%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : CSR138^1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 08:43:07 AM UTC 2026
% Result : Theorem 1.59s 1.34s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 19 unt; 0 typ; 2 def)
% Number of atoms : 299 ( 86 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 244 ( 73 ~; 43 |; 12 &; 112 @)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 130 ( 68 ^; 34 !; 28 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
num: $tType ).
thf(func_def_7,type,
likes_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_8,type,
parent_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_11,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_21,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f150,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f87,f95,f149]) ).
thf(f149,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[status(thm)],[f148]) ).
thf(f148,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ( $false = $true )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f53,f140]) ).
thf(f140,plain,
( ! [X2: $i,X1: $i] :
( ( parent_THFTYPE_IiioI @ X1 @ X2 )
= $true )
| ~ spl4_1 ),
inference(beta_eta_normalization,[status(thm)],[f139]) ).
thf(f139,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : $true
@ X2 )
= ( parent_THFTYPE_IiioI @ X1 @ X2 ) )
| ~ spl4_1 ),
inference(argument_congruence,[status(thm)],[f110]) ).
thf(f110,plain,
( ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ X1 )
= ( ^ [Y0: $i] : $true ) )
| ~ spl4_1 ),
inference(beta_eta_normalization,[status(thm)],[f109]) ).
thf(f109,plain,
( ! [X1: $i] :
( ( parent_THFTYPE_IiioI @ X1 )
= ( ^ [Y0: $i,Y1: $i] : $true
@ X1 ) )
| ~ spl4_1 ),
inference(argument_congruence,[status(thm)],[f100]) ).
thf(f100,plain,
( ( parent_THFTYPE_IiioI
= ( ^ [Y0: $i,Y1: $i] : $true ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ( parent_THFTYPE_IiioI
= ( ^ [Y0: $i,Y1: $i] : $true ) )
| ( $true != $true )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f62,f45]) ).
thf(f45,plain,
( ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i )
= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i,
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i,
file('/export/starexec/sandbox/tmp/tmp.QpZq09L7KZ/DTF2THF_7102.p',ax_008) ).
thf(f62,plain,
( ! [X0: $i > $i > $o] :
( ( $true
!= ( X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ) )
| ( ( ^ [Y0: $i,Y1: $i] : $true )
= X0 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl4_1
<=> ! [X0: $i > $i > $o] :
( ( ( ^ [Y0: $i,Y1: $i] : $true )
= X0 )
| ( $true
!= ( X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f53,plain,
( ( parent_THFTYPE_IiioI @ sK0 @ sK1 )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ~ ( parent_THFTYPE_IiioI @ sK0 @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ~ ( parent_THFTYPE_IiioI @ sK0 @ sK1 ) )
= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f20,f34]) ).
thf(f34,plain,
( ? [X0: $i,X1: $i] :
( ( ~ ( parent_THFTYPE_IiioI @ X0 @ X1 ) )
= $true )
=> ( ( ~ ( parent_THFTYPE_IiioI @ sK0 @ sK1 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
? [X0: $i,X1: $i] :
( ( ~ ( parent_THFTYPE_IiioI @ X0 @ X1 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
? [X0: $i,X1: $i] :
~ ( parent_THFTYPE_IiioI @ X0 @ X1 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
? [X0: $i,X1: $i] :
~ ( parent_THFTYPE_IiioI @ X0 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.QpZq09L7KZ/DTF2THF_7102.p',ax_002) ).
thf(f95,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f92,f61,f64]) ).
thf(f64,definition,
( spl4_2
<=> ( likes_THFTYPE_IiioI
= ( ^ [Y0: $i,Y1: $i] : $true ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f92,plain,
! [X0: $i > $i > $o] :
( ( likes_THFTYPE_IiioI
= ( ^ [Y0: $i,Y1: $i] : $true ) )
| ( $true
!= ( X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ) )
| ( ( ^ [Y0: $i,Y1: $i] : $true )
= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
! [X0: $i > $i > $o] :
( ( ( ^ [Y0: $i,Y1: $i] : $true )
= X0 )
| ( $true != $true )
| ( $true
!= ( X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ) )
| ( likes_THFTYPE_IiioI
= ( ^ [Y0: $i,Y1: $i] : $true ) ) ),
inference(superposition,[status(thm)],[f52,f42]) ).
thf(f42,plain,
( ( likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i )
= $true ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i )
= $true ),
inference(fool_elimination,[status(thm)],[f27]) ).
thf(f27,plain,
likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i,
file('/export/starexec/sandbox/tmp/tmp.QpZq09L7KZ/DTF2THF_7102.p',ax_001) ).
