%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP010^3 : 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 : n025.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 08:53:20 AM UTC 2026
% Result : Theorem 1.67s 1.48s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 6 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 102 ( 26 ~; 0 |; 0 &; 72 @)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 1 con; 0-4 aty)
% Number of variables : 24 ( 0 ^; 16 !; 8 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK1: $tType ).
thf(type_def_7,type,
sK2: $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_9,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_10,type,
c_2Ecardinal_2Ecardleq:
!>[X0: $tType,X1: $tType] : ( ( X0 > $o ) > ( X1 > $o ) > $o ) ).
thf(func_def_11,type,
c_2Ebool_2E_7E: $o > $o ).
thf(func_def_14,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_18,type,
sP0: $o > $o > $o > $o ).
thf(func_def_19,type,
sK3: sK1 > $o ).
thf(func_def_20,type,
sK4: sK2 > $o ).
thf(func_def_21,type,
sK5:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_22,type,
sK6:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f560,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f129]) ).
thf(f129,plain,
( ( ~ ( c_2Ecardinal_2Ecardleq @ sK1 @ sK2 @ sK3 @ sK4 ) )
!= ( ~ ( c_2Ecardinal_2Ecardleq @ sK1 @ sK2 @ sK3 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
thf(f90,plain,
( ( ~ ( c_2Ecardinal_2Ecardleq @ sK1 @ sK2 @ sK3 @ sK4 ) )
!= ( ~ ( c_2Ecardinal_2Ecardleq @ sK1 @ sK2 @ sK3 @ sK4 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f77,f89]) ).
thf(f89,plain,
( ? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) )
!= ( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) ) )
=> ( ( ~ ( c_2Ecardinal_2Ecardleq @ sK1 @ sK2 @ sK3 @ sK4 ) )
!= ( ~ ( c_2Ecardinal_2Ecardleq @ sK1 @ sK2 @ sK3 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f77,plain,
? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) )
!= ( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) ) ),
inference(ennf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) )
= ( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) ) ),
inference(fool_elimination,[status(thm)],[f40]) ).
thf(f40,plain,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 )
<=> ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,negated_conjecture,
~ ! [X0: $tType,X1: $tType,X8: X0 > $o,X9: X1 > $o] :
( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X8 @ X9 )
<=> ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X8 @ X9 ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f23,conjecture,
! [X0: $tType,X1: $tType,X8: X0 > $o,X9: X1 > $o] :
( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X8 @ X9 )
<=> ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X8 @ X9 ) ),
file('/export/starexec/sandbox2/tmp/tmp.IpL42N7Jx3/DTF2THF_10863.p',thm_2Ecardinal_2ECARD__NOT__LE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP010^3 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.35 % Computer : n025.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Feb 24 08:19:58 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.49 ---- Original DTF file ---
% 0.26/0.49 thf(spec,logic,$$dhol).
% 0.26/0.49 %------------------------------------------------------------------------------
% 0.26/0.49 % File : ITP010^3 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.26/0.49 % Domain : Interactive Theorem Proving
% 0.26/0.49 % Problem : HOL4 syntactic export of thm_2Ecardinal_2ECARD__NOT__LE.p, bushy mode
% 0.26/0.49 % Version : [BG+19] axioms.
% 0.26/0.49 % English :
% 0.26/0.49
% 0.26/0.49 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.26/0.49 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.26/0.49 % Source : [BG+19]
% 0.26/0.49 % Names : thm_2Ecardinal_2ECARD__NOT__LE.p [Gau19]
% 0.26/0.49 % : HL404501^3.p [TPAP]
% 0.26/0.49
% 0.26/0.49 % Status : Theorem
% 0.26/0.49 % Rating : 0.33 v8.1.0, 0.25 v7.5.0
% 0.26/0.49 % Syntax : Number of formulae : 35 ( 7 unt; 12 typ; 0 def)
% 0.26/0.49 % Number of atoms : 73 ( 7 equ; 28 cnn)
% 0.26/0.49 % Maximal formula atoms : 8 ( 3 avg)
% 0.26/0.49 % Number of connectives : 165 ( 28 ~; 14 |; 14 &; 60 @)
% 0.26/0.49 % ( 29 <=>; 20 =>; 0 <=; 0 <~>)
% 0.26/0.49 % Maximal formula depth : 11 ( 6 avg)
% 0.26/0.49 % Number of types : 2 ( 1 usr)
% 0.26/0.49 % Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% 0.26/0.49 % Number of symbols : 13 ( 11 usr; 3 con; 0-4 aty)
% 0.26/0.49 % Number of variables : 50 ( 0 ^; 44 !; 1 ?; 50 :)
% 0.26/0.49 % ( 5 !>; 0 ?*; 0 @-; 0 @+)
% 0.26/0.49 % SPC : TH1_THM_EQU_NAR
% 0.26/0.49
% 0.26/0.49 % Comments :
% 0.26/0.49 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.26/0.49 %------------------------------------------------------------------------------
% 0.26/0.49 thf(tyop_2Emin_2Ebool,type,
% 0.26/0.49 tyop_2Emin_2Ebool: $tType ).
