%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO263^5 : 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 : n025.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 09:53:48 AM UTC 2026
% Result : Theorem 1.60s 1.36s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 83 ( 2 unt; 0 typ; 8 def)
% Number of atoms : 806 ( 254 equ; 0 cnn)
% Maximal formula atoms : 18 ( 9 avg)
% Number of connectives : 994 ( 279 ~; 234 |; 40 &; 424 @)
% ( 13 <=>; 2 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 13 con; 0-3 aty)
% Number of variables : 178 ( 40 ^; 101 !; 37 ?; 178 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sP0: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
sK4: $i > $o ).
thf(func_def_8,type,
sK5: ( $i > $o ) > $i ).
thf(func_def_14,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f361,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f46,f50,f103,f119,f247,f256,f269,f297,f360]) ).
thf(f360,plain,
( ~ spl6_26
| ~ spl6_29 ),
inference(avatar_contradiction_clause,[status(thm)],[f359]) ).
thf(f359,plain,
( $false
| ~ spl6_26
| ~ spl6_29 ),
inference(subsumption_resolution,[status(thm)],[f358,f339]) ).
thf(f339,plain,
( ( $true
= ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) ) )
| ~ spl6_26
| ~ spl6_29 ),
inference(not_proxy_clausification,[status(thm)],[f338]) ).
thf(f338,plain,
( ( $true
!= ( ~ ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) ) ) )
| ~ spl6_26
| ~ spl6_29 ),
inference(beta_eta_normalization,[status(thm)],[f337]) ).
thf(f337,plain,
( ( ( ^ [Y0: $i] :
~ ( sK4 @ Y0 )
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) )
!= $true )
| ~ spl6_26
| ~ spl6_29 ),
inference(trivial_inequality_removal,[status(thm)],[f324]) ).
thf(f324,plain,
( ( $true = $false )
| ( $true != $true )
| ( ( ^ [Y0: $i] :
~ ( sK4 @ Y0 )
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) )
!= $true )
| ~ spl6_26
| ~ spl6_29 ),
inference(superposition,[status(thm)],[f285,f296]) ).
thf(f296,plain,
( ! [X0: $i > $o] :
( ( ( sK4 @ ( sK5 @ X0 ) )
= $true )
| ( ( X0 @ ( sK5 @ X0 ) )
!= $true ) )
| ~ spl6_29 ),
inference(avatar_component_clause,[status(thm)],[f295]) ).
thf(f295,definition,
( spl6_29
<=> ! [X0: $i > $o] :
( ( ( sK4 @ ( sK5 @ X0 ) )
= $true )
| ( ( X0 @ ( sK5 @ X0 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_29])],[avatar_definition]) ).
thf(f285,plain,
( ! [X3: $i > $o] :
( ( ( X3
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) )
= $false )
| ( ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) )
!= $true ) )
| ~ spl6_26 ),
inference(not_proxy_clausification,[status(thm)],[f284]) ).
thf(f284,plain,
( ! [X3: $i > $o] :
( ( ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) )
!= $true )
| ( ( ~ ( X3
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) ) )
= $true ) )
| ~ spl6_26 ),
inference(beta_eta_normalization,[status(thm)],[f276]) ).
thf(f276,plain,
( ! [X3: $i > $o] :
( ( ( ^ [Y0: $i] :
~ ( X3 @ Y0 )
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) )
= $true )
| ( ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) )
!= $true ) )
| ~ spl6_26 ),
inference(primitive_instantiation,[status(thm)],[f268]) ).
thf(f268,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ ( sK5 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK5 @ X0 ) )
!= $true ) )
| ~ spl6_26 ),
inference(avatar_component_clause,[status(thm)],[f267]) ).
thf(f267,definition,
( spl6_26
<=> ! [X0: $i > $o] :
( ( ( sK4 @ ( sK5 @ X0 ) )
!= $true )
| ( ( X0 @ ( sK5 @ X0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_26])],[avatar_definition]) ).
thf(f358,plain,
( ( $true
!= ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) ) )
| ~ spl6_26
| ~ spl6_29 ),
inference(trivial_inequality_removal,[status(thm)],[f354]) ).
thf(f354,plain,
( ( $true
!= ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) ) )
| ( $true = $false )
| ~ spl6_26
| ~ spl6_29 ),
inference(superposition,[status(thm)],[f339,f285]) ).
thf(f297,plain,
( spl6_29
| spl6_16
| ~ spl6_6 ),
inference(avatar_split_clause,[status(thm)],[f288,f48,f101,f295]) ).
thf(f101,definition,
( spl6_16
<=> ! [X1: $i > $o] :
( ( $true
!= ( X1 @ sK1 ) )
| ( ( X1 @ sK3 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_16])],[avatar_definition]) ).
thf(f48,definition,
( spl6_6
<=> ! [X4: $i > $o,X5: $i > $o] :
( ( $true
!= ( X4 @ sK1 ) )
| ( ( sK4 @ ( sK5 @ X5 ) )
= $true )
| ( ( X5 @ ( sK5 @ X5 ) )
!= $true )
| ( $true
= ( sP0 @ X5 @ X4 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_6])],[avatar_definition]) ).
thf(f288,plain,
( ! [X0: $i > $o,X1: $i > $o] :
( ( ( X1 @ sK3 )
!= $true )
| ( $true
!= ( X1 @ sK1 ) )
| ( ( sK4 @ ( sK5 @ X0 ) )
= $true )
| ( ( X0 @ ( sK5 @ X0 ) )
!= $true ) )
| ~ spl6_6 ),
inference(trivial_inequality_removal,[status(thm)],[f287]) ).
thf(f287,plain,
( ! [X0: $i > $o,X1: $i > $o] :
( ( $true != $true )
| ( ( sK4 @ ( sK5 @ X0 ) )
= $true )
| ( ( X1 @ sK3 )
!= $true )
| ( $true
!= ( X1 @ sK1 ) )
| ( ( X0 @ ( sK5 @ X0 ) )
!= $true ) )
| ~ spl6_6 ),
inference(superposition,[status(thm)],[f18,f49]) ).
thf(f49,plain,
( ! [X4: $i > $o,X5: $i > $o] :
( ( $true
= ( sP0 @ X5 @ X4 @ sK3 ) )
| ( ( sK4 @ ( sK5 @ X5 ) )
= $true )
| ( ( X5 @ ( sK5 @ X5 ) )
!= $true )
| ( $true
!= ( X4 @ sK1 ) ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f18,plain,
! [X2: $i > $o,X0: $i,X1: $i > $o] :
( ( $true
!= ( sP0 @ X2 @ X1 @ X0 ) )
| ( $true
!= ( X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i > $o,X2: $i > $o] :
( ( ( $true
!= ( X1 @ X0 ) )
& ( ( X2 @ X0 )
!= $true ) )
| ( $true
!= ( sP0 @ X2 @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X4: $i > $o,X5: $i > $o] :
( ( ( ( X4 @ X0 )
!= $true )
& ( ( X5 @ X0 )
!= $true ) )
| ( ( sP0 @ X5 @ X4 @ X0 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X4: $i > $o,X5: $i > $o] :
( ( ( ( X4 @ X0 )
!= $true )
& ( ( X5 @ X0 )
!= $true ) )
| ( ( sP0 @ X5 @ X4 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f269,plain,
( spl6_26
| spl6_16
| ~ spl6_5 ),
inference(avatar_split_clause,[status(thm)],[f265,f44,f101,f267]) ).
thf(f44,definition,
( spl6_5
<=> ! [X4: $i > $o,X5: $i > $o] :
( ( $true
= ( sP0 @ X5 @ X4 @ sK3 ) )
| ( ( X5 @ ( sK5 @ X5 ) )
= $true )
| ( $true
!= ( X4 @ sK1 ) )
| ( ( sK4 @ ( sK5 @ X5 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition]) ).
thf(f265,plain,
( ! [X0: $i > $o,X1: $i > $o] :
( ( ( X1 @ sK3 )
!= $true )
| ( ( sK4 @ ( sK5 @ X0 ) )
!= $true )
| ( ( X0 @ ( sK5 @ X0 ) )
= $true )
| ( $true
!= ( X1 @ sK1 ) ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[status(thm)],[f263]) ).
