%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU853^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 09:37:35 AM UTC 2026
% Result : Theorem 1.46s 1.28s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 1 unt; 0 typ; 5 def)
% Number of atoms : 561 ( 214 equ; 0 cnn)
% Maximal formula atoms : 36 ( 11 avg)
% Number of connectives : 605 ( 126 ~; 112 |; 82 &; 245 @)
% ( 10 <=>; 28 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 105 ( 0 ^; 75 !; 30 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a > $o ).
thf(func_def_7,type,
sK3: a ).
thf(func_def_8,type,
sK4: a ).
thf(f72,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f52,f55,f56,f57,f58,f65,f71]) ).
thf(f71,plain,
( ~ spl5_3
| spl5_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f70]) ).
thf(f70,plain,
( $false
| ~ spl5_3
| spl5_4 ),
inference(subsumption_resolution,[status(thm)],[f68,f47]) ).
thf(f47,plain,
( ( $true
!= ( sK2 @ sK4 ) )
| spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl5_4
<=> ( $true
= ( sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f68,plain,
( ( $true
= ( sK2 @ sK4 ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $true != $true )
| ( $true
= ( sK2 @ sK4 ) )
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f59,f42]) ).
thf(f42,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl5_3
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f59,plain,
! [X0: a] :
( ( $true
!= ( sK0 @ X0 ) )
| ( ( sK2 @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f30,f17]) ).
thf(f17,plain,
! [X7: a] :
( ( ( sK0 @ X7 )
!= $true )
| ( $true
= ( sK1 @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( ( $true
!= ( sK2 @ sK3 ) )
& ( $true
= ( sK0 @ sK3 ) ) )
| ( ( $true
= ( sK1 @ sK4 ) )
& ( $true
!= ( sK2 @ sK4 ) )
& ( ( $true
!= ( sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK4 ) ) )
& ( $true
= ( sK0 @ sK4 ) ) ) )
& ( ! [X5: a] :
( ( ( sK2 @ X5 )
= $true )
| ( $true
!= ( sK0 @ X5 ) ) )
| ! [X6: a] :
( ( $true
!= ( sK1 @ X6 ) )
| ( ( sK2 @ X6 )
= $true )
| ( ( $true
= ( sK1 @ X6 ) )
& ( $true
!= ( sK0 @ X6 ) ) )
| ( $true
!= ( sK0 @ X6 ) ) ) )
& ! [X7: a] :
( ( $true
= ( sK1 @ X7 ) )
| ( ( sK0 @ X7 )
!= $true ) )
& ! [X8: a] :
( ( $true
!= ( sK2 @ X8 ) )
| ( $true
= ( sK1 @ X8 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f11,f14,f13,f12]) ).
thf(f12,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X3: a] :
( ( ( X2 @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
| ? [X4: a] :
( ( ( X1 @ X4 )
= $true )
& ( ( X2 @ X4 )
!= $true )
& ( ( ( X1 @ X4 )
!= $true )
| ( $true
= ( X0 @ X4 ) ) )
& ( $true
= ( X0 @ X4 ) ) ) )
& ( ! [X5: a] :
( ( $true
= ( X2 @ X5 ) )
| ( ( X0 @ X5 )
!= $true ) )
| ! [X6: a] :
( ( $true
!= ( X1 @ X6 ) )
| ( $true
= ( X2 @ X6 ) )
| ( ( $true
= ( X1 @ X6 ) )
& ( ( X0 @ X6 )
!= $true ) )
| ( ( X0 @ X6 )
!= $true ) ) )
& ! [X7: a] :
( ( $true
= ( X1 @ X7 ) )
| ( $true
!= ( X0 @ X7 ) ) )
& ! [X8: a] :
( ( $true
!= ( X2 @ X8 ) )
| ( ( X1 @ X8 )
= $true ) ) )
=> ( ( ? [X3: a] :
( ( $true
!= ( sK2 @ X3 ) )
& ( ( sK0 @ X3 )
= $true ) )
| ? [X4: a] :
( ( ( sK1 @ X4 )
= $true )
& ( $true
!= ( sK2 @ X4 ) )
& ( ( ( sK1 @ X4 )
!= $true )
| ( $true
= ( sK0 @ X4 ) ) )
& ( $true
= ( sK0 @ X4 ) ) ) )
& ( ! [X5: a] :
( ( ( sK2 @ X5 )
= $true )
| ( $true
!= ( sK0 @ X5 ) ) )
| ! [X6: a] :
( ( $true
!= ( sK1 @ X6 ) )
| ( ( sK2 @ X6 )
= $true )
| ( ( $true
= ( sK1 @ X6 ) )
& ( $true
!= ( sK0 @ X6 ) ) )
| ( $true
!= ( sK0 @ X6 ) ) ) )
& ! [X7: a] :
( ( $true
= ( sK1 @ X7 ) )
| ( ( sK0 @ X7 )
!= $true ) )
& ! [X8: a] :
( ( $true
!= ( sK2 @ X8 ) )
| ( $true
= ( sK1 @ X8 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X3: a] :