thf(f52,plain,
! [X2: $i > $i > $o,X0: $i,X1: $i > $i > $o] :
( ( ( X2 @ X0 @ lBill_THFTYPE_i )
!= $true )
| ( ( ^ [Y0: $i,Y1: $i] : $true )
= X1 )
| ( ( ^ [Y0: $i,Y1: $i] : $true )
= X2 )
| ( ( X1 @ X0 @ lAnna_THFTYPE_i )
!= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i > $i > $o,X0: $i,X1: $i > $i > $o] :
( ( ( X2
= ( ^ [Y0: $i,Y1: $i] : $true ) )
= $true )
| ( ( ^ [Y0: $i,Y1: $i] : $true )
= X1 )
| ( ( X2 @ X0 @ lBill_THFTYPE_i )
!= $true )
| ( ( X1 @ X0 @ lAnna_THFTYPE_i )
!= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i > $i > $o,X0: $i,X1: $i > $i > $o] :
( ( ( X2
!= ( ^ [Y0: $i,Y1: $i] : $true ) )
!= $true )
| ( ( X1 @ X0 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X2 @ X0 @ lBill_THFTYPE_i )
!= $true )
| ( ( ^ [Y0: $i,Y1: $i] : $true )
= X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i > $i > $o,X0: $i,X1: $i > $i > $o] :
( ( ( X1 @ X0 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X1
= ( ^ [Y0: $i,Y1: $i] : $true ) )
= $true )
| ( ( X2
!= ( ^ [Y0: $i,Y1: $i] : $true ) )
!= $true )
| ( ( X2 @ X0 @ lBill_THFTYPE_i )
!= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i > $i > $o,X0: $i,X1: $i > $i > $o] :
( ( ( X1
!= ( ^ [Y0: $i,Y1: $i] : $true ) )
!= $true )
| ( ( X2
!= ( ^ [Y0: $i,Y1: $i] : $true ) )
!= $true )
| ( ( X1 @ X0 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X2 @ X0 @ lBill_THFTYPE_i )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: $i,X1: $i > $i > $o,X2: $i > $i > $o] :
( ( ( X2 @ X0 @ lBill_THFTYPE_i )
!= $true )
| ( ( X1 @ X0 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X1
!= ( ^ [Y0: $i,Y1: $i] : $true ) )
!= $true )
| ( ( X2
!= ( ^ [Y0: $i,Y1: $i] : $true ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
~ ? [X0: $i,X1: $i > $i > $o,X2: $i > $i > $o] :
( ( ( X1 @ X0 @ lAnna_THFTYPE_i )
= $true )
& ( ( X1
!= ( ^ [Y0: $i,Y1: $i] : $true ) )
= $true )
& ( ( X2 @ X0 @ lBill_THFTYPE_i )
= $true )
& ( ( X2
!= ( ^ [Y0: $i,Y1: $i] : $true ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
~ ? [X0: $i,X1: $i > $i > $o,X2: $i > $i > $o] :
( ( X1
!= ( ^ [X3: $i,X4: $i] : $true ) )
& ( X2
!= ( ^ [X5: $i,X6: $i] : $true ) )
& ( X1 @ X0 @ lAnna_THFTYPE_i )
& ( X2 @ X0 @ lBill_THFTYPE_i ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,negated_conjecture,
~ ? [X1: $i,X2: $i > $i > $o,X3: $i > $i > $o] :
( ( X2
!= ( ^ [X4: $i,X5: $i] : $true ) )
& ( X3
!= ( ^ [X4: $i,X5: $i] : $true ) )
& ( X2 @ X1 @ lAnna_THFTYPE_i )
& ( X3 @ X1 @ lBill_THFTYPE_i ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f10,conjecture,
? [X1: $i,X2: $i > $i > $o,X3: $i > $i > $o] :
( ( X2
!= ( ^ [X4: $i,X5: $i] : $true ) )
& ( X3
!= ( ^ [X4: $i,X5: $i] : $true ) )
& ( X2 @ X1 @ lAnna_THFTYPE_i )
& ( X3 @ X1 @ lBill_THFTYPE_i ) ),
file('/export/starexec/sandbox/tmp/tmp.QpZq09L7KZ/DTF2THF_7102.p',con) ).
thf(f87,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[status(thm)],[f86]) ).
thf(f86,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $false = $true )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f48,f81]) ).
thf(f81,plain,
( ! [X2: $i,X1: $i] :
( ( likes_THFTYPE_IiioI @ X1 @ X2 )
= $true )
| ~ spl4_2 ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : $true
@ X2 )
= ( likes_THFTYPE_IiioI @ X1 @ X2 ) )
| ~ spl4_2 ),
inference(argument_congruence,[status(thm)],[f78]) ).
thf(f78,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : $true )
= ( likes_THFTYPE_IiioI @ X1 ) )
| ~ spl4_2 ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
( ! [X1: $i] :
( ( likes_THFTYPE_IiioI @ X1 )
= ( ^ [Y0: $i,Y1: $i] : $true
@ X1 ) )
| ~ spl4_2 ),
inference(argument_congruence,[status(thm)],[f66]) ).
thf(f66,plain,
( ( likes_THFTYPE_IiioI
= ( ^ [Y0: $i,Y1: $i] : $true ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f48,plain,
( ( likes_THFTYPE_IiioI @ sK2 @ sK3 )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ~ ( likes_THFTYPE_IiioI @ sK2 @ sK3 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ~ ( likes_THFTYPE_IiioI @ sK2 @ sK3 ) )
= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f24,f36]) ).
thf(f36,plain,
( ? [X0: $i,X1: $i] :
( ( ~ ( likes_THFTYPE_IiioI @ X0 @ X1 ) )
= $true )
=> ( ( ~ ( likes_THFTYPE_IiioI @ sK2 @ sK3 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
? [X0: $i,X1: $i] :
( ( ~ ( likes_THFTYPE_IiioI @ X0 @ X1 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
? [X0: $i,X1: $i] :
~ ( likes_THFTYPE_IiioI @ X0 @ X1 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
? [X0: $i,X1: $i] :
~ ( likes_THFTYPE_IiioI @ X0 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.QpZq09L7KZ/DTF2THF_7102.p',ax_003) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : CSR138^1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n004.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 05:50:56 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : CSR138^1 : TPTP v9.2.1. Released v4.1.0.
