%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : CSR137^1 : 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 : n022.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 08:43:06 AM UTC 2026
% Result : Theorem 1.73s 1.45s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 315 ( 80 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 436 ( 81 ~; 53 |; 12 &; 254 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 11 con; 0-2 aty)
% ( 34 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 130 ( 28 ^; 90 !; 12 ?; 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_19,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f108,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f73,f99,f106]) ).
thf(f106,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f105]) ).
thf(f105,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f50,f69]) ).
thf(f69,plain,
( ! [X3: $i,X4: $i] :
( ( likes_THFTYPE_IiioI @ X3 @ X4 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f68]) ).
thf(f68,definition,
( spl0_1
<=> ! [X4: $i,X3: $i] :
( ( likes_THFTYPE_IiioI @ X3 @ X4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f50,plain,
( ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ~ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ~ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i ) )
= $true ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
~ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
~ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i ),
file('/export/starexec/sandbox/tmp/tmp.yKmfGHnlUw/DTF2THF_2804.p',ax_001) ).
thf(f99,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f98]) ).
thf(f98,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f49,f83]) ).
thf(f83,plain,
( ! [X0: $i,X1: $i] :
( ( parent_THFTYPE_IiioI @ X0 @ X1 )
= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ! [X0: $i,X1: $i] :
( ( ( parent_THFTYPE_IiioI @ X0 @ X1 )
= $true )
| ( $true != $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f72,f40]) ).
thf(f40,plain,
( ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i )
= $true ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i )
= $true ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,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.yKmfGHnlUw/DTF2THF_2804.p',ax_008) ).
thf(f72,plain,
( ! [X2: $i,X0: $i > $i > $o,X1: $i] :
( ( ( X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i )
!= $true )
| ( ( X0 @ X1 @ X2 )
= $true ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f71]) ).
thf(f71,definition,
( spl0_2
<=> ! [X2: $i,X0: $i > $i > $o,X1: $i] :
( ( ( X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i )
!= $true )
| ( ( X0 @ X1 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f49,plain,
( ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ~ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ~ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i ) )
= $true ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
~ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
~ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i ),
file('/export/starexec/sandbox/tmp/tmp.yKmfGHnlUw/DTF2THF_2804.p',ax_005) ).
thf(f73,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f66,f71,f68]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i,X4: $i] :
( ( ( X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i )
!= $true )
| ( ( likes_THFTYPE_IiioI @ X3 @ X4 )
= $true )
| ( ( X0 @ X1 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i,X4: $i] :
( ( ( X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i )
!= $true )
| ( ( X0 @ X1 @ X2 )
= $true )
| ( ( likes_THFTYPE_IiioI @ X3 @ X4 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f60,f42]) ).
thf(f42,plain,
( ( likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i )
= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i,
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i,
file('/export/starexec/sandbox/tmp/tmp.yKmfGHnlUw/DTF2THF_2804.p',ax_002) ).
thf(f60,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o,X6: $i,X4: $i,X5: $i] :
( ( ( X1 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( X0 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( $true
= ( X0 @ X5 @ X6 ) )
| ( ( X1 @ X4 @ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( ( X1 @ X4 @ X3 )
= $true )
| ( ( !! @ $i @ ( X0 @ X5 ) )
= $true )
| ( ( X0 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X1 @ X2 @ lBill_THFTYPE_i )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( ( X1 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( X0 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( ^ [Y0: $i] : ( !! @ $i @ ( X0 @ Y0 ) )
@ X5 )
= $true )
| ( ( X1 @ X4 @ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] : ( !! @ $i @ ( X0 @ Y0 ) ) )
= $true )
| ( ( X0 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X1 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( X1 @ X4 @ X3 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o,X4: $i] :
