TSTP Solution File: ITP003^3 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP003^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 : Mon May 20 22:21:17 EDT 2024
% Result : Theorem 120.44s 20.27s
% Output : Refutation 121.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 50
% Syntax : Number of formulae : 598 ( 250 unt; 18 typ; 0 def)
% Number of atoms : 1443 ( 773 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 6884 ( 706 ~; 426 |; 51 &;5651 @)
% ( 0 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 227 ( 227 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 1479 ( 126 ^1338 !; 14 ?;1479 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(c_2Earithmetic_2E_2A_type,type,
c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_2B_type,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Enum_2E0_type,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Eprim__rec_2E_3C_type,type,
c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2EBIT1_type,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EBIT2_type,type,
c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ECOND_type,type,
c_2Ebool_2ECOND:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(c_2Earithmetic_2EEVEN_type,type,
c_2Earithmetic_2EEVEN: tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2EF_type,type,
c_2Ebool_2EF: $o ).
thf(c_2Earithmetic_2EMOD_type,type,
c_2Earithmetic_2EMOD: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2ENUMERAL_type,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EODD_type,type,
c_2Earithmetic_2EODD: tyop_2Enum_2Enum > $o ).
thf(c_2Enum_2ESUC_type,type,
c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ET_type,type,
c_2Ebool_2ET: $o ).
thf(c_2Earithmetic_2EZERO_type,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(sk1_type,type,
sk1: tyop_2Enum_2Enum ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: $o,C: TB,D: TB] :
( ( A @ ( c_2Ebool_2ECOND @ TB @ B @ C @ D ) )
= ( c_2Ebool_2ECOND @ TA @ B @ ( A @ C ) @ ( A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__RAND) ).
thf(163,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: $o,C: TB,D: TB] :
( ( A @ ( c_2Ebool_2ECOND @ TB @ B @ C @ D ) )
= ( c_2Ebool_2ECOND @ TA @ B @ ( A @ C ) @ ( A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(164,plain,
! [TA: $tType,TB: $tType,D: TA,C: TA,B: $o,A: TA > TB] :
( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
= ( c_2Ebool_2ECOND @ TB @ B @ ( A @ C ) @ ( A @ D ) ) ),
inference(cnf,[status(esa)],[163]) ).
thf(165,plain,
! [TA: $tType,TB: $tType,D: TA,C: TA,B: $o,A: TA > TB] :
( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
= ( c_2Ebool_2ECOND @ TB @ B @ ( A @ C ) @ ( A @ D ) ) ),
inference(lifteq,[status(thm)],[164]) ).
thf(18,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__COMM) ).
thf(123,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(124,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ B @ A ) ),
inference(cnf,[status(esa)],[123]) ).
thf(125,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ B @ A ) ),
inference(lifteq,[status(thm)],[124]) ).
thf(24,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EODD__EXISTS) ).
thf(141,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(142,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
inference(cnf,[status(esa)],[141]) ).
thf(143,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(28,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EODD__EVEN) ).
thf(153,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(154,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
inference(cnf,[status(esa)],[153]) ).
thf(155,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
inference(lifteq,[status(thm)],[154]) ).
thf(567,plain,
! [A: tyop_2Enum_2Enum] :
( ( ~ ( c_2Earithmetic_2EEVEN @ A ) )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
inference(rewrite,[status(thm)],[143,155]) ).
thf(569,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2EEVEN @ A )
| ~ ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
inference(bool_ext,[status(thm)],[567]) ).
thf(574,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( A
!= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) )
| ~ ( c_2Earithmetic_2EEVEN @ A ) ),
inference(cnf,[status(esa)],[569]) ).
thf(575,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( A
!= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) )
| ~ ( c_2Earithmetic_2EEVEN @ A ) ),
inference(lifteq,[status(thm)],[574]) ).
thf(576,plain,
! [A: tyop_2Enum_2Enum] :
~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) ) ),
inference(simp,[status(thm)],[575]) ).
thf(581,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ B ) ) )
| ( ( c_2Earithmetic_2E_2A @ B @ A )
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[125,576]) ).
thf(582,plain,
! [A: tyop_2Enum_2Enum] :
~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(pattern_uni,[status(thm)],[581:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(1299,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,582]) ).
thf(1959,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1299:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2331,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(simp,[status(thm)],[1959]) ).
thf(29,axiom,
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ETWO) ).
thf(156,plain,
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(157,plain,
( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(lifteq,[status(thm)],[156]) ).
thf(1322,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( A @ D ) )
= ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[157,165]) ).
thf(1578,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1322:[bind(A,$thf( ^ [E: TA] : ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(1976,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[1578]) ).
thf(14140,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(rewrite,[status(thm)],[1976,157]) ).
thf(27,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__EXISTS) ).
thf(150,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(151,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
inference(cnf,[status(esa)],[150]) ).
thf(152,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
inference(lifteq,[status(thm)],[151]) ).
thf(938,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
| ~ ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ),
inference(bool_ext,[status(thm)],[152]) ).
thf(983,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( A
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) )
| ( c_2Earithmetic_2EEVEN @ A ) ),
inference(cnf,[status(esa)],[938]) ).
thf(984,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( A
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) )
| ( c_2Earithmetic_2EEVEN @ A ) ),
inference(lifteq,[status(thm)],[983]) ).
thf(985,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) ),
inference(simp,[status(thm)],[984]) ).
thf(25,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Enum_2ESUC @ A )
= ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD1) ).
thf(144,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Enum_2ESUC @ A )
= ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(145,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Enum_2ESUC @ A )
= ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(cnf,[status(esa)],[144]) ).
thf(146,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Enum_2ESUC @ A ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(32,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD__0) ).
thf(166,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(167,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
= A ),
inference(cnf,[status(esa)],[166]) ).
thf(168,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
= A ),
inference(lifteq,[status(thm)],[167]) ).
thf(313,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Enum_2ESUC @ A )
= B )
| ( ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2E_2B @ B @ c_2Enum_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[146,168]) ).
thf(316,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Enum_2ESUC @ A )
= B )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 ) ),
inference(simp,[status(thm)],[313]) ).
thf(318,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Enum_2ESUC @ A )
= A )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 ) ),
inference(simp,[status(thm)],[316]) ).
thf(23,axiom,
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
= ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EONE) ).
thf(139,plain,
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
= ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(140,plain,
( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(lifteq,[status(thm)],[139]) ).
thf(259,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[157,140]) ).
thf(263,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 ) ),
inference(simp,[status(thm)],[259]) ).
thf(588,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 )
| ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,582]) ).
thf(589,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 )
| ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[588:[]]) ).
thf(6664,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 )
| ~ ( c_2Earithmetic_2EEVEN @ A )
| ( ( c_2Enum_2ESUC @ A )
!= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[318,589]) ).
thf(6665,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 )
| ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(pattern_uni,[status(thm)],[6664:[bind(A,$thf( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )),bind(B,$thf( C ))]]) ).
thf(6687,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 )
| ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(simp,[status(thm)],[6665]) ).
thf(6830,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) )
!= ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[985,6687]) ).
thf(6831,plain,
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 ),
inference(pattern_uni,[status(thm)],[6830:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(6859,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) )
!= c_2Enum_2E0 )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[165,6831]) ).
thf(6862,plain,
! [A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 ),
inference(pre_uni,[status(thm)],[6859:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(6865,plain,
! [A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 ),
inference(simp,[status(thm)],[6862]) ).
thf(14151,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(paramod_ordered,[status(thm)],[14140,6865]) ).
thf(14278,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[14151]) ).
thf(14358,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[14278]) ).
thf(1454,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) )
| ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
!= ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[140,165]) ).
thf(1582,plain,
! [A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ),
inference(pre_uni,[status(thm)],[1454:[bind(A,$thf( ^ [E: TA] : ( c_2Enum_2ESUC @ c_2Enum_2E0 ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(1979,plain,
! [A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ),
inference(simp,[status(thm)],[1582]) ).
thf(3069,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(rewrite,[status(thm)],[1979,140]) ).
thf(1013,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ B ) )
| ( ( c_2Earithmetic_2E_2A @ B @ A )
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[125,985]) ).
thf(1014,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pattern_uni,[status(thm)],[1013:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).
thf(158,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(160,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
inference(cnf,[status(esa)],[158]) ).
thf(162,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
inference(lifteq,[status(thm)],[160]) ).
thf(6,axiom,
! [TA: $tType,A: TA] :
( ( A = A )
= c_2Ebool_2ET ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(52,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(413,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $true @ A @ B )
= A ),
inference(rewrite,[status(thm)],[162,52]) ).
thf(21,axiom,
! [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ELESS__0) ).
thf(134,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(135,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) ),
inference(cnf,[status(esa)],[134]) ).
thf(261,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[157,135]) ).
thf(262,plain,
c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(20,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ? [D: tyop_2Enum_2Enum] :
( ( B
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
& ( c_2Eprim__rec_2E_3C @ C @ A ) )
=> ( ( c_2Earithmetic_2EMOD @ B @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__UNIQUE) ).