% 0.26/0.49
% 0.26/0.49 thf(tyop_2Emin_2Efun,type,
% 0.26/0.49 tyop_2Emin_2Efun: $tType > $tType > $tType ).
% 0.26/0.49
% 0.26/0.49 thf(c_2Ebool_2E_21,type,
% 0.26/0.49 c_2Ebool_2E_21:
% 0.26/0.49 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 0.26/0.49
% 0.26/0.49 thf(c_2Ebool_2E_2F_5C,type,
% 0.26/0.49 c_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.26/0.49
% 0.26/0.49 thf(c_2Emin_2E_3D,type,
% 0.26/0.49 c_2Emin_2E_3D:
% 0.26/0.49 !>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
% 0.26/0.49
% 0.26/0.49 thf(c_2Emin_2E_3D_3D_3E,type,
% 0.26/0.49 c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.26/0.49
% 0.26/0.49 thf(c_2Ebool_2E_3F,type,
% 0.26/0.49 c_2Ebool_2E_3F:
% 0.26/0.49 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 0.26/0.49
% 0.26/0.49 thf(c_2Ebool_2EF,type,
% 0.26/0.49 c_2Ebool_2EF: $o ).
% 0.26/0.49
% 0.26/0.49 thf(c_2Ebool_2ET,type,
% 0.26/0.49 c_2Ebool_2ET: $o ).
% 0.26/0.49
% 0.26/0.49 thf(c_2Ebool_2E_5C_2F,type,
% 0.26/0.49 c_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.26/0.49
% 0.26/0.49 thf(c_2Ecardinal_2Ecardleq,type,
% 0.26/0.49 c_2Ecardinal_2Ecardleq:
% 0.26/0.49 !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > $o ) > ( A_27b > $o ) > $o ) ).
% 0.26/0.49
% 0.26/0.49 thf(c_2Ebool_2E_7E,type,
% 0.26/0.49 c_2Ebool_2E_7E: $o > $o ).
% 0.26/0.49
% 0.26/0.49 thf(logicdef_2E_2F_5C,axiom,
% 0.26/0.49 ! [V0: $o,V1: $o] :
% 0.26/0.49 ( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.26/0.49 <=> ( V0
% 0.26/0.49 & V1 ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(logicdef_2E_5C_2F,axiom,
% 0.26/0.49 ! [V0: $o,V1: $o] :
% 0.26/0.49 ( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.26/0.49 <=> ( V0
% 0.26/0.49 | V1 ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(logicdef_2E_7E,axiom,
% 0.26/0.49 ! [V0: $o] :
% 0.26/0.49 ( ( c_2Ebool_2E_7E @ V0 )
% 0.26/0.49 <=> ( (~) @ V0 ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(logicdef_2E_3D_3D_3E,axiom,
% 0.26/0.49 ! [V0: $o,V1: $o] :
% 0.26/0.49 ( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.26/0.49 <=> ( V0
% 0.26/0.49 => V1 ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(logicdef_2E_3D,axiom,
% 0.26/0.49 ! [A_27a: $tType,V0: A_27a,V1: A_27a] :
% 0.26/0.49 ( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
% 0.26/0.49 <=> ( V0 = V1 ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(quantdef_2E_21,axiom,
% 0.26/0.49 ! [A_27a: $tType,V0f: A_27a > $o] :
% 0.26/0.49 ( ( c_2Ebool_2E_21 @ A_27a @ V0f )
% 0.26/0.49 <=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(quantdef_2E_3F,axiom,
% 0.26/0.49 ! [A_27a: $tType,V0f: A_27a > $o] :
% 0.26/0.49 ( ( c_2Ebool_2E_3F @ A_27a @ V0f )
