%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV055^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 1.70s 1.47s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 231 ( 96 equ; 0 cnn)
% Maximal formula atoms : 22 ( 12 avg)
% Number of connectives : 462 ( 47 ~; 35 |; 46 &; 303 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 145 ( 5 ^; 116 !; 24 ?; 145 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: ( a > $o ) > a ).
thf(func_def_5,type,
sK1: a > a > $o ).
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(f37,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
$true != $true,
inference(superposition,[status(thm)],[f16,f33]) ).
thf(f33,plain,
! [X11: a] :
( $true
= ( sK1
@ ( sK0
@ ^ [Y0: a] : $false )
@ X11 ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X11: a] :
( ( $false = $true )
| ( $true
= ( sK1
@ ( sK0
@ ^ [Y0: a] : $false )
@ X11 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X11: a] :
( ( $true
= ( ^ [Y0: a] : $false
@ ( sK3 @ X11
@ ^ [Y0: a] : $false ) ) )
| ( $true
= ( sK1
@ ( sK0
@ ^ [Y0: a] : $false )
@ X11 ) ) ),
inference(primitive_instantiation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X11: a,X9: a > $o] :
( ( $true
= ( X9 @ ( sK3 @ X11 @ X9 ) ) )
| ( $true
= ( sK1 @ ( sK0 @ X9 ) @ X11 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X2: a,X3: a,X4: a] :
( ( ( sK1 @ X3 @ X2 )
!= $true )
| ( ( sK1 @ X2 @ X4 )
!= $true )
| ( ( sK1 @ X3 @ X4 )
= $true ) )
& ! [X6: a,X7: a] :
( ( $true
!= ( sK1 @ X6 @ X7 ) )
| ( ( sK1 @ ( sK2 @ X6 ) @ ( sK2 @ X7 ) )
= $true ) )
& ! [X8: a] :
( ( sK1 @ X8 @ ( sK2 @ X8 ) )
!= $true )
& ! [X9: a > $o] :
( ! [X10: a] :
( ( ( X9 @ X10 )
!= $true )
| ( $true
= ( sK1 @ X10 @ ( sK0 @ X9 ) ) ) )
& ! [X11: a] :
( ( $true
= ( sK1 @ ( sK0 @ X9 ) @ X11 ) )
| ( ( $true
= ( X9 @ ( sK3 @ X11 @ X9 ) ) )
& ( $true
!= ( sK1 @ ( sK3 @ X11 @ X9 ) @ X11 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: ( a > $o ) > a,X1: a > a > $o] :
( ! [X2: a,X3: a,X4: a] :
( ( $true
!= ( X1 @ X3 @ X2 ) )
| ( $true
!= ( X1 @ X2 @ X4 ) )
| ( ( X1 @ X3 @ X4 )
= $true ) )
& ? [X5: a > a] :
( ! [X6: a,X7: a] :
( ( ( X1 @ X6 @ X7 )
!= $true )
| ( $true
= ( X1 @ ( X5 @ X6 ) @ ( X5 @ X7 ) ) ) )
& ! [X8: a] :
( ( X1 @ X8 @ ( X5 @ X8 ) )
!= $true ) )
& ! [X9: a > $o] :
( ! [X10: a] :
( ( ( X9 @ X10 )
!= $true )
| ( $true
= ( X1 @ X10 @ ( X0 @ X9 ) ) ) )
& ! [X11: a] :
( ( $true
= ( X1 @ ( X0 @ X9 ) @ X11 ) )
| ? [X12: a] :
( ( $true
= ( X9 @ X12 ) )
& ( $true
!= ( X1 @ X12 @ X11 ) ) ) ) ) )
=> ( ! [X4: a,X3: a,X2: a] :
( ( ( sK1 @ X3 @ X2 )
!= $true )
| ( ( sK1 @ X2 @ X4 )
!= $true )
| ( ( sK1 @ X3 @ X4 )
= $true ) )
& ? [X5: a > a] :
( ! [X7: a,X6: a] :
( ( $true
!= ( sK1 @ X6 @ X7 ) )
| ( $true