( ( ( X0 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] : ( !! @ $i @ ( X0 @ Y0 ) ) ) )
!= $true )
| ( ( X1 @ X4 @ X3 )
= $true )
| ( ( X1 @ X2 @ lBill_THFTYPE_i )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o,X4: $i] :
( ( ( ^ [Y0: $i] : ( X1 @ Y0 @ X3 )
@ X4 )
= $true )
| ( ( X1 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( X0 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] : ( !! @ $i @ ( X0 @ Y0 ) ) ) )
!= $true ) ),
inference(pi_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] : ( X1 @ Y0 @ X3 ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] : ( !! @ $i @ ( X0 @ Y0 ) ) ) )
!= $true )
| ( ( X1 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( X0 @ X2 @ lAnna_THFTYPE_i )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( X1 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X1 @ Y1 @ Y0 ) )
@ X3 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] : ( !! @ $i @ ( X0 @ Y0 ) ) ) )
!= $true )
| ( ( X0 @ X2 @ lAnna_THFTYPE_i )
!= $true ) ),
inference(pi_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X1 @ Y1 @ Y0 ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] : ( !! @ $i @ ( X0 @ Y0 ) ) ) )
!= $true )
| ( ( X0 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X1 @ X2 @ lBill_THFTYPE_i )
!= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X1 @ Y1 @ Y0 ) ) ) )
!= $true )
| ( ( X1 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] : ( !! @ $i @ ( X0 @ Y0 ) ) ) )
!= $true )
| ( ( X0 @ X2 @ lAnna_THFTYPE_i )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( X0 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
!= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X1 @ Y1 @ Y0 ) ) ) )
!= $true )
| ( ( X1 @ X2 @ lBill_THFTYPE_i )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
!= $true )
| ( ( X0 @ X2 @ lAnna_THFTYPE_i )
!= $true )
| ( ( X1 @ X2 @ lBill_THFTYPE_i )
!= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X1 @ Y1 @ Y0 ) ) ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
~ ? [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i] :
( ( ( X0 @ X2 @ lAnna_THFTYPE_i )
= $true )
& ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
= $true )
& ( ( X1 @ X2 @ lBill_THFTYPE_i )
= $true )
& ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X1 @ Y1 @ Y0 ) ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
~ ? [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i] :
( ~ ! [X3: $i,X4: $i] : ( X0 @ X4 @ X3 )
& ~ ! [X5: $i,X6: $i] : ( X1 @ X5 @ X6 )
& ( X1 @ X2 @ lBill_THFTYPE_i )
& ( X0 @ X2 @ lAnna_THFTYPE_i ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,negated_conjecture,
~ ? [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i] :
( ~ ! [X4: $i,X3: $i] : ( X0 @ X3 @ X4 )
& ~ ! [X3: $i,X4: $i] : ( X1 @ X3 @ X4 )
& ( X1 @ X2 @ lBill_THFTYPE_i )
& ( X0 @ X2 @ lAnna_THFTYPE_i ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f11,conjecture,
? [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i] :
( ~ ! [X4: $i,X3: $i] : ( X0 @ X3 @ X4 )
& ~ ! [X3: $i,X4: $i] : ( X1 @ X3 @ X4 )
& ( X1 @ X2 @ lBill_THFTYPE_i )
& ( X0 @ X2 @ lAnna_THFTYPE_i ) ),
file('/export/starexec/sandbox/tmp/tmp.yKmfGHnlUw/DTF2THF_2804.p',con) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : CSR137^1 : 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
% 0.12/0.30 % Computer : n022.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 05:52:06 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.41 ---- Original DTF file ---
% 0.18/0.41 thf(spec,logic,$$dhol).
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 % File : CSR137^1 : TPTP v9.2.1. Released v4.1.0.
% 0.18/0.41 % Domain : Commonsense Reasoning
% 0.18/0.41 % Problem : Feelings from people to Bill and Anna
% 0.18/0.41 % Version : Especial.
% 0.18/0.41 % English : Do there exist relations ?R and ?Q so that ?R holds between a
% 0.18/0.41 % person ?Y and Bill and ?Q between ?Y and Anna.
% 0.18/0.41
% 0.18/0.41 % Refs : [Ben10] Benzmueller (2010), Email to Geoff Sutcliffe
% 0.18/0.41 % Source : [Ben10]
% 0.18/0.41 % Names : rv_3.tq_SUMO_local [Ben10]
% 0.18/0.41
% 0.18/0.41 % Status : Theorem
% 0.18/0.41 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 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 v6.1.0, 0.50 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.1.0
% 0.18/0.41 % Syntax : Number of formulae : 20 ( 7 unt; 9 typ; 0 def)
% 0.18/0.41 % Number of atoms : 15 ( 0 equ; 5 cnn)
% 0.18/0.41 % Maximal formula atoms : 2 ( 1 avg)
% 0.18/0.41 % Number of connectives : 41 ( 5 ~; 0 |; 3 &; 33 @)
% 0.18/0.41 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.41 % Maximal formula depth : 12 ( 4 avg)
% 0.18/0.41 % Number of types : 3 ( 1 usr)
% 0.18/0.41 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.18/0.41 % Number of symbols : 9 ( 8 usr; 7 con; 0-2 aty)
% 0.18/0.41 % Number of variables : 7 ( 0 ^; 4 !; 3 ?; 7 :)
% 0.18/0.41 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.41
% 0.18/0.41 % Comments : This is a simple test problem for reasoning in/about SUMO.