% 0.16/0.39 % Domain : Commonsense Reasoning
% 0.16/0.39 % Problem : Feelings from people to Bill and Anna
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : Do there exist relations ?R and ?Q so that ?R holds between a
% 0.16/0.39 % person ?Y and Bill and ?Q between ?Y and Anna.
% 0.16/0.39
% 0.16/0.39 % Refs : [Ben10] Benzmueller (2010), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Ben10]
% 0.16/0.39 % Names : rv_4.tq_SUMO_local [Ben10]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.11 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.57 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0
% 0.16/0.39 % Syntax : Number of formulae : 19 ( 7 unt; 9 typ; 0 def)
% 0.16/0.39 % Number of atoms : 17 ( 2 equ; 4 cnn)
% 0.16/0.39 % Maximal formula atoms : 4 ( 1 avg)
% 0.16/0.39 % Number of connectives : 33 ( 4 ~; 0 |; 3 &; 26 @)
% 0.16/0.39 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 8 ( 4 avg)
% 0.16/0.39 % Number of types : 3 ( 1 usr)
% 0.16/0.39 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 11 ( 4 ^; 0 !; 7 ?; 11 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This is a simple test problem for reasoning in/about SUMO.
% 0.16/0.39 % Initally the problem has been hand generated in KIF syntax in
% 0.16/0.39 % SigmaKEE and then automatically translated by Benzmueller's
% 0.16/0.39 % KIF2TH0 translator into THF syntax.
% 0.16/0.39 % : The translation has been applied in two modes: local and SInE.
% 0.16/0.39 % The local mode only translates the local assumptions and the
% 0.16/0.39 % query. The SInE mode additionally translates the SInE-extract
% 0.16/0.39 % of the loaded knowledge base (usually SUMO).
% 0.16/0.39 % : The examples are selected to illustrate the benefits of
% 0.16/0.39 % higher-order reasoning in ontology reasoning.
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 %----The extracted signature
% 0.16/0.39 thf(numbers,type,
% 0.16/0.39 num: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(lAnna_THFTYPE_i,type,
% 0.16/0.39 lAnna_THFTYPE_i: $i ).
% 0.16/0.39
% 0.16/0.39 thf(lBen_THFTYPE_i,type,
% 0.16/0.39 lBen_THFTYPE_i: $i ).
% 0.16/0.39
% 0.16/0.39 thf(lBill_THFTYPE_i,type,
% 0.16/0.39 lBill_THFTYPE_i: $i ).
% 0.16/0.39
% 0.16/0.39 thf(lBob_THFTYPE_i,type,
% 0.16/0.39 lBob_THFTYPE_i: $i ).
% 0.16/0.39
% 0.16/0.39 thf(lMary_THFTYPE_i,type,
% 0.16/0.39 lMary_THFTYPE_i: $i ).
% 0.16/0.39
% 0.16/0.39 thf(lSue_THFTYPE_i,type,
% 0.16/0.39 lSue_THFTYPE_i: $i ).
% 0.16/0.39
% 0.16/0.39 thf(likes_THFTYPE_IiioI,type,
% 0.16/0.39 likes_THFTYPE_IiioI: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(parent_THFTYPE_IiioI,type,
% 0.16/0.39 parent_THFTYPE_IiioI: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 %----The translated axioms
% 0.16/0.39 thf(ax,axiom,
% 0.16/0.39 likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i ).
% 0.16/0.39
% 0.16/0.39 thf(ax_001,axiom,
% 0.16/0.39 likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i ).
% 0.16/0.39
% 0.16/0.39 thf(ax_002,axiom,
% 0.16/0.39 ? [X: $i,Y: $i] : ( (~) @ ( parent_THFTYPE_IiioI @ X @ Y ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ax_003,axiom,
% 0.16/0.39 ? [X: $i,Y: $i] : ( (~) @ ( likes_THFTYPE_IiioI @ X @ Y ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ax_004,axiom,
% 0.16/0.39 parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i ).
% 0.16/0.39
% 0.16/0.39 thf(ax_005,axiom,
% 0.16/0.39 parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i ).
% 0.16/0.39
% 0.16/0.39 thf(ax_006,axiom,
% 0.16/0.39 likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i ).
% 0.16/0.39
% 0.16/0.39 thf(ax_007,axiom,
% 0.16/0.39 parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i ).
% 0.16/0.39
% 0.16/0.39 thf(ax_008,axiom,
% 0.16/0.39 parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ).
