%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET624^5 : 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 : n003.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 09:31:57 AM UTC 2026
% Result : Theorem 1.48s 1.26s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 61 ( 1 unt; 0 typ; 9 def)
% Number of atoms : 543 ( 179 equ; 0 cnn)
% Maximal formula atoms : 28 ( 8 avg)
% Number of connectives : 518 ( 107 ~; 140 |; 57 &; 196 @)
% ( 13 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 14 con; 0-2 aty)
% Number of variables : 86 ( 0 ^; 38 !; 48 ?; 86 :)
% 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_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a > $o ).
thf(func_def_7,type,
sK2: a > $o ).
thf(func_def_8,type,
sK3: a ).
thf(func_def_9,type,
sK4: a ).
thf(func_def_10,type,
sK5: a ).
thf(f85,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f46,f47,f64,f65,f66,f67,f68,f69,f71,f72,f75,f78,f81,f84]) ).
thf(f84,plain,
( ~ spl6_7
| ~ spl6_2
| ~ spl6_5 ),
inference(avatar_split_clause,[status(thm)],[f83,f43,f31,f53]) ).
thf(f53,definition,
( spl6_7
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_7])],[avatar_definition]) ).
thf(f31,definition,
( spl6_2
<=> ! [X4: a] :
( ( $true
!= ( sK0 @ X4 ) )
| ( $true
!= ( sK1 @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f43,definition,
( spl6_5
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition]) ).
thf(f83,plain,
( ( $true
!= ( sK0 @ sK4 ) )
| ~ spl6_2
| ~ spl6_5 ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK4 ) )
| ~ spl6_2
| ~ spl6_5 ),
inference(superposition,[status(thm)],[f32,f45]) ).
thf(f45,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f32,plain,
( ! [X4: a] :
( ( $true
!= ( sK1 @ X4 ) )
| ( $true
!= ( sK0 @ X4 ) ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f81,plain,
( ~ spl6_3
| ~ spl6_1
| ~ spl6_8 ),
inference(avatar_split_clause,[status(thm)],[f80,f57,f28,f35]) ).
thf(f35,definition,
( spl6_3
<=> ( $true
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition]) ).
thf(f28,definition,
( spl6_1
<=> ! [X5: a] :
( ( $true
!= ( sK2 @ X5 ) )
| ( $true
!= ( sK1 @ X5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f57,definition,
( spl6_8
<=> ( ( sK2 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_8])],[avatar_definition]) ).
thf(f80,plain,
( ( $true
!= ( sK1 @ sK5 ) )
| ~ spl6_1
| ~ spl6_8 ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $true != $true )
| ( $true
!= ( sK1 @ sK5 ) )
| ~ spl6_1
| ~ spl6_8 ),
inference(superposition,[status(thm)],[f29,f59]) ).
thf(f59,plain,
( ( ( sK2 @ sK5 )
= $true )
| ~ spl6_8 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f29,plain,
( ! [X5: a] :
( ( $true
!= ( sK2 @ X5 ) )
| ( $true
!= ( sK1 @ X5 ) ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f78,plain,
( ~ spl6_9
| ~ spl6_2
| ~ spl6_3 ),
inference(avatar_split_clause,[status(thm)],[f77,f35,f31,f61]) ).
thf(f61,definition,
( spl6_9
<=> ( $true
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition]) ).
thf(f77,plain,
( ( $true
!= ( sK0 @ sK5 ) )
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $true
!= ( sK0 @ sK5 ) )
| ( $true != $true )
| ~ spl6_2
| ~ spl6_3 ),
inference(superposition,[status(thm)],[f32,f37]) ).
thf(f37,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f75,plain,
( ~ spl6_6
| ~ spl6_1
| ~ spl6_4 ),
inference(avatar_split_clause,[status(thm)],[f74,f39,f28,f49]) ).
thf(f49,definition,
( spl6_6
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_6])],[avatar_definition]) ).
thf(f39,definition,
( spl6_4
<=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition]) ).
thf(f74,plain,
( ( $true
!= ( sK1 @ sK3 ) )
| ~ spl6_1
| ~ spl6_4 ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $true
!= ( sK1 @ sK3 ) )
| ( $true != $true )
| ~ spl6_1
| ~ spl6_4 ),
inference(superposition,[status(thm)],[f29,f41]) ).
thf(f41,plain,
( ( ( sK2 @ sK3 )
= $true )
| ~ spl6_4 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f72,plain,
( spl6_6
| spl6_8
| spl6_9
| spl6_5 ),
inference(avatar_split_clause,[status(thm)],[f18,f43,f61,f57,f49]) ).
