%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV067^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:12 AM UTC 2026
% Result : Theorem 1.49s 1.30s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 499 ( 148 equ; 0 cnn)
% Maximal formula atoms : 19 ( 14 avg)
% Number of connectives : 541 ( 81 ~; 76 |; 76 &; 276 @)
% ( 2 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 130 ( 0 ^; 122 !; 8 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cS: a > $o ).
thf(func_def_2,type,
cT: a > $o ).
thf(func_def_3,type,
cR: a > a > $o ).
thf(func_def_7,type,
sK0: a ).
thf(func_def_8,type,
sK1: a ).
thf(f58,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f39,f47,f57]) ).
thf(f57,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f56]) ).
thf(f56,plain,
( $false
| ~ spl2_1 ),
inference(subsumption_resolution,[status(thm)],[f55,f18]) ).
thf(f18,plain,
( ( cT @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $true
!= ( cT @ sK0 ) )
& ( ( cS @ sK0 )
= $true )
& ( ( cS @ sK1 )
!= $true )
& ( ( cT @ sK1 )
= $true )
& ! [X2: a] :
( $true
= ( cR @ X2 @ X2 ) )
& ! [X3: a,X4: a] :
( ( $true
!= ( cR @ X4 @ X3 ) )
| ( ( cS @ X4 )
= $true )
| ( ( cS @ X3 )
!= $true ) )
& ! [X5: a,X6: a] :
( ( ( cR @ X6 @ X5 )
!= $true )
| ( $true
!= ( cR @ X5 @ X6 ) )
| ( X5 = X6 ) )
& ! [X7: a,X8: a] :
( ( ( cR @ X8 @ X7 )
= $true )
| ( ( cR @ X7 @ X8 )
= $true ) )
& ! [X9: a,X10: a] :
( ( $true
!= ( cR @ X9 @ X10 ) )
| ( $true
= ( cT @ X9 ) )
| ( $true
!= ( cT @ X10 ) ) )
& ! [X11: a,X12: a,X13: a] :
( ( ( cR @ X12 @ X11 )
!= $true )
| ( $true
!= ( cR @ X11 @ X13 ) )
| ( ( cR @ X12 @ X13 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: a] :
( ( ( cT @ X0 )
!= $true )
& ( ( cS @ X0 )
= $true ) )
=> ( ( $true
!= ( cT @ sK0 ) )
& ( ( cS @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X1: a] :
( ( $true
!= ( cS @ X1 ) )
& ( $true
= ( cT @ X1 ) ) )
=> ( ( ( cS @ sK1 )
!= $true )
& ( ( cT @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X0: a] :
( ( ( cT @ X0 )
!= $true )
& ( ( cS @ X0 )
= $true ) )
& ? [X1: a] :
( ( $true
!= ( cS @ X1 ) )
& ( $true
= ( cT @ X1 ) ) )
& ! [X2: a] :
( $true
= ( cR @ X2 @ X2 ) )
& ! [X3: a,X4: a] :
( ( $true
!= ( cR @ X4 @ X3 ) )
| ( ( cS @ X4 )
= $true )
| ( ( cS @ X3 )
!= $true ) )
& ! [X5: a,X6: a] :
( ( ( cR @ X6 @ X5 )
!= $true )
| ( $true
!= ( cR @ X5 @ X6 ) )
| ( X5 = X6 ) )
& ! [X7: a,X8: a] :
( ( ( cR @ X8 @ X7 )
= $true )
| ( ( cR @ X7 @ X8 )
= $true ) )
& ! [X9: a,X10: a] :
( ( $true
!= ( cR @ X9 @ X10 ) )
| ( $true
= ( cT @ X9 ) )
| ( $true
!= ( cT @ X10 ) ) )
& ! [X11: a,X12: a,X13: a] :
( ( ( cR @ X12 @ X11 )
!= $true )
| ( $true
!= ( cR @ X11 @ X13 ) )
| ( ( cR @ X12 @ X13 )
= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X13: a] :
( ( $true
!= ( cT @ X13 ) )
& ( ( cS @ X13 )
= $true ) )
& ? [X12: a] :
( ( ( cS @ X12 )
!= $true )
& ( ( cT @ X12 )
= $true ) )
& ! [X9: a] :
( $true
= ( cR @ X9 @ X9 ) )
& ! [X1: a,X0: a] :
( ( ( cR @ X0 @ X1 )
!= $true )
| ( ( cS @ X0 )
= $true )
| ( $true
!= ( cS @ X1 ) ) )
& ! [X10: a,X11: a] :
( ( $true
!= ( cR @ X11 @ X10 ) )
| ( ( cR @ X10 @ X11 )
!= $true )
| ( X10 = X11 ) )
& ! [X5: a,X6: a] :
( ( ( cR @ X6 @ X5 )
= $true )
| ( $true
= ( cR @ X5 @ X6 ) ) )