( ( $true
!= ( sK2 @ X3 ) )
& ( ( sK0 @ X3 )
= $true ) )
=> ( ( $true
!= ( sK2 @ sK3 ) )
& ( $true
= ( sK0 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X4: a] :
( ( ( sK1 @ X4 )
= $true )
& ( $true
!= ( sK2 @ X4 ) )
& ( ( ( sK1 @ X4 )
!= $true )
| ( $true
= ( sK0 @ X4 ) ) )
& ( $true
= ( sK0 @ X4 ) ) )
=> ( ( $true
= ( sK1 @ sK4 ) )
& ( $true
!= ( sK2 @ sK4 ) )
& ( ( $true
!= ( sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK4 ) ) )
& ( $true
= ( sK0 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X3: a] :
( ( ( X2 @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
| ? [X4: a] :
( ( ( X1 @ X4 )
= $true )
& ( ( X2 @ X4 )
!= $true )
& ( ( ( X1 @ X4 )
!= $true )
| ( $true
= ( X0 @ X4 ) ) )
& ( $true
= ( X0 @ X4 ) ) ) )
& ( ! [X5: a] :
( ( $true
= ( X2 @ X5 ) )
| ( ( X0 @ X5 )
!= $true ) )
| ! [X6: a] :
( ( $true
!= ( X1 @ X6 ) )
| ( $true
= ( X2 @ X6 ) )
| ( ( $true
= ( X1 @ X6 ) )
& ( ( X0 @ X6 )
!= $true ) )
| ( ( X0 @ X6 )
!= $true ) ) )
& ! [X7: a] :
( ( $true
= ( X1 @ X7 ) )
| ( $true
!= ( X0 @ X7 ) ) )
& ! [X8: a] :
( ( $true
!= ( X2 @ X8 ) )
| ( ( X1 @ X8 )
= $true ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
? [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ? [X6: a] :
( ( $true
!= ( X2 @ X6 ) )
& ( $true
= ( X1 @ X6 ) ) )
| ? [X5: a] :
( ( ( X0 @ X5 )
= $true )
& ( $true
!= ( X2 @ X5 ) )
& ( ( ( X0 @ X5 )
!= $true )
| ( $true
= ( X1 @ X5 ) ) )
& ( $true
= ( X1 @ X5 ) ) ) )
& ( ! [X6: a] :
( ( $true
= ( X2 @ X6 ) )
| ( $true
!= ( X1 @ X6 ) ) )
| ! [X5: a] :
( ( ( X0 @ X5 )
!= $true )
| ( $true
= ( X2 @ X5 ) )
| ( ( ( X0 @ X5 )
= $true )
& ( $true
!= ( X1 @ X5 ) ) )
| ( $true
!= ( X1 @ X5 ) ) ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( ( X1 @ X4 )
!= $true ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
? [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ? [X6: a] :
( ( $true
!= ( X2 @ X6 ) )
& ( $true
= ( X1 @ X6 ) ) )
| ? [X5: a] :
( ( ( X0 @ X5 )
= $true )
& ( $true
!= ( X2 @ X5 ) )
& ( ( ( X0 @ X5 )
!= $true )
| ( $true
= ( X1 @ X5 ) ) )
& ( $true
= ( X1 @ X5 ) ) ) )
& ( ! [X6: a] :
( ( $true
= ( X2 @ X6 ) )
| ( $true
!= ( X1 @ X6 ) ) )
| ! [X5: a] :
( ( ( X0 @ X5 )
!= $true )
| ( $true
= ( X2 @ X5 ) )
| ( ( ( X0 @ X5 )
= $true )
& ( $true
!= ( X1 @ X5 ) ) )
| ( $true
!= ( X1 @ X5 ) ) ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( ( X1 @ X4 )
!= $true ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
? [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X5 )
!= $true )
| ( $true
= ( X2 @ X5 ) )
| ( ( ( X0 @ X5 )
= $true )
& ( $true
!= ( X1 @ X5 ) ) )
| ( $true
!= ( X1 @ X5 ) ) )
<~> ! [X6: a] :
( ( $true
= ( X2 @ X6 ) )
| ( $true
!= ( X1 @ X6 ) ) ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( ( X1 @ X4 )
!= $true ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X5: a] :
( ( ( ( X0 @ X5 )
= $true )
& ( $true
!= ( X1 @ X5 ) ) )
| ( ( X0 @ X5 )
!= $true )
| ( $true
!= ( X1 @ X5 ) )
| ( $true
= ( X2 @ X5 ) ) )
<~> ! [X6: a] :
( ( $true
= ( X2 @ X6 ) )
| ( $true
!= ( X1 @ X6 ) ) ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( ( X1 @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
=> ( $true
= ( X0 @ X4 ) ) ) )
=> ( ! [X5: a] :
( ( ( ( X0 @ X5 )
= $true )
& ( $true
= ( X1 @ X5 ) )
& ( $true
!= ( X2 @ X5 ) ) )
=> ( ( ( X0 @ X5 )
= $true )
& ( $true
!= ( X1 @ X5 ) ) ) )
<=> ! [X6: a] :
( ( $true
= ( X1 @ X6 ) )
=> ( $true
= ( X2 @ X6 ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
=> ( $true
= ( X0 @ X4 ) ) ) )
=> ( ! [X5: a] :
( ( ( $true
!= ( X2 @ X5 ) )
& ( ( X0 @ X5 )
= $true )
& ( $true
= ( X1 @ X5 ) ) )
=> ( ( ( X0 @ X5 )
