TSTP Solution File: ITP001^7 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP001^7 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 : Tue May 7 07:46:27 EDT 2024
% Result : Theorem 32.08s 23.29s
% Output : Refutation 32.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 54
% Syntax : Number of formulae : 86 ( 56 unt; 24 typ; 0 def)
% Number of atoms : 246 ( 58 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 418 ( 6 ~; 4 |; 4 &; 400 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 91 ( 91 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 3 con; 0-4 aty)
% Number of variables : 188 ( 94 ^ 72 !; 4 ?; 188 :)
% ( 18 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(c_2Ebool_2E_21_type,type,
c_2Ebool_2E_21:
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf(c_2Ebool_2E_2F_5C_type,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Emin_2E_3D_type,type,
c_2Emin_2E_3D:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(c_2Emin_2E_3D_3D_3E_type,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F_type,type,
c_2Ebool_2E_3F:
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf(c_2Ebool_2E_5C_2F_type,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ebool_2E_7E_type,type,
c_2Ebool_2E_7E: $o > $o ).
thf(tyop_2Emin_2Eind_type,type,
tyop_2Emin_2Eind: $tType ).
thf(c_2Ebool_2E_3F_21_type,type,
c_2Ebool_2E_3F_21:
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf(c_2Emin_2E_40_type,type,
c_2Emin_2E_40:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(c_2Ebool_2EBOUNDED_type,type,
c_2Ebool_2EBOUNDED: $o > $o ).
thf(c_2Ebool_2ECOND_type,type,
c_2Ebool_2ECOND:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(c_2Ebool_2EDATATYPE_type,type,
c_2Ebool_2EDATATYPE:
!>[TA: $tType] : ( TA > $o ) ).
thf(c_2Ebool_2EF_type,type,
c_2Ebool_2EF: $o ).
thf(c_2Ebool_2EIN_type,type,
c_2Ebool_2EIN:
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf(c_2Ebool_2EONE__ONE_type,type,
c_2Ebool_2EONE__ONE:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > $o ) ).
thf(c_2Ebool_2EONTO_type,type,
c_2Ebool_2EONTO:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > $o ) ).
thf(c_2Ebool_2ERES__EXISTS_type,type,
c_2Ebool_2ERES__EXISTS:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf(c_2Ebool_2ERES__EXISTS__UNIQUE_type,type,
c_2Ebool_2ERES__EXISTS__UNIQUE:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf(c_2Ebool_2ERES__FORALL_type,type,
c_2Ebool_2ERES__FORALL:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf(c_2Ebool_2ERES__SELECT_type,type,
c_2Ebool_2ERES__SELECT:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA ) ).
thf(c_2Ebool_2ET_type,type,
c_2Ebool_2ET: $o ).
thf(c_2Ebool_2ETYPE__DEFINITION_type,type,
c_2Ebool_2ETYPE__DEFINITION:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TA > TB ) > $o ) ).
thf(13,axiom,
( c_2Ebool_2EF
= ( ! [A: $o] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EF__DEF) ).
thf(69,plain,
( c_2Ebool_2EF
= ( ! [A: $o] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(27,axiom,
( c_2Ebool_2EBOUNDED
= ( ^ [A: $o] : c_2Ebool_2ET ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EBOUNDED__DEF) ).
thf(120,plain,
( c_2Ebool_2EBOUNDED
= ( ^ [A: $o] : c_2Ebool_2ET ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType] :
( ( c_2Ebool_2EONE__ONE @ TB @ TA )
= ( ^ [A: TB > TA] :
( c_2Ebool_2E_21 @ TB
@ ^ [B: TB] :
( c_2Ebool_2E_21 @ TB
@ ^ [C: TB] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D @ TA @ ( A @ B ) @ ( A @ C ) ) @ ( c_2Emin_2E_3D @ TB @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EONE__ONE__DEF) ).
thf(56,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Ebool_2EONE__ONE @ TB @ TA )
= ( ^ [A: TB > TA] :
( c_2Ebool_2E_21 @ TB
@ ^ [B: TB] :
( c_2Ebool_2E_21 @ TB
@ ^ [C: TB] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D @ TA @ ( A @ B ) @ ( A @ C ) ) @ ( c_2Emin_2E_3D @ TB @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Ebool_2E_3F @ TA @ A )
= ( ? [B: TA] : ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_3F) ).