% 0.16/0.39
% 0.16/0.39 %----The translated conjecture
% 0.16/0.39 thf(con,conjecture,
% 0.16/0.39 ? [Q: $i > $i > $o,R: $i > $i > $o,Y: $i] :
% 0.16/0.39 ( ( R @ Y @ lBill_THFTYPE_i )
% 0.16/0.39 & ( Q @ Y @ lAnna_THFTYPE_i )
% 0.16/0.39 & ( (~)
% 0.16/0.39 @ ( R
% 0.16/0.39 = ( ^ [Z: $i,W: $i] : $true ) ) )
% 0.16/0.39 & ( (~)
% 0.16/0.39 @ ( Q
% 0.16/0.39 = ( ^ [Z: $i,W: $i] : $true ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.59/1.30 ---- Embedded in THF ---
% 1.59/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.59/1.30 %%% Generated on Tue Feb 24 05:50:57 EST 2026
% 1.59/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.59/1.30 %%% Logic specification used:
% 1.59/1.30 %%% thf(spec, logic, $$dhol).
% 1.59/1.30
% 1.59/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QpZq09L7KZ/DTF2DTF7102.p
% See solution above
% 1.59/1.30 ------------------------
% 1.59/1.31 ---- Cleaned THF ---
% 1.59/1.31 thf(numbers,type,
% 1.59/1.31 num: $tType ).
% 1.59/1.31
% 1.59/1.31 thf(lAnna_THFTYPE_i,type,
% 1.59/1.31 lAnna_THFTYPE_i: $i ).
% 1.59/1.31
% 1.59/1.31 thf(lBen_THFTYPE_i,type,
% 1.59/1.31 lBen_THFTYPE_i: $i ).
% 1.59/1.31
% 1.59/1.31 thf(lBill_THFTYPE_i,type,
% 1.59/1.31 lBill_THFTYPE_i: $i ).
% 1.59/1.31
% 1.59/1.31 thf(lBob_THFTYPE_i,type,
% 1.59/1.31 lBob_THFTYPE_i: $i ).
% 1.59/1.31
% 1.59/1.31 thf(lMary_THFTYPE_i,type,
% 1.59/1.31 lMary_THFTYPE_i: $i ).
% 1.59/1.31
% 1.59/1.31 thf(lSue_THFTYPE_i,type,
% 1.59/1.31 lSue_THFTYPE_i: $i ).
% 1.59/1.31
% 1.59/1.31 thf(likes_THFTYPE_IiioI,type,
% 1.59/1.31 likes_THFTYPE_IiioI: $i > $i > $o ).
% 1.59/1.31
% 1.59/1.31 thf(parent_THFTYPE_IiioI,type,
% 1.59/1.31 parent_THFTYPE_IiioI: $i > $i > $o ).
% 1.59/1.31
% 1.59/1.31 thf(ax,axiom,
% 1.59/1.31 likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i ).
% 1.59/1.31
% 1.59/1.31 thf(ax_001,axiom,
% 1.59/1.31 likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i ).
% 1.59/1.31
% 1.59/1.31 thf(ax_002,axiom,
% 1.59/1.31 ? [X: $i,Y: $i] : ( (~) @ ( parent_THFTYPE_IiioI @ X @ Y ) ) ).
% 1.59/1.31
% 1.59/1.31 thf(ax_003,axiom,
% 1.59/1.31 ? [X: $i,Y: $i] : ( (~) @ ( likes_THFTYPE_IiioI @ X @ Y ) ) ).
% 1.59/1.31
% 1.59/1.31 thf(ax_004,axiom,
% 1.59/1.31 parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i ).
% 1.59/1.31
% 1.59/1.31 thf(ax_005,axiom,
% 1.59/1.31 parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i ).
% 1.59/1.31
% 1.59/1.31 thf(ax_006,axiom,
% 1.59/1.31 likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i ).
% 1.59/1.31
% 1.59/1.31 thf(ax_007,axiom,
% 1.59/1.31 parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i ).
% 1.59/1.31
% 1.59/1.31 thf(ax_008,axiom,
% 1.59/1.31 parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ).
% 1.59/1.31
% 1.59/1.31 thf(con,conjecture,
% 1.59/1.31 ? [Q: $i > $i > $o,R: $i > $i > $o,Y: $i] :
% 1.59/1.31 ( ( R @ Y @ lBill_THFTYPE_i )
% 1.59/1.31 & ( Q @ Y @ lAnna_THFTYPE_i )
% 1.59/1.31 & ( (~)
% 1.59/1.31 @ ( R
% 1.59/1.31 = ( ^ [Z: $i,W: $i] : $true ) ) )
% 1.59/1.31 & ( (~)
% 1.59/1.31 @ ( Q
% 1.59/1.31 = ( ^ [Z: $i,W: $i] : $true ) ) ) ) ).
