%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV088^5 : 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 : n010.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 09:40:15 AM UTC 2026
% Result : Theorem 1.48s 1.28s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 194 ( 67 equ; 0 cnn)
% Maximal formula atoms : 12 ( 12 avg)
% Number of connectives : 498 ( 38 ~; 35 |; 34 &; 384 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 173 ( 173 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 119 ( 24 ^; 61 !; 34 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_4,type,
sK1: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_5,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_6,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
sK4: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_8,type,
sK5: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(func_def_11,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f29,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
$true != $true,
inference(duplicate_literal_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $true != $true )
| ( $true != $true ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $true
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $true )
@ ( sK1 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $true )
@ ( sK0 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $true ) ) )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $true
@ ( sK2 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $true )
@ ( sK3 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $true )
@ ( sK5 @ X1
@ ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] : $true ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( $true
!= ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) ) )
| ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) ) )
& ( $true
!= ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) ) ) )
| ( ! [X7: $i] :
( ( $true
= ( X1 @ ( sK4 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 ) )
| ( ( X0 @ ( sK4 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 )
= $true ) )
& ( $true
!= ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) ) )
& ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) )
!= $true )
& ! [X9: $i] :
( ( $true
= ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) @ X9 ) )
| ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) @ X9 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X2: $i,X3: $i > $o] :
( ( $true
!= ( X1 @ X3 @ X3 @ X2 ) )
& ( $true
!= ( X0 @ X3 @ X3 @ X2 ) ) )
=> ( ( $true
!= ( X1 @ ( sK1 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) ) )
& ( $true
!= ( X0 @ ( sK1 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) @ ( sK0 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ! [X7: $i] :
( ( $true
= ( X1 @ X6 @ X5 @ X7 ) )
| ( $true
= ( X0 @ X6 @ X5 @ X7 ) ) )
& ? [X8: $i] :
( ( $true
!= ( X1 @ X4 @ X5 @ X8 ) )
& ( $true
!= ( X0 @ X4 @ X5 @ X8 ) ) )
& ! [X9: $i] :
( ( $true
= ( X0 @ X4 @ X6 @ X9 ) )
| ( $true
= ( X1 @ X4 @ X6 @ X9 ) ) ) )
=> ( ! [X7: $i] :
( ( $true
= ( X1 @ ( sK4 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 ) )
| ( ( X0 @ ( sK4 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X7 )
= $true ) )
& ? [X8: $i] :
( ( $true
!= ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X8 ) )
& ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X8 )
!= $true ) )
& ! [X9: $i] :
( ( $true
= ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) @ X9 ) )
| ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK4 @ X1 @ X0 ) @ X9 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X8: $i] :
