%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU859^5 : 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 : n014.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 09:37:36 AM UTC 2026
% Result : Theorem 0.32s 1.33s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 5 unt; 0 typ; 3 def)
% Number of atoms : 373 ( 145 equ; 0 cnn)
% Maximal formula atoms : 16 ( 9 avg)
% Number of connectives : 391 ( 57 ~; 89 |; 36 &; 178 @)
% ( 3 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 161 ( 72 ^; 68 !; 21 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_9,type,
sK0: a ).
thf(func_def_10,type,
sK1: a > $o ).
thf(func_def_11,type,
sK2: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_12,type,
sK3: ( ( a > $o ) > $o ) > a ).
thf(func_def_13,type,
sK4: ( a > $o ) > $o ).
thf(func_def_15,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f59,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f33,f47,f50,f58]) ).
thf(f58,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[status(thm)],[f57]) ).
thf(f57,plain,
( $false
| ~ spl5_1 ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true != $true )
| ~ spl5_1 ),
inference(superposition,[status(thm)],[f14,f52]) ).
thf(f52,plain,
( ! [X0: a] :
( ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( sK1 @ Y0 ) ) )
= $true )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ! [X0: a] :
( ( $true != $true )
| ( ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( sK1 @ Y0 ) ) )
= $true ) )
| ~ spl5_1 ),
inference(superposition,[status(thm)],[f15,f28]) ).
thf(f28,plain,
( ( ( sK4 @ sK1 )
= $true )
| ~ spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl5_1
<=> ( ( sK4 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f15,plain,
! [X6: a > $o,X7: a] :
( ( ( sK4 @ X6 )
!= $true )
| ( $true
= ( sK4
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( X6 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ sK1 )
= $true )
| ( ( X2
@ ^ [Y0: a] : $false )
!= $true )
| ( ( ( X2
@ ^ [Y0: a] :
( ( ( sK3 @ X2 )
= Y0 )
| ( sK2 @ X2 @ Y0 ) ) )
!= $true )
& ( ( X2 @ ( sK2 @ X2 ) )
= $true ) ) )
& ! [X6: a > $o,X7: a] :
( ( ( sK4 @ X6 )
!= $true )
| ( $true
= ( sK4
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( X6 @ Y0 ) ) ) ) )
& ( ( sK4
@ ^ [Y0: a] :
( ( sK0 = Y0 )
| ( sK1 @ Y0 ) ) )
!= $true )
& ( ( sK4
@ ^ [Y0: a] : $false )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a,X1: a > $o] :
( ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ X1 )
= $true )
| ( ( X2
@ ^ [Y0: a] : $false )
!= $true )
| ? [X3: a > $o,X4: a] :
( ( ( X2
@ ^ [Y0: a] :
( ( X4 = Y0 )
| ( X3 @ Y0 ) ) )
!= $true )
& ( ( X2 @ X3 )
= $true ) ) )
& ? [X5: ( a > $o ) > $o] :
( ! [X6: a > $o,X7: a] :
( ( ( X5 @ X6 )
!= $true )
| ( ( X5
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( X6 @ Y0 ) ) )
= $true ) )
& ( $true
!= ( X5
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) )
& ( ( X5
@ ^ [Y0: a] : $false )
= $true ) ) )
=> ( ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ sK1 )
= $true )
| ( ( X2
@ ^ [Y0: a] : $false )
!= $true )
| ? [X3: a > $o,X4: a] :
( ( ( X2
@ ^ [Y0: a] :
( ( X4 = Y0 )
| ( X3 @ Y0 ) ) )
!= $true )
& ( ( X2 @ X3 )
= $true ) ) )
& ? [X5: ( a > $o ) > $o] :
( ! [X6: a > $o,X7: a] :
( ( ( X5 @ X6 )
!= $true )
| ( ( X5
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( X6 @ Y0 ) ) )
= $true ) )
& ( ( X5
@ ^ [Y0: a] :
( ( sK0 = Y0 )
| ( sK1 @ Y0 ) ) )
!= $true )
& ( ( X5
@ ^ [Y0: a] : $false )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X2: ( a > $o ) > $o] :
( ? [X3: a > $o,X4: a] :
( ( ( X2
@ ^ [Y0: a] :
( ( X4 = Y0 )
| ( X3 @ Y0 ) ) )
!= $true )
& ( ( X2 @ X3 )
= $true ) )
=> ( ( ( X2
@ ^ [Y0: a] :
( ( ( sK3 @ X2 )
= Y0 )
| ( sK2 @ X2 @ Y0 ) ) )
!= $true )
& ( ( X2 @ ( sK2 @ X2 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X5: ( a > $o ) > $o] :
( ! [X6: a > $o,X7: a] :
( ( ( X5 @ X6 )
!= $true )
| ( ( X5
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( X6 @ Y0 ) ) )
= $true ) )
& ( ( X5
@ ^ [Y0: a] :
( ( sK0 = Y0 )
| ( sK1 @ Y0 ) ) )
!= $true )
& ( ( X5