& ! [X8: a,X7: a] :
( ( ( cR @ X8 @ X7 )
!= $true )
| ( ( cT @ X8 )
= $true )
| ( ( cT @ X7 )
!= $true ) )
& ! [X3: a,X4: a,X2: a] :
( ( $true
!= ( cR @ X4 @ X3 ) )
| ( ( cR @ X3 @ X2 )
!= $true )
| ( $true
= ( cR @ X4 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X13: a] :
( ( $true
!= ( cT @ X13 ) )
& ( ( cS @ X13 )
= $true ) )
& ? [X12: a] :
( ( ( cS @ X12 )
!= $true )
& ( ( cT @ X12 )
= $true ) )
& ! [X7: a,X8: a] :
( ( ( cT @ X8 )
= $true )
| ( ( cT @ X7 )
!= $true )
| ( ( cR @ X8 @ X7 )
!= $true ) )
& ! [X2: a,X4: a,X3: a] :
( ( $true
= ( cR @ X4 @ X2 ) )
| ( ( cR @ X3 @ X2 )
!= $true )
| ( $true
!= ( cR @ X4 @ X3 ) ) )
& ! [X1: a,X0: a] :
( ( ( cS @ X0 )
= $true )
| ( $true
!= ( cS @ X1 ) )
| ( ( cR @ X0 @ X1 )
!= $true ) )
& ! [X5: a,X6: a] :
( ( ( cR @ X6 @ X5 )
= $true )
| ( $true
= ( cR @ X5 @ X6 ) ) )
& ! [X9: a] :
( $true
= ( cR @ X9 @ X9 ) )
& ! [X11: a,X10: a] :
( ( X10 = X11 )
| ( $true
!= ( cR @ X11 @ X10 ) )
| ( ( cR @ X10 @ X11 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X7: a,X8: a] :
( ( ( ( cT @ X7 )
= $true )
& ( ( cR @ X8 @ X7 )
= $true ) )
=> ( ( cT @ X8 )
= $true ) )
& ! [X2: a,X4: a,X3: a] :
( ( ( ( cR @ X3 @ X2 )
= $true )
& ( $true
= ( cR @ X4 @ X3 ) ) )
=> ( $true
= ( cR @ X4 @ X2 ) ) )
& ! [X1: a,X0: a] :
( ( ( $true
= ( cS @ X1 ) )
& ( ( cR @ X0 @ X1 )
= $true ) )
=> ( ( cS @ X0 )
= $true ) )
& ! [X5: a,X6: a] :
( ( ( cR @ X6 @ X5 )
= $true )
| ( $true
= ( cR @ X5 @ X6 ) ) )
& ! [X9: a] :
( $true
= ( cR @ X9 @ X9 ) )
& ! [X11: a,X10: a] :
( ( ( $true
= ( cR @ X11 @ X10 ) )
& ( ( cR @ X10 @ X11 )
= $true ) )
=> ( X10 = X11 ) ) )
=> ( ! [X13: a] :
( ( ( cS @ X13 )
= $true )
=> ( $true
= ( cT @ X13 ) ) )
| ! [X12: a] :
( ( ( cT @ X12 )
= $true )
=> ( ( cS @ X12 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a,X1: a] :
( ( ( cR @ X0 @ X1 )
& ( cS @ X1 ) )
=> ( cS @ X0 ) )
& ! [X2: a,X3: a,X4: a] :
( ( ( cR @ X4 @ X3 )
& ( cR @ X3 @ X2 ) )
=> ( cR @ X4 @ X2 ) )
& ! [X5: a,X6: a] :
( ( cR @ X5 @ X6 )
| ( cR @ X6 @ X5 ) )
& ! [X7: a,X8: a] :
( ( ( cR @ X8 @ X7 )
& ( cT @ X7 ) )
=> ( cT @ X8 ) )
& ! [X9: a] : ( cR @ X9 @ X9 )
& ! [X10: a,X11: a] :
( ( ( cR @ X10 @ X11 )
& ( cR @ X11 @ X10 ) )
=> ( X10 = X11 ) ) )
=> ( ! [X12: a] :
( ( cT @ X12 )
=> ( cS @ X12 ) )
| ! [X13: a] :
( ( cS @ X13 )
=> ( cT @ X13 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: a,X4: a] :
( ( ( cR @ X3 @ X4 )
& ( cS @ X4 ) )
=> ( cS @ X3 ) )
& ! [X2: a,X1: a,X0: a] :
( ( ( cR @ X0 @ X1 )
& ( cR @ X1 @ X2 ) )
=> ( cR @ X0 @ X2 ) )
& ! [X1: a,X0: a] :
( ( cR @ X1 @ X0 )
| ( cR @ X0 @ X1 ) )
& ! [X4: a,X3: a] :
( ( ( cR @ X3 @ X4 )
& ( cT @ X4 ) )
=> ( cT @ X3 ) )
& ! [X0: a] : ( cR @ X0 @ X0 )
& ! [X0: a,X1: a] :
( ( ( cR @ X0 @ X1 )
& ( cR @ X1 @ X0 ) )
=> ( X0 = X1 ) ) )
=> ( ! [X0: a] :
( ( cT @ X0 )
=> ( cS @ X0 ) )
| ! [X0: a] :
( ( cS @ X0 )
=> ( cT @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X3: a,X4: a] :
( ( ( cR @ X3 @ X4 )
& ( cS @ X4 ) )
=> ( cS @ X3 ) )
& ! [X2: a,X1: a,X0: a] :
( ( ( cR @ X0 @ X1 )
& ( cR @ X1 @ X2 ) )
=> ( cR @ X0 @ X2 ) )
& ! [X1: a,X0: a] :
( ( cR @ X1 @ X0 )
| ( cR @ X0 @ X1 ) )
& ! [X4: a,X3: a] :
( ( ( cR @ X3 @ X4 )
& ( cT @ X4 ) )
=> ( cT @ X3 ) )
& ! [X0: a] : ( cR @ X0 @ X0 )