= $true )
& ( $true
!= ( X1 @ X5 ) ) ) )
<=> ! [X6: a] :
( ( $true
= ( X1 @ X6 ) )
=> ( $true
= ( X2 @ X6 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( X0 @ X3 ) )
& ! [X4: a] :
( ( X1 @ X4 )
=> ( X0 @ X4 ) ) )
=> ( ! [X5: a] :
( ( ~ ( X2 @ X5 )
& ( X0 @ X5 )
& ( X1 @ X5 ) )
=> ( ( X0 @ X5 )
& ~ ( X1 @ X5 ) ) )
<=> ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ! [X3: a] :
( ( ~ ( X1 @ X3 )
& ( X2 @ X3 )
& ( X0 @ X3 ) )
=> ( ( X2 @ X3 )
& ~ ( X0 @ X3 ) ) )
<=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ! [X3: a] :
( ( ~ ( X1 @ X3 )
& ( X2 @ X3 )
& ( X0 @ X3 ) )
=> ( ( X2 @ X3 )
& ~ ( X0 @ X3 ) ) )
<=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PkmVggdLr1/DTF2THF_22762.p',cGAZING_THM35_pme) ).
thf(f30,plain,
! [X0: a] :
( ( $true
!= ( sK1 @ X0 ) )
| ( ( sK2 @ X0 )
= $true )
| ( $true
!= ( sK0 @ X0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: a] :
( ( $true
!= ( sK0 @ X0 ) )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
!= ( sK1 @ X0 ) )
| ( ( sK2 @ X0 )
= $true ) ),
inference(condensation,[status(thm)],[f28]) ).
thf(f28,plain,
! [X6: a,X5: a] :
( ( ( sK2 @ X5 )
= $true )
| ( $true
!= ( sK0 @ X5 ) )
| ( $true
!= ( sK0 @ X6 ) )
| ( $true
!= ( sK1 @ X6 ) )
| ( ( sK2 @ X6 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f18]) ).
thf(f18,plain,
! [X6: a,X5: a] :
( ( $true
!= ( sK0 @ X6 ) )
| ( $true
!= ( sK0 @ X5 ) )
| ( $true
!= ( sK1 @ X6 ) )
| ( ( sK2 @ X5 )
= $true )
| ( ( sK2 @ X6 )
= $true )
| ( $true
!= ( sK0 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f65,plain,
( ~ spl5_2
| spl5_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| ~ spl5_2
| spl5_5 ),
inference(subsumption_resolution,[status(thm)],[f63,f51]) ).
thf(f51,plain,
( ( $true
!= ( sK2 @ sK3 ) )
| spl5_5 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl5_5
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition]) ).
thf(f63,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true != $true )
| ( $true
= ( sK2 @ sK3 ) )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f59,f38]) ).
thf(f38,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl5_2
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f58,plain,
( spl5_2
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f20,f40,f36]) ).
thf(f20,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f57,plain,
( spl5_1
| ~ spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f27,f49,f32]) ).
thf(f32,definition,
( spl5_1
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f27,plain,
( ( $true
!= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f56,plain,
( ~ spl5_4
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f22,f36,f45]) ).
thf(f22,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
!= ( sK2 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f55,plain,
( ~ spl5_5
| spl5_3
| ~ spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f25,f32,f40,f49]) ).
thf(f25,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
!= ( sK2 @ sK3 ) )
| ( $true
!= ( sK1 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f52,plain,
( ~ spl5_4
| ~ spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f26,f49,f45]) ).
thf(f26,plain,
( ( $true
!= ( sK2 @ sK4 ) )
| ( $true
!= ( sK2 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU853^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n007.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 12:34:53 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : SEU853^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.44 % Domain : Set Theory
% 0.18/0.44 % Problem : TPS problem GAZING-THM35
% 0.18/0.44 % Version : Especial.
