%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV076^5 : 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 : n001.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 09:40:13 AM UTC 2026
% Result : Theorem 1.45s 1.24s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 210 ( 90 equ; 0 cnn)
% Maximal formula atoms : 20 ( 11 avg)
% Number of connectives : 382 ( 45 ~; 26 |; 48 &; 235 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 129 ( 0 ^; 97 !; 32 ?; 129 :)
% 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 > $o ) > a ).
thf(func_def_7,type,
sK3: a > $o ).
thf(func_def_8,type,
sK4: a > a ).
thf(func_def_11,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f29,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
$true != $true,
inference(superposition,[status(thm)],[f21,f15]) ).
thf(f15,plain,
! [X10: a] :
( $true
= ( sK3 @ ( sK4 @ X10 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X2: a > $o] :
( ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( sK1 @ X3 @ ( sK0 @ X2 ) )
= $true ) )
& ! [X4: a] :
( ( $true
= ( sK1 @ ( sK0 @ X2 ) @ X4 ) )
| ( ( ( X2 @ ( sK2 @ X4 @ X2 ) )
= $true )
& ( ( sK1 @ ( sK2 @ X4 @ X2 ) @ X4 )
!= $true ) ) ) )
& ! [X6: a,X7: a,X8: a] :
( ( ( sK1 @ X8 @ X7 )
= $true )
| ( $true
!= ( sK1 @ X6 @ X7 ) )
| ( ( sK1 @ X8 @ X6 )
!= $true ) )
& ! [X10: a] :
( ( $true
= ( sK3 @ ( sK4 @ X10 ) ) )
& ( ( sK1 @ ( sK4 @ X10 ) @ X10 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: ( a > $o ) > a,X1: a > a > $o] :
( ! [X2: a > $o] :
( ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X1 @ X3 @ ( X0 @ X2 ) )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X1 @ ( X0 @ X2 ) @ X4 ) )
| ? [X5: a] :
( ( ( X2 @ X5 )
= $true )
& ( ( X1 @ X5 @ X4 )
!= $true ) ) ) )
& ! [X6: a,X7: a,X8: a] :
( ( ( X1 @ X8 @ X7 )
= $true )
| ( ( X1 @ X6 @ X7 )
!= $true )
| ( $true
!= ( X1 @ X8 @ X6 ) ) )
& ? [X9: a > $o] :
! [X10: a] :
? [X11: a] :
( ( ( X9 @ X11 )
= $true )
& ( ( X1 @ X11 @ X10 )
!= $true ) ) )
=> ( ! [X2: a > $o] :
( ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( sK1 @ X3 @ ( sK0 @ X2 ) )
= $true ) )
& ! [X4: a] :
( ( $true
= ( sK1 @ ( sK0 @ X2 ) @ X4 ) )
| ? [X5: a] :
( ( ( X2 @ X5 )
= $true )
& ( ( sK1 @ X5 @ X4 )
!= $true ) ) ) )
& ! [X8: a,X7: a,X6: a] :
( ( ( sK1 @ X8 @ X7 )
= $true )
| ( $true
!= ( sK1 @ X6 @ X7 ) )
| ( ( sK1 @ X8 @ X6 )
!= $true ) )
& ? [X9: a > $o] :
! [X10: a] :
? [X11: a] :
( ( ( X9 @ X11 )
= $true )
& ( ( sK1 @ X11 @ X10 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X2: a > $o,X4: a] :
( ? [X5: a] :
( ( ( X2 @ X5 )
= $true )
& ( ( sK1 @ X5 @ X4 )
!= $true ) )
=> ( ( ( X2 @ ( sK2 @ X4 @ X2 ) )
= $true )
& ( ( sK1 @ ( sK2 @ X4 @ X2 ) @ X4 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X9: a > $o] :
! [X10: a] :
? [X11: a] :
( ( ( X9 @ X11 )
= $true )
& ( ( sK1 @ X11 @ X10 )
!= $true ) )
=> ! [X10: a] :
? [X11: a] :
( ( ( sK3 @ X11 )
= $true )
& ( ( sK1 @ X11 @ X10 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X10: a] :
( ? [X11: a] :