& ! [X0: a,X1: a] :
( ( ( cR @ X0 @ X1 )
& ( cR @ X1 @ X0 ) )
=> ( X0 = X1 ) ) )
=> ( ! [X0: a] :
( ( cT @ X0 )
=> ( cS @ X0 ) )
| ! [X0: a] :
( ( cS @ X0 )
=> ( cT @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lbqzEspigo/DTF2THF_17603.p',cTHM553_pme) ).
thf(f55,plain,
( ( ( cT @ sK1 )
!= $true )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ( $true != $true )
| ( ( cT @ sK1 )
!= $true )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f19,f35]) ).
thf(f35,plain,
( ! [X0: a] :
( ( ( cS @ X0 )
= $true )
| ( ( cT @ X0 )
!= $true ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl2_1
<=> ! [X0: a] :
( ( ( cT @ X0 )
!= $true )
| ( ( cS @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f19,plain,
( ( cS @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f47,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f46]) ).
thf(f46,plain,
( $false
| ~ spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f45,f20]) ).
thf(f20,plain,
( ( cS @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f45,plain,
( ( ( cS @ sK0 )
!= $true )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( cS @ sK0 )
!= $true )
| ( $true != $true )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f21,f38]) ).
thf(f38,plain,
( ! [X1: a] :
( ( $true
= ( cT @ X1 ) )
| ( $true
!= ( cS @ X1 ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl2_2
<=> ! [X1: a] :
( ( $true
!= ( cS @ X1 ) )
| ( $true
= ( cT @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f21,plain,
( $true
!= ( cT @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f39,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f32,f37,f34]) ).
thf(f32,plain,
! [X0: a,X1: a] :
( ( $true
!= ( cS @ X1 ) )
| ( ( cT @ X0 )
!= $true )
| ( $true
= ( cT @ X1 ) )
| ( ( cS @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: a,X1: a] :
( ( ( cT @ X0 )
!= $true )
| ( $true != $true )
| ( ( cS @ X0 )
= $true )
| ( $true
= ( cT @ X1 ) )
| ( $true
!= ( cS @ X1 ) ) ),
inference(superposition,[status(thm)],[f16,f26]) ).
thf(f26,plain,
! [X0: a,X1: a] :
( ( ( cR @ X1 @ X0 )
= $true )
| ( $true
!= ( cT @ X1 ) )
| ( ( cT @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: a,X1: a] :
( ( $true != $true )
| ( ( cT @ X0 )
= $true )
| ( $true
!= ( cT @ X1 ) )
| ( ( cR @ X1 @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f13,f14]) ).
thf(f14,plain,
! [X8: a,X7: a] :
( ( ( cR @ X8 @ X7 )
= $true )
| ( ( cR @ X7 @ X8 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f13,plain,
! [X10: a,X9: a] :
( ( $true
!= ( cR @ X9 @ X10 ) )
| ( $true
!= ( cT @ X10 ) )
| ( $true
= ( cT @ X9 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f16,plain,
! [X3: a,X4: a] :
( ( $true
!= ( cR @ X4 @ X3 ) )
| ( ( cS @ X3 )
!= $true )
| ( ( cS @ X4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV067^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n028.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:39:42 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : SEV067^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.47 % Domain : Set Theory (Relations)
% 0.29/0.47 % Problem : TPS problem THM553
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English : Downward closed subsets of a linear order are comparable.