% 0.18/0.41 % Initally the problem has been hand generated in KIF syntax in
% 0.18/0.41 % SigmaKEE and then automatically translated by Benzmueller's
% 0.18/0.41 % KIF2TH0 translator into THF syntax.
% 0.18/0.41 % : The translation has been applied in two modes: local and SInE.
% 0.18/0.41 % The local mode only translates the local assumptions and the
% 0.18/0.41 % query. The SInE mode additionally translates the SInE-extract
% 0.18/0.41 % of the loaded knowledge base (usually SUMO).
% 0.18/0.41 % : The examples are selected to illustrate the benefits of
% 0.18/0.41 % higher-order reasoning in ontology reasoning.
% 0.18/0.41 % : Note that the universal predicates are excluded for ?R and Q?
% 0.18/0.41 % with the second and third conjuncts in the query.
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 %----The extracted signature
% 0.18/0.41 thf(numbers,type,
% 0.18/0.41 num: $tType ).
% 0.18/0.41
% 0.18/0.41 thf(lAnna_THFTYPE_i,type,
% 0.18/0.41 lAnna_THFTYPE_i: $i ).
% 0.18/0.41
% 0.18/0.41 thf(lBen_THFTYPE_i,type,
% 0.18/0.41 lBen_THFTYPE_i: $i ).
% 0.18/0.41
% 0.18/0.41 thf(lBill_THFTYPE_i,type,
% 0.18/0.41 lBill_THFTYPE_i: $i ).
% 0.18/0.41
% 0.18/0.41 thf(lBob_THFTYPE_i,type,
% 0.18/0.41 lBob_THFTYPE_i: $i ).
% 0.18/0.41
% 0.18/0.41 thf(lMary_THFTYPE_i,type,
% 0.18/0.41 lMary_THFTYPE_i: $i ).
% 0.18/0.41
% 0.18/0.41 thf(lSue_THFTYPE_i,type,
% 0.18/0.41 lSue_THFTYPE_i: $i ).
% 0.18/0.41
% 0.18/0.41 thf(likes_THFTYPE_IiioI,type,
% 0.18/0.41 likes_THFTYPE_IiioI: $i > $i > $o ).
% 0.18/0.41
% 0.18/0.41 thf(parent_THFTYPE_IiioI,type,
% 0.18/0.41 parent_THFTYPE_IiioI: $i > $i > $o ).
% 0.18/0.41
% 0.18/0.41 %----The translated axioms
% 0.18/0.41 thf(ax,axiom,
% 0.18/0.41 likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i ).
% 0.18/0.41
% 0.18/0.41 thf(ax_001,axiom,
% 0.18/0.41 (~) @ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i ) ).
% 0.18/0.41
% 0.18/0.41 thf(ax_002,axiom,
% 0.18/0.41 likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i ).
% 0.18/0.41
% 0.18/0.41 thf(ax_003,axiom,
% 0.18/0.41 parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i ).
% 0.18/0.41
% 0.18/0.41 thf(ax_004,axiom,
% 0.18/0.41 parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i ).
% 0.18/0.41
% 0.18/0.41 thf(ax_005,axiom,
% 0.18/0.41 (~) @ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i ) ).
% 0.18/0.41
% 0.18/0.41 thf(ax_006,axiom,
% 0.18/0.41 likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i ).
% 0.18/0.41
% 0.18/0.41 thf(ax_007,axiom,
% 0.18/0.41 parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i ).
% 0.18/0.41
% 0.18/0.41 thf(ax_008,axiom,
% 0.18/0.41 parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ).
% 0.18/0.41
% 0.18/0.41 thf(ax_009,axiom,
% 0.18/0.41 (~) @ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i ) ).
% 0.18/0.41
% 0.18/0.41 %----The translated conjecture
% 0.18/0.41 thf(con,conjecture,
% 0.18/0.41 ? [Q: $i > $i > $o,R: $i > $i > $o,Y: $i] :
% 0.18/0.41 ( ( R @ Y @ lBill_THFTYPE_i )
% 0.18/0.41 & ( Q @ Y @ lAnna_THFTYPE_i )
% 0.18/0.41 & ( (~)
% 0.18/0.41 @ ! [A: $i,B: $i] : ( R @ A @ B ) )
% 0.18/0.41 & ( (~)
% 0.18/0.41 @ ! [A: $i,B: $i] : ( Q @ A @ B ) ) ) ).
