,X5: $i > $o,X4: $i > $o] :
( ! [X7: $i] :
( ( ( X0 @ X3 @ X4 @ X7 )
= $true )
| ( $true
= ( X1 @ X3 @ X4 @ X7 ) ) )
& ? [X8: $i] :
( ( $true
!= ( X0 @ X5 @ X4 @ X8 ) )
& ( ( X1 @ X5 @ X4 @ X8 )
!= $true ) )
& ! [X6: $i] :
( ( ( X0 @ X5 @ X3 @ X6 )
= $true )
| ( $true
= ( X1 @ X5 @ X3 @ X6 ) ) ) )
| ? [X10: $i,X9: $i > $o] :
( ( $true
!= ( X1 @ X9 @ X9 @ X10 ) )
& ( $true
!= ( X0 @ X9 @ X9 @ X10 ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X3: $i > $o,X5: $i > $o,X4: $i > $o] :
( ? [X8: $i] :
( ( $true
!= ( X0 @ X5 @ X4 @ X8 ) )
& ( ( X1 @ X5 @ X4 @ X8 )
!= $true ) )
& ! [X6: $i] :
( ( ( X0 @ X5 @ X3 @ X6 )
= $true )
| ( $true
= ( X1 @ X5 @ X3 @ X6 ) ) )
& ! [X7: $i] :
( ( ( X0 @ X3 @ X4 @ X7 )
= $true )
| ( $true
= ( X1 @ X3 @ X4 @ X7 ) ) ) )
| ? [X10: $i,X9: $i > $o] :
( ( $true
!= ( X1 @ X9 @ X9 @ X10 ) )
& ( $true
!= ( X0 @ X9 @ X9 @ X10 ) ) )
| ! [X2: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 )
= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X3: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ! [X6: $i] :
( ( ( X0 @ X5 @ X3 @ X6 )
= $true )
| ( $true
= ( X1 @ X5 @ X3 @ X6 ) ) )
& ! [X7: $i] :
( ( ( X0 @ X3 @ X4 @ X7 )
= $true )
| ( $true
= ( X1 @ X3 @ X4 @ X7 ) ) ) )
=> ! [X8: $i] :
( ( ( X1 @ X5 @ X4 @ X8 )
= $true )
| ( $true
= ( X0 @ X5 @ X4 @ X8 ) ) ) )
& ! [X9: $i > $o,X10: $i] :
( ( $true
= ( X1 @ X9 @ X9 @ X10 ) )
| ( $true
= ( X0 @ X9 @ X9 @ X10 ) ) )
& ~ ! [X2: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 )
= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ! [X2: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 )
= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 ) ) )
& ! [X7: $i > $o,X8: $i > $o,X9: $i > $o] :
( ( ! [X10: $i] :
( ( ( X1 @ X9 @ X7 @ X10 )
= $true )
| ( $true
= ( X0 @ X9 @ X7 @ X10 ) ) )
& ! [X11: $i] :
( ( $true
= ( X1 @ X7 @ X8 @ X11 ) )
| ( $true
= ( X0 @ X7 @ X8 @ X11 ) ) ) )
=> ! [X12: $i] :
( ( ( X1 @ X9 @ X8 @ X12 )
= $true )
| ( $true
= ( X0 @ X9 @ X8 @ X12 ) ) ) )
& ! [X13: $i > $o,X14: $i] :
( ( ( X1 @ X13 @ X13 @ X14 )
= $true )
| ( $true
= ( X0 @ X13 @ X13 @ X14 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ! [X2: $i] :
( ( X0
@ ^ [X3: $i] :
( p
| ~ p )
@ ^ [X4: $i] :
( ~ p
& p )
@ X2 )
| ( X1
@ ^ [X5: $i] :
( p
| ~ p )
@ ^ [X6: $i] :
( ~ p
& p )
@ X2 ) )
& ! [X7: $i > $o,X8: $i > $o,X9: $i > $o] :
( ( ! [X10: $i] :
( ( X1 @ X9 @ X7 @ X10 )
| ( X0 @ X9 @ X7 @ X10 ) )
& ! [X11: $i] :
( ( X1 @ X7 @ X8 @ X11 )
| ( X0 @ X7 @ X8 @ X11 ) ) )
=> ! [X12: $i] :
( ( X1 @ X9 @ X8 @ X12 )
| ( X0 @ X9 @ X8 @ X12 ) ) )
& ! [X13: $i > $o,X14: $i] :
( ( X1 @ X13 @ X13 @ X14 )
| ( X0 @ X13 @ X13 @ X14 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ! [X5: $i] :
( ( X0
@ ^ [X2: $i] :
( p
| ~ p )
@ ^ [X2: $i] :
( ~ p
& p )
@ X5 )
| ( X1
@ ^ [X2: $i] :
( p
| ~ p )
@ ^ [X2: $i] :
( ~ p
& p )
@ X5 ) )
& ! [X3: $i > $o,X4: $i > $o,X2: $i > $o] :
( ( ! [X5: $i] :
( ( X1 @ X2 @ X3 @ X5 )
| ( X0 @ X2 @ X3 @ X5 ) )
& ! [X5: $i] :
( ( X1 @ X3 @ X4 @ X5 )
| ( X0 @ X3 @ X4 @ X5 ) ) )
=> ! [X5: $i] :
( ( X1 @ X2 @ X4 @ X5 )
| ( X0 @ X2 @ X4 @ X5 ) ) )
& ! [X2: $i > $o,X5: $i] :
( ( X1 @ X2 @ X2 @ X5 )
| ( X0 @ X2 @ X2 @ X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ! [X5: $i] :
( ( X0
@ ^ [X2: $i] :
( p
| ~ p )
@ ^ [X2: $i] :
( ~ p
& p )
@ X5 )
| ( X1
@ ^ [X2: $i] :
( p
| ~ p )
@ ^ [X2: $i] :
( ~ p
& p )
@ X5 ) )
& ! [X3: $i > $o,X4: $i > $o,X2: $i > $o] :
( ( ! [X5: $i] :
( ( X1 @ X2 @ X3 @ X5 )
| ( X0 @ X2 @ X3 @ X5 ) )
& ! [X5: $i] :
( ( X1 @ X3 @ X4 @ X5 )
| ( X0 @ X3 @ X4 @ X5 ) ) )
=> ! [X5: $i] :
( ( X1 @ X2 @ X4 @ X5 )
| ( X0 @ X2 @ X4 @ X5 ) ) )
& ! [X2: $i > $o,X5: $i] :
( ( X1 @ X2 @ X2 @ X5 )
| ( X0 @ X2 @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zrxScirKMq/DTF2THF_27682.p',cTHM120F_pme) ).
thf(f45,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true ) ),
inference(boolean_simplification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
= ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) )
| ( $true
= ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true ) ),
inference(boolean_simplification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( $true
= ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] : $false
@ X2 ) ) ),
inference(boolean_simplification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 ) )
| ( $true
= ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true ) ),
inference(boolean_simplification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) )
| ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 )
= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f376,plain,
( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f375]) ).
thf(f375,plain,
( ( $false = $true )
| ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| spl6_1 ),
inference(duplicate_literal_removal,[status(thm)],[f374]) ).
thf(f374,plain,
( ( $false = $true )
| ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ( $false = $true )
| spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f372]) ).
thf(f372,plain,
( ! [X2: $i,X6: $i] :
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false ) )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $false )
@ X6 )
= $true ) )
| spl6_1 ),
inference(primitive_instantiation,[status(thm)],[f241]) ).
thf(f241,plain,
( ! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( $true
= ( X0
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X6 ) )
| ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true ) )
| spl6_1 ),
inference(subsumption_resolution,[status(thm)],[f240,f75]) ).
thf(f240,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) )
| ( $true
= ( X0
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X6 ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f239]) ).
thf(f239,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( $true
= ( X0
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X6 ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f238]) ).
thf(f238,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) )
= $true )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( $true
= ( X0
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X6 ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f237]) ).
thf(f237,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( $true != $true )
| ( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) )
= $true )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( X0
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X6 ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) ) ),
inference(boolean_simplification,[status(thm)],[f236]) ).
thf(f236,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) )
!= $true )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= ( ^ [Y0: $i] : $true ) ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) )
= $true )
| ( $true
= ( X0
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X6 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f216]) ).
thf(f216,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( $true
= ( X0
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X6 ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ X6 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : ( Y1 = Y0 )
@ X0 ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( $true
= ( X0 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( X1 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) ) ),
inference(boolean_simplification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( $true
= ( X0 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) )
| ( $true
= ( X1 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) ) ),
inference(boolean_simplification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 ) )
| ( ( X0
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( $true
= ( X0 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) )
| ( $true
= ( X1 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) ) ),
inference(boolean_simplification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( $true
= ( X0 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) )
| ( $true
= ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] : $false
@ X2 ) )
| ( $true
= ( X1 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 ) ) ),
inference(boolean_simplification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: $i,X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( ( X1 @ ( sK5 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) )
!= $true )
| ( ( X0
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 )
= $true )
| ( $true
= ( X1
@ ^ [Y0: $i] :
( ~ p
| p )
@ ^ [Y0: $i] :
( p
& ~ p )
@ X2 ) )
| ( $true
= ( X1 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) )
| ( $true
= ( X0 @ ( sK0 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV100^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n018.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:40:01 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.48 ---- Original DTF file ---
% 0.33/0.49 thf(spec,logic,$$dhol).
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 % File : SEV100^5 : TPTP v9.2.1. Released v4.0.0.
% 0.33/0.49 % Domain : Set Theory (Relations)
% 0.33/0.49 % Problem : TPS problem from RELN-THMS
% 0.33/0.49 % Version : Especial.