% 1.59/1.31 ------------------------
% 1.59/1.33 % (7200)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7102 for (2999ds/183Mi)
% 1.59/1.33 % (7203)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7102 for (2999ds/2Mi)
% 1.59/1.33 % (7202)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_7102 for (2999ds/27Mi)
% 1.59/1.33 % (7206)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7102 for (2999ds/18Mi)
% 1.59/1.33 % (7204)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_7102 for (2999ds/2Mi)
% 1.59/1.33 % (7201)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_7102 for (2999ds/4Mi)
% 1.59/1.33 % (7205)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_7102 for (2999ds/275Mi)
% 1.59/1.34 % (7203)Instruction limit reached!
% 1.59/1.34 % (7203)------------------------------
% 1.59/1.34 % (7203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (7203)Termination reason: Unknown
% 1.59/1.34 % (7203)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (7204)Instruction limit reached!
% 1.59/1.34 % (7204)------------------------------
% 1.59/1.34 % (7204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (7203)Memory used [KB]: 5500
% 1.59/1.34 % (7203)Time elapsed: 0.003 s
% 1.59/1.34 % (7203)Instructions burned: 2 (million)
% 1.59/1.34 % (7203)------------------------------
% 1.59/1.34 % (7203)------------------------------
% 1.59/1.34 % (7204)Termination reason: Unknown
% 1.59/1.34 % (7204)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (7204)Memory used [KB]: 1023
% 1.59/1.34 % (7204)Time elapsed: 0.003 s
% 1.59/1.34 % (7204)Instructions burned: 2 (million)
% 1.59/1.34 % (7204)------------------------------
% 1.59/1.34 % (7204)------------------------------
% 1.59/1.34 % (7201)Instruction limit reached!
% 1.59/1.34 % (7201)------------------------------
% 1.59/1.34 % (7201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (7201)Termination reason: Unknown
% 1.59/1.34 % (7201)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (7201)Memory used [KB]: 5500
% 1.59/1.34 % (7201)Time elapsed: 0.005 s
% 1.59/1.34 % (7201)Instructions burned: 5 (million)
% 1.59/1.34 % (7201)------------------------------
% 1.59/1.34 % (7201)------------------------------
% 1.59/1.34 % (7202)First to succeed.
% 1.59/1.34 % (7206)Instruction limit reached!
% 1.59/1.34 % (7206)------------------------------
% 1.59/1.34 % (7206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (7206)Termination reason: Unknown
% 1.59/1.34 % (7206)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (7206)Memory used [KB]: 5628
% 1.59/1.34 % (7206)Time elapsed: 0.011 s
% 1.59/1.34 % (7206)Instructions burned: 18 (million)
% 1.59/1.34 % (7206)------------------------------
% 1.59/1.34 % (7206)------------------------------
% 1.59/1.34 % (7202)Refutation found. Thanks to Tanya!
% 1.59/1.34 % SZS status Theorem for DTF2THF_7102
% 1.59/1.34 % SZS output start Proof for DTF2THF_7102
% 1.59/1.34 thf(func_def_0, type, num: $tType).
% 1.59/1.34 thf(func_def_7, type, likes_THFTYPE_IiioI: $i > $i > $o).
% 1.59/1.34 thf(func_def_8, type, parent_THFTYPE_IiioI: $i > $i > $o).
% 1.59/1.34 thf(func_def_11, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.59/1.34 thf(func_def_21, type, ph5: !>[X0: $tType]:(X0)).
% 1.59/1.34 thf(f150,plain,(
% 1.59/1.34 $false),
% 1.59/1.34 inference(avatar_sat_refutation,[status(thm)],[f87,f95,f149])).
% 1.59/1.34 thf(f149,plain,(
% 1.59/1.34 ~spl4_1),
% 1.59/1.34 inference(avatar_contradiction_clause,[status(thm)],[f148])).
% 1.59/1.34 thf(f148,plain,(
% 1.59/1.34 $false | ~spl4_1),
% 1.59/1.34 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.59/1.34 thf(f144,plain,(
% 1.59/1.34 ($false = $true) | ~spl4_1),
% 1.59/1.34 inference(superposition,[status(thm)],[f53,f140])).
% 1.59/1.34 thf(f140,plain,(
% 1.59/1.34 ( ! [X2 : $i,X1 : $i] : (((parent_THFTYPE_IiioI @ X1 @ X2) = $true)) ) | ~spl4_1),
% 1.59/1.34 inference(beta_eta_normalization,[status(thm)],[f139])).
% 1.59/1.34 thf(f139,plain,(
% 1.59/1.34 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ($true)) @ X2) = (parent_THFTYPE_IiioI @ X1 @ X2))) ) | ~spl4_1),
% 1.59/1.34 inference(argument_congruence,[status(thm)],[f110])).
% 1.59/1.34 thf(f110,plain,(
% 1.59/1.34 ( ! [X1 : $i] : (((parent_THFTYPE_IiioI @ X1) = (^[Y0 : $i]: ($true)))) ) | ~spl4_1),
% 1.59/1.34 inference(beta_eta_normalization,[status(thm)],[f109])).
% 1.59/1.34 thf(f109,plain,(
% 1.59/1.34 ( ! [X1 : $i] : (((parent_THFTYPE_IiioI @ X1) = ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1))) ) | ~spl4_1),
% 1.59/1.34 inference(argument_congruence,[status(thm)],[f100])).
