%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU874^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 09:37:38 AM UTC 2026
% Result : Theorem 1.61s 1.32s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 12
% Syntax : Number of formulae : 144 ( 9 unt; 0 typ; 11 def)
% Number of atoms : 1566 ( 605 equ; 19 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 2169 ( 205 ~; 621 |; 62 &;1051 @)
% ( 11 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 245 ( 245 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 20 usr; 17 con; 0-2 aty)
% ( 92 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 467 ( 313 ^; 151 !; 3 ?; 467 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cX: a > $o ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
sK2: a ).
thf(func_def_20,type,
sK3: ( a > $o ) > a ).
thf(func_def_21,type,
sK4: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_22,type,
sK5: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_23,type,
sK6: a > $o ).
thf(func_def_24,type,
sK7: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_25,type,
sK8: ( ( a > $o ) > $o ) > a ).
thf(f523,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f73,f78,f98,f102,f106,f110,f114,f118,f121,f301,f504,f522]) ).
thf(f522,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f521]) ).
thf(f521,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f517]) ).
thf(f517,plain,
( ( $true = $false )
| ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f510,f77]) ).
thf(f77,plain,
( ( ( sK6 @ sK2 )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f75]) ).
thf(f75,definition,
( spl0_3
<=> ( ( sK6 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f510,plain,
( ( ( sK6 @ sK2 )
= $false )
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f508]) ).
thf(f508,plain,
( ( ( sK6 @ sK2 )
= $false )
| ( $true != $true )
| ~ spl0_1
| spl0_2 ),
inference(superposition,[status(thm)],[f71,f68]) ).
thf(f68,plain,
( ! [X1: a] :
( ( $true
= ( cX @ X1 ) )
| ( $false
= ( sK6 @ X1 ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f67,definition,
( spl0_1
<=> ! [X1: a] :
( ( $true
= ( cX @ X1 ) )
| ( $false
= ( sK6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f71,plain,
( ( $true
!= ( cX @ sK2 ) )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f70,definition,
( spl0_2
<=> ( $true
= ( cX @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f504,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f503]) ).
thf(f503,plain,
( $false
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f502]) ).
thf(f502,plain,
( ( sK2 != sK2 )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(duplicate_literal_removal,[status(thm)],[f500]) ).
thf(f500,plain,
( ( sK2 != sK2 )
| ( sK2 != sK2 )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(superposition,[status(thm)],[f130,f332]) ).
thf(f332,plain,
( ! [X0: a] :
( ( ( sK3 @ ( (=) @ X0 ) )
= X0 )
| ( sK2 != X0 ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(duplicate_literal_removal,[status(thm)],[f331]) ).
thf(f331,plain,
( ! [X0: a] :
( ( ( sK3 @ ( (=) @ X0 ) )
= X0 )
| ( sK2 != X0 )
| ( ( sK3 @ ( (=) @ X0 ) )
= X0 ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(equality_proxy_clausification,[status(thm)],[f330]) ).
thf(f330,plain,
( ! [X0: a] :
( ( sK2 != X0 )
| ( ( sK3 @ ( (=) @ X0 ) )
= X0 )
| ( $true
= ( X0
= ( sK3 @ ( (=) @ X0 ) ) ) ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(duplicate_literal_removal,[status(thm)],[f329]) ).
thf(f329,plain,
( ! [X0: a] :
( ( $true
= ( X0
= ( sK3 @ ( (=) @ X0 ) ) ) )
| ( ( sK3 @ ( (=) @ X0 ) )
= X0 )
| ( sK2 != X0 )
| ( sK2 != X0 ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(equality_proxy_clausification,[status(thm)],[f328]) ).
thf(f328,plain,
( ! [X0: a] :
( ( ( sK3 @ ( (=) @ X0 ) )
= X0 )
| ( sK2 != X0 )
| ( ( X0 = sK2 )
= $false )
| ( $true
= ( X0
= ( sK3 @ ( (=) @ X0 ) ) ) ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f327]) ).
thf(f327,plain,
( ! [X0: a] :
( ( $false
= ( ( X0 = sK2 )
| $false ) )
| ( $true
= ( X0
= ( sK3 @ ( (=) @ X0 ) ) ) )
| ( ( sK3 @ ( (=) @ X0 ) )
= X0 )
| ( sK2 != X0 ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f326]) ).
thf(f326,plain,
( ! [X0: a] :
( ( $true
= ( X0
= ( sK3 @ ( (=) @ X0 ) ) ) )
| ( ( sK3
@ ^ [Y0: a] : ( X0 = Y0 ) )
= X0 )
| ( $false
= ( ( X0 = sK2 )
| $false ) )
| ( sK2 != X0 ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f325]) ).
thf(f325,plain,
( ! [X0: a] :
( ( sK2 != X0 )
| ( ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| $false ) )
= X0 )
| ( $false
= ( ( X0 = sK2 )
| $false ) )
| ( $true
= ( X0
= ( sK3 @ ( (=) @ X0 ) ) ) ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f324]) ).
thf(f324,plain,
( ! [X0: a] :
( ( $false
= ( ( X0 = sK2 )
| $false ) )
| ( ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| $false ) )
= X0 )
| ( sK2 != X0 )
| ( $true
= ( X0
= ( sK3
@ ^ [Y0: a] : ( X0 = Y0 ) ) ) ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f323]) ).
thf(f323,plain,
( ! [X0: a] :
( ( $true
= ( X0
= ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| $false ) ) ) )
| ( ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| $false ) )
= X0 )
| ( $false
= ( ( X0 = sK2 )
| $false ) )
| ( sK2 != X0 ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f322]) ).
thf(f322,plain,
( ! [X0: a] :
( ( $true
= ( ( X0
= ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| $false ) ) )
| $false ) )
| ( $false
= ( ( X0 = sK2 )
| $false ) )
| ( sK2 != X0 )
| ( ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| $false ) )
= X0 ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f321]) ).
thf(f321,plain,
( ! [X0: a] :
( ( sK2 != X0 )
| ( $true = $false )
| ( $false
= ( ( X0 = sK2 )
| $false ) )
| ( ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| $false ) )
= X0 )
| ( $true
= ( ( X0
= ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| $false ) ) )
| $false ) ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f320]) ).
thf(f320,plain,
( ! [X0: a] :
( ( ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) ) )
= X0 )
| ( $true
= ( ^ [Y0: a] : $false
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) )
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) ) ) ) )
| ( sK2 != X0 )
| ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) )
@ sK2 ) ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f306]) ).
thf(f306,plain,
( ! [X0: a] :
( ( sK2 != X0 )
| ( $true
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) )
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) ) ) ) )
| ( $true = $false )
| ( ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) ) )
= X0 )
| ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: a] : $false
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) ) ) ) ) )
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f117,f201]) ).
thf(f201,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( X1
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( sK2 != X0 )
| ( ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) )
= X0 ) )
| ~ spl0_11
| ~ spl0_12 ),
inference(equality_proxy_clausification,[status(thm)],[f200]) ).
thf(f200,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( X0
= ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $true
= ( X1
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( sK2 != X0 ) )
| ~ spl0_11
| ~ spl0_12 ),
inference(equality_proxy_clausification,[status(thm)],[f199]) ).
thf(f199,plain,
( ! [X0: a,X1: a > $o] :
( ( $true
= ( X1
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( ( X0 = sK2 )
= $false )
| ( $false
= ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( X0
= ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) ) )
| ~ spl0_11
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f198]) ).
thf(f198,plain,
( ! [X0: a,X1: a > $o] :
( ( ( ( X0
= ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) )
| ( X1
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( ( X0 = sK2 )
= $false ) )
| ~ spl0_11
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f196]) ).
thf(f196,plain,
( ! [X0: a,X1: a > $o] :
( ( ( ( X0 = sK2 )
| ( X1 @ sK2 ) )
= $false )
| ( ( ( X0
= ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) )
| ( X1
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) ) )
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f195]) ).
thf(f195,plain,
( ! [X0: a,X1: a > $o] :
( ( ( ( X0 = sK2 )
| ( X1 @ sK2 ) )
= $false )
| ( ( ( X0
= ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) )
| ( X1
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
= $true )
| ( $true = $false )
| ( $false
= ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) ) )
| ~ spl0_11
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f194]) ).
thf(f194,plain,
( ! [X0: a,X1: a > $o] :
( ( ( ( X0 = sK2 )
| ( X1 @ sK2 ) )
= $false )
| ( $false
= ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( $true
| ( X1 @ X0 ) ) )
| ( ( ( X0
= ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) )
| ( X1
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
= $true ) )
| ~ spl0_11
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f193]) ).
thf(f193,plain,
( ! [X0: a,X1: a > $o] :
( ( ( ( X0 = sK2 )
| ( X1 @ sK2 ) )
= $false )
| ( ( ( X0 = X0 )
| ( X1 @ X0 ) )
= $false )
| ( $false
= ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( ( ( X0
= ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) )
| ( X1
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
= $true ) )
| ~ spl0_11
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f192]) ).
thf(f192,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X0 ) )
| ( $false
= ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) ) )
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f191]) ).
thf(f191,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $true = $false )
| ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X0 ) ) )
| ~ spl0_11
| ~ spl0_12 ),
inference(duplicate_literal_removal,[status(thm)],[f176]) ).
thf(f176,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X0 ) )
| ( $true
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $true = $false )
| ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ sK2 ) ) )
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f113,f109]) ).
thf(f109,plain,
( ! [X1: a > $o] :
( ( ( sK4 @ X1 @ X1 )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f108]) ).