thf(f263,plain,
( ! [X0: $i > $o,X1: $i > $o] :
( ( ( X1 @ sK3 )
!= $true )
| ( $true != $true )
| ( ( sK4 @ ( sK5 @ X0 ) )
!= $true )
| ( $true
!= ( X1 @ sK1 ) )
| ( ( X0 @ ( sK5 @ X0 ) )
= $true ) )
| ~ spl6_5 ),
inference(superposition,[status(thm)],[f18,f45]) ).
thf(f45,plain,
( ! [X4: $i > $o,X5: $i > $o] :
( ( $true
= ( sP0 @ X5 @ X4 @ sK3 ) )
| ( $true
!= ( X4 @ sK1 ) )
| ( ( X5 @ ( sK5 @ X5 ) )
= $true )
| ( ( sK4 @ ( sK5 @ X5 ) )
!= $true ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f256,plain,
~ spl6_16,
inference(avatar_contradiction_clause,[status(thm)],[f255]) ).
thf(f255,plain,
( $false
| ~ spl6_16 ),
inference(trivial_inequality_removal,[status(thm)],[f254]) ).
thf(f254,plain,
( ( $true != $true )
| ~ spl6_16 ),
inference(duplicate_literal_removal,[status(thm)],[f253]) ).
thf(f253,plain,
( ( $true != $true )
| ( $true != $true )
| ~ spl6_16 ),
inference(beta_eta_normalization,[status(thm)],[f248]) ).
thf(f248,plain,
( ( ( ^ [Y0: $i] : $true
@ sK3 )
!= $true )
| ( ( ^ [Y0: $i] : $true
@ sK1 )
!= $true )
| ~ spl6_16 ),
inference(primitive_instantiation,[status(thm)],[f102]) ).
thf(f102,plain,
( ! [X1: $i > $o] :
( ( $true
!= ( X1 @ sK1 ) )
| ( ( X1 @ sK3 )
!= $true ) )
| ~ spl6_16 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f247,plain,
( spl6_2
| ~ spl6_9
| ~ spl6_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f246]) ).
thf(f246,plain,
( $false
| spl6_2
| ~ spl6_9
| ~ spl6_11 ),
inference(subsumption_resolution,[status(thm)],[f245,f34]) ).
thf(f34,plain,
( ( $true
!= ( sK4 @ sK2 ) )
| spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl6_2
<=> ( $true
= ( sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f245,plain,
( ( $true
= ( sK4 @ sK2 ) )
| spl6_2
| ~ spl6_9
| ~ spl6_11 ),
inference(subsumption_resolution,[status(thm)],[f241,f227]) ).
thf(f227,plain,
( ( $true
= ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) ) )
| spl6_2
| ~ spl6_9
| ~ spl6_11 ),
inference(subsumption_resolution,[status(thm)],[f201,f34]) ).
thf(f201,plain,
( ( $true
= ( sK4 @ sK2 ) )
| ( $true
= ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) ) )
| ~ spl6_9
| ~ spl6_11 ),
inference(not_proxy_clausification,[status(thm)],[f200]) ).
thf(f200,plain,
( ( $true
!= ( ~ ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( sK4 @ sK2 ) )
| ~ spl6_9
| ~ spl6_11 ),
inference(duplicate_literal_removal,[status(thm)],[f199]) ).
thf(f199,plain,
( ( $true
= ( sK4 @ sK2 ) )
| ( $true
= ( sK4 @ sK2 ) )
| ( $true
!= ( ~ ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) ) ) )
| ~ spl6_9
| ~ spl6_11 ),
inference(not_proxy_clausification,[status(thm)],[f198]) ).
thf(f198,plain,
( ( $true
!= ( ~ ( sK4 @ sK2 ) ) )
| ( $true
!= ( ~ ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( sK4 @ sK2 ) )
| ~ spl6_9
| ~ spl6_11 ),
inference(beta_eta_normalization,[status(thm)],[f197]) ).
thf(f197,plain,
( ( ( ^ [Y0: $i] :
~ ( sK4 @ Y0 )
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) )
!= $true )
| ( $true
!= ( ^ [Y0: $i] :
~ ( sK4 @ Y0 )
@ sK2 ) )
| ( $true
= ( sK4 @ sK2 ) )
| ~ spl6_9
| ~ spl6_11 ),
inference(trivial_inequality_removal,[status(thm)],[f187]) ).
thf(f187,plain,
( ( ( ^ [Y0: $i] :
~ ( sK4 @ Y0 )
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) )
!= $true )
| ( $true
= ( sK4 @ sK2 ) )
| ( $true
!= ( ^ [Y0: $i] :
~ ( sK4 @ Y0 )
@ sK2 ) )
| ( $true != $true )
| ( $true = $false )
| ~ spl6_9
| ~ spl6_11 ),
inference(superposition,[status(thm)],[f151,f65]) ).
thf(f65,plain,
( ! [X0: $i > $o] :
( ( ( sK4 @ ( sK5 @ X0 ) )
= $true )
| ( ( X0 @ ( sK5 @ X0 ) )
!= $true )
| ( ( X0 @ sK2 )
!= $true ) )
| ~ spl6_9 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl6_9
<=> ! [X0: $i > $o] :
( ( ( X0 @ sK2 )
!= $true )
| ( ( X0 @ ( sK5 @ X0 ) )
!= $true )
| ( ( sK4 @ ( sK5 @ X0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition]) ).
thf(f151,plain,
( ! [X3: $i > $o] :
( ( ( X3
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) )
= $false )
| ( ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) )
!= $true )
| ( ( X3 @ sK2 )
= $true ) )
| ~ spl6_11 ),
inference(not_proxy_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
( ! [X3: $i > $o] :
( ( ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) )
!= $true )
| ( ( ~ ( X3 @ sK2 ) )
!= $true )
| ( ( X3
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) )
= $false ) )
| ~ spl6_11 ),
inference(not_proxy_clausification,[status(thm)],[f149]) ).
thf(f149,plain,
( ! [X3: $i > $o] :
( ( ( ~ ( X3
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) ) )
= $true )
| ( ( ~ ( X3 @ sK2 ) )
!= $true )
| ( ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) )
!= $true ) )
| ~ spl6_11 ),
inference(beta_eta_normalization,[status(thm)],[f143]) ).
thf(f143,plain,
( ! [X3: $i > $o] :
( ( ( ^ [Y0: $i] :
~ ( X3 @ Y0 )
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
~ ( X3 @ Y0 )
@ sK2 )
!= $true )
| ( ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( X3 @ Y0 ) ) )
!= $true ) )
| ~ spl6_11 ),
inference(primitive_instantiation,[status(thm)],[f77]) ).
thf(f77,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ ( sK5 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK5 @ X0 ) )
!= $true )
| ( ( X0 @ sK2 )
!= $true ) )
| ~ spl6_11 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f76,definition,
( spl6_11
<=> ! [X0: $i > $o] :
( ( ( sK4 @ ( sK5 @ X0 ) )
!= $true )
| ( ( X0 @ sK2 )
!= $true )
| ( ( X0 @ ( sK5 @ X0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_11])],[avatar_definition]) ).
thf(f241,plain,
( ( $true
!= ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) ) )
| ( $true
= ( sK4 @ sK2 ) )
| spl6_2
| ~ spl6_9
| ~ spl6_11 ),
inference(trivial_inequality_removal,[status(thm)],[f239]) ).
thf(f239,plain,
( ( $true
!= ( sK4
@ ( sK5
@ ^ [Y0: $i] :
~ ( sK4 @ Y0 ) ) ) )
| ( $true = $false )
| ( $true
= ( sK4 @ sK2 ) )
| spl6_2
| ~ spl6_9
| ~ spl6_11 ),
inference(superposition,[status(thm)],[f227,f151]) ).
thf(f119,plain,
( spl6_16
| spl6_9 ),
inference(avatar_split_clause,[status(thm)],[f113,f64,f101]) ).
