%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU897^5 : 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 09:37:41 AM UTC 2026
% Result : Theorem 1.81s 1.53s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 1 unt; 0 typ; 8 def)
% Number of atoms : 424 ( 145 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 464 ( 110 ~; 106 |; 34 &; 189 @)
% ( 12 <=>; 12 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 94 ( 2 ^; 66 !; 26 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cS: a > $o ).
thf(func_def_2,type,
cR: a > $o ).
thf(func_def_6,type,
sK0: a ).
thf(func_def_7,type,
sK1: a ).
thf(func_def_8,type,
sK2: a > a ).
thf(func_def_9,type,
sK3: a ).
thf(func_def_10,type,
sK4: ( a > a ) > a > a ).
thf(func_def_12,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f96,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f32,f36,f41,f48,f53,f57,f58,f59,f66,f68,f95]) ).
thf(f95,plain,
( spl5_5
| ~ spl5_6
| ~ spl5_8 ),
inference(avatar_split_clause,[status(thm)],[f94,f55,f46,f43]) ).
thf(f43,definition,
( spl5_5
<=> ! [X5: a] :
( ( ( cS @ X5 )
= $true )
| ( ( cR @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition]) ).
thf(f46,definition,
( spl5_6
<=> ! [X8: a,X7: a > a] :
( ( ( X7 @ ( sK4 @ X7 @ ( X7 @ X8 ) ) )
= ( X7 @ X8 ) )
| ( ( cR @ X8 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition]) ).
thf(f55,definition,
( spl5_8
<=> ! [X8: a,X7: a > a] :
( ( ( cR @ X8 )
!= $true )
| ( ( cS @ ( sK4 @ X7 @ ( X7 @ X8 ) ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition]) ).
thf(f94,plain,
( ! [X0: a] :
( ( ( cR @ X0 )
!= $true )
| ( ( cS @ X0 )
= $true ) )
| ~ spl5_6
| ~ spl5_8 ),
inference(beta_eta_normalization,[status(thm)],[f93]) ).
thf(f93,plain,
( ! [X0: a] :
( ( ( cR @ X0 )
!= $true )
| ( ( cS
@ ( ^ [Y0: a] : Y0
@ X0 ) )
= $true ) )
| ~ spl5_6
| ~ spl5_8 ),
inference(duplicate_literal_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ! [X0: a] :
( ( ( cR @ X0 )
!= $true )
| ( ( cR @ X0 )
!= $true )
| ( ( cS
@ ( ^ [Y0: a] : Y0
@ X0 ) )
= $true ) )
| ~ spl5_6
| ~ spl5_8 ),
inference(superposition,[status(thm)],[f56,f47]) ).
thf(f47,plain,
( ! [X8: a,X7: a > a] :
( ( ( X7 @ ( sK4 @ X7 @ ( X7 @ X8 ) ) )
= ( X7 @ X8 ) )
| ( ( cR @ X8 )
!= $true ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f56,plain,
( ! [X8: a,X7: a > a] :
( ( ( cS @ ( sK4 @ X7 @ ( X7 @ X8 ) ) )
= $true )
| ( ( cR @ X8 )
!= $true ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f68,plain,
( ~ spl5_2
| ~ spl5_3
| ~ spl5_4
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f67]) ).
thf(f67,plain,
( $false
| ~ spl5_2
| ~ spl5_3
| ~ spl5_4
| ~ spl5_5 ),
inference(subsumption_resolution,[status(thm)],[f64,f40]) ).
thf(f40,plain,
( ( ( cR @ sK3 )
= $true )
| ~ spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl5_4
<=> ( ( cR @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f64,plain,
( ( ( cR @ sK3 )
!= $true )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_5 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( cR @ sK3 )
!= $true )
| ( $true != $true )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_5 ),
inference(superposition,[status(thm)],[f61,f44]) ).
thf(f44,plain,
( ! [X5: a] :
( ( ( cS @ X5 )
= $true )
| ( ( cR @ X5 )
!= $true ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f61,plain,
( ( ( cS @ sK3 )
!= $true )
| ~ spl5_2
| ~ spl5_3 ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( cS @ sK3 )
!= $true )
| ( sK1 != sK1 )
| ~ spl5_2
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f35,f31]) ).
thf(f31,plain,
( ( sK1
= ( sK2 @ sK3 ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl5_2
<=> ( sK1
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f35,plain,
( ! [X4: a] :
( ( ( sK2 @ X4 )
!= sK1 )
| ( ( cS @ X4 )
!= $true ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl5_3
<=> ! [X4: a] :
( ( ( cS @ X4 )
!= $true )
| ( ( sK2 @ X4 )
!= sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f66,plain,
( ~ spl5_7
| spl5_1
| ~ spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f65,f43,f25,f50]) ).
thf(f50,definition,
( spl5_7
<=> ( $true
= ( cR @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition]) ).
thf(f25,definition,
( spl5_1
<=> ( ( cS @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f65,plain,
( ( $true
!= ( cR @ sK0 ) )
| spl5_1
| ~ spl5_5 ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true != $true )
| ( $true
!= ( cR @ sK0 ) )
| spl5_1
| ~ spl5_5 ),
inference(superposition,[status(thm)],[f27,f44]) ).