thf(f108,definition,
( spl0_11
<=> ! [X1: a > $o] :
( ( ( sK4 @ X1 @ X1 )
= $false )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( X1 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f113,plain,
( ! [X2: a > $o,X3: a,X1: a > $o] :
( ( $true
= ( sK4 @ X1
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( X1 @ sK2 ) )
| ( ( sK4 @ X1 @ X2 )
= $false )
| ( $false
= ( X1 @ X3 ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f112]) ).
thf(f112,definition,
( spl0_12
<=> ! [X2: a > $o,X1: a > $o,X3: a] :
( ( $true
= ( sK4 @ X1
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) ) )
| ( $false
= ( X1 @ X3 ) )
| ( ( sK4 @ X1 @ X2 )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f117,plain,
( ! [X1: a > $o] :
( ( $true
= ( sK4 @ X1
@ ^ [Y0: a] : $false ) )
| ( $false
= ( X1 @ sK2 ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f116]) ).
thf(f116,definition,
( spl0_13
<=> ! [X1: a > $o] :
( ( $true
= ( sK4 @ X1
@ ^ [Y0: a] : $false ) )
| ( $false
= ( X1 @ sK2 ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f130,plain,
( ( sK2
!= ( sK3 @ ( (=) @ sK2 ) ) )
| spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f129]) ).
thf(f129,definition,
( spl0_15
<=> ( sK2
= ( sK3 @ ( (=) @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f301,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f300]) ).
thf(f300,plain,
( $false
| spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(subsumption_resolution,[status(thm)],[f299,f93]) ).
thf(f93,plain,
( ( $false
!= ( cX @ sK2 ) )
| spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f92,definition,
( spl0_7
<=> ( $false
= ( cX @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f299,plain,
( ( $false
= ( cX @ sK2 ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f298]) ).
thf(f298,plain,
( ( $false
= ( cX @ sK2 ) )
| ( sK2 != sK2 )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f252,f131]) ).
thf(f131,plain,
( ( sK2
= ( sK3 @ ( (=) @ sK2 ) ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f129]) ).
thf(f252,plain,
( ! [X0: a] :
( ( $false
= ( cX @ ( sK3 @ ( (=) @ X0 ) ) ) )
| ( sK2 != X0 ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(duplicate_literal_removal,[status(thm)],[f251]) ).
thf(f251,plain,
( ! [X0: a] :
( ( sK2 != X0 )
| ( sK2 != X0 )
| ( $false
= ( cX @ ( sK3 @ ( (=) @ X0 ) ) ) ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(equality_proxy_clausification,[status(thm)],[f250]) ).
thf(f250,plain,
( ! [X0: a] :
( ( ( X0 = sK2 )
= $false )
| ( $false
= ( cX @ ( sK3 @ ( (=) @ X0 ) ) ) )
| ( sK2 != X0 ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f249]) ).
thf(f249,plain,
( ! [X0: a] :
( ( ( cX
@ ( sK3
@ ^ [Y0: a] : ( X0 = Y0 ) ) )
= $false )
| ( ( X0 = sK2 )
= $false )
| ( sK2 != X0 ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f248]) ).
thf(f248,plain,
( ! [X0: a] :
( ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| $false ) ) ) )
| ( ( X0 = sK2 )
= $false )
| ( sK2 != X0 ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f247]) ).
thf(f247,plain,
( ! [X0: a] :
( ( $false
= ( ( X0 = sK2 )
| $false ) )
| ( sK2 != X0 )
| ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| $false ) ) ) ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f246]) ).
thf(f246,plain,
( ! [X0: a] :
( ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) )
@ sK2 ) )
| ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) ) ) ) )
| ( sK2 != X0 ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f245]) ).
thf(f245,plain,
( ! [X0: a] :
( ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) )
@ sK2 ) )
| ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) ) ) ) )
| ( sK2 != X0 )
| ( $true = $false ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(duplicate_literal_removal,[status(thm)],[f208]) ).
thf(f208,plain,
( ! [X0: a] :
( ( $true = $false )
| ( sK2 != X0 )
| ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) )
@ sK2 ) )
| ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) ) ) ) ) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f105,f174]) ).
thf(f174,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( sK5
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( sK2 != X0 ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(equality_proxy_clausification,[status(thm)],[f173]) ).
thf(f173,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( sK5
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( ( X0 = sK2 )
= $false ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f171]) ).
thf(f171,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( sK5
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( ( ( X0 = sK2 )
| ( X1 @ sK2 ) )
= $false )
| ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f170]) ).
thf(f170,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $false
= ( sK5
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $true = $false )
| ( ( ( X0 = sK2 )
| ( X1 @ sK2 ) )
= $false ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f169]) ).
thf(f169,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( $true
| ( X1 @ X0 ) ) )
| ( ( ( X0 = sK2 )
| ( X1 @ sK2 ) )
= $false )
| ( $false
= ( sK5
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f168]) ).
thf(f168,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $false
= ( sK5
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( ( ( X0 = X0 )
| ( X1 @ X0 ) )
= $false )
| ( ( ( X0 = sK2 )
| ( X1 @ sK2 ) )
= $false ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f167]) ).
thf(f167,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X0 ) )
| ( $false
= ( sK5
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f166]) ).
thf(f166,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( sK5
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X0 ) )
| ( $true = $false ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(duplicate_literal_removal,[status(thm)],[f156]) ).
thf(f156,plain,
( ! [X0: a,X1: a > $o] :
( ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X0 ) )
| ( $false
= ( cX
@ ( sK3
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $false
= ( sK5
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ X1 ) )
| ( $true = $false )
| ( $false
= ( ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) )
@ sK2 ) ) )
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f97,f101]) ).
thf(f101,plain,
( ! [X2: a > $o,X3: a,X1: a > $o] :
( ( $true
= ( sK5 @ X1
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) ) )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( X1 @ X3 ) )
| ( ( sK5 @ X1 @ X2 )
= $false )
| ( ( cX @ ( sK3 @ X1 ) )
= $false ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f100]) ).
thf(f100,definition,
( spl0_9
<=> ! [X2: a > $o,X1: a > $o,X3: a] :
( ( ( sK5 @ X1 @ X2 )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( $true
= ( sK5 @ X1
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) ) )
| ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( $false
= ( X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f97,plain,
( ! [X1: a > $o] :
( ( ( sK5 @ X1 @ X1 )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( ( cX @ ( sK3 @ X1 ) )
= $false ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f96]) ).
thf(f96,definition,
( spl0_8
<=> ! [X1: a > $o] :
( ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( ( sK5 @ X1 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f105,plain,
( ! [X1: a > $o] :
( ( ( sK5 @ X1
@ ^ [Y0: a] : $false )
= $true )
| ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( $false
= ( X1 @ sK2 ) ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f104]) ).
thf(f104,definition,
( spl0_10
<=> ! [X1: a > $o] :
( ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( ( sK5 @ X1
@ ^ [Y0: a] : $false )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f121,plain,
( ~ spl0_2
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f120]) ).
thf(f120,plain,
( $false
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f72,f94]) ).
thf(f94,plain,
( ( $false
= ( cX @ sK2 ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f72,plain,
( ( $true
= ( cX @ sK2 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f118,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f25,f92,f116]) ).
thf(f25,plain,
! [X1: a > $o] :
( ( $true
= ( sK4 @ X1
@ ^ [Y0: a] : $false ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( cX @ sK2 ) )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: a > $o] :
( ( $true
= ( X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( cX @ sK2 ) )
| ( $true
= ( ( sK4 @ X1
@ ^ [Y0: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK4 @ X1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( sK4 @ X1
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: a > $o] :
( ( $false
= ( cX @ sK2 ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( ( ( sK4 @ X1
@ ^ [Y0: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK4 @ X1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( sK4 @ X1
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) )
=> ( sK4 @ X1 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: a > $o] :
( ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ X1 ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( cX @ sK2 ) ) ),
inference(sigma_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: a > $o] :
( ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ X1 ) ) ) )
| ( $false
= ( cX @ sK2 ) )
| ( $false
= ( X1 @ sK2 ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: a > $o] :
( ( $false
= ( cX @ sK2 ) )
| ( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ X1 ) ) )
& ( X1 @ sK2 ) )
= $false )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: a > $o] :
( ( $false
= ( ( X1 @ ( sK3 @ X1 ) )
=> ( cX @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( cX @ sK2 ) )
| ( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ X1 ) ) )
& ( X1 @ sK2 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: a > $o] :
( ( $false
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( cX @ Y0 ) )
@ ( sK3 @ X1 ) ) )
| ( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ X1 ) ) )
& ( X1 @ sK2 ) )
= $false )
| ( $false
= ( cX @ sK2 ) ) ),
inference(sigma_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: a > $o] :
( ( $false
= ( cX @ sK2 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( cX @ Y0 ) ) )
= $false )
| ( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ X1 ) ) )
& ( X1 @ sK2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: a > $o] :
( ( $false
= ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ X1 ) ) )
& ( X1 @ sK2 )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( cX @ Y0 ) ) ) ) )
| ( $false
= ( cX @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: a > $o] :
( ( $false
= ( cX @ sK2 ) )
| ( $false
= ( ^ [Y0: a > $o] :
( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( Y0 @ sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cX @ Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $false
= ( cX @ sK2 ) )
| ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( Y0 @ sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cX @ Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( Y0 @ sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cX @ Y1 ) ) ) ) )
!= ( cX @ sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( ( Y2
@ ^ [Y3: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y2
@ ^ [Y5: a] :
( ( Y4 = Y5 )
| ( Y3 @ Y5 ) ) ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cX @ Y2 ) ) ) ) )
@ sK2 )
!= ( cX @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f7]) ).