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.47 % Source : [Bro09]
% 0.29/0.47 % Names : tps_0441 [Bro09]
% 0.29/0.47 % : THM553 [TPS]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.29/0.47 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.29/0.47 % Number of atoms : 19 ( 1 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 19 ( 19 avg)
% 0.29/0.47 % Number of connectives : 46 ( 0 ~; 2 |; 9 &; 28 @)
% 0.29/0.47 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 13 ( 13 avg)
% 0.29/0.47 % Number of types : 2 ( 1 usr)
% 0.29/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.29/0.47 % Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.47 % : Polymorphic definitions expanded.
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(a_type,type,
% 0.29/0.47 a: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(cS,type,
% 0.29/0.47 cS: a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(cT,type,
% 0.29/0.47 cT: a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(cR,type,
% 0.29/0.47 cR: a > a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(cTHM553_pme,conjecture,
% 0.29/0.47 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 0.29/0.47 ( ( ( cR @ Xx @ Xy )
% 0.29/0.47 & ( cR @ Xy @ Xz ) )
% 0.29/0.47 => ( cR @ Xx @ Xz ) )
% 0.29/0.47 & ! [Xx: a] : ( cR @ Xx @ Xx )
% 0.29/0.47 & ! [Xx: a,Xy: a] :
% 0.29/0.47 ( ( ( cR @ Xx @ Xy )
% 0.29/0.47 & ( cR @ Xy @ Xx ) )
% 0.29/0.47 => ( Xx = Xy ) )
% 0.29/0.47 & ! [Xx: a,Xy: a] :
% 0.29/0.47 ( ( cR @ Xx @ Xy )
% 0.29/0.47 | ( cR @ Xy @ Xx ) )
% 0.29/0.47 & ! [Xu: a,Xv: a] :
% 0.29/0.47 ( ( ( cR @ Xu @ Xv )
% 0.29/0.47 & ( cS @ Xv ) )
% 0.29/0.47 => ( cS @ Xu ) )
% 0.29/0.47 & ! [Xu: a,Xv: a] :
% 0.29/0.47 ( ( ( cR @ Xu @ Xv )
% 0.29/0.47 & ( cT @ Xv ) )
% 0.29/0.47 => ( cT @ Xu ) ) )
% 0.29/0.47 => ( ! [Xx: a] :
% 0.29/0.47 ( ( cS @ Xx )
% 0.29/0.47 => ( cT @ Xx ) )
% 0.29/0.47 | ! [Xx: a] :
% 0.29/0.47 ( ( cT @ Xx )
% 0.29/0.47 => ( cS @ Xx ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.49/1.26 ---- Embedded in THF ---
% 1.49/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.26 %%% Generated on Tue Feb 24 12:39:43 EST 2026
% 1.49/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.26 %%% Logic specification used:
% 1.49/1.26 %%% thf(spec, logic, $$dhol).
% 1.49/1.26
% 1.49/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.lbqzEspigo/DTF2DTF17603.p
% See solution above
% 1.49/1.26 ------------------------
% 1.49/1.28 ---- Cleaned THF ---
% 1.49/1.28 thf(a_type,type,
% 1.49/1.28 a: $tType ).
% 1.49/1.28
% 1.49/1.28 thf(cS,type,
% 1.49/1.28 cS: a > $o ).
% 1.49/1.28
% 1.49/1.28 thf(cT,type,
% 1.49/1.28 cT: a > $o ).
% 1.49/1.28
% 1.49/1.28 thf(cR,type,
% 1.49/1.28 cR: a > a > $o ).
