%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV185^5 : 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 : n023.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 09:40:30 AM UTC 2026
% Result : Theorem 1.63s 1.32s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 382 ( 147 equ; 0 cnn)
% Maximal formula atoms : 22 ( 11 avg)
% Number of connectives : 455 ( 74 ~; 63 |; 48 &; 234 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 105 ( 105 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 134 ( 0 ^; 100 !; 34 ?; 134 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_4,type,
sK0: ( b > $o ) > b > $o ).
thf(func_def_5,type,
sK1: ( b > $o ) > $o ).
thf(func_def_6,type,
sK2: b > $o ).
thf(func_def_7,type,
sK3: b ).
thf(func_def_8,type,
sK4: b > $o ).
thf(func_def_9,type,
sK5: ( b > $o ) > ( b > $o ) > b ).
thf(func_def_12,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f36,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f35,f17]) ).
thf(f17,plain,
( $true
!= ( sK4 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X4: b] :
( ! [X5: b > $o] :
( ( ( X5 @ X4 )
= $true )
| ( ( sK1 @ X5 )
!= $true ) )
| ( $true
!= ( sK2 @ X4 ) ) )
& ( $true
= ( sK1 @ sK4 ) )
& ( $true
!= ( sK4 @ sK3 ) )
& ( $true
= ( sK0 @ sK2 @ sK3 ) )
& ! [X7: b > $o] :
( ! [X8: b,X9: b > $o] :
( ( ( sK0 @ X9 @ X8 )
!= $true )
| ( ( $true
= ( X9 @ ( sK5 @ X9 @ X7 ) ) )
& ( ( X7 @ ( sK5 @ X9 @ X7 ) )
!= $true ) )
| ( ( X7 @ X8 )
= $true ) )
| ( $true
!= ( sK1 @ X7 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: ( b > $o ) > b > $o,X1: ( b > $o ) > $o] :
( ? [X2: b > $o,X3: b] :
( ! [X4: b] :
( ! [X5: b > $o] :
( ( ( X5 @ X4 )
= $true )
| ( $true
!= ( X1 @ X5 ) ) )
| ( ( X2 @ X4 )
!= $true ) )
& ? [X6: b > $o] :
( ( ( X1 @ X6 )
= $true )
& ( $true
!= ( X6 @ X3 ) ) )
& ( ( X0 @ X2 @ X3 )
= $true ) )
& ! [X7: b > $o] :
( ! [X8: b,X9: b > $o] :
( ( $true
!= ( X0 @ X9 @ X8 ) )
| ? [X10: b] :
( ( ( X9 @ X10 )
= $true )
& ( $true
!= ( X7 @ X10 ) ) )
| ( ( X7 @ X8 )
= $true ) )
| ( $true
!= ( X1 @ X7 ) ) ) )
=> ( ? [X3: b,X2: b > $o] :
( ! [X4: b] :
( ! [X5: b > $o] :
( ( ( X5 @ X4 )
= $true )
| ( ( sK1 @ X5 )
!= $true ) )
| ( ( X2 @ X4 )
!= $true ) )
& ? [X6: b > $o] :
( ( $true
= ( sK1 @ X6 ) )
& ( $true
!= ( X6 @ X3 ) ) )
& ( $true
= ( sK0 @ X2 @ X3 ) ) )
& ! [X7: b > $o] :
( ! [X9: b > $o,X8: b] :
( ( ( sK0 @ X9 @ X8 )
!= $true )
| ? [X10: b] :
( ( ( X9 @ X10 )
= $true )
& ( $true
!= ( X7 @ X10 ) ) )
| ( ( X7 @ X8 )
= $true ) )
| ( $true
!= ( sK1 @ X7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: b,X2: b > $o] :
( ! [X4: b] :
( ! [X5: b > $o] :
( ( ( X5 @ X4 )
= $true )
| ( ( sK1 @ X5 )
!= $true ) )
| ( ( X2 @ X4 )
!= $true ) )
& ? [X6: b > $o] :
( ( $true
= ( sK1 @ X6 ) )
& ( $true
!= ( X6 @ X3 ) ) )
& ( $true
= ( sK0 @ X2 @ X3 ) ) )
=> ( ! [X4: b] :
( ! [X5: b > $o] :
( ( ( X5 @ X4 )
= $true )
| ( ( sK1 @ X5 )
!= $true ) )
| ( $true
!= ( sK2 @ X4 ) ) )
& ? [X6: b > $o] :
( ( $true
= ( sK1 @ X6 ) )
& ( $true
!= ( X6 @ sK3 ) ) )