thf(f7,plain,
( cX
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( ( Y2
@ ^ [Y3: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y2
@ ^ [Y5: a] :
( ( Y4 = Y5 )
| ( Y3 @ Y5 ) ) ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cX @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( cX
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( ( Y2
@ ^ [Y3: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y2
@ ^ [Y5: a] :
( ( Y4 = Y5 )
| ( Y3 @ Y5 ) ) ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cX @ Y2 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( cX
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( ( Y2
@ ^ [Y3: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y2
@ ^ [Y5: a] :
( ( Y4 = Y5 )
| ( Y3 @ Y5 ) ) ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cX @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ^ [X0: a] :
? [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cX @ X2 ) )
& ( X1 @ X0 )
& ! [X3: ( a > $o ) > $o] :
( ( ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X1 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ( X4 @ X6 )
| ( X5 = X6 ) ) ) ) )
& ( X3
@ ^ [X7: a] : $false ) )
=> ( X3 @ X1 ) ) ) )
!= cX ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a] :
? [X1: a > $o] :
( ! [X4: a] :
( ( X1 @ X4 )
=> ( cX @ X4 ) )
& ( X1 @ X0 )
& ! [X2: ( a > $o ) > $o] :
( ( ! [X4: a > $o] :
( ( X2 @ X4 )
=> ! [X5: a] :
( ( X1 @ X5 )
=> ( X2
@ ^ [X6: a] :
( ( X4 @ X6 )
| ( X5 = X6 ) ) ) ) )
& ( X2
@ ^ [X3: a] : $false ) )
=> ( X2 @ X1 ) ) ) )
!= cX ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X0: a] :
? [X1: a > $o] :
( ! [X4: a] :
( ( X1 @ X4 )
=> ( cX @ X4 ) )
& ( X1 @ X0 )
& ! [X2: ( a > $o ) > $o] :
( ( ! [X4: a > $o] :
( ( X2 @ X4 )
=> ! [X5: a] :
( ( X1 @ X5 )
=> ( X2
@ ^ [X6: a] :
( ( X4 @ X6 )
| ( X5 = X6 ) ) ) ) )
& ( X2
@ ^ [X3: a] : $false ) )
=> ( X2 @ X1 ) ) ) )
= cX ),
file('/export/starexec/sandbox2/tmp/tmp.vBFmgqyxdU/DTF2THF_20611.p',cDOMLEMMA3_pme) ).
thf(f114,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f31,f92,f112]) ).
thf(f31,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( $true
= ( sK4 @ X1
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( cX @ sK2 ) )
| ( ( sK4 @ X1 @ X2 )
= $false )
| ( $false
= ( X1 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( $true
= ( ( X1 @ X3 )
=> ( sK4 @ X1
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) ) ) )
| ( ( sK4 @ X1 @ X2 )
= $false )
| ( $false
= ( cX @ sK2 ) )
| ( $false
= ( X1 @ sK2 ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( $false
= ( cX @ sK2 ) )
| ( $false
= ( X1 @ sK2 ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) )
| ( $true
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ X1
@ ^ [Y1: a] :
( ( Y0 = Y1 )
| ( X2 @ Y1 ) ) ) )
@ X3 ) )
| ( ( sK4 @ X1 @ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: a > $o,X1: a > $o] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ X1
@ ^ [Y1: a] :
( ( Y0 = Y1 )
| ( X2 @ Y1 ) ) ) ) ) )
| ( ( sK4 @ X1 @ X2 )
= $false )
| ( $false
= ( cX @ sK2 ) )
| ( $false
= ( X1 @ sK2 ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: a > $o,X1: a > $o] :
( ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( cX @ sK2 ) )
| ( $true
= ( ( sK4 @ X1 @ X2 )
=> ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ X1
@ ^ [Y1: a] :
( ( Y0 = Y1 )
| ( X2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: a > $o,X1: a > $o] :
( ( $false
= ( X1 @ sK2 ) )
| ( $true
= ( ^ [Y0: a > $o] :
( ( sK4 @ X1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( sK4 @ X1
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) )
@ X2 ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( cX @ sK2 ) ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: a > $o] :
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK4 @ X1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( sK4 @ X1
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( cX @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f110,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[status(thm)],[f22,f108,f92]) ).
thf(f22,plain,
! [X1: a > $o] :
( ( $false
= ( cX @ sK2 ) )
| ( ( sK4 @ X1 @ X1 )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f106,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f38,f92,f104]) ).
thf(f38,plain,
! [X1: a > $o] :
( ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( $false
= ( cX @ sK2 ) )
| ( ( sK5 @ X1
@ ^ [Y0: a] : $false )
= $true )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: a > $o] :
( ( $false
= ( cX @ sK2 ) )
| ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( $true
= ( ( sK5 @ X1
@ ^ [Y0: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK5 @ X1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( sK5 @ X1
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: a > $o] :
( ( ( ( ( sK5 @ X1
@ ^ [Y0: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK5 @ X1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( sK5 @ X1
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) )
=> ( sK5 @ X1 @ X1 ) )
= $false )
| ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( $false
= ( cX @ sK2 ) )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: a > $o] :
( ( ( ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ X1 ) )
@ ( sK5 @ X1 ) )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( cX @ sK2 ) )
| ( ( cX @ ( sK3 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: a > $o] :
( ( $false
= ( cX @ sK2 ) )
| ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: a > $o] :
( ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ X1 ) ) )
& ( X1 @ sK2 ) )
= $false )
| ( $false
= ( cX @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f102,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f44,f92,f100]) ).
thf(f44,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( ( sK5 @ X1 @ X2 )
= $false )
| ( $false
= ( X1 @ X3 ) )
| ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( $true
= ( sK5 @ X1
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) ) )
| ( $false
= ( cX @ sK2 ) )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( $false
= ( X1 @ sK2 ) )
| ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( ( ( X1 @ X3 )
=> ( sK5 @ X1
@ ^ [Y0: a] :
( ( X3 = Y0 )
| ( X2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( cX @ sK2 ) )
| ( ( sK5 @ X1 @ X2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( ( sK5 @ X1 @ X2 )
= $false )
| ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK5 @ X1
@ ^ [Y1: a] :
( ( Y0 = Y1 )
| ( X2 @ Y1 ) ) ) )
@ X3 ) )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( cX @ sK2 ) ) ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: a > $o,X1: a > $o] :
( ( ( sK5 @ X1 @ X2 )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK5 @ X1
@ ^ [Y1: a] :
( ( Y0 = Y1 )
| ( X2 @ Y1 ) ) ) ) )
= $true )
| ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( $false
= ( cX @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: a > $o,X1: a > $o] :
( ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( $false
= ( cX @ sK2 ) )
| ( $true
= ( ( sK5 @ X1 @ X2 )
=> ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK5 @ X1
@ ^ [Y1: a] :
( ( Y0 = Y1 )
| ( X2 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: a > $o,X1: a > $o] :
( ( $true
= ( ^ [Y0: a > $o] :
( ( sK5 @ X1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( sK5 @ X1
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) )
@ X2 ) )
| ( $false
= ( cX @ sK2 ) )
| ( $false
= ( X1 @ sK2 ) )
| ( ( cX @ ( sK3 @ X1 ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: a > $o] :
( ( $false
= ( cX @ sK2 ) )
| ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( $false
= ( X1 @ sK2 ) )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK5 @ X1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( sK5 @ X1
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f98,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f35,f96,f92]) ).
thf(f35,plain,
! [X1: a > $o] :
( ( $false
= ( cX @ sK2 ) )
| ( ( cX @ ( sK3 @ X1 ) )
= $false )
| ( ( sK5 @ X1 @ X1 )
= $false )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f78,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f49,f70,f75]) ).
thf(f49,plain,
( ( $true
= ( cX @ sK2 ) )
| ( ( sK6 @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $true
= ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK6 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ sK6 ) ) )
& ( sK6 @ sK2 ) ) )
| ( $true
= ( cX @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $true
= ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK6 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ sK6 ) ) )
& ( sK6 @ sK2 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( cX @ Y0 ) ) ) ) )
| ( $true
= ( cX @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $true
= ( cX @ sK2 ) )
| ( $true
= ( ^ [Y0: a > $o] :
( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( Y0 @ sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cX @ Y1 ) ) ) )
@ sK6 ) ) ),
inference(sigma_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( $true
= ( cX @ sK2 ) )
| ( $true
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( Y0 @ sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cX @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f73,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f65,f70,f67]) ).
thf(f65,plain,
! [X1: a] :
( ( $true
= ( cX @ sK2 ) )
| ( $true
= ( cX @ X1 ) )
| ( $false
= ( sK6 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X1: a] :
( ( ( ( sK6 @ X1 )
=> ( cX @ X1 ) )
= $true )
| ( $true
= ( cX @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( cX @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( cX @ sK2 ) ) ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true
= ( cX @ sK2 ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( cX @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU874^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:36:35 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEU874^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Set Theory (Finite sets)
% 0.19/0.46 % Problem : TPS problem from SET-TOPOLOGY-THMS
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0922 [Bro09]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.43 v7.4.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.67 v5.4.0, 1.00 v5.3.0, 0.80 v5.2.0, 1.00 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 3 ( 1 unt; 2 typ; 0 def)
% 0.19/0.46 % Number of atoms : 5 ( 2 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 1 ( 5 avg)
% 0.19/0.46 % Number of connectives : 17 ( 0 ~; 1 |; 3 &; 9 @)
% 0.19/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 1 ( 1 avg)
% 0.19/0.46 % Number of types : 2 ( 1 usr)
% 0.19/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% 0.19/0.46 % Number of variables : 8 ( 3 ^; 4 !; 1 ?; 8 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(a_type,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(cX,type,
% 0.19/0.46 cX: a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cDOMLEMMA3_pme,conjecture,
% 0.19/0.46 ( cX
% 0.19/0.46 = ( ^ [Xx: a] :
% 0.19/0.46 ? [S: a > $o] :
% 0.19/0.46 ( ! [X0: ( a > $o ) > $o] :
% 0.19/0.46 ( ( ( X0
% 0.19/0.46 @ ^ [Xy: a] : $false )
% 0.19/0.46 & ! [Xx0: a > $o] :
% 0.19/0.46 ( ( X0 @ Xx0 )
% 0.19/0.46 => ! [Xt: a] :
% 0.19/0.46 ( ( S @ Xt )
% 0.19/0.46 => ( X0
% 0.19/0.46 @ ^ [Xz: a] :
% 0.19/0.46 ( ( Xx0 @ Xz )
% 0.19/0.46 | ( Xt = Xz ) ) ) ) ) )
% 0.19/0.46 => ( X0 @ S ) )
% 0.19/0.46 & ! [Xx0: a] :
% 0.19/0.46 ( ( S @ Xx0 )
% 0.19/0.46 => ( cX @ Xx0 ) )
% 0.19/0.46 & ( S @ Xx ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.44/1.27 ---- Embedded in THF ---
% 1.44/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.27 %%% Generated on Tue Feb 24 12:36:36 EST 2026
% 1.44/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.27 %%% Logic specification used:
% 1.44/1.27 %%% thf(spec, logic, $$dhol).
