%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU899^5 : 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 : n001.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 09:37:42 AM UTC 2026
% Result : Theorem 1.79s 1.55s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 66 ( 1 unt; 0 typ; 6 def)
% Number of atoms : 556 ( 213 equ; 0 cnn)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 599 ( 137 ~; 148 |; 55 &; 242 @)
% ( 11 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 85 ( 0 ^; 49 !; 36 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
cF: b > a ).
thf(func_def_3,type,
cS: b > $o ).
thf(func_def_4,type,
cR: b > $o ).
thf(func_def_8,type,
sP0: a > $o ).
thf(func_def_9,type,
sK1: a > b ).
thf(func_def_10,type,
sK2: a > b ).
thf(func_def_11,type,
sK3: a ).
thf(func_def_12,type,
sK4: b ).
thf(f102,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f40,f49,f53,f57,f87,f96,f101]) ).
thf(f101,plain,
( ~ spl5_1
| spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f100]) ).
thf(f100,plain,
( $false
| ~ spl5_1
| spl5_2
| ~ spl5_3 ),
inference(subsumption_resolution,[status(thm)],[f99,f38]) ).
thf(f38,plain,
( ( ( sP0 @ sK3 )
!= $true )
| spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl5_2
<=> ( ( sP0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f99,plain,
( ( ( sP0 @ sK3 )
= $true )
| ~ spl5_1
| ~ spl5_3 ),
inference(subsumption_resolution,[status(thm)],[f88,f44]) ).
thf(f44,plain,
( ( ( cR @ sK4 )
= $true )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f42,definition,
( spl5_3
<=> ( ( cR @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f88,plain,
( ( ( cR @ sK4 )
!= $true )
| ( ( sP0 @ sK3 )
= $true )
| ~ spl5_1 ),
inference(superposition,[status(thm)],[f31,f35]) ).
thf(f35,plain,
( ( sK3
= ( cF @ sK4 ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl5_1
<=> ( sK3
= ( cF @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f31,plain,
! [X2: b] :
( ( ( sP0 @ ( cF @ X2 ) )
= $true )
| ( ( cR @ X2 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: b,X0: a] :
( ( ( sP0 @ X0 )
= $true )
| ( ( cF @ X2 )
!= X0 )
| ( ( cR @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: a] :
( ( ( ( sP0 @ X0 )
= $true )
| ( ! [X1: b] :
( ( ( cS @ X1 )
!= $true )
| ( ( cF @ X1 )
!= X0 ) )
& ! [X2: b] :
( ( ( cF @ X2 )
!= X0 )
| ( ( cR @ X2 )
!= $true ) ) ) )
& ( ( ( ( cS @ ( sK1 @ X0 ) )
= $true )
& ( ( cF @ ( sK1 @ X0 ) )
= X0 ) )
| ( ( ( cF @ ( sK2 @ X0 ) )
= X0 )
& ( ( cR @ ( sK2 @ X0 ) )
= $true ) )
| ( ( sP0 @ X0 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f11,f13,f12]) ).
thf(f12,plain,
! [X0: a] :
( ? [X3: b] :
( ( ( cS @ X3 )
= $true )
& ( ( cF @ X3 )
= X0 ) )
=> ( ( ( cS @ ( sK1 @ X0 ) )
= $true )
& ( ( cF @ ( sK1 @ X0 ) )
= X0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X0: a] :
( ? [X4: b] :
( ( ( cF @ X4 )
= X0 )
& ( ( cR @ X4 )
= $true ) )
=> ( ( ( cF @ ( sK2 @ X0 ) )
= X0 )
& ( ( cR @ ( sK2 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: a] :
( ( ( ( sP0 @ X0 )
= $true )
| ( ! [X1: b] :
( ( ( cS @ X1 )
!= $true )
| ( ( cF @ X1 )
!= X0 ) )
& ! [X2: b] :
( ( ( cF @ X2 )
!= X0 )
| ( ( cR @ X2 )
!= $true ) ) ) )
& ( ? [X3: b] :
( ( ( cS @ X3 )
= $true )
& ( ( cF @ X3 )
= X0 ) )
| ? [X4: b] :
( ( ( cF @ X4 )
= X0 )
& ( ( cR @ X4 )
= $true ) )
| ( ( sP0 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: a] :
( ( ( ( sP0 @ X0 )
= $true )
| ( ! [X3: b] :
( ( ( cS @ X3 )
!= $true )
| ( ( cF @ X3 )
!= X0 ) )
& ! [X2: b] :
( ( ( cF @ X2 )
!= X0 )
| ( ( cR @ X2 )
!= $true ) ) ) )
& ( ? [X3: b] :
( ( ( cS @ X3 )
= $true )
& ( ( cF @ X3 )
= X0 ) )
| ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ( ( cR @ X2 )
= $true ) )
| ( ( sP0 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: a] :
( ( ( ( sP0 @ X0 )
= $true )
| ( ! [X3: b] :
( ( ( cS @ X3 )
!= $true )
| ( ( cF @ X3 )
!= X0 ) )
& ! [X2: b] :
( ( ( cF @ X2 )
!= X0 )
| ( ( cR @ X2 )
!= $true ) ) ) )
& ( ? [X3: b] :
( ( ( cS @ X3 )
= $true )
& ( ( cF @ X3 )
= X0 ) )
| ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ( ( cR @ X2 )
= $true ) )
| ( ( sP0 @ X0 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: a] :
( ( ( sP0 @ X0 )
= $true )
<=> ( ? [X3: b] :
( ( ( cS @ X3 )
= $true )
& ( ( cF @ X3 )
= X0 ) )
| ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ( ( cR @ X2 )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f96,plain,
( ~ spl5_4
| ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f95,f37,f33,f46]) ).
thf(f46,definition,
( spl5_4
<=> ( ( cS @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f95,plain,
( ( ( cS @ sK4 )
!= $true )
| ~ spl5_1
| spl5_2 ),
inference(subsumption_resolution,[status(thm)],[f89,f38]) ).