( ( ( sK3 @ X11 )
= $true )
& ( ( sK1 @ X11 @ X10 )
!= $true ) )
=> ( ( $true
= ( sK3 @ ( sK4 @ X10 ) ) )
& ( ( sK1 @ ( sK4 @ X10 ) @ X10 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: ( a > $o ) > a,X1: a > a > $o] :
( ! [X2: a > $o] :
( ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X1 @ X3 @ ( X0 @ X2 ) )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X1 @ ( X0 @ X2 ) @ X4 ) )
| ? [X5: a] :
( ( ( X2 @ X5 )
= $true )
& ( ( X1 @ X5 @ X4 )
!= $true ) ) ) )
& ! [X6: a,X7: a,X8: a] :
( ( ( X1 @ X8 @ X7 )
= $true )
| ( ( X1 @ X6 @ X7 )
!= $true )
| ( $true
!= ( X1 @ X8 @ X6 ) ) )
& ? [X9: a > $o] :
! [X10: a] :
? [X11: a] :
( ( ( X9 @ X11 )
= $true )
& ( ( X1 @ X11 @ X10 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: ( a > $o ) > a,X1: a > a > $o] :
( ! [X5: a > $o] :
( ! [X8: a] :
( ( ( X5 @ X8 )
!= $true )
| ( ( X1 @ X8 @ ( X0 @ X5 ) )
= $true ) )
& ! [X6: a] :
( ( ( X1 @ ( X0 @ X5 ) @ X6 )
= $true )
| ? [X7: a] :
( ( ( X5 @ X7 )
= $true )
& ( ( X1 @ X7 @ X6 )
!= $true ) ) ) )
& ! [X3: a,X2: a,X4: a] :
( ( ( X1 @ X4 @ X2 )
= $true )
| ( ( X1 @ X3 @ X2 )
!= $true )
| ( $true
!= ( X1 @ X4 @ X3 ) ) )
& ? [X9: a > $o] :
! [X10: a] :
? [X11: a] :
( ( ( X9 @ X11 )
= $true )
& ( ( X1 @ X11 @ X10 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: ( a > $o ) > a,X1: a > a > $o] :
( ? [X9: a > $o] :
! [X10: a] :
? [X11: a] :
( ( ( X9 @ X11 )
= $true )
& ( ( X1 @ X11 @ X10 )
!= $true ) )
& ! [X4: a,X2: a,X3: a] :
( ( ( X1 @ X4 @ X2 )
= $true )
| ( $true
!= ( X1 @ X4 @ X3 ) )
| ( ( X1 @ X3 @ X2 )
!= $true ) )
& ! [X5: a > $o] :
( ! [X8: a] :
( ( ( X5 @ X8 )
!= $true )
| ( ( X1 @ X8 @ ( X0 @ X5 ) )
= $true ) )
& ! [X6: a] :
( ( ( X1 @ ( X0 @ X5 ) @ X6 )
= $true )
| ? [X7: a] :
( ( ( X5 @ X7 )
= $true )
& ( ( X1 @ X7 @ X6 )
!= $true ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > $o ) > a,X1: a > a > $o] :
( ( ! [X4: a,X2: a,X3: a] :
( ( ( $true
= ( X1 @ X4 @ X3 ) )
& ( ( X1 @ X3 @ X2 )
= $true ) )
=> ( ( X1 @ X4 @ X2 )
= $true ) )
& ! [X5: a > $o] :
( ! [X6: a] :
( ! [X7: a] :
( ( ( X5 @ X7 )
= $true )
=> ( ( X1 @ X7 @ X6 )
= $true ) )
=> ( ( X1 @ ( X0 @ X5 ) @ X6 )
= $true ) )
& ! [X8: a] :
( ( ( X5 @ X8 )
= $true )
=> ( ( X1 @ X8 @ ( X0 @ X5 ) )
= $true ) ) ) )
=> ! [X9: a > $o] :
? [X10: a] :
! [X11: a] :
( ( ( X9 @ X11 )
= $true )
=> ( ( X1 @ X11 @ X10 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > $o ) > a,X1: a > a > $o] :
( ( ! [X2: a,X3: a,X4: a] :
( ( ( X1 @ X4 @ X3 )
& ( X1 @ X3 @ X2 ) )
=> ( X1 @ X4 @ X2 ) )
& ! [X5: a > $o] :
( ! [X6: a] :
( ! [X7: a] :
( ( X5 @ X7 )
=> ( X1 @ X7 @ X6 ) )
=> ( X1 @ ( X0 @ X5 ) @ X6 ) )
& ! [X8: a] :
( ( X5 @ X8 )
=> ( X1 @ X8 @ ( X0 @ X5 ) ) ) ) )
=> ! [X9: a > $o] :
? [X10: a] :
! [X11: a] :
( ( X9 @ X11 )
=> ( X1 @ X11 @ X10 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: ( a > $o ) > a,X0: a > a > $o] :
( ( ! [X4: a,X3: a,X2: 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 ) ) ) ) )
=> ! [X5: a > $o] :
? [X8: a] :
! [X4: a] :
( ( X5 @ X4 )