thf(f113,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( ( X1 @ sK3 )
!= $true )
| ( ( X0 @ sK2 )
!= $true )
| ( ( sK4 @ ( sK5 @ X0 ) )
= $true )
| ( ( X0 @ ( sK5 @ X0 ) )
!= $true )
| ( $true
!= ( X1 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( ( sK4 @ ( sK5 @ X0 ) )
= $true )
| ( $true
!= ( X1 @ sK1 ) )
| ( $true != $true )
| ( ( X1 @ sK3 )
!= $true )
| ( ( X0 @ ( sK5 @ X0 ) )
!= $true )
| ( ( X0 @ sK2 )
!= $true ) ),
inference(superposition,[status(thm)],[f18,f24]) ).
thf(f24,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( $true
= ( sP0 @ X5 @ X4 @ sK3 ) )
| ( $true
!= ( X4 @ sK1 ) )
| ( ( X5 @ ( sK5 @ X5 ) )
!= $true )
| ( ( sK4 @ ( sK5 @ X5 ) )
= $true )
| ( ( X5 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( ( $true
!= ( X4 @ sK1 ) )
& ( ( sK4 @ sK1 )
= $true ) )
| ( ( $true
!= ( sK4 @ sK2 ) )
& ( ( X5 @ sK2 )
!= $true ) )
| ( ( ( ( X5 @ ( sK5 @ X5 ) )
!= $true )
| ( ( sK4 @ ( sK5 @ X5 ) )
= $true ) )
& ( ( ( X5 @ ( sK5 @ X5 ) )
= $true )
| ( ( sK4 @ ( sK5 @ X5 ) )
!= $true ) ) )
| ( $true
= ( sP0 @ X5 @ X4 @ sK3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f13,f15,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i > $o] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( ( X4 @ X0 )
!= $true )
& ( ( X3 @ X0 )
= $true ) )
| ( ( ( X3 @ X1 )
!= $true )
& ( ( X5 @ X1 )
!= $true ) )
| ? [X6: $i] :
( ( ( ( X5 @ X6 )
!= $true )
| ( ( X3 @ X6 )
= $true ) )
& ( ( ( X5 @ X6 )
= $true )
| ( ( X3 @ X6 )
!= $true ) ) )
| ( ( sP0 @ X5 @ X4 @ X2 )
= $true ) )
=> ! [X5: $i > $o,X4: $i > $o] :
( ( ( $true
!= ( X4 @ sK1 ) )
& ( ( sK4 @ sK1 )
= $true ) )
| ( ( $true
!= ( sK4 @ sK2 ) )
& ( ( X5 @ sK2 )
!= $true ) )
| ? [X6: $i] :
( ( ( ( X5 @ X6 )
!= $true )
| ( ( sK4 @ X6 )
= $true ) )
& ( ( ( X5 @ X6 )
= $true )
| ( ( sK4 @ X6 )
!= $true ) ) )
| ( $true
= ( sP0 @ X5 @ X4 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X5: $i > $o] :
( ? [X6: $i] :
( ( ( ( X5 @ X6 )
!= $true )
| ( ( sK4 @ X6 )
= $true ) )
& ( ( ( X5 @ X6 )
= $true )
| ( ( sK4 @ X6 )
!= $true ) ) )
=> ( ( ( ( X5 @ ( sK5 @ X5 ) )
!= $true )
| ( ( sK4 @ ( sK5 @ X5 ) )
= $true ) )
& ( ( ( X5 @ ( sK5 @ X5 ) )
= $true )
| ( ( sK4 @ ( sK5 @ X5 ) )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: $i,X1: $i,X2: $i,X3: $i > $o] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( ( X4 @ X0 )
!= $true )
& ( ( X3 @ X0 )
= $true ) )
| ( ( ( X3 @ X1 )
!= $true )
& ( ( X5 @ X1 )
!= $true ) )
| ? [X6: $i] :
( ( ( ( X5 @ X6 )
!= $true )
| ( ( X3 @ X6 )
= $true ) )
& ( ( ( X5 @ X6 )
= $true )
| ( ( X3 @ X6 )
!= $true ) ) )
| ( ( sP0 @ X5 @ X4 @ X2 )
= $true ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
? [X3: $i,X2: $i,X0: $i,X1: $i > $o] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( ( X4 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) )
| ( ( ( X1 @ X2 )
!= $true )
& ( ( X5 @ X2 )
!= $true ) )
| ? [X6: $i] :
( ( ( ( X5 @ X6 )
!= $true )
| ( $true
= ( X1 @ X6 ) ) )
& ( ( ( X5 @ X6 )
= $true )
| ( $true
!= ( X1 @ X6 ) ) ) )
| ( ( sP0 @ X5 @ X4 @ X0 )
= $true ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
? [X3: $i,X2: $i,X0: $i,X1: $i > $o] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( ( X4 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) )
| ( ( ( X1 @ X2 )
!= $true )
& ( ( X5 @ X2 )
!= $true ) )
| ? [X6: $i] :
( ( $true
!= ( X1 @ X6 ) )
<~> ( ( X5 @ X6 )
= $true ) )
| ( ( sP0 @ X5 @ X4 @ X0 )
= $true ) ),
inference(definition_folding,[status(thm)],[f7,f8]) ).
thf(f7,plain,
? [X3: $i,X2: $i,X0: $i,X1: $i > $o] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( ( X4 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) )
| ( ( ( X1 @ X2 )
!= $true )
& ( ( X5 @ X2 )
!= $true ) )
| ? [X6: $i] :
( ( $true
!= ( X1 @ X6 ) )
<~> ( ( X5 @ X6 )
= $true ) )
| ( ( ( X4 @ X0 )
!= $true )
& ( ( X5 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X1: $i > $o,X2: $i,X0: $i,X3: $i] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( ( X1 @ X2 )
= $true )
| ( ( X5 @ X2 )
= $true ) )
& ( ( ( X4 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ( ( ( X4 @ X0 )
= $true )
| ( ( X5 @ X0 )
= $true ) )
& ! [X6: $i] :
( ( ( X5 @ X6 )
= $true )
<=> ( $true
!= ( X1 @ X6 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i > $o,X2: $i,X3: $i] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( ( X4 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ( ( ( X4 @ X0 )
= $true )
| ( ( X5 @ X0 )
= $true ) )
& ! [X6: $i] :
( ( $true
!= ( X1 @ X6 ) )
<=> ( ( X5 @ X6 )
= $true ) )
& ( ( ( X1 @ X2 )
= $true )
| ( ( X5 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i > $o,X2: $i,X3: $i] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( X4 @ X3 )
| ~ ( X1 @ X3 ) )
& ( ( X4 @ X0 )
| ( X5 @ X0 ) )
& ! [X6: $i] :
( ~ ( X1 @ X6 )
<=> ( X5 @ X6 ) )
& ( ( X1 @ X2 )
| ( X5 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X3: $i > $o,X1: $i,X2: $i] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( X4 @ X2 )
| ~ ( X3 @ X2 ) )
& ( ( X4 @ X0 )
| ( X5 @ X0 ) )
& ! [X6: $i] :
( ~ ( X3 @ X6 )
<=> ( X5 @ X6 ) )
& ( ( X3 @ X1 )
| ( X5 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i,X3: $i > $o,X1: $i,X2: $i] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( X4 @ X2 )
| ~ ( X3 @ X2 ) )
& ( ( X4 @ X0 )
| ( X5 @ X0 ) )
& ! [X6: $i] :
( ~ ( X3 @ X6 )
<=> ( X5 @ X6 ) )
& ( ( X3 @ X1 )
| ( X5 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ni0usXZvD3/DTF2THF_11946.p',cTHM125D) ).
thf(f103,plain,
( spl6_11
| spl6_16 ),
inference(avatar_split_clause,[status(thm)],[f95,f101,f76]) ).
thf(f95,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( ( sK4 @ ( sK5 @ X0 ) )
!= $true )
| ( $true
!= ( X1 @ sK1 ) )
| ( ( X0 @ ( sK5 @ X0 ) )
= $true )
| ( ( X1 @ sK3 )
!= $true )
| ( ( X0 @ sK2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( ( sK4 @ ( sK5 @ X0 ) )
!= $true )
| ( ( X0 @ sK2 )
!= $true )
| ( ( X1 @ sK3 )
!= $true )
| ( $true != $true )
| ( $true
!= ( X1 @ sK1 ) )
| ( ( X0 @ ( sK5 @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f18,f23]) ).