thf(f89,plain,
( ( ( sP0 @ sK3 )
= $true )
| ( ( cS @ sK4 )
!= $true )
| ~ spl5_1 ),
inference(superposition,[status(thm)],[f30,f35]) ).
thf(f30,plain,
! [X1: b] :
( ( ( sP0 @ ( cF @ X1 ) )
= $true )
| ( ( cS @ X1 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: a,X1: b] :
( ( ( sP0 @ X0 )
= $true )
| ( ( cS @ X1 )
!= $true )
| ( ( cF @ X1 )
!= X0 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f87,plain,
( ~ spl5_2
| ~ spl5_5
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f86]) ).
thf(f86,plain,
( $false
| ~ spl5_2
| ~ spl5_5
| ~ spl5_6 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true != $true )
| ( sK3 != sK3 )
| ~ spl5_2
| ~ spl5_5
| ~ spl5_6 ),
inference(superposition,[status(thm)],[f80,f39]) ).
thf(f39,plain,
( ( ( sP0 @ sK3 )
= $true )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f80,plain,
( ! [X0: a] :
( ( ( sP0 @ X0 )
!= $true )
| ( sK3 != X0 ) )
| ~ spl5_5
| ~ spl5_6 ),
inference(subsumption_resolution,[status(thm)],[f79,f73]) ).
thf(f73,plain,
( ! [X0: a] :
( ( ( cS @ ( sK1 @ X0 ) )
!= $true )
| ( sK3 != X0 )
| ( ( sP0 @ X0 )
!= $true ) )
| ~ spl5_5
| ~ spl5_6 ),
inference(duplicate_literal_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ! [X0: a] :
( ( sK3 != X0 )
| ( ( cS @ ( sK1 @ X0 ) )
!= $true )
| ( sK3 != X0 )
| ( ( sP0 @ X0 )
!= $true ) )
| ~ spl5_5
| ~ spl5_6 ),
inference(superposition,[status(thm)],[f52,f67]) ).
thf(f67,plain,
( ! [X0: a] :
( ( ( cF @ ( sK1 @ X0 ) )
= X0 )
| ( ( sP0 @ X0 )
!= $true )
| ( sK3 != X0 ) )
| ~ spl5_5
| ~ spl5_6 ),
inference(subsumption_resolution,[status(thm)],[f65,f62]) ).
thf(f62,plain,
( ! [X0: a] :
( ( ( cR @ ( sK2 @ X0 ) )
= $true )
| ( sK3 != X0 )
| ( ( sP0 @ X0 )
!= $true ) )
| ~ spl5_5 ),
inference(subsumption_resolution,[status(thm)],[f61,f22]) ).
thf(f22,plain,
! [X0: a] :
( ( ( cR @ ( sK2 @ X0 ) )
= $true )
| ( ( cS @ ( sK1 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f61,plain,
( ! [X0: a] :
( ( sK3 != X0 )
| ( ( sP0 @ X0 )
!= $true )
| ( ( cS @ ( sK1 @ X0 ) )
!= $true )
| ( ( cR @ ( sK2 @ X0 ) )
= $true ) )
| ~ spl5_5 ),
inference(superposition,[status(thm)],[f52,f20]) ).
thf(f20,plain,
! [X0: a] :
( ( ( cF @ ( sK1 @ X0 ) )
= X0 )
| ( ( sP0 @ X0 )
!= $true )
| ( ( cR @ ( sK2 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f65,plain,
( ! [X0: a] :
( ( ( cF @ ( sK1 @ X0 ) )
= X0 )
| ( sK3 != X0 )
| ( ( cR @ ( sK2 @ X0 ) )
!= $true )
| ( ( sP0 @ X0 )
!= $true ) )
| ~ spl5_6 ),
inference(superposition,[status(thm)],[f56,f21]) ).
thf(f21,plain,
! [X0: a] :
( ( ( cF @ ( sK2 @ X0 ) )
= X0 )
| ( ( sP0 @ X0 )
!= $true )
| ( ( cF @ ( sK1 @ X0 ) )
= X0 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f56,plain,
( ! [X1: b] :
( ( ( cF @ X1 )
!= sK3 )
| ( ( cR @ X1 )
!= $true ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl5_6
<=> ! [X1: b] :
( ( ( cR @ X1 )
!= $true )
| ( ( cF @ X1 )
!= sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition]) ).
thf(f52,plain,
( ! [X1: b] :
( ( ( cF @ X1 )
!= sK3 )
| ( ( cS @ X1 )
!= $true ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl5_5
<=> ! [X1: b] :
( ( ( cS @ X1 )
!= $true )
| ( ( cF @ X1 )
!= sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition]) ).
thf(f79,plain,
( ! [X0: a] :
( ( sK3 != X0 )
| ( ( cS @ ( sK1 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
!= $true ) )
| ~ spl5_6 ),
inference(subsumption_resolution,[status(thm)],[f76,f22]) ).
thf(f76,plain,
( ! [X0: a] :
( ( ( sP0 @ X0 )
!= $true )
| ( sK3 != X0 )
| ( ( cR @ ( sK2 @ X0 ) )
!= $true )
| ( ( cS @ ( sK1 @ X0 ) )
= $true ) )
| ~ spl5_6 ),
inference(superposition,[status(thm)],[f56,f23]) ).
thf(f23,plain,
! [X0: a] :
( ( ( cF @ ( sK2 @ X0 ) )
= X0 )
| ( ( cS @ ( sK1 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f57,plain,
( ~ spl5_2
| spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f29,f55,f37]) ).
thf(f29,plain,
! [X1: b] :
( ( ( cR @ X1 )
!= $true )
| ( ( sP0 @ sK3 )
!= $true )
| ( ( cF @ X1 )
!= sK3 ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ( sP0 @ sK3 )
!= $true )
| ! [X1: b] :
( ( ( cF @ X1 )
!= sK3 )
| ( ( ( cR @ X1 )
!= $true )
& ( ( cS @ X1 )
!= $true ) ) ) )
& ( ( ( sP0 @ sK3 )
= $true )
| ( ( sK3
= ( cF @ sK4 ) )
& ( ( ( cR @ sK4 )
= $true )
| ( ( cS @ sK4 )
= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f16,f18,f17]) ).