=> ( X0 @ X4 @ X8 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: ( a > $o ) > a,X0: a > a > $o] :
( ( ! [X4: a,X3: a,X2: 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 ) ) ) ) )
=> ! [X5: a > $o] :
? [X8: a] :
! [X4: a] :
( ( X5 @ X4 )
=> ( X0 @ X4 @ X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LdjnuxZbX7/DTF2THF_2945.p',cTHM401B_pme) ).
thf(f21,plain,
! [X0: a > $o] :
( ( X0 @ ( sK4 @ ( sK0 @ X0 ) ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: a > $o] :
( ( ( X0 @ ( sK4 @ ( sK0 @ X0 ) ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f14,f19]) ).
thf(f19,plain,
! [X2: a > $o,X3: a] :
( ( ( sK1 @ X3 @ ( sK0 @ X2 ) )
= $true )
| ( ( X2 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f14,plain,
! [X10: a] :
( ( sK1 @ ( sK4 @ X10 ) @ X10 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.15 % Problem : SEV076^5 : TPTP v9.2.1. Released v4.0.0.
% 0.10/0.16 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.38 % Computer : n001.cluster.edu
% 0.19/0.38 % Model : x86_64 x86_64
% 0.19/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.38 % Memory : 8042.1875MB
% 0.19/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.38 % CPULimit : 300
% 0.19/0.38 % WCLimit : 300
% 0.19/0.38 % DateTime : Tue Feb 24 12:40:35 EST 2026
% 0.19/0.38 % CPUTime :
% 0.19/0.38 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.49 ---- Original DTF file ---
% 0.27/0.49 thf(spec,logic,$$dhol).
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 % File : SEV076^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.49 % Domain : Set Theory (Relations)
% 0.27/0.49 % Problem : TPS problem THM401B
% 0.27/0.49 % Version : Especial.
% 0.27/0.49 % English : In a complete lattice, every set has an upper bound.
% 0.27/0.49
% 0.27/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.49 % Source : [Bro09]
% 0.27/0.49 % Names : tps_0556 [Bro09]
% 0.27/0.49 % : tps_0557 [Bro09]
% 0.27/0.49 % : THM401A [TPS]
% 0.27/0.49 % : THM401B [TPS]
% 0.27/0.49 % : THM401 [TPS]
% 0.27/0.49 % : THM401Z [TPS]
% 0.27/0.49
% 0.27/0.49 % Status : Theorem
% 0.27/0.49 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.27/0.49 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.27/0.49 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.27/0.49 % Maximal formula atoms : 0 ( 0 avg)
% 0.27/0.49 % Number of connectives : 28 ( 0 ~; 0 |; 3 &; 19 @)
% 0.27/0.49 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.27/0.49 % Maximal formula depth : 13 ( 13 avg)
% 0.27/0.49 % Number of types : 2 ( 1 usr)
% 0.27/0.49 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.27/0.49 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.27/0.49 % Number of variables : 12 ( 0 ^; 11 !; 1 ?; 12 :)
% 0.27/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.27/0.49
% 0.27/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.49 % : Polymorphic definitions expanded.
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 thf(a_type,type,
% 0.27/0.49 a: $tType ).