thf(129,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ? [D: tyop_2Enum_2Enum] :
( ( B
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
& ( c_2Eprim__rec_2E_3C @ C @ A ) )
=> ( ( c_2Earithmetic_2EMOD @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(130,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ? [D: tyop_2Enum_2Enum] :
( B
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
& ( c_2Eprim__rec_2E_3C @ C @ A ) )
=> ( ( c_2Earithmetic_2EMOD @ B @ A )
= C ) ),
inference(miniscope,[status(thm)],[129]) ).
thf(131,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( B
!= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
| ~ ( c_2Eprim__rec_2E_3C @ C @ A )
| ( ( c_2Earithmetic_2EMOD @ B @ A )
= C ) ),
inference(cnf,[status(esa)],[130]) ).
thf(132,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( B
!= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
| ( ( c_2Earithmetic_2EMOD @ B @ A )
= C )
| ~ ( c_2Eprim__rec_2E_3C @ C @ A ) ),
inference(lifteq,[status(thm)],[131]) ).
thf(133,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B ) @ A )
= B )
| ~ ( c_2Eprim__rec_2E_3C @ B @ A ) ),
inference(simp,[status(thm)],[132]) ).
thf(375,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B ) @ A )
= B )
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Eprim__rec_2E_3C @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[262,133]) ).
thf(376,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(pattern_uni,[status(thm)],[375:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( c_2Enum_2E0 )),bind(C,$thf( C ))]]) ).
thf(388,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(simp,[status(thm)],[376]) ).
thf(6248,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(rewrite,[status(thm)],[388,168]) ).
thf(1,conjecture,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ A ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__2) ).
thf(2,negated_conjecture,
~ ! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ A ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(34,plain,
~ ! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ A ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,plain,
( ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
( ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(6279,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6248,36]) ).
thf(6290,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[6279]) ).
thf(6303,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[6290]) ).
thf(6328,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( A != c_2Enum_2E0 )
| ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ $true @ A @ B )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[413,6303]) ).
thf(6337,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ~ ( c_2Earithmetic_2EEVEN @ sk1 )
| ( c_2Enum_2E0 != c_2Enum_2E0 )
| ( A
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[6328]) ).
thf(6355,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ~ ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(simp,[status(thm)],[6337]) ).
thf(6455,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EEVEN @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1014,6355]) ).
thf(6457,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[6455]) ).
thf(9795,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
| ( sk1 != sk1 ) ),
inference(eqfactor_ordered,[status(thm)],[6457]) ).
thf(9804,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[9795:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(9821,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ E @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) )
!= sk1 )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(paramod_ordered,[status(thm)],[165,9804]) ).
thf(9826,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[9821:[bind(A,$thf( ^ [F: TA] : ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(9830,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[9826]) ).
thf(13535,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3069,9830]) ).
thf(13554,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[13535]) ).
thf(13568,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[13554]) ).
thf(13840,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[13568]) ).
thf(13868,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
!= sk1 )
| ( ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[125,13840]) ).
thf(13869,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A )
!= sk1 )
| ( ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(pattern_uni,[status(thm)],[13868:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(370,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ B @ A )
| ( B
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
| ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B ) @ A )
!= ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[133,36]) ).
thf(378,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ A )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ A ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( A
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[370]) ).
thf(390,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[378]) ).
thf(491,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Enum_2ESUC @ A )
!= sk1 )
| ( ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[146,390]) ).
thf(498,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Enum_2ESUC @ A )
!= sk1 )
| ( A
!= ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[491]) ).
thf(511,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[498]) ).
thf(257,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[140,135]) ).
thf(258,plain,
c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( c_2Enum_2E0 ))]]) ).
thf(368,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B ) @ A )
= B )
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Eprim__rec_2E_3C @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[258,133]) ).
thf(369,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(pattern_uni,[status(thm)],[368:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( c_2Enum_2E0 )),bind(C,$thf( C ))]]) ).
thf(385,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(simp,[status(thm)],[369]) ).
thf(516,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(rewrite,[status(thm)],[385,168]) ).
thf(522,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[125,516]) ).
thf(523,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(pattern_uni,[status(thm)],[522:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(595,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[140,582]) ).
thf(597,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 ) ),
inference(simp,[status(thm)],[595]) ).
thf(9817,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[125,9804]) ).
thf(9818,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
!= sk1 ),
inference(pattern_uni,[status(thm)],[9817:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(366,plain,
! [E: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ B ) @ D ) @ C )
= D )
| ~ ( c_2Eprim__rec_2E_3C @ D @ C )
| ( ( c_2Earithmetic_2E_2A @ B @ A )
!= ( c_2Earithmetic_2E_2A @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[125,133]) ).
thf(367,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ B ) @ C ) @ A )
= C )
| ~ ( c_2Eprim__rec_2E_3C @ C @ A ) ),
inference(pattern_uni,[status(thm)],[366:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(384,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ B ) @ C ) @ A )
= C )
| ~ ( c_2Eprim__rec_2E_3C @ C @ A ) ),
inference(simp,[status(thm)],[367]) ).
thf(7266,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(paramod_ordered,[status(thm)],[3069,6865]) ).
thf(7283,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[7266]) ).
thf(7290,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[7283]) ).
thf(7323,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,7290]) ).
thf(7332,plain,
! [A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[7323:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7338,plain,
! [A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[7332]) ).
thf(14231,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[14140,7338]) ).
thf(14274,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14231]) ).
thf(14354,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14274]) ).
thf(4,axiom,
! [A: $o] :
( c_2Ebool_2EF
=> A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).
thf(42,plain,
! [A: $o] :
( c_2Ebool_2EF
=> A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MONO__EQ) ).
thf(126,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(127,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) ),
inference(cnf,[status(esa)],[126]) ).
thf(128,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) ),
inference(lifteq,[status(thm)],[127]) ).
thf(282,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) )
| ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[140,128]) ).
thf(283,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ A ) )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( c_2Enum_2E0 ))]]) ).
thf(301,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ A ) )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
inference(simp,[status(thm)],[283]) ).
thf(3,axiom,
! [A: $o] :
( ( A
=> c_2Ebool_2EF )
=> ~ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__F) ).
thf(37,plain,
! [A: $o] :
( ( A
=> c_2Ebool_2EF )
=> ~ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(377,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ A )
| ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ A ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ A )
!= ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(simp,[status(thm)],[370]) ).
thf(389,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ A )
| ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ A ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ A )
!= ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(simp,[status(thm)],[377]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: $o,B: TB > TA,C: TB > TA,D: TB] :
( ( c_2Ebool_2ECOND @ ( TB > TA ) @ A @ B @ C @ D )
= ( c_2Ebool_2ECOND @ TA @ A @ ( B @ D ) @ ( C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__RATOR) ).
thf(147,plain,
! [TA: $tType,TB: $tType,A: $o,B: TB > TA,C: TB > TA,D: TB] :
( ( c_2Ebool_2ECOND @ ( TB > TA ) @ A @ B @ C @ D )
= ( c_2Ebool_2ECOND @ TA @ A @ ( B @ D ) @ ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(148,plain,
! [TA: $tType,TB: $tType,D: TA,C: TA > TB,B: TA > TB,A: $o] :
( ( c_2Ebool_2ECOND @ ( TA > TB ) @ A @ B @ C @ D )
= ( c_2Ebool_2ECOND @ TB @ A @ ( B @ D ) @ ( C @ D ) ) ),
inference(cnf,[status(esa)],[147]) ).
thf(149,plain,
! [TA: $tType,TB: $tType,D: TA,C: TA > TB,B: TA > TB,A: $o] :
( ( c_2Ebool_2ECOND @ ( TA > TB ) @ A @ B @ C @ D )
= ( c_2Ebool_2ECOND @ TB @ A @ ( B @ D ) @ ( C @ D ) ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(6860,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
!= c_2Enum_2E0 )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,6831]) ).
thf(6863,plain,
! [A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 ),
inference(pre_uni,[status(thm)],[6860:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(6866,plain,
! [A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 ),
inference(simp,[status(thm)],[6863]) ).
thf(7245,plain,
! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[149,6866]) ).
thf(7255,plain,
! [TA: $tType,B: $o,A: TA] :
( ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT1
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ A ) ) )
!= c_2Enum_2E0 ),
inference(pre_uni,[status(thm)],[7245:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7262,plain,
! [TA: $tType,B: $o,A: TA] :
( ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT1
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ A ) ) )
!= c_2Enum_2E0 ),
inference(simp,[status(thm)],[7255]) ).
thf(280,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) )
| ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
!= ( c_2Enum_2ESUC @ B ) ) ),
inference(paramod_ordered,[status(thm)],[140,128]) ).
thf(281,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( A )),bind(B,$thf( c_2Enum_2E0 ))]]) ).
thf(3341,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[157,281]) ).
thf(3342,plain,
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ c_2Enum_2E0 ) ),
inference(pattern_uni,[status(thm)],[3341:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(15418,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,14358]) ).
thf(15424,plain,
! [A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[15418:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(15426,plain,
! [A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[15424]) ).
thf(7326,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,7290]) ).