thf(f17,plain,
( ? [X0: a] :
( ( ( ( sP0 @ X0 )
!= $true )
| ! [X1: b] :
( ( ( cF @ X1 )
!= X0 )
| ( ( ( cR @ X1 )
!= $true )
& ( ( cS @ X1 )
!= $true ) ) ) )
& ( ( ( sP0 @ X0 )
= $true )
| ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ( ( ( cR @ X2 )
= $true )
| ( ( cS @ X2 )
= $true ) ) ) ) )
=> ( ( ( ( sP0 @ sK3 )
!= $true )
| ! [X1: b] :
( ( ( cF @ X1 )
!= sK3 )
| ( ( ( cR @ X1 )
!= $true )
& ( ( cS @ X1 )
!= $true ) ) ) )
& ( ( ( sP0 @ sK3 )
= $true )
| ? [X2: b] :
( ( sK3
= ( cF @ X2 ) )
& ( ( ( cR @ X2 )
= $true )
| ( ( cS @ X2 )
= $true ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X2: b] :
( ( sK3
= ( cF @ X2 ) )
& ( ( ( cR @ X2 )
= $true )
| ( ( cS @ X2 )
= $true ) ) )
=> ( ( sK3
= ( cF @ sK4 ) )
& ( ( ( cR @ sK4 )
= $true )
| ( ( cS @ sK4 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
? [X0: a] :
( ( ( ( sP0 @ X0 )
!= $true )
| ! [X1: b] :
( ( ( cF @ X1 )
!= X0 )
| ( ( ( cR @ X1 )
!= $true )
& ( ( cS @ X1 )
!= $true ) ) ) )
& ( ( ( sP0 @ X0 )
= $true )
| ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ( ( ( cR @ X2 )
= $true )
| ( ( cS @ X2 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
? [X0: a] :
( ( ( ( sP0 @ X0 )
!= $true )
| ! [X1: b] :
( ( ( cF @ X1 )
!= X0 )
| ( ( ( cR @ X1 )
!= $true )
& ( ( cS @ X1 )
!= $true ) ) ) )
& ( ( ( sP0 @ X0 )
= $true )
| ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( ( cR @ X1 )
= $true )
| ( ( cS @ X1 )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a] :
( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( ( cR @ X1 )
= $true )
| ( ( cS @ X1 )
= $true ) ) )
<~> ( ( sP0 @ X0 )
= $true ) ),
inference(definition_folding,[status(thm)],[f6,f7]) ).
thf(f6,plain,
? [X0: a] :
( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( ( cR @ X1 )
= $true )
| ( ( cS @ X1 )
= $true ) ) )
<~> ( ? [X3: b] :
( ( ( cS @ X3 )
= $true )
& ( ( cF @ X3 )
= X0 ) )
| ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ( ( cR @ X2 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( ( cR @ X1 )
= $true )
| ( ( cS @ X1 )
= $true ) ) )
<=> ( ? [X3: b] :
( ( ( cS @ X3 )
= $true )
& ( ( cF @ X3 )
= X0 ) )
| ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ( ( cR @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( cR @ X1 )
| ( cS @ X1 ) ) )
<=> ( ? [X2: b] :
( ( cR @ X2 )
& ( ( cF @ X2 )
= X0 ) )
| ? [X3: b] :
( ( ( cF @ X3 )
= X0 )
& ( cS @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( cR @ X1 )
| ( cS @ X1 ) ) )
<=> ( ? [X1: b] :
( ( cR @ X1 )
& ( ( cF @ X1 )
= X0 ) )
| ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( cS @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a] :
( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( cR @ X1 )
| ( cS @ X1 ) ) )
<=> ( ? [X1: b] :
( ( cR @ X1 )
& ( ( cF @ X1 )
= X0 ) )
| ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( cS @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tTEChS5TMx/DTF2THF_25586.p',cTHM34_pme) ).
thf(f53,plain,
( spl5_5
| ~ spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f28,f37,f51]) ).
thf(f28,plain,
! [X1: b] :
( ( ( sP0 @ sK3 )
!= $true )
| ( ( cS @ X1 )
!= $true )
| ( ( cF @ X1 )
!= sK3 ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f49,plain,
( spl5_2
| spl5_3
| spl5_4 ),
inference(avatar_split_clause,[status(thm)],[f26,f46,f42,f37]) ).
thf(f26,plain,
( ( ( cS @ sK4 )
= $true )
| ( ( cR @ sK4 )
= $true )
| ( ( sP0 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f40,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f27,f37,f33]) ).
thf(f27,plain,
( ( ( sP0 @ sK3 )
= $true )
| ( sK3
= ( cF @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU899^5 : 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
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:37:35 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.50 ---- Original DTF file ---
% 0.29/0.50 thf(spec,logic,$$dhol).
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 % File : SEU899^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.50 % Domain : Set Theory
% 0.29/0.50 % Problem : TPS problem THM34
% 0.29/0.50 % Version : Especial.
% 0.29/0.50 % English :
% 0.29/0.50
% 0.29/0.50 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.50 % Source : [Bro09]
% 0.29/0.50 % Names : tps_0430 [Bro09]
% 0.29/0.50 % : THM34 [TPS]
% 0.29/0.50
% 0.29/0.50 % Status : Theorem
% 0.29/0.50 % Rating : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.29/0.50 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.29/0.50 % Number of atoms : 7 ( 3 equ; 0 cnn)
% 0.29/0.50 % Maximal formula atoms : 7 ( 7 avg)
% 0.29/0.50 % Number of connectives : 13 ( 0 ~; 2 |; 3 &; 7 @)
% 0.29/0.50 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.50 % Maximal formula depth : 7 ( 7 avg)
% 0.29/0.50 % Number of types : 3 ( 2 usr)
% 0.29/0.50 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.50 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.29/0.50 % Number of variables : 4 ( 0 ^; 1 !; 3 ?; 4 :)
% 0.29/0.50 % SPC : TH0_THM_EQU_NAR
% 0.29/0.50
% 0.29/0.50 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.50 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.50 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.50 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.50 % : Polymorphic definitions expanded.