% 1.44/1.27
% 1.44/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.vBFmgqyxdU/DTF2DTF20611.p
% See solution above
% 1.44/1.27 ------------------------
% 1.44/1.28 ---- Cleaned THF ---
% 1.44/1.28 thf(a_type,type,
% 1.44/1.28 a: $tType ).
% 1.44/1.28
% 1.44/1.28 thf(cX,type,
% 1.44/1.28 cX: a > $o ).
% 1.44/1.28
% 1.44/1.28 thf(cDOMLEMMA3_pme,conjecture,
% 1.44/1.28 ( cX
% 1.44/1.28 = ( ^ [Xx: a] :
% 1.44/1.28 ? [S: a > $o] :
% 1.44/1.28 ( ! [X0: ( a > $o ) > $o] :
% 1.44/1.28 ( ( ( X0
% 1.44/1.28 @ ^ [Xy: a] : $false )
% 1.44/1.28 & ! [Xx0: a > $o] :
% 1.44/1.28 ( ( X0 @ Xx0 )
% 1.44/1.28 => ! [Xt: a] :
% 1.44/1.28 ( ( S @ Xt )
% 1.44/1.28 => ( X0
% 1.44/1.28 @ ^ [Xz: a] :
% 1.44/1.28 ( ( Xx0 @ Xz )
% 1.44/1.28 | ( Xt = Xz ) ) ) ) ) )
% 1.44/1.28 => ( X0 @ S ) )
% 1.44/1.28 & ! [Xx0: a] :
% 1.44/1.28 ( ( S @ Xx0 )
% 1.44/1.28 => ( cX @ Xx0 ) )
% 1.44/1.28 & ( S @ Xx ) ) ) ) ).
% 1.44/1.28 ------------------------
% 1.44/1.29 % (20780)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_20611 for (2999ds/275Mi)
% 1.44/1.29 % (20777)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_20611 for (2999ds/27Mi)
% 1.44/1.29 % (20778)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20611 for (2999ds/2Mi)
% 1.44/1.30 % (20778)Instruction limit reached!
% 1.44/1.30 % (20778)------------------------------
% 1.44/1.30 % (20778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.30 % (20778)Termination reason: Unknown
% 1.44/1.30 % (20778)Termination phase: Saturation
% 1.44/1.30
% 1.44/1.30 % (20778)Memory used [KB]: 5500
% 1.44/1.30 % (20778)Time elapsed: 0.003 s
% 1.44/1.30 % (20778)Instructions burned: 2 (million)
% 1.44/1.30 % (20778)------------------------------
% 1.44/1.30 % (20778)------------------------------
% 1.61/1.30 % (20775)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20611 for (2999ds/183Mi)
% 1.61/1.30 % (20776)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_20611 for (2999ds/4Mi)
% 1.61/1.30 % (20781)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20611 for (2999ds/18Mi)
% 1.61/1.30 % (20779)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_20611 for (2999ds/2Mi)
% 1.61/1.30 % (20779)Instruction limit reached!
% 1.61/1.30 % (20779)------------------------------
% 1.61/1.30 % (20779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (20779)Termination reason: Unknown
% 1.61/1.30 % (20779)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (20779)Memory used [KB]: 5500
% 1.61/1.30 % (20779)Time elapsed: 0.004 s
% 1.61/1.30 % (20779)Instructions burned: 2 (million)
% 1.61/1.30 % (20779)------------------------------
% 1.61/1.30 % (20779)------------------------------
% 1.61/1.30 % (20776)Instruction limit reached!
% 1.61/1.30 % (20776)------------------------------
% 1.61/1.30 % (20776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (20776)Termination reason: Unknown
% 1.61/1.30 % (20776)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (20776)Memory used [KB]: 5500
% 1.61/1.30 % (20776)Time elapsed: 0.005 s
% 1.61/1.30 % (20776)Instructions burned: 5 (million)
% 1.61/1.30 % (20776)------------------------------
% 1.61/1.30 % (20776)------------------------------
% 1.61/1.30 % (20777)Instruction limit reached!
% 1.61/1.30 % (20777)------------------------------
% 1.61/1.30 % (20777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (20777)Termination reason: Unknown
% 1.61/1.30 % (20777)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (20777)Memory used [KB]: 5628
% 1.61/1.30 % (20777)Time elapsed: 0.011 s
% 1.61/1.30 % (20777)Instructions burned: 28 (million)
% 1.61/1.30 % (20777)------------------------------
% 1.61/1.30 % (20777)------------------------------
% 1.61/1.31 % (20781)Instruction limit reached!
% 1.61/1.31 % (20781)------------------------------
% 1.61/1.31 % (20781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (20781)Termination reason: Unknown
% 1.61/1.31 % (20781)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (20781)Memory used [KB]: 5628
% 1.61/1.31 % (20781)Time elapsed: 0.013 s
% 1.61/1.31 % (20781)Instructions burned: 18 (million)
% 1.61/1.31 % (20781)------------------------------
% 1.61/1.31 % (20781)------------------------------
% 1.61/1.31 % (20785)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_20611 for (2999ds/3Mi)
% 1.61/1.31 % (20780)First to succeed.
% 1.61/1.31 % (20785)Refutation not found, incomplete strategy
% 1.61/1.31 % (20785)------------------------------
% 1.61/1.31 % (20785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (20785)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.31
% 1.61/1.31
% 1.61/1.31 % (20785)Memory used [KB]: 5500
% 1.61/1.31 % (20785)Time elapsed: 0.002 s
% 1.61/1.31 % (20785)Instructions burned: 1 (million)
% 1.61/1.31 % (20785)------------------------------
% 1.61/1.31 % (20785)------------------------------
% 1.61/1.31 % (20782)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20611 for (2999ds/3Mi)
% 1.61/1.32 % (20780)Refutation found. Thanks to Tanya!
% 1.61/1.32 % SZS status Theorem for DTF2THF_20611
% 1.61/1.32 % SZS output start Proof for DTF2THF_20611
% 1.61/1.32 thf(type_def_5, type, a: $tType).
% 1.61/1.32 thf(func_def_0, type, a: $tType).
% 1.61/1.32 thf(func_def_1, type, cX: a > $o).
% 1.61/1.32 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 1.61/1.32 thf(func_def_19, type, sK2: a).
% 1.61/1.32 thf(func_def_20, type, sK3: (a > $o) > a).
% 1.61/1.32 thf(func_def_21, type, sK4: (a > $o) > (a > $o) > $o).
% 1.61/1.32 thf(func_def_22, type, sK5: (a > $o) > (a > $o) > $o).
% 1.61/1.32 thf(func_def_23, type, sK6: a > $o).
% 1.61/1.32 thf(func_def_24, type, sK7: ((a > $o) > $o) > a > $o).
% 1.61/1.32 thf(func_def_25, type, sK8: ((a > $o) > $o) > a).
% 1.61/1.32 thf(f523,plain,(
% 1.61/1.32 $false),
% 1.61/1.32 inference(avatar_sat_refutation,[status(thm)],[f73,f78,f98,f102,f106,f110,f114,f118,f121,f301,f504,f522])).
% 1.61/1.32 thf(f522,plain,(
% 1.61/1.32 ~spl0_1 | spl0_2 | ~spl0_3),
% 1.61/1.32 inference(avatar_contradiction_clause,[status(thm)],[f521])).
% 1.61/1.32 thf(f521,plain,(
% 1.61/1.32 $false | (~spl0_1 | spl0_2 | ~spl0_3)),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f517])).
% 1.61/1.32 thf(f517,plain,(
% 1.61/1.32 ($true = $false) | (~spl0_1 | spl0_2 | ~spl0_3)),
% 1.61/1.32 inference(superposition,[status(thm)],[f510,f77])).
% 1.61/1.32 thf(f77,plain,(
% 1.61/1.32 ((sK6 @ sK2) = $true) | ~spl0_3),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f75])).
% 1.61/1.32 thf(f75,definition,(
% 1.61/1.32 spl0_3 <=> ((sK6 @ sK2) = $true)),
% 1.61/1.32 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.61/1.32 thf(f510,plain,(
% 1.61/1.32 ((sK6 @ sK2) = $false) | (~spl0_1 | spl0_2)),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f508])).
% 1.61/1.32 thf(f508,plain,(
% 1.61/1.32 ((sK6 @ sK2) = $false) | ($true != $true) | (~spl0_1 | spl0_2)),
% 1.61/1.32 inference(superposition,[status(thm)],[f71,f68])).
