%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV171^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:28 AM UTC 2026
% Result : Theorem 1.56s 1.36s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 2 unt; 0 typ; 3 def)
% Number of atoms : 108 ( 81 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 582 ( 80 ~; 51 |; 8 &; 434 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 428 ( 428 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 4 con; 0-6 aty)
% Number of variables : 331 ( 246 ^; 69 !; 16 ?; 331 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_6,type,
sK0: ( a > ( a > a > a ) > a ) > a ).
thf(func_def_7,type,
sK1: ( a > ( a > a > a ) > a ) > a ).
thf(func_def_8,type,
sK2: ( a > ( a > a > a ) > a ) > a ).
thf(func_def_10,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK5: ( a > ( a > a > a ) > a ) > ( a > ( a > a > a ) > a ) > a > a > a > a ).
thf(func_def_18,type,
sK6: ( a > ( a > a > a ) > a ) > ( a > ( a > a > a ) > a ) > a > a > a > a ).
thf(func_def_19,type,
sK7: ( a > ( a > a > a ) > a ) > ( a > ( a > a > a ) > a ) > a > a > a ).
thf(func_def_20,type,
sK8: ( a > ( a > a > a ) > a ) > a ).
thf(func_def_21,type,
sK9: a > ( a > ( a > a > a ) > a ) > ( a > ( a > a > a ) > a ) > ( a > ( a > a > a ) > a > ( a > a > a ) > a ) > a > a > a ).
thf(func_def_22,type,
sK10: ( a > ( a > a > a ) > a ) > a > a > a ).
thf(func_def_23,type,
sK11: a > ( a > ( a > a > a ) > a ) > ( a > ( a > a > a ) > a ) > ( a > ( a > a > a ) > a > ( a > a > a ) > a ) > a > a > a ).
thf(f161,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f87,f103,f109,f160]) ).
thf(f160,plain,
( spl3_2
| ~ spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f153,f85,f81]) ).
thf(f81,definition,
( spl3_2
<=> ! [X8: a] :
( ( ^ [Y0: a > a > a] : X8 )
!= ( ^ [Y0: a > a > a] :
( sK2
@ ^ [Y1: a,Y2: a > a > a] : ( Y2 @ Y1 @ Y1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f85,definition,
( spl3_3
<=> ! [X4: a > ( a > a > a ) > a,X5: a] :
( ( ( ^ [Y0: a > a > a] : X5 )
!= ( X4
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X4 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK0
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ Y0 ) )
!= ( sK0
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X4 @ Y0 @ Y1 ) ) ) )
| ( ( ^ [Y0: a,Y1: a > a > a] : Y0 )
!= X4 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f153,plain,
( ! [X0: a] :
( ( ^ [Y0: a > a > a] :
( sK2
@ ^ [Y1: a,Y2: a > a > a] : ( Y2 @ Y1 @ Y1 ) ) )
!= ( ^ [Y0: a > a > a] : X0 ) )
| ~ spl3_3 ),
inference(beta_eta_normalization,[status(thm)],[f152]) ).
thf(f152,plain,
( ! [X0: a] :
( ( ^ [Y0: a,Y1: a > a > a] : Y0
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] :
( Y1 @ Y0
@ ( ^ [Y2: a,Y3: a > a > a] : Y2
@ Y0
@ Y1 ) ) ) )
!= ( ^ [Y0: a > a > a] : X0 ) )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f148]) ).
thf(f148,plain,
( ! [X0: a] :
( ( ( ^ [Y0: a,Y1: a > a > a] : Y0
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] :
( Y1 @ Y0
@ ( ^ [Y2: a,Y3: a > a > a] : Y2
@ Y0
@ Y1 ) ) ) )
!= ( ^ [Y0: a > a > a] : X0 ) )
| ( ( ^ [Y0: a,Y1: a > a > a] : Y0 )
!= ( ^ [Y0: a,Y1: a > a > a] : Y0 ) ) )
| ~ spl3_3 ),
inference(equality_resolution,[status(thm)],[f135]) ).
thf(f135,plain,
( ! [X0: a > ( a > a > a ) > a,X1: a] :
( ( ( sK10 @ X0 @ ( sK8 @ X0 ) @ ( X0 @ ( sK8 @ X0 ) @ ( sK10 @ X0 ) ) )
!= ( sK10 @ X0 @ ( sK8 @ X0 ) @ ( sK8 @ X0 ) ) )
| ( ( ^ [Y0: a,Y1: a > a > a] : Y0 )
!= X0 )
| ( ( ^ [Y0: a > a > a] : X1 )
!= ( X0
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl3_3 ),
inference(beta_eta_normalization,[status(thm)],[f133]) ).
thf(f133,plain,
( ! [X0: a > ( a > a > a ) > a,X1: a] :
( ( ( ^ [Y0: a > a > a] : ( Y0 @ ( sK8 @ X0 ) @ ( X0 @ ( sK8 @ X0 ) @ Y0 ) )
@ ( sK10 @ X0 ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ ( sK8 @ X0 ) @ ( sK8 @ X0 ) )
@ ( sK10 @ X0 ) ) )
| ( ( ^ [Y0: a > a > a] : X1 )
!= ( X0
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: a,Y1: a > a > a] : Y0 )
!= X0 ) )
| ~ spl3_3 ),
inference(negative_extensionality,[status(thm)],[f128]) ).
thf(f128,plain,
( ! [X0: a > ( a > a > a ) > a,X1: a] :
( ( ( ^ [Y0: a > a > a] : ( Y0 @ ( sK8 @ X0 ) @ ( X0 @ ( sK8 @ X0 ) @ Y0 ) ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ ( sK8 @ X0 ) @ ( sK8 @ X0 ) ) ) )
| ( ( ^ [Y0: a,Y1: a > a > a] : Y0 )
!= X0 )
| ( ( ^ [Y0: a > a > a] : X1 )
!= ( X0
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl3_3 ),
inference(beta_eta_normalization,[status(thm)],[f127]) ).
thf(f127,plain,
( ! [X0: a > ( a > a > a ) > a,X1: a] :
( ( ( ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X0 @ Y0 @ Y1 ) )
@ ( sK8 @ X0 ) )
!= ( ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ Y0 )
@ ( sK8 @ X0 ) ) )
| ( ( ^ [Y0: a > a > a] : X1 )
!= ( X0
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: a,Y1: a > a > a] : Y0 )
!= X0 ) )
| ~ spl3_3 ),
inference(negative_extensionality,[status(thm)],[f118]) ).
thf(f118,plain,
( ! [X0: a > ( a > a > a ) > a,X1: a] :
( ( ( ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ Y0 ) )
!= ( ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
| ( ( ^ [Y0: a,Y1: a > a > a] : Y0 )
!= X0 )
| ( ( ^ [Y0: a > a > a] : X1 )
!= ( X0
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl3_3 ),
inference(equality_resolution,[status(thm)],[f86]) ).
thf(f86,plain,
( ! [X4: a > ( a > a > a ) > a,X5: a] :
( ( ( sK0
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ Y0 ) )
!= ( sK0
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X4 @ Y0 @ Y1 ) ) ) )
| ( ( ^ [Y0: a,Y1: a > a > a] : Y0 )
!= X4 )
| ( ( ^ [Y0: a > a > a] : X5 )
!= ( X4
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X4 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f85]) ).
thf(f109,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[status(thm)],[f108]) ).
thf(f108,plain,
( $false
| ~ spl3_4 ),
inference(equality_resolution,[status(thm)],[f102]) ).