thf(f18,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( ( sK2 @ sK5 )
= $true )
| ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( ! [X3: a] :
( ( $true
!= ( sK2 @ X3 ) )
| ( $true
!= ( sK1 @ X3 ) ) )
& ! [X4: a] :
( ( $true
!= ( sK1 @ X4 ) )
| ( $true
!= ( sK0 @ X4 ) ) ) )
| ! [X5: a] :
( ( ( $true
!= ( sK2 @ X5 ) )
& ( $true
!= ( sK0 @ X5 ) ) )
| ( $true
!= ( sK1 @ X5 ) ) ) )
& ( ( ( ( sK2 @ sK3 )
= $true )
& ( $true
= ( sK1 @ sK3 ) ) )
| ( ( $true
= ( sK1 @ sK4 ) )
& ( $true
= ( sK0 @ sK4 ) ) )
| ( ( ( ( sK2 @ sK5 )
= $true )
| ( $true
= ( sK0 @ sK5 ) ) )
& ( $true
= ( sK1 @ sK5 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f9,f13,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
| ( $true
!= ( X0 @ X4 ) ) ) )
| ! [X5: a] :
( ( ( $true
!= ( X2 @ X5 ) )
& ( $true
!= ( X0 @ X5 ) ) )
| ( $true
!= ( X1 @ X5 ) ) ) )
& ( ? [X6: a] :
( ( $true
= ( X2 @ X6 ) )
& ( $true
= ( X1 @ X6 ) ) )
| ? [X7: a] :
( ( $true
= ( X1 @ X7 ) )
& ( $true
= ( X0 @ X7 ) ) )
| ? [X8: a] :
( ( ( $true
= ( X2 @ X8 ) )
| ( $true
= ( X0 @ X8 ) ) )
& ( $true
= ( X1 @ X8 ) ) ) ) )
=> ( ( ( ! [X3: a] :
( ( $true
!= ( sK2 @ X3 ) )
| ( $true
!= ( sK1 @ X3 ) ) )
& ! [X4: a] :
( ( $true
!= ( sK1 @ X4 ) )
| ( $true
!= ( sK0 @ X4 ) ) ) )
| ! [X5: a] :
( ( ( $true
!= ( sK2 @ X5 ) )
& ( $true
!= ( sK0 @ X5 ) ) )
| ( $true
!= ( sK1 @ X5 ) ) ) )
& ( ? [X6: a] :
( ( $true
= ( sK2 @ X6 ) )
& ( $true
= ( sK1 @ X6 ) ) )
| ? [X7: a] :
( ( $true
= ( sK1 @ X7 ) )
& ( $true
= ( sK0 @ X7 ) ) )
| ? [X8: a] :
( ( ( $true
= ( sK2 @ X8 ) )
| ( $true
= ( sK0 @ X8 ) ) )
& ( $true
= ( sK1 @ X8 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X6: a] :
( ( $true
= ( sK2 @ X6 ) )
& ( $true
= ( sK1 @ X6 ) ) )
=> ( ( ( sK2 @ sK3 )
= $true )
& ( $true
= ( sK1 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X7: a] :
( ( $true
= ( sK1 @ X7 ) )
& ( $true
= ( sK0 @ X7 ) ) )
=> ( ( $true
= ( sK1 @ sK4 ) )
& ( $true
= ( sK0 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X8: a] :
( ( ( $true
= ( sK2 @ X8 ) )
| ( $true
= ( sK0 @ X8 ) ) )
& ( $true
= ( sK1 @ X8 ) ) )
=> ( ( ( ( sK2 @ sK5 )
= $true )
| ( $true
= ( sK0 @ sK5 ) ) )
& ( $true
= ( sK1 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
| ( $true
!= ( X0 @ X4 ) ) ) )
| ! [X5: a] :
( ( ( $true
!= ( X2 @ X5 ) )
& ( $true
!= ( X0 @ X5 ) ) )
| ( $true
!= ( X1 @ X5 ) ) ) )
& ( ? [X6: a] :
( ( $true
= ( X2 @ X6 ) )
& ( $true
= ( X1 @ X6 ) ) )
| ? [X7: a] :
( ( $true
= ( X1 @ X7 ) )
& ( $true
= ( X0 @ X7 ) ) )
| ? [X8: a] :
( ( ( $true
= ( X2 @ X8 ) )
| ( $true
= ( X0 @ X8 ) ) )
& ( $true
= ( X1 @ X8 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ( ! [X5: a] :
( ( $true
!= ( X1 @ X5 ) )
| ( $true
!= ( X2 @ X5 ) ) )
& ! [X4: a] :
( ( $true
!= ( X2 @ X4 ) )
| ( $true
!= ( X0 @ X4 ) ) ) )
| ! [X3: a] :
( ( ( ( X1 @ X3 )
!= $true )
& ( ( X0 @ X3 )
!= $true ) )
| ( ( X2 @ X3 )
!= $true ) ) )
& ( ? [X5: a] :
( ( $true
= ( X1 @ X5 ) )
& ( $true
= ( X2 @ X5 ) ) )
| ? [X4: a] :
( ( $true
= ( X2 @ X4 ) )
& ( $true
= ( X0 @ X4 ) ) )
| ? [X3: a] :
( ( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true ) )
& ( ( X2 @ X3 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ( ! [X5: a] :
( ( $true
!= ( X1 @ X5 ) )
| ( $true