% 0.26/0.49 <=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Ebool_2ETRUTH,axiom,
% 0.26/0.49 c_2Ebool_2ET ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Ebool_2EFALSITY,axiom,
% 0.26/0.49 ! [V0t: $o] :
% 0.26/0.49 ( c_2Ebool_2EF
% 0.26/0.49 => V0t ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Ebool_2EFORALL__SIMP,axiom,
% 0.26/0.49 ! [A_27a: $tType,V0t: $o] :
% 0.26/0.49 ( ! [V1x: A_27a] : V0t
% 0.26/0.49 <=> V0t ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.26/0.49 ! [V0t: $o] :
% 0.26/0.49 ( ( ( c_2Ebool_2ET
% 0.26/0.49 => V0t )
% 0.26/0.49 <=> V0t )
% 0.26/0.49 & ( ( V0t
% 0.26/0.49 => c_2Ebool_2ET )
% 0.26/0.49 <=> c_2Ebool_2ET )
% 0.26/0.49 & ( ( c_2Ebool_2EF
% 0.26/0.49 => V0t )
% 0.26/0.49 <=> c_2Ebool_2ET )
% 0.26/0.49 & ( ( V0t
% 0.26/0.49 => V0t )
% 0.26/0.49 <=> c_2Ebool_2ET )
% 0.26/0.49 & ( ( V0t
% 0.26/0.49 => c_2Ebool_2EF )
% 0.26/0.49 <=> ( (~) @ V0t ) ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.26/0.49 ( ! [V0t: $o] :
% 0.26/0.49 ( ( (~) @ ( (~) @ V0t ) )
% 0.26/0.49 <=> V0t )
% 0.26/0.49 & ( ( (~) @ c_2Ebool_2ET )
% 0.26/0.49 <=> c_2Ebool_2EF )
% 0.26/0.49 & ( ( (~) @ c_2Ebool_2EF )
% 0.26/0.49 <=> c_2Ebool_2ET ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
% 0.26/0.49 ! [A_27a: $tType,V0x: A_27a] :
% 0.26/0.49 ( ( V0x = V0x )
% 0.26/0.49 <=> c_2Ebool_2ET ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.26/0.49 ! [V0t: $o] :
% 0.26/0.49 ( ( ( c_2Ebool_2ET = V0t )
% 0.26/0.49 <=> V0t )
% 0.26/0.49 & ( ( V0t = c_2Ebool_2ET )
% 0.26/0.49 <=> V0t )
% 0.26/0.49 & ( ( c_2Ebool_2EF = V0t )
% 0.26/0.49 <=> ( (~) @ V0t ) )
% 0.26/0.49 & ( ( V0t = c_2Ebool_2EF )
% 0.26/0.49 <=> ( (~) @ V0t ) ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Ecardinal_2ECARD__LE__TOTAL,axiom,
% 0.26/0.49 ! [A_27a: $tType,A_27b: $tType,V0s: A_27a > $o,V1t: A_27b > $o] :
% 0.26/0.49 ( ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b @ V0s @ V1t )
% 0.26/0.49 | ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a @ V1t @ V0s ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Esat_2ENOT__NOT,axiom,
% 0.26/0.49 ! [V0t: $o] :
% 0.26/0.49 ( ( (~) @ ( (~) @ V0t ) )
% 0.26/0.49 <=> V0t ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Esat_2EAND__INV__IMP,axiom,
% 0.26/0.49 ! [V0A: $o] :
% 0.26/0.49 ( V0A
% 0.26/0.49 => ( ( (~) @ V0A )
% 0.26/0.49 => c_2Ebool_2EF ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Esat_2EOR__DUAL2,axiom,
% 0.26/0.49 ! [V0B: $o,V1A: $o] :
% 0.26/0.49 ( ( ( (~)
% 0.26/0.49 @ ( V1A
% 0.26/0.49 | V0B ) )
% 0.26/0.49 => c_2Ebool_2EF )
% 0.26/0.49 <=> ( ( V1A
% 0.26/0.49 => c_2Ebool_2EF )
% 0.26/0.49 => ( ( (~) @ V0B )