thf(f27,plain,
( ( ( cS @ sK0 )
!= $true )
| spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f59,plain,
( spl5_4
| spl5_7 ),
inference(avatar_split_clause,[status(thm)],[f20,f50,f38]) ).
thf(f20,plain,
( ( $true
= ( cR @ sK0 ) )
| ( ( cR @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ( $true
= ( cR @ sK0 ) )
& ( ( cS @ sK0 )
!= $true ) )
| ( ( sK1
= ( sK2 @ sK3 ) )
& ( ( cR @ sK3 )
= $true )
& ! [X4: a] :
( ( ( cS @ X4 )
!= $true )
| ( ( sK2 @ X4 )
!= sK1 ) ) ) )
& ( ! [X5: a] :
( ( ( cR @ X5 )
!= $true )
| ( ( cS @ X5 )
= $true ) )
| ! [X6: a,X7: a > a] :
( ! [X8: a] :
( ( ( X7 @ X8 )
!= X6 )
| ( ( cR @ X8 )
!= $true ) )
| ( ( $true
= ( cS @ ( sK4 @ X7 @ X6 ) ) )
& ( ( X7 @ ( sK4 @ X7 @ X6 ) )
= X6 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a] :
( ( ( cR @ X0 )
= $true )
& ( ( cS @ X0 )
!= $true ) )
=> ( ( $true
= ( cR @ sK0 ) )
& ( ( cS @ sK0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X1: a,X2: a > a] :
( ? [X3: a] :
( ( ( X2 @ X3 )
= X1 )
& ( $true
= ( cR @ X3 ) ) )
& ! [X4: a] :
( ( ( cS @ X4 )
!= $true )
| ( ( X2 @ X4 )
!= X1 ) ) )
=> ( ? [X3: a] :
( ( sK1
= ( sK2 @ X3 ) )
& ( $true
= ( cR @ X3 ) ) )
& ! [X4: a] :
( ( ( cS @ X4 )
!= $true )
| ( ( sK2 @ X4 )
!= sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X3: a] :
( ( sK1
= ( sK2 @ X3 ) )
& ( $true
= ( cR @ X3 ) ) )
=> ( ( sK1
= ( sK2 @ sK3 ) )
& ( ( cR @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X6: a,X7: a > a] :
( ? [X9: a] :
( ( $true
= ( cS @ X9 ) )
& ( ( X7 @ X9 )
= X6 ) )
=> ( ( $true
= ( cS @ ( sK4 @ X7 @ X6 ) ) )
& ( ( X7 @ ( sK4 @ X7 @ X6 ) )
= X6 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ( ? [X0: a] :
( ( ( cR @ X0 )
= $true )
& ( ( cS @ X0 )
!= $true ) )
| ? [X1: a,X2: a > a] :
( ? [X3: a] :
( ( ( X2 @ X3 )
= X1 )
& ( $true
= ( cR @ X3 ) ) )
& ! [X4: a] :
( ( ( cS @ X4 )
!= $true )
| ( ( X2 @ X4 )
!= X1 ) ) ) )
& ( ! [X5: a] :
( ( ( cR @ X5 )
!= $true )
| ( ( cS @ X5 )
= $true ) )
| ! [X6: a,X7: a > a] :
( ! [X8: a] :
( ( ( X7 @ X8 )
!= X6 )
| ( ( cR @ X8 )
!= $true ) )
| ? [X9: a] :
( ( $true
= ( cS @ X9 ) )
& ( ( X7 @ X9 )
= X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ? [X4: a] :
( ( ( cR @ X4 )
= $true )
& ( ( cS @ X4 )
!= $true ) )
| ? [X0: a,X1: a > a] :
( ? [X2: a] :
( ( ( X1 @ X2 )
= X0 )
& ( ( cR @ X2 )
= $true ) )
& ! [X3: a] :
( ( ( cS @ X3 )
!= $true )
| ( ( X1 @ X3 )
!= X0 ) ) ) )
& ( ! [X4: a] :
( ( ( cR @ X4 )
!= $true )
| ( ( cS @ X4 )
= $true ) )
| ! [X0: a,X1: a > a] :
( ! [X2: a] :
( ( ( X1 @ X2 )
!= X0 )
| ( ( cR @ X2 )
!= $true ) )
| ? [X3: a] :
( ( ( cS @ X3 )
= $true )
& ( ( X1 @ X3 )
= X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: a,X1: a > a] :
( ! [X2: a] :
( ( ( X1 @ X2 )
!= X0 )
| ( ( cR @ X2 )
!= $true ) )
| ? [X3: a] :
( ( ( cS @ X3 )
= $true )
& ( ( X1 @ X3 )
= X0 ) ) )
<~> ! [X4: a] :
( ( ( cR @ X4 )
!= $true )
| ( ( cS @ X4 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X1: a > a,X0: a] :
( ? [X2: a] :
( ( ( X1 @ X2 )
= X0 )
& ( ( cR @ X2 )
= $true ) )
=> ? [X3: a] :
( ( ( cS @ X3 )
= $true )
& ( ( X1 @ X3 )
= X0 ) ) )
<=> ! [X4: a] :
( ( ( cR @ X4 )
= $true )
=> ( ( cS @ X4 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a,X1: a > a] :
( ? [X2: a] :
( ( ( X1 @ X2 )
= X0 )
& ( cR @ X2 ) )
=> ? [X3: a] :
( ( ( X1 @ X3 )
= X0 )
& ( cS @ X3 ) ) )
<=> ! [X4: a] :
( ( cR @ X4 )
=> ( cS @ X4 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a,X1: a > a] :
( ? [X2: a] :
( ( ( X1 @ X2 )
= X0 )
& ( cR @ X2 ) )
=> ? [X2: a] :
( ( ( X1 @ X2 )
= X0 )
& ( cS @ X2 ) ) )
<=> ! [X0: a] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: a,X1: a > a] :
( ? [X2: a] :
( ( ( X1 @ X2 )
= X0 )
& ( cR @ X2 ) )
=> ? [X2: a] :
( ( ( X1 @ X2 )
= X0 )
& ( cS @ X2 ) ) )
<=> ! [X0: a] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VbzzVtDKM4/DTF2THF_6797.p',cTHM30_pme) ).