% 0.33/0.49 % English :
% 0.33/0.49
% 0.33/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.33/0.49 % Source : [Bro09]
% 0.33/0.49 % Names : tps_1088 [Bro09]
% 0.33/0.49
% 0.33/0.49 % Status : Theorem
% 0.33/0.49 % Rating : 0.50 v9.0.0, 0.58 v8.2.0, 0.64 v8.1.0, 0.83 v7.5.0, 0.75 v7.4.0, 0.78 v7.3.0, 0.80 v7.2.0, 0.75 v7.1.0, 0.71 v7.0.0, 0.75 v6.4.0, 0.71 v6.3.0, 0.83 v5.5.0, 0.80 v5.4.0, 0.75 v5.2.0, 1.00 v4.0.0
% 0.33/0.49 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.33/0.49 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.33/0.49 % Maximal formula atoms : 8 ( 8 avg)
% 0.33/0.49 % Number of connectives : 48 ( 5 ~; 7 |; 5 &; 30 @)
% 0.33/0.49 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.33/0.49 % Maximal formula depth : 14 ( 14 avg)
% 0.33/0.49 % Number of types : 2 ( 0 usr)
% 0.33/0.49 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.33/0.49 % Number of symbols : 1 ( 1 usr; 1 con; 0-0 aty)
% 0.33/0.49 % Number of variables : 15 ( 4 ^; 9 !; 2 ?; 15 :)
% 0.33/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.33/0.49
% 0.33/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.33/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.33/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.33/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 thf(p,type,
% 0.33/0.49 p: $o ).
% 0.33/0.49
% 0.33/0.49 thf(cTHM120F_pme,conjecture,
% 0.33/0.49 ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
% 0.33/0.49 ( ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.33/0.49 ( ( ! [Xw_2: $i] :
% 0.33/0.49 ( ( Xr_27 @ Xx @ Xy @ Xw_2 )
% 0.33/0.49 | ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
% 0.33/0.49 & ! [Xw_2: $i] :
% 0.33/0.49 ( ( Xr_27 @ Xy @ Xz @ Xw_2 )
% 0.33/0.49 | ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
% 0.33/0.49 => ! [Xw_2: $i] :
% 0.33/0.49 ( ( Xr_27 @ Xx @ Xz @ Xw_2 )
% 0.33/0.49 | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) )
% 0.33/0.49 & ! [Xx: $i > $o,Xw_2: $i] :
% 0.33/0.49 ( ( Xr_27 @ Xx @ Xx @ Xw_2 )
% 0.33/0.49 | ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
% 0.33/0.49 & ~ ! [Xw_2: $i] :
% 0.33/0.49 ( ( Xr_27
% 0.33/0.49 @ ^ [Xx: $i] :
% 0.33/0.49 ( p
% 0.33/0.49 | ~ p )
% 0.33/0.49 @ ^ [Xx: $i] :
% 0.33/0.49 ( p
% 0.33/0.49 & ~ p )
% 0.33/0.49 @ Xw_2 )
% 0.33/0.49 | ( Xr_28
% 0.33/0.49 @ ^ [Xx: $i] :
% 0.33/0.49 ( p
% 0.33/0.49 | ~ p )
% 0.33/0.49 @ ^ [Xx: $i] :
% 0.33/0.49 ( p
% 0.33/0.49 & ~ p )
% 0.33/0.49 @ Xw_2 ) ) ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 1.40/1.26 ---- Embedded in THF ---
% 1.40/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.40/1.26 %%% Generated on Tue Feb 24 12:40:01 EST 2026
% 1.40/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.40/1.26 %%% Logic specification used:
% 1.40/1.26 %%% thf(spec, logic, $$dhol).
% 1.40/1.26
% 1.40/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zrxScirKMq/DTF2DTF27682.p
% See solution above
% 1.40/1.26 ------------------------
% 1.40/1.27 ---- Cleaned THF ---
% 1.40/1.27 thf(p,type,
% 1.40/1.27 p: $o ).