% 0.26/0.49 => c_2Ebool_2EF ) ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Esat_2EOR__DUAL3,axiom,
% 0.26/0.49 ! [V0B: $o,V1A: $o] :
% 0.26/0.49 ( ( ( (~)
% 0.26/0.49 @ ( ( (~) @ V1A )
% 0.26/0.49 | V0B ) )
% 0.26/0.49 => c_2Ebool_2EF )
% 0.26/0.49 <=> ( V1A
% 0.26/0.49 => ( ( (~) @ V0B )
% 0.26/0.49 => c_2Ebool_2EF ) ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Esat_2EAND__INV2,axiom,
% 0.26/0.49 ! [V0A: $o] :
% 0.26/0.49 ( ( ( (~) @ V0A )
% 0.26/0.49 => c_2Ebool_2EF )
% 0.26/0.49 => ( ( V0A
% 0.26/0.49 => c_2Ebool_2EF )
% 0.26/0.49 => c_2Ebool_2EF ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Esat_2Edc__eq,axiom,
% 0.26/0.49 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.26/0.49 ( ( V2p
% 0.26/0.49 <=> ( V1q = V0r ) )
% 0.26/0.49 <=> ( ( V2p
% 0.26/0.49 | V1q
% 0.26/0.49 | V0r )
% 0.26/0.49 & ( V2p
% 0.26/0.49 | ( (~) @ V0r )
% 0.26/0.49 | ( (~) @ V1q ) )
% 0.26/0.49 & ( V1q
% 0.26/0.49 | ( (~) @ V0r )
% 0.26/0.49 | ( (~) @ V2p ) )
% 0.26/0.49 & ( V0r
% 0.26/0.49 | ( (~) @ V1q )
% 0.26/0.49 | ( (~) @ V2p ) ) ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Esat_2Edc__neg,axiom,
% 0.26/0.49 ! [V0q: $o,V1p: $o] :
% 0.26/0.49 ( ( V1p
% 0.26/0.49 <=> ( (~) @ V0q ) )
% 0.26/0.49 <=> ( ( V1p
% 0.26/0.49 | V0q )
% 0.26/0.49 & ( ( (~) @ V0q )
% 0.26/0.49 | ( (~) @ V1p ) ) ) ) ).
% 0.26/0.49
% 0.26/0.49 thf(thm_2Ecardinal_2ECARD__NOT__LE,conjecture,
% 0.26/0.49 ! [A_27a: $tType,A_27b: $tType,V0s: A_27a > $o,V1t: A_27b > $o] :
% 0.26/0.49 ( ( (~) @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b @ V0s @ V1t ) )
% 0.26/0.49 <=> ( (~) @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b @ V0s @ V1t ) ) ) ).
% 0.26/0.49
% 0.26/0.49 %------------------------------------------------------------------------------
% 0.26/0.49 ------------------------
% 1.67/1.45 ---- Embedded in THF ---
% 1.67/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.45 %%% Generated on Tue Feb 24 08:19:59 EST 2026
% 1.67/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.45 %%% Logic specification used:
% 1.67/1.45 %%% thf(spec, logic, $$dhol).
% 1.67/1.45
% 1.67/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.IpL42N7Jx3/DTF2DTF10863.p
% See solution above
% 1.67/1.45 ------------------------
% 1.67/1.46 ---- Cleaned THF ---
% 1.67/1.46 thf(tyop_2Emin_2Ebool,type,
% 1.67/1.46 tyop_2Emin_2Ebool: $tType ).
% 1.67/1.46
% 1.67/1.46 thf(tyop_2Emin_2Efun,type,
% 1.67/1.46 tyop_2Emin_2Efun: $tType > $tType > $tType ).
% 1.67/1.46
% 1.67/1.46 thf(c_2Ebool_2E_21,type,
% 1.67/1.46 c_2Ebool_2E_21:
% 1.67/1.46 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 1.67/1.46
% 1.67/1.46 thf(c_2Ebool_2E_2F_5C,type,
% 1.67/1.46 c_2Ebool_2E_2F_5C: $o > $o > $o ).