thf(f58,plain,
( spl5_2
| spl5_7 ),
inference(avatar_split_clause,[status(thm)],[f21,f50,f29]) ).
thf(f21,plain,
( ( sK1
= ( sK2 @ sK3 ) )
| ( $true
= ( cR @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f57,plain,
( spl5_8
| spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f22,f43,f55]) ).
thf(f22,plain,
! [X8: a,X7: a > a,X5: a] :
( ( ( cS @ X5 )
= $true )
| ( ( cR @ X8 )
!= $true )
| ( ( cS @ ( sK4 @ X7 @ ( X7 @ X8 ) ) )
= $true )
| ( ( cR @ X5 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f15]) ).
thf(f15,plain,
! [X8: a,X6: a,X7: a > a,X5: a] :
( ( ( cR @ X5 )
!= $true )
| ( ( cS @ X5 )
= $true )
| ( ( X7 @ X8 )
!= X6 )
| ( ( cR @ X8 )
!= $true )
| ( $true
= ( cS @ ( sK4 @ X7 @ X6 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f53,plain,
( spl5_3
| spl5_7 ),
inference(avatar_split_clause,[status(thm)],[f19,f50,f34]) ).
thf(f19,plain,
! [X4: a] :
( ( ( cS @ X4 )
!= $true )
| ( ( sK2 @ X4 )
!= sK1 )
| ( $true
= ( cR @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f48,plain,
( spl5_5
| spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f23,f46,f43]) ).
thf(f23,plain,
! [X8: a,X7: a > a,X5: a] :
( ( ( X7 @ ( sK4 @ X7 @ ( X7 @ X8 ) ) )
= ( X7 @ X8 ) )
| ( ( cS @ X5 )
= $true )
| ( ( cR @ X8 )
!= $true )
| ( ( cR @ X5 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f14]) ).
thf(f14,plain,
! [X8: a,X6: a,X7: a > a,X5: a] :
( ( ( cR @ X5 )
!= $true )
| ( ( cS @ X5 )
= $true )
| ( ( X7 @ X8 )
!= X6 )
| ( ( cR @ X8 )
!= $true )
| ( ( X7 @ ( sK4 @ X7 @ X6 ) )
= X6 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f41,plain,
( spl5_4
| ~ spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f17,f25,f38]) ).
thf(f17,plain,
( ( ( cR @ sK3 )
= $true )
| ( ( cS @ sK0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f36,plain,
( ~ spl5_1
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f16,f34,f25]) ).
thf(f16,plain,
! [X4: a] :
( ( ( cS @ sK0 )
!= $true )
| ( ( cS @ X4 )
!= $true )
| ( ( sK2 @ X4 )
!= sK1 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f32,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f18,f29,f25]) ).
thf(f18,plain,
( ( ( cS @ sK0 )
!= $true )
| ( sK1
= ( sK2 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU897^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n027.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:36:37 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.48 ---- Original DTF file ---
% 0.31/0.48 thf(spec,logic,$$dhol).
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 % File : SEU897^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.48 % Domain : Set Theory
% 0.31/0.48 % Problem : TPS problem THM30
% 0.31/0.48 % Version : Especial.
% 0.31/0.48 % English :
% 0.31/0.48
% 0.31/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.48 % Source : [Bro09]
% 0.31/0.48 % Names : tps_0413 [Bro09]
% 0.31/0.48 % : THM30 [TPS]
% 0.31/0.48
% 0.31/0.48 % Status : Theorem
% 0.31/0.48 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.22 v7.3.0, 0.33 v7.2.0, 0.25 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.43 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.0.0, 0.60 v4.1.0, 0.67 v4.0.0
% 0.31/0.48 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.31/0.48 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.31/0.48 % Maximal formula atoms : 6 ( 6 avg)
% 0.31/0.48 % Number of connectives : 11 ( 0 ~; 0 |; 2 &; 6 @)
% 0.31/0.48 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.31/0.48 % Maximal formula depth : 8 ( 8 avg)
% 0.31/0.48 % Number of types : 2 ( 1 usr)
% 0.31/0.48 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.31/0.48 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.31/0.48 % Number of variables : 5 ( 0 ^; 3 !; 2 ?; 5 :)
% 0.31/0.48 % SPC : TH0_THM_EQU_NAR
% 0.31/0.48
% 0.31/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.48 % : Polymorphic definitions expanded.