@ ^ [Y0: a] : $false )
= $true ) )
=> ( ! [X7: a,X6: a > $o] :
( ( ( sK4 @ X6 )
!= $true )
| ( $true
= ( sK4
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( X6 @ Y0 ) ) ) ) )
& ( ( sK4
@ ^ [Y0: a] :
( ( sK0 = Y0 )
| ( sK1 @ Y0 ) ) )
!= $true )
& ( ( sK4
@ ^ [Y0: a] : $false )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a,X1: a > $o] :
( ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ X1 )
= $true )
| ( ( X2
@ ^ [Y0: a] : $false )
!= $true )
| ? [X3: a > $o,X4: a] :
( ( ( X2
@ ^ [Y0: a] :
( ( X4 = Y0 )
| ( X3 @ Y0 ) ) )
!= $true )
& ( ( X2 @ X3 )
= $true ) ) )
& ? [X5: ( a > $o ) > $o] :
( ! [X6: a > $o,X7: a] :
( ( ( X5 @ X6 )
!= $true )
| ( ( X5
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( X6 @ Y0 ) ) )
= $true ) )
& ( $true
!= ( X5
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) )
& ( ( X5
@ ^ [Y0: a] : $false )
= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a,X1: a > $o] :
( ? [X5: ( a > $o ) > $o] :
( ( $true
!= ( X5
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) )
& ! [X6: a > $o,X7: a] :
( ( ( X5 @ X6 )
!= $true )
| ( ( X5
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( X6 @ Y0 ) ) )
= $true ) )
& ( ( X5
@ ^ [Y0: a] : $false )
= $true ) )
& ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ X1 )
= $true )
| ( ( X2
@ ^ [Y0: a] : $false )
!= $true )
| ? [X3: a > $o,X4: a] :
( ( ( X2
@ ^ [Y0: a] :
( ( X4 = Y0 )
| ( X3 @ Y0 ) ) )
!= $true )
& ( ( X2 @ X3 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a,X1: a > $o] :
( ! [X2: ( a > $o ) > $o] :
( ( ( ( X2
@ ^ [Y0: a] : $false )
= $true )
& ! [X3: a > $o,X4: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X2
@ ^ [Y0: a] :
( ( X4 = Y0 )
| ( X3 @ Y0 ) ) )
= $true ) ) )
=> ( ( X2 @ X1 )
= $true ) )
=> ! [X5: ( a > $o ) > $o] :
( ( ! [X6: a > $o,X7: a] :
( ( ( X5 @ X6 )
= $true )
=> ( ( X5
@ ^ [Y0: a] :
( ( X7 = Y0 )
| ( X6 @ Y0 ) ) )
= $true ) )
& ( ( X5
@ ^ [Y0: a] : $false )
= $true ) )
=> ( $true
= ( X5
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a,X1: a > $o] :
( ! [X2: ( a > $o ) > $o] :
( ( ( ( X2
@ ^ [Y0: a] : $false )
= $true )
& ! [X4: a > $o,X5: a] :
( ( ( X2 @ X4 )
= $true )
=> ( ( X2
@ ^ [Y0: a] :
( ( X5 = Y0 )
| ( X4 @ Y0 ) ) )
= $true ) ) )
=> ( ( X2 @ X1 )
= $true ) )
=> ! [X7: ( a > $o ) > $o] :
( ( ( ( X7
@ ^ [Y0: a] : $false )
= $true )
& ! [X9: a > $o,X10: a] :
( ( ( X7 @ X9 )
= $true )
=> ( ( X7
@ ^ [Y0: a] :
( ( X10 = Y0 )
| ( X9 @ Y0 ) ) )
= $true ) ) )
=> ( ( X7
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( X1 @ Y0 ) ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > $o] :
( ! [X2: ( a > $o ) > $o] :
( ( ( X2
@ ^ [X3: a] : $false )
& ! [X4: a > $o,X5: a] :
( ( X2 @ X4 )
=> ( X2
@ ^ [X6: a] :
( ( X4 @ X6 )
| ( X5 = X6 ) ) ) ) )
=> ( X2 @ X1 ) )
=> ! [X7: ( a > $o ) > $o] :
( ( ( X7
@ ^ [X8: a] : $false )
& ! [X9: a > $o,X10: a] :
( ( X7 @ X9 )
=> ( X7
@ ^ [X11: a] :
( ( X9 @ X11 )
| ( X10 = X11 ) ) ) ) )
=> ( X7
@ ^ [X12: a] :
( ( X1 @ X12 )
| ( X0 = X12 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a,X0: a > $o] :
( ! [X2: ( a > $o ) > $o] :
( ( ( X2
@ ^ [X3: a] : $false )
& ! [X4: a > $o,X3: a] :
( ( X2 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ( X4 @ X5 )
| ( X3 = X5 ) ) ) ) )
=> ( X2 @ X0 ) )
=> ! [X2: ( a > $o ) > $o] :
( ( ( X2
@ ^ [X3: a] : $false )
& ! [X4: a > $o,X3: a] :
( ( X2 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ( X4 @ X5 )
| ( X3 = X5 ) ) ) ) )
=> ( X2
@ ^ [X5: a] :
( ( X0 @ X5 )
| ( X1 = X5 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a,X0: a > $o] :
( ! [X2: ( a > $o ) > $o] :
( ( ( X2
@ ^ [X3: a] : $false )
& ! [X4: a > $o,X3: a] :
( ( X2 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ( X4 @ X5 )
| ( X3 = X5 ) ) ) ) )
=> ( X2 @ X0 ) )
=> ! [X2: ( a > $o ) > $o] :
( ( ( X2
@ ^ [X3: a] : $false )
& ! [X4: a > $o,X3: a] :
( ( X2 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ( X4 @ X5 )
| ( X3 = X5 ) ) ) ) )
=> ( X2
@ ^ [X5: a] :
( ( X0 @ X5 )
| ( X1 = X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TYOR3p4e0d/DTF2THF_19603.p',cTHM164_pme) ).