% 1.61/1.32 thf(f68,plain,(
% 1.61/1.32 ( ! [X1 : a] : (($true = (cX @ X1)) | ($false = (sK6 @ X1))) ) | ~spl0_1),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.61/1.32 thf(f67,definition,(
% 1.61/1.32 spl0_1 <=> ! [X1 : a] : (($true = (cX @ X1)) | ($false = (sK6 @ X1)))),
% 1.61/1.32 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.61/1.32 thf(f71,plain,(
% 1.61/1.32 ($true != (cX @ sK2)) | spl0_2),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.61/1.32 thf(f70,definition,(
% 1.61/1.32 spl0_2 <=> ($true = (cX @ sK2))),
% 1.61/1.32 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.61/1.32 thf(f504,plain,(
% 1.61/1.32 ~spl0_11 | ~spl0_12 | ~spl0_13 | spl0_15),
% 1.61/1.32 inference(avatar_contradiction_clause,[status(thm)],[f503])).
% 1.61/1.32 thf(f503,plain,(
% 1.61/1.32 $false | (~spl0_11 | ~spl0_12 | ~spl0_13 | spl0_15)),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f502])).
% 1.61/1.32 thf(f502,plain,(
% 1.61/1.32 (sK2 != sK2) | (~spl0_11 | ~spl0_12 | ~spl0_13 | spl0_15)),
% 1.61/1.32 inference(duplicate_literal_removal,[status(thm)],[f500])).
% 1.61/1.32 thf(f500,plain,(
% 1.61/1.32 (sK2 != sK2) | (sK2 != sK2) | (~spl0_11 | ~spl0_12 | ~spl0_13 | spl0_15)),
% 1.61/1.32 inference(superposition,[status(thm)],[f130,f332])).
% 1.61/1.32 thf(f332,plain,(
% 1.61/1.32 ( ! [X0 : a] : (((sK3 @ (= @ X0)) = X0) | (sK2 != X0)) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(duplicate_literal_removal,[status(thm)],[f331])).
% 1.61/1.32 thf(f331,plain,(
% 1.61/1.32 ( ! [X0 : a] : (((sK3 @ (= @ X0)) = X0) | (sK2 != X0) | ((sK3 @ (= @ X0)) = X0)) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(equality_proxy_clausification,[status(thm)],[f330])).
% 1.61/1.32 thf(f330,plain,(
% 1.61/1.32 ( ! [X0 : a] : ((sK2 != X0) | ((sK3 @ (= @ X0)) = X0) | ($true = (X0 = (sK3 @ (= @ X0))))) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(duplicate_literal_removal,[status(thm)],[f329])).
% 1.61/1.32 thf(f329,plain,(
% 1.61/1.32 ( ! [X0 : a] : (($true = (X0 = (sK3 @ (= @ X0)))) | ((sK3 @ (= @ X0)) = X0) | (sK2 != X0) | (sK2 != X0)) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(equality_proxy_clausification,[status(thm)],[f328])).
% 1.61/1.32 thf(f328,plain,(
% 1.61/1.32 ( ! [X0 : a] : (((sK3 @ (= @ X0)) = X0) | (sK2 != X0) | ((X0 = sK2) = $false) | ($true = (X0 = (sK3 @ (= @ X0))))) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(boolean_simplification,[status(thm)],[f327])).
% 1.61/1.32 thf(f327,plain,(
% 1.61/1.32 ( ! [X0 : a] : (($false = ((X0 = sK2) | $false)) | ($true = (X0 = (sK3 @ (= @ X0)))) | ((sK3 @ (= @ X0)) = X0) | (sK2 != X0)) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f326])).
% 1.61/1.32 thf(f326,plain,(
% 1.61/1.32 ( ! [X0 : a] : (($true = (X0 = (sK3 @ (= @ X0)))) | ((sK3 @ (^[Y0 : a]: (X0 = Y0))) = X0) | ($false = ((X0 = sK2) | $false)) | (sK2 != X0)) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(boolean_simplification,[status(thm)],[f325])).
% 1.61/1.32 thf(f325,plain,(
% 1.61/1.32 ( ! [X0 : a] : ((sK2 != X0) | ((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false))) = X0) | ($false = ((X0 = sK2) | $false)) | ($true = (X0 = (sK3 @ (= @ X0))))) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f324])).
% 1.61/1.32 thf(f324,plain,(
% 1.61/1.32 ( ! [X0 : a] : (($false = ((X0 = sK2) | $false)) | ((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false))) = X0) | (sK2 != X0) | ($true = (X0 = (sK3 @ (^[Y0 : a]: (X0 = Y0)))))) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(boolean_simplification,[status(thm)],[f323])).
% 1.61/1.32 thf(f323,plain,(
% 1.61/1.32 ( ! [X0 : a] : (($true = (X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false))))) | ((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false))) = X0) | ($false = ((X0 = sK2) | $false)) | (sK2 != X0)) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(boolean_simplification,[status(thm)],[f322])).
% 1.61/1.32 thf(f322,plain,(
% 1.61/1.32 ( ! [X0 : a] : (($true = ((X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) | $false)) | ($false = ((X0 = sK2) | $false)) | (sK2 != X0) | ((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false))) = X0)) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f321])).
% 1.61/1.32 thf(f321,plain,(
% 1.61/1.32 ( ! [X0 : a] : ((sK2 != X0) | ($true = $false) | ($false = ((X0 = sK2) | $false)) | ((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false))) = X0) | ($true = ((X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) | $false))) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f320])).
% 1.61/1.32 thf(f320,plain,(
% 1.61/1.32 ( ! [X0 : a] : (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))) = X0) | ($true = ((^[Y0 : a]: ($false)) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) | ($true = ((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) | (sK2 != X0) | ($false = ((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK2))) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f306])).
% 1.61/1.32 thf(f306,plain,(
% 1.61/1.32 ( ! [X0 : a] : ((sK2 != X0) | ($true = ((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) | ($true = $false) | ((sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))) = X0) | ($false = ((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK2)) | ($true = ((^[Y0 : a]: ($false)) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))))) ) | (~spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.61/1.32 inference(superposition,[status(thm)],[f117,f201])).
% 1.61/1.32 thf(f201,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = (sK4 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($true = (X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | (sK2 != X0) | ((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))) = X0)) ) | (~spl0_11 | ~spl0_12)),
% 1.61/1.32 inference(equality_proxy_clausification,[status(thm)],[f200])).
% 1.61/1.32 thf(f200,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = (sK4 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($true = (X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($true = (X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | (sK2 != X0)) ) | (~spl0_11 | ~spl0_12)),
% 1.61/1.32 inference(equality_proxy_clausification,[status(thm)],[f199])).
% 1.61/1.32 thf(f199,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($true = (X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ((X0 = sK2) = $false) | ($false = (sK4 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($true = (X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) ) | (~spl0_11 | ~spl0_12)),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f198])).
% 1.61/1.32 thf(f198,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : ((((X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) | (X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | ($false = (sK4 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ((X0 = sK2) = $false)) ) | (~spl0_11 | ~spl0_12)),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f196])).
% 1.61/1.32 thf(f196,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : ((((X0 = sK2) | (X1 @ sK2)) = $false) | (((X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) | (X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | ($false = (sK4 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1))) ) | (~spl0_11 | ~spl0_12)),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f195])).
% 1.61/1.32 thf(f195,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : ((((X0 = sK2) | (X1 @ sK2)) = $false) | (((X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) | (X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | ($true = $false) | ($false = (sK4 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1))) ) | (~spl0_11 | ~spl0_12)),
% 1.61/1.32 inference(boolean_simplification,[status(thm)],[f194])).
% 1.61/1.32 thf(f194,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : ((((X0 = sK2) | (X1 @ sK2)) = $false) | ($false = (sK4 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($false = ($true | (X1 @ X0))) | (((X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) | (X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true)) ) | (~spl0_11 | ~spl0_12)),
% 1.61/1.32 inference(boolean_simplification,[status(thm)],[f193])).
% 1.61/1.32 thf(f193,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : ((((X0 = sK2) | (X1 @ sK2)) = $false) | (((X0 = X0) | (X1 @ X0)) = $false) | ($false = (sK4 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | (((X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) | (X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true)) ) | (~spl0_11 | ~spl0_12)),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f192])).
% 1.61/1.32 thf(f192,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK2)) | ($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0)) | ($false = (sK4 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($true = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) ) | (~spl0_11 | ~spl0_12)),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f191])).
% 1.61/1.32 thf(f191,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = (sK4 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($true = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($true = $false) | ($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK2)) | ($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0))) ) | (~spl0_11 | ~spl0_12)),
% 1.61/1.32 inference(duplicate_literal_removal,[status(thm)],[f176])).
% 1.61/1.32 thf(f176,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0)) | ($true = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($true = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK2)) | ($false = (sK4 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($true = $false) | ($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK2))) ) | (~spl0_11 | ~spl0_12)),
% 1.61/1.32 inference(superposition,[status(thm)],[f113,f109])).
% 1.61/1.32 thf(f109,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (((sK4 @ X1 @ X1) = $false) | ($false = (X1 @ sK2)) | ($true = (X1 @ (sK3 @ X1)))) ) | ~spl0_11),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f108])).
% 1.61/1.32 thf(f108,definition,(
% 1.61/1.32 spl0_11 <=> ! [X1 : a > $o] : (((sK4 @ X1 @ X1) = $false) | ($true = (X1 @ (sK3 @ X1))) | ($false = (X1 @ sK2)))),
% 1.61/1.32 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.61/1.32 thf(f113,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : (($true = (sK4 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0))))) | ($true = (X1 @ (sK3 @ X1))) | ($false = (X1 @ sK2)) | ((sK4 @ X1 @ X2) = $false) | ($false = (X1 @ X3))) ) | ~spl0_12),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f112])).