thf(f102,plain,
( ! [X1: a > ( a > a > a ) > a] :
( ( ^ [Y0: a > a > a,Y1: a,Y2: a > a > a] : Y1 )
!= ( ^ [Y0: a > a > a] : X1 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f101,definition,
( spl3_4
<=> ! [X1: a > ( a > a > a ) > a] :
( ( ^ [Y0: a > a > a,Y1: a,Y2: a > a > a] : Y1 )
!= ( ^ [Y0: a > a > a] : X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f103,plain,
( spl3_4
| spl3_4
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f99,f81,f101,f101]) ).
thf(f99,plain,
( ! [X0: a > ( a > a > a ) > a,X1: a > ( a > a > a ) > a] :
( ( ( ^ [Y0: a > a > a] : X0 )
!= ( ^ [Y0: a > a > a,Y1: a,Y2: a > a > a] : Y1 ) )
| ( ( ^ [Y0: a > a > a,Y1: a,Y2: a > a > a] : Y1 )
!= ( ^ [Y0: a > a > a] : X1 ) ) )
| ~ spl3_2 ),
inference(beta_eta_normalization,[status(thm)],[f98]) ).
thf(f98,plain,
( ! [X0: a > ( a > a > a ) > a,X1: a > ( a > a > a ) > a] :
( ( ( ^ [Y0: a > a > a,Y1: a,Y2: a > a > a] : ( X0 @ Y1 @ Y2 ) )
!= ( ^ [Y0: a > a > a,Y1: a,Y2: a > a > a] : Y1 ) )
| ( ( ^ [Y0: a > a > a,Y1: a,Y2: a > a > a] : ( X1 @ Y1 @ Y2 ) )
!= ( ^ [Y0: a > a > a,Y1: a,Y2: a > a > a] : Y1 ) ) )
| ~ spl3_2 ),
inference(equality_resolution,[status(thm)],[f82]) ).
thf(f82,plain,
( ! [X8: a] :
( ( ^ [Y0: a > a > a] : X8 )
!= ( ^ [Y0: a > a > a] :
( sK2
@ ^ [Y1: a,Y2: a > a > a] : ( Y2 @ Y1 @ Y1 ) ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f87,plain,
( spl3_2
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f63,f85,f81]) ).
thf(f63,plain,
! [X6: a,X4: a > ( a > a > a ) > a,X5: a] :
( ( ( ^ [Y0: a > a > a] : X5 )
!= ( X4
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X4 @ Y0 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: a,Y1: a > a > a] : Y0 )
!= X4 )
| ( ( sK0
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ Y0 ) )
!= ( sK0
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X4 @ Y0 @ Y1 ) ) ) )
| ( ( ^ [Y0: a > a > a] : X6 )
!= ( ^ [Y0: a > a > a] :
( sK2
@ ^ [Y1: a,Y2: a > a > a] : ( Y2 @ Y1 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X6: a,X4: a > ( a > a > a ) > a,X5: a] :
( ( ( ^ [Y0: a > a > a] : X6 )
!= ( ^ [Y0: a,Y1: a > a > a] : Y0
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] :
( Y1 @ Y0
@ ( ^ [Y2: a,Y3: a > a > a] : Y2
@ Y0
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: a,Y1: a] : Y1
@ ( sK0
@ ^ [Y0: a,Y1: a > a > a] :
( Y1 @ Y0
@ ( ^ [Y2: a,Y3: a > a > a] : Y2
@ Y0
@ Y1 ) ) )
@ ( ^ [Y0: a,Y1: a > a > a] : Y0
@ ( sK0
@ ^ [Y0: a,Y1: a > a > a] :
( Y1 @ Y0
@ ( ^ [Y2: a,Y3: a > a > a] : Y2
@ Y0
@ Y1 ) ) )
@ ^ [Y0: a,Y1: a] : Y1 ) )
!= ( sK0
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X4 @ Y0 @ Y1 ) ) ) )
| ( ( ^ [Y0: a > a > a] : X5 )
!= ( X4
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X4 @ Y0 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: a,Y1: a > a > a] : ( X4 @ Y0 @ Y1 ) )
!= ( ^ [Y0: a,Y1: a > a > a] : Y0 ) ) ),
inference(constrained_superposition,[status(thm)],[f15,f28]) ).
thf(f28,plain,
! [X2: a > a > a,X0: a,X1: a > ( a > a > a ) > a] :
( ( ( X2
@ ( sK0
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ( X1
@ ( sK0
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ X2 ) )
= ( X2
@ ( sK1
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ( X1
@ ( sK1
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ X2 ) ) )
| ( ( X1
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X1 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a > a > a] : X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: a > a > a,X0: a,X1: a > ( a > a > a ) > a] :
( ( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK1
@ ^ [Y1: a,Y2: a > a > a] : ( Y2 @ Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ( X1
@ ( sK1
@ ^ [Y1: a,Y2: a > a > a] : ( Y2 @ Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ Y0 ) )
@ X2 )
= ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a > a > a] : ( Y2 @ Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ( X1
@ ( sK0
@ ^ [Y1: a,Y2: a > a > a] : ( Y2 @ Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ Y0 ) )
@ X2 ) )
| ( ( X1
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X1 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a > a > a] : X0 ) ) ),
inference(argument_congruence,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: a,X1: a > ( a > a > a ) > a] :
( ( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK1
@ ^ [Y1: a,Y2: a > a > a] : ( Y2 @ Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ( X1
@ ( sK1
@ ^ [Y1: a,Y2: a > a > a] : ( Y2 @ Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ Y0 ) ) )
= ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a > a > a] : ( Y2 @ Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ( X1
@ ( sK0
@ ^ [Y1: a,Y2: a > a > a] : ( Y2 @ Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ Y0 ) ) ) )
| ( ( X1
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X1 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a > a > a] : X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: a,X1: a > ( a > a > a ) > a] :
( ( ( ^ [Y0: a > a > a] :
( X1
@ ( sK2
@ ^ [Y1: a,Y2: a > a > a] :
( Y2
@ ( ^ [Y3: a,Y4: a > a > a] : Y3
@ Y1
@ Y2 )
@ ( X1 @ Y1 @ Y2 ) ) )
@ Y0 ) )
!= ( ^ [Y0: a > a > a] : X0 ) )
| ( ( ^ [Y0: a,Y1: a > a > a] :
( Y1
@ ( ^ [Y2: a,Y3: a > a > a] : Y2
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) )
@ ( sK1
@ ^ [Y0: a,Y1: a > a > a] :
( Y1
@ ( ^ [Y2: a,Y3: a > a > a] : Y2
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a > a > a] :
( Y1
@ ( ^ [Y2: a,Y3: a > a > a] : Y2
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) )
@ ( sK0
@ ^ [Y0: a,Y1: a > a > a] :
( Y1
@ ( ^ [Y2: a,Y3: a > a > a] : Y2
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: a > ( a > a > a ) > a,X4: a] :
( ( ( ^ [Y0: a > a > a] : ( Y0 @ ( sK2 @ X0 ) @ X4 ) )
!= ( X0 @ ( sK2 @ X0 ) ) )
| ( ( X0 @ ( sK0 @ X0 ) )
= ( X0 @ ( sK1 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: a > ( a > a > a ) > a] :
( ( ( ( X0 @ ( sK0 @ X0 ) )
= ( X0 @ ( sK1 @ X0 ) ) )
& ( ( sK1 @ X0 )
!= ( sK0 @ X0 ) ) )
| ! [X4: a] :
( ( ^ [Y0: a > a > a] : ( Y0 @ ( sK2 @ X0 ) @ X4 ) )
!= ( X0 @ ( sK2 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f8,f7]) ).