thf(7328,plain,
! [A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[7326:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7334,plain,
! [A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[7328]) ).
thf(14214,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[14140,7334]) ).
thf(14311,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14214]) ).
thf(14391,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14311]) ).
thf(1574,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[165,262]) ).
thf(1805,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1574:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(2185,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[1805]) ).
thf(159,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(cnf,[status(esa)],[158]) ).
thf(161,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(lifteq,[status(thm)],[159]) ).
thf(38,plain,
( ( $true
=> c_2Ebool_2EF )
=> ~ $true ),
inference(instance,[status(thm)],[37]) ).
thf(39,plain,
~ c_2Ebool_2EF,
inference(simp,[status(thm)],[38]) ).
thf(328,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $false @ A @ B )
= B ),
inference(rewrite,[status(thm)],[161,39]) ).
thf(474,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ $false @ A @ B )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[328,390]) ).
thf(497,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( c_2Earithmetic_2EEVEN @ sk1 )
| ( A != c_2Enum_2E0 )
| ( B
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[474]) ).
thf(510,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(simp,[status(thm)],[497]) ).
thf(286,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Enum_2ESUC @ B ) ) ),
inference(paramod_ordered,[status(thm)],[157,128]) ).
thf(287,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pattern_uni,[status(thm)],[286:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(3926,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
| ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[140,287]) ).
thf(3927,plain,
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pattern_uni,[status(thm)],[3926:[bind(A,$thf( c_2Enum_2E0 ))]]) ).
thf(4104,plain,
c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ),
inference(rewrite,[status(thm)],[3927,258]) ).
thf(15501,plain,
! [A: tyop_2Enum_2Enum] :
( ~ $true
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(rewrite,[status(thm)],[510,4104]) ).
thf(15502,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(simp,[status(thm)],[15501]) ).
thf(15525,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
!= sk1 )
| ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ $false @ A @ B )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[328,15502]) ).
thf(15549,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
!= sk1 )
| ( c_2Earithmetic_2EEVEN @ sk1 )
| ( A != c_2Enum_2E0 )
| ( B
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[15525]) ).
thf(15593,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[15549]) ).
thf(18385,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ) ),
inference(rewrite,[status(thm)],[15593,146]) ).
thf(18194,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[3069,15426]) ).
thf(18221,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[18194]) ).
thf(18236,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[18221]) ).
thf(6252,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[125,6248]) ).
thf(6253,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(pattern_uni,[status(thm)],[6252:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(9839,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) @ E )
!= sk1 )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,9818]) ).
thf(9844,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B )
!= sk1 ),
inference(pre_uni,[status(thm)],[9839:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(9848,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B )
!= sk1 ),
inference(simp,[status(thm)],[9844]) ).
thf(9959,plain,
! [D: tyop_2Enum_2Enum,C: $o,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[125,9848]) ).
thf(9960,plain,
! [B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[9959:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ G @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( B ))]]) ).
thf(9985,plain,
! [B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[9960]) ).
thf(14192,plain,
! [C: $o,B: tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[14140,9985]) ).
thf(14252,plain,
! [C: $o,B: tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
!= sk1 )
| ( A != C )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14192]) ).
thf(14331,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14252]) ).
thf(7237,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[3069,6866]) ).
thf(7250,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[7237]) ).
thf(7258,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[7250]) ).
thf(7303,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
!= c_2Earithmetic_2EZERO )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,7258]) ).
thf(7306,plain,
! [A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
!= c_2Earithmetic_2EZERO ) ),
inference(pre_uni,[status(thm)],[7303:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7314,plain,
! [A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[7306]) ).
thf(14174,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[14140,7314]) ).
thf(14268,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Earithmetic_2EZERO )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14174]) ).
thf(14346,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14268]) ).
thf(9841,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) @ E )
!= sk1 )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[165,9818]) ).
thf(9843,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
!= sk1 ),
inference(pre_uni,[status(thm)],[9841:[bind(A,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(9847,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
!= sk1 ),
inference(simp,[status(thm)],[9843]) ).
thf(11755,plain,
! [D: tyop_2Enum_2Enum,C: $o,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[125,9847]) ).
thf(11756,plain,
! [B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[11755:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ F @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( B ))]]) ).
thf(11793,plain,
! [B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[11756]) ).
thf(33,axiom,
! [A: $o,B: $o,C: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
= ( ( ~ A
| B )
& ( A
| C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__EXPAND) ).
thf(169,plain,
! [A: $o,B: $o,C: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
= ( ( ~ A
| B )
& ( A
| C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(184,plain,
( ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $false )
= ( ( ~ $true
| $false )
& ( $true
| $false ) ) ),
inference(instance,[status(thm)],[169]) ).
thf(185,plain,
~ ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $false ),
inference(simp,[status(thm)],[184]) ).
thf(329,plain,
! [B: $o,A: $o] :
( ~ B
| ( ( c_2Ebool_2ECOND @ $o @ $false @ A @ B )
!= ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $false ) ) ),
inference(paramod_ordered,[status(thm)],[328,185]) ).
thf(349,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ $o @ $false @ A @ $true )
!= ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $false ) ),
inference(simp,[status(thm)],[329]) ).
thf(393,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ $false @ A @ $true ),
inference(rewrite,[status(thm)],[349,185]) ).
thf(681,plain,
! [TA: $tType,E: $o,D: TA,C: TA > $o,B: TA > $o,A: $o] :
( ( c_2Ebool_2ECOND @ ( TA > $o ) @ A @ B @ C @ D )
| ( ( c_2Ebool_2ECOND @ $o @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ $o @ $false @ E @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[149,393]) ).
thf(773,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ $false @ A
@ ^ [C: TA] : $true
@ B ),
inference(pre_uni,[status(thm)],[681:[bind(A,$thf( $false )),bind(B,$thf( B )),bind(C,$thf( ^ [F: TA] : $true )),bind(D,$thf( D )),bind(E,$thf( B @ D ))]]) ).
thf(806,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ $false @ A
@ ^ [C: TA] : $true
@ B ),
inference(simp,[status(thm)],[773]) ).
thf(1451,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > $o] :
( ~ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Ebool_2EF ) ),
inference(paramod_ordered,[status(thm)],[165,39]) ).
thf(1745,plain,
! [A: $o] :
~ ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2EF @ c_2Ebool_2EF ),
inference(pre_uni,[status(thm)],[1451:[bind(A,$thf( ^ [E: TA] : c_2Ebool_2EF ))]]) ).
thf(2131,plain,
! [A: $o] :
~ ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2EF @ c_2Ebool_2EF ),
inference(simp,[status(thm)],[1745]) ).
thf(2410,plain,
! [A: $o] :
~ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ),
inference(rewrite,[status(thm)],[2131,39]) ).
thf(2417,plain,
! [TA: $tType,E: $o,D: TA,C: TA > $o,B: TA > $o,A: $o] :
( ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A @ B @ C @ D )
| ( ( c_2Ebool_2ECOND @ $o @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ $o @ E @ $false @ $false ) ) ),
inference(paramod_ordered,[status(thm)],[149,2410]) ).
thf(2435,plain,
! [TA: $tType,B: $o,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ B
@ ^ [C: TA] : $false
@ ^ [C: TA] : $false
@ A ),
inference(pre_uni,[status(thm)],[2417:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : $false )),bind(C,$thf( ^ [F: TA] : $false ))]]) ).
thf(2437,plain,
! [TA: $tType,B: $o,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ B
@ ^ [C: TA] : $false
@ ^ [C: TA] : $false
@ A ),
inference(simp,[status(thm)],[2435]) ).
thf(9,axiom,
! [A: $o] :
( A
=> ( ~ A
=> c_2Ebool_2EF ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV__IMP) ).
thf(61,plain,
! [A: $o] :
( A
=> ( ~ A
=> c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18213,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[14140,15426]) ).
thf(18229,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[18213]) ).
thf(18241,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[18229]) ).
thf(1453,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Enum_2ESUC @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Enum_2E0 ) ),
inference(paramod_ordered,[status(thm)],[165,140]) ).
thf(1903,plain,
! [A: $o] :
( ( c_2Enum_2ESUC @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[1453:[bind(A,$thf( ^ [E: TA] : c_2Enum_2E0 ))]]) ).
thf(2278,plain,
! [A: $o] :
( ( c_2Enum_2ESUC @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[1903]) ).
thf(2854,plain,
! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Enum_2ESUC @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Enum_2E0 @ c_2Enum_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[149,2278]) ).
thf(2869,plain,
! [TA: $tType,B: $o,A: TA] :
( ( c_2Enum_2ESUC
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Enum_2E0
@ ^ [C: TA] : c_2Enum_2E0
@ A ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[2854:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Enum_2E0 )),bind(C,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).
thf(2884,plain,
! [TA: $tType,B: $o,A: TA] :
( ( c_2Enum_2ESUC
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Enum_2E0
@ ^ [C: TA] : c_2Enum_2E0
@ A ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[2869]) ).
thf(174,plain,
( ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false )
= ( ( ~ $false
| $true )
& ( $false
| $false ) ) ),
inference(instance,[status(thm)],[169]) ).