= ( sK1 @ ( X5 @ X6 ) @ ( X5 @ X7 ) ) ) )
& ! [X8: a] :
( ( sK1 @ X8 @ ( X5 @ X8 ) )
!= $true ) )
& ! [X9: a > $o] :
( ! [X10: a] :
( ( ( X9 @ X10 )
!= $true )
| ( $true
= ( sK1 @ X10 @ ( sK0 @ X9 ) ) ) )
& ! [X11: a] :
( ( $true
= ( sK1 @ ( sK0 @ X9 ) @ X11 ) )
| ? [X12: a] :
( ( $true
= ( X9 @ X12 ) )
& ( $true
!= ( sK1 @ X12 @ X11 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X5: a > a] :
( ! [X7: a,X6: a] :
( ( $true
!= ( sK1 @ X6 @ X7 ) )
| ( $true
= ( sK1 @ ( X5 @ X6 ) @ ( X5 @ X7 ) ) ) )
& ! [X8: a] :
( ( sK1 @ X8 @ ( X5 @ X8 ) )
!= $true ) )
=> ( ! [X7: a,X6: a] :
( ( $true
!= ( sK1 @ X6 @ X7 ) )
| ( ( sK1 @ ( sK2 @ X6 ) @ ( sK2 @ X7 ) )
= $true ) )
& ! [X8: a] :
( ( sK1 @ X8 @ ( sK2 @ X8 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X9: a > $o,X11: a] :
( ? [X12: a] :
( ( $true
= ( X9 @ X12 ) )
& ( $true
!= ( sK1 @ X12 @ X11 ) ) )
=> ( ( $true
= ( X9 @ ( sK3 @ X11 @ X9 ) ) )
& ( $true
!= ( sK1 @ ( sK3 @ X11 @ X9 ) @ X11 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: ( a > $o ) > a,X1: a > a > $o] :
( ! [X2: a,X3: a,X4: a] :
( ( $true
!= ( X1 @ X3 @ X2 ) )
| ( $true
!= ( X1 @ X2 @ X4 ) )
| ( ( X1 @ X3 @ X4 )
= $true ) )
& ? [X5: a > a] :
( ! [X6: a,X7: a] :
( ( ( X1 @ X6 @ X7 )
!= $true )
| ( $true
= ( X1 @ ( X5 @ X6 ) @ ( X5 @ X7 ) ) ) )
& ! [X8: a] :
( ( X1 @ X8 @ ( X5 @ X8 ) )
!= $true ) )
& ! [X9: a > $o] :
( ! [X10: a] :
( ( ( X9 @ X10 )
!= $true )
| ( $true
= ( X1 @ X10 @ ( X0 @ X9 ) ) ) )
& ! [X11: a] :
( ( $true
= ( X1 @ ( X0 @ X9 ) @ X11 ) )
| ? [X12: a] :
( ( $true
= ( X9 @ X12 ) )
& ( $true
!= ( X1 @ X12 @ X11 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: ( a > $o ) > a,X1: a > a > $o] :
( ! [X8: a,X7: a,X6: a] :
( ( $true
!= ( X1 @ X7 @ X8 ) )
| ( $true
!= ( X1 @ X8 @ X6 ) )
| ( $true
= ( X1 @ X7 @ X6 ) ) )
& ? [X9: a > a] :
( ! [X11: a,X10: a] :
( ( $true
!= ( X1 @ X11 @ X10 ) )
| ( ( X1 @ ( X9 @ X11 ) @ ( X9 @ X10 ) )
= $true ) )
& ! [X12: a] :
( $true
!= ( X1 @ X12 @ ( X9 @ X12 ) ) ) )
& ! [X2: a > $o] :
( ! [X3: a] :
( ( $true
!= ( X2 @ X3 ) )
| ( ( X1 @ X3 @ ( X0 @ X2 ) )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X1 @ ( X0 @ X2 ) @ X4 ) )
| ? [X5: a] :
( ( $true
= ( X2 @ X5 ) )
& ( ( X1 @ X5 @ X4 )
!= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: ( a > $o ) > a,X1: a > a > $o] :
( ? [X9: a > a] :
( ! [X11: a,X10: a] :
( ( $true
!= ( X1 @ X11 @ X10 ) )
| ( ( X1 @ ( X9 @ X11 ) @ ( X9 @ X10 ) )
= $true ) )
& ! [X12: a] :
( $true
!= ( X1 @ X12 @ ( X9 @ X12 ) ) ) )
& ! [X2: a > $o] :
( ! [X3: a] :
( ( $true
!= ( X2 @ X3 ) )
| ( ( X1 @ X3 @ ( X0 @ X2 ) )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X1 @ ( X0 @ X2 ) @ X4 ) )
| ? [X5: a] :
( ( $true
= ( X2 @ X5 ) )
& ( ( X1 @ X5 @ X4 )
!= $true ) ) ) )