% 0.27/0.49
% 0.27/0.49 thf(cTHM401B_pme,conjecture,
% 0.27/0.49 ! [RRR: a > a > $o,U: ( a > $o ) > a] :
% 0.27/0.49 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 0.27/0.49 ( ( ( RRR @ Xx @ Xy )
% 0.27/0.49 & ( RRR @ Xy @ Xz ) )
% 0.27/0.49 => ( RRR @ Xx @ Xz ) )
% 0.27/0.49 & ! [Xs: a > $o] :
% 0.27/0.49 ( ! [Xz: a] :
% 0.27/0.49 ( ( Xs @ Xz )
% 0.27/0.49 => ( RRR @ Xz @ ( U @ Xs ) ) )
% 0.27/0.49 & ! [Xj: a] :
% 0.27/0.49 ( ! [Xk: a] :
% 0.27/0.49 ( ( Xs @ Xk )
% 0.27/0.49 => ( RRR @ Xk @ Xj ) )
% 0.27/0.49 => ( RRR @ ( U @ Xs ) @ Xj ) ) ) )
% 0.27/0.49 => ! [Xs: a > $o] :
% 0.27/0.49 ? [Xb: a] :
% 0.27/0.49 ! [Xz: a] :
% 0.27/0.49 ( ( Xs @ Xz )
% 0.27/0.49 => ( RRR @ Xz @ Xb ) ) ) ).
% 0.27/0.49
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 ------------------------
% 1.45/1.22 ---- Embedded in THF ---
% 1.45/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.22 %%% Generated on Tue Feb 24 12:40:36 EST 2026
% 1.45/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.22 %%% Logic specification used:
% 1.45/1.22 %%% thf(spec, logic, $$dhol).
% 1.45/1.22
% 1.45/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.LdjnuxZbX7/DTF2DTF2945.p
% See solution above
% 1.45/1.22 ------------------------
% 1.45/1.23 ---- Cleaned THF ---
% 1.45/1.23 thf(a_type,type,
% 1.45/1.23 a: $tType ).
% 1.45/1.23
% 1.45/1.23 thf(cTHM401B_pme,conjecture,
% 1.45/1.23 ! [RRR: a > a > $o,U: ( a > $o ) > a] :
% 1.45/1.23 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 1.45/1.23 ( ( ( RRR @ Xx @ Xy )
% 1.45/1.23 & ( RRR @ Xy @ Xz ) )
% 1.45/1.23 => ( RRR @ Xx @ Xz ) )
% 1.45/1.23 & ! [Xs: a > $o] :
% 1.45/1.23 ( ! [Xz: a] :
% 1.45/1.23 ( ( Xs @ Xz )
% 1.45/1.23 => ( RRR @ Xz @ ( U @ Xs ) ) )
% 1.45/1.23 & ! [Xj: a] :
% 1.45/1.23 ( ! [Xk: a] :
% 1.45/1.23 ( ( Xs @ Xk )
% 1.45/1.23 => ( RRR @ Xk @ Xj ) )
% 1.45/1.23 => ( RRR @ ( U @ Xs ) @ Xj ) ) ) )
% 1.45/1.23 => ! [Xs: a > $o] :
% 1.45/1.23 ? [Xb: a] :
% 1.45/1.23 ! [Xz: a] :
% 1.45/1.23 ( ( Xs @ Xz )
% 1.45/1.23 => ( RRR @ Xz @ Xb ) ) ) ).
% 1.45/1.23 ------------------------
% 1.45/1.24 % (3043)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2945 for (3000ds/183Mi)
% 1.45/1.24 % (3045)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_2945 for (3000ds/27Mi)
% 1.45/1.24 % (3043)First to succeed.
% 1.45/1.24 % (3045)Also succeeded, but the first one will report.
% 1.45/1.24 % (3043)Refutation found. Thanks to Tanya!
% 1.45/1.24 % SZS status Theorem for DTF2THF_2945
% 1.45/1.24 % SZS output start Proof for DTF2THF_2945
% 1.45/1.24 thf(type_def_5, type, a: $tType).
% 1.45/1.24 thf(func_def_0, type, a: $tType).
% 1.45/1.24 thf(func_def_4, type, sK0: (a > $o) > a).