thf(175,plain,
~ ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false ),
inference(simp,[status(thm)],[174]) ).
thf(419,plain,
! [B: $o,A: $o] :
( ~ A
| ( ( c_2Ebool_2ECOND @ $o @ $true @ A @ B )
!= ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false ) ) ),
inference(paramod_ordered,[status(thm)],[413,175]) ).
thf(434,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A )
!= ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false ) ),
inference(simp,[status(thm)],[419]) ).
thf(442,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A )
!= ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false ) ),
inference(simp,[status(thm)],[434]) ).
thf(448,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A ),
inference(rewrite,[status(thm)],[442,175]) ).
thf(668,plain,
! [TA: $tType,E: TA,D: TA > $o,C: TA > $o,B: $o,A: $o] :
( ( c_2Ebool_2ECOND @ ( TA > $o ) @ B @ C @ D @ E )
| ( ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A )
!= ( c_2Ebool_2ECOND @ $o @ B @ ( C @ E ) @ ( D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[448,149]) ).
thf(777,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [C: TA] : $true
@ A
@ B ),
inference(pre_uni,[status(thm)],[668:[bind(A,$thf( D @ E )),bind(B,$thf( $true )),bind(C,$thf( ^ [F: TA] : $true ))]]) ).
thf(810,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [C: TA] : $true
@ A
@ B ),
inference(simp,[status(thm)],[777]) ).
thf(360,plain,
! [E: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ E @ C ) @ D ) @ C )
= D )
| ~ ( c_2Eprim__rec_2E_3C @ A @ B )
| ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
!= ( c_2Eprim__rec_2E_3C @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[128,133]) ).
thf(361,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Enum_2ESUC @ C ) ) @ ( c_2Enum_2ESUC @ B ) ) @ ( c_2Enum_2ESUC @ C ) )
= ( c_2Enum_2ESUC @ B ) )
| ~ ( c_2Eprim__rec_2E_3C @ B @ C ) ),
inference(pattern_uni,[status(thm)],[360:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( c_2Enum_2ESUC @ G )),bind(D,$thf( c_2Enum_2ESUC @ F ))]]) ).
thf(381,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Enum_2ESUC @ C ) ) @ ( c_2Enum_2ESUC @ B ) ) @ ( c_2Enum_2ESUC @ C ) )
= ( c_2Enum_2ESUC @ B ) )
| ~ ( c_2Eprim__rec_2E_3C @ B @ C ) ),
inference(simp,[status(thm)],[361]) ).
thf(7296,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,7258]) ).
thf(7310,plain,
! [A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(pre_uni,[status(thm)],[7296:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7318,plain,
! [A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[7310]) ).
thf(12095,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[3069,7318]) ).
thf(12119,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[12095]) ).
thf(12132,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[12119]) ).
thf(176,plain,
( ( c_2Ebool_2ECOND @ $o @ $false @ $false @ $false )
= ( ( ~ $false
| $false )
& ( $false
| $false ) ) ),
inference(instance,[status(thm)],[169]) ).
thf(177,plain,
~ ( c_2Ebool_2ECOND @ $o @ $false @ $false @ $false ),
inference(simp,[status(thm)],[176]) ).
thf(725,plain,
! [TA: $tType,D: TA,C: TA > $o,B: TA > $o,A: $o] :
( ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A @ B @ C @ D )
| ( ( c_2Ebool_2ECOND @ $o @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ $o @ $false @ $false @ $false ) ) ),
inference(paramod_ordered,[status(thm)],[149,177]) ).
thf(756,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
@ ^ [B: TA] : $false
@ ^ [B: TA] : $false
@ A ),
inference(pre_uni,[status(thm)],[725:[bind(A,$thf( $false )),bind(B,$thf( ^ [E: TA] : $false )),bind(C,$thf( ^ [E: TA] : $false ))]]) ).
thf(847,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
@ ^ [B: TA] : $false
@ ^ [B: TA] : $false
@ A ),
inference(simp,[status(thm)],[756]) ).
thf(1394,plain,
! [TA: $tType,TC: $tType,E: TC,D: TA,C: TA,B: $o,A: TA > $o] :
( ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $false
@ ^ [F: TC] : ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) )
@ ^ [F: TC] : $false
@ E )
| ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[165,847]) ).
thf(1674,plain,
! [TC: $tType,B: TC,A: $o] :
~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $false
@ ^ [C: TC] : ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
@ ^ [C: TC] : $false
@ B ),
inference(pre_uni,[status(thm)],[1394:[bind(A,$thf( ^ [F: TA] : $false ))]]) ).
thf(2061,plain,
! [TA: $tType,B: TA,A: $o] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
@ ^ [C: TA] : ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
@ ^ [C: TA] : $false
@ B ),
inference(simp,[status(thm)],[1674]) ).
thf(2424,plain,
! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > $o] :
( ~ ( c_2Ebool_2ECOND @ $o @ E @ $false @ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) ) )
| ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[165,2410]) ).
thf(2430,plain,
! [B: $o,A: $o] :
~ ( c_2Ebool_2ECOND @ $o @ B @ $false @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ) ),
inference(pre_uni,[status(thm)],[2424:[bind(A,$thf( ^ [F: TA] : $false ))]]) ).
thf(2439,plain,
! [B: $o,A: $o] :
~ ( c_2Ebool_2ECOND @ $o @ B @ $false @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ) ),
inference(simp,[status(thm)],[2430]) ).
thf(4069,plain,
! [A: $o] :
~ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ),
inference(rewrite,[status(thm)],[2439,2410]) ).
thf(5334,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
@ ^ [B: TA] : $false
@ ^ [B: TA] : $false
@ A ),
inference(rewrite,[status(thm)],[2061,4069]) ).
thf(4121,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[165,4104]) ).
thf(4151,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[4121:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(4172,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[4151]) ).
thf(1305,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > $o] :
( ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) )
| ( c_2Ebool_2ET
!= ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[52,165]) ).
thf(1601,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2ET @ c_2Ebool_2ET ),
inference(pre_uni,[status(thm)],[1305:[bind(A,$thf( ^ [E: TA] : c_2Ebool_2ET ))]]) ).
thf(1996,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2ET @ c_2Ebool_2ET ),
inference(simp,[status(thm)],[1601]) ).
thf(2346,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ),
inference(rewrite,[status(thm)],[1996,52]) ).
thf(2364,plain,
! [TB: $tType,E: $o,D: $o,C: $o,B: $o > TB,A: $o] :
( ( ( B @ $true )
= ( c_2Ebool_2ECOND @ TB @ C @ ( B @ D ) @ ( B @ E ) ) )
| ( ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true )
!= ( c_2Ebool_2ECOND @ $o @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[2346,165]) ).
thf(2365,plain,
! [TB: $tType,B: $o > TB,A: $o] :
( ( c_2Ebool_2ECOND @ TB @ A @ ( B @ $true ) @ ( B @ $true ) )
= ( B @ $true ) ),
inference(pattern_uni,[status(thm)],[2364:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( $true )),bind(E,$thf( $true ))]]) ).
thf(2409,plain,
! [TA: $tType,B: $o > TA,A: $o] :
( ( c_2Ebool_2ECOND @ TA @ A @ ( B @ $true ) @ ( B @ $true ) )
= ( B @ $true ) ),
inference(simp,[status(thm)],[2365]) ).
thf(284,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
| ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
!= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[128,135]) ).
thf(297,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
| ( ( c_2Enum_2ESUC @ A )
!= c_2Enum_2E0 )
| ( ( c_2Enum_2ESUC @ B )
!= ( c_2Enum_2ESUC @ C ) ) ),
inference(simp,[status(thm)],[284]) ).
thf(4119,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,4104]) ).
thf(4136,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[4119:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(4160,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[4136]) ).
thf(9963,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ C )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[3069,9848]) ).
thf(9980,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ C )
!= sk1 )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[9963]) ).
thf(9993,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ A )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[9980]) ).
thf(1564,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[165,36]) ).
thf(1681,plain,
! [A: $o] :
( ( c_2Earithmetic_2EMOD @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ sk1 @ sk1 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1564:[bind(A,$thf( ^ [E: TA] : sk1 ))]]) ).
thf(2068,plain,
! [A: $o] :
( ( c_2Earithmetic_2EMOD @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ sk1 @ sk1 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[1681]) ).
thf(3076,plain,
! [TB: $tType,E: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,C: $o,B: tyop_2Enum_2Enum > TB,A: $o] :
( ( ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Ebool_2ECOND @ TB @ C @ ( B @ D ) @ ( B @ E ) ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[3069,165]) ).
thf(3077,plain,
! [TB: $tType,B: tyop_2Enum_2Enum > TB,A: $o] :
( ( c_2Ebool_2ECOND @ TB @ A @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pattern_uni,[status(thm)],[3076:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(E,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(3144,plain,
! [TA: $tType,B: tyop_2Enum_2Enum > TA,A: $o] :
( ( c_2Ebool_2ECOND @ TA @ A @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[3077]) ).
thf(9822,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
!= sk1 )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,9804]) ).