% 0.18/0.41
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 ------------------------
% 1.73/1.41 ---- Embedded in THF ---
% 1.73/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.73/1.41 %%% Generated on Tue Feb 24 05:52:07 EST 2026
% 1.73/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.73/1.41 %%% Logic specification used:
% 1.73/1.41 %%% thf(spec, logic, $$dhol).
% 1.73/1.41
% 1.73/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.yKmfGHnlUw/DTF2DTF2804.p
% See solution above
% 1.73/1.41 ------------------------
% 1.73/1.42 ---- Cleaned THF ---
% 1.73/1.42 thf(numbers,type,
% 1.73/1.42 num: $tType ).
% 1.73/1.42
% 1.73/1.42 thf(lAnna_THFTYPE_i,type,
% 1.73/1.42 lAnna_THFTYPE_i: $i ).
% 1.73/1.42
% 1.73/1.42 thf(lBen_THFTYPE_i,type,
% 1.73/1.42 lBen_THFTYPE_i: $i ).
% 1.73/1.42
% 1.73/1.42 thf(lBill_THFTYPE_i,type,
% 1.73/1.42 lBill_THFTYPE_i: $i ).
% 1.73/1.42
% 1.73/1.42 thf(lBob_THFTYPE_i,type,
% 1.73/1.42 lBob_THFTYPE_i: $i ).
% 1.73/1.42
% 1.73/1.42 thf(lMary_THFTYPE_i,type,
% 1.73/1.42 lMary_THFTYPE_i: $i ).
% 1.73/1.42
% 1.73/1.42 thf(lSue_THFTYPE_i,type,
% 1.73/1.42 lSue_THFTYPE_i: $i ).
% 1.73/1.42
% 1.73/1.42 thf(likes_THFTYPE_IiioI,type,
% 1.73/1.42 likes_THFTYPE_IiioI: $i > $i > $o ).
% 1.73/1.42
% 1.73/1.42 thf(parent_THFTYPE_IiioI,type,
% 1.73/1.42 parent_THFTYPE_IiioI: $i > $i > $o ).
% 1.73/1.42
% 1.73/1.42 thf(ax,axiom,
% 1.73/1.42 likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i ).
% 1.73/1.42
% 1.73/1.42 thf(ax_001,axiom,
% 1.73/1.42 (~) @ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i ) ).
% 1.73/1.42
% 1.73/1.42 thf(ax_002,axiom,
% 1.73/1.42 likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i ).
% 1.73/1.42
% 1.73/1.42 thf(ax_003,axiom,
% 1.73/1.42 parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i ).
% 1.73/1.42
% 1.73/1.42 thf(ax_004,axiom,
% 1.73/1.42 parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i ).
% 1.73/1.42
% 1.73/1.42 thf(ax_005,axiom,
% 1.73/1.42 (~) @ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i ) ).
% 1.73/1.42
% 1.73/1.42 thf(ax_006,axiom,
% 1.73/1.42 likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i ).
% 1.73/1.42
% 1.73/1.42 thf(ax_007,axiom,
% 1.73/1.42 parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i ).
% 1.73/1.42
% 1.73/1.42 thf(ax_008,axiom,
% 1.73/1.42 parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ).
% 1.73/1.42
% 1.73/1.42 thf(ax_009,axiom,
% 1.73/1.42 (~) @ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i ) ).
% 1.73/1.42
% 1.73/1.42 thf(con,conjecture,
% 1.73/1.42 ? [Q: $i > $i > $o,R: $i > $i > $o,Y: $i] :
% 1.73/1.42 ( ( R @ Y @ lBill_THFTYPE_i )
% 1.73/1.42 & ( Q @ Y @ lAnna_THFTYPE_i )
% 1.73/1.42 & ( (~)
% 1.73/1.42 @ ! [A: $i,B: $i] : ( R @ A @ B ) )
% 1.73/1.42 & ( (~)
% 1.73/1.42 @ ! [A: $i,B: $i] : ( Q @ A @ B ) ) ) ).
% 1.73/1.42 ------------------------
% 1.73/1.44 % (2907)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2804 for (2999ds/18Mi)
% 1.73/1.44 % (2903)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_2804 for (2999ds/27Mi)
% 1.73/1.44 % (2906)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_2804 for (2999ds/275Mi)
% 1.73/1.44 % (2901)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2804 for (2999ds/183Mi)
% 1.73/1.44 % (2902)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_2804 for (2999ds/4Mi)
% 1.73/1.44 % (2904)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2804 for (2999ds/2Mi)
% 1.73/1.44 % (2904)Instruction limit reached!