& ! [X8: a,X6: a,X7: a] :
( ( $true
= ( X1 @ X7 @ X6 ) )
| ( $true
!= ( X1 @ X8 @ X6 ) )
| ( $true
!= ( X1 @ X7 @ X8 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > $o ) > a,X1: a > a > $o] :
( ( ! [X2: a > $o] :
( ! [X4: a] :
( ! [X5: a] :
( ( $true
= ( X2 @ X5 ) )
=> ( ( X1 @ X5 @ X4 )
= $true ) )
=> ( $true
= ( X1 @ ( X0 @ X2 ) @ X4 ) ) )
& ! [X3: a] :
( ( $true
= ( X2 @ X3 ) )
=> ( ( X1 @ X3 @ ( X0 @ X2 ) )
= $true ) ) )
& ! [X8: a,X6: a,X7: a] :
( ( ( $true
= ( X1 @ X8 @ X6 ) )
& ( $true
= ( X1 @ X7 @ X8 ) ) )
=> ( $true
= ( X1 @ X7 @ X6 ) ) ) )
=> ! [X9: a > a] :
( ! [X10: a,X11: a] :
( ( $true
= ( X1 @ X11 @ X10 ) )
=> ( ( X1 @ ( X9 @ X11 ) @ ( X9 @ X10 ) )
= $true ) )
=> ? [X12: a] :
( $true
= ( X1 @ X12 @ ( X9 @ X12 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > $o ) > a,X1: a > a > $o] :
( ( ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 @ ( X0 @ X2 ) ) )
& ! [X4: a] :
( ! [X5: a] :
( ( X2 @ X5 )
=> ( X1 @ X5 @ X4 ) )
=> ( X1 @ ( X0 @ X2 ) @ X4 ) ) )
& ! [X6: a,X7: a,X8: a] :
( ( ( X1 @ X7 @ X8 )
& ( X1 @ X8 @ X6 ) )
=> ( X1 @ X7 @ X6 ) ) )
=> ! [X9: a > a] :
( ! [X10: a,X11: a] :
( ( X1 @ X11 @ X10 )
=> ( X1 @ ( X9 @ X11 ) @ ( X9 @ X10 ) ) )
=> ? [X12: a] : ( X1 @ X12 @ ( X9 @ X12 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: ( a > $o ) > a,X0: a > a > $o] :
( ( ! [X5: a > $o] :
( ! [X4: a] :
( ( X5 @ X4 )
=> ( X0 @ X4 @ ( X1 @ X5 ) ) )
& ! [X6: a] :
( ! [X7: a] :
( ( X5 @ X7 )
=> ( X0 @ X7 @ X6 ) )
=> ( X0 @ ( X1 @ X5 ) @ X6 ) ) )
& ! [X4: a,X2: a,X3: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X4 ) )
=> ( X0 @ X2 @ X4 ) ) )
=> ! [X8: a > a] :
( ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ ( X8 @ X2 ) @ ( X8 @ X3 ) ) )
=> ? [X9: a] : ( X0 @ X9 @ ( X8 @ X9 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: ( a > $o ) > a,X0: a > a > $o] :
( ( ! [X5: a > $o] :
( ! [X4: a] :
( ( X5 @ X4 )
=> ( X0 @ X4 @ ( X1 @ X5 ) ) )
& ! [X6: a] :
( ! [X7: a] :
( ( X5 @ X7 )
=> ( X0 @ X7 @ X6 ) )
=> ( X0 @ ( X1 @ X5 ) @ X6 ) ) )
& ! [X4: a,X2: a,X3: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X4 ) )
=> ( X0 @ X2 @ X4 ) ) )
=> ! [X8: a > a] :
( ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ ( X8 @ X2 ) @ ( X8 @ X3 ) ) )
=> ? [X9: a] : ( X0 @ X9 @ ( X8 @ X9 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1tz59creLT/DTF2THF_7061.p',cTHM402_pme) ).
thf(f16,plain,
! [X8: a] :
( ( sK1 @ X8 @ ( sK2 @ X8 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV055^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n006.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 12:39:30 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.42 ---- Original DTF file ---
% 0.17/0.42 thf(spec,logic,$$dhol).