thf(f7,plain,
! [X0: a > ( a > a > a ) > a] :
( ? [X1: a,X2: a] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
& ( X1 != X2 ) )
=> ( ( ( X0 @ ( sK0 @ X0 ) )
= ( X0 @ ( sK1 @ X0 ) ) )
& ( ( sK1 @ X0 )
!= ( sK0 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: a > ( a > a > a ) > a] :
( ? [X3: a] :
! [X4: a] :
( ( X0 @ X3 )
!= ( ^ [Y0: a > a > a] : ( Y0 @ X3 @ X4 ) ) )
=> ! [X4: a] :
( ( ^ [Y0: a > a > a] : ( Y0 @ ( sK2 @ X0 ) @ X4 ) )
!= ( X0 @ ( sK2 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
! [X0: a > ( a > a > a ) > a] :
( ? [X1: a,X2: a] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
& ( X1 != X2 ) )
| ? [X3: a] :
! [X4: a] :
( ( X0 @ X3 )
!= ( ^ [Y0: a > a > a] : ( Y0 @ X3 @ X4 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: a > ( a > a > a ) > a] :
( ! [X1: a,X2: a] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
& ! [X3: a] :
? [X4: a] :
( ( X0 @ X3 )
= ( ^ [Y0: a > a > a] : ( Y0 @ X3 @ X4 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: a > ( a > a > a ) > a] :
( ! [X1: a,X2: a] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
& ! [X3: a] :
? [X4: a] :
( ( X0 @ X3 )
= ( ^ [X6: a > a > a] : ( X6 @ X3 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: a > ( a > a > a ) > a] :
( ! [X1: a,X2: a] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
& ! [X3: a] :
? [X4: a,X5: a] :
( ( X0 @ X3 )
= ( ^ [X6: a > a > a] : ( X6 @ X3 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: a > ( a > a > a ) > a] :
( ! [X1: a,X2: a] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
& ! [X3: a] :
? [X4: a,X5: a] :
( ( X0 @ X3 )
= ( ^ [X6: a > a > a] : ( X6 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7mWr8eznfP/DTF2THF_21975.p',cTHM33_pme) ).
thf(f15,plain,
! [X0: a,X1: a > ( a > a > a ) > a] :
( ( ( sK1
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X1 @ Y0 @ Y1 ) ) )
!= ( sK0
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X1 @ Y0 @ Y1 ) ) ) )
| ( ( X1
@ ( sK2
@ ^ [Y0: a,Y1: a > a > a] : ( Y1 @ Y0 @ ( X1 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a > a > a] : X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: a,X1: a > ( a > a > a ) > a] :
( ( ( ^ [Y0: a > a > a] :
( X1
@ ( sK2
@ ^ [Y1: a,Y2: a > a > a] :
( Y2
@ ( ^ [Y3: a,Y4: a > a > a] : Y3
@ Y1
@ Y2 )
@ ( X1 @ Y1 @ Y2 ) ) )
@ Y0 ) )
!= ( ^ [Y0: a > a > a] : X0 ) )
| ( ( sK1
@ ^ [Y0: a,Y1: a > a > a] :
( Y1
@ ( ^ [Y2: a,Y3: a > a > a] : Y2
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) )
!= ( sK0
@ ^ [Y0: a,Y1: a > a > a] :
( Y1
@ ( ^ [Y2: a,Y3: a > a > a] : Y2
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: a > ( a > a > a ) > a,X4: a] :
( ( ( ^ [Y0: a > a > a] : ( Y0 @ ( sK2 @ X0 ) @ X4 ) )
!= ( X0 @ ( sK2 @ X0 ) ) )
| ( ( sK1 @ X0 )
!= ( sK0 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV171^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:41:37 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SEV171^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.45 % Domain : Set Theory
% 0.29/0.45 % Problem : TPS problem from PAIRS-FUNS-THMS
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : tps_0844 [Bro09]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.69 v8.1.0, 0.64 v7.5.0, 0.43 v7.4.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v4.1.0, 0.67 v4.0.0
% 0.29/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.29/0.45 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 3 ( 3 avg)
% 0.29/0.45 % Number of connectives : 7 ( 0 ~; 0 |; 1 &; 5 @)
% 0.29/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 6 ( 6 avg)
% 0.29/0.45 % Number of types : 1 ( 1 usr)
% 0.29/0.45 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.29/0.45 % Number of variables : 7 ( 1 ^; 3 !; 3 ?; 7 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(a_type,type,
% 0.29/0.45 a: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(cTHM33_pme,conjecture,
% 0.29/0.45 ? [F: a > ( a > a > a ) > a] :
% 0.29/0.45 ( ! [Xx: a,Xy: a] :
% 0.29/0.45 ( ( ( F @ Xx )
% 0.29/0.45 = ( F @ Xy ) )
% 0.29/0.45 => ( Xx = Xy ) )
% 0.29/0.45 & ! [X: a] :
% 0.29/0.45 ? [Y: a,Z: a] :
% 0.29/0.45 ( ( F @ X )
% 0.29/0.45 = ( ^ [G: a > a > a] : ( G @ X @ Y ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.53/1.22 ---- Embedded in THF ---
% 1.53/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.22 %%% Generated on Tue Feb 24 12:41:37 EST 2026
% 1.53/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.22 %%% Logic specification used:
% 1.53/1.22 %%% thf(spec, logic, $$dhol).
% 1.53/1.22
% 1.53/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.7mWr8eznfP/DTF2DTF21975.p
% See solution above
% 1.53/1.22 ------------------------
% 1.53/1.23 ---- Cleaned THF ---
% 1.53/1.23 thf(a_type,type,
% 1.53/1.23 a: $tType ).
% 1.53/1.23
% 1.53/1.23 thf(cTHM33_pme,conjecture,
% 1.53/1.23 ? [F: a > ( a > a > a ) > a] :
% 1.53/1.23 ( ! [Xx: a,Xy: a] :
% 1.53/1.23 ( ( ( F @ Xx )
% 1.53/1.23 = ( F @ Xy ) )
% 1.53/1.23 => ( Xx = Xy ) )
% 1.53/1.23 & ! [X: a] :
% 1.53/1.23 ? [Y: a,Z: a] :
% 1.53/1.23 ( ( F @ X )
% 1.53/1.23 = ( ^ [G: a > a > a] : ( G @ X @ Y ) ) ) ) ).
% 1.53/1.23 ------------------------
% 1.53/1.24 % (22075)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_21975 for (2999ds/27Mi)
% 1.53/1.24 % (22077)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_21975 for (2999ds/2Mi)
% 1.53/1.24 % (22075)Refutation not found, incomplete strategy
% 1.53/1.24 % (22075)------------------------------
% 1.53/1.24 % (22075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.24 % (22075)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.24
% 1.53/1.24
% 1.53/1.24 % (22075)Memory used [KB]: 5500
% 1.53/1.24 % (22075)Time elapsed: 0.002 s
% 1.53/1.24 % (22075)Instructions burned: 1 (million)
% 1.53/1.24 % (22075)------------------------------
% 1.53/1.24 % (22075)------------------------------
% 1.53/1.25 % (22077)Instruction limit reached!