% 0.18/0.44 % English :
% 0.18/0.44
% 0.18/0.44 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.18/0.44 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.44 % Source : [Bro09]
% 0.18/0.44 % Names : tps_0396 [Bro09]
% 0.18/0.44 % : 35 [Bar92]
% 0.18/0.44 % : GAZING-THM35 [TPS]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.18/0.44 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.18/0.44 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 0 ( 0 avg)
% 0.18/0.44 % Number of connectives : 23 ( 2 ~; 0 |; 4 &; 11 @)
% 0.18/0.44 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 12 ( 12 avg)
% 0.18/0.44 % Number of types : 2 ( 1 usr)
% 0.18/0.44 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.18/0.44 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.18/0.44 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.44
% 0.18/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.44 % : Polymorphic definitions expanded.
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 thf(a_type,type,
% 0.18/0.44 a: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(cGAZING_THM35_pme,conjecture,
% 0.18/0.44 ! [S: a > $o,T: a > $o,U: a > $o] :
% 0.18/0.44 ( ( ! [Xx: a] :
% 0.18/0.44 ( ( S @ Xx )
% 0.18/0.44 => ( U @ Xx ) )
% 0.18/0.44 & ! [Xx: a] :
% 0.18/0.44 ( ( T @ Xx )
% 0.18/0.44 => ( U @ Xx ) ) )
% 0.18/0.44 => ( ! [Xx: a] :
% 0.18/0.44 ( ( S @ Xx )
% 0.18/0.44 => ( T @ Xx ) )
% 0.18/0.44 <=> ! [Xx: a] :
% 0.18/0.44 ( ( ( S @ Xx )
% 0.18/0.44 & ( U @ Xx )
% 0.18/0.44 & ~ ( T @ Xx ) )
% 0.18/0.44 => ( ( U @ Xx )
% 0.18/0.44 & ~ ( S @ Xx ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 ------------------------
% 1.46/1.25 ---- Embedded in THF ---
% 1.46/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.25 %%% Generated on Tue Feb 24 12:34:54 EST 2026
% 1.46/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.25 %%% Logic specification used:
% 1.46/1.25 %%% thf(spec, logic, $$dhol).
% 1.46/1.25
% 1.46/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.PkmVggdLr1/DTF2DTF22762.p
% See solution above
% 1.46/1.25 ------------------------
% 1.46/1.26 ---- Cleaned THF ---
% 1.46/1.26 thf(a_type,type,
% 1.46/1.26 a: $tType ).
% 1.46/1.26
% 1.46/1.26 thf(cGAZING_THM35_pme,conjecture,
% 1.46/1.26 ! [S: a > $o,T: a > $o,U: a > $o] :
% 1.46/1.26 ( ( ! [Xx: a] :
% 1.46/1.26 ( ( S @ Xx )
% 1.46/1.26 => ( U @ Xx ) )
% 1.46/1.26 & ! [Xx: a] :
% 1.46/1.26 ( ( T @ Xx )
% 1.46/1.26 => ( U @ Xx ) ) )
% 1.46/1.26 => ( ! [Xx: a] :
% 1.46/1.26 ( ( S @ Xx )
% 1.46/1.26 => ( T @ Xx ) )
% 1.46/1.26 <=> ! [Xx: a] :
% 1.46/1.26 ( ( ( S @ Xx )
% 1.46/1.26 & ( U @ Xx )
% 1.46/1.26 & ~ ( T @ Xx ) )
% 1.46/1.26 => ( ( U @ Xx )
% 1.46/1.26 & ~ ( S @ Xx ) ) ) ) ) ).
% 1.46/1.26 ------------------------
% 1.46/1.28 % (22985)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22762 for (2999ds/18Mi)
% 1.46/1.28 % (22982)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22762 for (2999ds/2Mi)
% 1.46/1.28 % (22982)Instruction limit reached!
% 1.46/1.28 % (22982)------------------------------
% 1.46/1.28 % (22982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (22982)Termination reason: Unknown
% 1.46/1.28 % (22982)Termination phase: Saturation
% 1.46/1.28
% 1.46/1.28 % (22982)Memory used [KB]: 5500
% 1.46/1.28 % (22982)Time elapsed: 0.002 s
% 1.46/1.28 % (22982)Instructions burned: 2 (million)
% 1.46/1.28 % (22982)------------------------------
% 1.46/1.28 % (22982)------------------------------
% 1.46/1.28 % (22985)First to succeed.
% 1.46/1.28 % (22985)Refutation found. Thanks to Tanya!
% 1.46/1.28 % SZS status Theorem for DTF2THF_22762
% 1.46/1.28 % SZS output start Proof for DTF2THF_22762
% 1.46/1.28 thf(type_def_5, type, a: $tType).
% 1.46/1.28 thf(func_def_0, type, a: $tType).
% 1.46/1.28 thf(func_def_4, type, sK0: a > $o).