& ( $true
= ( sK0 @ sK2 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X6: b > $o] :
( ( $true
= ( sK1 @ X6 ) )
& ( $true
!= ( X6 @ sK3 ) ) )
=> ( ( $true
= ( sK1 @ sK4 ) )
& ( $true
!= ( sK4 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X7: b > $o,X9: b > $o] :
( ? [X10: b] :
( ( ( X9 @ X10 )
= $true )
& ( $true
!= ( X7 @ X10 ) ) )
=> ( ( $true
= ( X9 @ ( sK5 @ X9 @ X7 ) ) )
& ( ( X7 @ ( sK5 @ X9 @ X7 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: ( b > $o ) > b > $o,X1: ( b > $o ) > $o] :
( ? [X2: b > $o,X3: b] :
( ! [X4: b] :
( ! [X5: b > $o] :
( ( ( X5 @ X4 )
= $true )
| ( $true
!= ( X1 @ X5 ) ) )
| ( ( X2 @ X4 )
!= $true ) )
& ? [X6: b > $o] :
( ( ( X1 @ X6 )
= $true )
& ( $true
!= ( X6 @ X3 ) ) )
& ( ( X0 @ X2 @ X3 )
= $true ) )
& ! [X7: b > $o] :
( ! [X8: b,X9: b > $o] :
( ( $true
!= ( X0 @ X9 @ X8 ) )
| ? [X10: b] :
( ( ( X9 @ X10 )
= $true )
& ( $true
!= ( X7 @ X10 ) ) )
| ( ( X7 @ X8 )
= $true ) )
| ( $true
!= ( X1 @ X7 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: ( b > $o ) > b > $o,X1: ( b > $o ) > $o] :
( ? [X7: b > $o,X6: b] :
( ! [X8: b] :
( ! [X9: b > $o] :
( ( $true
= ( X9 @ X8 ) )
| ( $true
!= ( X1 @ X9 ) ) )
| ( ( X7 @ X8 )
!= $true ) )
& ? [X10: b > $o] :
( ( ( X1 @ X10 )
= $true )
& ( $true
!= ( X10 @ X6 ) ) )
& ( $true
= ( X0 @ X7 @ X6 ) ) )
& ! [X2: b > $o] :
( ! [X4: b,X3: b > $o] :
( ( ( X0 @ X3 @ X4 )
!= $true )
| ? [X5: b] :
( ( ( X3 @ X5 )
= $true )
& ( ( X2 @ X5 )
!= $true ) )
| ( ( X2 @ X4 )
= $true ) )
| ( ( X1 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: ( b > $o ) > $o,X0: ( b > $o ) > b > $o] :
( ? [X6: b,X7: b > $o] :
( ? [X10: b > $o] :
( ( ( X1 @ X10 )
= $true )
& ( $true
!= ( X10 @ X6 ) ) )
& ( $true
= ( X0 @ X7 @ X6 ) )
& ! [X8: b] :
( ! [X9: b > $o] :
( ( $true
= ( X9 @ X8 ) )
| ( $true
!= ( X1 @ X9 ) ) )
| ( ( X7 @ X8 )
!= $true ) ) )
& ! [X2: b > $o] :
( ! [X4: b,X3: b > $o] :
( ( ( X2 @ X4 )
= $true )
| ? [X5: b] :
( ( ( X3 @ X5 )
= $true )
& ( ( X2 @ X5 )
!= $true ) )
| ( ( X0 @ X3 @ X4 )
!= $true ) )
| ( ( X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: ( b > $o ) > $o,X0: ( b > $o ) > b > $o] :
( ! [X2: b > $o] :
( ( ( X1 @ X2 )
= $true )
=> ! [X4: b,X3: b > $o] :
( ( ! [X5: b] :
( ( ( X3 @ X5 )
= $true )
=> ( ( X2 @ X5 )
= $true ) )
& ( ( X0 @ X3 @ X4 )
= $true ) )
=> ( ( X2 @ X4 )
= $true ) ) )
=> ! [X6: b,X7: b > $o] :
( ( ( $true
= ( X0 @ X7 @ X6 ) )
& ! [X8: b] :
( ( ( X7 @ X8 )
= $true )
=> ! [X9: b > $o] :
( ( $true
= ( X1 @ X9 ) )
=> ( $true
= ( X9 @ X8 ) ) ) ) )
=> ! [X10: b > $o] :
( ( ( X1 @ X10 )
= $true )
=> ( $true
= ( X10 @ X6 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( b > $o ) > b > $o,X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ! [X3: b > $o,X4: b] :
( ( ( X0 @ X3 @ X4 )
& ! [X5: b] :
( ( X3 @ X5 )
=> ( X2 @ X5 ) ) )
=> ( X2 @ X4 ) ) )
=> ! [X6: b,X7: b > $o] :
( ( ( X0 @ X7 @ X6 )
& ! [X8: b] :
( ( X7 @ X8 )
=> ! [X9: b > $o] :
( ( X1 @ X9 )
=> ( X9 @ X8 ) ) ) )
=> ! [X10: b > $o] :