% 1.61/1.32 thf(f112,definition,(
% 1.61/1.32 spl0_12 <=> ! [X2 : a > $o,X1 : a > $o,X3 : a] : (($true = (sK4 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0))))) | ($false = (X1 @ X3)) | ((sK4 @ X1 @ X2) = $false) | ($false = (X1 @ sK2)) | ($true = (X1 @ (sK3 @ X1))))),
% 1.61/1.32 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.61/1.32 thf(f117,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($true = (sK4 @ X1 @ (^[Y0 : a]: ($false)))) | ($false = (X1 @ sK2)) | ($true = (X1 @ (sK3 @ X1)))) ) | ~spl0_13),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f116])).
% 1.61/1.32 thf(f116,definition,(
% 1.61/1.32 spl0_13 <=> ! [X1 : a > $o] : (($true = (sK4 @ X1 @ (^[Y0 : a]: ($false)))) | ($false = (X1 @ sK2)) | ($true = (X1 @ (sK3 @ X1))))),
% 1.61/1.32 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.61/1.32 thf(f130,plain,(
% 1.61/1.32 (sK2 != (sK3 @ (= @ sK2))) | spl0_15),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f129])).
% 1.61/1.32 thf(f129,definition,(
% 1.61/1.32 spl0_15 <=> (sK2 = (sK3 @ (= @ sK2)))),
% 1.61/1.32 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 1.61/1.32 thf(f301,plain,(
% 1.61/1.32 spl0_7 | ~spl0_8 | ~spl0_9 | ~spl0_10 | ~spl0_15),
% 1.61/1.32 inference(avatar_contradiction_clause,[status(thm)],[f300])).
% 1.61/1.32 thf(f300,plain,(
% 1.61/1.32 $false | (spl0_7 | ~spl0_8 | ~spl0_9 | ~spl0_10 | ~spl0_15)),
% 1.61/1.32 inference(subsumption_resolution,[status(thm)],[f299,f93])).
% 1.61/1.32 thf(f93,plain,(
% 1.61/1.32 ($false != (cX @ sK2)) | spl0_7),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.61/1.32 thf(f92,definition,(
% 1.61/1.32 spl0_7 <=> ($false = (cX @ sK2))),
% 1.61/1.32 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.61/1.32 thf(f299,plain,(
% 1.61/1.32 ($false = (cX @ sK2)) | (~spl0_8 | ~spl0_9 | ~spl0_10 | ~spl0_15)),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f298])).
% 1.61/1.32 thf(f298,plain,(
% 1.61/1.32 ($false = (cX @ sK2)) | (sK2 != sK2) | (~spl0_8 | ~spl0_9 | ~spl0_10 | ~spl0_15)),
% 1.61/1.32 inference(superposition,[status(thm)],[f252,f131])).
% 1.61/1.32 thf(f131,plain,(
% 1.61/1.32 (sK2 = (sK3 @ (= @ sK2))) | ~spl0_15),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f129])).
% 1.61/1.32 thf(f252,plain,(
% 1.61/1.32 ( ! [X0 : a] : (($false = (cX @ (sK3 @ (= @ X0)))) | (sK2 != X0)) ) | (~spl0_8 | ~spl0_9 | ~spl0_10)),
% 1.61/1.32 inference(duplicate_literal_removal,[status(thm)],[f251])).
% 1.61/1.32 thf(f251,plain,(
% 1.61/1.32 ( ! [X0 : a] : ((sK2 != X0) | (sK2 != X0) | ($false = (cX @ (sK3 @ (= @ X0))))) ) | (~spl0_8 | ~spl0_9 | ~spl0_10)),
% 1.61/1.32 inference(equality_proxy_clausification,[status(thm)],[f250])).
% 1.61/1.32 thf(f250,plain,(
% 1.61/1.32 ( ! [X0 : a] : (((X0 = sK2) = $false) | ($false = (cX @ (sK3 @ (= @ X0)))) | (sK2 != X0)) ) | (~spl0_8 | ~spl0_9 | ~spl0_10)),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f249])).
% 1.61/1.32 thf(f249,plain,(
% 1.61/1.32 ( ! [X0 : a] : (((cX @ (sK3 @ (^[Y0 : a]: (X0 = Y0)))) = $false) | ((X0 = sK2) = $false) | (sK2 != X0)) ) | (~spl0_8 | ~spl0_9 | ~spl0_10)),
% 1.61/1.32 inference(boolean_simplification,[status(thm)],[f248])).
% 1.61/1.32 thf(f248,plain,(
% 1.61/1.32 ( ! [X0 : a] : (($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false))))) | ((X0 = sK2) = $false) | (sK2 != X0)) ) | (~spl0_8 | ~spl0_9 | ~spl0_10)),
% 1.61/1.32 inference(boolean_simplification,[status(thm)],[f247])).
% 1.61/1.32 thf(f247,plain,(
% 1.61/1.32 ( ! [X0 : a] : (($false = ((X0 = sK2) | $false)) | (sK2 != X0) | ($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))))) ) | (~spl0_8 | ~spl0_9 | ~spl0_10)),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f246])).
% 1.61/1.32 thf(f246,plain,(
% 1.61/1.32 ( ! [X0 : a] : (($false = ((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK2)) | ($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) | (sK2 != X0)) ) | (~spl0_8 | ~spl0_9 | ~spl0_10)),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f245])).
% 1.61/1.32 thf(f245,plain,(
% 1.61/1.32 ( ! [X0 : a] : (($false = ((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK2)) | ($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) | (sK2 != X0) | ($true = $false)) ) | (~spl0_8 | ~spl0_9 | ~spl0_10)),
% 1.61/1.32 inference(duplicate_literal_removal,[status(thm)],[f208])).
% 1.61/1.32 thf(f208,plain,(
% 1.61/1.32 ( ! [X0 : a] : (($true = $false) | (sK2 != X0) | ($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) | ($false = ((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK2)) | ($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))))) ) | (~spl0_8 | ~spl0_9 | ~spl0_10)),
% 1.61/1.32 inference(superposition,[status(thm)],[f105,f174])).
% 1.61/1.32 thf(f174,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = (sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | (sK2 != X0)) ) | (~spl0_8 | ~spl0_9)),
% 1.61/1.32 inference(equality_proxy_clausification,[status(thm)],[f173])).
% 1.61/1.32 thf(f173,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = (sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ((X0 = sK2) = $false)) ) | (~spl0_8 | ~spl0_9)),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f171])).
% 1.61/1.32 thf(f171,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = (sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | (((X0 = sK2) | (X1 @ sK2)) = $false) | ($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) ) | (~spl0_8 | ~spl0_9)),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f170])).
% 1.61/1.32 thf(f170,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($false = (sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($true = $false) | (((X0 = sK2) | (X1 @ sK2)) = $false)) ) | (~spl0_8 | ~spl0_9)),
% 1.61/1.32 inference(boolean_simplification,[status(thm)],[f169])).
% 1.61/1.32 thf(f169,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = ($true | (X1 @ X0))) | (((X0 = sK2) | (X1 @ sK2)) = $false) | ($false = (sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) ) | (~spl0_8 | ~spl0_9)),
% 1.61/1.32 inference(boolean_simplification,[status(thm)],[f168])).
% 1.61/1.32 thf(f168,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($false = (sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | (((X0 = X0) | (X1 @ X0)) = $false) | (((X0 = sK2) | (X1 @ sK2)) = $false)) ) | (~spl0_8 | ~spl0_9)),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f167])).
% 1.61/1.32 thf(f167,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK2)) | ($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0)) | ($false = (sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) ) | (~spl0_8 | ~spl0_9)),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f166])).
% 1.61/1.32 thf(f166,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK2)) | ($false = (sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0)) | ($true = $false)) ) | (~spl0_8 | ~spl0_9)),
% 1.61/1.32 inference(duplicate_literal_removal,[status(thm)],[f156])).
% 1.61/1.32 thf(f156,plain,(
% 1.61/1.32 ( ! [X0 : a,X1 : a > $o] : (($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK2)) | ($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0)) | ($false = (cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) | ($false = (sK5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) | ($true = $false) | ($false = ((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK2))) ) | (~spl0_8 | ~spl0_9)),
% 1.61/1.32 inference(superposition,[status(thm)],[f97,f101])).
% 1.61/1.32 thf(f101,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : (($true = (sK5 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0))))) | ($false = (X1 @ sK2)) | ($false = (X1 @ X3)) | ((sK5 @ X1 @ X2) = $false) | ((cX @ (sK3 @ X1)) = $false)) ) | ~spl0_9),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f100])).
% 1.61/1.32 thf(f100,definition,(
% 1.61/1.32 spl0_9 <=> ! [X2 : a > $o,X1 : a > $o,X3 : a] : (((sK5 @ X1 @ X2) = $false) | ($false = (X1 @ sK2)) | ($true = (sK5 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0))))) | ((cX @ (sK3 @ X1)) = $false) | ($false = (X1 @ X3)))),
% 1.61/1.32 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.61/1.32 thf(f97,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (((sK5 @ X1 @ X1) = $false) | ($false = (X1 @ sK2)) | ((cX @ (sK3 @ X1)) = $false)) ) | ~spl0_8),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f96])).
% 1.61/1.32 thf(f96,definition,(
% 1.61/1.32 spl0_8 <=> ! [X1 : a > $o] : (((cX @ (sK3 @ X1)) = $false) | ($false = (X1 @ sK2)) | ((sK5 @ X1 @ X1) = $false))),
% 1.61/1.32 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.61/1.32 thf(f105,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (((sK5 @ X1 @ (^[Y0 : a]: ($false))) = $true) | ((cX @ (sK3 @ X1)) = $false) | ($false = (X1 @ sK2))) ) | ~spl0_10),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f104])).
