%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV054^5 : 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 : n015.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 09:40:10 AM UTC 2026
% Result : Theorem 1.63s 1.36s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 216 ( 93 equ; 0 cnn)
% Maximal formula atoms : 22 ( 13 avg)
% Number of connectives : 456 ( 50 ~; 34 |; 46 &; 295 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 139 ( 0 ^; 115 !; 24 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > a > $o ).
thf(func_def_5,type,
sK1: ( a > $o ) > a ).
thf(func_def_6,type,
sK2: a > a ).
thf(func_def_7,type,
sK3: a > ( a > $o ) > a ).
thf(func_def_10,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f25,plain,
$false,
inference(equality_resolution,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: a > $o] :
( $true
!= ( X0 @ ( sK2 @ ( sK1 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( $true
!= ( X0 @ ( sK2 @ ( sK1 @ X0 ) ) ) ) ),
inference(superposition,[status(thm)],[f16,f13]) ).
thf(f13,plain,
! [X9: a > $o,X12: a] :
( ( ( sK0 @ X12 @ ( sK1 @ X9 ) )
= $true )
| ( $true
!= ( X9 @ X12 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X2: a,X3: a,X4: a] :
( ( $true
!= ( sK0 @ X2 @ X3 ) )
| ( $true
!= ( sK0 @ X3 @ X4 ) )
| ( $true
= ( sK0 @ X2 @ X4 ) ) )
& ! [X6: a,X7: a] :
( ( $true
= ( sK0 @ ( sK2 @ X7 ) @ ( sK2 @ X6 ) ) )
| ( $true
!= ( sK0 @ X7 @ X6 ) ) )
& ! [X8: a] :
( $true
!= ( sK0 @ ( sK2 @ X8 ) @ X8 ) )
& ! [X9: a > $o] :
( ! [X10: a] :
( ( ( $true
!= ( sK0 @ ( sK3 @ X10 @ X9 ) @ X10 ) )
& ( $true
= ( X9 @ ( sK3 @ X10 @ X9 ) ) ) )
| ( $true
= ( sK0 @ ( sK1 @ X9 ) @ X10 ) ) )
& ! [X12: a] :
( ( $true
!= ( X9 @ X12 ) )
| ( ( sK0 @ X12 @ ( sK1 @ X9 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > a > $o,X1: ( a > $o ) > a] :
( ! [X2: a,X3: a,X4: a] :
( ( ( X0 @ X2 @ X3 )
!= $true )
| ( ( X0 @ X3 @ X4 )
!= $true )
| ( ( X0 @ X2 @ X4 )
= $true ) )
& ? [X5: a > a] :
( ! [X6: a,X7: a] :
( ( $true
= ( X0 @ ( X5 @ X7 ) @ ( X5 @ X6 ) ) )
| ( ( X0 @ X7 @ X6 )
!= $true ) )
& ! [X8: a] :
( $true
!= ( X0 @ ( X5 @ X8 ) @ X8 ) ) )
& ! [X9: a > $o] :
( ! [X10: a] :
( ? [X11: a] :
( ( $true
!= ( X0 @ X11 @ X10 ) )
& ( $true
= ( X9 @ X11 ) ) )
| ( $true
= ( X0 @ ( X1 @ X9 ) @ X10 ) ) )
& ! [X12: a] :
( ( $true
!= ( X9 @ X12 ) )
| ( $true
= ( X0 @ X12 @ ( X1 @ X9 ) ) ) ) ) )
=> ( ! [X4: a,X3: a,X2: a] :
( ( $true
!= ( sK0 @ X2 @ X3 ) )
| ( $true
!= ( sK0 @ X3 @ X4 ) )
| ( $true
= ( sK0 @ X2 @ X4 ) ) )
& ? [X5: a > a] :
( ! [X7: a,X6: a] :
( ( $true