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 thf(b_type,type,
% 0.29/0.50 b: $tType ).
% 0.29/0.50
% 0.29/0.50 thf(a_type,type,
% 0.29/0.50 a: $tType ).
% 0.29/0.50
% 0.29/0.50 thf(cF,type,
% 0.29/0.50 cF: b > a ).
% 0.29/0.50
% 0.29/0.50 thf(cS,type,
% 0.29/0.50 cS: b > $o ).
% 0.29/0.50
% 0.29/0.50 thf(cR,type,
% 0.29/0.50 cR: b > $o ).
% 0.29/0.50
% 0.29/0.50 thf(cTHM34_pme,conjecture,
% 0.29/0.50 ! [Xx: a] :
% 0.29/0.50 ( ? [Xt: b] :
% 0.29/0.50 ( ( ( cR @ Xt )
% 0.29/0.50 | ( cS @ Xt ) )
% 0.29/0.50 & ( Xx
% 0.29/0.50 = ( cF @ Xt ) ) )
% 0.29/0.50 <=> ( ? [Xt: b] :
% 0.29/0.50 ( ( cR @ Xt )
% 0.29/0.50 & ( Xx
% 0.29/0.50 = ( cF @ Xt ) ) )
% 0.29/0.50 | ? [Xt: b] :
% 0.29/0.50 ( ( cS @ Xt )
% 0.29/0.50 & ( Xx
% 0.29/0.50 = ( cF @ Xt ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 ------------------------
% 1.79/1.51 ---- Embedded in THF ---
% 1.79/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.79/1.51 %%% Generated on Tue Feb 24 12:37:36 EST 2026
% 1.79/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 1.79/1.51 %%% Logic specification used:
% 1.79/1.51 %%% thf(spec, logic, $$dhol).
% 1.79/1.51
% 1.79/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.tTEChS5TMx/DTF2DTF25586.p
% See solution above
% 1.79/1.51 ------------------------
% 1.79/1.52 ---- Cleaned THF ---
% 1.79/1.52 thf(b_type,type,
% 1.79/1.52 b: $tType ).
% 1.79/1.52
% 1.79/1.52 thf(a_type,type,
% 1.79/1.52 a: $tType ).
% 1.79/1.52
% 1.79/1.52 thf(cF,type,
% 1.79/1.52 cF: b > a ).
% 1.79/1.52
% 1.79/1.52 thf(cS,type,
% 1.79/1.52 cS: b > $o ).
% 1.79/1.52
% 1.79/1.52 thf(cR,type,
% 1.79/1.52 cR: b > $o ).
% 1.79/1.52
% 1.79/1.52 thf(cTHM34_pme,conjecture,
% 1.79/1.52 ! [Xx: a] :
% 1.79/1.52 ( ? [Xt: b] :
% 1.79/1.52 ( ( ( cR @ Xt )
% 1.79/1.52 | ( cS @ Xt ) )
% 1.79/1.52 & ( Xx
% 1.79/1.52 = ( cF @ Xt ) ) )
% 1.79/1.52 <=> ( ? [Xt: b] :
% 1.79/1.52 ( ( cR @ Xt )
% 1.79/1.52 & ( Xx
% 1.79/1.52 = ( cF @ Xt ) ) )
% 1.79/1.52 | ? [Xt: b] :
% 1.79/1.52 ( ( cS @ Xt )
% 1.79/1.52 & ( Xx
% 1.79/1.52 = ( cF @ Xt ) ) ) ) ) ).
% 1.79/1.52 ------------------------
% 1.79/1.54 % (25702)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25586 for (2999ds/2Mi)
% 1.79/1.54 % (25703)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_25586 for (2999ds/2Mi)
% 1.79/1.54 % (25705)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25586 for (2999ds/18Mi)
% 1.79/1.54 % (25700)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_25586 for (2999ds/4Mi)
% 1.79/1.54 % (25699)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25586 for (2999ds/183Mi)
% 1.79/1.54 % (25704)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_25586 for (2999ds/275Mi)
% 1.79/1.55 % (25702)Instruction limit reached!
% 1.79/1.55 % (25702)------------------------------
% 1.79/1.55 % (25702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.55 % (25702)Termination reason: Unknown
% 1.79/1.55 % (25702)Termination phase: Saturation
% 1.79/1.55 % (25703)Instruction limit reached!
% 1.79/1.55 % (25703)------------------------------
% 1.79/1.55 % (25703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.55
% 1.79/1.55 % (25702)Memory used [KB]: 5500
% 1.79/1.55 % (25702)Time elapsed: 0.003 s
% 1.79/1.55 % (25702)Instructions burned: 2 (million)
% 1.79/1.55 % (25702)------------------------------
% 1.79/1.55 % (25702)------------------------------
% 1.79/1.55 % (25703)Termination reason: Unknown
% 1.79/1.55 % (25703)Termination phase: Saturation
% 1.79/1.55
% 1.79/1.55 % (25703)Memory used [KB]: 5500
% 1.79/1.55 % (25703)Time elapsed: 0.003 s
% 1.79/1.55 % (25703)Instructions burned: 3 (million)
% 1.79/1.55 % (25703)------------------------------
% 1.79/1.55 % (25703)------------------------------
% 1.79/1.55 % (25700)Instruction limit reached!
% 1.79/1.55 % (25700)------------------------------
% 1.79/1.55 % (25700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.55 % (25700)Termination reason: Unknown
% 1.79/1.55 % (25700)Termination phase: Saturation
% 1.79/1.55
% 1.79/1.55 % (25700)Memory used [KB]: 5500
% 1.79/1.55 % (25700)Time elapsed: 0.004 s
% 1.79/1.55 % (25700)Instructions burned: 4 (million)
% 1.79/1.55 % (25700)------------------------------
% 1.79/1.55 % (25700)------------------------------
% 1.79/1.55 % (25701)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_25586 for (2999ds/27Mi)
% 1.79/1.55 % (25699)First to succeed.
% 1.79/1.55 % (25704)Also succeeded, but the first one will report.