!= ( X2 @ X5 ) ) )
& ! [X4: a] :
( ( $true
!= ( X2 @ X4 ) )
| ( $true
!= ( X0 @ X4 ) ) ) )
| ! [X3: a] :
( ( ( ( X1 @ X3 )
!= $true )
& ( ( X0 @ X3 )
!= $true ) )
| ( ( X2 @ X3 )
!= $true ) ) )
& ( ? [X5: a] :
( ( $true
= ( X1 @ X5 ) )
& ( $true
= ( X2 @ X5 ) ) )
| ? [X4: a] :
( ( $true
= ( X2 @ X4 ) )
& ( $true
= ( X0 @ X4 ) ) )
| ? [X3: a] :
( ( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true ) )
& ( ( X2 @ X3 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ? [X3: a] :
( ( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true ) )
& ( ( X2 @ X3 )
= $true ) )
<~> ( ? [X5: a] :
( ( $true
= ( X1 @ X5 ) )
& ( $true
= ( X2 @ X5 ) ) )
| ? [X4: a] :
( ( $true
= ( X2 @ X4 ) )
& ( $true
= ( X0 @ X4 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true ) )
& ( ( X2 @ X3 )
= $true ) )
<=> ( ? [X5: a] :
( ( $true
= ( X1 @ X5 ) )
& ( $true
= ( X2 @ X5 ) ) )
| ? [X4: a] :
( ( $true
= ( X2 @ X4 ) )
& ( $true
= ( X0 @ X4 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( ( X0 @ X3 )
| ( X1 @ X3 ) )
& ( X2 @ X3 ) )
<=> ( ? [X4: a] :
( ( X0 @ X4 )
& ( X2 @ X4 ) )
| ? [X5: a] :
( ( X1 @ X5 )
& ( X2 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ? [X3: a] :
( ( ( X1 @ X3 )
| ( X2 @ X3 ) )
& ( X0 @ X3 ) )
<=> ( ? [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 ) )
| ? [X3: a] :
( ( X2 @ X3 )
& ( X0 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ? [X3: a] :
( ( ( X1 @ X3 )
| ( X2 @ X3 ) )
& ( X0 @ X3 ) )
<=> ( ? [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 ) )
| ? [X3: a] :
( ( X2 @ X3 )
& ( X0 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bHLU3G5kF0/DTF2THF_411.p',cBOOL_PROP_100_pme) ).
thf(f71,plain,
( spl6_9
| spl6_8
| spl6_4
| spl6_7 ),
inference(avatar_split_clause,[status(thm)],[f20,f53,f39,f57,f61]) ).
thf(f20,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f69,plain,
( spl6_8
| spl6_4
| spl6_5
| spl6_9 ),
inference(avatar_split_clause,[status(thm)],[f22,f61,f43,f39,f57]) ).
thf(f22,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( ( sK2 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK5 ) )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f68,plain,
( spl6_1
| spl6_1 ),
inference(avatar_split_clause,[status(thm)],[f26,f28,f28]) ).
thf(f26,plain,
! [X3: a,X5: a] :
( ( $true
!= ( sK1 @ X3 ) )
| ( $true
!= ( sK2 @ X5 ) )
| ( $true
!= ( sK1 @ X5 ) )
| ( $true
!= ( sK2 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f67,plain,
( spl6_7
| spl6_6
| spl6_3 ),
inference(avatar_split_clause,[status(thm)],[f15,f35,f49,f53]) ).
thf(f15,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f66,plain,
( spl6_4
| spl6_7
| spl6_3 ),
inference(avatar_split_clause,[status(thm)],[f19,f35,f53,f39]) ).
thf(f19,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f65,plain,
( spl6_3
| spl6_6
| spl6_5 ),
inference(avatar_split_clause,[status(thm)],[f17,f43,f49,f35]) ).
thf(f17,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f64,plain,
( spl6_6
| spl6_7
| spl6_8
| spl6_9 ),
inference(avatar_split_clause,[status(thm)],[f16,f61,f57,f53,f49]) ).
thf(f16,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f47,plain,
( spl6_2
| spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f23,f31,f31]) ).
