%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP004^3 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:53:04 AM UTC 2026
% Result : Theorem 1.71s 1.47s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 261 ( 78 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 420 ( 39 ~; 25 |; 15 &; 329 @)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 2 con; 0-4 aty)
% Number of variables : 101 ( 0 ^; 94 !; 7 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
tyop_2Emin_2Ebool: $tType ).
thf(func_def_1,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
thf(func_def_2,type,
c_2Ebool_2E_21:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_4,type,
c_2Emin_2E_3D:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_5,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_6,type,
c_2Ebool_2E_3F:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
c_2Epred__set_2ECHOICE:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_8,type,
c_2Epred__set_2EDELETE:
!>[X0: $tType] : ( ( X0 > $o ) > X0 > X0 > $o ) ).
thf(func_def_9,type,
c_2Ebool_2EIN:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
c_2Epred__set_2EREST:
!>[X0: $tType] : ( ( X0 > $o ) > X0 > $o ) ).
thf(func_def_11,type,
c_2Epred__set_2ESUBSET:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_13,type,
c_2Ebool_2E_7E: $o > $o ).
thf(func_def_19,type,
sK1: sK0 > $o ).
thf(func_def_20,type,
sK2:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_22,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f110,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
$true != $true,
inference(superposition,[status(thm)],[f46,f95]) ).
thf(f95,plain,
! [X0: $tType,X1: X0 > $o] :
( ( c_2Epred__set_2ESUBSET @ X0 @ ( c_2Epred__set_2EREST @ X0 @ X1 ) @ X1 )
= $true ),
inference(superposition,[status(thm)],[f92,f45]) ).
thf(f45,plain,
! [X0: $tType,X1: X0 > $o] :
( ( c_2Epred__set_2EREST @ X0 @ X1 )
= ( c_2Epred__set_2EDELETE @ X0 @ X1 @ ( c_2Epred__set_2ECHOICE @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: $tType,X1: X0 > $o] :
( ( c_2Epred__set_2EREST @ X0 @ X1 )
= ( c_2Epred__set_2EDELETE @ X0 @ X1 @ ( c_2Epred__set_2ECHOICE @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
! [X0: $tType,X5: X0 > $o] :
( ( c_2Epred__set_2EREST @ X0 @ X5 )
= ( c_2Epred__set_2EDELETE @ X0 @ X5 @ ( c_2Epred__set_2ECHOICE @ X0 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2IJ2M6QJHF/DTF2THF_13408.p',thm_2Epred__set_2EREST__DEF) ).
thf(f92,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( c_2Epred__set_2ESUBSET @ X0 @ ( c_2Epred__set_2EDELETE @ X0 @ X1 @ X2 ) @ X1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $true != $true )
| ( ( c_2Epred__set_2ESUBSET @ X0 @ ( c_2Epred__set_2EDELETE @ X0 @ X1 @ X2 ) @ X1 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f86]) ).
thf(f86,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $true != $true )
| ( ( c_2Epred__set_2ESUBSET @ X0 @ ( c_2Epred__set_2EDELETE @ X0 @ X1 @ X2 ) @ X1 )
= $true )
| ( ( c_2Epred__set_2ESUBSET @ X0 @ ( c_2Epred__set_2EDELETE @ X0 @ X1 @ X2 ) @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f51,f65]) ).
thf(f65,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( $true
= ( c_2Ebool_2EIN @ X0 @ ( sK2 @ X0 @ X1 @ ( c_2Epred__set_2EDELETE @ X0 @ X2 @ X3 ) ) @ X2 ) )
| ( ( c_2Epred__set_2ESUBSET @ X0 @ ( c_2Epred__set_2EDELETE @ X0 @ X2 @ X3 ) @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( $true != $true )
| ( $true
= ( c_2Ebool_2EIN @ X0 @ ( sK2 @ X0 @ X1 @ ( c_2Epred__set_2EDELETE @ X0 @ X2 @ X3 ) ) @ X2 ) )
| ( ( c_2Epred__set_2ESUBSET @ X0 @ ( c_2Epred__set_2EDELETE @ X0 @ X2 @ X3 ) @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f47,f50]) ).
thf(f50,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( $true
= ( c_2Ebool_2EIN @ X0 @ ( sK2 @ X0 @ X2 @ X1 ) @ X1 ) )
| ( ( c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( ( c_2Ebool_2EIN @ X0 @ X3 @ X2 )
= $true )
| ( ( c_2Ebool_2EIN @ X0 @ X3 @ X1 )
!= $true ) )
| ( ( c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2 )
= $true )
| ( ( ( c_2Ebool_2EIN @ X0 @ ( sK2 @ X0 @ X2 @ X1 ) @ X2 )
!= $true )
& ( $true
= ( c_2Ebool_2EIN @ X0 @ ( sK2 @ X0 @ X2 @ X1 ) @ X1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f42,f43]) ).
thf(f43,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ? [X4: X0] :
( ( ( c_2Ebool_2EIN @ X0 @ X4 @ X2 )
!= $true )
& ( $true
= ( c_2Ebool_2EIN @ X0 @ X4 @ X1 ) ) )
=> ( ( ( c_2Ebool_2EIN @ X0 @ ( sK2 @ X0 @ X2 @ X1 ) @ X2 )
!= $true )
& ( $true
= ( c_2Ebool_2EIN @ X0 @ ( sK2 @ X0 @ X2 @ X1 ) @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( ( c_2Ebool_2EIN @ X0 @ X3 @ X2 )
= $true )
| ( ( c_2Ebool_2EIN @ X0 @ X3 @ X1 )
!= $true ) )
| ( ( c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2 )
= $true )
| ? [X4: X0] :
( ( ( c_2Ebool_2EIN @ X0 @ X4 @ X2 )
!= $true )
& ( $true
= ( c_2Ebool_2EIN @ X0 @ X4 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( ( c_2Ebool_2EIN @ X0 @ X3 @ X2 )
= $true )
| ( ( c_2Ebool_2EIN @ X0 @ X3 @ X1 )
!= $true ) )
| ( ( c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2 )
= $true )
| ? [X3: X0] :
( ( ( c_2Ebool_2EIN @ X0 @ X3 @ X2 )
!= $true )
& ( ( c_2Ebool_2EIN @ X0 @ X3 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ! [X3: X0] :
( ( ( c_2Ebool_2EIN @ X0 @ X3 @ X2 )
= $true )
| ( ( c_2Ebool_2EIN @ X0 @ X3 @ X1 )
!= $true ) )
<=> ( ( c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2 )
= $true )
<=> ! [X3: X0] :
( ( ( c_2Ebool_2EIN @ X0 @ X3 @ X1 )
= $true )
=> ( ( c_2Ebool_2EIN @ X0 @ X3 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ! [X3: X0] :
( ( c_2Ebool_2EIN @ X0 @ X3 @ X1 )
=> ( c_2Ebool_2EIN @ X0 @ X3 @ X2 ) )
<=> ( c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2 ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X0: $tType,X5: X0 > $o,X6: X0 > $o] :
( ! [X7: X0] :
( ( c_2Ebool_2EIN @ X0 @ X7 @ X5 )
=> ( c_2Ebool_2EIN @ X0 @ X7 @ X6 ) )
<=> ( c_2Epred__set_2ESUBSET @ X0 @ X5 @ X6 ) ),
file('/export/starexec/sandbox2/tmp/tmp.2IJ2M6QJHF/DTF2THF_13408.p',thm_2Epred__set_2ESUBSET__DEF) ).