( ( X1 @ X10 )
=> ( X10 @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( b > $o ) > b > $o,X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ! [X3: b > $o,X4: b] :
( ( ( X0 @ X3 @ X4 )
& ! [X5: b] :
( ( X3 @ X5 )
=> ( X2 @ X5 ) ) )
=> ( X2 @ X4 ) ) )
=> ! [X4: b,X3: b > $o] :
( ( ( X0 @ X3 @ X4 )
& ! [X2: b] :
( ( X3 @ X2 )
=> ! [X6: b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 ) ) ) )
=> ! [X6: b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( b > $o ) > b > $o,X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ! [X3: b > $o,X4: b] :
( ( ( X0 @ X3 @ X4 )
& ! [X5: b] :
( ( X3 @ X5 )
=> ( X2 @ X5 ) ) )
=> ( X2 @ X4 ) ) )
=> ! [X4: b,X3: b > $o] :
( ( ( X0 @ X3 @ X4 )
& ! [X2: b] :
( ( X3 @ X2 )
=> ! [X6: b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 ) ) ) )
=> ! [X6: b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QtEV7U1CkB/DTF2THF_7812.p',cTHM564_pme) ).
thf(f35,plain,
( $true
= ( sK4 @ sK3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true != $true )
| ( $true
= ( sK4 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f33,f16]) ).
thf(f16,plain,
( $true
= ( sK0 @ sK2 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f33,plain,
! [X0: b] :
( ( ( sK0 @ sK2 @ X0 )
!= $true )
| ( $true
= ( sK4 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: b] :
( ( ( sK0 @ sK2 @ X0 )
!= $true )
| ( $true != $true )
| ( $true
= ( sK4 @ X0 ) ) ),
inference(superposition,[status(thm)],[f24,f31]) ).
thf(f31,plain,
( ( sK4 @ ( sK5 @ sK2 @ sK4 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( sK4 @ ( sK5 @ sK2 @ sK4 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f21,f29]) ).
thf(f29,plain,
( $true
= ( sK2 @ ( sK5 @ sK2 @ sK4 ) ) ),
inference(subsumption_resolution,[status(thm)],[f28,f17]) ).
thf(f28,plain,
( ( $true
= ( sK4 @ sK3 ) )
| ( $true
= ( sK2 @ ( sK5 @ sK2 @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $true != $true )
| ( $true
= ( sK4 @ sK3 ) )
| ( $true
= ( sK2 @ ( sK5 @ sK2 @ sK4 ) ) ) ),
inference(superposition,[status(thm)],[f26,f16]) ).
thf(f26,plain,
! [X0: b > $o,X1: b] :
( ( $true
!= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( X0 @ ( sK5 @ X0 @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: b > $o,X1: b] :
( ( $true
= ( X0 @ ( sK5 @ X0 @ sK4 ) ) )
| ( $true != $true )
| ( $true
!= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(superposition,[status(thm)],[f15,f18]) ).
thf(f18,plain,
( $true
= ( sK1 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f15,plain,
! [X8: b,X9: b > $o,X7: b > $o] :
( ( $true
!= ( sK1 @ X7 ) )
| ( $true
= ( X9 @ ( sK5 @ X9 @ X7 ) ) )
| ( ( sK0 @ X9 @ X8 )
!= $true )
| ( ( X7 @ X8 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f21,plain,
! [X0: b] :
( ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( sK4 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: b] :
( ( $true != $true )
| ( $true
!= ( sK2 @ X0 ) )
| ( $true
= ( sK4 @ X0 ) ) ),
inference(superposition,[status(thm)],[f19,f18]) ).