thf(f23,plain,
! [X4: a,X5: a] :
( ( $true
!= ( sK0 @ X4 ) )
| ( $true
!= ( sK1 @ X4 ) )
| ( $true
!= ( sK0 @ X5 ) )
| ( $true
!= ( sK1 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f46,plain,
( spl6_3
| spl6_4
| spl6_5 ),
inference(avatar_split_clause,[status(thm)],[f21,f43,f39,f35]) ).
thf(f21,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET624^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n003.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:00:40 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SET624^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : TPS problem BOOL-PROP-100
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English : Trybulec's 100th Boolean property of sets
% 0.18/0.45
% 0.18/0.45 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.18/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : tps_0385 [Bro09]
% 0.18/0.45 % : BOOL-PROP-100 [TPS]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.18/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.18/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.18/0.45 % Number of connectives : 13 ( 0 ~; 2 |; 3 &; 7 @)
% 0.18/0.45 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 9 ( 9 avg)
% 0.18/0.45 % Number of types : 2 ( 1 usr)
% 0.18/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.18/0.45 % Number of variables : 6 ( 0 ^; 3 !; 3 ?; 6 :)
% 0.18/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.45 % : Polymorphic definitions expanded.
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(a_type,type,
% 0.18/0.45 a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(cBOOL_PROP_100_pme,conjecture,
% 0.18/0.45 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.18/0.45 ( ? [Xx: a] :
% 0.18/0.45 ( ( X @ Xx )
% 0.18/0.45 & ( ( Y @ Xx )
% 0.18/0.45 | ( Z @ Xx ) ) )
% 0.18/0.45 <=> ( ? [Xx: a] :
% 0.18/0.45 ( ( X @ Xx )
% 0.18/0.45 & ( Y @ Xx ) )
% 0.18/0.45 | ? [Xx: a] :
% 0.18/0.45 ( ( X @ Xx )
% 0.18/0.45 & ( Z @ Xx ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.48/1.23 ---- Embedded in THF ---
% 1.48/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.23 %%% Generated on Tue Feb 24 12:00:41 EST 2026
% 1.48/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.23 %%% Logic specification used:
% 1.48/1.23 %%% thf(spec, logic, $$dhol).
% 1.48/1.23
% 1.48/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.bHLU3G5kF0/DTF2DTF411.p
% See solution above
% 1.48/1.23 ------------------------
% 1.48/1.24 ---- Cleaned THF ---
% 1.48/1.24 thf(a_type,type,
% 1.48/1.24 a: $tType ).
% 1.48/1.24
% 1.48/1.24 thf(cBOOL_PROP_100_pme,conjecture,
% 1.48/1.24 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.48/1.24 ( ? [Xx: a] :
% 1.48/1.24 ( ( X @ Xx )
% 1.48/1.24 & ( ( Y @ Xx )
% 1.48/1.24 | ( Z @ Xx ) ) )
% 1.48/1.24 <=> ( ? [Xx: a] :
% 1.48/1.24 ( ( X @ Xx )
% 1.48/1.24 & ( Y @ Xx ) )
% 1.48/1.24 | ? [Xx: a] :
% 1.48/1.24 ( ( X @ Xx )
% 1.48/1.24 & ( Z @ Xx ) ) ) ) ).
% 1.48/1.24 ------------------------
% 1.48/1.25 % (555)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_411 for (2999ds/2Mi)
% 1.48/1.25 % (555)Instruction limit reached!
% 1.48/1.25 % (555)------------------------------
% 1.48/1.25 % (555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (555)Termination reason: Unknown
% 1.48/1.25 % (555)Termination phase: Saturation
% 1.48/1.25
% 1.48/1.25 % (555)Memory used [KB]: 895
% 1.48/1.25 % (555)Time elapsed: 0.002 s
% 1.48/1.25 % (555)Instructions burned: 2 (million)
% 1.48/1.25 % (553)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_411 for (2999ds/27Mi)
% 1.48/1.25 % (555)------------------------------
% 1.48/1.25 % (555)------------------------------
% 1.48/1.26 % (553)First to succeed.
% 1.48/1.26 % (553)Refutation found. Thanks to Tanya!
% 1.48/1.26 % SZS status Theorem for DTF2THF_411
% 1.48/1.26 % SZS output start Proof for DTF2THF_411
% 1.48/1.26 thf(type_def_5, type, a: $tType).
% 1.48/1.26 thf(func_def_0, type, a: $tType).
% 1.48/1.26 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.48/1.26 thf(func_def_5, type, sK0: a > $o).
% 1.48/1.26 thf(func_def_6, type, sK1: a > $o).
% 1.48/1.26 thf(func_def_7, type, sK2: a > $o).
% 1.48/1.26 thf(func_def_8, type, sK3: a).
% 1.48/1.26 thf(func_def_9, type, sK4: a).
% 1.48/1.26 thf(func_def_10, type, sK5: a).