thf(f47,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0 > $o] :
( ( ( c_2Ebool_2EIN @ X0 @ X2 @ ( c_2Epred__set_2EDELETE @ X0 @ X1 @ X3 ) )
!= $true )
| ( ( c_2Ebool_2EIN @ X0 @ X2 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0] :
( ( ( ( c_2Ebool_2EIN @ X0 @ X2 @ ( c_2Epred__set_2EDELETE @ X0 @ X1 @ X3 ) )
= $true )
| ( ( X2 != X3 )
!= $true )
| ( ( c_2Ebool_2EIN @ X0 @ X2 @ X1 )
!= $true ) )
& ( ( ( ( X2 != X3 )
= $true )
& ( ( c_2Ebool_2EIN @ X0 @ X2 @ X1 )
= $true ) )
| ( ( c_2Ebool_2EIN @ X0 @ X2 @ ( c_2Epred__set_2EDELETE @ X0 @ X1 @ X3 ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0] :
( ( ( ( c_2Ebool_2EIN @ X0 @ X2 @ ( c_2Epred__set_2EDELETE @ X0 @ X1 @ X3 ) )
= $true )
| ( ( X2 != X3 )
!= $true )
| ( ( c_2Ebool_2EIN @ X0 @ X2 @ X1 )
!= $true ) )
& ( ( ( ( X2 != X3 )
= $true )
& ( ( c_2Ebool_2EIN @ X0 @ X2 @ X1 )
= $true ) )
| ( ( c_2Ebool_2EIN @ X0 @ X2 @ ( c_2Epred__set_2EDELETE @ X0 @ X1 @ X3 ) )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0] :
( ( ( c_2Ebool_2EIN @ X0 @ X2 @ ( c_2Epred__set_2EDELETE @ X0 @ X1 @ X3 ) )
= $true )
<=> ( ( ( X2 != X3 )
= $true )
& ( ( c_2Ebool_2EIN @ X0 @ X2 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0] :
( ( c_2Ebool_2EIN @ X0 @ X2 @ ( c_2Epred__set_2EDELETE @ X0 @ X1 @ X3 ) )
<=> ( ( c_2Ebool_2EIN @ X0 @ X2 @ X1 )
& ( X2 != X3 ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X0: $tType,X5: X0 > $o,X4: X0,X8: X0] :
( ( c_2Ebool_2EIN @ X0 @ X4 @ ( c_2Epred__set_2EDELETE @ X0 @ X5 @ X8 ) )
<=> ( ( c_2Ebool_2EIN @ X0 @ X4 @ X5 )
& ( X4 != X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2IJ2M6QJHF/DTF2THF_13408.p',thm_2Epred__set_2EIN__DELETE) ).
thf(f51,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( c_2Ebool_2EIN @ X0 @ ( sK2 @ X0 @ X2 @ X1 ) @ X2 )
!= $true )
| ( ( c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f46,plain,
( ( c_2Epred__set_2ESUBSET @ sK0 @ ( c_2Epred__set_2EREST @ sK0 @ sK1 ) @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( c_2Epred__set_2ESUBSET @ sK0 @ ( c_2Epred__set_2EREST @ sK0 @ sK1 ) @ sK1 )
!= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f36,f37]) ).
thf(f37,plain,
( ? [X0: $tType,X1: X0 > $o] :
( ( c_2Epred__set_2ESUBSET @ X0 @ ( c_2Epred__set_2EREST @ X0 @ X1 ) @ X1 )
!= $true )
=> ( ( c_2Epred__set_2ESUBSET @ sK0 @ ( c_2Epred__set_2EREST @ sK0 @ sK1 ) @ sK1 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
? [X0: $tType,X1: X0 > $o] :
( ( c_2Epred__set_2ESUBSET @ X0 @ ( c_2Epred__set_2EREST @ X0 @ X1 ) @ X1 )
!= $true ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
~ ! [X0: $tType,X1: X0 > $o] :
( ( c_2Epred__set_2ESUBSET @ X0 @ ( c_2Epred__set_2EREST @ X0 @ X1 ) @ X1 )
= $true ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
~ ! [X0: $tType,X1: X0 > $o] : ( c_2Epred__set_2ESUBSET @ X0 @ ( c_2Epred__set_2EREST @ X0 @ X1 ) @ X1 ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,negated_conjecture,
~ ! [X0: $tType,X5: X0 > $o] : ( c_2Epred__set_2ESUBSET @ X0 @ ( c_2Epred__set_2EREST @ X0 @ X5 ) @ X5 ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f11,conjecture,
! [X0: $tType,X5: X0 > $o] : ( c_2Epred__set_2ESUBSET @ X0 @ ( c_2Epred__set_2EREST @ X0 @ X5 ) @ X5 ),
file('/export/starexec/sandbox2/tmp/tmp.2IJ2M6QJHF/DTF2THF_13408.p',thm_2Epred__set_2EREST__SUBSET) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP004^3 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n015.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Feb 24 08:18:31 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : ITP004^3 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.27/0.47 % Domain : Interactive Theorem Proving
% 0.27/0.47 % Problem : HOL4 syntactic export of thm_2Epred__set_2EREST__SUBSET.p, bushy mode
% 0.27/0.47 % Version : [BG+19] axioms.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.27/0.47 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [BG+19]
% 0.27/0.47 % Names : thm_2Epred__set_2EREST__SUBSET.p [Gau19]
% 0.27/0.47 % : HL401501^3.p [TPAP]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.33 v8.1.0, 0.25 v7.5.0
% 0.27/0.47 % Syntax : Number of formulae : 25 ( 6 unt; 14 typ; 0 def)
% 0.27/0.47 % Number of atoms : 22 ( 3 equ; 2 cnn)
% 0.27/0.47 % Maximal formula atoms : 5 ( 2 avg)
% 0.27/0.47 % Number of connectives : 64 ( 2 ~; 1 |; 2 &; 48 @)
% 0.27/0.47 % ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 10 ( 7 avg)
% 0.27/0.47 % Number of types : 2 ( 1 usr)
% 0.27/0.47 % Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 15 ( 13 usr; 1 con; 0-4 aty)
% 0.27/0.47 % Number of variables : 36 ( 0 ^; 27 !; 1 ?; 36 :)
% 0.27/0.47 % ( 8 !>; 0 ?*; 0 @-; 0 @+)
% 0.27/0.47 % SPC : TH1_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments :
% 0.27/0.47 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(tyop_2Emin_2Ebool,type,
% 0.27/0.47 tyop_2Emin_2Ebool: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(tyop_2Emin_2Efun,type,
% 0.27/0.47 tyop_2Emin_2Efun: $tType > $tType > $tType ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ebool_2E_21,type,
% 0.27/0.47 c_2Ebool_2E_21:
% 0.27/0.47 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ebool_2E_2F_5C,type,
% 0.27/0.47 c_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Emin_2E_3D,type,
% 0.27/0.47 c_2Emin_2E_3D:
% 0.27/0.47 !>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Emin_2E_3D_3D_3E,type,
% 0.27/0.47 c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ebool_2E_3F,type,
% 0.27/0.47 c_2Ebool_2E_3F:
% 0.27/0.47 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Epred__set_2ECHOICE,type,
% 0.27/0.47 c_2Epred__set_2ECHOICE:
% 0.27/0.47 !>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a ) ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Epred__set_2EDELETE,type,
% 0.27/0.47 c_2Epred__set_2EDELETE:
% 0.27/0.47 !>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a > A_27a > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ebool_2EIN,type,
% 0.27/0.47 c_2Ebool_2EIN:
% 0.27/0.47 !>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Epred__set_2EREST,type,
% 0.27/0.47 c_2Epred__set_2EREST:
% 0.27/0.47 !>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Epred__set_2ESUBSET,type,
% 0.27/0.47 c_2Epred__set_2ESUBSET:
% 0.27/0.47 !>[A_27a: $tType] : ( ( A_27a > $o ) > ( A_27a > $o ) > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ebool_2E_5C_2F,type,
% 0.27/0.47 c_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ebool_2E_7E,type,
% 0.27/0.47 c_2Ebool_2E_7E: $o > $o ).