% 1.79/1.55 % (25701)Also succeeded, but the first one will report.
% 1.79/1.55 % (25699)Refutation found. Thanks to Tanya!
% 1.79/1.55 % SZS status Theorem for DTF2THF_25586
% 1.79/1.55 % SZS output start Proof for DTF2THF_25586
% 1.79/1.55 thf(type_def_5, type, b: $tType).
% 1.79/1.55 thf(type_def_6, type, a: $tType).
% 1.79/1.55 thf(func_def_0, type, b: $tType).
% 1.79/1.55 thf(func_def_1, type, a: $tType).
% 1.79/1.55 thf(func_def_2, type, cF: b > a).
% 1.79/1.55 thf(func_def_3, type, cS: b > $o).
% 1.79/1.55 thf(func_def_4, type, cR: b > $o).
% 1.79/1.55 thf(func_def_8, type, sP0: a > $o).
% 1.79/1.55 thf(func_def_9, type, sK1: a > b).
% 1.79/1.55 thf(func_def_10, type, sK2: a > b).
% 1.79/1.55 thf(func_def_11, type, sK3: a).
% 1.79/1.55 thf(func_def_12, type, sK4: b).
% 1.79/1.55 thf(f102,plain,(
% 1.79/1.55 $false),
% 1.79/1.55 inference(avatar_sat_refutation,[status(thm)],[f40,f49,f53,f57,f87,f96,f101])).
% 1.79/1.55 thf(f101,plain,(
% 1.79/1.55 ~spl5_1 | spl5_2 | ~spl5_3),
% 1.79/1.55 inference(avatar_contradiction_clause,[status(thm)],[f100])).
% 1.79/1.55 thf(f100,plain,(
% 1.79/1.55 $false | (~spl5_1 | spl5_2 | ~spl5_3)),
% 1.79/1.55 inference(subsumption_resolution,[status(thm)],[f99,f38])).
% 1.79/1.55 thf(f38,plain,(
% 1.79/1.55 ((sP0 @ sK3) != $true) | spl5_2),
% 1.79/1.55 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.79/1.55 thf(f37,definition,(
% 1.79/1.55 spl5_2 <=> ((sP0 @ sK3) = $true)),
% 1.79/1.55 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.79/1.55 thf(f99,plain,(
% 1.79/1.55 ((sP0 @ sK3) = $true) | (~spl5_1 | ~spl5_3)),
% 1.79/1.55 inference(subsumption_resolution,[status(thm)],[f88,f44])).
% 1.79/1.55 thf(f44,plain,(
% 1.79/1.55 ((cR @ sK4) = $true) | ~spl5_3),
% 1.79/1.55 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.79/1.55 thf(f42,definition,(
% 1.79/1.55 spl5_3 <=> ((cR @ sK4) = $true)),
% 1.79/1.55 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.79/1.55 thf(f88,plain,(
% 1.79/1.55 ((cR @ sK4) != $true) | ((sP0 @ sK3) = $true) | ~spl5_1),
% 1.79/1.55 inference(superposition,[status(thm)],[f31,f35])).
% 1.79/1.55 thf(f35,plain,(
% 1.79/1.55 (sK3 = (cF @ sK4)) | ~spl5_1),
% 1.79/1.55 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.79/1.55 thf(f33,definition,(
% 1.79/1.55 spl5_1 <=> (sK3 = (cF @ sK4))),
% 1.79/1.55 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.79/1.55 thf(f31,plain,(
% 1.79/1.55 ( ! [X2 : b] : (((sP0 @ (cF @ X2)) = $true) | ((cR @ X2) != $true)) )),
% 1.79/1.55 inference(equality_resolution,[status(thm)],[f24])).
% 1.79/1.55 thf(f24,plain,(
% 1.79/1.55 ( ! [X2 : b,X0 : a] : (((sP0 @ X0) = $true) | ((cF @ X2) != X0) | ((cR @ X2) != $true)) )),
% 1.79/1.55 inference(cnf_transformation,[status(thm)],[f14])).
% 1.79/1.55 thf(f14,plain,(
% 1.79/1.55 ! [X0 : a] : ((((sP0 @ X0) = $true) | (! [X1 : b] : (((cS @ X1) != $true) | ((cF @ X1) != X0)) & ! [X2 : b] : (((cF @ X2) != X0) | ((cR @ X2) != $true)))) & ((((cS @ (sK1 @ X0)) = $true) & ((cF @ (sK1 @ X0)) = X0)) | (((cF @ (sK2 @ X0)) = X0) & ((cR @ (sK2 @ X0)) = $true)) | ((sP0 @ X0) != $true)))),
% 1.79/1.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f11,f13,f12])).
% 1.79/1.55 thf(f12,plain,(
% 1.79/1.55 ! [X0 : a] : (? [X3 : b] : (((cS @ X3) = $true) & ((cF @ X3) = X0)) => (((cS @ (sK1 @ X0)) = $true) & ((cF @ (sK1 @ X0)) = X0)))),
% 1.79/1.55 introduced(definition,[],[choice_axiom])).
% 1.79/1.55 thf(f13,plain,(
% 1.79/1.55 ! [X0 : a] : (? [X4 : b] : (((cF @ X4) = X0) & ((cR @ X4) = $true)) => (((cF @ (sK2 @ X0)) = X0) & ((cR @ (sK2 @ X0)) = $true)))),
% 1.79/1.55 introduced(definition,[],[choice_axiom])).
% 1.79/1.55 thf(f11,plain,(
% 1.79/1.55 ! [X0 : a] : ((((sP0 @ X0) = $true) | (! [X1 : b] : (((cS @ X1) != $true) | ((cF @ X1) != X0)) & ! [X2 : b] : (((cF @ X2) != X0) | ((cR @ X2) != $true)))) & (? [X3 : b] : (((cS @ X3) = $true) & ((cF @ X3) = X0)) | ? [X4 : b] : (((cF @ X4) = X0) & ((cR @ X4) = $true)) | ((sP0 @ X0) != $true)))),
% 1.79/1.55 inference(rectify,[status(thm)],[f10])).