% 1.46/1.28 thf(func_def_5, type, sK1: a > $o).
% 1.46/1.28 thf(func_def_6, type, sK2: a > $o).
% 1.46/1.28 thf(func_def_7, type, sK3: a).
% 1.46/1.28 thf(func_def_8, type, sK4: a).
% 1.46/1.28 thf(f72,plain,(
% 1.46/1.28 $false),
% 1.46/1.28 inference(avatar_sat_refutation,[status(thm)],[f52,f55,f56,f57,f58,f65,f71])).
% 1.46/1.28 thf(f71,plain,(
% 1.46/1.28 ~spl5_3 | spl5_4),
% 1.46/1.28 inference(avatar_contradiction_clause,[status(thm)],[f70])).
% 1.46/1.28 thf(f70,plain,(
% 1.46/1.28 $false | (~spl5_3 | spl5_4)),
% 1.46/1.28 inference(subsumption_resolution,[status(thm)],[f68,f47])).
% 1.46/1.28 thf(f47,plain,(
% 1.46/1.28 ($true != (sK2 @ sK4)) | spl5_4),
% 1.46/1.28 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.46/1.28 thf(f45,definition,(
% 1.46/1.28 spl5_4 <=> ($true = (sK2 @ sK4))),
% 1.46/1.28 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.46/1.28 thf(f68,plain,(
% 1.46/1.28 ($true = (sK2 @ sK4)) | ~spl5_3),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.46/1.28 thf(f66,plain,(
% 1.46/1.28 ($true != $true) | ($true = (sK2 @ sK4)) | ~spl5_3),
% 1.46/1.28 inference(superposition,[status(thm)],[f59,f42])).
% 1.46/1.28 thf(f42,plain,(
% 1.46/1.28 ($true = (sK0 @ sK4)) | ~spl5_3),
% 1.46/1.28 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.46/1.28 thf(f40,definition,(
% 1.46/1.28 spl5_3 <=> ($true = (sK0 @ sK4))),
% 1.46/1.28 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.46/1.28 thf(f59,plain,(
% 1.46/1.28 ( ! [X0 : a] : (($true != (sK0 @ X0)) | ((sK2 @ X0) = $true)) )),
% 1.46/1.28 inference(subsumption_resolution,[status(thm)],[f30,f17])).
% 1.46/1.28 thf(f17,plain,(
% 1.46/1.28 ( ! [X7 : a] : (((sK0 @ X7) != $true) | ($true = (sK1 @ X7))) )),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f15])).
% 1.46/1.28 thf(f15,plain,(
% 1.46/1.28 ((($true != (sK2 @ sK3)) & ($true = (sK0 @ sK3))) | (($true = (sK1 @ sK4)) & ($true != (sK2 @ sK4)) & (($true != (sK1 @ sK4)) | ($true = (sK0 @ sK4))) & ($true = (sK0 @ sK4)))) & (! [X5 : a] : (((sK2 @ X5) = $true) | ($true != (sK0 @ X5))) | ! [X6 : a] : (($true != (sK1 @ X6)) | ((sK2 @ X6) = $true) | (($true = (sK1 @ X6)) & ($true != (sK0 @ X6))) | ($true != (sK0 @ X6)))) & ! [X7 : a] : (($true = (sK1 @ X7)) | ((sK0 @ X7) != $true)) & ! [X8 : a] : (($true != (sK2 @ X8)) | ($true = (sK1 @ X8)))),
% 1.46/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f11,f14,f13,f12])).
% 1.46/1.28 thf(f12,plain,(
% 1.46/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((? [X3 : a] : (((X2 @ X3) != $true) & ((X0 @ X3) = $true)) | ? [X4 : a] : (((X1 @ X4) = $true) & ((X2 @ X4) != $true) & (((X1 @ X4) != $true) | ($true = (X0 @ X4))) & ($true = (X0 @ X4)))) & (! [X5 : a] : (($true = (X2 @ X5)) | ((X0 @ X5) != $true)) | ! [X6 : a] : (($true != (X1 @ X6)) | ($true = (X2 @ X6)) | (($true = (X1 @ X6)) & ((X0 @ X6) != $true)) | ((X0 @ X6) != $true))) & ! [X7 : a] : (($true = (X1 @ X7)) | ($true != (X0 @ X7))) & ! [X8 : a] : (($true != (X2 @ X8)) | ((X1 @ X8) = $true))) => ((? [X3 : a] : (($true != (sK2 @ X3)) & ((sK0 @ X3) = $true)) | ? [X4 : a] : (((sK1 @ X4) = $true) & ($true != (sK2 @ X4)) & (((sK1 @ X4) != $true) | ($true = (sK0 @ X4))) & ($true = (sK0 @ X4)))) & (! [X5 : a] : (((sK2 @ X5) = $true) | ($true != (sK0 @ X5))) | ! [X6 : a] : (($true != (sK1 @ X6)) | ((sK2 @ X6) = $true) | (($true = (sK1 @ X6)) & ($true != (sK0 @ X6))) | ($true != (sK0 @ X6)))) & ! [X7 : a] : (($true = (sK1 @ X7)) | ((sK0 @ X7) != $true)) & ! [X8 : a] : (($true != (sK2 @ X8)) | ($true = (sK1 @ X8))))),
% 1.46/1.28 introduced(definition,[],[choice_axiom])).