% 0.27/0.47
% 0.27/0.47 thf(logicdef_2E_2F_5C,axiom,
% 0.27/0.47 ! [V0: $o,V1: $o] :
% 0.27/0.47 ( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.27/0.47 <=> ( V0
% 0.27/0.47 & V1 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(logicdef_2E_5C_2F,axiom,
% 0.27/0.47 ! [V0: $o,V1: $o] :
% 0.27/0.47 ( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.27/0.47 <=> ( V0
% 0.27/0.47 | V1 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(logicdef_2E_7E,axiom,
% 0.27/0.47 ! [V0: $o] :
% 0.27/0.47 ( ( c_2Ebool_2E_7E @ V0 )
% 0.27/0.47 <=> ( (~) @ V0 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(logicdef_2E_3D_3D_3E,axiom,
% 0.27/0.47 ! [V0: $o,V1: $o] :
% 0.27/0.47 ( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.27/0.47 <=> ( V0
% 0.27/0.47 => V1 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(logicdef_2E_3D,axiom,
% 0.27/0.47 ! [A_27a: $tType,V0: A_27a,V1: A_27a] :
% 0.27/0.47 ( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
% 0.27/0.47 <=> ( V0 = V1 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(quantdef_2E_21,axiom,
% 0.27/0.47 ! [A_27a: $tType,V0f: A_27a > $o] :
% 0.27/0.47 ( ( c_2Ebool_2E_21 @ A_27a @ V0f )
% 0.27/0.47 <=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(quantdef_2E_3F,axiom,
% 0.27/0.47 ! [A_27a: $tType,V0f: A_27a > $o] :
% 0.27/0.47 ( ( c_2Ebool_2E_3F @ A_27a @ V0f )
% 0.27/0.47 <=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(thm_2Epred__set_2ESUBSET__DEF,axiom,
% 0.27/0.47 ! [A_27a: $tType,V0s: A_27a > $o,V1t: A_27a > $o] :
% 0.27/0.47 ( ( c_2Epred__set_2ESUBSET @ A_27a @ V0s @ V1t )
% 0.27/0.47 <=> ! [V2x: A_27a] :
% 0.27/0.47 ( ( c_2Ebool_2EIN @ A_27a @ V2x @ V0s )
% 0.27/0.47 => ( c_2Ebool_2EIN @ A_27a @ V2x @ V1t ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(thm_2Epred__set_2EIN__DELETE,axiom,
% 0.27/0.47 ! [A_27a: $tType,V0s: A_27a > $o,V1x: A_27a,V2y: A_27a] :
% 0.27/0.47 ( ( c_2Ebool_2EIN @ A_27a @ V1x @ ( c_2Epred__set_2EDELETE @ A_27a @ V0s @ V2y ) )
% 0.27/0.47 <=> ( ( c_2Ebool_2EIN @ A_27a @ V1x @ V0s )
% 0.27/0.47 & ( (~) @ ( V1x = V2y ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(thm_2Epred__set_2EREST__DEF,axiom,
% 0.27/0.47 ! [A_27a: $tType,V0s: A_27a > $o] :
% 0.27/0.47 ( ( c_2Epred__set_2EREST @ A_27a @ V0s )
% 0.27/0.47 = ( c_2Epred__set_2EDELETE @ A_27a @ V0s @ ( c_2Epred__set_2ECHOICE @ A_27a @ V0s ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(thm_2Epred__set_2EREST__SUBSET,conjecture,
% 0.27/0.47 ! [A_27a: $tType,V0s: A_27a > $o] : ( c_2Epred__set_2ESUBSET @ A_27a @ ( c_2Epred__set_2EREST @ A_27a @ V0s ) @ V0s ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.50/1.29 ---- Embedded in THF ---
% 1.50/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.29 %%% Generated on Tue Feb 24 08:18:32 EST 2026
% 1.50/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.29 %%% Logic specification used:
% 1.50/1.29 %%% thf(spec, logic, $$dhol).
% 1.50/1.29
% 1.50/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.2IJ2M6QJHF/DTF2DTF13408.p
% See solution above
% 1.50/1.29 ------------------------
% 1.69/1.30 ---- Cleaned THF ---
% 1.69/1.30 thf(tyop_2Emin_2Ebool,type,
% 1.69/1.30 tyop_2Emin_2Ebool: $tType ).
% 1.69/1.30
% 1.69/1.30 thf(tyop_2Emin_2Efun,type,
% 1.69/1.30 tyop_2Emin_2Efun: $tType > $tType > $tType ).
% 1.69/1.30
% 1.69/1.30 thf(c_2Ebool_2E_21,type,
% 1.69/1.30 c_2Ebool_2E_21:
% 1.69/1.30 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 1.69/1.30
% 1.69/1.30 thf(c_2Ebool_2E_2F_5C,type,
% 1.69/1.30 c_2Ebool_2E_2F_5C: $o > $o > $o ).
% 1.69/1.30
% 1.69/1.30 thf(c_2Emin_2E_3D,type,
% 1.69/1.30 c_2Emin_2E_3D:
% 1.69/1.30 !>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
% 1.69/1.30
% 1.69/1.30 thf(c_2Emin_2E_3D_3D_3E,type,
% 1.69/1.30 c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 1.69/1.30
% 1.69/1.30 thf(c_2Ebool_2E_3F,type,
% 1.69/1.30 c_2Ebool_2E_3F:
% 1.69/1.30 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 1.69/1.30
% 1.69/1.30 thf(c_2Epred__set_2ECHOICE,type,
% 1.69/1.30 c_2Epred__set_2ECHOICE:
% 1.69/1.30 !>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a ) ).
% 1.69/1.30
% 1.69/1.30 thf(c_2Epred__set_2EDELETE,type,
% 1.69/1.30 c_2Epred__set_2EDELETE:
% 1.69/1.30 !>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a > A_27a > $o ) ).
% 1.69/1.30
% 1.69/1.30 thf(c_2Ebool_2EIN,type,
% 1.69/1.30 c_2Ebool_2EIN:
% 1.69/1.30 !>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > $o ) ).
% 1.69/1.30
% 1.69/1.30 thf(c_2Epred__set_2EREST,type,
% 1.69/1.30 c_2Epred__set_2EREST:
% 1.69/1.30 !>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a > $o ) ).
% 1.69/1.30
% 1.69/1.30 thf(c_2Epred__set_2ESUBSET,type,
% 1.69/1.30 c_2Epred__set_2ESUBSET:
% 1.69/1.30 !>[A_27a: $tType] : ( ( A_27a > $o ) > ( A_27a > $o ) > $o ) ).
% 1.69/1.30
% 1.69/1.30 thf(c_2Ebool_2E_5C_2F,type,
% 1.69/1.30 c_2Ebool_2E_5C_2F: $o > $o > $o ).