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 % File : SEV055^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.42 % Domain : Set Theory (Relations)
% 0.17/0.42 % Problem : TPS problem THM402
% 0.17/0.42 % Version : Especial.
% 0.17/0.42 % English :
% 0.17/0.42
% 0.17/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.42 % Source : [Bro09]
% 0.17/0.42 % Names : tps_0276 [Bro09]
% 0.17/0.42 % : THM402 [TPS]
% 0.17/0.42
% 0.17/0.42 % Status : Theorem
% 0.17/0.42 % 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, 0.20 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 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 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
% 0.17/0.42 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.17/0.42 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.17/0.42 % Maximal formula atoms : 0 ( 0 avg)
% 0.17/0.42 % Number of connectives : 35 ( 0 ~; 0 |; 3 &; 25 @)
% 0.17/0.42 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.17/0.42 % Maximal formula depth : 13 ( 13 avg)
% 0.17/0.42 % Number of types : 2 ( 1 usr)
% 0.17/0.42 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.17/0.42 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.17/0.42 % Number of variables : 13 ( 0 ^; 12 !; 1 ?; 13 :)
% 0.17/0.42 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.42
% 0.17/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.42 % : Polymorphic definitions expanded.
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 thf(a_type,type,
% 0.17/0.42 a: $tType ).
% 0.17/0.42
% 0.17/0.42 thf(cTHM402_pme,conjecture,
% 0.17/0.42 ! [R: a > a > $o,U: ( a > $o ) > a] :
% 0.17/0.42 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 0.17/0.42 ( ( ( R @ Xx @ Xy )
% 0.17/0.42 & ( R @ Xy @ Xz ) )
% 0.17/0.42 => ( R @ Xx @ Xz ) )
% 0.17/0.42 & ! [Xs: a > $o] :
% 0.17/0.42 ( ! [Xz: a] :
% 0.17/0.42 ( ( Xs @ Xz )
% 0.17/0.42 => ( R @ Xz @ ( U @ Xs ) ) )
% 0.17/0.42 & ! [Xj: a] :
% 0.17/0.42 ( ! [Xk: a] :
% 0.17/0.42 ( ( Xs @ Xk )
% 0.17/0.42 => ( R @ Xk @ Xj ) )
% 0.17/0.42 => ( R @ ( U @ Xs ) @ Xj ) ) ) )
% 0.17/0.42 => ! [Xf: a > a] :
% 0.17/0.42 ( ! [Xx: a,Xy: a] :
% 0.17/0.42 ( ( R @ Xx @ Xy )
% 0.17/0.42 => ( R @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) )
% 0.17/0.42 => ? [Xw: a] : ( R @ Xw @ ( Xf @ Xw ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 ------------------------
% 1.70/1.43 ---- Embedded in THF ---
% 1.70/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.70/1.43 %%% Generated on Tue Feb 24 12:39:31 EST 2026
% 1.70/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.70/1.43 %%% Logic specification used:
% 1.70/1.43 %%% thf(spec, logic, $$dhol).
% 1.70/1.43
% 1.70/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1tz59creLT/DTF2DTF7061.p
% See solution above
% 1.70/1.43 ------------------------
% 1.70/1.44 ---- Cleaned THF ---
% 1.70/1.44 thf(a_type,type,
% 1.70/1.44 a: $tType ).
% 1.70/1.44
% 1.70/1.44 thf(cTHM402_pme,conjecture,
% 1.70/1.44 ! [R: a > a > $o,U: ( a > $o ) > a] :
% 1.70/1.44 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 1.70/1.44 ( ( ( R @ Xx @ Xy )
% 1.70/1.44 & ( R @ Xy @ Xz ) )
% 1.70/1.44 => ( R @ Xx @ Xz ) )
% 1.70/1.44 & ! [Xs: a > $o] :
% 1.70/1.44 ( ! [Xz: a] :
% 1.70/1.44 ( ( Xs @ Xz )
% 1.70/1.44 => ( R @ Xz @ ( U @ Xs ) ) )
% 1.70/1.44 & ! [Xj: a] :
% 1.70/1.44 ( ! [Xk: a] :
% 1.70/1.44 ( ( Xs @ Xk )
% 1.70/1.44 => ( R @ Xk @ Xj ) )
% 1.70/1.44 => ( R @ ( U @ Xs ) @ Xj ) ) ) )
% 1.70/1.44 => ! [Xf: a > a] :
% 1.70/1.44 ( ! [Xx: a,Xy: a] :
% 1.70/1.44 ( ( R @ Xx @ Xy )
% 1.70/1.44 => ( R @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) )
% 1.70/1.44 => ? [Xw: a] : ( R @ Xw @ ( Xf @ Xw ) ) ) ) ).