thf(9825,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[9822:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(9829,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[9825]) ).
thf(1512,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[165,258]) ).
thf(1927,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1512:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(2300,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[1927]) ).
thf(7,axiom,
c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(53,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1508,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,258]) ).
thf(1910,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1508:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2284,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[1910]) ).
thf(3030,plain,
! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[149,2284]) ).
thf(3050,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT1
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ A ) ) ) ),
inference(pre_uni,[status(thm)],[3030:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(3060,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT1
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ A ) ) ) ),
inference(simp,[status(thm)],[3050]) ).
thf(3308,plain,
! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(paramod_ordered,[status(thm)],[149,2300]) ).
thf(3312,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
@ A ) ) ),
inference(pre_uni,[status(thm)],[3308:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(3326,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
@ A ) ) ),
inference(simp,[status(thm)],[3312]) ).
thf(13486,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[3069,7338]) ).
thf(13515,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[13486]) ).
thf(13527,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[13515]) ).
thf(9919,plain,
! [D: tyop_2Enum_2Enum,C: $o,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[125,9829]) ).
thf(9920,plain,
! [B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ A )
!= sk1 ),
inference(pattern_uni,[status(thm)],[9919:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ G @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )),bind(C,$thf( G )),bind(D,$thf( A ))]]) ).
thf(9944,plain,
! [B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ A )
!= sk1 ),
inference(simp,[status(thm)],[9920]) ).
thf(10081,plain,
! [TA: $tType,F: $o,E: tyop_2Enum_2Enum,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) ) @ E )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ F @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[149,9944]) ).
thf(10084,plain,
! [TA: $tType,C: $o,B: tyop_2Enum_2Enum,A: TA] :
( ( c_2Earithmetic_2E_2A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ C
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ A ) ) )
@ B )
!= sk1 ),
inference(pre_uni,[status(thm)],[10081:[bind(A,$thf( F )),bind(B,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(10094,plain,
! [TA: $tType,C: $o,B: tyop_2Enum_2Enum,A: TA] :
( ( c_2Earithmetic_2E_2A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ C
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ A ) ) )
@ B )
!= sk1 ),
inference(simp,[status(thm)],[10084]) ).
thf(16,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET
& A )
= A )
& ( ( A
& c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF
& A )
= c_2Ebool_2EF )
& ( ( A
& c_2Ebool_2EF )
= c_2Ebool_2EF )
& ( ( A
& A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__CLAUSES) ).
thf(109,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET
& A )
= A )
& ( ( A
& c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF
& A )
= c_2Ebool_2EF )
& ( ( A
& c_2Ebool_2EF )
= c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(493,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[262,390]) ).
thf(504,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[493]) ).
thf(515,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 ) ),
inference(simp,[status(thm)],[504]) ).
thf(14160,plain,
! [TB: $tType,E: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,C: $o,B: tyop_2Enum_2Enum > TB,A: $o] :
( ( ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Ebool_2ECOND @ TB @ C @ ( B @ D ) @ ( B @ E ) ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[14140,165]) ).
thf(14161,plain,
! [TB: $tType,B: tyop_2Enum_2Enum > TB,A: $o] :
( ( c_2Ebool_2ECOND @ TB @ A @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
= ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pattern_uni,[status(thm)],[14160:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(E,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(14369,plain,
! [TA: $tType,B: tyop_2Enum_2Enum > TA,A: $o] :
( ( c_2Ebool_2ECOND @ TA @ A @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
= ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[14161]) ).
thf(3363,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ) )
| ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[140,281]) ).
thf(3364,plain,
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ c_2Enum_2E0 ) ),
inference(pattern_uni,[status(thm)],[3363:[bind(A,$thf( c_2Enum_2E0 ))]]) ).
thf(9824,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
!= sk1 )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[165,9804]) ).
thf(9827,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[9824:[bind(A,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(9831,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[9827]) ).
thf(10787,plain,
! [D: tyop_2Enum_2Enum,C: $o,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[125,9831]) ).
thf(10788,plain,
! [B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ A )
!= sk1 ),
inference(pattern_uni,[status(thm)],[10787:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ F @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )),bind(C,$thf( F )),bind(D,$thf( A ))]]) ).
thf(10815,plain,
! [B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ A )
!= sk1 ),
inference(simp,[status(thm)],[10788]) ).
thf(1319,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,157]) ).
thf(1652,plain,
! [A: $o] :
( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[1319:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2043,plain,
! [A: $o] :
( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[1652]) ).
thf(9972,plain,
! [TA: $tType,F: tyop_2Enum_2Enum,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) ) @ F )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[149,9848]) ).
thf(9983,plain,
! [TA: $tType,C: tyop_2Enum_2Enum,B: $o,A: TA] :
( ( c_2Earithmetic_2E_2A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ A ) ) )
@ C )
!= sk1 ),
inference(pre_uni,[status(thm)],[9972:[bind(A,$thf( E )),bind(B,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(9996,plain,
! [TA: $tType,C: tyop_2Enum_2Enum,B: $o,A: TA] :
( ( c_2Earithmetic_2E_2A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ A ) ) )
@ C )
!= sk1 ),
inference(simp,[status(thm)],[9983]) ).
thf(14395,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: $o,C: TA,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ D
@ ^ [F: TA] : c_2Earithmetic_2EZERO
@ ^ [F: TA] : c_2Earithmetic_2EZERO
@ C ) ) )
@ E ) ) ),
inference(paramod_ordered,[status(thm)],[125,9996]) ).
thf(14396,plain,
! [TA: $tType,C: TA,B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ C ) ) ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[14395:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ H @ ^ [H: TA] : c_2Earithmetic_2EZERO @ ^ [H: TA] : c_2Earithmetic_2EZERO @ K ) ) )),bind(B,$thf( B )),bind(C,$thf( K )),bind(D,$thf( H )),bind(E,$thf( B ))]]) ).
thf(14433,plain,
! [TA: $tType,C: TA,B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ C ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[14396]) ).
thf(584,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) )
!= ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[140,576]) ).
thf(586,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
!= c_2Enum_2E0 ) ),
inference(simp,[status(thm)],[584]) ).
thf(14232,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ C )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[14140,9848]) ).
thf(14257,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ C )
!= sk1 )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14232]) ).
thf(14335,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ A )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14257]) ).
thf(1318,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[165,157]) ).
thf(1761,plain,
! [A: $o] :
( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[1318:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(2144,plain,
! [A: $o] :
( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[1761]) ).
thf(291,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
| ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
!= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[258,128]) ).
thf(298,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
| ( ( c_2Enum_2ESUC @ A )
!= c_2Enum_2E0 )
| ( ( c_2Enum_2ESUC @ B )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[291]) ).
thf(362,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ B ) @ C ) @ B )
= C )
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) )
!= ( c_2Eprim__rec_2E_3C @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[135,133]) ).
thf(363,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Enum_2ESUC @ B ) ) @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ B ) )
= c_2Enum_2E0 ),
inference(pattern_uni,[status(thm)],[362:[bind(A,$thf( E )),bind(B,$thf( c_2Enum_2ESUC @ E )),bind(C,$thf( c_2Enum_2E0 ))]]) ).
thf(382,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Enum_2ESUC @ B ) ) @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ B ) )
= c_2Enum_2E0 ),
inference(simp,[status(thm)],[363]) ).
thf(7459,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Enum_2ESUC @ B ) ) @ ( c_2Enum_2ESUC @ B ) )
= c_2Enum_2E0 ),
inference(rewrite,[status(thm)],[382,168]) ).
thf(1337,plain,
! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > $o] :
( ( c_2Ebool_2ECOND @ $o @ $true @ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) ) @ E )
| ~ ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[165,448]) ).
thf(1580,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ $true @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) @ B ),
inference(pre_uni,[status(thm)],[1337:[bind(A,$thf( ^ [F: TA] : $true ))]]) ).
thf(1977,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ $true @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) @ B ),
inference(simp,[status(thm)],[1580]) ).
thf(3523,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A ),
inference(rewrite,[status(thm)],[1977,2346]) ).
thf(285,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ B @ C )
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) )
!= ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ B ) @ ( c_2Enum_2ESUC @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[135,128]) ).
thf(296,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ B @ C )
| ( ( c_2Enum_2ESUC @ B )
!= c_2Enum_2E0 )
| ( ( c_2Enum_2ESUC @ A )
!= ( c_2Enum_2ESUC @ C ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(3254,plain,
! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(paramod_ordered,[status(thm)],[149,2185]) ).
thf(3268,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
@ A ) ) ),
inference(pre_uni,[status(thm)],[3254:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(3274,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
@ A ) ) ),
inference(simp,[status(thm)],[3268]) ).
thf(1572,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Enum_2E0 ) ),
inference(paramod_ordered,[status(thm)],[165,262]) ).
thf(1657,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[1572:[bind(A,$thf( ^ [E: TA] : c_2Enum_2E0 ))]]) ).
thf(2048,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[1657]) ).
thf(1571,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,262]) ).
thf(1811,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1571:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2191,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[1811]) ).
thf(2757,plain,
! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[149,2191]) ).