= ( sK0 @ ( X5 @ X7 ) @ ( X5 @ X6 ) ) )
| ( $true
!= ( sK0 @ X7 @ X6 ) ) )
& ! [X8: a] :
( $true
!= ( sK0 @ ( X5 @ X8 ) @ X8 ) ) )
& ! [X9: a > $o] :
( ! [X10: a] :
( ? [X11: a] :
( ( $true
!= ( sK0 @ X11 @ X10 ) )
& ( $true
= ( X9 @ X11 ) ) )
| ( $true
= ( sK0 @ ( sK1 @ X9 ) @ X10 ) ) )
& ! [X12: a] :
( ( $true
!= ( X9 @ X12 ) )
| ( ( sK0 @ X12 @ ( sK1 @ X9 ) )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X5: a > a] :
( ! [X7: a,X6: a] :
( ( $true
= ( sK0 @ ( X5 @ X7 ) @ ( X5 @ X6 ) ) )
| ( $true
!= ( sK0 @ X7 @ X6 ) ) )
& ! [X8: a] :
( $true
!= ( sK0 @ ( X5 @ X8 ) @ X8 ) ) )
=> ( ! [X7: a,X6: a] :
( ( $true
= ( sK0 @ ( sK2 @ X7 ) @ ( sK2 @ X6 ) ) )
| ( $true
!= ( sK0 @ X7 @ X6 ) ) )
& ! [X8: a] :
( $true
!= ( sK0 @ ( sK2 @ X8 ) @ X8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X9: a > $o,X10: a] :
( ? [X11: a] :
( ( $true
!= ( sK0 @ X11 @ X10 ) )
& ( $true
= ( X9 @ X11 ) ) )
=> ( ( $true
!= ( sK0 @ ( sK3 @ X10 @ X9 ) @ X10 ) )
& ( $true
= ( X9 @ ( sK3 @ X10 @ X9 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > a > $o,X1: ( a > $o ) > a] :
( ! [X2: a,X3: a,X4: a] :
( ( ( X0 @ X2 @ X3 )
!= $true )
| ( ( X0 @ X3 @ X4 )
!= $true )
| ( ( X0 @ X2 @ X4 )
= $true ) )
& ? [X5: a > a] :
( ! [X6: a,X7: a] :
( ( $true
= ( X0 @ ( X5 @ X7 ) @ ( X5 @ X6 ) ) )
| ( ( X0 @ X7 @ X6 )
!= $true ) )
& ! [X8: a] :
( $true
!= ( X0 @ ( X5 @ X8 ) @ X8 ) ) )
& ! [X9: a > $o] :
( ! [X10: a] :
( ? [X11: a] :
( ( $true
!= ( X0 @ X11 @ X10 ) )
& ( $true
= ( X9 @ X11 ) ) )
| ( $true
= ( X0 @ ( X1 @ X9 ) @ X10 ) ) )
& ! [X12: a] :
( ( $true
!= ( X9 @ X12 ) )
| ( $true
= ( X0 @ X12 @ ( X1 @ X9 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > a > $o,X1: ( a > $o ) > a] :
( ! [X3: a,X4: a,X2: a] :
( ( ( X0 @ X3 @ X4 )
!= $true )
| ( $true
!= ( X0 @ X4 @ X2 ) )
| ( $true
= ( X0 @ X3 @ X2 ) ) )
& ? [X9: a > a] :
( ! [X11: a,X10: a] :
( ( $true
= ( X0 @ ( X9 @ X10 ) @ ( X9 @ X11 ) ) )
| ( $true
!= ( X0 @ X10 @ X11 ) ) )
& ! [X12: a] :
( $true
!= ( X0 @ ( X9 @ X12 ) @ X12 ) ) )
& ! [X5: a > $o] :
( ! [X6: a] :
( ? [X7: a] :
( ( ( X0 @ X7 @ X6 )
!= $true )
& ( ( X5 @ X7 )
= $true ) )
| ( ( X0 @ ( X1 @ X5 ) @ X6 )
= $true ) )
& ! [X8: a] :
( ( $true
!= ( X5 @ X8 ) )
| ( ( X0 @ X8 @ ( X1 @ X5 ) )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: ( a > $o ) > a,X0: a > a > $o] :
( ? [X9: a > a] :
( ! [X11: a,X10: a] :
( ( $true
= ( X0 @ ( X9 @ X10 ) @ ( X9 @ X11 ) ) )
| ( $true
!= ( X0 @ X10 @ X11 ) ) )
& ! [X12: a] :
( $true
!= ( X0 @ ( X9 @ X12 ) @ X12 ) ) )
& ! [X3: a,X4: a,X2: a] :
( ( $true