% 1.40/1.27
% 1.40/1.27 thf(cTHM120F_pme,conjecture,
% 1.40/1.27 ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
% 1.40/1.27 ( ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 1.40/1.27 ( ( ! [Xw_2: $i] :
% 1.40/1.27 ( ( Xr_27 @ Xx @ Xy @ Xw_2 )
% 1.40/1.27 | ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
% 1.40/1.27 & ! [Xw_2: $i] :
% 1.40/1.27 ( ( Xr_27 @ Xy @ Xz @ Xw_2 )
% 1.40/1.27 | ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
% 1.40/1.27 => ! [Xw_2: $i] :
% 1.40/1.27 ( ( Xr_27 @ Xx @ Xz @ Xw_2 )
% 1.40/1.27 | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) )
% 1.40/1.27 & ! [Xx: $i > $o,Xw_2: $i] :
% 1.40/1.27 ( ( Xr_27 @ Xx @ Xx @ Xw_2 )
% 1.40/1.27 | ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
% 1.40/1.27 & ~ ! [Xw_2: $i] :
% 1.40/1.27 ( ( Xr_27
% 1.40/1.27 @ ^ [Xx: $i] :
% 1.40/1.27 ( p
% 1.40/1.27 | ~ p )
% 1.40/1.27 @ ^ [Xx: $i] :
% 1.40/1.27 ( p
% 1.40/1.27 & ~ p )
% 1.40/1.27 @ Xw_2 )
% 1.40/1.27 | ( Xr_28
% 1.40/1.27 @ ^ [Xx: $i] :
% 1.40/1.27 ( p
% 1.40/1.27 | ~ p )
% 1.40/1.27 @ ^ [Xx: $i] :
% 1.40/1.27 ( p
% 1.40/1.27 & ~ p )
% 1.40/1.27 @ Xw_2 ) ) ) ).
% 1.40/1.27 ------------------------
% 1.40/1.28 % (27793)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27682 for (3000ds/183Mi)
% 1.40/1.28 % (27799)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27682 for (3000ds/18Mi)
% 1.40/1.29 % (27799)Instruction limit reached!
% 1.40/1.29 % (27799)------------------------------
% 1.40/1.29 % (27799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.29 % (27799)Termination reason: Unknown
% 1.40/1.29 % (27799)Termination phase: Saturation
% 1.40/1.29
% 1.40/1.29 % (27799)Memory used [KB]: 5628
% 1.40/1.29 % (27799)Time elapsed: 0.007 s
% 1.40/1.29 % (27799)Instructions burned: 19 (million)
% 1.40/1.29 % (27799)------------------------------
% 1.40/1.29 % (27799)------------------------------
% 1.40/1.29 % (27794)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_27682 for (3000ds/4Mi)
% 1.40/1.29 % (27794)Instruction limit reached!
% 1.40/1.29 % (27794)------------------------------
% 1.40/1.29 % (27794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.29 % (27794)Termination reason: Unknown
% 1.40/1.29 % (27794)Termination phase: Saturation
% 1.40/1.29
% 1.40/1.29 % (27794)Memory used [KB]: 5500
% 1.40/1.29 % (27794)Time elapsed: 0.005 s
% 1.40/1.29 % (27794)Instructions burned: 5 (million)
% 1.40/1.29 % (27794)------------------------------
% 1.40/1.29 % (27794)------------------------------
% 1.40/1.29 % (27798)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_27682 for (3000ds/275Mi)
% 1.40/1.29 % (27795)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_27682 for (3000ds/27Mi)
% 1.40/1.29 % (27797)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_27682 for (3000ds/2Mi)
% 1.40/1.30 % (27800)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27682 for (2999ds/3Mi)
% 1.40/1.30 % (27797)Instruction limit reached!
% 1.40/1.30 % (27797)------------------------------
% 1.40/1.30 % (27797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.30 % (27797)Termination reason: Unknown
% 1.40/1.30 % (27797)Termination phase: shuffling
% 1.40/1.30
% 1.40/1.30 % (27797)Memory used [KB]: 1023
% 1.40/1.30 % (27797)Time elapsed: 0.003 s
% 1.40/1.30 % (27797)Instructions burned: 2 (million)
% 1.40/1.30 % (27797)------------------------------
% 1.40/1.30 % (27797)------------------------------
% 1.51/1.30 % (27800)Instruction limit reached!
% 1.51/1.30 % (27800)------------------------------
% 1.51/1.30 % (27800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.30 % (27800)Termination reason: Unknown
% 1.51/1.30 % (27800)Termination phase: Property scanning
% 1.51/1.30
% 1.51/1.30 % (27800)Memory used [KB]: 1023
% 1.51/1.30 % (27800)Time elapsed: 0.002 s
% 1.51/1.30 % (27800)Instructions burned: 3 (million)
% 1.51/1.30 % (27800)------------------------------
% 1.51/1.30 % (27800)------------------------------
% 1.51/1.30 % (27795)Refutation not found, incomplete strategy
% 1.51/1.30 % (27795)------------------------------
% 1.51/1.30 % (27795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.30 % (27795)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.30
% 1.51/1.30
% 1.51/1.30 % (27795)Memory used [KB]: 5500
% 1.51/1.30 % (27795)Time elapsed: 0.006 s
% 1.51/1.30 % (27795)Instructions burned: 8 (million)
% 1.51/1.30 % (27795)------------------------------
% 1.51/1.30 % (27795)------------------------------
% 1.51/1.30 % (27796)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27682 for (3000ds/2Mi)
% 1.51/1.30 % (27796)Instruction limit reached!