% 1.49/1.28
% 1.49/1.28 thf(cTHM553_pme,conjecture,
% 1.49/1.28 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 1.49/1.28 ( ( ( cR @ Xx @ Xy )
% 1.49/1.28 & ( cR @ Xy @ Xz ) )
% 1.49/1.28 => ( cR @ Xx @ Xz ) )
% 1.49/1.28 & ! [Xx: a] : ( cR @ Xx @ Xx )
% 1.49/1.28 & ! [Xx: a,Xy: a] :
% 1.49/1.28 ( ( ( cR @ Xx @ Xy )
% 1.49/1.28 & ( cR @ Xy @ Xx ) )
% 1.49/1.28 => ( Xx = Xy ) )
% 1.49/1.28 & ! [Xx: a,Xy: a] :
% 1.49/1.28 ( ( cR @ Xx @ Xy )
% 1.49/1.28 | ( cR @ Xy @ Xx ) )
% 1.49/1.28 & ! [Xu: a,Xv: a] :
% 1.49/1.28 ( ( ( cR @ Xu @ Xv )
% 1.49/1.28 & ( cS @ Xv ) )
% 1.49/1.28 => ( cS @ Xu ) )
% 1.49/1.28 & ! [Xu: a,Xv: a] :
% 1.49/1.28 ( ( ( cR @ Xu @ Xv )
% 1.49/1.28 & ( cT @ Xv ) )
% 1.49/1.28 => ( cT @ Xu ) ) )
% 1.49/1.28 => ( ! [Xx: a] :
% 1.49/1.28 ( ( cS @ Xx )
% 1.49/1.28 => ( cT @ Xx ) )
% 1.49/1.28 | ! [Xx: a] :
% 1.49/1.28 ( ( cT @ Xx )
% 1.49/1.28 => ( cS @ Xx ) ) ) ) ).
% 1.49/1.28 ------------------------
% 1.49/1.29 % (17879)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_17603 for (2999ds/275Mi)
% 1.49/1.29 % (17877)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17603 for (2999ds/2Mi)
% 1.49/1.29 % (17877)Instruction limit reached!
% 1.49/1.29 % (17877)------------------------------
% 1.49/1.29 % (17877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (17877)Termination reason: Unknown
% 1.49/1.29 % (17877)Termination phase: Saturation
% 1.49/1.29
% 1.49/1.29 % (17877)Memory used [KB]: 5500
% 1.49/1.29 % (17877)Time elapsed: 0.002 s
% 1.49/1.29 % (17877)Instructions burned: 2 (million)
% 1.49/1.29 % (17877)------------------------------
% 1.49/1.29 % (17877)------------------------------
% 1.49/1.29 % (17879)First to succeed.
% 1.49/1.30 % (17879)Refutation found. Thanks to Tanya!
% 1.49/1.30 % SZS status Theorem for DTF2THF_17603
% 1.49/1.30 % SZS output start Proof for DTF2THF_17603
% 1.49/1.30 thf(type_def_5, type, a: $tType).
% 1.49/1.30 thf(func_def_0, type, a: $tType).
% 1.49/1.30 thf(func_def_1, type, cS: a > $o).
% 1.49/1.30 thf(func_def_2, type, cT: a > $o).
% 1.49/1.30 thf(func_def_3, type, cR: a > a > $o).
% 1.49/1.30 thf(func_def_7, type, sK0: a).
% 1.49/1.30 thf(func_def_8, type, sK1: a).
% 1.49/1.30 thf(f58,plain,(
% 1.49/1.30 $false),
% 1.49/1.30 inference(avatar_sat_refutation,[status(thm)],[f39,f47,f57])).
% 1.49/1.30 thf(f57,plain,(
% 1.49/1.30 ~spl2_1),
% 1.49/1.30 inference(avatar_contradiction_clause,[status(thm)],[f56])).
% 1.49/1.30 thf(f56,plain,(
% 1.49/1.30 $false | ~spl2_1),
% 1.49/1.30 inference(subsumption_resolution,[status(thm)],[f55,f18])).
% 1.49/1.30 thf(f18,plain,(
% 1.49/1.30 ((cT @ sK1) = $true)),
% 1.49/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.30 thf(f11,plain,(
% 1.49/1.30 (($true != (cT @ sK0)) & ((cS @ sK0) = $true)) & (((cS @ sK1) != $true) & ((cT @ sK1) = $true)) & ! [X2 : a] : ($true = (cR @ X2 @ X2)) & ! [X3 : a,X4 : a] : (($true != (cR @ X4 @ X3)) | ((cS @ X4) = $true) | ((cS @ X3) != $true)) & ! [X5 : a,X6 : a] : (((cR @ X6 @ X5) != $true) | ($true != (cR @ X5 @ X6)) | (X5 = X6)) & ! [X7 : a,X8 : a] : (((cR @ X8 @ X7) = $true) | ((cR @ X7 @ X8) = $true)) & ! [X9 : a,X10 : a] : (($true != (cR @ X9 @ X10)) | ($true = (cT @ X9)) | ($true != (cT @ X10))) & ! [X11 : a,X12 : a,X13 : a] : (((cR @ X12 @ X11) != $true) | ($true != (cR @ X11 @ X13)) | ((cR @ X12 @ X13) = $true))),
% 1.49/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9])).