% 1.67/1.46
% 1.67/1.46 thf(c_2Emin_2E_3D,type,
% 1.67/1.46 c_2Emin_2E_3D:
% 1.67/1.46 !>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
% 1.67/1.46
% 1.67/1.46 thf(c_2Emin_2E_3D_3D_3E,type,
% 1.67/1.46 c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 1.67/1.46
% 1.67/1.46 thf(c_2Ebool_2E_3F,type,
% 1.67/1.46 c_2Ebool_2E_3F:
% 1.67/1.46 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 1.67/1.46
% 1.67/1.46 thf(c_2Ebool_2EF,type,
% 1.67/1.46 c_2Ebool_2EF: $o ).
% 1.67/1.46
% 1.67/1.46 thf(c_2Ebool_2ET,type,
% 1.67/1.46 c_2Ebool_2ET: $o ).
% 1.67/1.46
% 1.67/1.46 thf(c_2Ebool_2E_5C_2F,type,
% 1.67/1.46 c_2Ebool_2E_5C_2F: $o > $o > $o ).
% 1.67/1.46
% 1.67/1.46 thf(c_2Ecardinal_2Ecardleq,type,
% 1.67/1.46 c_2Ecardinal_2Ecardleq:
% 1.67/1.46 !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > $o ) > ( A_27b > $o ) > $o ) ).
% 1.67/1.46
% 1.67/1.46 thf(c_2Ebool_2E_7E,type,
% 1.67/1.46 c_2Ebool_2E_7E: $o > $o ).
% 1.67/1.46
% 1.67/1.46 thf(logicdef_2E_2F_5C,axiom,
% 1.67/1.46 ! [V0: $o,V1: $o] :
% 1.67/1.46 ( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
% 1.67/1.46 <=> ( V0
% 1.67/1.46 & V1 ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(logicdef_2E_5C_2F,axiom,
% 1.67/1.46 ! [V0: $o,V1: $o] :
% 1.67/1.46 ( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
% 1.67/1.46 <=> ( V0
% 1.67/1.46 | V1 ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(logicdef_2E_7E,axiom,
% 1.67/1.46 ! [V0: $o] :
% 1.67/1.46 ( ( c_2Ebool_2E_7E @ V0 )
% 1.67/1.46 <=> ( (~) @ V0 ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(logicdef_2E_3D_3D_3E,axiom,
% 1.67/1.46 ! [V0: $o,V1: $o] :
% 1.67/1.46 ( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 1.67/1.46 <=> ( V0
% 1.67/1.46 => V1 ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(logicdef_2E_3D,axiom,
% 1.67/1.46 ! [A_27a: $tType,V0: A_27a,V1: A_27a] :
% 1.67/1.46 ( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
% 1.67/1.46 <=> ( V0 = V1 ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(quantdef_2E_21,axiom,
% 1.67/1.46 ! [A_27a: $tType,V0f: A_27a > $o] :
% 1.67/1.46 ( ( c_2Ebool_2E_21 @ A_27a @ V0f )
% 1.67/1.46 <=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(quantdef_2E_3F,axiom,
% 1.67/1.46 ! [A_27a: $tType,V0f: A_27a > $o] :
% 1.67/1.46 ( ( c_2Ebool_2E_3F @ A_27a @ V0f )
% 1.67/1.46 <=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Ebool_2ETRUTH,axiom,
% 1.67/1.46 c_2Ebool_2ET ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Ebool_2EFALSITY,axiom,
% 1.67/1.46 ! [V0t: $o] :
% 1.67/1.46 ( c_2Ebool_2EF
% 1.67/1.46 => V0t ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Ebool_2EFORALL__SIMP,axiom,
% 1.67/1.46 ! [A_27a: $tType,V0t: $o] :
% 1.67/1.46 ( ! [V1x: A_27a] : V0t
% 1.67/1.46 <=> V0t ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 1.67/1.46 ! [V0t: $o] :