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 thf(a_type,type,
% 0.31/0.48 a: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(cS,type,
% 0.31/0.48 cS: a > $o ).
% 0.31/0.48
% 0.31/0.48 thf(cR,type,
% 0.31/0.48 cR: a > $o ).
% 0.31/0.48
% 0.31/0.48 thf(cTHM30_pme,conjecture,
% 0.31/0.48 ( ! [Xx: a] :
% 0.31/0.48 ( ( cR @ Xx )
% 0.31/0.48 => ( cS @ Xx ) )
% 0.31/0.48 <=> ! [F: a > a,Xx: a] :
% 0.31/0.48 ( ? [Xt: a] :
% 0.31/0.48 ( ( cR @ Xt )
% 0.31/0.48 & ( Xx
% 0.31/0.48 = ( F @ Xt ) ) )
% 0.31/0.48 => ? [Xt: a] :
% 0.31/0.48 ( ( cS @ Xt )
% 0.31/0.48 & ( Xx
% 0.31/0.48 = ( F @ Xt ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 1.61/1.49 ---- Embedded in THF ---
% 1.61/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.49 %%% Generated on Tue Feb 24 12:36:38 EST 2026
% 1.61/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.49 %%% Logic specification used:
% 1.61/1.49 %%% thf(spec, logic, $$dhol).
% 1.61/1.49
% 1.61/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VbzzVtDKM4/DTF2DTF6797.p
% See solution above
% 1.61/1.49 ------------------------
% 1.81/1.50 ---- Cleaned THF ---
% 1.81/1.50 thf(a_type,type,
% 1.81/1.50 a: $tType ).
% 1.81/1.50
% 1.81/1.50 thf(cS,type,
% 1.81/1.50 cS: a > $o ).
% 1.81/1.50
% 1.81/1.50 thf(cR,type,
% 1.81/1.50 cR: a > $o ).
% 1.81/1.50
% 1.81/1.50 thf(cTHM30_pme,conjecture,
% 1.81/1.50 ( ! [Xx: a] :
% 1.81/1.50 ( ( cR @ Xx )
% 1.81/1.50 => ( cS @ Xx ) )
% 1.81/1.50 <=> ! [F: a > a,Xx: a] :
% 1.81/1.50 ( ? [Xt: a] :
% 1.81/1.50 ( ( cR @ Xt )
% 1.81/1.50 & ( Xx
% 1.81/1.50 = ( F @ Xt ) ) )
% 1.81/1.50 => ? [Xt: a] :
% 1.81/1.50 ( ( cS @ Xt )
% 1.81/1.50 & ( Xx
% 1.81/1.50 = ( F @ Xt ) ) ) ) ) ).
% 1.81/1.50 ------------------------
% 1.81/1.52 % (6927)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_6797 for (3000ds/27Mi)
% 1.81/1.52 % (6928)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6797 for (3000ds/2Mi)
% 1.81/1.52 % (6931)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6797 for (3000ds/18Mi)
% 1.81/1.52 % (6925)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6797 for (3000ds/183Mi)
% 1.81/1.52 % (6929)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_6797 for (3000ds/2Mi)
% 1.81/1.52 % (6930)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_6797 for (3000ds/275Mi)
% 1.81/1.52 % (6926)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_6797 for (3000ds/4Mi)
% 1.81/1.52 % (6928)Instruction limit reached!
% 1.81/1.52 % (6928)------------------------------
% 1.81/1.52 % (6928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.52 % (6928)Termination reason: Unknown
% 1.81/1.52 % (6928)Termination phase: Property scanning
% 1.81/1.52
% 1.81/1.52 % (6929)Instruction limit reached!
% 1.81/1.52 % (6929)------------------------------
% 1.81/1.52 % (6929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.52 % (6929)Termination reason: Unknown
% 1.81/1.52 % (6929)Termination phase: Saturation
% 1.81/1.52
% 1.81/1.52 % (6929)Memory used [KB]: 895
% 1.81/1.52 % (6929)Time elapsed: 0.003 s
% 1.81/1.52 % (6929)Instructions burned: 2 (million)
% 1.81/1.52 % (6929)------------------------------
% 1.81/1.52 % (6929)------------------------------
% 1.81/1.52 % (6928)Memory used [KB]: 895
% 1.81/1.52 % (6928)Time elapsed: 0.003 s
% 1.81/1.52 % (6928)Instructions burned: 2 (million)
% 1.81/1.52 % (6928)------------------------------
% 1.81/1.52 % (6928)------------------------------
% 1.81/1.52 % (6926)Instruction limit reached!