% 1.49/1.30 thf(f9,plain,(
% 1.49/1.30 ? [X0 : a] : (((cT @ X0) != $true) & ((cS @ X0) = $true)) => (($true != (cT @ sK0)) & ((cS @ sK0) = $true))),
% 1.49/1.30 introduced(definition,[],[choice_axiom])).
% 1.49/1.30 thf(f10,plain,(
% 1.49/1.30 ? [X1 : a] : (($true != (cS @ X1)) & ($true = (cT @ X1))) => (((cS @ sK1) != $true) & ((cT @ sK1) = $true))),
% 1.49/1.30 introduced(definition,[],[choice_axiom])).
% 1.49/1.30 thf(f8,plain,(
% 1.49/1.30 ? [X0 : a] : (((cT @ X0) != $true) & ((cS @ X0) = $true)) & ? [X1 : a] : (($true != (cS @ X1)) & ($true = (cT @ X1))) & ! [X2 : a] : ($true = (cR @ X2 @ X2)) & ! [X3 : a,X4 : a] : (($true != (cR @ X4 @ X3)) | ((cS @ X4) = $true) | ((cS @ X3) != $true)) & ! [X5 : a,X6 : a] : (((cR @ X6 @ X5) != $true) | ($true != (cR @ X5 @ X6)) | (X5 = X6)) & ! [X7 : a,X8 : a] : (((cR @ X8 @ X7) = $true) | ((cR @ X7 @ X8) = $true)) & ! [X9 : a,X10 : a] : (($true != (cR @ X9 @ X10)) | ($true = (cT @ X9)) | ($true != (cT @ X10))) & ! [X11 : a,X12 : a,X13 : a] : (((cR @ X12 @ X11) != $true) | ($true != (cR @ X11 @ X13)) | ((cR @ X12 @ X13) = $true))),
% 1.49/1.30 inference(rectify,[status(thm)],[f7])).
% 1.49/1.30 thf(f7,plain,(
% 1.49/1.30 ? [X13 : a] : (($true != (cT @ X13)) & ((cS @ X13) = $true)) & ? [X12 : a] : (((cS @ X12) != $true) & ((cT @ X12) = $true)) & ! [X9 : a] : ($true = (cR @ X9 @ X9)) & ! [X1 : a,X0 : a] : (((cR @ X0 @ X1) != $true) | ((cS @ X0) = $true) | ($true != (cS @ X1))) & ! [X10 : a,X11 : a] : (($true != (cR @ X11 @ X10)) | ((cR @ X10 @ X11) != $true) | (X10 = X11)) & ! [X5 : a,X6 : a] : (((cR @ X6 @ X5) = $true) | ($true = (cR @ X5 @ X6))) & ! [X8 : a,X7 : a] : (((cR @ X8 @ X7) != $true) | ((cT @ X8) = $true) | ((cT @ X7) != $true)) & ! [X3 : a,X4 : a,X2 : a] : (($true != (cR @ X4 @ X3)) | ((cR @ X3 @ X2) != $true) | ($true = (cR @ X4 @ X2)))),
% 1.49/1.30 inference(flattening,[status(thm)],[f6])).
% 1.49/1.30 thf(f6,plain,(
% 1.49/1.30 (? [X13 : a] : (($true != (cT @ X13)) & ((cS @ X13) = $true)) & ? [X12 : a] : (((cS @ X12) != $true) & ((cT @ X12) = $true))) & (! [X7 : a,X8 : a] : (((cT @ X8) = $true) | (((cT @ X7) != $true) | ((cR @ X8 @ X7) != $true))) & ! [X2 : a,X4 : a,X3 : a] : (($true = (cR @ X4 @ X2)) | (((cR @ X3 @ X2) != $true) | ($true != (cR @ X4 @ X3)))) & ! [X1 : a,X0 : a] : (((cS @ X0) = $true) | (($true != (cS @ X1)) | ((cR @ X0 @ X1) != $true))) & ! [X5 : a,X6 : a] : (((cR @ X6 @ X5) = $true) | ($true = (cR @ X5 @ X6))) & ! [X9 : a] : ($true = (cR @ X9 @ X9)) & ! [X11 : a,X10 : a] : ((X10 = X11) | (($true != (cR @ X11 @ X10)) | ((cR @ X10 @ X11) != $true))))),
% 1.49/1.30 inference(ennf_transformation,[status(thm)],[f5])).
