%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : CSR153^1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 08:43:16 AM UTC 2026
% Result : Theorem 1.56s 1.37s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 259 ( 91 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 203 ( 57 ~; 31 |; 11 &; 94 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 6 con; 0-2 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 61 ( 18 ^; 39 !; 4 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
num: $tType ).
thf(func_def_1,type,
brother_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_6,type,
sister_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f99,plain,
$false,
inference(flex-flex_simplify,[status(thm)],[f98]) ).
thf(f98,plain,
! [X2: $i,X1: $i] : ( X1 != X2 ),
inference(subsumption_resolution,[status(thm)],[f97,f39]) ).
thf(f39,plain,
lBill_THFTYPE_i != lBob_THFTYPE_i,
inference(equality_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( lBill_THFTYPE_i = lBob_THFTYPE_i )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( $true
= ( lBill_THFTYPE_i != lBob_THFTYPE_i ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( lBill_THFTYPE_i != lBob_THFTYPE_i ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
lBill_THFTYPE_i != lBob_THFTYPE_i,
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
lBill_THFTYPE_i != lBob_THFTYPE_i,
file('/export/starexec/sandbox2/tmp/tmp.A8QmIi1PxN/DTF2THF_29136.p',ax_004) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( ( lBill_THFTYPE_i = lBob_THFTYPE_i )
| ( X1 != X2 ) ),
inference(subsumption_resolution,[status(thm)],[f92,f53]) ).
thf(f53,plain,
lSue_THFTYPE_i != lBob_THFTYPE_i,
inference(equality_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
= ( lSue_THFTYPE_i = lBob_THFTYPE_i ) ),
inference(not_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( $true
= ( lSue_THFTYPE_i != lBob_THFTYPE_i ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $true
= ( lSue_THFTYPE_i != lBill_THFTYPE_i ) )
& ( $true
= ( lSue_THFTYPE_i != lBob_THFTYPE_i ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( ( lSue_THFTYPE_i != lBob_THFTYPE_i )
& ( lSue_THFTYPE_i != lBill_THFTYPE_i ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( lSue_THFTYPE_i != lBob_THFTYPE_i )
& ( lSue_THFTYPE_i != lBill_THFTYPE_i ) ),
file('/export/starexec/sandbox2/tmp/tmp.A8QmIi1PxN/DTF2THF_29136.p',ax_002) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( ( lSue_THFTYPE_i = lBob_THFTYPE_i )
| ( X1 != X2 )
| ( lBill_THFTYPE_i = lBob_THFTYPE_i ) ),
inference(equality_proxy_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: $i,X1: $i] :
( ( lSue_THFTYPE_i = lBob_THFTYPE_i )
| ( X1 != X2 )
| ( $true
= ( lBill_THFTYPE_i = lBob_THFTYPE_i ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( X1 = X2 ) )
| ( lSue_THFTYPE_i = lBob_THFTYPE_i )
| ( $true
= ( lBill_THFTYPE_i = lBob_THFTYPE_i ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( lBob_THFTYPE_i = lSue_THFTYPE_i ) )
| ( $true
= ( lBill_THFTYPE_i = lBob_THFTYPE_i ) )
| ( $false
= ( X1 = X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: $i,X1: $i] :
( ( $true
!= ( lBill_THFTYPE_i != lBob_THFTYPE_i ) )
| ( $false
= ( X1 = X2 ) )
| ( $true
= ( lBob_THFTYPE_i = lSue_THFTYPE_i ) ) ),
inference(not_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( X1 != X2 ) )
| ( $true
!= ( lBill_THFTYPE_i != lBob_THFTYPE_i ) )
| ( $true
= ( lBob_THFTYPE_i = lSue_THFTYPE_i ) ) ),
inference(not_proxy_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
! [X2: $i,X1: $i] :
( ( $true
!= ( lBob_THFTYPE_i != lSue_THFTYPE_i ) )
| ( $true
!= ( lBill_THFTYPE_i != lBob_THFTYPE_i ) )
| ( $true
= ( X1 != X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i,Y1: $i] : ( Y1 != Y0 )
@ X2
@ X1 ) )
| ( $true
!= ( ^ [Y0: $i,Y1: $i] : ( Y1 != Y0 )
@ lBob_THFTYPE_i
@ lBill_THFTYPE_i ) )
| ( $true
!= ( ^ [Y0: $i,Y1: $i] : ( Y1 != Y0 )
@ lSue_THFTYPE_i
@ lBob_THFTYPE_i ) ) ),
inference(primitive_instantiation,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( X0 @ X2 @ X1 ) )
| ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true )
| ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i] :
( ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true )
| ( $true
= ( ^ [Y0: $i] : ( X0 @ Y0 @ X1 )
@ X2 ) )
| ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true ) ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true )
| ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( X0 @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) )
@ X1 ) )
| ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true )
| ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true ) ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $i > $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) ) )
| ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true )
| ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $i > $i > $o] :
( ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true )
| ( $true
!= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) ) ) )
| ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $i > $i > $o] :
( ( $true
!= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) ) ) )
| ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true )
| ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ? [X0: $i > $i > $o] :
( ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
= $true )
& ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
= $true )
& ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ? [X0: $i > $i > $o] :
( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
& ~ ! [X1: $i,X2: $i] : ( X0 @ X1 @ X2 )
& ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ? [X0: $i > $i > $o] :
( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
& ~ ! [X1: $i,X2: $i] : ( X0 @ X1 @ X2 )
& ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
? [X0: $i > $i > $o] :
( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
& ~ ! [X1: $i,X2: $i] : ( X0 @ X1 @ X2 )
& ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i ) ),
file('/export/starexec/sandbox2/tmp/tmp.A8QmIi1PxN/DTF2THF_29136.p',con) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : CSR153^1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n019.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 05:56:39 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : CSR153^1 : TPTP v9.2.1. Released v4.1.0.
% 0.17/0.39 % Domain : Commonsense Reasoning
% 0.17/0.39 % Problem : Is there a common relation?
% 0.17/0.39 % Version : Especial > Reduced > Especial.
% 0.17/0.39 % English : Mary, Sue, Bill and Bob are mutually distinct. Mary is neither a
% 0.17/0.39 % sister of Sue nor of Bill. Bob is not a brother of Mary. Sue is a
% 0.17/0.39 % sister of Bill and of Bob. Bob is a brother of Bill. Is there a
% 0.17/0.39 % relation that holds both between Bob and Bill and between Sue and
% 0.17/0.39 % Bob?
% 0.17/0.39
% 0.17/0.39 % Refs : [PS07] Pease & Sutcliffe (2007), First Order Reasoning on a L
% 0.17/0.39 % : [BP10] Benzmueller & Pease (2010), Progress in Automating Hig
% 0.17/0.39 % : [Ben10] Benzmueller (2010), Email to Geoff Sutcliffe
% 0.17/0.39 % Source : [Ben10]
% 0.17/0.39 % Names : paar_9.tq_SUMO_local [Ben10]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.46 v8.1.0, 0.45 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, 0.60 v4.1.0
% 0.17/0.39 % Syntax : Number of formulae : 13 ( 1 unt; 7 typ; 0 def)
% 0.17/0.39 % Number of atoms : 22 ( 6 equ; 10 cnn)
% 0.17/0.39 % Maximal formula atoms : 6 ( 3 avg)
% 0.17/0.39 % Number of connectives : 47 ( 10 ~; 0 |; 9 &; 28 @)
% 0.17/0.39 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 9 ( 5 avg)
% 0.17/0.39 % Number of types : 3 ( 1 usr)
% 0.17/0.39 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% 0.17/0.39 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.17/0.39 % SPC : TH0_THM_EQU_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : This is a simple test problem for reasoning in/about SUMO.