= ( X0 @ X3 @ X2 ) )
| ( $true
!= ( X0 @ X4 @ X2 ) )
| ( ( X0 @ X3 @ X4 )
!= $true ) )
& ! [X5: a > $o] :
( ! [X6: a] :
( ? [X7: a] :
( ( ( X0 @ X7 @ X6 )
!= $true )
& ( ( X5 @ X7 )
= $true ) )
| ( ( X0 @ ( X1 @ X5 ) @ X6 )
= $true ) )
& ! [X8: a] :
( ( $true
!= ( X5 @ X8 ) )
| ( ( X0 @ X8 @ ( X1 @ X5 ) )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: ( a > $o ) > a,X0: a > a > $o] :
( ( ! [X3: a,X4: a,X2: a] :
( ( ( $true
= ( X0 @ X4 @ X2 ) )
& ( ( X0 @ X3 @ X4 )
= $true ) )
=> ( $true
= ( X0 @ X3 @ X2 ) ) )
& ! [X5: a > $o] :
( ! [X8: a] :
( ( $true
= ( X5 @ X8 ) )
=> ( ( X0 @ X8 @ ( X1 @ X5 ) )
= $true ) )
& ! [X6: a] :
( ! [X7: a] :
( ( ( X5 @ X7 )
= $true )
=> ( ( X0 @ X7 @ X6 )
= $true ) )
=> ( ( X0 @ ( X1 @ X5 ) @ X6 )
= $true ) ) ) )
=> ! [X9: a > a] :
( ! [X11: a,X10: a] :
( ( $true
= ( X0 @ X10 @ X11 ) )
=> ( $true
= ( X0 @ ( X9 @ X10 ) @ ( X9 @ X11 ) ) ) )
=> ? [X12: a] :
( $true
= ( X0 @ ( X9 @ X12 ) @ X12 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: ( a > $o ) > a] :
( ( ! [X2: a,X3: a,X4: a] :
( ( ( X0 @ X3 @ X4 )
& ( X0 @ X4 @ X2 ) )
=> ( X0 @ X3 @ X2 ) )
& ! [X5: a > $o] :
( ! [X6: a] :
( ! [X7: a] :
( ( X5 @ X7 )
=> ( X0 @ X7 @ X6 ) )
=> ( X0 @ ( X1 @ X5 ) @ X6 ) )
& ! [X8: a] :
( ( X5 @ X8 )
=> ( X0 @ X8 @ ( X1 @ X5 ) ) ) ) )
=> ! [X9: a > a] :
( ! [X10: a,X11: a] :
( ( X0 @ X10 @ X11 )
=> ( X0 @ ( X9 @ X10 ) @ ( X9 @ X11 ) ) )
=> ? [X12: a] : ( X0 @ ( X9 @ X12 ) @ X12 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: ( a > $o ) > a] :
( ( ! [X4: a,X2: a,X3: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X4 ) )
=> ( X0 @ X2 @ X4 ) )
& ! [X5: a > $o] :
( ! [X6: a] :
( ! [X7: a] :
( ( X5 @ X7 )
=> ( X0 @ X7 @ X6 ) )
=> ( X0 @ ( X1 @ X5 ) @ X6 ) )
& ! [X4: a] :
( ( X5 @ X4 )
=> ( X0 @ X4 @ ( X1 @ X5 ) ) ) ) )
=> ! [X8: a > a] :
( ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ ( X8 @ X2 ) @ ( X8 @ X3 ) ) )
=> ? [X9: a] : ( X0 @ ( X8 @ X9 ) @ X9 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X1: ( a > $o ) > a] :
( ( ! [X4: a,X2: a,X3: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X4 ) )
=> ( X0 @ X2 @ X4 ) )
& ! [X5: a > $o] :
( ! [X6: a] :
( ! [X7: a] :
( ( X5 @ X7 )
=> ( X0 @ X7 @ X6 ) )
=> ( X0 @ ( X1 @ X5 ) @ X6 ) )
& ! [X4: a] :
( ( X5 @ X4 )
=> ( X0 @ X4 @ ( X1 @ X5 ) ) ) ) )
=> ! [X8: a > a] :
( ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ ( X8 @ X2 ) @ ( X8 @ X3 ) ) )
=> ? [X9: a] : ( X0 @ ( X8 @ X9 ) @ X9 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.bpULcMaiAU/DTF2THF_11526.p',cTHM403_pme) ).