thf(f19,plain,
! [X4: b,X5: b > $o] :
( ( ( sK1 @ X5 )
!= $true )
| ( $true
!= ( sK2 @ X4 ) )
| ( ( X5 @ X4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f24,plain,
! [X0: b,X1: b > $o] :
( ( ( sK4 @ ( sK5 @ X1 @ sK4 ) )
!= $true )
| ( $true
= ( sK4 @ X0 ) )
| ( $true
!= ( sK0 @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: b,X1: b > $o] :
( ( ( sK4 @ ( sK5 @ X1 @ sK4 ) )
!= $true )
| ( $true
!= ( sK0 @ X1 @ X0 ) )
| ( $true
= ( sK4 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f14,f18]) ).
thf(f14,plain,
! [X8: b,X9: b > $o,X7: b > $o] :
( ( $true
!= ( sK1 @ X7 ) )
| ( ( X7 @ X8 )
= $true )
| ( ( X7 @ ( sK5 @ X9 @ X7 ) )
!= $true )
| ( ( sK0 @ X9 @ X8 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV185^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n023.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:42:19 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : SEV185^5 : TPTP v9.2.1. Released v4.0.0.
% 0.21/0.47 % Domain : Set Theory (Sets of sets)
% 0.21/0.47 % Problem : TPS problem THM564
% 0.21/0.47 % Version : Especial.
% 0.21/0.47 % English :
% 0.21/0.47
% 0.21/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.47 % Source : [Bro09]
% 0.21/0.47 % Names : tps_0453 [Bro09]
% 0.21/0.47 % : THM564 [TPS]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.21/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.21/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.21/0.47 % Number of connectives : 23 ( 0 ~; 0 |; 2 &; 13 @)
% 0.21/0.47 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 13 ( 13 avg)
% 0.21/0.47 % Number of types : 2 ( 1 usr)
% 0.21/0.47 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.21/0.47 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.21/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.47 % : Polymorphic definitions expanded.
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 thf(b_type,type,
% 0.21/0.47 b: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(cTHM564_pme,conjecture,
% 0.21/0.47 ! [P: ( b > $o ) > b > $o,S: ( b > $o ) > $o] :
% 0.21/0.47 ( ! [Xx: b > $o] :
% 0.21/0.47 ( ( S @ Xx )
% 0.21/0.47 => ! [X: b > $o,Xy: b] :
% 0.21/0.47 ( ( ! [Xx0: b] :
% 0.21/0.47 ( ( X @ Xx0 )
% 0.21/0.47 => ( Xx @ Xx0 ) )
% 0.21/0.47 & ( P @ X @ Xy ) )
% 0.21/0.47 => ( Xx @ Xy ) ) )
% 0.21/0.47 => ! [X: b > $o,Xy: b] :
% 0.21/0.47 ( ( ! [Xx: b] :
% 0.21/0.47 ( ( X @ Xx )
% 0.21/0.47 => ! [S0: b > $o] :
% 0.21/0.47 ( ( S @ S0 )
% 0.21/0.47 => ( S0 @ Xx ) ) )
% 0.21/0.47 & ( P @ X @ Xy ) )
% 0.21/0.47 => ! [S0: b > $o] :
% 0.21/0.47 ( ( S @ S0 )
% 0.21/0.47 => ( S0 @ Xy ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 1.45/1.29 ---- Embedded in THF ---
% 1.45/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.29 %%% Generated on Tue Feb 24 12:42:20 EST 2026
% 1.45/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.29 %%% Logic specification used:
% 1.45/1.29 %%% thf(spec, logic, $$dhol).
% 1.45/1.29
% 1.45/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QtEV7U1CkB/DTF2DTF7812.p
% See solution above
% 1.45/1.29 ------------------------
% 1.63/1.30 ---- Cleaned THF ---
% 1.63/1.30 thf(b_type,type,
% 1.63/1.30 b: $tType ).