thf(f14,plain,
( ( sK4
@ ^ [Y0: a] :
( ( sK0 = Y0 )
| ( sK1 @ Y0 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f50,plain,
spl5_3,
inference(avatar_contradiction_clause,[status(thm)],[f49]) ).
thf(f49,plain,
( $false
| spl5_3 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $true != $true )
| spl5_3 ),
inference(superposition,[status(thm)],[f46,f13]) ).
thf(f13,plain,
( ( sK4
@ ^ [Y0: a] : $false )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f46,plain,
( ( ( sK4
@ ^ [Y0: a] : $false )
!= $true )
| spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl5_3
<=> ( ( sK4
@ ^ [Y0: a] : $false )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f47,plain,
( ~ spl5_3
| spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f42,f30,f26,f44]) ).
thf(f30,definition,
( spl5_2
<=> ( ( sK4 @ ( sK2 @ sK4 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f42,plain,
( ( ( sK4
@ ^ [Y0: a] : $false )
!= $true )
| ( ( sK4 @ sK1 )
= $true )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( sK4
@ ^ [Y0: a] : $false )
!= $true )
| ( $true != $true )
| ( ( sK4 @ sK1 )
= $true )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f17,f37]) ).
thf(f37,plain,
( ! [X0: a] :
( ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( sK2 @ sK4 @ Y0 ) ) )
= $true )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ! [X0: a] :
( ( ( sK4
@ ^ [Y0: a] :
( ( X0 = Y0 )
| ( sK2 @ sK4 @ Y0 ) ) )
= $true )
| ( $true != $true ) )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f15,f32]) ).
thf(f32,plain,
( ( ( sK4 @ ( sK2 @ sK4 ) )
= $true )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f17,plain,
! [X2: ( a > $o ) > $o] :
( ( ( X2
@ ^ [Y0: a] :
( ( ( sK3 @ X2 )
= Y0 )
| ( sK2 @ X2 @ Y0 ) ) )
!= $true )
| ( ( X2
@ ^ [Y0: a] : $false )
!= $true )
| ( ( X2 @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f33,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f24,f30,f26]) ).
thf(f24,plain,
( ( ( sK4 @ ( sK2 @ sK4 ) )
= $true )
| ( ( sK4 @ sK1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true != $true )
| ( ( sK4 @ ( sK2 @ sK4 ) )
= $true )
| ( ( sK4 @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f16,f13]) ).
thf(f16,plain,
! [X2: ( a > $o ) > $o] :
( ( ( X2
@ ^ [Y0: a] : $false )
!= $true )
| ( ( X2 @ sK1 )
= $true )
| ( ( X2 @ ( sK2 @ X2 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU859^5 : 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
% 0.18/0.34 % Computer : n014.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:35:57 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SEU859^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.47 % Domain : Set Theory (Finite sets)
% 0.31/0.47 % Problem : TPS problem THM164
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English : Direct consequence of the definition of FINITE1.
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Bro09]
% 0.31/0.47 % Names : tps_0333 [Bro09]
% 0.31/0.47 % : THM164 [TPS]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 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 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.31/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.31/0.47 % Number of atoms : 5 ( 3 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 5 ( 5 avg)
% 0.31/0.47 % Number of connectives : 21 ( 0 ~; 3 |; 2 &; 11 @)
% 0.31/0.47 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 14 ( 14 avg)
% 0.31/0.47 % Number of types : 2 ( 1 usr)
% 0.31/0.47 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.31/0.47 % Number of variables : 13 ( 5 ^; 8 !; 0 ?; 13 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.47 % : Polymorphic definitions expanded.