% 1.70/1.44 ------------------------
% 1.70/1.46 % (7165)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7061 for (2999ds/18Mi)
% 1.70/1.46 % (7164)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_7061 for (2999ds/275Mi)
% 1.70/1.46 % (7161)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_7061 for (2999ds/27Mi)
% 1.70/1.46 % (7159)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7061 for (2999ds/183Mi)
% 1.70/1.46 % (7160)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_7061 for (2999ds/4Mi)
% 1.70/1.46 % (7163)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_7061 for (2999ds/2Mi)
% 1.70/1.46 % (7162)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7061 for (2999ds/2Mi)
% 1.70/1.46 % (7163)Instruction limit reached!
% 1.70/1.46 % (7163)------------------------------
% 1.70/1.46 % (7163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.46 % (7163)Termination reason: Unknown
% 1.70/1.46 % (7163)Termination phase: Saturation
% 1.70/1.46
% 1.70/1.46 % (7163)Memory used [KB]: 5500
% 1.70/1.46 % (7163)Time elapsed: 0.003 s
% 1.70/1.46 % (7163)Instructions burned: 3 (million)
% 1.70/1.46 % (7163)------------------------------
% 1.70/1.46 % (7163)------------------------------
% 1.70/1.46 % (7160)Instruction limit reached!
% 1.70/1.46 % (7160)------------------------------
% 1.70/1.46 % (7160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.46 % (7160)Termination reason: Unknown
% 1.70/1.46 % (7160)Termination phase: Saturation
% 1.70/1.46
% 1.70/1.46 % (7160)Memory used [KB]: 5500
% 1.70/1.46 % (7160)Time elapsed: 0.005 s
% 1.70/1.46 % (7160)Instructions burned: 4 (million)
% 1.70/1.46 % (7160)------------------------------
% 1.70/1.46 % (7160)------------------------------
% 1.70/1.46 % (7162)Instruction limit reached!
% 1.70/1.46 % (7162)------------------------------
% 1.70/1.46 % (7162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.46 % (7162)Termination reason: Unknown
% 1.70/1.46 % (7162)Termination phase: Saturation
% 1.70/1.46
% 1.70/1.46 % (7162)Memory used [KB]: 5500
% 1.70/1.46 % (7162)Time elapsed: 0.003 s
% 1.70/1.46 % (7162)Instructions burned: 2 (million)
% 1.70/1.46 % (7162)------------------------------
% 1.70/1.46 % (7162)------------------------------
% 1.70/1.46 % (7164)First to succeed.
% 1.70/1.47 % (7164)Refutation found. Thanks to Tanya!
% 1.70/1.47 % SZS status Theorem for DTF2THF_7061
% 1.70/1.47 % SZS output start Proof for DTF2THF_7061
% 1.70/1.47 thf(type_def_5, type, a: $tType).
% 1.70/1.47 thf(func_def_0, type, a: $tType).
% 1.70/1.47 thf(func_def_4, type, sK0: (a > $o) > a).
% 1.70/1.47 thf(func_def_5, type, sK1: a > a > $o).
% 1.70/1.47 thf(func_def_6, type, sK2: a > a).
% 1.70/1.47 thf(func_def_7, type, sK3: a > (a > $o) > a).
% 1.70/1.47 thf(func_def_10, type, ph5: !>[X0: $tType]:(X0)).
% 1.70/1.47 thf(f37,plain,(
% 1.70/1.47 $false),
% 1.70/1.47 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.70/1.47 thf(f35,plain,(
% 1.70/1.47 ($true != $true)),
% 1.70/1.47 inference(superposition,[status(thm)],[f16,f33])).