% 1.45/1.24 thf(func_def_5, type, sK1: a > a > $o).
% 1.45/1.24 thf(func_def_6, type, sK2: a > (a > $o) > a).
% 1.45/1.24 thf(func_def_7, type, sK3: a > $o).
% 1.45/1.24 thf(func_def_8, type, sK4: a > a).
% 1.45/1.24 thf(func_def_11, type, ph6: !>[X0: $tType]:(X0)).
% 1.45/1.24 thf(f29,plain,(
% 1.45/1.24 $false),
% 1.45/1.24 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.45/1.24 thf(f25,plain,(
% 1.45/1.24 ($true != $true)),
% 1.45/1.24 inference(superposition,[status(thm)],[f21,f15])).
% 1.45/1.24 thf(f15,plain,(
% 1.45/1.24 ( ! [X10 : a] : (($true = (sK3 @ (sK4 @ X10)))) )),
% 1.45/1.24 inference(cnf_transformation,[status(thm)],[f13])).
% 1.45/1.24 thf(f13,plain,(
% 1.45/1.24 ! [X2 : a > $o] : (! [X3 : a] : (((X2 @ X3) != $true) | ((sK1 @ X3 @ (sK0 @ X2)) = $true)) & ! [X4 : a] : (($true = (sK1 @ (sK0 @ X2) @ X4)) | (((X2 @ (sK2 @ X4 @ X2)) = $true) & ((sK1 @ (sK2 @ X4 @ X2) @ X4) != $true)))) & ! [X6 : a,X7 : a,X8 : a] : (((sK1 @ X8 @ X7) = $true) | ($true != (sK1 @ X6 @ X7)) | ((sK1 @ X8 @ X6) != $true)) & ! [X10 : a] : (($true = (sK3 @ (sK4 @ X10))) & ((sK1 @ (sK4 @ X10) @ X10) != $true))),
% 1.45/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f12,f11,f10,f9])).
% 1.45/1.24 thf(f9,plain,(
% 1.45/1.24 ? [X0 : (a > $o) > a,X1 : a > a > $o] : (! [X2 : a > $o] : (! [X3 : a] : (((X2 @ X3) != $true) | ((X1 @ X3 @ (X0 @ X2)) = $true)) & ! [X4 : a] : (($true = (X1 @ (X0 @ X2) @ X4)) | ? [X5 : a] : (((X2 @ X5) = $true) & ((X1 @ X5 @ X4) != $true)))) & ! [X6 : a,X7 : a,X8 : a] : (((X1 @ X8 @ X7) = $true) | ((X1 @ X6 @ X7) != $true) | ($true != (X1 @ X8 @ X6))) & ? [X9 : a > $o] : ! [X10 : a] : ? [X11 : a] : (((X9 @ X11) = $true) & ((X1 @ X11 @ X10) != $true))) => (! [X2 : a > $o] : (! [X3 : a] : (((X2 @ X3) != $true) | ((sK1 @ X3 @ (sK0 @ X2)) = $true)) & ! [X4 : a] : (($true = (sK1 @ (sK0 @ X2) @ X4)) | ? [X5 : a] : (((X2 @ X5) = $true) & ((sK1 @ X5 @ X4) != $true)))) & ! [X8 : a,X7 : a,X6 : a] : (((sK1 @ X8 @ X7) = $true) | ($true != (sK1 @ X6 @ X7)) | ((sK1 @ X8 @ X6) != $true)) & ? [X9 : a > $o] : ! [X10 : a] : ? [X11 : a] : (((X9 @ X11) = $true) & ((sK1 @ X11 @ X10) != $true)))),
% 1.45/1.24 introduced(definition,[],[choice_axiom])).
% 1.45/1.24 thf(f10,plain,(
% 1.45/1.24 ! [X2 : a > $o,X4 : a] : (? [X5 : a] : (((X2 @ X5) = $true) & ((sK1 @ X5 @ X4) != $true)) => (((X2 @ (sK2 @ X4 @ X2)) = $true) & ((sK1 @ (sK2 @ X4 @ X2) @ X4) != $true)))),
% 1.45/1.24 introduced(definition,[],[choice_axiom])).