% 1.51/1.30 % (27796)------------------------------
% 1.51/1.30 % (27796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.30 % (27796)Termination reason: Unknown
% 1.51/1.30 % (27796)Termination phase: Property scanning
% 1.51/1.30
% 1.51/1.30 % (27796)Memory used [KB]: 895
% 1.51/1.30 % (27796)Time elapsed: 0.003 s
% 1.51/1.30 % (27796)Instructions burned: 2 (million)
% 1.51/1.30 % (27796)------------------------------
% 1.51/1.30 % (27796)------------------------------
% 1.51/1.31 % (27803)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_27682 for (2999ds/3Mi)
% 1.51/1.31 % (27803)Instruction limit reached!
% 1.51/1.31 % (27803)------------------------------
% 1.51/1.31 % (27803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.31 % (27803)Termination reason: Unknown
% 1.51/1.31 % (27803)Termination phase: Property scanning
% 1.51/1.31
% 1.51/1.31 % (27803)Memory used [KB]: 1023
% 1.51/1.31 % (27803)Time elapsed: 0.002 s
% 1.51/1.31 % (27803)Instructions burned: 3 (million)
% 1.51/1.31 % (27803)------------------------------
% 1.51/1.31 % (27803)------------------------------
% 1.51/1.31 % (27801)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_27682 for (2999ds/37Mi)
% 1.51/1.31 % (27802)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_27682 for (2999ds/15Mi)
% 1.51/1.32 % (27804)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_27682 for (2999ds/1041Mi)
% 1.51/1.32 % (27798)First to succeed.
% 1.51/1.32 % (27806)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27682 for (2999ds/16Mi)
% 1.51/1.32 % (27805)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27682 for (2999ds/7Mi)
% 1.51/1.32 % (27798)Refutation found. Thanks to Tanya!
% 1.51/1.32 % SZS status Theorem for DTF2THF_27682
% 1.51/1.32 % SZS output start Proof for DTF2THF_27682
% 1.51/1.32 thf(func_def_8, type, sK0: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.51/1.32 thf(func_def_9, type, sK1: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.51/1.32 thf(func_def_10, type, sK2: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.51/1.32 thf(func_def_11, type, sK3: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.51/1.32 thf(func_def_12, type, sK4: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.51/1.32 thf(func_def_13, type, sK5: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.51/1.32 thf(func_def_15, type, ph7: !>[X0: $tType]:(X0)).
% 1.51/1.32 thf(func_def_21, type, sK9: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.51/1.32 thf(func_def_22, type, sK10: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.51/1.32 thf(f459,plain,(
% 1.51/1.32 $false),
% 1.51/1.32 inference(avatar_sat_refutation,[status(thm)],[f392,f458])).
% 1.51/1.32 thf(f458,plain,(
% 1.51/1.32 ~spl6_1),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f457])).
% 1.51/1.32 thf(f457,plain,(
% 1.51/1.32 $false | ~spl6_1),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f456])).
% 1.51/1.32 thf(f456,plain,(
% 1.51/1.32 ($false = $true) | ~spl6_1),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f455])).
% 1.51/1.32 thf(f455,plain,(
% 1.51/1.32 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($true)) @ X1) = ((^[Y0 : $i]: ($false)) @ X1))) ) | ~spl6_1),
% 1.51/1.32 inference(argument_congruence,[status(thm)],[f74])).
% 1.51/1.32 thf(f74,plain,(
% 1.51/1.32 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_1),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f73])).
% 1.51/1.32 thf(f73,definition,(
% 1.51/1.32 spl6_1 <=> ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.51/1.32 thf(f392,plain,(
% 1.51/1.32 spl6_1),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f391])).
% 1.51/1.32 thf(f391,plain,(
% 1.51/1.32 $false | spl6_1),
% 1.51/1.32 inference(subsumption_resolution,[status(thm)],[f376,f368])).
% 1.51/1.32 thf(f368,plain,(
% 1.51/1.32 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) != (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | spl6_1),
% 1.51/1.32 inference(subsumption_resolution,[status(thm)],[f364,f75])).
% 1.51/1.32 thf(f75,plain,(
% 1.51/1.32 ((^[Y0 : $i]: ($false)) != (^[Y0 : $i]: ($true))) | spl6_1),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f73])).
% 1.51/1.32 thf(f364,plain,(
% 1.51/1.32 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) != (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | spl6_1),
% 1.51/1.32 inference(equality_proxy_clausification,[status(thm)],[f363])).
% 1.51/1.32 thf(f363,plain,(
% 1.51/1.32 ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) != (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | spl6_1),
% 1.51/1.32 inference(equality_proxy_clausification,[status(thm)],[f362])).
% 1.51/1.32 thf(f362,plain,(
% 1.51/1.32 ($true != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | spl6_1),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f361])).
% 1.51/1.32 thf(f361,plain,(
% 1.51/1.32 ($true != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true != $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | spl6_1),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f360])).
% 1.51/1.32 thf(f360,plain,(
% 1.51/1.32 (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_1),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f359])).