% 1.48/1.26 thf(f85,plain,(
% 1.48/1.26 $false),
% 1.48/1.26 inference(avatar_sat_refutation,[status(thm)],[f46,f47,f64,f65,f66,f67,f68,f69,f71,f72,f75,f78,f81,f84])).
% 1.48/1.26 thf(f84,plain,(
% 1.48/1.26 ~spl6_7 | ~spl6_2 | ~spl6_5),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f83,f43,f31,f53])).
% 1.48/1.26 thf(f53,definition,(
% 1.48/1.26 spl6_7 <=> ($true = (sK0 @ sK4))),
% 1.48/1.26 introduced(definition,[new_symbols(naming,[spl6_7])],[avatar_definition])).
% 1.48/1.26 thf(f31,definition,(
% 1.48/1.26 spl6_2 <=> ! [X4 : a] : (($true != (sK0 @ X4)) | ($true != (sK1 @ X4)))),
% 1.48/1.26 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.48/1.26 thf(f43,definition,(
% 1.48/1.26 spl6_5 <=> ($true = (sK1 @ sK4))),
% 1.48/1.26 introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition])).
% 1.48/1.26 thf(f83,plain,(
% 1.48/1.26 ($true != (sK0 @ sK4)) | (~spl6_2 | ~spl6_5)),
% 1.48/1.26 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.48/1.26 thf(f82,plain,(
% 1.48/1.26 ($true != $true) | ($true != (sK0 @ sK4)) | (~spl6_2 | ~spl6_5)),
% 1.48/1.26 inference(superposition,[status(thm)],[f32,f45])).
% 1.48/1.26 thf(f45,plain,(
% 1.48/1.26 ($true = (sK1 @ sK4)) | ~spl6_5),
% 1.48/1.26 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.48/1.26 thf(f32,plain,(
% 1.48/1.26 ( ! [X4 : a] : (($true != (sK1 @ X4)) | ($true != (sK0 @ X4))) ) | ~spl6_2),
% 1.48/1.26 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.48/1.26 thf(f81,plain,(
% 1.48/1.26 ~spl6_3 | ~spl6_1 | ~spl6_8),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f80,f57,f28,f35])).
% 1.48/1.26 thf(f35,definition,(
% 1.48/1.26 spl6_3 <=> ($true = (sK1 @ sK5))),
% 1.48/1.26 introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition])).
% 1.48/1.26 thf(f28,definition,(
% 1.48/1.26 spl6_1 <=> ! [X5 : a] : (($true != (sK2 @ X5)) | ($true != (sK1 @ X5)))),
% 1.48/1.26 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.48/1.26 thf(f57,definition,(
% 1.48/1.26 spl6_8 <=> ((sK2 @ sK5) = $true)),
% 1.48/1.26 introduced(definition,[new_symbols(naming,[spl6_8])],[avatar_definition])).
% 1.48/1.26 thf(f80,plain,(
% 1.48/1.26 ($true != (sK1 @ sK5)) | (~spl6_1 | ~spl6_8)),
% 1.48/1.26 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.48/1.26 thf(f79,plain,(
% 1.48/1.26 ($true != $true) | ($true != (sK1 @ sK5)) | (~spl6_1 | ~spl6_8)),
% 1.48/1.26 inference(superposition,[status(thm)],[f29,f59])).
% 1.48/1.26 thf(f59,plain,(
% 1.48/1.26 ((sK2 @ sK5) = $true) | ~spl6_8),
% 1.48/1.26 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.48/1.26 thf(f29,plain,(
% 1.48/1.26 ( ! [X5 : a] : (($true != (sK2 @ X5)) | ($true != (sK1 @ X5))) ) | ~spl6_1),
% 1.48/1.26 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.48/1.26 thf(f78,plain,(
% 1.48/1.26 ~spl6_9 | ~spl6_2 | ~spl6_3),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f77,f35,f31,f61])).
% 1.48/1.26 thf(f61,definition,(
% 1.48/1.26 spl6_9 <=> ($true = (sK0 @ sK5))),
% 1.48/1.26 introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition])).
% 1.48/1.26 thf(f77,plain,(
% 1.48/1.26 ($true != (sK0 @ sK5)) | (~spl6_2 | ~spl6_3)),
% 1.48/1.26 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.48/1.26 thf(f76,plain,(
% 1.48/1.26 ($true != (sK0 @ sK5)) | ($true != $true) | (~spl6_2 | ~spl6_3)),
% 1.48/1.26 inference(superposition,[status(thm)],[f32,f37])).
% 1.48/1.26 thf(f37,plain,(
% 1.48/1.26 ($true = (sK1 @ sK5)) | ~spl6_3),
% 1.48/1.26 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.48/1.26 thf(f75,plain,(
% 1.48/1.26 ~spl6_6 | ~spl6_1 | ~spl6_4),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f74,f39,f28,f49])).