thf(f23,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( $true
= ( sP0 @ X5 @ X4 @ sK3 ) )
| ( ( X5 @ sK2 )
!= $true )
| ( ( sK4 @ ( sK5 @ X5 ) )
!= $true )
| ( ( X5 @ ( sK5 @ X5 ) )
= $true )
| ( $true
!= ( X4 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f50,plain,
( spl6_6
| ~ spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f26,f32,f48]) ).
thf(f26,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( $true
!= ( X4 @ sK1 ) )
| ( ( X5 @ ( sK5 @ X5 ) )
!= $true )
| ( $true
= ( sP0 @ X5 @ X4 @ sK3 ) )
| ( ( sK4 @ ( sK5 @ X5 ) )
= $true )
| ( $true
!= ( sK4 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f46,plain,
( ~ spl6_2
| spl6_5 ),
inference(avatar_split_clause,[status(thm)],[f25,f44,f32]) ).
thf(f25,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( $true
= ( sP0 @ X5 @ X4 @ sK3 ) )
| ( $true
!= ( sK4 @ sK2 ) )
| ( ( sK4 @ ( sK5 @ X5 ) )
!= $true )
| ( $true
!= ( X4 @ sK1 ) )
| ( ( X5 @ ( sK5 @ X5 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO263^5 : 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
% 0.16/0.34 % Computer : n025.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:27:12 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SYO263^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.47 % Domain : Syntactic
% 0.31/0.47 % Problem : TPS problem THM125D
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English : Trivial theorem to test flexible-flexible pairs.
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Bro09]
% 0.31/0.47 % Names : tps_0157 [Bro09]
% 0.31/0.47 % : THM125D [TPS]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.50 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v5.1.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.31/0.47 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.31/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.31/0.47 % Number of connectives : 17 ( 2 ~; 3 |; 3 &; 8 @)
% 0.31/0.47 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 14 ( 14 avg)
% 0.31/0.47 % Number of types : 2 ( 0 usr)
% 0.31/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.31/0.47 % Number of variables : 7 ( 0 ^; 5 !; 2 ?; 7 :)
% 0.31/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(cTHM125D,conjecture,
% 0.31/0.47 ! [Xa: $i,Xb: $i,Xc: $i,P: $i > $o] :
% 0.31/0.47 ? [Xm: $i > $o,Xn: $i > $o] :
% 0.31/0.47 ( ( ( Xn @ Xa )
% 0.31/0.47 | ( Xm @ Xa ) )
% 0.31/0.47 & ( ( P @ Xb )
% 0.31/0.47 | ( Xn @ Xb ) )
% 0.31/0.47 & ( ( Xm @ Xc )
% 0.31/0.47 | ~ ( P @ Xc ) )
% 0.31/0.47 & ! [Xx: $i] :
% 0.31/0.47 ( ( Xn @ Xx )
% 0.31/0.47 <=> ~ ( P @ Xx ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.60/1.31 ---- Embedded in THF ---
% 1.60/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.60/1.31 %%% Generated on Tue Feb 24 14:27:13 EST 2026
% 1.60/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.60/1.31 %%% Logic specification used:
% 1.60/1.31 %%% thf(spec, logic, $$dhol).
% 1.60/1.31
% 1.60/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ni0usXZvD3/DTF2DTF11946.p
% See solution above
% 1.60/1.31 ------------------------
% 1.60/1.32 ---- Cleaned THF ---
% 1.60/1.32 thf(cTHM125D,conjecture,
% 1.60/1.32 ! [Xa: $i,Xb: $i,Xc: $i,P: $i > $o] :
% 1.60/1.32 ? [Xm: $i > $o,Xn: $i > $o] :
% 1.60/1.32 ( ( ( Xn @ Xa )
% 1.60/1.32 | ( Xm @ Xa ) )
% 1.60/1.32 & ( ( P @ Xb )
% 1.60/1.32 | ( Xn @ Xb ) )
% 1.60/1.32 & ( ( Xm @ Xc )
% 1.60/1.32 | ~ ( P @ Xc ) )
% 1.60/1.32 & ! [Xx: $i] :
% 1.60/1.32 ( ( Xn @ Xx )
% 1.60/1.32 <=> ~ ( P @ Xx ) ) ) ).
% 1.60/1.32 ------------------------
% 1.60/1.33 % (12109)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11946 for (3000ds/18Mi)
% 1.60/1.33 % (12108)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_11946 for (3000ds/275Mi)
% 1.60/1.34 % (12104)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_11946 for (3000ds/4Mi)
% 1.60/1.34 % (12103)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11946 for (3000ds/183Mi)
% 1.60/1.34 % (12109)Instruction limit reached!
% 1.60/1.34 % (12109)------------------------------
% 1.60/1.34 % (12109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (12109)Termination reason: Unknown
% 1.60/1.34 % (12109)Termination phase: Saturation
% 1.60/1.34
% 1.60/1.34 % (12109)Memory used [KB]: 5628
% 1.60/1.34 % (12109)Time elapsed: 0.008 s
% 1.60/1.34 % (12109)Instructions burned: 18 (million)
% 1.60/1.34 % (12109)------------------------------
% 1.60/1.34 % (12109)------------------------------
% 1.60/1.34 % (12106)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11946 for (3000ds/2Mi)
% 1.60/1.34 % (12105)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_11946 for (3000ds/27Mi)
% 1.60/1.34 % (12107)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_11946 for (3000ds/2Mi)
% 1.60/1.34 % (12106)Instruction limit reached!
% 1.60/1.34 % (12106)------------------------------
% 1.60/1.34 % (12106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (12107)Instruction limit reached!
% 1.60/1.34 % (12107)------------------------------
% 1.60/1.34 % (12107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (12106)Termination reason: Unknown
% 1.60/1.34 % (12106)Termination phase: Property scanning
% 1.60/1.34
% 1.60/1.34 % (12106)Memory used [KB]: 895
% 1.60/1.34 % (12106)Time elapsed: 0.003 s
% 1.60/1.34 % (12106)Instructions burned: 2 (million)
% 1.60/1.34 % (12106)------------------------------
% 1.60/1.34 % (12106)------------------------------
% 1.60/1.34 % (12107)Termination reason: Unknown
% 1.60/1.34 % (12107)Termination phase: shuffling
% 1.60/1.34
% 1.60/1.34 % (12107)Memory used [KB]: 895
% 1.60/1.34 % (12107)Time elapsed: 0.003 s
% 1.60/1.34 % (12107)Instructions burned: 2 (million)
% 1.60/1.34 % (12107)------------------------------
% 1.60/1.34 % (12107)------------------------------
% 1.60/1.34 % (12104)Instruction limit reached!
% 1.60/1.34 % (12104)------------------------------
% 1.60/1.34 % (12104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (12104)Termination reason: Unknown
% 1.60/1.34 % (12104)Termination phase: Saturation
% 1.60/1.34
% 1.60/1.34 % (12104)Memory used [KB]: 5500
% 1.60/1.34 % (12104)Time elapsed: 0.005 s
% 1.60/1.34 % (12104)Instructions burned: 4 (million)
% 1.60/1.34 % (12104)------------------------------
% 1.60/1.34 % (12104)------------------------------
% 1.60/1.34 % (12105)Refutation not found, incomplete strategy
% 1.60/1.34 % (12105)------------------------------
% 1.60/1.34 % (12105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (12105)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.34
% 1.60/1.34
% 1.60/1.34 % (12105)Memory used [KB]: 5500
% 1.60/1.34 % (12105)Time elapsed: 0.005 s
% 1.60/1.34 % (12105)Instructions burned: 5 (million)
% 1.60/1.34 % (12105)------------------------------
% 1.60/1.34 % (12105)------------------------------
% 1.60/1.35 % (12110)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11946 for (2999ds/3Mi)
% 1.60/1.35 % (12110)Instruction limit reached!
% 1.60/1.35 % (12110)------------------------------
% 1.60/1.35 % (12110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.35 % (12110)Termination reason: Unknown
% 1.60/1.35 % (12110)Termination phase: Saturation
% 1.60/1.35
% 1.60/1.35 % (12110)Memory used [KB]: 5500
% 1.60/1.35 % (12110)Time elapsed: 0.003 s
% 1.60/1.35 % (12110)Instructions burned: 3 (million)
% 1.60/1.35 % (12110)------------------------------
% 1.60/1.35 % (12110)------------------------------
% 1.60/1.36 % (12108)First to succeed.