thf(f16,plain,
! [X8: a] :
( $true
!= ( sK0 @ ( sK2 @ X8 ) @ X8 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV054^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n015.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:39:46 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEV054^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Set Theory (Relations)
% 0.29/0.46 % Problem : TPS problem THM403
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0275 [Bro09]
% 0.29/0.46 % : THM403 [TPS]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.17 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, 0.20 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 v6.2.0, 0.33 v6.1.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.50 v5.3.0, 0.25 v5.2.0, 0.50 v5.1.0, 0.25 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.29/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.29/0.46 % Number of connectives : 35 ( 0 ~; 0 |; 3 &; 25 @)
% 0.29/0.46 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 13 ( 13 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.29/0.46 % Number of variables : 13 ( 0 ^; 12 !; 1 ?; 13 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 % : Polymorphic definitions expanded.
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(a_type,type,
% 0.29/0.46 a: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(cTHM403_pme,conjecture,
% 0.29/0.46 ! [R: a > a > $o,U: ( a > $o ) > a] :
% 0.29/0.46 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 0.29/0.46 ( ( ( R @ Xx @ Xy )
% 0.29/0.46 & ( R @ Xy @ Xz ) )
% 0.29/0.46 => ( R @ Xx @ Xz ) )
% 0.29/0.46 & ! [Xs: a > $o] :
% 0.29/0.46 ( ! [Xz: a] :
% 0.29/0.46 ( ( Xs @ Xz )
% 0.29/0.46 => ( R @ Xz @ ( U @ Xs ) ) )
% 0.29/0.46 & ! [Xj: a] :
% 0.29/0.46 ( ! [Xk: a] :
% 0.29/0.46 ( ( Xs @ Xk )
% 0.29/0.46 => ( R @ Xk @ Xj ) )
% 0.29/0.46 => ( R @ ( U @ Xs ) @ Xj ) ) ) )
% 0.29/0.46 => ! [Xf: a > a] :
% 0.29/0.46 ( ! [Xx: a,Xy: a] :
% 0.29/0.46 ( ( R @ Xx @ Xy )
% 0.29/0.46 => ( R @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) )
% 0.29/0.46 => ? [Xw: a] : ( R @ ( Xf @ Xw ) @ Xw ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.63/1.32 ---- Embedded in THF ---
% 1.63/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.32 %%% Generated on Tue Feb 24 12:39:47 EST 2026
% 1.63/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.32 %%% Logic specification used:
% 1.63/1.32 %%% thf(spec, logic, $$dhol).
% 1.63/1.32
% 1.63/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.bpULcMaiAU/DTF2DTF11526.p
% See solution above
% 1.63/1.32 ------------------------
% 1.63/1.33 ---- Cleaned THF ---
% 1.63/1.33 thf(a_type,type,
% 1.63/1.33 a: $tType ).
% 1.63/1.33
% 1.63/1.33 thf(cTHM403_pme,conjecture,
% 1.63/1.33 ! [R: a > a > $o,U: ( a > $o ) > a] :
% 1.63/1.33 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 1.63/1.33 ( ( ( R @ Xx @ Xy )
% 1.63/1.33 & ( R @ Xy @ Xz ) )
% 1.63/1.33 => ( R @ Xx @ Xz ) )
% 1.63/1.33 & ! [Xs: a > $o] :
% 1.63/1.33 ( ! [Xz: a] :
% 1.63/1.33 ( ( Xs @ Xz )
% 1.63/1.33 => ( R @ Xz @ ( U @ Xs ) ) )
% 1.63/1.33 & ! [Xj: a] :
% 1.63/1.33 ( ! [Xk: a] :
% 1.63/1.33 ( ( Xs @ Xk )
% 1.63/1.33 => ( R @ Xk @ Xj ) )
% 1.63/1.33 => ( R @ ( U @ Xs ) @ Xj ) ) ) )
% 1.63/1.33 => ! [Xf: a > a] :
% 1.63/1.33 ( ! [Xx: a,Xy: a] :
% 1.63/1.33 ( ( R @ Xx @ Xy )
% 1.63/1.33 => ( R @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) )
% 1.63/1.33 => ? [Xw: a] : ( R @ ( Xf @ Xw ) @ Xw ) ) ) ).