thf(2775,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ A ) ) ) ),
inference(pre_uni,[status(thm)],[2757:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2791,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ A ) ) ) ),
inference(simp,[status(thm)],[2775]) ).
thf(2354,plain,
! [TA: $tType,E: TA,D: TA > $o,C: TA > $o,B: $o,A: $o] :
( ( c_2Ebool_2ECOND @ ( TA > $o ) @ B @ C @ D @ E )
| ( ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true )
!= ( c_2Ebool_2ECOND @ $o @ B @ ( C @ E ) @ ( D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[2346,149]) ).
thf(2383,plain,
! [TA: $tType,B: TA,A: $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ A
@ ^ [C: TA] : $true
@ ^ [C: TA] : $true
@ B ),
inference(pre_uni,[status(thm)],[2354:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( ^ [F: TA] : $true )),bind(D,$thf( ^ [F: TA] : $true ))]]) ).
thf(2398,plain,
! [TA: $tType,B: TA,A: $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ A
@ ^ [C: TA] : $true
@ ^ [C: TA] : $true
@ B ),
inference(simp,[status(thm)],[2383]) ).
thf(11,axiom,
! [A: $o,B: $o] :
( ( ~ ( ~ B
| A )
=> c_2Ebool_2EF )
= ( B
=> ( ~ A
=> c_2Ebool_2EF ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL3) ).
thf(71,plain,
! [A: $o,B: $o] :
( ( ~ ( ~ B
| A )
=> c_2Ebool_2EF )
= ( B
=> ( ~ A
=> c_2Ebool_2EF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1248,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,1014]) ).
thf(1936,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(pre_uni,[status(thm)],[1248:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2308,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(simp,[status(thm)],[1936]) ).
thf(3900,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[157,287]) ).
thf(3901,plain,
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pattern_uni,[status(thm)],[3900:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(5033,plain,
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ c_2Enum_2E0 ) ),
inference(rewrite,[status(thm)],[3901,3364]) ).
thf(8,axiom,
! [A: $o] :
( ( A = c_2Ebool_2ET )
| ( A = c_2Ebool_2EF ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EBOOL__CASES__AX) ).
thf(54,plain,
! [A: $o] :
( ( A = c_2Ebool_2ET )
| ( A = c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1420,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) @ E ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[165,985]) ).
thf(1842,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B ) ),
inference(pre_uni,[status(thm)],[1420:[bind(A,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(2220,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B ) ),
inference(simp,[status(thm)],[1842]) ).
thf(1510,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Enum_2E0 ) ),
inference(paramod_ordered,[status(thm)],[165,258]) ).
thf(1772,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[1510:[bind(A,$thf( ^ [E: TA] : c_2Enum_2E0 ))]]) ).
thf(2155,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[1772]) ).
thf(2693,plain,
! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Enum_2E0 @ c_2Enum_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[149,2155]) ).
thf(2703,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Enum_2E0
@ ^ [C: TA] : c_2Enum_2E0
@ A )
@ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[2693:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Enum_2E0 )),bind(C,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).
thf(2721,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Enum_2E0
@ ^ [C: TA] : c_2Enum_2E0
@ A )
@ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[2703]) ).
thf(14218,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ C )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(paramod_ordered,[status(thm)],[14140,9847]) ).
thf(14284,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ C )
!= sk1 )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[14218]) ).
thf(14364,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ A )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[14284]) ).
thf(4118,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,4104]) ).
thf(4156,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[4118:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(4176,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[4156]) ).
thf(373,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ A @ B )
= C )
| ~ ( c_2Eprim__rec_2E_3C @ C @ B )
| ( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
!= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[168,133]) ).
thf(374,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ B )
= c_2Enum_2E0 )
| ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) ),
inference(pattern_uni,[status(thm)],[373:[bind(A,$thf( c_2Earithmetic_2E_2A @ E @ F )),bind(B,$thf( F )),bind(C,$thf( c_2Enum_2E0 )),bind(D,$thf( E ))]]) ).
thf(387,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ B )
= c_2Enum_2E0 )
| ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) ),
inference(simp,[status(thm)],[374]) ).
thf(1417,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) @ E ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,985]) ).
thf(1973,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B ) ),
inference(pre_uni,[status(thm)],[1417:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2343,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B ) ),
inference(simp,[status(thm)],[1973]) ).
thf(10,axiom,
( ! [A: $o] :
( ( ~ ~ A )
= A )
& ( ~ c_2Ebool_2ET = c_2Ebool_2EF )
& ( ~ c_2Ebool_2EF = c_2Ebool_2ET ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__CLAUSES) ).
thf(66,plain,
( ( ~ c_2Ebool_2ET = c_2Ebool_2EF )
& ( ~ c_2Ebool_2EF = c_2Ebool_2ET ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1503,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) @ E ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,576]) ).
thf(1789,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B ) ) ),
inference(pre_uni,[status(thm)],[1503:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2171,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B ) ) ),
inference(simp,[status(thm)],[1789]) ).
thf(1560,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,36]) ).
thf(1700,plain,
! [A: $o] :
( ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1560:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2086,plain,
! [A: $o] :
( ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[1700]) ).
thf(13075,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[3069,7334]) ).
thf(13098,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[13075]) ).
thf(13112,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[13098]) ).
thf(12,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET
=> A )
= A )
& ( ( A
=> c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> A )
= c_2Ebool_2ET )
& ( ( A
=> A )
= c_2Ebool_2ET )
& ( ( A
=> c_2Ebool_2EF )
= ~ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
thf(80,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET
=> A )
= A )
& ( ( A
=> c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> A )
= c_2Ebool_2ET )
& c_2Ebool_2ET
& ( ( A
=> c_2Ebool_2EF )
= ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(476,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ A @ B )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
!= ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[128,390]) ).
thf(505,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ A @ B )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Enum_2ESUC @ A )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
| ( ( c_2Enum_2ESUC @ B )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[476]) ).
thf(1251,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[165,1014]) ).
thf(1773,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(pre_uni,[status(thm)],[1251:[bind(A,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(2156,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(simp,[status(thm)],[1773]) ).
thf(7239,plain,
! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Earithmetic_2EZERO @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,6866]) ).
thf(7253,plain,
! [B: $o,A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 ),
inference(pre_uni,[status(thm)],[7239:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7260,plain,
! [B: $o,A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 ),
inference(simp,[status(thm)],[7253]) ).
thf(486,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ A ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[125,390]) ).
thf(487,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[486:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(14,axiom,
! [A: $o,B: $o] :
( ( ~ ( B
| A )
=> c_2Ebool_2EF )
= ( ( B
=> c_2Ebool_2EF )
=> ( ~ A
=> c_2Ebool_2EF ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL2) ).
thf(95,plain,
! [A: $o,B: $o] :
( ( ~ ( B
| A )
=> c_2Ebool_2EF )
= ( ( B
=> c_2Ebool_2EF )
=> ( ~ A
=> c_2Ebool_2EF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9932,plain,
! [TA: $tType,F: tyop_2Enum_2Enum,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ F @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[149,9829]) ).
thf(9936,plain,
! [TA: $tType,C: tyop_2Enum_2Enum,B: $o,A: TA] :
( ( c_2Earithmetic_2E_2A @ C
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ A ) ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[9932:[bind(A,$thf( E )),bind(B,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(9948,plain,
! [TA: $tType,C: tyop_2Enum_2Enum,B: $o,A: TA] :
( ( c_2Earithmetic_2E_2A @ C
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ A ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[9936]) ).
thf(10503,plain,
! [TA: $tType,F: $o,E: tyop_2Enum_2Enum,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ F @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[149,9985]) ).
thf(10511,plain,
! [TA: $tType,C: $o,B: tyop_2Enum_2Enum,A: TA] :
( ( c_2Earithmetic_2E_2A @ B
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ C
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ A ) ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[10503:[bind(A,$thf( F )),bind(B,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(10521,plain,
! [TA: $tType,C: $o,B: tyop_2Enum_2Enum,A: TA] :
( ( c_2Earithmetic_2E_2A @ B
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ C
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ A ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[10511]) ).
thf(701,plain,
! [TA: $tType,D: TA,C: TA > $o,B: TA > $o,A: $o] :
( ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A @ B @ C @ D )
| ( ( c_2Ebool_2ECOND @ $o @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false ) ) ),
inference(paramod_ordered,[status(thm)],[149,175]) ).
thf(761,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
@ ^ [B: TA] : $true
@ ^ [B: TA] : $false
@ A ),
inference(pre_uni,[status(thm)],[701:[bind(A,$thf( $false )),bind(B,$thf( ^ [E: TA] : $true )),bind(C,$thf( ^ [E: TA] : $false ))]]) ).
thf(852,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
@ ^ [B: TA] : $true
@ ^ [B: TA] : $false
@ A ),
inference(simp,[status(thm)],[761]) ).
thf(1401,plain,
! [TA: $tType,TC: $tType,E: TC,D: TA,C: TA,B: $o,A: TA > $o] :
( ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) )
@ ^ [F: TC] : $true
@ ^ [F: TC] : $false
@ E )
| ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[165,852]) ).