% 1.46/1.28 thf(f13,plain,(
% 1.46/1.28 ? [X3 : a] : (($true != (sK2 @ X3)) & ((sK0 @ X3) = $true)) => (($true != (sK2 @ sK3)) & ($true = (sK0 @ sK3)))),
% 1.46/1.28 introduced(definition,[],[choice_axiom])).
% 1.46/1.28 thf(f14,plain,(
% 1.46/1.28 ? [X4 : a] : (((sK1 @ X4) = $true) & ($true != (sK2 @ X4)) & (((sK1 @ X4) != $true) | ($true = (sK0 @ X4))) & ($true = (sK0 @ X4))) => (($true = (sK1 @ sK4)) & ($true != (sK2 @ sK4)) & (($true != (sK1 @ sK4)) | ($true = (sK0 @ sK4))) & ($true = (sK0 @ sK4)))),
% 1.46/1.28 introduced(definition,[],[choice_axiom])).
% 1.46/1.28 thf(f11,plain,(
% 1.46/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((? [X3 : a] : (((X2 @ X3) != $true) & ((X0 @ X3) = $true)) | ? [X4 : a] : (((X1 @ X4) = $true) & ((X2 @ X4) != $true) & (((X1 @ X4) != $true) | ($true = (X0 @ X4))) & ($true = (X0 @ X4)))) & (! [X5 : a] : (($true = (X2 @ X5)) | ((X0 @ X5) != $true)) | ! [X6 : a] : (($true != (X1 @ X6)) | ($true = (X2 @ X6)) | (($true = (X1 @ X6)) & ((X0 @ X6) != $true)) | ((X0 @ X6) != $true))) & ! [X7 : a] : (($true = (X1 @ X7)) | ($true != (X0 @ X7))) & ! [X8 : a] : (($true != (X2 @ X8)) | ((X1 @ X8) = $true)))),
% 1.46/1.28 inference(rectify,[status(thm)],[f10])).
% 1.46/1.28 thf(f10,plain,(
% 1.46/1.28 ? [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((? [X6 : a] : (($true != (X2 @ X6)) & ($true = (X1 @ X6))) | ? [X5 : a] : (((X0 @ X5) = $true) & ($true != (X2 @ X5)) & (((X0 @ X5) != $true) | ($true = (X1 @ X5))) & ($true = (X1 @ X5)))) & (! [X6 : a] : (($true = (X2 @ X6)) | ($true != (X1 @ X6))) | ! [X5 : a] : (((X0 @ X5) != $true) | ($true = (X2 @ X5)) | (((X0 @ X5) = $true) & ($true != (X1 @ X5))) | ($true != (X1 @ X5)))) & ! [X4 : a] : (($true = (X0 @ X4)) | ((X1 @ X4) != $true)) & ! [X3 : a] : (((X2 @ X3) != $true) | ((X0 @ X3) = $true)))),
% 1.46/1.28 inference(flattening,[status(thm)],[f9])).
% 1.46/1.28 thf(f9,plain,(
% 1.46/1.28 ? [X1 : a > $o,X0 : a > $o,X2 : a > $o] : (((? [X6 : a] : (($true != (X2 @ X6)) & ($true = (X1 @ X6))) | ? [X5 : a] : (((X0 @ X5) = $true) & ($true != (X2 @ X5)) & (((X0 @ X5) != $true) | ($true = (X1 @ X5))) & ($true = (X1 @ X5)))) & (! [X6 : a] : (($true = (X2 @ X6)) | ($true != (X1 @ X6))) | ! [X5 : a] : (((X0 @ X5) != $true) | ($true = (X2 @ X5)) | (((X0 @ X5) = $true) & ($true != (X1 @ X5))) | ($true != (X1 @ X5))))) & ! [X4 : a] : (($true = (X0 @ X4)) | ((X1 @ X4) != $true)) & ! [X3 : a] : (((X2 @ X3) != $true) | ((X0 @ X3) = $true)))),
% 1.46/1.28 inference(nnf_transformation,[status(thm)],[f8])).