% 1.61/1.32 thf(f104,definition,(
% 1.61/1.32 spl0_10 <=> ! [X1 : a > $o] : (((cX @ (sK3 @ X1)) = $false) | ($false = (X1 @ sK2)) | ((sK5 @ X1 @ (^[Y0 : a]: ($false))) = $true))),
% 1.61/1.32 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.61/1.32 thf(f121,plain,(
% 1.61/1.32 ~spl0_2 | ~spl0_7),
% 1.61/1.32 inference(avatar_contradiction_clause,[status(thm)],[f120])).
% 1.61/1.32 thf(f120,plain,(
% 1.61/1.32 $false | (~spl0_2 | ~spl0_7)),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.61/1.32 thf(f119,plain,(
% 1.61/1.32 ($true = $false) | (~spl0_2 | ~spl0_7)),
% 1.61/1.32 inference(forward_demodulation,[status(thm)],[f72,f94])).
% 1.61/1.32 thf(f94,plain,(
% 1.61/1.32 ($false = (cX @ sK2)) | ~spl0_7),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.61/1.32 thf(f72,plain,(
% 1.61/1.32 ($true = (cX @ sK2)) | ~spl0_2),
% 1.61/1.32 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.61/1.32 thf(f118,plain,(
% 1.61/1.32 spl0_13 | spl0_7),
% 1.61/1.32 inference(avatar_split_clause,[status(thm)],[f25,f92,f116])).
% 1.61/1.32 thf(f25,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($true = (sK4 @ X1 @ (^[Y0 : a]: ($false)))) | ($true = (X1 @ (sK3 @ X1))) | ($false = (cX @ sK2)) | ($false = (X1 @ sK2))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.61/1.32 thf(f23,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($true = (X1 @ (sK3 @ X1))) | ($false = (cX @ sK2)) | ($true = ((sK4 @ X1 @ (^[Y0 : a]: ($false))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK4 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK4 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2)))))))))))) | ($false = (X1 @ sK2))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.61/1.32 thf(f21,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = (cX @ sK2)) | ($true = (X1 @ (sK3 @ X1))) | ($false = (X1 @ sK2)) | ($false = (((sK4 @ X1 @ (^[Y0 : a]: ($false))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK4 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK4 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))))) => (sK4 @ X1 @ X1)))) )),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.61/1.32 thf(f20,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = (X1 @ sK2)) | ($false = ((^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1))) @ (sK4 @ X1))) | ($true = (X1 @ (sK3 @ X1))) | ($false = (cX @ sK2))) )),
% 1.61/1.32 inference(sigma_clausification,[status(thm)],[f19])).
% 1.61/1.32 thf(f19,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1))))) | ($false = (cX @ sK2)) | ($false = (X1 @ sK2)) | ($true = (X1 @ (sK3 @ X1)))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.61/1.32 thf(f18,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = (cX @ sK2)) | (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1)))) & (X1 @ sK2)) = $false) | ($true = (X1 @ (sK3 @ X1)))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.61/1.32 thf(f16,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = ((X1 @ (sK3 @ X1)) => (cX @ (sK3 @ X1)))) | ($false = (cX @ sK2)) | (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1)))) & (X1 @ sK2)) = $false)) )),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.61/1.32 thf(f15,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = ((^[Y0 : a]: ((X1 @ Y0) => (cX @ Y0))) @ (sK3 @ X1))) | (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1)))) & (X1 @ sK2)) = $false) | ($false = (cX @ sK2))) )),
% 1.61/1.32 inference(sigma_clausification,[status(thm)],[f14])).
% 1.61/1.32 thf(f14,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = (cX @ sK2)) | ((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cX @ Y0)))) = $false) | (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1)))) & (X1 @ sK2)) = $false)) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.61/1.32 thf(f13,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1)))) & (X1 @ sK2)) & (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cX @ Y0)))))) | ($false = (cX @ sK2))) )),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.61/1.32 thf(f12,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = (cX @ sK2)) | ($false = ((^[Y0 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: (((Y1 @ (^[Y2 : a]: ($false))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ (^[Y4 : a]: ((Y3 = Y4) | (Y2 @ Y4))))))))))) => (Y1 @ Y0)))) & (Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cX @ Y1)))))) @ X1))) )),
% 1.61/1.32 inference(pi_clausification,[status(thm)],[f11])).
% 1.61/1.32 thf(f11,plain,(
% 1.61/1.32 ($false = (cX @ sK2)) | ((?? @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: (((Y1 @ (^[Y2 : a]: ($false))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ (^[Y4 : a]: ((Y3 = Y4) | (Y2 @ Y4))))))))))) => (Y1 @ Y0)))) & (Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cX @ Y1))))))) = $false)),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.61/1.32 thf(f9,plain,(
% 1.61/1.32 ((?? @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: (((Y1 @ (^[Y2 : a]: ($false))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ (^[Y4 : a]: ((Y3 = Y4) | (Y2 @ Y4))))))))))) => (Y1 @ Y0)))) & (Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cX @ Y1))))))) != (cX @ sK2))),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.61/1.32 thf(f8,plain,(
% 1.61/1.32 (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((Y2 @ (^[Y3 : a]: ($false))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5))))))))))) => (Y2 @ Y1)))) & (Y1 @ Y0)) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2)))))))) @ sK2) != (cX @ sK2))),
% 1.61/1.32 inference(negative_extensionality,[status(thm)],[f7])).
% 1.61/1.32 thf(f7,plain,(
% 1.61/1.32 (cX != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((Y2 @ (^[Y3 : a]: ($false))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5))))))))))) => (Y2 @ Y1)))) & (Y1 @ Y0)) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2)))))))))),
% 1.61/1.32 inference(cnf_transformation,[status(thm)],[f6])).
% 1.61/1.32 thf(f6,plain,(
% 1.61/1.32 (cX != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((Y2 @ (^[Y3 : a]: ($false))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5))))))))))) => (Y2 @ Y1)))) & (Y1 @ Y0)) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2)))))))))),
% 1.61/1.32 inference(flattening,[status(thm)],[f5])).
% 1.61/1.32 thf(f5,plain,(
% 1.61/1.32 ~(cX = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((Y2 @ (^[Y3 : a]: ($false))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5))))))))))) => (Y2 @ Y1)))) & (Y1 @ Y0)) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2)))))))))),
% 1.61/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.61/1.32 thf(f4,plain,(
% 1.61/1.32 ~((^[X0 : a] : (? [X1 : a > $o] : (! [X2 : a] : ((X1 @ X2) => (cX @ X2)) & (X1 @ X0) & ! [X3 : (a > $o) > $o] : ((! [X4 : a > $o] : ((X3 @ X4) => ! [X5 : a] : ((X1 @ X5) => (X3 @ (^[X6 : a] : ((X4 @ X6) | (X5 = X6)))))) & (X3 @ (^[X7 : a] : ($false)))) => (X3 @ X1))))) = cX)),
% 1.61/1.32 inference(rectify,[status(thm)],[f2])).
% 1.61/1.32 thf(f2,negated_conjecture,(
% 1.61/1.32 ~((^[X0 : a] : (? [X1 : a > $o] : (! [X4 : a] : ((X1 @ X4) => (cX @ X4)) & (X1 @ X0) & ! [X2 : (a > $o) > $o] : ((! [X4 : a > $o] : ((X2 @ X4) => ! [X5 : a] : ((X1 @ X5) => (X2 @ (^[X6 : a] : ((X4 @ X6) | (X5 = X6)))))) & (X2 @ (^[X3 : a] : ($false)))) => (X2 @ X1))))) = cX)),
% 1.61/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.61/1.32 thf(f1,conjecture,(
% 1.61/1.32 ((^[X0 : a] : (? [X1 : a > $o] : (! [X4 : a] : ((X1 @ X4) => (cX @ X4)) & (X1 @ X0) & ! [X2 : (a > $o) > $o] : ((! [X4 : a > $o] : ((X2 @ X4) => ! [X5 : a] : ((X1 @ X5) => (X2 @ (^[X6 : a] : ((X4 @ X6) | (X5 = X6)))))) & (X2 @ (^[X3 : a] : ($false)))) => (X2 @ X1))))) = cX)),
% 1.61/1.32 file('/export/starexec/sandbox2/tmp/tmp.vBFmgqyxdU/DTF2THF_20611.p',cDOMLEMMA3_pme)).
% 1.61/1.32 thf(f114,plain,(
% 1.61/1.32 spl0_12 | spl0_7),
% 1.61/1.32 inference(avatar_split_clause,[status(thm)],[f31,f92,f112])).
% 1.61/1.32 thf(f31,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : (($true = (sK4 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0))))) | ($true = (X1 @ (sK3 @ X1))) | ($false = (X1 @ sK2)) | ($false = (cX @ sK2)) | ((sK4 @ X1 @ X2) = $false) | ($false = (X1 @ X3))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.61/1.32 thf(f30,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : (($true = ((X1 @ X3) => (sK4 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) | ((sK4 @ X1 @ X2) = $false) | ($false = (cX @ sK2)) | ($false = (X1 @ sK2)) | ($true = (X1 @ (sK3 @ X1)))) )),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.61/1.32 thf(f29,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : (($false = (cX @ sK2)) | ($false = (X1 @ sK2)) | ($true = (X1 @ (sK3 @ X1))) | ($true = ((^[Y0 : a]: ((X1 @ Y0) => (sK4 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1)))))) @ X3)) | ((sK4 @ X1 @ X2) = $false)) )),
% 1.61/1.32 inference(pi_clausification,[status(thm)],[f28])).