% 1.63/1.30
% 1.63/1.30 thf(cTHM564_pme,conjecture,
% 1.63/1.30 ! [P: ( b > $o ) > b > $o,S: ( b > $o ) > $o] :
% 1.63/1.30 ( ! [Xx: b > $o] :
% 1.63/1.30 ( ( S @ Xx )
% 1.63/1.30 => ! [X: b > $o,Xy: b] :
% 1.63/1.30 ( ( ! [Xx0: b] :
% 1.63/1.30 ( ( X @ Xx0 )
% 1.63/1.30 => ( Xx @ Xx0 ) )
% 1.63/1.30 & ( P @ X @ Xy ) )
% 1.63/1.30 => ( Xx @ Xy ) ) )
% 1.63/1.30 => ! [X: b > $o,Xy: b] :
% 1.63/1.30 ( ( ! [Xx: b] :
% 1.63/1.30 ( ( X @ Xx )
% 1.63/1.30 => ! [S0: b > $o] :
% 1.63/1.30 ( ( S @ S0 )
% 1.63/1.30 => ( S0 @ Xx ) ) )
% 1.63/1.30 & ( P @ X @ Xy ) )
% 1.63/1.30 => ! [S0: b > $o] :
% 1.63/1.30 ( ( S @ S0 )
% 1.63/1.30 => ( S0 @ Xy ) ) ) ) ).
% 1.63/1.30 ------------------------
% 1.63/1.31 % (8147)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7812 for (2999ds/18Mi)
% 1.63/1.32 % (8147)First to succeed.
% 1.63/1.32 % (8147)Refutation found. Thanks to Tanya!
% 1.63/1.32 % SZS status Theorem for DTF2THF_7812
% 1.63/1.32 % SZS output start Proof for DTF2THF_7812
% 1.63/1.32 thf(type_def_5, type, b: $tType).
% 1.63/1.32 thf(func_def_0, type, b: $tType).
% 1.63/1.32 thf(func_def_4, type, sK0: (b > $o) > b > $o).
% 1.63/1.32 thf(func_def_5, type, sK1: (b > $o) > $o).
% 1.63/1.32 thf(func_def_6, type, sK2: b > $o).
% 1.63/1.32 thf(func_def_7, type, sK3: b).
% 1.63/1.32 thf(func_def_8, type, sK4: b > $o).
% 1.63/1.32 thf(func_def_9, type, sK5: (b > $o) > (b > $o) > b).
% 1.63/1.32 thf(func_def_12, type, ph7: !>[X0: $tType]:(X0)).
% 1.63/1.32 thf(f36,plain,(
% 1.63/1.32 $false),
% 1.63/1.32 inference(subsumption_resolution,[status(thm)],[f35,f17])).
% 1.63/1.32 thf(f17,plain,(
% 1.63/1.32 ($true != (sK4 @ sK3))),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.32 thf(f13,plain,(
% 1.63/1.32 (! [X4 : b] : (! [X5 : b > $o] : (((X5 @ X4) = $true) | ((sK1 @ X5) != $true)) | ($true != (sK2 @ X4))) & (($true = (sK1 @ sK4)) & ($true != (sK4 @ sK3))) & ($true = (sK0 @ sK2 @ sK3))) & ! [X7 : b > $o] : (! [X8 : b,X9 : b > $o] : (((sK0 @ X9 @ X8) != $true) | (($true = (X9 @ (sK5 @ X9 @ X7))) & ((X7 @ (sK5 @ X9 @ X7)) != $true)) | ((X7 @ X8) = $true)) | ($true != (sK1 @ X7)))),
% 1.63/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f12,f11,f10,f9])).
% 1.63/1.32 thf(f9,plain,(