% 1.53/1.25 % (22077)------------------------------
% 1.53/1.25 % (22077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.25 % (22077)Termination reason: Unknown
% 1.53/1.25 % (22077)Termination phase: Saturation
% 1.53/1.25
% 1.53/1.25 % (22077)Memory used [KB]: 5500
% 1.53/1.25 % (22077)Time elapsed: 0.003 s
% 1.53/1.25 % (22077)Instructions burned: 3 (million)
% 1.53/1.25 % (22077)------------------------------
% 1.53/1.25 % (22077)------------------------------
% 1.53/1.25 % (22072)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/183Mi)
% 1.53/1.25 % (22073)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_21975 for (2999ds/4Mi)
% 1.53/1.25 % (22076)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/2Mi)
% 1.53/1.25 % (22078)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_21975 for (2999ds/275Mi)
% 1.53/1.25 % (22076)Refutation not found, incomplete strategy
% 1.53/1.25 % (22076)------------------------------
% 1.53/1.25 % (22076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.25 % (22076)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.25
% 1.53/1.25
% 1.53/1.25 % (22078)Refutation not found, incomplete strategy
% 1.53/1.25 % (22078)------------------------------
% 1.53/1.25 % (22078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.25 % (22078)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.25
% 1.53/1.25
% 1.53/1.25 % (22078)Memory used [KB]: 5500
% 1.53/1.25 % (22078)Time elapsed: 0.003 s
% 1.53/1.25 % (22078)Instructions burned: 1 (million)
% 1.53/1.25 % (22078)------------------------------
% 1.53/1.25 % (22078)------------------------------
% 1.53/1.25 % (22076)Memory used [KB]: 5500
% 1.53/1.25 % (22076)Time elapsed: 0.003 s
% 1.53/1.25 % (22076)Instructions burned: 1 (million)
% 1.53/1.25 % (22076)------------------------------
% 1.53/1.25 % (22076)------------------------------
% 1.53/1.25 % (22073)Instruction limit reached!
% 1.53/1.25 % (22073)------------------------------
% 1.53/1.25 % (22073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.25 % (22079)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/18Mi)
% 1.53/1.25 % (22073)Termination reason: Unknown
% 1.53/1.25 % (22073)Termination phase: Saturation
% 1.53/1.25
% 1.53/1.25 % (22073)Memory used [KB]: 5500
% 1.53/1.25 % (22073)Time elapsed: 0.005 s
% 1.53/1.25 % (22073)Instructions burned: 4 (million)
% 1.53/1.25 % (22073)------------------------------
% 1.53/1.25 % (22073)------------------------------
% 1.53/1.26 % (22080)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/3Mi)
% 1.53/1.26 % (22080)Instruction limit reached!
% 1.53/1.26 % (22080)------------------------------
% 1.53/1.26 % (22080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.26 % (22080)Termination reason: Unknown
% 1.53/1.26 % (22080)Termination phase: Saturation
% 1.53/1.26
% 1.53/1.26 % (22080)Memory used [KB]: 5500
% 1.53/1.26 % (22080)Time elapsed: 0.003 s
% 1.53/1.26 % (22080)Instructions burned: 3 (million)
% 1.53/1.26 % (22080)------------------------------
% 1.53/1.26 % (22080)------------------------------
% 1.53/1.26 % (22079)Instruction limit reached!
% 1.53/1.26 % (22079)------------------------------
% 1.53/1.26 % (22079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.26 % (22079)Termination reason: Unknown
% 1.53/1.26 % (22079)Termination phase: Saturation
% 1.53/1.26
% 1.53/1.26 % (22079)Memory used [KB]: 5628
% 1.53/1.26 % (22079)Time elapsed: 0.007 s
% 1.53/1.26 % (22079)Instructions burned: 21 (million)
% 1.53/1.26 % (22079)------------------------------
% 1.53/1.26 % (22079)------------------------------
% 1.53/1.26 % (22081)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_21975 for (2999ds/37Mi)
% 1.53/1.27 % (22085)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/7Mi)
% 1.53/1.27 % (22086)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/16Mi)
% 1.53/1.27 % (22085)Instruction limit reached!
% 1.53/1.27 % (22085)------------------------------
% 1.53/1.27 % (22085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.27 % (22085)Termination reason: Unknown
% 1.53/1.27 % (22085)Termination phase: Saturation
% 1.53/1.27
% 1.53/1.27 % (22085)Memory used [KB]: 1023
% 1.53/1.27 % (22085)Time elapsed: 0.005 s
% 1.53/1.27 % (22085)Instructions burned: 9 (million)
% 1.53/1.27 % (22085)------------------------------
% 1.53/1.27 % (22085)------------------------------
% 1.53/1.27 % (22082)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_21975 for (2999ds/15Mi)
% 1.53/1.27 % (22083)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_21975 for (2999ds/3Mi)
% 1.53/1.27 % (22082)Refutation not found, incomplete strategy
% 1.53/1.27 % (22082)------------------------------
% 1.53/1.27 % (22082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.27 % (22082)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.27
% 1.53/1.27
% 1.53/1.27 % (22082)Memory used [KB]: 5500
% 1.53/1.27 % (22082)Time elapsed: 0.003 s
% 1.53/1.27 % (22082)Instructions burned: 1 (million)
% 1.53/1.27 % (22082)------------------------------
% 1.53/1.27 % (22082)------------------------------
% 1.53/1.27 % (22084)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/1041Mi)
% 1.53/1.27 % (22083)Instruction limit reached!
% 1.53/1.27 % (22083)------------------------------
% 1.53/1.27 % (22083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.27 % (22083)Termination reason: Unknown
% 1.53/1.27 % (22083)Termination phase: Saturation
% 1.53/1.27
% 1.53/1.27 % (22083)Memory used [KB]: 5500
% 1.53/1.27 % (22083)Time elapsed: 0.004 s
% 1.53/1.27 % (22083)Instructions burned: 3 (million)
% 1.53/1.27 % (22083)------------------------------
% 1.53/1.27 % (22083)------------------------------
% 1.53/1.28 % (22086)Instruction limit reached!
% 1.53/1.28 % (22086)------------------------------
% 1.53/1.28 % (22086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (22086)Termination reason: Unknown
% 1.53/1.28 % (22086)Termination phase: Saturation
% 1.53/1.28
% 1.53/1.28 % (22086)Memory used [KB]: 5628
% 1.53/1.28 % (22086)Time elapsed: 0.007 s
% 1.53/1.28 % (22086)Instructions burned: 19 (million)
% 1.53/1.28 % (22086)------------------------------
% 1.53/1.28 % (22086)------------------------------
% 1.53/1.28 % (22087)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/3Mi)
% 1.53/1.28 % (22087)Instruction limit reached!
% 1.53/1.28 % (22087)------------------------------
% 1.53/1.28 % (22087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (22087)Termination reason: Unknown
% 1.53/1.28 % (22087)Termination phase: Saturation
% 1.53/1.28
% 1.53/1.28 % (22087)Memory used [KB]: 5500
% 1.53/1.28 % (22087)Time elapsed: 0.003 s
% 1.53/1.28 % (22087)Instructions burned: 3 (million)
% 1.53/1.28 % (22087)------------------------------
% 1.53/1.28 % (22087)------------------------------
% 1.53/1.28 % (22084)Refutation not found, incomplete strategy
% 1.53/1.28 % (22084)------------------------------
% 1.53/1.28 % (22084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (22084)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.28
% 1.53/1.28
% 1.53/1.28 % (22084)Memory used [KB]: 5500
% 1.53/1.28 % (22084)Time elapsed: 0.011 s
% 1.53/1.28 % (22084)Instructions burned: 15 (million)
% 1.53/1.28 % (22084)------------------------------
% 1.53/1.28 % (22084)------------------------------
% 1.53/1.28 % (22090)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/3Mi)
% 1.53/1.29 % (22081)Instruction limit reached!
% 1.53/1.29 % (22081)------------------------------
% 1.53/1.29 % (22081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (22081)Termination reason: Unknown
% 1.53/1.29 % (22081)Termination phase: Saturation
% 1.53/1.29
% 1.53/1.29 % (22081)Memory used [KB]: 5628
% 1.53/1.29 % (22081)Time elapsed: 0.023 s
% 1.53/1.29 % (22081)Instructions burned: 38 (million)
% 1.53/1.29 % (22090)Instruction limit reached!