% 1.69/1.30
% 1.69/1.30 thf(c_2Ebool_2E_7E,type,
% 1.69/1.30 c_2Ebool_2E_7E: $o > $o ).
% 1.69/1.30
% 1.69/1.30 thf(logicdef_2E_2F_5C,axiom,
% 1.69/1.30 ! [V0: $o,V1: $o] :
% 1.69/1.30 ( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
% 1.69/1.30 <=> ( V0
% 1.69/1.30 & V1 ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(logicdef_2E_5C_2F,axiom,
% 1.69/1.30 ! [V0: $o,V1: $o] :
% 1.69/1.30 ( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
% 1.69/1.30 <=> ( V0
% 1.69/1.30 | V1 ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(logicdef_2E_7E,axiom,
% 1.69/1.30 ! [V0: $o] :
% 1.69/1.30 ( ( c_2Ebool_2E_7E @ V0 )
% 1.69/1.30 <=> ( (~) @ V0 ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(logicdef_2E_3D_3D_3E,axiom,
% 1.69/1.30 ! [V0: $o,V1: $o] :
% 1.69/1.30 ( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 1.69/1.30 <=> ( V0
% 1.69/1.30 => V1 ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(logicdef_2E_3D,axiom,
% 1.69/1.30 ! [A_27a: $tType,V0: A_27a,V1: A_27a] :
% 1.69/1.30 ( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
% 1.69/1.30 <=> ( V0 = V1 ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(quantdef_2E_21,axiom,
% 1.69/1.30 ! [A_27a: $tType,V0f: A_27a > $o] :
% 1.69/1.30 ( ( c_2Ebool_2E_21 @ A_27a @ V0f )
% 1.69/1.30 <=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(quantdef_2E_3F,axiom,
% 1.69/1.30 ! [A_27a: $tType,V0f: A_27a > $o] :
% 1.69/1.30 ( ( c_2Ebool_2E_3F @ A_27a @ V0f )
% 1.69/1.30 <=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(thm_2Epred__set_2ESUBSET__DEF,axiom,
% 1.69/1.30 ! [A_27a: $tType,V0s: A_27a > $o,V1t: A_27a > $o] :
% 1.69/1.30 ( ( c_2Epred__set_2ESUBSET @ A_27a @ V0s @ V1t )
% 1.69/1.30 <=> ! [V2x: A_27a] :
% 1.69/1.30 ( ( c_2Ebool_2EIN @ A_27a @ V2x @ V0s )
% 1.69/1.30 => ( c_2Ebool_2EIN @ A_27a @ V2x @ V1t ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(thm_2Epred__set_2EIN__DELETE,axiom,
% 1.69/1.30 ! [A_27a: $tType,V0s: A_27a > $o,V1x: A_27a,V2y: A_27a] :
% 1.69/1.30 ( ( c_2Ebool_2EIN @ A_27a @ V1x @ ( c_2Epred__set_2EDELETE @ A_27a @ V0s @ V2y ) )
% 1.69/1.30 <=> ( ( c_2Ebool_2EIN @ A_27a @ V1x @ V0s )
% 1.69/1.30 & ( (~) @ ( V1x = V2y ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(thm_2Epred__set_2EREST__DEF,axiom,
% 1.69/1.30 ! [A_27a: $tType,V0s: A_27a > $o] :
% 1.69/1.30 ( ( c_2Epred__set_2EREST @ A_27a @ V0s )
% 1.69/1.30 = ( c_2Epred__set_2EDELETE @ A_27a @ V0s @ ( c_2Epred__set_2ECHOICE @ A_27a @ V0s ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(thm_2Epred__set_2EREST__SUBSET,conjecture,
% 1.69/1.30 ! [A_27a: $tType,V0s: A_27a > $o] : ( c_2Epred__set_2ESUBSET @ A_27a @ ( c_2Epred__set_2EREST @ A_27a @ V0s ) @ V0s ) ).
% 1.69/1.30 ------------------------
% 1.69/1.31 % (13831)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_13408 for (2999ds/2Mi)
% 1.69/1.32 % (13831)Instruction limit reached!
% 1.69/1.32 % (13831)------------------------------
% 1.69/1.32 % (13831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (13831)Termination reason: Unknown
% 1.69/1.32 % (13831)Termination phase: shuffling
% 1.69/1.32
% 1.69/1.32 % (13831)Memory used [KB]: 1023
% 1.69/1.32 % (13831)Time elapsed: 0.002 s
% 1.69/1.32 % (13831)Instructions burned: 2 (million)
% 1.69/1.32 % (13831)------------------------------
% 1.69/1.32 % (13831)------------------------------
% 1.69/1.32 % (13830)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/2Mi)
% 1.69/1.32 % (13830)Instruction limit reached!
% 1.69/1.32 % (13830)------------------------------
% 1.69/1.32 % (13830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (13830)Termination reason: Unknown
% 1.69/1.32 % (13830)Termination phase: Property scanning
% 1.69/1.32
% 1.69/1.32 % (13830)Memory used [KB]: 1023
% 1.69/1.32 % (13830)Time elapsed: 0.002 s
% 1.69/1.32 % (13830)Instructions burned: 3 (million)
% 1.69/1.32 % (13830)------------------------------
% 1.69/1.32 % (13830)------------------------------
% 1.69/1.32 % (13827)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/183Mi)
% 1.69/1.32 % (13828)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_13408 for (2999ds/4Mi)
% 1.69/1.32 % (13829)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_13408 for (2999ds/27Mi)
% 1.69/1.32 % (13832)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_13408 for (2999ds/275Mi)
% 1.69/1.32 % (13833)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/18Mi)
% 1.69/1.32 % (13832)Refutation not found, incomplete strategy
% 1.69/1.32 % (13832)------------------------------
% 1.69/1.32 % (13832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (13832)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.32
% 1.69/1.32
% 1.69/1.32 % (13832)Memory used [KB]: 5500
% 1.69/1.32 % (13832)Time elapsed: 0.004 s
% 1.69/1.32 % (13832)Instructions burned: 2 (million)
% 1.69/1.32 % (13832)------------------------------
% 1.69/1.32 % (13832)------------------------------
% 1.69/1.32 % (13839)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/3Mi)
% 1.69/1.33 % (13828)Instruction limit reached!
% 1.69/1.33 % (13828)------------------------------
% 1.69/1.33 % (13828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (13828)Termination reason: Unknown
% 1.69/1.33 % (13828)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (13828)Memory used [KB]: 5500
% 1.69/1.33 % (13828)Time elapsed: 0.005 s
% 1.69/1.33 % (13828)Instructions burned: 5 (million)
% 1.69/1.33 % (13828)------------------------------
% 1.69/1.33 % (13828)------------------------------
% 1.69/1.33 % (13839)Instruction limit reached!
% 1.69/1.33 % (13839)------------------------------
% 1.69/1.33 % (13839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (13839)Termination reason: Unknown
% 1.69/1.33 % (13839)Termination phase: Property scanning
% 1.69/1.33
% 1.69/1.33 % (13839)Memory used [KB]: 1023
% 1.69/1.33 % (13839)Time elapsed: 0.002 s
% 1.69/1.33 % (13839)Instructions burned: 3 (million)
% 1.69/1.33 % (13839)------------------------------
% 1.69/1.33 % (13839)------------------------------
% 1.69/1.33 % (13841)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/37Mi)
% 1.69/1.33 % Exception at run slice level
% 1.69/1.33 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.69/1.33 % (13833)Instruction limit reached!