% 1.59/1.34 thf(f100,plain,(
% 1.59/1.34 (parent_THFTYPE_IiioI = (^[Y0 : $i]: ((^[Y1 : $i]: ($true))))) | ~spl4_1),
% 1.59/1.34 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.59/1.34 thf(f99,plain,(
% 1.59/1.34 (parent_THFTYPE_IiioI = (^[Y0 : $i]: ((^[Y1 : $i]: ($true))))) | ($true != $true) | ~spl4_1),
% 1.59/1.34 inference(superposition,[status(thm)],[f62,f45])).
% 1.59/1.34 thf(f45,plain,(
% 1.59/1.34 ((parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i) = $true)),
% 1.59/1.34 inference(cnf_transformation,[status(thm)],[f14])).
% 1.59/1.34 thf(f14,plain,(
% 1.59/1.34 ((parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i) = $true)),
% 1.59/1.34 inference(fool_elimination,[status(thm)],[f13])).
% 1.59/1.34 thf(f13,plain,(
% 1.59/1.34 (parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i)),
% 1.59/1.34 inference(rectify,[status(thm)],[f9])).
% 1.59/1.34 thf(f9,axiom,(
% 1.59/1.34 (parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i)),
% 1.59/1.34 file('/export/starexec/sandbox/tmp/tmp.QpZq09L7KZ/DTF2THF_7102.p',ax_008)).
% 1.59/1.34 thf(f62,plain,(
% 1.59/1.34 ( ! [X0 : $i > $i > $o] : (($true != (X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i)) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = X0)) ) | ~spl4_1),
% 1.59/1.34 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.59/1.34 thf(f61,definition,(
% 1.59/1.34 spl4_1 <=> ! [X0 : $i > $i > $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = X0) | ($true != (X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i)))),
% 1.59/1.34 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.59/1.34 thf(f53,plain,(
% 1.59/1.34 ((parent_THFTYPE_IiioI @ sK0 @ sK1) = $false)),
% 1.59/1.34 inference(not_proxy_clausification,[status(thm)],[f44])).
% 1.59/1.34 thf(f44,plain,(
% 1.59/1.34 ((~ (parent_THFTYPE_IiioI @ sK0 @ sK1)) = $true)),
% 1.59/1.34 inference(cnf_transformation,[status(thm)],[f35])).
% 1.59/1.34 thf(f35,plain,(
% 1.59/1.34 ((~ (parent_THFTYPE_IiioI @ sK0 @ sK1)) = $true)),
% 1.59/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f20,f34])).
% 1.59/1.34 thf(f34,plain,(
% 1.59/1.34 ? [X0 : $i,X1 : $i] : ((~ (parent_THFTYPE_IiioI @ X0 @ X1)) = $true) => ((~ (parent_THFTYPE_IiioI @ sK0 @ sK1)) = $true)),
% 1.59/1.34 introduced(definition,[],[choice_axiom])).
% 1.59/1.34 thf(f20,plain,(
% 1.59/1.34 ? [X0 : $i,X1 : $i] : ((~ (parent_THFTYPE_IiioI @ X0 @ X1)) = $true)),
% 1.59/1.34 inference(fool_elimination,[status(thm)],[f19])).
% 1.59/1.34 thf(f19,plain,(
% 1.59/1.34 ? [X0 : $i,X1 : $i] : (~ (parent_THFTYPE_IiioI @ X0 @ X1))),
% 1.59/1.34 inference(rectify,[status(thm)],[f3])).
% 1.59/1.34 thf(f3,axiom,(
% 1.59/1.34 ? [X0 : $i,X1 : $i] : (~ (parent_THFTYPE_IiioI @ X0 @ X1))),
% 1.59/1.34 file('/export/starexec/sandbox/tmp/tmp.QpZq09L7KZ/DTF2THF_7102.p',ax_002)).
% 1.59/1.34 thf(f95,plain,(
% 1.59/1.34 spl4_2 | spl4_1),
% 1.59/1.34 inference(avatar_split_clause,[status(thm)],[f92,f61,f64])).
% 1.59/1.34 thf(f64,definition,(
% 1.59/1.34 spl4_2 <=> (likes_THFTYPE_IiioI = (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))))),
% 1.59/1.34 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.59/1.34 thf(f92,plain,(
% 1.59/1.34 ( ! [X0 : $i > $i > $o] : ((likes_THFTYPE_IiioI = (^[Y0 : $i]: ((^[Y1 : $i]: ($true))))) | ($true != (X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i)) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = X0)) )),
% 1.59/1.34 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.59/1.34 thf(f90,plain,(
% 1.59/1.34 ( ! [X0 : $i > $i > $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = X0) | ($true != $true) | ($true != (X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i)) | (likes_THFTYPE_IiioI = (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))))) )),
% 1.59/1.34 inference(superposition,[status(thm)],[f52,f42])).
% 1.59/1.34 thf(f42,plain,(
% 1.59/1.34 ((likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i) = $true)),
% 1.59/1.34 inference(cnf_transformation,[status(thm)],[f28])).
% 1.59/1.34 thf(f28,plain,(
% 1.59/1.34 ((likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i) = $true)),
% 1.59/1.34 inference(fool_elimination,[status(thm)],[f27])).