% 1.67/1.46 ( ( ( c_2Ebool_2ET
% 1.67/1.46 => V0t )
% 1.67/1.46 <=> V0t )
% 1.67/1.46 & ( ( V0t
% 1.67/1.46 => c_2Ebool_2ET )
% 1.67/1.46 <=> c_2Ebool_2ET )
% 1.67/1.46 & ( ( c_2Ebool_2EF
% 1.67/1.46 => V0t )
% 1.67/1.46 <=> c_2Ebool_2ET )
% 1.67/1.46 & ( ( V0t
% 1.67/1.46 => V0t )
% 1.67/1.46 <=> c_2Ebool_2ET )
% 1.67/1.46 & ( ( V0t
% 1.67/1.46 => c_2Ebool_2EF )
% 1.67/1.46 <=> ( (~) @ V0t ) ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
% 1.67/1.46 ( ! [V0t: $o] :
% 1.67/1.46 ( ( (~) @ ( (~) @ V0t ) )
% 1.67/1.46 <=> V0t )
% 1.67/1.46 & ( ( (~) @ c_2Ebool_2ET )
% 1.67/1.46 <=> c_2Ebool_2EF )
% 1.67/1.46 & ( ( (~) @ c_2Ebool_2EF )
% 1.67/1.46 <=> c_2Ebool_2ET ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
% 1.67/1.46 ! [A_27a: $tType,V0x: A_27a] :
% 1.67/1.46 ( ( V0x = V0x )
% 1.67/1.46 <=> c_2Ebool_2ET ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
% 1.67/1.46 ! [V0t: $o] :
% 1.67/1.46 ( ( ( c_2Ebool_2ET = V0t )
% 1.67/1.46 <=> V0t )
% 1.67/1.46 & ( ( V0t = c_2Ebool_2ET )
% 1.67/1.46 <=> V0t )
% 1.67/1.46 & ( ( c_2Ebool_2EF = V0t )
% 1.67/1.46 <=> ( (~) @ V0t ) )
% 1.67/1.46 & ( ( V0t = c_2Ebool_2EF )
% 1.67/1.46 <=> ( (~) @ V0t ) ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Ecardinal_2ECARD__LE__TOTAL,axiom,
% 1.67/1.46 ! [A_27a: $tType,A_27b: $tType,V0s: A_27a > $o,V1t: A_27b > $o] :
% 1.67/1.46 ( ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b @ V0s @ V1t )
% 1.67/1.46 | ( c_2Ecardinal_2Ecardleq @ A_27b @ A_27a @ V1t @ V0s ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Esat_2ENOT__NOT,axiom,
% 1.67/1.46 ! [V0t: $o] :
% 1.67/1.46 ( ( (~) @ ( (~) @ V0t ) )
% 1.67/1.46 <=> V0t ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Esat_2EAND__INV__IMP,axiom,
% 1.67/1.46 ! [V0A: $o] :
% 1.67/1.46 ( V0A
% 1.67/1.46 => ( ( (~) @ V0A )
% 1.67/1.46 => c_2Ebool_2EF ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Esat_2EOR__DUAL2,axiom,
% 1.67/1.46 ! [V0B: $o,V1A: $o] :
% 1.67/1.46 ( ( ( (~)
% 1.67/1.46 @ ( V1A
% 1.67/1.46 | V0B ) )
% 1.67/1.46 => c_2Ebool_2EF )
% 1.67/1.46 <=> ( ( V1A
% 1.67/1.46 => c_2Ebool_2EF )
% 1.67/1.46 => ( ( (~) @ V0B )
% 1.67/1.46 => c_2Ebool_2EF ) ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Esat_2EOR__DUAL3,axiom,
% 1.67/1.46 ! [V0B: $o,V1A: $o] :
% 1.67/1.46 ( ( ( (~)
% 1.67/1.46 @ ( ( (~) @ V1A )
% 1.67/1.46 | V0B ) )
% 1.67/1.46 => c_2Ebool_2EF )
% 1.67/1.46 <=> ( V1A
% 1.67/1.46 => ( ( (~) @ V0B )
% 1.67/1.46 => c_2Ebool_2EF ) ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Esat_2EAND__INV2,axiom,
% 1.67/1.46 ! [V0A: $o] :
% 1.67/1.46 ( ( ( (~) @ V0A )
% 1.67/1.46 => c_2Ebool_2EF )
% 1.67/1.46 => ( ( V0A
% 1.67/1.46 => c_2Ebool_2EF )
% 1.67/1.46 => c_2Ebool_2EF ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Esat_2Edc__eq,axiom,