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(a_type,type,
% 0.31/0.47 a: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(cTHM164_pme,conjecture,
% 0.31/0.47 ! [Xr: a > $o,Xx: a] :
% 0.31/0.47 ( ! [Xw: ( a > $o ) > $o] :
% 0.31/0.47 ( ( ( Xw
% 0.31/0.47 @ ^ [Xx0: a] : $false )
% 0.31/0.47 & ! [Xr0: a > $o,Xx0: a] :
% 0.31/0.47 ( ( Xw @ Xr0 )
% 0.31/0.47 => ( Xw
% 0.31/0.47 @ ^ [Xt: a] :
% 0.31/0.47 ( ( Xr0 @ Xt )
% 0.31/0.47 | ( Xt = Xx0 ) ) ) ) )
% 0.31/0.47 => ( Xw @ Xr ) )
% 0.31/0.47 => ! [Xw: ( a > $o ) > $o] :
% 0.31/0.47 ( ( ( Xw
% 0.31/0.47 @ ^ [Xx0: a] : $false )
% 0.31/0.47 & ! [Xr0: a > $o,Xx0: a] :
% 0.31/0.47 ( ( Xw @ Xr0 )
% 0.31/0.47 => ( Xw
% 0.31/0.47 @ ^ [Xt: a] :
% 0.31/0.47 ( ( Xr0 @ Xt )
% 0.31/0.47 | ( Xt = Xx0 ) ) ) ) )
% 0.31/0.47 => ( Xw
% 0.31/0.47 @ ^ [Xt: a] :
% 0.31/0.47 ( ( Xr @ Xt )
% 0.31/0.47 | ( Xt = Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 0.32/1.30 ---- Embedded in THF ---
% 0.32/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.31 %%% Generated on Tue Feb 24 12:35:58 EST 2026
% 0.32/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.31 %%% Logic specification used:
% 0.32/1.31 %%% thf(spec, logic, $$dhol).
% 0.32/1.31
% 0.32/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.TYOR3p4e0d/DTF2DTF19603.p
% See solution above
% 0.32/1.31 ------------------------
% 0.32/1.31 ---- Cleaned THF ---
% 0.32/1.32 thf(a_type,type,
% 0.32/1.32 a: $tType ).
% 0.32/1.32
% 0.32/1.32 thf(cTHM164_pme,conjecture,
% 0.32/1.32 ! [Xr: a > $o,Xx: a] :
% 0.32/1.32 ( ! [Xw: ( a > $o ) > $o] :
% 0.32/1.32 ( ( ( Xw
% 0.32/1.32 @ ^ [Xx0: a] : $false )
% 0.32/1.32 & ! [Xr0: a > $o,Xx0: a] :
% 0.32/1.32 ( ( Xw @ Xr0 )
% 0.32/1.32 => ( Xw
% 0.32/1.32 @ ^ [Xt: a] :
% 0.32/1.32 ( ( Xr0 @ Xt )
% 0.32/1.32 | ( Xt = Xx0 ) ) ) ) )
% 0.32/1.32 => ( Xw @ Xr ) )
% 0.32/1.32 => ! [Xw: ( a > $o ) > $o] :
% 0.32/1.32 ( ( ( Xw
% 0.32/1.32 @ ^ [Xx0: a] : $false )
% 0.32/1.32 & ! [Xr0: a > $o,Xx0: a] :
% 0.32/1.32 ( ( Xw @ Xr0 )
% 0.32/1.32 => ( Xw
% 0.32/1.32 @ ^ [Xt: a] :
% 0.32/1.32 ( ( Xr0 @ Xt )
% 0.32/1.32 | ( Xt = Xx0 ) ) ) ) )
% 0.32/1.32 => ( Xw
% 0.32/1.32 @ ^ [Xt: a] :
% 0.32/1.32 ( ( Xr @ Xt )
% 0.32/1.32 | ( Xt = Xx ) ) ) ) ) ).
% 0.32/1.32 ------------------------
% 0.32/1.33 % (19794)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_19603 for (2999ds/27Mi)
% 0.32/1.33 % (19793)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_19603 for (2999ds/4Mi)
% 0.32/1.33 % (19792)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19603 for (2999ds/183Mi)
% 0.32/1.33 % (19793)Instruction limit reached!
% 0.32/1.33 % (19793)------------------------------
% 0.32/1.33 % (19793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.33 % (19793)Termination reason: Unknown
% 0.32/1.33 % (19793)Termination phase: Saturation
% 0.32/1.33
% 0.32/1.33 % (19793)Memory used [KB]: 5500
% 0.32/1.33 % (19793)Time elapsed: 0.004 s
% 0.32/1.33 % (19793)Instructions burned: 6 (million)
% 0.32/1.33 % (19793)------------------------------
% 0.32/1.33 % (19793)------------------------------
% 0.32/1.33 % (19795)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19603 for (2999ds/2Mi)
% 0.32/1.33 % (19794)First to succeed.