% 1.48/1.26 thf(f49,definition,(
% 1.48/1.26 spl6_6 <=> ($true = (sK1 @ sK3))),
% 1.48/1.26 introduced(definition,[new_symbols(naming,[spl6_6])],[avatar_definition])).
% 1.48/1.26 thf(f39,definition,(
% 1.48/1.26 spl6_4 <=> ((sK2 @ sK3) = $true)),
% 1.48/1.26 introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition])).
% 1.48/1.26 thf(f74,plain,(
% 1.48/1.26 ($true != (sK1 @ sK3)) | (~spl6_1 | ~spl6_4)),
% 1.48/1.26 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.48/1.26 thf(f73,plain,(
% 1.48/1.26 ($true != (sK1 @ sK3)) | ($true != $true) | (~spl6_1 | ~spl6_4)),
% 1.48/1.26 inference(superposition,[status(thm)],[f29,f41])).
% 1.48/1.26 thf(f41,plain,(
% 1.48/1.26 ((sK2 @ sK3) = $true) | ~spl6_4),
% 1.48/1.26 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.48/1.26 thf(f72,plain,(
% 1.48/1.26 spl6_6 | spl6_8 | spl6_9 | spl6_5),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f18,f43,f61,f57,f49])).
% 1.48/1.26 thf(f18,plain,(
% 1.48/1.26 ($true = (sK1 @ sK3)) | ((sK2 @ sK5) = $true) | ($true = (sK0 @ sK5)) | ($true = (sK1 @ sK4))),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.26 thf(f14,plain,(
% 1.48/1.26 ((! [X3 : a] : (($true != (sK2 @ X3)) | ($true != (sK1 @ X3))) & ! [X4 : a] : (($true != (sK1 @ X4)) | ($true != (sK0 @ X4)))) | ! [X5 : a] : ((($true != (sK2 @ X5)) & ($true != (sK0 @ X5))) | ($true != (sK1 @ X5)))) & ((((sK2 @ sK3) = $true) & ($true = (sK1 @ sK3))) | (($true = (sK1 @ sK4)) & ($true = (sK0 @ sK4))) | ((((sK2 @ sK5) = $true) | ($true = (sK0 @ sK5))) & ($true = (sK1 @ sK5))))),
% 1.48/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f9,f13,f12,f11,f10])).
% 1.48/1.26 thf(f10,plain,(
% 1.48/1.26 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((! [X3 : a] : (((X2 @ X3) != $true) | ((X1 @ X3) != $true)) & ! [X4 : a] : (($true != (X1 @ X4)) | ($true != (X0 @ X4)))) | ! [X5 : a] : ((($true != (X2 @ X5)) & ($true != (X0 @ X5))) | ($true != (X1 @ X5)))) & (? [X6 : a] : (($true = (X2 @ X6)) & ($true = (X1 @ X6))) | ? [X7 : a] : (($true = (X1 @ X7)) & ($true = (X0 @ X7))) | ? [X8 : a] : ((($true = (X2 @ X8)) | ($true = (X0 @ X8))) & ($true = (X1 @ X8))))) => (((! [X3 : a] : (($true != (sK2 @ X3)) | ($true != (sK1 @ X3))) & ! [X4 : a] : (($true != (sK1 @ X4)) | ($true != (sK0 @ X4)))) | ! [X5 : a] : ((($true != (sK2 @ X5)) & ($true != (sK0 @ X5))) | ($true != (sK1 @ X5)))) & (? [X6 : a] : (($true = (sK2 @ X6)) & ($true = (sK1 @ X6))) | ? [X7 : a] : (($true = (sK1 @ X7)) & ($true = (sK0 @ X7))) | ? [X8 : a] : ((($true = (sK2 @ X8)) | ($true = (sK0 @ X8))) & ($true = (sK1 @ X8)))))),
% 1.48/1.26 introduced(definition,[],[choice_axiom])).
% 1.48/1.26 thf(f11,plain,(
% 1.48/1.26 ? [X6 : a] : (($true = (sK2 @ X6)) & ($true = (sK1 @ X6))) => (((sK2 @ sK3) = $true) & ($true = (sK1 @ sK3)))),
% 1.48/1.26 introduced(definition,[],[choice_axiom])).
% 1.48/1.26 thf(f12,plain,(
% 1.48/1.26 ? [X7 : a] : (($true = (sK1 @ X7)) & ($true = (sK0 @ X7))) => (($true = (sK1 @ sK4)) & ($true = (sK0 @ sK4)))),
% 1.48/1.26 introduced(definition,[],[choice_axiom])).