% 1.60/1.36 % (12111)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_11946 for (2999ds/37Mi)
% 1.60/1.36 % (12112)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_11946 for (2999ds/15Mi)
% 1.60/1.36 % (12113)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_11946 for (2999ds/3Mi)
% 1.60/1.36 % (12115)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_11946 for (2999ds/7Mi)
% 1.60/1.36 % (12108)Refutation found. Thanks to Tanya!
% 1.60/1.36 % SZS status Theorem for DTF2THF_11946
% 1.60/1.36 % SZS output start Proof for DTF2THF_11946
% 1.60/1.36 thf(func_def_3, type, sP0: ($i > $o) > ($i > $o) > $i > $o).
% 1.60/1.36 thf(func_def_7, type, sK4: $i > $o).
% 1.60/1.36 thf(func_def_8, type, sK5: ($i > $o) > $i).
% 1.60/1.36 thf(func_def_14, type, ph7: !>[X0: $tType]:(X0)).
% 1.60/1.36 thf(f361,plain,(
% 1.60/1.36 $false),
% 1.60/1.36 inference(avatar_sat_refutation,[status(thm)],[f46,f50,f103,f119,f247,f256,f269,f297,f360])).
% 1.60/1.36 thf(f360,plain,(
% 1.60/1.36 ~spl6_26 | ~spl6_29),
% 1.60/1.36 inference(avatar_contradiction_clause,[status(thm)],[f359])).
% 1.60/1.36 thf(f359,plain,(
% 1.60/1.36 $false | (~spl6_26 | ~spl6_29)),
% 1.60/1.36 inference(subsumption_resolution,[status(thm)],[f358,f339])).
% 1.60/1.36 thf(f339,plain,(
% 1.60/1.36 ($true = (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) | (~spl6_26 | ~spl6_29)),
% 1.60/1.36 inference(not_proxy_clausification,[status(thm)],[f338])).
% 1.60/1.36 thf(f338,plain,(
% 1.60/1.36 ($true != (~ (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | (~spl6_26 | ~spl6_29)),
% 1.60/1.36 inference(beta_eta_normalization,[status(thm)],[f337])).
% 1.60/1.36 thf(f337,plain,(
% 1.60/1.36 (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))) != $true) | (~spl6_26 | ~spl6_29)),
% 1.60/1.36 inference(trivial_inequality_removal,[status(thm)],[f324])).
% 1.60/1.36 thf(f324,plain,(
% 1.60/1.36 ($true = $false) | ($true != $true) | (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))) != $true) | (~spl6_26 | ~spl6_29)),
% 1.60/1.36 inference(superposition,[status(thm)],[f285,f296])).
% 1.60/1.36 thf(f296,plain,(
% 1.60/1.36 ( ! [X0 : $i > $o] : (((sK4 @ (sK5 @ X0)) = $true) | ((X0 @ (sK5 @ X0)) != $true)) ) | ~spl6_29),
% 1.60/1.36 inference(avatar_component_clause,[status(thm)],[f295])).
% 1.60/1.36 thf(f295,definition,(
% 1.60/1.36 spl6_29 <=> ! [X0 : $i > $o] : (((sK4 @ (sK5 @ X0)) = $true) | ((X0 @ (sK5 @ X0)) != $true))),
% 1.60/1.36 introduced(definition,[new_symbols(naming,[spl6_29])],[avatar_definition])).
% 1.60/1.36 thf(f285,plain,(
% 1.60/1.36 ( ! [X3 : $i > $o] : (((X3 @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0))))) = $false) | ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0))))) != $true)) ) | ~spl6_26),
% 1.60/1.36 inference(not_proxy_clausification,[status(thm)],[f284])).
% 1.60/1.36 thf(f284,plain,(
% 1.60/1.36 ( ! [X3 : $i > $o] : (((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0))))) != $true) | ((~ (X3 @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0)))))) = $true)) ) | ~spl6_26),
% 1.60/1.36 inference(beta_eta_normalization,[status(thm)],[f276])).
% 1.60/1.36 thf(f276,plain,(
% 1.60/1.36 ( ! [X3 : $i > $o] : ((((^[Y0 : $i]: (~ (X3 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0))))) = $true) | ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0))))) != $true)) ) | ~spl6_26),
% 1.60/1.36 inference(primitive_instantiation,[status(thm)],[f268])).
% 1.60/1.36 thf(f268,plain,(
% 1.60/1.36 ( ! [X0 : $i > $o] : (((X0 @ (sK5 @ X0)) = $true) | ((sK4 @ (sK5 @ X0)) != $true)) ) | ~spl6_26),
% 1.60/1.36 inference(avatar_component_clause,[status(thm)],[f267])).
% 1.60/1.36 thf(f267,definition,(
% 1.60/1.36 spl6_26 <=> ! [X0 : $i > $o] : (((sK4 @ (sK5 @ X0)) != $true) | ((X0 @ (sK5 @ X0)) = $true))),
% 1.60/1.36 introduced(definition,[new_symbols(naming,[spl6_26])],[avatar_definition])).
% 1.60/1.36 thf(f358,plain,(
% 1.60/1.36 ($true != (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) | (~spl6_26 | ~spl6_29)),
% 1.60/1.36 inference(trivial_inequality_removal,[status(thm)],[f354])).
% 1.60/1.36 thf(f354,plain,(
% 1.60/1.36 ($true != (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) | ($true = $false) | (~spl6_26 | ~spl6_29)),
% 1.60/1.36 inference(superposition,[status(thm)],[f339,f285])).
% 1.60/1.36 thf(f297,plain,(
% 1.60/1.36 spl6_29 | spl6_16 | ~spl6_6),
% 1.60/1.36 inference(avatar_split_clause,[status(thm)],[f288,f48,f101,f295])).
% 1.60/1.36 thf(f101,definition,(
% 1.60/1.36 spl6_16 <=> ! [X1 : $i > $o] : (($true != (X1 @ sK1)) | ((X1 @ sK3) != $true))),
% 1.60/1.36 introduced(definition,[new_symbols(naming,[spl6_16])],[avatar_definition])).
% 1.60/1.36 thf(f48,definition,(
% 1.60/1.36 spl6_6 <=> ! [X4 : $i > $o,X5 : $i > $o] : (($true != (X4 @ sK1)) | ((sK4 @ (sK5 @ X5)) = $true) | ((X5 @ (sK5 @ X5)) != $true) | ($true = (sP0 @ X5 @ X4 @ sK3)))),
% 1.60/1.36 introduced(definition,[new_symbols(naming,[spl6_6])],[avatar_definition])).
% 1.60/1.36 thf(f288,plain,(
% 1.60/1.36 ( ! [X0 : $i > $o,X1 : $i > $o] : (((X1 @ sK3) != $true) | ($true != (X1 @ sK1)) | ((sK4 @ (sK5 @ X0)) = $true) | ((X0 @ (sK5 @ X0)) != $true)) ) | ~spl6_6),
% 1.60/1.36 inference(trivial_inequality_removal,[status(thm)],[f287])).
% 1.60/1.36 thf(f287,plain,(
% 1.60/1.36 ( ! [X0 : $i > $o,X1 : $i > $o] : (($true != $true) | ((sK4 @ (sK5 @ X0)) = $true) | ((X1 @ sK3) != $true) | ($true != (X1 @ sK1)) | ((X0 @ (sK5 @ X0)) != $true)) ) | ~spl6_6),
% 1.60/1.36 inference(superposition,[status(thm)],[f18,f49])).
% 1.60/1.36 thf(f49,plain,(
% 1.60/1.36 ( ! [X4 : $i > $o,X5 : $i > $o] : (($true = (sP0 @ X5 @ X4 @ sK3)) | ((sK4 @ (sK5 @ X5)) = $true) | ((X5 @ (sK5 @ X5)) != $true) | ($true != (X4 @ sK1))) ) | ~spl6_6),
% 1.60/1.36 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.60/1.36 thf(f18,plain,(
% 1.60/1.36 ( ! [X2 : $i > $o,X0 : $i,X1 : $i > $o] : (($true != (sP0 @ X2 @ X1 @ X0)) | ($true != (X1 @ X0))) )),
% 1.60/1.36 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.36 thf(f11,plain,(
% 1.60/1.36 ! [X0 : $i,X1 : $i > $o,X2 : $i > $o] : ((($true != (X1 @ X0)) & ((X2 @ X0) != $true)) | ($true != (sP0 @ X2 @ X1 @ X0)))),
% 1.60/1.36 inference(rectify,[status(thm)],[f10])).