% 1.53/1.29 % (22090)------------------------------
% 1.53/1.29 % (22090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (22090)Termination reason: Unknown
% 1.53/1.29 % (22090)Termination phase: Saturation
% 1.53/1.29
% 1.53/1.29 % (22090)Memory used [KB]: 5500
% 1.53/1.29 % (22090)Time elapsed: 0.002 s
% 1.53/1.29 % (22090)Instructions burned: 3 (million)
% 1.53/1.29 % (22090)------------------------------
% 1.53/1.29 % (22090)------------------------------
% 1.53/1.29 % (22081)------------------------------
% 1.53/1.29 % (22081)------------------------------
% 1.53/1.29 % (22088)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/3Mi)
% 1.53/1.29 % (22089)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/7Mi)
% 1.53/1.29 % (22091)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/4Mi)
% 1.53/1.29 % (22088)Instruction limit reached!
% 1.53/1.29 % (22088)------------------------------
% 1.53/1.29 % (22088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (22088)Termination reason: Unknown
% 1.53/1.29 % (22088)Termination phase: Saturation
% 1.53/1.29
% 1.53/1.29 % (22088)Memory used [KB]: 5500
% 1.53/1.29 % (22088)Time elapsed: 0.004 s
% 1.53/1.29 % (22088)Instructions burned: 3 (million)
% 1.53/1.29 % (22088)------------------------------
% 1.53/1.29 % (22088)------------------------------
% 1.53/1.29 % (22091)Instruction limit reached!
% 1.53/1.29 % (22091)------------------------------
% 1.53/1.29 % (22091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (22091)Termination reason: Unknown
% 1.53/1.29 % (22091)Termination phase: Saturation
% 1.53/1.29
% 1.53/1.29 % (22091)Memory used [KB]: 5500
% 1.53/1.29 % (22091)Time elapsed: 0.004 s
% 1.53/1.29 % (22091)Instructions burned: 6 (million)
% 1.53/1.29 % (22091)------------------------------
% 1.53/1.29 % (22091)------------------------------
% 1.53/1.29 % (22089)Refutation not found, incomplete strategy
% 1.53/1.29 % (22089)------------------------------
% 1.53/1.29 % (22089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (22089)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.29
% 1.53/1.29
% 1.53/1.29 % (22089)Memory used [KB]: 5500
% 1.53/1.29 % (22089)Time elapsed: 0.005 s
% 1.53/1.29 % (22089)Instructions burned: 5 (million)
% 1.53/1.29 % (22089)------------------------------
% 1.53/1.29 % (22089)------------------------------
% 1.53/1.29 % (22093)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/710Mi)
% 1.56/1.30 % (22092)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/18Mi)
% 1.56/1.30 % (22092)Refutation not found, incomplete strategy
% 1.56/1.30 % (22092)------------------------------
% 1.56/1.30 % (22092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.30 % (22092)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.30
% 1.56/1.30
% 1.56/1.30 % (22092)Memory used [KB]: 5500
% 1.56/1.30 % (22092)Time elapsed: 0.003 s
% 1.56/1.30 % (22092)Instructions burned: 1 (million)
% 1.56/1.30 % (22092)------------------------------
% 1.56/1.30 % (22092)------------------------------
% 1.56/1.30 % (22096)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/21Mi)
% 1.56/1.31 % (22094)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/6Mi)
% 1.56/1.31 % (22095)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/902Mi)
% 1.56/1.31 % (22095)Refutation not found, incomplete strategy
% 1.56/1.31 % (22095)------------------------------
% 1.56/1.31 % (22095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (22095)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.31
% 1.56/1.31
% 1.56/1.31 % (22095)Memory used [KB]: 5373
% 1.56/1.31 % (22095)Time elapsed: 0.024 s
% 1.56/1.31 % (22095)Instructions burned: 1 (million)
% 1.56/1.31 % (22095)------------------------------
% 1.56/1.31 % (22095)------------------------------
% 1.56/1.31 % (22094)Instruction limit reached!
% 1.56/1.31 % (22094)------------------------------
% 1.56/1.31 % (22094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (22094)Termination reason: Unknown
% 1.56/1.31 % (22094)Termination phase: Saturation
% 1.56/1.31
% 1.56/1.31 % (22094)Memory used [KB]: 5500
% 1.56/1.31 % (22094)Time elapsed: 0.031 s
% 1.56/1.31 % (22094)Instructions burned: 6 (million)
% 1.56/1.31 % (22094)------------------------------
% 1.56/1.31 % (22094)------------------------------
% 1.56/1.31 % (22096)Instruction limit reached!
% 1.56/1.31 % (22096)------------------------------
% 1.56/1.31 % (22096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (22096)Termination reason: Unknown
% 1.56/1.31 % (22096)Termination phase: Saturation
% 1.56/1.31
% 1.56/1.31 % (22096)Memory used [KB]: 5628
% 1.56/1.31 % (22096)Time elapsed: 0.035 s
% 1.56/1.31 % (22096)Instructions burned: 22 (million)
% 1.56/1.31 % (22096)------------------------------
% 1.56/1.31 % (22096)------------------------------
% 1.56/1.31 % (22097)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/5Mi)
% 1.56/1.32 % (22097)Instruction limit reached!
% 1.56/1.32 % (22097)------------------------------
% 1.56/1.32 % (22097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (22097)Termination reason: Unknown
% 1.56/1.32 % (22097)Termination phase: Saturation
% 1.56/1.32
% 1.56/1.32 % (22097)Memory used [KB]: 5500
% 1.56/1.32 % (22097)Time elapsed: 0.005 s
% 1.56/1.32 % (22097)Instructions burned: 5 (million)
% 1.56/1.32 % (22097)------------------------------
% 1.56/1.32 % (22097)------------------------------
% 1.56/1.32 % (22098)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/6Mi)
% 1.56/1.32 % (22101)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/19Mi)
% 1.56/1.32 % (22098)Instruction limit reached!
% 1.56/1.32 % (22098)------------------------------
% 1.56/1.32 % (22098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (22098)Termination reason: Unknown
% 1.56/1.32 % (22098)Termination phase: Saturation
% 1.56/1.32
% 1.56/1.32 % (22098)Memory used [KB]: 5500
% 1.56/1.32 % (22098)Time elapsed: 0.006 s
% 1.56/1.32 % (22098)Instructions burned: 6 (million)
% 1.56/1.32 % (22098)------------------------------
% 1.56/1.32 % (22098)------------------------------
% 1.56/1.33 % (22099)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/377Mi)
% 1.56/1.33 % (22099)Refutation not found, incomplete strategy
% 1.56/1.33 % (22099)------------------------------
% 1.56/1.33 % (22099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (22099)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.33
% 1.56/1.33
% 1.56/1.33 % (22099)Memory used [KB]: 5500
% 1.56/1.33 % (22099)Time elapsed: 0.002 s
% 1.56/1.33 % (22099)Instructions burned: 2 (million)
% 1.56/1.33 % (22099)------------------------------
% 1.56/1.33 % (22099)------------------------------
% 1.56/1.33 % (22101)Instruction limit reached!