% 0.17/0.39 % Initally the problem has been hand generated in KIF syntax in
% 0.17/0.39 % SigmaKEE and then automatically translated by Benzmueller's
% 0.17/0.39 % KIF2TH0 translator into THF syntax.
% 0.17/0.39 % : The translation has been applied in two modes: local and SInE.
% 0.17/0.39 % The local mode only translates the local assumptions and the
% 0.17/0.39 % query. The SInE mode additionally translates the SInE-extract
% 0.17/0.39 % of the loaded knowledge base (usually SUMO).
% 0.17/0.39 % : The examples are selected to illustrate the benefits of
% 0.17/0.39 % higher-order reasoning in ontology reasoning.
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 %----The extracted Signature
% 0.17/0.39 thf(numbers,type,
% 0.17/0.39 num: $tType ).
% 0.17/0.39
% 0.17/0.39 thf(brother_THFTYPE_IiioI,type,
% 0.17/0.39 brother_THFTYPE_IiioI: $i > $i > $o ).
% 0.17/0.39
% 0.17/0.39 thf(lBill_THFTYPE_i,type,
% 0.17/0.39 lBill_THFTYPE_i: $i ).
% 0.17/0.39
% 0.17/0.39 thf(lBob_THFTYPE_i,type,
% 0.17/0.39 lBob_THFTYPE_i: $i ).
% 0.17/0.39
% 0.17/0.39 thf(lMary_THFTYPE_i,type,
% 0.17/0.39 lMary_THFTYPE_i: $i ).
% 0.17/0.39
% 0.17/0.39 thf(lSue_THFTYPE_i,type,
% 0.17/0.39 lSue_THFTYPE_i: $i ).
% 0.17/0.39
% 0.17/0.39 thf(sister_THFTYPE_IiioI,type,
% 0.17/0.39 sister_THFTYPE_IiioI: $i > $i > $o ).
% 0.17/0.39
% 0.17/0.39 %----The translated axioms
% 0.17/0.39 thf(ax,axiom,
% 0.17/0.39 ( ( sister_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
% 0.17/0.39 & ( sister_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
% 0.17/0.39 & ( brother_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(ax_001,axiom,
% 0.17/0.39 ( ( (~) @ ( lMary_THFTYPE_i = lSue_THFTYPE_i ) )
% 0.17/0.39 & ( (~) @ ( lMary_THFTYPE_i = lBill_THFTYPE_i ) )
% 0.17/0.39 & ( (~) @ ( lBob_THFTYPE_i = lMary_THFTYPE_i ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(ax_002,axiom,
% 0.17/0.39 ( ( (~) @ ( lSue_THFTYPE_i = lBill_THFTYPE_i ) )
% 0.17/0.39 & ( (~) @ ( lSue_THFTYPE_i = lBob_THFTYPE_i ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(ax_003,axiom,
% 0.17/0.39 ( ( (~) @ ( sister_THFTYPE_IiioI @ lMary_THFTYPE_i @ lSue_THFTYPE_i ) )
% 0.17/0.39 & ( (~) @ ( sister_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i ) )
% 0.17/0.39 & ( (~) @ ( brother_THFTYPE_IiioI @ lBob_THFTYPE_i @ lMary_THFTYPE_i ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(ax_004,axiom,
% 0.17/0.39 (~) @ ( lBob_THFTYPE_i = lBill_THFTYPE_i ) ).
% 0.17/0.39
% 0.17/0.39 %----The translated conjectures
% 0.17/0.39 thf(con,conjecture,
% 0.17/0.39 ? [R: $i > $i > $o] :
% 0.17/0.39 ( ( R @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
% 0.17/0.39 & ( R @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
% 0.17/0.39 & ( (~)
% 0.17/0.39 @ ! [X: $i,Y: $i] : ( R @ X @ Y ) ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.56/1.33 ---- Embedded in THF ---
% 1.56/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.34 %%% Generated on Tue Feb 24 05:56:40 EST 2026
% 1.56/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.34 %%% Logic specification used:
% 1.56/1.34 %%% thf(spec, logic, $$dhol).