% 1.48/1.26 thf(f13,plain,(
% 1.48/1.26 ? [X8 : a] : ((($true = (sK2 @ X8)) | ($true = (sK0 @ X8))) & ($true = (sK1 @ X8))) => ((((sK2 @ sK5) = $true) | ($true = (sK0 @ sK5))) & ($true = (sK1 @ sK5)))),
% 1.48/1.26 introduced(definition,[],[choice_axiom])).
% 1.48/1.26 thf(f9,plain,(
% 1.48/1.26 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((! [X3 : a] : (((X2 @ X3) != $true) | ((X1 @ X3) != $true)) & ! [X4 : a] : (($true != (X1 @ X4)) | ($true != (X0 @ X4)))) | ! [X5 : a] : ((($true != (X2 @ X5)) & ($true != (X0 @ X5))) | ($true != (X1 @ X5)))) & (? [X6 : a] : (($true = (X2 @ X6)) & ($true = (X1 @ X6))) | ? [X7 : a] : (($true = (X1 @ X7)) & ($true = (X0 @ X7))) | ? [X8 : a] : ((($true = (X2 @ X8)) | ($true = (X0 @ X8))) & ($true = (X1 @ X8)))))),
% 1.48/1.26 inference(rectify,[status(thm)],[f8])).
% 1.48/1.26 thf(f8,plain,(
% 1.48/1.26 ? [X0 : a > $o,X2 : a > $o,X1 : a > $o] : (((! [X5 : a] : (($true != (X1 @ X5)) | ($true != (X2 @ X5))) & ! [X4 : a] : (($true != (X2 @ X4)) | ($true != (X0 @ X4)))) | ! [X3 : a] : ((((X1 @ X3) != $true) & ((X0 @ X3) != $true)) | ((X2 @ X3) != $true))) & (? [X5 : a] : (($true = (X1 @ X5)) & ($true = (X2 @ X5))) | ? [X4 : a] : (($true = (X2 @ X4)) & ($true = (X0 @ X4))) | ? [X3 : a] : ((((X1 @ X3) = $true) | ((X0 @ X3) = $true)) & ((X2 @ X3) = $true))))),
% 1.48/1.26 inference(flattening,[status(thm)],[f7])).
% 1.48/1.26 thf(f7,plain,(
% 1.48/1.26 ? [X0 : a > $o,X2 : a > $o,X1 : a > $o] : (((! [X5 : a] : (($true != (X1 @ X5)) | ($true != (X2 @ X5))) & ! [X4 : a] : (($true != (X2 @ X4)) | ($true != (X0 @ X4)))) | ! [X3 : a] : ((((X1 @ X3) != $true) & ((X0 @ X3) != $true)) | ((X2 @ X3) != $true))) & ((? [X5 : a] : (($true = (X1 @ X5)) & ($true = (X2 @ X5))) | ? [X4 : a] : (($true = (X2 @ X4)) & ($true = (X0 @ X4)))) | ? [X3 : a] : ((((X1 @ X3) = $true) | ((X0 @ X3) = $true)) & ((X2 @ X3) = $true))))),
% 1.48/1.26 inference(nnf_transformation,[status(thm)],[f6])).
% 1.48/1.26 thf(f6,plain,(
% 1.48/1.26 ? [X0 : a > $o,X2 : a > $o,X1 : a > $o] : (? [X3 : a] : ((((X1 @ X3) = $true) | ((X0 @ X3) = $true)) & ((X2 @ X3) = $true)) <~> (? [X5 : a] : (($true = (X1 @ X5)) & ($true = (X2 @ X5))) | ? [X4 : a] : (($true = (X2 @ X4)) & ($true = (X0 @ X4)))))),
% 1.48/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.26 thf(f5,plain,(
% 1.48/1.26 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (? [X3 : a] : ((((X1 @ X3) = $true) | ((X0 @ X3) = $true)) & ((X2 @ X3) = $true)) <=> (? [X5 : a] : (($true = (X1 @ X5)) & ($true = (X2 @ X5))) | ? [X4 : a] : (($true = (X2 @ X4)) & ($true = (X0 @ X4)))))),
% 1.48/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.26 thf(f4,plain,(
% 1.48/1.26 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (? [X3 : a] : (((X0 @ X3) | (X1 @ X3)) & (X2 @ X3)) <=> (? [X4 : a] : ((X0 @ X4) & (X2 @ X4)) | ? [X5 : a] : ((X1 @ X5) & (X2 @ X5))))),
% 1.48/1.26 inference(rectify,[status(thm)],[f2])).