% 1.73/1.44 % (2904)------------------------------
% 1.73/1.44 % (2904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.44 % (2904)Termination reason: Unknown
% 1.73/1.44 % (2904)Termination phase: Unused predicate definition removal
% 1.73/1.44
% 1.73/1.44 % (2904)Memory used [KB]: 895
% 1.73/1.44 % (2904)Time elapsed: 0.003 s
% 1.73/1.44 % (2904)Instructions burned: 2 (million)
% 1.73/1.44 % (2904)------------------------------
% 1.73/1.44 % (2904)------------------------------
% 1.73/1.44 % (2905)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_2804 for (2999ds/2Mi)
% 1.73/1.45 % (2905)Instruction limit reached!
% 1.73/1.45 % (2905)------------------------------
% 1.73/1.45 % (2905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.45 % (2905)Termination reason: Unknown
% 1.73/1.45 % (2905)Termination phase: Saturation
% 1.73/1.45
% 1.73/1.45 % (2905)Memory used [KB]: 895
% 1.73/1.45 % (2905)Time elapsed: 0.003 s
% 1.73/1.45 % (2905)Instructions burned: 2 (million)
% 1.73/1.45 % (2905)------------------------------
% 1.73/1.45 % (2905)------------------------------
% 1.73/1.45 % (2902)Instruction limit reached!
% 1.73/1.45 % (2902)------------------------------
% 1.73/1.45 % (2902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.45 % (2902)Termination reason: Unknown
% 1.73/1.45 % (2902)Termination phase: Saturation
% 1.73/1.45
% 1.73/1.45 % (2902)Memory used [KB]: 5500
% 1.73/1.45 % (2902)Time elapsed: 0.005 s
% 1.73/1.45 % (2902)Instructions burned: 4 (million)
% 1.73/1.45 % (2902)------------------------------
% 1.73/1.45 % (2902)------------------------------
% 1.73/1.45 % (2903)First to succeed.
% 1.73/1.45 % (2903)Refutation found. Thanks to Tanya!
% 1.73/1.45 % SZS status Theorem for DTF2THF_2804
% 1.73/1.45 % SZS output start Proof for DTF2THF_2804
% 1.73/1.45 thf(func_def_0, type, num: $tType).
% 1.73/1.45 thf(func_def_7, type, likes_THFTYPE_IiioI: $i > $i > $o).
% 1.73/1.45 thf(func_def_8, type, parent_THFTYPE_IiioI: $i > $i > $o).
% 1.73/1.45 thf(func_def_11, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.73/1.45 thf(func_def_19, type, ph1: !>[X0: $tType]:(X0)).
% 1.73/1.45 thf(f108,plain,(
% 1.73/1.45 $false),
% 1.73/1.45 inference(avatar_sat_refutation,[status(thm)],[f73,f99,f106])).
% 1.73/1.45 thf(f106,plain,(
% 1.73/1.45 ~spl0_1),
% 1.73/1.45 inference(avatar_contradiction_clause,[status(thm)],[f105])).
% 1.73/1.45 thf(f105,plain,(
% 1.73/1.45 $false | ~spl0_1),
% 1.73/1.45 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.73/1.45 thf(f101,plain,(
% 1.73/1.45 ($false = $true) | ~spl0_1),
% 1.73/1.45 inference(superposition,[status(thm)],[f50,f69])).
% 1.73/1.45 thf(f69,plain,(
% 1.73/1.45 ( ! [X3 : $i,X4 : $i] : (((likes_THFTYPE_IiioI @ X3 @ X4) = $true)) ) | ~spl0_1),
% 1.73/1.45 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.73/1.45 thf(f68,definition,(
% 1.73/1.45 spl0_1 <=> ! [X4 : $i,X3 : $i] : ((likes_THFTYPE_IiioI @ X3 @ X4) = $true)),
% 1.73/1.45 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.73/1.45 thf(f50,plain,(
% 1.73/1.45 ((likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i) = $false)),
% 1.73/1.45 inference(not_proxy_clausification,[status(thm)],[f46])).
% 1.73/1.45 thf(f46,plain,(
% 1.73/1.45 ((~ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i)) = $true)),
% 1.73/1.45 inference(cnf_transformation,[status(thm)],[f25])).
% 1.73/1.45 thf(f25,plain,(
% 1.73/1.45 ((~ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i)) = $true)),
% 1.73/1.45 inference(fool_elimination,[status(thm)],[f24])).
% 1.73/1.45 thf(f24,plain,(
% 1.73/1.45 (~ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i))),
% 1.73/1.45 inference(rectify,[status(thm)],[f2])).