% 1.60/1.36 thf(f10,plain,(
% 1.60/1.36 ! [X0 : $i,X4 : $i > $o,X5 : $i > $o] : ((((X4 @ X0) != $true) & ((X5 @ X0) != $true)) | ((sP0 @ X5 @ X4 @ X0) != $true))),
% 1.60/1.36 inference(nnf_transformation,[status(thm)],[f8])).
% 1.60/1.36 thf(f8,plain,(
% 1.60/1.36 ! [X0 : $i,X4 : $i > $o,X5 : $i > $o] : ((((X4 @ X0) != $true) & ((X5 @ X0) != $true)) | ~((sP0 @ X5 @ X4 @ X0) = $true))),
% 1.60/1.36 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.60/1.36 thf(f269,plain,(
% 1.60/1.36 spl6_26 | spl6_16 | ~spl6_5),
% 1.60/1.36 inference(avatar_split_clause,[status(thm)],[f265,f44,f101,f267])).
% 1.60/1.36 thf(f44,definition,(
% 1.60/1.36 spl6_5 <=> ! [X4 : $i > $o,X5 : $i > $o] : (($true = (sP0 @ X5 @ X4 @ sK3)) | ((X5 @ (sK5 @ X5)) = $true) | ($true != (X4 @ sK1)) | ((sK4 @ (sK5 @ X5)) != $true))),
% 1.60/1.36 introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition])).
% 1.60/1.36 thf(f265,plain,(
% 1.60/1.36 ( ! [X0 : $i > $o,X1 : $i > $o] : (((X1 @ sK3) != $true) | ((sK4 @ (sK5 @ X0)) != $true) | ((X0 @ (sK5 @ X0)) = $true) | ($true != (X1 @ sK1))) ) | ~spl6_5),
% 1.60/1.36 inference(trivial_inequality_removal,[status(thm)],[f263])).
% 1.60/1.36 thf(f263,plain,(
% 1.60/1.36 ( ! [X0 : $i > $o,X1 : $i > $o] : (((X1 @ sK3) != $true) | ($true != $true) | ((sK4 @ (sK5 @ X0)) != $true) | ($true != (X1 @ sK1)) | ((X0 @ (sK5 @ X0)) = $true)) ) | ~spl6_5),
% 1.60/1.36 inference(superposition,[status(thm)],[f18,f45])).
% 1.60/1.36 thf(f45,plain,(
% 1.60/1.36 ( ! [X4 : $i > $o,X5 : $i > $o] : (($true = (sP0 @ X5 @ X4 @ sK3)) | ($true != (X4 @ sK1)) | ((X5 @ (sK5 @ X5)) = $true) | ((sK4 @ (sK5 @ X5)) != $true)) ) | ~spl6_5),
% 1.60/1.36 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.60/1.36 thf(f256,plain,(
% 1.60/1.36 ~spl6_16),
% 1.60/1.36 inference(avatar_contradiction_clause,[status(thm)],[f255])).
% 1.60/1.36 thf(f255,plain,(
% 1.60/1.36 $false | ~spl6_16),
% 1.60/1.36 inference(trivial_inequality_removal,[status(thm)],[f254])).
% 1.60/1.36 thf(f254,plain,(
% 1.60/1.36 ($true != $true) | ~spl6_16),
% 1.60/1.36 inference(duplicate_literal_removal,[status(thm)],[f253])).
% 1.60/1.36 thf(f253,plain,(
% 1.60/1.36 ($true != $true) | ($true != $true) | ~spl6_16),
% 1.60/1.36 inference(beta_eta_normalization,[status(thm)],[f248])).
% 1.60/1.36 thf(f248,plain,(
% 1.60/1.36 (((^[Y0 : $i]: ($true)) @ sK3) != $true) | (((^[Y0 : $i]: ($true)) @ sK1) != $true) | ~spl6_16),
% 1.60/1.36 inference(primitive_instantiation,[status(thm)],[f102])).
% 1.60/1.36 thf(f102,plain,(
% 1.60/1.36 ( ! [X1 : $i > $o] : (($true != (X1 @ sK1)) | ((X1 @ sK3) != $true)) ) | ~spl6_16),
% 1.60/1.36 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.60/1.36 thf(f247,plain,(
% 1.60/1.36 spl6_2 | ~spl6_9 | ~spl6_11),
% 1.60/1.36 inference(avatar_contradiction_clause,[status(thm)],[f246])).
% 1.60/1.36 thf(f246,plain,(
% 1.60/1.36 $false | (spl6_2 | ~spl6_9 | ~spl6_11)),
% 1.60/1.36 inference(subsumption_resolution,[status(thm)],[f245,f34])).
% 1.60/1.36 thf(f34,plain,(
% 1.60/1.36 ($true != (sK4 @ sK2)) | spl6_2),
% 1.60/1.36 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.60/1.36 thf(f32,definition,(
% 1.60/1.36 spl6_2 <=> ($true = (sK4 @ sK2))),
% 1.60/1.36 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.60/1.36 thf(f245,plain,(
% 1.60/1.36 ($true = (sK4 @ sK2)) | (spl6_2 | ~spl6_9 | ~spl6_11)),
% 1.60/1.36 inference(subsumption_resolution,[status(thm)],[f241,f227])).
% 1.60/1.36 thf(f227,plain,(
% 1.60/1.36 ($true = (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) | (spl6_2 | ~spl6_9 | ~spl6_11)),
% 1.60/1.36 inference(subsumption_resolution,[status(thm)],[f201,f34])).
% 1.60/1.36 thf(f201,plain,(
% 1.60/1.36 ($true = (sK4 @ sK2)) | ($true = (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) | (~spl6_9 | ~spl6_11)),
% 1.60/1.36 inference(not_proxy_clausification,[status(thm)],[f200])).
% 1.60/1.36 thf(f200,plain,(
% 1.60/1.36 ($true != (~ (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ($true = (sK4 @ sK2)) | (~spl6_9 | ~spl6_11)),
% 1.60/1.36 inference(duplicate_literal_removal,[status(thm)],[f199])).
% 1.60/1.36 thf(f199,plain,(
% 1.60/1.36 ($true = (sK4 @ sK2)) | ($true = (sK4 @ sK2)) | ($true != (~ (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | (~spl6_9 | ~spl6_11)),
% 1.60/1.36 inference(not_proxy_clausification,[status(thm)],[f198])).
% 1.60/1.36 thf(f198,plain,(
% 1.60/1.36 ($true != (~ (sK4 @ sK2))) | ($true != (~ (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ($true = (sK4 @ sK2)) | (~spl6_9 | ~spl6_11)),
% 1.60/1.36 inference(beta_eta_normalization,[status(thm)],[f197])).
% 1.60/1.36 thf(f197,plain,(
% 1.60/1.36 (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))) != $true) | ($true != ((^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK2)) | ($true = (sK4 @ sK2)) | (~spl6_9 | ~spl6_11)),
% 1.60/1.36 inference(trivial_inequality_removal,[status(thm)],[f187])).
% 1.60/1.36 thf(f187,plain,(
% 1.60/1.36 (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))) != $true) | ($true = (sK4 @ sK2)) | ($true != ((^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK2)) | ($true != $true) | ($true = $false) | (~spl6_9 | ~spl6_11)),
% 1.60/1.36 inference(superposition,[status(thm)],[f151,f65])).
% 1.60/1.36 thf(f65,plain,(
% 1.60/1.36 ( ! [X0 : $i > $o] : (((sK4 @ (sK5 @ X0)) = $true) | ((X0 @ (sK5 @ X0)) != $true) | ((X0 @ sK2) != $true)) ) | ~spl6_9),
% 1.60/1.36 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.60/1.36 thf(f64,definition,(
% 1.60/1.36 spl6_9 <=> ! [X0 : $i > $o] : (((X0 @ sK2) != $true) | ((X0 @ (sK5 @ X0)) != $true) | ((sK4 @ (sK5 @ X0)) = $true))),
% 1.60/1.36 introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition])).