% 0.32/1.33 % (19795)Instruction limit reached!
% 0.32/1.33 % (19795)------------------------------
% 0.32/1.33 % (19795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.33 % (19795)Termination reason: Unknown
% 0.32/1.33 % (19795)Termination phase: Saturation
% 0.32/1.33
% 0.32/1.33 % (19795)Memory used [KB]: 5500
% 0.32/1.33 % (19795)Time elapsed: 0.002 s
% 0.32/1.33 % (19795)Instructions burned: 2 (million)
% 0.32/1.33 % (19795)------------------------------
% 0.32/1.33 % (19795)------------------------------
% 0.32/1.33 % (19794)Refutation found. Thanks to Tanya!
% 0.32/1.33 % SZS status Theorem for DTF2THF_19603
% 0.32/1.33 % SZS output start Proof for DTF2THF_19603
% 0.32/1.33 thf(type_def_5, type, a: $tType).
% 0.32/1.33 thf(func_def_0, type, a: $tType).
% 0.32/1.33 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.32/1.33 thf(func_def_9, type, sK0: a).
% 0.32/1.33 thf(func_def_10, type, sK1: a > $o).
% 0.32/1.33 thf(func_def_11, type, sK2: ((a > $o) > $o) > a > $o).
% 0.32/1.33 thf(func_def_12, type, sK3: ((a > $o) > $o) > a).
% 0.32/1.33 thf(func_def_13, type, sK4: (a > $o) > $o).
% 0.32/1.33 thf(func_def_15, type, ph6: !>[X0: $tType]:(X0)).
% 0.32/1.33 thf(f59,plain,(
% 0.32/1.33 $false),
% 0.32/1.33 inference(avatar_sat_refutation,[status(thm)],[f33,f47,f50,f58])).
% 0.32/1.33 thf(f58,plain,(
% 0.32/1.33 ~spl5_1),
% 0.32/1.33 inference(avatar_contradiction_clause,[status(thm)],[f57])).
% 0.32/1.33 thf(f57,plain,(
% 0.32/1.33 $false | ~spl5_1),
% 0.32/1.33 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 0.32/1.33 thf(f53,plain,(
% 0.32/1.33 ($true != $true) | ~spl5_1),
% 0.32/1.33 inference(superposition,[status(thm)],[f14,f52])).
% 0.32/1.33 thf(f52,plain,(
% 0.32/1.33 ( ! [X0 : a] : (((sK4 @ (^[Y0 : a]: ((X0 = Y0) | (sK1 @ Y0)))) = $true)) ) | ~spl5_1),
% 0.32/1.33 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 0.32/1.33 thf(f51,plain,(
% 0.32/1.33 ( ! [X0 : a] : (($true != $true) | ((sK4 @ (^[Y0 : a]: ((X0 = Y0) | (sK1 @ Y0)))) = $true)) ) | ~spl5_1),
% 0.32/1.33 inference(superposition,[status(thm)],[f15,f28])).
% 0.32/1.33 thf(f28,plain,(
% 0.32/1.33 ((sK4 @ sK1) = $true) | ~spl5_1),
% 0.32/1.33 inference(avatar_component_clause,[status(thm)],[f26])).
% 0.32/1.33 thf(f26,definition,(
% 0.32/1.33 spl5_1 <=> ((sK4 @ sK1) = $true)),
% 0.32/1.33 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 0.32/1.33 thf(f15,plain,(
% 0.32/1.33 ( ! [X6 : a > $o,X7 : a] : (((sK4 @ X6) != $true) | ($true = (sK4 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0)))))) )),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 0.32/1.33 thf(f12,plain,(
% 0.32/1.33 ! [X2 : (a > $o) > $o] : (((X2 @ sK1) = $true) | ((X2 @ (^[Y0 : a]: ($false))) != $true) | (((X2 @ (^[Y0 : a]: (((sK3 @ X2) = Y0) | (sK2 @ X2 @ Y0)))) != $true) & ((X2 @ (sK2 @ X2)) = $true))) & (! [X6 : a > $o,X7 : a] : (((sK4 @ X6) != $true) | ($true = (sK4 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0)))))) & ((sK4 @ (^[Y0 : a]: ((sK0 = Y0) | (sK1 @ Y0)))) != $true) & ((sK4 @ (^[Y0 : a]: ($false))) = $true))),
% 0.32/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f11,f10,f9])).