% 1.70/1.47 thf(f33,plain,(
% 1.70/1.47 ( ! [X11 : a] : (($true = (sK1 @ (sK0 @ (^[Y0 : a]: ($false))) @ X11))) )),
% 1.70/1.47 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.70/1.47 thf(f32,plain,(
% 1.70/1.47 ( ! [X11 : a] : (($false = $true) | ($true = (sK1 @ (sK0 @ (^[Y0 : a]: ($false))) @ X11))) )),
% 1.70/1.47 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.70/1.47 thf(f28,plain,(
% 1.70/1.47 ( ! [X11 : a] : (($true = ((^[Y0 : a]: ($false)) @ (sK3 @ X11 @ (^[Y0 : a]: ($false))))) | ($true = (sK1 @ (sK0 @ (^[Y0 : a]: ($false))) @ X11))) )),
% 1.70/1.47 inference(primitive_instantiation,[status(thm)],[f14])).
% 1.70/1.47 thf(f14,plain,(
% 1.70/1.47 ( ! [X11 : a,X9 : a > $o] : (($true = (X9 @ (sK3 @ X11 @ X9))) | ($true = (sK1 @ (sK0 @ X9) @ X11))) )),
% 1.70/1.47 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.47 thf(f12,plain,(
% 1.70/1.47 ! [X2 : a,X3 : a,X4 : a] : (((sK1 @ X3 @ X2) != $true) | ((sK1 @ X2 @ X4) != $true) | ((sK1 @ X3 @ X4) = $true)) & (! [X6 : a,X7 : a] : (($true != (sK1 @ X6 @ X7)) | ((sK1 @ (sK2 @ X6) @ (sK2 @ X7)) = $true)) & ! [X8 : a] : ((sK1 @ X8 @ (sK2 @ X8)) != $true)) & ! [X9 : a > $o] : (! [X10 : a] : (((X9 @ X10) != $true) | ($true = (sK1 @ X10 @ (sK0 @ X9)))) & ! [X11 : a] : (($true = (sK1 @ (sK0 @ X9) @ X11)) | (($true = (X9 @ (sK3 @ X11 @ X9))) & ($true != (sK1 @ (sK3 @ X11 @ X9) @ X11)))))),
% 1.70/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f11,f10,f9])).
% 1.70/1.47 thf(f9,plain,(
% 1.70/1.47 ? [X0 : (a > $o) > a,X1 : a > a > $o] : (! [X2 : a,X3 : a,X4 : a] : (($true != (X1 @ X3 @ X2)) | ($true != (X1 @ X2 @ X4)) | ((X1 @ X3 @ X4) = $true)) & ? [X5 : a > a] : (! [X6 : a,X7 : a] : (((X1 @ X6 @ X7) != $true) | ($true = (X1 @ (X5 @ X6) @ (X5 @ X7)))) & ! [X8 : a] : ((X1 @ X8 @ (X5 @ X8)) != $true)) & ! [X9 : a > $o] : (! [X10 : a] : (((X9 @ X10) != $true) | ($true = (X1 @ X10 @ (X0 @ X9)))) & ! [X11 : a] : (($true = (X1 @ (X0 @ X9) @ X11)) | ? [X12 : a] : (($true = (X9 @ X12)) & ($true != (X1 @ X12 @ X11)))))) => (! [X4 : a,X3 : a,X2 : a] : (((sK1 @ X3 @ X2) != $true) | ((sK1 @ X2 @ X4) != $true) | ((sK1 @ X3 @ X4) = $true)) & ? [X5 : a > a] : (! [X7 : a,X6 : a] : (($true != (sK1 @ X6 @ X7)) | ($true = (sK1 @ (X5 @ X6) @ (X5 @ X7)))) & ! [X8 : a] : ((sK1 @ X8 @ (X5 @ X8)) != $true)) & ! [X9 : a > $o] : (! [X10 : a] : (((X9 @ X10) != $true) | ($true = (sK1 @ X10 @ (sK0 @ X9)))) & ! [X11 : a] : (($true = (sK1 @ (sK0 @ X9) @ X11)) | ? [X12 : a] : (($true = (X9 @ X12)) & ($true != (sK1 @ X12 @ X11))))))),
% 1.70/1.47 introduced(definition,[],[choice_axiom])).
% 1.70/1.47 thf(f10,plain,(
% 1.70/1.47 ? [X5 : a > a] : (! [X7 : a,X6 : a] : (($true != (sK1 @ X6 @ X7)) | ($true = (sK1 @ (X5 @ X6) @ (X5 @ X7)))) & ! [X8 : a] : ((sK1 @ X8 @ (X5 @ X8)) != $true)) => (! [X7 : a,X6 : a] : (($true != (sK1 @ X6 @ X7)) | ((sK1 @ (sK2 @ X6) @ (sK2 @ X7)) = $true)) & ! [X8 : a] : ((sK1 @ X8 @ (sK2 @ X8)) != $true))),
% 1.70/1.47 introduced(definition,[],[choice_axiom])).