% 1.79/1.55 thf(f10,plain,(
% 1.79/1.55 ! [X0 : a] : ((((sP0 @ X0) = $true) | (! [X3 : b] : (((cS @ X3) != $true) | ((cF @ X3) != X0)) & ! [X2 : b] : (((cF @ X2) != X0) | ((cR @ X2) != $true)))) & (? [X3 : b] : (((cS @ X3) = $true) & ((cF @ X3) = X0)) | ? [X2 : b] : (((cF @ X2) = X0) & ((cR @ X2) = $true)) | ((sP0 @ X0) != $true)))),
% 1.79/1.55 inference(flattening,[status(thm)],[f9])).
% 1.79/1.55 thf(f9,plain,(
% 1.79/1.55 ! [X0 : a] : ((((sP0 @ X0) = $true) | (! [X3 : b] : (((cS @ X3) != $true) | ((cF @ X3) != X0)) & ! [X2 : b] : (((cF @ X2) != X0) | ((cR @ X2) != $true)))) & ((? [X3 : b] : (((cS @ X3) = $true) & ((cF @ X3) = X0)) | ? [X2 : b] : (((cF @ X2) = X0) & ((cR @ X2) = $true))) | ((sP0 @ X0) != $true)))),
% 1.79/1.55 inference(nnf_transformation,[status(thm)],[f7])).
% 1.79/1.55 thf(f7,plain,(
% 1.79/1.55 ! [X0 : a] : (((sP0 @ X0) = $true) <=> (? [X3 : b] : (((cS @ X3) = $true) & ((cF @ X3) = X0)) | ? [X2 : b] : (((cF @ X2) = X0) & ((cR @ X2) = $true))))),
% 1.79/1.55 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.79/1.55 thf(f96,plain,(
% 1.79/1.55 ~spl5_4 | ~spl5_1 | spl5_2),
% 1.79/1.55 inference(avatar_split_clause,[status(thm)],[f95,f37,f33,f46])).
% 1.79/1.55 thf(f46,definition,(
% 1.79/1.55 spl5_4 <=> ((cS @ sK4) = $true)),
% 1.79/1.55 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.79/1.55 thf(f95,plain,(
% 1.79/1.55 ((cS @ sK4) != $true) | (~spl5_1 | spl5_2)),
% 1.79/1.55 inference(subsumption_resolution,[status(thm)],[f89,f38])).
% 1.79/1.55 thf(f89,plain,(
% 1.79/1.55 ((sP0 @ sK3) = $true) | ((cS @ sK4) != $true) | ~spl5_1),
% 1.79/1.55 inference(superposition,[status(thm)],[f30,f35])).
% 1.79/1.55 thf(f30,plain,(
% 1.79/1.55 ( ! [X1 : b] : (((sP0 @ (cF @ X1)) = $true) | ((cS @ X1) != $true)) )),
% 1.79/1.55 inference(equality_resolution,[status(thm)],[f25])).
% 1.79/1.55 thf(f25,plain,(
% 1.79/1.55 ( ! [X0 : a,X1 : b] : (((sP0 @ X0) = $true) | ((cS @ X1) != $true) | ((cF @ X1) != X0)) )),
% 1.79/1.55 inference(cnf_transformation,[status(thm)],[f14])).
% 1.79/1.55 thf(f87,plain,(
% 1.79/1.55 ~spl5_2 | ~spl5_5 | ~spl5_6),
% 1.79/1.55 inference(avatar_contradiction_clause,[status(thm)],[f86])).
% 1.79/1.55 thf(f86,plain,(
% 1.79/1.55 $false | (~spl5_2 | ~spl5_5 | ~spl5_6)),
% 1.79/1.55 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.79/1.55 thf(f81,plain,(
% 1.79/1.55 ($true != $true) | (sK3 != sK3) | (~spl5_2 | ~spl5_5 | ~spl5_6)),
% 1.79/1.55 inference(superposition,[status(thm)],[f80,f39])).
% 1.79/1.55 thf(f39,plain,(
% 1.79/1.55 ((sP0 @ sK3) = $true) | ~spl5_2),
% 1.79/1.55 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.79/1.55 thf(f80,plain,(
% 1.79/1.55 ( ! [X0 : a] : (((sP0 @ X0) != $true) | (sK3 != X0)) ) | (~spl5_5 | ~spl5_6)),
% 1.79/1.55 inference(subsumption_resolution,[status(thm)],[f79,f73])).
% 1.79/1.55 thf(f73,plain,(
% 1.79/1.55 ( ! [X0 : a] : (((cS @ (sK1 @ X0)) != $true) | (sK3 != X0) | ((sP0 @ X0) != $true)) ) | (~spl5_5 | ~spl5_6)),
% 1.79/1.55 inference(duplicate_literal_removal,[status(thm)],[f71])).
% 1.79/1.55 thf(f71,plain,(
% 1.79/1.55 ( ! [X0 : a] : ((sK3 != X0) | ((cS @ (sK1 @ X0)) != $true) | (sK3 != X0) | ((sP0 @ X0) != $true)) ) | (~spl5_5 | ~spl5_6)),
% 1.79/1.55 inference(superposition,[status(thm)],[f52,f67])).
% 1.79/1.55 thf(f67,plain,(
% 1.79/1.55 ( ! [X0 : a] : (((cF @ (sK1 @ X0)) = X0) | ((sP0 @ X0) != $true) | (sK3 != X0)) ) | (~spl5_5 | ~spl5_6)),
% 1.79/1.55 inference(subsumption_resolution,[status(thm)],[f65,f62])).
% 1.79/1.55 thf(f62,plain,(
% 1.79/1.55 ( ! [X0 : a] : (((cR @ (sK2 @ X0)) = $true) | (sK3 != X0) | ((sP0 @ X0) != $true)) ) | ~spl5_5),
% 1.79/1.55 inference(subsumption_resolution,[status(thm)],[f61,f22])).
% 1.79/1.55 thf(f22,plain,(
% 1.79/1.55 ( ! [X0 : a] : (((cR @ (sK2 @ X0)) = $true) | ((cS @ (sK1 @ X0)) = $true) | ((sP0 @ X0) != $true)) )),
% 1.79/1.55 inference(cnf_transformation,[status(thm)],[f14])).