thf(42,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Ebool_2E_3F @ TA @ A )
= ( ? [B: TA] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_5C_2F @ A @ B )
= ( A
| B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).
thf(33,plain,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_5C_2F @ A @ B )
= ( A
| B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [TA: $tType] :
( ( c_2Ebool_2EIN @ TA )
= ( ^ [A: TA,B: TA > $o] : ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIN__DEF) ).
thf(53,plain,
! [TA: $tType] :
( ( c_2Ebool_2EIN @ TA )
= ( ^ [A: TA,B: TA > $o] : ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Ebool_2E_21 @ TA @ A )
= ( ! [B: TA] : ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_21) ).
thf(96,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Ebool_2E_21 @ TA @ A )
= ( ! [B: TA] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(24,axiom,
! [A: $o,B: $o] :
( ( c_2Emin_2E_3D_3D_3E @ A @ B )
= ( A
=> B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).
thf(105,plain,
! [A: $o,B: $o] :
( ( c_2Emin_2E_3D_3D_3E @ A @ B )
= ( A
=> B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(9,axiom,
( c_2Ebool_2E_5C_2F
= ( ^ [A: $o,B: $o] :
( c_2Ebool_2E_21 @ $o
@ ^ [C: $o] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D_3D_3E @ A @ C ) @ ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D_3D_3E @ B @ C ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__DEF) ).
thf(59,plain,
( c_2Ebool_2E_5C_2F
= ( ^ [A: $o,B: $o] :
( c_2Ebool_2E_21 @ $o
@ ^ [C: $o] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D_3D_3E @ A @ C ) @ ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D_3D_3E @ B @ C ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [TA: $tType] :
( ( c_2Ebool_2E_3F @ TA )
= ( ^ [A: TA > $o] : ( A @ ( c_2Emin_2E_40 @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEXISTS__DEF) ).
thf(71,plain,
! [TA: $tType] :
( ( c_2Ebool_2E_3F @ TA )
= ( ^ [A: TA > $o] : ( A @ ( c_2Emin_2E_40 @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( c_2Emin_2E_3D @ TA @ A @ B )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D) ).
thf(76,plain,
! [TA: $tType,A: TA,B: TA] :
( ( c_2Emin_2E_3D @ TA @ A @ B )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [TA: $tType] :
( ( c_2Ebool_2ERES__SELECT @ TA )
= ( ^ [A: TA > $o,B: TA > $o] :
( c_2Emin_2E_40 @ TA
@ ^ [C: TA] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2EIN @ TA @ C @ A ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERES__SELECT__DEF) ).
thf(66,plain,
! [TA: $tType] :
( ( c_2Ebool_2ERES__SELECT @ TA )
= ( ^ [A: TA > $o,B: TA > $o] :
( c_2Emin_2E_40 @ TA
@ ^ [C: TA] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2EIN @ TA @ C @ A ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(29,axiom,
! [TA: $tType] :
( ( c_2Ebool_2E_21 @ TA )
= ( ^ [A: TA > $o] :
( c_2Emin_2E_3D @ ( TA > $o ) @ A
@ ^ [B: TA] : c_2Ebool_2ET ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFORALL__DEF) ).
thf(123,plain,
! [TA: $tType] :
( ( c_2Ebool_2E_21 @ TA )
= ( ^ [A: TA > $o] :
( c_2Emin_2E_3D @ ( TA > $o ) @ A
@ ^ [B: TA] : c_2Ebool_2ET ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(6,axiom,
? [A: tyop_2Emin_2Eind > tyop_2Emin_2Eind] :
( ( c_2Ebool_2EONE__ONE @ tyop_2Emin_2Eind @ tyop_2Emin_2Eind @ A )
& ~ ( c_2Ebool_2EONTO @ tyop_2Emin_2Eind @ tyop_2Emin_2Eind @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EINFINITY__AX) ).