% 1.63/1.33 ------------------------
% 1.63/1.35 % (11745)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_11526 for (2999ds/27Mi)
% 1.63/1.35 % (11743)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11526 for (2999ds/183Mi)
% 1.63/1.35 % (11744)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_11526 for (2999ds/4Mi)
% 1.63/1.35 % (11746)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11526 for (2999ds/2Mi)
% 1.63/1.35 % (11747)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_11526 for (2999ds/2Mi)
% 1.63/1.35 % (11749)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11526 for (2999ds/18Mi)
% 1.63/1.35 % (11748)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_11526 for (2999ds/275Mi)
% 1.63/1.35 % (11746)Instruction limit reached!
% 1.63/1.35 % (11746)------------------------------
% 1.63/1.35 % (11746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (11746)Termination reason: Unknown
% 1.63/1.35 % (11746)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (11746)Memory used [KB]: 5500
% 1.63/1.35 % (11746)Time elapsed: 0.004 s
% 1.63/1.35 % (11746)Instructions burned: 2 (million)
% 1.63/1.35 % (11746)------------------------------
% 1.63/1.35 % (11746)------------------------------
% 1.63/1.35 % (11747)Instruction limit reached!
% 1.63/1.35 % (11747)------------------------------
% 1.63/1.35 % (11747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (11747)Termination reason: Unknown
% 1.63/1.35 % (11747)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (11747)Memory used [KB]: 5500
% 1.63/1.35 % (11747)Time elapsed: 0.004 s
% 1.63/1.35 % (11747)Instructions burned: 3 (million)
% 1.63/1.35 % (11747)------------------------------
% 1.63/1.35 % (11747)------------------------------
% 1.63/1.35 % (11743)First to succeed.
% 1.63/1.35 % (11744)Instruction limit reached!
% 1.63/1.35 % (11744)------------------------------
% 1.63/1.35 % (11744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (11744)Termination reason: Unknown
% 1.63/1.35 % (11744)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (11744)Memory used [KB]: 5500
% 1.63/1.35 % (11744)Time elapsed: 0.005 s
% 1.63/1.35 % (11744)Instructions burned: 4 (million)
% 1.63/1.35 % (11744)------------------------------
% 1.63/1.35 % (11744)------------------------------
% 1.63/1.36 % (11745)Instruction limit reached!
% 1.63/1.36 % (11745)------------------------------
% 1.63/1.36 % (11745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (11745)Termination reason: Unknown
% 1.63/1.36 % (11745)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (11745)Memory used [KB]: 5628
% 1.63/1.36 % (11745)Time elapsed: 0.012 s
% 1.63/1.36 % (11745)Instructions burned: 28 (million)
% 1.63/1.36 % (11745)------------------------------
% 1.63/1.36 % (11745)------------------------------
% 1.63/1.36 % (11748)Also succeeded, but the first one will report.
% 1.63/1.36 % (11743)Refutation found. Thanks to Tanya!
% 1.63/1.36 % SZS status Theorem for DTF2THF_11526
% 1.63/1.36 % SZS output start Proof for DTF2THF_11526
% 1.63/1.36 thf(type_def_5, type, a: $tType).
% 1.63/1.36 thf(func_def_0, type, a: $tType).
% 1.63/1.36 thf(func_def_4, type, sK0: a > a > $o).
% 1.63/1.36 thf(func_def_5, type, sK1: (a > $o) > a).
% 1.63/1.36 thf(func_def_6, type, sK2: a > a).
% 1.63/1.36 thf(func_def_7, type, sK3: a > (a > $o) > a).
% 1.63/1.36 thf(func_def_10, type, ph5: !>[X0: $tType]:(X0)).
% 1.63/1.36 thf(f25,plain,(
% 1.63/1.36 $false),
% 1.63/1.36 inference(equality_resolution,[status(thm)],[f20])).