% 1.46/1.28 thf(f8,plain,(
% 1.46/1.28 ? [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((! [X5 : a] : (((X0 @ X5) != $true) | ($true = (X2 @ X5)) | (((X0 @ X5) = $true) & ($true != (X1 @ X5))) | ($true != (X1 @ X5))) <~> ! [X6 : a] : (($true = (X2 @ X6)) | ($true != (X1 @ X6)))) & ! [X4 : a] : (($true = (X0 @ X4)) | ((X1 @ X4) != $true)) & ! [X3 : a] : (((X2 @ X3) != $true) | ((X0 @ X3) = $true)))),
% 1.46/1.28 inference(flattening,[status(thm)],[f7])).
% 1.46/1.28 thf(f7,plain,(
% 1.46/1.28 ? [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((! [X5 : a] : ((((X0 @ X5) = $true) & ($true != (X1 @ X5))) | (((X0 @ X5) != $true) | ($true != (X1 @ X5)) | ($true = (X2 @ X5)))) <~> ! [X6 : a] : (($true = (X2 @ X6)) | ($true != (X1 @ X6)))) & (! [X3 : a] : (((X2 @ X3) != $true) | ((X0 @ X3) = $true)) & ! [X4 : a] : (($true = (X0 @ X4)) | ((X1 @ X4) != $true))))),
% 1.46/1.28 inference(ennf_transformation,[status(thm)],[f6])).
% 1.46/1.28 thf(f6,plain,(
% 1.46/1.28 ~! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((! [X3 : a] : (((X2 @ X3) = $true) => ((X0 @ X3) = $true)) & ! [X4 : a] : (((X1 @ X4) = $true) => ($true = (X0 @ X4)))) => (! [X5 : a] : ((((X0 @ X5) = $true) & ($true = (X1 @ X5)) & ($true != (X2 @ X5))) => (((X0 @ X5) = $true) & ($true != (X1 @ X5)))) <=> ! [X6 : a] : (($true = (X1 @ X6)) => ($true = (X2 @ X6)))))),
% 1.46/1.28 inference(flattening,[status(thm)],[f5])).
% 1.46/1.28 thf(f5,plain,(
% 1.46/1.28 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : (((X2 @ X3) = $true) => ((X0 @ X3) = $true)) & ! [X4 : a] : (((X1 @ X4) = $true) => ($true = (X0 @ X4)))) => (! [X5 : a] : ((~($true = (X2 @ X5)) & ((X0 @ X5) = $true) & ($true = (X1 @ X5))) => (((X0 @ X5) = $true) & ~($true = (X1 @ X5)))) <=> ! [X6 : a] : (($true = (X1 @ X6)) => ($true = (X2 @ X6)))))),
% 1.46/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.28 thf(f4,plain,(
% 1.46/1.28 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X2 @ X3) => (X0 @ X3)) & ! [X4 : a] : ((X1 @ X4) => (X0 @ X4))) => (! [X5 : a] : ((~(X2 @ X5) & (X0 @ X5) & (X1 @ X5)) => ((X0 @ X5) & ~(X1 @ X5))) <=> ! [X6 : a] : ((X1 @ X6) => (X2 @ X6))))),
% 1.46/1.28 inference(rectify,[status(thm)],[f2])).
% 1.46/1.28 thf(f2,negated_conjecture,(
% 1.46/1.28 ~! [X2 : a > $o,X0 : a > $o,X1 : a > $o] : ((! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3))) => (! [X3 : a] : ((~(X1 @ X3) & (X2 @ X3) & (X0 @ X3)) => ((X2 @ X3) & ~(X0 @ X3))) <=> ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))))),
% 1.46/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.28 thf(f1,conjecture,(
% 1.46/1.28 ! [X2 : a > $o,X0 : a > $o,X1 : a > $o] : ((! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3))) => (! [X3 : a] : ((~(X1 @ X3) & (X2 @ X3) & (X0 @ X3)) => ((X2 @ X3) & ~(X0 @ X3))) <=> ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))))),
% 1.46/1.28 file('/export/starexec/sandbox2/tmp/tmp.PkmVggdLr1/DTF2THF_22762.p',cGAZING_THM35_pme)).
% 1.46/1.28 thf(f30,plain,(
% 1.46/1.28 ( ! [X0 : a] : (($true != (sK1 @ X0)) | ((sK2 @ X0) = $true) | ($true != (sK0 @ X0))) )),
% 1.46/1.28 inference(duplicate_literal_removal,[status(thm)],[f29])).
% 1.46/1.28 thf(f29,plain,(
% 1.46/1.28 ( ! [X0 : a] : (($true != (sK0 @ X0)) | ($true != (sK0 @ X0)) | ($true != (sK1 @ X0)) | ((sK2 @ X0) = $true)) )),
% 1.46/1.28 inference(condensation,[status(thm)],[f28])).
% 1.46/1.28 thf(f28,plain,(
% 1.46/1.28 ( ! [X6 : a,X5 : a] : (((sK2 @ X5) = $true) | ($true != (sK0 @ X5)) | ($true != (sK0 @ X6)) | ($true != (sK1 @ X6)) | ((sK2 @ X6) = $true)) )),
% 1.46/1.28 inference(duplicate_literal_removal,[status(thm)],[f18])).