thf(50,plain,
? [A: tyop_2Emin_2Eind > tyop_2Emin_2Eind] :
( ( c_2Ebool_2EONE__ONE @ tyop_2Emin_2Eind @ tyop_2Emin_2Eind @ A )
& ~ ( c_2Ebool_2EONTO @ tyop_2Emin_2Eind @ tyop_2Emin_2Eind @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,axiom,
! [TA: $tType] :
( ( c_2Ebool_2ERES__EXISTS @ TA )
= ( ^ [A: TA > $o,B: TA > $o] :
( c_2Ebool_2E_3F @ TA
@ ^ [C: TA] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2EIN @ TA @ C @ A ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERES__EXISTS__DEF) ).
thf(114,plain,
! [TA: $tType] :
( ( c_2Ebool_2ERES__EXISTS @ TA )
= ( ^ [A: TA > $o,B: TA > $o] :
( c_2Ebool_2E_3F @ TA
@ ^ [C: TA] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2EIN @ TA @ C @ A ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType] :
( ( c_2Ebool_2ETYPE__DEFINITION @ TB @ TA )
= ( ^ [A: TB > $o,B: TA > TB] :
( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_21 @ TA
@ ^ [C: TA] :
( c_2Ebool_2E_21 @ TA
@ ^ [D: TA] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D @ TB @ ( B @ C ) @ ( B @ D ) ) @ ( c_2Emin_2E_3D @ TA @ C @ D ) ) ) )
@ ( c_2Ebool_2E_21 @ TB
@ ^ [C: TB] :
( c_2Emin_2E_3D @ $o @ ( A @ C )
@ ( c_2Ebool_2E_3F @ TA
@ ^ [D: TA] : ( c_2Emin_2E_3D @ TB @ C @ ( B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETYPE__DEFINITION) ).
thf(82,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Ebool_2ETYPE__DEFINITION @ TB @ TA )
= ( ^ [A: TB > $o,B: TA > TB] :
( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_21 @ TA
@ ^ [C: TA] :
( c_2Ebool_2E_21 @ TA
@ ^ [D: TA] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D @ TB @ ( B @ C ) @ ( B @ D ) ) @ ( c_2Emin_2E_3D @ TA @ C @ D ) ) ) )
@ ( c_2Ebool_2E_21 @ TB
@ ^ [C: TB] :
( c_2Emin_2E_3D @ $o @ ( A @ C )
@ ( c_2Ebool_2E_3F @ TA
@ ^ [D: TA] : ( c_2Emin_2E_3D @ TB @ C @ ( B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(28,axiom,
( c_2Ebool_2ET
= ( ( ^ [A: $o] : A )
= ( ^ [A: $o] : A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ET__DEF) ).
thf(122,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10,axiom,
! [TA: $tType] :
( ( c_2Ebool_2ERES__FORALL @ TA )
= ( ^ [A: TA > $o,B: TA > $o] :
( c_2Ebool_2E_21 @ TA
@ ^ [C: TA] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2EIN @ TA @ C @ A ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERES__FORALL__DEF) ).
thf(61,plain,
! [TA: $tType] :
( ( c_2Ebool_2ERES__FORALL @ TA )
= ( ^ [A: TA > $o,B: TA > $o] :
( c_2Ebool_2E_21 @ TA
@ ^ [C: TA] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2EIN @ TA @ C @ A ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,axiom,
! [TA: $tType] :
( ( c_2Ebool_2ECOND @ TA )
= ( ^ [A: $o,B: TA,C: TA] :
( c_2Emin_2E_40 @ TA
@ ^ [D: TA] : ( c_2Ebool_2E_2F_5C @ ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D @ $o @ A @ c_2Ebool_2ET ) @ ( c_2Emin_2E_3D @ TA @ D @ B ) ) @ ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D @ $o @ A @ c_2Ebool_2EF ) @ ( c_2Emin_2E_3D @ TA @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__DEF) ).