% 1.59/1.34 thf(f27,plain,(
% 1.59/1.34 (likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i)),
% 1.59/1.34 inference(rectify,[status(thm)],[f2])).
% 1.59/1.34 thf(f2,axiom,(
% 1.59/1.34 (likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i)),
% 1.59/1.34 file('/export/starexec/sandbox/tmp/tmp.QpZq09L7KZ/DTF2THF_7102.p',ax_001)).
% 1.59/1.34 thf(f52,plain,(
% 1.59/1.34 ( ! [X2 : $i > $i > $o,X0 : $i,X1 : $i > $i > $o] : (((X2 @ X0 @ lBill_THFTYPE_i) != $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = X1) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = X2) | ((X1 @ X0 @ lAnna_THFTYPE_i) != $true)) )),
% 1.59/1.34 inference(equality_proxy_clausification,[status(thm)],[f51])).
% 1.59/1.34 thf(f51,plain,(
% 1.59/1.34 ( ! [X2 : $i > $i > $o,X0 : $i,X1 : $i > $i > $o] : (((X2 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true))))) = $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = X1) | ((X2 @ X0 @ lBill_THFTYPE_i) != $true) | ((X1 @ X0 @ lAnna_THFTYPE_i) != $true)) )),
% 1.59/1.34 inference(not_proxy_clausification,[status(thm)],[f50])).
% 1.59/1.34 thf(f50,plain,(
% 1.59/1.34 ( ! [X2 : $i > $i > $o,X0 : $i,X1 : $i > $i > $o] : (((~ (X2 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))))) != $true) | ((X1 @ X0 @ lAnna_THFTYPE_i) != $true) | ((X2 @ X0 @ lBill_THFTYPE_i) != $true) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = X1)) )),
% 1.59/1.34 inference(equality_proxy_clausification,[status(thm)],[f49])).
% 1.59/1.34 thf(f49,plain,(
% 1.59/1.34 ( ! [X2 : $i > $i > $o,X0 : $i,X1 : $i > $i > $o] : (((X1 @ X0 @ lAnna_THFTYPE_i) != $true) | ((X1 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true))))) = $true) | ((~ (X2 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))))) != $true) | ((X2 @ X0 @ lBill_THFTYPE_i) != $true)) )),
% 1.59/1.34 inference(not_proxy_clausification,[status(thm)],[f38])).
% 1.59/1.34 thf(f38,plain,(
% 1.59/1.34 ( ! [X2 : $i > $i > $o,X0 : $i,X1 : $i > $i > $o] : (((~ (X1 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))))) != $true) | ((~ (X2 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))))) != $true) | ((X1 @ X0 @ lAnna_THFTYPE_i) != $true) | ((X2 @ X0 @ lBill_THFTYPE_i) != $true)) )),
% 1.59/1.34 inference(cnf_transformation,[status(thm)],[f33])).
% 1.59/1.34 thf(f33,plain,(
% 1.59/1.34 ! [X0 : $i,X1 : $i > $i > $o,X2 : $i > $i > $o] : (((X2 @ X0 @ lBill_THFTYPE_i) != $true) | ((X1 @ X0 @ lAnna_THFTYPE_i) != $true) | ((~ (X1 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))))) != $true) | ((~ (X2 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))))) != $true))),
% 1.59/1.34 inference(ennf_transformation,[status(thm)],[f16])).
% 1.59/1.34 thf(f16,plain,(
% 1.59/1.34 ~? [X0 : $i,X1 : $i > $i > $o,X2 : $i > $i > $o] : (((X1 @ X0 @ lAnna_THFTYPE_i) = $true) & ((~ (X1 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))))) = $true) & ((X2 @ X0 @ lBill_THFTYPE_i) = $true) & ((~ (X2 = (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))))) = $true))),
% 1.59/1.34 inference(fool_elimination,[status(thm)],[f15])).
% 1.59/1.34 thf(f15,plain,(
% 1.59/1.34 ~? [X0 : $i,X1 : $i > $i > $o,X2 : $i > $i > $o] : ((~ (X1 = (^[X3 : $i, X4 : $i] : ($true)))) & (~ (X2 = (^[X5 : $i, X6 : $i] : ($true)))) & (X1 @ X0 @ lAnna_THFTYPE_i) & (X2 @ X0 @ lBill_THFTYPE_i))),
% 1.59/1.34 inference(rectify,[status(thm)],[f11])).
% 1.59/1.34 thf(f11,negated_conjecture,(
% 1.59/1.34 ~? [X1 : $i,X2 : $i > $i > $o,X3 : $i > $i > $o] : ((~ (X2 = (^[X4 : $i, X5 : $i] : ($true)))) & (~ (X3 = (^[X4 : $i, X5 : $i] : ($true)))) & (X2 @ X1 @ lAnna_THFTYPE_i) & (X3 @ X1 @ lBill_THFTYPE_i))),
% 1.59/1.34 inference(negated_conjecture,[status(cth)],[f10])).