% 1.45/1.24 thf(f11,plain,(
% 1.45/1.24 ? [X9 : a > $o] : ! [X10 : a] : ? [X11 : a] : (((X9 @ X11) = $true) & ((sK1 @ X11 @ X10) != $true)) => ! [X10 : a] : ? [X11 : a] : (((sK3 @ X11) = $true) & ((sK1 @ X11 @ X10) != $true))),
% 1.45/1.24 introduced(definition,[],[choice_axiom])).
% 1.45/1.24 thf(f12,plain,(
% 1.45/1.24 ! [X10 : a] : (? [X11 : a] : (((sK3 @ X11) = $true) & ((sK1 @ X11 @ X10) != $true)) => (($true = (sK3 @ (sK4 @ X10))) & ((sK1 @ (sK4 @ X10) @ X10) != $true)))),
% 1.45/1.24 introduced(definition,[],[choice_axiom])).
% 1.45/1.24 thf(f8,plain,(
% 1.45/1.24 ? [X0 : (a > $o) > a,X1 : a > a > $o] : (! [X2 : a > $o] : (! [X3 : a] : (((X2 @ X3) != $true) | ((X1 @ X3 @ (X0 @ X2)) = $true)) & ! [X4 : a] : (($true = (X1 @ (X0 @ X2) @ X4)) | ? [X5 : a] : (((X2 @ X5) = $true) & ((X1 @ X5 @ X4) != $true)))) & ! [X6 : a,X7 : a,X8 : a] : (((X1 @ X8 @ X7) = $true) | ((X1 @ X6 @ X7) != $true) | ($true != (X1 @ X8 @ X6))) & ? [X9 : a > $o] : ! [X10 : a] : ? [X11 : a] : (((X9 @ X11) = $true) & ((X1 @ X11 @ X10) != $true)))),
% 1.45/1.24 inference(rectify,[status(thm)],[f7])).
% 1.45/1.24 thf(f7,plain,(
% 1.45/1.24 ? [X0 : (a > $o) > a,X1 : a > a > $o] : (! [X5 : a > $o] : (! [X8 : a] : (((X5 @ X8) != $true) | ((X1 @ X8 @ (X0 @ X5)) = $true)) & ! [X6 : a] : (((X1 @ (X0 @ X5) @ X6) = $true) | ? [X7 : a] : (((X5 @ X7) = $true) & ((X1 @ X7 @ X6) != $true)))) & ! [X3 : a,X2 : a,X4 : a] : (((X1 @ X4 @ X2) = $true) | ((X1 @ X3 @ X2) != $true) | ($true != (X1 @ X4 @ X3))) & ? [X9 : a > $o] : ! [X10 : a] : ? [X11 : a] : (((X9 @ X11) = $true) & ((X1 @ X11 @ X10) != $true)))),
% 1.45/1.24 inference(flattening,[status(thm)],[f6])).
% 1.45/1.24 thf(f6,plain,(
% 1.45/1.24 ? [X0 : (a > $o) > a,X1 : a > a > $o] : (? [X9 : a > $o] : ! [X10 : a] : ? [X11 : a] : (((X9 @ X11) = $true) & ((X1 @ X11 @ X10) != $true)) & (! [X4 : a,X2 : a,X3 : a] : (((X1 @ X4 @ X2) = $true) | (($true != (X1 @ X4 @ X3)) | ((X1 @ X3 @ X2) != $true))) & ! [X5 : a > $o] : (! [X8 : a] : (((X5 @ X8) != $true) | ((X1 @ X8 @ (X0 @ X5)) = $true)) & ! [X6 : a] : (((X1 @ (X0 @ X5) @ X6) = $true) | ? [X7 : a] : (((X5 @ X7) = $true) & ((X1 @ X7 @ X6) != $true))))))),
% 1.45/1.24 inference(ennf_transformation,[status(thm)],[f5])).