% 1.81/1.52 % (6926)------------------------------
% 1.81/1.52 % (6926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.52 % (6926)Termination reason: Unknown
% 1.81/1.52 % (6926)Termination phase: Saturation
% 1.81/1.52
% 1.81/1.52 % (6926)Memory used [KB]: 5500
% 1.81/1.52 % (6927)Refutation not found, incomplete strategy
% 1.81/1.52 % (6927)------------------------------
% 1.81/1.52 % (6927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.52 % (6927)Termination reason: Refutation not found, incomplete strategy
% 1.81/1.52
% 1.81/1.52
% 1.81/1.52 % (6927)Memory used [KB]: 5500
% 1.81/1.52 % (6927)Time elapsed: 0.004 s
% 1.81/1.52 % (6927)Instructions burned: 4 (million)
% 1.81/1.52 % (6927)------------------------------
% 1.81/1.52 % (6927)------------------------------
% 1.81/1.52 % (6926)Time elapsed: 0.004 s
% 1.81/1.52 % (6926)Instructions burned: 4 (million)
% 1.81/1.52 % (6926)------------------------------
% 1.81/1.52 % (6926)------------------------------
% 1.81/1.53 % (6930)Refutation not found, incomplete strategy
% 1.81/1.53 % (6930)------------------------------
% 1.81/1.53 % (6930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.53 % (6930)Termination reason: Refutation not found, incomplete strategy
% 1.81/1.53
% 1.81/1.53
% 1.81/1.53 % (6930)Memory used [KB]: 5500
% 1.81/1.53 % (6930)Time elapsed: 0.006 s
% 1.81/1.53 % (6930)Instructions burned: 6 (million)
% 1.81/1.53 % (6930)------------------------------
% 1.81/1.53 % (6930)------------------------------
% 1.81/1.53 % (6925)First to succeed.
% 1.81/1.53 % (6925)Refutation found. Thanks to Tanya!
% 1.81/1.53 % SZS status Theorem for DTF2THF_6797
% 1.81/1.53 % SZS output start Proof for DTF2THF_6797
% 1.81/1.53 thf(type_def_5, type, a: $tType).
% 1.81/1.53 thf(func_def_0, type, a: $tType).
% 1.81/1.53 thf(func_def_1, type, cS: a > $o).
% 1.81/1.53 thf(func_def_2, type, cR: a > $o).
% 1.81/1.53 thf(func_def_6, type, sK0: a).
% 1.81/1.53 thf(func_def_7, type, sK1: a).
% 1.81/1.53 thf(func_def_8, type, sK2: a > a).
% 1.81/1.53 thf(func_def_9, type, sK3: a).
% 1.81/1.53 thf(func_def_10, type, sK4: (a > a) > a > a).
% 1.81/1.53 thf(func_def_12, type, ph6: !>[X0: $tType]:(X0)).
% 1.81/1.53 thf(f96,plain,(
% 1.81/1.53 $false),
% 1.81/1.53 inference(avatar_sat_refutation,[status(thm)],[f32,f36,f41,f48,f53,f57,f58,f59,f66,f68,f95])).
% 1.81/1.53 thf(f95,plain,(
% 1.81/1.53 spl5_5 | ~spl5_6 | ~spl5_8),
% 1.81/1.53 inference(avatar_split_clause,[status(thm)],[f94,f55,f46,f43])).
% 1.81/1.53 thf(f43,definition,(
% 1.81/1.53 spl5_5 <=> ! [X5 : a] : (((cS @ X5) = $true) | ((cR @ X5) != $true))),
% 1.81/1.53 introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition])).
% 1.81/1.53 thf(f46,definition,(
% 1.81/1.53 spl5_6 <=> ! [X8 : a,X7 : a > a] : (((X7 @ (sK4 @ X7 @ (X7 @ X8))) = (X7 @ X8)) | ((cR @ X8) != $true))),
% 1.81/1.53 introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition])).
% 1.81/1.53 thf(f55,definition,(
% 1.81/1.53 spl5_8 <=> ! [X8 : a,X7 : a > a] : (((cR @ X8) != $true) | ((cS @ (sK4 @ X7 @ (X7 @ X8))) = $true))),
% 1.81/1.53 introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition])).
% 1.81/1.53 thf(f94,plain,(
% 1.81/1.53 ( ! [X0 : a] : (((cR @ X0) != $true) | ((cS @ X0) = $true)) ) | (~spl5_6 | ~spl5_8)),
% 1.81/1.53 inference(beta_eta_normalization,[status(thm)],[f93])).
% 1.81/1.53 thf(f93,plain,(
% 1.81/1.53 ( ! [X0 : a] : (((cR @ X0) != $true) | ((cS @ ((^[Y0 : a]: (Y0)) @ X0)) = $true)) ) | (~spl5_6 | ~spl5_8)),
% 1.81/1.53 inference(duplicate_literal_removal,[status(thm)],[f87])).
% 1.81/1.53 thf(f87,plain,(
% 1.81/1.53 ( ! [X0 : a] : (((cR @ X0) != $true) | ((cR @ X0) != $true) | ((cS @ ((^[Y0 : a]: (Y0)) @ X0)) = $true)) ) | (~spl5_6 | ~spl5_8)),
% 1.81/1.53 inference(superposition,[status(thm)],[f56,f47])).
% 1.81/1.53 thf(f47,plain,(
% 1.81/1.53 ( ! [X8 : a,X7 : a > a] : (((X7 @ (sK4 @ X7 @ (X7 @ X8))) = (X7 @ X8)) | ((cR @ X8) != $true)) ) | ~spl5_6),
% 1.81/1.53 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.81/1.53 thf(f56,plain,(
% 1.81/1.53 ( ! [X8 : a,X7 : a > a] : (((cS @ (sK4 @ X7 @ (X7 @ X8))) = $true) | ((cR @ X8) != $true)) ) | ~spl5_8),
% 1.81/1.53 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.81/1.53 thf(f68,plain,(
% 1.81/1.53 ~spl5_2 | ~spl5_3 | ~spl5_4 | ~spl5_5),
% 1.81/1.53 inference(avatar_contradiction_clause,[status(thm)],[f67])).