% 1.69/1.33 % (13833)------------------------------
% 1.69/1.33 % (13833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (13833)Termination reason: Unknown
% 1.69/1.33 % (13833)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (13833)Memory used [KB]: 5628
% 1.69/1.33 % (13833)Time elapsed: 0.014 s
% 1.69/1.33 % (13833)Instructions burned: 18 (million)
% 1.69/1.33 % (13833)------------------------------
% 1.69/1.33 % (13833)------------------------------
% 1.69/1.34 % (13845)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/1041Mi)
% 1.69/1.34 % Exception at run slice level
% 1.69/1.34 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.69/1.34 % (13847)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/7Mi)
% 1.69/1.34 % (13847)Instruction limit reached!
% 1.69/1.34 % (13847)------------------------------
% 1.69/1.34 % (13847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (13847)Termination reason: Unknown
% 1.69/1.34 % (13847)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (13847)Memory used [KB]: 1023
% 1.69/1.34 % (13847)Time elapsed: 0.005 s
% 1.69/1.34 % (13847)Instructions burned: 9 (million)
% 1.69/1.34 % (13847)------------------------------
% 1.69/1.34 % (13847)------------------------------
% 1.69/1.34 % (13829)Instruction limit reached!
% 1.69/1.34 % (13829)------------------------------
% 1.69/1.34 % (13829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (13829)Termination reason: Unknown
% 1.69/1.34 % (13829)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (13829)Memory used [KB]: 5628
% 1.69/1.34 % (13829)Time elapsed: 0.021 s
% 1.69/1.34 % (13829)Instructions burned: 27 (million)
% 1.69/1.34 % (13829)------------------------------
% 1.69/1.34 % (13829)------------------------------
% 1.69/1.34 % (13843)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/15Mi)
% 1.69/1.34 % (13844)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/3Mi)
% 1.69/1.34 % (13844)Instruction limit reached!
% 1.69/1.34 % (13844)------------------------------
% 1.69/1.34 % (13844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (13844)Termination reason: Unknown
% 1.69/1.34 % (13844)Termination phase: Saturation
% 1.69/1.34
% 1.69/1.34 % (13844)Memory used [KB]: 1023
% 1.69/1.34 % (13844)Time elapsed: 0.004 s
% 1.69/1.34 % (13844)Instructions burned: 4 (million)
% 1.69/1.34 % (13844)------------------------------
% 1.69/1.34 % (13844)------------------------------
% 1.69/1.34 % (13851)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/3Mi)
% 1.69/1.35 % (13851)Instruction limit reached!
% 1.69/1.35 % (13851)------------------------------
% 1.69/1.35 % (13851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (13851)Termination reason: Unknown
% 1.69/1.35 % (13851)Termination phase: Property scanning
% 1.69/1.35
% 1.69/1.35 % (13851)Memory used [KB]: 1023
% 1.69/1.35 % (13851)Time elapsed: 0.002 s
% 1.69/1.35 % (13851)Instructions burned: 3 (million)
% 1.69/1.35 % (13851)------------------------------
% 1.69/1.35 % (13851)------------------------------
% 1.69/1.35 % (13855)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/3Mi)
% 1.69/1.35 % (13855)Instruction limit reached!
% 1.69/1.35 % (13855)------------------------------
% 1.69/1.35 % (13855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (13855)Termination reason: Unknown
% 1.69/1.35 % (13855)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (13855)Memory used [KB]: 1023
% 1.69/1.35 % (13855)Time elapsed: 0.003 s
% 1.69/1.35 % (13855)Instructions burned: 4 (million)
% 1.69/1.35 % (13855)------------------------------
% 1.69/1.35 % (13855)------------------------------
% 1.69/1.35 % (13850)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/16Mi)
% 1.69/1.35 % (13843)Instruction limit reached!
% 1.69/1.35 % (13843)------------------------------
% 1.69/1.35 % (13843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (13843)Termination reason: Unknown
% 1.69/1.35 % (13843)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (13843)Memory used [KB]: 5628
% 1.69/1.35 % (13843)Time elapsed: 0.012 s
% 1.69/1.35 % (13843)Instructions burned: 15 (million)
% 1.69/1.35 % (13843)------------------------------
% 1.69/1.35 % (13843)------------------------------
% 1.69/1.36 % (13859)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/4Mi)
% 1.69/1.36 % (13859)Instruction limit reached!
% 1.69/1.36 % (13859)------------------------------
% 1.69/1.36 % (13859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (13859)Termination reason: Unknown
% 1.69/1.36 % (13859)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (13859)Memory used [KB]: 5500
% 1.69/1.36 % (13859)Time elapsed: 0.002 s
% 1.69/1.36 % (13859)Instructions burned: 4 (million)
% 1.69/1.36 % (13859)------------------------------
% 1.69/1.36 % (13859)------------------------------
% 1.69/1.36 % (13856)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/7Mi)
% 1.69/1.36 % (13863)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/18Mi)
% 1.69/1.36 % (13858)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/3Mi)
% 1.69/1.36 % Exception at run slice level
% 1.69/1.36 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.69/1.36 % (13850)Instruction limit reached!
% 1.69/1.36 % (13850)------------------------------
% 1.69/1.36 % (13850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (13850)Termination reason: Unknown
% 1.69/1.36 % (13850)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (13850)Memory used [KB]: 5628
% 1.69/1.36 % (13850)Time elapsed: 0.013 s
% 1.69/1.36 % (13850)Instructions burned: 16 (million)
% 1.69/1.36 % (13850)------------------------------
% 1.69/1.36 % (13850)------------------------------
% 1.69/1.36 % (13856)Instruction limit reached!
% 1.69/1.36 % (13856)------------------------------
% 1.69/1.36 % (13856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (13856)Termination reason: Unknown
% 1.69/1.36 % (13856)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (13856)Memory used [KB]: 5500
% 1.69/1.36 % (13856)Time elapsed: 0.007 s
% 1.69/1.36 % (13856)Instructions burned: 8 (million)
% 1.69/1.36 % (13856)------------------------------
% 1.69/1.36 % (13856)------------------------------
% 1.69/1.37 % (13867)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/6Mi)
% 1.69/1.37 % (13867)Instruction limit reached!
% 1.69/1.37 % (13867)------------------------------
% 1.69/1.37 % (13867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (13867)Termination reason: Unknown
% 1.69/1.37 % (13867)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (13867)Memory used [KB]: 5500
% 1.69/1.37 % (13867)Time elapsed: 0.003 s
% 1.69/1.37 % (13867)Instructions burned: 6 (million)
% 1.69/1.37 % (13867)------------------------------
% 1.69/1.37 % (13867)------------------------------
% 1.69/1.37 % (13865)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/710Mi)
% 1.69/1.37 % (13863)Instruction limit reached!
% 1.69/1.37 % (13863)------------------------------
% 1.69/1.37 % (13863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (13863)Termination reason: Unknown
% 1.69/1.37 % (13863)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (13863)Memory used [KB]: 5628
% 1.69/1.37 % (13863)Time elapsed: 0.009 s
% 1.69/1.37 % (13863)Instructions burned: 19 (million)
% 1.69/1.37 % (13863)------------------------------
% 1.69/1.37 % (13863)------------------------------
% 1.69/1.38 % (13876)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/6Mi)
% 1.69/1.38 % Exception at run slice level
% 1.69/1.38 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.69/1.38 % (13877)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/377Mi)
% 1.69/1.38 % (13871)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/902Mi)
% 1.69/1.38 % (13872)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/21Mi)
% 1.69/1.38 % (13873)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/5Mi)
% 1.69/1.38 % Exception at run slice level
% 1.69/1.38 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.69/1.38 % (13871)Refutation not found, incomplete strategy
% 1.69/1.38 % (13871)------------------------------
% 1.69/1.38 % (13871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (13871)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.38
% 1.69/1.38
% 1.69/1.38 % (13871)Memory used [KB]: 5500
% 1.69/1.38 % (13871)Time elapsed: 0.005 s
% 1.69/1.38 % (13871)Instructions burned: 4 (million)
% 1.69/1.38 % (13871)------------------------------
% 1.69/1.38 % (13871)------------------------------
% 1.69/1.39 % (13880)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/779Mi)
% 1.69/1.39 % Exception at run slice level
% 1.69/1.39 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.69/1.39 % (13872)Instruction limit reached!