thf(133,plain,
! [TA: $tType] :
( ( c_2Ebool_2ECOND @ TA )
= ( ^ [A: $o,B: TA,C: TA] :
( c_2Emin_2E_40 @ TA
@ ^ [D: TA] : ( c_2Ebool_2E_2F_5C @ ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D @ $o @ A @ c_2Ebool_2ET ) @ ( c_2Emin_2E_3D @ TA @ D @ B ) ) @ ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D @ $o @ A @ c_2Ebool_2EF ) @ ( c_2Emin_2E_3D @ TA @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(15,axiom,
( c_2Ebool_2E_2F_5C
= ( ^ [A: $o,B: $o] :
( c_2Ebool_2E_21 @ $o
@ ^ [C: $o] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D_3D_3E @ A @ ( c_2Emin_2E_3D_3D_3E @ B @ C ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__DEF) ).
thf(74,plain,
( c_2Ebool_2E_2F_5C
= ( ^ [A: $o,B: $o] :
( c_2Ebool_2E_21 @ $o
@ ^ [C: $o] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Emin_2E_3D_3D_3E @ A @ ( c_2Emin_2E_3D_3D_3E @ B @ C ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
! [TA: $tType] :
( ( c_2Ebool_2EDATATYPE @ TA )
= ( ^ [A: TA] : c_2Ebool_2ET ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EDATATYPE__TAG__DEF) ).
thf(117,plain,
! [TA: $tType] :
( ( c_2Ebool_2EDATATYPE @ TA )
= ( ^ [A: TA] : c_2Ebool_2ET ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(19,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( A @ ( c_2Emin_2E_40 @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ESELECT__AX) ).
thf(85,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( A @ ( c_2Emin_2E_40 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( c_2Ebool_2EONTO @ TB @ TA )
= ( ^ [A: TB > TA] :
( c_2Ebool_2E_21 @ TA
@ ^ [B: TA] :
( c_2Ebool_2E_3F @ TB
@ ^ [C: TB] : ( c_2Emin_2E_3D @ TA @ B @ ( A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EONTO__DEF) ).
thf(102,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Ebool_2EONTO @ TB @ TA )
= ( ^ [A: TB > TA] :
( c_2Ebool_2E_21 @ TA
@ ^ [B: TA] :
( c_2Ebool_2E_3F @ TB
@ ^ [C: TB] : ( c_2Emin_2E_3D @ TA @ B @ ( A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,conjecture,
c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(2,negated_conjecture,
~ c_2Ebool_2ET,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(32,plain,
~ c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $o] :
( ( c_2Ebool_2E_7E @ A )
= ~ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_7E) ).
thf(45,plain,
! [A: $o] :
( ( c_2Ebool_2E_7E @ A )
= ~ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
( c_2Ebool_2E_7E
= ( ^ [A: $o] : ( c_2Emin_2E_3D_3D_3E @ A @ c_2Ebool_2EF ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__DEF) ).
thf(64,plain,
( c_2Ebool_2E_7E
= ( ^ [A: $o] : ( c_2Emin_2E_3D_3D_3E @ A @ c_2Ebool_2EF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(22,axiom,
! [TA: $tType] :
( ( c_2Ebool_2E_3F_21 @ TA )
= ( ^ [A: TA > $o] :
( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_3F @ TA @ A )
@ ( c_2Ebool_2E_21 @ TA
@ ^ [B: TA] :
( c_2Ebool_2E_21 @ TA
@ ^ [C: TA] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2E_2F_5C @ ( A @ B ) @ ( A @ C ) ) @ ( c_2Emin_2E_3D @ TA @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEXISTS__UNIQUE__DEF) ).
thf(99,plain,
! [TA: $tType] :
( ( c_2Ebool_2E_3F_21 @ TA )
= ( ^ [A: TA > $o] :
( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_3F @ TA @ A )
@ ( c_2Ebool_2E_21 @ TA
@ ^ [B: TA] :
( c_2Ebool_2E_21 @ TA
@ ^ [C: TA] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2E_2F_5C @ ( A @ B ) @ ( A @ C ) ) @ ( c_2Emin_2E_3D @ TA @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(20,axiom,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_2F_5C @ A @ B )
= ( A
& B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).
thf(87,plain,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_2F_5C @ A @ B )
= ( A
& B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(30,axiom,
! [A: $o] :
( ( A = c_2Ebool_2ET )
| ( A = c_2Ebool_2EF ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EBOOL__CASES__AX) ).