( ( $true
!= ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X8 ) )
& ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ X8 )
!= $true ) )
=> ( ( $true
!= ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) ) )
& ( ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) @ ( sK5 @ X1 @ X0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X2: $i,X3: $i > $o] :
( ( $true
!= ( X1 @ X3 @ X3 @ X2 ) )
& ( $true
!= ( X0 @ X3 @ X3 @ X2 ) ) )
| ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ! [X7: $i] :
( ( $true
= ( X1 @ X6 @ X5 @ X7 ) )
| ( $true
= ( X0 @ X6 @ X5 @ X7 ) ) )
& ? [X8: $i] :
( ( $true
!= ( X1 @ X4 @ X5 @ X8 ) )
& ( $true
!= ( X0 @ X4 @ X5 @ X8 ) ) )
& ! [X9: $i] :
( ( $true
= ( X0 @ X4 @ X6 @ X9 ) )
| ( $true
= ( X1 @ X4 @ X6 @ X9 ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X3: $i,X2: $i > $o] :
( ( $true
!= ( X0 @ X2 @ X2 @ X3 ) )
& ( $true
!= ( X1 @ X2 @ X2 @ X3 ) ) )
| ? [X5: $i > $o,X6: $i > $o,X4: $i > $o] :
( ! [X7: $i] :
( ( $true
= ( X0 @ X4 @ X6 @ X7 ) )
| ( $true
= ( X1 @ X4 @ X6 @ X7 ) ) )
& ? [X9: $i] :
( ( $true
!= ( X0 @ X5 @ X6 @ X9 ) )
& ( $true
!= ( X1 @ X5 @ X6 @ X9 ) ) )
& ! [X8: $i] :
( ( $true
= ( X1 @ X5 @ X4 @ X8 ) )
| ( $true
= ( X0 @ X5 @ X4 @ X8 ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ? [X3: $i,X2: $i > $o] :
( ( $true
!= ( X0 @ X2 @ X2 @ X3 ) )
& ( $true
!= ( X1 @ X2 @ X2 @ X3 ) ) )
| ? [X4: $i > $o,X6: $i > $o,X5: $i > $o] :
( ? [X9: $i] :
( ( $true
!= ( X0 @ X5 @ X6 @ X9 ) )
& ( $true
!= ( X1 @ X5 @ X6 @ X9 ) ) )
& ! [X7: $i] :
( ( $true
= ( X0 @ X4 @ X6 @ X7 ) )
| ( $true
= ( X1 @ X4 @ X6 @ X7 ) ) )
& ! [X8: $i] :
( ( $true
= ( X1 @ X5 @ X4 @ X8 ) )
| ( $true
= ( X0 @ X5 @ X4 @ X8 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i] :
( ( $true
= ( X0 @ X2 @ X2 @ X3 ) )
| ( $true
= ( X1 @ X2 @ X2 @ X3 ) ) )
& ! [X4: $i > $o,X6: $i > $o,X5: $i > $o] :
( ( ! [X7: $i] :
( ( $true
= ( X0 @ X4 @ X6 @ X7 ) )
| ( $true
= ( X1 @ X4 @ X6 @ X7 ) ) )
& ! [X8: $i] :
( ( $true
= ( X1 @ X5 @ X4 @ X8 ) )
| ( $true
= ( X0 @ X5 @ X4 @ X8 ) ) ) )
=> ! [X9: $i] :
( ( $true
= ( X0 @ X5 @ X6 @ X9 ) )
| ( $true
= ( X1 @ X5 @ X6 @ X9 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i] :
( ( X0 @ X2 @ X2 @ X3 )
| ( X1 @ X2 @ X2 @ X3 ) )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ! [X7: $i] :
( ( X1 @ X4 @ X6 @ X7 )
| ( X0 @ X4 @ X6 @ X7 ) )
& ! [X8: $i] :
( ( X0 @ X5 @ X4 @ X8 )
| ( X1 @ X5 @ X4 @ X8 ) ) )
=> ! [X9: $i] :
( ( X0 @ X5 @ X6 @ X9 )
| ( X1 @ X5 @ X6 @ X9 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X5: $i] :
( ( X0 @ X2 @ X2 @ X5 )
| ( X1 @ X2 @ X2 @ X5 ) )
& ! [X3: $i > $o,X2: $i > $o,X4: $i > $o] :
( ( ! [X5: $i] :
( ( X1 @ X3 @ X4 @ X5 )
| ( X0 @ X3 @ X4 @ X5 ) )
& ! [X5: $i] :
( ( X0 @ X2 @ X3 @ X5 )
| ( X1 @ X2 @ X3 @ X5 ) ) )
=> ! [X5: $i] :
( ( X0 @ X2 @ X4 @ X5 )
| ( X1 @ X2 @ X4 @ X5 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X5: $i] :
( ( X0 @ X2 @ X2 @ X5 )
| ( X1 @ X2 @ X2 @ X5 ) )
& ! [X3: $i > $o,X2: $i > $o,X4: $i > $o] :
( ( ! [X5: $i] :
( ( X1 @ X3 @ X4 @ X5 )
| ( X0 @ X3 @ X4 @ X5 ) )
& ! [X5: $i] :
( ( X0 @ X2 @ X3 @ X5 )
| ( X1 @ X2 @ X3 @ X5 ) ) )
=> ! [X5: $i] :
( ( X0 @ X2 @ X4 @ X5 )
| ( X1 @ X2 @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LJbsQv27eM/DTF2THF_9619.p',cTHM120G_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV088^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n010.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:39:48 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEV088^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Set Theory (Relations)
% 0.30/0.46 % Problem : TPS problem from RELN-THMS