% 1.56/1.34
% 1.56/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.A8QmIi1PxN/DTF2DTF29136.p
% See solution above
% 1.56/1.34 ------------------------
% 1.56/1.34 ---- Cleaned THF ---
% 1.56/1.35 thf(numbers,type,
% 1.56/1.35 num: $tType ).
% 1.56/1.35
% 1.56/1.35 thf(brother_THFTYPE_IiioI,type,
% 1.56/1.35 brother_THFTYPE_IiioI: $i > $i > $o ).
% 1.56/1.35
% 1.56/1.35 thf(lBill_THFTYPE_i,type,
% 1.56/1.35 lBill_THFTYPE_i: $i ).
% 1.56/1.35
% 1.56/1.35 thf(lBob_THFTYPE_i,type,
% 1.56/1.35 lBob_THFTYPE_i: $i ).
% 1.56/1.35
% 1.56/1.35 thf(lMary_THFTYPE_i,type,
% 1.56/1.35 lMary_THFTYPE_i: $i ).
% 1.56/1.35
% 1.56/1.35 thf(lSue_THFTYPE_i,type,
% 1.56/1.35 lSue_THFTYPE_i: $i ).
% 1.56/1.35
% 1.56/1.35 thf(sister_THFTYPE_IiioI,type,
% 1.56/1.35 sister_THFTYPE_IiioI: $i > $i > $o ).
% 1.56/1.35
% 1.56/1.35 thf(ax,axiom,
% 1.56/1.35 ( ( sister_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
% 1.56/1.35 & ( sister_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
% 1.56/1.35 & ( brother_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i ) ) ).
% 1.56/1.35
% 1.56/1.35 thf(ax_001,axiom,
% 1.56/1.35 ( ( (~) @ ( lMary_THFTYPE_i = lSue_THFTYPE_i ) )
% 1.56/1.35 & ( (~) @ ( lMary_THFTYPE_i = lBill_THFTYPE_i ) )
% 1.56/1.35 & ( (~) @ ( lBob_THFTYPE_i = lMary_THFTYPE_i ) ) ) ).
% 1.56/1.35
% 1.56/1.35 thf(ax_002,axiom,
% 1.56/1.35 ( ( (~) @ ( lSue_THFTYPE_i = lBill_THFTYPE_i ) )
% 1.56/1.35 & ( (~) @ ( lSue_THFTYPE_i = lBob_THFTYPE_i ) ) ) ).
% 1.56/1.35
% 1.56/1.35 thf(ax_003,axiom,
% 1.56/1.35 ( ( (~) @ ( sister_THFTYPE_IiioI @ lMary_THFTYPE_i @ lSue_THFTYPE_i ) )
% 1.56/1.35 & ( (~) @ ( sister_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i ) )
% 1.56/1.35 & ( (~) @ ( brother_THFTYPE_IiioI @ lBob_THFTYPE_i @ lMary_THFTYPE_i ) ) ) ).
% 1.56/1.35
% 1.56/1.35 thf(ax_004,axiom,
% 1.56/1.35 (~) @ ( lBob_THFTYPE_i = lBill_THFTYPE_i ) ).
% 1.56/1.35
% 1.56/1.35 thf(con,conjecture,
% 1.56/1.35 ? [R: $i > $i > $o] :
% 1.56/1.35 ( ( R @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
% 1.56/1.35 & ( R @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
% 1.56/1.35 & ( (~)
% 1.56/1.35 @ ! [X: $i,Y: $i] : ( R @ X @ Y ) ) ) ).