% 0.32/1.33 thf(f9,plain,(
% 0.32/1.33 ? [X0 : a,X1 : a > $o] : (! [X2 : (a > $o) > $o] : (((X2 @ X1) = $true) | ((X2 @ (^[Y0 : a]: ($false))) != $true) | ? [X3 : a > $o,X4 : a] : (((X2 @ (^[Y0 : a]: ((X4 = Y0) | (X3 @ Y0)))) != $true) & ((X2 @ X3) = $true))) & ? [X5 : (a > $o) > $o] : (! [X6 : a > $o,X7 : a] : (((X5 @ X6) != $true) | ((X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0)))) = $true)) & ($true != (X5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) & ((X5 @ (^[Y0 : a]: ($false))) = $true))) => (! [X2 : (a > $o) > $o] : (((X2 @ sK1) = $true) | ((X2 @ (^[Y0 : a]: ($false))) != $true) | ? [X3 : a > $o,X4 : a] : (((X2 @ (^[Y0 : a]: ((X4 = Y0) | (X3 @ Y0)))) != $true) & ((X2 @ X3) = $true))) & ? [X5 : (a > $o) > $o] : (! [X6 : a > $o,X7 : a] : (((X5 @ X6) != $true) | ((X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0)))) = $true)) & ((X5 @ (^[Y0 : a]: ((sK0 = Y0) | (sK1 @ Y0)))) != $true) & ((X5 @ (^[Y0 : a]: ($false))) = $true)))),
% 0.32/1.33 introduced(definition,[],[choice_axiom])).
% 0.32/1.33 thf(f10,plain,(
% 0.32/1.33 ! [X2 : (a > $o) > $o] : (? [X3 : a > $o,X4 : a] : (((X2 @ (^[Y0 : a]: ((X4 = Y0) | (X3 @ Y0)))) != $true) & ((X2 @ X3) = $true)) => (((X2 @ (^[Y0 : a]: (((sK3 @ X2) = Y0) | (sK2 @ X2 @ Y0)))) != $true) & ((X2 @ (sK2 @ X2)) = $true)))),
% 0.32/1.33 introduced(definition,[],[choice_axiom])).
% 0.32/1.33 thf(f11,plain,(
% 0.32/1.33 ? [X5 : (a > $o) > $o] : (! [X6 : a > $o,X7 : a] : (((X5 @ X6) != $true) | ((X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0)))) = $true)) & ((X5 @ (^[Y0 : a]: ((sK0 = Y0) | (sK1 @ Y0)))) != $true) & ((X5 @ (^[Y0 : a]: ($false))) = $true)) => (! [X7 : a,X6 : a > $o] : (((sK4 @ X6) != $true) | ($true = (sK4 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0)))))) & ((sK4 @ (^[Y0 : a]: ((sK0 = Y0) | (sK1 @ Y0)))) != $true) & ((sK4 @ (^[Y0 : a]: ($false))) = $true))),
% 0.32/1.33 introduced(definition,[],[choice_axiom])).
% 0.32/1.33 thf(f8,plain,(
% 0.32/1.33 ? [X0 : a,X1 : a > $o] : (! [X2 : (a > $o) > $o] : (((X2 @ X1) = $true) | ((X2 @ (^[Y0 : a]: ($false))) != $true) | ? [X3 : a > $o,X4 : a] : (((X2 @ (^[Y0 : a]: ((X4 = Y0) | (X3 @ Y0)))) != $true) & ((X2 @ X3) = $true))) & ? [X5 : (a > $o) > $o] : (! [X6 : a > $o,X7 : a] : (((X5 @ X6) != $true) | ((X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0)))) = $true)) & ($true != (X5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) & ((X5 @ (^[Y0 : a]: ($false))) = $true)))),
% 0.32/1.33 inference(flattening,[status(thm)],[f7])).
% 0.32/1.33 thf(f7,plain,(
% 0.32/1.33 ? [X0 : a,X1 : a > $o] : (? [X5 : (a > $o) > $o] : (($true != (X5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) & (! [X6 : a > $o,X7 : a] : (((X5 @ X6) != $true) | ((X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0)))) = $true)) & ((X5 @ (^[Y0 : a]: ($false))) = $true))) & ! [X2 : (a > $o) > $o] : (((X2 @ X1) = $true) | (((X2 @ (^[Y0 : a]: ($false))) != $true) | ? [X3 : a > $o,X4 : a] : (((X2 @ (^[Y0 : a]: ((X4 = Y0) | (X3 @ Y0)))) != $true) & ((X2 @ X3) = $true)))))),
% 0.32/1.33 inference(ennf_transformation,[status(thm)],[f6])).