% 1.56/1.33 % (22101)------------------------------
% 1.56/1.33 % (22101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (22101)Termination reason: Unknown
% 1.56/1.33 % (22101)Termination phase: Saturation
% 1.56/1.33
% 1.56/1.33 % (22101)Memory used [KB]: 5628
% 1.56/1.33 % (22101)Time elapsed: 0.008 s
% 1.56/1.33 % (22101)Instructions burned: 20 (million)
% 1.56/1.33 % (22101)------------------------------
% 1.56/1.33 % (22101)------------------------------
% 1.56/1.33 % (22100)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/779Mi)
% 1.56/1.33 % (22102)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/879Mi)
% 1.56/1.33 % (22102)Refutation not found, incomplete strategy
% 1.56/1.33 % (22102)------------------------------
% 1.56/1.33 % (22102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (22102)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.33
% 1.56/1.33
% 1.56/1.33 % (22102)Memory used [KB]: 5500
% 1.56/1.33 % (22102)Time elapsed: 0.003 s
% 1.56/1.33 % (22102)Instructions burned: 2 (million)
% 1.56/1.33 % (22102)------------------------------
% 1.56/1.33 % (22102)------------------------------
% 1.56/1.34 % (22104)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/3Mi)
% 1.56/1.34 % (22104)Instruction limit reached!
% 1.56/1.34 % (22104)------------------------------
% 1.56/1.34 % (22104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.34 % (22104)Termination reason: Unknown
% 1.56/1.34 % (22104)Termination phase: Saturation
% 1.56/1.34
% 1.56/1.34 % (22104)Memory used [KB]: 5500
% 1.56/1.34 % (22104)Time elapsed: 0.003 s
% 1.56/1.34 % (22104)Instructions burned: 4 (million)
% 1.56/1.34 % (22104)------------------------------
% 1.56/1.34 % (22104)------------------------------
% 1.56/1.34 % (22105)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/30Mi)
% 1.56/1.34 % (22103)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/17Mi)
% 1.56/1.35 % (22105)Instruction limit reached!
% 1.56/1.35 % (22105)------------------------------
% 1.56/1.35 % (22105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.35 % (22105)Termination reason: Unknown
% 1.56/1.35 % (22105)Termination phase: Saturation
% 1.56/1.35
% 1.56/1.35 % (22105)Memory used [KB]: 5628
% 1.56/1.35 % (22105)Time elapsed: 0.011 s
% 1.56/1.35 % (22105)Instructions burned: 30 (million)
% 1.56/1.35 % (22105)------------------------------
% 1.56/1.35 % (22105)------------------------------
% 1.56/1.35 % (22107)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_21975 for (2998ds/100Mi)
% 1.56/1.35 % (22107)Refutation not found, incomplete strategy
% 1.56/1.35 % (22107)------------------------------
% 1.56/1.35 % (22107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.35 % (22107)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.35
% 1.56/1.35
% 1.56/1.35 % (22107)Memory used [KB]: 5500
% 1.56/1.35 % (22107)Time elapsed: 0.002 s
% 1.56/1.35 % (22107)Instructions burned: 1 (million)
% 1.56/1.35 % (22107)------------------------------
% 1.56/1.35 % (22107)------------------------------
% 1.56/1.35 % (22103)Instruction limit reached!
% 1.56/1.35 % (22103)------------------------------
% 1.56/1.35 % (22103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.35 % (22103)Termination reason: Unknown
% 1.56/1.35 % (22103)Termination phase: Saturation
% 1.56/1.35
% 1.56/1.35 % (22103)Memory used [KB]: 5500
% 1.56/1.35 % (22103)Time elapsed: 0.011 s
% 1.56/1.35 % (22103)Instructions burned: 17 (million)
% 1.56/1.35 % (22103)------------------------------
% 1.56/1.35 % (22103)------------------------------
% 1.56/1.35 % (22106)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_21975 for (2999ds/127Mi)
% 1.56/1.35 % (22093)First to succeed.
% 1.56/1.36 % (22093)Refutation found. Thanks to Tanya!
% 1.56/1.36 % SZS status Theorem for DTF2THF_21975
% 1.56/1.36 % SZS output start Proof for DTF2THF_21975
% 1.56/1.36 thf(type_def_5, type, a: $tType).
% 1.56/1.36 thf(func_def_0, type, a: $tType).
% 1.56/1.36 thf(func_def_6, type, sK0: (a > (a > a > a) > a) > a).
% 1.56/1.36 thf(func_def_7, type, sK1: (a > (a > a > a) > a) > a).
% 1.56/1.36 thf(func_def_8, type, sK2: (a > (a > a > a) > a) > a).
% 1.56/1.36 thf(func_def_10, type, ph4: !>[X0: $tType]:(X0)).
% 1.56/1.36 thf(func_def_17, type, sK5: (a > (a > a > a) > a) > (a > (a > a > a) > a) > a > a > a > a).
% 1.56/1.36 thf(func_def_18, type, sK6: (a > (a > a > a) > a) > (a > (a > a > a) > a) > a > a > a > a).
% 1.56/1.36 thf(func_def_19, type, sK7: (a > (a > a > a) > a) > (a > (a > a > a) > a) > a > a > a).
% 1.56/1.36 thf(func_def_20, type, sK8: (a > (a > a > a) > a) > a).
% 1.56/1.36 thf(func_def_21, type, sK9: a > (a > (a > a > a) > a) > (a > (a > a > a) > a) > (a > (a > a > a) > a > (a > a > a) > a) > a > a > a).
% 1.56/1.36 thf(func_def_22, type, sK10: (a > (a > a > a) > a) > a > a > a).
% 1.56/1.36 thf(func_def_23, type, sK11: a > (a > (a > a > a) > a) > (a > (a > a > a) > a) > (a > (a > a > a) > a > (a > a > a) > a) > a > a > a).
% 1.56/1.36 thf(f161,plain,(
% 1.56/1.36 $false),
% 1.56/1.36 inference(avatar_sat_refutation,[status(thm)],[f87,f103,f109,f160])).
% 1.56/1.36 thf(f160,plain,(
% 1.56/1.36 spl3_2 | ~spl3_3),
% 1.56/1.36 inference(avatar_split_clause,[status(thm)],[f153,f85,f81])).
% 1.56/1.36 thf(f81,definition,(
% 1.56/1.36 spl3_2 <=> ! [X8 : a] : ((^[Y0 : a > a > a]: (X8)) != (^[Y0 : a > a > a]: (sK2 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ Y1)))))))),
% 1.56/1.36 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.56/1.36 thf(f85,definition,(
% 1.56/1.36 spl3_3 <=> ! [X4 : a > (a > a > a) > a,X5 : a] : (((^[Y0 : a > a > a]: (X5)) != (X4 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X4 @ Y0 @ Y1)))))))) | ((sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0))))) != (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X4 @ Y0 @ Y1))))))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) != X4))),
% 1.56/1.36 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.56/1.36 thf(f153,plain,(
% 1.56/1.36 ( ! [X0 : a] : (((^[Y0 : a > a > a]: (sK2 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ Y1)))))) != (^[Y0 : a > a > a]: (X0)))) ) | ~spl3_3),
% 1.56/1.36 inference(beta_eta_normalization,[status(thm)],[f152])).
% 1.56/1.36 thf(f152,plain,(
% 1.56/1.36 ( ! [X0 : a] : ((((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1))))))) != (^[Y0 : a > a > a]: (X0)))) ) | ~spl3_3),
% 1.56/1.36 inference(trivial_inequality_removal,[status(thm)],[f148])).
% 1.56/1.36 thf(f148,plain,(
% 1.56/1.36 ( ! [X0 : a] : ((((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1))))))) != (^[Y0 : a > a > a]: (X0))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) != (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))))) ) | ~spl3_3),
% 1.56/1.36 inference(equality_resolution,[status(thm)],[f135])).