thf(1598,plain,
! [TC: $tType,B: TC,A: $o] :
~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
@ ^ [C: TC] : $true
@ ^ [C: TC] : $false
@ B ),
inference(pre_uni,[status(thm)],[1401:[bind(A,$thf( ^ [F: TA] : $false ))]]) ).
thf(1993,plain,
! [TA: $tType,B: TA,A: $o] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
@ ^ [C: TA] : $true
@ ^ [C: TA] : $false
@ B ),
inference(simp,[status(thm)],[1598]) ).
thf(4961,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
@ ^ [B: TA] : $true
@ ^ [B: TA] : $false
@ A ),
inference(rewrite,[status(thm)],[1993,4069]) ).
thf(10791,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(paramod_ordered,[status(thm)],[3069,9831]) ).
thf(10806,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[10791]) ).
thf(10820,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[10806]) ).
thf(583,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) )
!= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[157,576]) ).
thf(585,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[583]) ).
thf(1237,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) @ ( c_2Enum_2ESUC @ E ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Enum_2E0 ) ),
inference(paramod_ordered,[status(thm)],[165,135]) ).
thf(1583,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ B ) ),
inference(pre_uni,[status(thm)],[1237:[bind(A,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).
thf(1980,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ B ) ),
inference(simp,[status(thm)],[1583]) ).
thf(18386,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ B @ A ) )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[125,18385]) ).
thf(18387,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[18386:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(14208,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[14140,6866]) ).
thf(14309,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14208]) ).
thf(14389,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14309]) ).
thf(16761,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( c_2Earithmetic_2EZERO != c_2Earithmetic_2EZERO ) ),
inference(eqfactor_ordered,[status(thm)],[14346]) ).
thf(16766,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[16761]) ).
thf(371,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Enum_2ESUC @ A ) @ B )
= C )
| ~ ( c_2Eprim__rec_2E_3C @ C @ B )
| ( ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[146,133]) ).
thf(372,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ B ) ) @ B )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ~ ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ B ) ),
inference(pattern_uni,[status(thm)],[371:[bind(A,$thf( c_2Earithmetic_2E_2A @ E @ F )),bind(B,$thf( F )),bind(C,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(D,$thf( E ))]]) ).
thf(386,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ B ) ) @ B )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ~ ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ B ) ),
inference(simp,[status(thm)],[372]) ).
thf(4123,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[165,4104]) ).
thf(4143,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[4123:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(4165,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[4143]) ).
thf(663,plain,
! [TA: $tType,D: TA,C: TA > $o,B: TA > $o,A: $o] :
( ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A @ B @ C @ D )
| ( ( c_2Ebool_2ECOND @ $o @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $false ) ) ),
inference(paramod_ordered,[status(thm)],[149,185]) ).
thf(782,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [B: TA] : $false
@ ^ [B: TA] : $false
@ A ),
inference(pre_uni,[status(thm)],[663:[bind(A,$thf( $true )),bind(B,$thf( ^ [E: TA] : $false )),bind(C,$thf( ^ [E: TA] : $false ))]]) ).
thf(815,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [B: TA] : $false
@ ^ [B: TA] : $false
@ A ),
inference(simp,[status(thm)],[782]) ).
thf(1386,plain,
! [TA: $tType,TC: $tType,E: TC,D: TA,C: TA,B: $o,A: TA > TC > $o] :
( ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $true
@ ^ [F: TC] : $false
@ ( c_2Ebool_2ECOND @ ( TC > $o ) @ B @ ( A @ C ) @ ( A @ D ) )
@ E )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( ^ [F: TC] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[165,815]) ).
thf(1624,plain,
! [TC: $tType,B: TC,A: $o] :
~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $true
@ ^ [C: TC] : $false
@ ( c_2Ebool_2ECOND @ ( TC > $o ) @ A
@ ^ [C: TC] : $false
@ ^ [C: TC] : $false )
@ B ),
inference(pre_uni,[status(thm)],[1386:[bind(A,$thf( ^ [F: TA] : ^ [G: TC] : $false ))]]) ).
thf(2016,plain,
! [TA: $tType,B: TA,A: $o] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [C: TA] : $false
@ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A
@ ^ [C: TA] : $false
@ ^ [C: TA] : $false )
@ B ),
inference(simp,[status(thm)],[1624]) ).
thf(4997,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [B: TA] : $false
@ ^ [B: TA] : $false
@ A ),
inference(rewrite,[status(thm)],[2016,2437]) ).
thf(7275,plain,
! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) )
!= c_2Enum_2E0 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(paramod_ordered,[status(thm)],[149,6865]) ).
thf(7281,plain,
! [TA: $tType,B: $o,A: TA] :
( ( c_2Earithmetic_2ENUMERAL
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
@ A ) )
!= c_2Enum_2E0 ),
inference(pre_uni,[status(thm)],[7275:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(7288,plain,
! [TA: $tType,B: $o,A: TA] :
( ( c_2Earithmetic_2ENUMERAL
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
@ A ) )
!= c_2Enum_2E0 ),
inference(simp,[status(thm)],[7281]) ).
thf(15,axiom,
! [A: $o] :
( ( ~ A
=> c_2Ebool_2EF )
=> ( ( A
=> c_2Ebool_2EF )
=> c_2Ebool_2EF ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV2) ).
thf(104,plain,
! [A: $o] :
( ( ~ A
=> c_2Ebool_2EF )
=> ( ( A
=> c_2Ebool_2EF )
=> c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13992,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: $o,C: TA,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ E
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ D
@ ^ [F: TA] : c_2Earithmetic_2EZERO
@ ^ [F: TA] : c_2Earithmetic_2EZERO
@ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[125,9948]) ).
thf(13993,plain,
! [TA: $tType,C: TA,B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ C ) ) )
@ A )
!= sk1 ),
inference(pattern_uni,[status(thm)],[13992:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ H @ ^ [H: TA] : c_2Earithmetic_2EZERO @ ^ [H: TA] : c_2Earithmetic_2EZERO @ K ) ) )),bind(C,$thf( K )),bind(D,$thf( H )),bind(E,$thf( A ))]]) ).
thf(14026,plain,
! [TA: $tType,C: TA,B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ C ) ) )
@ A )
!= sk1 ),
inference(simp,[status(thm)],[13993]) ).
thf(17,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET = A )
= A )
& ( ( A = c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF = A )
= ~ A )
& ( ( A = c_2Ebool_2EF )
= ~ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(114,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET = A )
= A )
& ( ( A = c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF = A )
= ~ A )
& ( ( A = c_2Ebool_2EF )
= ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1407,plain,
! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > $o] :
( ( c_2Ebool_2ECOND @ $o @ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) ) @ E @ $true )
| ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[165,393]) ).
thf(1713,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ) @ B @ $true ),
inference(pre_uni,[status(thm)],[1407:[bind(A,$thf( ^ [F: TA] : $false ))]]) ).
thf(2098,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ) @ B @ $true ),
inference(simp,[status(thm)],[1713]) ).
thf(3662,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ $false @ A @ $true ),
inference(rewrite,[status(thm)],[2098,2410]) ).
thf(9923,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[3069,9829]) ).
thf(9943,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
!= sk1 )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[9923]) ).
thf(9955,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[9943]) ).
thf(364,plain,
! [E: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ A ) @ D ) @ C )
= D )
| ~ ( c_2Eprim__rec_2E_3C @ D @ C )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[125,133]) ).
thf(365,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ B )
= C )
| ~ ( c_2Eprim__rec_2E_3C @ C @ B ) ),
inference(pattern_uni,[status(thm)],[364:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(383,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ B )
= C )
| ~ ( c_2Eprim__rec_2E_3C @ C @ B ) ),
inference(simp,[status(thm)],[365]) ).
thf(1566,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2B @ E @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) )
= E )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Enum_2E0 ) ),
inference(paramod_ordered,[status(thm)],[165,168]) ).
thf(1852,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2B @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) )
= B ),
inference(pre_uni,[status(thm)],[1566:[bind(A,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).
thf(2230,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2B @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) )
= B ),
inference(simp,[status(thm)],[1852]) ).
thf(288,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[157,128]) ).
thf(289,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ A ) )
= ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B ))]]) ).
thf(300,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ A ) )
= ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A ) ),
inference(simp,[status(thm)],[289]) ).
thf(7238,plain,
! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[165,6866]) ).
thf(7251,plain,
! [B: $o,A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 ),
inference(pre_uni,[status(thm)],[7238:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7259,plain,
! [B: $o,A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 ),
inference(simp,[status(thm)],[7251]) ).
thf(182,plain,
( ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $true )
= ( ( ~ $true
| $false )
& ( $true
| $true ) ) ),
inference(instance,[status(thm)],[169]) ).
thf(183,plain,
~ ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $true ),
inference(simp,[status(thm)],[182]) ).
thf(735,plain,
! [TA: $tType,D: TA,C: TA > $o,B: TA > $o,A: $o] :
( ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A @ B @ C @ D )
| ( ( c_2Ebool_2ECOND @ $o @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[149,183]) ).