% 1.59/1.34 thf(f10,conjecture,(
% 1.59/1.34 ? [X1 : $i,X2 : $i > $i > $o,X3 : $i > $i > $o] : ((~ (X2 = (^[X4 : $i, X5 : $i] : ($true)))) & (~ (X3 = (^[X4 : $i, X5 : $i] : ($true)))) & (X2 @ X1 @ lAnna_THFTYPE_i) & (X3 @ X1 @ lBill_THFTYPE_i))),
% 1.59/1.34 file('/export/starexec/sandbox/tmp/tmp.QpZq09L7KZ/DTF2THF_7102.p',con)).
% 1.59/1.34 thf(f87,plain,(
% 1.59/1.34 ~spl4_2),
% 1.59/1.34 inference(avatar_contradiction_clause,[status(thm)],[f86])).
% 1.59/1.34 thf(f86,plain,(
% 1.59/1.34 $false | ~spl4_2),
% 1.59/1.34 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.59/1.34 thf(f83,plain,(
% 1.59/1.34 ($false = $true) | ~spl4_2),
% 1.59/1.34 inference(superposition,[status(thm)],[f48,f81])).
% 1.59/1.34 thf(f81,plain,(
% 1.59/1.34 ( ! [X2 : $i,X1 : $i] : (((likes_THFTYPE_IiioI @ X1 @ X2) = $true)) ) | ~spl4_2),
% 1.59/1.34 inference(beta_eta_normalization,[status(thm)],[f80])).
% 1.59/1.34 thf(f80,plain,(
% 1.59/1.34 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ($true)) @ X2) = (likes_THFTYPE_IiioI @ X1 @ X2))) ) | ~spl4_2),
% 1.59/1.34 inference(argument_congruence,[status(thm)],[f78])).
% 1.59/1.34 thf(f78,plain,(
% 1.59/1.34 ( ! [X1 : $i] : (((^[Y0 : $i]: ($true)) = (likes_THFTYPE_IiioI @ X1))) ) | ~spl4_2),
% 1.59/1.34 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.59/1.34 thf(f77,plain,(
% 1.59/1.34 ( ! [X1 : $i] : (((likes_THFTYPE_IiioI @ X1) = ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1))) ) | ~spl4_2),
% 1.59/1.34 inference(argument_congruence,[status(thm)],[f66])).
% 1.59/1.34 thf(f66,plain,(
% 1.59/1.34 (likes_THFTYPE_IiioI = (^[Y0 : $i]: ((^[Y1 : $i]: ($true))))) | ~spl4_2),
% 1.59/1.34 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.59/1.34 thf(f48,plain,(
% 1.59/1.34 ((likes_THFTYPE_IiioI @ sK2 @ sK3) = $false)),
% 1.59/1.34 inference(not_proxy_clausification,[status(thm)],[f46])).
% 1.59/1.34 thf(f46,plain,(
% 1.59/1.34 ((~ (likes_THFTYPE_IiioI @ sK2 @ sK3)) = $true)),
% 1.59/1.34 inference(cnf_transformation,[status(thm)],[f37])).
% 1.59/1.34 thf(f37,plain,(
% 1.59/1.34 ((~ (likes_THFTYPE_IiioI @ sK2 @ sK3)) = $true)),
% 1.59/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f24,f36])).
% 1.59/1.34 thf(f36,plain,(
% 1.59/1.34 ? [X0 : $i,X1 : $i] : ((~ (likes_THFTYPE_IiioI @ X0 @ X1)) = $true) => ((~ (likes_THFTYPE_IiioI @ sK2 @ sK3)) = $true)),
% 1.59/1.34 introduced(definition,[],[choice_axiom])).
% 1.59/1.34 thf(f24,plain,(
% 1.59/1.34 ? [X0 : $i,X1 : $i] : ((~ (likes_THFTYPE_IiioI @ X0 @ X1)) = $true)),
% 1.59/1.34 inference(fool_elimination,[status(thm)],[f23])).
% 1.59/1.34 thf(f23,plain,(
% 1.59/1.34 ? [X0 : $i,X1 : $i] : (~ (likes_THFTYPE_IiioI @ X0 @ X1))),
% 1.59/1.34 inference(rectify,[status(thm)],[f4])).
% 1.59/1.34 thf(f4,axiom,(
% 1.59/1.34 ? [X0 : $i,X1 : $i] : (~ (likes_THFTYPE_IiioI @ X0 @ X1))),
% 1.59/1.34 file('/export/starexec/sandbox/tmp/tmp.QpZq09L7KZ/DTF2THF_7102.p',ax_003)).
% 1.59/1.34 % SZS output end Proof for DTF2THF_7102
% 1.59/1.34 % (7202)------------------------------
% 1.59/1.34 % (7202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (7202)Termination reason: Refutation
% 1.59/1.34
% 1.59/1.34 % (7202)Memory used [KB]: 5628
% 1.59/1.34 % (7202)Time elapsed: 0.010 s
% 1.59/1.34 % (7202)Instructions burned: 12 (million)
% 1.59/1.34 % (7202)------------------------------
% 1.59/1.34 % (7202)------------------------------
% 1.59/1.34 % (7199)Success in time 0.025 s
%------------------------------------------------------------------------------