% 1.67/1.46 ! [V0r: $o,V1q: $o,V2p: $o] :
% 1.67/1.46 ( ( V2p
% 1.67/1.46 <=> ( V1q = V0r ) )
% 1.67/1.46 <=> ( ( V2p
% 1.67/1.46 | V1q
% 1.67/1.46 | V0r )
% 1.67/1.46 & ( V2p
% 1.67/1.46 | ( (~) @ V0r )
% 1.67/1.46 | ( (~) @ V1q ) )
% 1.67/1.46 & ( V1q
% 1.67/1.46 | ( (~) @ V0r )
% 1.67/1.46 | ( (~) @ V2p ) )
% 1.67/1.46 & ( V0r
% 1.67/1.46 | ( (~) @ V1q )
% 1.67/1.46 | ( (~) @ V2p ) ) ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Esat_2Edc__neg,axiom,
% 1.67/1.46 ! [V0q: $o,V1p: $o] :
% 1.67/1.46 ( ( V1p
% 1.67/1.46 <=> ( (~) @ V0q ) )
% 1.67/1.46 <=> ( ( V1p
% 1.67/1.46 | V0q )
% 1.67/1.46 & ( ( (~) @ V0q )
% 1.67/1.46 | ( (~) @ V1p ) ) ) ) ).
% 1.67/1.46
% 1.67/1.46 thf(thm_2Ecardinal_2ECARD__NOT__LE,conjecture,
% 1.67/1.46 ! [A_27a: $tType,A_27b: $tType,V0s: A_27a > $o,V1t: A_27b > $o] :
% 1.67/1.46 ( ( (~) @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b @ V0s @ V1t ) )
% 1.67/1.46 <=> ( (~) @ ( c_2Ecardinal_2Ecardleq @ A_27a @ A_27b @ V0s @ V1t ) ) ) ).
% 1.67/1.46 ------------------------
% 1.67/1.47 % (11265)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_10863 for (2999ds/27Mi)
% 1.67/1.47 % (11264)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_10863 for (2999ds/4Mi)
% 1.67/1.48 % (11264)Instruction limit reached!
% 1.67/1.48 % (11264)------------------------------
% 1.67/1.48 % (11264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.48 % (11264)Termination reason: Unknown
% 1.67/1.48 % (11264)Termination phase: Function definition elimination
% 1.67/1.48
% 1.67/1.48 % (11264)Memory used [KB]: 1023
% 1.67/1.48 % (11264)Time elapsed: 0.003 s
% 1.67/1.48 % (11264)Instructions burned: 7 (million)
% 1.67/1.48 % (11264)------------------------------
% 1.67/1.48 % (11264)------------------------------
% 1.67/1.48 % (11265)First to succeed.
% 1.67/1.48 % (11265)Refutation found. Thanks to Tanya!
% 1.67/1.48 % SZS status Theorem for DTF2THF_10863
% 1.67/1.48 % SZS output start Proof for DTF2THF_10863
% 1.67/1.48 thf(type_def_6, type, sK1: $tType).
% 1.67/1.48 thf(type_def_7, type, sK2: $tType).
% 1.67/1.48 thf(func_def_0, type, tyop_2Emin_2Ebool: $tType).
% 1.67/1.48 thf(func_def_1, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 1.67/1.48 thf(func_def_2, type, c_2Ebool_2E_21: !>[X0: $tType]:((X0 > $o) > $o)).
% 1.67/1.48 thf(func_def_3, type, c_2Ebool_2E_2F_5C: $o > $o > $o).
% 1.67/1.48 thf(func_def_4, type, c_2Emin_2E_3D: !>[X0: $tType]:(X0 > X0 > $o)).
% 1.67/1.48 thf(func_def_5, type, c_2Emin_2E_3D_3D_3E: $o > $o > $o).
% 1.67/1.48 thf(func_def_6, type, c_2Ebool_2E_3F: !>[X0: $tType]:((X0 > $o) > $o)).
% 1.67/1.48 thf(func_def_9, type, c_2Ebool_2E_5C_2F: $o > $o > $o).
% 1.67/1.48 thf(func_def_10, type, c_2Ecardinal_2Ecardleq: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > $o)).