% 1.46/1.28 thf(f18,plain,(
% 1.46/1.28 ( ! [X6 : a,X5 : a] : (($true != (sK0 @ X6)) | ($true != (sK0 @ X5)) | ($true != (sK1 @ X6)) | ((sK2 @ X5) = $true) | ((sK2 @ X6) = $true) | ($true != (sK0 @ X6))) )),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f15])).
% 1.46/1.28 thf(f65,plain,(
% 1.46/1.28 ~spl5_2 | spl5_5),
% 1.46/1.28 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.46/1.28 thf(f64,plain,(
% 1.46/1.28 $false | (~spl5_2 | spl5_5)),
% 1.46/1.28 inference(subsumption_resolution,[status(thm)],[f63,f51])).
% 1.46/1.28 thf(f51,plain,(
% 1.46/1.28 ($true != (sK2 @ sK3)) | spl5_5),
% 1.46/1.28 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.46/1.28 thf(f49,definition,(
% 1.46/1.28 spl5_5 <=> ($true = (sK2 @ sK3))),
% 1.46/1.28 introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition])).
% 1.46/1.28 thf(f63,plain,(
% 1.46/1.28 ($true = (sK2 @ sK3)) | ~spl5_2),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.46/1.28 thf(f62,plain,(
% 1.46/1.28 ($true != $true) | ($true = (sK2 @ sK3)) | ~spl5_2),
% 1.46/1.28 inference(superposition,[status(thm)],[f59,f38])).
% 1.46/1.28 thf(f38,plain,(
% 1.46/1.28 ($true = (sK0 @ sK3)) | ~spl5_2),
% 1.46/1.28 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.46/1.28 thf(f36,definition,(
% 1.46/1.28 spl5_2 <=> ($true = (sK0 @ sK3))),
% 1.46/1.28 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.46/1.28 thf(f58,plain,(
% 1.46/1.28 spl5_2 | spl5_3),
% 1.46/1.28 inference(avatar_split_clause,[status(thm)],[f20,f40,f36])).
% 1.46/1.28 thf(f20,plain,(
% 1.46/1.28 ($true = (sK0 @ sK3)) | ($true = (sK0 @ sK4))),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f15])).
% 1.46/1.28 thf(f57,plain,(
% 1.46/1.28 spl5_1 | ~spl5_5),
% 1.46/1.28 inference(avatar_split_clause,[status(thm)],[f27,f49,f32])).
% 1.46/1.28 thf(f32,definition,(
% 1.46/1.28 spl5_1 <=> ($true = (sK1 @ sK4))),
% 1.46/1.28 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.46/1.28 thf(f27,plain,(
% 1.46/1.28 ($true != (sK2 @ sK3)) | ($true = (sK1 @ sK4))),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f15])).
% 1.46/1.28 thf(f56,plain,(
% 1.46/1.28 ~spl5_4 | spl5_2),
% 1.46/1.28 inference(avatar_split_clause,[status(thm)],[f22,f36,f45])).
% 1.46/1.28 thf(f22,plain,(
% 1.46/1.28 ($true = (sK0 @ sK3)) | ($true != (sK2 @ sK4))),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f15])).
% 1.46/1.28 thf(f55,plain,(
% 1.46/1.28 ~spl5_5 | spl5_3 | ~spl5_1),
% 1.46/1.28 inference(avatar_split_clause,[status(thm)],[f25,f32,f40,f49])).
% 1.46/1.28 thf(f25,plain,(
% 1.46/1.28 ($true = (sK0 @ sK4)) | ($true != (sK2 @ sK3)) | ($true != (sK1 @ sK4))),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f15])).
% 1.46/1.28 thf(f52,plain,(
% 1.46/1.28 ~spl5_4 | ~spl5_5),
% 1.46/1.28 inference(avatar_split_clause,[status(thm)],[f26,f49,f45])).
% 1.46/1.28 thf(f26,plain,(
% 1.46/1.28 ($true != (sK2 @ sK4)) | ($true != (sK2 @ sK3))),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f15])).
% 1.46/1.28 % SZS output end Proof for DTF2THF_22762
% 1.46/1.28 % (22985)------------------------------
% 1.46/1.28 % (22985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (22985)Termination reason: Refutation
% 1.46/1.28
% 1.46/1.28 % (22985)Memory used [KB]: 5500
% 1.46/1.28 % (22985)Time elapsed: 0.004 s
% 1.46/1.28 % (22985)Instructions burned: 4 (million)
% 1.46/1.28 % (22985)------------------------------
% 1.46/1.28 % (22985)------------------------------
% 1.46/1.28 % (22978)Success in time 0.013 s
%------------------------------------------------------------------------------