% 1.73/1.45 thf(f2,axiom,(
% 1.73/1.45 (~ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i))),
% 1.73/1.45 file('/export/starexec/sandbox/tmp/tmp.yKmfGHnlUw/DTF2THF_2804.p',ax_001)).
% 1.73/1.45 thf(f99,plain,(
% 1.73/1.45 ~spl0_2),
% 1.73/1.45 inference(avatar_contradiction_clause,[status(thm)],[f98])).
% 1.73/1.45 thf(f98,plain,(
% 1.73/1.45 $false | ~spl0_2),
% 1.73/1.45 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.73/1.45 thf(f87,plain,(
% 1.73/1.45 ($false = $true) | ~spl0_2),
% 1.73/1.45 inference(superposition,[status(thm)],[f49,f83])).
% 1.73/1.45 thf(f83,plain,(
% 1.73/1.45 ( ! [X0 : $i,X1 : $i] : (((parent_THFTYPE_IiioI @ X0 @ X1) = $true)) ) | ~spl0_2),
% 1.73/1.45 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.73/1.45 thf(f82,plain,(
% 1.73/1.45 ( ! [X0 : $i,X1 : $i] : (((parent_THFTYPE_IiioI @ X0 @ X1) = $true) | ($true != $true)) ) | ~spl0_2),
% 1.73/1.45 inference(superposition,[status(thm)],[f72,f40])).
% 1.73/1.45 thf(f40,plain,(
% 1.73/1.45 ((parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i) = $true)),
% 1.73/1.45 inference(cnf_transformation,[status(thm)],[f27])).
% 1.73/1.45 thf(f27,plain,(
% 1.73/1.45 ((parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i) = $true)),
% 1.73/1.45 inference(fool_elimination,[status(thm)],[f26])).
% 1.73/1.45 thf(f26,plain,(
% 1.73/1.45 (parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i)),
% 1.73/1.45 inference(rectify,[status(thm)],[f9])).
% 1.73/1.45 thf(f9,axiom,(
% 1.73/1.45 (parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i)),
% 1.73/1.45 file('/export/starexec/sandbox/tmp/tmp.yKmfGHnlUw/DTF2THF_2804.p',ax_008)).
% 1.73/1.45 thf(f72,plain,(
% 1.73/1.45 ( ! [X2 : $i,X0 : $i > $i > $o,X1 : $i] : (((X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i) != $true) | ((X0 @ X1 @ X2) = $true)) ) | ~spl0_2),
% 1.73/1.45 inference(avatar_component_clause,[status(thm)],[f71])).
% 1.73/1.45 thf(f71,definition,(
% 1.73/1.45 spl0_2 <=> ! [X2 : $i,X0 : $i > $i > $o,X1 : $i] : (((X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i) != $true) | ((X0 @ X1 @ X2) = $true))),
% 1.73/1.45 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.73/1.45 thf(f49,plain,(
% 1.73/1.45 ((parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i) = $false)),
% 1.73/1.45 inference(not_proxy_clausification,[status(thm)],[f43])).
% 1.73/1.45 thf(f43,plain,(
% 1.73/1.45 ((~ (parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i)) = $true)),
% 1.73/1.45 inference(cnf_transformation,[status(thm)],[f31])).
% 1.73/1.45 thf(f31,plain,(
% 1.73/1.45 ((~ (parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i)) = $true)),
% 1.73/1.45 inference(fool_elimination,[status(thm)],[f30])).
% 1.73/1.45 thf(f30,plain,(
% 1.73/1.45 (~ (parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i))),
% 1.73/1.45 inference(rectify,[status(thm)],[f6])).
% 1.73/1.45 thf(f6,axiom,(
% 1.73/1.45 (~ (parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i))),
% 1.73/1.45 file('/export/starexec/sandbox/tmp/tmp.yKmfGHnlUw/DTF2THF_2804.p',ax_005)).
% 1.73/1.45 thf(f73,plain,(
% 1.73/1.45 spl0_1 | spl0_2),
% 1.73/1.45 inference(avatar_split_clause,[status(thm)],[f66,f71,f68])).
% 1.73/1.45 thf(f66,plain,(
% 1.73/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i,X4 : $i] : (((X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i) != $true) | ((likes_THFTYPE_IiioI @ X3 @ X4) = $true) | ((X0 @ X1 @ X2) = $true)) )),
% 1.73/1.45 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.73/1.45 thf(f62,plain,(
% 1.73/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i,X4 : $i] : (((X0 @ lMary_THFTYPE_i @ lAnna_THFTYPE_i) != $true) | ((X0 @ X1 @ X2) = $true) | ((likes_THFTYPE_IiioI @ X3 @ X4) = $true) | ($true != $true)) )),
% 1.73/1.45 inference(superposition,[status(thm)],[f60,f42])).