% 1.45/1.24 thf(f5,plain,(
% 1.45/1.24 ~! [X0 : (a > $o) > a,X1 : a > a > $o] : ((! [X4 : a,X2 : a,X3 : a] : ((($true = (X1 @ X4 @ X3)) & ((X1 @ X3 @ X2) = $true)) => ((X1 @ X4 @ X2) = $true)) & ! [X5 : a > $o] : (! [X6 : a] : (! [X7 : a] : (((X5 @ X7) = $true) => ((X1 @ X7 @ X6) = $true)) => ((X1 @ (X0 @ X5) @ X6) = $true)) & ! [X8 : a] : (((X5 @ X8) = $true) => ((X1 @ X8 @ (X0 @ X5)) = $true)))) => ! [X9 : a > $o] : ? [X10 : a] : ! [X11 : a] : (((X9 @ X11) = $true) => ((X1 @ X11 @ X10) = $true)))),
% 1.45/1.24 inference(fool_elimination,[status(thm)],[f4])).
% 1.45/1.24 thf(f4,plain,(
% 1.45/1.24 ~! [X0 : (a > $o) > a,X1 : a > a > $o] : ((! [X2 : a,X3 : a,X4 : a] : (((X1 @ X4 @ X3) & (X1 @ X3 @ X2)) => (X1 @ X4 @ X2)) & ! [X5 : a > $o] : (! [X6 : a] : (! [X7 : a] : ((X5 @ X7) => (X1 @ X7 @ X6)) => (X1 @ (X0 @ X5) @ X6)) & ! [X8 : a] : ((X5 @ X8) => (X1 @ X8 @ (X0 @ X5))))) => ! [X9 : a > $o] : ? [X10 : a] : ! [X11 : a] : ((X9 @ X11) => (X1 @ X11 @ X10)))),
% 1.45/1.24 inference(rectify,[status(thm)],[f2])).
% 1.45/1.24 thf(f2,negated_conjecture,(
% 1.45/1.24 ~! [X1 : (a > $o) > a,X0 : a > a > $o] : ((! [X4 : a,X3 : a,X2 : 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))))) => ! [X5 : a > $o] : ? [X8 : a] : ! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ X8)))),
% 1.45/1.24 inference(negated_conjecture,[status(cth)],[f1])).
% 1.45/1.24 thf(f1,conjecture,(
% 1.45/1.24 ! [X1 : (a > $o) > a,X0 : a > a > $o] : ((! [X4 : a,X3 : a,X2 : 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))))) => ! [X5 : a > $o] : ? [X8 : a] : ! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ X8)))),
% 1.45/1.24 file('/export/starexec/sandbox2/tmp/tmp.LdjnuxZbX7/DTF2THF_2945.p',cTHM401B_pme)).
% 1.45/1.24 thf(f21,plain,(
% 1.45/1.24 ( ! [X0 : a > $o] : (((X0 @ (sK4 @ (sK0 @ X0))) != $true)) )),
% 1.45/1.24 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.45/1.24 thf(f20,plain,(
% 1.45/1.24 ( ! [X0 : a > $o] : (((X0 @ (sK4 @ (sK0 @ X0))) != $true) | ($true != $true)) )),
% 1.45/1.24 inference(superposition,[status(thm)],[f14,f19])).
% 1.45/1.24 thf(f19,plain,(
% 1.45/1.24 ( ! [X2 : a > $o,X3 : a] : (((sK1 @ X3 @ (sK0 @ X2)) = $true) | ((X2 @ X3) != $true)) )),
% 1.45/1.24 inference(cnf_transformation,[status(thm)],[f13])).
% 1.45/1.24 thf(f14,plain,(
% 1.45/1.24 ( ! [X10 : a] : (((sK1 @ (sK4 @ X10) @ X10) != $true)) )),
% 1.45/1.24 inference(cnf_transformation,[status(thm)],[f13])).
% 1.45/1.24 % SZS output end Proof for DTF2THF_2945
% 1.45/1.24 % (3043)------------------------------
% 1.45/1.24 % (3043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.24 % (3043)Termination reason: Refutation
% 1.45/1.24
% 1.45/1.24 % (3043)Memory used [KB]: 5500
% 1.45/1.24 % (3043)Time elapsed: 0.003 s
% 1.45/1.24 % (3043)Instructions burned: 2 (million)
% 1.45/1.24 % (3043)------------------------------
% 1.45/1.24 % (3043)------------------------------
% 1.45/1.24 % (3042)Success in time 0.012 s
%------------------------------------------------------------------------------