% 0.32/1.33 thf(f6,plain,(
% 0.32/1.33 ~! [X0 : a,X1 : a > $o] : (! [X2 : (a > $o) > $o] : ((((X2 @ (^[Y0 : a]: ($false))) = $true) & ! [X3 : a > $o,X4 : a] : (((X2 @ X3) = $true) => ((X2 @ (^[Y0 : a]: ((X4 = Y0) | (X3 @ Y0)))) = $true))) => ((X2 @ X1) = $true)) => ! [X5 : (a > $o) > $o] : ((! [X6 : a > $o,X7 : a] : (((X5 @ X6) = $true) => ((X5 @ (^[Y0 : a]: ((X7 = Y0) | (X6 @ Y0)))) = $true)) & ((X5 @ (^[Y0 : a]: ($false))) = $true)) => ($true = (X5 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))))),
% 0.32/1.33 inference(rectify,[status(thm)],[f5])).
% 0.32/1.33 thf(f5,plain,(
% 0.32/1.33 ~! [X0 : a,X1 : a > $o] : (! [X2 : (a > $o) > $o] : ((((X2 @ (^[Y0 : a]: ($false))) = $true) & ! [X4 : a > $o,X5 : a] : (((X2 @ X4) = $true) => ((X2 @ (^[Y0 : a]: ((X5 = Y0) | (X4 @ Y0)))) = $true))) => ((X2 @ X1) = $true)) => ! [X7 : (a > $o) > $o] : ((((X7 @ (^[Y0 : a]: ($false))) = $true) & ! [X9 : a > $o,X10 : a] : (((X7 @ X9) = $true) => ((X7 @ (^[Y0 : a]: ((X10 = Y0) | (X9 @ Y0)))) = $true))) => ((X7 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))) = $true)))),
% 0.32/1.33 inference(fool_elimination,[status(thm)],[f4])).
% 0.32/1.33 thf(f4,plain,(
% 0.32/1.33 ~! [X0 : a,X1 : a > $o] : (! [X2 : (a > $o) > $o] : (((X2 @ (^[X3 : a] : ($false))) & ! [X4 : a > $o,X5 : a] : ((X2 @ X4) => (X2 @ (^[X6 : a] : ((X4 @ X6) | (X5 = X6)))))) => (X2 @ X1)) => ! [X7 : (a > $o) > $o] : (((X7 @ (^[X8 : a] : ($false))) & ! [X9 : a > $o,X10 : a] : ((X7 @ X9) => (X7 @ (^[X11 : a] : ((X9 @ X11) | (X10 = X11)))))) => (X7 @ (^[X12 : a] : ((X1 @ X12) | (X0 = X12))))))),
% 0.32/1.33 inference(rectify,[status(thm)],[f2])).
% 0.32/1.33 thf(f2,negated_conjecture,(
% 0.32/1.33 ~! [X1 : a,X0 : a > $o] : (! [X2 : (a > $o) > $o] : (((X2 @ (^[X3 : a] : ($false))) & ! [X4 : a > $o,X3 : a] : ((X2 @ X4) => (X2 @ (^[X5 : a] : ((X4 @ X5) | (X3 = X5)))))) => (X2 @ X0)) => ! [X2 : (a > $o) > $o] : (((X2 @ (^[X3 : a] : ($false))) & ! [X4 : a > $o,X3 : a] : ((X2 @ X4) => (X2 @ (^[X5 : a] : ((X4 @ X5) | (X3 = X5)))))) => (X2 @ (^[X5 : a] : ((X0 @ X5) | (X1 = X5))))))),
% 0.32/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 0.32/1.33 thf(f1,conjecture,(
% 0.32/1.33 ! [X1 : a,X0 : a > $o] : (! [X2 : (a > $o) > $o] : (((X2 @ (^[X3 : a] : ($false))) & ! [X4 : a > $o,X3 : a] : ((X2 @ X4) => (X2 @ (^[X5 : a] : ((X4 @ X5) | (X3 = X5)))))) => (X2 @ X0)) => ! [X2 : (a > $o) > $o] : (((X2 @ (^[X3 : a] : ($false))) & ! [X4 : a > $o,X3 : a] : ((X2 @ X4) => (X2 @ (^[X5 : a] : ((X4 @ X5) | (X3 = X5)))))) => (X2 @ (^[X5 : a] : ((X0 @ X5) | (X1 = X5))))))),
% 0.32/1.33 file('/export/starexec/sandbox/tmp/tmp.TYOR3p4e0d/DTF2THF_19603.p',cTHM164_pme)).
% 0.32/1.33 thf(f14,plain,(
% 0.32/1.33 ((sK4 @ (^[Y0 : a]: ((sK0 = Y0) | (sK1 @ Y0)))) != $true)),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 0.32/1.33 thf(f50,plain,(
% 0.32/1.33 spl5_3),
% 0.32/1.33 inference(avatar_contradiction_clause,[status(thm)],[f49])).