% 1.51/1.32 thf(f359,plain,(
% 1.51/1.32 ($false = $true) | (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_1),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f355])).
% 1.51/1.32 thf(f355,plain,(
% 1.51/1.32 ( ! [X0 : $i] : (($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0)) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0))) ) | spl6_1),
% 1.51/1.32 inference(superposition,[status(thm)],[f45,f348])).
% 1.51/1.32 thf(f348,plain,(
% 1.51/1.32 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | spl6_1),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f347])).
% 1.51/1.32 thf(f347,plain,(
% 1.51/1.32 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($false = $true) | spl6_1),
% 1.51/1.32 inference(duplicate_literal_removal,[status(thm)],[f346])).
% 1.51/1.32 thf(f346,plain,(
% 1.51/1.32 ($false = $true) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($false = $true) | spl6_1),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f333])).
% 1.51/1.32 thf(f333,plain,(
% 1.51/1.32 ( ! [X2 : $i,X8 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X8))) ) | spl6_1),
% 1.51/1.32 inference(primitive_instantiation,[status(thm)],[f215])).
% 1.51/1.32 thf(f215,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) ) | spl6_1),
% 1.51/1.32 inference(subsumption_resolution,[status(thm)],[f212,f75])).
% 1.51/1.32 thf(f212,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true)) )),
% 1.51/1.32 inference(equality_proxy_clausification,[status(thm)],[f211])).
% 1.51/1.32 thf(f211,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )),
% 1.51/1.32 inference(equality_proxy_clausification,[status(thm)],[f210])).
% 1.51/1.32 thf(f210,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true)) )),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f209])).
% 1.51/1.32 thf(f209,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true != $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true)) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f208])).
% 1.51/1.32 thf(f208,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : ((((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f190])).
% 1.51/1.32 thf(f190,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8)) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true)) )),
% 1.51/1.32 inference(primitive_instantiation,[status(thm)],[f29])).
% 1.51/1.32 thf(f29,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8))) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f28])).
% 1.51/1.32 thf(f28,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = (X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8)) | ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8) = $true)) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f27])).
% 1.51/1.32 thf(f27,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = (X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8)) | ($true = (X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8) = $true) | ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X2))) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f26])).
% 1.51/1.32 thf(f26,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ($true = (X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8)) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X2))) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f15])).
% 1.51/1.32 thf(f15,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8) = $true) | ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2)) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ($true = (X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8))) )),
% 1.51/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.32 thf(f13,plain,(
% 1.51/1.32 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i] : (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | (! [X6 : $i] : (($true = (X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6))) & (((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) & ($true != (X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) & ! [X8 : $i] : (((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8) = $true) | ($true = (X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8)))) | (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) & ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true)))),
% 1.51/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f9,f12,f11,f10])).
% 1.51/1.32 thf(f10,plain,(
% 1.51/1.32 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X3 : $i > $o,X4 : $i > $o,X5 : $i > $o] : (! [X6 : $i] : (((X0 @ X3 @ X5 @ X6) = $true) | ($true = (X1 @ X3 @ X5 @ X6))) & ? [X7 : $i] : (((X0 @ X4 @ X5 @ X7) != $true) & ($true != (X1 @ X4 @ X5 @ X7))) & ! [X8 : $i] : (($true = (X0 @ X4 @ X3 @ X8)) | ($true = (X1 @ X4 @ X3 @ X8)))) => (! [X6 : $i] : (($true = (X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6))) & ? [X7 : $i] : (((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7) != $true) & ($true != (X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) & ! [X8 : $i] : (((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8) = $true) | ($true = (X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8)))))),
% 1.51/1.32 introduced(definition,[],[choice_axiom])).
% 1.51/1.32 thf(f11,plain,(
% 1.51/1.32 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X7 : $i] : (((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7) != $true) & ($true != (X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) => (((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) & ($true != (X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))))),
% 1.51/1.32 introduced(definition,[],[choice_axiom])).
% 1.51/1.32 thf(f12,plain,(
% 1.51/1.32 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X9 : $i,X10 : $i > $o] : (((X1 @ X10 @ X10 @ X9) != $true) & ((X0 @ X10 @ X10 @ X9) != $true)) => (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) & ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true)))),
% 1.51/1.32 introduced(definition,[],[choice_axiom])).
% 1.51/1.32 thf(f9,plain,(
% 1.51/1.32 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i] : (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ? [X3 : $i > $o,X4 : $i > $o,X5 : $i > $o] : (! [X6 : $i] : (((X0 @ X3 @ X5 @ X6) = $true) | ($true = (X1 @ X3 @ X5 @ X6))) & ? [X7 : $i] : (((X0 @ X4 @ X5 @ X7) != $true) & ($true != (X1 @ X4 @ X5 @ X7))) & ! [X8 : $i] : (($true = (X0 @ X4 @ X3 @ X8)) | ($true = (X1 @ X4 @ X3 @ X8)))) | ? [X9 : $i,X10 : $i > $o] : (((X1 @ X10 @ X10 @ X9) != $true) & ((X0 @ X10 @ X10 @ X9) != $true)))),
% 1.51/1.32 inference(rectify,[status(thm)],[f8])).