% 1.56/1.35 ------------------------
% 1.56/1.37 % (29235)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_29136 for (2999ds/4Mi)
% 1.56/1.37 % (29238)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_29136 for (2999ds/2Mi)
% 1.56/1.37 % (29234)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29136 for (2999ds/183Mi)
% 1.56/1.37 % (29237)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29136 for (2999ds/2Mi)
% 1.56/1.37 % (29240)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29136 for (2999ds/18Mi)
% 1.56/1.37 % (29236)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_29136 for (2999ds/27Mi)
% 1.56/1.37 % (29239)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_29136 for (2999ds/275Mi)
% 1.56/1.37 % (29237)Instruction limit reached!
% 1.56/1.37 % (29237)------------------------------
% 1.56/1.37 % (29237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (29237)Termination reason: Unknown
% 1.56/1.37 % (29238)Instruction limit reached!
% 1.56/1.37 % (29238)------------------------------
% 1.56/1.37 % (29238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (29238)Termination reason: Unknown
% 1.56/1.37 % (29238)Termination phase: Saturation
% 1.56/1.37
% 1.56/1.37 % (29238)Memory used [KB]: 895
% 1.56/1.37 % (29238)Time elapsed: 0.003 s
% 1.56/1.37 % (29238)Instructions burned: 2 (million)
% 1.56/1.37 % (29238)------------------------------
% 1.56/1.37 % (29238)------------------------------
% 1.56/1.37 % (29237)Termination phase: Saturation
% 1.56/1.37
% 1.56/1.37 % (29237)Memory used [KB]: 895
% 1.56/1.37 % (29237)Time elapsed: 0.003 s
% 1.56/1.37 % (29237)Instructions burned: 2 (million)
% 1.56/1.37 % (29237)------------------------------
% 1.56/1.37 % (29237)------------------------------
% 1.56/1.37 % (29235)Instruction limit reached!
% 1.56/1.37 % (29235)------------------------------
% 1.56/1.37 % (29235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (29235)Termination reason: Unknown
% 1.56/1.37 % (29235)Termination phase: Saturation
% 1.56/1.37
% 1.56/1.37 % (29235)Memory used [KB]: 5500
% 1.56/1.37 % (29235)Time elapsed: 0.005 s
% 1.56/1.37 % (29235)Instructions burned: 4 (million)
% 1.56/1.37 % (29235)------------------------------
% 1.56/1.37 % (29235)------------------------------
% 1.56/1.37 % (29236)Refutation not found, incomplete strategy
% 1.56/1.37 % (29236)------------------------------
% 1.56/1.37 % (29236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (29236)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.37
% 1.56/1.37
% 1.56/1.37 % (29236)Memory used [KB]: 5500
% 1.56/1.37 % (29236)Time elapsed: 0.005 s
% 1.56/1.37 % (29236)Instructions burned: 4 (million)
% 1.56/1.37 % (29236)------------------------------
% 1.56/1.37 % (29236)------------------------------
% 1.56/1.37 % (29234)First to succeed.
% 1.56/1.37 % (29239)Refutation not found, incomplete strategy
% 1.56/1.37 % (29239)------------------------------
% 1.56/1.37 % (29239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (29239)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.37
% 1.56/1.37
% 1.56/1.37 % (29239)Memory used [KB]: 5500
% 1.56/1.37 % (29239)Time elapsed: 0.007 s
% 1.56/1.37 % (29239)Instructions burned: 8 (million)
% 1.56/1.37 % (29239)------------------------------
% 1.56/1.37 % (29239)------------------------------
% 1.56/1.37 % (29240)Also succeeded, but the first one will report.
% 1.56/1.37 % (29234)Refutation found. Thanks to Tanya!
% 1.56/1.37 % SZS status Theorem for DTF2THF_29136
% 1.56/1.37 % SZS output start Proof for DTF2THF_29136
% 1.56/1.37 thf(func_def_0, type, num: $tType).
% 1.56/1.37 thf(func_def_1, type, brother_THFTYPE_IiioI: $i > $i > $o).
% 1.56/1.37 thf(func_def_6, type, sister_THFTYPE_IiioI: $i > $i > $o).