% 1.56/1.36 thf(f135,plain,(
% 1.56/1.36 ( ! [X0 : a > (a > a > a) > a,X1 : a] : (((sK10 @ X0 @ (sK8 @ X0) @ (X0 @ (sK8 @ X0) @ (sK10 @ X0))) != (sK10 @ X0 @ (sK8 @ X0) @ (sK8 @ X0))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) != X0) | ((^[Y0 : a > a > a]: (X1)) != (X0 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1))))))))) ) | ~spl3_3),
% 1.56/1.36 inference(beta_eta_normalization,[status(thm)],[f133])).
% 1.56/1.36 thf(f133,plain,(
% 1.56/1.36 ( ! [X0 : a > (a > a > a) > a,X1 : a] : ((((^[Y0 : a > a > a]: (Y0 @ (sK8 @ X0) @ (X0 @ (sK8 @ X0) @ Y0))) @ (sK10 @ X0)) != ((^[Y0 : a > a > a]: (Y0 @ (sK8 @ X0) @ (sK8 @ X0))) @ (sK10 @ X0))) | ((^[Y0 : a > a > a]: (X1)) != (X0 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1)))))))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) != X0)) ) | ~spl3_3),
% 1.56/1.36 inference(negative_extensionality,[status(thm)],[f128])).
% 1.56/1.36 thf(f128,plain,(
% 1.56/1.36 ( ! [X0 : a > (a > a > a) > a,X1 : a] : (((^[Y0 : a > a > a]: (Y0 @ (sK8 @ X0) @ (X0 @ (sK8 @ X0) @ Y0))) != (^[Y0 : a > a > a]: (Y0 @ (sK8 @ X0) @ (sK8 @ X0)))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) != X0) | ((^[Y0 : a > a > a]: (X1)) != (X0 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1))))))))) ) | ~spl3_3),
% 1.56/1.36 inference(beta_eta_normalization,[status(thm)],[f127])).
% 1.56/1.36 thf(f127,plain,(
% 1.56/1.36 ( ! [X0 : a > (a > a > a) > a,X1 : a] : ((((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1))))) @ (sK8 @ X0)) != ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0)))) @ (sK8 @ X0))) | ((^[Y0 : a > a > a]: (X1)) != (X0 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1)))))))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) != X0)) ) | ~spl3_3),
% 1.56/1.36 inference(negative_extensionality,[status(thm)],[f118])).
% 1.56/1.36 thf(f118,plain,(
% 1.56/1.36 ( ! [X0 : a > (a > a > a) > a,X1 : a] : (((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0)))) != (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1)))))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) != X0) | ((^[Y0 : a > a > a]: (X1)) != (X0 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1))))))))) ) | ~spl3_3),
% 1.56/1.36 inference(equality_resolution,[status(thm)],[f86])).
% 1.56/1.36 thf(f86,plain,(
% 1.56/1.36 ( ! [X4 : a > (a > a > a) > a,X5 : a] : (((sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0))))) != (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X4 @ Y0 @ Y1))))))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) != X4) | ((^[Y0 : a > a > a]: (X5)) != (X4 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X4 @ Y0 @ Y1))))))))) ) | ~spl3_3),
% 1.56/1.36 inference(avatar_component_clause,[status(thm)],[f85])).
% 1.56/1.36 thf(f109,plain,(
% 1.56/1.36 ~spl3_4),
% 1.56/1.36 inference(avatar_contradiction_clause,[status(thm)],[f108])).
% 1.56/1.36 thf(f108,plain,(
% 1.56/1.36 $false | ~spl3_4),
% 1.56/1.36 inference(equality_resolution,[status(thm)],[f102])).
% 1.56/1.36 thf(f102,plain,(
% 1.56/1.36 ( ! [X1 : a > (a > a > a) > a] : (((^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y1)))))) != (^[Y0 : a > a > a]: (X1)))) ) | ~spl3_4),
% 1.56/1.36 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.56/1.36 thf(f101,definition,(
% 1.56/1.36 spl3_4 <=> ! [X1 : a > (a > a > a) > a] : ((^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y1)))))) != (^[Y0 : a > a > a]: (X1)))),
% 1.56/1.36 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.56/1.36 thf(f103,plain,(
% 1.56/1.36 spl3_4 | spl3_4 | ~spl3_2),
% 1.56/1.36 inference(avatar_split_clause,[status(thm)],[f99,f81,f101,f101])).
% 1.56/1.36 thf(f99,plain,(
% 1.56/1.36 ( ! [X0 : a > (a > a > a) > a,X1 : a > (a > a > a) > a] : (((^[Y0 : a > a > a]: (X0)) != (^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y1))))))) | ((^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y1)))))) != (^[Y0 : a > a > a]: (X1)))) ) | ~spl3_2),
% 1.56/1.36 inference(beta_eta_normalization,[status(thm)],[f98])).
% 1.56/1.36 thf(f98,plain,(
% 1.56/1.36 ( ! [X0 : a > (a > a > a) > a,X1 : a > (a > a > a) > a] : (((^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (X0 @ Y1 @ Y2)))))) != (^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y1))))))) | ((^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (X1 @ Y1 @ Y2)))))) != (^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y1)))))))) ) | ~spl3_2),
% 1.56/1.36 inference(equality_resolution,[status(thm)],[f82])).
% 1.56/1.36 thf(f82,plain,(
% 1.56/1.36 ( ! [X8 : a] : (((^[Y0 : a > a > a]: (X8)) != (^[Y0 : a > a > a]: (sK2 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ Y1)))))))) ) | ~spl3_2),
% 1.56/1.36 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.56/1.36 thf(f87,plain,(
% 1.56/1.36 spl3_2 | spl3_3),
% 1.56/1.36 inference(avatar_split_clause,[status(thm)],[f63,f85,f81])).
% 1.56/1.36 thf(f63,plain,(
% 1.56/1.36 ( ! [X6 : a,X4 : a > (a > a > a) > a,X5 : a] : (((^[Y0 : a > a > a]: (X5)) != (X4 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X4 @ Y0 @ Y1)))))))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) != X4) | ((sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0))))) != (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X4 @ Y0 @ Y1))))))) | ((^[Y0 : a > a > a]: (X6)) != (^[Y0 : a > a > a]: (sK2 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ Y1)))))))) )),
% 1.56/1.36 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.56/1.36 thf(f50,plain,(
% 1.56/1.36 ( ! [X6 : a,X4 : a > (a > a > a) > a,X5 : a] : (((^[Y0 : a > a > a]: (X6)) != ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1)))))))) | (((^[Y0 : a]: ((^[Y1 : a]: (Y1)))) @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1)))))) @ ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1)))))) @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) != (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X4 @ Y0 @ Y1))))))) | ((^[Y0 : a > a > a]: (X5)) != (X4 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X4 @ Y0 @ Y1)))))))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (X4 @ Y0 @ Y1)))) != (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))))) )),
% 1.56/1.36 inference(constrained_superposition,[status(thm)],[f15,f28])).
% 1.56/1.36 thf(f28,plain,(
% 1.56/1.36 ( ! [X2 : a > a > a,X0 : a,X1 : a > (a > a > a) > a] : (((X2 @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X1 @ Y0 @ Y1)))))) @ (X1 @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X1 @ Y0 @ Y1)))))) @ X2)) = (X2 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X1 @ Y0 @ Y1)))))) @ (X1 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X1 @ Y0 @ Y1)))))) @ X2))) | ((X1 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X1 @ Y0 @ Y1))))))) != (^[Y0 : a > a > a]: (X0)))) )),
% 1.56/1.36 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.56/1.36 thf(f20,plain,(
% 1.56/1.36 ( ! [X2 : a > a > a,X0 : a,X1 : a > (a > a > a) > a] : ((((^[Y0 : a > a > a]: (Y0 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X1 @ Y1 @ Y2)))))) @ (X1 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X1 @ Y1 @ Y2)))))) @ Y0))) @ X2) = ((^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X1 @ Y1 @ Y2)))))) @ (X1 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X1 @ Y1 @ Y2)))))) @ Y0))) @ X2)) | ((X1 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X1 @ Y0 @ Y1))))))) != (^[Y0 : a > a > a]: (X0)))) )),
% 1.56/1.36 inference(argument_congruence,[status(thm)],[f18])).