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0985 [Bro09]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.30/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.30/0.46 % Number of connectives : 31 ( 0 ~; 4 |; 2 &; 24 @)
% 0.30/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 14 ( 14 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.30/0.46 % Number of variables : 10 ( 0 ^; 8 !; 2 ?; 10 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(cTHM120G_pme,conjecture,
% 0.30/0.46 ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
% 0.30/0.46 ( ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.30/0.46 ( ( ! [Xw_2: $i] :
% 0.30/0.46 ( ( Xr_27 @ Xx @ Xy @ Xw_2 )
% 0.30/0.46 | ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
% 0.30/0.46 & ! [Xw_2: $i] :
% 0.30/0.46 ( ( Xr_27 @ Xy @ Xz @ Xw_2 )
% 0.30/0.46 | ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
% 0.30/0.46 => ! [Xw_2: $i] :
% 0.30/0.46 ( ( Xr_27 @ Xx @ Xz @ Xw_2 )
% 0.30/0.46 | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) )
% 0.30/0.46 & ! [Xx: $i > $o,Xw_2: $i] :
% 0.30/0.46 ( ( Xr_27 @ Xx @ Xx @ Xw_2 )
% 0.30/0.46 | ( Xr_28 @ Xx @ Xx @ Xw_2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.48/1.24 ---- Embedded in THF ---
% 1.48/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.24 %%% Generated on Tue Feb 24 12:39:49 EST 2026
% 1.48/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.24 %%% Logic specification used:
% 1.48/1.24 %%% thf(spec, logic, $$dhol).
% 1.48/1.24
% 1.48/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LJbsQv27eM/DTF2DTF9619.p
% See solution above
% 1.48/1.24 ------------------------
% 1.48/1.25 ---- Cleaned THF ---
% 1.48/1.25 thf(cTHM120G_pme,conjecture,
% 1.48/1.25 ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
% 1.48/1.25 ( ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 1.48/1.25 ( ( ! [Xw_2: $i] :
% 1.48/1.25 ( ( Xr_27 @ Xx @ Xy @ Xw_2 )
% 1.48/1.25 | ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
% 1.48/1.25 & ! [Xw_2: $i] :
% 1.48/1.25 ( ( Xr_27 @ Xy @ Xz @ Xw_2 )
% 1.48/1.25 | ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
% 1.48/1.25 => ! [Xw_2: $i] :
% 1.48/1.25 ( ( Xr_27 @ Xx @ Xz @ Xw_2 )
% 1.48/1.25 | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) )
% 1.48/1.25 & ! [Xx: $i > $o,Xw_2: $i] :
% 1.48/1.25 ( ( Xr_27 @ Xx @ Xx @ Xw_2 )
% 1.48/1.25 | ( Xr_28 @ Xx @ Xx @ Xw_2 ) ) ) ).
% 1.48/1.25 ------------------------
% 1.48/1.27 % (9900)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_9619 for (2999ds/27Mi)
% 1.48/1.27 % (9900)Refutation not found, incomplete strategy
% 1.48/1.27 % (9900)------------------------------
% 1.48/1.27 % (9900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (9900)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.27
% 1.48/1.27
% 1.48/1.27 % (9900)Memory used [KB]: 5500
% 1.48/1.27 % (9900)Time elapsed: 0.003 s
% 1.48/1.27 % (9900)Instructions burned: 4 (million)
% 1.48/1.27 % (9900)------------------------------
% 1.48/1.27 % (9900)------------------------------
% 1.48/1.27 % (9899)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_9619 for (2999ds/4Mi)
% 1.48/1.27 % (9898)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9619 for (2999ds/183Mi)
% 1.48/1.27 % (9901)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9619 for (2999ds/2Mi)
% 1.48/1.27 % (9902)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_9619 for (2999ds/2Mi)
% 1.48/1.27 % (9903)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_9619 for (2999ds/275Mi)
% 1.48/1.27 % (9904)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9619 for (2999ds/18Mi)
% 1.48/1.27 % (9901)Instruction limit reached!