% 1.56/1.37 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 1.56/1.37 thf(f99,plain,(
% 1.56/1.37 $false),
% 1.56/1.37 inference(flex-flex_simplify,[status(thm)],[f98])).
% 1.56/1.37 thf(f98,plain,(
% 1.56/1.37 ( ! [X2 : $i,X1 : $i] : ((X1 != X2)) )),
% 1.56/1.37 inference(subsumption_resolution,[status(thm)],[f97,f39])).
% 1.56/1.37 thf(f39,plain,(
% 1.56/1.37 (lBill_THFTYPE_i != lBob_THFTYPE_i)),
% 1.56/1.37 inference(equality_proxy_clausification,[status(thm)],[f38])).
% 1.56/1.37 thf(f38,plain,(
% 1.56/1.37 ((lBill_THFTYPE_i = lBob_THFTYPE_i) = $false)),
% 1.56/1.37 inference(not_proxy_clausification,[status(thm)],[f26])).
% 1.56/1.37 thf(f26,plain,(
% 1.56/1.37 ($true = (~ (lBill_THFTYPE_i = lBob_THFTYPE_i)))),
% 1.56/1.37 inference(cnf_transformation,[status(thm)],[f20])).
% 1.56/1.37 thf(f20,plain,(
% 1.56/1.37 ($true = (~ (lBill_THFTYPE_i = lBob_THFTYPE_i)))),
% 1.56/1.37 inference(fool_elimination,[status(thm)],[f19])).
% 1.56/1.37 thf(f19,plain,(
% 1.56/1.37 (~ (lBill_THFTYPE_i = lBob_THFTYPE_i))),
% 1.56/1.37 inference(rectify,[status(thm)],[f5])).
% 1.56/1.37 thf(f5,axiom,(
% 1.56/1.37 (~ (lBill_THFTYPE_i = lBob_THFTYPE_i))),
% 1.56/1.37 file('/export/starexec/sandbox2/tmp/tmp.A8QmIi1PxN/DTF2THF_29136.p',ax_004)).
% 1.56/1.37 thf(f97,plain,(
% 1.56/1.37 ( ! [X2 : $i,X1 : $i] : ((lBill_THFTYPE_i = lBob_THFTYPE_i) | (X1 != X2)) )),
% 1.56/1.37 inference(subsumption_resolution,[status(thm)],[f92,f53])).
% 1.56/1.37 thf(f53,plain,(
% 1.56/1.37 (lSue_THFTYPE_i != lBob_THFTYPE_i)),
% 1.56/1.37 inference(equality_proxy_clausification,[status(thm)],[f52])).
% 1.56/1.37 thf(f52,plain,(
% 1.56/1.37 ($false = (lSue_THFTYPE_i = lBob_THFTYPE_i))),
% 1.56/1.37 inference(not_proxy_clausification,[status(thm)],[f30])).
% 1.56/1.37 thf(f30,plain,(
% 1.56/1.37 ($true = (~ (lSue_THFTYPE_i = lBob_THFTYPE_i)))),
% 1.56/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.56/1.37 thf(f14,plain,(
% 1.56/1.37 ($true = (~ (lSue_THFTYPE_i = lBill_THFTYPE_i))) & ($true = (~ (lSue_THFTYPE_i = lBob_THFTYPE_i)))),
% 1.56/1.37 inference(fool_elimination,[status(thm)],[f13])).
% 1.56/1.37 thf(f13,plain,(
% 1.56/1.37 (~ (lSue_THFTYPE_i = lBob_THFTYPE_i)) & (~ (lSue_THFTYPE_i = lBill_THFTYPE_i))),
% 1.56/1.37 inference(rectify,[status(thm)],[f3])).
% 1.56/1.37 thf(f3,axiom,(
% 1.56/1.37 (~ (lSue_THFTYPE_i = lBob_THFTYPE_i)) & (~ (lSue_THFTYPE_i = lBill_THFTYPE_i))),
% 1.56/1.37 file('/export/starexec/sandbox2/tmp/tmp.A8QmIi1PxN/DTF2THF_29136.p',ax_002)).