% 1.61/1.32 thf(f28,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X1 : a > $o] : (($true = (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK4 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1)))))))) | ((sK4 @ X1 @ X2) = $false) | ($false = (cX @ sK2)) | ($false = (X1 @ sK2)) | ($true = (X1 @ (sK3 @ X1)))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.61/1.32 thf(f27,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X1 : a > $o] : (($false = (X1 @ sK2)) | ($false = (cX @ sK2)) | ($true = ((sK4 @ X1 @ X2) => (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK4 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1))))))))) | ($true = (X1 @ (sK3 @ X1)))) )),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.61/1.32 thf(f26,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X1 : a > $o] : (($false = (X1 @ sK2)) | ($true = ((^[Y0 : a > $o]: ((sK4 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK4 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))) @ X2)) | ($true = (X1 @ (sK3 @ X1))) | ($false = (cX @ sK2))) )),
% 1.61/1.32 inference(pi_clausification,[status(thm)],[f24])).
% 1.61/1.32 thf(f24,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK4 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK4 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))))) | ($true = (X1 @ (sK3 @ X1))) | ($false = (X1 @ sK2)) | ($false = (cX @ sK2))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.61/1.32 thf(f110,plain,(
% 1.61/1.32 spl0_7 | spl0_11),
% 1.61/1.32 inference(avatar_split_clause,[status(thm)],[f22,f108,f92])).
% 1.61/1.32 thf(f22,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = (cX @ sK2)) | ((sK4 @ X1 @ X1) = $false) | ($false = (X1 @ sK2)) | ($true = (X1 @ (sK3 @ X1)))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.61/1.32 thf(f106,plain,(
% 1.61/1.32 spl0_10 | spl0_7),
% 1.61/1.32 inference(avatar_split_clause,[status(thm)],[f38,f92,f104])).
% 1.61/1.32 thf(f38,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (((cX @ (sK3 @ X1)) = $false) | ($false = (cX @ sK2)) | ((sK5 @ X1 @ (^[Y0 : a]: ($false))) = $true) | ($false = (X1 @ sK2))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.61/1.32 thf(f36,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = (cX @ sK2)) | ((cX @ (sK3 @ X1)) = $false) | ($true = ((sK5 @ X1 @ (^[Y0 : a]: ($false))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK5 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK5 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2)))))))))))) | ($false = (X1 @ sK2))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.61/1.32 thf(f34,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (((((sK5 @ X1 @ (^[Y0 : a]: ($false))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK5 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK5 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))))) => (sK5 @ X1 @ X1)) = $false) | ((cX @ (sK3 @ X1)) = $false) | ($false = (cX @ sK2)) | ($false = (X1 @ sK2))) )),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.61/1.32 thf(f33,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : ((((^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1))) @ (sK5 @ X1)) = $false) | ($false = (X1 @ sK2)) | ($false = (cX @ sK2)) | ((cX @ (sK3 @ X1)) = $false)) )),
% 1.61/1.32 inference(sigma_clausification,[status(thm)],[f32])).
% 1.61/1.32 thf(f32,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = (cX @ sK2)) | ((cX @ (sK3 @ X1)) = $false) | ($false = (X1 @ sK2)) | ($false = (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1)))))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.61/1.32 thf(f17,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (((cX @ (sK3 @ X1)) = $false) | (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1)))) & (X1 @ sK2)) = $false) | ($false = (cX @ sK2))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.61/1.32 thf(f102,plain,(
% 1.61/1.32 spl0_9 | spl0_7),
% 1.61/1.32 inference(avatar_split_clause,[status(thm)],[f44,f92,f100])).
% 1.61/1.32 thf(f44,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : (((sK5 @ X1 @ X2) = $false) | ($false = (X1 @ X3)) | ((cX @ (sK3 @ X1)) = $false) | ($true = (sK5 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0))))) | ($false = (cX @ sK2)) | ($false = (X1 @ sK2))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.61/1.32 thf(f43,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : (($false = (X1 @ sK2)) | ((cX @ (sK3 @ X1)) = $false) | (((X1 @ X3) => (sK5 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0))))) = $true) | ($false = (cX @ sK2)) | ((sK5 @ X1 @ X2) = $false)) )),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.61/1.32 thf(f42,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : (((sK5 @ X1 @ X2) = $false) | ((cX @ (sK3 @ X1)) = $false) | ($true = ((^[Y0 : a]: ((X1 @ Y0) => (sK5 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1)))))) @ X3)) | ($false = (X1 @ sK2)) | ($false = (cX @ sK2))) )),
% 1.61/1.32 inference(pi_clausification,[status(thm)],[f41])).
% 1.61/1.32 thf(f41,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X1 : a > $o] : (((sK5 @ X1 @ X2) = $false) | ((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK5 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1))))))) = $true) | ((cX @ (sK3 @ X1)) = $false) | ($false = (X1 @ sK2)) | ($false = (cX @ sK2))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.61/1.32 thf(f40,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X1 : a > $o] : (((cX @ (sK3 @ X1)) = $false) | ($false = (cX @ sK2)) | ($true = ((sK5 @ X1 @ X2) => (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK5 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1))))))))) | ($false = (X1 @ sK2))) )),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.61/1.32 thf(f39,plain,(
% 1.61/1.32 ( ! [X2 : a > $o,X1 : a > $o] : (($true = ((^[Y0 : a > $o]: ((sK5 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK5 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))) @ X2)) | ($false = (cX @ sK2)) | ($false = (X1 @ sK2)) | ((cX @ (sK3 @ X1)) = $false)) )),
% 1.61/1.32 inference(pi_clausification,[status(thm)],[f37])).
% 1.61/1.32 thf(f37,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = (cX @ sK2)) | ((cX @ (sK3 @ X1)) = $false) | ($false = (X1 @ sK2)) | ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK5 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK5 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2)))))))))))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.61/1.32 thf(f98,plain,(
% 1.61/1.32 spl0_7 | spl0_8),
% 1.61/1.32 inference(avatar_split_clause,[status(thm)],[f35,f96,f92])).
% 1.61/1.32 thf(f35,plain,(
% 1.61/1.32 ( ! [X1 : a > $o] : (($false = (cX @ sK2)) | ((cX @ (sK3 @ X1)) = $false) | ((sK5 @ X1 @ X1) = $false) | ($false = (X1 @ sK2))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.61/1.32 thf(f78,plain,(
% 1.61/1.32 spl0_3 | spl0_2),
% 1.61/1.32 inference(avatar_split_clause,[status(thm)],[f49,f70,f75])).
% 1.61/1.32 thf(f49,plain,(
% 1.61/1.32 ($true = (cX @ sK2)) | ((sK6 @ sK2) = $true)),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.61/1.32 thf(f48,plain,(
% 1.61/1.32 ($true = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK6 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ sK6)))) & (sK6 @ sK2))) | ($true = (cX @ sK2))),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.61/1.32 thf(f46,plain,(
% 1.61/1.32 ($true = (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK6 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ sK6)))) & (sK6 @ sK2)) & (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (cX @ Y0)))))) | ($true = (cX @ sK2))),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.61/1.32 thf(f45,plain,(
% 1.61/1.32 ($true = (cX @ sK2)) | ($true = ((^[Y0 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: (((Y1 @ (^[Y2 : a]: ($false))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ (^[Y4 : a]: ((Y3 = Y4) | (Y2 @ Y4))))))))))) => (Y1 @ Y0)))) & (Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cX @ Y1)))))) @ sK6))),
% 1.61/1.32 inference(sigma_clausification,[status(thm)],[f10])).
% 1.61/1.32 thf(f10,plain,(
% 1.61/1.32 ($true = (cX @ sK2)) | ($true = (?? @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: (((Y1 @ (^[Y2 : a]: ($false))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ (^[Y4 : a]: ((Y3 = Y4) | (Y2 @ Y4))))))))))) => (Y1 @ Y0)))) & (Y0 @ sK2)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cX @ Y1))))))))),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.61/1.32 thf(f73,plain,(
% 1.61/1.32 spl0_1 | spl0_2),
% 1.61/1.32 inference(avatar_split_clause,[status(thm)],[f65,f70,f67])).
% 1.61/1.32 thf(f65,plain,(
% 1.61/1.32 ( ! [X1 : a] : (($true = (cX @ sK2)) | ($true = (cX @ X1)) | ($false = (sK6 @ X1))) )),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.61/1.32 thf(f64,plain,(
% 1.61/1.32 ( ! [X1 : a] : ((((sK6 @ X1) => (cX @ X1)) = $true) | ($true = (cX @ sK2))) )),
% 1.61/1.32 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.61/1.32 thf(f63,plain,(
% 1.61/1.32 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK6 @ Y0) => (cX @ Y0))) @ X1) = $true) | ($true = (cX @ sK2))) )),
% 1.61/1.32 inference(pi_clausification,[status(thm)],[f47])).
% 1.61/1.32 thf(f47,plain,(
% 1.61/1.32 ($true = (cX @ sK2)) | ($true = (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (cX @ Y0)))))),
% 1.61/1.32 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.61/1.32 % SZS output end Proof for DTF2THF_20611
% 1.61/1.32 % (20780)------------------------------
% 1.61/1.32 % (20780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (20780)Termination reason: Refutation
% 1.61/1.32
% 1.61/1.32 % (20780)Memory used [KB]: 5756
% 1.61/1.32 % (20780)Time elapsed: 0.026 s
% 1.61/1.32 % (20780)Instructions burned: 69 (million)
% 1.61/1.32 % (20780)------------------------------
% 1.61/1.32 % (20780)------------------------------
% 1.61/1.32 % (20774)Success in time 0.033 s
%------------------------------------------------------------------------------