% 1.70/1.47 thf(f11,plain,(
% 1.70/1.47 ! [X9 : a > $o,X11 : a] : (? [X12 : a] : (($true = (X9 @ X12)) & ($true != (sK1 @ X12 @ X11))) => (($true = (X9 @ (sK3 @ X11 @ X9))) & ($true != (sK1 @ (sK3 @ X11 @ X9) @ X11))))),
% 1.70/1.47 introduced(definition,[],[choice_axiom])).
% 1.70/1.47 thf(f8,plain,(
% 1.70/1.47 ? [X0 : (a > $o) > a,X1 : a > a > $o] : (! [X2 : a,X3 : a,X4 : a] : (($true != (X1 @ X3 @ X2)) | ($true != (X1 @ X2 @ X4)) | ((X1 @ X3 @ X4) = $true)) & ? [X5 : a > a] : (! [X6 : a,X7 : a] : (((X1 @ X6 @ X7) != $true) | ($true = (X1 @ (X5 @ X6) @ (X5 @ X7)))) & ! [X8 : a] : ((X1 @ X8 @ (X5 @ X8)) != $true)) & ! [X9 : a > $o] : (! [X10 : a] : (((X9 @ X10) != $true) | ($true = (X1 @ X10 @ (X0 @ X9)))) & ! [X11 : a] : (($true = (X1 @ (X0 @ X9) @ X11)) | ? [X12 : a] : (($true = (X9 @ X12)) & ($true != (X1 @ X12 @ X11))))))),
% 1.70/1.47 inference(rectify,[status(thm)],[f7])).
% 1.70/1.47 thf(f7,plain,(
% 1.70/1.47 ? [X0 : (a > $o) > a,X1 : a > a > $o] : (! [X8 : a,X7 : a,X6 : a] : (($true != (X1 @ X7 @ X8)) | ($true != (X1 @ X8 @ X6)) | ($true = (X1 @ X7 @ X6))) & ? [X9 : a > a] : (! [X11 : a,X10 : a] : (($true != (X1 @ X11 @ X10)) | ((X1 @ (X9 @ X11) @ (X9 @ X10)) = $true)) & ! [X12 : a] : ($true != (X1 @ X12 @ (X9 @ X12)))) & ! [X2 : a > $o] : (! [X3 : a] : (($true != (X2 @ X3)) | ((X1 @ X3 @ (X0 @ X2)) = $true)) & ! [X4 : a] : (($true = (X1 @ (X0 @ X2) @ X4)) | ? [X5 : a] : (($true = (X2 @ X5)) & ((X1 @ X5 @ X4) != $true)))))),
% 1.70/1.47 inference(flattening,[status(thm)],[f6])).
% 1.70/1.47 thf(f6,plain,(
% 1.70/1.47 ? [X0 : (a > $o) > a,X1 : a > a > $o] : (? [X9 : a > a] : (! [X11 : a,X10 : a] : (($true != (X1 @ X11 @ X10)) | ((X1 @ (X9 @ X11) @ (X9 @ X10)) = $true)) & ! [X12 : a] : ($true != (X1 @ X12 @ (X9 @ X12)))) & (! [X2 : a > $o] : (! [X3 : a] : (($true != (X2 @ X3)) | ((X1 @ X3 @ (X0 @ X2)) = $true)) & ! [X4 : a] : (($true = (X1 @ (X0 @ X2) @ X4)) | ? [X5 : a] : (($true = (X2 @ X5)) & ((X1 @ X5 @ X4) != $true)))) & ! [X8 : a,X6 : a,X7 : a] : (($true = (X1 @ X7 @ X6)) | (($true != (X1 @ X8 @ X6)) | ($true != (X1 @ X7 @ X8))))))),
% 1.70/1.47 inference(ennf_transformation,[status(thm)],[f5])).