% 1.67/1.48 thf(func_def_11, type, c_2Ebool_2E_7E: $o > $o).
% 1.67/1.48 thf(func_def_14, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.67/1.48 thf(func_def_18, type, sP0: $o > $o > $o > $o).
% 1.67/1.48 thf(func_def_19, type, sK3: sK1 > $o).
% 1.67/1.48 thf(func_def_20, type, sK4: sK2 > $o).
% 1.67/1.48 thf(func_def_21, type, sK5: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.67/1.48 thf(func_def_22, type, sK6: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.67/1.48 thf(f560,plain,(
% 1.67/1.48 $false),
% 1.67/1.48 inference(trivial_inequality_removal,[status(thm)],[f129])).
% 1.67/1.48 thf(f129,plain,(
% 1.67/1.48 ((~ (c_2Ecardinal_2Ecardleq @ sK1 @ sK2 @ sK3 @ sK4)) != (~ (c_2Ecardinal_2Ecardleq @ sK1 @ sK2 @ sK3 @ sK4)))),
% 1.67/1.48 inference(cnf_transformation,[status(thm)],[f90])).
% 1.67/1.48 thf(f90,plain,(
% 1.67/1.48 ((~ (c_2Ecardinal_2Ecardleq @ sK1 @ sK2 @ sK3 @ sK4)) != (~ (c_2Ecardinal_2Ecardleq @ sK1 @ sK2 @ sK3 @ sK4)))),
% 1.67/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f77,f89])).
% 1.67/1.48 thf(f89,plain,(
% 1.67/1.48 ? [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o] : ((~ (c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3)) != (~ (c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3))) => ((~ (c_2Ecardinal_2Ecardleq @ sK1 @ sK2 @ sK3 @ sK4)) != (~ (c_2Ecardinal_2Ecardleq @ sK1 @ sK2 @ sK3 @ sK4)))),
% 1.67/1.48 introduced(definition,[],[choice_axiom])).
% 1.67/1.48 thf(f77,plain,(
% 1.67/1.48 ? [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o] : ((~ (c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3)) != (~ (c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3)))),
% 1.67/1.48 inference(ennf_transformation,[status(thm)],[f41])).
% 1.67/1.48 thf(f41,plain,(
% 1.67/1.48 ~! [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o] : ((~ (c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3)) = (~ (c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3)))),
% 1.67/1.48 inference(fool_elimination,[status(thm)],[f40])).
% 1.67/1.48 thf(f40,plain,(
% 1.67/1.48 ~! [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o] : ((~ (c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3)) <=> (~ (c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3)))),
% 1.67/1.48 inference(rectify,[status(thm)],[f24])).
% 1.67/1.48 thf(f24,negated_conjecture,(
% 1.67/1.48 ~! [X0 : $tType,X1 : $tType,X8 : X0 > $o,X9 : X1 > $o] : ((~ (c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X8 @ X9)) <=> (~ (c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X8 @ X9)))),
% 1.67/1.48 inference(negated_conjecture,[status(cth)],[f23])).
% 1.67/1.48 thf(f23,conjecture,(
% 1.67/1.48 ! [X0 : $tType,X1 : $tType,X8 : X0 > $o,X9 : X1 > $o] : ((~ (c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X8 @ X9)) <=> (~ (c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X8 @ X9)))),
% 1.67/1.48 file('/export/starexec/sandbox2/tmp/tmp.IpL42N7Jx3/DTF2THF_10863.p',thm_2Ecardinal_2ECARD__NOT__LE)).
% 1.67/1.48 % SZS output end Proof for DTF2THF_10863
% 1.67/1.48 % (11265)------------------------------
% 1.67/1.48 % (11265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.48 % (11265)Termination reason: Refutation
% 1.67/1.48
% 1.67/1.48 % (11265)Memory used [KB]: 5628
% 1.67/1.48 % (11265)Time elapsed: 0.005 s
% 1.67/1.48 % (11265)Instructions burned: 12 (million)
% 1.67/1.48 % (11265)------------------------------
% 1.67/1.48 % (11265)------------------------------
% 1.67/1.48 % (11259)Success in time 0.015 s
%------------------------------------------------------------------------------