% 1.69/1.39 % (13872)------------------------------
% 1.69/1.39 % (13872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (13872)Termination reason: Unknown
% 1.69/1.39 % (13872)Termination phase: Saturation
% 1.69/1.39
% 1.69/1.39 % (13872)Memory used [KB]: 5628
% 1.69/1.39 % (13872)Time elapsed: 0.016 s
% 1.69/1.39 % (13872)Instructions burned: 21 (million)
% 1.69/1.39 % (13872)------------------------------
% 1.69/1.39 % (13872)------------------------------
% 1.71/1.40 % (13886)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/17Mi)
% 1.71/1.40 % (13882)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/19Mi)
% 1.71/1.40 % Exception at run slice level
% 1.71/1.40 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.71/1.40 % (13884)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/879Mi)
% 1.71/1.40 % (13886)Instruction limit reached!
% 1.71/1.40 % (13886)------------------------------
% 1.71/1.40 % (13886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.40 % (13886)Termination reason: Unknown
% 1.71/1.40 % (13886)Termination phase: Saturation
% 1.71/1.40
% 1.71/1.40 % (13886)Memory used [KB]: 5628
% 1.71/1.40 % (13886)Time elapsed: 0.007 s
% 1.71/1.40 % (13886)Instructions burned: 17 (million)
% 1.71/1.40 % (13886)------------------------------
% 1.71/1.40 % (13886)------------------------------
% 1.71/1.41 % (13893)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13408 for (2998ds/127Mi)
% 1.71/1.41 % (13888)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13408 for (2999ds/3Mi)
% 1.71/1.41 % (13888)Instruction limit reached!
% 1.71/1.41 % (13888)------------------------------
% 1.71/1.41 % (13888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.41 % (13888)Termination reason: Unknown
% 1.71/1.41 % (13888)Termination phase: Property scanning
% 1.71/1.41
% 1.71/1.41 % (13888)Memory used [KB]: 1023
% 1.71/1.41 % (13888)Time elapsed: 0.004 s
% 1.71/1.41 % (13888)Instructions burned: 4 (million)
% 1.71/1.41 % (13888)------------------------------
% 1.71/1.41 % (13888)------------------------------
% 1.71/1.42 % (13892)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13408 for (2998ds/30Mi)
% 1.71/1.42 % (13827)Instruction limit reached!
% 1.71/1.42 % (13827)------------------------------
% 1.71/1.42 % (13827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.42 % (13827)Termination reason: Unknown
% 1.71/1.42 % (13827)Termination phase: Saturation
% 1.71/1.42
% 1.71/1.42 % (13827)Memory used [KB]: 6652
% 1.71/1.42 % (13827)Time elapsed: 0.104 s
% 1.71/1.42 % (13827)Instructions burned: 184 (million)
% 1.71/1.42 % (13827)------------------------------
% 1.71/1.42 % (13827)------------------------------
% 1.71/1.43 % (13895)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13408 for (2998ds/100Mi)
% 1.71/1.44 % (13901)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_13408 for (2998ds/3Mi)
% 1.71/1.44 % Exception at run slice level
% 1.71/1.44 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.71/1.44 % (13892)Instruction limit reached!
% 1.71/1.44 % (13892)------------------------------
% 1.71/1.44 % (13892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.44 % (13892)Termination reason: Unknown
% 1.71/1.44 % (13892)Termination phase: Saturation
% 1.71/1.44
% 1.71/1.44 % (13892)Memory used [KB]: 5756
% 1.71/1.44 % (13892)Time elapsed: 0.020 s
% 1.71/1.44 % (13892)Instructions burned: 30 (million)
% 1.71/1.44 % (13892)------------------------------
% 1.71/1.44 % (13892)------------------------------
% 1.71/1.45 % (13905)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_13408 for (2998ds/20Mi)
% 1.71/1.45 % (13906)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_13408 for (2998ds/86Mi)
% 1.71/1.45 % (13905)Refutation not found, incomplete strategy
% 1.71/1.45 % (13905)------------------------------
% 1.71/1.45 % (13905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.45 % (13905)Termination reason: Refutation not found, incomplete strategy
% 1.71/1.45
% 1.71/1.45
% 1.71/1.45 % (13905)Memory used [KB]: 5500
% 1.71/1.45 % (13905)Time elapsed: 0.003 s
% 1.71/1.45 % (13905)Instructions burned: 3 (million)
% 1.71/1.45 % (13905)------------------------------
% 1.71/1.45 % (13905)------------------------------
% 1.71/1.45 % (13893)Instruction limit reached!
% 1.71/1.45 % (13893)------------------------------
% 1.71/1.45 % (13893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.45 % (13893)Termination reason: Unknown
% 1.71/1.45 % (13893)Termination phase: Saturation
% 1.71/1.45
% 1.71/1.45 % (13893)Memory used [KB]: 6012
% 1.71/1.45 % (13893)Time elapsed: 0.043 s
% 1.71/1.45 % (13893)Instructions burned: 130 (million)
% 1.71/1.45 % (13893)------------------------------
% 1.71/1.45 % (13893)------------------------------
% 1.71/1.46 % (13912)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_13408 for (2998ds/107Mi)
% 1.71/1.46 % (13913)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_13408 for (2998ds/39Mi)
% 1.71/1.46 % Exception at run slice level
% 1.71/1.46 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.71/1.47 % (13912)First to succeed.
% 1.71/1.47 % (13895)Instruction limit reached!
% 1.71/1.47 % (13895)------------------------------
% 1.71/1.47 % (13895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.47 % (13895)Termination reason: Unknown
% 1.71/1.47 % (13895)Termination phase: Saturation
% 1.71/1.47
% 1.71/1.47 % (13895)Memory used [KB]: 5884
% 1.71/1.47 % (13895)Time elapsed: 0.039 s
% 1.71/1.47 % (13895)Instructions burned: 100 (million)
% 1.71/1.47 % (13895)------------------------------
% 1.71/1.47 % (13895)------------------------------
% 1.71/1.47 % (13912)Refutation found. Thanks to Tanya!
% 1.71/1.47 % SZS status Theorem for DTF2THF_13408
% 1.71/1.47 % SZS output start Proof for DTF2THF_13408
% 1.71/1.47 thf(type_def_6, type, sK0: $tType).
% 1.71/1.47 thf(func_def_0, type, tyop_2Emin_2Ebool: $tType).
% 1.71/1.47 thf(func_def_1, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 1.71/1.47 thf(func_def_2, type, c_2Ebool_2E_21: !>[X0: $tType]:((X0 > $o) > $o)).
% 1.71/1.47 thf(func_def_3, type, c_2Ebool_2E_2F_5C: $o > $o > $o).