% 1.49/1.30 thf(f5,plain,(
% 1.49/1.30 ~((! [X7 : a,X8 : a] : ((((cT @ X7) = $true) & ((cR @ X8 @ X7) = $true)) => ((cT @ X8) = $true)) & ! [X2 : a,X4 : a,X3 : a] : ((((cR @ X3 @ X2) = $true) & ($true = (cR @ X4 @ X3))) => ($true = (cR @ X4 @ X2))) & ! [X1 : a,X0 : a] : ((($true = (cS @ X1)) & ((cR @ X0 @ X1) = $true)) => ((cS @ X0) = $true)) & ! [X5 : a,X6 : a] : (((cR @ X6 @ X5) = $true) | ($true = (cR @ X5 @ X6))) & ! [X9 : a] : ($true = (cR @ X9 @ X9)) & ! [X11 : a,X10 : a] : ((($true = (cR @ X11 @ X10)) & ((cR @ X10 @ X11) = $true)) => (X10 = X11))) => (! [X13 : a] : (((cS @ X13) = $true) => ($true = (cT @ X13))) | ! [X12 : a] : (((cT @ X12) = $true) => ((cS @ X12) = $true))))),
% 1.49/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.30 thf(f4,plain,(
% 1.49/1.30 ~((! [X0 : a,X1 : a] : (((cR @ X0 @ X1) & (cS @ X1)) => (cS @ X0)) & ! [X2 : a,X3 : a,X4 : a] : (((cR @ X4 @ X3) & (cR @ X3 @ X2)) => (cR @ X4 @ X2)) & ! [X5 : a,X6 : a] : ((cR @ X5 @ X6) | (cR @ X6 @ X5)) & ! [X7 : a,X8 : a] : (((cR @ X8 @ X7) & (cT @ X7)) => (cT @ X8)) & ! [X9 : a] : (cR @ X9 @ X9) & ! [X10 : a,X11 : a] : (((cR @ X10 @ X11) & (cR @ X11 @ X10)) => (X10 = X11))) => (! [X12 : a] : ((cT @ X12) => (cS @ X12)) | ! [X13 : a] : ((cS @ X13) => (cT @ X13))))),
% 1.49/1.30 inference(rectify,[status(thm)],[f2])).
% 1.49/1.30 thf(f2,negated_conjecture,(
% 1.49/1.30 ~((! [X3 : a,X4 : a] : (((cR @ X3 @ X4) & (cS @ X4)) => (cS @ X3)) & ! [X2 : a,X1 : a,X0 : a] : (((cR @ X0 @ X1) & (cR @ X1 @ X2)) => (cR @ X0 @ X2)) & ! [X1 : a,X0 : a] : ((cR @ X1 @ X0) | (cR @ X0 @ X1)) & ! [X4 : a,X3 : a] : (((cR @ X3 @ X4) & (cT @ X4)) => (cT @ X3)) & ! [X0 : a] : (cR @ X0 @ X0) & ! [X0 : a,X1 : a] : (((cR @ X0 @ X1) & (cR @ X1 @ X0)) => (X0 = X1))) => (! [X0 : a] : ((cT @ X0) => (cS @ X0)) | ! [X0 : a] : ((cS @ X0) => (cT @ X0))))),
% 1.49/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.30 thf(f1,conjecture,(
% 1.49/1.30 (! [X3 : a,X4 : a] : (((cR @ X3 @ X4) & (cS @ X4)) => (cS @ X3)) & ! [X2 : a,X1 : a,X0 : a] : (((cR @ X0 @ X1) & (cR @ X1 @ X2)) => (cR @ X0 @ X2)) & ! [X1 : a,X0 : a] : ((cR @ X1 @ X0) | (cR @ X0 @ X1)) & ! [X4 : a,X3 : a] : (((cR @ X3 @ X4) & (cT @ X4)) => (cT @ X3)) & ! [X0 : a] : (cR @ X0 @ X0) & ! [X0 : a,X1 : a] : (((cR @ X0 @ X1) & (cR @ X1 @ X0)) => (X0 = X1))) => (! [X0 : a] : ((cT @ X0) => (cS @ X0)) | ! [X0 : a] : ((cS @ X0) => (cT @ X0)))),
% 1.49/1.30 file('/export/starexec/sandbox2/tmp/tmp.lbqzEspigo/DTF2THF_17603.p',cTHM553_pme)).
% 1.49/1.30 thf(f55,plain,(
% 1.49/1.30 ((cT @ sK1) != $true) | ~spl2_1),
% 1.49/1.30 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.49/1.30 thf(f54,plain,(
% 1.49/1.30 ($true != $true) | ((cT @ sK1) != $true) | ~spl2_1),
% 1.49/1.30 inference(superposition,[status(thm)],[f19,f35])).