% 1.51/1.32 thf(f8,plain,(
% 1.51/1.32 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i] : (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ? [X3 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (! [X7 : $i] : (((X0 @ X3 @ X4 @ X7) = $true) | ($true = (X1 @ X3 @ X4 @ X7))) & ? [X8 : $i] : (($true != (X0 @ X5 @ X4 @ X8)) & ((X1 @ X5 @ X4 @ X8) != $true)) & ! [X6 : $i] : (((X0 @ X5 @ X3 @ X6) = $true) | ($true = (X1 @ X5 @ X3 @ X6)))) | ? [X10 : $i,X9 : $i > $o] : (($true != (X1 @ X9 @ X9 @ X10)) & ($true != (X0 @ X9 @ X9 @ X10))))),
% 1.51/1.32 inference(flattening,[status(thm)],[f7])).
% 1.51/1.32 thf(f7,plain,(
% 1.51/1.32 ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (? [X3 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (? [X8 : $i] : (($true != (X0 @ X5 @ X4 @ X8)) & ((X1 @ X5 @ X4 @ X8) != $true)) & (! [X6 : $i] : (((X0 @ X5 @ X3 @ X6) = $true) | ($true = (X1 @ X5 @ X3 @ X6))) & ! [X7 : $i] : (((X0 @ X3 @ X4 @ X7) = $true) | ($true = (X1 @ X3 @ X4 @ X7))))) | ? [X10 : $i,X9 : $i > $o] : (($true != (X1 @ X9 @ X9 @ X10)) & ($true != (X0 @ X9 @ X9 @ X10))) | ! [X2 : $i] : (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2))))),
% 1.51/1.32 inference(ennf_transformation,[status(thm)],[f6])).
% 1.51/1.32 thf(f6,plain,(
% 1.51/1.32 ~? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X3 : $i > $o,X5 : $i > $o,X4 : $i > $o] : ((! [X6 : $i] : (((X0 @ X5 @ X3 @ X6) = $true) | ($true = (X1 @ X5 @ X3 @ X6))) & ! [X7 : $i] : (((X0 @ X3 @ X4 @ X7) = $true) | ($true = (X1 @ X3 @ X4 @ X7)))) => ! [X8 : $i] : (((X1 @ X5 @ X4 @ X8) = $true) | ($true = (X0 @ X5 @ X4 @ X8)))) & ! [X9 : $i > $o,X10 : $i] : (($true = (X1 @ X9 @ X9 @ X10)) | ($true = (X0 @ X9 @ X9 @ X10))) & ~! [X2 : $i] : (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2))))),
% 1.51/1.32 inference(rectify,[status(thm)],[f5])).
% 1.51/1.32 thf(f5,plain,(
% 1.51/1.32 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X2 : $i] : (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) & ! [X7 : $i > $o,X8 : $i > $o,X9 : $i > $o] : ((! [X10 : $i] : (((X1 @ X9 @ X7 @ X10) = $true) | ($true = (X0 @ X9 @ X7 @ X10))) & ! [X11 : $i] : (($true = (X1 @ X7 @ X8 @ X11)) | ($true = (X0 @ X7 @ X8 @ X11)))) => ! [X12 : $i] : (((X1 @ X9 @ X8 @ X12) = $true) | ($true = (X0 @ X9 @ X8 @ X12)))) & ! [X13 : $i > $o,X14 : $i] : (((X1 @ X13 @ X13 @ X14) = $true) | ($true = (X0 @ X13 @ X13 @ X14))))),
% 1.51/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.32 thf(f4,plain,(
% 1.51/1.32 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X2 : $i] : ((X0 @ (^[X3 : $i] : (p | ~p)) @ (^[X4 : $i] : (~p & p)) @ X2) | (X1 @ (^[X5 : $i] : (p | ~p)) @ (^[X6 : $i] : (~p & p)) @ X2)) & ! [X7 : $i > $o,X8 : $i > $o,X9 : $i > $o] : ((! [X10 : $i] : ((X1 @ X9 @ X7 @ X10) | (X0 @ X9 @ X7 @ X10)) & ! [X11 : $i] : ((X1 @ X7 @ X8 @ X11) | (X0 @ X7 @ X8 @ X11))) => ! [X12 : $i] : ((X1 @ X9 @ X8 @ X12) | (X0 @ X9 @ X8 @ X12))) & ! [X13 : $i > $o,X14 : $i] : ((X1 @ X13 @ X13 @ X14) | (X0 @ X13 @ X13 @ X14)))),
% 1.51/1.32 inference(rectify,[status(thm)],[f2])).