% 1.81/1.53 thf(f67,plain,(
% 1.81/1.53 $false | (~spl5_2 | ~spl5_3 | ~spl5_4 | ~spl5_5)),
% 1.81/1.53 inference(subsumption_resolution,[status(thm)],[f64,f40])).
% 1.81/1.53 thf(f40,plain,(
% 1.81/1.53 ((cR @ sK3) = $true) | ~spl5_4),
% 1.81/1.53 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.81/1.53 thf(f38,definition,(
% 1.81/1.53 spl5_4 <=> ((cR @ sK3) = $true)),
% 1.81/1.53 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.81/1.53 thf(f64,plain,(
% 1.81/1.53 ((cR @ sK3) != $true) | (~spl5_2 | ~spl5_3 | ~spl5_5)),
% 1.81/1.53 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.81/1.53 thf(f63,plain,(
% 1.81/1.53 ((cR @ sK3) != $true) | ($true != $true) | (~spl5_2 | ~spl5_3 | ~spl5_5)),
% 1.81/1.53 inference(superposition,[status(thm)],[f61,f44])).
% 1.81/1.53 thf(f44,plain,(
% 1.81/1.53 ( ! [X5 : a] : (((cS @ X5) = $true) | ((cR @ X5) != $true)) ) | ~spl5_5),
% 1.81/1.53 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.81/1.53 thf(f61,plain,(
% 1.81/1.53 ((cS @ sK3) != $true) | (~spl5_2 | ~spl5_3)),
% 1.81/1.53 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.81/1.53 thf(f60,plain,(
% 1.81/1.53 ((cS @ sK3) != $true) | (sK1 != sK1) | (~spl5_2 | ~spl5_3)),
% 1.81/1.53 inference(superposition,[status(thm)],[f35,f31])).
% 1.81/1.53 thf(f31,plain,(
% 1.81/1.53 (sK1 = (sK2 @ sK3)) | ~spl5_2),
% 1.81/1.53 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.81/1.53 thf(f29,definition,(
% 1.81/1.53 spl5_2 <=> (sK1 = (sK2 @ sK3))),
% 1.81/1.53 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.81/1.53 thf(f35,plain,(
% 1.81/1.53 ( ! [X4 : a] : (((sK2 @ X4) != sK1) | ((cS @ X4) != $true)) ) | ~spl5_3),
% 1.81/1.53 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.81/1.53 thf(f34,definition,(
% 1.81/1.53 spl5_3 <=> ! [X4 : a] : (((cS @ X4) != $true) | ((sK2 @ X4) != sK1))),
% 1.81/1.53 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.81/1.53 thf(f66,plain,(
% 1.81/1.53 ~spl5_7 | spl5_1 | ~spl5_5),
% 1.81/1.53 inference(avatar_split_clause,[status(thm)],[f65,f43,f25,f50])).
% 1.81/1.53 thf(f50,definition,(
% 1.81/1.53 spl5_7 <=> ($true = (cR @ sK0))),
% 1.81/1.53 introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition])).
% 1.81/1.53 thf(f25,definition,(
% 1.81/1.53 spl5_1 <=> ((cS @ sK0) = $true)),
% 1.81/1.53 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.81/1.53 thf(f65,plain,(
% 1.81/1.53 ($true != (cR @ sK0)) | (spl5_1 | ~spl5_5)),
% 1.81/1.53 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.81/1.53 thf(f62,plain,(
% 1.81/1.53 ($true != $true) | ($true != (cR @ sK0)) | (spl5_1 | ~spl5_5)),
% 1.81/1.53 inference(superposition,[status(thm)],[f27,f44])).
% 1.81/1.53 thf(f27,plain,(
% 1.81/1.53 ((cS @ sK0) != $true) | spl5_1),
% 1.81/1.53 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.81/1.53 thf(f59,plain,(
% 1.81/1.53 spl5_4 | spl5_7),
% 1.81/1.53 inference(avatar_split_clause,[status(thm)],[f20,f50,f38])).
% 1.81/1.53 thf(f20,plain,(
% 1.81/1.53 ($true = (cR @ sK0)) | ((cR @ sK3) = $true)),
% 1.81/1.53 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.53 thf(f13,plain,(
% 1.81/1.53 ((($true = (cR @ sK0)) & ((cS @ sK0) != $true)) | (((sK1 = (sK2 @ sK3)) & ((cR @ sK3) = $true)) & ! [X4 : a] : (((cS @ X4) != $true) | ((sK2 @ X4) != sK1)))) & (! [X5 : a] : (((cR @ X5) != $true) | ((cS @ X5) = $true)) | ! [X6 : a,X7 : a > a] : (! [X8 : a] : (((X7 @ X8) != X6) | ((cR @ X8) != $true)) | (($true = (cS @ (sK4 @ X7 @ X6))) & ((X7 @ (sK4 @ X7 @ X6)) = X6))))),
% 1.81/1.53 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f12,f11,f10,f9])).
% 1.81/1.53 thf(f9,plain,(
% 1.81/1.53 ? [X0 : a] : (((cR @ X0) = $true) & ((cS @ X0) != $true)) => (($true = (cR @ sK0)) & ((cS @ sK0) != $true))),
% 1.81/1.53 introduced(definition,[],[choice_axiom])).