% 1.71/1.47 thf(func_def_4, type, c_2Emin_2E_3D: !>[X0: $tType]:(X0 > X0 > $o)).
% 1.71/1.47 thf(func_def_5, type, c_2Emin_2E_3D_3D_3E: $o > $o > $o).
% 1.71/1.47 thf(func_def_6, type, c_2Ebool_2E_3F: !>[X0: $tType]:((X0 > $o) > $o)).
% 1.71/1.47 thf(func_def_7, type, c_2Epred__set_2ECHOICE: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.71/1.47 thf(func_def_8, type, c_2Epred__set_2EDELETE: !>[X0: $tType]:((X0 > $o) > X0 > X0 > $o)).
% 1.71/1.47 thf(func_def_9, type, c_2Ebool_2EIN: !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.71/1.47 thf(func_def_10, type, c_2Epred__set_2EREST: !>[X0: $tType]:((X0 > $o) > X0 > $o)).
% 1.71/1.47 thf(func_def_11, type, c_2Epred__set_2ESUBSET: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 1.71/1.47 thf(func_def_12, type, c_2Ebool_2E_5C_2F: $o > $o > $o).
% 1.71/1.47 thf(func_def_13, type, c_2Ebool_2E_7E: $o > $o).
% 1.71/1.47 thf(func_def_19, type, sK1: sK0 > $o).
% 1.71/1.47 thf(func_def_20, type, sK2: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 1.71/1.47 thf(func_def_22, type, ph4: !>[X0: $tType]:(X0)).
% 1.71/1.47 thf(f110,plain,(
% 1.71/1.47 $false),
% 1.71/1.47 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.71/1.47 thf(f107,plain,(
% 1.71/1.47 ($true != $true)),
% 1.71/1.47 inference(superposition,[status(thm)],[f46,f95])).
% 1.71/1.47 thf(f95,plain,(
% 1.71/1.47 ( ! [X0 : $tType,X1 : X0 > $o] : (((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EREST @ X0 @ X1) @ X1) = $true)) )),
% 1.71/1.47 inference(superposition,[status(thm)],[f92,f45])).
% 1.71/1.47 thf(f45,plain,(
% 1.71/1.47 ( ! [X0 : $tType,X1 : X0 > $o] : (((c_2Epred__set_2EREST @ X0 @ X1) = (c_2Epred__set_2EDELETE @ X0 @ X1 @ (c_2Epred__set_2ECHOICE @ X0 @ X1)))) )),
% 1.71/1.47 inference(cnf_transformation,[status(thm)],[f34])).
% 1.71/1.47 thf(f34,plain,(
% 1.71/1.47 ! [X0 : $tType,X1 : X0 > $o] : ((c_2Epred__set_2EREST @ X0 @ X1) = (c_2Epred__set_2EDELETE @ X0 @ X1 @ (c_2Epred__set_2ECHOICE @ X0 @ X1)))),
% 1.71/1.47 inference(rectify,[status(thm)],[f10])).
% 1.71/1.47 thf(f10,axiom,(
% 1.71/1.47 ! [X0 : $tType,X5 : X0 > $o] : ((c_2Epred__set_2EREST @ X0 @ X5) = (c_2Epred__set_2EDELETE @ X0 @ X5 @ (c_2Epred__set_2ECHOICE @ X0 @ X5)))),
% 1.71/1.47 file('/export/starexec/sandbox2/tmp/tmp.2IJ2M6QJHF/DTF2THF_13408.p',thm_2Epred__set_2EREST__DEF)).
% 1.71/1.47 thf(f92,plain,(
% 1.71/1.47 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X2) @ X1) = $true)) )),
% 1.71/1.47 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.71/1.47 thf(f91,plain,(
% 1.71/1.47 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != $true) | ((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X2) @ X1) = $true)) )),
% 1.71/1.47 inference(duplicate_literal_removal,[status(thm)],[f86])).
% 1.71/1.47 thf(f86,plain,(
% 1.71/1.47 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != $true) | ((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X2) @ X1) = $true) | ((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X2) @ X1) = $true)) )),
% 1.71/1.47 inference(superposition,[status(thm)],[f51,f65])).
% 1.71/1.47 thf(f65,plain,(
% 1.71/1.47 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : (($true = (c_2Ebool_2EIN @ X0 @ (sK2 @ X0 @ X1 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3)) @ X2)) | ((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3) @ X1) = $true)) )),
% 1.71/1.47 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.71/1.47 thf(f63,plain,(
% 1.71/1.47 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true = (c_2Ebool_2EIN @ X0 @ (sK2 @ X0 @ X1 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3)) @ X2)) | ((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3) @ X1) = $true)) )),
% 1.71/1.47 inference(superposition,[status(thm)],[f47,f50])).
% 1.71/1.47 thf(f50,plain,(
% 1.71/1.47 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = (c_2Ebool_2EIN @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X1)) | ((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2) = $true)) )),
% 1.71/1.47 inference(cnf_transformation,[status(thm)],[f44])).
% 1.71/1.47 thf(f44,plain,(
% 1.71/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : (((c_2Ebool_2EIN @ X0 @ X3 @ X2) = $true) | ((c_2Ebool_2EIN @ X0 @ X3 @ X1) != $true)) | ((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2) != $true)) & (((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2) = $true) | (((c_2Ebool_2EIN @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X2) != $true) & ($true = (c_2Ebool_2EIN @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X1)))))),
% 1.71/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f42,f43])).
% 1.71/1.47 thf(f43,plain,(
% 1.71/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X4 : X0] : (((c_2Ebool_2EIN @ X0 @ X4 @ X2) != $true) & ($true = (c_2Ebool_2EIN @ X0 @ X4 @ X1))) => (((c_2Ebool_2EIN @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X2) != $true) & ($true = (c_2Ebool_2EIN @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X1))))),
% 1.71/1.47 introduced(definition,[],[choice_axiom])).
% 1.71/1.47 thf(f42,plain,(
% 1.71/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : (((c_2Ebool_2EIN @ X0 @ X3 @ X2) = $true) | ((c_2Ebool_2EIN @ X0 @ X3 @ X1) != $true)) | ((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2) != $true)) & (((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2) = $true) | ? [X4 : X0] : (((c_2Ebool_2EIN @ X0 @ X4 @ X2) != $true) & ($true = (c_2Ebool_2EIN @ X0 @ X4 @ X1)))))),
% 1.71/1.47 inference(rectify,[status(thm)],[f41])).
% 1.71/1.47 thf(f41,plain,(
% 1.71/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : (((c_2Ebool_2EIN @ X0 @ X3 @ X2) = $true) | ((c_2Ebool_2EIN @ X0 @ X3 @ X1) != $true)) | ((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2) != $true)) & (((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2) = $true) | ? [X3 : X0] : (((c_2Ebool_2EIN @ X0 @ X3 @ X2) != $true) & ((c_2Ebool_2EIN @ X0 @ X3 @ X1) = $true))))),
% 1.71/1.47 inference(nnf_transformation,[status(thm)],[f35])).
% 1.71/1.47 thf(f35,plain,(
% 1.71/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (((c_2Ebool_2EIN @ X0 @ X3 @ X2) = $true) | ((c_2Ebool_2EIN @ X0 @ X3 @ X1) != $true)) <=> ((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2) = $true))),
% 1.71/1.47 inference(ennf_transformation,[status(thm)],[f21])).