% 1.56/1.37 thf(f92,plain,(
% 1.56/1.37 ( ! [X2 : $i,X1 : $i] : ((lSue_THFTYPE_i = lBob_THFTYPE_i) | (X1 != X2) | (lBill_THFTYPE_i = lBob_THFTYPE_i)) )),
% 1.56/1.37 inference(equality_proxy_clausification,[status(thm)],[f91])).
% 1.56/1.37 thf(f91,plain,(
% 1.56/1.37 ( ! [X2 : $i,X1 : $i] : ((lSue_THFTYPE_i = lBob_THFTYPE_i) | (X1 != X2) | ($true = (lBill_THFTYPE_i = lBob_THFTYPE_i))) )),
% 1.56/1.37 inference(equality_proxy_clausification,[status(thm)],[f90])).
% 1.56/1.37 thf(f90,plain,(
% 1.56/1.37 ( ! [X2 : $i,X1 : $i] : (($false = (X1 = X2)) | (lSue_THFTYPE_i = lBob_THFTYPE_i) | ($true = (lBill_THFTYPE_i = lBob_THFTYPE_i))) )),
% 1.56/1.37 inference(equality_proxy_clausification,[status(thm)],[f89])).
% 1.56/1.37 thf(f89,plain,(
% 1.56/1.37 ( ! [X2 : $i,X1 : $i] : (($true = (lBob_THFTYPE_i = lSue_THFTYPE_i)) | ($true = (lBill_THFTYPE_i = lBob_THFTYPE_i)) | ($false = (X1 = X2))) )),
% 1.56/1.37 inference(not_proxy_clausification,[status(thm)],[f88])).
% 1.56/1.37 thf(f88,plain,(
% 1.56/1.37 ( ! [X2 : $i,X1 : $i] : (($true != (~ (lBill_THFTYPE_i = lBob_THFTYPE_i))) | ($false = (X1 = X2)) | ($true = (lBob_THFTYPE_i = lSue_THFTYPE_i))) )),
% 1.56/1.37 inference(not_proxy_clausification,[status(thm)],[f87])).
% 1.56/1.37 thf(f87,plain,(
% 1.56/1.37 ( ! [X2 : $i,X1 : $i] : (($true = (~ (X1 = X2))) | ($true != (~ (lBill_THFTYPE_i = lBob_THFTYPE_i))) | ($true = (lBob_THFTYPE_i = lSue_THFTYPE_i))) )),
% 1.56/1.37 inference(not_proxy_clausification,[status(thm)],[f86])).
% 1.56/1.37 thf(f86,plain,(
% 1.56/1.37 ( ! [X2 : $i,X1 : $i] : (($true != (~ (lBob_THFTYPE_i = lSue_THFTYPE_i))) | ($true != (~ (lBill_THFTYPE_i = lBob_THFTYPE_i))) | ($true = (~ (X1 = X2)))) )),
% 1.56/1.37 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.56/1.37 thf(f56,plain,(
% 1.56/1.37 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y1 = Y0))))) @ X2 @ X1)) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y1 = Y0))))) @ lBob_THFTYPE_i @ lBill_THFTYPE_i)) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y1 = Y0))))) @ lSue_THFTYPE_i @ lBob_THFTYPE_i))) )),
% 1.56/1.37 inference(primitive_instantiation,[status(thm)],[f44])).
% 1.56/1.37 thf(f44,plain,(
% 1.56/1.37 ( ! [X2 : $i,X0 : $i > $i > $o,X1 : $i] : (($true = (X0 @ X2 @ X1)) | ((X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i) != $true) | ((X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i) != $true)) )),
% 1.56/1.37 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.56/1.37 thf(f43,plain,(
% 1.56/1.37 ( ! [X2 : $i,X0 : $i > $i > $o,X1 : $i] : (((X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i) != $true) | ($true = ((^[Y0 : $i]: (X0 @ Y0 @ X1)) @ X2)) | ((X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i) != $true)) )),
% 1.56/1.37 inference(pi_clausification,[status(thm)],[f42])).