% 1.56/1.36 thf(f18,plain,(
% 1.56/1.36 ( ! [X0 : a,X1 : a > (a > a > a) > a] : (((^[Y0 : a > a > a]: (Y0 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X1 @ Y1 @ Y2)))))) @ (X1 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X1 @ Y1 @ Y2)))))) @ Y0))) = (^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X1 @ Y1 @ Y2)))))) @ (X1 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X1 @ Y1 @ Y2)))))) @ Y0)))) | ((X1 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X1 @ Y0 @ Y1))))))) != (^[Y0 : a > a > a]: (X0)))) )),
% 1.56/1.36 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.56/1.36 thf(f16,plain,(
% 1.56/1.36 ( ! [X0 : a,X1 : a > (a > a > a) > a] : (((^[Y0 : a > a > a]: (X1 @ (sK2 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ ((^[Y3 : a]: ((^[Y4 : a > a > a]: (Y3)))) @ Y1 @ Y2) @ (X1 @ Y1 @ Y2)))))) @ Y0)) != (^[Y0 : a > a > a]: (X0))) | (((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))))) = ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))) @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))))))) )),
% 1.56/1.36 inference(equality_resolution,[status(thm)],[f11])).
% 1.56/1.36 thf(f11,plain,(
% 1.56/1.36 ( ! [X0 : a > (a > a > a) > a,X4 : a] : (((^[Y0 : a > a > a]: (Y0 @ (sK2 @ X0) @ X4)) != (X0 @ (sK2 @ X0))) | ((X0 @ (sK0 @ X0)) = (X0 @ (sK1 @ X0)))) )),
% 1.56/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.56/1.36 thf(f9,plain,(
% 1.56/1.36 ! [X0 : a > (a > a > a) > a] : ((((X0 @ (sK0 @ X0)) = (X0 @ (sK1 @ X0))) & ((sK1 @ X0) != (sK0 @ X0))) | ! [X4 : a] : ((^[Y0 : a > a > a]: (Y0 @ (sK2 @ X0) @ X4)) != (X0 @ (sK2 @ X0))))),
% 1.56/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f8,f7])).
% 1.56/1.36 thf(f7,plain,(
% 1.56/1.36 ! [X0 : a > (a > a > a) > a] : (? [X1 : a,X2 : a] : (((X0 @ X1) = (X0 @ X2)) & (X1 != X2)) => (((X0 @ (sK0 @ X0)) = (X0 @ (sK1 @ X0))) & ((sK1 @ X0) != (sK0 @ X0))))),
% 1.56/1.36 introduced(definition,[],[choice_axiom])).
% 1.56/1.36 thf(f8,plain,(
% 1.56/1.36 ! [X0 : a > (a > a > a) > a] : (? [X3 : a] : ! [X4 : a] : ((X0 @ X3) != (^[Y0 : a > a > a]: (Y0 @ X3 @ X4))) => ! [X4 : a] : ((^[Y0 : a > a > a]: (Y0 @ (sK2 @ X0) @ X4)) != (X0 @ (sK2 @ X0))))),
% 1.56/1.36 introduced(definition,[],[choice_axiom])).
% 1.56/1.36 thf(f6,plain,(
% 1.56/1.36 ! [X0 : a > (a > a > a) > a] : (? [X1 : a,X2 : a] : (((X0 @ X1) = (X0 @ X2)) & (X1 != X2)) | ? [X3 : a] : ! [X4 : a] : ((X0 @ X3) != (^[Y0 : a > a > a]: (Y0 @ X3 @ X4))))),
% 1.56/1.36 inference(ennf_transformation,[status(thm)],[f5])).
% 1.56/1.36 thf(f5,plain,(
% 1.56/1.36 ~? [X0 : a > (a > a > a) > a] : (! [X1 : a,X2 : a] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) & ! [X3 : a] : ? [X4 : a] : ((X0 @ X3) = (^[Y0 : a > a > a]: (Y0 @ X3 @ X4))))),
% 1.56/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 1.56/1.36 thf(f4,plain,(
% 1.56/1.36 ~? [X0 : a > (a > a > a) > a] : (! [X1 : a,X2 : a] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) & ! [X3 : a] : ? [X4 : a] : ((X0 @ X3) = (^[X6 : a > a > a] : (X6 @ X3 @ X4))))),
% 1.56/1.36 inference(rectify,[status(thm)],[f2])).
% 1.56/1.36 thf(f2,negated_conjecture,(
% 1.56/1.36 ~? [X0 : a > (a > a > a) > a] : (! [X1 : a,X2 : a] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) & ! [X3 : a] : ? [X4 : a,X5 : a] : ((X0 @ X3) = (^[X6 : a > a > a] : (X6 @ X3 @ X4))))),
% 1.56/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.56/1.36 thf(f1,conjecture,(
% 1.56/1.36 ? [X0 : a > (a > a > a) > a] : (! [X1 : a,X2 : a] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) & ! [X3 : a] : ? [X4 : a,X5 : a] : ((X0 @ X3) = (^[X6 : a > a > a] : (X6 @ X3 @ X4))))),
% 1.56/1.36 file('/export/starexec/sandbox/tmp/tmp.7mWr8eznfP/DTF2THF_21975.p',cTHM33_pme)).
% 1.56/1.36 thf(f15,plain,(
% 1.56/1.36 ( ! [X0 : a,X1 : a > (a > a > a) > a] : (((sK1 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X1 @ Y0 @ Y1)))))) != (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X1 @ Y0 @ Y1))))))) | ((X1 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X1 @ Y0 @ Y1))))))) != (^[Y0 : a > a > a]: (X0)))) )),
% 1.56/1.36 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.56/1.36 thf(f12,plain,(
% 1.56/1.36 ( ! [X0 : a,X1 : a > (a > a > a) > a] : (((^[Y0 : a > a > a]: (X1 @ (sK2 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ ((^[Y3 : a]: ((^[Y4 : a > a > a]: (Y3)))) @ Y1 @ Y2) @ (X1 @ Y1 @ Y2)))))) @ Y0)) != (^[Y0 : a > a > a]: (X0))) | ((sK1 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1)))))) != (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1)))))))) )),
% 1.56/1.36 inference(equality_resolution,[status(thm)],[f10])).
% 1.56/1.36 thf(f10,plain,(
% 1.56/1.36 ( ! [X0 : a > (a > a > a) > a,X4 : a] : (((^[Y0 : a > a > a]: (Y0 @ (sK2 @ X0) @ X4)) != (X0 @ (sK2 @ X0))) | ((sK1 @ X0) != (sK0 @ X0))) )),
% 1.56/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.56/1.36 % SZS output end Proof for DTF2THF_21975
% 1.56/1.36 % (22093)------------------------------
% 1.56/1.36 % (22093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (22093)Termination reason: Refutation
% 1.56/1.36
% 1.56/1.36 % (22093)Memory used [KB]: 6780
% 1.56/1.36 % (22093)Time elapsed: 0.085 s
% 1.56/1.36 % (22093)Instructions burned: 217 (million)
% 1.56/1.36 % (22093)------------------------------
% 1.56/1.36 % (22093)------------------------------
% 1.56/1.36 % (22071)Success in time 0.118 s
%------------------------------------------------------------------------------