% 0.32/1.33 thf(f49,plain,(
% 0.32/1.33 $false | spl5_3),
% 0.32/1.33 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 0.32/1.33 thf(f48,plain,(
% 0.32/1.33 ($true != $true) | spl5_3),
% 0.32/1.33 inference(superposition,[status(thm)],[f46,f13])).
% 0.32/1.33 thf(f13,plain,(
% 0.32/1.33 ((sK4 @ (^[Y0 : a]: ($false))) = $true)),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 0.32/1.33 thf(f46,plain,(
% 0.32/1.33 ((sK4 @ (^[Y0 : a]: ($false))) != $true) | spl5_3),
% 0.32/1.33 inference(avatar_component_clause,[status(thm)],[f44])).
% 0.32/1.33 thf(f44,definition,(
% 0.32/1.33 spl5_3 <=> ((sK4 @ (^[Y0 : a]: ($false))) = $true)),
% 0.32/1.33 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 0.32/1.33 thf(f47,plain,(
% 0.32/1.33 ~spl5_3 | spl5_1 | ~spl5_2),
% 0.32/1.33 inference(avatar_split_clause,[status(thm)],[f42,f30,f26,f44])).
% 0.32/1.33 thf(f30,definition,(
% 0.32/1.33 spl5_2 <=> ((sK4 @ (sK2 @ sK4)) = $true)),
% 0.32/1.33 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 0.32/1.33 thf(f42,plain,(
% 0.32/1.33 ((sK4 @ (^[Y0 : a]: ($false))) != $true) | ((sK4 @ sK1) = $true) | ~spl5_2),
% 0.32/1.33 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 0.32/1.33 thf(f41,plain,(
% 0.32/1.33 ((sK4 @ (^[Y0 : a]: ($false))) != $true) | ($true != $true) | ((sK4 @ sK1) = $true) | ~spl5_2),
% 0.32/1.33 inference(superposition,[status(thm)],[f17,f37])).
% 0.32/1.33 thf(f37,plain,(
% 0.32/1.33 ( ! [X0 : a] : (((sK4 @ (^[Y0 : a]: ((X0 = Y0) | (sK2 @ sK4 @ Y0)))) = $true)) ) | ~spl5_2),
% 0.32/1.33 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 0.32/1.33 thf(f36,plain,(
% 0.32/1.33 ( ! [X0 : a] : (((sK4 @ (^[Y0 : a]: ((X0 = Y0) | (sK2 @ sK4 @ Y0)))) = $true) | ($true != $true)) ) | ~spl5_2),
% 0.32/1.33 inference(superposition,[status(thm)],[f15,f32])).
% 0.32/1.33 thf(f32,plain,(
% 0.32/1.33 ((sK4 @ (sK2 @ sK4)) = $true) | ~spl5_2),
% 0.32/1.33 inference(avatar_component_clause,[status(thm)],[f30])).
% 0.32/1.33 thf(f17,plain,(
% 0.32/1.33 ( ! [X2 : (a > $o) > $o] : (((X2 @ (^[Y0 : a]: (((sK3 @ X2) = Y0) | (sK2 @ X2 @ Y0)))) != $true) | ((X2 @ (^[Y0 : a]: ($false))) != $true) | ((X2 @ sK1) = $true)) )),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 0.32/1.33 thf(f33,plain,(
% 0.32/1.33 spl5_1 | spl5_2),
% 0.32/1.33 inference(avatar_split_clause,[status(thm)],[f24,f30,f26])).
% 0.32/1.33 thf(f24,plain,(
% 0.32/1.33 ((sK4 @ (sK2 @ sK4)) = $true) | ((sK4 @ sK1) = $true)),
% 0.32/1.33 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 0.32/1.33 thf(f23,plain,(
% 0.32/1.33 ($true != $true) | ((sK4 @ (sK2 @ sK4)) = $true) | ((sK4 @ sK1) = $true)),
% 0.32/1.33 inference(superposition,[status(thm)],[f16,f13])).
% 0.32/1.33 thf(f16,plain,(
% 0.32/1.33 ( ! [X2 : (a > $o) > $o] : (((X2 @ (^[Y0 : a]: ($false))) != $true) | ((X2 @ sK1) = $true) | ((X2 @ (sK2 @ X2)) = $true)) )),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 0.32/1.33 % SZS output end Proof for DTF2THF_19603
% 0.32/1.33 % (19794)------------------------------
% 0.32/1.33 % (19794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.33 % (19794)Termination reason: Refutation
% 0.32/1.33
% 0.32/1.33 % (19794)Memory used [KB]: 5500
% 0.32/1.33 % (19794)Time elapsed: 0.005 s
% 0.32/1.33 % (19794)Instructions burned: 6 (million)
% 0.32/1.33 % (19794)------------------------------
% 0.32/1.33 % (19794)------------------------------
% 0.32/1.33 % (19790)Success in time 0.014 s
%------------------------------------------------------------------------------