% 1.71/1.47 thf(f21,plain,(
% 1.71/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2) = $true) <=> ! [X3 : X0] : (((c_2Ebool_2EIN @ X0 @ X3 @ X1) = $true) => ((c_2Ebool_2EIN @ X0 @ X3 @ X2) = $true)))),
% 1.71/1.47 inference(fool_elimination,[status(thm)],[f20])).
% 1.71/1.47 thf(f20,plain,(
% 1.71/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : ((c_2Ebool_2EIN @ X0 @ X3 @ X1) => (c_2Ebool_2EIN @ X0 @ X3 @ X2)) <=> (c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2))),
% 1.71/1.47 inference(rectify,[status(thm)],[f8])).
% 1.71/1.47 thf(f8,axiom,(
% 1.71/1.47 ! [X0 : $tType,X5 : X0 > $o,X6 : X0 > $o] : (! [X7 : X0] : ((c_2Ebool_2EIN @ X0 @ X7 @ X5) => (c_2Ebool_2EIN @ X0 @ X7 @ X6)) <=> (c_2Epred__set_2ESUBSET @ X0 @ X5 @ X6))),
% 1.71/1.47 file('/export/starexec/sandbox2/tmp/tmp.2IJ2M6QJHF/DTF2THF_13408.p',thm_2Epred__set_2ESUBSET__DEF)).
% 1.71/1.47 thf(f47,plain,(
% 1.71/1.47 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (((c_2Ebool_2EIN @ X0 @ X2 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X3)) != $true) | ((c_2Ebool_2EIN @ X0 @ X2 @ X1) = $true)) )),
% 1.71/1.47 inference(cnf_transformation,[status(thm)],[f40])).
% 1.71/1.47 thf(f40,plain,(
% 1.71/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : ((((c_2Ebool_2EIN @ X0 @ X2 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X3)) = $true) | ((~ (X2 = X3)) != $true) | ((c_2Ebool_2EIN @ X0 @ X2 @ X1) != $true)) & ((((~ (X2 = X3)) = $true) & ((c_2Ebool_2EIN @ X0 @ X2 @ X1) = $true)) | ((c_2Ebool_2EIN @ X0 @ X2 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X3)) != $true)))),
% 1.71/1.47 inference(flattening,[status(thm)],[f39])).
% 1.71/1.47 thf(f39,plain,(
% 1.71/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : ((((c_2Ebool_2EIN @ X0 @ X2 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X3)) = $true) | (((~ (X2 = X3)) != $true) | ((c_2Ebool_2EIN @ X0 @ X2 @ X1) != $true))) & ((((~ (X2 = X3)) = $true) & ((c_2Ebool_2EIN @ X0 @ X2 @ X1) = $true)) | ((c_2Ebool_2EIN @ X0 @ X2 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X3)) != $true)))),
% 1.71/1.47 inference(nnf_transformation,[status(thm)],[f23])).
% 1.71/1.47 thf(f23,plain,(
% 1.71/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : (((c_2Ebool_2EIN @ X0 @ X2 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X3)) = $true) <=> (((~ (X2 = X3)) = $true) & ((c_2Ebool_2EIN @ X0 @ X2 @ X1) = $true)))),
% 1.71/1.47 inference(fool_elimination,[status(thm)],[f22])).
% 1.71/1.47 thf(f22,plain,(
% 1.71/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : ((c_2Ebool_2EIN @ X0 @ X2 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X3)) <=> ((c_2Ebool_2EIN @ X0 @ X2 @ X1) & (~ (X2 = X3))))),
% 1.71/1.47 inference(rectify,[status(thm)],[f9])).
% 1.71/1.47 thf(f9,axiom,(
% 1.71/1.47 ! [X0 : $tType,X5 : X0 > $o,X4 : X0,X8 : X0] : ((c_2Ebool_2EIN @ X0 @ X4 @ (c_2Epred__set_2EDELETE @ X0 @ X5 @ X8)) <=> ((c_2Ebool_2EIN @ X0 @ X4 @ X5) & (~ (X4 = X8))))),
% 1.71/1.47 file('/export/starexec/sandbox2/tmp/tmp.2IJ2M6QJHF/DTF2THF_13408.p',thm_2Epred__set_2EIN__DELETE)).
% 1.71/1.47 thf(f51,plain,(
% 1.71/1.47 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (((c_2Ebool_2EIN @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X2) != $true) | ((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2) = $true)) )),
% 1.71/1.47 inference(cnf_transformation,[status(thm)],[f44])).
% 1.71/1.47 thf(f46,plain,(
% 1.71/1.47 ((c_2Epred__set_2ESUBSET @ sK0 @ (c_2Epred__set_2EREST @ sK0 @ sK1) @ sK1) != $true)),
% 1.71/1.47 inference(cnf_transformation,[status(thm)],[f38])).
% 1.71/1.47 thf(f38,plain,(
% 1.71/1.47 ((c_2Epred__set_2ESUBSET @ sK0 @ (c_2Epred__set_2EREST @ sK0 @ sK1) @ sK1) != $true)),
% 1.71/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f36,f37])).
% 1.71/1.47 thf(f37,plain,(
% 1.71/1.47 ? [X0 : $tType,X1 : X0 > $o] : ((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EREST @ X0 @ X1) @ X1) != $true) => ((c_2Epred__set_2ESUBSET @ sK0 @ (c_2Epred__set_2EREST @ sK0 @ sK1) @ sK1) != $true)),
% 1.71/1.47 introduced(definition,[],[choice_axiom])).
% 1.71/1.47 thf(f36,plain,(
% 1.71/1.47 ? [X0 : $tType,X1 : X0 > $o] : ((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EREST @ X0 @ X1) @ X1) != $true)),
% 1.71/1.47 inference(ennf_transformation,[status(thm)],[f15])).
% 1.71/1.47 thf(f15,plain,(
% 1.71/1.47 ~! [X0 : $tType,X1 : X0 > $o] : ((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EREST @ X0 @ X1) @ X1) = $true)),
% 1.71/1.47 inference(fool_elimination,[status(thm)],[f14])).
% 1.71/1.47 thf(f14,plain,(
% 1.71/1.47 ~! [X0 : $tType,X1 : X0 > $o] : (c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EREST @ X0 @ X1) @ X1)),
% 1.71/1.47 inference(rectify,[status(thm)],[f12])).
% 1.71/1.47 thf(f12,negated_conjecture,(
% 1.71/1.47 ~! [X0 : $tType,X5 : X0 > $o] : (c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EREST @ X0 @ X5) @ X5)),
% 1.71/1.47 inference(negated_conjecture,[status(cth)],[f11])).
% 1.71/1.47 thf(f11,conjecture,(
% 1.71/1.47 ! [X0 : $tType,X5 : X0 > $o] : (c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EREST @ X0 @ X5) @ X5)),
% 1.71/1.47 file('/export/starexec/sandbox2/tmp/tmp.2IJ2M6QJHF/DTF2THF_13408.p',thm_2Epred__set_2EREST__SUBSET)).
% 1.71/1.47 % SZS output end Proof for DTF2THF_13408
% 1.71/1.47 % (13912)------------------------------
% 1.71/1.47 % (13912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.47 % (13912)Termination reason: Refutation
% 1.71/1.47
% 1.71/1.47 % (13912)Memory used [KB]: 5628
% 1.71/1.47 % (13912)Time elapsed: 0.011 s
% 1.71/1.47 % (13912)Instructions burned: 24 (million)
% 1.71/1.47 % (13912)------------------------------
% 1.71/1.47 % (13912)------------------------------
% 1.71/1.47 % (13826)Success in time 0.164 s
%------------------------------------------------------------------------------