% 1.63/1.36 thf(f20,plain,(
% 1.63/1.36 ( ! [X0 : a > $o] : (($true != (X0 @ (sK2 @ (sK1 @ X0))))) )),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.63/1.36 thf(f19,plain,(
% 1.63/1.36 ( ! [X0 : a > $o] : (($true != $true) | ($true != (X0 @ (sK2 @ (sK1 @ X0))))) )),
% 1.63/1.36 inference(superposition,[status(thm)],[f16,f13])).
% 1.63/1.36 thf(f13,plain,(
% 1.63/1.36 ( ! [X9 : a > $o,X12 : a] : (((sK0 @ X12 @ (sK1 @ X9)) = $true) | ($true != (X9 @ X12))) )),
% 1.63/1.36 inference(cnf_transformation,[status(thm)],[f12])).
% 1.63/1.36 thf(f12,plain,(
% 1.63/1.36 ! [X2 : a,X3 : a,X4 : a] : (($true != (sK0 @ X2 @ X3)) | ($true != (sK0 @ X3 @ X4)) | ($true = (sK0 @ X2 @ X4))) & (! [X6 : a,X7 : a] : (($true = (sK0 @ (sK2 @ X7) @ (sK2 @ X6))) | ($true != (sK0 @ X7 @ X6))) & ! [X8 : a] : ($true != (sK0 @ (sK2 @ X8) @ X8))) & ! [X9 : a > $o] : (! [X10 : a] : ((($true != (sK0 @ (sK3 @ X10 @ X9) @ X10)) & ($true = (X9 @ (sK3 @ X10 @ X9)))) | ($true = (sK0 @ (sK1 @ X9) @ X10))) & ! [X12 : a] : (($true != (X9 @ X12)) | ((sK0 @ X12 @ (sK1 @ X9)) = $true)))),
% 1.63/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f11,f10,f9])).
% 1.63/1.36 thf(f9,plain,(
% 1.63/1.36 ? [X0 : a > a > $o,X1 : (a > $o) > a] : (! [X2 : a,X3 : a,X4 : a] : (((X0 @ X2 @ X3) != $true) | ((X0 @ X3 @ X4) != $true) | ((X0 @ X2 @ X4) = $true)) & ? [X5 : a > a] : (! [X6 : a,X7 : a] : (($true = (X0 @ (X5 @ X7) @ (X5 @ X6))) | ((X0 @ X7 @ X6) != $true)) & ! [X8 : a] : ($true != (X0 @ (X5 @ X8) @ X8))) & ! [X9 : a > $o] : (! [X10 : a] : (? [X11 : a] : (($true != (X0 @ X11 @ X10)) & ($true = (X9 @ X11))) | ($true = (X0 @ (X1 @ X9) @ X10))) & ! [X12 : a] : (($true != (X9 @ X12)) | ($true = (X0 @ X12 @ (X1 @ X9)))))) => (! [X4 : a,X3 : a,X2 : a] : (($true != (sK0 @ X2 @ X3)) | ($true != (sK0 @ X3 @ X4)) | ($true = (sK0 @ X2 @ X4))) & ? [X5 : a > a] : (! [X7 : a,X6 : a] : (($true = (sK0 @ (X5 @ X7) @ (X5 @ X6))) | ($true != (sK0 @ X7 @ X6))) & ! [X8 : a] : ($true != (sK0 @ (X5 @ X8) @ X8))) & ! [X9 : a > $o] : (! [X10 : a] : (? [X11 : a] : (($true != (sK0 @ X11 @ X10)) & ($true = (X9 @ X11))) | ($true = (sK0 @ (sK1 @ X9) @ X10))) & ! [X12 : a] : (($true != (X9 @ X12)) | ((sK0 @ X12 @ (sK1 @ X9)) = $true))))),
% 1.63/1.36 introduced(definition,[],[choice_axiom])).
% 1.63/1.36 thf(f10,plain,(
% 1.63/1.36 ? [X5 : a > a] : (! [X7 : a,X6 : a] : (($true = (sK0 @ (X5 @ X7) @ (X5 @ X6))) | ($true != (sK0 @ X7 @ X6))) & ! [X8 : a] : ($true != (sK0 @ (X5 @ X8) @ X8))) => (! [X7 : a,X6 : a] : (($true = (sK0 @ (sK2 @ X7) @ (sK2 @ X6))) | ($true != (sK0 @ X7 @ X6))) & ! [X8 : a] : ($true != (sK0 @ (sK2 @ X8) @ X8)))),
% 1.63/1.36 introduced(definition,[],[choice_axiom])).