% 1.48/1.26 thf(f2,negated_conjecture,(
% 1.48/1.26 ~! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : (? [X3 : a] : (((X1 @ X3) | (X2 @ X3)) & (X0 @ X3)) <=> (? [X3 : a] : ((X1 @ X3) & (X0 @ X3)) | ? [X3 : a] : ((X2 @ X3) & (X0 @ X3))))),
% 1.48/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.26 thf(f1,conjecture,(
% 1.48/1.26 ! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : (? [X3 : a] : (((X1 @ X3) | (X2 @ X3)) & (X0 @ X3)) <=> (? [X3 : a] : ((X1 @ X3) & (X0 @ X3)) | ? [X3 : a] : ((X2 @ X3) & (X0 @ X3))))),
% 1.48/1.26 file('/export/starexec/sandbox/tmp/tmp.bHLU3G5kF0/DTF2THF_411.p',cBOOL_PROP_100_pme)).
% 1.48/1.26 thf(f71,plain,(
% 1.48/1.26 spl6_9 | spl6_8 | spl6_4 | spl6_7),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f20,f53,f39,f57,f61])).
% 1.48/1.26 thf(f20,plain,(
% 1.48/1.26 ((sK2 @ sK5) = $true) | ((sK2 @ sK3) = $true) | ($true = (sK0 @ sK5)) | ($true = (sK0 @ sK4))),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.26 thf(f69,plain,(
% 1.48/1.26 spl6_8 | spl6_4 | spl6_5 | spl6_9),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f22,f61,f43,f39,f57])).
% 1.48/1.26 thf(f22,plain,(
% 1.48/1.26 ($true = (sK1 @ sK4)) | ((sK2 @ sK3) = $true) | ($true = (sK0 @ sK5)) | ((sK2 @ sK5) = $true)),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.26 thf(f68,plain,(
% 1.48/1.26 spl6_1 | spl6_1),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f26,f28,f28])).
% 1.48/1.26 thf(f26,plain,(
% 1.48/1.26 ( ! [X3 : a,X5 : a] : (($true != (sK1 @ X3)) | ($true != (sK2 @ X5)) | ($true != (sK1 @ X5)) | ($true != (sK2 @ X3))) )),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.26 thf(f67,plain,(
% 1.48/1.26 spl6_7 | spl6_6 | spl6_3),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f15,f35,f49,f53])).
% 1.48/1.26 thf(f15,plain,(
% 1.48/1.26 ($true = (sK0 @ sK4)) | ($true = (sK1 @ sK5)) | ($true = (sK1 @ sK3))),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.26 thf(f66,plain,(
% 1.48/1.26 spl6_4 | spl6_7 | spl6_3),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f19,f35,f53,f39])).
% 1.48/1.26 thf(f19,plain,(
% 1.48/1.26 ((sK2 @ sK3) = $true) | ($true = (sK1 @ sK5)) | ($true = (sK0 @ sK4))),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.26 thf(f65,plain,(
% 1.48/1.26 spl6_3 | spl6_6 | spl6_5),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f17,f43,f49,f35])).
% 1.48/1.26 thf(f17,plain,(
% 1.48/1.26 ($true = (sK1 @ sK4)) | ($true = (sK1 @ sK3)) | ($true = (sK1 @ sK5))),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.26 thf(f64,plain,(
% 1.48/1.26 spl6_6 | spl6_7 | spl6_8 | spl6_9),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f16,f61,f57,f53,f49])).
% 1.48/1.26 thf(f16,plain,(
% 1.48/1.26 ((sK2 @ sK5) = $true) | ($true = (sK1 @ sK3)) | ($true = (sK0 @ sK4)) | ($true = (sK0 @ sK5))),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.26 thf(f47,plain,(
% 1.48/1.26 spl6_2 | spl6_2),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f23,f31,f31])).
% 1.48/1.26 thf(f23,plain,(
% 1.48/1.26 ( ! [X4 : a,X5 : a] : (($true != (sK0 @ X4)) | ($true != (sK1 @ X4)) | ($true != (sK0 @ X5)) | ($true != (sK1 @ X5))) )),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.26 thf(f46,plain,(
% 1.48/1.26 spl6_3 | spl6_4 | spl6_5),
% 1.48/1.26 inference(avatar_split_clause,[status(thm)],[f21,f43,f39,f35])).
% 1.48/1.26 thf(f21,plain,(
% 1.48/1.26 ($true = (sK1 @ sK4)) | ($true = (sK1 @ sK5)) | ((sK2 @ sK3) = $true)),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.26 % SZS output end Proof for DTF2THF_411
% 1.48/1.26 % (553)------------------------------
% 1.48/1.26 % (553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (553)Termination reason: Refutation
% 1.48/1.26
% 1.48/1.26 % (553)Memory used [KB]: 5500
% 1.48/1.26 % (553)Time elapsed: 0.004 s
% 1.48/1.26 % (553)Instructions burned: 4 (million)
% 1.48/1.26 % (553)------------------------------
% 1.48/1.26 % (553)------------------------------
% 1.48/1.26 % (550)Success in time 0.007 s
%------------------------------------------------------------------------------