% 1.79/1.55 thf(f61,plain,(
% 1.79/1.55 ( ! [X0 : a] : ((sK3 != X0) | ((sP0 @ X0) != $true) | ((cS @ (sK1 @ X0)) != $true) | ((cR @ (sK2 @ X0)) = $true)) ) | ~spl5_5),
% 1.79/1.55 inference(superposition,[status(thm)],[f52,f20])).
% 1.79/1.55 thf(f20,plain,(
% 1.79/1.55 ( ! [X0 : a] : (((cF @ (sK1 @ X0)) = X0) | ((sP0 @ X0) != $true) | ((cR @ (sK2 @ X0)) = $true)) )),
% 1.79/1.55 inference(cnf_transformation,[status(thm)],[f14])).
% 1.79/1.55 thf(f65,plain,(
% 1.79/1.55 ( ! [X0 : a] : (((cF @ (sK1 @ X0)) = X0) | (sK3 != X0) | ((cR @ (sK2 @ X0)) != $true) | ((sP0 @ X0) != $true)) ) | ~spl5_6),
% 1.79/1.55 inference(superposition,[status(thm)],[f56,f21])).
% 1.79/1.55 thf(f21,plain,(
% 1.79/1.55 ( ! [X0 : a] : (((cF @ (sK2 @ X0)) = X0) | ((sP0 @ X0) != $true) | ((cF @ (sK1 @ X0)) = X0)) )),
% 1.79/1.55 inference(cnf_transformation,[status(thm)],[f14])).
% 1.79/1.55 thf(f56,plain,(
% 1.79/1.55 ( ! [X1 : b] : (((cF @ X1) != sK3) | ((cR @ X1) != $true)) ) | ~spl5_6),
% 1.79/1.55 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.79/1.55 thf(f55,definition,(
% 1.79/1.55 spl5_6 <=> ! [X1 : b] : (((cR @ X1) != $true) | ((cF @ X1) != sK3))),
% 1.79/1.55 introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition])).
% 1.79/1.55 thf(f52,plain,(
% 1.79/1.55 ( ! [X1 : b] : (((cF @ X1) != sK3) | ((cS @ X1) != $true)) ) | ~spl5_5),
% 1.79/1.55 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.79/1.55 thf(f51,definition,(
% 1.79/1.55 spl5_5 <=> ! [X1 : b] : (((cS @ X1) != $true) | ((cF @ X1) != sK3))),
% 1.79/1.55 introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition])).
% 1.79/1.55 thf(f79,plain,(
% 1.79/1.55 ( ! [X0 : a] : ((sK3 != X0) | ((cS @ (sK1 @ X0)) = $true) | ((sP0 @ X0) != $true)) ) | ~spl5_6),
% 1.79/1.55 inference(subsumption_resolution,[status(thm)],[f76,f22])).
% 1.79/1.55 thf(f76,plain,(
% 1.79/1.55 ( ! [X0 : a] : (((sP0 @ X0) != $true) | (sK3 != X0) | ((cR @ (sK2 @ X0)) != $true) | ((cS @ (sK1 @ X0)) = $true)) ) | ~spl5_6),
% 1.79/1.55 inference(superposition,[status(thm)],[f56,f23])).
% 1.79/1.55 thf(f23,plain,(
% 1.79/1.55 ( ! [X0 : a] : (((cF @ (sK2 @ X0)) = X0) | ((cS @ (sK1 @ X0)) = $true) | ((sP0 @ X0) != $true)) )),
% 1.79/1.55 inference(cnf_transformation,[status(thm)],[f14])).
% 1.79/1.55 thf(f57,plain,(
% 1.79/1.55 ~spl5_2 | spl5_6),
% 1.79/1.55 inference(avatar_split_clause,[status(thm)],[f29,f55,f37])).
% 1.79/1.55 thf(f29,plain,(
% 1.79/1.55 ( ! [X1 : b] : (((cR @ X1) != $true) | ((sP0 @ sK3) != $true) | ((cF @ X1) != sK3)) )),
% 1.79/1.55 inference(cnf_transformation,[status(thm)],[f19])).
% 1.79/1.55 thf(f19,plain,(
% 1.79/1.55 (((sP0 @ sK3) != $true) | ! [X1 : b] : (((cF @ X1) != sK3) | (((cR @ X1) != $true) & ((cS @ X1) != $true)))) & (((sP0 @ sK3) = $true) | ((sK3 = (cF @ sK4)) & (((cR @ sK4) = $true) | ((cS @ sK4) = $true))))),
% 1.79/1.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f16,f18,f17])).
% 1.79/1.55 thf(f17,plain,(
% 1.79/1.55 ? [X0 : a] : ((((sP0 @ X0) != $true) | ! [X1 : b] : (((cF @ X1) != X0) | (((cR @ X1) != $true) & ((cS @ X1) != $true)))) & (((sP0 @ X0) = $true) | ? [X2 : b] : (((cF @ X2) = X0) & (((cR @ X2) = $true) | ((cS @ X2) = $true))))) => ((((sP0 @ sK3) != $true) | ! [X1 : b] : (((cF @ X1) != sK3) | (((cR @ X1) != $true) & ((cS @ X1) != $true)))) & (((sP0 @ sK3) = $true) | ? [X2 : b] : ((sK3 = (cF @ X2)) & (((cR @ X2) = $true) | ((cS @ X2) = $true)))))),
% 1.79/1.55 introduced(definition,[],[choice_axiom])).
% 1.79/1.55 thf(f18,plain,(
% 1.79/1.55 ? [X2 : b] : ((sK3 = (cF @ X2)) & (((cR @ X2) = $true) | ((cS @ X2) = $true))) => ((sK3 = (cF @ sK4)) & (((cR @ sK4) = $true) | ((cS @ sK4) = $true)))),
% 1.79/1.55 introduced(definition,[],[choice_axiom])).