% 1.63/1.36 thf(f11,plain,(
% 1.63/1.36 ! [X9 : a > $o,X10 : a] : (? [X11 : a] : (($true != (sK0 @ X11 @ X10)) & ($true = (X9 @ X11))) => (($true != (sK0 @ (sK3 @ X10 @ X9) @ X10)) & ($true = (X9 @ (sK3 @ X10 @ X9)))))),
% 1.63/1.36 introduced(definition,[],[choice_axiom])).
% 1.63/1.36 thf(f8,plain,(
% 1.63/1.36 ? [X0 : a > a > $o,X1 : (a > $o) > a] : (! [X2 : a,X3 : a,X4 : a] : (((X0 @ X2 @ X3) != $true) | ((X0 @ X3 @ X4) != $true) | ((X0 @ X2 @ X4) = $true)) & ? [X5 : a > a] : (! [X6 : a,X7 : a] : (($true = (X0 @ (X5 @ X7) @ (X5 @ X6))) | ((X0 @ X7 @ X6) != $true)) & ! [X8 : a] : ($true != (X0 @ (X5 @ X8) @ X8))) & ! [X9 : a > $o] : (! [X10 : a] : (? [X11 : a] : (($true != (X0 @ X11 @ X10)) & ($true = (X9 @ X11))) | ($true = (X0 @ (X1 @ X9) @ X10))) & ! [X12 : a] : (($true != (X9 @ X12)) | ($true = (X0 @ X12 @ (X1 @ X9))))))),
% 1.63/1.36 inference(rectify,[status(thm)],[f7])).
% 1.63/1.36 thf(f7,plain,(
% 1.63/1.36 ? [X0 : a > a > $o,X1 : (a > $o) > a] : (! [X3 : a,X4 : a,X2 : a] : (((X0 @ X3 @ X4) != $true) | ($true != (X0 @ X4 @ X2)) | ($true = (X0 @ X3 @ X2))) & ? [X9 : a > a] : (! [X11 : a,X10 : a] : (($true = (X0 @ (X9 @ X10) @ (X9 @ X11))) | ($true != (X0 @ X10 @ X11))) & ! [X12 : a] : ($true != (X0 @ (X9 @ X12) @ X12))) & ! [X5 : a > $o] : (! [X6 : a] : (? [X7 : a] : (((X0 @ X7 @ X6) != $true) & ((X5 @ X7) = $true)) | ((X0 @ (X1 @ X5) @ X6) = $true)) & ! [X8 : a] : (($true != (X5 @ X8)) | ((X0 @ X8 @ (X1 @ X5)) = $true))))),
% 1.63/1.36 inference(flattening,[status(thm)],[f6])).
% 1.63/1.36 thf(f6,plain,(
% 1.63/1.36 ? [X1 : (a > $o) > a,X0 : a > a > $o] : (? [X9 : a > a] : (! [X11 : a,X10 : a] : (($true = (X0 @ (X9 @ X10) @ (X9 @ X11))) | ($true != (X0 @ X10 @ X11))) & ! [X12 : a] : ($true != (X0 @ (X9 @ X12) @ X12))) & (! [X3 : a,X4 : a,X2 : a] : (($true = (X0 @ X3 @ X2)) | (($true != (X0 @ X4 @ X2)) | ((X0 @ X3 @ X4) != $true))) & ! [X5 : a > $o] : (! [X6 : a] : (? [X7 : a] : (((X0 @ X7 @ X6) != $true) & ((X5 @ X7) = $true)) | ((X0 @ (X1 @ X5) @ X6) = $true)) & ! [X8 : a] : (($true != (X5 @ X8)) | ((X0 @ X8 @ (X1 @ X5)) = $true)))))),
% 1.63/1.36 inference(ennf_transformation,[status(thm)],[f5])).