% 1.81/1.53 thf(f10,plain,(
% 1.81/1.53 ? [X1 : a,X2 : a > a] : (? [X3 : a] : (((X2 @ X3) = X1) & ($true = (cR @ X3))) & ! [X4 : a] : (((cS @ X4) != $true) | ((X2 @ X4) != X1))) => (? [X3 : a] : ((sK1 = (sK2 @ X3)) & ($true = (cR @ X3))) & ! [X4 : a] : (((cS @ X4) != $true) | ((sK2 @ X4) != sK1)))),
% 1.81/1.53 introduced(definition,[],[choice_axiom])).
% 1.81/1.53 thf(f11,plain,(
% 1.81/1.53 ? [X3 : a] : ((sK1 = (sK2 @ X3)) & ($true = (cR @ X3))) => ((sK1 = (sK2 @ sK3)) & ((cR @ sK3) = $true))),
% 1.81/1.53 introduced(definition,[],[choice_axiom])).
% 1.81/1.53 thf(f12,plain,(
% 1.81/1.53 ! [X6 : a,X7 : a > a] : (? [X9 : a] : (($true = (cS @ X9)) & ((X7 @ X9) = X6)) => (($true = (cS @ (sK4 @ X7 @ X6))) & ((X7 @ (sK4 @ X7 @ X6)) = X6)))),
% 1.81/1.53 introduced(definition,[],[choice_axiom])).
% 1.81/1.53 thf(f8,plain,(
% 1.81/1.53 (? [X0 : a] : (((cR @ X0) = $true) & ((cS @ X0) != $true)) | ? [X1 : a,X2 : a > a] : (? [X3 : a] : (((X2 @ X3) = X1) & ($true = (cR @ X3))) & ! [X4 : a] : (((cS @ X4) != $true) | ((X2 @ X4) != X1)))) & (! [X5 : a] : (((cR @ X5) != $true) | ((cS @ X5) = $true)) | ! [X6 : a,X7 : a > a] : (! [X8 : a] : (((X7 @ X8) != X6) | ((cR @ X8) != $true)) | ? [X9 : a] : (($true = (cS @ X9)) & ((X7 @ X9) = X6))))),
% 1.81/1.53 inference(rectify,[status(thm)],[f7])).
% 1.81/1.53 thf(f7,plain,(
% 1.81/1.53 (? [X4 : a] : (((cR @ X4) = $true) & ((cS @ X4) != $true)) | ? [X0 : a,X1 : a > a] : (? [X2 : a] : (((X1 @ X2) = X0) & ((cR @ X2) = $true)) & ! [X3 : a] : (((cS @ X3) != $true) | ((X1 @ X3) != X0)))) & (! [X4 : a] : (((cR @ X4) != $true) | ((cS @ X4) = $true)) | ! [X0 : a,X1 : a > a] : (! [X2 : a] : (((X1 @ X2) != X0) | ((cR @ X2) != $true)) | ? [X3 : a] : (((cS @ X3) = $true) & ((X1 @ X3) = X0))))),
% 1.81/1.53 inference(nnf_transformation,[status(thm)],[f6])).
% 1.81/1.53 thf(f6,plain,(
% 1.81/1.53 ! [X0 : a,X1 : a > a] : (! [X2 : a] : (((X1 @ X2) != X0) | ((cR @ X2) != $true)) | ? [X3 : a] : (((cS @ X3) = $true) & ((X1 @ X3) = X0))) <~> ! [X4 : a] : (((cR @ X4) != $true) | ((cS @ X4) = $true))),
% 1.81/1.53 inference(ennf_transformation,[status(thm)],[f5])).
% 1.81/1.53 thf(f5,plain,(
% 1.81/1.53 ~(! [X1 : a > a,X0 : a] : (? [X2 : a] : (((X1 @ X2) = X0) & ((cR @ X2) = $true)) => ? [X3 : a] : (((cS @ X3) = $true) & ((X1 @ X3) = X0))) <=> ! [X4 : a] : (((cR @ X4) = $true) => ((cS @ X4) = $true)))),
% 1.81/1.53 inference(fool_elimination,[status(thm)],[f4])).
% 1.81/1.53 thf(f4,plain,(
% 1.81/1.53 ~(! [X0 : a,X1 : a > a] : (? [X2 : a] : (((X1 @ X2) = X0) & (cR @ X2)) => ? [X3 : a] : (((X1 @ X3) = X0) & (cS @ X3))) <=> ! [X4 : a] : ((cR @ X4) => (cS @ X4)))),
% 1.81/1.53 inference(rectify,[status(thm)],[f2])).
% 1.81/1.53 thf(f2,negated_conjecture,(
% 1.81/1.53 ~(! [X0 : a,X1 : a > a] : (? [X2 : a] : (((X1 @ X2) = X0) & (cR @ X2)) => ? [X2 : a] : (((X1 @ X2) = X0) & (cS @ X2))) <=> ! [X0 : a] : ((cR @ X0) => (cS @ X0)))),
% 1.81/1.53 inference(negated_conjecture,[status(cth)],[f1])).