% 1.70/1.47 thf(f5,plain,(
% 1.70/1.47 ~! [X0 : (a > $o) > a,X1 : a > a > $o] : ((! [X2 : a > $o] : (! [X4 : a] : (! [X5 : a] : (($true = (X2 @ X5)) => ((X1 @ X5 @ X4) = $true)) => ($true = (X1 @ (X0 @ X2) @ X4))) & ! [X3 : a] : (($true = (X2 @ X3)) => ((X1 @ X3 @ (X0 @ X2)) = $true))) & ! [X8 : a,X6 : a,X7 : a] : ((($true = (X1 @ X8 @ X6)) & ($true = (X1 @ X7 @ X8))) => ($true = (X1 @ X7 @ X6)))) => ! [X9 : a > a] : (! [X10 : a,X11 : a] : (($true = (X1 @ X11 @ X10)) => ((X1 @ (X9 @ X11) @ (X9 @ X10)) = $true)) => ? [X12 : a] : ($true = (X1 @ X12 @ (X9 @ X12)))))),
% 1.70/1.47 inference(fool_elimination,[status(thm)],[f4])).
% 1.70/1.47 thf(f4,plain,(
% 1.70/1.47 ~! [X0 : (a > $o) > a,X1 : a > a > $o] : ((! [X2 : a > $o] : (! [X3 : a] : ((X2 @ X3) => (X1 @ X3 @ (X0 @ X2))) & ! [X4 : a] : (! [X5 : a] : ((X2 @ X5) => (X1 @ X5 @ X4)) => (X1 @ (X0 @ X2) @ X4))) & ! [X6 : a,X7 : a,X8 : a] : (((X1 @ X7 @ X8) & (X1 @ X8 @ X6)) => (X1 @ X7 @ X6))) => ! [X9 : a > a] : (! [X10 : a,X11 : a] : ((X1 @ X11 @ X10) => (X1 @ (X9 @ X11) @ (X9 @ X10))) => ? [X12 : a] : (X1 @ X12 @ (X9 @ X12))))),
% 1.70/1.47 inference(rectify,[status(thm)],[f2])).
% 1.70/1.47 thf(f2,negated_conjecture,(
% 1.70/1.47 ~! [X1 : (a > $o) > a,X0 : a > a > $o] : ((! [X5 : a > $o] : (! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ (X1 @ X5))) & ! [X6 : a] : (! [X7 : a] : ((X5 @ X7) => (X0 @ X7 @ X6)) => (X0 @ (X1 @ X5) @ X6))) & ! [X4 : a,X2 : a,X3 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X4)) => (X0 @ X2 @ X4))) => ! [X8 : a > a] : (! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X0 @ (X8 @ X2) @ (X8 @ X3))) => ? [X9 : a] : (X0 @ X9 @ (X8 @ X9))))),
% 1.70/1.47 inference(negated_conjecture,[status(cth)],[f1])).
% 1.70/1.47 thf(f1,conjecture,(
% 1.70/1.47 ! [X1 : (a > $o) > a,X0 : a > a > $o] : ((! [X5 : a > $o] : (! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ (X1 @ X5))) & ! [X6 : a] : (! [X7 : a] : ((X5 @ X7) => (X0 @ X7 @ X6)) => (X0 @ (X1 @ X5) @ X6))) & ! [X4 : a,X2 : a,X3 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X4)) => (X0 @ X2 @ X4))) => ! [X8 : a > a] : (! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X0 @ (X8 @ X2) @ (X8 @ X3))) => ? [X9 : a] : (X0 @ X9 @ (X8 @ X9))))),
% 1.70/1.47 file('/export/starexec/sandbox/tmp/tmp.1tz59creLT/DTF2THF_7061.p',cTHM402_pme)).
% 1.70/1.47 thf(f16,plain,(
% 1.70/1.47 ( ! [X8 : a] : (((sK1 @ X8 @ (sK2 @ X8)) != $true)) )),
% 1.70/1.47 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.47 % SZS output end Proof for DTF2THF_7061
% 1.70/1.47 % (7164)------------------------------
% 1.70/1.47 % (7164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.47 % (7164)Termination reason: Refutation
% 1.70/1.47
% 1.70/1.47 % (7164)Memory used [KB]: 5500
% 1.70/1.47 % (7164)Time elapsed: 0.007 s
% 1.70/1.47 % (7164)Instructions burned: 7 (million)
% 1.70/1.47 % (7164)------------------------------
% 1.70/1.47 % (7164)------------------------------
% 1.70/1.47 % (7158)Success in time 0.022 s
%------------------------------------------------------------------------------