% 1.60/1.36 thf(f151,plain,(
% 1.60/1.36 ( ! [X3 : $i > $o] : (((X3 @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0))))) = $false) | ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0))))) != $true) | ((X3 @ sK2) = $true)) ) | ~spl6_11),
% 1.60/1.36 inference(not_proxy_clausification,[status(thm)],[f150])).
% 1.60/1.36 thf(f150,plain,(
% 1.60/1.36 ( ! [X3 : $i > $o] : (((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0))))) != $true) | ((~ (X3 @ sK2)) != $true) | ((X3 @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0))))) = $false)) ) | ~spl6_11),
% 1.60/1.36 inference(not_proxy_clausification,[status(thm)],[f149])).
% 1.60/1.36 thf(f149,plain,(
% 1.60/1.36 ( ! [X3 : $i > $o] : (((~ (X3 @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0)))))) = $true) | ((~ (X3 @ sK2)) != $true) | ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0))))) != $true)) ) | ~spl6_11),
% 1.60/1.36 inference(beta_eta_normalization,[status(thm)],[f143])).
% 1.60/1.36 thf(f143,plain,(
% 1.60/1.36 ( ! [X3 : $i > $o] : ((((^[Y0 : $i]: (~ (X3 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0))))) = $true) | (((^[Y0 : $i]: (~ (X3 @ Y0))) @ sK2) != $true) | ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X3 @ Y0))))) != $true)) ) | ~spl6_11),
% 1.60/1.36 inference(primitive_instantiation,[status(thm)],[f77])).
% 1.60/1.36 thf(f77,plain,(
% 1.60/1.36 ( ! [X0 : $i > $o] : (((X0 @ (sK5 @ X0)) = $true) | ((sK4 @ (sK5 @ X0)) != $true) | ((X0 @ sK2) != $true)) ) | ~spl6_11),
% 1.60/1.36 inference(avatar_component_clause,[status(thm)],[f76])).
% 1.60/1.36 thf(f76,definition,(
% 1.60/1.36 spl6_11 <=> ! [X0 : $i > $o] : (((sK4 @ (sK5 @ X0)) != $true) | ((X0 @ sK2) != $true) | ((X0 @ (sK5 @ X0)) = $true))),
% 1.60/1.36 introduced(definition,[new_symbols(naming,[spl6_11])],[avatar_definition])).
% 1.60/1.36 thf(f241,plain,(
% 1.60/1.36 ($true != (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) | ($true = (sK4 @ sK2)) | (spl6_2 | ~spl6_9 | ~spl6_11)),
% 1.60/1.36 inference(trivial_inequality_removal,[status(thm)],[f239])).
% 1.60/1.36 thf(f239,plain,(
% 1.60/1.36 ($true != (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) | ($true = $false) | ($true = (sK4 @ sK2)) | (spl6_2 | ~spl6_9 | ~spl6_11)),
% 1.60/1.36 inference(superposition,[status(thm)],[f227,f151])).
% 1.60/1.36 thf(f119,plain,(
% 1.60/1.36 spl6_16 | spl6_9),
% 1.60/1.36 inference(avatar_split_clause,[status(thm)],[f113,f64,f101])).
% 1.60/1.36 thf(f113,plain,(
% 1.60/1.36 ( ! [X0 : $i > $o,X1 : $i > $o] : (((X1 @ sK3) != $true) | ((X0 @ sK2) != $true) | ((sK4 @ (sK5 @ X0)) = $true) | ((X0 @ (sK5 @ X0)) != $true) | ($true != (X1 @ sK1))) )),
% 1.60/1.36 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.60/1.36 thf(f112,plain,(
% 1.60/1.36 ( ! [X0 : $i > $o,X1 : $i > $o] : (((sK4 @ (sK5 @ X0)) = $true) | ($true != (X1 @ sK1)) | ($true != $true) | ((X1 @ sK3) != $true) | ((X0 @ (sK5 @ X0)) != $true) | ((X0 @ sK2) != $true)) )),
% 1.60/1.36 inference(superposition,[status(thm)],[f18,f24])).
% 1.60/1.36 thf(f24,plain,(
% 1.60/1.36 ( ! [X4 : $i > $o,X5 : $i > $o] : (($true = (sP0 @ X5 @ X4 @ sK3)) | ($true != (X4 @ sK1)) | ((X5 @ (sK5 @ X5)) != $true) | ((sK4 @ (sK5 @ X5)) = $true) | ((X5 @ sK2) != $true)) )),
% 1.60/1.36 inference(cnf_transformation,[status(thm)],[f16])).
% 1.60/1.36 thf(f16,plain,(
% 1.60/1.36 ! [X4 : $i > $o,X5 : $i > $o] : ((($true != (X4 @ sK1)) & ((sK4 @ sK1) = $true)) | (($true != (sK4 @ sK2)) & ((X5 @ sK2) != $true)) | ((((X5 @ (sK5 @ X5)) != $true) | ((sK4 @ (sK5 @ X5)) = $true)) & (((X5 @ (sK5 @ X5)) = $true) | ((sK4 @ (sK5 @ X5)) != $true))) | ($true = (sP0 @ X5 @ X4 @ sK3)))),
% 1.60/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f13,f15,f14])).
% 1.60/1.36 thf(f14,plain,(
% 1.60/1.36 ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i > $o] : ! [X4 : $i > $o,X5 : $i > $o] : ((((X4 @ X0) != $true) & ((X3 @ X0) = $true)) | (((X3 @ X1) != $true) & ((X5 @ X1) != $true)) | ? [X6 : $i] : ((((X5 @ X6) != $true) | ((X3 @ X6) = $true)) & (((X5 @ X6) = $true) | ((X3 @ X6) != $true))) | ((sP0 @ X5 @ X4 @ X2) = $true)) => ! [X5 : $i > $o,X4 : $i > $o] : ((($true != (X4 @ sK1)) & ((sK4 @ sK1) = $true)) | (($true != (sK4 @ sK2)) & ((X5 @ sK2) != $true)) | ? [X6 : $i] : ((((X5 @ X6) != $true) | ((sK4 @ X6) = $true)) & (((X5 @ X6) = $true) | ((sK4 @ X6) != $true))) | ($true = (sP0 @ X5 @ X4 @ sK3)))),
% 1.60/1.36 introduced(definition,[],[choice_axiom])).
% 1.60/1.36 thf(f15,plain,(
% 1.60/1.36 ! [X5 : $i > $o] : (? [X6 : $i] : ((((X5 @ X6) != $true) | ((sK4 @ X6) = $true)) & (((X5 @ X6) = $true) | ((sK4 @ X6) != $true))) => ((((X5 @ (sK5 @ X5)) != $true) | ((sK4 @ (sK5 @ X5)) = $true)) & (((X5 @ (sK5 @ X5)) = $true) | ((sK4 @ (sK5 @ X5)) != $true))))),
% 1.60/1.36 introduced(definition,[],[choice_axiom])).
% 1.60/1.36 thf(f13,plain,(
% 1.60/1.36 ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i > $o] : ! [X4 : $i > $o,X5 : $i > $o] : ((((X4 @ X0) != $true) & ((X3 @ X0) = $true)) | (((X3 @ X1) != $true) & ((X5 @ X1) != $true)) | ? [X6 : $i] : ((((X5 @ X6) != $true) | ((X3 @ X6) = $true)) & (((X5 @ X6) = $true) | ((X3 @ X6) != $true))) | ((sP0 @ X5 @ X4 @ X2) = $true))),
% 1.60/1.36 inference(rectify,[status(thm)],[f12])).
% 1.60/1.36 thf(f12,plain,(
% 1.60/1.36 ? [X3 : $i,X2 : $i,X0 : $i,X1 : $i > $o] : ! [X4 : $i > $o,X5 : $i > $o] : ((((X4 @ X3) != $true) & ((X1 @ X3) = $true)) | (((X1 @ X2) != $true) & ((X5 @ X2) != $true)) | ? [X6 : $i] : ((((X5 @ X6) != $true) | ($true = (X1 @ X6))) & (((X5 @ X6) = $true) | ($true != (X1 @ X6)))) | ((sP0 @ X5 @ X4 @ X0) = $true))),
% 1.60/1.36 inference(nnf_transformation,[status(thm)],[f9])).