% 1.79/1.55 thf(f16,plain,(
% 1.79/1.55 ? [X0 : a] : ((((sP0 @ X0) != $true) | ! [X1 : b] : (((cF @ X1) != X0) | (((cR @ X1) != $true) & ((cS @ X1) != $true)))) & (((sP0 @ X0) = $true) | ? [X2 : b] : (((cF @ X2) = X0) & (((cR @ X2) = $true) | ((cS @ X2) = $true)))))),
% 1.79/1.55 inference(rectify,[status(thm)],[f15])).
% 1.79/1.55 thf(f15,plain,(
% 1.79/1.55 ? [X0 : a] : ((((sP0 @ X0) != $true) | ! [X1 : b] : (((cF @ X1) != X0) | (((cR @ X1) != $true) & ((cS @ X1) != $true)))) & (((sP0 @ X0) = $true) | ? [X1 : b] : (((cF @ X1) = X0) & (((cR @ X1) = $true) | ((cS @ X1) = $true)))))),
% 1.79/1.55 inference(nnf_transformation,[status(thm)],[f8])).
% 1.79/1.55 thf(f8,plain,(
% 1.79/1.55 ? [X0 : a] : (? [X1 : b] : (((cF @ X1) = X0) & (((cR @ X1) = $true) | ((cS @ X1) = $true))) <~> ((sP0 @ X0) = $true))),
% 1.79/1.55 inference(definition_folding,[status(thm)],[f6,f7])).
% 1.79/1.55 thf(f6,plain,(
% 1.79/1.55 ? [X0 : a] : (? [X1 : b] : (((cF @ X1) = X0) & (((cR @ X1) = $true) | ((cS @ X1) = $true))) <~> (? [X3 : b] : (((cS @ X3) = $true) & ((cF @ X3) = X0)) | ? [X2 : b] : (((cF @ X2) = X0) & ((cR @ X2) = $true))))),
% 1.79/1.55 inference(ennf_transformation,[status(thm)],[f5])).
% 1.79/1.55 thf(f5,plain,(
% 1.79/1.55 ~! [X0 : a] : (? [X1 : b] : (((cF @ X1) = X0) & (((cR @ X1) = $true) | ((cS @ X1) = $true))) <=> (? [X3 : b] : (((cS @ X3) = $true) & ((cF @ X3) = X0)) | ? [X2 : b] : (((cF @ X2) = X0) & ((cR @ X2) = $true))))),
% 1.79/1.55 inference(fool_elimination,[status(thm)],[f4])).
% 1.79/1.55 thf(f4,plain,(
% 1.79/1.55 ~! [X0 : a] : (? [X1 : b] : (((cF @ X1) = X0) & ((cR @ X1) | (cS @ X1))) <=> (? [X2 : b] : ((cR @ X2) & ((cF @ X2) = X0)) | ? [X3 : b] : (((cF @ X3) = X0) & (cS @ X3))))),
% 1.79/1.55 inference(rectify,[status(thm)],[f2])).
% 1.79/1.55 thf(f2,negated_conjecture,(
% 1.79/1.55 ~! [X0 : a] : (? [X1 : b] : (((cF @ X1) = X0) & ((cR @ X1) | (cS @ X1))) <=> (? [X1 : b] : ((cR @ X1) & ((cF @ X1) = X0)) | ? [X1 : b] : (((cF @ X1) = X0) & (cS @ X1))))),
% 1.79/1.55 inference(negated_conjecture,[status(cth)],[f1])).
% 1.79/1.55 thf(f1,conjecture,(
% 1.79/1.55 ! [X0 : a] : (? [X1 : b] : (((cF @ X1) = X0) & ((cR @ X1) | (cS @ X1))) <=> (? [X1 : b] : ((cR @ X1) & ((cF @ X1) = X0)) | ? [X1 : b] : (((cF @ X1) = X0) & (cS @ X1))))),
% 1.79/1.55 file('/export/starexec/sandbox/tmp/tmp.tTEChS5TMx/DTF2THF_25586.p',cTHM34_pme)).
% 1.79/1.55 thf(f53,plain,(
% 1.79/1.55 spl5_5 | ~spl5_2),
% 1.79/1.55 inference(avatar_split_clause,[status(thm)],[f28,f37,f51])).
% 1.79/1.55 thf(f28,plain,(
% 1.79/1.55 ( ! [X1 : b] : (((sP0 @ sK3) != $true) | ((cS @ X1) != $true) | ((cF @ X1) != sK3)) )),
% 1.79/1.55 inference(cnf_transformation,[status(thm)],[f19])).
% 1.79/1.55 thf(f49,plain,(
% 1.79/1.55 spl5_2 | spl5_3 | spl5_4),
% 1.79/1.55 inference(avatar_split_clause,[status(thm)],[f26,f46,f42,f37])).
% 1.79/1.55 thf(f26,plain,(
% 1.79/1.55 ((cS @ sK4) = $true) | ((cR @ sK4) = $true) | ((sP0 @ sK3) = $true)),
% 1.79/1.55 inference(cnf_transformation,[status(thm)],[f19])).
% 1.79/1.55 thf(f40,plain,(
% 1.79/1.55 spl5_1 | spl5_2),
% 1.79/1.55 inference(avatar_split_clause,[status(thm)],[f27,f37,f33])).
% 1.79/1.55 thf(f27,plain,(
% 1.79/1.55 ((sP0 @ sK3) = $true) | (sK3 = (cF @ sK4))),
% 1.79/1.55 inference(cnf_transformation,[status(thm)],[f19])).
% 1.79/1.55 % SZS output end Proof for DTF2THF_25586
% 1.79/1.55 % (25699)------------------------------
% 1.79/1.55 % (25699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.55 % (25699)Termination reason: Refutation
% 1.79/1.55
% 1.79/1.55 % (25699)Memory used [KB]: 5500
% 1.79/1.55 % (25699)Time elapsed: 0.009 s
% 1.79/1.55 % (25699)Instructions burned: 9 (million)
% 1.79/1.55 % (25699)------------------------------
% 1.79/1.55 % (25699)------------------------------
% 1.79/1.55 % (25698)Success in time 0.013 s
%------------------------------------------------------------------------------