% 1.48/1.27 % (9901)------------------------------
% 1.48/1.27 % (9901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (9901)Termination reason: Unknown
% 1.48/1.27 % (9901)Termination phase: Preprocessing 3
% 1.48/1.27
% 1.48/1.27 % (9901)Memory used [KB]: 895
% 1.48/1.27 % (9901)Time elapsed: 0.003 s
% 1.48/1.27 % (9901)Instructions burned: 2 (million)
% 1.48/1.27 % (9901)------------------------------
% 1.48/1.27 % (9901)------------------------------
% 1.48/1.27 % (9902)Instruction limit reached!
% 1.48/1.27 % (9902)------------------------------
% 1.48/1.27 % (9902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (9902)Termination reason: Unknown
% 1.48/1.27 % (9902)Termination phase: Preprocessing 2
% 1.48/1.27
% 1.48/1.27 % (9902)Memory used [KB]: 895
% 1.48/1.27 % (9902)Time elapsed: 0.003 s
% 1.48/1.27 % (9902)Instructions burned: 2 (million)
% 1.48/1.27 % (9902)------------------------------
% 1.48/1.27 % (9902)------------------------------
% 1.48/1.28 % (9899)Instruction limit reached!
% 1.48/1.28 % (9899)------------------------------
% 1.48/1.28 % (9899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (9899)Termination reason: Unknown
% 1.48/1.28 % (9899)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (9899)Memory used [KB]: 5500
% 1.48/1.28 % (9899)Time elapsed: 0.004 s
% 1.48/1.28 % (9899)Instructions burned: 4 (million)
% 1.48/1.28 % (9899)------------------------------
% 1.48/1.28 % (9899)------------------------------
% 1.48/1.28 % (9898)First to succeed.
% 1.48/1.28 % (9905)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9619 for (2999ds/3Mi)
% 1.48/1.28 % (9903)Also succeeded, but the first one will report.
% 1.48/1.28 % (9905)Instruction limit reached!
% 1.48/1.28 % (9905)------------------------------
% 1.48/1.28 % (9905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (9905)Termination reason: Unknown
% 1.48/1.28 % (9905)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (9905)Memory used [KB]: 5500
% 1.48/1.28 % (9905)Time elapsed: 0.002 s
% 1.48/1.28 % (9905)Instructions burned: 4 (million)
% 1.48/1.28 % (9905)------------------------------
% 1.48/1.28 % (9905)------------------------------
% 1.48/1.28 % (9898)Refutation found. Thanks to Tanya!
% 1.48/1.28 % SZS status Theorem for DTF2THF_9619
% 1.48/1.28 % SZS output start Proof for DTF2THF_9619
% 1.48/1.28 thf(func_def_3, type, sK0: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.48/1.28 thf(func_def_4, type, sK1: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.48/1.28 thf(func_def_5, type, sK2: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.48/1.28 thf(func_def_6, type, sK3: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.48/1.28 thf(func_def_7, type, sK4: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 1.48/1.28 thf(func_def_8, type, sK5: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 1.48/1.28 thf(func_def_11, type, ph7: !>[X0: $tType]:(X0)).
% 1.48/1.28 thf(f29,plain,(
% 1.48/1.28 $false),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.48/1.28 thf(f28,plain,(
% 1.48/1.28 ($true != $true)),
% 1.48/1.28 inference(duplicate_literal_removal,[status(thm)],[f27])).
% 1.48/1.28 thf(f27,plain,(
% 1.48/1.28 ($true != $true) | ($true != $true)),
% 1.48/1.28 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.48/1.28 thf(f23,plain,(
% 1.48/1.28 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true)))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true))))))))) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true)))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($true)))))))))) )),
% 1.48/1.28 inference(primitive_instantiation,[status(thm)],[f14])).