% 1.60/1.36 thf(f9,plain,(
% 1.60/1.36 ? [X3 : $i,X2 : $i,X0 : $i,X1 : $i > $o] : ! [X4 : $i > $o,X5 : $i > $o] : ((((X4 @ X3) != $true) & ((X1 @ X3) = $true)) | (((X1 @ X2) != $true) & ((X5 @ X2) != $true)) | ? [X6 : $i] : (($true != (X1 @ X6)) <~> ((X5 @ X6) = $true)) | ((sP0 @ X5 @ X4 @ X0) = $true))),
% 1.60/1.36 inference(definition_folding,[status(thm)],[f7,f8])).
% 1.60/1.36 thf(f7,plain,(
% 1.60/1.36 ? [X3 : $i,X2 : $i,X0 : $i,X1 : $i > $o] : ! [X4 : $i > $o,X5 : $i > $o] : ((((X4 @ X3) != $true) & ((X1 @ X3) = $true)) | (((X1 @ X2) != $true) & ((X5 @ X2) != $true)) | ? [X6 : $i] : (($true != (X1 @ X6)) <~> ((X5 @ X6) = $true)) | (((X4 @ X0) != $true) & ((X5 @ X0) != $true)))),
% 1.60/1.36 inference(ennf_transformation,[status(thm)],[f6])).
% 1.60/1.36 thf(f6,plain,(
% 1.60/1.36 ~! [X1 : $i > $o,X2 : $i,X0 : $i,X3 : $i] : ? [X4 : $i > $o,X5 : $i > $o] : ((((X1 @ X2) = $true) | ((X5 @ X2) = $true)) & (((X4 @ X3) = $true) | ((X1 @ X3) != $true)) & (((X4 @ X0) = $true) | ((X5 @ X0) = $true)) & ! [X6 : $i] : (((X5 @ X6) = $true) <=> ($true != (X1 @ X6))))),
% 1.60/1.36 inference(flattening,[status(thm)],[f5])).
% 1.60/1.36 thf(f5,plain,(
% 1.60/1.36 ~! [X0 : $i,X1 : $i > $o,X2 : $i,X3 : $i] : ? [X4 : $i > $o,X5 : $i > $o] : ((((X4 @ X3) = $true) | ~((X1 @ X3) = $true)) & (((X4 @ X0) = $true) | ((X5 @ X0) = $true)) & ! [X6 : $i] : (~($true = (X1 @ X6)) <=> ((X5 @ X6) = $true)) & (((X1 @ X2) = $true) | ((X5 @ X2) = $true)))),
% 1.60/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 1.60/1.36 thf(f4,plain,(
% 1.60/1.36 ~! [X0 : $i,X1 : $i > $o,X2 : $i,X3 : $i] : ? [X4 : $i > $o,X5 : $i > $o] : (((X4 @ X3) | ~(X1 @ X3)) & ((X4 @ X0) | (X5 @ X0)) & ! [X6 : $i] : (~(X1 @ X6) <=> (X5 @ X6)) & ((X1 @ X2) | (X5 @ X2)))),
% 1.60/1.36 inference(rectify,[status(thm)],[f2])).
% 1.60/1.36 thf(f2,negated_conjecture,(
% 1.60/1.36 ~! [X0 : $i,X3 : $i > $o,X1 : $i,X2 : $i] : ? [X4 : $i > $o,X5 : $i > $o] : (((X4 @ X2) | ~(X3 @ X2)) & ((X4 @ X0) | (X5 @ X0)) & ! [X6 : $i] : (~(X3 @ X6) <=> (X5 @ X6)) & ((X3 @ X1) | (X5 @ X1)))),
% 1.60/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.60/1.36 thf(f1,conjecture,(
% 1.60/1.36 ! [X0 : $i,X3 : $i > $o,X1 : $i,X2 : $i] : ? [X4 : $i > $o,X5 : $i > $o] : (((X4 @ X2) | ~(X3 @ X2)) & ((X4 @ X0) | (X5 @ X0)) & ! [X6 : $i] : (~(X3 @ X6) <=> (X5 @ X6)) & ((X3 @ X1) | (X5 @ X1)))),
% 1.60/1.36 file('/export/starexec/sandbox2/tmp/tmp.ni0usXZvD3/DTF2THF_11946.p',cTHM125D)).
% 1.60/1.36 thf(f103,plain,(
% 1.60/1.36 spl6_11 | spl6_16),
% 1.60/1.36 inference(avatar_split_clause,[status(thm)],[f95,f101,f76])).
% 1.60/1.36 thf(f95,plain,(
% 1.60/1.36 ( ! [X0 : $i > $o,X1 : $i > $o] : (((sK4 @ (sK5 @ X0)) != $true) | ($true != (X1 @ sK1)) | ((X0 @ (sK5 @ X0)) = $true) | ((X1 @ sK3) != $true) | ((X0 @ sK2) != $true)) )),
% 1.60/1.36 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.60/1.36 thf(f93,plain,(
% 1.60/1.36 ( ! [X0 : $i > $o,X1 : $i > $o] : (((sK4 @ (sK5 @ X0)) != $true) | ((X0 @ sK2) != $true) | ((X1 @ sK3) != $true) | ($true != $true) | ($true != (X1 @ sK1)) | ((X0 @ (sK5 @ X0)) = $true)) )),
% 1.60/1.36 inference(superposition,[status(thm)],[f18,f23])).
% 1.60/1.36 thf(f23,plain,(
% 1.60/1.36 ( ! [X4 : $i > $o,X5 : $i > $o] : (($true = (sP0 @ X5 @ X4 @ sK3)) | ((X5 @ sK2) != $true) | ((sK4 @ (sK5 @ X5)) != $true) | ((X5 @ (sK5 @ X5)) = $true) | ($true != (X4 @ sK1))) )),
% 1.60/1.36 inference(cnf_transformation,[status(thm)],[f16])).
% 1.60/1.36 thf(f50,plain,(
% 1.60/1.36 spl6_6 | ~spl6_2),
% 1.60/1.36 inference(avatar_split_clause,[status(thm)],[f26,f32,f48])).
% 1.60/1.36 thf(f26,plain,(
% 1.60/1.36 ( ! [X4 : $i > $o,X5 : $i > $o] : (($true != (X4 @ sK1)) | ((X5 @ (sK5 @ X5)) != $true) | ($true = (sP0 @ X5 @ X4 @ sK3)) | ((sK4 @ (sK5 @ X5)) = $true) | ($true != (sK4 @ sK2))) )),
% 1.60/1.36 inference(cnf_transformation,[status(thm)],[f16])).
% 1.60/1.36 thf(f46,plain,(
% 1.60/1.36 ~spl6_2 | spl6_5),
% 1.60/1.36 inference(avatar_split_clause,[status(thm)],[f25,f44,f32])).
% 1.60/1.36 thf(f25,plain,(
% 1.60/1.36 ( ! [X4 : $i > $o,X5 : $i > $o] : (($true = (sP0 @ X5 @ X4 @ sK3)) | ($true != (sK4 @ sK2)) | ((sK4 @ (sK5 @ X5)) != $true) | ($true != (X4 @ sK1)) | ((X5 @ (sK5 @ X5)) = $true)) )),
% 1.60/1.36 inference(cnf_transformation,[status(thm)],[f16])).
% 1.60/1.36 % SZS output end Proof for DTF2THF_11946
% 1.60/1.36 % (12108)------------------------------
% 1.60/1.36 % (12108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.36 % (12108)Termination reason: Refutation
% 1.60/1.36
% 1.60/1.36 % (12108)Memory used [KB]: 5756
% 1.60/1.36 % (12108)Time elapsed: 0.029 s
% 1.60/1.36 % (12108)Instructions burned: 36 (million)
% 1.60/1.36 % (12108)------------------------------
% 1.60/1.36 % (12108)------------------------------
% 1.60/1.36 % (12102)Success in time 0.022 s
%------------------------------------------------------------------------------