thf(741,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [B: TA] : $false
@ ^ [B: TA] : $true
@ A ),
inference(pre_uni,[status(thm)],[735:[bind(A,$thf( $true )),bind(B,$thf( ^ [E: TA] : $false )),bind(C,$thf( ^ [E: TA] : $true ))]]) ).
thf(833,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [B: TA] : $false
@ ^ [B: TA] : $true
@ A ),
inference(simp,[status(thm)],[741]) ).
thf(1555,plain,
! [TA: $tType,TC: $tType,E: TC,D: TA,C: TA,B: $o,A: TA > $o] :
( ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $true
@ ^ [F: TC] : ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) )
@ ^ [F: TC] : $true
@ E )
| ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[165,833]) ).
thf(1705,plain,
! [TC: $tType,B: TC,A: $o] :
~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $true
@ ^ [C: TC] : ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
@ ^ [C: TC] : $true
@ B ),
inference(pre_uni,[status(thm)],[1555:[bind(A,$thf( ^ [F: TA] : $false ))]]) ).
thf(2091,plain,
! [TA: $tType,B: TA,A: $o] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [C: TA] : ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
@ ^ [C: TA] : $true
@ B ),
inference(simp,[status(thm)],[1705]) ).
thf(5371,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [B: TA] : $false
@ ^ [B: TA] : $true
@ A ),
inference(rewrite,[status(thm)],[2091,4069]) ).
thf(11694,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[125,10820]) ).
thf(11695,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ A )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(pattern_uni,[status(thm)],[11694:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )),bind(C,$thf( A ))]]) ).
thf(1515,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > $o] :
( ( ( c_2Ebool_2ECOND @ $o @ B @ $true @ ( A @ D ) )
= ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) )
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[258,165]) ).
thf(1769,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ $true @ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1515:[bind(A,$thf( ^ [E: TA] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(2152,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ $true @ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[1769]) ).
thf(18278,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ),
inference(rewrite,[status(thm)],[2152,258]) ).
thf(18293,plain,
! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > $o] :
( ( c_2Ebool_2ECOND @ $o @ E @ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) ) @ $true )
| ~ ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[165,18278]) ).
thf(18335,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ B @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) @ $true ),
inference(pre_uni,[status(thm)],[18293:[bind(A,$thf( ^ [F: TA] : $true ))]]) ).
thf(18370,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ B @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) @ $true ),
inference(simp,[status(thm)],[18335]) ).
thf(18453,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ),
inference(rewrite,[status(thm)],[18370,18278]) ).
thf(14149,plain,
! [C: $o,B: tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(paramod_ordered,[status(thm)],[14140,11793]) ).
thf(14236,plain,
! [C: $o,B: tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( A != C )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[14149]) ).
thf(14315,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[14236]) ).
thf(13841,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[125,13568]) ).
thf(13842,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pattern_uni,[status(thm)],[13841:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(2627,plain,
! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Enum_2E0 @ c_2Enum_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[149,2048]) ).
thf(2635,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Enum_2E0
@ ^ [C: TA] : c_2Enum_2E0
@ A )
@ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[2627:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Enum_2E0 )),bind(C,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).
thf(2651,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Enum_2E0
@ ^ [C: TA] : c_2Enum_2E0
@ A )
@ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[2635]) ).
thf(293,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
| ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
!= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[262,128]) ).
thf(294,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
| ( ( c_2Enum_2ESUC @ A )
!= c_2Enum_2E0 )
| ( ( c_2Enum_2ESUC @ B )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[293]) ).
thf(22,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
= ( ~ ( c_2Earithmetic_2EODD @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__ODD) ).
thf(136,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
= ( ~ ( c_2Earithmetic_2EODD @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(594,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[157,582]) ).
thf(596,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[594]) ).
thf(5,axiom,
! [A: $o] :
( ~ A
=> ( A
=> c_2Ebool_2EF ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EF__IMP) ).
thf(47,plain,
! [A: $o] :
( ~ A
=> ( A
=> c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET
| A )
= c_2Ebool_2ET )
& ( ( A
| c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
| A )
= A )
& ( ( A
| c_2Ebool_2EF )
= A )
& ( ( A
| A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__CLAUSES) ).
thf(90,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET
| A )
= c_2Ebool_2ET )
& ( ( A
| c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
| A )
= A )
& ( ( A
| c_2Ebool_2EF )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14189,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[14140,7318]) ).
thf(14267,plain,
! [B: $o,A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( A != B )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14189]) ).
thf(14345,plain,
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[14267]) ).
thf(477,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ $true @ A @ B )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[413,390]) ).
thf(494,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ~ ( c_2Earithmetic_2EEVEN @ sk1 )
| ( A != c_2Enum_2E0 )
| ( B
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[477]) ).
thf(508,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ~ ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(simp,[status(thm)],[494]) ).
thf(14032,plain,
! [A: tyop_2Enum_2Enum] :
( ~ $true
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ~ ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(rewrite,[status(thm)],[508,262]) ).
thf(14033,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ~ ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(simp,[status(thm)],[14032]) ).
thf(22141,plain,
$false,
inference(e,[status(thm)],[2331,14358,13869,511,523,582,597,9818,384,153,14354,42,301,37,389,52,7262,3342,15426,125,14391,2185,18385,157,18236,6253,14331,152,7258,7290,14346,11793,806,147,2437,61,18241,133,2884,810,381,6865,12132,5334,4172,2409,297,3069,165,4160,9993,7314,13568,2068,3144,4104,9829,2300,9804,156,53,169,141,3060,3326,7318,13527,10094,109,328,985,515,14369,129,4069,3364,134,128,10815,2043,14433,9985,586,14335,2144,298,7459,166,34,3523,149,296,3274,2048,2791,9996,281,413,15502,2398,71,2308,144,6248,5033,54,2220,2721,14364,6866,2284,567,39,4176,387,2343,140,66,2278,155,2171,2086,7334,13112,135,80,13840,505,2156,7260,487,516,123,9847,150,95,9948,10521,4961,10820,585,1980,576,18387,14389,16766,175,386,4165,4997,7288,104,6831,14026,258,158,390,114,139,3662,14140,9955,383,2230,287,300,2155,146,7259,183,5371,9944,11695,18453,36,168,262,14315,13842,2651,294,126,136,7338,596,47,163,9848,90,14345,14033,2191,9831,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ITP003^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 17:32:54 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.89/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/1.15 % [INFO] Parsing done (236ms).
% 1.43/1.16 % [INFO] Running in sequential loop mode.
% 1.87/1.42 % [INFO] eprover registered as external prover.
% 1.87/1.42 % [INFO] cvc4 registered as external prover.
% 2.02/1.43 % [INFO] Scanning for conjecture ...
% 2.09/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 64 axioms. Running axiom selection ...
% 2.31/1.59 % [INFO] Axiom selection finished. Selected 31 axioms (removed 33 axioms).
% 2.53/1.65 % [INFO] Problem is higher-order (TPTP THF).
% 2.53/1.66 % [INFO] Type checking passed.
% 2.53/1.66 % [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 ...
% 120.44/20.26 % External prover 'e' found a proof!
% 120.44/20.27 % [INFO] Killing All external provers ...
% 120.44/20.27 % Time passed: 19781ms (effective reasoning time: 19100ms)
% 120.44/20.27 % 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)>
% 120.44/20.27 % Axioms used in derivation (31): thm_2Ebool_2EBOOL__CASES__AX, thm_2Ebool_2ENOT__CLAUSES, thm_2Ebool_2ECOND__CLAUSES, thm_2Earithmetic_2ETWO, thm_2Ebool_2EOR__CLAUSES, thm_2Earithmetic_2EADD__0, thm_2Ebool_2EAND__CLAUSES, thm_2Esat_2EOR__DUAL2, thm_2Earithmetic_2ELESS__MONO__EQ, thm_2Esat_2EAND__INV__IMP, thm_2Esat_2EOR__DUAL3, thm_2Ebool_2EREFL__CLAUSE, thm_2Ebool_2ECOND__RAND, thm_2Ebool_2EEQ__CLAUSES, thm_2Ebool_2EIMP__F, thm_2Earithmetic_2EODD__EXISTS, thm_2Earithmetic_2EEVEN__EXISTS, thm_2Ebool_2EFALSITY, thm_2Eprim__rec_2ELESS__0, thm_2Earithmetic_2EONE, thm_2Ebool_2ECOND__EXPAND, thm_2Ebool_2EIMP__CLAUSES, thm_2Ebool_2ETRUTH, thm_2Earithmetic_2EODD__EVEN, thm_2Ebool_2EF__IMP, thm_2Earithmetic_2EMOD__UNIQUE, thm_2Esat_2EAND__INV2, thm_2Earithmetic_2EMULT__COMM, thm_2Earithmetic_2EADD1, thm_2Ebool_2ECOND__RATOR, thm_2Earithmetic_2EEVEN__ODD
% 120.44/20.27 % No. of inferences in proof: 580
% 120.44/20.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19781 ms resp. 19100 ms w/o parsing
% 121.07/20.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 121.07/20.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------