% 1.48/1.28 thf(f14,plain,(
% 1.48/1.28 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0))) | ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.28 thf(f12,plain,(
% 1.48/1.28 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : ((($true != (X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0))) & ($true != (X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)))) | (! [X7 : $i] : (($true = (X1 @ (sK4 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7)) | ((X0 @ (sK4 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7) = $true)) & (($true != (X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)) & ! [X9 : $i] : (($true = (X0 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9)) | ($true = (X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9)))))),
% 1.48/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9])).
% 1.48/1.28 thf(f9,plain,(
% 1.48/1.28 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i,X3 : $i > $o] : (($true != (X1 @ X3 @ X3 @ X2)) & ($true != (X0 @ X3 @ X3 @ X2))) => (($true != (X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0))) & ($true != (X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)))))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f10,plain,(
% 1.48/1.28 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (! [X7 : $i] : (($true = (X1 @ X6 @ X5 @ X7)) | ($true = (X0 @ X6 @ X5 @ X7))) & ? [X8 : $i] : (($true != (X1 @ X4 @ X5 @ X8)) & ($true != (X0 @ X4 @ X5 @ X8))) & ! [X9 : $i] : (($true = (X0 @ X4 @ X6 @ X9)) | ($true = (X1 @ X4 @ X6 @ X9)))) => (! [X7 : $i] : (($true = (X1 @ (sK4 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7)) | ((X0 @ (sK4 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X7) = $true)) & ? [X8 : $i] : (($true != (X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X8)) & ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X8) != $true)) & ! [X9 : $i] : (($true = (X0 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9)) | ($true = (X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9)))))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f11,plain,(
% 1.48/1.28 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X8 : $i] : (($true != (X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X8)) & ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X8) != $true)) => (($true != (X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f8,plain,(
% 1.48/1.28 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i,X3 : $i > $o] : (($true != (X1 @ X3 @ X3 @ X2)) & ($true != (X0 @ X3 @ X3 @ X2))) | ? [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (! [X7 : $i] : (($true = (X1 @ X6 @ X5 @ X7)) | ($true = (X0 @ X6 @ X5 @ X7))) & ? [X8 : $i] : (($true != (X1 @ X4 @ X5 @ X8)) & ($true != (X0 @ X4 @ X5 @ X8))) & ! [X9 : $i] : (($true = (X0 @ X4 @ X6 @ X9)) | ($true = (X1 @ X4 @ X6 @ X9)))))),
% 1.48/1.28 inference(rectify,[status(thm)],[f7])).
% 1.48/1.28 thf(f7,plain,(
% 1.48/1.28 ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (? [X3 : $i,X2 : $i > $o] : (($true != (X0 @ X2 @ X2 @ X3)) & ($true != (X1 @ X2 @ X2 @ X3))) | ? [X5 : $i > $o,X6 : $i > $o,X4 : $i > $o] : (! [X7 : $i] : (($true = (X0 @ X4 @ X6 @ X7)) | ($true = (X1 @ X4 @ X6 @ X7))) & ? [X9 : $i] : (($true != (X0 @ X5 @ X6 @ X9)) & ($true != (X1 @ X5 @ X6 @ X9))) & ! [X8 : $i] : (($true = (X1 @ X5 @ X4 @ X8)) | ($true = (X0 @ X5 @ X4 @ X8)))))),
% 1.48/1.28 inference(flattening,[status(thm)],[f6])).