thf(126,plain,
! [A: $o] :
( ( A = c_2Ebool_2ET )
| ( A = c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(17,axiom,
! [TA: $tType] :
( ( c_2Ebool_2ERES__EXISTS__UNIQUE @ TA )
= ( ^ [A: TA > $o,B: TA > $o] :
( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2ERES__EXISTS @ TA @ A @ B )
@ ( c_2Ebool_2ERES__FORALL @ TA @ A
@ ^ [C: TA] :
( c_2Ebool_2ERES__FORALL @ TA @ A
@ ^ [D: TA] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2E_2F_5C @ ( B @ C ) @ ( B @ D ) ) @ ( c_2Emin_2E_3D @ TA @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) ).
thf(79,plain,
! [TA: $tType] :
( ( c_2Ebool_2ERES__EXISTS__UNIQUE @ TA )
= ( ^ [A: TA > $o,B: TA > $o] :
( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2ERES__EXISTS @ TA @ A @ B )
@ ( c_2Ebool_2ERES__FORALL @ TA @ A
@ ^ [C: TA] :
( c_2Ebool_2ERES__FORALL @ TA @ A
@ ^ [D: TA] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2E_2F_5C @ ( B @ C ) @ ( B @ D ) ) @ ( c_2Emin_2E_3D @ TA @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(136,plain,
$false,
inference(e,[status(thm)],[69,120,56,42,33,53,96,105,59,71,76,66,123,50,114,82,122,61,133,74,117,85,102,32,45,64,99,87,126,79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ITP001^7 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.14/0.16 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 6 14:34:39 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.93/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/0.99 % [INFO] Parsing done (161ms).
% 1.33/1.00 % [INFO] Running in sequential loop mode.
% 1.87/1.19 % [INFO] eprover registered as external prover.
% 1.87/1.20 % [INFO] cvc4 registered as external prover.
% 1.87/1.20 % [INFO] Scanning for conjecture ...
% 2.03/1.26 % [INFO] Found a conjecture and 39 axioms. Running axiom selection ...
% 2.03/1.30 % [INFO] Axiom selection finished. Selected 29 axioms (removed 10 axioms).
% 2.20/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 2.43/1.36 % [INFO] Type checking passed.
% 2.43/1.36 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 32.08/23.28 % External prover 'e' found a proof!
% 32.08/23.28 % [INFO] Killing All external provers ...
% 32.08/23.29 % Time passed: 22776ms (effective reasoning time: 22279ms)
% 32.08/23.29 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 32.08/23.29 % Axioms used in derivation (29): thm_2Ebool_2EBOOL__CASES__AX, thm_2Ebool_2EDATATYPE__TAG__DEF, thm_2Ebool_2EINFINITY__AX, thm_2Ebool_2EEXISTS__DEF, thm_2Ebool_2ENOT__DEF, logicdef_2E_3D_3D_3E, thm_2Ebool_2EF__DEF, thm_2Ebool_2ESELECT__AX, thm_2Ebool_2EAND__DEF, thm_2Ebool_2ERES__FORALL__DEF, quantdef_2E_3F, thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF, logicdef_2E_3D, thm_2Ebool_2EIN__DEF, logicdef_2E_5C_2F, thm_2Ebool_2EONE__ONE__DEF, thm_2Ebool_2EBOUNDED__DEF, thm_2Ebool_2EOR__DEF, quantdef_2E_21, thm_2Ebool_2ERES__SELECT__DEF, thm_2Ebool_2ECOND__DEF, thm_2Ebool_2ET__DEF, thm_2Ebool_2ETYPE__DEFINITION, thm_2Ebool_2EFORALL__DEF, thm_2Ebool_2EEXISTS__UNIQUE__DEF, thm_2Ebool_2EONTO__DEF, logicdef_2E_2F_5C, thm_2Ebool_2ERES__EXISTS__DEF, logicdef_2E_7E
% 32.08/23.29 % No. of inferences in proof: 62
% 32.08/23.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 22776 ms resp. 22279 ms w/o parsing
% 32.30/23.33 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 32.30/23.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------