% 1.81/1.53 thf(f1,conjecture,(
% 1.81/1.53 ! [X0 : a,X1 : a > a] : (? [X2 : a] : (((X1 @ X2) = X0) & (cR @ X2)) => ? [X2 : a] : (((X1 @ X2) = X0) & (cS @ X2))) <=> ! [X0 : a] : ((cR @ X0) => (cS @ X0))),
% 1.81/1.53 file('/export/starexec/sandbox/tmp/tmp.VbzzVtDKM4/DTF2THF_6797.p',cTHM30_pme)).
% 1.81/1.53 thf(f58,plain,(
% 1.81/1.53 spl5_2 | spl5_7),
% 1.81/1.53 inference(avatar_split_clause,[status(thm)],[f21,f50,f29])).
% 1.81/1.53 thf(f21,plain,(
% 1.81/1.53 (sK1 = (sK2 @ sK3)) | ($true = (cR @ sK0))),
% 1.81/1.53 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.53 thf(f57,plain,(
% 1.81/1.53 spl5_8 | spl5_5),
% 1.81/1.53 inference(avatar_split_clause,[status(thm)],[f22,f43,f55])).
% 1.81/1.53 thf(f22,plain,(
% 1.81/1.53 ( ! [X8 : a,X7 : a > a,X5 : a] : (((cS @ X5) = $true) | ((cR @ X8) != $true) | ((cS @ (sK4 @ X7 @ (X7 @ X8))) = $true) | ((cR @ X5) != $true)) )),
% 1.81/1.53 inference(equality_resolution,[status(thm)],[f15])).
% 1.81/1.53 thf(f15,plain,(
% 1.81/1.53 ( ! [X8 : a,X6 : a,X7 : a > a,X5 : a] : (((cR @ X5) != $true) | ((cS @ X5) = $true) | ((X7 @ X8) != X6) | ((cR @ X8) != $true) | ($true = (cS @ (sK4 @ X7 @ X6)))) )),
% 1.81/1.53 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.53 thf(f53,plain,(
% 1.81/1.53 spl5_3 | spl5_7),
% 1.81/1.53 inference(avatar_split_clause,[status(thm)],[f19,f50,f34])).
% 1.81/1.53 thf(f19,plain,(
% 1.81/1.53 ( ! [X4 : a] : (((cS @ X4) != $true) | ((sK2 @ X4) != sK1) | ($true = (cR @ sK0))) )),
% 1.81/1.53 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.53 thf(f48,plain,(
% 1.81/1.53 spl5_5 | spl5_6),
% 1.81/1.53 inference(avatar_split_clause,[status(thm)],[f23,f46,f43])).
% 1.81/1.53 thf(f23,plain,(
% 1.81/1.53 ( ! [X8 : a,X7 : a > a,X5 : a] : (((X7 @ (sK4 @ X7 @ (X7 @ X8))) = (X7 @ X8)) | ((cS @ X5) = $true) | ((cR @ X8) != $true) | ((cR @ X5) != $true)) )),
% 1.81/1.53 inference(equality_resolution,[status(thm)],[f14])).
% 1.81/1.53 thf(f14,plain,(
% 1.81/1.53 ( ! [X8 : a,X6 : a,X7 : a > a,X5 : a] : (((cR @ X5) != $true) | ((cS @ X5) = $true) | ((X7 @ X8) != X6) | ((cR @ X8) != $true) | ((X7 @ (sK4 @ X7 @ X6)) = X6)) )),
% 1.81/1.53 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.53 thf(f41,plain,(
% 1.81/1.53 spl5_4 | ~spl5_1),
% 1.81/1.53 inference(avatar_split_clause,[status(thm)],[f17,f25,f38])).
% 1.81/1.53 thf(f17,plain,(
% 1.81/1.53 ((cR @ sK3) = $true) | ((cS @ sK0) != $true)),
% 1.81/1.53 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.53 thf(f36,plain,(
% 1.81/1.53 ~spl5_1 | spl5_3),
% 1.81/1.53 inference(avatar_split_clause,[status(thm)],[f16,f34,f25])).
% 1.81/1.53 thf(f16,plain,(
% 1.81/1.53 ( ! [X4 : a] : (((cS @ sK0) != $true) | ((cS @ X4) != $true) | ((sK2 @ X4) != sK1)) )),
% 1.81/1.53 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.53 thf(f32,plain,(
% 1.81/1.53 ~spl5_1 | spl5_2),
% 1.81/1.53 inference(avatar_split_clause,[status(thm)],[f18,f29,f25])).
% 1.81/1.53 thf(f18,plain,(
% 1.81/1.53 ((cS @ sK0) != $true) | (sK1 = (sK2 @ sK3))),
% 1.81/1.53 inference(cnf_transformation,[status(thm)],[f13])).
% 1.81/1.53 % SZS output end Proof for DTF2THF_6797
% 1.81/1.53 % (6925)------------------------------
% 1.81/1.53 % (6925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.53 % (6925)Termination reason: Refutation
% 1.81/1.53
% 1.81/1.53 % (6925)Memory used [KB]: 5628
% 1.81/1.53 % (6925)Time elapsed: 0.007 s
% 1.81/1.53 % (6925)Instructions burned: 8 (million)
% 1.81/1.53 % (6925)------------------------------
% 1.81/1.53 % (6925)------------------------------
% 1.81/1.53 % (6924)Success in time 0.02 s
%------------------------------------------------------------------------------