% 1.73/1.45 thf(f42,plain,(
% 1.73/1.45 ((likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i) = $true)),
% 1.73/1.45 inference(cnf_transformation,[status(thm)],[f17])).
% 1.73/1.45 thf(f17,plain,(
% 1.73/1.45 ((likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i) = $true)),
% 1.73/1.45 inference(fool_elimination,[status(thm)],[f16])).
% 1.73/1.45 thf(f16,plain,(
% 1.73/1.45 (likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i)),
% 1.73/1.45 inference(rectify,[status(thm)],[f3])).
% 1.73/1.45 thf(f3,axiom,(
% 1.73/1.45 (likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i)),
% 1.73/1.45 file('/export/starexec/sandbox/tmp/tmp.yKmfGHnlUw/DTF2THF_2804.p',ax_002)).
% 1.73/1.45 thf(f60,plain,(
% 1.73/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o,X6 : $i,X4 : $i,X5 : $i] : (((X1 @ X2 @ lBill_THFTYPE_i) != $true) | ((X0 @ X2 @ lAnna_THFTYPE_i) != $true) | ($true = (X0 @ X5 @ X6)) | ((X1 @ X4 @ X3) = $true)) )),
% 1.73/1.45 inference(pi_clausification,[status(thm)],[f59])).
% 1.73/1.45 thf(f59,plain,(
% 1.73/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (((X1 @ X4 @ X3) = $true) | ((!! @ $i @ (X0 @ X5)) = $true) | ((X0 @ X2 @ lAnna_THFTYPE_i) != $true) | ((X1 @ X2 @ lBill_THFTYPE_i) != $true)) )),
% 1.73/1.45 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.73/1.45 thf(f58,plain,(
% 1.73/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (((X1 @ X2 @ lBill_THFTYPE_i) != $true) | ((X0 @ X2 @ lAnna_THFTYPE_i) != $true) | (((^[Y0 : $i]: (!! @ $i @ (X0 @ Y0))) @ X5) = $true) | ((X1 @ X4 @ X3) = $true)) )),
% 1.73/1.45 inference(pi_clausification,[status(thm)],[f57])).
% 1.73/1.45 thf(f57,plain,(
% 1.73/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (X0 @ Y0)))) = $true) | ((X0 @ X2 @ lAnna_THFTYPE_i) != $true) | ((X1 @ X2 @ lBill_THFTYPE_i) != $true) | ((X1 @ X4 @ X3) = $true)) )),
% 1.73/1.45 inference(not_proxy_clausification,[status(thm)],[f56])).
% 1.73/1.45 thf(f56,plain,(
% 1.73/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o,X4 : $i] : (((X0 @ X2 @ lAnna_THFTYPE_i) != $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (X0 @ Y0))))) != $true) | ((X1 @ X4 @ X3) = $true) | ((X1 @ X2 @ lBill_THFTYPE_i) != $true)) )),
% 1.73/1.45 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.73/1.45 thf(f55,plain,(
% 1.73/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o,X4 : $i] : ((((^[Y0 : $i]: (X1 @ Y0 @ X3)) @ X4) = $true) | ((X1 @ X2 @ lBill_THFTYPE_i) != $true) | ((X0 @ X2 @ lAnna_THFTYPE_i) != $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (X0 @ Y0))))) != $true)) )),
% 1.73/1.45 inference(pi_clausification,[status(thm)],[f54])).
% 1.73/1.45 thf(f54,plain,(
% 1.73/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (X1 @ Y0 @ X3))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (X0 @ Y0))))) != $true) | ((X1 @ X2 @ lBill_THFTYPE_i) != $true) | ((X0 @ X2 @ lAnna_THFTYPE_i) != $true)) )),
% 1.73/1.45 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.73/1.45 thf(f53,plain,(
% 1.73/1.45 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o] : (((X1 @ X2 @ lBill_THFTYPE_i) != $true) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X1 @ Y1 @ Y0)))) @ X3) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (X0 @ Y0))))) != $true) | ((X0 @ X2 @ lAnna_THFTYPE_i) != $true)) )),
% 1.73/1.45 inference(pi_clausification,[status(thm)],[f52])).