% 1.63/1.32 ? [X0 : (b > $o) > b > $o,X1 : (b > $o) > $o] : (? [X2 : b > $o,X3 : b] : (! [X4 : b] : (! [X5 : b > $o] : (((X5 @ X4) = $true) | ($true != (X1 @ X5))) | ((X2 @ X4) != $true)) & ? [X6 : b > $o] : (((X1 @ X6) = $true) & ($true != (X6 @ X3))) & ((X0 @ X2 @ X3) = $true)) & ! [X7 : b > $o] : (! [X8 : b,X9 : b > $o] : (($true != (X0 @ X9 @ X8)) | ? [X10 : b] : (((X9 @ X10) = $true) & ($true != (X7 @ X10))) | ((X7 @ X8) = $true)) | ($true != (X1 @ X7)))) => (? [X3 : b,X2 : b > $o] : (! [X4 : b] : (! [X5 : b > $o] : (((X5 @ X4) = $true) | ((sK1 @ X5) != $true)) | ((X2 @ X4) != $true)) & ? [X6 : b > $o] : (($true = (sK1 @ X6)) & ($true != (X6 @ X3))) & ($true = (sK0 @ X2 @ X3))) & ! [X7 : b > $o] : (! [X9 : b > $o,X8 : b] : (((sK0 @ X9 @ X8) != $true) | ? [X10 : b] : (((X9 @ X10) = $true) & ($true != (X7 @ X10))) | ((X7 @ X8) = $true)) | ($true != (sK1 @ X7))))),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 thf(f10,plain,(
% 1.63/1.32 ? [X3 : b,X2 : b > $o] : (! [X4 : b] : (! [X5 : b > $o] : (((X5 @ X4) = $true) | ((sK1 @ X5) != $true)) | ((X2 @ X4) != $true)) & ? [X6 : b > $o] : (($true = (sK1 @ X6)) & ($true != (X6 @ X3))) & ($true = (sK0 @ X2 @ X3))) => (! [X4 : b] : (! [X5 : b > $o] : (((X5 @ X4) = $true) | ((sK1 @ X5) != $true)) | ($true != (sK2 @ X4))) & ? [X6 : b > $o] : (($true = (sK1 @ X6)) & ($true != (X6 @ sK3))) & ($true = (sK0 @ sK2 @ sK3)))),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 thf(f11,plain,(
% 1.63/1.32 ? [X6 : b > $o] : (($true = (sK1 @ X6)) & ($true != (X6 @ sK3))) => (($true = (sK1 @ sK4)) & ($true != (sK4 @ sK3)))),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 thf(f12,plain,(
% 1.63/1.32 ! [X7 : b > $o,X9 : b > $o] : (? [X10 : b] : (((X9 @ X10) = $true) & ($true != (X7 @ X10))) => (($true = (X9 @ (sK5 @ X9 @ X7))) & ((X7 @ (sK5 @ X9 @ X7)) != $true)))),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 thf(f8,plain,(
% 1.63/1.32 ? [X0 : (b > $o) > b > $o,X1 : (b > $o) > $o] : (? [X2 : b > $o,X3 : b] : (! [X4 : b] : (! [X5 : b > $o] : (((X5 @ X4) = $true) | ($true != (X1 @ X5))) | ((X2 @ X4) != $true)) & ? [X6 : b > $o] : (((X1 @ X6) = $true) & ($true != (X6 @ X3))) & ((X0 @ X2 @ X3) = $true)) & ! [X7 : b > $o] : (! [X8 : b,X9 : b > $o] : (($true != (X0 @ X9 @ X8)) | ? [X10 : b] : (((X9 @ X10) = $true) & ($true != (X7 @ X10))) | ((X7 @ X8) = $true)) | ($true != (X1 @ X7))))),
% 1.63/1.32 inference(rectify,[status(thm)],[f7])).
% 1.63/1.32 thf(f7,plain,(
% 1.63/1.32 ? [X0 : (b > $o) > b > $o,X1 : (b > $o) > $o] : (? [X7 : b > $o,X6 : b] : (! [X8 : b] : (! [X9 : b > $o] : (($true = (X9 @ X8)) | ($true != (X1 @ X9))) | ((X7 @ X8) != $true)) & ? [X10 : b > $o] : (((X1 @ X10) = $true) & ($true != (X10 @ X6))) & ($true = (X0 @ X7 @ X6))) & ! [X2 : b > $o] : (! [X4 : b,X3 : b > $o] : (((X0 @ X3 @ X4) != $true) | ? [X5 : b] : (((X3 @ X5) = $true) & ((X2 @ X5) != $true)) | ((X2 @ X4) = $true)) | ((X1 @ X2) != $true)))),
% 1.63/1.32 inference(flattening,[status(thm)],[f6])).