% 1.48/1.28 thf(f6,plain,(
% 1.48/1.28 ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (? [X3 : $i,X2 : $i > $o] : (($true != (X0 @ X2 @ X2 @ X3)) & ($true != (X1 @ X2 @ X2 @ X3))) | ? [X4 : $i > $o,X6 : $i > $o,X5 : $i > $o] : (? [X9 : $i] : (($true != (X0 @ X5 @ X6 @ X9)) & ($true != (X1 @ X5 @ X6 @ X9))) & (! [X7 : $i] : (($true = (X0 @ X4 @ X6 @ X7)) | ($true = (X1 @ X4 @ X6 @ X7))) & ! [X8 : $i] : (($true = (X1 @ X5 @ X4 @ X8)) | ($true = (X0 @ X5 @ X4 @ X8))))))),
% 1.48/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.28 thf(f5,plain,(
% 1.48/1.28 ~? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i > $o,X3 : $i] : (($true = (X0 @ X2 @ X2 @ X3)) | ($true = (X1 @ X2 @ X2 @ X3))) & ! [X4 : $i > $o,X6 : $i > $o,X5 : $i > $o] : ((! [X7 : $i] : (($true = (X0 @ X4 @ X6 @ X7)) | ($true = (X1 @ X4 @ X6 @ X7))) & ! [X8 : $i] : (($true = (X1 @ X5 @ X4 @ X8)) | ($true = (X0 @ X5 @ X4 @ X8)))) => ! [X9 : $i] : (($true = (X0 @ X5 @ X6 @ X9)) | ($true = (X1 @ X5 @ X6 @ X9)))))),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.28 thf(f4,plain,(
% 1.48/1.28 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i > $o,X3 : $i] : ((X0 @ X2 @ X2 @ X3) | (X1 @ X2 @ X2 @ X3)) & ! [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : ((! [X7 : $i] : ((X1 @ X4 @ X6 @ X7) | (X0 @ X4 @ X6 @ X7)) & ! [X8 : $i] : ((X0 @ X5 @ X4 @ X8) | (X1 @ X5 @ X4 @ X8))) => ! [X9 : $i] : ((X0 @ X5 @ X6 @ X9) | (X1 @ X5 @ X6 @ X9))))),
% 1.48/1.28 inference(rectify,[status(thm)],[f2])).
% 1.48/1.28 thf(f2,negated_conjecture,(
% 1.48/1.28 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i > $o,X5 : $i] : ((X0 @ X2 @ X2 @ X5) | (X1 @ X2 @ X2 @ X5)) & ! [X3 : $i > $o,X2 : $i > $o,X4 : $i > $o] : ((! [X5 : $i] : ((X1 @ X3 @ X4 @ X5) | (X0 @ X3 @ X4 @ X5)) & ! [X5 : $i] : ((X0 @ X2 @ X3 @ X5) | (X1 @ X2 @ X3 @ X5))) => ! [X5 : $i] : ((X0 @ X2 @ X4 @ X5) | (X1 @ X2 @ X4 @ X5))))),
% 1.48/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.28 thf(f1,conjecture,(
% 1.48/1.28 ? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i > $o,X5 : $i] : ((X0 @ X2 @ X2 @ X5) | (X1 @ X2 @ X2 @ X5)) & ! [X3 : $i > $o,X2 : $i > $o,X4 : $i > $o] : ((! [X5 : $i] : ((X1 @ X3 @ X4 @ X5) | (X0 @ X3 @ X4 @ X5)) & ! [X5 : $i] : ((X0 @ X2 @ X3 @ X5) | (X1 @ X2 @ X3 @ X5))) => ! [X5 : $i] : ((X0 @ X2 @ X4 @ X5) | (X1 @ X2 @ X4 @ X5))))),
% 1.48/1.28 file('/export/starexec/sandbox/tmp/tmp.LJbsQv27eM/DTF2THF_9619.p',cTHM120G_pme)).
% 1.48/1.28 % SZS output end Proof for DTF2THF_9619
% 1.48/1.28 % (9898)------------------------------
% 1.48/1.28 % (9898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (9898)Termination reason: Refutation
% 1.48/1.28
% 1.48/1.28 % (9898)Memory used [KB]: 5500
% 1.48/1.28 % (9898)Time elapsed: 0.007 s
% 1.48/1.28 % (9898)Instructions burned: 5 (million)
% 1.48/1.28 % (9898)------------------------------
% 1.48/1.28 % (9898)------------------------------
% 1.48/1.28 % (9897)Success in time 0.022 s
%------------------------------------------------------------------------------