% 1.73/1.45 thf(f52,plain,(
% 1.73/1.45 ( ! [X2 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X1 @ Y1 @ Y0))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (X0 @ Y0))))) != $true) | ((X0 @ X2 @ lAnna_THFTYPE_i) != $true) | ((X1 @ X2 @ lBill_THFTYPE_i) != $true)) )),
% 1.73/1.45 inference(not_proxy_clausification,[status(thm)],[f51])).
% 1.73/1.45 thf(f51,plain,(
% 1.73/1.45 ( ! [X2 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o] : (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X1 @ Y1 @ Y0)))))) != $true) | ((X1 @ X2 @ lBill_THFTYPE_i) != $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (X0 @ Y0))))) != $true) | ((X0 @ X2 @ lAnna_THFTYPE_i) != $true)) )),
% 1.73/1.45 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.73/1.45 thf(f38,plain,(
% 1.73/1.45 ( ! [X2 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o] : (((X0 @ X2 @ lAnna_THFTYPE_i) != $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) != $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X1 @ Y1 @ Y0)))))) != $true) | ((X1 @ X2 @ lBill_THFTYPE_i) != $true)) )),
% 1.73/1.45 inference(cnf_transformation,[status(thm)],[f36])).
% 1.73/1.45 thf(f36,plain,(
% 1.73/1.45 ! [X0 : $i > $i > $o,X1 : $i > $i > $o,X2 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) != $true) | ((X0 @ X2 @ lAnna_THFTYPE_i) != $true) | ((X1 @ X2 @ lBill_THFTYPE_i) != $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X1 @ Y1 @ Y0)))))) != $true))),
% 1.73/1.45 inference(ennf_transformation,[status(thm)],[f23])).
% 1.73/1.45 thf(f23,plain,(
% 1.73/1.45 ~? [X0 : $i > $i > $o,X1 : $i > $i > $o,X2 : $i] : (((X0 @ X2 @ lAnna_THFTYPE_i) = $true) & ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) = $true) & ((X1 @ X2 @ lBill_THFTYPE_i) = $true) & ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X1 @ Y1 @ Y0)))))) = $true))),
% 1.73/1.45 inference(fool_elimination,[status(thm)],[f22])).
% 1.73/1.45 thf(f22,plain,(
% 1.73/1.45 ~? [X0 : $i > $i > $o,X1 : $i > $i > $o,X2 : $i] : ((~ ! [X3 : $i,X4 : $i] : (X0 @ X4 @ X3)) & (~ ! [X5 : $i,X6 : $i] : (X1 @ X5 @ X6)) & (X1 @ X2 @ lBill_THFTYPE_i) & (X0 @ X2 @ lAnna_THFTYPE_i))),
% 1.73/1.45 inference(rectify,[status(thm)],[f12])).
% 1.73/1.45 thf(f12,negated_conjecture,(
% 1.73/1.45 ~? [X0 : $i > $i > $o,X1 : $i > $i > $o,X2 : $i] : ((~ ! [X4 : $i,X3 : $i] : (X0 @ X3 @ X4)) & (~ ! [X3 : $i,X4 : $i] : (X1 @ X3 @ X4)) & (X1 @ X2 @ lBill_THFTYPE_i) & (X0 @ X2 @ lAnna_THFTYPE_i))),
% 1.73/1.45 inference(negated_conjecture,[status(cth)],[f11])).
% 1.73/1.45 thf(f11,conjecture,(
% 1.73/1.45 ? [X0 : $i > $i > $o,X1 : $i > $i > $o,X2 : $i] : ((~ ! [X4 : $i,X3 : $i] : (X0 @ X3 @ X4)) & (~ ! [X3 : $i,X4 : $i] : (X1 @ X3 @ X4)) & (X1 @ X2 @ lBill_THFTYPE_i) & (X0 @ X2 @ lAnna_THFTYPE_i))),
% 1.73/1.45 file('/export/starexec/sandbox/tmp/tmp.yKmfGHnlUw/DTF2THF_2804.p',con)).
% 1.73/1.45 % SZS output end Proof for DTF2THF_2804
% 1.73/1.45 % (2903)------------------------------
% 1.73/1.45 % (2903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.45 % (2903)Termination reason: Refutation
% 1.73/1.45
% 1.73/1.45 % (2903)Memory used [KB]: 5500
% 1.73/1.45 % (2903)Time elapsed: 0.008 s
% 1.73/1.45 % (2903)Instructions burned: 8 (million)
% 1.73/1.45 % (2903)------------------------------
% 1.73/1.45 % (2903)------------------------------
% 1.73/1.45 % (2900)Success in time 0.022 s
%------------------------------------------------------------------------------