% 1.63/1.32 thf(f6,plain,(
% 1.63/1.32 ? [X1 : (b > $o) > $o,X0 : (b > $o) > b > $o] : (? [X6 : b,X7 : b > $o] : (? [X10 : b > $o] : (((X1 @ X10) = $true) & ($true != (X10 @ X6))) & (($true = (X0 @ X7 @ X6)) & ! [X8 : b] : (! [X9 : b > $o] : (($true = (X9 @ X8)) | ($true != (X1 @ X9))) | ((X7 @ X8) != $true)))) & ! [X2 : b > $o] : (! [X4 : b,X3 : b > $o] : (((X2 @ X4) = $true) | (? [X5 : b] : (((X3 @ X5) = $true) & ((X2 @ X5) != $true)) | ((X0 @ X3 @ X4) != $true))) | ((X1 @ X2) != $true)))),
% 1.63/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.63/1.32 thf(f5,plain,(
% 1.63/1.32 ~! [X1 : (b > $o) > $o,X0 : (b > $o) > b > $o] : (! [X2 : b > $o] : (((X1 @ X2) = $true) => ! [X4 : b,X3 : b > $o] : ((! [X5 : b] : (((X3 @ X5) = $true) => ((X2 @ X5) = $true)) & ((X0 @ X3 @ X4) = $true)) => ((X2 @ X4) = $true))) => ! [X6 : b,X7 : b > $o] : ((($true = (X0 @ X7 @ X6)) & ! [X8 : b] : (((X7 @ X8) = $true) => ! [X9 : b > $o] : (($true = (X1 @ X9)) => ($true = (X9 @ X8))))) => ! [X10 : b > $o] : (((X1 @ X10) = $true) => ($true = (X10 @ X6)))))),
% 1.63/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.32 thf(f4,plain,(
% 1.63/1.32 ~! [X0 : (b > $o) > b > $o,X1 : (b > $o) > $o] : (! [X2 : b > $o] : ((X1 @ X2) => ! [X3 : b > $o,X4 : b] : (((X0 @ X3 @ X4) & ! [X5 : b] : ((X3 @ X5) => (X2 @ X5))) => (X2 @ X4))) => ! [X6 : b,X7 : b > $o] : (((X0 @ X7 @ X6) & ! [X8 : b] : ((X7 @ X8) => ! [X9 : b > $o] : ((X1 @ X9) => (X9 @ X8)))) => ! [X10 : b > $o] : ((X1 @ X10) => (X10 @ X6))))),
% 1.63/1.32 inference(rectify,[status(thm)],[f2])).
% 1.63/1.32 thf(f2,negated_conjecture,(
% 1.63/1.32 ~! [X0 : (b > $o) > b > $o,X1 : (b > $o) > $o] : (! [X2 : b > $o] : ((X1 @ X2) => ! [X3 : b > $o,X4 : b] : (((X0 @ X3 @ X4) & ! [X5 : b] : ((X3 @ X5) => (X2 @ X5))) => (X2 @ X4))) => ! [X4 : b,X3 : b > $o] : (((X0 @ X3 @ X4) & ! [X2 : b] : ((X3 @ X2) => ! [X6 : b > $o] : ((X1 @ X6) => (X6 @ X2)))) => ! [X6 : b > $o] : ((X1 @ X6) => (X6 @ X4))))),
% 1.63/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.32 thf(f1,conjecture,(
% 1.63/1.32 ! [X0 : (b > $o) > b > $o,X1 : (b > $o) > $o] : (! [X2 : b > $o] : ((X1 @ X2) => ! [X3 : b > $o,X4 : b] : (((X0 @ X3 @ X4) & ! [X5 : b] : ((X3 @ X5) => (X2 @ X5))) => (X2 @ X4))) => ! [X4 : b,X3 : b > $o] : (((X0 @ X3 @ X4) & ! [X2 : b] : ((X3 @ X2) => ! [X6 : b > $o] : ((X1 @ X6) => (X6 @ X2)))) => ! [X6 : b > $o] : ((X1 @ X6) => (X6 @ X4))))),
% 1.63/1.32 file('/export/starexec/sandbox/tmp/tmp.QtEV7U1CkB/DTF2THF_7812.p',cTHM564_pme)).
% 1.63/1.32 thf(f35,plain,(
% 1.63/1.32 ($true = (sK4 @ sK3))),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.63/1.32 thf(f34,plain,(
% 1.63/1.32 ($true != $true) | ($true = (sK4 @ sK3))),
% 1.63/1.32 inference(superposition,[status(thm)],[f33,f16])).
% 1.63/1.32 thf(f16,plain,(
% 1.63/1.32 ($true = (sK0 @ sK2 @ sK3))),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.32 thf(f33,plain,(
% 1.63/1.32 ( ! [X0 : b] : (((sK0 @ sK2 @ X0) != $true) | ($true = (sK4 @ X0))) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.63/1.32 thf(f32,plain,(
% 1.63/1.32 ( ! [X0 : b] : (((sK0 @ sK2 @ X0) != $true) | ($true != $true) | ($true = (sK4 @ X0))) )),
% 1.63/1.32 inference(superposition,[status(thm)],[f24,f31])).
% 1.63/1.32 thf(f31,plain,(
% 1.63/1.32 ((sK4 @ (sK5 @ sK2 @ sK4)) = $true)),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.63/1.32 thf(f30,plain,(
% 1.63/1.32 ((sK4 @ (sK5 @ sK2 @ sK4)) = $true) | ($true != $true)),
% 1.63/1.32 inference(superposition,[status(thm)],[f21,f29])).