% 1.56/1.37 thf(f42,plain,(
% 1.56/1.37 ( ! [X0 : $i > $i > $o,X1 : $i] : (((X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i) != $true) | ((X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i) != $true) | ($true = (!! @ $i @ (^[Y0 : $i]: (X0 @ Y0 @ X1))))) )),
% 1.56/1.37 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.56/1.37 thf(f41,plain,(
% 1.56/1.37 ( ! [X0 : $i > $i > $o,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X0 @ Y1 @ Y0)))) @ X1)) | ((X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i) != $true) | ((X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i) != $true)) )),
% 1.56/1.37 inference(pi_clausification,[status(thm)],[f40])).
% 1.56/1.37 thf(f40,plain,(
% 1.56/1.37 ( ! [X0 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X0 @ Y1 @ Y0)))))) | ((X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i) != $true) | ((X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i) != $true)) )),
% 1.56/1.37 inference(not_proxy_clausification,[status(thm)],[f25])).
% 1.56/1.37 thf(f25,plain,(
% 1.56/1.37 ( ! [X0 : $i > $i > $o] : (((X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i) != $true) | ($true != (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X0 @ Y1 @ Y0))))))) | ((X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i) != $true)) )),
% 1.56/1.37 inference(cnf_transformation,[status(thm)],[f21])).
% 1.56/1.37 thf(f21,plain,(
% 1.56/1.37 ! [X0 : $i > $i > $o] : (($true != (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X0 @ Y1 @ Y0))))))) | ((X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i) != $true) | ((X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i) != $true))),
% 1.56/1.37 inference(ennf_transformation,[status(thm)],[f10])).
% 1.56/1.37 thf(f10,plain,(
% 1.56/1.37 ~? [X0 : $i > $i > $o] : (((X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i) = $true) & ((X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i) = $true) & ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X0 @ Y1 @ Y0))))))))),
% 1.56/1.37 inference(fool_elimination,[status(thm)],[f9])).
% 1.56/1.37 thf(f9,plain,(
% 1.56/1.37 ~? [X0 : $i > $i > $o] : ((X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i) & (~ ! [X1 : $i,X2 : $i] : (X0 @ X1 @ X2)) & (X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i))),
% 1.56/1.37 inference(rectify,[status(thm)],[f7])).
% 1.56/1.37 thf(f7,negated_conjecture,(
% 1.56/1.37 ~? [X0 : $i > $i > $o] : ((X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i) & (~ ! [X1 : $i,X2 : $i] : (X0 @ X1 @ X2)) & (X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i))),
% 1.56/1.37 inference(negated_conjecture,[status(cth)],[f6])).
% 1.56/1.37 thf(f6,conjecture,(
% 1.56/1.37 ? [X0 : $i > $i > $o] : ((X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i) & (~ ! [X1 : $i,X2 : $i] : (X0 @ X1 @ X2)) & (X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i))),
% 1.56/1.37 file('/export/starexec/sandbox2/tmp/tmp.A8QmIi1PxN/DTF2THF_29136.p',con)).
% 1.56/1.37 % SZS output end Proof for DTF2THF_29136
% 1.56/1.37 % (29234)------------------------------
% 1.56/1.37 % (29234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (29234)Termination reason: Refutation
% 1.56/1.37
% 1.56/1.37 % (29234)Memory used [KB]: 5500
% 1.56/1.37 % (29234)Time elapsed: 0.008 s
% 1.56/1.37 % (29234)Instructions burned: 8 (million)
% 1.56/1.37 % (29234)------------------------------
% 1.56/1.37 % (29234)------------------------------
% 1.56/1.37 % (29233)Success in time 0.021 s
%------------------------------------------------------------------------------