% 1.63/1.36 thf(f5,plain,(
% 1.63/1.36 ~! [X1 : (a > $o) > a,X0 : a > a > $o] : ((! [X3 : a,X4 : a,X2 : a] : ((($true = (X0 @ X4 @ X2)) & ((X0 @ X3 @ X4) = $true)) => ($true = (X0 @ X3 @ X2))) & ! [X5 : a > $o] : (! [X8 : a] : (($true = (X5 @ X8)) => ((X0 @ X8 @ (X1 @ X5)) = $true)) & ! [X6 : a] : (! [X7 : a] : (((X5 @ X7) = $true) => ((X0 @ X7 @ X6) = $true)) => ((X0 @ (X1 @ X5) @ X6) = $true)))) => ! [X9 : a > a] : (! [X11 : a,X10 : a] : (($true = (X0 @ X10 @ X11)) => ($true = (X0 @ (X9 @ X10) @ (X9 @ X11)))) => ? [X12 : a] : ($true = (X0 @ (X9 @ X12) @ X12))))),
% 1.63/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.36 thf(f4,plain,(
% 1.63/1.36 ~! [X0 : a > a > $o,X1 : (a > $o) > a] : ((! [X2 : a,X3 : a,X4 : a] : (((X0 @ X3 @ X4) & (X0 @ X4 @ X2)) => (X0 @ X3 @ X2)) & ! [X5 : a > $o] : (! [X6 : a] : (! [X7 : a] : ((X5 @ X7) => (X0 @ X7 @ X6)) => (X0 @ (X1 @ X5) @ X6)) & ! [X8 : a] : ((X5 @ X8) => (X0 @ X8 @ (X1 @ X5))))) => ! [X9 : a > a] : (! [X10 : a,X11 : a] : ((X0 @ X10 @ X11) => (X0 @ (X9 @ X10) @ (X9 @ X11))) => ? [X12 : a] : (X0 @ (X9 @ X12) @ X12)))),
% 1.63/1.36 inference(rectify,[status(thm)],[f2])).
% 1.63/1.36 thf(f2,negated_conjecture,(
% 1.63/1.36 ~! [X0 : a > a > $o,X1 : (a > $o) > a] : ((! [X4 : a,X2 : a,X3 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X4)) => (X0 @ X2 @ X4)) & ! [X5 : a > $o] : (! [X6 : a] : (! [X7 : a] : ((X5 @ X7) => (X0 @ X7 @ X6)) => (X0 @ (X1 @ X5) @ X6)) & ! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ (X1 @ X5))))) => ! [X8 : a > a] : (! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X0 @ (X8 @ X2) @ (X8 @ X3))) => ? [X9 : a] : (X0 @ (X8 @ X9) @ X9)))),
% 1.63/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.36 thf(f1,conjecture,(
% 1.63/1.36 ! [X0 : a > a > $o,X1 : (a > $o) > a] : ((! [X4 : a,X2 : a,X3 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X4)) => (X0 @ X2 @ X4)) & ! [X5 : a > $o] : (! [X6 : a] : (! [X7 : a] : ((X5 @ X7) => (X0 @ X7 @ X6)) => (X0 @ (X1 @ X5) @ X6)) & ! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ (X1 @ X5))))) => ! [X8 : a > a] : (! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X0 @ (X8 @ X2) @ (X8 @ X3))) => ? [X9 : a] : (X0 @ (X8 @ X9) @ X9)))),
% 1.63/1.36 file('/export/starexec/sandbox2/tmp/tmp.bpULcMaiAU/DTF2THF_11526.p',cTHM403_pme)).
% 1.63/1.36 thf(f16,plain,(
% 1.63/1.36 ( ! [X8 : a] : (($true != (sK0 @ (sK2 @ X8) @ X8))) )),
% 1.63/1.36 inference(cnf_transformation,[status(thm)],[f12])).
% 1.63/1.36 % SZS output end Proof for DTF2THF_11526
% 1.63/1.36 % (11743)------------------------------
% 1.63/1.36 % (11743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (11743)Termination reason: Refutation
% 1.63/1.36
% 1.63/1.36 % (11743)Memory used [KB]: 5500
% 1.63/1.36 % (11743)Time elapsed: 0.006 s
% 1.63/1.36 % (11743)Instructions burned: 3 (million)
% 1.63/1.36 % (11743)------------------------------
% 1.63/1.36 % (11743)------------------------------
% 1.63/1.36 % (11742)Success in time 0.02 s
%------------------------------------------------------------------------------