% 1.51/1.32 thf(f2,negated_conjecture,(
% 1.51/1.32 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X5 : $i] : ((X0 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (~p & p)) @ X5) | (X1 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (~p & p)) @ X5)) & ! [X3 : $i > $o,X4 : $i > $o,X2 : $i > $o] : ((! [X5 : $i] : ((X1 @ X2 @ X3 @ X5) | (X0 @ X2 @ X3 @ X5)) & ! [X5 : $i] : ((X1 @ X3 @ X4 @ X5) | (X0 @ X3 @ X4 @ X5))) => ! [X5 : $i] : ((X1 @ X2 @ X4 @ X5) | (X0 @ X2 @ X4 @ X5))) & ! [X2 : $i > $o,X5 : $i] : ((X1 @ X2 @ X2 @ X5) | (X0 @ X2 @ X2 @ X5)))),
% 1.51/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.32 thf(f1,conjecture,(
% 1.51/1.32 ? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X5 : $i] : ((X0 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (~p & p)) @ X5) | (X1 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (~p & p)) @ X5)) & ! [X3 : $i > $o,X4 : $i > $o,X2 : $i > $o] : ((! [X5 : $i] : ((X1 @ X2 @ X3 @ X5) | (X0 @ X2 @ X3 @ X5)) & ! [X5 : $i] : ((X1 @ X3 @ X4 @ X5) | (X0 @ X3 @ X4 @ X5))) => ! [X5 : $i] : ((X1 @ X2 @ X4 @ X5) | (X0 @ X2 @ X4 @ X5))) & ! [X2 : $i > $o,X5 : $i] : ((X1 @ X2 @ X2 @ X5) | (X0 @ X2 @ X2 @ X5)))),
% 1.51/1.32 file('/export/starexec/sandbox/tmp/tmp.zrxScirKMq/DTF2THF_27682.p',cTHM120F_pme)).
% 1.51/1.32 thf(f45,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true)) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f44])).
% 1.51/1.32 thf(f44,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true != (X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) | ($true = (X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true)) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f43])).
% 1.51/1.32 thf(f43,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ($true != (X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X2))) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f42])).
% 1.51/1.32 thf(f42,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2)) | ($true = (X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true)) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f17])).
% 1.51/1.32 thf(f17,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) | ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) )),
% 1.51/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.32 thf(f376,plain,(
% 1.51/1.32 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | spl6_1),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f375])).
% 1.51/1.32 thf(f375,plain,(
% 1.51/1.32 ($false = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | spl6_1),
% 1.51/1.32 inference(duplicate_literal_removal,[status(thm)],[f374])).
% 1.51/1.32 thf(f374,plain,(
% 1.51/1.32 ($false = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($false = $true) | spl6_1),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f372])).
% 1.51/1.32 thf(f372,plain,(
% 1.51/1.32 ( ! [X2 : $i,X6 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X6) = $true)) ) | spl6_1),
% 1.51/1.32 inference(primitive_instantiation,[status(thm)],[f241])).
% 1.51/1.32 thf(f241,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6)) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) ) | spl6_1),
% 1.51/1.32 inference(subsumption_resolution,[status(thm)],[f240,f75])).
% 1.51/1.32 thf(f240,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) )),
% 1.51/1.32 inference(equality_proxy_clausification,[status(thm)],[f239])).
% 1.51/1.32 thf(f239,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )),
% 1.51/1.32 inference(equality_proxy_clausification,[status(thm)],[f238])).
% 1.51/1.32 thf(f238,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : ((((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f237])).
% 1.51/1.32 thf(f237,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true != $true) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6)) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f236])).
% 1.51/1.32 thf(f236,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : ((((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | ($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6))) )),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f216])).
% 1.51/1.32 thf(f216,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)))) )),
% 1.51/1.32 inference(primitive_instantiation,[status(thm)],[f33])).
% 1.51/1.32 thf(f33,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6))) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f32])).
% 1.51/1.32 thf(f32,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6))) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f31])).
% 1.51/1.32 thf(f31,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ($true = (X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6))) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f30])).
% 1.51/1.32 thf(f30,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ($true = (X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ($true = (X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) )),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f21])).
% 1.51/1.32 thf(f21,plain,(
% 1.51/1.32 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)) != $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ($true = (X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2)) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ($true = (X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6))) )),
% 1.51/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.32 % SZS output end Proof for DTF2THF_27682
% 1.51/1.32 % (27798)------------------------------
% 1.51/1.32 % (27798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.32 % (27798)Termination reason: Refutation
% 1.51/1.32
% 1.51/1.32 % (27798)Memory used [KB]: 6012
% 1.51/1.32 % (27798)Time elapsed: 0.028 s
% 1.51/1.32 % (27798)Instructions burned: 76 (million)
% 1.51/1.32 % (27798)------------------------------
% 1.51/1.32 % (27798)------------------------------
% 1.51/1.32 % (27792)Success in time 0.046 s
%------------------------------------------------------------------------------