% 1.63/1.32 thf(f29,plain,(
% 1.63/1.32 ($true = (sK2 @ (sK5 @ sK2 @ sK4)))),
% 1.63/1.32 inference(subsumption_resolution,[status(thm)],[f28,f17])).
% 1.63/1.32 thf(f28,plain,(
% 1.63/1.32 ($true = (sK4 @ sK3)) | ($true = (sK2 @ (sK5 @ sK2 @ sK4)))),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.63/1.32 thf(f27,plain,(
% 1.63/1.32 ($true != $true) | ($true = (sK4 @ sK3)) | ($true = (sK2 @ (sK5 @ sK2 @ sK4)))),
% 1.63/1.32 inference(superposition,[status(thm)],[f26,f16])).
% 1.63/1.32 thf(f26,plain,(
% 1.63/1.32 ( ! [X0 : b > $o,X1 : b] : (($true != (sK0 @ X0 @ X1)) | ($true = (sK4 @ X1)) | ($true = (X0 @ (sK5 @ X0 @ sK4)))) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.63/1.32 thf(f25,plain,(
% 1.63/1.32 ( ! [X0 : b > $o,X1 : b] : (($true = (X0 @ (sK5 @ X0 @ sK4))) | ($true != $true) | ($true != (sK0 @ X0 @ X1)) | ($true = (sK4 @ X1))) )),
% 1.63/1.32 inference(superposition,[status(thm)],[f15,f18])).
% 1.63/1.32 thf(f18,plain,(
% 1.63/1.32 ($true = (sK1 @ sK4))),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.32 thf(f15,plain,(
% 1.63/1.32 ( ! [X8 : b,X9 : b > $o,X7 : b > $o] : (($true != (sK1 @ X7)) | ($true = (X9 @ (sK5 @ X9 @ X7))) | ((sK0 @ X9 @ X8) != $true) | ((X7 @ X8) = $true)) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.32 thf(f21,plain,(
% 1.63/1.32 ( ! [X0 : b] : (($true != (sK2 @ X0)) | ($true = (sK4 @ X0))) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.63/1.32 thf(f20,plain,(
% 1.63/1.32 ( ! [X0 : b] : (($true != $true) | ($true != (sK2 @ X0)) | ($true = (sK4 @ X0))) )),
% 1.63/1.32 inference(superposition,[status(thm)],[f19,f18])).
% 1.63/1.32 thf(f19,plain,(
% 1.63/1.32 ( ! [X4 : b,X5 : b > $o] : (((sK1 @ X5) != $true) | ($true != (sK2 @ X4)) | ((X5 @ X4) = $true)) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.32 thf(f24,plain,(
% 1.63/1.32 ( ! [X0 : b,X1 : b > $o] : (((sK4 @ (sK5 @ X1 @ sK4)) != $true) | ($true = (sK4 @ X0)) | ($true != (sK0 @ X1 @ X0))) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.63/1.32 thf(f23,plain,(
% 1.63/1.32 ( ! [X0 : b,X1 : b > $o] : (((sK4 @ (sK5 @ X1 @ sK4)) != $true) | ($true != (sK0 @ X1 @ X0)) | ($true = (sK4 @ X0)) | ($true != $true)) )),
% 1.63/1.32 inference(superposition,[status(thm)],[f14,f18])).
% 1.63/1.32 thf(f14,plain,(
% 1.63/1.32 ( ! [X8 : b,X9 : b > $o,X7 : b > $o] : (($true != (sK1 @ X7)) | ((X7 @ X8) = $true) | ((X7 @ (sK5 @ X9 @ X7)) != $true) | ((sK0 @ X9 @ X8) != $true)) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.32 % SZS output end Proof for DTF2THF_7812
% 1.63/1.32 % (8147)------------------------------
% 1.63/1.32 % (8147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (8147)Termination reason: Refutation
% 1.63/1.32
% 1.63/1.32 % (8147)Memory used [KB]: 5500
% 1.63/1.32 % (8147)Time elapsed: 0.005 s
% 1.63/1.32 % (8147)Instructions burned: 6 (million)
% 1.63/1.32 % (8147)------------------------------
% 1.63/1.32 % (8147)------------------------------
% 1.63/1.32 % (8140)Success in time 0.015 s
%------------------------------------------------------------------------------