% 1.49/1.30 thf(f35,plain,(
% 1.49/1.30 ( ! [X0 : a] : (((cS @ X0) = $true) | ((cT @ X0) != $true)) ) | ~spl2_1),
% 1.49/1.30 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.49/1.30 thf(f34,definition,(
% 1.49/1.30 spl2_1 <=> ! [X0 : a] : (((cT @ X0) != $true) | ((cS @ X0) = $true))),
% 1.49/1.30 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.49/1.30 thf(f19,plain,(
% 1.49/1.30 ((cS @ sK1) != $true)),
% 1.49/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.30 thf(f47,plain,(
% 1.49/1.30 ~spl2_2),
% 1.49/1.30 inference(avatar_contradiction_clause,[status(thm)],[f46])).
% 1.49/1.30 thf(f46,plain,(
% 1.49/1.30 $false | ~spl2_2),
% 1.49/1.30 inference(subsumption_resolution,[status(thm)],[f45,f20])).
% 1.49/1.30 thf(f20,plain,(
% 1.49/1.30 ((cS @ sK0) = $true)),
% 1.49/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.30 thf(f45,plain,(
% 1.49/1.30 ((cS @ sK0) != $true) | ~spl2_2),
% 1.49/1.30 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.49/1.30 thf(f44,plain,(
% 1.49/1.30 ((cS @ sK0) != $true) | ($true != $true) | ~spl2_2),
% 1.49/1.30 inference(superposition,[status(thm)],[f21,f38])).
% 1.49/1.30 thf(f38,plain,(
% 1.49/1.30 ( ! [X1 : a] : (($true = (cT @ X1)) | ($true != (cS @ X1))) ) | ~spl2_2),
% 1.49/1.30 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.49/1.30 thf(f37,definition,(
% 1.49/1.30 spl2_2 <=> ! [X1 : a] : (($true != (cS @ X1)) | ($true = (cT @ X1)))),
% 1.49/1.30 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.49/1.30 thf(f21,plain,(
% 1.49/1.30 ($true != (cT @ sK0))),
% 1.49/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.30 thf(f39,plain,(
% 1.49/1.30 spl2_1 | spl2_2),
% 1.49/1.30 inference(avatar_split_clause,[status(thm)],[f32,f37,f34])).
% 1.49/1.30 thf(f32,plain,(
% 1.49/1.30 ( ! [X0 : a,X1 : a] : (($true != (cS @ X1)) | ((cT @ X0) != $true) | ($true = (cT @ X1)) | ((cS @ X0) = $true)) )),
% 1.49/1.30 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.49/1.30 thf(f30,plain,(
% 1.49/1.30 ( ! [X0 : a,X1 : a] : (((cT @ X0) != $true) | ($true != $true) | ((cS @ X0) = $true) | ($true = (cT @ X1)) | ($true != (cS @ X1))) )),
% 1.49/1.30 inference(superposition,[status(thm)],[f16,f26])).
% 1.49/1.30 thf(f26,plain,(
% 1.49/1.30 ( ! [X0 : a,X1 : a] : (((cR @ X1 @ X0) = $true) | ($true != (cT @ X1)) | ((cT @ X0) = $true)) )),
% 1.49/1.30 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.49/1.30 thf(f25,plain,(
% 1.49/1.30 ( ! [X0 : a,X1 : a] : (($true != $true) | ((cT @ X0) = $true) | ($true != (cT @ X1)) | ((cR @ X1 @ X0) = $true)) )),
% 1.49/1.30 inference(superposition,[status(thm)],[f13,f14])).
% 1.49/1.30 thf(f14,plain,(
% 1.49/1.30 ( ! [X8 : a,X7 : a] : (((cR @ X8 @ X7) = $true) | ((cR @ X7 @ X8) = $true)) )),
% 1.49/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.30 thf(f13,plain,(
% 1.49/1.30 ( ! [X10 : a,X9 : a] : (($true != (cR @ X9 @ X10)) | ($true != (cT @ X10)) | ($true = (cT @ X9))) )),
% 1.49/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.30 thf(f16,plain,(
% 1.49/1.30 ( ! [X3 : a,X4 : a] : (($true != (cR @ X4 @ X3)) | ((cS @ X3) != $true) | ((cS @ X4) = $true)) )),
% 1.49/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.30 % SZS output end Proof for DTF2THF_17603
% 1.49/1.30 % (17879)------------------------------
% 1.49/1.30 % (17879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.30 % (17879)Termination reason: Refutation
% 1.49/1.30
% 1.49/1.30 % (17879)Memory used [KB]: 5500
% 1.49/1.30 % (17879)Time elapsed: 0.005 s
% 1.49/1.30 % (17879)Instructions burned: 6 (million)
% 1.49/1.30 % (17879)------------------------------
% 1.49/1.30 % (17879)------------------------------
% 1.49/1.30 % (17873)Success in time 0.015 s
%------------------------------------------------------------------------------